Education and economic growth in Pakistan: A cointegration and causality analysis
15
Education and economic growth in Pakistan: A cointegration and causality analysis Muhammad Afzal, Hafeez Ur Rehman, Muhammad Shahid Farooq *, Kafeel Sarwar University of the Punjab, Pakistan 1. Introduction Progress and prosperity of a country depends upon the educational choices available to the masses. Education not only trains the young ones to understand and cope with the complexities of economic growth, but also serves as a lever for its enhancement. It guarantees the quality of human life which ensures socioeconomic growth in a country (United Nations, 1997). Asian countries such as South Korea, India and China have achieved wonderful economic growth in the last few decades through agricultural and educational reforms. The economic growth especially growth in agricultural yield of Indian Punjab has beaten the Pakistan’s economic growth by a wide margin in last six decades only because of land reforms and mass education. The three land reforms in Pakistan (one in 1959 and others in 1972 and 1977) have failed to lessen the strong hold of landlords on the economic and political decision making (Chaudhry, Malik, & Ashraf, 2006). The expenditures on education and health have always remained very low (about 2.5% of GDP) even lower than military expenditures in Pakistan. The cut in current high military spending of both Pakistan and India can further raise their education level and hence economic development. Poor and corrupt taxation system failed to generate sufficient revenue to uplift the schooling and health facilities for masses in Pakistan. The poor and fixed income groups pay most of the taxes. The rich especially big International Journal of Educational Research 50 (2011) 321–335 A R T I C L E I N F O Article history: Received 8 June 2010 Received in revised form 19 September 2011 Accepted 10 October 2011 Available online 17 November 2011 JEL classification: C13 C51 I21 N1 O51 O53 Keywords: Education Economic growth Causality Cointegration A B S T R A C T This study explored the cointegration and causality between education and economic growth in Pakistan by using time series data on real gross domestic product (RGDP), labour force, physical capital and education from 1970–1971 to 2008–2009 were used. Autoregressive Distributed Lag (ARDL) Model of Cointegration and the Augmented Granger Causality Approach given by Toda and Yamamoto (1995) were applied. Cointegration among economic growth and education has been found. The findings of this study also indicate the existence of the feedback causality between education and all levels of education with economic growth. Among all levels of education, general higher education causes economic growth highly and most significantly while the level of confidence of causing economic growth to school education is found to be the highest. Labour force as compare to physical capital appeared to be a key factor in understanding the relationship between education and economic growth. This study recommends more investment in university education so that economic growth can be further accelerated, that in turn, leads to further education and hence economic growth. ß 2011 Elsevier Ltd. All rights reserved. * Corresponding author. E-mail address: [email protected] (M.S. Farooq). Contents lists available at SciVerse ScienceDirect International Journal of Educational Research jo u r nal h o mep age: w ww.els evier.c o m/lo c ate/ijed ur es 0883-0355/$ – see front matter ß 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijer.2011.10.004
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Transcript of Education and economic growth in Pakistan: A cointegration and causality analysis
International Journal of Educational Research 50 (2011) 321ndash335
Contents lists available at SciVerse ScienceDirect
International Journal of Educational Research
jo u r nal h o mep age w wwels evier c o mlo c ate i jed ur es
Education and economic growth in Pakistan A cointegration andcausality analysis
Muhammad Afzal Hafeez Ur Rehman Muhammad Shahid Farooq Kafeel Sarwar
University of the Punjab Pakistan
A R T I C L E I N F O
Article history
Received 8 June 2010
Received in revised form 19 September 2011
Accepted 10 October 2011
Available online 17 November 2011
JEL classification
C13
C51
I21
N1
O51
O53
Keywords
Education
Economic growth
Causality
Cointegration
A B S T R A C T
This study explored the cointegration and causality between education and economic
growth in Pakistan by using time series data on real gross domestic product (RGDP) labour
force physical capital and education from 1970ndash1971 to 2008ndash2009 were used
Autoregressive Distributed Lag (ARDL) Model of Cointegration and the Augmented
Granger Causality Approach given by Toda and Yamamoto (1995) were applied
Cointegration among economic growth and education has been found The findings of
this study also indicate the existence of the feedback causality between education and all
levels of education with economic growth Among all levels of education general higher
education causes economic growth highly and most significantly while the level of
confidence of causing economic growth to school education is found to be the highest
Labour force as compare to physical capital appeared to be a key factor in understanding
the relationship between education and economic growth This study recommends more
investment in university education so that economic growth can be further accelerated
that in turn leads to further education and hence economic growth
2011 Elsevier Ltd All rights reserved
1 Introduction
Progress and prosperity of a country depends upon the educational choices available to the masses Education not onlytrains the young ones to understand and cope with the complexities of economic growth but also serves as a lever for itsenhancement It guarantees the quality of human life which ensures socioeconomic growth in a country (United Nations1997) Asian countries such as South Korea India and China have achieved wonderful economic growth in the last fewdecades through agricultural and educational reforms The economic growth especially growth in agricultural yield of IndianPunjab has beaten the Pakistanrsquos economic growth by a wide margin in last six decades only because of land reforms andmass education The three land reforms in Pakistan (one in 1959 and others in 1972 and 1977) have failed to lessen the stronghold of landlords on the economic and political decision making (Chaudhry Malik amp Ashraf 2006) The expenditures oneducation and health have always remained very low (about 25 of GDP) even lower than military expenditures in PakistanThe cut in current high military spending of both Pakistan and India can further raise their education level and henceeconomic development Poor and corrupt taxation system failed to generate sufficient revenue to uplift the schooling andhealth facilities for masses in Pakistan The poor and fixed income groups pay most of the taxes The rich especially big
Corresponding author
E-mail address drdrmshahidgmailcom (MS Farooq)
0883-0355$ ndash see front matter 2011 Elsevier Ltd All rights reserved
doi101016jijer201110004
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335322
landlords pay even no income tax Galor and Moav (2000) noted that big landowners in Pakistan would have little incentiveto tax themselves to pay for schooling of the masses The additional tax revenue can be generated by abolishing VIP cultureand can be used in raising education health economic growth levels and hence development in Pakistan Pakistan is said tobe a country having growth miracles without development (Easterly 2001) The VIP and elite culture the high ethnicity andpolarization the foreign involvement in economic and political decision making and last but not the least the dictatorshiphave always been remained obstruction in the way of economic social human political and institutional developmentprocess of Pakistan South Asia (being poor neglected illiterate malnourished and less gender sensitive region of the world)in general and Pakistan in particular can enter in the global competition and enhance their economic growth by moreinvesting in their people The enormous potential of South Asia and Pakistanrsquos economy can easily be exploited by makingmore investment in human resources and carrying out some solid reforms especially in education system
In spite of carrying out number of reforms economic development in Pakistan is still lacking behind than even most ofdeveloping nations like Bangladesh There seems no clear-cut direction and strength of relationship between education andeconomic growth and between levels of education and economic growth in Pakistan Whether education causes economicgrowth or economic growth causes education Which level of education causes to economic growth more and vice versaThis study was designed to empirically answer such questions by using ARDL approach to cointegration and TodandashYamamoto causality technique
The Primary objective of this study is to examine the causal linkage firstly between education and RGDP secondlybetween different levels of education (ie school education college education and university education) and RGDP withinclusion and exclusion of stock of physical capital and stock of labour force as third and fourth variables
This empirical study has its significance in various aspects This study will be helpful for policy makers and higherauthorities It will provide a guideline for designing the future education planning Present study also provides motivation forthe future researchers for working in this domain Present study is a significant addition in existing literature It provides thedirection and enthusiasm to new researchers to explore more and more on this issue
2 Review of literature
Education one of the most important ingredients of human capital is considered as an important determinant ofsustainable economic growth (Goode 1959 Schultz 1961) The importance of the relationship between education andeconomic growth is acknowledged by the endogenous growth theory in late 1980s and early 1990s Productivity can beenhanced by investing more in education Human capital is the key component for boosting productivity which leads tohigher economic growth (Lucas 1988 Romer 1990) Human capital directly or indirectly serves as the determinant ofeconomic growth Education as components of human capital improves the socio-economic factors In the last century thefocus of researchers remained on the impacts of human capital on economic growth by increasing the facilities of educationand health A direct and significant linkage between human capital through educational developments and economic growthwas being observed
Education possesses multidimensional impacts on human beings and the economy It influences positively on theeconomic growth and employability of the persons while on the other hand it also helps in shaping the behavior of society topromote a cordial political social and economic environment which provides basis for further domestic and foreigninvestments in the country This socio-political polite educated workforce gets more respect more monetary rewards andstable employment prospects (Abbas amp Peck 2008 Fernandez amp Mauro 2000 Grossman amp Helpman 1991 Gylfason ampZoega 2003 Hassan amp Ahmed 2008 Loening 2004 Lucas 1988 Momete 2007 Quah amp Rauch 1990 Rivera-Batiz amp Romer1991 Romer 1986 1989 1990) Baldacci Clements Cui and Gupta (2005) found positive linkage between enrollment ratesandor years of schooling and GDP growth for developing countries
Economic growth and holistic development depend upon the highly skilled manpower Education and economic growthis not a one way process it is a two way process (Gylfason amp Zoega 2003 Hassan amp Ahmed 2008 Islam Wadud amp Islam2007 Jin 2009 Rondinelli amp Montgomery 1995) There does not exist one to one relationship between education andeconomic growth It is also affected by some other economic and non-economic variables like labour force physical capitaltrade openness happiness and health (Morote 2000) Better-educated workforce appeared to have a positive and significantimpact on economic growth (Loening 2004) Better-educated labour force had a considerable influence on economic growthby showing that human capital accumulation was one of the sources of economic growth (Babatunde amp Adefabi 2005)Morote (2000) estimated the causality between economic growth and higher education in the presence of employment as athird variable He used higher education enrollment per capita and per capita GDP growth rate as a proxy variable for highereducation and economic growth respectively This study revealed that the employment variable was a key factor in thehigher education and growth relationship Higher education had a positive effect on economic growth in both the short run(SR) and the long run (LR) (Francis amp Iyare 2006 Katırcıoglu 2009 Macerinskiene amp Vaiksnoraite 2006 Permani 2008)
More and better education geared up economic growth directly as well as indirectly by more equality and cohesion(Changzheng Zhijian amp Huaizu 2007 Gylfason amp Zoega 2003) Jin (2009) examined the Granger causal association betweenresearch productivity and economic growth for five East Asian countries He took total publications as the proxy of quality ofeducation at university level and RGDP as a measure of economic growth Bidirectional causal linkage between researchproductivity and economic growth was found in the case of Hong Kong due to its open economy focus on services sector suchas financial services trading and tourism In the case of Japan one-way causality running from economic growth to research
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 323
productivities was observed The reason behind this was the faster growth in 1960s and 1970s and increasing the share ofinvestment in tertiary education Economic growth caused by research publications was observed in Korea and TaiwanMoreover the significant causal flow running from publications to economic growth was no longer found in case ofSingapore This insignificant causal flow was perhaps found due to small number of universities in Singapore
Basic education causes economic growth while on the other side economic growth only causes higher education otherthan primary education No cointegration between education and national income was found (Kui 2005) Pradhan (2009)found unidirectional causality running from economic growth to education in India Islam et al (2007) examined linkagebetween education and GDP in the case of Bangladesh They used multivariate approach (Vector Error Correction ModelVECM) which is assumed more robust than the bivariate approach in the presence of labour and capital for the time seriesdata of 1976ndash2003 They found long run linkage between economic growth and education and further concluded that thereis bidirectional causality between education and economic growth It shows that Bangladesh is in that condition where GDPand education are helping each other to grow Bidirectional causality in economic growth and education could be possiblebecause education produces more accomplished labour force that directs to more productivity and ultimately economicgrowth Finally the general education has the greater returns than the vocational education (Hassan amp Ahmed 2008) Abbasand Peck (2008) explored the linkages between human capital and economic growth for Pakistan by utilizing cointegrationand error correction mechanism on time series data from 1960 to 2003 They found that human capital explained as much as39 of the increase in GDP per person in 1990 From this one can easily conclude that human capital positively contributedto economic growth in Pakistan (Chaudhary Iqbal amp Gillani 2009 Stengos amp Aurangzeb 2008) Thus human capital througheducation plays a major role in economic growth of a country
Majority of the above studies reveal that education and economic growth have the long run relationship and both thevariables have the causal relationship either one way or two way The present study is planned to explore the causalconnection between education (measured by 10 different indicators of education) and economic growth in Pakistan in theabsence and presence of third and fourth variables known as stock of capital and stock of labour force
3 Method and procedure
In light of objectives of the study the time series data on RGDP stock of capital stock of labour and ten different indicatorsof education have been used in Pakistani context for the period 1970ndash1971 to 2008ndash2009 The data were taken from differentissues of lsquolsquoPakistan Economic Surveyrsquorsquo and lsquolsquoAnnual Reports of State Bank of Pakistanrsquorsquo Furthermore a comprehensivemeasure of education known as education index was constructed for the period 1970ndash1971 to 2008ndash2009 by adopting UNDPmethodology given in 1999ndash2000 Education index is constructed by adding together adult literacy rate index (ALI) withtwo-third weightage and the combined primary secondary and tertiary gross enrollment ratio index (GEI) with one-thirdweightage The adult literacy rate (ALR) gives an indication of the ability to read and write while the gross enrolment ratio(GER) gives an indication of the level of education
Education Index frac14 2
3 ALI thorn 1
3 GEI
Adult Literacy Index ethALITHORN frac14 ALR 0
100 0
Gross Enrollment Index ethGEITHORN frac14 GER 0
100 0
where lsquo0rsquo and lsquo100rsquo are the minimum and maximum values of the variables adult literacy rate and gross enrollment ratioKeeping in view the theoretical postulates of the connection among RGDPt real physical capital (RPCt) labour force (LFt)
and education (Edut) the following models have been specified as
ln RGDPt frac14 f ethln RPCt ln LFt ln EduitTHORN (A)
ln Eduit frac14 f ethln RGDPt ln RPCt ln LFtTHORN (B)
To find out the relationship between Eduit and RGDPt various functional forms have been tested and the most appropriatefunctional forms ie log linear form for the variables RGDPt and Eduit were specified as
ln RGDPt frac14 b0 thorn b1 ln RPCt thorn b2 ln LFt thorn b3 ln Eduit thorn e1 (Model 1)
ln Eduit frac14 g0 thorn g1 RGDPt thorn g2 ln RPCt thorn g3 ln LFt thorn e2 (Model 2)
where ln = natural logarithm RGDPt = a proxy used to measure economic growth RPCt = stock of physical capital in realterms gross fixed capital formation deflated by GDP deflator LFt = stock of labour force Eduit = educational capital as takenby Ayara (2002) Mankiw Romer and Weil (1992) and Pritchett (2001) in extended Solow Model In literature education wasmeasured by using different indicators such as Edu1t = education index a key indicator used as a proxy to measure
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335324
educational development Edu2t = school enrollment ratio Edu3t = college enrollment ratio Edu4t = professional collegeenrollment ratio Edu5t = university enrollment ratio Edu6t = total enrollment ratio Edu7t = total general enrollment ratioEdu8t = higher education including professional education enrollment ratio Edu9t = general higher education enrollmentratio and Edu10t = education expenditure as percentage of GNP
RGDPt as a proxy to measure economic growth has also been utilized by Islam et al (2007) Abbas and Peck (2008) Jin(2009) Katırcıoglu (2009) and Chaudhary et al (2009) Gross fixed capital formation deflated by GDP deflator has also beenused as a proxy for RPC by Abbas and Peck (2008) Khorasgani (2008) and Chaudhary et al (2009) Stock of labour force as aproxy for measuring stock of labour has been already utilized by Islam et al (2007) and Chaudhary et al (2009)
Enrollment ratios are derived by dividing total enrollment of each category or level of education to the population of thatrespective age group These indicators have been used by Diebolt and Litago (1997) Gylfason and Zoega (2003) Islam et al(2007) and Pradhan (2009)
A number of cointegration techniques such as residual based EnglendashGranger (1987) test Johansen (1988) Johansen andJuselius (1990) Gregory and Hansen (1996) Saikkonen and Lutkepohl (2000) were available in literature This study used arelatively new and more robust cointegration approach known as Autoregressive Distributed Lag Model (ARDL) to determinethe long run relationship among variables of interest Although ARDL Approach can be applied whether the variables are I(0)
or I(1) or fractionally integrated but it is still pre requisite for the ARDL model to apply that none of the variables underconsideration is integrated of order lsquolsquo2rsquorsquo or higher In order to examine the causal nexus between Eduit and RGDPt theAugmented Granger Causality approach given by Toda and Yamamoto (1995) is applied
4 Empirical results
41 Unit root results
The study utilized different unit root tests such as Augmented Dickey-Fuller Test (ADF) Phillips-Perron Test (PP) Dickey-Fuller Generalized Least Square Test (DF-GLS) and Ng-Perron in order to make sure that none of the variables is of I(2) orhigher order A summary of unit root results regarding order of integration based on different above unit root criteria is givenin Table 1
According to ADF PP DF-GLS and Ng-Perron tests results in Table 1 RPCt LFt Edu2t Edu3t Edu4t Edu5t Edu6t Edu7t andEdu8t are of I(1) with constant while Edu1t is of I(0) with intercept and trend RGDPt is of I(1) according to ADF PP and DF-GLSwhile Ng-Perron exhibits RGDPt is of I(0) The order of the integration for Edu10t is zero according to all criteriarsquos Edu9t is ofI(1) with intercept and trend I(1) with constant I(0) with constant and I(0) with constant and trend according to ADF PP DF-GLS and Ng-Perron criteriarsquos respectively Edu9t is of I(1) according to ADF and PP while it is of I(0) according to DF-GLS andNg-Perron criteriarsquos so Edu9t seems to be fractionally integrated None of the variables is of I(2) according all criteriarsquos So theappropriate technique to cointegration is the ARDL approach to cointegration
To examine the long run (LR) relationship between RGDPt RPCt LFt and Eduit this study used the error-correction versionof ARDL approach of Model 1 and Model 2 by following Pesaran and Pesaran (1997) and Pesaran and Shin (1999) as
Dln RGDPt frac14 a0RGDPtthornXn
ifrac141
biRGDPtDln RGDPti thorn
Xn
ifrac141
ciRGDPtDln RPCti thorn
Xn
ifrac141
diRGDPtDln LFti
thornXn
ifrac141
eiRGDPtDln Eduiti thorn d1RGDPt
ln RGDPt1 thorn d2RGDPtln RPCt1 thorn d3RGDPt
ln LFt1
thorn d4RGDPtln Eduit1 (Model 1A)
Table 1
Order of integration
Variable ADF PP DF-GLS Ng-Perron
Intercept Intercept
and trend
Intercept Intercept
and trend
Intercept Interpret
and trend
Intercept Intercept
and trend
RGDPt I(1) I(1) I(1) I(0)
RPCt I(1) I(1) I(1) I(1)
LFt I(1) I(1) I(1) I(1)
Edu1t I(0) I(0) I(0) I(0)
Edu2t I(1) I(1) I(1) I(1)
Edu3t I(1) I(1) I(1) I(1)
Edu4t I(1) I(1) I(1) I(1)
Edu5t I(1) I(1) I(1) I(1)
Edu6t I(1) I(1) I(1) I(1)
Edu7t I(1) I(1) I(1) I(1)
Edu8t I(1) I(1) I(1) I(1)
Edu9t I(1) I(1) I(0) I(0)
Edu10t I(0) I(0) I(0) I(0)
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 325
Dln Eduit frac14 a0EduitthornXn
ifrac141
biEduitDln Eduiti thorn
Xn
ifrac141
ciEduitDln RPCti thorn
Xn
ifrac141
diEduitDln RGDPti thorn
Xn
ifrac141
eiEduitDln LFti
thorn d1Eduitln Eduit1 thorn d2Eduitln RPCt1 thorn d3Eduitln RGDPt1 thorn d4Eduitln LFt1 (Model 2A)
The coefficients (b c d and e) of the part one of the Model 1A and Model 2A represent SR dynamics and ds determine LRrelationship The first step in ARDL model was to examine long run linkage among the variables by calculating familiar F-statistic on the differenced variables components of Unrestricted Error Correction Mechanism (UECM) model for the jointsignificance of the coefficients of lagged level of the variables In this first step the regression equation estimated for thedependent variable RGDPt is defined as
Dln RGDPt frac14 a0RGDPtthornXn
ifrac141
biRGDPtDln RGDPti thorn
Xn
ifrac141
ciRGDPtDln RPCti thorn
Xn
ifrac141
diRGDPtDln LFti
thornXn
ifrac141
eiRGDPtDln Eduiti (Model 1B)
To create error correction mechanism in this equation 1st lag of the level of each variable is added to Model 1B and a variableaddition test is conducted by calculating F-test on the joint significance of all the added lagged level variables
Dln RGDPt frac14 a0RGDPtthornXn
ifrac141
biRGDPtDln RGDPti thorn
Xn
ifrac141
ciRGDPtDln RPCti thorn
Xn
ifrac141
diRGDPtDln LFti
thornXn
ifrac141
eiRGDPtDln Eduiti thorn d1RDGPt
ln RGDPt1 thorn d2RGDPtln RPCt1 thorn d3RGDPt
ln LFt1
thorn d4RGDPt ln Eduit1 (Model 1C)
The null hypothesis for no cointegration for the variable RGDPt against alternative hypothesis is given as
H0 d1RGDPtfrac14 d2RGDPt
frac14 d3RGDPtfrac14 d4RGDPt
frac14 0
H1 d1RGDPt6frac14 d2RGDPt
6frac14 d3RGDPt6frac14 d4RGDPt
6frac14 0
This is denoted as FRGDPt (RGDPtRPCt LFt Eduit)This hypothesis is being tested by the familiar F-testIf the calculated F-statistic is higher than the upper bounds critical value given by Pesaran Shin and Smith (2001) and
Narayan (2005) the null hypothesis of no cointegration is rejected implying that there exists a LR relationship among theRGDPt RPCt LFt Eduit when RGDPt is the dependent variable If the calculated F-statistic is less than the lower bounds criticalvalue then the null hypothesis of no cointegration cannot be rejected If the F-value falls in between lower and upper boundscritical values the test statistic will be inconclusive The value of the F depends upon the sample size constant andor a trendof ARDL and number of explanatory variables
42 Cointegration
The ARDL approach is applied to examine the long run relationship by conducting F-statistic The cointegration resultsare presented in Tables 2 and 3 The values of estimated F-test for RGDPt are shown in Table 2
Pesaran et al (2001) lower and upper critical values for bounds testing ARDL for 1 5 and 10 significance levels are365ndash466 279ndash367 and 237ndash320 respectively Narayan (2005) lower and upper critical values for Bound Testing ARDL for1 5 and 10 significance level are 502ndash661 355ndash480 and 293ndash402 respectively
All the indicators of education except Edu8 indicate that there exists cointegration relationship among RGDPt RPCt LFt
and Eduit when RGDPt is the dependent variable according to Pesaran et al (2001) CVs because there is at least one F-valuethat is greater than the upper critical bounds value Cointegration exists among RGDPt RPCt LFt and Eduit (as Eduit ismeasured by Edu1t Edu2t Edu4t Edu5t Edu9t) when RGDPt is the dependent variable according to Narayan (2005) CVs Thenull hypothesis of no cointegration is not rejected for Edu8t according to both CVs
Pesaran et al (2001) lower and upper critical values for bounds testing ARDL for 1 5 and 10 significance levels are365ndash466 279ndash367 and 237ndash320 respectively Narayan (2005) lower and upper critical values for Bound Testing ARDL for1 5 and 10 significance level are 502ndash661 355ndash480 and 293ndash402 respectively
The cointegration results in Table 3 shows that there is LR linkage between Eduit RGDPt LFt and RPCt when Eduit (as Eduit
is represented by Edu1t Edu2t Edu5t Edu6t Edu7t Edu9t and Edu10t) is the dependent variable according to both Pesaran et al(2001) and Narayan (2005) CVs because at least one partial F statistic is greater than the upper critical bounds value There
Table 2
Cointegration
Dependent variable when RGDPt serves as dependent variable Lag length Cointegration results based on critical
values (CVs) given by
1 2 3 4 Pesaran et al (2001) Narayan (2005)
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu1t)] 167 419 203 214 Cointegration Cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu2t)] 281 340 226 179 Cointegration No cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu3t)] 209 644 203 145 Cointegration Cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu4t)] 234 619 263 190 Cointegration Cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu5t)] 253 454 257 236 Cointegration Cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu6t)] 287 336 231 181 Cointegration No cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu7t)] 277 338 230 181 Cointegration No cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu8t)] 114 172 203 165 No cointegration No cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu9t)] 274 482 188 117 Cointegration Cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu10t)] 237 392 246 203 Cointegration No cointegration
Table 3
Cointegration
Dependent variable when Eduit serves as dependent variable Lag length Cointegration results based on critical
values (CV) given by Results
1 2 3 4 Pesaran et al (2001) Narayan (2005)
DEdu1t [FEdu1t (Edu1tRGDPt RPCt LFt)] 711 502 548 447 Cointegration Cointegration
DEdu2t [FEdu2t (Edu2tRGDPt RPCt LFt)] 446 336 192 308 Cointegration Cointegration
DEdu3t [FEdu3t (Edu3tRGDPt RPCt LFt)] 157 280 195 295 No cointegration No cointegration
DEdu4t [FEdu4t (Edu4tRGDPt RPCt LFt)] 202 156 295 223 No cointegration No cointegration
DEdu5t [FEdu5t (Edu5tRGDPt RPCt LFt)] 152 629 081 069 Cointegration Cointegration
DEdu6t [FEdu6t (Edu6tRGDPt RPCt LFt)] 488 366 225 305 Cointegration Cointegration
DEdu7t [FEdu7t (Edu7tRGDPt RPCt LFt)] 475 362 226 314 Cointegration Cointegration
DEdu8t [FEdu8t (Edu8tRGDPt RPCt LFt)] 156 182 089 101 No cointegration No cointegration
DEdu9t [FEdu9t (Edu9tRGDPt RPCt LFt)] 322 443 417 286 Cointegration Cointegration
DEdu10t [FEdu10t (Edu10tRGDPt RPCt LFt)] 341 527 523 842 Cointegration Cointegration
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335326
exists no cointegration among Eduit RGDPt RPCt and LFt when Eduit is represented by Edu3t Edu4t and Edu8t In conclusioneducation and RGDPt are found to be cointegrated ie they possess LR relationship
43 TodandashYamamoto Augmented Granger Causality (TYAGC) Test
Keeping in view the objectives of the study TYAGC was applied for data analysis To examine Augmented GrangerCausality Test among RGDPt RPCt LFt and Eduit the following equations are being estimated The estimated results of TYAGCprocedure are presented in Tables IndashIV
44 Bivariate TYAGC framework
The bivariate causality between RGDPt and Eduit (Eqs (1) and (2)) between RGDPt and RPCt (Eqs (3) and (4)) betweenRGDPt and LFt (Eqs (5) and (6)) between Eduit and RPCt (Eqs (7) and (8)) and between Eduit and LFt (Eqs (9) and (10)) wasestimated by using TYAGC technique and in presented in Table I
RGDPt frac14 a1 thornX3
ifrac141
b1iRGDPti thornX3
ifrac141
g1iEduiti thorn u1t (1)
Eduit frac14 a2 thornX3
ifrac141
b2iRGDPti thornX3
ifrac141
g2iEduiti thorn u2t (2)
RGDPt frac14 a3 thornX3
ifrac141
b3iRGDPti thornX3
ifrac141
g3iRPCti thorn u3t (3)
RPCt frac14 a4 thornX3
ifrac141
b4iRGDPti thornX3
ifrac141
g4iRPCti thorn u4t (4)
RGDPt frac14 a5 thornX3
ifrac141
b5iRGDPti thornX3
ifrac141
g5iLFti thorn u5t (5)
LFt frac14 a6 thornX3
ifrac141
b6iRGDPti thornX3
ifrac141
g6iLFti thorn u6t (6)
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 327
Eduit frac14 a7 thornX3
ifrac141
b7iEduiti thornX3
ifrac141
g7iRPCti thorn u7t (7)
RPCt frac14 a8 thornX3
ifrac141
b8iEduiti thornX3
ifrac141
g8iRPCti thorn u8t (8)
Eduit frac14 a9 thornX3
ifrac141
b9iEduiti thornX3
ifrac141
g9iLFti thorn u9t (9)
LFt frac14 a10 thornX3
ifrac141
b10iEduiti thornX3
ifrac141
g10iLFti thorn u10t (10)
The null hypothesis that all the indicators of education and all levels of education do not Granger cause RGDPt was tested inTable I Bivariate TYAGC results indicate that the null hypothesis was rejected (Table I) Similarly the null hypothesis thatRGDPt does not Granger cause all the indicators and all levels of education is rejected except Edu8t and Edu10t It means thatthere exists two-way causality between education and RGDPt RGDPt fails to cause higher education and expenditures oneducation
The estimated results from Eqs (3) and (4) in Table I show the feedback Granger causality between RPCt and RGDPt LFt isfound to cause RGDPt at 99 level of confidence while its reverse is not true The results of Eqs (7) and (8) in Table I show thatthe feedback causality between Eduit and RPCt seems to exist because majority of the indicators of education are causingRPCt and vice versa The results from Eq (9) and (10) in Table I reveal that LFt Granger causes education while reverseseemed to be not true In conclusion education and all levels of education (school college and university) Granger causeRGDPt and RGDPt also Granger causes education and all levels of education Feedback causality between education andRGDPt is found in bivariate case
45 Trivariate TYAGC framework
The trivariate causality among RGDPt RPCt and Eduit (Eqs (11)ndash(13)) and among RGDPt LFt and Eduit (Eqs (14)ndash(16)) wasestimated by using TYAGC framework and is presented in Tables II and III
RGDPt frac14 a11 thornX3
ifrac141
b11iRGDPti thornX3
ifrac141
l11iRPCti thornX3
ifrac141
g11iEduiti thorn u11t (11)
Eduit frac14 a12 thornX3
ifrac141
b12iRGDPti thornX3
ifrac141
l12iRPCti thornX3
ifrac141
g12iEduiti thorn u12t (12)
RPCt frac14 a13 thornX3
ifrac141
b13iRGDPti thornX3
ifrac141
l13iRPCti thornX3
ifrac141
g13iEduiti thorn u13t (13)
RGDPt frac14 a14 thornX3
ifrac141
b14iRGDPti thornX3
ifrac141
l14iLFti thornX3
ifrac141
g14iEduiti thorn u14t (14)
Edut frac14 a15 thornX3
ifrac141
b15iRGDPti thornX3
ifrac141
l15iLFti thornX3
ifrac141
g15iEduiti thorn u15t (15)
LFt frac14 a16 thornX3
ifrac141
b16iRGDPti thornX3
ifrac141
l16iLFti thornX3
ifrac141
g16iEduiti thorn u16t (16)
The estimated results presented in Table II indicate that the null hypothesis of no Granger causality between majority of theindicators of education and RGDPt is rejected This also supports our previous bivariate causality results that there existsfeedback causality between education and RGDPt The trivariate result in Table II seems to support the previous bivariateresult regarding causality between education and RPCt and between RPCt and RGDPt
In case of trivariate causality analysis among RGDPt LFt and Eduit the results in Table III again indicate the two waycausality running between education and RGDPt Six out of ten indicators of education does Granger cause LFt while LFt
Granger causes nine indicators out of ten indicators of education The null hypothesis that LFt does not Granger cause RGDPt
in the presence of all indicators of education is rejected at 99 level of confidence So LFt seems to be a very importantvariable that affects two main variables of the study ie education and RGDPt
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335328
In conclusion education and all levels of education Granger cause RGDPt where as its revere ie Granger causalityrunning from RGDPt to education and all levels of education is only true in case of trivariate causality among RGDPt LFt andeducation From here one can easily conclude that the role of LFt as compared to RPCt is very important in understanding therelationship between education and RGDPt Feedback causality between education and RGDPt is also found in trivariate case
46 Tetravariate TYAGC framework
The tetravariate causality among RGDPt RPCt LFt and Eduit (Eqs (17)ndash(20)) was also estimated by using TYAGC techniqueand their results are presented in Table IV
RGDPt frac14 a17 thornX3
ifrac141
b17iRGDPti thornX3
ifrac141
g17iRPCti thornX3
ifrac141
l17iLFti thornX3
ifrac141
d17iEduiti thorn u17t (17)
Eduit frac14 a18 thornX3
ifrac141
b18iRGDPti thornX3
ifrac141
g18iRPCti thornX3
ifrac141
l18iLFti thornX3
ifrac141
d18iEduiti thorn u18t (18)
RPCt frac14 a19 thornX3
ifrac141
b19iRGDPti thornX3
ifrac141
g19iRPCti thornX3
ifrac141
l19iLFti thornX3
ifrac141
d19iEduiti thorn u19t (19)
LFt frac14 a20 thornX3
ifrac141
b20iRGDPti thornX3
ifrac141
g20iRPCti thornX3
ifrac141
l20iLFti thornX3
ifrac141
d20iEduiti thorn u20t (20)
The tetravariate TYAGC results presented in Table IV indicate that all the indicators of education Granger cause RGDPt whileRGDPt does Granger cause majority of the indicators of education (seven out of ten) RGDPt does not Granger cause Edu5t
(university education) Edu8t (higher education) and Edu10t (education expenditure) From this one can easily conclude thatthere exists two way causality between education and RGDPt in case of tetravariate causality analysis as have been the caseof bivariate and trivariate causality Regarding levels of education all levels of education (ie school education collegeeducation and university education) do Granger cause RGDPt while RGDPt does only cause school education and collegeeducation RGDPt does not Granger cause university education
LFt Granger causes RGDPt at 99 confidence level while RGDPt only Granger causes LFt in case of Edu3t Edu5t Edu9t andEdu10t In case of testing causality between RPCt and RGDPt in the presence of all indicators of education RPCt does Grangercause RGDPt and in reverse case RGDPt does not Granger cause RPCt in the presence of Edu1t Edu3t Edu8t Edu9t and Edu10tThese results show the unidirectional causality running from RPCt to RGDPt
The research hypothesis that LFt does not Granger cause Eduit is rejected at 99 confidence interval except wheneducation is measured by Eduit Labour force has been found to cause all levels of education On the other side education onlyGranger causes the LFt in the presence of Edu3t Edu4t Edu5t Edu8t and Edu10t RPC does not Granger cause education whenEdu3t and Edu4t are used as proxies of education All indicators of education except Edu1t Edu2t and Edu10t do Granger causeRPCt This implies that feedback causality between RPCt and education is observed
It can easily be concluded from the TYAGC results of Eq (17) in Table IV that among all levels of education General highereducation (Edu9t) causes RGDPt highly and most significantly (999 confidence level) The level of confidence of collegeeducation (Edu3t) and school education (Edu2t) causing RGDPt is found to be 2nd highest (significance at 997 confidencelevel) and 3rd highest (significance at 989 confidence level) respectively From Eq (18) in Table IV it can also be found thatthe level of confidence (999) of causing RGDPt to school education (Edu2t) is found to be highest
From the bivariate trivariate and tetravariate TYAGC tests results in Tables IndashIV the overall results of the study abouteducation and different levels of education (School College and University) are summarized in Table 4
Table 4
Causal nexus between education different levels of education with RGDPt
Hypothesis TYAGC procedure
Bivariate Trivariate Tetravariate
RGDPt and Edut RGDPt RPCt Edut RGDPt LFt Edut RGDPt LFt RPCt Edut
Education (Edu1t) does Granger cause RGDPt Yes (0089) No (0459) Yes (0009) Yes (0087)
RGDPt does Granger cause education (Edu1t) Yes (0000) Yes (0000) Yes (0000) Yes (0000)
School education (Edu2t) does Granger cause RGDPt Yes (0000) Yes (0001) Yes (0002) Yes (0010)
RGDPt does Granger cause school education (Edu2t) Yes (0000) Yes (0000) Yes (0000) Yes (0000)
College education (Edu3t) does Granger cause RGDPt Yes (0038) Yes (0081) Yes (0000) Yes (0002)
RGDPt does Granger cause college education (Edu3t) Yes (0003) No (0172) Yes (0001) Yes (0032)
University education (Edu5t) does Granger cause RGDPt Yes (0000) Yes (0000) Yes (0001) Yes (0001)
RGDPt does Granger cause university education (Edu5t) Yes (0089) Yes (0000) Yes (0025) No (0515)
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 329
47 Figures in parentheses are p-values
From the above results presented in Table 4 it can be concluded that there existed feedback causality between educationand RGDPt in all bivariate trivariate and tetravariate TYAGC causality cases All levels of education ie school educationcollege education and university education do Granger cause RGDPt in all causality cases RGDPt does Granger cause schooleducation in all causality cases RGDPt does Granger cause college education in all causality cases except trivariate causalitythat is running from RGDPt to education when RPCt serves as a third variable Table 4 also reveals that RGDPt does Grangercause university education only in a bivariate and trivariate causality cases RGDPt fails to Granger cause to universityeducation in tetravariate case
5 Conclusions and recommendations
This study aimed to explore the cointegration and causal relationship between education (measured by different indicatorsof education) and economic growth in Pakistan It is very essential for a country to invest more in education because it is one ofthe most important ingredients of human capital and hence economic development The nature and strength of the relationshipbetween education and economic growth is still not clear in case of Pakistan The main focus of this empirical study remained toobserve the causality and cointegration between education and economic growth in the absence and presence physical capitaland labour force Cointegration between education and economic growth was investigated using ARDL approach and the causallinkage between education and economic growth was examined in bivariate trivariate and tetravariate TYAGC frameworkDifferent indicators of education were utilized in this study to show the robustness of empirical results The causality betweeneducation and economic growth was examined in the presence and absence of stock of physical capital and stock of labour as athird and fourth variable The causality results indicate that there exist two-way causality between education and economicgrowth and between all levels of education and economic growth in case of bivariate TYAGC framework Education and alllevels of education do Granger cause economic growth in the presence of real physical capital as a third variable while economicgrowth causes all the indicators of education except college education professional college education and educationalexpenditures in the presence of real physical capital as a third variable in case of trivariate causality analysis In the presence oflabour force as a third variable feedback causality exists between education and economic growth and between all levels ofeducation and economic growth The results of tetravariate TYAGC Test indicate that education and all level of education doGranger cause economic growth while economic growth does Granger cause majority of the indicators of education (ie sevenout of ten) Economic growth does not Granger cause university education higher education including professional educationand expenditures on education The rise in university education higher education including professional education andexpenditures on education were considered as the key indicators to gauge human and social progress Economic growth doesnot seem to affect important educational indicators like university education higher education including professionaleducation and expenditures on education This seems to be consistent with Easterlyrsquos findings Easterly (2001) said thatPakistan is a country that made little social progress for given rates of GDP Among all levels of education General highereducation causes economic growth highly and most significantly as was explored by Stengos and Aurangzeb (2008) The level ofconfidence of causing economic growth to school education found to be highest This study also confirms the long runrelationship between education and economic growth
On the basis of the results of this study it is recommended that the government should focus more on higher educationparticularly to university education More funds should be allocated to education in line with others sectors particularly touniversity and higher education levels so that the economic growth can be further accelerated This will in turn leads tofurther education and hence development Poor should be facilitated to get higher education so that the polarization inhigher education may further be minimized Primary schooling should also be given priority because primary educationserves as an input for all higher levels of education The inverted educational expenditure pyramid may also be taken intoaccount Since the role of labour force seems to be very important in understanding the relationship between education andeconomic growth so it is suggested that labour force should be given more chances to enhance their skills The variablelabour force must be included while examining the causality between education and economic growth It is alsorecommended that the nexus between education and economic growth with inclusion of other variables other than physicalcapital and labour force should further be tested and generalized
Appendix A
Table I
Bivariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Bivariate-RGDPt and Eduit
Eq (1) Edu1t does not Granger cause RGDPt 028998 [0089] 1 Reject H0
Edu2t does not Granger cause RGDPt 144869 [0000] 1 Reject H0
Edu3t does not Granger cause RGDPt 043243 [0038] 1 Reject H0
Edu4t does not Granger cause RGDPt 039797 [0046] 1 Reject H0
Table I (Continued )
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Edu5t does not Granger cause RGDPt 217739 [0000] 1 Reject H0
Edu6t does not Granger cause RGDPt 137788 [0000] 1 Reject H0
Edu7t does not Granger cause RGDPt 126682 [0000] 1 Reject H0
Edu8t does not Granger cause RGDPt 041335 [0042] 1 Reject H0
Edu9t does not Granger cause RGDPt 160963 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 028642 [0091] 1 Reject H0
Eq (2) RGDPt does not Granger cause Edu1t 260926 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 230094 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 085441 [0003] 1 Reject H0
RGDPt does not Granger cause Edu4t 107403 [0001] 1 Reject H0
RGDPt does not Granger cause Edu5t 028935 [0089] 1 Reject H0
RGDPt does not Granger cause Edu6t 270343 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 273974 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 003162 [0574] 1 Cannot reject H0
RGDPt does not Granger cause Edu9t 027588 [0097] 1 Reject H0
RGDPt does not Granger cause Edu10t 000851 [0770] 1 Cannot reject H0
Bivariate-RGDPt and RPCt
Eq (3) RPCt does not Granger cause RGDPt 054972 [0019] 1 Reject H0
Eq (4) RGDPt does not Granger cause RPCt 167511 [0000] 1 Reject H0
Bivariate-RGDPt and LFt
Eq (5) LFt does not Granger cause RGDPt 227888 [0000] 1 Reject H0
Eq (6) RGDPt does not Granger cause LFt 012380 [0266] 1 Cannot reject H0
Bivariate-Eduit and RPCt
Eq (7) Edu1t does not Granger cause RPCt 094596 [0002] 1 Reject H0
Edu2t does not Granger cause RPCt 015434 [0214] 1 Cannot reject H0
Edu3t does not Granger cause RPCt 038233 [0051] 1 Reject H0
Edu4t does not Granger cause RPCt 000506 [0822] 1 Cannot reject H0
Edu5t does not Granger cause RPCt 298085 [0000] 1 Reject H0
Edu6t does not Granger cause RPCt 018289 [0176] 1 Cannot reject H0
Edu7t does not Granger cause RPCt 018976 [0168] 1 Cannot reject H0
Edu8t does not Granger cause RPCt 176399 [0000] 1 Reject H0
Edu9t does not Granger cause RPCt 224647 [0000] 1 Reject H0
Edu10t does not Granger cause RPCt 039174 [0048] 1 Reject H0
Eq (8) RPCt does not Granger cause Edu1t 091477 [0002] 1 Reject H0
RPCt does not Granger cause Edu2t 098821 [0002] 1 Reject H0
RPCt does not Granger cause Edu3t 066148 [0010] 1 Reject H0
RPCt does not Granger cause Edu4t 084218 [0004] 1 Reject H0
RPCt does not Granger cause Edu5t 001684 [0682] 1 Cannot reject H0
RPCt does not Granger cause Edu6t 107553 [0001] 1 Reject H0
RPCt does not Granger cause Edu7t 108798 [0001] 1 Reject H0
RPCt does not Granger cause Edu8t 004283 [0513] 1 Cannot reject H0
RPCt does not Granger cause Edu9t 005627 [0453] 1 Cannot reject H0
RPCt does not Granger cause Edu10t 000417 [0838] 1 Cannot reject H0
Bivariate-Eduit and LFt
Eq (9) Edu1t does not Granger cause LFt 026469 [0104] 1 Reject H0
Edu2t does not Granger cause LFt 012355 [0266] 1 Cannot reject H0
Edu3t does not Granger cause LFt 020468 [0153] 1 Cannot reject H0
Edu4t does not Granger cause LFt 098042 [0002] 1 Reject H0
Edu5t does not Granger cause LFt 049986 [0025] 1 Reject H0
Edu6t does not Granger cause LFt 016896 [0194] 1 Cannot reject H0
Edu7t does not Granger cause LFt 015167 [0218] 1 Cannot reject H0
Edu8t does not Granger cause LFt 184475 [0000] 1 Reject H0
Edu9t does not Granger cause LFt 003986 [0528] 1 Cannot reject H0
Edu10t does not Granger cause LFt 010899 [0296] 1 Cannot reject H0
Eq (10) LFt does not Granger cause Edu1t 107709 [0001] 1 Reject H0
LFt does not Granger cause Edu2t 071204 [0008] 1 Reject H0
LFt does not Granger cause Edu3t 136419 [0000] 1 Reject H0
LFt does not Granger cause Edu4t 056225 [0018] 1 Reject H0
LFt does not Granger cause Edu5t 057141 [0017] 1 Reject H0
LFt does not Granger cause Edu6t 091531 [0002] 1 Reject H0
LFt does not Granger cause Edu7t 095063 [0002] 1 Reject H0
LFt does not Granger cause Edu8t 021313 [0144] 1 Cannot reject H0
LFt does not Granger cause Edu9t 069389 [0008] 1 Reject H0
LFt does not Granger cause Edu10t 000743 [0785] 1 Cannot reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335330
Table II
Trivariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Trivariate-RGDPt RPCt and Eduit
Eq (11) Edu1t does not Granger cause RGDPt 005481 [0459] 1 Cannot reject H0
Edu2t does not Granger cause RGDPt 105415 [0001] 1 Reject H0
Edu3t does not Granger cause RGDPt 030370 [0081] 1 Reject H0
Edu4t does not Granger cause RGDPt 022525 [0133] 1 Cannot reject H0
Edu5t does not Granger cause RGDPt 227510 [0000] 1 Reject H0
Edu6t does not Granger cause RGDPt 098494 [0002] 1 Reject H0
Edu7t does not Granger cause RGDPt 090460 [0003] 1 Reject H0
Edu8t does not Granger cause RGDPt 067381 [0009] 1 Reject H0
Edu9t does not Granger cause RGDPt 168617 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 085842 [0003] Reject H0
Eq (11a) RPCt does not Granger cause RGDP (Edu1 as a 3rd variable) 029029 [0088] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu2 as a 3rd variable) 024880 [0115] 1 Cannot reject H0
RPCt does not Granger cause RGDPt (Edu3t as a 3rd variable) 041380 [0042] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu4t as a 3rd variable) 036580 [0056] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu5t as a 3rd variable) 064811 [0011] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu6t as a 3rd variable) 024405 [0118] 1 Cannot reject H0
RPCt does not Granger cause RGDPt (Edu7t as a 3rd variable) 026008 [0107] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu8t as a 3rd variable) 081607 [0004] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu9t as a 3rd variable) 063133 [0012] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu10t as a 3rd variable) 115637 [0001] 1 Reject H0
Eq (12) RGDPt does not Granger cause Edu1t 176454 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 129776 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 018626 [0172] 1 Cannot reject H0
RGDPt does not Granger cause Edu4t 020449 [0153] 1 Cannot reject H0
RGDPt does not Granger cause Edu5t 144658 [0000] 1 Reject H0
RGDPt does not Granger cause Edu6t 175431 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 178356 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 042497 [0039] 1 Reject H0
RGDPt does not Granger cause Edu9t 082506 [0004] 1 Reject H0
RGDPt does not Granger cause Edu10t 008026 [0370] 1 Cannot reject H0
Eq (12a) RPCt does not Granger cause Edu1t 000122 [0912] 1 Cannot reject H0
RPCt does not Granger cause Edu2t 028750 [0090] 1 Reject H0
RPCt does not Granger cause Edu3t 058586 [0016] 1 Reject H0
RPCt does not Granger cause Edu4t 071372 [0008] 1 Reject H0
RPCt does not Granger cause Edu5t 302364 [0000] 1 Reject H0
RPCt does not Granger cause Edu6t 020474 [0152] 1 Cannot reject H0
RPCt does not Granger cause Edu7t 017533 [0185] 1 Cannot reject H0
RPCt does not Granger cause Edu8t 044926 [0034] 1 Reject H0
RPCt does not Granger cause Edu9t 240955 [0000] 1 Reject H0
RPCt does not Granger cause Edu10t 021006 [0147] 1 Cannot reject H0
Eq (13) RGDPt does not Granger cause RPCt (Edu1t as a 3rd variable) 055095 [0019] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu2t as a 3rd variable) 182287 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu3t as a 3rd variable) 191499 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu4t as a 3rd variable) 269133 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu5t as a 3rd variable) 172979 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu6t as a 3rd variable) 166347 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu7t as a 3rd variable) 161198 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu8t as a 3rd variable) 038521 [0050] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu9tas a 3rd variable) 183169 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu10t as a 3rd variable) 139552 [0000] 1 Reject H0
Eq (13a) Edu1t does not Granger cause RPCt 000122 [0912] 1 Cannot reject H0
Edu2t does not Granger cause RPCt 028750 [0090] 1 Reject H0
Edu3t does not Granger cause RPCt 058586 [0016] 1 Reject H0
Edu4t does not Granger cause RPCt 071372 [0008] 1 Reject H0
Edu5t does not Granger cause RPCt 302364 [0000] 1 Reject H0
Edu6t does not Granger cause RPCt 020474 [0152] 1 Cannot reject H0
Edu7t does not Granger cause RPCt 017533 [0185] 1 Cannot reject H0
Edu8t does not Granger cause RPCt 044926 [0034] 1 Reject H0
Edu9t does not Granger cause RPCt 240955 [0000] 1 Reject H0
Edu10t does not Granger cause RPCt 021006 [0147] 1 Cannot reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 331
Table III
Trivariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Trivariate-RGDPt LFt and Eduit
Eq (14) Edu1t does not Granger cause RGDPt 068472 [0009] 1 Reject H0
Edu2t does not Granger cause RGDPt 092326 [0002] 1 Reject H0
Edu3t does not Granger cause RGDPt 180477 [0000] 1 Reject H0
Edu4t does not Granger cause RGDPt 132070 [0000] 1 Reject H0
Edu5t does not Granger cause RGDPt 109716 [0001] 1 Reject H0
Edu6t does not Granger cause RGDPt 086017 [0003] 1 Reject H0
Edu7t does not Granger cause RGDPt 078604 [0005] 1 Reject H0
Edu8t does not Granger cause RGDPt 020470 [0153] 1 Cannot reject H0
Edu9t does not Granger cause RGDPt 293293 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 005754 [0448] 1 Cannot reject H0
Eq (14a) LFt does not Granger cause RGDPt (Edu1t as a 3rd variable) 409533 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu2t as a 3rd variable) 332636 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu3t as a 3rd variable) 701171 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu4t as a 3rd variable) 605496 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu5t as a 3rd variable) 240867 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu6t as a 3rd variable) 330495 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu7t as a 3rd variable) 332860 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu8t as a 3rd variable) 352003 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu9t as a 3rd variable) 573087 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu10t as a 3rd variable) 343199 [0000] 1 Reject H0
Eq (15) RGDPt does not Granger cause Edu1t 134939 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 804323 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 109273 [0001] 1 Reject H0
RGDPt does not Granger cause Edu4t 278785 [0000] 1 Reject H0
RGDPt does not Granger cause Edu5t 050547 [0025] 1 Reject H0
RGDPt does not Granger cause Edu6t 790307 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 738342 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 043402 [0037] 1 Reject H0
RGDPt does not Granger cause Edu9t 175731 [0000] 1 Reject H0
RGDPt does not Granger cause Edu10t 061709 [0013] 1 Reject H0
Eq (15a) LFt does not Granger cause Edu1t 009324 [0334] 1 Cannot reject H0
LFt does not Granger cause Edu2t 377339 [0000] 1 Reject H0
LFt does not Granger cause Edu3t 176565 [0000] 1 Reject H0
LFt does not Granger cause Edu4t 180046 [0000] 1 Reject H0
LFt does not Granger cause Edu5t 091061 [0003] 1 Reject H0
LFt does not Granger cause Edu6t 355203 [0000] 1 Reject H0
LFt does not Granger cause Edu7t 327354 [0000] 1 Reject H0
LFt does not Granger cause Edu8t 053664 [0021] 1 Reject H0
LFt does not Granger cause Edu9t 251724 [0000] 1 Reject H0
LFt does not Granger cause Edu10t 060787 [0014] 1 Reject H0
Eq (16) Edu1t does not Granger cause LFt 036697 [0055] 1 Reject H0
Edu2t does not Granger cause LFt 004605 [0497] 1 Cannot reject H0
Edu3t does not Granger cause LFt 093988 [0002] 1 Reject H0
Edu4t does not Granger cause LFt 177287 [0000] 1 Reject H0
Edu5t does not Granger cause LFt 059203 [0015] 1 Reject H0
Edu6t does not Granger cause LFt 007202 [0396] 1 Cannot reject H0
Edu7t does not Granger cause LFt 005520 [0458] 1 Cannot reject H0
Edu8t does not Granger cause LFt 241662 [0000] 1 Reject H0
Edu9t does not Granger cause LFt 004009 [0527] 1 Cannot reject H0
Edu10t does not Granger cause LFt 058477 [0016] 1 Reject H0
Eq (16a) RGDPt does not Granger cause LFt (Edu1t as a 3rd variable) 002436 [0622] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu2t as a 3rd variable) 004276 [0513] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu3t as a 3rd variable) 047690 [0029] 1 Reject H0
RGDPt does not Granger cause LFt (Edu4t as a 3rd variable) 015207 [0218] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu5t as a 3rd variable) 040757 [0044] 1 Reject H0
RGDPt does not Granger cause LFt (Edu6t as a 3rd variable) 003392 [0560] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu7t as a 3rd variable) 004309 [0512] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu8t as a 3rd variable) 003145 [0575] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu9t as a 3rd variable) 017426 [0187] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu10t as a 3rd variable) 048448 [0028] 1 Reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335332
Table IV
Tetravariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Tetravariate-RGDPt RPCt LFt and Edut
Eq (17) Edu1t does not Granger cause RGDPt 029350 [0087] 1 Reject H0
Edu2t does not Granger cause RGDPt 065661 [0010] 1 Reject H0
Edu3t does not Granger cause RGDPt 097521 [0002] 1 Reject H0
Edu4t does not Granger cause RGDPt 071590 [0007] 1 Reject H0
Edu5t does not Granger cause RGDPt 116263 [0001] 1 Reject H0
Edu6t does not Granger cause RGDPt 059569 [0015] 1 Reject H0
Edu7t does not Granger cause RGDPt 054327 [0020] 1 Reject H0
Edu8t does not Granger cause RGDPt 040033 [0045] 1 Reject H0
Edu9t does not Granger cause RGDPt 195734 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 034374 [0064] 1 Reject H0
Eq (17a) LFt does not Granger cause RGDPt (Edut = Edu1) 251518 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu2) 165581 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu3) 316418 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu4) 289993 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu5) 109302 [0001] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu6) 165606 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu7) 168037 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu8) 176645 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu9) 247435 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu10) 146998 [0000] 1 Reject H0
Eq (17b) RPCt does not Granger cause RGDPt (Edut = Edu1) 042975 [0038] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu2) 039280 [0047] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu3) 034296 [0064] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu4) 027068 [0100] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu5) 062858 [0012] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu6) 039537 [0047] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu7) 040022 [0045] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu8) 045487 [0033] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu9) 068323 [0009] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu10) 083479 [0004] 1 Reject H0
Eq (18) RGDPt does not Granger cause Edu1t 150200 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 633103 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 045767 [0032] 1 Reject H0
RGDPt does not Granger cause Edu4t 122392 [0000] 1 Reject H0
RGDPt does not Granger cause Edu5t 004235 [0515] 1 Cannot reject H0
RGDPt does not Granger cause Edu6t 453644 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 418611 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 055973 [0454] 1 Cannot reject H0
RGDPt does not Granger cause Edu9t 053890 [0020] 1 Reject H0
RGDPt does not Granger cause Edu10t 011119 [0292] 1 Cannot reject H0
Eq (18a) LFt does not Granger cause Edu1t 006023 [0438] 1 Cannot reject H0
LFt does not Granger cause Edu2t 364559 [0000] 1 Reject H0
LFt does not Granger cause Edu3t 197423 [0000] 1 Reject H0
LFt does not Granger cause Edu4t 166511 [0000] 1 Reject H0
LFt does not Granger cause Edu5t 383886 [0000] 1 Reject H0
LFt does not Granger cause Edu6t 359377 [0000] 1 Reject H0
LFt does not Granger cause Edu7t 328249 [0000] 1 Reject H0
LFt does not Granger cause Edu8t 135310 [0000] 1 Reject H0
LFt does not Granger cause Edu9t 630068 [0000] 1 Reject H0
LFt does not Granger cause Edu01t 109365 [0001] 1 Reject H0
Eq (18b) RPCt does not Granger cause Edu1t 114248 [0001] 1 Reject H0
RPCt does not Granger cause Edu2t 036828 [0055] 1 Reject H0
RPCt does not Granger cause Edu3t 021023 [0147] 1 Cannot reject H0
RPCt does not Granger cause Edu4t 000484 [0826] 1 Cannot reject H0
RPCt does not Granger cause Edu5t 610934 [0000] 1 Reject H0
RPCt does not Granger cause Edu6t 070279 [0008] 1 Reject H0
RPCt does not Granger cause Edu7t 051166 [0024] 1 Reject H0
RPCt does not Granger cause Edu8t 167481 [0000] 1 Reject H0
RPCt does not Granger cause Edu9t 335271 [0000] 1 Reject H0
RPCt does not Granger cause Edu10t 067481 [0009] 1 Reject H0
Eq (19) Edu1 does not Granger cause RPCt 005154 [0473] 1 Cannot reject H0
Edu2 does not Granger cause RPCt 011954 [0274] 1 Cannot reject H0
Edu3 does not Granger cause RPCt 162365 [0000] 1 Reject H0
Edu4 does not Granger cause RPCt 148964 [0000] 1 Reject H0
Edu5 does not Granger cause RPCt 243978 [0000] 1 Reject H0
Edu6 does not Granger cause RPCt 040262 [0045] 1 Reject H0
Edu7 does not Granger cause RPCt 035138 [0061] 1 Reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 333
able IV (Continued )
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Edu8 does not Granger cause RPCt 030100 [0083] 1 Reject H0
Edu9 does not Granger cause RPCt 462564 [0000] 1 Reject H0
Edu10 does not Granger cause RPCt 009580 [0328] 1 Cannot reject H0
Eq (19a) RGDPt does not Granger cause RPCt (Edu1t as a 3rd variable) 009936 [0319] 1 Cannot reject H0
RGDPt does not Granger cause RPCt (Edu2t as a 3rd variable) 039369 [0047] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu3t as a 3rd variable) 003822 [0536] 1 Cannot reject H0
RGDPt does not Granger cause RPCt (Edu4t as a 3rd variable) 028000 [0094] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu5t as a 3rd variable) 039910 [0046] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu6t as a 3rd variable) 033500 [0067] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu7t as a 3rd variable) 029924 [0084] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu8t as a 3rd variable) 002803 [0597] 1 Cannot Reject H0
RGDPt does not Granger cause RPCt (Edu9t as a 3rd variable) 011416 [0285] 1 Cannot reject H0
RGDPt does not Granger cause RPCt (Edu10t as a 3rd variable) 006944 [0405] 1 Cannot reject H0
Eq (20) Edu1t does not Granger cause LFt 015302 [0216] 1 Cannot reject H0
Edu2t does not Granger cause LFt 001053 [0746] 1 Cannot reject H0
Edu3t does not Granger cause LFt 080072 [0005] 1 Reject H0
Edu4t does not Granger cause LFt 143854 [0000] 1 Reject H0
Edu5t does not Granger cause LFt 061159 [0013] 1 Reject H0
Edu6t does not Granger cause LFt 003113 [0577] 1 Cannot reject H0
Edu7t does not Granger cause LFt 002394 [0625] 1 Cannot reject H0
Edu8t does not Granger cause LFt 196804 [0000] 1 Reject H0
Edu9t does not Granger cause LFt 046285 [0496] 1 Cannot reject H0
Edu10t does not Granger cause LFt 04161 1 [0041] 1 Reject H0
Eq (20a) RGDPt does not Granger cause LFt (Edu1t as a 3rd variable) 006872 [0407] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu2t as a 3rd variable) 018604 [0173] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu3t as a 3rd variable) 066905 [0010] 1 Reject H0
RGDPt does not Granger cause LFt (Edu4t as a 3rd variable) 023249 [0127] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu5t as a 3rd variable) 070835 [0008] 1 Reject H0
RGDPt does not Granger cause LFt (Edu6t as a 3rd variable) 016501 [0199] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu7t as a 3rd variable) 018532 [0173] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu8t as a 3rd variable) 003730 [0541] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu9t as a 3rd variable) 039255 [0048] 1 Reject H0
RGDPt does not Granger cause LFt (Edu10t as a 3rd variable) 055266 [0019] 1 Reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335334
T
References
Abbas Q amp Peck J F (2008) Human capital and economic growth Pakistan 1960ndash2003 The Lahore Journal of Economics 13(1) 1ndash28Ayara N A (2002) The paradox of education and economic growth in Nigeria Empirical evidence The Nigerian Economic Society (NES) Pt 2 371ndash393Babatunde M A amp Adefabi R A (2005) Long run relationship between education and economic growth in Nigeria Evidence from the Johansenrsquos cointegration
approach Paper presented at the regional conference on education in West Africa Constraints and Opportunities Dakar Senegal November 1stndash2nd 2005Cornell UniversityCREAMinisterede lrsquoEducation du Senegal
Baldacci E Clements B Cui Q amp Gupta S (2005) What does it take to help the poor Finance and Development The Quarterly Magazine of the IMF 42(2)Changzheng Z Zhijian H amp Huaizu L (2007) An empirical study on education equity in China 1978ndash2004 Frontier in Economics of China 2(4) 536ndash544Chaudhary A R Asim I amp Gillani S Y M (2009) The nexus between higher education and economic growth An empirical investigation for Pakistan Pakistan
Journal of Commerce and Social Sciences 3Chaudhry I S Malik S amp Ashraf M (2006) Rural poverty in Pakistan Some related concepts issues and empirical analysis Pakistan Economic and Social Review
44(2) 259ndash276Diebolt C amp Litago J (1997) Education and economic growth in Germany before the Second World War An econometric analysis of dynamic relations Historical
Social Research 2(22) 132ndash149Easterly W (2001) The middle class consensus and economic development Journal of Economic Growth 6(4) 317ndash335Engle R F amp Granger C W J (1987) Cointegration and error correction Representation estimation and testing Econometrica 55 251ndash276Fernandez E amp Mauro P (2000) The role of human capital in economic growth The case of Spain (IMF Working Paper) International Monetary FundFrancis B amp Iyare S (2006) Education and development in the Caribbean A cointegration and causality approach Economics Bulletin 15(2) 1ndash13Galor O amp Moav O (2000) Das human capital Retrieved from httpeconpstcn brownedufacultygalorindexhtmlGoode R B (1959) Adding to the stock of physical and human capital American Economic Review 49(2) 147Government of Pakistan (1970ndash2009) Pakistan economic survey various issues Finance Division Islamabad Economic Advisorrsquos WingGregory A W amp Hansen B E (1996) Residual-based tests for cointegration in models with regime shifts Journal of Econometrics 70 99ndash126Grossman G M amp Helpman E (1991) Innovation and growth in the global economy Cambridge MIT PressGylfason T amp Zoega G (2003) Education social equality and economic growth A view of the landscape CESifo Economic Studies 49(4) 557ndash579Hassan S amp Ahmed H (2008) Educationrsquos contribution to the economic growth of sub-Saharan Africa Southwestern Economic Review 1(32) 175ndash190Islam T S Wadud M A amp Islam Q B T (2007) Relationship between education and GDP growth A multivariate causality analysis for Bangladesh Economics
Bulletin 3(35) 1ndash7Jin J C (2009) Economic research and economic growth Evidence from East Asian Economies Journal of Asian Economics 20 150ndash155Johansen S (1988) Statistical analysis of cointegration vectors Journal of Economic Dynamics and Control 12 231ndash254Johansen S amp Juselius K (1990) Maximum likelihood estimation and inference on cointegration with applications to the demand for money Oxford Bulletin of
Economics and Statistics 52 169ndash210Katırcıoglu S T (2009) Investigating higher-education-led growth hypothesis in a small Island Time series evidence from Northern Cyprus Paper presented at
Econ Anadolu 2009 Anadolu International Conference in Economics June 17ndash19 2009 TurkeyKhorasgani M F (2008) Higher education development and economic growth in Iran Education Business and Society Contemporary Middle Eastern Issues 1
162ndash174
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 335
Kui L (2005) The interactive causality between education and economic growth in China Retrieved from httppapersssrncomsol3paperscfmAbstrac-tid=920624
Loening J L (2004) Time series evidence on education and growth The case of Guatemala 1951ndash2002 Revista de Analisis Economico 19(2) 3ndash40Lucas R E (1988) On the mechanics of economic development Journal of Monetary Economics 22 3ndash42Macerinskiene I amp Vaiksnoraite B (2006) The role of higher education to economic development VadybaManagement 2(11)Mankiw N G Romer D amp Weil D N (1992) A contribution to the empirics of economic growth Quarterly Journal of Economics 107 407ndash437Momete D C (2007) Analysis of the relationship between employment and economic growth in Romania Fascicle of Management and Technological Engineering
VI(XVI)Morote E S (2000) Higher education employment and economic growth Mexico and Peru Retrieved from httpwwwamericanprofessororgdocumentation
lasapa perdocNarayan P K (2005) The saving and investment nexus for China Evidence from cointegration tests Applied Economics 37 1979ndash1990Permani R (2008) Education as a determinant of economic growth in East Asia Historical trends and empirical evidences (1965ndash2000) Retrieved from http
wwwuoweduaucommerceeconehsanzpdfsPermani202008pdfPesaran M H amp Pesaran B (1997) Working with Microfit 40 Interactive econometric analysis Oxford Oxford University PressPesaran M H amp Shin Y (1999) An autoregressive distributed lag modeling approach to cointegration analysis In S Strom (Ed) Econometrics and economic theory
in the 20th century Cambridge Cambridge University PressPesaran M H Shin Y amp Smith R J (2001) Bounds testing approaches to the analysis of level relationships Journal of Applied Econometrics 16 289ndash326Pradhan R P (2009) Education and economic growth in India Using error correction modeling International Research Journal of Finance and Economics 25Pritchett L (2001) Where has all the education gone The World Bank Economic Review 15(3)Quah D amp Rauch J E (1990) Openness and the rate of economic growth Journal Development of Studies 2(49) 307ndash335Rivera-Batiz L A amp Romer P M (1991) Economic integration and endogenous growth Quarterly Journal of Economics 106 531ndash555Romer P M (1986) Increasing returns and long run growth Journal of Political Economy 6(90) 1002ndash1037Romer P M (1989) Human capital and growth Theory and evidence (NBER Working Papers 3173) National Bureau of Economic Research IncRomer P M (1990) Endogenous technological change Journal of Political Economy 5(98) 71ndash101Rondinelli D amp Montgomery J (1995) Great policies Strategic innovations in Asia and the Pacific Basin Westport Praeger PublishingSaikkonen P amp Lutkepohl H (2000) Testing for the cointegration rank of a VAR process with structural shifts Journal of Business and Economic Statistics 18(4)
451ndash464Schultz T W (1961) Investment in human capital American Economic Review 51(1) 1State Bank of Pakistan (1972ndash2009) Annual reports Karachi SBP PressStengos T amp Aurangzeb A (2008) An empirical investigation of the relationship between education and growth in pakistan International Economic Journal 3
345ndash359 Retrieved from httpwwwinformaworldcomsmpptitledb=allcontent=t713685453tab=issueslistbranches=22-v2222Toda H Y amp Yamamoto T (1995) Statistical inference in vector autoregressive with possible integrated processes Journal of Econometrics 66 225ndash250United Nations (1997) Human Development Report New York Oxford University Press
- Education and economic growth in Pakistan A cointegration and causality analysis
-
- Introduction
- Review of literature
- Method and procedure
- Empirical results
-
- Unit root results
- Cointegration
- Toda-Yamamoto Augmented Granger Causality (TYAGC) Test
- Bivariate TYAGC framework
- Trivariate TYAGC framework
- Tetravariate TYAGC framework
- Figures in parentheses are p-values
-
- Conclusions and recommendations
-
- References
-
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335322
landlords pay even no income tax Galor and Moav (2000) noted that big landowners in Pakistan would have little incentiveto tax themselves to pay for schooling of the masses The additional tax revenue can be generated by abolishing VIP cultureand can be used in raising education health economic growth levels and hence development in Pakistan Pakistan is said tobe a country having growth miracles without development (Easterly 2001) The VIP and elite culture the high ethnicity andpolarization the foreign involvement in economic and political decision making and last but not the least the dictatorshiphave always been remained obstruction in the way of economic social human political and institutional developmentprocess of Pakistan South Asia (being poor neglected illiterate malnourished and less gender sensitive region of the world)in general and Pakistan in particular can enter in the global competition and enhance their economic growth by moreinvesting in their people The enormous potential of South Asia and Pakistanrsquos economy can easily be exploited by makingmore investment in human resources and carrying out some solid reforms especially in education system
In spite of carrying out number of reforms economic development in Pakistan is still lacking behind than even most ofdeveloping nations like Bangladesh There seems no clear-cut direction and strength of relationship between education andeconomic growth and between levels of education and economic growth in Pakistan Whether education causes economicgrowth or economic growth causes education Which level of education causes to economic growth more and vice versaThis study was designed to empirically answer such questions by using ARDL approach to cointegration and TodandashYamamoto causality technique
The Primary objective of this study is to examine the causal linkage firstly between education and RGDP secondlybetween different levels of education (ie school education college education and university education) and RGDP withinclusion and exclusion of stock of physical capital and stock of labour force as third and fourth variables
This empirical study has its significance in various aspects This study will be helpful for policy makers and higherauthorities It will provide a guideline for designing the future education planning Present study also provides motivation forthe future researchers for working in this domain Present study is a significant addition in existing literature It provides thedirection and enthusiasm to new researchers to explore more and more on this issue
2 Review of literature
Education one of the most important ingredients of human capital is considered as an important determinant ofsustainable economic growth (Goode 1959 Schultz 1961) The importance of the relationship between education andeconomic growth is acknowledged by the endogenous growth theory in late 1980s and early 1990s Productivity can beenhanced by investing more in education Human capital is the key component for boosting productivity which leads tohigher economic growth (Lucas 1988 Romer 1990) Human capital directly or indirectly serves as the determinant ofeconomic growth Education as components of human capital improves the socio-economic factors In the last century thefocus of researchers remained on the impacts of human capital on economic growth by increasing the facilities of educationand health A direct and significant linkage between human capital through educational developments and economic growthwas being observed
Education possesses multidimensional impacts on human beings and the economy It influences positively on theeconomic growth and employability of the persons while on the other hand it also helps in shaping the behavior of society topromote a cordial political social and economic environment which provides basis for further domestic and foreigninvestments in the country This socio-political polite educated workforce gets more respect more monetary rewards andstable employment prospects (Abbas amp Peck 2008 Fernandez amp Mauro 2000 Grossman amp Helpman 1991 Gylfason ampZoega 2003 Hassan amp Ahmed 2008 Loening 2004 Lucas 1988 Momete 2007 Quah amp Rauch 1990 Rivera-Batiz amp Romer1991 Romer 1986 1989 1990) Baldacci Clements Cui and Gupta (2005) found positive linkage between enrollment ratesandor years of schooling and GDP growth for developing countries
Economic growth and holistic development depend upon the highly skilled manpower Education and economic growthis not a one way process it is a two way process (Gylfason amp Zoega 2003 Hassan amp Ahmed 2008 Islam Wadud amp Islam2007 Jin 2009 Rondinelli amp Montgomery 1995) There does not exist one to one relationship between education andeconomic growth It is also affected by some other economic and non-economic variables like labour force physical capitaltrade openness happiness and health (Morote 2000) Better-educated workforce appeared to have a positive and significantimpact on economic growth (Loening 2004) Better-educated labour force had a considerable influence on economic growthby showing that human capital accumulation was one of the sources of economic growth (Babatunde amp Adefabi 2005)Morote (2000) estimated the causality between economic growth and higher education in the presence of employment as athird variable He used higher education enrollment per capita and per capita GDP growth rate as a proxy variable for highereducation and economic growth respectively This study revealed that the employment variable was a key factor in thehigher education and growth relationship Higher education had a positive effect on economic growth in both the short run(SR) and the long run (LR) (Francis amp Iyare 2006 Katırcıoglu 2009 Macerinskiene amp Vaiksnoraite 2006 Permani 2008)
More and better education geared up economic growth directly as well as indirectly by more equality and cohesion(Changzheng Zhijian amp Huaizu 2007 Gylfason amp Zoega 2003) Jin (2009) examined the Granger causal association betweenresearch productivity and economic growth for five East Asian countries He took total publications as the proxy of quality ofeducation at university level and RGDP as a measure of economic growth Bidirectional causal linkage between researchproductivity and economic growth was found in the case of Hong Kong due to its open economy focus on services sector suchas financial services trading and tourism In the case of Japan one-way causality running from economic growth to research
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 323
productivities was observed The reason behind this was the faster growth in 1960s and 1970s and increasing the share ofinvestment in tertiary education Economic growth caused by research publications was observed in Korea and TaiwanMoreover the significant causal flow running from publications to economic growth was no longer found in case ofSingapore This insignificant causal flow was perhaps found due to small number of universities in Singapore
Basic education causes economic growth while on the other side economic growth only causes higher education otherthan primary education No cointegration between education and national income was found (Kui 2005) Pradhan (2009)found unidirectional causality running from economic growth to education in India Islam et al (2007) examined linkagebetween education and GDP in the case of Bangladesh They used multivariate approach (Vector Error Correction ModelVECM) which is assumed more robust than the bivariate approach in the presence of labour and capital for the time seriesdata of 1976ndash2003 They found long run linkage between economic growth and education and further concluded that thereis bidirectional causality between education and economic growth It shows that Bangladesh is in that condition where GDPand education are helping each other to grow Bidirectional causality in economic growth and education could be possiblebecause education produces more accomplished labour force that directs to more productivity and ultimately economicgrowth Finally the general education has the greater returns than the vocational education (Hassan amp Ahmed 2008) Abbasand Peck (2008) explored the linkages between human capital and economic growth for Pakistan by utilizing cointegrationand error correction mechanism on time series data from 1960 to 2003 They found that human capital explained as much as39 of the increase in GDP per person in 1990 From this one can easily conclude that human capital positively contributedto economic growth in Pakistan (Chaudhary Iqbal amp Gillani 2009 Stengos amp Aurangzeb 2008) Thus human capital througheducation plays a major role in economic growth of a country
Majority of the above studies reveal that education and economic growth have the long run relationship and both thevariables have the causal relationship either one way or two way The present study is planned to explore the causalconnection between education (measured by 10 different indicators of education) and economic growth in Pakistan in theabsence and presence of third and fourth variables known as stock of capital and stock of labour force
3 Method and procedure
In light of objectives of the study the time series data on RGDP stock of capital stock of labour and ten different indicatorsof education have been used in Pakistani context for the period 1970ndash1971 to 2008ndash2009 The data were taken from differentissues of lsquolsquoPakistan Economic Surveyrsquorsquo and lsquolsquoAnnual Reports of State Bank of Pakistanrsquorsquo Furthermore a comprehensivemeasure of education known as education index was constructed for the period 1970ndash1971 to 2008ndash2009 by adopting UNDPmethodology given in 1999ndash2000 Education index is constructed by adding together adult literacy rate index (ALI) withtwo-third weightage and the combined primary secondary and tertiary gross enrollment ratio index (GEI) with one-thirdweightage The adult literacy rate (ALR) gives an indication of the ability to read and write while the gross enrolment ratio(GER) gives an indication of the level of education
Education Index frac14 2
3 ALI thorn 1
3 GEI
Adult Literacy Index ethALITHORN frac14 ALR 0
100 0
Gross Enrollment Index ethGEITHORN frac14 GER 0
100 0
where lsquo0rsquo and lsquo100rsquo are the minimum and maximum values of the variables adult literacy rate and gross enrollment ratioKeeping in view the theoretical postulates of the connection among RGDPt real physical capital (RPCt) labour force (LFt)
and education (Edut) the following models have been specified as
ln RGDPt frac14 f ethln RPCt ln LFt ln EduitTHORN (A)
ln Eduit frac14 f ethln RGDPt ln RPCt ln LFtTHORN (B)
To find out the relationship between Eduit and RGDPt various functional forms have been tested and the most appropriatefunctional forms ie log linear form for the variables RGDPt and Eduit were specified as
ln RGDPt frac14 b0 thorn b1 ln RPCt thorn b2 ln LFt thorn b3 ln Eduit thorn e1 (Model 1)
ln Eduit frac14 g0 thorn g1 RGDPt thorn g2 ln RPCt thorn g3 ln LFt thorn e2 (Model 2)
where ln = natural logarithm RGDPt = a proxy used to measure economic growth RPCt = stock of physical capital in realterms gross fixed capital formation deflated by GDP deflator LFt = stock of labour force Eduit = educational capital as takenby Ayara (2002) Mankiw Romer and Weil (1992) and Pritchett (2001) in extended Solow Model In literature education wasmeasured by using different indicators such as Edu1t = education index a key indicator used as a proxy to measure
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335324
educational development Edu2t = school enrollment ratio Edu3t = college enrollment ratio Edu4t = professional collegeenrollment ratio Edu5t = university enrollment ratio Edu6t = total enrollment ratio Edu7t = total general enrollment ratioEdu8t = higher education including professional education enrollment ratio Edu9t = general higher education enrollmentratio and Edu10t = education expenditure as percentage of GNP
RGDPt as a proxy to measure economic growth has also been utilized by Islam et al (2007) Abbas and Peck (2008) Jin(2009) Katırcıoglu (2009) and Chaudhary et al (2009) Gross fixed capital formation deflated by GDP deflator has also beenused as a proxy for RPC by Abbas and Peck (2008) Khorasgani (2008) and Chaudhary et al (2009) Stock of labour force as aproxy for measuring stock of labour has been already utilized by Islam et al (2007) and Chaudhary et al (2009)
Enrollment ratios are derived by dividing total enrollment of each category or level of education to the population of thatrespective age group These indicators have been used by Diebolt and Litago (1997) Gylfason and Zoega (2003) Islam et al(2007) and Pradhan (2009)
A number of cointegration techniques such as residual based EnglendashGranger (1987) test Johansen (1988) Johansen andJuselius (1990) Gregory and Hansen (1996) Saikkonen and Lutkepohl (2000) were available in literature This study used arelatively new and more robust cointegration approach known as Autoregressive Distributed Lag Model (ARDL) to determinethe long run relationship among variables of interest Although ARDL Approach can be applied whether the variables are I(0)
or I(1) or fractionally integrated but it is still pre requisite for the ARDL model to apply that none of the variables underconsideration is integrated of order lsquolsquo2rsquorsquo or higher In order to examine the causal nexus between Eduit and RGDPt theAugmented Granger Causality approach given by Toda and Yamamoto (1995) is applied
4 Empirical results
41 Unit root results
The study utilized different unit root tests such as Augmented Dickey-Fuller Test (ADF) Phillips-Perron Test (PP) Dickey-Fuller Generalized Least Square Test (DF-GLS) and Ng-Perron in order to make sure that none of the variables is of I(2) orhigher order A summary of unit root results regarding order of integration based on different above unit root criteria is givenin Table 1
According to ADF PP DF-GLS and Ng-Perron tests results in Table 1 RPCt LFt Edu2t Edu3t Edu4t Edu5t Edu6t Edu7t andEdu8t are of I(1) with constant while Edu1t is of I(0) with intercept and trend RGDPt is of I(1) according to ADF PP and DF-GLSwhile Ng-Perron exhibits RGDPt is of I(0) The order of the integration for Edu10t is zero according to all criteriarsquos Edu9t is ofI(1) with intercept and trend I(1) with constant I(0) with constant and I(0) with constant and trend according to ADF PP DF-GLS and Ng-Perron criteriarsquos respectively Edu9t is of I(1) according to ADF and PP while it is of I(0) according to DF-GLS andNg-Perron criteriarsquos so Edu9t seems to be fractionally integrated None of the variables is of I(2) according all criteriarsquos So theappropriate technique to cointegration is the ARDL approach to cointegration
To examine the long run (LR) relationship between RGDPt RPCt LFt and Eduit this study used the error-correction versionof ARDL approach of Model 1 and Model 2 by following Pesaran and Pesaran (1997) and Pesaran and Shin (1999) as
Dln RGDPt frac14 a0RGDPtthornXn
ifrac141
biRGDPtDln RGDPti thorn
Xn
ifrac141
ciRGDPtDln RPCti thorn
Xn
ifrac141
diRGDPtDln LFti
thornXn
ifrac141
eiRGDPtDln Eduiti thorn d1RGDPt
ln RGDPt1 thorn d2RGDPtln RPCt1 thorn d3RGDPt
ln LFt1
thorn d4RGDPtln Eduit1 (Model 1A)
Table 1
Order of integration
Variable ADF PP DF-GLS Ng-Perron
Intercept Intercept
and trend
Intercept Intercept
and trend
Intercept Interpret
and trend
Intercept Intercept
and trend
RGDPt I(1) I(1) I(1) I(0)
RPCt I(1) I(1) I(1) I(1)
LFt I(1) I(1) I(1) I(1)
Edu1t I(0) I(0) I(0) I(0)
Edu2t I(1) I(1) I(1) I(1)
Edu3t I(1) I(1) I(1) I(1)
Edu4t I(1) I(1) I(1) I(1)
Edu5t I(1) I(1) I(1) I(1)
Edu6t I(1) I(1) I(1) I(1)
Edu7t I(1) I(1) I(1) I(1)
Edu8t I(1) I(1) I(1) I(1)
Edu9t I(1) I(1) I(0) I(0)
Edu10t I(0) I(0) I(0) I(0)
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 325
Dln Eduit frac14 a0EduitthornXn
ifrac141
biEduitDln Eduiti thorn
Xn
ifrac141
ciEduitDln RPCti thorn
Xn
ifrac141
diEduitDln RGDPti thorn
Xn
ifrac141
eiEduitDln LFti
thorn d1Eduitln Eduit1 thorn d2Eduitln RPCt1 thorn d3Eduitln RGDPt1 thorn d4Eduitln LFt1 (Model 2A)
The coefficients (b c d and e) of the part one of the Model 1A and Model 2A represent SR dynamics and ds determine LRrelationship The first step in ARDL model was to examine long run linkage among the variables by calculating familiar F-statistic on the differenced variables components of Unrestricted Error Correction Mechanism (UECM) model for the jointsignificance of the coefficients of lagged level of the variables In this first step the regression equation estimated for thedependent variable RGDPt is defined as
Dln RGDPt frac14 a0RGDPtthornXn
ifrac141
biRGDPtDln RGDPti thorn
Xn
ifrac141
ciRGDPtDln RPCti thorn
Xn
ifrac141
diRGDPtDln LFti
thornXn
ifrac141
eiRGDPtDln Eduiti (Model 1B)
To create error correction mechanism in this equation 1st lag of the level of each variable is added to Model 1B and a variableaddition test is conducted by calculating F-test on the joint significance of all the added lagged level variables
Dln RGDPt frac14 a0RGDPtthornXn
ifrac141
biRGDPtDln RGDPti thorn
Xn
ifrac141
ciRGDPtDln RPCti thorn
Xn
ifrac141
diRGDPtDln LFti
thornXn
ifrac141
eiRGDPtDln Eduiti thorn d1RDGPt
ln RGDPt1 thorn d2RGDPtln RPCt1 thorn d3RGDPt
ln LFt1
thorn d4RGDPt ln Eduit1 (Model 1C)
The null hypothesis for no cointegration for the variable RGDPt against alternative hypothesis is given as
H0 d1RGDPtfrac14 d2RGDPt
frac14 d3RGDPtfrac14 d4RGDPt
frac14 0
H1 d1RGDPt6frac14 d2RGDPt
6frac14 d3RGDPt6frac14 d4RGDPt
6frac14 0
This is denoted as FRGDPt (RGDPtRPCt LFt Eduit)This hypothesis is being tested by the familiar F-testIf the calculated F-statistic is higher than the upper bounds critical value given by Pesaran Shin and Smith (2001) and
Narayan (2005) the null hypothesis of no cointegration is rejected implying that there exists a LR relationship among theRGDPt RPCt LFt Eduit when RGDPt is the dependent variable If the calculated F-statistic is less than the lower bounds criticalvalue then the null hypothesis of no cointegration cannot be rejected If the F-value falls in between lower and upper boundscritical values the test statistic will be inconclusive The value of the F depends upon the sample size constant andor a trendof ARDL and number of explanatory variables
42 Cointegration
The ARDL approach is applied to examine the long run relationship by conducting F-statistic The cointegration resultsare presented in Tables 2 and 3 The values of estimated F-test for RGDPt are shown in Table 2
Pesaran et al (2001) lower and upper critical values for bounds testing ARDL for 1 5 and 10 significance levels are365ndash466 279ndash367 and 237ndash320 respectively Narayan (2005) lower and upper critical values for Bound Testing ARDL for1 5 and 10 significance level are 502ndash661 355ndash480 and 293ndash402 respectively
All the indicators of education except Edu8 indicate that there exists cointegration relationship among RGDPt RPCt LFt
and Eduit when RGDPt is the dependent variable according to Pesaran et al (2001) CVs because there is at least one F-valuethat is greater than the upper critical bounds value Cointegration exists among RGDPt RPCt LFt and Eduit (as Eduit ismeasured by Edu1t Edu2t Edu4t Edu5t Edu9t) when RGDPt is the dependent variable according to Narayan (2005) CVs Thenull hypothesis of no cointegration is not rejected for Edu8t according to both CVs
Pesaran et al (2001) lower and upper critical values for bounds testing ARDL for 1 5 and 10 significance levels are365ndash466 279ndash367 and 237ndash320 respectively Narayan (2005) lower and upper critical values for Bound Testing ARDL for1 5 and 10 significance level are 502ndash661 355ndash480 and 293ndash402 respectively
The cointegration results in Table 3 shows that there is LR linkage between Eduit RGDPt LFt and RPCt when Eduit (as Eduit
is represented by Edu1t Edu2t Edu5t Edu6t Edu7t Edu9t and Edu10t) is the dependent variable according to both Pesaran et al(2001) and Narayan (2005) CVs because at least one partial F statistic is greater than the upper critical bounds value There
Table 2
Cointegration
Dependent variable when RGDPt serves as dependent variable Lag length Cointegration results based on critical
values (CVs) given by
1 2 3 4 Pesaran et al (2001) Narayan (2005)
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu1t)] 167 419 203 214 Cointegration Cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu2t)] 281 340 226 179 Cointegration No cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu3t)] 209 644 203 145 Cointegration Cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu4t)] 234 619 263 190 Cointegration Cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu5t)] 253 454 257 236 Cointegration Cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu6t)] 287 336 231 181 Cointegration No cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu7t)] 277 338 230 181 Cointegration No cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu8t)] 114 172 203 165 No cointegration No cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu9t)] 274 482 188 117 Cointegration Cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu10t)] 237 392 246 203 Cointegration No cointegration
Table 3
Cointegration
Dependent variable when Eduit serves as dependent variable Lag length Cointegration results based on critical
values (CV) given by Results
1 2 3 4 Pesaran et al (2001) Narayan (2005)
DEdu1t [FEdu1t (Edu1tRGDPt RPCt LFt)] 711 502 548 447 Cointegration Cointegration
DEdu2t [FEdu2t (Edu2tRGDPt RPCt LFt)] 446 336 192 308 Cointegration Cointegration
DEdu3t [FEdu3t (Edu3tRGDPt RPCt LFt)] 157 280 195 295 No cointegration No cointegration
DEdu4t [FEdu4t (Edu4tRGDPt RPCt LFt)] 202 156 295 223 No cointegration No cointegration
DEdu5t [FEdu5t (Edu5tRGDPt RPCt LFt)] 152 629 081 069 Cointegration Cointegration
DEdu6t [FEdu6t (Edu6tRGDPt RPCt LFt)] 488 366 225 305 Cointegration Cointegration
DEdu7t [FEdu7t (Edu7tRGDPt RPCt LFt)] 475 362 226 314 Cointegration Cointegration
DEdu8t [FEdu8t (Edu8tRGDPt RPCt LFt)] 156 182 089 101 No cointegration No cointegration
DEdu9t [FEdu9t (Edu9tRGDPt RPCt LFt)] 322 443 417 286 Cointegration Cointegration
DEdu10t [FEdu10t (Edu10tRGDPt RPCt LFt)] 341 527 523 842 Cointegration Cointegration
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335326
exists no cointegration among Eduit RGDPt RPCt and LFt when Eduit is represented by Edu3t Edu4t and Edu8t In conclusioneducation and RGDPt are found to be cointegrated ie they possess LR relationship
43 TodandashYamamoto Augmented Granger Causality (TYAGC) Test
Keeping in view the objectives of the study TYAGC was applied for data analysis To examine Augmented GrangerCausality Test among RGDPt RPCt LFt and Eduit the following equations are being estimated The estimated results of TYAGCprocedure are presented in Tables IndashIV
44 Bivariate TYAGC framework
The bivariate causality between RGDPt and Eduit (Eqs (1) and (2)) between RGDPt and RPCt (Eqs (3) and (4)) betweenRGDPt and LFt (Eqs (5) and (6)) between Eduit and RPCt (Eqs (7) and (8)) and between Eduit and LFt (Eqs (9) and (10)) wasestimated by using TYAGC technique and in presented in Table I
RGDPt frac14 a1 thornX3
ifrac141
b1iRGDPti thornX3
ifrac141
g1iEduiti thorn u1t (1)
Eduit frac14 a2 thornX3
ifrac141
b2iRGDPti thornX3
ifrac141
g2iEduiti thorn u2t (2)
RGDPt frac14 a3 thornX3
ifrac141
b3iRGDPti thornX3
ifrac141
g3iRPCti thorn u3t (3)
RPCt frac14 a4 thornX3
ifrac141
b4iRGDPti thornX3
ifrac141
g4iRPCti thorn u4t (4)
RGDPt frac14 a5 thornX3
ifrac141
b5iRGDPti thornX3
ifrac141
g5iLFti thorn u5t (5)
LFt frac14 a6 thornX3
ifrac141
b6iRGDPti thornX3
ifrac141
g6iLFti thorn u6t (6)
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 327
Eduit frac14 a7 thornX3
ifrac141
b7iEduiti thornX3
ifrac141
g7iRPCti thorn u7t (7)
RPCt frac14 a8 thornX3
ifrac141
b8iEduiti thornX3
ifrac141
g8iRPCti thorn u8t (8)
Eduit frac14 a9 thornX3
ifrac141
b9iEduiti thornX3
ifrac141
g9iLFti thorn u9t (9)
LFt frac14 a10 thornX3
ifrac141
b10iEduiti thornX3
ifrac141
g10iLFti thorn u10t (10)
The null hypothesis that all the indicators of education and all levels of education do not Granger cause RGDPt was tested inTable I Bivariate TYAGC results indicate that the null hypothesis was rejected (Table I) Similarly the null hypothesis thatRGDPt does not Granger cause all the indicators and all levels of education is rejected except Edu8t and Edu10t It means thatthere exists two-way causality between education and RGDPt RGDPt fails to cause higher education and expenditures oneducation
The estimated results from Eqs (3) and (4) in Table I show the feedback Granger causality between RPCt and RGDPt LFt isfound to cause RGDPt at 99 level of confidence while its reverse is not true The results of Eqs (7) and (8) in Table I show thatthe feedback causality between Eduit and RPCt seems to exist because majority of the indicators of education are causingRPCt and vice versa The results from Eq (9) and (10) in Table I reveal that LFt Granger causes education while reverseseemed to be not true In conclusion education and all levels of education (school college and university) Granger causeRGDPt and RGDPt also Granger causes education and all levels of education Feedback causality between education andRGDPt is found in bivariate case
45 Trivariate TYAGC framework
The trivariate causality among RGDPt RPCt and Eduit (Eqs (11)ndash(13)) and among RGDPt LFt and Eduit (Eqs (14)ndash(16)) wasestimated by using TYAGC framework and is presented in Tables II and III
RGDPt frac14 a11 thornX3
ifrac141
b11iRGDPti thornX3
ifrac141
l11iRPCti thornX3
ifrac141
g11iEduiti thorn u11t (11)
Eduit frac14 a12 thornX3
ifrac141
b12iRGDPti thornX3
ifrac141
l12iRPCti thornX3
ifrac141
g12iEduiti thorn u12t (12)
RPCt frac14 a13 thornX3
ifrac141
b13iRGDPti thornX3
ifrac141
l13iRPCti thornX3
ifrac141
g13iEduiti thorn u13t (13)
RGDPt frac14 a14 thornX3
ifrac141
b14iRGDPti thornX3
ifrac141
l14iLFti thornX3
ifrac141
g14iEduiti thorn u14t (14)
Edut frac14 a15 thornX3
ifrac141
b15iRGDPti thornX3
ifrac141
l15iLFti thornX3
ifrac141
g15iEduiti thorn u15t (15)
LFt frac14 a16 thornX3
ifrac141
b16iRGDPti thornX3
ifrac141
l16iLFti thornX3
ifrac141
g16iEduiti thorn u16t (16)
The estimated results presented in Table II indicate that the null hypothesis of no Granger causality between majority of theindicators of education and RGDPt is rejected This also supports our previous bivariate causality results that there existsfeedback causality between education and RGDPt The trivariate result in Table II seems to support the previous bivariateresult regarding causality between education and RPCt and between RPCt and RGDPt
In case of trivariate causality analysis among RGDPt LFt and Eduit the results in Table III again indicate the two waycausality running between education and RGDPt Six out of ten indicators of education does Granger cause LFt while LFt
Granger causes nine indicators out of ten indicators of education The null hypothesis that LFt does not Granger cause RGDPt
in the presence of all indicators of education is rejected at 99 level of confidence So LFt seems to be a very importantvariable that affects two main variables of the study ie education and RGDPt
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335328
In conclusion education and all levels of education Granger cause RGDPt where as its revere ie Granger causalityrunning from RGDPt to education and all levels of education is only true in case of trivariate causality among RGDPt LFt andeducation From here one can easily conclude that the role of LFt as compared to RPCt is very important in understanding therelationship between education and RGDPt Feedback causality between education and RGDPt is also found in trivariate case
46 Tetravariate TYAGC framework
The tetravariate causality among RGDPt RPCt LFt and Eduit (Eqs (17)ndash(20)) was also estimated by using TYAGC techniqueand their results are presented in Table IV
RGDPt frac14 a17 thornX3
ifrac141
b17iRGDPti thornX3
ifrac141
g17iRPCti thornX3
ifrac141
l17iLFti thornX3
ifrac141
d17iEduiti thorn u17t (17)
Eduit frac14 a18 thornX3
ifrac141
b18iRGDPti thornX3
ifrac141
g18iRPCti thornX3
ifrac141
l18iLFti thornX3
ifrac141
d18iEduiti thorn u18t (18)
RPCt frac14 a19 thornX3
ifrac141
b19iRGDPti thornX3
ifrac141
g19iRPCti thornX3
ifrac141
l19iLFti thornX3
ifrac141
d19iEduiti thorn u19t (19)
LFt frac14 a20 thornX3
ifrac141
b20iRGDPti thornX3
ifrac141
g20iRPCti thornX3
ifrac141
l20iLFti thornX3
ifrac141
d20iEduiti thorn u20t (20)
The tetravariate TYAGC results presented in Table IV indicate that all the indicators of education Granger cause RGDPt whileRGDPt does Granger cause majority of the indicators of education (seven out of ten) RGDPt does not Granger cause Edu5t
(university education) Edu8t (higher education) and Edu10t (education expenditure) From this one can easily conclude thatthere exists two way causality between education and RGDPt in case of tetravariate causality analysis as have been the caseof bivariate and trivariate causality Regarding levels of education all levels of education (ie school education collegeeducation and university education) do Granger cause RGDPt while RGDPt does only cause school education and collegeeducation RGDPt does not Granger cause university education
LFt Granger causes RGDPt at 99 confidence level while RGDPt only Granger causes LFt in case of Edu3t Edu5t Edu9t andEdu10t In case of testing causality between RPCt and RGDPt in the presence of all indicators of education RPCt does Grangercause RGDPt and in reverse case RGDPt does not Granger cause RPCt in the presence of Edu1t Edu3t Edu8t Edu9t and Edu10tThese results show the unidirectional causality running from RPCt to RGDPt
The research hypothesis that LFt does not Granger cause Eduit is rejected at 99 confidence interval except wheneducation is measured by Eduit Labour force has been found to cause all levels of education On the other side education onlyGranger causes the LFt in the presence of Edu3t Edu4t Edu5t Edu8t and Edu10t RPC does not Granger cause education whenEdu3t and Edu4t are used as proxies of education All indicators of education except Edu1t Edu2t and Edu10t do Granger causeRPCt This implies that feedback causality between RPCt and education is observed
It can easily be concluded from the TYAGC results of Eq (17) in Table IV that among all levels of education General highereducation (Edu9t) causes RGDPt highly and most significantly (999 confidence level) The level of confidence of collegeeducation (Edu3t) and school education (Edu2t) causing RGDPt is found to be 2nd highest (significance at 997 confidencelevel) and 3rd highest (significance at 989 confidence level) respectively From Eq (18) in Table IV it can also be found thatthe level of confidence (999) of causing RGDPt to school education (Edu2t) is found to be highest
From the bivariate trivariate and tetravariate TYAGC tests results in Tables IndashIV the overall results of the study abouteducation and different levels of education (School College and University) are summarized in Table 4
Table 4
Causal nexus between education different levels of education with RGDPt
Hypothesis TYAGC procedure
Bivariate Trivariate Tetravariate
RGDPt and Edut RGDPt RPCt Edut RGDPt LFt Edut RGDPt LFt RPCt Edut
Education (Edu1t) does Granger cause RGDPt Yes (0089) No (0459) Yes (0009) Yes (0087)
RGDPt does Granger cause education (Edu1t) Yes (0000) Yes (0000) Yes (0000) Yes (0000)
School education (Edu2t) does Granger cause RGDPt Yes (0000) Yes (0001) Yes (0002) Yes (0010)
RGDPt does Granger cause school education (Edu2t) Yes (0000) Yes (0000) Yes (0000) Yes (0000)
College education (Edu3t) does Granger cause RGDPt Yes (0038) Yes (0081) Yes (0000) Yes (0002)
RGDPt does Granger cause college education (Edu3t) Yes (0003) No (0172) Yes (0001) Yes (0032)
University education (Edu5t) does Granger cause RGDPt Yes (0000) Yes (0000) Yes (0001) Yes (0001)
RGDPt does Granger cause university education (Edu5t) Yes (0089) Yes (0000) Yes (0025) No (0515)
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 329
47 Figures in parentheses are p-values
From the above results presented in Table 4 it can be concluded that there existed feedback causality between educationand RGDPt in all bivariate trivariate and tetravariate TYAGC causality cases All levels of education ie school educationcollege education and university education do Granger cause RGDPt in all causality cases RGDPt does Granger cause schooleducation in all causality cases RGDPt does Granger cause college education in all causality cases except trivariate causalitythat is running from RGDPt to education when RPCt serves as a third variable Table 4 also reveals that RGDPt does Grangercause university education only in a bivariate and trivariate causality cases RGDPt fails to Granger cause to universityeducation in tetravariate case
5 Conclusions and recommendations
This study aimed to explore the cointegration and causal relationship between education (measured by different indicatorsof education) and economic growth in Pakistan It is very essential for a country to invest more in education because it is one ofthe most important ingredients of human capital and hence economic development The nature and strength of the relationshipbetween education and economic growth is still not clear in case of Pakistan The main focus of this empirical study remained toobserve the causality and cointegration between education and economic growth in the absence and presence physical capitaland labour force Cointegration between education and economic growth was investigated using ARDL approach and the causallinkage between education and economic growth was examined in bivariate trivariate and tetravariate TYAGC frameworkDifferent indicators of education were utilized in this study to show the robustness of empirical results The causality betweeneducation and economic growth was examined in the presence and absence of stock of physical capital and stock of labour as athird and fourth variable The causality results indicate that there exist two-way causality between education and economicgrowth and between all levels of education and economic growth in case of bivariate TYAGC framework Education and alllevels of education do Granger cause economic growth in the presence of real physical capital as a third variable while economicgrowth causes all the indicators of education except college education professional college education and educationalexpenditures in the presence of real physical capital as a third variable in case of trivariate causality analysis In the presence oflabour force as a third variable feedback causality exists between education and economic growth and between all levels ofeducation and economic growth The results of tetravariate TYAGC Test indicate that education and all level of education doGranger cause economic growth while economic growth does Granger cause majority of the indicators of education (ie sevenout of ten) Economic growth does not Granger cause university education higher education including professional educationand expenditures on education The rise in university education higher education including professional education andexpenditures on education were considered as the key indicators to gauge human and social progress Economic growth doesnot seem to affect important educational indicators like university education higher education including professionaleducation and expenditures on education This seems to be consistent with Easterlyrsquos findings Easterly (2001) said thatPakistan is a country that made little social progress for given rates of GDP Among all levels of education General highereducation causes economic growth highly and most significantly as was explored by Stengos and Aurangzeb (2008) The level ofconfidence of causing economic growth to school education found to be highest This study also confirms the long runrelationship between education and economic growth
On the basis of the results of this study it is recommended that the government should focus more on higher educationparticularly to university education More funds should be allocated to education in line with others sectors particularly touniversity and higher education levels so that the economic growth can be further accelerated This will in turn leads tofurther education and hence development Poor should be facilitated to get higher education so that the polarization inhigher education may further be minimized Primary schooling should also be given priority because primary educationserves as an input for all higher levels of education The inverted educational expenditure pyramid may also be taken intoaccount Since the role of labour force seems to be very important in understanding the relationship between education andeconomic growth so it is suggested that labour force should be given more chances to enhance their skills The variablelabour force must be included while examining the causality between education and economic growth It is alsorecommended that the nexus between education and economic growth with inclusion of other variables other than physicalcapital and labour force should further be tested and generalized
Appendix A
Table I
Bivariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Bivariate-RGDPt and Eduit
Eq (1) Edu1t does not Granger cause RGDPt 028998 [0089] 1 Reject H0
Edu2t does not Granger cause RGDPt 144869 [0000] 1 Reject H0
Edu3t does not Granger cause RGDPt 043243 [0038] 1 Reject H0
Edu4t does not Granger cause RGDPt 039797 [0046] 1 Reject H0
Table I (Continued )
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Edu5t does not Granger cause RGDPt 217739 [0000] 1 Reject H0
Edu6t does not Granger cause RGDPt 137788 [0000] 1 Reject H0
Edu7t does not Granger cause RGDPt 126682 [0000] 1 Reject H0
Edu8t does not Granger cause RGDPt 041335 [0042] 1 Reject H0
Edu9t does not Granger cause RGDPt 160963 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 028642 [0091] 1 Reject H0
Eq (2) RGDPt does not Granger cause Edu1t 260926 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 230094 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 085441 [0003] 1 Reject H0
RGDPt does not Granger cause Edu4t 107403 [0001] 1 Reject H0
RGDPt does not Granger cause Edu5t 028935 [0089] 1 Reject H0
RGDPt does not Granger cause Edu6t 270343 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 273974 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 003162 [0574] 1 Cannot reject H0
RGDPt does not Granger cause Edu9t 027588 [0097] 1 Reject H0
RGDPt does not Granger cause Edu10t 000851 [0770] 1 Cannot reject H0
Bivariate-RGDPt and RPCt
Eq (3) RPCt does not Granger cause RGDPt 054972 [0019] 1 Reject H0
Eq (4) RGDPt does not Granger cause RPCt 167511 [0000] 1 Reject H0
Bivariate-RGDPt and LFt
Eq (5) LFt does not Granger cause RGDPt 227888 [0000] 1 Reject H0
Eq (6) RGDPt does not Granger cause LFt 012380 [0266] 1 Cannot reject H0
Bivariate-Eduit and RPCt
Eq (7) Edu1t does not Granger cause RPCt 094596 [0002] 1 Reject H0
Edu2t does not Granger cause RPCt 015434 [0214] 1 Cannot reject H0
Edu3t does not Granger cause RPCt 038233 [0051] 1 Reject H0
Edu4t does not Granger cause RPCt 000506 [0822] 1 Cannot reject H0
Edu5t does not Granger cause RPCt 298085 [0000] 1 Reject H0
Edu6t does not Granger cause RPCt 018289 [0176] 1 Cannot reject H0
Edu7t does not Granger cause RPCt 018976 [0168] 1 Cannot reject H0
Edu8t does not Granger cause RPCt 176399 [0000] 1 Reject H0
Edu9t does not Granger cause RPCt 224647 [0000] 1 Reject H0
Edu10t does not Granger cause RPCt 039174 [0048] 1 Reject H0
Eq (8) RPCt does not Granger cause Edu1t 091477 [0002] 1 Reject H0
RPCt does not Granger cause Edu2t 098821 [0002] 1 Reject H0
RPCt does not Granger cause Edu3t 066148 [0010] 1 Reject H0
RPCt does not Granger cause Edu4t 084218 [0004] 1 Reject H0
RPCt does not Granger cause Edu5t 001684 [0682] 1 Cannot reject H0
RPCt does not Granger cause Edu6t 107553 [0001] 1 Reject H0
RPCt does not Granger cause Edu7t 108798 [0001] 1 Reject H0
RPCt does not Granger cause Edu8t 004283 [0513] 1 Cannot reject H0
RPCt does not Granger cause Edu9t 005627 [0453] 1 Cannot reject H0
RPCt does not Granger cause Edu10t 000417 [0838] 1 Cannot reject H0
Bivariate-Eduit and LFt
Eq (9) Edu1t does not Granger cause LFt 026469 [0104] 1 Reject H0
Edu2t does not Granger cause LFt 012355 [0266] 1 Cannot reject H0
Edu3t does not Granger cause LFt 020468 [0153] 1 Cannot reject H0
Edu4t does not Granger cause LFt 098042 [0002] 1 Reject H0
Edu5t does not Granger cause LFt 049986 [0025] 1 Reject H0
Edu6t does not Granger cause LFt 016896 [0194] 1 Cannot reject H0
Edu7t does not Granger cause LFt 015167 [0218] 1 Cannot reject H0
Edu8t does not Granger cause LFt 184475 [0000] 1 Reject H0
Edu9t does not Granger cause LFt 003986 [0528] 1 Cannot reject H0
Edu10t does not Granger cause LFt 010899 [0296] 1 Cannot reject H0
Eq (10) LFt does not Granger cause Edu1t 107709 [0001] 1 Reject H0
LFt does not Granger cause Edu2t 071204 [0008] 1 Reject H0
LFt does not Granger cause Edu3t 136419 [0000] 1 Reject H0
LFt does not Granger cause Edu4t 056225 [0018] 1 Reject H0
LFt does not Granger cause Edu5t 057141 [0017] 1 Reject H0
LFt does not Granger cause Edu6t 091531 [0002] 1 Reject H0
LFt does not Granger cause Edu7t 095063 [0002] 1 Reject H0
LFt does not Granger cause Edu8t 021313 [0144] 1 Cannot reject H0
LFt does not Granger cause Edu9t 069389 [0008] 1 Reject H0
LFt does not Granger cause Edu10t 000743 [0785] 1 Cannot reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335330
Table II
Trivariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Trivariate-RGDPt RPCt and Eduit
Eq (11) Edu1t does not Granger cause RGDPt 005481 [0459] 1 Cannot reject H0
Edu2t does not Granger cause RGDPt 105415 [0001] 1 Reject H0
Edu3t does not Granger cause RGDPt 030370 [0081] 1 Reject H0
Edu4t does not Granger cause RGDPt 022525 [0133] 1 Cannot reject H0
Edu5t does not Granger cause RGDPt 227510 [0000] 1 Reject H0
Edu6t does not Granger cause RGDPt 098494 [0002] 1 Reject H0
Edu7t does not Granger cause RGDPt 090460 [0003] 1 Reject H0
Edu8t does not Granger cause RGDPt 067381 [0009] 1 Reject H0
Edu9t does not Granger cause RGDPt 168617 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 085842 [0003] Reject H0
Eq (11a) RPCt does not Granger cause RGDP (Edu1 as a 3rd variable) 029029 [0088] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu2 as a 3rd variable) 024880 [0115] 1 Cannot reject H0
RPCt does not Granger cause RGDPt (Edu3t as a 3rd variable) 041380 [0042] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu4t as a 3rd variable) 036580 [0056] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu5t as a 3rd variable) 064811 [0011] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu6t as a 3rd variable) 024405 [0118] 1 Cannot reject H0
RPCt does not Granger cause RGDPt (Edu7t as a 3rd variable) 026008 [0107] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu8t as a 3rd variable) 081607 [0004] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu9t as a 3rd variable) 063133 [0012] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu10t as a 3rd variable) 115637 [0001] 1 Reject H0
Eq (12) RGDPt does not Granger cause Edu1t 176454 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 129776 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 018626 [0172] 1 Cannot reject H0
RGDPt does not Granger cause Edu4t 020449 [0153] 1 Cannot reject H0
RGDPt does not Granger cause Edu5t 144658 [0000] 1 Reject H0
RGDPt does not Granger cause Edu6t 175431 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 178356 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 042497 [0039] 1 Reject H0
RGDPt does not Granger cause Edu9t 082506 [0004] 1 Reject H0
RGDPt does not Granger cause Edu10t 008026 [0370] 1 Cannot reject H0
Eq (12a) RPCt does not Granger cause Edu1t 000122 [0912] 1 Cannot reject H0
RPCt does not Granger cause Edu2t 028750 [0090] 1 Reject H0
RPCt does not Granger cause Edu3t 058586 [0016] 1 Reject H0
RPCt does not Granger cause Edu4t 071372 [0008] 1 Reject H0
RPCt does not Granger cause Edu5t 302364 [0000] 1 Reject H0
RPCt does not Granger cause Edu6t 020474 [0152] 1 Cannot reject H0
RPCt does not Granger cause Edu7t 017533 [0185] 1 Cannot reject H0
RPCt does not Granger cause Edu8t 044926 [0034] 1 Reject H0
RPCt does not Granger cause Edu9t 240955 [0000] 1 Reject H0
RPCt does not Granger cause Edu10t 021006 [0147] 1 Cannot reject H0
Eq (13) RGDPt does not Granger cause RPCt (Edu1t as a 3rd variable) 055095 [0019] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu2t as a 3rd variable) 182287 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu3t as a 3rd variable) 191499 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu4t as a 3rd variable) 269133 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu5t as a 3rd variable) 172979 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu6t as a 3rd variable) 166347 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu7t as a 3rd variable) 161198 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu8t as a 3rd variable) 038521 [0050] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu9tas a 3rd variable) 183169 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu10t as a 3rd variable) 139552 [0000] 1 Reject H0
Eq (13a) Edu1t does not Granger cause RPCt 000122 [0912] 1 Cannot reject H0
Edu2t does not Granger cause RPCt 028750 [0090] 1 Reject H0
Edu3t does not Granger cause RPCt 058586 [0016] 1 Reject H0
Edu4t does not Granger cause RPCt 071372 [0008] 1 Reject H0
Edu5t does not Granger cause RPCt 302364 [0000] 1 Reject H0
Edu6t does not Granger cause RPCt 020474 [0152] 1 Cannot reject H0
Edu7t does not Granger cause RPCt 017533 [0185] 1 Cannot reject H0
Edu8t does not Granger cause RPCt 044926 [0034] 1 Reject H0
Edu9t does not Granger cause RPCt 240955 [0000] 1 Reject H0
Edu10t does not Granger cause RPCt 021006 [0147] 1 Cannot reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 331
Table III
Trivariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Trivariate-RGDPt LFt and Eduit
Eq (14) Edu1t does not Granger cause RGDPt 068472 [0009] 1 Reject H0
Edu2t does not Granger cause RGDPt 092326 [0002] 1 Reject H0
Edu3t does not Granger cause RGDPt 180477 [0000] 1 Reject H0
Edu4t does not Granger cause RGDPt 132070 [0000] 1 Reject H0
Edu5t does not Granger cause RGDPt 109716 [0001] 1 Reject H0
Edu6t does not Granger cause RGDPt 086017 [0003] 1 Reject H0
Edu7t does not Granger cause RGDPt 078604 [0005] 1 Reject H0
Edu8t does not Granger cause RGDPt 020470 [0153] 1 Cannot reject H0
Edu9t does not Granger cause RGDPt 293293 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 005754 [0448] 1 Cannot reject H0
Eq (14a) LFt does not Granger cause RGDPt (Edu1t as a 3rd variable) 409533 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu2t as a 3rd variable) 332636 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu3t as a 3rd variable) 701171 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu4t as a 3rd variable) 605496 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu5t as a 3rd variable) 240867 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu6t as a 3rd variable) 330495 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu7t as a 3rd variable) 332860 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu8t as a 3rd variable) 352003 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu9t as a 3rd variable) 573087 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu10t as a 3rd variable) 343199 [0000] 1 Reject H0
Eq (15) RGDPt does not Granger cause Edu1t 134939 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 804323 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 109273 [0001] 1 Reject H0
RGDPt does not Granger cause Edu4t 278785 [0000] 1 Reject H0
RGDPt does not Granger cause Edu5t 050547 [0025] 1 Reject H0
RGDPt does not Granger cause Edu6t 790307 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 738342 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 043402 [0037] 1 Reject H0
RGDPt does not Granger cause Edu9t 175731 [0000] 1 Reject H0
RGDPt does not Granger cause Edu10t 061709 [0013] 1 Reject H0
Eq (15a) LFt does not Granger cause Edu1t 009324 [0334] 1 Cannot reject H0
LFt does not Granger cause Edu2t 377339 [0000] 1 Reject H0
LFt does not Granger cause Edu3t 176565 [0000] 1 Reject H0
LFt does not Granger cause Edu4t 180046 [0000] 1 Reject H0
LFt does not Granger cause Edu5t 091061 [0003] 1 Reject H0
LFt does not Granger cause Edu6t 355203 [0000] 1 Reject H0
LFt does not Granger cause Edu7t 327354 [0000] 1 Reject H0
LFt does not Granger cause Edu8t 053664 [0021] 1 Reject H0
LFt does not Granger cause Edu9t 251724 [0000] 1 Reject H0
LFt does not Granger cause Edu10t 060787 [0014] 1 Reject H0
Eq (16) Edu1t does not Granger cause LFt 036697 [0055] 1 Reject H0
Edu2t does not Granger cause LFt 004605 [0497] 1 Cannot reject H0
Edu3t does not Granger cause LFt 093988 [0002] 1 Reject H0
Edu4t does not Granger cause LFt 177287 [0000] 1 Reject H0
Edu5t does not Granger cause LFt 059203 [0015] 1 Reject H0
Edu6t does not Granger cause LFt 007202 [0396] 1 Cannot reject H0
Edu7t does not Granger cause LFt 005520 [0458] 1 Cannot reject H0
Edu8t does not Granger cause LFt 241662 [0000] 1 Reject H0
Edu9t does not Granger cause LFt 004009 [0527] 1 Cannot reject H0
Edu10t does not Granger cause LFt 058477 [0016] 1 Reject H0
Eq (16a) RGDPt does not Granger cause LFt (Edu1t as a 3rd variable) 002436 [0622] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu2t as a 3rd variable) 004276 [0513] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu3t as a 3rd variable) 047690 [0029] 1 Reject H0
RGDPt does not Granger cause LFt (Edu4t as a 3rd variable) 015207 [0218] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu5t as a 3rd variable) 040757 [0044] 1 Reject H0
RGDPt does not Granger cause LFt (Edu6t as a 3rd variable) 003392 [0560] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu7t as a 3rd variable) 004309 [0512] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu8t as a 3rd variable) 003145 [0575] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu9t as a 3rd variable) 017426 [0187] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu10t as a 3rd variable) 048448 [0028] 1 Reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335332
Table IV
Tetravariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Tetravariate-RGDPt RPCt LFt and Edut
Eq (17) Edu1t does not Granger cause RGDPt 029350 [0087] 1 Reject H0
Edu2t does not Granger cause RGDPt 065661 [0010] 1 Reject H0
Edu3t does not Granger cause RGDPt 097521 [0002] 1 Reject H0
Edu4t does not Granger cause RGDPt 071590 [0007] 1 Reject H0
Edu5t does not Granger cause RGDPt 116263 [0001] 1 Reject H0
Edu6t does not Granger cause RGDPt 059569 [0015] 1 Reject H0
Edu7t does not Granger cause RGDPt 054327 [0020] 1 Reject H0
Edu8t does not Granger cause RGDPt 040033 [0045] 1 Reject H0
Edu9t does not Granger cause RGDPt 195734 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 034374 [0064] 1 Reject H0
Eq (17a) LFt does not Granger cause RGDPt (Edut = Edu1) 251518 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu2) 165581 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu3) 316418 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu4) 289993 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu5) 109302 [0001] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu6) 165606 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu7) 168037 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu8) 176645 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu9) 247435 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu10) 146998 [0000] 1 Reject H0
Eq (17b) RPCt does not Granger cause RGDPt (Edut = Edu1) 042975 [0038] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu2) 039280 [0047] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu3) 034296 [0064] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu4) 027068 [0100] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu5) 062858 [0012] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu6) 039537 [0047] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu7) 040022 [0045] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu8) 045487 [0033] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu9) 068323 [0009] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu10) 083479 [0004] 1 Reject H0
Eq (18) RGDPt does not Granger cause Edu1t 150200 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 633103 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 045767 [0032] 1 Reject H0
RGDPt does not Granger cause Edu4t 122392 [0000] 1 Reject H0
RGDPt does not Granger cause Edu5t 004235 [0515] 1 Cannot reject H0
RGDPt does not Granger cause Edu6t 453644 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 418611 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 055973 [0454] 1 Cannot reject H0
RGDPt does not Granger cause Edu9t 053890 [0020] 1 Reject H0
RGDPt does not Granger cause Edu10t 011119 [0292] 1 Cannot reject H0
Eq (18a) LFt does not Granger cause Edu1t 006023 [0438] 1 Cannot reject H0
LFt does not Granger cause Edu2t 364559 [0000] 1 Reject H0
LFt does not Granger cause Edu3t 197423 [0000] 1 Reject H0
LFt does not Granger cause Edu4t 166511 [0000] 1 Reject H0
LFt does not Granger cause Edu5t 383886 [0000] 1 Reject H0
LFt does not Granger cause Edu6t 359377 [0000] 1 Reject H0
LFt does not Granger cause Edu7t 328249 [0000] 1 Reject H0
LFt does not Granger cause Edu8t 135310 [0000] 1 Reject H0
LFt does not Granger cause Edu9t 630068 [0000] 1 Reject H0
LFt does not Granger cause Edu01t 109365 [0001] 1 Reject H0
Eq (18b) RPCt does not Granger cause Edu1t 114248 [0001] 1 Reject H0
RPCt does not Granger cause Edu2t 036828 [0055] 1 Reject H0
RPCt does not Granger cause Edu3t 021023 [0147] 1 Cannot reject H0
RPCt does not Granger cause Edu4t 000484 [0826] 1 Cannot reject H0
RPCt does not Granger cause Edu5t 610934 [0000] 1 Reject H0
RPCt does not Granger cause Edu6t 070279 [0008] 1 Reject H0
RPCt does not Granger cause Edu7t 051166 [0024] 1 Reject H0
RPCt does not Granger cause Edu8t 167481 [0000] 1 Reject H0
RPCt does not Granger cause Edu9t 335271 [0000] 1 Reject H0
RPCt does not Granger cause Edu10t 067481 [0009] 1 Reject H0
Eq (19) Edu1 does not Granger cause RPCt 005154 [0473] 1 Cannot reject H0
Edu2 does not Granger cause RPCt 011954 [0274] 1 Cannot reject H0
Edu3 does not Granger cause RPCt 162365 [0000] 1 Reject H0
Edu4 does not Granger cause RPCt 148964 [0000] 1 Reject H0
Edu5 does not Granger cause RPCt 243978 [0000] 1 Reject H0
Edu6 does not Granger cause RPCt 040262 [0045] 1 Reject H0
Edu7 does not Granger cause RPCt 035138 [0061] 1 Reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 333
able IV (Continued )
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Edu8 does not Granger cause RPCt 030100 [0083] 1 Reject H0
Edu9 does not Granger cause RPCt 462564 [0000] 1 Reject H0
Edu10 does not Granger cause RPCt 009580 [0328] 1 Cannot reject H0
Eq (19a) RGDPt does not Granger cause RPCt (Edu1t as a 3rd variable) 009936 [0319] 1 Cannot reject H0
RGDPt does not Granger cause RPCt (Edu2t as a 3rd variable) 039369 [0047] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu3t as a 3rd variable) 003822 [0536] 1 Cannot reject H0
RGDPt does not Granger cause RPCt (Edu4t as a 3rd variable) 028000 [0094] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu5t as a 3rd variable) 039910 [0046] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu6t as a 3rd variable) 033500 [0067] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu7t as a 3rd variable) 029924 [0084] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu8t as a 3rd variable) 002803 [0597] 1 Cannot Reject H0
RGDPt does not Granger cause RPCt (Edu9t as a 3rd variable) 011416 [0285] 1 Cannot reject H0
RGDPt does not Granger cause RPCt (Edu10t as a 3rd variable) 006944 [0405] 1 Cannot reject H0
Eq (20) Edu1t does not Granger cause LFt 015302 [0216] 1 Cannot reject H0
Edu2t does not Granger cause LFt 001053 [0746] 1 Cannot reject H0
Edu3t does not Granger cause LFt 080072 [0005] 1 Reject H0
Edu4t does not Granger cause LFt 143854 [0000] 1 Reject H0
Edu5t does not Granger cause LFt 061159 [0013] 1 Reject H0
Edu6t does not Granger cause LFt 003113 [0577] 1 Cannot reject H0
Edu7t does not Granger cause LFt 002394 [0625] 1 Cannot reject H0
Edu8t does not Granger cause LFt 196804 [0000] 1 Reject H0
Edu9t does not Granger cause LFt 046285 [0496] 1 Cannot reject H0
Edu10t does not Granger cause LFt 04161 1 [0041] 1 Reject H0
Eq (20a) RGDPt does not Granger cause LFt (Edu1t as a 3rd variable) 006872 [0407] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu2t as a 3rd variable) 018604 [0173] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu3t as a 3rd variable) 066905 [0010] 1 Reject H0
RGDPt does not Granger cause LFt (Edu4t as a 3rd variable) 023249 [0127] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu5t as a 3rd variable) 070835 [0008] 1 Reject H0
RGDPt does not Granger cause LFt (Edu6t as a 3rd variable) 016501 [0199] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu7t as a 3rd variable) 018532 [0173] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu8t as a 3rd variable) 003730 [0541] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu9t as a 3rd variable) 039255 [0048] 1 Reject H0
RGDPt does not Granger cause LFt (Edu10t as a 3rd variable) 055266 [0019] 1 Reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335334
T
References
Abbas Q amp Peck J F (2008) Human capital and economic growth Pakistan 1960ndash2003 The Lahore Journal of Economics 13(1) 1ndash28Ayara N A (2002) The paradox of education and economic growth in Nigeria Empirical evidence The Nigerian Economic Society (NES) Pt 2 371ndash393Babatunde M A amp Adefabi R A (2005) Long run relationship between education and economic growth in Nigeria Evidence from the Johansenrsquos cointegration
approach Paper presented at the regional conference on education in West Africa Constraints and Opportunities Dakar Senegal November 1stndash2nd 2005Cornell UniversityCREAMinisterede lrsquoEducation du Senegal
Baldacci E Clements B Cui Q amp Gupta S (2005) What does it take to help the poor Finance and Development The Quarterly Magazine of the IMF 42(2)Changzheng Z Zhijian H amp Huaizu L (2007) An empirical study on education equity in China 1978ndash2004 Frontier in Economics of China 2(4) 536ndash544Chaudhary A R Asim I amp Gillani S Y M (2009) The nexus between higher education and economic growth An empirical investigation for Pakistan Pakistan
Journal of Commerce and Social Sciences 3Chaudhry I S Malik S amp Ashraf M (2006) Rural poverty in Pakistan Some related concepts issues and empirical analysis Pakistan Economic and Social Review
44(2) 259ndash276Diebolt C amp Litago J (1997) Education and economic growth in Germany before the Second World War An econometric analysis of dynamic relations Historical
Social Research 2(22) 132ndash149Easterly W (2001) The middle class consensus and economic development Journal of Economic Growth 6(4) 317ndash335Engle R F amp Granger C W J (1987) Cointegration and error correction Representation estimation and testing Econometrica 55 251ndash276Fernandez E amp Mauro P (2000) The role of human capital in economic growth The case of Spain (IMF Working Paper) International Monetary FundFrancis B amp Iyare S (2006) Education and development in the Caribbean A cointegration and causality approach Economics Bulletin 15(2) 1ndash13Galor O amp Moav O (2000) Das human capital Retrieved from httpeconpstcn brownedufacultygalorindexhtmlGoode R B (1959) Adding to the stock of physical and human capital American Economic Review 49(2) 147Government of Pakistan (1970ndash2009) Pakistan economic survey various issues Finance Division Islamabad Economic Advisorrsquos WingGregory A W amp Hansen B E (1996) Residual-based tests for cointegration in models with regime shifts Journal of Econometrics 70 99ndash126Grossman G M amp Helpman E (1991) Innovation and growth in the global economy Cambridge MIT PressGylfason T amp Zoega G (2003) Education social equality and economic growth A view of the landscape CESifo Economic Studies 49(4) 557ndash579Hassan S amp Ahmed H (2008) Educationrsquos contribution to the economic growth of sub-Saharan Africa Southwestern Economic Review 1(32) 175ndash190Islam T S Wadud M A amp Islam Q B T (2007) Relationship between education and GDP growth A multivariate causality analysis for Bangladesh Economics
Bulletin 3(35) 1ndash7Jin J C (2009) Economic research and economic growth Evidence from East Asian Economies Journal of Asian Economics 20 150ndash155Johansen S (1988) Statistical analysis of cointegration vectors Journal of Economic Dynamics and Control 12 231ndash254Johansen S amp Juselius K (1990) Maximum likelihood estimation and inference on cointegration with applications to the demand for money Oxford Bulletin of
Economics and Statistics 52 169ndash210Katırcıoglu S T (2009) Investigating higher-education-led growth hypothesis in a small Island Time series evidence from Northern Cyprus Paper presented at
Econ Anadolu 2009 Anadolu International Conference in Economics June 17ndash19 2009 TurkeyKhorasgani M F (2008) Higher education development and economic growth in Iran Education Business and Society Contemporary Middle Eastern Issues 1
162ndash174
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 335
Kui L (2005) The interactive causality between education and economic growth in China Retrieved from httppapersssrncomsol3paperscfmAbstrac-tid=920624
Loening J L (2004) Time series evidence on education and growth The case of Guatemala 1951ndash2002 Revista de Analisis Economico 19(2) 3ndash40Lucas R E (1988) On the mechanics of economic development Journal of Monetary Economics 22 3ndash42Macerinskiene I amp Vaiksnoraite B (2006) The role of higher education to economic development VadybaManagement 2(11)Mankiw N G Romer D amp Weil D N (1992) A contribution to the empirics of economic growth Quarterly Journal of Economics 107 407ndash437Momete D C (2007) Analysis of the relationship between employment and economic growth in Romania Fascicle of Management and Technological Engineering
VI(XVI)Morote E S (2000) Higher education employment and economic growth Mexico and Peru Retrieved from httpwwwamericanprofessororgdocumentation
lasapa perdocNarayan P K (2005) The saving and investment nexus for China Evidence from cointegration tests Applied Economics 37 1979ndash1990Permani R (2008) Education as a determinant of economic growth in East Asia Historical trends and empirical evidences (1965ndash2000) Retrieved from http
wwwuoweduaucommerceeconehsanzpdfsPermani202008pdfPesaran M H amp Pesaran B (1997) Working with Microfit 40 Interactive econometric analysis Oxford Oxford University PressPesaran M H amp Shin Y (1999) An autoregressive distributed lag modeling approach to cointegration analysis In S Strom (Ed) Econometrics and economic theory
in the 20th century Cambridge Cambridge University PressPesaran M H Shin Y amp Smith R J (2001) Bounds testing approaches to the analysis of level relationships Journal of Applied Econometrics 16 289ndash326Pradhan R P (2009) Education and economic growth in India Using error correction modeling International Research Journal of Finance and Economics 25Pritchett L (2001) Where has all the education gone The World Bank Economic Review 15(3)Quah D amp Rauch J E (1990) Openness and the rate of economic growth Journal Development of Studies 2(49) 307ndash335Rivera-Batiz L A amp Romer P M (1991) Economic integration and endogenous growth Quarterly Journal of Economics 106 531ndash555Romer P M (1986) Increasing returns and long run growth Journal of Political Economy 6(90) 1002ndash1037Romer P M (1989) Human capital and growth Theory and evidence (NBER Working Papers 3173) National Bureau of Economic Research IncRomer P M (1990) Endogenous technological change Journal of Political Economy 5(98) 71ndash101Rondinelli D amp Montgomery J (1995) Great policies Strategic innovations in Asia and the Pacific Basin Westport Praeger PublishingSaikkonen P amp Lutkepohl H (2000) Testing for the cointegration rank of a VAR process with structural shifts Journal of Business and Economic Statistics 18(4)
451ndash464Schultz T W (1961) Investment in human capital American Economic Review 51(1) 1State Bank of Pakistan (1972ndash2009) Annual reports Karachi SBP PressStengos T amp Aurangzeb A (2008) An empirical investigation of the relationship between education and growth in pakistan International Economic Journal 3
345ndash359 Retrieved from httpwwwinformaworldcomsmpptitledb=allcontent=t713685453tab=issueslistbranches=22-v2222Toda H Y amp Yamamoto T (1995) Statistical inference in vector autoregressive with possible integrated processes Journal of Econometrics 66 225ndash250United Nations (1997) Human Development Report New York Oxford University Press
- Education and economic growth in Pakistan A cointegration and causality analysis
-
- Introduction
- Review of literature
- Method and procedure
- Empirical results
-
- Unit root results
- Cointegration
- Toda-Yamamoto Augmented Granger Causality (TYAGC) Test
- Bivariate TYAGC framework
- Trivariate TYAGC framework
- Tetravariate TYAGC framework
- Figures in parentheses are p-values
-
- Conclusions and recommendations
-
- References
-
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 323
productivities was observed The reason behind this was the faster growth in 1960s and 1970s and increasing the share ofinvestment in tertiary education Economic growth caused by research publications was observed in Korea and TaiwanMoreover the significant causal flow running from publications to economic growth was no longer found in case ofSingapore This insignificant causal flow was perhaps found due to small number of universities in Singapore
Basic education causes economic growth while on the other side economic growth only causes higher education otherthan primary education No cointegration between education and national income was found (Kui 2005) Pradhan (2009)found unidirectional causality running from economic growth to education in India Islam et al (2007) examined linkagebetween education and GDP in the case of Bangladesh They used multivariate approach (Vector Error Correction ModelVECM) which is assumed more robust than the bivariate approach in the presence of labour and capital for the time seriesdata of 1976ndash2003 They found long run linkage between economic growth and education and further concluded that thereis bidirectional causality between education and economic growth It shows that Bangladesh is in that condition where GDPand education are helping each other to grow Bidirectional causality in economic growth and education could be possiblebecause education produces more accomplished labour force that directs to more productivity and ultimately economicgrowth Finally the general education has the greater returns than the vocational education (Hassan amp Ahmed 2008) Abbasand Peck (2008) explored the linkages between human capital and economic growth for Pakistan by utilizing cointegrationand error correction mechanism on time series data from 1960 to 2003 They found that human capital explained as much as39 of the increase in GDP per person in 1990 From this one can easily conclude that human capital positively contributedto economic growth in Pakistan (Chaudhary Iqbal amp Gillani 2009 Stengos amp Aurangzeb 2008) Thus human capital througheducation plays a major role in economic growth of a country
Majority of the above studies reveal that education and economic growth have the long run relationship and both thevariables have the causal relationship either one way or two way The present study is planned to explore the causalconnection between education (measured by 10 different indicators of education) and economic growth in Pakistan in theabsence and presence of third and fourth variables known as stock of capital and stock of labour force
3 Method and procedure
In light of objectives of the study the time series data on RGDP stock of capital stock of labour and ten different indicatorsof education have been used in Pakistani context for the period 1970ndash1971 to 2008ndash2009 The data were taken from differentissues of lsquolsquoPakistan Economic Surveyrsquorsquo and lsquolsquoAnnual Reports of State Bank of Pakistanrsquorsquo Furthermore a comprehensivemeasure of education known as education index was constructed for the period 1970ndash1971 to 2008ndash2009 by adopting UNDPmethodology given in 1999ndash2000 Education index is constructed by adding together adult literacy rate index (ALI) withtwo-third weightage and the combined primary secondary and tertiary gross enrollment ratio index (GEI) with one-thirdweightage The adult literacy rate (ALR) gives an indication of the ability to read and write while the gross enrolment ratio(GER) gives an indication of the level of education
Education Index frac14 2
3 ALI thorn 1
3 GEI
Adult Literacy Index ethALITHORN frac14 ALR 0
100 0
Gross Enrollment Index ethGEITHORN frac14 GER 0
100 0
where lsquo0rsquo and lsquo100rsquo are the minimum and maximum values of the variables adult literacy rate and gross enrollment ratioKeeping in view the theoretical postulates of the connection among RGDPt real physical capital (RPCt) labour force (LFt)
and education (Edut) the following models have been specified as
ln RGDPt frac14 f ethln RPCt ln LFt ln EduitTHORN (A)
ln Eduit frac14 f ethln RGDPt ln RPCt ln LFtTHORN (B)
To find out the relationship between Eduit and RGDPt various functional forms have been tested and the most appropriatefunctional forms ie log linear form for the variables RGDPt and Eduit were specified as
ln RGDPt frac14 b0 thorn b1 ln RPCt thorn b2 ln LFt thorn b3 ln Eduit thorn e1 (Model 1)
ln Eduit frac14 g0 thorn g1 RGDPt thorn g2 ln RPCt thorn g3 ln LFt thorn e2 (Model 2)
where ln = natural logarithm RGDPt = a proxy used to measure economic growth RPCt = stock of physical capital in realterms gross fixed capital formation deflated by GDP deflator LFt = stock of labour force Eduit = educational capital as takenby Ayara (2002) Mankiw Romer and Weil (1992) and Pritchett (2001) in extended Solow Model In literature education wasmeasured by using different indicators such as Edu1t = education index a key indicator used as a proxy to measure
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335324
educational development Edu2t = school enrollment ratio Edu3t = college enrollment ratio Edu4t = professional collegeenrollment ratio Edu5t = university enrollment ratio Edu6t = total enrollment ratio Edu7t = total general enrollment ratioEdu8t = higher education including professional education enrollment ratio Edu9t = general higher education enrollmentratio and Edu10t = education expenditure as percentage of GNP
RGDPt as a proxy to measure economic growth has also been utilized by Islam et al (2007) Abbas and Peck (2008) Jin(2009) Katırcıoglu (2009) and Chaudhary et al (2009) Gross fixed capital formation deflated by GDP deflator has also beenused as a proxy for RPC by Abbas and Peck (2008) Khorasgani (2008) and Chaudhary et al (2009) Stock of labour force as aproxy for measuring stock of labour has been already utilized by Islam et al (2007) and Chaudhary et al (2009)
Enrollment ratios are derived by dividing total enrollment of each category or level of education to the population of thatrespective age group These indicators have been used by Diebolt and Litago (1997) Gylfason and Zoega (2003) Islam et al(2007) and Pradhan (2009)
A number of cointegration techniques such as residual based EnglendashGranger (1987) test Johansen (1988) Johansen andJuselius (1990) Gregory and Hansen (1996) Saikkonen and Lutkepohl (2000) were available in literature This study used arelatively new and more robust cointegration approach known as Autoregressive Distributed Lag Model (ARDL) to determinethe long run relationship among variables of interest Although ARDL Approach can be applied whether the variables are I(0)
or I(1) or fractionally integrated but it is still pre requisite for the ARDL model to apply that none of the variables underconsideration is integrated of order lsquolsquo2rsquorsquo or higher In order to examine the causal nexus between Eduit and RGDPt theAugmented Granger Causality approach given by Toda and Yamamoto (1995) is applied
4 Empirical results
41 Unit root results
The study utilized different unit root tests such as Augmented Dickey-Fuller Test (ADF) Phillips-Perron Test (PP) Dickey-Fuller Generalized Least Square Test (DF-GLS) and Ng-Perron in order to make sure that none of the variables is of I(2) orhigher order A summary of unit root results regarding order of integration based on different above unit root criteria is givenin Table 1
According to ADF PP DF-GLS and Ng-Perron tests results in Table 1 RPCt LFt Edu2t Edu3t Edu4t Edu5t Edu6t Edu7t andEdu8t are of I(1) with constant while Edu1t is of I(0) with intercept and trend RGDPt is of I(1) according to ADF PP and DF-GLSwhile Ng-Perron exhibits RGDPt is of I(0) The order of the integration for Edu10t is zero according to all criteriarsquos Edu9t is ofI(1) with intercept and trend I(1) with constant I(0) with constant and I(0) with constant and trend according to ADF PP DF-GLS and Ng-Perron criteriarsquos respectively Edu9t is of I(1) according to ADF and PP while it is of I(0) according to DF-GLS andNg-Perron criteriarsquos so Edu9t seems to be fractionally integrated None of the variables is of I(2) according all criteriarsquos So theappropriate technique to cointegration is the ARDL approach to cointegration
To examine the long run (LR) relationship between RGDPt RPCt LFt and Eduit this study used the error-correction versionof ARDL approach of Model 1 and Model 2 by following Pesaran and Pesaran (1997) and Pesaran and Shin (1999) as
Dln RGDPt frac14 a0RGDPtthornXn
ifrac141
biRGDPtDln RGDPti thorn
Xn
ifrac141
ciRGDPtDln RPCti thorn
Xn
ifrac141
diRGDPtDln LFti
thornXn
ifrac141
eiRGDPtDln Eduiti thorn d1RGDPt
ln RGDPt1 thorn d2RGDPtln RPCt1 thorn d3RGDPt
ln LFt1
thorn d4RGDPtln Eduit1 (Model 1A)
Table 1
Order of integration
Variable ADF PP DF-GLS Ng-Perron
Intercept Intercept
and trend
Intercept Intercept
and trend
Intercept Interpret
and trend
Intercept Intercept
and trend
RGDPt I(1) I(1) I(1) I(0)
RPCt I(1) I(1) I(1) I(1)
LFt I(1) I(1) I(1) I(1)
Edu1t I(0) I(0) I(0) I(0)
Edu2t I(1) I(1) I(1) I(1)
Edu3t I(1) I(1) I(1) I(1)
Edu4t I(1) I(1) I(1) I(1)
Edu5t I(1) I(1) I(1) I(1)
Edu6t I(1) I(1) I(1) I(1)
Edu7t I(1) I(1) I(1) I(1)
Edu8t I(1) I(1) I(1) I(1)
Edu9t I(1) I(1) I(0) I(0)
Edu10t I(0) I(0) I(0) I(0)
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 325
Dln Eduit frac14 a0EduitthornXn
ifrac141
biEduitDln Eduiti thorn
Xn
ifrac141
ciEduitDln RPCti thorn
Xn
ifrac141
diEduitDln RGDPti thorn
Xn
ifrac141
eiEduitDln LFti
thorn d1Eduitln Eduit1 thorn d2Eduitln RPCt1 thorn d3Eduitln RGDPt1 thorn d4Eduitln LFt1 (Model 2A)
The coefficients (b c d and e) of the part one of the Model 1A and Model 2A represent SR dynamics and ds determine LRrelationship The first step in ARDL model was to examine long run linkage among the variables by calculating familiar F-statistic on the differenced variables components of Unrestricted Error Correction Mechanism (UECM) model for the jointsignificance of the coefficients of lagged level of the variables In this first step the regression equation estimated for thedependent variable RGDPt is defined as
Dln RGDPt frac14 a0RGDPtthornXn
ifrac141
biRGDPtDln RGDPti thorn
Xn
ifrac141
ciRGDPtDln RPCti thorn
Xn
ifrac141
diRGDPtDln LFti
thornXn
ifrac141
eiRGDPtDln Eduiti (Model 1B)
To create error correction mechanism in this equation 1st lag of the level of each variable is added to Model 1B and a variableaddition test is conducted by calculating F-test on the joint significance of all the added lagged level variables
Dln RGDPt frac14 a0RGDPtthornXn
ifrac141
biRGDPtDln RGDPti thorn
Xn
ifrac141
ciRGDPtDln RPCti thorn
Xn
ifrac141
diRGDPtDln LFti
thornXn
ifrac141
eiRGDPtDln Eduiti thorn d1RDGPt
ln RGDPt1 thorn d2RGDPtln RPCt1 thorn d3RGDPt
ln LFt1
thorn d4RGDPt ln Eduit1 (Model 1C)
The null hypothesis for no cointegration for the variable RGDPt against alternative hypothesis is given as
H0 d1RGDPtfrac14 d2RGDPt
frac14 d3RGDPtfrac14 d4RGDPt
frac14 0
H1 d1RGDPt6frac14 d2RGDPt
6frac14 d3RGDPt6frac14 d4RGDPt
6frac14 0
This is denoted as FRGDPt (RGDPtRPCt LFt Eduit)This hypothesis is being tested by the familiar F-testIf the calculated F-statistic is higher than the upper bounds critical value given by Pesaran Shin and Smith (2001) and
Narayan (2005) the null hypothesis of no cointegration is rejected implying that there exists a LR relationship among theRGDPt RPCt LFt Eduit when RGDPt is the dependent variable If the calculated F-statistic is less than the lower bounds criticalvalue then the null hypothesis of no cointegration cannot be rejected If the F-value falls in between lower and upper boundscritical values the test statistic will be inconclusive The value of the F depends upon the sample size constant andor a trendof ARDL and number of explanatory variables
42 Cointegration
The ARDL approach is applied to examine the long run relationship by conducting F-statistic The cointegration resultsare presented in Tables 2 and 3 The values of estimated F-test for RGDPt are shown in Table 2
Pesaran et al (2001) lower and upper critical values for bounds testing ARDL for 1 5 and 10 significance levels are365ndash466 279ndash367 and 237ndash320 respectively Narayan (2005) lower and upper critical values for Bound Testing ARDL for1 5 and 10 significance level are 502ndash661 355ndash480 and 293ndash402 respectively
All the indicators of education except Edu8 indicate that there exists cointegration relationship among RGDPt RPCt LFt
and Eduit when RGDPt is the dependent variable according to Pesaran et al (2001) CVs because there is at least one F-valuethat is greater than the upper critical bounds value Cointegration exists among RGDPt RPCt LFt and Eduit (as Eduit ismeasured by Edu1t Edu2t Edu4t Edu5t Edu9t) when RGDPt is the dependent variable according to Narayan (2005) CVs Thenull hypothesis of no cointegration is not rejected for Edu8t according to both CVs
Pesaran et al (2001) lower and upper critical values for bounds testing ARDL for 1 5 and 10 significance levels are365ndash466 279ndash367 and 237ndash320 respectively Narayan (2005) lower and upper critical values for Bound Testing ARDL for1 5 and 10 significance level are 502ndash661 355ndash480 and 293ndash402 respectively
The cointegration results in Table 3 shows that there is LR linkage between Eduit RGDPt LFt and RPCt when Eduit (as Eduit
is represented by Edu1t Edu2t Edu5t Edu6t Edu7t Edu9t and Edu10t) is the dependent variable according to both Pesaran et al(2001) and Narayan (2005) CVs because at least one partial F statistic is greater than the upper critical bounds value There
Table 2
Cointegration
Dependent variable when RGDPt serves as dependent variable Lag length Cointegration results based on critical
values (CVs) given by
1 2 3 4 Pesaran et al (2001) Narayan (2005)
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu1t)] 167 419 203 214 Cointegration Cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu2t)] 281 340 226 179 Cointegration No cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu3t)] 209 644 203 145 Cointegration Cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu4t)] 234 619 263 190 Cointegration Cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu5t)] 253 454 257 236 Cointegration Cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu6t)] 287 336 231 181 Cointegration No cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu7t)] 277 338 230 181 Cointegration No cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu8t)] 114 172 203 165 No cointegration No cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu9t)] 274 482 188 117 Cointegration Cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu10t)] 237 392 246 203 Cointegration No cointegration
Table 3
Cointegration
Dependent variable when Eduit serves as dependent variable Lag length Cointegration results based on critical
values (CV) given by Results
1 2 3 4 Pesaran et al (2001) Narayan (2005)
DEdu1t [FEdu1t (Edu1tRGDPt RPCt LFt)] 711 502 548 447 Cointegration Cointegration
DEdu2t [FEdu2t (Edu2tRGDPt RPCt LFt)] 446 336 192 308 Cointegration Cointegration
DEdu3t [FEdu3t (Edu3tRGDPt RPCt LFt)] 157 280 195 295 No cointegration No cointegration
DEdu4t [FEdu4t (Edu4tRGDPt RPCt LFt)] 202 156 295 223 No cointegration No cointegration
DEdu5t [FEdu5t (Edu5tRGDPt RPCt LFt)] 152 629 081 069 Cointegration Cointegration
DEdu6t [FEdu6t (Edu6tRGDPt RPCt LFt)] 488 366 225 305 Cointegration Cointegration
DEdu7t [FEdu7t (Edu7tRGDPt RPCt LFt)] 475 362 226 314 Cointegration Cointegration
DEdu8t [FEdu8t (Edu8tRGDPt RPCt LFt)] 156 182 089 101 No cointegration No cointegration
DEdu9t [FEdu9t (Edu9tRGDPt RPCt LFt)] 322 443 417 286 Cointegration Cointegration
DEdu10t [FEdu10t (Edu10tRGDPt RPCt LFt)] 341 527 523 842 Cointegration Cointegration
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335326
exists no cointegration among Eduit RGDPt RPCt and LFt when Eduit is represented by Edu3t Edu4t and Edu8t In conclusioneducation and RGDPt are found to be cointegrated ie they possess LR relationship
43 TodandashYamamoto Augmented Granger Causality (TYAGC) Test
Keeping in view the objectives of the study TYAGC was applied for data analysis To examine Augmented GrangerCausality Test among RGDPt RPCt LFt and Eduit the following equations are being estimated The estimated results of TYAGCprocedure are presented in Tables IndashIV
44 Bivariate TYAGC framework
The bivariate causality between RGDPt and Eduit (Eqs (1) and (2)) between RGDPt and RPCt (Eqs (3) and (4)) betweenRGDPt and LFt (Eqs (5) and (6)) between Eduit and RPCt (Eqs (7) and (8)) and between Eduit and LFt (Eqs (9) and (10)) wasestimated by using TYAGC technique and in presented in Table I
RGDPt frac14 a1 thornX3
ifrac141
b1iRGDPti thornX3
ifrac141
g1iEduiti thorn u1t (1)
Eduit frac14 a2 thornX3
ifrac141
b2iRGDPti thornX3
ifrac141
g2iEduiti thorn u2t (2)
RGDPt frac14 a3 thornX3
ifrac141
b3iRGDPti thornX3
ifrac141
g3iRPCti thorn u3t (3)
RPCt frac14 a4 thornX3
ifrac141
b4iRGDPti thornX3
ifrac141
g4iRPCti thorn u4t (4)
RGDPt frac14 a5 thornX3
ifrac141
b5iRGDPti thornX3
ifrac141
g5iLFti thorn u5t (5)
LFt frac14 a6 thornX3
ifrac141
b6iRGDPti thornX3
ifrac141
g6iLFti thorn u6t (6)
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 327
Eduit frac14 a7 thornX3
ifrac141
b7iEduiti thornX3
ifrac141
g7iRPCti thorn u7t (7)
RPCt frac14 a8 thornX3
ifrac141
b8iEduiti thornX3
ifrac141
g8iRPCti thorn u8t (8)
Eduit frac14 a9 thornX3
ifrac141
b9iEduiti thornX3
ifrac141
g9iLFti thorn u9t (9)
LFt frac14 a10 thornX3
ifrac141
b10iEduiti thornX3
ifrac141
g10iLFti thorn u10t (10)
The null hypothesis that all the indicators of education and all levels of education do not Granger cause RGDPt was tested inTable I Bivariate TYAGC results indicate that the null hypothesis was rejected (Table I) Similarly the null hypothesis thatRGDPt does not Granger cause all the indicators and all levels of education is rejected except Edu8t and Edu10t It means thatthere exists two-way causality between education and RGDPt RGDPt fails to cause higher education and expenditures oneducation
The estimated results from Eqs (3) and (4) in Table I show the feedback Granger causality between RPCt and RGDPt LFt isfound to cause RGDPt at 99 level of confidence while its reverse is not true The results of Eqs (7) and (8) in Table I show thatthe feedback causality between Eduit and RPCt seems to exist because majority of the indicators of education are causingRPCt and vice versa The results from Eq (9) and (10) in Table I reveal that LFt Granger causes education while reverseseemed to be not true In conclusion education and all levels of education (school college and university) Granger causeRGDPt and RGDPt also Granger causes education and all levels of education Feedback causality between education andRGDPt is found in bivariate case
45 Trivariate TYAGC framework
The trivariate causality among RGDPt RPCt and Eduit (Eqs (11)ndash(13)) and among RGDPt LFt and Eduit (Eqs (14)ndash(16)) wasestimated by using TYAGC framework and is presented in Tables II and III
RGDPt frac14 a11 thornX3
ifrac141
b11iRGDPti thornX3
ifrac141
l11iRPCti thornX3
ifrac141
g11iEduiti thorn u11t (11)
Eduit frac14 a12 thornX3
ifrac141
b12iRGDPti thornX3
ifrac141
l12iRPCti thornX3
ifrac141
g12iEduiti thorn u12t (12)
RPCt frac14 a13 thornX3
ifrac141
b13iRGDPti thornX3
ifrac141
l13iRPCti thornX3
ifrac141
g13iEduiti thorn u13t (13)
RGDPt frac14 a14 thornX3
ifrac141
b14iRGDPti thornX3
ifrac141
l14iLFti thornX3
ifrac141
g14iEduiti thorn u14t (14)
Edut frac14 a15 thornX3
ifrac141
b15iRGDPti thornX3
ifrac141
l15iLFti thornX3
ifrac141
g15iEduiti thorn u15t (15)
LFt frac14 a16 thornX3
ifrac141
b16iRGDPti thornX3
ifrac141
l16iLFti thornX3
ifrac141
g16iEduiti thorn u16t (16)
The estimated results presented in Table II indicate that the null hypothesis of no Granger causality between majority of theindicators of education and RGDPt is rejected This also supports our previous bivariate causality results that there existsfeedback causality between education and RGDPt The trivariate result in Table II seems to support the previous bivariateresult regarding causality between education and RPCt and between RPCt and RGDPt
In case of trivariate causality analysis among RGDPt LFt and Eduit the results in Table III again indicate the two waycausality running between education and RGDPt Six out of ten indicators of education does Granger cause LFt while LFt
Granger causes nine indicators out of ten indicators of education The null hypothesis that LFt does not Granger cause RGDPt
in the presence of all indicators of education is rejected at 99 level of confidence So LFt seems to be a very importantvariable that affects two main variables of the study ie education and RGDPt
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335328
In conclusion education and all levels of education Granger cause RGDPt where as its revere ie Granger causalityrunning from RGDPt to education and all levels of education is only true in case of trivariate causality among RGDPt LFt andeducation From here one can easily conclude that the role of LFt as compared to RPCt is very important in understanding therelationship between education and RGDPt Feedback causality between education and RGDPt is also found in trivariate case
46 Tetravariate TYAGC framework
The tetravariate causality among RGDPt RPCt LFt and Eduit (Eqs (17)ndash(20)) was also estimated by using TYAGC techniqueand their results are presented in Table IV
RGDPt frac14 a17 thornX3
ifrac141
b17iRGDPti thornX3
ifrac141
g17iRPCti thornX3
ifrac141
l17iLFti thornX3
ifrac141
d17iEduiti thorn u17t (17)
Eduit frac14 a18 thornX3
ifrac141
b18iRGDPti thornX3
ifrac141
g18iRPCti thornX3
ifrac141
l18iLFti thornX3
ifrac141
d18iEduiti thorn u18t (18)
RPCt frac14 a19 thornX3
ifrac141
b19iRGDPti thornX3
ifrac141
g19iRPCti thornX3
ifrac141
l19iLFti thornX3
ifrac141
d19iEduiti thorn u19t (19)
LFt frac14 a20 thornX3
ifrac141
b20iRGDPti thornX3
ifrac141
g20iRPCti thornX3
ifrac141
l20iLFti thornX3
ifrac141
d20iEduiti thorn u20t (20)
The tetravariate TYAGC results presented in Table IV indicate that all the indicators of education Granger cause RGDPt whileRGDPt does Granger cause majority of the indicators of education (seven out of ten) RGDPt does not Granger cause Edu5t
(university education) Edu8t (higher education) and Edu10t (education expenditure) From this one can easily conclude thatthere exists two way causality between education and RGDPt in case of tetravariate causality analysis as have been the caseof bivariate and trivariate causality Regarding levels of education all levels of education (ie school education collegeeducation and university education) do Granger cause RGDPt while RGDPt does only cause school education and collegeeducation RGDPt does not Granger cause university education
LFt Granger causes RGDPt at 99 confidence level while RGDPt only Granger causes LFt in case of Edu3t Edu5t Edu9t andEdu10t In case of testing causality between RPCt and RGDPt in the presence of all indicators of education RPCt does Grangercause RGDPt and in reverse case RGDPt does not Granger cause RPCt in the presence of Edu1t Edu3t Edu8t Edu9t and Edu10tThese results show the unidirectional causality running from RPCt to RGDPt
The research hypothesis that LFt does not Granger cause Eduit is rejected at 99 confidence interval except wheneducation is measured by Eduit Labour force has been found to cause all levels of education On the other side education onlyGranger causes the LFt in the presence of Edu3t Edu4t Edu5t Edu8t and Edu10t RPC does not Granger cause education whenEdu3t and Edu4t are used as proxies of education All indicators of education except Edu1t Edu2t and Edu10t do Granger causeRPCt This implies that feedback causality between RPCt and education is observed
It can easily be concluded from the TYAGC results of Eq (17) in Table IV that among all levels of education General highereducation (Edu9t) causes RGDPt highly and most significantly (999 confidence level) The level of confidence of collegeeducation (Edu3t) and school education (Edu2t) causing RGDPt is found to be 2nd highest (significance at 997 confidencelevel) and 3rd highest (significance at 989 confidence level) respectively From Eq (18) in Table IV it can also be found thatthe level of confidence (999) of causing RGDPt to school education (Edu2t) is found to be highest
From the bivariate trivariate and tetravariate TYAGC tests results in Tables IndashIV the overall results of the study abouteducation and different levels of education (School College and University) are summarized in Table 4
Table 4
Causal nexus between education different levels of education with RGDPt
Hypothesis TYAGC procedure
Bivariate Trivariate Tetravariate
RGDPt and Edut RGDPt RPCt Edut RGDPt LFt Edut RGDPt LFt RPCt Edut
Education (Edu1t) does Granger cause RGDPt Yes (0089) No (0459) Yes (0009) Yes (0087)
RGDPt does Granger cause education (Edu1t) Yes (0000) Yes (0000) Yes (0000) Yes (0000)
School education (Edu2t) does Granger cause RGDPt Yes (0000) Yes (0001) Yes (0002) Yes (0010)
RGDPt does Granger cause school education (Edu2t) Yes (0000) Yes (0000) Yes (0000) Yes (0000)
College education (Edu3t) does Granger cause RGDPt Yes (0038) Yes (0081) Yes (0000) Yes (0002)
RGDPt does Granger cause college education (Edu3t) Yes (0003) No (0172) Yes (0001) Yes (0032)
University education (Edu5t) does Granger cause RGDPt Yes (0000) Yes (0000) Yes (0001) Yes (0001)
RGDPt does Granger cause university education (Edu5t) Yes (0089) Yes (0000) Yes (0025) No (0515)
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 329
47 Figures in parentheses are p-values
From the above results presented in Table 4 it can be concluded that there existed feedback causality between educationand RGDPt in all bivariate trivariate and tetravariate TYAGC causality cases All levels of education ie school educationcollege education and university education do Granger cause RGDPt in all causality cases RGDPt does Granger cause schooleducation in all causality cases RGDPt does Granger cause college education in all causality cases except trivariate causalitythat is running from RGDPt to education when RPCt serves as a third variable Table 4 also reveals that RGDPt does Grangercause university education only in a bivariate and trivariate causality cases RGDPt fails to Granger cause to universityeducation in tetravariate case
5 Conclusions and recommendations
This study aimed to explore the cointegration and causal relationship between education (measured by different indicatorsof education) and economic growth in Pakistan It is very essential for a country to invest more in education because it is one ofthe most important ingredients of human capital and hence economic development The nature and strength of the relationshipbetween education and economic growth is still not clear in case of Pakistan The main focus of this empirical study remained toobserve the causality and cointegration between education and economic growth in the absence and presence physical capitaland labour force Cointegration between education and economic growth was investigated using ARDL approach and the causallinkage between education and economic growth was examined in bivariate trivariate and tetravariate TYAGC frameworkDifferent indicators of education were utilized in this study to show the robustness of empirical results The causality betweeneducation and economic growth was examined in the presence and absence of stock of physical capital and stock of labour as athird and fourth variable The causality results indicate that there exist two-way causality between education and economicgrowth and between all levels of education and economic growth in case of bivariate TYAGC framework Education and alllevels of education do Granger cause economic growth in the presence of real physical capital as a third variable while economicgrowth causes all the indicators of education except college education professional college education and educationalexpenditures in the presence of real physical capital as a third variable in case of trivariate causality analysis In the presence oflabour force as a third variable feedback causality exists between education and economic growth and between all levels ofeducation and economic growth The results of tetravariate TYAGC Test indicate that education and all level of education doGranger cause economic growth while economic growth does Granger cause majority of the indicators of education (ie sevenout of ten) Economic growth does not Granger cause university education higher education including professional educationand expenditures on education The rise in university education higher education including professional education andexpenditures on education were considered as the key indicators to gauge human and social progress Economic growth doesnot seem to affect important educational indicators like university education higher education including professionaleducation and expenditures on education This seems to be consistent with Easterlyrsquos findings Easterly (2001) said thatPakistan is a country that made little social progress for given rates of GDP Among all levels of education General highereducation causes economic growth highly and most significantly as was explored by Stengos and Aurangzeb (2008) The level ofconfidence of causing economic growth to school education found to be highest This study also confirms the long runrelationship between education and economic growth
On the basis of the results of this study it is recommended that the government should focus more on higher educationparticularly to university education More funds should be allocated to education in line with others sectors particularly touniversity and higher education levels so that the economic growth can be further accelerated This will in turn leads tofurther education and hence development Poor should be facilitated to get higher education so that the polarization inhigher education may further be minimized Primary schooling should also be given priority because primary educationserves as an input for all higher levels of education The inverted educational expenditure pyramid may also be taken intoaccount Since the role of labour force seems to be very important in understanding the relationship between education andeconomic growth so it is suggested that labour force should be given more chances to enhance their skills The variablelabour force must be included while examining the causality between education and economic growth It is alsorecommended that the nexus between education and economic growth with inclusion of other variables other than physicalcapital and labour force should further be tested and generalized
Appendix A
Table I
Bivariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Bivariate-RGDPt and Eduit
Eq (1) Edu1t does not Granger cause RGDPt 028998 [0089] 1 Reject H0
Edu2t does not Granger cause RGDPt 144869 [0000] 1 Reject H0
Edu3t does not Granger cause RGDPt 043243 [0038] 1 Reject H0
Edu4t does not Granger cause RGDPt 039797 [0046] 1 Reject H0
Table I (Continued )
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Edu5t does not Granger cause RGDPt 217739 [0000] 1 Reject H0
Edu6t does not Granger cause RGDPt 137788 [0000] 1 Reject H0
Edu7t does not Granger cause RGDPt 126682 [0000] 1 Reject H0
Edu8t does not Granger cause RGDPt 041335 [0042] 1 Reject H0
Edu9t does not Granger cause RGDPt 160963 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 028642 [0091] 1 Reject H0
Eq (2) RGDPt does not Granger cause Edu1t 260926 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 230094 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 085441 [0003] 1 Reject H0
RGDPt does not Granger cause Edu4t 107403 [0001] 1 Reject H0
RGDPt does not Granger cause Edu5t 028935 [0089] 1 Reject H0
RGDPt does not Granger cause Edu6t 270343 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 273974 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 003162 [0574] 1 Cannot reject H0
RGDPt does not Granger cause Edu9t 027588 [0097] 1 Reject H0
RGDPt does not Granger cause Edu10t 000851 [0770] 1 Cannot reject H0
Bivariate-RGDPt and RPCt
Eq (3) RPCt does not Granger cause RGDPt 054972 [0019] 1 Reject H0
Eq (4) RGDPt does not Granger cause RPCt 167511 [0000] 1 Reject H0
Bivariate-RGDPt and LFt
Eq (5) LFt does not Granger cause RGDPt 227888 [0000] 1 Reject H0
Eq (6) RGDPt does not Granger cause LFt 012380 [0266] 1 Cannot reject H0
Bivariate-Eduit and RPCt
Eq (7) Edu1t does not Granger cause RPCt 094596 [0002] 1 Reject H0
Edu2t does not Granger cause RPCt 015434 [0214] 1 Cannot reject H0
Edu3t does not Granger cause RPCt 038233 [0051] 1 Reject H0
Edu4t does not Granger cause RPCt 000506 [0822] 1 Cannot reject H0
Edu5t does not Granger cause RPCt 298085 [0000] 1 Reject H0
Edu6t does not Granger cause RPCt 018289 [0176] 1 Cannot reject H0
Edu7t does not Granger cause RPCt 018976 [0168] 1 Cannot reject H0
Edu8t does not Granger cause RPCt 176399 [0000] 1 Reject H0
Edu9t does not Granger cause RPCt 224647 [0000] 1 Reject H0
Edu10t does not Granger cause RPCt 039174 [0048] 1 Reject H0
Eq (8) RPCt does not Granger cause Edu1t 091477 [0002] 1 Reject H0
RPCt does not Granger cause Edu2t 098821 [0002] 1 Reject H0
RPCt does not Granger cause Edu3t 066148 [0010] 1 Reject H0
RPCt does not Granger cause Edu4t 084218 [0004] 1 Reject H0
RPCt does not Granger cause Edu5t 001684 [0682] 1 Cannot reject H0
RPCt does not Granger cause Edu6t 107553 [0001] 1 Reject H0
RPCt does not Granger cause Edu7t 108798 [0001] 1 Reject H0
RPCt does not Granger cause Edu8t 004283 [0513] 1 Cannot reject H0
RPCt does not Granger cause Edu9t 005627 [0453] 1 Cannot reject H0
RPCt does not Granger cause Edu10t 000417 [0838] 1 Cannot reject H0
Bivariate-Eduit and LFt
Eq (9) Edu1t does not Granger cause LFt 026469 [0104] 1 Reject H0
Edu2t does not Granger cause LFt 012355 [0266] 1 Cannot reject H0
Edu3t does not Granger cause LFt 020468 [0153] 1 Cannot reject H0
Edu4t does not Granger cause LFt 098042 [0002] 1 Reject H0
Edu5t does not Granger cause LFt 049986 [0025] 1 Reject H0
Edu6t does not Granger cause LFt 016896 [0194] 1 Cannot reject H0
Edu7t does not Granger cause LFt 015167 [0218] 1 Cannot reject H0
Edu8t does not Granger cause LFt 184475 [0000] 1 Reject H0
Edu9t does not Granger cause LFt 003986 [0528] 1 Cannot reject H0
Edu10t does not Granger cause LFt 010899 [0296] 1 Cannot reject H0
Eq (10) LFt does not Granger cause Edu1t 107709 [0001] 1 Reject H0
LFt does not Granger cause Edu2t 071204 [0008] 1 Reject H0
LFt does not Granger cause Edu3t 136419 [0000] 1 Reject H0
LFt does not Granger cause Edu4t 056225 [0018] 1 Reject H0
LFt does not Granger cause Edu5t 057141 [0017] 1 Reject H0
LFt does not Granger cause Edu6t 091531 [0002] 1 Reject H0
LFt does not Granger cause Edu7t 095063 [0002] 1 Reject H0
LFt does not Granger cause Edu8t 021313 [0144] 1 Cannot reject H0
LFt does not Granger cause Edu9t 069389 [0008] 1 Reject H0
LFt does not Granger cause Edu10t 000743 [0785] 1 Cannot reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335330
Table II
Trivariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Trivariate-RGDPt RPCt and Eduit
Eq (11) Edu1t does not Granger cause RGDPt 005481 [0459] 1 Cannot reject H0
Edu2t does not Granger cause RGDPt 105415 [0001] 1 Reject H0
Edu3t does not Granger cause RGDPt 030370 [0081] 1 Reject H0
Edu4t does not Granger cause RGDPt 022525 [0133] 1 Cannot reject H0
Edu5t does not Granger cause RGDPt 227510 [0000] 1 Reject H0
Edu6t does not Granger cause RGDPt 098494 [0002] 1 Reject H0
Edu7t does not Granger cause RGDPt 090460 [0003] 1 Reject H0
Edu8t does not Granger cause RGDPt 067381 [0009] 1 Reject H0
Edu9t does not Granger cause RGDPt 168617 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 085842 [0003] Reject H0
Eq (11a) RPCt does not Granger cause RGDP (Edu1 as a 3rd variable) 029029 [0088] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu2 as a 3rd variable) 024880 [0115] 1 Cannot reject H0
RPCt does not Granger cause RGDPt (Edu3t as a 3rd variable) 041380 [0042] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu4t as a 3rd variable) 036580 [0056] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu5t as a 3rd variable) 064811 [0011] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu6t as a 3rd variable) 024405 [0118] 1 Cannot reject H0
RPCt does not Granger cause RGDPt (Edu7t as a 3rd variable) 026008 [0107] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu8t as a 3rd variable) 081607 [0004] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu9t as a 3rd variable) 063133 [0012] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu10t as a 3rd variable) 115637 [0001] 1 Reject H0
Eq (12) RGDPt does not Granger cause Edu1t 176454 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 129776 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 018626 [0172] 1 Cannot reject H0
RGDPt does not Granger cause Edu4t 020449 [0153] 1 Cannot reject H0
RGDPt does not Granger cause Edu5t 144658 [0000] 1 Reject H0
RGDPt does not Granger cause Edu6t 175431 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 178356 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 042497 [0039] 1 Reject H0
RGDPt does not Granger cause Edu9t 082506 [0004] 1 Reject H0
RGDPt does not Granger cause Edu10t 008026 [0370] 1 Cannot reject H0
Eq (12a) RPCt does not Granger cause Edu1t 000122 [0912] 1 Cannot reject H0
RPCt does not Granger cause Edu2t 028750 [0090] 1 Reject H0
RPCt does not Granger cause Edu3t 058586 [0016] 1 Reject H0
RPCt does not Granger cause Edu4t 071372 [0008] 1 Reject H0
RPCt does not Granger cause Edu5t 302364 [0000] 1 Reject H0
RPCt does not Granger cause Edu6t 020474 [0152] 1 Cannot reject H0
RPCt does not Granger cause Edu7t 017533 [0185] 1 Cannot reject H0
RPCt does not Granger cause Edu8t 044926 [0034] 1 Reject H0
RPCt does not Granger cause Edu9t 240955 [0000] 1 Reject H0
RPCt does not Granger cause Edu10t 021006 [0147] 1 Cannot reject H0
Eq (13) RGDPt does not Granger cause RPCt (Edu1t as a 3rd variable) 055095 [0019] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu2t as a 3rd variable) 182287 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu3t as a 3rd variable) 191499 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu4t as a 3rd variable) 269133 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu5t as a 3rd variable) 172979 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu6t as a 3rd variable) 166347 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu7t as a 3rd variable) 161198 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu8t as a 3rd variable) 038521 [0050] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu9tas a 3rd variable) 183169 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu10t as a 3rd variable) 139552 [0000] 1 Reject H0
Eq (13a) Edu1t does not Granger cause RPCt 000122 [0912] 1 Cannot reject H0
Edu2t does not Granger cause RPCt 028750 [0090] 1 Reject H0
Edu3t does not Granger cause RPCt 058586 [0016] 1 Reject H0
Edu4t does not Granger cause RPCt 071372 [0008] 1 Reject H0
Edu5t does not Granger cause RPCt 302364 [0000] 1 Reject H0
Edu6t does not Granger cause RPCt 020474 [0152] 1 Cannot reject H0
Edu7t does not Granger cause RPCt 017533 [0185] 1 Cannot reject H0
Edu8t does not Granger cause RPCt 044926 [0034] 1 Reject H0
Edu9t does not Granger cause RPCt 240955 [0000] 1 Reject H0
Edu10t does not Granger cause RPCt 021006 [0147] 1 Cannot reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 331
Table III
Trivariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Trivariate-RGDPt LFt and Eduit
Eq (14) Edu1t does not Granger cause RGDPt 068472 [0009] 1 Reject H0
Edu2t does not Granger cause RGDPt 092326 [0002] 1 Reject H0
Edu3t does not Granger cause RGDPt 180477 [0000] 1 Reject H0
Edu4t does not Granger cause RGDPt 132070 [0000] 1 Reject H0
Edu5t does not Granger cause RGDPt 109716 [0001] 1 Reject H0
Edu6t does not Granger cause RGDPt 086017 [0003] 1 Reject H0
Edu7t does not Granger cause RGDPt 078604 [0005] 1 Reject H0
Edu8t does not Granger cause RGDPt 020470 [0153] 1 Cannot reject H0
Edu9t does not Granger cause RGDPt 293293 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 005754 [0448] 1 Cannot reject H0
Eq (14a) LFt does not Granger cause RGDPt (Edu1t as a 3rd variable) 409533 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu2t as a 3rd variable) 332636 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu3t as a 3rd variable) 701171 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu4t as a 3rd variable) 605496 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu5t as a 3rd variable) 240867 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu6t as a 3rd variable) 330495 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu7t as a 3rd variable) 332860 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu8t as a 3rd variable) 352003 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu9t as a 3rd variable) 573087 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu10t as a 3rd variable) 343199 [0000] 1 Reject H0
Eq (15) RGDPt does not Granger cause Edu1t 134939 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 804323 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 109273 [0001] 1 Reject H0
RGDPt does not Granger cause Edu4t 278785 [0000] 1 Reject H0
RGDPt does not Granger cause Edu5t 050547 [0025] 1 Reject H0
RGDPt does not Granger cause Edu6t 790307 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 738342 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 043402 [0037] 1 Reject H0
RGDPt does not Granger cause Edu9t 175731 [0000] 1 Reject H0
RGDPt does not Granger cause Edu10t 061709 [0013] 1 Reject H0
Eq (15a) LFt does not Granger cause Edu1t 009324 [0334] 1 Cannot reject H0
LFt does not Granger cause Edu2t 377339 [0000] 1 Reject H0
LFt does not Granger cause Edu3t 176565 [0000] 1 Reject H0
LFt does not Granger cause Edu4t 180046 [0000] 1 Reject H0
LFt does not Granger cause Edu5t 091061 [0003] 1 Reject H0
LFt does not Granger cause Edu6t 355203 [0000] 1 Reject H0
LFt does not Granger cause Edu7t 327354 [0000] 1 Reject H0
LFt does not Granger cause Edu8t 053664 [0021] 1 Reject H0
LFt does not Granger cause Edu9t 251724 [0000] 1 Reject H0
LFt does not Granger cause Edu10t 060787 [0014] 1 Reject H0
Eq (16) Edu1t does not Granger cause LFt 036697 [0055] 1 Reject H0
Edu2t does not Granger cause LFt 004605 [0497] 1 Cannot reject H0
Edu3t does not Granger cause LFt 093988 [0002] 1 Reject H0
Edu4t does not Granger cause LFt 177287 [0000] 1 Reject H0
Edu5t does not Granger cause LFt 059203 [0015] 1 Reject H0
Edu6t does not Granger cause LFt 007202 [0396] 1 Cannot reject H0
Edu7t does not Granger cause LFt 005520 [0458] 1 Cannot reject H0
Edu8t does not Granger cause LFt 241662 [0000] 1 Reject H0
Edu9t does not Granger cause LFt 004009 [0527] 1 Cannot reject H0
Edu10t does not Granger cause LFt 058477 [0016] 1 Reject H0
Eq (16a) RGDPt does not Granger cause LFt (Edu1t as a 3rd variable) 002436 [0622] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu2t as a 3rd variable) 004276 [0513] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu3t as a 3rd variable) 047690 [0029] 1 Reject H0
RGDPt does not Granger cause LFt (Edu4t as a 3rd variable) 015207 [0218] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu5t as a 3rd variable) 040757 [0044] 1 Reject H0
RGDPt does not Granger cause LFt (Edu6t as a 3rd variable) 003392 [0560] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu7t as a 3rd variable) 004309 [0512] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu8t as a 3rd variable) 003145 [0575] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu9t as a 3rd variable) 017426 [0187] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu10t as a 3rd variable) 048448 [0028] 1 Reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335332
Table IV
Tetravariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Tetravariate-RGDPt RPCt LFt and Edut
Eq (17) Edu1t does not Granger cause RGDPt 029350 [0087] 1 Reject H0
Edu2t does not Granger cause RGDPt 065661 [0010] 1 Reject H0
Edu3t does not Granger cause RGDPt 097521 [0002] 1 Reject H0
Edu4t does not Granger cause RGDPt 071590 [0007] 1 Reject H0
Edu5t does not Granger cause RGDPt 116263 [0001] 1 Reject H0
Edu6t does not Granger cause RGDPt 059569 [0015] 1 Reject H0
Edu7t does not Granger cause RGDPt 054327 [0020] 1 Reject H0
Edu8t does not Granger cause RGDPt 040033 [0045] 1 Reject H0
Edu9t does not Granger cause RGDPt 195734 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 034374 [0064] 1 Reject H0
Eq (17a) LFt does not Granger cause RGDPt (Edut = Edu1) 251518 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu2) 165581 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu3) 316418 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu4) 289993 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu5) 109302 [0001] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu6) 165606 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu7) 168037 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu8) 176645 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu9) 247435 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu10) 146998 [0000] 1 Reject H0
Eq (17b) RPCt does not Granger cause RGDPt (Edut = Edu1) 042975 [0038] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu2) 039280 [0047] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu3) 034296 [0064] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu4) 027068 [0100] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu5) 062858 [0012] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu6) 039537 [0047] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu7) 040022 [0045] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu8) 045487 [0033] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu9) 068323 [0009] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu10) 083479 [0004] 1 Reject H0
Eq (18) RGDPt does not Granger cause Edu1t 150200 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 633103 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 045767 [0032] 1 Reject H0
RGDPt does not Granger cause Edu4t 122392 [0000] 1 Reject H0
RGDPt does not Granger cause Edu5t 004235 [0515] 1 Cannot reject H0
RGDPt does not Granger cause Edu6t 453644 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 418611 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 055973 [0454] 1 Cannot reject H0
RGDPt does not Granger cause Edu9t 053890 [0020] 1 Reject H0
RGDPt does not Granger cause Edu10t 011119 [0292] 1 Cannot reject H0
Eq (18a) LFt does not Granger cause Edu1t 006023 [0438] 1 Cannot reject H0
LFt does not Granger cause Edu2t 364559 [0000] 1 Reject H0
LFt does not Granger cause Edu3t 197423 [0000] 1 Reject H0
LFt does not Granger cause Edu4t 166511 [0000] 1 Reject H0
LFt does not Granger cause Edu5t 383886 [0000] 1 Reject H0
LFt does not Granger cause Edu6t 359377 [0000] 1 Reject H0
LFt does not Granger cause Edu7t 328249 [0000] 1 Reject H0
LFt does not Granger cause Edu8t 135310 [0000] 1 Reject H0
LFt does not Granger cause Edu9t 630068 [0000] 1 Reject H0
LFt does not Granger cause Edu01t 109365 [0001] 1 Reject H0
Eq (18b) RPCt does not Granger cause Edu1t 114248 [0001] 1 Reject H0
RPCt does not Granger cause Edu2t 036828 [0055] 1 Reject H0
RPCt does not Granger cause Edu3t 021023 [0147] 1 Cannot reject H0
RPCt does not Granger cause Edu4t 000484 [0826] 1 Cannot reject H0
RPCt does not Granger cause Edu5t 610934 [0000] 1 Reject H0
RPCt does not Granger cause Edu6t 070279 [0008] 1 Reject H0
RPCt does not Granger cause Edu7t 051166 [0024] 1 Reject H0
RPCt does not Granger cause Edu8t 167481 [0000] 1 Reject H0
RPCt does not Granger cause Edu9t 335271 [0000] 1 Reject H0
RPCt does not Granger cause Edu10t 067481 [0009] 1 Reject H0
Eq (19) Edu1 does not Granger cause RPCt 005154 [0473] 1 Cannot reject H0
Edu2 does not Granger cause RPCt 011954 [0274] 1 Cannot reject H0
Edu3 does not Granger cause RPCt 162365 [0000] 1 Reject H0
Edu4 does not Granger cause RPCt 148964 [0000] 1 Reject H0
Edu5 does not Granger cause RPCt 243978 [0000] 1 Reject H0
Edu6 does not Granger cause RPCt 040262 [0045] 1 Reject H0
Edu7 does not Granger cause RPCt 035138 [0061] 1 Reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 333
able IV (Continued )
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Edu8 does not Granger cause RPCt 030100 [0083] 1 Reject H0
Edu9 does not Granger cause RPCt 462564 [0000] 1 Reject H0
Edu10 does not Granger cause RPCt 009580 [0328] 1 Cannot reject H0
Eq (19a) RGDPt does not Granger cause RPCt (Edu1t as a 3rd variable) 009936 [0319] 1 Cannot reject H0
RGDPt does not Granger cause RPCt (Edu2t as a 3rd variable) 039369 [0047] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu3t as a 3rd variable) 003822 [0536] 1 Cannot reject H0
RGDPt does not Granger cause RPCt (Edu4t as a 3rd variable) 028000 [0094] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu5t as a 3rd variable) 039910 [0046] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu6t as a 3rd variable) 033500 [0067] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu7t as a 3rd variable) 029924 [0084] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu8t as a 3rd variable) 002803 [0597] 1 Cannot Reject H0
RGDPt does not Granger cause RPCt (Edu9t as a 3rd variable) 011416 [0285] 1 Cannot reject H0
RGDPt does not Granger cause RPCt (Edu10t as a 3rd variable) 006944 [0405] 1 Cannot reject H0
Eq (20) Edu1t does not Granger cause LFt 015302 [0216] 1 Cannot reject H0
Edu2t does not Granger cause LFt 001053 [0746] 1 Cannot reject H0
Edu3t does not Granger cause LFt 080072 [0005] 1 Reject H0
Edu4t does not Granger cause LFt 143854 [0000] 1 Reject H0
Edu5t does not Granger cause LFt 061159 [0013] 1 Reject H0
Edu6t does not Granger cause LFt 003113 [0577] 1 Cannot reject H0
Edu7t does not Granger cause LFt 002394 [0625] 1 Cannot reject H0
Edu8t does not Granger cause LFt 196804 [0000] 1 Reject H0
Edu9t does not Granger cause LFt 046285 [0496] 1 Cannot reject H0
Edu10t does not Granger cause LFt 04161 1 [0041] 1 Reject H0
Eq (20a) RGDPt does not Granger cause LFt (Edu1t as a 3rd variable) 006872 [0407] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu2t as a 3rd variable) 018604 [0173] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu3t as a 3rd variable) 066905 [0010] 1 Reject H0
RGDPt does not Granger cause LFt (Edu4t as a 3rd variable) 023249 [0127] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu5t as a 3rd variable) 070835 [0008] 1 Reject H0
RGDPt does not Granger cause LFt (Edu6t as a 3rd variable) 016501 [0199] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu7t as a 3rd variable) 018532 [0173] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu8t as a 3rd variable) 003730 [0541] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu9t as a 3rd variable) 039255 [0048] 1 Reject H0
RGDPt does not Granger cause LFt (Edu10t as a 3rd variable) 055266 [0019] 1 Reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335334
T
References
Abbas Q amp Peck J F (2008) Human capital and economic growth Pakistan 1960ndash2003 The Lahore Journal of Economics 13(1) 1ndash28Ayara N A (2002) The paradox of education and economic growth in Nigeria Empirical evidence The Nigerian Economic Society (NES) Pt 2 371ndash393Babatunde M A amp Adefabi R A (2005) Long run relationship between education and economic growth in Nigeria Evidence from the Johansenrsquos cointegration
approach Paper presented at the regional conference on education in West Africa Constraints and Opportunities Dakar Senegal November 1stndash2nd 2005Cornell UniversityCREAMinisterede lrsquoEducation du Senegal
Baldacci E Clements B Cui Q amp Gupta S (2005) What does it take to help the poor Finance and Development The Quarterly Magazine of the IMF 42(2)Changzheng Z Zhijian H amp Huaizu L (2007) An empirical study on education equity in China 1978ndash2004 Frontier in Economics of China 2(4) 536ndash544Chaudhary A R Asim I amp Gillani S Y M (2009) The nexus between higher education and economic growth An empirical investigation for Pakistan Pakistan
Journal of Commerce and Social Sciences 3Chaudhry I S Malik S amp Ashraf M (2006) Rural poverty in Pakistan Some related concepts issues and empirical analysis Pakistan Economic and Social Review
44(2) 259ndash276Diebolt C amp Litago J (1997) Education and economic growth in Germany before the Second World War An econometric analysis of dynamic relations Historical
Social Research 2(22) 132ndash149Easterly W (2001) The middle class consensus and economic development Journal of Economic Growth 6(4) 317ndash335Engle R F amp Granger C W J (1987) Cointegration and error correction Representation estimation and testing Econometrica 55 251ndash276Fernandez E amp Mauro P (2000) The role of human capital in economic growth The case of Spain (IMF Working Paper) International Monetary FundFrancis B amp Iyare S (2006) Education and development in the Caribbean A cointegration and causality approach Economics Bulletin 15(2) 1ndash13Galor O amp Moav O (2000) Das human capital Retrieved from httpeconpstcn brownedufacultygalorindexhtmlGoode R B (1959) Adding to the stock of physical and human capital American Economic Review 49(2) 147Government of Pakistan (1970ndash2009) Pakistan economic survey various issues Finance Division Islamabad Economic Advisorrsquos WingGregory A W amp Hansen B E (1996) Residual-based tests for cointegration in models with regime shifts Journal of Econometrics 70 99ndash126Grossman G M amp Helpman E (1991) Innovation and growth in the global economy Cambridge MIT PressGylfason T amp Zoega G (2003) Education social equality and economic growth A view of the landscape CESifo Economic Studies 49(4) 557ndash579Hassan S amp Ahmed H (2008) Educationrsquos contribution to the economic growth of sub-Saharan Africa Southwestern Economic Review 1(32) 175ndash190Islam T S Wadud M A amp Islam Q B T (2007) Relationship between education and GDP growth A multivariate causality analysis for Bangladesh Economics
Bulletin 3(35) 1ndash7Jin J C (2009) Economic research and economic growth Evidence from East Asian Economies Journal of Asian Economics 20 150ndash155Johansen S (1988) Statistical analysis of cointegration vectors Journal of Economic Dynamics and Control 12 231ndash254Johansen S amp Juselius K (1990) Maximum likelihood estimation and inference on cointegration with applications to the demand for money Oxford Bulletin of
Economics and Statistics 52 169ndash210Katırcıoglu S T (2009) Investigating higher-education-led growth hypothesis in a small Island Time series evidence from Northern Cyprus Paper presented at
Econ Anadolu 2009 Anadolu International Conference in Economics June 17ndash19 2009 TurkeyKhorasgani M F (2008) Higher education development and economic growth in Iran Education Business and Society Contemporary Middle Eastern Issues 1
162ndash174
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 335
Kui L (2005) The interactive causality between education and economic growth in China Retrieved from httppapersssrncomsol3paperscfmAbstrac-tid=920624
Loening J L (2004) Time series evidence on education and growth The case of Guatemala 1951ndash2002 Revista de Analisis Economico 19(2) 3ndash40Lucas R E (1988) On the mechanics of economic development Journal of Monetary Economics 22 3ndash42Macerinskiene I amp Vaiksnoraite B (2006) The role of higher education to economic development VadybaManagement 2(11)Mankiw N G Romer D amp Weil D N (1992) A contribution to the empirics of economic growth Quarterly Journal of Economics 107 407ndash437Momete D C (2007) Analysis of the relationship between employment and economic growth in Romania Fascicle of Management and Technological Engineering
VI(XVI)Morote E S (2000) Higher education employment and economic growth Mexico and Peru Retrieved from httpwwwamericanprofessororgdocumentation
lasapa perdocNarayan P K (2005) The saving and investment nexus for China Evidence from cointegration tests Applied Economics 37 1979ndash1990Permani R (2008) Education as a determinant of economic growth in East Asia Historical trends and empirical evidences (1965ndash2000) Retrieved from http
wwwuoweduaucommerceeconehsanzpdfsPermani202008pdfPesaran M H amp Pesaran B (1997) Working with Microfit 40 Interactive econometric analysis Oxford Oxford University PressPesaran M H amp Shin Y (1999) An autoregressive distributed lag modeling approach to cointegration analysis In S Strom (Ed) Econometrics and economic theory
in the 20th century Cambridge Cambridge University PressPesaran M H Shin Y amp Smith R J (2001) Bounds testing approaches to the analysis of level relationships Journal of Applied Econometrics 16 289ndash326Pradhan R P (2009) Education and economic growth in India Using error correction modeling International Research Journal of Finance and Economics 25Pritchett L (2001) Where has all the education gone The World Bank Economic Review 15(3)Quah D amp Rauch J E (1990) Openness and the rate of economic growth Journal Development of Studies 2(49) 307ndash335Rivera-Batiz L A amp Romer P M (1991) Economic integration and endogenous growth Quarterly Journal of Economics 106 531ndash555Romer P M (1986) Increasing returns and long run growth Journal of Political Economy 6(90) 1002ndash1037Romer P M (1989) Human capital and growth Theory and evidence (NBER Working Papers 3173) National Bureau of Economic Research IncRomer P M (1990) Endogenous technological change Journal of Political Economy 5(98) 71ndash101Rondinelli D amp Montgomery J (1995) Great policies Strategic innovations in Asia and the Pacific Basin Westport Praeger PublishingSaikkonen P amp Lutkepohl H (2000) Testing for the cointegration rank of a VAR process with structural shifts Journal of Business and Economic Statistics 18(4)
451ndash464Schultz T W (1961) Investment in human capital American Economic Review 51(1) 1State Bank of Pakistan (1972ndash2009) Annual reports Karachi SBP PressStengos T amp Aurangzeb A (2008) An empirical investigation of the relationship between education and growth in pakistan International Economic Journal 3
345ndash359 Retrieved from httpwwwinformaworldcomsmpptitledb=allcontent=t713685453tab=issueslistbranches=22-v2222Toda H Y amp Yamamoto T (1995) Statistical inference in vector autoregressive with possible integrated processes Journal of Econometrics 66 225ndash250United Nations (1997) Human Development Report New York Oxford University Press
- Education and economic growth in Pakistan A cointegration and causality analysis
-
- Introduction
- Review of literature
- Method and procedure
- Empirical results
-
- Unit root results
- Cointegration
- Toda-Yamamoto Augmented Granger Causality (TYAGC) Test
- Bivariate TYAGC framework
- Trivariate TYAGC framework
- Tetravariate TYAGC framework
- Figures in parentheses are p-values
-
- Conclusions and recommendations
-
- References
-
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335324
educational development Edu2t = school enrollment ratio Edu3t = college enrollment ratio Edu4t = professional collegeenrollment ratio Edu5t = university enrollment ratio Edu6t = total enrollment ratio Edu7t = total general enrollment ratioEdu8t = higher education including professional education enrollment ratio Edu9t = general higher education enrollmentratio and Edu10t = education expenditure as percentage of GNP
RGDPt as a proxy to measure economic growth has also been utilized by Islam et al (2007) Abbas and Peck (2008) Jin(2009) Katırcıoglu (2009) and Chaudhary et al (2009) Gross fixed capital formation deflated by GDP deflator has also beenused as a proxy for RPC by Abbas and Peck (2008) Khorasgani (2008) and Chaudhary et al (2009) Stock of labour force as aproxy for measuring stock of labour has been already utilized by Islam et al (2007) and Chaudhary et al (2009)
Enrollment ratios are derived by dividing total enrollment of each category or level of education to the population of thatrespective age group These indicators have been used by Diebolt and Litago (1997) Gylfason and Zoega (2003) Islam et al(2007) and Pradhan (2009)
A number of cointegration techniques such as residual based EnglendashGranger (1987) test Johansen (1988) Johansen andJuselius (1990) Gregory and Hansen (1996) Saikkonen and Lutkepohl (2000) were available in literature This study used arelatively new and more robust cointegration approach known as Autoregressive Distributed Lag Model (ARDL) to determinethe long run relationship among variables of interest Although ARDL Approach can be applied whether the variables are I(0)
or I(1) or fractionally integrated but it is still pre requisite for the ARDL model to apply that none of the variables underconsideration is integrated of order lsquolsquo2rsquorsquo or higher In order to examine the causal nexus between Eduit and RGDPt theAugmented Granger Causality approach given by Toda and Yamamoto (1995) is applied
4 Empirical results
41 Unit root results
The study utilized different unit root tests such as Augmented Dickey-Fuller Test (ADF) Phillips-Perron Test (PP) Dickey-Fuller Generalized Least Square Test (DF-GLS) and Ng-Perron in order to make sure that none of the variables is of I(2) orhigher order A summary of unit root results regarding order of integration based on different above unit root criteria is givenin Table 1
According to ADF PP DF-GLS and Ng-Perron tests results in Table 1 RPCt LFt Edu2t Edu3t Edu4t Edu5t Edu6t Edu7t andEdu8t are of I(1) with constant while Edu1t is of I(0) with intercept and trend RGDPt is of I(1) according to ADF PP and DF-GLSwhile Ng-Perron exhibits RGDPt is of I(0) The order of the integration for Edu10t is zero according to all criteriarsquos Edu9t is ofI(1) with intercept and trend I(1) with constant I(0) with constant and I(0) with constant and trend according to ADF PP DF-GLS and Ng-Perron criteriarsquos respectively Edu9t is of I(1) according to ADF and PP while it is of I(0) according to DF-GLS andNg-Perron criteriarsquos so Edu9t seems to be fractionally integrated None of the variables is of I(2) according all criteriarsquos So theappropriate technique to cointegration is the ARDL approach to cointegration
To examine the long run (LR) relationship between RGDPt RPCt LFt and Eduit this study used the error-correction versionof ARDL approach of Model 1 and Model 2 by following Pesaran and Pesaran (1997) and Pesaran and Shin (1999) as
Dln RGDPt frac14 a0RGDPtthornXn
ifrac141
biRGDPtDln RGDPti thorn
Xn
ifrac141
ciRGDPtDln RPCti thorn
Xn
ifrac141
diRGDPtDln LFti
thornXn
ifrac141
eiRGDPtDln Eduiti thorn d1RGDPt
ln RGDPt1 thorn d2RGDPtln RPCt1 thorn d3RGDPt
ln LFt1
thorn d4RGDPtln Eduit1 (Model 1A)
Table 1
Order of integration
Variable ADF PP DF-GLS Ng-Perron
Intercept Intercept
and trend
Intercept Intercept
and trend
Intercept Interpret
and trend
Intercept Intercept
and trend
RGDPt I(1) I(1) I(1) I(0)
RPCt I(1) I(1) I(1) I(1)
LFt I(1) I(1) I(1) I(1)
Edu1t I(0) I(0) I(0) I(0)
Edu2t I(1) I(1) I(1) I(1)
Edu3t I(1) I(1) I(1) I(1)
Edu4t I(1) I(1) I(1) I(1)
Edu5t I(1) I(1) I(1) I(1)
Edu6t I(1) I(1) I(1) I(1)
Edu7t I(1) I(1) I(1) I(1)
Edu8t I(1) I(1) I(1) I(1)
Edu9t I(1) I(1) I(0) I(0)
Edu10t I(0) I(0) I(0) I(0)
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 325
Dln Eduit frac14 a0EduitthornXn
ifrac141
biEduitDln Eduiti thorn
Xn
ifrac141
ciEduitDln RPCti thorn
Xn
ifrac141
diEduitDln RGDPti thorn
Xn
ifrac141
eiEduitDln LFti
thorn d1Eduitln Eduit1 thorn d2Eduitln RPCt1 thorn d3Eduitln RGDPt1 thorn d4Eduitln LFt1 (Model 2A)
The coefficients (b c d and e) of the part one of the Model 1A and Model 2A represent SR dynamics and ds determine LRrelationship The first step in ARDL model was to examine long run linkage among the variables by calculating familiar F-statistic on the differenced variables components of Unrestricted Error Correction Mechanism (UECM) model for the jointsignificance of the coefficients of lagged level of the variables In this first step the regression equation estimated for thedependent variable RGDPt is defined as
Dln RGDPt frac14 a0RGDPtthornXn
ifrac141
biRGDPtDln RGDPti thorn
Xn
ifrac141
ciRGDPtDln RPCti thorn
Xn
ifrac141
diRGDPtDln LFti
thornXn
ifrac141
eiRGDPtDln Eduiti (Model 1B)
To create error correction mechanism in this equation 1st lag of the level of each variable is added to Model 1B and a variableaddition test is conducted by calculating F-test on the joint significance of all the added lagged level variables
Dln RGDPt frac14 a0RGDPtthornXn
ifrac141
biRGDPtDln RGDPti thorn
Xn
ifrac141
ciRGDPtDln RPCti thorn
Xn
ifrac141
diRGDPtDln LFti
thornXn
ifrac141
eiRGDPtDln Eduiti thorn d1RDGPt
ln RGDPt1 thorn d2RGDPtln RPCt1 thorn d3RGDPt
ln LFt1
thorn d4RGDPt ln Eduit1 (Model 1C)
The null hypothesis for no cointegration for the variable RGDPt against alternative hypothesis is given as
H0 d1RGDPtfrac14 d2RGDPt
frac14 d3RGDPtfrac14 d4RGDPt
frac14 0
H1 d1RGDPt6frac14 d2RGDPt
6frac14 d3RGDPt6frac14 d4RGDPt
6frac14 0
This is denoted as FRGDPt (RGDPtRPCt LFt Eduit)This hypothesis is being tested by the familiar F-testIf the calculated F-statistic is higher than the upper bounds critical value given by Pesaran Shin and Smith (2001) and
Narayan (2005) the null hypothesis of no cointegration is rejected implying that there exists a LR relationship among theRGDPt RPCt LFt Eduit when RGDPt is the dependent variable If the calculated F-statistic is less than the lower bounds criticalvalue then the null hypothesis of no cointegration cannot be rejected If the F-value falls in between lower and upper boundscritical values the test statistic will be inconclusive The value of the F depends upon the sample size constant andor a trendof ARDL and number of explanatory variables
42 Cointegration
The ARDL approach is applied to examine the long run relationship by conducting F-statistic The cointegration resultsare presented in Tables 2 and 3 The values of estimated F-test for RGDPt are shown in Table 2
Pesaran et al (2001) lower and upper critical values for bounds testing ARDL for 1 5 and 10 significance levels are365ndash466 279ndash367 and 237ndash320 respectively Narayan (2005) lower and upper critical values for Bound Testing ARDL for1 5 and 10 significance level are 502ndash661 355ndash480 and 293ndash402 respectively
All the indicators of education except Edu8 indicate that there exists cointegration relationship among RGDPt RPCt LFt
and Eduit when RGDPt is the dependent variable according to Pesaran et al (2001) CVs because there is at least one F-valuethat is greater than the upper critical bounds value Cointegration exists among RGDPt RPCt LFt and Eduit (as Eduit ismeasured by Edu1t Edu2t Edu4t Edu5t Edu9t) when RGDPt is the dependent variable according to Narayan (2005) CVs Thenull hypothesis of no cointegration is not rejected for Edu8t according to both CVs
Pesaran et al (2001) lower and upper critical values for bounds testing ARDL for 1 5 and 10 significance levels are365ndash466 279ndash367 and 237ndash320 respectively Narayan (2005) lower and upper critical values for Bound Testing ARDL for1 5 and 10 significance level are 502ndash661 355ndash480 and 293ndash402 respectively
The cointegration results in Table 3 shows that there is LR linkage between Eduit RGDPt LFt and RPCt when Eduit (as Eduit
is represented by Edu1t Edu2t Edu5t Edu6t Edu7t Edu9t and Edu10t) is the dependent variable according to both Pesaran et al(2001) and Narayan (2005) CVs because at least one partial F statistic is greater than the upper critical bounds value There
Table 2
Cointegration
Dependent variable when RGDPt serves as dependent variable Lag length Cointegration results based on critical
values (CVs) given by
1 2 3 4 Pesaran et al (2001) Narayan (2005)
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu1t)] 167 419 203 214 Cointegration Cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu2t)] 281 340 226 179 Cointegration No cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu3t)] 209 644 203 145 Cointegration Cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu4t)] 234 619 263 190 Cointegration Cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu5t)] 253 454 257 236 Cointegration Cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu6t)] 287 336 231 181 Cointegration No cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu7t)] 277 338 230 181 Cointegration No cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu8t)] 114 172 203 165 No cointegration No cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu9t)] 274 482 188 117 Cointegration Cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu10t)] 237 392 246 203 Cointegration No cointegration
Table 3
Cointegration
Dependent variable when Eduit serves as dependent variable Lag length Cointegration results based on critical
values (CV) given by Results
1 2 3 4 Pesaran et al (2001) Narayan (2005)
DEdu1t [FEdu1t (Edu1tRGDPt RPCt LFt)] 711 502 548 447 Cointegration Cointegration
DEdu2t [FEdu2t (Edu2tRGDPt RPCt LFt)] 446 336 192 308 Cointegration Cointegration
DEdu3t [FEdu3t (Edu3tRGDPt RPCt LFt)] 157 280 195 295 No cointegration No cointegration
DEdu4t [FEdu4t (Edu4tRGDPt RPCt LFt)] 202 156 295 223 No cointegration No cointegration
DEdu5t [FEdu5t (Edu5tRGDPt RPCt LFt)] 152 629 081 069 Cointegration Cointegration
DEdu6t [FEdu6t (Edu6tRGDPt RPCt LFt)] 488 366 225 305 Cointegration Cointegration
DEdu7t [FEdu7t (Edu7tRGDPt RPCt LFt)] 475 362 226 314 Cointegration Cointegration
DEdu8t [FEdu8t (Edu8tRGDPt RPCt LFt)] 156 182 089 101 No cointegration No cointegration
DEdu9t [FEdu9t (Edu9tRGDPt RPCt LFt)] 322 443 417 286 Cointegration Cointegration
DEdu10t [FEdu10t (Edu10tRGDPt RPCt LFt)] 341 527 523 842 Cointegration Cointegration
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335326
exists no cointegration among Eduit RGDPt RPCt and LFt when Eduit is represented by Edu3t Edu4t and Edu8t In conclusioneducation and RGDPt are found to be cointegrated ie they possess LR relationship
43 TodandashYamamoto Augmented Granger Causality (TYAGC) Test
Keeping in view the objectives of the study TYAGC was applied for data analysis To examine Augmented GrangerCausality Test among RGDPt RPCt LFt and Eduit the following equations are being estimated The estimated results of TYAGCprocedure are presented in Tables IndashIV
44 Bivariate TYAGC framework
The bivariate causality between RGDPt and Eduit (Eqs (1) and (2)) between RGDPt and RPCt (Eqs (3) and (4)) betweenRGDPt and LFt (Eqs (5) and (6)) between Eduit and RPCt (Eqs (7) and (8)) and between Eduit and LFt (Eqs (9) and (10)) wasestimated by using TYAGC technique and in presented in Table I
RGDPt frac14 a1 thornX3
ifrac141
b1iRGDPti thornX3
ifrac141
g1iEduiti thorn u1t (1)
Eduit frac14 a2 thornX3
ifrac141
b2iRGDPti thornX3
ifrac141
g2iEduiti thorn u2t (2)
RGDPt frac14 a3 thornX3
ifrac141
b3iRGDPti thornX3
ifrac141
g3iRPCti thorn u3t (3)
RPCt frac14 a4 thornX3
ifrac141
b4iRGDPti thornX3
ifrac141
g4iRPCti thorn u4t (4)
RGDPt frac14 a5 thornX3
ifrac141
b5iRGDPti thornX3
ifrac141
g5iLFti thorn u5t (5)
LFt frac14 a6 thornX3
ifrac141
b6iRGDPti thornX3
ifrac141
g6iLFti thorn u6t (6)
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 327
Eduit frac14 a7 thornX3
ifrac141
b7iEduiti thornX3
ifrac141
g7iRPCti thorn u7t (7)
RPCt frac14 a8 thornX3
ifrac141
b8iEduiti thornX3
ifrac141
g8iRPCti thorn u8t (8)
Eduit frac14 a9 thornX3
ifrac141
b9iEduiti thornX3
ifrac141
g9iLFti thorn u9t (9)
LFt frac14 a10 thornX3
ifrac141
b10iEduiti thornX3
ifrac141
g10iLFti thorn u10t (10)
The null hypothesis that all the indicators of education and all levels of education do not Granger cause RGDPt was tested inTable I Bivariate TYAGC results indicate that the null hypothesis was rejected (Table I) Similarly the null hypothesis thatRGDPt does not Granger cause all the indicators and all levels of education is rejected except Edu8t and Edu10t It means thatthere exists two-way causality between education and RGDPt RGDPt fails to cause higher education and expenditures oneducation
The estimated results from Eqs (3) and (4) in Table I show the feedback Granger causality between RPCt and RGDPt LFt isfound to cause RGDPt at 99 level of confidence while its reverse is not true The results of Eqs (7) and (8) in Table I show thatthe feedback causality between Eduit and RPCt seems to exist because majority of the indicators of education are causingRPCt and vice versa The results from Eq (9) and (10) in Table I reveal that LFt Granger causes education while reverseseemed to be not true In conclusion education and all levels of education (school college and university) Granger causeRGDPt and RGDPt also Granger causes education and all levels of education Feedback causality between education andRGDPt is found in bivariate case
45 Trivariate TYAGC framework
The trivariate causality among RGDPt RPCt and Eduit (Eqs (11)ndash(13)) and among RGDPt LFt and Eduit (Eqs (14)ndash(16)) wasestimated by using TYAGC framework and is presented in Tables II and III
RGDPt frac14 a11 thornX3
ifrac141
b11iRGDPti thornX3
ifrac141
l11iRPCti thornX3
ifrac141
g11iEduiti thorn u11t (11)
Eduit frac14 a12 thornX3
ifrac141
b12iRGDPti thornX3
ifrac141
l12iRPCti thornX3
ifrac141
g12iEduiti thorn u12t (12)
RPCt frac14 a13 thornX3
ifrac141
b13iRGDPti thornX3
ifrac141
l13iRPCti thornX3
ifrac141
g13iEduiti thorn u13t (13)
RGDPt frac14 a14 thornX3
ifrac141
b14iRGDPti thornX3
ifrac141
l14iLFti thornX3
ifrac141
g14iEduiti thorn u14t (14)
Edut frac14 a15 thornX3
ifrac141
b15iRGDPti thornX3
ifrac141
l15iLFti thornX3
ifrac141
g15iEduiti thorn u15t (15)
LFt frac14 a16 thornX3
ifrac141
b16iRGDPti thornX3
ifrac141
l16iLFti thornX3
ifrac141
g16iEduiti thorn u16t (16)
The estimated results presented in Table II indicate that the null hypothesis of no Granger causality between majority of theindicators of education and RGDPt is rejected This also supports our previous bivariate causality results that there existsfeedback causality between education and RGDPt The trivariate result in Table II seems to support the previous bivariateresult regarding causality between education and RPCt and between RPCt and RGDPt
In case of trivariate causality analysis among RGDPt LFt and Eduit the results in Table III again indicate the two waycausality running between education and RGDPt Six out of ten indicators of education does Granger cause LFt while LFt
Granger causes nine indicators out of ten indicators of education The null hypothesis that LFt does not Granger cause RGDPt
in the presence of all indicators of education is rejected at 99 level of confidence So LFt seems to be a very importantvariable that affects two main variables of the study ie education and RGDPt
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335328
In conclusion education and all levels of education Granger cause RGDPt where as its revere ie Granger causalityrunning from RGDPt to education and all levels of education is only true in case of trivariate causality among RGDPt LFt andeducation From here one can easily conclude that the role of LFt as compared to RPCt is very important in understanding therelationship between education and RGDPt Feedback causality between education and RGDPt is also found in trivariate case
46 Tetravariate TYAGC framework
The tetravariate causality among RGDPt RPCt LFt and Eduit (Eqs (17)ndash(20)) was also estimated by using TYAGC techniqueand their results are presented in Table IV
RGDPt frac14 a17 thornX3
ifrac141
b17iRGDPti thornX3
ifrac141
g17iRPCti thornX3
ifrac141
l17iLFti thornX3
ifrac141
d17iEduiti thorn u17t (17)
Eduit frac14 a18 thornX3
ifrac141
b18iRGDPti thornX3
ifrac141
g18iRPCti thornX3
ifrac141
l18iLFti thornX3
ifrac141
d18iEduiti thorn u18t (18)
RPCt frac14 a19 thornX3
ifrac141
b19iRGDPti thornX3
ifrac141
g19iRPCti thornX3
ifrac141
l19iLFti thornX3
ifrac141
d19iEduiti thorn u19t (19)
LFt frac14 a20 thornX3
ifrac141
b20iRGDPti thornX3
ifrac141
g20iRPCti thornX3
ifrac141
l20iLFti thornX3
ifrac141
d20iEduiti thorn u20t (20)
The tetravariate TYAGC results presented in Table IV indicate that all the indicators of education Granger cause RGDPt whileRGDPt does Granger cause majority of the indicators of education (seven out of ten) RGDPt does not Granger cause Edu5t
(university education) Edu8t (higher education) and Edu10t (education expenditure) From this one can easily conclude thatthere exists two way causality between education and RGDPt in case of tetravariate causality analysis as have been the caseof bivariate and trivariate causality Regarding levels of education all levels of education (ie school education collegeeducation and university education) do Granger cause RGDPt while RGDPt does only cause school education and collegeeducation RGDPt does not Granger cause university education
LFt Granger causes RGDPt at 99 confidence level while RGDPt only Granger causes LFt in case of Edu3t Edu5t Edu9t andEdu10t In case of testing causality between RPCt and RGDPt in the presence of all indicators of education RPCt does Grangercause RGDPt and in reverse case RGDPt does not Granger cause RPCt in the presence of Edu1t Edu3t Edu8t Edu9t and Edu10tThese results show the unidirectional causality running from RPCt to RGDPt
The research hypothesis that LFt does not Granger cause Eduit is rejected at 99 confidence interval except wheneducation is measured by Eduit Labour force has been found to cause all levels of education On the other side education onlyGranger causes the LFt in the presence of Edu3t Edu4t Edu5t Edu8t and Edu10t RPC does not Granger cause education whenEdu3t and Edu4t are used as proxies of education All indicators of education except Edu1t Edu2t and Edu10t do Granger causeRPCt This implies that feedback causality between RPCt and education is observed
It can easily be concluded from the TYAGC results of Eq (17) in Table IV that among all levels of education General highereducation (Edu9t) causes RGDPt highly and most significantly (999 confidence level) The level of confidence of collegeeducation (Edu3t) and school education (Edu2t) causing RGDPt is found to be 2nd highest (significance at 997 confidencelevel) and 3rd highest (significance at 989 confidence level) respectively From Eq (18) in Table IV it can also be found thatthe level of confidence (999) of causing RGDPt to school education (Edu2t) is found to be highest
From the bivariate trivariate and tetravariate TYAGC tests results in Tables IndashIV the overall results of the study abouteducation and different levels of education (School College and University) are summarized in Table 4
Table 4
Causal nexus between education different levels of education with RGDPt
Hypothesis TYAGC procedure
Bivariate Trivariate Tetravariate
RGDPt and Edut RGDPt RPCt Edut RGDPt LFt Edut RGDPt LFt RPCt Edut
Education (Edu1t) does Granger cause RGDPt Yes (0089) No (0459) Yes (0009) Yes (0087)
RGDPt does Granger cause education (Edu1t) Yes (0000) Yes (0000) Yes (0000) Yes (0000)
School education (Edu2t) does Granger cause RGDPt Yes (0000) Yes (0001) Yes (0002) Yes (0010)
RGDPt does Granger cause school education (Edu2t) Yes (0000) Yes (0000) Yes (0000) Yes (0000)
College education (Edu3t) does Granger cause RGDPt Yes (0038) Yes (0081) Yes (0000) Yes (0002)
RGDPt does Granger cause college education (Edu3t) Yes (0003) No (0172) Yes (0001) Yes (0032)
University education (Edu5t) does Granger cause RGDPt Yes (0000) Yes (0000) Yes (0001) Yes (0001)
RGDPt does Granger cause university education (Edu5t) Yes (0089) Yes (0000) Yes (0025) No (0515)
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 329
47 Figures in parentheses are p-values
From the above results presented in Table 4 it can be concluded that there existed feedback causality between educationand RGDPt in all bivariate trivariate and tetravariate TYAGC causality cases All levels of education ie school educationcollege education and university education do Granger cause RGDPt in all causality cases RGDPt does Granger cause schooleducation in all causality cases RGDPt does Granger cause college education in all causality cases except trivariate causalitythat is running from RGDPt to education when RPCt serves as a third variable Table 4 also reveals that RGDPt does Grangercause university education only in a bivariate and trivariate causality cases RGDPt fails to Granger cause to universityeducation in tetravariate case
5 Conclusions and recommendations
This study aimed to explore the cointegration and causal relationship between education (measured by different indicatorsof education) and economic growth in Pakistan It is very essential for a country to invest more in education because it is one ofthe most important ingredients of human capital and hence economic development The nature and strength of the relationshipbetween education and economic growth is still not clear in case of Pakistan The main focus of this empirical study remained toobserve the causality and cointegration between education and economic growth in the absence and presence physical capitaland labour force Cointegration between education and economic growth was investigated using ARDL approach and the causallinkage between education and economic growth was examined in bivariate trivariate and tetravariate TYAGC frameworkDifferent indicators of education were utilized in this study to show the robustness of empirical results The causality betweeneducation and economic growth was examined in the presence and absence of stock of physical capital and stock of labour as athird and fourth variable The causality results indicate that there exist two-way causality between education and economicgrowth and between all levels of education and economic growth in case of bivariate TYAGC framework Education and alllevels of education do Granger cause economic growth in the presence of real physical capital as a third variable while economicgrowth causes all the indicators of education except college education professional college education and educationalexpenditures in the presence of real physical capital as a third variable in case of trivariate causality analysis In the presence oflabour force as a third variable feedback causality exists between education and economic growth and between all levels ofeducation and economic growth The results of tetravariate TYAGC Test indicate that education and all level of education doGranger cause economic growth while economic growth does Granger cause majority of the indicators of education (ie sevenout of ten) Economic growth does not Granger cause university education higher education including professional educationand expenditures on education The rise in university education higher education including professional education andexpenditures on education were considered as the key indicators to gauge human and social progress Economic growth doesnot seem to affect important educational indicators like university education higher education including professionaleducation and expenditures on education This seems to be consistent with Easterlyrsquos findings Easterly (2001) said thatPakistan is a country that made little social progress for given rates of GDP Among all levels of education General highereducation causes economic growth highly and most significantly as was explored by Stengos and Aurangzeb (2008) The level ofconfidence of causing economic growth to school education found to be highest This study also confirms the long runrelationship between education and economic growth
On the basis of the results of this study it is recommended that the government should focus more on higher educationparticularly to university education More funds should be allocated to education in line with others sectors particularly touniversity and higher education levels so that the economic growth can be further accelerated This will in turn leads tofurther education and hence development Poor should be facilitated to get higher education so that the polarization inhigher education may further be minimized Primary schooling should also be given priority because primary educationserves as an input for all higher levels of education The inverted educational expenditure pyramid may also be taken intoaccount Since the role of labour force seems to be very important in understanding the relationship between education andeconomic growth so it is suggested that labour force should be given more chances to enhance their skills The variablelabour force must be included while examining the causality between education and economic growth It is alsorecommended that the nexus between education and economic growth with inclusion of other variables other than physicalcapital and labour force should further be tested and generalized
Appendix A
Table I
Bivariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Bivariate-RGDPt and Eduit
Eq (1) Edu1t does not Granger cause RGDPt 028998 [0089] 1 Reject H0
Edu2t does not Granger cause RGDPt 144869 [0000] 1 Reject H0
Edu3t does not Granger cause RGDPt 043243 [0038] 1 Reject H0
Edu4t does not Granger cause RGDPt 039797 [0046] 1 Reject H0
Table I (Continued )
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Edu5t does not Granger cause RGDPt 217739 [0000] 1 Reject H0
Edu6t does not Granger cause RGDPt 137788 [0000] 1 Reject H0
Edu7t does not Granger cause RGDPt 126682 [0000] 1 Reject H0
Edu8t does not Granger cause RGDPt 041335 [0042] 1 Reject H0
Edu9t does not Granger cause RGDPt 160963 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 028642 [0091] 1 Reject H0
Eq (2) RGDPt does not Granger cause Edu1t 260926 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 230094 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 085441 [0003] 1 Reject H0
RGDPt does not Granger cause Edu4t 107403 [0001] 1 Reject H0
RGDPt does not Granger cause Edu5t 028935 [0089] 1 Reject H0
RGDPt does not Granger cause Edu6t 270343 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 273974 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 003162 [0574] 1 Cannot reject H0
RGDPt does not Granger cause Edu9t 027588 [0097] 1 Reject H0
RGDPt does not Granger cause Edu10t 000851 [0770] 1 Cannot reject H0
Bivariate-RGDPt and RPCt
Eq (3) RPCt does not Granger cause RGDPt 054972 [0019] 1 Reject H0
Eq (4) RGDPt does not Granger cause RPCt 167511 [0000] 1 Reject H0
Bivariate-RGDPt and LFt
Eq (5) LFt does not Granger cause RGDPt 227888 [0000] 1 Reject H0
Eq (6) RGDPt does not Granger cause LFt 012380 [0266] 1 Cannot reject H0
Bivariate-Eduit and RPCt
Eq (7) Edu1t does not Granger cause RPCt 094596 [0002] 1 Reject H0
Edu2t does not Granger cause RPCt 015434 [0214] 1 Cannot reject H0
Edu3t does not Granger cause RPCt 038233 [0051] 1 Reject H0
Edu4t does not Granger cause RPCt 000506 [0822] 1 Cannot reject H0
Edu5t does not Granger cause RPCt 298085 [0000] 1 Reject H0
Edu6t does not Granger cause RPCt 018289 [0176] 1 Cannot reject H0
Edu7t does not Granger cause RPCt 018976 [0168] 1 Cannot reject H0
Edu8t does not Granger cause RPCt 176399 [0000] 1 Reject H0
Edu9t does not Granger cause RPCt 224647 [0000] 1 Reject H0
Edu10t does not Granger cause RPCt 039174 [0048] 1 Reject H0
Eq (8) RPCt does not Granger cause Edu1t 091477 [0002] 1 Reject H0
RPCt does not Granger cause Edu2t 098821 [0002] 1 Reject H0
RPCt does not Granger cause Edu3t 066148 [0010] 1 Reject H0
RPCt does not Granger cause Edu4t 084218 [0004] 1 Reject H0
RPCt does not Granger cause Edu5t 001684 [0682] 1 Cannot reject H0
RPCt does not Granger cause Edu6t 107553 [0001] 1 Reject H0
RPCt does not Granger cause Edu7t 108798 [0001] 1 Reject H0
RPCt does not Granger cause Edu8t 004283 [0513] 1 Cannot reject H0
RPCt does not Granger cause Edu9t 005627 [0453] 1 Cannot reject H0
RPCt does not Granger cause Edu10t 000417 [0838] 1 Cannot reject H0
Bivariate-Eduit and LFt
Eq (9) Edu1t does not Granger cause LFt 026469 [0104] 1 Reject H0
Edu2t does not Granger cause LFt 012355 [0266] 1 Cannot reject H0
Edu3t does not Granger cause LFt 020468 [0153] 1 Cannot reject H0
Edu4t does not Granger cause LFt 098042 [0002] 1 Reject H0
Edu5t does not Granger cause LFt 049986 [0025] 1 Reject H0
Edu6t does not Granger cause LFt 016896 [0194] 1 Cannot reject H0
Edu7t does not Granger cause LFt 015167 [0218] 1 Cannot reject H0
Edu8t does not Granger cause LFt 184475 [0000] 1 Reject H0
Edu9t does not Granger cause LFt 003986 [0528] 1 Cannot reject H0
Edu10t does not Granger cause LFt 010899 [0296] 1 Cannot reject H0
Eq (10) LFt does not Granger cause Edu1t 107709 [0001] 1 Reject H0
LFt does not Granger cause Edu2t 071204 [0008] 1 Reject H0
LFt does not Granger cause Edu3t 136419 [0000] 1 Reject H0
LFt does not Granger cause Edu4t 056225 [0018] 1 Reject H0
LFt does not Granger cause Edu5t 057141 [0017] 1 Reject H0
LFt does not Granger cause Edu6t 091531 [0002] 1 Reject H0
LFt does not Granger cause Edu7t 095063 [0002] 1 Reject H0
LFt does not Granger cause Edu8t 021313 [0144] 1 Cannot reject H0
LFt does not Granger cause Edu9t 069389 [0008] 1 Reject H0
LFt does not Granger cause Edu10t 000743 [0785] 1 Cannot reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335330
Table II
Trivariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Trivariate-RGDPt RPCt and Eduit
Eq (11) Edu1t does not Granger cause RGDPt 005481 [0459] 1 Cannot reject H0
Edu2t does not Granger cause RGDPt 105415 [0001] 1 Reject H0
Edu3t does not Granger cause RGDPt 030370 [0081] 1 Reject H0
Edu4t does not Granger cause RGDPt 022525 [0133] 1 Cannot reject H0
Edu5t does not Granger cause RGDPt 227510 [0000] 1 Reject H0
Edu6t does not Granger cause RGDPt 098494 [0002] 1 Reject H0
Edu7t does not Granger cause RGDPt 090460 [0003] 1 Reject H0
Edu8t does not Granger cause RGDPt 067381 [0009] 1 Reject H0
Edu9t does not Granger cause RGDPt 168617 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 085842 [0003] Reject H0
Eq (11a) RPCt does not Granger cause RGDP (Edu1 as a 3rd variable) 029029 [0088] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu2 as a 3rd variable) 024880 [0115] 1 Cannot reject H0
RPCt does not Granger cause RGDPt (Edu3t as a 3rd variable) 041380 [0042] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu4t as a 3rd variable) 036580 [0056] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu5t as a 3rd variable) 064811 [0011] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu6t as a 3rd variable) 024405 [0118] 1 Cannot reject H0
RPCt does not Granger cause RGDPt (Edu7t as a 3rd variable) 026008 [0107] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu8t as a 3rd variable) 081607 [0004] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu9t as a 3rd variable) 063133 [0012] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu10t as a 3rd variable) 115637 [0001] 1 Reject H0
Eq (12) RGDPt does not Granger cause Edu1t 176454 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 129776 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 018626 [0172] 1 Cannot reject H0
RGDPt does not Granger cause Edu4t 020449 [0153] 1 Cannot reject H0
RGDPt does not Granger cause Edu5t 144658 [0000] 1 Reject H0
RGDPt does not Granger cause Edu6t 175431 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 178356 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 042497 [0039] 1 Reject H0
RGDPt does not Granger cause Edu9t 082506 [0004] 1 Reject H0
RGDPt does not Granger cause Edu10t 008026 [0370] 1 Cannot reject H0
Eq (12a) RPCt does not Granger cause Edu1t 000122 [0912] 1 Cannot reject H0
RPCt does not Granger cause Edu2t 028750 [0090] 1 Reject H0
RPCt does not Granger cause Edu3t 058586 [0016] 1 Reject H0
RPCt does not Granger cause Edu4t 071372 [0008] 1 Reject H0
RPCt does not Granger cause Edu5t 302364 [0000] 1 Reject H0
RPCt does not Granger cause Edu6t 020474 [0152] 1 Cannot reject H0
RPCt does not Granger cause Edu7t 017533 [0185] 1 Cannot reject H0
RPCt does not Granger cause Edu8t 044926 [0034] 1 Reject H0
RPCt does not Granger cause Edu9t 240955 [0000] 1 Reject H0
RPCt does not Granger cause Edu10t 021006 [0147] 1 Cannot reject H0
Eq (13) RGDPt does not Granger cause RPCt (Edu1t as a 3rd variable) 055095 [0019] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu2t as a 3rd variable) 182287 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu3t as a 3rd variable) 191499 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu4t as a 3rd variable) 269133 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu5t as a 3rd variable) 172979 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu6t as a 3rd variable) 166347 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu7t as a 3rd variable) 161198 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu8t as a 3rd variable) 038521 [0050] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu9tas a 3rd variable) 183169 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu10t as a 3rd variable) 139552 [0000] 1 Reject H0
Eq (13a) Edu1t does not Granger cause RPCt 000122 [0912] 1 Cannot reject H0
Edu2t does not Granger cause RPCt 028750 [0090] 1 Reject H0
Edu3t does not Granger cause RPCt 058586 [0016] 1 Reject H0
Edu4t does not Granger cause RPCt 071372 [0008] 1 Reject H0
Edu5t does not Granger cause RPCt 302364 [0000] 1 Reject H0
Edu6t does not Granger cause RPCt 020474 [0152] 1 Cannot reject H0
Edu7t does not Granger cause RPCt 017533 [0185] 1 Cannot reject H0
Edu8t does not Granger cause RPCt 044926 [0034] 1 Reject H0
Edu9t does not Granger cause RPCt 240955 [0000] 1 Reject H0
Edu10t does not Granger cause RPCt 021006 [0147] 1 Cannot reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 331
Table III
Trivariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Trivariate-RGDPt LFt and Eduit
Eq (14) Edu1t does not Granger cause RGDPt 068472 [0009] 1 Reject H0
Edu2t does not Granger cause RGDPt 092326 [0002] 1 Reject H0
Edu3t does not Granger cause RGDPt 180477 [0000] 1 Reject H0
Edu4t does not Granger cause RGDPt 132070 [0000] 1 Reject H0
Edu5t does not Granger cause RGDPt 109716 [0001] 1 Reject H0
Edu6t does not Granger cause RGDPt 086017 [0003] 1 Reject H0
Edu7t does not Granger cause RGDPt 078604 [0005] 1 Reject H0
Edu8t does not Granger cause RGDPt 020470 [0153] 1 Cannot reject H0
Edu9t does not Granger cause RGDPt 293293 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 005754 [0448] 1 Cannot reject H0
Eq (14a) LFt does not Granger cause RGDPt (Edu1t as a 3rd variable) 409533 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu2t as a 3rd variable) 332636 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu3t as a 3rd variable) 701171 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu4t as a 3rd variable) 605496 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu5t as a 3rd variable) 240867 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu6t as a 3rd variable) 330495 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu7t as a 3rd variable) 332860 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu8t as a 3rd variable) 352003 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu9t as a 3rd variable) 573087 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu10t as a 3rd variable) 343199 [0000] 1 Reject H0
Eq (15) RGDPt does not Granger cause Edu1t 134939 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 804323 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 109273 [0001] 1 Reject H0
RGDPt does not Granger cause Edu4t 278785 [0000] 1 Reject H0
RGDPt does not Granger cause Edu5t 050547 [0025] 1 Reject H0
RGDPt does not Granger cause Edu6t 790307 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 738342 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 043402 [0037] 1 Reject H0
RGDPt does not Granger cause Edu9t 175731 [0000] 1 Reject H0
RGDPt does not Granger cause Edu10t 061709 [0013] 1 Reject H0
Eq (15a) LFt does not Granger cause Edu1t 009324 [0334] 1 Cannot reject H0
LFt does not Granger cause Edu2t 377339 [0000] 1 Reject H0
LFt does not Granger cause Edu3t 176565 [0000] 1 Reject H0
LFt does not Granger cause Edu4t 180046 [0000] 1 Reject H0
LFt does not Granger cause Edu5t 091061 [0003] 1 Reject H0
LFt does not Granger cause Edu6t 355203 [0000] 1 Reject H0
LFt does not Granger cause Edu7t 327354 [0000] 1 Reject H0
LFt does not Granger cause Edu8t 053664 [0021] 1 Reject H0
LFt does not Granger cause Edu9t 251724 [0000] 1 Reject H0
LFt does not Granger cause Edu10t 060787 [0014] 1 Reject H0
Eq (16) Edu1t does not Granger cause LFt 036697 [0055] 1 Reject H0
Edu2t does not Granger cause LFt 004605 [0497] 1 Cannot reject H0
Edu3t does not Granger cause LFt 093988 [0002] 1 Reject H0
Edu4t does not Granger cause LFt 177287 [0000] 1 Reject H0
Edu5t does not Granger cause LFt 059203 [0015] 1 Reject H0
Edu6t does not Granger cause LFt 007202 [0396] 1 Cannot reject H0
Edu7t does not Granger cause LFt 005520 [0458] 1 Cannot reject H0
Edu8t does not Granger cause LFt 241662 [0000] 1 Reject H0
Edu9t does not Granger cause LFt 004009 [0527] 1 Cannot reject H0
Edu10t does not Granger cause LFt 058477 [0016] 1 Reject H0
Eq (16a) RGDPt does not Granger cause LFt (Edu1t as a 3rd variable) 002436 [0622] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu2t as a 3rd variable) 004276 [0513] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu3t as a 3rd variable) 047690 [0029] 1 Reject H0
RGDPt does not Granger cause LFt (Edu4t as a 3rd variable) 015207 [0218] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu5t as a 3rd variable) 040757 [0044] 1 Reject H0
RGDPt does not Granger cause LFt (Edu6t as a 3rd variable) 003392 [0560] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu7t as a 3rd variable) 004309 [0512] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu8t as a 3rd variable) 003145 [0575] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu9t as a 3rd variable) 017426 [0187] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu10t as a 3rd variable) 048448 [0028] 1 Reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335332
Table IV
Tetravariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Tetravariate-RGDPt RPCt LFt and Edut
Eq (17) Edu1t does not Granger cause RGDPt 029350 [0087] 1 Reject H0
Edu2t does not Granger cause RGDPt 065661 [0010] 1 Reject H0
Edu3t does not Granger cause RGDPt 097521 [0002] 1 Reject H0
Edu4t does not Granger cause RGDPt 071590 [0007] 1 Reject H0
Edu5t does not Granger cause RGDPt 116263 [0001] 1 Reject H0
Edu6t does not Granger cause RGDPt 059569 [0015] 1 Reject H0
Edu7t does not Granger cause RGDPt 054327 [0020] 1 Reject H0
Edu8t does not Granger cause RGDPt 040033 [0045] 1 Reject H0
Edu9t does not Granger cause RGDPt 195734 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 034374 [0064] 1 Reject H0
Eq (17a) LFt does not Granger cause RGDPt (Edut = Edu1) 251518 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu2) 165581 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu3) 316418 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu4) 289993 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu5) 109302 [0001] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu6) 165606 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu7) 168037 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu8) 176645 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu9) 247435 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu10) 146998 [0000] 1 Reject H0
Eq (17b) RPCt does not Granger cause RGDPt (Edut = Edu1) 042975 [0038] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu2) 039280 [0047] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu3) 034296 [0064] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu4) 027068 [0100] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu5) 062858 [0012] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu6) 039537 [0047] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu7) 040022 [0045] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu8) 045487 [0033] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu9) 068323 [0009] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu10) 083479 [0004] 1 Reject H0
Eq (18) RGDPt does not Granger cause Edu1t 150200 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 633103 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 045767 [0032] 1 Reject H0
RGDPt does not Granger cause Edu4t 122392 [0000] 1 Reject H0
RGDPt does not Granger cause Edu5t 004235 [0515] 1 Cannot reject H0
RGDPt does not Granger cause Edu6t 453644 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 418611 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 055973 [0454] 1 Cannot reject H0
RGDPt does not Granger cause Edu9t 053890 [0020] 1 Reject H0
RGDPt does not Granger cause Edu10t 011119 [0292] 1 Cannot reject H0
Eq (18a) LFt does not Granger cause Edu1t 006023 [0438] 1 Cannot reject H0
LFt does not Granger cause Edu2t 364559 [0000] 1 Reject H0
LFt does not Granger cause Edu3t 197423 [0000] 1 Reject H0
LFt does not Granger cause Edu4t 166511 [0000] 1 Reject H0
LFt does not Granger cause Edu5t 383886 [0000] 1 Reject H0
LFt does not Granger cause Edu6t 359377 [0000] 1 Reject H0
LFt does not Granger cause Edu7t 328249 [0000] 1 Reject H0
LFt does not Granger cause Edu8t 135310 [0000] 1 Reject H0
LFt does not Granger cause Edu9t 630068 [0000] 1 Reject H0
LFt does not Granger cause Edu01t 109365 [0001] 1 Reject H0
Eq (18b) RPCt does not Granger cause Edu1t 114248 [0001] 1 Reject H0
RPCt does not Granger cause Edu2t 036828 [0055] 1 Reject H0
RPCt does not Granger cause Edu3t 021023 [0147] 1 Cannot reject H0
RPCt does not Granger cause Edu4t 000484 [0826] 1 Cannot reject H0
RPCt does not Granger cause Edu5t 610934 [0000] 1 Reject H0
RPCt does not Granger cause Edu6t 070279 [0008] 1 Reject H0
RPCt does not Granger cause Edu7t 051166 [0024] 1 Reject H0
RPCt does not Granger cause Edu8t 167481 [0000] 1 Reject H0
RPCt does not Granger cause Edu9t 335271 [0000] 1 Reject H0
RPCt does not Granger cause Edu10t 067481 [0009] 1 Reject H0
Eq (19) Edu1 does not Granger cause RPCt 005154 [0473] 1 Cannot reject H0
Edu2 does not Granger cause RPCt 011954 [0274] 1 Cannot reject H0
Edu3 does not Granger cause RPCt 162365 [0000] 1 Reject H0
Edu4 does not Granger cause RPCt 148964 [0000] 1 Reject H0
Edu5 does not Granger cause RPCt 243978 [0000] 1 Reject H0
Edu6 does not Granger cause RPCt 040262 [0045] 1 Reject H0
Edu7 does not Granger cause RPCt 035138 [0061] 1 Reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 333
able IV (Continued )
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Edu8 does not Granger cause RPCt 030100 [0083] 1 Reject H0
Edu9 does not Granger cause RPCt 462564 [0000] 1 Reject H0
Edu10 does not Granger cause RPCt 009580 [0328] 1 Cannot reject H0
Eq (19a) RGDPt does not Granger cause RPCt (Edu1t as a 3rd variable) 009936 [0319] 1 Cannot reject H0
RGDPt does not Granger cause RPCt (Edu2t as a 3rd variable) 039369 [0047] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu3t as a 3rd variable) 003822 [0536] 1 Cannot reject H0
RGDPt does not Granger cause RPCt (Edu4t as a 3rd variable) 028000 [0094] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu5t as a 3rd variable) 039910 [0046] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu6t as a 3rd variable) 033500 [0067] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu7t as a 3rd variable) 029924 [0084] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu8t as a 3rd variable) 002803 [0597] 1 Cannot Reject H0
RGDPt does not Granger cause RPCt (Edu9t as a 3rd variable) 011416 [0285] 1 Cannot reject H0
RGDPt does not Granger cause RPCt (Edu10t as a 3rd variable) 006944 [0405] 1 Cannot reject H0
Eq (20) Edu1t does not Granger cause LFt 015302 [0216] 1 Cannot reject H0
Edu2t does not Granger cause LFt 001053 [0746] 1 Cannot reject H0
Edu3t does not Granger cause LFt 080072 [0005] 1 Reject H0
Edu4t does not Granger cause LFt 143854 [0000] 1 Reject H0
Edu5t does not Granger cause LFt 061159 [0013] 1 Reject H0
Edu6t does not Granger cause LFt 003113 [0577] 1 Cannot reject H0
Edu7t does not Granger cause LFt 002394 [0625] 1 Cannot reject H0
Edu8t does not Granger cause LFt 196804 [0000] 1 Reject H0
Edu9t does not Granger cause LFt 046285 [0496] 1 Cannot reject H0
Edu10t does not Granger cause LFt 04161 1 [0041] 1 Reject H0
Eq (20a) RGDPt does not Granger cause LFt (Edu1t as a 3rd variable) 006872 [0407] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu2t as a 3rd variable) 018604 [0173] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu3t as a 3rd variable) 066905 [0010] 1 Reject H0
RGDPt does not Granger cause LFt (Edu4t as a 3rd variable) 023249 [0127] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu5t as a 3rd variable) 070835 [0008] 1 Reject H0
RGDPt does not Granger cause LFt (Edu6t as a 3rd variable) 016501 [0199] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu7t as a 3rd variable) 018532 [0173] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu8t as a 3rd variable) 003730 [0541] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu9t as a 3rd variable) 039255 [0048] 1 Reject H0
RGDPt does not Granger cause LFt (Edu10t as a 3rd variable) 055266 [0019] 1 Reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335334
T
References
Abbas Q amp Peck J F (2008) Human capital and economic growth Pakistan 1960ndash2003 The Lahore Journal of Economics 13(1) 1ndash28Ayara N A (2002) The paradox of education and economic growth in Nigeria Empirical evidence The Nigerian Economic Society (NES) Pt 2 371ndash393Babatunde M A amp Adefabi R A (2005) Long run relationship between education and economic growth in Nigeria Evidence from the Johansenrsquos cointegration
approach Paper presented at the regional conference on education in West Africa Constraints and Opportunities Dakar Senegal November 1stndash2nd 2005Cornell UniversityCREAMinisterede lrsquoEducation du Senegal
Baldacci E Clements B Cui Q amp Gupta S (2005) What does it take to help the poor Finance and Development The Quarterly Magazine of the IMF 42(2)Changzheng Z Zhijian H amp Huaizu L (2007) An empirical study on education equity in China 1978ndash2004 Frontier in Economics of China 2(4) 536ndash544Chaudhary A R Asim I amp Gillani S Y M (2009) The nexus between higher education and economic growth An empirical investigation for Pakistan Pakistan
Journal of Commerce and Social Sciences 3Chaudhry I S Malik S amp Ashraf M (2006) Rural poverty in Pakistan Some related concepts issues and empirical analysis Pakistan Economic and Social Review
44(2) 259ndash276Diebolt C amp Litago J (1997) Education and economic growth in Germany before the Second World War An econometric analysis of dynamic relations Historical
Social Research 2(22) 132ndash149Easterly W (2001) The middle class consensus and economic development Journal of Economic Growth 6(4) 317ndash335Engle R F amp Granger C W J (1987) Cointegration and error correction Representation estimation and testing Econometrica 55 251ndash276Fernandez E amp Mauro P (2000) The role of human capital in economic growth The case of Spain (IMF Working Paper) International Monetary FundFrancis B amp Iyare S (2006) Education and development in the Caribbean A cointegration and causality approach Economics Bulletin 15(2) 1ndash13Galor O amp Moav O (2000) Das human capital Retrieved from httpeconpstcn brownedufacultygalorindexhtmlGoode R B (1959) Adding to the stock of physical and human capital American Economic Review 49(2) 147Government of Pakistan (1970ndash2009) Pakistan economic survey various issues Finance Division Islamabad Economic Advisorrsquos WingGregory A W amp Hansen B E (1996) Residual-based tests for cointegration in models with regime shifts Journal of Econometrics 70 99ndash126Grossman G M amp Helpman E (1991) Innovation and growth in the global economy Cambridge MIT PressGylfason T amp Zoega G (2003) Education social equality and economic growth A view of the landscape CESifo Economic Studies 49(4) 557ndash579Hassan S amp Ahmed H (2008) Educationrsquos contribution to the economic growth of sub-Saharan Africa Southwestern Economic Review 1(32) 175ndash190Islam T S Wadud M A amp Islam Q B T (2007) Relationship between education and GDP growth A multivariate causality analysis for Bangladesh Economics
Bulletin 3(35) 1ndash7Jin J C (2009) Economic research and economic growth Evidence from East Asian Economies Journal of Asian Economics 20 150ndash155Johansen S (1988) Statistical analysis of cointegration vectors Journal of Economic Dynamics and Control 12 231ndash254Johansen S amp Juselius K (1990) Maximum likelihood estimation and inference on cointegration with applications to the demand for money Oxford Bulletin of
Economics and Statistics 52 169ndash210Katırcıoglu S T (2009) Investigating higher-education-led growth hypothesis in a small Island Time series evidence from Northern Cyprus Paper presented at
Econ Anadolu 2009 Anadolu International Conference in Economics June 17ndash19 2009 TurkeyKhorasgani M F (2008) Higher education development and economic growth in Iran Education Business and Society Contemporary Middle Eastern Issues 1
162ndash174
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 335
Kui L (2005) The interactive causality between education and economic growth in China Retrieved from httppapersssrncomsol3paperscfmAbstrac-tid=920624
Loening J L (2004) Time series evidence on education and growth The case of Guatemala 1951ndash2002 Revista de Analisis Economico 19(2) 3ndash40Lucas R E (1988) On the mechanics of economic development Journal of Monetary Economics 22 3ndash42Macerinskiene I amp Vaiksnoraite B (2006) The role of higher education to economic development VadybaManagement 2(11)Mankiw N G Romer D amp Weil D N (1992) A contribution to the empirics of economic growth Quarterly Journal of Economics 107 407ndash437Momete D C (2007) Analysis of the relationship between employment and economic growth in Romania Fascicle of Management and Technological Engineering
VI(XVI)Morote E S (2000) Higher education employment and economic growth Mexico and Peru Retrieved from httpwwwamericanprofessororgdocumentation
lasapa perdocNarayan P K (2005) The saving and investment nexus for China Evidence from cointegration tests Applied Economics 37 1979ndash1990Permani R (2008) Education as a determinant of economic growth in East Asia Historical trends and empirical evidences (1965ndash2000) Retrieved from http
wwwuoweduaucommerceeconehsanzpdfsPermani202008pdfPesaran M H amp Pesaran B (1997) Working with Microfit 40 Interactive econometric analysis Oxford Oxford University PressPesaran M H amp Shin Y (1999) An autoregressive distributed lag modeling approach to cointegration analysis In S Strom (Ed) Econometrics and economic theory
in the 20th century Cambridge Cambridge University PressPesaran M H Shin Y amp Smith R J (2001) Bounds testing approaches to the analysis of level relationships Journal of Applied Econometrics 16 289ndash326Pradhan R P (2009) Education and economic growth in India Using error correction modeling International Research Journal of Finance and Economics 25Pritchett L (2001) Where has all the education gone The World Bank Economic Review 15(3)Quah D amp Rauch J E (1990) Openness and the rate of economic growth Journal Development of Studies 2(49) 307ndash335Rivera-Batiz L A amp Romer P M (1991) Economic integration and endogenous growth Quarterly Journal of Economics 106 531ndash555Romer P M (1986) Increasing returns and long run growth Journal of Political Economy 6(90) 1002ndash1037Romer P M (1989) Human capital and growth Theory and evidence (NBER Working Papers 3173) National Bureau of Economic Research IncRomer P M (1990) Endogenous technological change Journal of Political Economy 5(98) 71ndash101Rondinelli D amp Montgomery J (1995) Great policies Strategic innovations in Asia and the Pacific Basin Westport Praeger PublishingSaikkonen P amp Lutkepohl H (2000) Testing for the cointegration rank of a VAR process with structural shifts Journal of Business and Economic Statistics 18(4)
451ndash464Schultz T W (1961) Investment in human capital American Economic Review 51(1) 1State Bank of Pakistan (1972ndash2009) Annual reports Karachi SBP PressStengos T amp Aurangzeb A (2008) An empirical investigation of the relationship between education and growth in pakistan International Economic Journal 3
345ndash359 Retrieved from httpwwwinformaworldcomsmpptitledb=allcontent=t713685453tab=issueslistbranches=22-v2222Toda H Y amp Yamamoto T (1995) Statistical inference in vector autoregressive with possible integrated processes Journal of Econometrics 66 225ndash250United Nations (1997) Human Development Report New York Oxford University Press
- Education and economic growth in Pakistan A cointegration and causality analysis
-
- Introduction
- Review of literature
- Method and procedure
- Empirical results
-
- Unit root results
- Cointegration
- Toda-Yamamoto Augmented Granger Causality (TYAGC) Test
- Bivariate TYAGC framework
- Trivariate TYAGC framework
- Tetravariate TYAGC framework
- Figures in parentheses are p-values
-
- Conclusions and recommendations
-
- References
-
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 325
Dln Eduit frac14 a0EduitthornXn
ifrac141
biEduitDln Eduiti thorn
Xn
ifrac141
ciEduitDln RPCti thorn
Xn
ifrac141
diEduitDln RGDPti thorn
Xn
ifrac141
eiEduitDln LFti
thorn d1Eduitln Eduit1 thorn d2Eduitln RPCt1 thorn d3Eduitln RGDPt1 thorn d4Eduitln LFt1 (Model 2A)
The coefficients (b c d and e) of the part one of the Model 1A and Model 2A represent SR dynamics and ds determine LRrelationship The first step in ARDL model was to examine long run linkage among the variables by calculating familiar F-statistic on the differenced variables components of Unrestricted Error Correction Mechanism (UECM) model for the jointsignificance of the coefficients of lagged level of the variables In this first step the regression equation estimated for thedependent variable RGDPt is defined as
Dln RGDPt frac14 a0RGDPtthornXn
ifrac141
biRGDPtDln RGDPti thorn
Xn
ifrac141
ciRGDPtDln RPCti thorn
Xn
ifrac141
diRGDPtDln LFti
thornXn
ifrac141
eiRGDPtDln Eduiti (Model 1B)
To create error correction mechanism in this equation 1st lag of the level of each variable is added to Model 1B and a variableaddition test is conducted by calculating F-test on the joint significance of all the added lagged level variables
Dln RGDPt frac14 a0RGDPtthornXn
ifrac141
biRGDPtDln RGDPti thorn
Xn
ifrac141
ciRGDPtDln RPCti thorn
Xn
ifrac141
diRGDPtDln LFti
thornXn
ifrac141
eiRGDPtDln Eduiti thorn d1RDGPt
ln RGDPt1 thorn d2RGDPtln RPCt1 thorn d3RGDPt
ln LFt1
thorn d4RGDPt ln Eduit1 (Model 1C)
The null hypothesis for no cointegration for the variable RGDPt against alternative hypothesis is given as
H0 d1RGDPtfrac14 d2RGDPt
frac14 d3RGDPtfrac14 d4RGDPt
frac14 0
H1 d1RGDPt6frac14 d2RGDPt
6frac14 d3RGDPt6frac14 d4RGDPt
6frac14 0
This is denoted as FRGDPt (RGDPtRPCt LFt Eduit)This hypothesis is being tested by the familiar F-testIf the calculated F-statistic is higher than the upper bounds critical value given by Pesaran Shin and Smith (2001) and
Narayan (2005) the null hypothesis of no cointegration is rejected implying that there exists a LR relationship among theRGDPt RPCt LFt Eduit when RGDPt is the dependent variable If the calculated F-statistic is less than the lower bounds criticalvalue then the null hypothesis of no cointegration cannot be rejected If the F-value falls in between lower and upper boundscritical values the test statistic will be inconclusive The value of the F depends upon the sample size constant andor a trendof ARDL and number of explanatory variables
42 Cointegration
The ARDL approach is applied to examine the long run relationship by conducting F-statistic The cointegration resultsare presented in Tables 2 and 3 The values of estimated F-test for RGDPt are shown in Table 2
Pesaran et al (2001) lower and upper critical values for bounds testing ARDL for 1 5 and 10 significance levels are365ndash466 279ndash367 and 237ndash320 respectively Narayan (2005) lower and upper critical values for Bound Testing ARDL for1 5 and 10 significance level are 502ndash661 355ndash480 and 293ndash402 respectively
All the indicators of education except Edu8 indicate that there exists cointegration relationship among RGDPt RPCt LFt
and Eduit when RGDPt is the dependent variable according to Pesaran et al (2001) CVs because there is at least one F-valuethat is greater than the upper critical bounds value Cointegration exists among RGDPt RPCt LFt and Eduit (as Eduit ismeasured by Edu1t Edu2t Edu4t Edu5t Edu9t) when RGDPt is the dependent variable according to Narayan (2005) CVs Thenull hypothesis of no cointegration is not rejected for Edu8t according to both CVs
Pesaran et al (2001) lower and upper critical values for bounds testing ARDL for 1 5 and 10 significance levels are365ndash466 279ndash367 and 237ndash320 respectively Narayan (2005) lower and upper critical values for Bound Testing ARDL for1 5 and 10 significance level are 502ndash661 355ndash480 and 293ndash402 respectively
The cointegration results in Table 3 shows that there is LR linkage between Eduit RGDPt LFt and RPCt when Eduit (as Eduit
is represented by Edu1t Edu2t Edu5t Edu6t Edu7t Edu9t and Edu10t) is the dependent variable according to both Pesaran et al(2001) and Narayan (2005) CVs because at least one partial F statistic is greater than the upper critical bounds value There
Table 2
Cointegration
Dependent variable when RGDPt serves as dependent variable Lag length Cointegration results based on critical
values (CVs) given by
1 2 3 4 Pesaran et al (2001) Narayan (2005)
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu1t)] 167 419 203 214 Cointegration Cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu2t)] 281 340 226 179 Cointegration No cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu3t)] 209 644 203 145 Cointegration Cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu4t)] 234 619 263 190 Cointegration Cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu5t)] 253 454 257 236 Cointegration Cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu6t)] 287 336 231 181 Cointegration No cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu7t)] 277 338 230 181 Cointegration No cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu8t)] 114 172 203 165 No cointegration No cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu9t)] 274 482 188 117 Cointegration Cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu10t)] 237 392 246 203 Cointegration No cointegration
Table 3
Cointegration
Dependent variable when Eduit serves as dependent variable Lag length Cointegration results based on critical
values (CV) given by Results
1 2 3 4 Pesaran et al (2001) Narayan (2005)
DEdu1t [FEdu1t (Edu1tRGDPt RPCt LFt)] 711 502 548 447 Cointegration Cointegration
DEdu2t [FEdu2t (Edu2tRGDPt RPCt LFt)] 446 336 192 308 Cointegration Cointegration
DEdu3t [FEdu3t (Edu3tRGDPt RPCt LFt)] 157 280 195 295 No cointegration No cointegration
DEdu4t [FEdu4t (Edu4tRGDPt RPCt LFt)] 202 156 295 223 No cointegration No cointegration
DEdu5t [FEdu5t (Edu5tRGDPt RPCt LFt)] 152 629 081 069 Cointegration Cointegration
DEdu6t [FEdu6t (Edu6tRGDPt RPCt LFt)] 488 366 225 305 Cointegration Cointegration
DEdu7t [FEdu7t (Edu7tRGDPt RPCt LFt)] 475 362 226 314 Cointegration Cointegration
DEdu8t [FEdu8t (Edu8tRGDPt RPCt LFt)] 156 182 089 101 No cointegration No cointegration
DEdu9t [FEdu9t (Edu9tRGDPt RPCt LFt)] 322 443 417 286 Cointegration Cointegration
DEdu10t [FEdu10t (Edu10tRGDPt RPCt LFt)] 341 527 523 842 Cointegration Cointegration
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335326
exists no cointegration among Eduit RGDPt RPCt and LFt when Eduit is represented by Edu3t Edu4t and Edu8t In conclusioneducation and RGDPt are found to be cointegrated ie they possess LR relationship
43 TodandashYamamoto Augmented Granger Causality (TYAGC) Test
Keeping in view the objectives of the study TYAGC was applied for data analysis To examine Augmented GrangerCausality Test among RGDPt RPCt LFt and Eduit the following equations are being estimated The estimated results of TYAGCprocedure are presented in Tables IndashIV
44 Bivariate TYAGC framework
The bivariate causality between RGDPt and Eduit (Eqs (1) and (2)) between RGDPt and RPCt (Eqs (3) and (4)) betweenRGDPt and LFt (Eqs (5) and (6)) between Eduit and RPCt (Eqs (7) and (8)) and between Eduit and LFt (Eqs (9) and (10)) wasestimated by using TYAGC technique and in presented in Table I
RGDPt frac14 a1 thornX3
ifrac141
b1iRGDPti thornX3
ifrac141
g1iEduiti thorn u1t (1)
Eduit frac14 a2 thornX3
ifrac141
b2iRGDPti thornX3
ifrac141
g2iEduiti thorn u2t (2)
RGDPt frac14 a3 thornX3
ifrac141
b3iRGDPti thornX3
ifrac141
g3iRPCti thorn u3t (3)
RPCt frac14 a4 thornX3
ifrac141
b4iRGDPti thornX3
ifrac141
g4iRPCti thorn u4t (4)
RGDPt frac14 a5 thornX3
ifrac141
b5iRGDPti thornX3
ifrac141
g5iLFti thorn u5t (5)
LFt frac14 a6 thornX3
ifrac141
b6iRGDPti thornX3
ifrac141
g6iLFti thorn u6t (6)
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 327
Eduit frac14 a7 thornX3
ifrac141
b7iEduiti thornX3
ifrac141
g7iRPCti thorn u7t (7)
RPCt frac14 a8 thornX3
ifrac141
b8iEduiti thornX3
ifrac141
g8iRPCti thorn u8t (8)
Eduit frac14 a9 thornX3
ifrac141
b9iEduiti thornX3
ifrac141
g9iLFti thorn u9t (9)
LFt frac14 a10 thornX3
ifrac141
b10iEduiti thornX3
ifrac141
g10iLFti thorn u10t (10)
The null hypothesis that all the indicators of education and all levels of education do not Granger cause RGDPt was tested inTable I Bivariate TYAGC results indicate that the null hypothesis was rejected (Table I) Similarly the null hypothesis thatRGDPt does not Granger cause all the indicators and all levels of education is rejected except Edu8t and Edu10t It means thatthere exists two-way causality between education and RGDPt RGDPt fails to cause higher education and expenditures oneducation
The estimated results from Eqs (3) and (4) in Table I show the feedback Granger causality between RPCt and RGDPt LFt isfound to cause RGDPt at 99 level of confidence while its reverse is not true The results of Eqs (7) and (8) in Table I show thatthe feedback causality between Eduit and RPCt seems to exist because majority of the indicators of education are causingRPCt and vice versa The results from Eq (9) and (10) in Table I reveal that LFt Granger causes education while reverseseemed to be not true In conclusion education and all levels of education (school college and university) Granger causeRGDPt and RGDPt also Granger causes education and all levels of education Feedback causality between education andRGDPt is found in bivariate case
45 Trivariate TYAGC framework
The trivariate causality among RGDPt RPCt and Eduit (Eqs (11)ndash(13)) and among RGDPt LFt and Eduit (Eqs (14)ndash(16)) wasestimated by using TYAGC framework and is presented in Tables II and III
RGDPt frac14 a11 thornX3
ifrac141
b11iRGDPti thornX3
ifrac141
l11iRPCti thornX3
ifrac141
g11iEduiti thorn u11t (11)
Eduit frac14 a12 thornX3
ifrac141
b12iRGDPti thornX3
ifrac141
l12iRPCti thornX3
ifrac141
g12iEduiti thorn u12t (12)
RPCt frac14 a13 thornX3
ifrac141
b13iRGDPti thornX3
ifrac141
l13iRPCti thornX3
ifrac141
g13iEduiti thorn u13t (13)
RGDPt frac14 a14 thornX3
ifrac141
b14iRGDPti thornX3
ifrac141
l14iLFti thornX3
ifrac141
g14iEduiti thorn u14t (14)
Edut frac14 a15 thornX3
ifrac141
b15iRGDPti thornX3
ifrac141
l15iLFti thornX3
ifrac141
g15iEduiti thorn u15t (15)
LFt frac14 a16 thornX3
ifrac141
b16iRGDPti thornX3
ifrac141
l16iLFti thornX3
ifrac141
g16iEduiti thorn u16t (16)
The estimated results presented in Table II indicate that the null hypothesis of no Granger causality between majority of theindicators of education and RGDPt is rejected This also supports our previous bivariate causality results that there existsfeedback causality between education and RGDPt The trivariate result in Table II seems to support the previous bivariateresult regarding causality between education and RPCt and between RPCt and RGDPt
In case of trivariate causality analysis among RGDPt LFt and Eduit the results in Table III again indicate the two waycausality running between education and RGDPt Six out of ten indicators of education does Granger cause LFt while LFt
Granger causes nine indicators out of ten indicators of education The null hypothesis that LFt does not Granger cause RGDPt
in the presence of all indicators of education is rejected at 99 level of confidence So LFt seems to be a very importantvariable that affects two main variables of the study ie education and RGDPt
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335328
In conclusion education and all levels of education Granger cause RGDPt where as its revere ie Granger causalityrunning from RGDPt to education and all levels of education is only true in case of trivariate causality among RGDPt LFt andeducation From here one can easily conclude that the role of LFt as compared to RPCt is very important in understanding therelationship between education and RGDPt Feedback causality between education and RGDPt is also found in trivariate case
46 Tetravariate TYAGC framework
The tetravariate causality among RGDPt RPCt LFt and Eduit (Eqs (17)ndash(20)) was also estimated by using TYAGC techniqueand their results are presented in Table IV
RGDPt frac14 a17 thornX3
ifrac141
b17iRGDPti thornX3
ifrac141
g17iRPCti thornX3
ifrac141
l17iLFti thornX3
ifrac141
d17iEduiti thorn u17t (17)
Eduit frac14 a18 thornX3
ifrac141
b18iRGDPti thornX3
ifrac141
g18iRPCti thornX3
ifrac141
l18iLFti thornX3
ifrac141
d18iEduiti thorn u18t (18)
RPCt frac14 a19 thornX3
ifrac141
b19iRGDPti thornX3
ifrac141
g19iRPCti thornX3
ifrac141
l19iLFti thornX3
ifrac141
d19iEduiti thorn u19t (19)
LFt frac14 a20 thornX3
ifrac141
b20iRGDPti thornX3
ifrac141
g20iRPCti thornX3
ifrac141
l20iLFti thornX3
ifrac141
d20iEduiti thorn u20t (20)
The tetravariate TYAGC results presented in Table IV indicate that all the indicators of education Granger cause RGDPt whileRGDPt does Granger cause majority of the indicators of education (seven out of ten) RGDPt does not Granger cause Edu5t
(university education) Edu8t (higher education) and Edu10t (education expenditure) From this one can easily conclude thatthere exists two way causality between education and RGDPt in case of tetravariate causality analysis as have been the caseof bivariate and trivariate causality Regarding levels of education all levels of education (ie school education collegeeducation and university education) do Granger cause RGDPt while RGDPt does only cause school education and collegeeducation RGDPt does not Granger cause university education
LFt Granger causes RGDPt at 99 confidence level while RGDPt only Granger causes LFt in case of Edu3t Edu5t Edu9t andEdu10t In case of testing causality between RPCt and RGDPt in the presence of all indicators of education RPCt does Grangercause RGDPt and in reverse case RGDPt does not Granger cause RPCt in the presence of Edu1t Edu3t Edu8t Edu9t and Edu10tThese results show the unidirectional causality running from RPCt to RGDPt
The research hypothesis that LFt does not Granger cause Eduit is rejected at 99 confidence interval except wheneducation is measured by Eduit Labour force has been found to cause all levels of education On the other side education onlyGranger causes the LFt in the presence of Edu3t Edu4t Edu5t Edu8t and Edu10t RPC does not Granger cause education whenEdu3t and Edu4t are used as proxies of education All indicators of education except Edu1t Edu2t and Edu10t do Granger causeRPCt This implies that feedback causality between RPCt and education is observed
It can easily be concluded from the TYAGC results of Eq (17) in Table IV that among all levels of education General highereducation (Edu9t) causes RGDPt highly and most significantly (999 confidence level) The level of confidence of collegeeducation (Edu3t) and school education (Edu2t) causing RGDPt is found to be 2nd highest (significance at 997 confidencelevel) and 3rd highest (significance at 989 confidence level) respectively From Eq (18) in Table IV it can also be found thatthe level of confidence (999) of causing RGDPt to school education (Edu2t) is found to be highest
From the bivariate trivariate and tetravariate TYAGC tests results in Tables IndashIV the overall results of the study abouteducation and different levels of education (School College and University) are summarized in Table 4
Table 4
Causal nexus between education different levels of education with RGDPt
Hypothesis TYAGC procedure
Bivariate Trivariate Tetravariate
RGDPt and Edut RGDPt RPCt Edut RGDPt LFt Edut RGDPt LFt RPCt Edut
Education (Edu1t) does Granger cause RGDPt Yes (0089) No (0459) Yes (0009) Yes (0087)
RGDPt does Granger cause education (Edu1t) Yes (0000) Yes (0000) Yes (0000) Yes (0000)
School education (Edu2t) does Granger cause RGDPt Yes (0000) Yes (0001) Yes (0002) Yes (0010)
RGDPt does Granger cause school education (Edu2t) Yes (0000) Yes (0000) Yes (0000) Yes (0000)
College education (Edu3t) does Granger cause RGDPt Yes (0038) Yes (0081) Yes (0000) Yes (0002)
RGDPt does Granger cause college education (Edu3t) Yes (0003) No (0172) Yes (0001) Yes (0032)
University education (Edu5t) does Granger cause RGDPt Yes (0000) Yes (0000) Yes (0001) Yes (0001)
RGDPt does Granger cause university education (Edu5t) Yes (0089) Yes (0000) Yes (0025) No (0515)
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 329
47 Figures in parentheses are p-values
From the above results presented in Table 4 it can be concluded that there existed feedback causality between educationand RGDPt in all bivariate trivariate and tetravariate TYAGC causality cases All levels of education ie school educationcollege education and university education do Granger cause RGDPt in all causality cases RGDPt does Granger cause schooleducation in all causality cases RGDPt does Granger cause college education in all causality cases except trivariate causalitythat is running from RGDPt to education when RPCt serves as a third variable Table 4 also reveals that RGDPt does Grangercause university education only in a bivariate and trivariate causality cases RGDPt fails to Granger cause to universityeducation in tetravariate case
5 Conclusions and recommendations
This study aimed to explore the cointegration and causal relationship between education (measured by different indicatorsof education) and economic growth in Pakistan It is very essential for a country to invest more in education because it is one ofthe most important ingredients of human capital and hence economic development The nature and strength of the relationshipbetween education and economic growth is still not clear in case of Pakistan The main focus of this empirical study remained toobserve the causality and cointegration between education and economic growth in the absence and presence physical capitaland labour force Cointegration between education and economic growth was investigated using ARDL approach and the causallinkage between education and economic growth was examined in bivariate trivariate and tetravariate TYAGC frameworkDifferent indicators of education were utilized in this study to show the robustness of empirical results The causality betweeneducation and economic growth was examined in the presence and absence of stock of physical capital and stock of labour as athird and fourth variable The causality results indicate that there exist two-way causality between education and economicgrowth and between all levels of education and economic growth in case of bivariate TYAGC framework Education and alllevels of education do Granger cause economic growth in the presence of real physical capital as a third variable while economicgrowth causes all the indicators of education except college education professional college education and educationalexpenditures in the presence of real physical capital as a third variable in case of trivariate causality analysis In the presence oflabour force as a third variable feedback causality exists between education and economic growth and between all levels ofeducation and economic growth The results of tetravariate TYAGC Test indicate that education and all level of education doGranger cause economic growth while economic growth does Granger cause majority of the indicators of education (ie sevenout of ten) Economic growth does not Granger cause university education higher education including professional educationand expenditures on education The rise in university education higher education including professional education andexpenditures on education were considered as the key indicators to gauge human and social progress Economic growth doesnot seem to affect important educational indicators like university education higher education including professionaleducation and expenditures on education This seems to be consistent with Easterlyrsquos findings Easterly (2001) said thatPakistan is a country that made little social progress for given rates of GDP Among all levels of education General highereducation causes economic growth highly and most significantly as was explored by Stengos and Aurangzeb (2008) The level ofconfidence of causing economic growth to school education found to be highest This study also confirms the long runrelationship between education and economic growth
On the basis of the results of this study it is recommended that the government should focus more on higher educationparticularly to university education More funds should be allocated to education in line with others sectors particularly touniversity and higher education levels so that the economic growth can be further accelerated This will in turn leads tofurther education and hence development Poor should be facilitated to get higher education so that the polarization inhigher education may further be minimized Primary schooling should also be given priority because primary educationserves as an input for all higher levels of education The inverted educational expenditure pyramid may also be taken intoaccount Since the role of labour force seems to be very important in understanding the relationship between education andeconomic growth so it is suggested that labour force should be given more chances to enhance their skills The variablelabour force must be included while examining the causality between education and economic growth It is alsorecommended that the nexus between education and economic growth with inclusion of other variables other than physicalcapital and labour force should further be tested and generalized
Appendix A
Table I
Bivariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Bivariate-RGDPt and Eduit
Eq (1) Edu1t does not Granger cause RGDPt 028998 [0089] 1 Reject H0
Edu2t does not Granger cause RGDPt 144869 [0000] 1 Reject H0
Edu3t does not Granger cause RGDPt 043243 [0038] 1 Reject H0
Edu4t does not Granger cause RGDPt 039797 [0046] 1 Reject H0
Table I (Continued )
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Edu5t does not Granger cause RGDPt 217739 [0000] 1 Reject H0
Edu6t does not Granger cause RGDPt 137788 [0000] 1 Reject H0
Edu7t does not Granger cause RGDPt 126682 [0000] 1 Reject H0
Edu8t does not Granger cause RGDPt 041335 [0042] 1 Reject H0
Edu9t does not Granger cause RGDPt 160963 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 028642 [0091] 1 Reject H0
Eq (2) RGDPt does not Granger cause Edu1t 260926 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 230094 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 085441 [0003] 1 Reject H0
RGDPt does not Granger cause Edu4t 107403 [0001] 1 Reject H0
RGDPt does not Granger cause Edu5t 028935 [0089] 1 Reject H0
RGDPt does not Granger cause Edu6t 270343 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 273974 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 003162 [0574] 1 Cannot reject H0
RGDPt does not Granger cause Edu9t 027588 [0097] 1 Reject H0
RGDPt does not Granger cause Edu10t 000851 [0770] 1 Cannot reject H0
Bivariate-RGDPt and RPCt
Eq (3) RPCt does not Granger cause RGDPt 054972 [0019] 1 Reject H0
Eq (4) RGDPt does not Granger cause RPCt 167511 [0000] 1 Reject H0
Bivariate-RGDPt and LFt
Eq (5) LFt does not Granger cause RGDPt 227888 [0000] 1 Reject H0
Eq (6) RGDPt does not Granger cause LFt 012380 [0266] 1 Cannot reject H0
Bivariate-Eduit and RPCt
Eq (7) Edu1t does not Granger cause RPCt 094596 [0002] 1 Reject H0
Edu2t does not Granger cause RPCt 015434 [0214] 1 Cannot reject H0
Edu3t does not Granger cause RPCt 038233 [0051] 1 Reject H0
Edu4t does not Granger cause RPCt 000506 [0822] 1 Cannot reject H0
Edu5t does not Granger cause RPCt 298085 [0000] 1 Reject H0
Edu6t does not Granger cause RPCt 018289 [0176] 1 Cannot reject H0
Edu7t does not Granger cause RPCt 018976 [0168] 1 Cannot reject H0
Edu8t does not Granger cause RPCt 176399 [0000] 1 Reject H0
Edu9t does not Granger cause RPCt 224647 [0000] 1 Reject H0
Edu10t does not Granger cause RPCt 039174 [0048] 1 Reject H0
Eq (8) RPCt does not Granger cause Edu1t 091477 [0002] 1 Reject H0
RPCt does not Granger cause Edu2t 098821 [0002] 1 Reject H0
RPCt does not Granger cause Edu3t 066148 [0010] 1 Reject H0
RPCt does not Granger cause Edu4t 084218 [0004] 1 Reject H0
RPCt does not Granger cause Edu5t 001684 [0682] 1 Cannot reject H0
RPCt does not Granger cause Edu6t 107553 [0001] 1 Reject H0
RPCt does not Granger cause Edu7t 108798 [0001] 1 Reject H0
RPCt does not Granger cause Edu8t 004283 [0513] 1 Cannot reject H0
RPCt does not Granger cause Edu9t 005627 [0453] 1 Cannot reject H0
RPCt does not Granger cause Edu10t 000417 [0838] 1 Cannot reject H0
Bivariate-Eduit and LFt
Eq (9) Edu1t does not Granger cause LFt 026469 [0104] 1 Reject H0
Edu2t does not Granger cause LFt 012355 [0266] 1 Cannot reject H0
Edu3t does not Granger cause LFt 020468 [0153] 1 Cannot reject H0
Edu4t does not Granger cause LFt 098042 [0002] 1 Reject H0
Edu5t does not Granger cause LFt 049986 [0025] 1 Reject H0
Edu6t does not Granger cause LFt 016896 [0194] 1 Cannot reject H0
Edu7t does not Granger cause LFt 015167 [0218] 1 Cannot reject H0
Edu8t does not Granger cause LFt 184475 [0000] 1 Reject H0
Edu9t does not Granger cause LFt 003986 [0528] 1 Cannot reject H0
Edu10t does not Granger cause LFt 010899 [0296] 1 Cannot reject H0
Eq (10) LFt does not Granger cause Edu1t 107709 [0001] 1 Reject H0
LFt does not Granger cause Edu2t 071204 [0008] 1 Reject H0
LFt does not Granger cause Edu3t 136419 [0000] 1 Reject H0
LFt does not Granger cause Edu4t 056225 [0018] 1 Reject H0
LFt does not Granger cause Edu5t 057141 [0017] 1 Reject H0
LFt does not Granger cause Edu6t 091531 [0002] 1 Reject H0
LFt does not Granger cause Edu7t 095063 [0002] 1 Reject H0
LFt does not Granger cause Edu8t 021313 [0144] 1 Cannot reject H0
LFt does not Granger cause Edu9t 069389 [0008] 1 Reject H0
LFt does not Granger cause Edu10t 000743 [0785] 1 Cannot reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335330
Table II
Trivariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Trivariate-RGDPt RPCt and Eduit
Eq (11) Edu1t does not Granger cause RGDPt 005481 [0459] 1 Cannot reject H0
Edu2t does not Granger cause RGDPt 105415 [0001] 1 Reject H0
Edu3t does not Granger cause RGDPt 030370 [0081] 1 Reject H0
Edu4t does not Granger cause RGDPt 022525 [0133] 1 Cannot reject H0
Edu5t does not Granger cause RGDPt 227510 [0000] 1 Reject H0
Edu6t does not Granger cause RGDPt 098494 [0002] 1 Reject H0
Edu7t does not Granger cause RGDPt 090460 [0003] 1 Reject H0
Edu8t does not Granger cause RGDPt 067381 [0009] 1 Reject H0
Edu9t does not Granger cause RGDPt 168617 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 085842 [0003] Reject H0
Eq (11a) RPCt does not Granger cause RGDP (Edu1 as a 3rd variable) 029029 [0088] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu2 as a 3rd variable) 024880 [0115] 1 Cannot reject H0
RPCt does not Granger cause RGDPt (Edu3t as a 3rd variable) 041380 [0042] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu4t as a 3rd variable) 036580 [0056] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu5t as a 3rd variable) 064811 [0011] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu6t as a 3rd variable) 024405 [0118] 1 Cannot reject H0
RPCt does not Granger cause RGDPt (Edu7t as a 3rd variable) 026008 [0107] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu8t as a 3rd variable) 081607 [0004] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu9t as a 3rd variable) 063133 [0012] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu10t as a 3rd variable) 115637 [0001] 1 Reject H0
Eq (12) RGDPt does not Granger cause Edu1t 176454 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 129776 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 018626 [0172] 1 Cannot reject H0
RGDPt does not Granger cause Edu4t 020449 [0153] 1 Cannot reject H0
RGDPt does not Granger cause Edu5t 144658 [0000] 1 Reject H0
RGDPt does not Granger cause Edu6t 175431 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 178356 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 042497 [0039] 1 Reject H0
RGDPt does not Granger cause Edu9t 082506 [0004] 1 Reject H0
RGDPt does not Granger cause Edu10t 008026 [0370] 1 Cannot reject H0
Eq (12a) RPCt does not Granger cause Edu1t 000122 [0912] 1 Cannot reject H0
RPCt does not Granger cause Edu2t 028750 [0090] 1 Reject H0
RPCt does not Granger cause Edu3t 058586 [0016] 1 Reject H0
RPCt does not Granger cause Edu4t 071372 [0008] 1 Reject H0
RPCt does not Granger cause Edu5t 302364 [0000] 1 Reject H0
RPCt does not Granger cause Edu6t 020474 [0152] 1 Cannot reject H0
RPCt does not Granger cause Edu7t 017533 [0185] 1 Cannot reject H0
RPCt does not Granger cause Edu8t 044926 [0034] 1 Reject H0
RPCt does not Granger cause Edu9t 240955 [0000] 1 Reject H0
RPCt does not Granger cause Edu10t 021006 [0147] 1 Cannot reject H0
Eq (13) RGDPt does not Granger cause RPCt (Edu1t as a 3rd variable) 055095 [0019] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu2t as a 3rd variable) 182287 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu3t as a 3rd variable) 191499 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu4t as a 3rd variable) 269133 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu5t as a 3rd variable) 172979 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu6t as a 3rd variable) 166347 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu7t as a 3rd variable) 161198 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu8t as a 3rd variable) 038521 [0050] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu9tas a 3rd variable) 183169 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu10t as a 3rd variable) 139552 [0000] 1 Reject H0
Eq (13a) Edu1t does not Granger cause RPCt 000122 [0912] 1 Cannot reject H0
Edu2t does not Granger cause RPCt 028750 [0090] 1 Reject H0
Edu3t does not Granger cause RPCt 058586 [0016] 1 Reject H0
Edu4t does not Granger cause RPCt 071372 [0008] 1 Reject H0
Edu5t does not Granger cause RPCt 302364 [0000] 1 Reject H0
Edu6t does not Granger cause RPCt 020474 [0152] 1 Cannot reject H0
Edu7t does not Granger cause RPCt 017533 [0185] 1 Cannot reject H0
Edu8t does not Granger cause RPCt 044926 [0034] 1 Reject H0
Edu9t does not Granger cause RPCt 240955 [0000] 1 Reject H0
Edu10t does not Granger cause RPCt 021006 [0147] 1 Cannot reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 331
Table III
Trivariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Trivariate-RGDPt LFt and Eduit
Eq (14) Edu1t does not Granger cause RGDPt 068472 [0009] 1 Reject H0
Edu2t does not Granger cause RGDPt 092326 [0002] 1 Reject H0
Edu3t does not Granger cause RGDPt 180477 [0000] 1 Reject H0
Edu4t does not Granger cause RGDPt 132070 [0000] 1 Reject H0
Edu5t does not Granger cause RGDPt 109716 [0001] 1 Reject H0
Edu6t does not Granger cause RGDPt 086017 [0003] 1 Reject H0
Edu7t does not Granger cause RGDPt 078604 [0005] 1 Reject H0
Edu8t does not Granger cause RGDPt 020470 [0153] 1 Cannot reject H0
Edu9t does not Granger cause RGDPt 293293 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 005754 [0448] 1 Cannot reject H0
Eq (14a) LFt does not Granger cause RGDPt (Edu1t as a 3rd variable) 409533 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu2t as a 3rd variable) 332636 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu3t as a 3rd variable) 701171 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu4t as a 3rd variable) 605496 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu5t as a 3rd variable) 240867 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu6t as a 3rd variable) 330495 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu7t as a 3rd variable) 332860 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu8t as a 3rd variable) 352003 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu9t as a 3rd variable) 573087 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu10t as a 3rd variable) 343199 [0000] 1 Reject H0
Eq (15) RGDPt does not Granger cause Edu1t 134939 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 804323 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 109273 [0001] 1 Reject H0
RGDPt does not Granger cause Edu4t 278785 [0000] 1 Reject H0
RGDPt does not Granger cause Edu5t 050547 [0025] 1 Reject H0
RGDPt does not Granger cause Edu6t 790307 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 738342 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 043402 [0037] 1 Reject H0
RGDPt does not Granger cause Edu9t 175731 [0000] 1 Reject H0
RGDPt does not Granger cause Edu10t 061709 [0013] 1 Reject H0
Eq (15a) LFt does not Granger cause Edu1t 009324 [0334] 1 Cannot reject H0
LFt does not Granger cause Edu2t 377339 [0000] 1 Reject H0
LFt does not Granger cause Edu3t 176565 [0000] 1 Reject H0
LFt does not Granger cause Edu4t 180046 [0000] 1 Reject H0
LFt does not Granger cause Edu5t 091061 [0003] 1 Reject H0
LFt does not Granger cause Edu6t 355203 [0000] 1 Reject H0
LFt does not Granger cause Edu7t 327354 [0000] 1 Reject H0
LFt does not Granger cause Edu8t 053664 [0021] 1 Reject H0
LFt does not Granger cause Edu9t 251724 [0000] 1 Reject H0
LFt does not Granger cause Edu10t 060787 [0014] 1 Reject H0
Eq (16) Edu1t does not Granger cause LFt 036697 [0055] 1 Reject H0
Edu2t does not Granger cause LFt 004605 [0497] 1 Cannot reject H0
Edu3t does not Granger cause LFt 093988 [0002] 1 Reject H0
Edu4t does not Granger cause LFt 177287 [0000] 1 Reject H0
Edu5t does not Granger cause LFt 059203 [0015] 1 Reject H0
Edu6t does not Granger cause LFt 007202 [0396] 1 Cannot reject H0
Edu7t does not Granger cause LFt 005520 [0458] 1 Cannot reject H0
Edu8t does not Granger cause LFt 241662 [0000] 1 Reject H0
Edu9t does not Granger cause LFt 004009 [0527] 1 Cannot reject H0
Edu10t does not Granger cause LFt 058477 [0016] 1 Reject H0
Eq (16a) RGDPt does not Granger cause LFt (Edu1t as a 3rd variable) 002436 [0622] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu2t as a 3rd variable) 004276 [0513] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu3t as a 3rd variable) 047690 [0029] 1 Reject H0
RGDPt does not Granger cause LFt (Edu4t as a 3rd variable) 015207 [0218] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu5t as a 3rd variable) 040757 [0044] 1 Reject H0
RGDPt does not Granger cause LFt (Edu6t as a 3rd variable) 003392 [0560] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu7t as a 3rd variable) 004309 [0512] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu8t as a 3rd variable) 003145 [0575] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu9t as a 3rd variable) 017426 [0187] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu10t as a 3rd variable) 048448 [0028] 1 Reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335332
Table IV
Tetravariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Tetravariate-RGDPt RPCt LFt and Edut
Eq (17) Edu1t does not Granger cause RGDPt 029350 [0087] 1 Reject H0
Edu2t does not Granger cause RGDPt 065661 [0010] 1 Reject H0
Edu3t does not Granger cause RGDPt 097521 [0002] 1 Reject H0
Edu4t does not Granger cause RGDPt 071590 [0007] 1 Reject H0
Edu5t does not Granger cause RGDPt 116263 [0001] 1 Reject H0
Edu6t does not Granger cause RGDPt 059569 [0015] 1 Reject H0
Edu7t does not Granger cause RGDPt 054327 [0020] 1 Reject H0
Edu8t does not Granger cause RGDPt 040033 [0045] 1 Reject H0
Edu9t does not Granger cause RGDPt 195734 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 034374 [0064] 1 Reject H0
Eq (17a) LFt does not Granger cause RGDPt (Edut = Edu1) 251518 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu2) 165581 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu3) 316418 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu4) 289993 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu5) 109302 [0001] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu6) 165606 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu7) 168037 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu8) 176645 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu9) 247435 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu10) 146998 [0000] 1 Reject H0
Eq (17b) RPCt does not Granger cause RGDPt (Edut = Edu1) 042975 [0038] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu2) 039280 [0047] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu3) 034296 [0064] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu4) 027068 [0100] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu5) 062858 [0012] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu6) 039537 [0047] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu7) 040022 [0045] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu8) 045487 [0033] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu9) 068323 [0009] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu10) 083479 [0004] 1 Reject H0
Eq (18) RGDPt does not Granger cause Edu1t 150200 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 633103 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 045767 [0032] 1 Reject H0
RGDPt does not Granger cause Edu4t 122392 [0000] 1 Reject H0
RGDPt does not Granger cause Edu5t 004235 [0515] 1 Cannot reject H0
RGDPt does not Granger cause Edu6t 453644 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 418611 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 055973 [0454] 1 Cannot reject H0
RGDPt does not Granger cause Edu9t 053890 [0020] 1 Reject H0
RGDPt does not Granger cause Edu10t 011119 [0292] 1 Cannot reject H0
Eq (18a) LFt does not Granger cause Edu1t 006023 [0438] 1 Cannot reject H0
LFt does not Granger cause Edu2t 364559 [0000] 1 Reject H0
LFt does not Granger cause Edu3t 197423 [0000] 1 Reject H0
LFt does not Granger cause Edu4t 166511 [0000] 1 Reject H0
LFt does not Granger cause Edu5t 383886 [0000] 1 Reject H0
LFt does not Granger cause Edu6t 359377 [0000] 1 Reject H0
LFt does not Granger cause Edu7t 328249 [0000] 1 Reject H0
LFt does not Granger cause Edu8t 135310 [0000] 1 Reject H0
LFt does not Granger cause Edu9t 630068 [0000] 1 Reject H0
LFt does not Granger cause Edu01t 109365 [0001] 1 Reject H0
Eq (18b) RPCt does not Granger cause Edu1t 114248 [0001] 1 Reject H0
RPCt does not Granger cause Edu2t 036828 [0055] 1 Reject H0
RPCt does not Granger cause Edu3t 021023 [0147] 1 Cannot reject H0
RPCt does not Granger cause Edu4t 000484 [0826] 1 Cannot reject H0
RPCt does not Granger cause Edu5t 610934 [0000] 1 Reject H0
RPCt does not Granger cause Edu6t 070279 [0008] 1 Reject H0
RPCt does not Granger cause Edu7t 051166 [0024] 1 Reject H0
RPCt does not Granger cause Edu8t 167481 [0000] 1 Reject H0
RPCt does not Granger cause Edu9t 335271 [0000] 1 Reject H0
RPCt does not Granger cause Edu10t 067481 [0009] 1 Reject H0
Eq (19) Edu1 does not Granger cause RPCt 005154 [0473] 1 Cannot reject H0
Edu2 does not Granger cause RPCt 011954 [0274] 1 Cannot reject H0
Edu3 does not Granger cause RPCt 162365 [0000] 1 Reject H0
Edu4 does not Granger cause RPCt 148964 [0000] 1 Reject H0
Edu5 does not Granger cause RPCt 243978 [0000] 1 Reject H0
Edu6 does not Granger cause RPCt 040262 [0045] 1 Reject H0
Edu7 does not Granger cause RPCt 035138 [0061] 1 Reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 333
able IV (Continued )
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Edu8 does not Granger cause RPCt 030100 [0083] 1 Reject H0
Edu9 does not Granger cause RPCt 462564 [0000] 1 Reject H0
Edu10 does not Granger cause RPCt 009580 [0328] 1 Cannot reject H0
Eq (19a) RGDPt does not Granger cause RPCt (Edu1t as a 3rd variable) 009936 [0319] 1 Cannot reject H0
RGDPt does not Granger cause RPCt (Edu2t as a 3rd variable) 039369 [0047] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu3t as a 3rd variable) 003822 [0536] 1 Cannot reject H0
RGDPt does not Granger cause RPCt (Edu4t as a 3rd variable) 028000 [0094] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu5t as a 3rd variable) 039910 [0046] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu6t as a 3rd variable) 033500 [0067] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu7t as a 3rd variable) 029924 [0084] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu8t as a 3rd variable) 002803 [0597] 1 Cannot Reject H0
RGDPt does not Granger cause RPCt (Edu9t as a 3rd variable) 011416 [0285] 1 Cannot reject H0
RGDPt does not Granger cause RPCt (Edu10t as a 3rd variable) 006944 [0405] 1 Cannot reject H0
Eq (20) Edu1t does not Granger cause LFt 015302 [0216] 1 Cannot reject H0
Edu2t does not Granger cause LFt 001053 [0746] 1 Cannot reject H0
Edu3t does not Granger cause LFt 080072 [0005] 1 Reject H0
Edu4t does not Granger cause LFt 143854 [0000] 1 Reject H0
Edu5t does not Granger cause LFt 061159 [0013] 1 Reject H0
Edu6t does not Granger cause LFt 003113 [0577] 1 Cannot reject H0
Edu7t does not Granger cause LFt 002394 [0625] 1 Cannot reject H0
Edu8t does not Granger cause LFt 196804 [0000] 1 Reject H0
Edu9t does not Granger cause LFt 046285 [0496] 1 Cannot reject H0
Edu10t does not Granger cause LFt 04161 1 [0041] 1 Reject H0
Eq (20a) RGDPt does not Granger cause LFt (Edu1t as a 3rd variable) 006872 [0407] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu2t as a 3rd variable) 018604 [0173] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu3t as a 3rd variable) 066905 [0010] 1 Reject H0
RGDPt does not Granger cause LFt (Edu4t as a 3rd variable) 023249 [0127] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu5t as a 3rd variable) 070835 [0008] 1 Reject H0
RGDPt does not Granger cause LFt (Edu6t as a 3rd variable) 016501 [0199] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu7t as a 3rd variable) 018532 [0173] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu8t as a 3rd variable) 003730 [0541] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu9t as a 3rd variable) 039255 [0048] 1 Reject H0
RGDPt does not Granger cause LFt (Edu10t as a 3rd variable) 055266 [0019] 1 Reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335334
T
References
Abbas Q amp Peck J F (2008) Human capital and economic growth Pakistan 1960ndash2003 The Lahore Journal of Economics 13(1) 1ndash28Ayara N A (2002) The paradox of education and economic growth in Nigeria Empirical evidence The Nigerian Economic Society (NES) Pt 2 371ndash393Babatunde M A amp Adefabi R A (2005) Long run relationship between education and economic growth in Nigeria Evidence from the Johansenrsquos cointegration
approach Paper presented at the regional conference on education in West Africa Constraints and Opportunities Dakar Senegal November 1stndash2nd 2005Cornell UniversityCREAMinisterede lrsquoEducation du Senegal
Baldacci E Clements B Cui Q amp Gupta S (2005) What does it take to help the poor Finance and Development The Quarterly Magazine of the IMF 42(2)Changzheng Z Zhijian H amp Huaizu L (2007) An empirical study on education equity in China 1978ndash2004 Frontier in Economics of China 2(4) 536ndash544Chaudhary A R Asim I amp Gillani S Y M (2009) The nexus between higher education and economic growth An empirical investigation for Pakistan Pakistan
Journal of Commerce and Social Sciences 3Chaudhry I S Malik S amp Ashraf M (2006) Rural poverty in Pakistan Some related concepts issues and empirical analysis Pakistan Economic and Social Review
44(2) 259ndash276Diebolt C amp Litago J (1997) Education and economic growth in Germany before the Second World War An econometric analysis of dynamic relations Historical
Social Research 2(22) 132ndash149Easterly W (2001) The middle class consensus and economic development Journal of Economic Growth 6(4) 317ndash335Engle R F amp Granger C W J (1987) Cointegration and error correction Representation estimation and testing Econometrica 55 251ndash276Fernandez E amp Mauro P (2000) The role of human capital in economic growth The case of Spain (IMF Working Paper) International Monetary FundFrancis B amp Iyare S (2006) Education and development in the Caribbean A cointegration and causality approach Economics Bulletin 15(2) 1ndash13Galor O amp Moav O (2000) Das human capital Retrieved from httpeconpstcn brownedufacultygalorindexhtmlGoode R B (1959) Adding to the stock of physical and human capital American Economic Review 49(2) 147Government of Pakistan (1970ndash2009) Pakistan economic survey various issues Finance Division Islamabad Economic Advisorrsquos WingGregory A W amp Hansen B E (1996) Residual-based tests for cointegration in models with regime shifts Journal of Econometrics 70 99ndash126Grossman G M amp Helpman E (1991) Innovation and growth in the global economy Cambridge MIT PressGylfason T amp Zoega G (2003) Education social equality and economic growth A view of the landscape CESifo Economic Studies 49(4) 557ndash579Hassan S amp Ahmed H (2008) Educationrsquos contribution to the economic growth of sub-Saharan Africa Southwestern Economic Review 1(32) 175ndash190Islam T S Wadud M A amp Islam Q B T (2007) Relationship between education and GDP growth A multivariate causality analysis for Bangladesh Economics
Bulletin 3(35) 1ndash7Jin J C (2009) Economic research and economic growth Evidence from East Asian Economies Journal of Asian Economics 20 150ndash155Johansen S (1988) Statistical analysis of cointegration vectors Journal of Economic Dynamics and Control 12 231ndash254Johansen S amp Juselius K (1990) Maximum likelihood estimation and inference on cointegration with applications to the demand for money Oxford Bulletin of
Economics and Statistics 52 169ndash210Katırcıoglu S T (2009) Investigating higher-education-led growth hypothesis in a small Island Time series evidence from Northern Cyprus Paper presented at
Econ Anadolu 2009 Anadolu International Conference in Economics June 17ndash19 2009 TurkeyKhorasgani M F (2008) Higher education development and economic growth in Iran Education Business and Society Contemporary Middle Eastern Issues 1
162ndash174
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 335
Kui L (2005) The interactive causality between education and economic growth in China Retrieved from httppapersssrncomsol3paperscfmAbstrac-tid=920624
Loening J L (2004) Time series evidence on education and growth The case of Guatemala 1951ndash2002 Revista de Analisis Economico 19(2) 3ndash40Lucas R E (1988) On the mechanics of economic development Journal of Monetary Economics 22 3ndash42Macerinskiene I amp Vaiksnoraite B (2006) The role of higher education to economic development VadybaManagement 2(11)Mankiw N G Romer D amp Weil D N (1992) A contribution to the empirics of economic growth Quarterly Journal of Economics 107 407ndash437Momete D C (2007) Analysis of the relationship between employment and economic growth in Romania Fascicle of Management and Technological Engineering
VI(XVI)Morote E S (2000) Higher education employment and economic growth Mexico and Peru Retrieved from httpwwwamericanprofessororgdocumentation
lasapa perdocNarayan P K (2005) The saving and investment nexus for China Evidence from cointegration tests Applied Economics 37 1979ndash1990Permani R (2008) Education as a determinant of economic growth in East Asia Historical trends and empirical evidences (1965ndash2000) Retrieved from http
wwwuoweduaucommerceeconehsanzpdfsPermani202008pdfPesaran M H amp Pesaran B (1997) Working with Microfit 40 Interactive econometric analysis Oxford Oxford University PressPesaran M H amp Shin Y (1999) An autoregressive distributed lag modeling approach to cointegration analysis In S Strom (Ed) Econometrics and economic theory
in the 20th century Cambridge Cambridge University PressPesaran M H Shin Y amp Smith R J (2001) Bounds testing approaches to the analysis of level relationships Journal of Applied Econometrics 16 289ndash326Pradhan R P (2009) Education and economic growth in India Using error correction modeling International Research Journal of Finance and Economics 25Pritchett L (2001) Where has all the education gone The World Bank Economic Review 15(3)Quah D amp Rauch J E (1990) Openness and the rate of economic growth Journal Development of Studies 2(49) 307ndash335Rivera-Batiz L A amp Romer P M (1991) Economic integration and endogenous growth Quarterly Journal of Economics 106 531ndash555Romer P M (1986) Increasing returns and long run growth Journal of Political Economy 6(90) 1002ndash1037Romer P M (1989) Human capital and growth Theory and evidence (NBER Working Papers 3173) National Bureau of Economic Research IncRomer P M (1990) Endogenous technological change Journal of Political Economy 5(98) 71ndash101Rondinelli D amp Montgomery J (1995) Great policies Strategic innovations in Asia and the Pacific Basin Westport Praeger PublishingSaikkonen P amp Lutkepohl H (2000) Testing for the cointegration rank of a VAR process with structural shifts Journal of Business and Economic Statistics 18(4)
451ndash464Schultz T W (1961) Investment in human capital American Economic Review 51(1) 1State Bank of Pakistan (1972ndash2009) Annual reports Karachi SBP PressStengos T amp Aurangzeb A (2008) An empirical investigation of the relationship between education and growth in pakistan International Economic Journal 3
345ndash359 Retrieved from httpwwwinformaworldcomsmpptitledb=allcontent=t713685453tab=issueslistbranches=22-v2222Toda H Y amp Yamamoto T (1995) Statistical inference in vector autoregressive with possible integrated processes Journal of Econometrics 66 225ndash250United Nations (1997) Human Development Report New York Oxford University Press
- Education and economic growth in Pakistan A cointegration and causality analysis
-
- Introduction
- Review of literature
- Method and procedure
- Empirical results
-
- Unit root results
- Cointegration
- Toda-Yamamoto Augmented Granger Causality (TYAGC) Test
- Bivariate TYAGC framework
- Trivariate TYAGC framework
- Tetravariate TYAGC framework
- Figures in parentheses are p-values
-
- Conclusions and recommendations
-
- References
-
Table 2
Cointegration
Dependent variable when RGDPt serves as dependent variable Lag length Cointegration results based on critical
values (CVs) given by
1 2 3 4 Pesaran et al (2001) Narayan (2005)
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu1t)] 167 419 203 214 Cointegration Cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu2t)] 281 340 226 179 Cointegration No cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu3t)] 209 644 203 145 Cointegration Cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu4t)] 234 619 263 190 Cointegration Cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu5t)] 253 454 257 236 Cointegration Cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu6t)] 287 336 231 181 Cointegration No cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu7t)] 277 338 230 181 Cointegration No cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu8t)] 114 172 203 165 No cointegration No cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu9t)] 274 482 188 117 Cointegration Cointegration
DRGDPt [FRGDPt (RGDPtRPCt LFt Edu10t)] 237 392 246 203 Cointegration No cointegration
Table 3
Cointegration
Dependent variable when Eduit serves as dependent variable Lag length Cointegration results based on critical
values (CV) given by Results
1 2 3 4 Pesaran et al (2001) Narayan (2005)
DEdu1t [FEdu1t (Edu1tRGDPt RPCt LFt)] 711 502 548 447 Cointegration Cointegration
DEdu2t [FEdu2t (Edu2tRGDPt RPCt LFt)] 446 336 192 308 Cointegration Cointegration
DEdu3t [FEdu3t (Edu3tRGDPt RPCt LFt)] 157 280 195 295 No cointegration No cointegration
DEdu4t [FEdu4t (Edu4tRGDPt RPCt LFt)] 202 156 295 223 No cointegration No cointegration
DEdu5t [FEdu5t (Edu5tRGDPt RPCt LFt)] 152 629 081 069 Cointegration Cointegration
DEdu6t [FEdu6t (Edu6tRGDPt RPCt LFt)] 488 366 225 305 Cointegration Cointegration
DEdu7t [FEdu7t (Edu7tRGDPt RPCt LFt)] 475 362 226 314 Cointegration Cointegration
DEdu8t [FEdu8t (Edu8tRGDPt RPCt LFt)] 156 182 089 101 No cointegration No cointegration
DEdu9t [FEdu9t (Edu9tRGDPt RPCt LFt)] 322 443 417 286 Cointegration Cointegration
DEdu10t [FEdu10t (Edu10tRGDPt RPCt LFt)] 341 527 523 842 Cointegration Cointegration
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335326
exists no cointegration among Eduit RGDPt RPCt and LFt when Eduit is represented by Edu3t Edu4t and Edu8t In conclusioneducation and RGDPt are found to be cointegrated ie they possess LR relationship
43 TodandashYamamoto Augmented Granger Causality (TYAGC) Test
Keeping in view the objectives of the study TYAGC was applied for data analysis To examine Augmented GrangerCausality Test among RGDPt RPCt LFt and Eduit the following equations are being estimated The estimated results of TYAGCprocedure are presented in Tables IndashIV
44 Bivariate TYAGC framework
The bivariate causality between RGDPt and Eduit (Eqs (1) and (2)) between RGDPt and RPCt (Eqs (3) and (4)) betweenRGDPt and LFt (Eqs (5) and (6)) between Eduit and RPCt (Eqs (7) and (8)) and between Eduit and LFt (Eqs (9) and (10)) wasestimated by using TYAGC technique and in presented in Table I
RGDPt frac14 a1 thornX3
ifrac141
b1iRGDPti thornX3
ifrac141
g1iEduiti thorn u1t (1)
Eduit frac14 a2 thornX3
ifrac141
b2iRGDPti thornX3
ifrac141
g2iEduiti thorn u2t (2)
RGDPt frac14 a3 thornX3
ifrac141
b3iRGDPti thornX3
ifrac141
g3iRPCti thorn u3t (3)
RPCt frac14 a4 thornX3
ifrac141
b4iRGDPti thornX3
ifrac141
g4iRPCti thorn u4t (4)
RGDPt frac14 a5 thornX3
ifrac141
b5iRGDPti thornX3
ifrac141
g5iLFti thorn u5t (5)
LFt frac14 a6 thornX3
ifrac141
b6iRGDPti thornX3
ifrac141
g6iLFti thorn u6t (6)
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 327
Eduit frac14 a7 thornX3
ifrac141
b7iEduiti thornX3
ifrac141
g7iRPCti thorn u7t (7)
RPCt frac14 a8 thornX3
ifrac141
b8iEduiti thornX3
ifrac141
g8iRPCti thorn u8t (8)
Eduit frac14 a9 thornX3
ifrac141
b9iEduiti thornX3
ifrac141
g9iLFti thorn u9t (9)
LFt frac14 a10 thornX3
ifrac141
b10iEduiti thornX3
ifrac141
g10iLFti thorn u10t (10)
The null hypothesis that all the indicators of education and all levels of education do not Granger cause RGDPt was tested inTable I Bivariate TYAGC results indicate that the null hypothesis was rejected (Table I) Similarly the null hypothesis thatRGDPt does not Granger cause all the indicators and all levels of education is rejected except Edu8t and Edu10t It means thatthere exists two-way causality between education and RGDPt RGDPt fails to cause higher education and expenditures oneducation
The estimated results from Eqs (3) and (4) in Table I show the feedback Granger causality between RPCt and RGDPt LFt isfound to cause RGDPt at 99 level of confidence while its reverse is not true The results of Eqs (7) and (8) in Table I show thatthe feedback causality between Eduit and RPCt seems to exist because majority of the indicators of education are causingRPCt and vice versa The results from Eq (9) and (10) in Table I reveal that LFt Granger causes education while reverseseemed to be not true In conclusion education and all levels of education (school college and university) Granger causeRGDPt and RGDPt also Granger causes education and all levels of education Feedback causality between education andRGDPt is found in bivariate case
45 Trivariate TYAGC framework
The trivariate causality among RGDPt RPCt and Eduit (Eqs (11)ndash(13)) and among RGDPt LFt and Eduit (Eqs (14)ndash(16)) wasestimated by using TYAGC framework and is presented in Tables II and III
RGDPt frac14 a11 thornX3
ifrac141
b11iRGDPti thornX3
ifrac141
l11iRPCti thornX3
ifrac141
g11iEduiti thorn u11t (11)
Eduit frac14 a12 thornX3
ifrac141
b12iRGDPti thornX3
ifrac141
l12iRPCti thornX3
ifrac141
g12iEduiti thorn u12t (12)
RPCt frac14 a13 thornX3
ifrac141
b13iRGDPti thornX3
ifrac141
l13iRPCti thornX3
ifrac141
g13iEduiti thorn u13t (13)
RGDPt frac14 a14 thornX3
ifrac141
b14iRGDPti thornX3
ifrac141
l14iLFti thornX3
ifrac141
g14iEduiti thorn u14t (14)
Edut frac14 a15 thornX3
ifrac141
b15iRGDPti thornX3
ifrac141
l15iLFti thornX3
ifrac141
g15iEduiti thorn u15t (15)
LFt frac14 a16 thornX3
ifrac141
b16iRGDPti thornX3
ifrac141
l16iLFti thornX3
ifrac141
g16iEduiti thorn u16t (16)
The estimated results presented in Table II indicate that the null hypothesis of no Granger causality between majority of theindicators of education and RGDPt is rejected This also supports our previous bivariate causality results that there existsfeedback causality between education and RGDPt The trivariate result in Table II seems to support the previous bivariateresult regarding causality between education and RPCt and between RPCt and RGDPt
In case of trivariate causality analysis among RGDPt LFt and Eduit the results in Table III again indicate the two waycausality running between education and RGDPt Six out of ten indicators of education does Granger cause LFt while LFt
Granger causes nine indicators out of ten indicators of education The null hypothesis that LFt does not Granger cause RGDPt
in the presence of all indicators of education is rejected at 99 level of confidence So LFt seems to be a very importantvariable that affects two main variables of the study ie education and RGDPt
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335328
In conclusion education and all levels of education Granger cause RGDPt where as its revere ie Granger causalityrunning from RGDPt to education and all levels of education is only true in case of trivariate causality among RGDPt LFt andeducation From here one can easily conclude that the role of LFt as compared to RPCt is very important in understanding therelationship between education and RGDPt Feedback causality between education and RGDPt is also found in trivariate case
46 Tetravariate TYAGC framework
The tetravariate causality among RGDPt RPCt LFt and Eduit (Eqs (17)ndash(20)) was also estimated by using TYAGC techniqueand their results are presented in Table IV
RGDPt frac14 a17 thornX3
ifrac141
b17iRGDPti thornX3
ifrac141
g17iRPCti thornX3
ifrac141
l17iLFti thornX3
ifrac141
d17iEduiti thorn u17t (17)
Eduit frac14 a18 thornX3
ifrac141
b18iRGDPti thornX3
ifrac141
g18iRPCti thornX3
ifrac141
l18iLFti thornX3
ifrac141
d18iEduiti thorn u18t (18)
RPCt frac14 a19 thornX3
ifrac141
b19iRGDPti thornX3
ifrac141
g19iRPCti thornX3
ifrac141
l19iLFti thornX3
ifrac141
d19iEduiti thorn u19t (19)
LFt frac14 a20 thornX3
ifrac141
b20iRGDPti thornX3
ifrac141
g20iRPCti thornX3
ifrac141
l20iLFti thornX3
ifrac141
d20iEduiti thorn u20t (20)
The tetravariate TYAGC results presented in Table IV indicate that all the indicators of education Granger cause RGDPt whileRGDPt does Granger cause majority of the indicators of education (seven out of ten) RGDPt does not Granger cause Edu5t
(university education) Edu8t (higher education) and Edu10t (education expenditure) From this one can easily conclude thatthere exists two way causality between education and RGDPt in case of tetravariate causality analysis as have been the caseof bivariate and trivariate causality Regarding levels of education all levels of education (ie school education collegeeducation and university education) do Granger cause RGDPt while RGDPt does only cause school education and collegeeducation RGDPt does not Granger cause university education
LFt Granger causes RGDPt at 99 confidence level while RGDPt only Granger causes LFt in case of Edu3t Edu5t Edu9t andEdu10t In case of testing causality between RPCt and RGDPt in the presence of all indicators of education RPCt does Grangercause RGDPt and in reverse case RGDPt does not Granger cause RPCt in the presence of Edu1t Edu3t Edu8t Edu9t and Edu10tThese results show the unidirectional causality running from RPCt to RGDPt
The research hypothesis that LFt does not Granger cause Eduit is rejected at 99 confidence interval except wheneducation is measured by Eduit Labour force has been found to cause all levels of education On the other side education onlyGranger causes the LFt in the presence of Edu3t Edu4t Edu5t Edu8t and Edu10t RPC does not Granger cause education whenEdu3t and Edu4t are used as proxies of education All indicators of education except Edu1t Edu2t and Edu10t do Granger causeRPCt This implies that feedback causality between RPCt and education is observed
It can easily be concluded from the TYAGC results of Eq (17) in Table IV that among all levels of education General highereducation (Edu9t) causes RGDPt highly and most significantly (999 confidence level) The level of confidence of collegeeducation (Edu3t) and school education (Edu2t) causing RGDPt is found to be 2nd highest (significance at 997 confidencelevel) and 3rd highest (significance at 989 confidence level) respectively From Eq (18) in Table IV it can also be found thatthe level of confidence (999) of causing RGDPt to school education (Edu2t) is found to be highest
From the bivariate trivariate and tetravariate TYAGC tests results in Tables IndashIV the overall results of the study abouteducation and different levels of education (School College and University) are summarized in Table 4
Table 4
Causal nexus between education different levels of education with RGDPt
Hypothesis TYAGC procedure
Bivariate Trivariate Tetravariate
RGDPt and Edut RGDPt RPCt Edut RGDPt LFt Edut RGDPt LFt RPCt Edut
Education (Edu1t) does Granger cause RGDPt Yes (0089) No (0459) Yes (0009) Yes (0087)
RGDPt does Granger cause education (Edu1t) Yes (0000) Yes (0000) Yes (0000) Yes (0000)
School education (Edu2t) does Granger cause RGDPt Yes (0000) Yes (0001) Yes (0002) Yes (0010)
RGDPt does Granger cause school education (Edu2t) Yes (0000) Yes (0000) Yes (0000) Yes (0000)
College education (Edu3t) does Granger cause RGDPt Yes (0038) Yes (0081) Yes (0000) Yes (0002)
RGDPt does Granger cause college education (Edu3t) Yes (0003) No (0172) Yes (0001) Yes (0032)
University education (Edu5t) does Granger cause RGDPt Yes (0000) Yes (0000) Yes (0001) Yes (0001)
RGDPt does Granger cause university education (Edu5t) Yes (0089) Yes (0000) Yes (0025) No (0515)
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 329
47 Figures in parentheses are p-values
From the above results presented in Table 4 it can be concluded that there existed feedback causality between educationand RGDPt in all bivariate trivariate and tetravariate TYAGC causality cases All levels of education ie school educationcollege education and university education do Granger cause RGDPt in all causality cases RGDPt does Granger cause schooleducation in all causality cases RGDPt does Granger cause college education in all causality cases except trivariate causalitythat is running from RGDPt to education when RPCt serves as a third variable Table 4 also reveals that RGDPt does Grangercause university education only in a bivariate and trivariate causality cases RGDPt fails to Granger cause to universityeducation in tetravariate case
5 Conclusions and recommendations
This study aimed to explore the cointegration and causal relationship between education (measured by different indicatorsof education) and economic growth in Pakistan It is very essential for a country to invest more in education because it is one ofthe most important ingredients of human capital and hence economic development The nature and strength of the relationshipbetween education and economic growth is still not clear in case of Pakistan The main focus of this empirical study remained toobserve the causality and cointegration between education and economic growth in the absence and presence physical capitaland labour force Cointegration between education and economic growth was investigated using ARDL approach and the causallinkage between education and economic growth was examined in bivariate trivariate and tetravariate TYAGC frameworkDifferent indicators of education were utilized in this study to show the robustness of empirical results The causality betweeneducation and economic growth was examined in the presence and absence of stock of physical capital and stock of labour as athird and fourth variable The causality results indicate that there exist two-way causality between education and economicgrowth and between all levels of education and economic growth in case of bivariate TYAGC framework Education and alllevels of education do Granger cause economic growth in the presence of real physical capital as a third variable while economicgrowth causes all the indicators of education except college education professional college education and educationalexpenditures in the presence of real physical capital as a third variable in case of trivariate causality analysis In the presence oflabour force as a third variable feedback causality exists between education and economic growth and between all levels ofeducation and economic growth The results of tetravariate TYAGC Test indicate that education and all level of education doGranger cause economic growth while economic growth does Granger cause majority of the indicators of education (ie sevenout of ten) Economic growth does not Granger cause university education higher education including professional educationand expenditures on education The rise in university education higher education including professional education andexpenditures on education were considered as the key indicators to gauge human and social progress Economic growth doesnot seem to affect important educational indicators like university education higher education including professionaleducation and expenditures on education This seems to be consistent with Easterlyrsquos findings Easterly (2001) said thatPakistan is a country that made little social progress for given rates of GDP Among all levels of education General highereducation causes economic growth highly and most significantly as was explored by Stengos and Aurangzeb (2008) The level ofconfidence of causing economic growth to school education found to be highest This study also confirms the long runrelationship between education and economic growth
On the basis of the results of this study it is recommended that the government should focus more on higher educationparticularly to university education More funds should be allocated to education in line with others sectors particularly touniversity and higher education levels so that the economic growth can be further accelerated This will in turn leads tofurther education and hence development Poor should be facilitated to get higher education so that the polarization inhigher education may further be minimized Primary schooling should also be given priority because primary educationserves as an input for all higher levels of education The inverted educational expenditure pyramid may also be taken intoaccount Since the role of labour force seems to be very important in understanding the relationship between education andeconomic growth so it is suggested that labour force should be given more chances to enhance their skills The variablelabour force must be included while examining the causality between education and economic growth It is alsorecommended that the nexus between education and economic growth with inclusion of other variables other than physicalcapital and labour force should further be tested and generalized
Appendix A
Table I
Bivariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Bivariate-RGDPt and Eduit
Eq (1) Edu1t does not Granger cause RGDPt 028998 [0089] 1 Reject H0
Edu2t does not Granger cause RGDPt 144869 [0000] 1 Reject H0
Edu3t does not Granger cause RGDPt 043243 [0038] 1 Reject H0
Edu4t does not Granger cause RGDPt 039797 [0046] 1 Reject H0
Table I (Continued )
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Edu5t does not Granger cause RGDPt 217739 [0000] 1 Reject H0
Edu6t does not Granger cause RGDPt 137788 [0000] 1 Reject H0
Edu7t does not Granger cause RGDPt 126682 [0000] 1 Reject H0
Edu8t does not Granger cause RGDPt 041335 [0042] 1 Reject H0
Edu9t does not Granger cause RGDPt 160963 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 028642 [0091] 1 Reject H0
Eq (2) RGDPt does not Granger cause Edu1t 260926 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 230094 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 085441 [0003] 1 Reject H0
RGDPt does not Granger cause Edu4t 107403 [0001] 1 Reject H0
RGDPt does not Granger cause Edu5t 028935 [0089] 1 Reject H0
RGDPt does not Granger cause Edu6t 270343 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 273974 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 003162 [0574] 1 Cannot reject H0
RGDPt does not Granger cause Edu9t 027588 [0097] 1 Reject H0
RGDPt does not Granger cause Edu10t 000851 [0770] 1 Cannot reject H0
Bivariate-RGDPt and RPCt
Eq (3) RPCt does not Granger cause RGDPt 054972 [0019] 1 Reject H0
Eq (4) RGDPt does not Granger cause RPCt 167511 [0000] 1 Reject H0
Bivariate-RGDPt and LFt
Eq (5) LFt does not Granger cause RGDPt 227888 [0000] 1 Reject H0
Eq (6) RGDPt does not Granger cause LFt 012380 [0266] 1 Cannot reject H0
Bivariate-Eduit and RPCt
Eq (7) Edu1t does not Granger cause RPCt 094596 [0002] 1 Reject H0
Edu2t does not Granger cause RPCt 015434 [0214] 1 Cannot reject H0
Edu3t does not Granger cause RPCt 038233 [0051] 1 Reject H0
Edu4t does not Granger cause RPCt 000506 [0822] 1 Cannot reject H0
Edu5t does not Granger cause RPCt 298085 [0000] 1 Reject H0
Edu6t does not Granger cause RPCt 018289 [0176] 1 Cannot reject H0
Edu7t does not Granger cause RPCt 018976 [0168] 1 Cannot reject H0
Edu8t does not Granger cause RPCt 176399 [0000] 1 Reject H0
Edu9t does not Granger cause RPCt 224647 [0000] 1 Reject H0
Edu10t does not Granger cause RPCt 039174 [0048] 1 Reject H0
Eq (8) RPCt does not Granger cause Edu1t 091477 [0002] 1 Reject H0
RPCt does not Granger cause Edu2t 098821 [0002] 1 Reject H0
RPCt does not Granger cause Edu3t 066148 [0010] 1 Reject H0
RPCt does not Granger cause Edu4t 084218 [0004] 1 Reject H0
RPCt does not Granger cause Edu5t 001684 [0682] 1 Cannot reject H0
RPCt does not Granger cause Edu6t 107553 [0001] 1 Reject H0
RPCt does not Granger cause Edu7t 108798 [0001] 1 Reject H0
RPCt does not Granger cause Edu8t 004283 [0513] 1 Cannot reject H0
RPCt does not Granger cause Edu9t 005627 [0453] 1 Cannot reject H0
RPCt does not Granger cause Edu10t 000417 [0838] 1 Cannot reject H0
Bivariate-Eduit and LFt
Eq (9) Edu1t does not Granger cause LFt 026469 [0104] 1 Reject H0
Edu2t does not Granger cause LFt 012355 [0266] 1 Cannot reject H0
Edu3t does not Granger cause LFt 020468 [0153] 1 Cannot reject H0
Edu4t does not Granger cause LFt 098042 [0002] 1 Reject H0
Edu5t does not Granger cause LFt 049986 [0025] 1 Reject H0
Edu6t does not Granger cause LFt 016896 [0194] 1 Cannot reject H0
Edu7t does not Granger cause LFt 015167 [0218] 1 Cannot reject H0
Edu8t does not Granger cause LFt 184475 [0000] 1 Reject H0
Edu9t does not Granger cause LFt 003986 [0528] 1 Cannot reject H0
Edu10t does not Granger cause LFt 010899 [0296] 1 Cannot reject H0
Eq (10) LFt does not Granger cause Edu1t 107709 [0001] 1 Reject H0
LFt does not Granger cause Edu2t 071204 [0008] 1 Reject H0
LFt does not Granger cause Edu3t 136419 [0000] 1 Reject H0
LFt does not Granger cause Edu4t 056225 [0018] 1 Reject H0
LFt does not Granger cause Edu5t 057141 [0017] 1 Reject H0
LFt does not Granger cause Edu6t 091531 [0002] 1 Reject H0
LFt does not Granger cause Edu7t 095063 [0002] 1 Reject H0
LFt does not Granger cause Edu8t 021313 [0144] 1 Cannot reject H0
LFt does not Granger cause Edu9t 069389 [0008] 1 Reject H0
LFt does not Granger cause Edu10t 000743 [0785] 1 Cannot reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335330
Table II
Trivariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Trivariate-RGDPt RPCt and Eduit
Eq (11) Edu1t does not Granger cause RGDPt 005481 [0459] 1 Cannot reject H0
Edu2t does not Granger cause RGDPt 105415 [0001] 1 Reject H0
Edu3t does not Granger cause RGDPt 030370 [0081] 1 Reject H0
Edu4t does not Granger cause RGDPt 022525 [0133] 1 Cannot reject H0
Edu5t does not Granger cause RGDPt 227510 [0000] 1 Reject H0
Edu6t does not Granger cause RGDPt 098494 [0002] 1 Reject H0
Edu7t does not Granger cause RGDPt 090460 [0003] 1 Reject H0
Edu8t does not Granger cause RGDPt 067381 [0009] 1 Reject H0
Edu9t does not Granger cause RGDPt 168617 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 085842 [0003] Reject H0
Eq (11a) RPCt does not Granger cause RGDP (Edu1 as a 3rd variable) 029029 [0088] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu2 as a 3rd variable) 024880 [0115] 1 Cannot reject H0
RPCt does not Granger cause RGDPt (Edu3t as a 3rd variable) 041380 [0042] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu4t as a 3rd variable) 036580 [0056] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu5t as a 3rd variable) 064811 [0011] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu6t as a 3rd variable) 024405 [0118] 1 Cannot reject H0
RPCt does not Granger cause RGDPt (Edu7t as a 3rd variable) 026008 [0107] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu8t as a 3rd variable) 081607 [0004] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu9t as a 3rd variable) 063133 [0012] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu10t as a 3rd variable) 115637 [0001] 1 Reject H0
Eq (12) RGDPt does not Granger cause Edu1t 176454 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 129776 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 018626 [0172] 1 Cannot reject H0
RGDPt does not Granger cause Edu4t 020449 [0153] 1 Cannot reject H0
RGDPt does not Granger cause Edu5t 144658 [0000] 1 Reject H0
RGDPt does not Granger cause Edu6t 175431 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 178356 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 042497 [0039] 1 Reject H0
RGDPt does not Granger cause Edu9t 082506 [0004] 1 Reject H0
RGDPt does not Granger cause Edu10t 008026 [0370] 1 Cannot reject H0
Eq (12a) RPCt does not Granger cause Edu1t 000122 [0912] 1 Cannot reject H0
RPCt does not Granger cause Edu2t 028750 [0090] 1 Reject H0
RPCt does not Granger cause Edu3t 058586 [0016] 1 Reject H0
RPCt does not Granger cause Edu4t 071372 [0008] 1 Reject H0
RPCt does not Granger cause Edu5t 302364 [0000] 1 Reject H0
RPCt does not Granger cause Edu6t 020474 [0152] 1 Cannot reject H0
RPCt does not Granger cause Edu7t 017533 [0185] 1 Cannot reject H0
RPCt does not Granger cause Edu8t 044926 [0034] 1 Reject H0
RPCt does not Granger cause Edu9t 240955 [0000] 1 Reject H0
RPCt does not Granger cause Edu10t 021006 [0147] 1 Cannot reject H0
Eq (13) RGDPt does not Granger cause RPCt (Edu1t as a 3rd variable) 055095 [0019] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu2t as a 3rd variable) 182287 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu3t as a 3rd variable) 191499 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu4t as a 3rd variable) 269133 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu5t as a 3rd variable) 172979 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu6t as a 3rd variable) 166347 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu7t as a 3rd variable) 161198 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu8t as a 3rd variable) 038521 [0050] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu9tas a 3rd variable) 183169 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu10t as a 3rd variable) 139552 [0000] 1 Reject H0
Eq (13a) Edu1t does not Granger cause RPCt 000122 [0912] 1 Cannot reject H0
Edu2t does not Granger cause RPCt 028750 [0090] 1 Reject H0
Edu3t does not Granger cause RPCt 058586 [0016] 1 Reject H0
Edu4t does not Granger cause RPCt 071372 [0008] 1 Reject H0
Edu5t does not Granger cause RPCt 302364 [0000] 1 Reject H0
Edu6t does not Granger cause RPCt 020474 [0152] 1 Cannot reject H0
Edu7t does not Granger cause RPCt 017533 [0185] 1 Cannot reject H0
Edu8t does not Granger cause RPCt 044926 [0034] 1 Reject H0
Edu9t does not Granger cause RPCt 240955 [0000] 1 Reject H0
Edu10t does not Granger cause RPCt 021006 [0147] 1 Cannot reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 331
Table III
Trivariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Trivariate-RGDPt LFt and Eduit
Eq (14) Edu1t does not Granger cause RGDPt 068472 [0009] 1 Reject H0
Edu2t does not Granger cause RGDPt 092326 [0002] 1 Reject H0
Edu3t does not Granger cause RGDPt 180477 [0000] 1 Reject H0
Edu4t does not Granger cause RGDPt 132070 [0000] 1 Reject H0
Edu5t does not Granger cause RGDPt 109716 [0001] 1 Reject H0
Edu6t does not Granger cause RGDPt 086017 [0003] 1 Reject H0
Edu7t does not Granger cause RGDPt 078604 [0005] 1 Reject H0
Edu8t does not Granger cause RGDPt 020470 [0153] 1 Cannot reject H0
Edu9t does not Granger cause RGDPt 293293 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 005754 [0448] 1 Cannot reject H0
Eq (14a) LFt does not Granger cause RGDPt (Edu1t as a 3rd variable) 409533 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu2t as a 3rd variable) 332636 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu3t as a 3rd variable) 701171 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu4t as a 3rd variable) 605496 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu5t as a 3rd variable) 240867 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu6t as a 3rd variable) 330495 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu7t as a 3rd variable) 332860 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu8t as a 3rd variable) 352003 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu9t as a 3rd variable) 573087 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu10t as a 3rd variable) 343199 [0000] 1 Reject H0
Eq (15) RGDPt does not Granger cause Edu1t 134939 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 804323 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 109273 [0001] 1 Reject H0
RGDPt does not Granger cause Edu4t 278785 [0000] 1 Reject H0
RGDPt does not Granger cause Edu5t 050547 [0025] 1 Reject H0
RGDPt does not Granger cause Edu6t 790307 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 738342 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 043402 [0037] 1 Reject H0
RGDPt does not Granger cause Edu9t 175731 [0000] 1 Reject H0
RGDPt does not Granger cause Edu10t 061709 [0013] 1 Reject H0
Eq (15a) LFt does not Granger cause Edu1t 009324 [0334] 1 Cannot reject H0
LFt does not Granger cause Edu2t 377339 [0000] 1 Reject H0
LFt does not Granger cause Edu3t 176565 [0000] 1 Reject H0
LFt does not Granger cause Edu4t 180046 [0000] 1 Reject H0
LFt does not Granger cause Edu5t 091061 [0003] 1 Reject H0
LFt does not Granger cause Edu6t 355203 [0000] 1 Reject H0
LFt does not Granger cause Edu7t 327354 [0000] 1 Reject H0
LFt does not Granger cause Edu8t 053664 [0021] 1 Reject H0
LFt does not Granger cause Edu9t 251724 [0000] 1 Reject H0
LFt does not Granger cause Edu10t 060787 [0014] 1 Reject H0
Eq (16) Edu1t does not Granger cause LFt 036697 [0055] 1 Reject H0
Edu2t does not Granger cause LFt 004605 [0497] 1 Cannot reject H0
Edu3t does not Granger cause LFt 093988 [0002] 1 Reject H0
Edu4t does not Granger cause LFt 177287 [0000] 1 Reject H0
Edu5t does not Granger cause LFt 059203 [0015] 1 Reject H0
Edu6t does not Granger cause LFt 007202 [0396] 1 Cannot reject H0
Edu7t does not Granger cause LFt 005520 [0458] 1 Cannot reject H0
Edu8t does not Granger cause LFt 241662 [0000] 1 Reject H0
Edu9t does not Granger cause LFt 004009 [0527] 1 Cannot reject H0
Edu10t does not Granger cause LFt 058477 [0016] 1 Reject H0
Eq (16a) RGDPt does not Granger cause LFt (Edu1t as a 3rd variable) 002436 [0622] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu2t as a 3rd variable) 004276 [0513] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu3t as a 3rd variable) 047690 [0029] 1 Reject H0
RGDPt does not Granger cause LFt (Edu4t as a 3rd variable) 015207 [0218] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu5t as a 3rd variable) 040757 [0044] 1 Reject H0
RGDPt does not Granger cause LFt (Edu6t as a 3rd variable) 003392 [0560] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu7t as a 3rd variable) 004309 [0512] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu8t as a 3rd variable) 003145 [0575] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu9t as a 3rd variable) 017426 [0187] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu10t as a 3rd variable) 048448 [0028] 1 Reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335332
Table IV
Tetravariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Tetravariate-RGDPt RPCt LFt and Edut
Eq (17) Edu1t does not Granger cause RGDPt 029350 [0087] 1 Reject H0
Edu2t does not Granger cause RGDPt 065661 [0010] 1 Reject H0
Edu3t does not Granger cause RGDPt 097521 [0002] 1 Reject H0
Edu4t does not Granger cause RGDPt 071590 [0007] 1 Reject H0
Edu5t does not Granger cause RGDPt 116263 [0001] 1 Reject H0
Edu6t does not Granger cause RGDPt 059569 [0015] 1 Reject H0
Edu7t does not Granger cause RGDPt 054327 [0020] 1 Reject H0
Edu8t does not Granger cause RGDPt 040033 [0045] 1 Reject H0
Edu9t does not Granger cause RGDPt 195734 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 034374 [0064] 1 Reject H0
Eq (17a) LFt does not Granger cause RGDPt (Edut = Edu1) 251518 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu2) 165581 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu3) 316418 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu4) 289993 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu5) 109302 [0001] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu6) 165606 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu7) 168037 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu8) 176645 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu9) 247435 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu10) 146998 [0000] 1 Reject H0
Eq (17b) RPCt does not Granger cause RGDPt (Edut = Edu1) 042975 [0038] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu2) 039280 [0047] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu3) 034296 [0064] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu4) 027068 [0100] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu5) 062858 [0012] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu6) 039537 [0047] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu7) 040022 [0045] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu8) 045487 [0033] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu9) 068323 [0009] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu10) 083479 [0004] 1 Reject H0
Eq (18) RGDPt does not Granger cause Edu1t 150200 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 633103 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 045767 [0032] 1 Reject H0
RGDPt does not Granger cause Edu4t 122392 [0000] 1 Reject H0
RGDPt does not Granger cause Edu5t 004235 [0515] 1 Cannot reject H0
RGDPt does not Granger cause Edu6t 453644 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 418611 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 055973 [0454] 1 Cannot reject H0
RGDPt does not Granger cause Edu9t 053890 [0020] 1 Reject H0
RGDPt does not Granger cause Edu10t 011119 [0292] 1 Cannot reject H0
Eq (18a) LFt does not Granger cause Edu1t 006023 [0438] 1 Cannot reject H0
LFt does not Granger cause Edu2t 364559 [0000] 1 Reject H0
LFt does not Granger cause Edu3t 197423 [0000] 1 Reject H0
LFt does not Granger cause Edu4t 166511 [0000] 1 Reject H0
LFt does not Granger cause Edu5t 383886 [0000] 1 Reject H0
LFt does not Granger cause Edu6t 359377 [0000] 1 Reject H0
LFt does not Granger cause Edu7t 328249 [0000] 1 Reject H0
LFt does not Granger cause Edu8t 135310 [0000] 1 Reject H0
LFt does not Granger cause Edu9t 630068 [0000] 1 Reject H0
LFt does not Granger cause Edu01t 109365 [0001] 1 Reject H0
Eq (18b) RPCt does not Granger cause Edu1t 114248 [0001] 1 Reject H0
RPCt does not Granger cause Edu2t 036828 [0055] 1 Reject H0
RPCt does not Granger cause Edu3t 021023 [0147] 1 Cannot reject H0
RPCt does not Granger cause Edu4t 000484 [0826] 1 Cannot reject H0
RPCt does not Granger cause Edu5t 610934 [0000] 1 Reject H0
RPCt does not Granger cause Edu6t 070279 [0008] 1 Reject H0
RPCt does not Granger cause Edu7t 051166 [0024] 1 Reject H0
RPCt does not Granger cause Edu8t 167481 [0000] 1 Reject H0
RPCt does not Granger cause Edu9t 335271 [0000] 1 Reject H0
RPCt does not Granger cause Edu10t 067481 [0009] 1 Reject H0
Eq (19) Edu1 does not Granger cause RPCt 005154 [0473] 1 Cannot reject H0
Edu2 does not Granger cause RPCt 011954 [0274] 1 Cannot reject H0
Edu3 does not Granger cause RPCt 162365 [0000] 1 Reject H0
Edu4 does not Granger cause RPCt 148964 [0000] 1 Reject H0
Edu5 does not Granger cause RPCt 243978 [0000] 1 Reject H0
Edu6 does not Granger cause RPCt 040262 [0045] 1 Reject H0
Edu7 does not Granger cause RPCt 035138 [0061] 1 Reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 333
able IV (Continued )
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Edu8 does not Granger cause RPCt 030100 [0083] 1 Reject H0
Edu9 does not Granger cause RPCt 462564 [0000] 1 Reject H0
Edu10 does not Granger cause RPCt 009580 [0328] 1 Cannot reject H0
Eq (19a) RGDPt does not Granger cause RPCt (Edu1t as a 3rd variable) 009936 [0319] 1 Cannot reject H0
RGDPt does not Granger cause RPCt (Edu2t as a 3rd variable) 039369 [0047] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu3t as a 3rd variable) 003822 [0536] 1 Cannot reject H0
RGDPt does not Granger cause RPCt (Edu4t as a 3rd variable) 028000 [0094] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu5t as a 3rd variable) 039910 [0046] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu6t as a 3rd variable) 033500 [0067] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu7t as a 3rd variable) 029924 [0084] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu8t as a 3rd variable) 002803 [0597] 1 Cannot Reject H0
RGDPt does not Granger cause RPCt (Edu9t as a 3rd variable) 011416 [0285] 1 Cannot reject H0
RGDPt does not Granger cause RPCt (Edu10t as a 3rd variable) 006944 [0405] 1 Cannot reject H0
Eq (20) Edu1t does not Granger cause LFt 015302 [0216] 1 Cannot reject H0
Edu2t does not Granger cause LFt 001053 [0746] 1 Cannot reject H0
Edu3t does not Granger cause LFt 080072 [0005] 1 Reject H0
Edu4t does not Granger cause LFt 143854 [0000] 1 Reject H0
Edu5t does not Granger cause LFt 061159 [0013] 1 Reject H0
Edu6t does not Granger cause LFt 003113 [0577] 1 Cannot reject H0
Edu7t does not Granger cause LFt 002394 [0625] 1 Cannot reject H0
Edu8t does not Granger cause LFt 196804 [0000] 1 Reject H0
Edu9t does not Granger cause LFt 046285 [0496] 1 Cannot reject H0
Edu10t does not Granger cause LFt 04161 1 [0041] 1 Reject H0
Eq (20a) RGDPt does not Granger cause LFt (Edu1t as a 3rd variable) 006872 [0407] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu2t as a 3rd variable) 018604 [0173] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu3t as a 3rd variable) 066905 [0010] 1 Reject H0
RGDPt does not Granger cause LFt (Edu4t as a 3rd variable) 023249 [0127] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu5t as a 3rd variable) 070835 [0008] 1 Reject H0
RGDPt does not Granger cause LFt (Edu6t as a 3rd variable) 016501 [0199] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu7t as a 3rd variable) 018532 [0173] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu8t as a 3rd variable) 003730 [0541] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu9t as a 3rd variable) 039255 [0048] 1 Reject H0
RGDPt does not Granger cause LFt (Edu10t as a 3rd variable) 055266 [0019] 1 Reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335334
T
References
Abbas Q amp Peck J F (2008) Human capital and economic growth Pakistan 1960ndash2003 The Lahore Journal of Economics 13(1) 1ndash28Ayara N A (2002) The paradox of education and economic growth in Nigeria Empirical evidence The Nigerian Economic Society (NES) Pt 2 371ndash393Babatunde M A amp Adefabi R A (2005) Long run relationship between education and economic growth in Nigeria Evidence from the Johansenrsquos cointegration
approach Paper presented at the regional conference on education in West Africa Constraints and Opportunities Dakar Senegal November 1stndash2nd 2005Cornell UniversityCREAMinisterede lrsquoEducation du Senegal
Baldacci E Clements B Cui Q amp Gupta S (2005) What does it take to help the poor Finance and Development The Quarterly Magazine of the IMF 42(2)Changzheng Z Zhijian H amp Huaizu L (2007) An empirical study on education equity in China 1978ndash2004 Frontier in Economics of China 2(4) 536ndash544Chaudhary A R Asim I amp Gillani S Y M (2009) The nexus between higher education and economic growth An empirical investigation for Pakistan Pakistan
Journal of Commerce and Social Sciences 3Chaudhry I S Malik S amp Ashraf M (2006) Rural poverty in Pakistan Some related concepts issues and empirical analysis Pakistan Economic and Social Review
44(2) 259ndash276Diebolt C amp Litago J (1997) Education and economic growth in Germany before the Second World War An econometric analysis of dynamic relations Historical
Social Research 2(22) 132ndash149Easterly W (2001) The middle class consensus and economic development Journal of Economic Growth 6(4) 317ndash335Engle R F amp Granger C W J (1987) Cointegration and error correction Representation estimation and testing Econometrica 55 251ndash276Fernandez E amp Mauro P (2000) The role of human capital in economic growth The case of Spain (IMF Working Paper) International Monetary FundFrancis B amp Iyare S (2006) Education and development in the Caribbean A cointegration and causality approach Economics Bulletin 15(2) 1ndash13Galor O amp Moav O (2000) Das human capital Retrieved from httpeconpstcn brownedufacultygalorindexhtmlGoode R B (1959) Adding to the stock of physical and human capital American Economic Review 49(2) 147Government of Pakistan (1970ndash2009) Pakistan economic survey various issues Finance Division Islamabad Economic Advisorrsquos WingGregory A W amp Hansen B E (1996) Residual-based tests for cointegration in models with regime shifts Journal of Econometrics 70 99ndash126Grossman G M amp Helpman E (1991) Innovation and growth in the global economy Cambridge MIT PressGylfason T amp Zoega G (2003) Education social equality and economic growth A view of the landscape CESifo Economic Studies 49(4) 557ndash579Hassan S amp Ahmed H (2008) Educationrsquos contribution to the economic growth of sub-Saharan Africa Southwestern Economic Review 1(32) 175ndash190Islam T S Wadud M A amp Islam Q B T (2007) Relationship between education and GDP growth A multivariate causality analysis for Bangladesh Economics
Bulletin 3(35) 1ndash7Jin J C (2009) Economic research and economic growth Evidence from East Asian Economies Journal of Asian Economics 20 150ndash155Johansen S (1988) Statistical analysis of cointegration vectors Journal of Economic Dynamics and Control 12 231ndash254Johansen S amp Juselius K (1990) Maximum likelihood estimation and inference on cointegration with applications to the demand for money Oxford Bulletin of
Economics and Statistics 52 169ndash210Katırcıoglu S T (2009) Investigating higher-education-led growth hypothesis in a small Island Time series evidence from Northern Cyprus Paper presented at
Econ Anadolu 2009 Anadolu International Conference in Economics June 17ndash19 2009 TurkeyKhorasgani M F (2008) Higher education development and economic growth in Iran Education Business and Society Contemporary Middle Eastern Issues 1
162ndash174
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 335
Kui L (2005) The interactive causality between education and economic growth in China Retrieved from httppapersssrncomsol3paperscfmAbstrac-tid=920624
Loening J L (2004) Time series evidence on education and growth The case of Guatemala 1951ndash2002 Revista de Analisis Economico 19(2) 3ndash40Lucas R E (1988) On the mechanics of economic development Journal of Monetary Economics 22 3ndash42Macerinskiene I amp Vaiksnoraite B (2006) The role of higher education to economic development VadybaManagement 2(11)Mankiw N G Romer D amp Weil D N (1992) A contribution to the empirics of economic growth Quarterly Journal of Economics 107 407ndash437Momete D C (2007) Analysis of the relationship between employment and economic growth in Romania Fascicle of Management and Technological Engineering
VI(XVI)Morote E S (2000) Higher education employment and economic growth Mexico and Peru Retrieved from httpwwwamericanprofessororgdocumentation
lasapa perdocNarayan P K (2005) The saving and investment nexus for China Evidence from cointegration tests Applied Economics 37 1979ndash1990Permani R (2008) Education as a determinant of economic growth in East Asia Historical trends and empirical evidences (1965ndash2000) Retrieved from http
wwwuoweduaucommerceeconehsanzpdfsPermani202008pdfPesaran M H amp Pesaran B (1997) Working with Microfit 40 Interactive econometric analysis Oxford Oxford University PressPesaran M H amp Shin Y (1999) An autoregressive distributed lag modeling approach to cointegration analysis In S Strom (Ed) Econometrics and economic theory
in the 20th century Cambridge Cambridge University PressPesaran M H Shin Y amp Smith R J (2001) Bounds testing approaches to the analysis of level relationships Journal of Applied Econometrics 16 289ndash326Pradhan R P (2009) Education and economic growth in India Using error correction modeling International Research Journal of Finance and Economics 25Pritchett L (2001) Where has all the education gone The World Bank Economic Review 15(3)Quah D amp Rauch J E (1990) Openness and the rate of economic growth Journal Development of Studies 2(49) 307ndash335Rivera-Batiz L A amp Romer P M (1991) Economic integration and endogenous growth Quarterly Journal of Economics 106 531ndash555Romer P M (1986) Increasing returns and long run growth Journal of Political Economy 6(90) 1002ndash1037Romer P M (1989) Human capital and growth Theory and evidence (NBER Working Papers 3173) National Bureau of Economic Research IncRomer P M (1990) Endogenous technological change Journal of Political Economy 5(98) 71ndash101Rondinelli D amp Montgomery J (1995) Great policies Strategic innovations in Asia and the Pacific Basin Westport Praeger PublishingSaikkonen P amp Lutkepohl H (2000) Testing for the cointegration rank of a VAR process with structural shifts Journal of Business and Economic Statistics 18(4)
451ndash464Schultz T W (1961) Investment in human capital American Economic Review 51(1) 1State Bank of Pakistan (1972ndash2009) Annual reports Karachi SBP PressStengos T amp Aurangzeb A (2008) An empirical investigation of the relationship between education and growth in pakistan International Economic Journal 3
345ndash359 Retrieved from httpwwwinformaworldcomsmpptitledb=allcontent=t713685453tab=issueslistbranches=22-v2222Toda H Y amp Yamamoto T (1995) Statistical inference in vector autoregressive with possible integrated processes Journal of Econometrics 66 225ndash250United Nations (1997) Human Development Report New York Oxford University Press
- Education and economic growth in Pakistan A cointegration and causality analysis
-
- Introduction
- Review of literature
- Method and procedure
- Empirical results
-
- Unit root results
- Cointegration
- Toda-Yamamoto Augmented Granger Causality (TYAGC) Test
- Bivariate TYAGC framework
- Trivariate TYAGC framework
- Tetravariate TYAGC framework
- Figures in parentheses are p-values
-
- Conclusions and recommendations
-
- References
-
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 327
Eduit frac14 a7 thornX3
ifrac141
b7iEduiti thornX3
ifrac141
g7iRPCti thorn u7t (7)
RPCt frac14 a8 thornX3
ifrac141
b8iEduiti thornX3
ifrac141
g8iRPCti thorn u8t (8)
Eduit frac14 a9 thornX3
ifrac141
b9iEduiti thornX3
ifrac141
g9iLFti thorn u9t (9)
LFt frac14 a10 thornX3
ifrac141
b10iEduiti thornX3
ifrac141
g10iLFti thorn u10t (10)
The null hypothesis that all the indicators of education and all levels of education do not Granger cause RGDPt was tested inTable I Bivariate TYAGC results indicate that the null hypothesis was rejected (Table I) Similarly the null hypothesis thatRGDPt does not Granger cause all the indicators and all levels of education is rejected except Edu8t and Edu10t It means thatthere exists two-way causality between education and RGDPt RGDPt fails to cause higher education and expenditures oneducation
The estimated results from Eqs (3) and (4) in Table I show the feedback Granger causality between RPCt and RGDPt LFt isfound to cause RGDPt at 99 level of confidence while its reverse is not true The results of Eqs (7) and (8) in Table I show thatthe feedback causality between Eduit and RPCt seems to exist because majority of the indicators of education are causingRPCt and vice versa The results from Eq (9) and (10) in Table I reveal that LFt Granger causes education while reverseseemed to be not true In conclusion education and all levels of education (school college and university) Granger causeRGDPt and RGDPt also Granger causes education and all levels of education Feedback causality between education andRGDPt is found in bivariate case
45 Trivariate TYAGC framework
The trivariate causality among RGDPt RPCt and Eduit (Eqs (11)ndash(13)) and among RGDPt LFt and Eduit (Eqs (14)ndash(16)) wasestimated by using TYAGC framework and is presented in Tables II and III
RGDPt frac14 a11 thornX3
ifrac141
b11iRGDPti thornX3
ifrac141
l11iRPCti thornX3
ifrac141
g11iEduiti thorn u11t (11)
Eduit frac14 a12 thornX3
ifrac141
b12iRGDPti thornX3
ifrac141
l12iRPCti thornX3
ifrac141
g12iEduiti thorn u12t (12)
RPCt frac14 a13 thornX3
ifrac141
b13iRGDPti thornX3
ifrac141
l13iRPCti thornX3
ifrac141
g13iEduiti thorn u13t (13)
RGDPt frac14 a14 thornX3
ifrac141
b14iRGDPti thornX3
ifrac141
l14iLFti thornX3
ifrac141
g14iEduiti thorn u14t (14)
Edut frac14 a15 thornX3
ifrac141
b15iRGDPti thornX3
ifrac141
l15iLFti thornX3
ifrac141
g15iEduiti thorn u15t (15)
LFt frac14 a16 thornX3
ifrac141
b16iRGDPti thornX3
ifrac141
l16iLFti thornX3
ifrac141
g16iEduiti thorn u16t (16)
The estimated results presented in Table II indicate that the null hypothesis of no Granger causality between majority of theindicators of education and RGDPt is rejected This also supports our previous bivariate causality results that there existsfeedback causality between education and RGDPt The trivariate result in Table II seems to support the previous bivariateresult regarding causality between education and RPCt and between RPCt and RGDPt
In case of trivariate causality analysis among RGDPt LFt and Eduit the results in Table III again indicate the two waycausality running between education and RGDPt Six out of ten indicators of education does Granger cause LFt while LFt
Granger causes nine indicators out of ten indicators of education The null hypothesis that LFt does not Granger cause RGDPt
in the presence of all indicators of education is rejected at 99 level of confidence So LFt seems to be a very importantvariable that affects two main variables of the study ie education and RGDPt
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335328
In conclusion education and all levels of education Granger cause RGDPt where as its revere ie Granger causalityrunning from RGDPt to education and all levels of education is only true in case of trivariate causality among RGDPt LFt andeducation From here one can easily conclude that the role of LFt as compared to RPCt is very important in understanding therelationship between education and RGDPt Feedback causality between education and RGDPt is also found in trivariate case
46 Tetravariate TYAGC framework
The tetravariate causality among RGDPt RPCt LFt and Eduit (Eqs (17)ndash(20)) was also estimated by using TYAGC techniqueand their results are presented in Table IV
RGDPt frac14 a17 thornX3
ifrac141
b17iRGDPti thornX3
ifrac141
g17iRPCti thornX3
ifrac141
l17iLFti thornX3
ifrac141
d17iEduiti thorn u17t (17)
Eduit frac14 a18 thornX3
ifrac141
b18iRGDPti thornX3
ifrac141
g18iRPCti thornX3
ifrac141
l18iLFti thornX3
ifrac141
d18iEduiti thorn u18t (18)
RPCt frac14 a19 thornX3
ifrac141
b19iRGDPti thornX3
ifrac141
g19iRPCti thornX3
ifrac141
l19iLFti thornX3
ifrac141
d19iEduiti thorn u19t (19)
LFt frac14 a20 thornX3
ifrac141
b20iRGDPti thornX3
ifrac141
g20iRPCti thornX3
ifrac141
l20iLFti thornX3
ifrac141
d20iEduiti thorn u20t (20)
The tetravariate TYAGC results presented in Table IV indicate that all the indicators of education Granger cause RGDPt whileRGDPt does Granger cause majority of the indicators of education (seven out of ten) RGDPt does not Granger cause Edu5t
(university education) Edu8t (higher education) and Edu10t (education expenditure) From this one can easily conclude thatthere exists two way causality between education and RGDPt in case of tetravariate causality analysis as have been the caseof bivariate and trivariate causality Regarding levels of education all levels of education (ie school education collegeeducation and university education) do Granger cause RGDPt while RGDPt does only cause school education and collegeeducation RGDPt does not Granger cause university education
LFt Granger causes RGDPt at 99 confidence level while RGDPt only Granger causes LFt in case of Edu3t Edu5t Edu9t andEdu10t In case of testing causality between RPCt and RGDPt in the presence of all indicators of education RPCt does Grangercause RGDPt and in reverse case RGDPt does not Granger cause RPCt in the presence of Edu1t Edu3t Edu8t Edu9t and Edu10tThese results show the unidirectional causality running from RPCt to RGDPt
The research hypothesis that LFt does not Granger cause Eduit is rejected at 99 confidence interval except wheneducation is measured by Eduit Labour force has been found to cause all levels of education On the other side education onlyGranger causes the LFt in the presence of Edu3t Edu4t Edu5t Edu8t and Edu10t RPC does not Granger cause education whenEdu3t and Edu4t are used as proxies of education All indicators of education except Edu1t Edu2t and Edu10t do Granger causeRPCt This implies that feedback causality between RPCt and education is observed
It can easily be concluded from the TYAGC results of Eq (17) in Table IV that among all levels of education General highereducation (Edu9t) causes RGDPt highly and most significantly (999 confidence level) The level of confidence of collegeeducation (Edu3t) and school education (Edu2t) causing RGDPt is found to be 2nd highest (significance at 997 confidencelevel) and 3rd highest (significance at 989 confidence level) respectively From Eq (18) in Table IV it can also be found thatthe level of confidence (999) of causing RGDPt to school education (Edu2t) is found to be highest
From the bivariate trivariate and tetravariate TYAGC tests results in Tables IndashIV the overall results of the study abouteducation and different levels of education (School College and University) are summarized in Table 4
Table 4
Causal nexus between education different levels of education with RGDPt
Hypothesis TYAGC procedure
Bivariate Trivariate Tetravariate
RGDPt and Edut RGDPt RPCt Edut RGDPt LFt Edut RGDPt LFt RPCt Edut
Education (Edu1t) does Granger cause RGDPt Yes (0089) No (0459) Yes (0009) Yes (0087)
RGDPt does Granger cause education (Edu1t) Yes (0000) Yes (0000) Yes (0000) Yes (0000)
School education (Edu2t) does Granger cause RGDPt Yes (0000) Yes (0001) Yes (0002) Yes (0010)
RGDPt does Granger cause school education (Edu2t) Yes (0000) Yes (0000) Yes (0000) Yes (0000)
College education (Edu3t) does Granger cause RGDPt Yes (0038) Yes (0081) Yes (0000) Yes (0002)
RGDPt does Granger cause college education (Edu3t) Yes (0003) No (0172) Yes (0001) Yes (0032)
University education (Edu5t) does Granger cause RGDPt Yes (0000) Yes (0000) Yes (0001) Yes (0001)
RGDPt does Granger cause university education (Edu5t) Yes (0089) Yes (0000) Yes (0025) No (0515)
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 329
47 Figures in parentheses are p-values
From the above results presented in Table 4 it can be concluded that there existed feedback causality between educationand RGDPt in all bivariate trivariate and tetravariate TYAGC causality cases All levels of education ie school educationcollege education and university education do Granger cause RGDPt in all causality cases RGDPt does Granger cause schooleducation in all causality cases RGDPt does Granger cause college education in all causality cases except trivariate causalitythat is running from RGDPt to education when RPCt serves as a third variable Table 4 also reveals that RGDPt does Grangercause university education only in a bivariate and trivariate causality cases RGDPt fails to Granger cause to universityeducation in tetravariate case
5 Conclusions and recommendations
This study aimed to explore the cointegration and causal relationship between education (measured by different indicatorsof education) and economic growth in Pakistan It is very essential for a country to invest more in education because it is one ofthe most important ingredients of human capital and hence economic development The nature and strength of the relationshipbetween education and economic growth is still not clear in case of Pakistan The main focus of this empirical study remained toobserve the causality and cointegration between education and economic growth in the absence and presence physical capitaland labour force Cointegration between education and economic growth was investigated using ARDL approach and the causallinkage between education and economic growth was examined in bivariate trivariate and tetravariate TYAGC frameworkDifferent indicators of education were utilized in this study to show the robustness of empirical results The causality betweeneducation and economic growth was examined in the presence and absence of stock of physical capital and stock of labour as athird and fourth variable The causality results indicate that there exist two-way causality between education and economicgrowth and between all levels of education and economic growth in case of bivariate TYAGC framework Education and alllevels of education do Granger cause economic growth in the presence of real physical capital as a third variable while economicgrowth causes all the indicators of education except college education professional college education and educationalexpenditures in the presence of real physical capital as a third variable in case of trivariate causality analysis In the presence oflabour force as a third variable feedback causality exists between education and economic growth and between all levels ofeducation and economic growth The results of tetravariate TYAGC Test indicate that education and all level of education doGranger cause economic growth while economic growth does Granger cause majority of the indicators of education (ie sevenout of ten) Economic growth does not Granger cause university education higher education including professional educationand expenditures on education The rise in university education higher education including professional education andexpenditures on education were considered as the key indicators to gauge human and social progress Economic growth doesnot seem to affect important educational indicators like university education higher education including professionaleducation and expenditures on education This seems to be consistent with Easterlyrsquos findings Easterly (2001) said thatPakistan is a country that made little social progress for given rates of GDP Among all levels of education General highereducation causes economic growth highly and most significantly as was explored by Stengos and Aurangzeb (2008) The level ofconfidence of causing economic growth to school education found to be highest This study also confirms the long runrelationship between education and economic growth
On the basis of the results of this study it is recommended that the government should focus more on higher educationparticularly to university education More funds should be allocated to education in line with others sectors particularly touniversity and higher education levels so that the economic growth can be further accelerated This will in turn leads tofurther education and hence development Poor should be facilitated to get higher education so that the polarization inhigher education may further be minimized Primary schooling should also be given priority because primary educationserves as an input for all higher levels of education The inverted educational expenditure pyramid may also be taken intoaccount Since the role of labour force seems to be very important in understanding the relationship between education andeconomic growth so it is suggested that labour force should be given more chances to enhance their skills The variablelabour force must be included while examining the causality between education and economic growth It is alsorecommended that the nexus between education and economic growth with inclusion of other variables other than physicalcapital and labour force should further be tested and generalized
Appendix A
Table I
Bivariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Bivariate-RGDPt and Eduit
Eq (1) Edu1t does not Granger cause RGDPt 028998 [0089] 1 Reject H0
Edu2t does not Granger cause RGDPt 144869 [0000] 1 Reject H0
Edu3t does not Granger cause RGDPt 043243 [0038] 1 Reject H0
Edu4t does not Granger cause RGDPt 039797 [0046] 1 Reject H0
Table I (Continued )
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Edu5t does not Granger cause RGDPt 217739 [0000] 1 Reject H0
Edu6t does not Granger cause RGDPt 137788 [0000] 1 Reject H0
Edu7t does not Granger cause RGDPt 126682 [0000] 1 Reject H0
Edu8t does not Granger cause RGDPt 041335 [0042] 1 Reject H0
Edu9t does not Granger cause RGDPt 160963 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 028642 [0091] 1 Reject H0
Eq (2) RGDPt does not Granger cause Edu1t 260926 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 230094 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 085441 [0003] 1 Reject H0
RGDPt does not Granger cause Edu4t 107403 [0001] 1 Reject H0
RGDPt does not Granger cause Edu5t 028935 [0089] 1 Reject H0
RGDPt does not Granger cause Edu6t 270343 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 273974 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 003162 [0574] 1 Cannot reject H0
RGDPt does not Granger cause Edu9t 027588 [0097] 1 Reject H0
RGDPt does not Granger cause Edu10t 000851 [0770] 1 Cannot reject H0
Bivariate-RGDPt and RPCt
Eq (3) RPCt does not Granger cause RGDPt 054972 [0019] 1 Reject H0
Eq (4) RGDPt does not Granger cause RPCt 167511 [0000] 1 Reject H0
Bivariate-RGDPt and LFt
Eq (5) LFt does not Granger cause RGDPt 227888 [0000] 1 Reject H0
Eq (6) RGDPt does not Granger cause LFt 012380 [0266] 1 Cannot reject H0
Bivariate-Eduit and RPCt
Eq (7) Edu1t does not Granger cause RPCt 094596 [0002] 1 Reject H0
Edu2t does not Granger cause RPCt 015434 [0214] 1 Cannot reject H0
Edu3t does not Granger cause RPCt 038233 [0051] 1 Reject H0
Edu4t does not Granger cause RPCt 000506 [0822] 1 Cannot reject H0
Edu5t does not Granger cause RPCt 298085 [0000] 1 Reject H0
Edu6t does not Granger cause RPCt 018289 [0176] 1 Cannot reject H0
Edu7t does not Granger cause RPCt 018976 [0168] 1 Cannot reject H0
Edu8t does not Granger cause RPCt 176399 [0000] 1 Reject H0
Edu9t does not Granger cause RPCt 224647 [0000] 1 Reject H0
Edu10t does not Granger cause RPCt 039174 [0048] 1 Reject H0
Eq (8) RPCt does not Granger cause Edu1t 091477 [0002] 1 Reject H0
RPCt does not Granger cause Edu2t 098821 [0002] 1 Reject H0
RPCt does not Granger cause Edu3t 066148 [0010] 1 Reject H0
RPCt does not Granger cause Edu4t 084218 [0004] 1 Reject H0
RPCt does not Granger cause Edu5t 001684 [0682] 1 Cannot reject H0
RPCt does not Granger cause Edu6t 107553 [0001] 1 Reject H0
RPCt does not Granger cause Edu7t 108798 [0001] 1 Reject H0
RPCt does not Granger cause Edu8t 004283 [0513] 1 Cannot reject H0
RPCt does not Granger cause Edu9t 005627 [0453] 1 Cannot reject H0
RPCt does not Granger cause Edu10t 000417 [0838] 1 Cannot reject H0
Bivariate-Eduit and LFt
Eq (9) Edu1t does not Granger cause LFt 026469 [0104] 1 Reject H0
Edu2t does not Granger cause LFt 012355 [0266] 1 Cannot reject H0
Edu3t does not Granger cause LFt 020468 [0153] 1 Cannot reject H0
Edu4t does not Granger cause LFt 098042 [0002] 1 Reject H0
Edu5t does not Granger cause LFt 049986 [0025] 1 Reject H0
Edu6t does not Granger cause LFt 016896 [0194] 1 Cannot reject H0
Edu7t does not Granger cause LFt 015167 [0218] 1 Cannot reject H0
Edu8t does not Granger cause LFt 184475 [0000] 1 Reject H0
Edu9t does not Granger cause LFt 003986 [0528] 1 Cannot reject H0
Edu10t does not Granger cause LFt 010899 [0296] 1 Cannot reject H0
Eq (10) LFt does not Granger cause Edu1t 107709 [0001] 1 Reject H0
LFt does not Granger cause Edu2t 071204 [0008] 1 Reject H0
LFt does not Granger cause Edu3t 136419 [0000] 1 Reject H0
LFt does not Granger cause Edu4t 056225 [0018] 1 Reject H0
LFt does not Granger cause Edu5t 057141 [0017] 1 Reject H0
LFt does not Granger cause Edu6t 091531 [0002] 1 Reject H0
LFt does not Granger cause Edu7t 095063 [0002] 1 Reject H0
LFt does not Granger cause Edu8t 021313 [0144] 1 Cannot reject H0
LFt does not Granger cause Edu9t 069389 [0008] 1 Reject H0
LFt does not Granger cause Edu10t 000743 [0785] 1 Cannot reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335330
Table II
Trivariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Trivariate-RGDPt RPCt and Eduit
Eq (11) Edu1t does not Granger cause RGDPt 005481 [0459] 1 Cannot reject H0
Edu2t does not Granger cause RGDPt 105415 [0001] 1 Reject H0
Edu3t does not Granger cause RGDPt 030370 [0081] 1 Reject H0
Edu4t does not Granger cause RGDPt 022525 [0133] 1 Cannot reject H0
Edu5t does not Granger cause RGDPt 227510 [0000] 1 Reject H0
Edu6t does not Granger cause RGDPt 098494 [0002] 1 Reject H0
Edu7t does not Granger cause RGDPt 090460 [0003] 1 Reject H0
Edu8t does not Granger cause RGDPt 067381 [0009] 1 Reject H0
Edu9t does not Granger cause RGDPt 168617 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 085842 [0003] Reject H0
Eq (11a) RPCt does not Granger cause RGDP (Edu1 as a 3rd variable) 029029 [0088] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu2 as a 3rd variable) 024880 [0115] 1 Cannot reject H0
RPCt does not Granger cause RGDPt (Edu3t as a 3rd variable) 041380 [0042] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu4t as a 3rd variable) 036580 [0056] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu5t as a 3rd variable) 064811 [0011] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu6t as a 3rd variable) 024405 [0118] 1 Cannot reject H0
RPCt does not Granger cause RGDPt (Edu7t as a 3rd variable) 026008 [0107] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu8t as a 3rd variable) 081607 [0004] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu9t as a 3rd variable) 063133 [0012] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu10t as a 3rd variable) 115637 [0001] 1 Reject H0
Eq (12) RGDPt does not Granger cause Edu1t 176454 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 129776 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 018626 [0172] 1 Cannot reject H0
RGDPt does not Granger cause Edu4t 020449 [0153] 1 Cannot reject H0
RGDPt does not Granger cause Edu5t 144658 [0000] 1 Reject H0
RGDPt does not Granger cause Edu6t 175431 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 178356 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 042497 [0039] 1 Reject H0
RGDPt does not Granger cause Edu9t 082506 [0004] 1 Reject H0
RGDPt does not Granger cause Edu10t 008026 [0370] 1 Cannot reject H0
Eq (12a) RPCt does not Granger cause Edu1t 000122 [0912] 1 Cannot reject H0
RPCt does not Granger cause Edu2t 028750 [0090] 1 Reject H0
RPCt does not Granger cause Edu3t 058586 [0016] 1 Reject H0
RPCt does not Granger cause Edu4t 071372 [0008] 1 Reject H0
RPCt does not Granger cause Edu5t 302364 [0000] 1 Reject H0
RPCt does not Granger cause Edu6t 020474 [0152] 1 Cannot reject H0
RPCt does not Granger cause Edu7t 017533 [0185] 1 Cannot reject H0
RPCt does not Granger cause Edu8t 044926 [0034] 1 Reject H0
RPCt does not Granger cause Edu9t 240955 [0000] 1 Reject H0
RPCt does not Granger cause Edu10t 021006 [0147] 1 Cannot reject H0
Eq (13) RGDPt does not Granger cause RPCt (Edu1t as a 3rd variable) 055095 [0019] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu2t as a 3rd variable) 182287 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu3t as a 3rd variable) 191499 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu4t as a 3rd variable) 269133 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu5t as a 3rd variable) 172979 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu6t as a 3rd variable) 166347 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu7t as a 3rd variable) 161198 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu8t as a 3rd variable) 038521 [0050] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu9tas a 3rd variable) 183169 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu10t as a 3rd variable) 139552 [0000] 1 Reject H0
Eq (13a) Edu1t does not Granger cause RPCt 000122 [0912] 1 Cannot reject H0
Edu2t does not Granger cause RPCt 028750 [0090] 1 Reject H0
Edu3t does not Granger cause RPCt 058586 [0016] 1 Reject H0
Edu4t does not Granger cause RPCt 071372 [0008] 1 Reject H0
Edu5t does not Granger cause RPCt 302364 [0000] 1 Reject H0
Edu6t does not Granger cause RPCt 020474 [0152] 1 Cannot reject H0
Edu7t does not Granger cause RPCt 017533 [0185] 1 Cannot reject H0
Edu8t does not Granger cause RPCt 044926 [0034] 1 Reject H0
Edu9t does not Granger cause RPCt 240955 [0000] 1 Reject H0
Edu10t does not Granger cause RPCt 021006 [0147] 1 Cannot reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 331
Table III
Trivariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Trivariate-RGDPt LFt and Eduit
Eq (14) Edu1t does not Granger cause RGDPt 068472 [0009] 1 Reject H0
Edu2t does not Granger cause RGDPt 092326 [0002] 1 Reject H0
Edu3t does not Granger cause RGDPt 180477 [0000] 1 Reject H0
Edu4t does not Granger cause RGDPt 132070 [0000] 1 Reject H0
Edu5t does not Granger cause RGDPt 109716 [0001] 1 Reject H0
Edu6t does not Granger cause RGDPt 086017 [0003] 1 Reject H0
Edu7t does not Granger cause RGDPt 078604 [0005] 1 Reject H0
Edu8t does not Granger cause RGDPt 020470 [0153] 1 Cannot reject H0
Edu9t does not Granger cause RGDPt 293293 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 005754 [0448] 1 Cannot reject H0
Eq (14a) LFt does not Granger cause RGDPt (Edu1t as a 3rd variable) 409533 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu2t as a 3rd variable) 332636 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu3t as a 3rd variable) 701171 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu4t as a 3rd variable) 605496 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu5t as a 3rd variable) 240867 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu6t as a 3rd variable) 330495 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu7t as a 3rd variable) 332860 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu8t as a 3rd variable) 352003 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu9t as a 3rd variable) 573087 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu10t as a 3rd variable) 343199 [0000] 1 Reject H0
Eq (15) RGDPt does not Granger cause Edu1t 134939 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 804323 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 109273 [0001] 1 Reject H0
RGDPt does not Granger cause Edu4t 278785 [0000] 1 Reject H0
RGDPt does not Granger cause Edu5t 050547 [0025] 1 Reject H0
RGDPt does not Granger cause Edu6t 790307 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 738342 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 043402 [0037] 1 Reject H0
RGDPt does not Granger cause Edu9t 175731 [0000] 1 Reject H0
RGDPt does not Granger cause Edu10t 061709 [0013] 1 Reject H0
Eq (15a) LFt does not Granger cause Edu1t 009324 [0334] 1 Cannot reject H0
LFt does not Granger cause Edu2t 377339 [0000] 1 Reject H0
LFt does not Granger cause Edu3t 176565 [0000] 1 Reject H0
LFt does not Granger cause Edu4t 180046 [0000] 1 Reject H0
LFt does not Granger cause Edu5t 091061 [0003] 1 Reject H0
LFt does not Granger cause Edu6t 355203 [0000] 1 Reject H0
LFt does not Granger cause Edu7t 327354 [0000] 1 Reject H0
LFt does not Granger cause Edu8t 053664 [0021] 1 Reject H0
LFt does not Granger cause Edu9t 251724 [0000] 1 Reject H0
LFt does not Granger cause Edu10t 060787 [0014] 1 Reject H0
Eq (16) Edu1t does not Granger cause LFt 036697 [0055] 1 Reject H0
Edu2t does not Granger cause LFt 004605 [0497] 1 Cannot reject H0
Edu3t does not Granger cause LFt 093988 [0002] 1 Reject H0
Edu4t does not Granger cause LFt 177287 [0000] 1 Reject H0
Edu5t does not Granger cause LFt 059203 [0015] 1 Reject H0
Edu6t does not Granger cause LFt 007202 [0396] 1 Cannot reject H0
Edu7t does not Granger cause LFt 005520 [0458] 1 Cannot reject H0
Edu8t does not Granger cause LFt 241662 [0000] 1 Reject H0
Edu9t does not Granger cause LFt 004009 [0527] 1 Cannot reject H0
Edu10t does not Granger cause LFt 058477 [0016] 1 Reject H0
Eq (16a) RGDPt does not Granger cause LFt (Edu1t as a 3rd variable) 002436 [0622] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu2t as a 3rd variable) 004276 [0513] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu3t as a 3rd variable) 047690 [0029] 1 Reject H0
RGDPt does not Granger cause LFt (Edu4t as a 3rd variable) 015207 [0218] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu5t as a 3rd variable) 040757 [0044] 1 Reject H0
RGDPt does not Granger cause LFt (Edu6t as a 3rd variable) 003392 [0560] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu7t as a 3rd variable) 004309 [0512] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu8t as a 3rd variable) 003145 [0575] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu9t as a 3rd variable) 017426 [0187] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu10t as a 3rd variable) 048448 [0028] 1 Reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335332
Table IV
Tetravariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Tetravariate-RGDPt RPCt LFt and Edut
Eq (17) Edu1t does not Granger cause RGDPt 029350 [0087] 1 Reject H0
Edu2t does not Granger cause RGDPt 065661 [0010] 1 Reject H0
Edu3t does not Granger cause RGDPt 097521 [0002] 1 Reject H0
Edu4t does not Granger cause RGDPt 071590 [0007] 1 Reject H0
Edu5t does not Granger cause RGDPt 116263 [0001] 1 Reject H0
Edu6t does not Granger cause RGDPt 059569 [0015] 1 Reject H0
Edu7t does not Granger cause RGDPt 054327 [0020] 1 Reject H0
Edu8t does not Granger cause RGDPt 040033 [0045] 1 Reject H0
Edu9t does not Granger cause RGDPt 195734 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 034374 [0064] 1 Reject H0
Eq (17a) LFt does not Granger cause RGDPt (Edut = Edu1) 251518 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu2) 165581 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu3) 316418 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu4) 289993 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu5) 109302 [0001] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu6) 165606 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu7) 168037 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu8) 176645 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu9) 247435 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu10) 146998 [0000] 1 Reject H0
Eq (17b) RPCt does not Granger cause RGDPt (Edut = Edu1) 042975 [0038] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu2) 039280 [0047] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu3) 034296 [0064] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu4) 027068 [0100] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu5) 062858 [0012] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu6) 039537 [0047] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu7) 040022 [0045] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu8) 045487 [0033] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu9) 068323 [0009] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu10) 083479 [0004] 1 Reject H0
Eq (18) RGDPt does not Granger cause Edu1t 150200 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 633103 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 045767 [0032] 1 Reject H0
RGDPt does not Granger cause Edu4t 122392 [0000] 1 Reject H0
RGDPt does not Granger cause Edu5t 004235 [0515] 1 Cannot reject H0
RGDPt does not Granger cause Edu6t 453644 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 418611 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 055973 [0454] 1 Cannot reject H0
RGDPt does not Granger cause Edu9t 053890 [0020] 1 Reject H0
RGDPt does not Granger cause Edu10t 011119 [0292] 1 Cannot reject H0
Eq (18a) LFt does not Granger cause Edu1t 006023 [0438] 1 Cannot reject H0
LFt does not Granger cause Edu2t 364559 [0000] 1 Reject H0
LFt does not Granger cause Edu3t 197423 [0000] 1 Reject H0
LFt does not Granger cause Edu4t 166511 [0000] 1 Reject H0
LFt does not Granger cause Edu5t 383886 [0000] 1 Reject H0
LFt does not Granger cause Edu6t 359377 [0000] 1 Reject H0
LFt does not Granger cause Edu7t 328249 [0000] 1 Reject H0
LFt does not Granger cause Edu8t 135310 [0000] 1 Reject H0
LFt does not Granger cause Edu9t 630068 [0000] 1 Reject H0
LFt does not Granger cause Edu01t 109365 [0001] 1 Reject H0
Eq (18b) RPCt does not Granger cause Edu1t 114248 [0001] 1 Reject H0
RPCt does not Granger cause Edu2t 036828 [0055] 1 Reject H0
RPCt does not Granger cause Edu3t 021023 [0147] 1 Cannot reject H0
RPCt does not Granger cause Edu4t 000484 [0826] 1 Cannot reject H0
RPCt does not Granger cause Edu5t 610934 [0000] 1 Reject H0
RPCt does not Granger cause Edu6t 070279 [0008] 1 Reject H0
RPCt does not Granger cause Edu7t 051166 [0024] 1 Reject H0
RPCt does not Granger cause Edu8t 167481 [0000] 1 Reject H0
RPCt does not Granger cause Edu9t 335271 [0000] 1 Reject H0
RPCt does not Granger cause Edu10t 067481 [0009] 1 Reject H0
Eq (19) Edu1 does not Granger cause RPCt 005154 [0473] 1 Cannot reject H0
Edu2 does not Granger cause RPCt 011954 [0274] 1 Cannot reject H0
Edu3 does not Granger cause RPCt 162365 [0000] 1 Reject H0
Edu4 does not Granger cause RPCt 148964 [0000] 1 Reject H0
Edu5 does not Granger cause RPCt 243978 [0000] 1 Reject H0
Edu6 does not Granger cause RPCt 040262 [0045] 1 Reject H0
Edu7 does not Granger cause RPCt 035138 [0061] 1 Reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 333
able IV (Continued )
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Edu8 does not Granger cause RPCt 030100 [0083] 1 Reject H0
Edu9 does not Granger cause RPCt 462564 [0000] 1 Reject H0
Edu10 does not Granger cause RPCt 009580 [0328] 1 Cannot reject H0
Eq (19a) RGDPt does not Granger cause RPCt (Edu1t as a 3rd variable) 009936 [0319] 1 Cannot reject H0
RGDPt does not Granger cause RPCt (Edu2t as a 3rd variable) 039369 [0047] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu3t as a 3rd variable) 003822 [0536] 1 Cannot reject H0
RGDPt does not Granger cause RPCt (Edu4t as a 3rd variable) 028000 [0094] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu5t as a 3rd variable) 039910 [0046] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu6t as a 3rd variable) 033500 [0067] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu7t as a 3rd variable) 029924 [0084] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu8t as a 3rd variable) 002803 [0597] 1 Cannot Reject H0
RGDPt does not Granger cause RPCt (Edu9t as a 3rd variable) 011416 [0285] 1 Cannot reject H0
RGDPt does not Granger cause RPCt (Edu10t as a 3rd variable) 006944 [0405] 1 Cannot reject H0
Eq (20) Edu1t does not Granger cause LFt 015302 [0216] 1 Cannot reject H0
Edu2t does not Granger cause LFt 001053 [0746] 1 Cannot reject H0
Edu3t does not Granger cause LFt 080072 [0005] 1 Reject H0
Edu4t does not Granger cause LFt 143854 [0000] 1 Reject H0
Edu5t does not Granger cause LFt 061159 [0013] 1 Reject H0
Edu6t does not Granger cause LFt 003113 [0577] 1 Cannot reject H0
Edu7t does not Granger cause LFt 002394 [0625] 1 Cannot reject H0
Edu8t does not Granger cause LFt 196804 [0000] 1 Reject H0
Edu9t does not Granger cause LFt 046285 [0496] 1 Cannot reject H0
Edu10t does not Granger cause LFt 04161 1 [0041] 1 Reject H0
Eq (20a) RGDPt does not Granger cause LFt (Edu1t as a 3rd variable) 006872 [0407] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu2t as a 3rd variable) 018604 [0173] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu3t as a 3rd variable) 066905 [0010] 1 Reject H0
RGDPt does not Granger cause LFt (Edu4t as a 3rd variable) 023249 [0127] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu5t as a 3rd variable) 070835 [0008] 1 Reject H0
RGDPt does not Granger cause LFt (Edu6t as a 3rd variable) 016501 [0199] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu7t as a 3rd variable) 018532 [0173] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu8t as a 3rd variable) 003730 [0541] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu9t as a 3rd variable) 039255 [0048] 1 Reject H0
RGDPt does not Granger cause LFt (Edu10t as a 3rd variable) 055266 [0019] 1 Reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335334
T
References
Abbas Q amp Peck J F (2008) Human capital and economic growth Pakistan 1960ndash2003 The Lahore Journal of Economics 13(1) 1ndash28Ayara N A (2002) The paradox of education and economic growth in Nigeria Empirical evidence The Nigerian Economic Society (NES) Pt 2 371ndash393Babatunde M A amp Adefabi R A (2005) Long run relationship between education and economic growth in Nigeria Evidence from the Johansenrsquos cointegration
approach Paper presented at the regional conference on education in West Africa Constraints and Opportunities Dakar Senegal November 1stndash2nd 2005Cornell UniversityCREAMinisterede lrsquoEducation du Senegal
Baldacci E Clements B Cui Q amp Gupta S (2005) What does it take to help the poor Finance and Development The Quarterly Magazine of the IMF 42(2)Changzheng Z Zhijian H amp Huaizu L (2007) An empirical study on education equity in China 1978ndash2004 Frontier in Economics of China 2(4) 536ndash544Chaudhary A R Asim I amp Gillani S Y M (2009) The nexus between higher education and economic growth An empirical investigation for Pakistan Pakistan
Journal of Commerce and Social Sciences 3Chaudhry I S Malik S amp Ashraf M (2006) Rural poverty in Pakistan Some related concepts issues and empirical analysis Pakistan Economic and Social Review
44(2) 259ndash276Diebolt C amp Litago J (1997) Education and economic growth in Germany before the Second World War An econometric analysis of dynamic relations Historical
Social Research 2(22) 132ndash149Easterly W (2001) The middle class consensus and economic development Journal of Economic Growth 6(4) 317ndash335Engle R F amp Granger C W J (1987) Cointegration and error correction Representation estimation and testing Econometrica 55 251ndash276Fernandez E amp Mauro P (2000) The role of human capital in economic growth The case of Spain (IMF Working Paper) International Monetary FundFrancis B amp Iyare S (2006) Education and development in the Caribbean A cointegration and causality approach Economics Bulletin 15(2) 1ndash13Galor O amp Moav O (2000) Das human capital Retrieved from httpeconpstcn brownedufacultygalorindexhtmlGoode R B (1959) Adding to the stock of physical and human capital American Economic Review 49(2) 147Government of Pakistan (1970ndash2009) Pakistan economic survey various issues Finance Division Islamabad Economic Advisorrsquos WingGregory A W amp Hansen B E (1996) Residual-based tests for cointegration in models with regime shifts Journal of Econometrics 70 99ndash126Grossman G M amp Helpman E (1991) Innovation and growth in the global economy Cambridge MIT PressGylfason T amp Zoega G (2003) Education social equality and economic growth A view of the landscape CESifo Economic Studies 49(4) 557ndash579Hassan S amp Ahmed H (2008) Educationrsquos contribution to the economic growth of sub-Saharan Africa Southwestern Economic Review 1(32) 175ndash190Islam T S Wadud M A amp Islam Q B T (2007) Relationship between education and GDP growth A multivariate causality analysis for Bangladesh Economics
Bulletin 3(35) 1ndash7Jin J C (2009) Economic research and economic growth Evidence from East Asian Economies Journal of Asian Economics 20 150ndash155Johansen S (1988) Statistical analysis of cointegration vectors Journal of Economic Dynamics and Control 12 231ndash254Johansen S amp Juselius K (1990) Maximum likelihood estimation and inference on cointegration with applications to the demand for money Oxford Bulletin of
Economics and Statistics 52 169ndash210Katırcıoglu S T (2009) Investigating higher-education-led growth hypothesis in a small Island Time series evidence from Northern Cyprus Paper presented at
Econ Anadolu 2009 Anadolu International Conference in Economics June 17ndash19 2009 TurkeyKhorasgani M F (2008) Higher education development and economic growth in Iran Education Business and Society Contemporary Middle Eastern Issues 1
162ndash174
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 335
Kui L (2005) The interactive causality between education and economic growth in China Retrieved from httppapersssrncomsol3paperscfmAbstrac-tid=920624
Loening J L (2004) Time series evidence on education and growth The case of Guatemala 1951ndash2002 Revista de Analisis Economico 19(2) 3ndash40Lucas R E (1988) On the mechanics of economic development Journal of Monetary Economics 22 3ndash42Macerinskiene I amp Vaiksnoraite B (2006) The role of higher education to economic development VadybaManagement 2(11)Mankiw N G Romer D amp Weil D N (1992) A contribution to the empirics of economic growth Quarterly Journal of Economics 107 407ndash437Momete D C (2007) Analysis of the relationship between employment and economic growth in Romania Fascicle of Management and Technological Engineering
VI(XVI)Morote E S (2000) Higher education employment and economic growth Mexico and Peru Retrieved from httpwwwamericanprofessororgdocumentation
lasapa perdocNarayan P K (2005) The saving and investment nexus for China Evidence from cointegration tests Applied Economics 37 1979ndash1990Permani R (2008) Education as a determinant of economic growth in East Asia Historical trends and empirical evidences (1965ndash2000) Retrieved from http
wwwuoweduaucommerceeconehsanzpdfsPermani202008pdfPesaran M H amp Pesaran B (1997) Working with Microfit 40 Interactive econometric analysis Oxford Oxford University PressPesaran M H amp Shin Y (1999) An autoregressive distributed lag modeling approach to cointegration analysis In S Strom (Ed) Econometrics and economic theory
in the 20th century Cambridge Cambridge University PressPesaran M H Shin Y amp Smith R J (2001) Bounds testing approaches to the analysis of level relationships Journal of Applied Econometrics 16 289ndash326Pradhan R P (2009) Education and economic growth in India Using error correction modeling International Research Journal of Finance and Economics 25Pritchett L (2001) Where has all the education gone The World Bank Economic Review 15(3)Quah D amp Rauch J E (1990) Openness and the rate of economic growth Journal Development of Studies 2(49) 307ndash335Rivera-Batiz L A amp Romer P M (1991) Economic integration and endogenous growth Quarterly Journal of Economics 106 531ndash555Romer P M (1986) Increasing returns and long run growth Journal of Political Economy 6(90) 1002ndash1037Romer P M (1989) Human capital and growth Theory and evidence (NBER Working Papers 3173) National Bureau of Economic Research IncRomer P M (1990) Endogenous technological change Journal of Political Economy 5(98) 71ndash101Rondinelli D amp Montgomery J (1995) Great policies Strategic innovations in Asia and the Pacific Basin Westport Praeger PublishingSaikkonen P amp Lutkepohl H (2000) Testing for the cointegration rank of a VAR process with structural shifts Journal of Business and Economic Statistics 18(4)
451ndash464Schultz T W (1961) Investment in human capital American Economic Review 51(1) 1State Bank of Pakistan (1972ndash2009) Annual reports Karachi SBP PressStengos T amp Aurangzeb A (2008) An empirical investigation of the relationship between education and growth in pakistan International Economic Journal 3
345ndash359 Retrieved from httpwwwinformaworldcomsmpptitledb=allcontent=t713685453tab=issueslistbranches=22-v2222Toda H Y amp Yamamoto T (1995) Statistical inference in vector autoregressive with possible integrated processes Journal of Econometrics 66 225ndash250United Nations (1997) Human Development Report New York Oxford University Press
- Education and economic growth in Pakistan A cointegration and causality analysis
-
- Introduction
- Review of literature
- Method and procedure
- Empirical results
-
- Unit root results
- Cointegration
- Toda-Yamamoto Augmented Granger Causality (TYAGC) Test
- Bivariate TYAGC framework
- Trivariate TYAGC framework
- Tetravariate TYAGC framework
- Figures in parentheses are p-values
-
- Conclusions and recommendations
-
- References
-
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335328
In conclusion education and all levels of education Granger cause RGDPt where as its revere ie Granger causalityrunning from RGDPt to education and all levels of education is only true in case of trivariate causality among RGDPt LFt andeducation From here one can easily conclude that the role of LFt as compared to RPCt is very important in understanding therelationship between education and RGDPt Feedback causality between education and RGDPt is also found in trivariate case
46 Tetravariate TYAGC framework
The tetravariate causality among RGDPt RPCt LFt and Eduit (Eqs (17)ndash(20)) was also estimated by using TYAGC techniqueand their results are presented in Table IV
RGDPt frac14 a17 thornX3
ifrac141
b17iRGDPti thornX3
ifrac141
g17iRPCti thornX3
ifrac141
l17iLFti thornX3
ifrac141
d17iEduiti thorn u17t (17)
Eduit frac14 a18 thornX3
ifrac141
b18iRGDPti thornX3
ifrac141
g18iRPCti thornX3
ifrac141
l18iLFti thornX3
ifrac141
d18iEduiti thorn u18t (18)
RPCt frac14 a19 thornX3
ifrac141
b19iRGDPti thornX3
ifrac141
g19iRPCti thornX3
ifrac141
l19iLFti thornX3
ifrac141
d19iEduiti thorn u19t (19)
LFt frac14 a20 thornX3
ifrac141
b20iRGDPti thornX3
ifrac141
g20iRPCti thornX3
ifrac141
l20iLFti thornX3
ifrac141
d20iEduiti thorn u20t (20)
The tetravariate TYAGC results presented in Table IV indicate that all the indicators of education Granger cause RGDPt whileRGDPt does Granger cause majority of the indicators of education (seven out of ten) RGDPt does not Granger cause Edu5t
(university education) Edu8t (higher education) and Edu10t (education expenditure) From this one can easily conclude thatthere exists two way causality between education and RGDPt in case of tetravariate causality analysis as have been the caseof bivariate and trivariate causality Regarding levels of education all levels of education (ie school education collegeeducation and university education) do Granger cause RGDPt while RGDPt does only cause school education and collegeeducation RGDPt does not Granger cause university education
LFt Granger causes RGDPt at 99 confidence level while RGDPt only Granger causes LFt in case of Edu3t Edu5t Edu9t andEdu10t In case of testing causality between RPCt and RGDPt in the presence of all indicators of education RPCt does Grangercause RGDPt and in reverse case RGDPt does not Granger cause RPCt in the presence of Edu1t Edu3t Edu8t Edu9t and Edu10tThese results show the unidirectional causality running from RPCt to RGDPt
The research hypothesis that LFt does not Granger cause Eduit is rejected at 99 confidence interval except wheneducation is measured by Eduit Labour force has been found to cause all levels of education On the other side education onlyGranger causes the LFt in the presence of Edu3t Edu4t Edu5t Edu8t and Edu10t RPC does not Granger cause education whenEdu3t and Edu4t are used as proxies of education All indicators of education except Edu1t Edu2t and Edu10t do Granger causeRPCt This implies that feedback causality between RPCt and education is observed
It can easily be concluded from the TYAGC results of Eq (17) in Table IV that among all levels of education General highereducation (Edu9t) causes RGDPt highly and most significantly (999 confidence level) The level of confidence of collegeeducation (Edu3t) and school education (Edu2t) causing RGDPt is found to be 2nd highest (significance at 997 confidencelevel) and 3rd highest (significance at 989 confidence level) respectively From Eq (18) in Table IV it can also be found thatthe level of confidence (999) of causing RGDPt to school education (Edu2t) is found to be highest
From the bivariate trivariate and tetravariate TYAGC tests results in Tables IndashIV the overall results of the study abouteducation and different levels of education (School College and University) are summarized in Table 4
Table 4
Causal nexus between education different levels of education with RGDPt
Hypothesis TYAGC procedure
Bivariate Trivariate Tetravariate
RGDPt and Edut RGDPt RPCt Edut RGDPt LFt Edut RGDPt LFt RPCt Edut
Education (Edu1t) does Granger cause RGDPt Yes (0089) No (0459) Yes (0009) Yes (0087)
RGDPt does Granger cause education (Edu1t) Yes (0000) Yes (0000) Yes (0000) Yes (0000)
School education (Edu2t) does Granger cause RGDPt Yes (0000) Yes (0001) Yes (0002) Yes (0010)
RGDPt does Granger cause school education (Edu2t) Yes (0000) Yes (0000) Yes (0000) Yes (0000)
College education (Edu3t) does Granger cause RGDPt Yes (0038) Yes (0081) Yes (0000) Yes (0002)
RGDPt does Granger cause college education (Edu3t) Yes (0003) No (0172) Yes (0001) Yes (0032)
University education (Edu5t) does Granger cause RGDPt Yes (0000) Yes (0000) Yes (0001) Yes (0001)
RGDPt does Granger cause university education (Edu5t) Yes (0089) Yes (0000) Yes (0025) No (0515)
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 329
47 Figures in parentheses are p-values
From the above results presented in Table 4 it can be concluded that there existed feedback causality between educationand RGDPt in all bivariate trivariate and tetravariate TYAGC causality cases All levels of education ie school educationcollege education and university education do Granger cause RGDPt in all causality cases RGDPt does Granger cause schooleducation in all causality cases RGDPt does Granger cause college education in all causality cases except trivariate causalitythat is running from RGDPt to education when RPCt serves as a third variable Table 4 also reveals that RGDPt does Grangercause university education only in a bivariate and trivariate causality cases RGDPt fails to Granger cause to universityeducation in tetravariate case
5 Conclusions and recommendations
This study aimed to explore the cointegration and causal relationship between education (measured by different indicatorsof education) and economic growth in Pakistan It is very essential for a country to invest more in education because it is one ofthe most important ingredients of human capital and hence economic development The nature and strength of the relationshipbetween education and economic growth is still not clear in case of Pakistan The main focus of this empirical study remained toobserve the causality and cointegration between education and economic growth in the absence and presence physical capitaland labour force Cointegration between education and economic growth was investigated using ARDL approach and the causallinkage between education and economic growth was examined in bivariate trivariate and tetravariate TYAGC frameworkDifferent indicators of education were utilized in this study to show the robustness of empirical results The causality betweeneducation and economic growth was examined in the presence and absence of stock of physical capital and stock of labour as athird and fourth variable The causality results indicate that there exist two-way causality between education and economicgrowth and between all levels of education and economic growth in case of bivariate TYAGC framework Education and alllevels of education do Granger cause economic growth in the presence of real physical capital as a third variable while economicgrowth causes all the indicators of education except college education professional college education and educationalexpenditures in the presence of real physical capital as a third variable in case of trivariate causality analysis In the presence oflabour force as a third variable feedback causality exists between education and economic growth and between all levels ofeducation and economic growth The results of tetravariate TYAGC Test indicate that education and all level of education doGranger cause economic growth while economic growth does Granger cause majority of the indicators of education (ie sevenout of ten) Economic growth does not Granger cause university education higher education including professional educationand expenditures on education The rise in university education higher education including professional education andexpenditures on education were considered as the key indicators to gauge human and social progress Economic growth doesnot seem to affect important educational indicators like university education higher education including professionaleducation and expenditures on education This seems to be consistent with Easterlyrsquos findings Easterly (2001) said thatPakistan is a country that made little social progress for given rates of GDP Among all levels of education General highereducation causes economic growth highly and most significantly as was explored by Stengos and Aurangzeb (2008) The level ofconfidence of causing economic growth to school education found to be highest This study also confirms the long runrelationship between education and economic growth
On the basis of the results of this study it is recommended that the government should focus more on higher educationparticularly to university education More funds should be allocated to education in line with others sectors particularly touniversity and higher education levels so that the economic growth can be further accelerated This will in turn leads tofurther education and hence development Poor should be facilitated to get higher education so that the polarization inhigher education may further be minimized Primary schooling should also be given priority because primary educationserves as an input for all higher levels of education The inverted educational expenditure pyramid may also be taken intoaccount Since the role of labour force seems to be very important in understanding the relationship between education andeconomic growth so it is suggested that labour force should be given more chances to enhance their skills The variablelabour force must be included while examining the causality between education and economic growth It is alsorecommended that the nexus between education and economic growth with inclusion of other variables other than physicalcapital and labour force should further be tested and generalized
Appendix A
Table I
Bivariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Bivariate-RGDPt and Eduit
Eq (1) Edu1t does not Granger cause RGDPt 028998 [0089] 1 Reject H0
Edu2t does not Granger cause RGDPt 144869 [0000] 1 Reject H0
Edu3t does not Granger cause RGDPt 043243 [0038] 1 Reject H0
Edu4t does not Granger cause RGDPt 039797 [0046] 1 Reject H0
Table I (Continued )
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Edu5t does not Granger cause RGDPt 217739 [0000] 1 Reject H0
Edu6t does not Granger cause RGDPt 137788 [0000] 1 Reject H0
Edu7t does not Granger cause RGDPt 126682 [0000] 1 Reject H0
Edu8t does not Granger cause RGDPt 041335 [0042] 1 Reject H0
Edu9t does not Granger cause RGDPt 160963 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 028642 [0091] 1 Reject H0
Eq (2) RGDPt does not Granger cause Edu1t 260926 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 230094 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 085441 [0003] 1 Reject H0
RGDPt does not Granger cause Edu4t 107403 [0001] 1 Reject H0
RGDPt does not Granger cause Edu5t 028935 [0089] 1 Reject H0
RGDPt does not Granger cause Edu6t 270343 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 273974 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 003162 [0574] 1 Cannot reject H0
RGDPt does not Granger cause Edu9t 027588 [0097] 1 Reject H0
RGDPt does not Granger cause Edu10t 000851 [0770] 1 Cannot reject H0
Bivariate-RGDPt and RPCt
Eq (3) RPCt does not Granger cause RGDPt 054972 [0019] 1 Reject H0
Eq (4) RGDPt does not Granger cause RPCt 167511 [0000] 1 Reject H0
Bivariate-RGDPt and LFt
Eq (5) LFt does not Granger cause RGDPt 227888 [0000] 1 Reject H0
Eq (6) RGDPt does not Granger cause LFt 012380 [0266] 1 Cannot reject H0
Bivariate-Eduit and RPCt
Eq (7) Edu1t does not Granger cause RPCt 094596 [0002] 1 Reject H0
Edu2t does not Granger cause RPCt 015434 [0214] 1 Cannot reject H0
Edu3t does not Granger cause RPCt 038233 [0051] 1 Reject H0
Edu4t does not Granger cause RPCt 000506 [0822] 1 Cannot reject H0
Edu5t does not Granger cause RPCt 298085 [0000] 1 Reject H0
Edu6t does not Granger cause RPCt 018289 [0176] 1 Cannot reject H0
Edu7t does not Granger cause RPCt 018976 [0168] 1 Cannot reject H0
Edu8t does not Granger cause RPCt 176399 [0000] 1 Reject H0
Edu9t does not Granger cause RPCt 224647 [0000] 1 Reject H0
Edu10t does not Granger cause RPCt 039174 [0048] 1 Reject H0
Eq (8) RPCt does not Granger cause Edu1t 091477 [0002] 1 Reject H0
RPCt does not Granger cause Edu2t 098821 [0002] 1 Reject H0
RPCt does not Granger cause Edu3t 066148 [0010] 1 Reject H0
RPCt does not Granger cause Edu4t 084218 [0004] 1 Reject H0
RPCt does not Granger cause Edu5t 001684 [0682] 1 Cannot reject H0
RPCt does not Granger cause Edu6t 107553 [0001] 1 Reject H0
RPCt does not Granger cause Edu7t 108798 [0001] 1 Reject H0
RPCt does not Granger cause Edu8t 004283 [0513] 1 Cannot reject H0
RPCt does not Granger cause Edu9t 005627 [0453] 1 Cannot reject H0
RPCt does not Granger cause Edu10t 000417 [0838] 1 Cannot reject H0
Bivariate-Eduit and LFt
Eq (9) Edu1t does not Granger cause LFt 026469 [0104] 1 Reject H0
Edu2t does not Granger cause LFt 012355 [0266] 1 Cannot reject H0
Edu3t does not Granger cause LFt 020468 [0153] 1 Cannot reject H0
Edu4t does not Granger cause LFt 098042 [0002] 1 Reject H0
Edu5t does not Granger cause LFt 049986 [0025] 1 Reject H0
Edu6t does not Granger cause LFt 016896 [0194] 1 Cannot reject H0
Edu7t does not Granger cause LFt 015167 [0218] 1 Cannot reject H0
Edu8t does not Granger cause LFt 184475 [0000] 1 Reject H0
Edu9t does not Granger cause LFt 003986 [0528] 1 Cannot reject H0
Edu10t does not Granger cause LFt 010899 [0296] 1 Cannot reject H0
Eq (10) LFt does not Granger cause Edu1t 107709 [0001] 1 Reject H0
LFt does not Granger cause Edu2t 071204 [0008] 1 Reject H0
LFt does not Granger cause Edu3t 136419 [0000] 1 Reject H0
LFt does not Granger cause Edu4t 056225 [0018] 1 Reject H0
LFt does not Granger cause Edu5t 057141 [0017] 1 Reject H0
LFt does not Granger cause Edu6t 091531 [0002] 1 Reject H0
LFt does not Granger cause Edu7t 095063 [0002] 1 Reject H0
LFt does not Granger cause Edu8t 021313 [0144] 1 Cannot reject H0
LFt does not Granger cause Edu9t 069389 [0008] 1 Reject H0
LFt does not Granger cause Edu10t 000743 [0785] 1 Cannot reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335330
Table II
Trivariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Trivariate-RGDPt RPCt and Eduit
Eq (11) Edu1t does not Granger cause RGDPt 005481 [0459] 1 Cannot reject H0
Edu2t does not Granger cause RGDPt 105415 [0001] 1 Reject H0
Edu3t does not Granger cause RGDPt 030370 [0081] 1 Reject H0
Edu4t does not Granger cause RGDPt 022525 [0133] 1 Cannot reject H0
Edu5t does not Granger cause RGDPt 227510 [0000] 1 Reject H0
Edu6t does not Granger cause RGDPt 098494 [0002] 1 Reject H0
Edu7t does not Granger cause RGDPt 090460 [0003] 1 Reject H0
Edu8t does not Granger cause RGDPt 067381 [0009] 1 Reject H0
Edu9t does not Granger cause RGDPt 168617 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 085842 [0003] Reject H0
Eq (11a) RPCt does not Granger cause RGDP (Edu1 as a 3rd variable) 029029 [0088] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu2 as a 3rd variable) 024880 [0115] 1 Cannot reject H0
RPCt does not Granger cause RGDPt (Edu3t as a 3rd variable) 041380 [0042] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu4t as a 3rd variable) 036580 [0056] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu5t as a 3rd variable) 064811 [0011] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu6t as a 3rd variable) 024405 [0118] 1 Cannot reject H0
RPCt does not Granger cause RGDPt (Edu7t as a 3rd variable) 026008 [0107] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu8t as a 3rd variable) 081607 [0004] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu9t as a 3rd variable) 063133 [0012] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu10t as a 3rd variable) 115637 [0001] 1 Reject H0
Eq (12) RGDPt does not Granger cause Edu1t 176454 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 129776 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 018626 [0172] 1 Cannot reject H0
RGDPt does not Granger cause Edu4t 020449 [0153] 1 Cannot reject H0
RGDPt does not Granger cause Edu5t 144658 [0000] 1 Reject H0
RGDPt does not Granger cause Edu6t 175431 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 178356 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 042497 [0039] 1 Reject H0
RGDPt does not Granger cause Edu9t 082506 [0004] 1 Reject H0
RGDPt does not Granger cause Edu10t 008026 [0370] 1 Cannot reject H0
Eq (12a) RPCt does not Granger cause Edu1t 000122 [0912] 1 Cannot reject H0
RPCt does not Granger cause Edu2t 028750 [0090] 1 Reject H0
RPCt does not Granger cause Edu3t 058586 [0016] 1 Reject H0
RPCt does not Granger cause Edu4t 071372 [0008] 1 Reject H0
RPCt does not Granger cause Edu5t 302364 [0000] 1 Reject H0
RPCt does not Granger cause Edu6t 020474 [0152] 1 Cannot reject H0
RPCt does not Granger cause Edu7t 017533 [0185] 1 Cannot reject H0
RPCt does not Granger cause Edu8t 044926 [0034] 1 Reject H0
RPCt does not Granger cause Edu9t 240955 [0000] 1 Reject H0
RPCt does not Granger cause Edu10t 021006 [0147] 1 Cannot reject H0
Eq (13) RGDPt does not Granger cause RPCt (Edu1t as a 3rd variable) 055095 [0019] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu2t as a 3rd variable) 182287 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu3t as a 3rd variable) 191499 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu4t as a 3rd variable) 269133 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu5t as a 3rd variable) 172979 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu6t as a 3rd variable) 166347 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu7t as a 3rd variable) 161198 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu8t as a 3rd variable) 038521 [0050] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu9tas a 3rd variable) 183169 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu10t as a 3rd variable) 139552 [0000] 1 Reject H0
Eq (13a) Edu1t does not Granger cause RPCt 000122 [0912] 1 Cannot reject H0
Edu2t does not Granger cause RPCt 028750 [0090] 1 Reject H0
Edu3t does not Granger cause RPCt 058586 [0016] 1 Reject H0
Edu4t does not Granger cause RPCt 071372 [0008] 1 Reject H0
Edu5t does not Granger cause RPCt 302364 [0000] 1 Reject H0
Edu6t does not Granger cause RPCt 020474 [0152] 1 Cannot reject H0
Edu7t does not Granger cause RPCt 017533 [0185] 1 Cannot reject H0
Edu8t does not Granger cause RPCt 044926 [0034] 1 Reject H0
Edu9t does not Granger cause RPCt 240955 [0000] 1 Reject H0
Edu10t does not Granger cause RPCt 021006 [0147] 1 Cannot reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 331
Table III
Trivariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Trivariate-RGDPt LFt and Eduit
Eq (14) Edu1t does not Granger cause RGDPt 068472 [0009] 1 Reject H0
Edu2t does not Granger cause RGDPt 092326 [0002] 1 Reject H0
Edu3t does not Granger cause RGDPt 180477 [0000] 1 Reject H0
Edu4t does not Granger cause RGDPt 132070 [0000] 1 Reject H0
Edu5t does not Granger cause RGDPt 109716 [0001] 1 Reject H0
Edu6t does not Granger cause RGDPt 086017 [0003] 1 Reject H0
Edu7t does not Granger cause RGDPt 078604 [0005] 1 Reject H0
Edu8t does not Granger cause RGDPt 020470 [0153] 1 Cannot reject H0
Edu9t does not Granger cause RGDPt 293293 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 005754 [0448] 1 Cannot reject H0
Eq (14a) LFt does not Granger cause RGDPt (Edu1t as a 3rd variable) 409533 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu2t as a 3rd variable) 332636 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu3t as a 3rd variable) 701171 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu4t as a 3rd variable) 605496 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu5t as a 3rd variable) 240867 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu6t as a 3rd variable) 330495 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu7t as a 3rd variable) 332860 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu8t as a 3rd variable) 352003 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu9t as a 3rd variable) 573087 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu10t as a 3rd variable) 343199 [0000] 1 Reject H0
Eq (15) RGDPt does not Granger cause Edu1t 134939 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 804323 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 109273 [0001] 1 Reject H0
RGDPt does not Granger cause Edu4t 278785 [0000] 1 Reject H0
RGDPt does not Granger cause Edu5t 050547 [0025] 1 Reject H0
RGDPt does not Granger cause Edu6t 790307 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 738342 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 043402 [0037] 1 Reject H0
RGDPt does not Granger cause Edu9t 175731 [0000] 1 Reject H0
RGDPt does not Granger cause Edu10t 061709 [0013] 1 Reject H0
Eq (15a) LFt does not Granger cause Edu1t 009324 [0334] 1 Cannot reject H0
LFt does not Granger cause Edu2t 377339 [0000] 1 Reject H0
LFt does not Granger cause Edu3t 176565 [0000] 1 Reject H0
LFt does not Granger cause Edu4t 180046 [0000] 1 Reject H0
LFt does not Granger cause Edu5t 091061 [0003] 1 Reject H0
LFt does not Granger cause Edu6t 355203 [0000] 1 Reject H0
LFt does not Granger cause Edu7t 327354 [0000] 1 Reject H0
LFt does not Granger cause Edu8t 053664 [0021] 1 Reject H0
LFt does not Granger cause Edu9t 251724 [0000] 1 Reject H0
LFt does not Granger cause Edu10t 060787 [0014] 1 Reject H0
Eq (16) Edu1t does not Granger cause LFt 036697 [0055] 1 Reject H0
Edu2t does not Granger cause LFt 004605 [0497] 1 Cannot reject H0
Edu3t does not Granger cause LFt 093988 [0002] 1 Reject H0
Edu4t does not Granger cause LFt 177287 [0000] 1 Reject H0
Edu5t does not Granger cause LFt 059203 [0015] 1 Reject H0
Edu6t does not Granger cause LFt 007202 [0396] 1 Cannot reject H0
Edu7t does not Granger cause LFt 005520 [0458] 1 Cannot reject H0
Edu8t does not Granger cause LFt 241662 [0000] 1 Reject H0
Edu9t does not Granger cause LFt 004009 [0527] 1 Cannot reject H0
Edu10t does not Granger cause LFt 058477 [0016] 1 Reject H0
Eq (16a) RGDPt does not Granger cause LFt (Edu1t as a 3rd variable) 002436 [0622] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu2t as a 3rd variable) 004276 [0513] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu3t as a 3rd variable) 047690 [0029] 1 Reject H0
RGDPt does not Granger cause LFt (Edu4t as a 3rd variable) 015207 [0218] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu5t as a 3rd variable) 040757 [0044] 1 Reject H0
RGDPt does not Granger cause LFt (Edu6t as a 3rd variable) 003392 [0560] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu7t as a 3rd variable) 004309 [0512] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu8t as a 3rd variable) 003145 [0575] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu9t as a 3rd variable) 017426 [0187] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu10t as a 3rd variable) 048448 [0028] 1 Reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335332
Table IV
Tetravariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Tetravariate-RGDPt RPCt LFt and Edut
Eq (17) Edu1t does not Granger cause RGDPt 029350 [0087] 1 Reject H0
Edu2t does not Granger cause RGDPt 065661 [0010] 1 Reject H0
Edu3t does not Granger cause RGDPt 097521 [0002] 1 Reject H0
Edu4t does not Granger cause RGDPt 071590 [0007] 1 Reject H0
Edu5t does not Granger cause RGDPt 116263 [0001] 1 Reject H0
Edu6t does not Granger cause RGDPt 059569 [0015] 1 Reject H0
Edu7t does not Granger cause RGDPt 054327 [0020] 1 Reject H0
Edu8t does not Granger cause RGDPt 040033 [0045] 1 Reject H0
Edu9t does not Granger cause RGDPt 195734 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 034374 [0064] 1 Reject H0
Eq (17a) LFt does not Granger cause RGDPt (Edut = Edu1) 251518 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu2) 165581 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu3) 316418 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu4) 289993 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu5) 109302 [0001] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu6) 165606 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu7) 168037 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu8) 176645 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu9) 247435 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu10) 146998 [0000] 1 Reject H0
Eq (17b) RPCt does not Granger cause RGDPt (Edut = Edu1) 042975 [0038] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu2) 039280 [0047] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu3) 034296 [0064] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu4) 027068 [0100] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu5) 062858 [0012] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu6) 039537 [0047] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu7) 040022 [0045] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu8) 045487 [0033] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu9) 068323 [0009] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu10) 083479 [0004] 1 Reject H0
Eq (18) RGDPt does not Granger cause Edu1t 150200 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 633103 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 045767 [0032] 1 Reject H0
RGDPt does not Granger cause Edu4t 122392 [0000] 1 Reject H0
RGDPt does not Granger cause Edu5t 004235 [0515] 1 Cannot reject H0
RGDPt does not Granger cause Edu6t 453644 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 418611 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 055973 [0454] 1 Cannot reject H0
RGDPt does not Granger cause Edu9t 053890 [0020] 1 Reject H0
RGDPt does not Granger cause Edu10t 011119 [0292] 1 Cannot reject H0
Eq (18a) LFt does not Granger cause Edu1t 006023 [0438] 1 Cannot reject H0
LFt does not Granger cause Edu2t 364559 [0000] 1 Reject H0
LFt does not Granger cause Edu3t 197423 [0000] 1 Reject H0
LFt does not Granger cause Edu4t 166511 [0000] 1 Reject H0
LFt does not Granger cause Edu5t 383886 [0000] 1 Reject H0
LFt does not Granger cause Edu6t 359377 [0000] 1 Reject H0
LFt does not Granger cause Edu7t 328249 [0000] 1 Reject H0
LFt does not Granger cause Edu8t 135310 [0000] 1 Reject H0
LFt does not Granger cause Edu9t 630068 [0000] 1 Reject H0
LFt does not Granger cause Edu01t 109365 [0001] 1 Reject H0
Eq (18b) RPCt does not Granger cause Edu1t 114248 [0001] 1 Reject H0
RPCt does not Granger cause Edu2t 036828 [0055] 1 Reject H0
RPCt does not Granger cause Edu3t 021023 [0147] 1 Cannot reject H0
RPCt does not Granger cause Edu4t 000484 [0826] 1 Cannot reject H0
RPCt does not Granger cause Edu5t 610934 [0000] 1 Reject H0
RPCt does not Granger cause Edu6t 070279 [0008] 1 Reject H0
RPCt does not Granger cause Edu7t 051166 [0024] 1 Reject H0
RPCt does not Granger cause Edu8t 167481 [0000] 1 Reject H0
RPCt does not Granger cause Edu9t 335271 [0000] 1 Reject H0
RPCt does not Granger cause Edu10t 067481 [0009] 1 Reject H0
Eq (19) Edu1 does not Granger cause RPCt 005154 [0473] 1 Cannot reject H0
Edu2 does not Granger cause RPCt 011954 [0274] 1 Cannot reject H0
Edu3 does not Granger cause RPCt 162365 [0000] 1 Reject H0
Edu4 does not Granger cause RPCt 148964 [0000] 1 Reject H0
Edu5 does not Granger cause RPCt 243978 [0000] 1 Reject H0
Edu6 does not Granger cause RPCt 040262 [0045] 1 Reject H0
Edu7 does not Granger cause RPCt 035138 [0061] 1 Reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 333
able IV (Continued )
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Edu8 does not Granger cause RPCt 030100 [0083] 1 Reject H0
Edu9 does not Granger cause RPCt 462564 [0000] 1 Reject H0
Edu10 does not Granger cause RPCt 009580 [0328] 1 Cannot reject H0
Eq (19a) RGDPt does not Granger cause RPCt (Edu1t as a 3rd variable) 009936 [0319] 1 Cannot reject H0
RGDPt does not Granger cause RPCt (Edu2t as a 3rd variable) 039369 [0047] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu3t as a 3rd variable) 003822 [0536] 1 Cannot reject H0
RGDPt does not Granger cause RPCt (Edu4t as a 3rd variable) 028000 [0094] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu5t as a 3rd variable) 039910 [0046] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu6t as a 3rd variable) 033500 [0067] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu7t as a 3rd variable) 029924 [0084] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu8t as a 3rd variable) 002803 [0597] 1 Cannot Reject H0
RGDPt does not Granger cause RPCt (Edu9t as a 3rd variable) 011416 [0285] 1 Cannot reject H0
RGDPt does not Granger cause RPCt (Edu10t as a 3rd variable) 006944 [0405] 1 Cannot reject H0
Eq (20) Edu1t does not Granger cause LFt 015302 [0216] 1 Cannot reject H0
Edu2t does not Granger cause LFt 001053 [0746] 1 Cannot reject H0
Edu3t does not Granger cause LFt 080072 [0005] 1 Reject H0
Edu4t does not Granger cause LFt 143854 [0000] 1 Reject H0
Edu5t does not Granger cause LFt 061159 [0013] 1 Reject H0
Edu6t does not Granger cause LFt 003113 [0577] 1 Cannot reject H0
Edu7t does not Granger cause LFt 002394 [0625] 1 Cannot reject H0
Edu8t does not Granger cause LFt 196804 [0000] 1 Reject H0
Edu9t does not Granger cause LFt 046285 [0496] 1 Cannot reject H0
Edu10t does not Granger cause LFt 04161 1 [0041] 1 Reject H0
Eq (20a) RGDPt does not Granger cause LFt (Edu1t as a 3rd variable) 006872 [0407] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu2t as a 3rd variable) 018604 [0173] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu3t as a 3rd variable) 066905 [0010] 1 Reject H0
RGDPt does not Granger cause LFt (Edu4t as a 3rd variable) 023249 [0127] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu5t as a 3rd variable) 070835 [0008] 1 Reject H0
RGDPt does not Granger cause LFt (Edu6t as a 3rd variable) 016501 [0199] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu7t as a 3rd variable) 018532 [0173] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu8t as a 3rd variable) 003730 [0541] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu9t as a 3rd variable) 039255 [0048] 1 Reject H0
RGDPt does not Granger cause LFt (Edu10t as a 3rd variable) 055266 [0019] 1 Reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335334
T
References
Abbas Q amp Peck J F (2008) Human capital and economic growth Pakistan 1960ndash2003 The Lahore Journal of Economics 13(1) 1ndash28Ayara N A (2002) The paradox of education and economic growth in Nigeria Empirical evidence The Nigerian Economic Society (NES) Pt 2 371ndash393Babatunde M A amp Adefabi R A (2005) Long run relationship between education and economic growth in Nigeria Evidence from the Johansenrsquos cointegration
approach Paper presented at the regional conference on education in West Africa Constraints and Opportunities Dakar Senegal November 1stndash2nd 2005Cornell UniversityCREAMinisterede lrsquoEducation du Senegal
Baldacci E Clements B Cui Q amp Gupta S (2005) What does it take to help the poor Finance and Development The Quarterly Magazine of the IMF 42(2)Changzheng Z Zhijian H amp Huaizu L (2007) An empirical study on education equity in China 1978ndash2004 Frontier in Economics of China 2(4) 536ndash544Chaudhary A R Asim I amp Gillani S Y M (2009) The nexus between higher education and economic growth An empirical investigation for Pakistan Pakistan
Journal of Commerce and Social Sciences 3Chaudhry I S Malik S amp Ashraf M (2006) Rural poverty in Pakistan Some related concepts issues and empirical analysis Pakistan Economic and Social Review
44(2) 259ndash276Diebolt C amp Litago J (1997) Education and economic growth in Germany before the Second World War An econometric analysis of dynamic relations Historical
Social Research 2(22) 132ndash149Easterly W (2001) The middle class consensus and economic development Journal of Economic Growth 6(4) 317ndash335Engle R F amp Granger C W J (1987) Cointegration and error correction Representation estimation and testing Econometrica 55 251ndash276Fernandez E amp Mauro P (2000) The role of human capital in economic growth The case of Spain (IMF Working Paper) International Monetary FundFrancis B amp Iyare S (2006) Education and development in the Caribbean A cointegration and causality approach Economics Bulletin 15(2) 1ndash13Galor O amp Moav O (2000) Das human capital Retrieved from httpeconpstcn brownedufacultygalorindexhtmlGoode R B (1959) Adding to the stock of physical and human capital American Economic Review 49(2) 147Government of Pakistan (1970ndash2009) Pakistan economic survey various issues Finance Division Islamabad Economic Advisorrsquos WingGregory A W amp Hansen B E (1996) Residual-based tests for cointegration in models with regime shifts Journal of Econometrics 70 99ndash126Grossman G M amp Helpman E (1991) Innovation and growth in the global economy Cambridge MIT PressGylfason T amp Zoega G (2003) Education social equality and economic growth A view of the landscape CESifo Economic Studies 49(4) 557ndash579Hassan S amp Ahmed H (2008) Educationrsquos contribution to the economic growth of sub-Saharan Africa Southwestern Economic Review 1(32) 175ndash190Islam T S Wadud M A amp Islam Q B T (2007) Relationship between education and GDP growth A multivariate causality analysis for Bangladesh Economics
Bulletin 3(35) 1ndash7Jin J C (2009) Economic research and economic growth Evidence from East Asian Economies Journal of Asian Economics 20 150ndash155Johansen S (1988) Statistical analysis of cointegration vectors Journal of Economic Dynamics and Control 12 231ndash254Johansen S amp Juselius K (1990) Maximum likelihood estimation and inference on cointegration with applications to the demand for money Oxford Bulletin of
Economics and Statistics 52 169ndash210Katırcıoglu S T (2009) Investigating higher-education-led growth hypothesis in a small Island Time series evidence from Northern Cyprus Paper presented at
Econ Anadolu 2009 Anadolu International Conference in Economics June 17ndash19 2009 TurkeyKhorasgani M F (2008) Higher education development and economic growth in Iran Education Business and Society Contemporary Middle Eastern Issues 1
162ndash174
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 335
Kui L (2005) The interactive causality between education and economic growth in China Retrieved from httppapersssrncomsol3paperscfmAbstrac-tid=920624
Loening J L (2004) Time series evidence on education and growth The case of Guatemala 1951ndash2002 Revista de Analisis Economico 19(2) 3ndash40Lucas R E (1988) On the mechanics of economic development Journal of Monetary Economics 22 3ndash42Macerinskiene I amp Vaiksnoraite B (2006) The role of higher education to economic development VadybaManagement 2(11)Mankiw N G Romer D amp Weil D N (1992) A contribution to the empirics of economic growth Quarterly Journal of Economics 107 407ndash437Momete D C (2007) Analysis of the relationship between employment and economic growth in Romania Fascicle of Management and Technological Engineering
VI(XVI)Morote E S (2000) Higher education employment and economic growth Mexico and Peru Retrieved from httpwwwamericanprofessororgdocumentation
lasapa perdocNarayan P K (2005) The saving and investment nexus for China Evidence from cointegration tests Applied Economics 37 1979ndash1990Permani R (2008) Education as a determinant of economic growth in East Asia Historical trends and empirical evidences (1965ndash2000) Retrieved from http
wwwuoweduaucommerceeconehsanzpdfsPermani202008pdfPesaran M H amp Pesaran B (1997) Working with Microfit 40 Interactive econometric analysis Oxford Oxford University PressPesaran M H amp Shin Y (1999) An autoregressive distributed lag modeling approach to cointegration analysis In S Strom (Ed) Econometrics and economic theory
in the 20th century Cambridge Cambridge University PressPesaran M H Shin Y amp Smith R J (2001) Bounds testing approaches to the analysis of level relationships Journal of Applied Econometrics 16 289ndash326Pradhan R P (2009) Education and economic growth in India Using error correction modeling International Research Journal of Finance and Economics 25Pritchett L (2001) Where has all the education gone The World Bank Economic Review 15(3)Quah D amp Rauch J E (1990) Openness and the rate of economic growth Journal Development of Studies 2(49) 307ndash335Rivera-Batiz L A amp Romer P M (1991) Economic integration and endogenous growth Quarterly Journal of Economics 106 531ndash555Romer P M (1986) Increasing returns and long run growth Journal of Political Economy 6(90) 1002ndash1037Romer P M (1989) Human capital and growth Theory and evidence (NBER Working Papers 3173) National Bureau of Economic Research IncRomer P M (1990) Endogenous technological change Journal of Political Economy 5(98) 71ndash101Rondinelli D amp Montgomery J (1995) Great policies Strategic innovations in Asia and the Pacific Basin Westport Praeger PublishingSaikkonen P amp Lutkepohl H (2000) Testing for the cointegration rank of a VAR process with structural shifts Journal of Business and Economic Statistics 18(4)
451ndash464Schultz T W (1961) Investment in human capital American Economic Review 51(1) 1State Bank of Pakistan (1972ndash2009) Annual reports Karachi SBP PressStengos T amp Aurangzeb A (2008) An empirical investigation of the relationship between education and growth in pakistan International Economic Journal 3
345ndash359 Retrieved from httpwwwinformaworldcomsmpptitledb=allcontent=t713685453tab=issueslistbranches=22-v2222Toda H Y amp Yamamoto T (1995) Statistical inference in vector autoregressive with possible integrated processes Journal of Econometrics 66 225ndash250United Nations (1997) Human Development Report New York Oxford University Press
- Education and economic growth in Pakistan A cointegration and causality analysis
-
- Introduction
- Review of literature
- Method and procedure
- Empirical results
-
- Unit root results
- Cointegration
- Toda-Yamamoto Augmented Granger Causality (TYAGC) Test
- Bivariate TYAGC framework
- Trivariate TYAGC framework
- Tetravariate TYAGC framework
- Figures in parentheses are p-values
-
- Conclusions and recommendations
-
- References
-
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 329
47 Figures in parentheses are p-values
From the above results presented in Table 4 it can be concluded that there existed feedback causality between educationand RGDPt in all bivariate trivariate and tetravariate TYAGC causality cases All levels of education ie school educationcollege education and university education do Granger cause RGDPt in all causality cases RGDPt does Granger cause schooleducation in all causality cases RGDPt does Granger cause college education in all causality cases except trivariate causalitythat is running from RGDPt to education when RPCt serves as a third variable Table 4 also reveals that RGDPt does Grangercause university education only in a bivariate and trivariate causality cases RGDPt fails to Granger cause to universityeducation in tetravariate case
5 Conclusions and recommendations
This study aimed to explore the cointegration and causal relationship between education (measured by different indicatorsof education) and economic growth in Pakistan It is very essential for a country to invest more in education because it is one ofthe most important ingredients of human capital and hence economic development The nature and strength of the relationshipbetween education and economic growth is still not clear in case of Pakistan The main focus of this empirical study remained toobserve the causality and cointegration between education and economic growth in the absence and presence physical capitaland labour force Cointegration between education and economic growth was investigated using ARDL approach and the causallinkage between education and economic growth was examined in bivariate trivariate and tetravariate TYAGC frameworkDifferent indicators of education were utilized in this study to show the robustness of empirical results The causality betweeneducation and economic growth was examined in the presence and absence of stock of physical capital and stock of labour as athird and fourth variable The causality results indicate that there exist two-way causality between education and economicgrowth and between all levels of education and economic growth in case of bivariate TYAGC framework Education and alllevels of education do Granger cause economic growth in the presence of real physical capital as a third variable while economicgrowth causes all the indicators of education except college education professional college education and educationalexpenditures in the presence of real physical capital as a third variable in case of trivariate causality analysis In the presence oflabour force as a third variable feedback causality exists between education and economic growth and between all levels ofeducation and economic growth The results of tetravariate TYAGC Test indicate that education and all level of education doGranger cause economic growth while economic growth does Granger cause majority of the indicators of education (ie sevenout of ten) Economic growth does not Granger cause university education higher education including professional educationand expenditures on education The rise in university education higher education including professional education andexpenditures on education were considered as the key indicators to gauge human and social progress Economic growth doesnot seem to affect important educational indicators like university education higher education including professionaleducation and expenditures on education This seems to be consistent with Easterlyrsquos findings Easterly (2001) said thatPakistan is a country that made little social progress for given rates of GDP Among all levels of education General highereducation causes economic growth highly and most significantly as was explored by Stengos and Aurangzeb (2008) The level ofconfidence of causing economic growth to school education found to be highest This study also confirms the long runrelationship between education and economic growth
On the basis of the results of this study it is recommended that the government should focus more on higher educationparticularly to university education More funds should be allocated to education in line with others sectors particularly touniversity and higher education levels so that the economic growth can be further accelerated This will in turn leads tofurther education and hence development Poor should be facilitated to get higher education so that the polarization inhigher education may further be minimized Primary schooling should also be given priority because primary educationserves as an input for all higher levels of education The inverted educational expenditure pyramid may also be taken intoaccount Since the role of labour force seems to be very important in understanding the relationship between education andeconomic growth so it is suggested that labour force should be given more chances to enhance their skills The variablelabour force must be included while examining the causality between education and economic growth It is alsorecommended that the nexus between education and economic growth with inclusion of other variables other than physicalcapital and labour force should further be tested and generalized
Appendix A
Table I
Bivariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Bivariate-RGDPt and Eduit
Eq (1) Edu1t does not Granger cause RGDPt 028998 [0089] 1 Reject H0
Edu2t does not Granger cause RGDPt 144869 [0000] 1 Reject H0
Edu3t does not Granger cause RGDPt 043243 [0038] 1 Reject H0
Edu4t does not Granger cause RGDPt 039797 [0046] 1 Reject H0
Table I (Continued )
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Edu5t does not Granger cause RGDPt 217739 [0000] 1 Reject H0
Edu6t does not Granger cause RGDPt 137788 [0000] 1 Reject H0
Edu7t does not Granger cause RGDPt 126682 [0000] 1 Reject H0
Edu8t does not Granger cause RGDPt 041335 [0042] 1 Reject H0
Edu9t does not Granger cause RGDPt 160963 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 028642 [0091] 1 Reject H0
Eq (2) RGDPt does not Granger cause Edu1t 260926 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 230094 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 085441 [0003] 1 Reject H0
RGDPt does not Granger cause Edu4t 107403 [0001] 1 Reject H0
RGDPt does not Granger cause Edu5t 028935 [0089] 1 Reject H0
RGDPt does not Granger cause Edu6t 270343 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 273974 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 003162 [0574] 1 Cannot reject H0
RGDPt does not Granger cause Edu9t 027588 [0097] 1 Reject H0
RGDPt does not Granger cause Edu10t 000851 [0770] 1 Cannot reject H0
Bivariate-RGDPt and RPCt
Eq (3) RPCt does not Granger cause RGDPt 054972 [0019] 1 Reject H0
Eq (4) RGDPt does not Granger cause RPCt 167511 [0000] 1 Reject H0
Bivariate-RGDPt and LFt
Eq (5) LFt does not Granger cause RGDPt 227888 [0000] 1 Reject H0
Eq (6) RGDPt does not Granger cause LFt 012380 [0266] 1 Cannot reject H0
Bivariate-Eduit and RPCt
Eq (7) Edu1t does not Granger cause RPCt 094596 [0002] 1 Reject H0
Edu2t does not Granger cause RPCt 015434 [0214] 1 Cannot reject H0
Edu3t does not Granger cause RPCt 038233 [0051] 1 Reject H0
Edu4t does not Granger cause RPCt 000506 [0822] 1 Cannot reject H0
Edu5t does not Granger cause RPCt 298085 [0000] 1 Reject H0
Edu6t does not Granger cause RPCt 018289 [0176] 1 Cannot reject H0
Edu7t does not Granger cause RPCt 018976 [0168] 1 Cannot reject H0
Edu8t does not Granger cause RPCt 176399 [0000] 1 Reject H0
Edu9t does not Granger cause RPCt 224647 [0000] 1 Reject H0
Edu10t does not Granger cause RPCt 039174 [0048] 1 Reject H0
Eq (8) RPCt does not Granger cause Edu1t 091477 [0002] 1 Reject H0
RPCt does not Granger cause Edu2t 098821 [0002] 1 Reject H0
RPCt does not Granger cause Edu3t 066148 [0010] 1 Reject H0
RPCt does not Granger cause Edu4t 084218 [0004] 1 Reject H0
RPCt does not Granger cause Edu5t 001684 [0682] 1 Cannot reject H0
RPCt does not Granger cause Edu6t 107553 [0001] 1 Reject H0
RPCt does not Granger cause Edu7t 108798 [0001] 1 Reject H0
RPCt does not Granger cause Edu8t 004283 [0513] 1 Cannot reject H0
RPCt does not Granger cause Edu9t 005627 [0453] 1 Cannot reject H0
RPCt does not Granger cause Edu10t 000417 [0838] 1 Cannot reject H0
Bivariate-Eduit and LFt
Eq (9) Edu1t does not Granger cause LFt 026469 [0104] 1 Reject H0
Edu2t does not Granger cause LFt 012355 [0266] 1 Cannot reject H0
Edu3t does not Granger cause LFt 020468 [0153] 1 Cannot reject H0
Edu4t does not Granger cause LFt 098042 [0002] 1 Reject H0
Edu5t does not Granger cause LFt 049986 [0025] 1 Reject H0
Edu6t does not Granger cause LFt 016896 [0194] 1 Cannot reject H0
Edu7t does not Granger cause LFt 015167 [0218] 1 Cannot reject H0
Edu8t does not Granger cause LFt 184475 [0000] 1 Reject H0
Edu9t does not Granger cause LFt 003986 [0528] 1 Cannot reject H0
Edu10t does not Granger cause LFt 010899 [0296] 1 Cannot reject H0
Eq (10) LFt does not Granger cause Edu1t 107709 [0001] 1 Reject H0
LFt does not Granger cause Edu2t 071204 [0008] 1 Reject H0
LFt does not Granger cause Edu3t 136419 [0000] 1 Reject H0
LFt does not Granger cause Edu4t 056225 [0018] 1 Reject H0
LFt does not Granger cause Edu5t 057141 [0017] 1 Reject H0
LFt does not Granger cause Edu6t 091531 [0002] 1 Reject H0
LFt does not Granger cause Edu7t 095063 [0002] 1 Reject H0
LFt does not Granger cause Edu8t 021313 [0144] 1 Cannot reject H0
LFt does not Granger cause Edu9t 069389 [0008] 1 Reject H0
LFt does not Granger cause Edu10t 000743 [0785] 1 Cannot reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335330
Table II
Trivariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Trivariate-RGDPt RPCt and Eduit
Eq (11) Edu1t does not Granger cause RGDPt 005481 [0459] 1 Cannot reject H0
Edu2t does not Granger cause RGDPt 105415 [0001] 1 Reject H0
Edu3t does not Granger cause RGDPt 030370 [0081] 1 Reject H0
Edu4t does not Granger cause RGDPt 022525 [0133] 1 Cannot reject H0
Edu5t does not Granger cause RGDPt 227510 [0000] 1 Reject H0
Edu6t does not Granger cause RGDPt 098494 [0002] 1 Reject H0
Edu7t does not Granger cause RGDPt 090460 [0003] 1 Reject H0
Edu8t does not Granger cause RGDPt 067381 [0009] 1 Reject H0
Edu9t does not Granger cause RGDPt 168617 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 085842 [0003] Reject H0
Eq (11a) RPCt does not Granger cause RGDP (Edu1 as a 3rd variable) 029029 [0088] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu2 as a 3rd variable) 024880 [0115] 1 Cannot reject H0
RPCt does not Granger cause RGDPt (Edu3t as a 3rd variable) 041380 [0042] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu4t as a 3rd variable) 036580 [0056] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu5t as a 3rd variable) 064811 [0011] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu6t as a 3rd variable) 024405 [0118] 1 Cannot reject H0
RPCt does not Granger cause RGDPt (Edu7t as a 3rd variable) 026008 [0107] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu8t as a 3rd variable) 081607 [0004] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu9t as a 3rd variable) 063133 [0012] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu10t as a 3rd variable) 115637 [0001] 1 Reject H0
Eq (12) RGDPt does not Granger cause Edu1t 176454 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 129776 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 018626 [0172] 1 Cannot reject H0
RGDPt does not Granger cause Edu4t 020449 [0153] 1 Cannot reject H0
RGDPt does not Granger cause Edu5t 144658 [0000] 1 Reject H0
RGDPt does not Granger cause Edu6t 175431 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 178356 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 042497 [0039] 1 Reject H0
RGDPt does not Granger cause Edu9t 082506 [0004] 1 Reject H0
RGDPt does not Granger cause Edu10t 008026 [0370] 1 Cannot reject H0
Eq (12a) RPCt does not Granger cause Edu1t 000122 [0912] 1 Cannot reject H0
RPCt does not Granger cause Edu2t 028750 [0090] 1 Reject H0
RPCt does not Granger cause Edu3t 058586 [0016] 1 Reject H0
RPCt does not Granger cause Edu4t 071372 [0008] 1 Reject H0
RPCt does not Granger cause Edu5t 302364 [0000] 1 Reject H0
RPCt does not Granger cause Edu6t 020474 [0152] 1 Cannot reject H0
RPCt does not Granger cause Edu7t 017533 [0185] 1 Cannot reject H0
RPCt does not Granger cause Edu8t 044926 [0034] 1 Reject H0
RPCt does not Granger cause Edu9t 240955 [0000] 1 Reject H0
RPCt does not Granger cause Edu10t 021006 [0147] 1 Cannot reject H0
Eq (13) RGDPt does not Granger cause RPCt (Edu1t as a 3rd variable) 055095 [0019] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu2t as a 3rd variable) 182287 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu3t as a 3rd variable) 191499 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu4t as a 3rd variable) 269133 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu5t as a 3rd variable) 172979 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu6t as a 3rd variable) 166347 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu7t as a 3rd variable) 161198 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu8t as a 3rd variable) 038521 [0050] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu9tas a 3rd variable) 183169 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu10t as a 3rd variable) 139552 [0000] 1 Reject H0
Eq (13a) Edu1t does not Granger cause RPCt 000122 [0912] 1 Cannot reject H0
Edu2t does not Granger cause RPCt 028750 [0090] 1 Reject H0
Edu3t does not Granger cause RPCt 058586 [0016] 1 Reject H0
Edu4t does not Granger cause RPCt 071372 [0008] 1 Reject H0
Edu5t does not Granger cause RPCt 302364 [0000] 1 Reject H0
Edu6t does not Granger cause RPCt 020474 [0152] 1 Cannot reject H0
Edu7t does not Granger cause RPCt 017533 [0185] 1 Cannot reject H0
Edu8t does not Granger cause RPCt 044926 [0034] 1 Reject H0
Edu9t does not Granger cause RPCt 240955 [0000] 1 Reject H0
Edu10t does not Granger cause RPCt 021006 [0147] 1 Cannot reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 331
Table III
Trivariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Trivariate-RGDPt LFt and Eduit
Eq (14) Edu1t does not Granger cause RGDPt 068472 [0009] 1 Reject H0
Edu2t does not Granger cause RGDPt 092326 [0002] 1 Reject H0
Edu3t does not Granger cause RGDPt 180477 [0000] 1 Reject H0
Edu4t does not Granger cause RGDPt 132070 [0000] 1 Reject H0
Edu5t does not Granger cause RGDPt 109716 [0001] 1 Reject H0
Edu6t does not Granger cause RGDPt 086017 [0003] 1 Reject H0
Edu7t does not Granger cause RGDPt 078604 [0005] 1 Reject H0
Edu8t does not Granger cause RGDPt 020470 [0153] 1 Cannot reject H0
Edu9t does not Granger cause RGDPt 293293 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 005754 [0448] 1 Cannot reject H0
Eq (14a) LFt does not Granger cause RGDPt (Edu1t as a 3rd variable) 409533 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu2t as a 3rd variable) 332636 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu3t as a 3rd variable) 701171 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu4t as a 3rd variable) 605496 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu5t as a 3rd variable) 240867 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu6t as a 3rd variable) 330495 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu7t as a 3rd variable) 332860 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu8t as a 3rd variable) 352003 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu9t as a 3rd variable) 573087 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu10t as a 3rd variable) 343199 [0000] 1 Reject H0
Eq (15) RGDPt does not Granger cause Edu1t 134939 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 804323 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 109273 [0001] 1 Reject H0
RGDPt does not Granger cause Edu4t 278785 [0000] 1 Reject H0
RGDPt does not Granger cause Edu5t 050547 [0025] 1 Reject H0
RGDPt does not Granger cause Edu6t 790307 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 738342 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 043402 [0037] 1 Reject H0
RGDPt does not Granger cause Edu9t 175731 [0000] 1 Reject H0
RGDPt does not Granger cause Edu10t 061709 [0013] 1 Reject H0
Eq (15a) LFt does not Granger cause Edu1t 009324 [0334] 1 Cannot reject H0
LFt does not Granger cause Edu2t 377339 [0000] 1 Reject H0
LFt does not Granger cause Edu3t 176565 [0000] 1 Reject H0
LFt does not Granger cause Edu4t 180046 [0000] 1 Reject H0
LFt does not Granger cause Edu5t 091061 [0003] 1 Reject H0
LFt does not Granger cause Edu6t 355203 [0000] 1 Reject H0
LFt does not Granger cause Edu7t 327354 [0000] 1 Reject H0
LFt does not Granger cause Edu8t 053664 [0021] 1 Reject H0
LFt does not Granger cause Edu9t 251724 [0000] 1 Reject H0
LFt does not Granger cause Edu10t 060787 [0014] 1 Reject H0
Eq (16) Edu1t does not Granger cause LFt 036697 [0055] 1 Reject H0
Edu2t does not Granger cause LFt 004605 [0497] 1 Cannot reject H0
Edu3t does not Granger cause LFt 093988 [0002] 1 Reject H0
Edu4t does not Granger cause LFt 177287 [0000] 1 Reject H0
Edu5t does not Granger cause LFt 059203 [0015] 1 Reject H0
Edu6t does not Granger cause LFt 007202 [0396] 1 Cannot reject H0
Edu7t does not Granger cause LFt 005520 [0458] 1 Cannot reject H0
Edu8t does not Granger cause LFt 241662 [0000] 1 Reject H0
Edu9t does not Granger cause LFt 004009 [0527] 1 Cannot reject H0
Edu10t does not Granger cause LFt 058477 [0016] 1 Reject H0
Eq (16a) RGDPt does not Granger cause LFt (Edu1t as a 3rd variable) 002436 [0622] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu2t as a 3rd variable) 004276 [0513] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu3t as a 3rd variable) 047690 [0029] 1 Reject H0
RGDPt does not Granger cause LFt (Edu4t as a 3rd variable) 015207 [0218] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu5t as a 3rd variable) 040757 [0044] 1 Reject H0
RGDPt does not Granger cause LFt (Edu6t as a 3rd variable) 003392 [0560] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu7t as a 3rd variable) 004309 [0512] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu8t as a 3rd variable) 003145 [0575] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu9t as a 3rd variable) 017426 [0187] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu10t as a 3rd variable) 048448 [0028] 1 Reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335332
Table IV
Tetravariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Tetravariate-RGDPt RPCt LFt and Edut
Eq (17) Edu1t does not Granger cause RGDPt 029350 [0087] 1 Reject H0
Edu2t does not Granger cause RGDPt 065661 [0010] 1 Reject H0
Edu3t does not Granger cause RGDPt 097521 [0002] 1 Reject H0
Edu4t does not Granger cause RGDPt 071590 [0007] 1 Reject H0
Edu5t does not Granger cause RGDPt 116263 [0001] 1 Reject H0
Edu6t does not Granger cause RGDPt 059569 [0015] 1 Reject H0
Edu7t does not Granger cause RGDPt 054327 [0020] 1 Reject H0
Edu8t does not Granger cause RGDPt 040033 [0045] 1 Reject H0
Edu9t does not Granger cause RGDPt 195734 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 034374 [0064] 1 Reject H0
Eq (17a) LFt does not Granger cause RGDPt (Edut = Edu1) 251518 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu2) 165581 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu3) 316418 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu4) 289993 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu5) 109302 [0001] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu6) 165606 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu7) 168037 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu8) 176645 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu9) 247435 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu10) 146998 [0000] 1 Reject H0
Eq (17b) RPCt does not Granger cause RGDPt (Edut = Edu1) 042975 [0038] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu2) 039280 [0047] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu3) 034296 [0064] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu4) 027068 [0100] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu5) 062858 [0012] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu6) 039537 [0047] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu7) 040022 [0045] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu8) 045487 [0033] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu9) 068323 [0009] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu10) 083479 [0004] 1 Reject H0
Eq (18) RGDPt does not Granger cause Edu1t 150200 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 633103 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 045767 [0032] 1 Reject H0
RGDPt does not Granger cause Edu4t 122392 [0000] 1 Reject H0
RGDPt does not Granger cause Edu5t 004235 [0515] 1 Cannot reject H0
RGDPt does not Granger cause Edu6t 453644 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 418611 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 055973 [0454] 1 Cannot reject H0
RGDPt does not Granger cause Edu9t 053890 [0020] 1 Reject H0
RGDPt does not Granger cause Edu10t 011119 [0292] 1 Cannot reject H0
Eq (18a) LFt does not Granger cause Edu1t 006023 [0438] 1 Cannot reject H0
LFt does not Granger cause Edu2t 364559 [0000] 1 Reject H0
LFt does not Granger cause Edu3t 197423 [0000] 1 Reject H0
LFt does not Granger cause Edu4t 166511 [0000] 1 Reject H0
LFt does not Granger cause Edu5t 383886 [0000] 1 Reject H0
LFt does not Granger cause Edu6t 359377 [0000] 1 Reject H0
LFt does not Granger cause Edu7t 328249 [0000] 1 Reject H0
LFt does not Granger cause Edu8t 135310 [0000] 1 Reject H0
LFt does not Granger cause Edu9t 630068 [0000] 1 Reject H0
LFt does not Granger cause Edu01t 109365 [0001] 1 Reject H0
Eq (18b) RPCt does not Granger cause Edu1t 114248 [0001] 1 Reject H0
RPCt does not Granger cause Edu2t 036828 [0055] 1 Reject H0
RPCt does not Granger cause Edu3t 021023 [0147] 1 Cannot reject H0
RPCt does not Granger cause Edu4t 000484 [0826] 1 Cannot reject H0
RPCt does not Granger cause Edu5t 610934 [0000] 1 Reject H0
RPCt does not Granger cause Edu6t 070279 [0008] 1 Reject H0
RPCt does not Granger cause Edu7t 051166 [0024] 1 Reject H0
RPCt does not Granger cause Edu8t 167481 [0000] 1 Reject H0
RPCt does not Granger cause Edu9t 335271 [0000] 1 Reject H0
RPCt does not Granger cause Edu10t 067481 [0009] 1 Reject H0
Eq (19) Edu1 does not Granger cause RPCt 005154 [0473] 1 Cannot reject H0
Edu2 does not Granger cause RPCt 011954 [0274] 1 Cannot reject H0
Edu3 does not Granger cause RPCt 162365 [0000] 1 Reject H0
Edu4 does not Granger cause RPCt 148964 [0000] 1 Reject H0
Edu5 does not Granger cause RPCt 243978 [0000] 1 Reject H0
Edu6 does not Granger cause RPCt 040262 [0045] 1 Reject H0
Edu7 does not Granger cause RPCt 035138 [0061] 1 Reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 333
able IV (Continued )
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Edu8 does not Granger cause RPCt 030100 [0083] 1 Reject H0
Edu9 does not Granger cause RPCt 462564 [0000] 1 Reject H0
Edu10 does not Granger cause RPCt 009580 [0328] 1 Cannot reject H0
Eq (19a) RGDPt does not Granger cause RPCt (Edu1t as a 3rd variable) 009936 [0319] 1 Cannot reject H0
RGDPt does not Granger cause RPCt (Edu2t as a 3rd variable) 039369 [0047] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu3t as a 3rd variable) 003822 [0536] 1 Cannot reject H0
RGDPt does not Granger cause RPCt (Edu4t as a 3rd variable) 028000 [0094] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu5t as a 3rd variable) 039910 [0046] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu6t as a 3rd variable) 033500 [0067] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu7t as a 3rd variable) 029924 [0084] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu8t as a 3rd variable) 002803 [0597] 1 Cannot Reject H0
RGDPt does not Granger cause RPCt (Edu9t as a 3rd variable) 011416 [0285] 1 Cannot reject H0
RGDPt does not Granger cause RPCt (Edu10t as a 3rd variable) 006944 [0405] 1 Cannot reject H0
Eq (20) Edu1t does not Granger cause LFt 015302 [0216] 1 Cannot reject H0
Edu2t does not Granger cause LFt 001053 [0746] 1 Cannot reject H0
Edu3t does not Granger cause LFt 080072 [0005] 1 Reject H0
Edu4t does not Granger cause LFt 143854 [0000] 1 Reject H0
Edu5t does not Granger cause LFt 061159 [0013] 1 Reject H0
Edu6t does not Granger cause LFt 003113 [0577] 1 Cannot reject H0
Edu7t does not Granger cause LFt 002394 [0625] 1 Cannot reject H0
Edu8t does not Granger cause LFt 196804 [0000] 1 Reject H0
Edu9t does not Granger cause LFt 046285 [0496] 1 Cannot reject H0
Edu10t does not Granger cause LFt 04161 1 [0041] 1 Reject H0
Eq (20a) RGDPt does not Granger cause LFt (Edu1t as a 3rd variable) 006872 [0407] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu2t as a 3rd variable) 018604 [0173] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu3t as a 3rd variable) 066905 [0010] 1 Reject H0
RGDPt does not Granger cause LFt (Edu4t as a 3rd variable) 023249 [0127] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu5t as a 3rd variable) 070835 [0008] 1 Reject H0
RGDPt does not Granger cause LFt (Edu6t as a 3rd variable) 016501 [0199] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu7t as a 3rd variable) 018532 [0173] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu8t as a 3rd variable) 003730 [0541] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu9t as a 3rd variable) 039255 [0048] 1 Reject H0
RGDPt does not Granger cause LFt (Edu10t as a 3rd variable) 055266 [0019] 1 Reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335334
T
References
Abbas Q amp Peck J F (2008) Human capital and economic growth Pakistan 1960ndash2003 The Lahore Journal of Economics 13(1) 1ndash28Ayara N A (2002) The paradox of education and economic growth in Nigeria Empirical evidence The Nigerian Economic Society (NES) Pt 2 371ndash393Babatunde M A amp Adefabi R A (2005) Long run relationship between education and economic growth in Nigeria Evidence from the Johansenrsquos cointegration
approach Paper presented at the regional conference on education in West Africa Constraints and Opportunities Dakar Senegal November 1stndash2nd 2005Cornell UniversityCREAMinisterede lrsquoEducation du Senegal
Baldacci E Clements B Cui Q amp Gupta S (2005) What does it take to help the poor Finance and Development The Quarterly Magazine of the IMF 42(2)Changzheng Z Zhijian H amp Huaizu L (2007) An empirical study on education equity in China 1978ndash2004 Frontier in Economics of China 2(4) 536ndash544Chaudhary A R Asim I amp Gillani S Y M (2009) The nexus between higher education and economic growth An empirical investigation for Pakistan Pakistan
Journal of Commerce and Social Sciences 3Chaudhry I S Malik S amp Ashraf M (2006) Rural poverty in Pakistan Some related concepts issues and empirical analysis Pakistan Economic and Social Review
44(2) 259ndash276Diebolt C amp Litago J (1997) Education and economic growth in Germany before the Second World War An econometric analysis of dynamic relations Historical
Social Research 2(22) 132ndash149Easterly W (2001) The middle class consensus and economic development Journal of Economic Growth 6(4) 317ndash335Engle R F amp Granger C W J (1987) Cointegration and error correction Representation estimation and testing Econometrica 55 251ndash276Fernandez E amp Mauro P (2000) The role of human capital in economic growth The case of Spain (IMF Working Paper) International Monetary FundFrancis B amp Iyare S (2006) Education and development in the Caribbean A cointegration and causality approach Economics Bulletin 15(2) 1ndash13Galor O amp Moav O (2000) Das human capital Retrieved from httpeconpstcn brownedufacultygalorindexhtmlGoode R B (1959) Adding to the stock of physical and human capital American Economic Review 49(2) 147Government of Pakistan (1970ndash2009) Pakistan economic survey various issues Finance Division Islamabad Economic Advisorrsquos WingGregory A W amp Hansen B E (1996) Residual-based tests for cointegration in models with regime shifts Journal of Econometrics 70 99ndash126Grossman G M amp Helpman E (1991) Innovation and growth in the global economy Cambridge MIT PressGylfason T amp Zoega G (2003) Education social equality and economic growth A view of the landscape CESifo Economic Studies 49(4) 557ndash579Hassan S amp Ahmed H (2008) Educationrsquos contribution to the economic growth of sub-Saharan Africa Southwestern Economic Review 1(32) 175ndash190Islam T S Wadud M A amp Islam Q B T (2007) Relationship between education and GDP growth A multivariate causality analysis for Bangladesh Economics
Bulletin 3(35) 1ndash7Jin J C (2009) Economic research and economic growth Evidence from East Asian Economies Journal of Asian Economics 20 150ndash155Johansen S (1988) Statistical analysis of cointegration vectors Journal of Economic Dynamics and Control 12 231ndash254Johansen S amp Juselius K (1990) Maximum likelihood estimation and inference on cointegration with applications to the demand for money Oxford Bulletin of
Economics and Statistics 52 169ndash210Katırcıoglu S T (2009) Investigating higher-education-led growth hypothesis in a small Island Time series evidence from Northern Cyprus Paper presented at
Econ Anadolu 2009 Anadolu International Conference in Economics June 17ndash19 2009 TurkeyKhorasgani M F (2008) Higher education development and economic growth in Iran Education Business and Society Contemporary Middle Eastern Issues 1
162ndash174
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 335
Kui L (2005) The interactive causality between education and economic growth in China Retrieved from httppapersssrncomsol3paperscfmAbstrac-tid=920624
Loening J L (2004) Time series evidence on education and growth The case of Guatemala 1951ndash2002 Revista de Analisis Economico 19(2) 3ndash40Lucas R E (1988) On the mechanics of economic development Journal of Monetary Economics 22 3ndash42Macerinskiene I amp Vaiksnoraite B (2006) The role of higher education to economic development VadybaManagement 2(11)Mankiw N G Romer D amp Weil D N (1992) A contribution to the empirics of economic growth Quarterly Journal of Economics 107 407ndash437Momete D C (2007) Analysis of the relationship between employment and economic growth in Romania Fascicle of Management and Technological Engineering
VI(XVI)Morote E S (2000) Higher education employment and economic growth Mexico and Peru Retrieved from httpwwwamericanprofessororgdocumentation
lasapa perdocNarayan P K (2005) The saving and investment nexus for China Evidence from cointegration tests Applied Economics 37 1979ndash1990Permani R (2008) Education as a determinant of economic growth in East Asia Historical trends and empirical evidences (1965ndash2000) Retrieved from http
wwwuoweduaucommerceeconehsanzpdfsPermani202008pdfPesaran M H amp Pesaran B (1997) Working with Microfit 40 Interactive econometric analysis Oxford Oxford University PressPesaran M H amp Shin Y (1999) An autoregressive distributed lag modeling approach to cointegration analysis In S Strom (Ed) Econometrics and economic theory
in the 20th century Cambridge Cambridge University PressPesaran M H Shin Y amp Smith R J (2001) Bounds testing approaches to the analysis of level relationships Journal of Applied Econometrics 16 289ndash326Pradhan R P (2009) Education and economic growth in India Using error correction modeling International Research Journal of Finance and Economics 25Pritchett L (2001) Where has all the education gone The World Bank Economic Review 15(3)Quah D amp Rauch J E (1990) Openness and the rate of economic growth Journal Development of Studies 2(49) 307ndash335Rivera-Batiz L A amp Romer P M (1991) Economic integration and endogenous growth Quarterly Journal of Economics 106 531ndash555Romer P M (1986) Increasing returns and long run growth Journal of Political Economy 6(90) 1002ndash1037Romer P M (1989) Human capital and growth Theory and evidence (NBER Working Papers 3173) National Bureau of Economic Research IncRomer P M (1990) Endogenous technological change Journal of Political Economy 5(98) 71ndash101Rondinelli D amp Montgomery J (1995) Great policies Strategic innovations in Asia and the Pacific Basin Westport Praeger PublishingSaikkonen P amp Lutkepohl H (2000) Testing for the cointegration rank of a VAR process with structural shifts Journal of Business and Economic Statistics 18(4)
451ndash464Schultz T W (1961) Investment in human capital American Economic Review 51(1) 1State Bank of Pakistan (1972ndash2009) Annual reports Karachi SBP PressStengos T amp Aurangzeb A (2008) An empirical investigation of the relationship between education and growth in pakistan International Economic Journal 3
345ndash359 Retrieved from httpwwwinformaworldcomsmpptitledb=allcontent=t713685453tab=issueslistbranches=22-v2222Toda H Y amp Yamamoto T (1995) Statistical inference in vector autoregressive with possible integrated processes Journal of Econometrics 66 225ndash250United Nations (1997) Human Development Report New York Oxford University Press
- Education and economic growth in Pakistan A cointegration and causality analysis
-
- Introduction
- Review of literature
- Method and procedure
- Empirical results
-
- Unit root results
- Cointegration
- Toda-Yamamoto Augmented Granger Causality (TYAGC) Test
- Bivariate TYAGC framework
- Trivariate TYAGC framework
- Tetravariate TYAGC framework
- Figures in parentheses are p-values
-
- Conclusions and recommendations
-
- References
-
Table I (Continued )
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Edu5t does not Granger cause RGDPt 217739 [0000] 1 Reject H0
Edu6t does not Granger cause RGDPt 137788 [0000] 1 Reject H0
Edu7t does not Granger cause RGDPt 126682 [0000] 1 Reject H0
Edu8t does not Granger cause RGDPt 041335 [0042] 1 Reject H0
Edu9t does not Granger cause RGDPt 160963 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 028642 [0091] 1 Reject H0
Eq (2) RGDPt does not Granger cause Edu1t 260926 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 230094 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 085441 [0003] 1 Reject H0
RGDPt does not Granger cause Edu4t 107403 [0001] 1 Reject H0
RGDPt does not Granger cause Edu5t 028935 [0089] 1 Reject H0
RGDPt does not Granger cause Edu6t 270343 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 273974 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 003162 [0574] 1 Cannot reject H0
RGDPt does not Granger cause Edu9t 027588 [0097] 1 Reject H0
RGDPt does not Granger cause Edu10t 000851 [0770] 1 Cannot reject H0
Bivariate-RGDPt and RPCt
Eq (3) RPCt does not Granger cause RGDPt 054972 [0019] 1 Reject H0
Eq (4) RGDPt does not Granger cause RPCt 167511 [0000] 1 Reject H0
Bivariate-RGDPt and LFt
Eq (5) LFt does not Granger cause RGDPt 227888 [0000] 1 Reject H0
Eq (6) RGDPt does not Granger cause LFt 012380 [0266] 1 Cannot reject H0
Bivariate-Eduit and RPCt
Eq (7) Edu1t does not Granger cause RPCt 094596 [0002] 1 Reject H0
Edu2t does not Granger cause RPCt 015434 [0214] 1 Cannot reject H0
Edu3t does not Granger cause RPCt 038233 [0051] 1 Reject H0
Edu4t does not Granger cause RPCt 000506 [0822] 1 Cannot reject H0
Edu5t does not Granger cause RPCt 298085 [0000] 1 Reject H0
Edu6t does not Granger cause RPCt 018289 [0176] 1 Cannot reject H0
Edu7t does not Granger cause RPCt 018976 [0168] 1 Cannot reject H0
Edu8t does not Granger cause RPCt 176399 [0000] 1 Reject H0
Edu9t does not Granger cause RPCt 224647 [0000] 1 Reject H0
Edu10t does not Granger cause RPCt 039174 [0048] 1 Reject H0
Eq (8) RPCt does not Granger cause Edu1t 091477 [0002] 1 Reject H0
RPCt does not Granger cause Edu2t 098821 [0002] 1 Reject H0
RPCt does not Granger cause Edu3t 066148 [0010] 1 Reject H0
RPCt does not Granger cause Edu4t 084218 [0004] 1 Reject H0
RPCt does not Granger cause Edu5t 001684 [0682] 1 Cannot reject H0
RPCt does not Granger cause Edu6t 107553 [0001] 1 Reject H0
RPCt does not Granger cause Edu7t 108798 [0001] 1 Reject H0
RPCt does not Granger cause Edu8t 004283 [0513] 1 Cannot reject H0
RPCt does not Granger cause Edu9t 005627 [0453] 1 Cannot reject H0
RPCt does not Granger cause Edu10t 000417 [0838] 1 Cannot reject H0
Bivariate-Eduit and LFt
Eq (9) Edu1t does not Granger cause LFt 026469 [0104] 1 Reject H0
Edu2t does not Granger cause LFt 012355 [0266] 1 Cannot reject H0
Edu3t does not Granger cause LFt 020468 [0153] 1 Cannot reject H0
Edu4t does not Granger cause LFt 098042 [0002] 1 Reject H0
Edu5t does not Granger cause LFt 049986 [0025] 1 Reject H0
Edu6t does not Granger cause LFt 016896 [0194] 1 Cannot reject H0
Edu7t does not Granger cause LFt 015167 [0218] 1 Cannot reject H0
Edu8t does not Granger cause LFt 184475 [0000] 1 Reject H0
Edu9t does not Granger cause LFt 003986 [0528] 1 Cannot reject H0
Edu10t does not Granger cause LFt 010899 [0296] 1 Cannot reject H0
Eq (10) LFt does not Granger cause Edu1t 107709 [0001] 1 Reject H0
LFt does not Granger cause Edu2t 071204 [0008] 1 Reject H0
LFt does not Granger cause Edu3t 136419 [0000] 1 Reject H0
LFt does not Granger cause Edu4t 056225 [0018] 1 Reject H0
LFt does not Granger cause Edu5t 057141 [0017] 1 Reject H0
LFt does not Granger cause Edu6t 091531 [0002] 1 Reject H0
LFt does not Granger cause Edu7t 095063 [0002] 1 Reject H0
LFt does not Granger cause Edu8t 021313 [0144] 1 Cannot reject H0
LFt does not Granger cause Edu9t 069389 [0008] 1 Reject H0
LFt does not Granger cause Edu10t 000743 [0785] 1 Cannot reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335330
Table II
Trivariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Trivariate-RGDPt RPCt and Eduit
Eq (11) Edu1t does not Granger cause RGDPt 005481 [0459] 1 Cannot reject H0
Edu2t does not Granger cause RGDPt 105415 [0001] 1 Reject H0
Edu3t does not Granger cause RGDPt 030370 [0081] 1 Reject H0
Edu4t does not Granger cause RGDPt 022525 [0133] 1 Cannot reject H0
Edu5t does not Granger cause RGDPt 227510 [0000] 1 Reject H0
Edu6t does not Granger cause RGDPt 098494 [0002] 1 Reject H0
Edu7t does not Granger cause RGDPt 090460 [0003] 1 Reject H0
Edu8t does not Granger cause RGDPt 067381 [0009] 1 Reject H0
Edu9t does not Granger cause RGDPt 168617 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 085842 [0003] Reject H0
Eq (11a) RPCt does not Granger cause RGDP (Edu1 as a 3rd variable) 029029 [0088] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu2 as a 3rd variable) 024880 [0115] 1 Cannot reject H0
RPCt does not Granger cause RGDPt (Edu3t as a 3rd variable) 041380 [0042] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu4t as a 3rd variable) 036580 [0056] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu5t as a 3rd variable) 064811 [0011] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu6t as a 3rd variable) 024405 [0118] 1 Cannot reject H0
RPCt does not Granger cause RGDPt (Edu7t as a 3rd variable) 026008 [0107] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu8t as a 3rd variable) 081607 [0004] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu9t as a 3rd variable) 063133 [0012] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu10t as a 3rd variable) 115637 [0001] 1 Reject H0
Eq (12) RGDPt does not Granger cause Edu1t 176454 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 129776 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 018626 [0172] 1 Cannot reject H0
RGDPt does not Granger cause Edu4t 020449 [0153] 1 Cannot reject H0
RGDPt does not Granger cause Edu5t 144658 [0000] 1 Reject H0
RGDPt does not Granger cause Edu6t 175431 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 178356 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 042497 [0039] 1 Reject H0
RGDPt does not Granger cause Edu9t 082506 [0004] 1 Reject H0
RGDPt does not Granger cause Edu10t 008026 [0370] 1 Cannot reject H0
Eq (12a) RPCt does not Granger cause Edu1t 000122 [0912] 1 Cannot reject H0
RPCt does not Granger cause Edu2t 028750 [0090] 1 Reject H0
RPCt does not Granger cause Edu3t 058586 [0016] 1 Reject H0
RPCt does not Granger cause Edu4t 071372 [0008] 1 Reject H0
RPCt does not Granger cause Edu5t 302364 [0000] 1 Reject H0
RPCt does not Granger cause Edu6t 020474 [0152] 1 Cannot reject H0
RPCt does not Granger cause Edu7t 017533 [0185] 1 Cannot reject H0
RPCt does not Granger cause Edu8t 044926 [0034] 1 Reject H0
RPCt does not Granger cause Edu9t 240955 [0000] 1 Reject H0
RPCt does not Granger cause Edu10t 021006 [0147] 1 Cannot reject H0
Eq (13) RGDPt does not Granger cause RPCt (Edu1t as a 3rd variable) 055095 [0019] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu2t as a 3rd variable) 182287 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu3t as a 3rd variable) 191499 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu4t as a 3rd variable) 269133 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu5t as a 3rd variable) 172979 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu6t as a 3rd variable) 166347 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu7t as a 3rd variable) 161198 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu8t as a 3rd variable) 038521 [0050] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu9tas a 3rd variable) 183169 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu10t as a 3rd variable) 139552 [0000] 1 Reject H0
Eq (13a) Edu1t does not Granger cause RPCt 000122 [0912] 1 Cannot reject H0
Edu2t does not Granger cause RPCt 028750 [0090] 1 Reject H0
Edu3t does not Granger cause RPCt 058586 [0016] 1 Reject H0
Edu4t does not Granger cause RPCt 071372 [0008] 1 Reject H0
Edu5t does not Granger cause RPCt 302364 [0000] 1 Reject H0
Edu6t does not Granger cause RPCt 020474 [0152] 1 Cannot reject H0
Edu7t does not Granger cause RPCt 017533 [0185] 1 Cannot reject H0
Edu8t does not Granger cause RPCt 044926 [0034] 1 Reject H0
Edu9t does not Granger cause RPCt 240955 [0000] 1 Reject H0
Edu10t does not Granger cause RPCt 021006 [0147] 1 Cannot reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 331
Table III
Trivariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Trivariate-RGDPt LFt and Eduit
Eq (14) Edu1t does not Granger cause RGDPt 068472 [0009] 1 Reject H0
Edu2t does not Granger cause RGDPt 092326 [0002] 1 Reject H0
Edu3t does not Granger cause RGDPt 180477 [0000] 1 Reject H0
Edu4t does not Granger cause RGDPt 132070 [0000] 1 Reject H0
Edu5t does not Granger cause RGDPt 109716 [0001] 1 Reject H0
Edu6t does not Granger cause RGDPt 086017 [0003] 1 Reject H0
Edu7t does not Granger cause RGDPt 078604 [0005] 1 Reject H0
Edu8t does not Granger cause RGDPt 020470 [0153] 1 Cannot reject H0
Edu9t does not Granger cause RGDPt 293293 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 005754 [0448] 1 Cannot reject H0
Eq (14a) LFt does not Granger cause RGDPt (Edu1t as a 3rd variable) 409533 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu2t as a 3rd variable) 332636 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu3t as a 3rd variable) 701171 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu4t as a 3rd variable) 605496 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu5t as a 3rd variable) 240867 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu6t as a 3rd variable) 330495 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu7t as a 3rd variable) 332860 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu8t as a 3rd variable) 352003 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu9t as a 3rd variable) 573087 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu10t as a 3rd variable) 343199 [0000] 1 Reject H0
Eq (15) RGDPt does not Granger cause Edu1t 134939 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 804323 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 109273 [0001] 1 Reject H0
RGDPt does not Granger cause Edu4t 278785 [0000] 1 Reject H0
RGDPt does not Granger cause Edu5t 050547 [0025] 1 Reject H0
RGDPt does not Granger cause Edu6t 790307 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 738342 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 043402 [0037] 1 Reject H0
RGDPt does not Granger cause Edu9t 175731 [0000] 1 Reject H0
RGDPt does not Granger cause Edu10t 061709 [0013] 1 Reject H0
Eq (15a) LFt does not Granger cause Edu1t 009324 [0334] 1 Cannot reject H0
LFt does not Granger cause Edu2t 377339 [0000] 1 Reject H0
LFt does not Granger cause Edu3t 176565 [0000] 1 Reject H0
LFt does not Granger cause Edu4t 180046 [0000] 1 Reject H0
LFt does not Granger cause Edu5t 091061 [0003] 1 Reject H0
LFt does not Granger cause Edu6t 355203 [0000] 1 Reject H0
LFt does not Granger cause Edu7t 327354 [0000] 1 Reject H0
LFt does not Granger cause Edu8t 053664 [0021] 1 Reject H0
LFt does not Granger cause Edu9t 251724 [0000] 1 Reject H0
LFt does not Granger cause Edu10t 060787 [0014] 1 Reject H0
Eq (16) Edu1t does not Granger cause LFt 036697 [0055] 1 Reject H0
Edu2t does not Granger cause LFt 004605 [0497] 1 Cannot reject H0
Edu3t does not Granger cause LFt 093988 [0002] 1 Reject H0
Edu4t does not Granger cause LFt 177287 [0000] 1 Reject H0
Edu5t does not Granger cause LFt 059203 [0015] 1 Reject H0
Edu6t does not Granger cause LFt 007202 [0396] 1 Cannot reject H0
Edu7t does not Granger cause LFt 005520 [0458] 1 Cannot reject H0
Edu8t does not Granger cause LFt 241662 [0000] 1 Reject H0
Edu9t does not Granger cause LFt 004009 [0527] 1 Cannot reject H0
Edu10t does not Granger cause LFt 058477 [0016] 1 Reject H0
Eq (16a) RGDPt does not Granger cause LFt (Edu1t as a 3rd variable) 002436 [0622] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu2t as a 3rd variable) 004276 [0513] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu3t as a 3rd variable) 047690 [0029] 1 Reject H0
RGDPt does not Granger cause LFt (Edu4t as a 3rd variable) 015207 [0218] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu5t as a 3rd variable) 040757 [0044] 1 Reject H0
RGDPt does not Granger cause LFt (Edu6t as a 3rd variable) 003392 [0560] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu7t as a 3rd variable) 004309 [0512] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu8t as a 3rd variable) 003145 [0575] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu9t as a 3rd variable) 017426 [0187] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu10t as a 3rd variable) 048448 [0028] 1 Reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335332
Table IV
Tetravariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Tetravariate-RGDPt RPCt LFt and Edut
Eq (17) Edu1t does not Granger cause RGDPt 029350 [0087] 1 Reject H0
Edu2t does not Granger cause RGDPt 065661 [0010] 1 Reject H0
Edu3t does not Granger cause RGDPt 097521 [0002] 1 Reject H0
Edu4t does not Granger cause RGDPt 071590 [0007] 1 Reject H0
Edu5t does not Granger cause RGDPt 116263 [0001] 1 Reject H0
Edu6t does not Granger cause RGDPt 059569 [0015] 1 Reject H0
Edu7t does not Granger cause RGDPt 054327 [0020] 1 Reject H0
Edu8t does not Granger cause RGDPt 040033 [0045] 1 Reject H0
Edu9t does not Granger cause RGDPt 195734 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 034374 [0064] 1 Reject H0
Eq (17a) LFt does not Granger cause RGDPt (Edut = Edu1) 251518 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu2) 165581 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu3) 316418 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu4) 289993 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu5) 109302 [0001] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu6) 165606 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu7) 168037 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu8) 176645 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu9) 247435 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu10) 146998 [0000] 1 Reject H0
Eq (17b) RPCt does not Granger cause RGDPt (Edut = Edu1) 042975 [0038] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu2) 039280 [0047] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu3) 034296 [0064] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu4) 027068 [0100] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu5) 062858 [0012] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu6) 039537 [0047] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu7) 040022 [0045] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu8) 045487 [0033] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu9) 068323 [0009] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu10) 083479 [0004] 1 Reject H0
Eq (18) RGDPt does not Granger cause Edu1t 150200 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 633103 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 045767 [0032] 1 Reject H0
RGDPt does not Granger cause Edu4t 122392 [0000] 1 Reject H0
RGDPt does not Granger cause Edu5t 004235 [0515] 1 Cannot reject H0
RGDPt does not Granger cause Edu6t 453644 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 418611 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 055973 [0454] 1 Cannot reject H0
RGDPt does not Granger cause Edu9t 053890 [0020] 1 Reject H0
RGDPt does not Granger cause Edu10t 011119 [0292] 1 Cannot reject H0
Eq (18a) LFt does not Granger cause Edu1t 006023 [0438] 1 Cannot reject H0
LFt does not Granger cause Edu2t 364559 [0000] 1 Reject H0
LFt does not Granger cause Edu3t 197423 [0000] 1 Reject H0
LFt does not Granger cause Edu4t 166511 [0000] 1 Reject H0
LFt does not Granger cause Edu5t 383886 [0000] 1 Reject H0
LFt does not Granger cause Edu6t 359377 [0000] 1 Reject H0
LFt does not Granger cause Edu7t 328249 [0000] 1 Reject H0
LFt does not Granger cause Edu8t 135310 [0000] 1 Reject H0
LFt does not Granger cause Edu9t 630068 [0000] 1 Reject H0
LFt does not Granger cause Edu01t 109365 [0001] 1 Reject H0
Eq (18b) RPCt does not Granger cause Edu1t 114248 [0001] 1 Reject H0
RPCt does not Granger cause Edu2t 036828 [0055] 1 Reject H0
RPCt does not Granger cause Edu3t 021023 [0147] 1 Cannot reject H0
RPCt does not Granger cause Edu4t 000484 [0826] 1 Cannot reject H0
RPCt does not Granger cause Edu5t 610934 [0000] 1 Reject H0
RPCt does not Granger cause Edu6t 070279 [0008] 1 Reject H0
RPCt does not Granger cause Edu7t 051166 [0024] 1 Reject H0
RPCt does not Granger cause Edu8t 167481 [0000] 1 Reject H0
RPCt does not Granger cause Edu9t 335271 [0000] 1 Reject H0
RPCt does not Granger cause Edu10t 067481 [0009] 1 Reject H0
Eq (19) Edu1 does not Granger cause RPCt 005154 [0473] 1 Cannot reject H0
Edu2 does not Granger cause RPCt 011954 [0274] 1 Cannot reject H0
Edu3 does not Granger cause RPCt 162365 [0000] 1 Reject H0
Edu4 does not Granger cause RPCt 148964 [0000] 1 Reject H0
Edu5 does not Granger cause RPCt 243978 [0000] 1 Reject H0
Edu6 does not Granger cause RPCt 040262 [0045] 1 Reject H0
Edu7 does not Granger cause RPCt 035138 [0061] 1 Reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 333
able IV (Continued )
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Edu8 does not Granger cause RPCt 030100 [0083] 1 Reject H0
Edu9 does not Granger cause RPCt 462564 [0000] 1 Reject H0
Edu10 does not Granger cause RPCt 009580 [0328] 1 Cannot reject H0
Eq (19a) RGDPt does not Granger cause RPCt (Edu1t as a 3rd variable) 009936 [0319] 1 Cannot reject H0
RGDPt does not Granger cause RPCt (Edu2t as a 3rd variable) 039369 [0047] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu3t as a 3rd variable) 003822 [0536] 1 Cannot reject H0
RGDPt does not Granger cause RPCt (Edu4t as a 3rd variable) 028000 [0094] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu5t as a 3rd variable) 039910 [0046] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu6t as a 3rd variable) 033500 [0067] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu7t as a 3rd variable) 029924 [0084] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu8t as a 3rd variable) 002803 [0597] 1 Cannot Reject H0
RGDPt does not Granger cause RPCt (Edu9t as a 3rd variable) 011416 [0285] 1 Cannot reject H0
RGDPt does not Granger cause RPCt (Edu10t as a 3rd variable) 006944 [0405] 1 Cannot reject H0
Eq (20) Edu1t does not Granger cause LFt 015302 [0216] 1 Cannot reject H0
Edu2t does not Granger cause LFt 001053 [0746] 1 Cannot reject H0
Edu3t does not Granger cause LFt 080072 [0005] 1 Reject H0
Edu4t does not Granger cause LFt 143854 [0000] 1 Reject H0
Edu5t does not Granger cause LFt 061159 [0013] 1 Reject H0
Edu6t does not Granger cause LFt 003113 [0577] 1 Cannot reject H0
Edu7t does not Granger cause LFt 002394 [0625] 1 Cannot reject H0
Edu8t does not Granger cause LFt 196804 [0000] 1 Reject H0
Edu9t does not Granger cause LFt 046285 [0496] 1 Cannot reject H0
Edu10t does not Granger cause LFt 04161 1 [0041] 1 Reject H0
Eq (20a) RGDPt does not Granger cause LFt (Edu1t as a 3rd variable) 006872 [0407] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu2t as a 3rd variable) 018604 [0173] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu3t as a 3rd variable) 066905 [0010] 1 Reject H0
RGDPt does not Granger cause LFt (Edu4t as a 3rd variable) 023249 [0127] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu5t as a 3rd variable) 070835 [0008] 1 Reject H0
RGDPt does not Granger cause LFt (Edu6t as a 3rd variable) 016501 [0199] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu7t as a 3rd variable) 018532 [0173] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu8t as a 3rd variable) 003730 [0541] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu9t as a 3rd variable) 039255 [0048] 1 Reject H0
RGDPt does not Granger cause LFt (Edu10t as a 3rd variable) 055266 [0019] 1 Reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335334
T
References
Abbas Q amp Peck J F (2008) Human capital and economic growth Pakistan 1960ndash2003 The Lahore Journal of Economics 13(1) 1ndash28Ayara N A (2002) The paradox of education and economic growth in Nigeria Empirical evidence The Nigerian Economic Society (NES) Pt 2 371ndash393Babatunde M A amp Adefabi R A (2005) Long run relationship between education and economic growth in Nigeria Evidence from the Johansenrsquos cointegration
approach Paper presented at the regional conference on education in West Africa Constraints and Opportunities Dakar Senegal November 1stndash2nd 2005Cornell UniversityCREAMinisterede lrsquoEducation du Senegal
Baldacci E Clements B Cui Q amp Gupta S (2005) What does it take to help the poor Finance and Development The Quarterly Magazine of the IMF 42(2)Changzheng Z Zhijian H amp Huaizu L (2007) An empirical study on education equity in China 1978ndash2004 Frontier in Economics of China 2(4) 536ndash544Chaudhary A R Asim I amp Gillani S Y M (2009) The nexus between higher education and economic growth An empirical investigation for Pakistan Pakistan
Journal of Commerce and Social Sciences 3Chaudhry I S Malik S amp Ashraf M (2006) Rural poverty in Pakistan Some related concepts issues and empirical analysis Pakistan Economic and Social Review
44(2) 259ndash276Diebolt C amp Litago J (1997) Education and economic growth in Germany before the Second World War An econometric analysis of dynamic relations Historical
Social Research 2(22) 132ndash149Easterly W (2001) The middle class consensus and economic development Journal of Economic Growth 6(4) 317ndash335Engle R F amp Granger C W J (1987) Cointegration and error correction Representation estimation and testing Econometrica 55 251ndash276Fernandez E amp Mauro P (2000) The role of human capital in economic growth The case of Spain (IMF Working Paper) International Monetary FundFrancis B amp Iyare S (2006) Education and development in the Caribbean A cointegration and causality approach Economics Bulletin 15(2) 1ndash13Galor O amp Moav O (2000) Das human capital Retrieved from httpeconpstcn brownedufacultygalorindexhtmlGoode R B (1959) Adding to the stock of physical and human capital American Economic Review 49(2) 147Government of Pakistan (1970ndash2009) Pakistan economic survey various issues Finance Division Islamabad Economic Advisorrsquos WingGregory A W amp Hansen B E (1996) Residual-based tests for cointegration in models with regime shifts Journal of Econometrics 70 99ndash126Grossman G M amp Helpman E (1991) Innovation and growth in the global economy Cambridge MIT PressGylfason T amp Zoega G (2003) Education social equality and economic growth A view of the landscape CESifo Economic Studies 49(4) 557ndash579Hassan S amp Ahmed H (2008) Educationrsquos contribution to the economic growth of sub-Saharan Africa Southwestern Economic Review 1(32) 175ndash190Islam T S Wadud M A amp Islam Q B T (2007) Relationship between education and GDP growth A multivariate causality analysis for Bangladesh Economics
Bulletin 3(35) 1ndash7Jin J C (2009) Economic research and economic growth Evidence from East Asian Economies Journal of Asian Economics 20 150ndash155Johansen S (1988) Statistical analysis of cointegration vectors Journal of Economic Dynamics and Control 12 231ndash254Johansen S amp Juselius K (1990) Maximum likelihood estimation and inference on cointegration with applications to the demand for money Oxford Bulletin of
Economics and Statistics 52 169ndash210Katırcıoglu S T (2009) Investigating higher-education-led growth hypothesis in a small Island Time series evidence from Northern Cyprus Paper presented at
Econ Anadolu 2009 Anadolu International Conference in Economics June 17ndash19 2009 TurkeyKhorasgani M F (2008) Higher education development and economic growth in Iran Education Business and Society Contemporary Middle Eastern Issues 1
162ndash174
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 335
Kui L (2005) The interactive causality between education and economic growth in China Retrieved from httppapersssrncomsol3paperscfmAbstrac-tid=920624
Loening J L (2004) Time series evidence on education and growth The case of Guatemala 1951ndash2002 Revista de Analisis Economico 19(2) 3ndash40Lucas R E (1988) On the mechanics of economic development Journal of Monetary Economics 22 3ndash42Macerinskiene I amp Vaiksnoraite B (2006) The role of higher education to economic development VadybaManagement 2(11)Mankiw N G Romer D amp Weil D N (1992) A contribution to the empirics of economic growth Quarterly Journal of Economics 107 407ndash437Momete D C (2007) Analysis of the relationship between employment and economic growth in Romania Fascicle of Management and Technological Engineering
VI(XVI)Morote E S (2000) Higher education employment and economic growth Mexico and Peru Retrieved from httpwwwamericanprofessororgdocumentation
lasapa perdocNarayan P K (2005) The saving and investment nexus for China Evidence from cointegration tests Applied Economics 37 1979ndash1990Permani R (2008) Education as a determinant of economic growth in East Asia Historical trends and empirical evidences (1965ndash2000) Retrieved from http
wwwuoweduaucommerceeconehsanzpdfsPermani202008pdfPesaran M H amp Pesaran B (1997) Working with Microfit 40 Interactive econometric analysis Oxford Oxford University PressPesaran M H amp Shin Y (1999) An autoregressive distributed lag modeling approach to cointegration analysis In S Strom (Ed) Econometrics and economic theory
in the 20th century Cambridge Cambridge University PressPesaran M H Shin Y amp Smith R J (2001) Bounds testing approaches to the analysis of level relationships Journal of Applied Econometrics 16 289ndash326Pradhan R P (2009) Education and economic growth in India Using error correction modeling International Research Journal of Finance and Economics 25Pritchett L (2001) Where has all the education gone The World Bank Economic Review 15(3)Quah D amp Rauch J E (1990) Openness and the rate of economic growth Journal Development of Studies 2(49) 307ndash335Rivera-Batiz L A amp Romer P M (1991) Economic integration and endogenous growth Quarterly Journal of Economics 106 531ndash555Romer P M (1986) Increasing returns and long run growth Journal of Political Economy 6(90) 1002ndash1037Romer P M (1989) Human capital and growth Theory and evidence (NBER Working Papers 3173) National Bureau of Economic Research IncRomer P M (1990) Endogenous technological change Journal of Political Economy 5(98) 71ndash101Rondinelli D amp Montgomery J (1995) Great policies Strategic innovations in Asia and the Pacific Basin Westport Praeger PublishingSaikkonen P amp Lutkepohl H (2000) Testing for the cointegration rank of a VAR process with structural shifts Journal of Business and Economic Statistics 18(4)
451ndash464Schultz T W (1961) Investment in human capital American Economic Review 51(1) 1State Bank of Pakistan (1972ndash2009) Annual reports Karachi SBP PressStengos T amp Aurangzeb A (2008) An empirical investigation of the relationship between education and growth in pakistan International Economic Journal 3
345ndash359 Retrieved from httpwwwinformaworldcomsmpptitledb=allcontent=t713685453tab=issueslistbranches=22-v2222Toda H Y amp Yamamoto T (1995) Statistical inference in vector autoregressive with possible integrated processes Journal of Econometrics 66 225ndash250United Nations (1997) Human Development Report New York Oxford University Press
- Education and economic growth in Pakistan A cointegration and causality analysis
-
- Introduction
- Review of literature
- Method and procedure
- Empirical results
-
- Unit root results
- Cointegration
- Toda-Yamamoto Augmented Granger Causality (TYAGC) Test
- Bivariate TYAGC framework
- Trivariate TYAGC framework
- Tetravariate TYAGC framework
- Figures in parentheses are p-values
-
- Conclusions and recommendations
-
- References
-
Table II
Trivariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Trivariate-RGDPt RPCt and Eduit
Eq (11) Edu1t does not Granger cause RGDPt 005481 [0459] 1 Cannot reject H0
Edu2t does not Granger cause RGDPt 105415 [0001] 1 Reject H0
Edu3t does not Granger cause RGDPt 030370 [0081] 1 Reject H0
Edu4t does not Granger cause RGDPt 022525 [0133] 1 Cannot reject H0
Edu5t does not Granger cause RGDPt 227510 [0000] 1 Reject H0
Edu6t does not Granger cause RGDPt 098494 [0002] 1 Reject H0
Edu7t does not Granger cause RGDPt 090460 [0003] 1 Reject H0
Edu8t does not Granger cause RGDPt 067381 [0009] 1 Reject H0
Edu9t does not Granger cause RGDPt 168617 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 085842 [0003] Reject H0
Eq (11a) RPCt does not Granger cause RGDP (Edu1 as a 3rd variable) 029029 [0088] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu2 as a 3rd variable) 024880 [0115] 1 Cannot reject H0
RPCt does not Granger cause RGDPt (Edu3t as a 3rd variable) 041380 [0042] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu4t as a 3rd variable) 036580 [0056] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu5t as a 3rd variable) 064811 [0011] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu6t as a 3rd variable) 024405 [0118] 1 Cannot reject H0
RPCt does not Granger cause RGDPt (Edu7t as a 3rd variable) 026008 [0107] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu8t as a 3rd variable) 081607 [0004] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu9t as a 3rd variable) 063133 [0012] 1 Reject H0
RPCt does not Granger cause RGDPt (Edu10t as a 3rd variable) 115637 [0001] 1 Reject H0
Eq (12) RGDPt does not Granger cause Edu1t 176454 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 129776 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 018626 [0172] 1 Cannot reject H0
RGDPt does not Granger cause Edu4t 020449 [0153] 1 Cannot reject H0
RGDPt does not Granger cause Edu5t 144658 [0000] 1 Reject H0
RGDPt does not Granger cause Edu6t 175431 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 178356 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 042497 [0039] 1 Reject H0
RGDPt does not Granger cause Edu9t 082506 [0004] 1 Reject H0
RGDPt does not Granger cause Edu10t 008026 [0370] 1 Cannot reject H0
Eq (12a) RPCt does not Granger cause Edu1t 000122 [0912] 1 Cannot reject H0
RPCt does not Granger cause Edu2t 028750 [0090] 1 Reject H0
RPCt does not Granger cause Edu3t 058586 [0016] 1 Reject H0
RPCt does not Granger cause Edu4t 071372 [0008] 1 Reject H0
RPCt does not Granger cause Edu5t 302364 [0000] 1 Reject H0
RPCt does not Granger cause Edu6t 020474 [0152] 1 Cannot reject H0
RPCt does not Granger cause Edu7t 017533 [0185] 1 Cannot reject H0
RPCt does not Granger cause Edu8t 044926 [0034] 1 Reject H0
RPCt does not Granger cause Edu9t 240955 [0000] 1 Reject H0
RPCt does not Granger cause Edu10t 021006 [0147] 1 Cannot reject H0
Eq (13) RGDPt does not Granger cause RPCt (Edu1t as a 3rd variable) 055095 [0019] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu2t as a 3rd variable) 182287 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu3t as a 3rd variable) 191499 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu4t as a 3rd variable) 269133 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu5t as a 3rd variable) 172979 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu6t as a 3rd variable) 166347 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu7t as a 3rd variable) 161198 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu8t as a 3rd variable) 038521 [0050] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu9tas a 3rd variable) 183169 [0000] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu10t as a 3rd variable) 139552 [0000] 1 Reject H0
Eq (13a) Edu1t does not Granger cause RPCt 000122 [0912] 1 Cannot reject H0
Edu2t does not Granger cause RPCt 028750 [0090] 1 Reject H0
Edu3t does not Granger cause RPCt 058586 [0016] 1 Reject H0
Edu4t does not Granger cause RPCt 071372 [0008] 1 Reject H0
Edu5t does not Granger cause RPCt 302364 [0000] 1 Reject H0
Edu6t does not Granger cause RPCt 020474 [0152] 1 Cannot reject H0
Edu7t does not Granger cause RPCt 017533 [0185] 1 Cannot reject H0
Edu8t does not Granger cause RPCt 044926 [0034] 1 Reject H0
Edu9t does not Granger cause RPCt 240955 [0000] 1 Reject H0
Edu10t does not Granger cause RPCt 021006 [0147] 1 Cannot reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 331
Table III
Trivariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Trivariate-RGDPt LFt and Eduit
Eq (14) Edu1t does not Granger cause RGDPt 068472 [0009] 1 Reject H0
Edu2t does not Granger cause RGDPt 092326 [0002] 1 Reject H0
Edu3t does not Granger cause RGDPt 180477 [0000] 1 Reject H0
Edu4t does not Granger cause RGDPt 132070 [0000] 1 Reject H0
Edu5t does not Granger cause RGDPt 109716 [0001] 1 Reject H0
Edu6t does not Granger cause RGDPt 086017 [0003] 1 Reject H0
Edu7t does not Granger cause RGDPt 078604 [0005] 1 Reject H0
Edu8t does not Granger cause RGDPt 020470 [0153] 1 Cannot reject H0
Edu9t does not Granger cause RGDPt 293293 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 005754 [0448] 1 Cannot reject H0
Eq (14a) LFt does not Granger cause RGDPt (Edu1t as a 3rd variable) 409533 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu2t as a 3rd variable) 332636 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu3t as a 3rd variable) 701171 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu4t as a 3rd variable) 605496 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu5t as a 3rd variable) 240867 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu6t as a 3rd variable) 330495 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu7t as a 3rd variable) 332860 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu8t as a 3rd variable) 352003 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu9t as a 3rd variable) 573087 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu10t as a 3rd variable) 343199 [0000] 1 Reject H0
Eq (15) RGDPt does not Granger cause Edu1t 134939 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 804323 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 109273 [0001] 1 Reject H0
RGDPt does not Granger cause Edu4t 278785 [0000] 1 Reject H0
RGDPt does not Granger cause Edu5t 050547 [0025] 1 Reject H0
RGDPt does not Granger cause Edu6t 790307 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 738342 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 043402 [0037] 1 Reject H0
RGDPt does not Granger cause Edu9t 175731 [0000] 1 Reject H0
RGDPt does not Granger cause Edu10t 061709 [0013] 1 Reject H0
Eq (15a) LFt does not Granger cause Edu1t 009324 [0334] 1 Cannot reject H0
LFt does not Granger cause Edu2t 377339 [0000] 1 Reject H0
LFt does not Granger cause Edu3t 176565 [0000] 1 Reject H0
LFt does not Granger cause Edu4t 180046 [0000] 1 Reject H0
LFt does not Granger cause Edu5t 091061 [0003] 1 Reject H0
LFt does not Granger cause Edu6t 355203 [0000] 1 Reject H0
LFt does not Granger cause Edu7t 327354 [0000] 1 Reject H0
LFt does not Granger cause Edu8t 053664 [0021] 1 Reject H0
LFt does not Granger cause Edu9t 251724 [0000] 1 Reject H0
LFt does not Granger cause Edu10t 060787 [0014] 1 Reject H0
Eq (16) Edu1t does not Granger cause LFt 036697 [0055] 1 Reject H0
Edu2t does not Granger cause LFt 004605 [0497] 1 Cannot reject H0
Edu3t does not Granger cause LFt 093988 [0002] 1 Reject H0
Edu4t does not Granger cause LFt 177287 [0000] 1 Reject H0
Edu5t does not Granger cause LFt 059203 [0015] 1 Reject H0
Edu6t does not Granger cause LFt 007202 [0396] 1 Cannot reject H0
Edu7t does not Granger cause LFt 005520 [0458] 1 Cannot reject H0
Edu8t does not Granger cause LFt 241662 [0000] 1 Reject H0
Edu9t does not Granger cause LFt 004009 [0527] 1 Cannot reject H0
Edu10t does not Granger cause LFt 058477 [0016] 1 Reject H0
Eq (16a) RGDPt does not Granger cause LFt (Edu1t as a 3rd variable) 002436 [0622] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu2t as a 3rd variable) 004276 [0513] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu3t as a 3rd variable) 047690 [0029] 1 Reject H0
RGDPt does not Granger cause LFt (Edu4t as a 3rd variable) 015207 [0218] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu5t as a 3rd variable) 040757 [0044] 1 Reject H0
RGDPt does not Granger cause LFt (Edu6t as a 3rd variable) 003392 [0560] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu7t as a 3rd variable) 004309 [0512] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu8t as a 3rd variable) 003145 [0575] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu9t as a 3rd variable) 017426 [0187] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu10t as a 3rd variable) 048448 [0028] 1 Reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335332
Table IV
Tetravariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Tetravariate-RGDPt RPCt LFt and Edut
Eq (17) Edu1t does not Granger cause RGDPt 029350 [0087] 1 Reject H0
Edu2t does not Granger cause RGDPt 065661 [0010] 1 Reject H0
Edu3t does not Granger cause RGDPt 097521 [0002] 1 Reject H0
Edu4t does not Granger cause RGDPt 071590 [0007] 1 Reject H0
Edu5t does not Granger cause RGDPt 116263 [0001] 1 Reject H0
Edu6t does not Granger cause RGDPt 059569 [0015] 1 Reject H0
Edu7t does not Granger cause RGDPt 054327 [0020] 1 Reject H0
Edu8t does not Granger cause RGDPt 040033 [0045] 1 Reject H0
Edu9t does not Granger cause RGDPt 195734 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 034374 [0064] 1 Reject H0
Eq (17a) LFt does not Granger cause RGDPt (Edut = Edu1) 251518 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu2) 165581 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu3) 316418 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu4) 289993 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu5) 109302 [0001] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu6) 165606 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu7) 168037 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu8) 176645 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu9) 247435 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu10) 146998 [0000] 1 Reject H0
Eq (17b) RPCt does not Granger cause RGDPt (Edut = Edu1) 042975 [0038] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu2) 039280 [0047] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu3) 034296 [0064] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu4) 027068 [0100] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu5) 062858 [0012] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu6) 039537 [0047] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu7) 040022 [0045] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu8) 045487 [0033] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu9) 068323 [0009] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu10) 083479 [0004] 1 Reject H0
Eq (18) RGDPt does not Granger cause Edu1t 150200 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 633103 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 045767 [0032] 1 Reject H0
RGDPt does not Granger cause Edu4t 122392 [0000] 1 Reject H0
RGDPt does not Granger cause Edu5t 004235 [0515] 1 Cannot reject H0
RGDPt does not Granger cause Edu6t 453644 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 418611 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 055973 [0454] 1 Cannot reject H0
RGDPt does not Granger cause Edu9t 053890 [0020] 1 Reject H0
RGDPt does not Granger cause Edu10t 011119 [0292] 1 Cannot reject H0
Eq (18a) LFt does not Granger cause Edu1t 006023 [0438] 1 Cannot reject H0
LFt does not Granger cause Edu2t 364559 [0000] 1 Reject H0
LFt does not Granger cause Edu3t 197423 [0000] 1 Reject H0
LFt does not Granger cause Edu4t 166511 [0000] 1 Reject H0
LFt does not Granger cause Edu5t 383886 [0000] 1 Reject H0
LFt does not Granger cause Edu6t 359377 [0000] 1 Reject H0
LFt does not Granger cause Edu7t 328249 [0000] 1 Reject H0
LFt does not Granger cause Edu8t 135310 [0000] 1 Reject H0
LFt does not Granger cause Edu9t 630068 [0000] 1 Reject H0
LFt does not Granger cause Edu01t 109365 [0001] 1 Reject H0
Eq (18b) RPCt does not Granger cause Edu1t 114248 [0001] 1 Reject H0
RPCt does not Granger cause Edu2t 036828 [0055] 1 Reject H0
RPCt does not Granger cause Edu3t 021023 [0147] 1 Cannot reject H0
RPCt does not Granger cause Edu4t 000484 [0826] 1 Cannot reject H0
RPCt does not Granger cause Edu5t 610934 [0000] 1 Reject H0
RPCt does not Granger cause Edu6t 070279 [0008] 1 Reject H0
RPCt does not Granger cause Edu7t 051166 [0024] 1 Reject H0
RPCt does not Granger cause Edu8t 167481 [0000] 1 Reject H0
RPCt does not Granger cause Edu9t 335271 [0000] 1 Reject H0
RPCt does not Granger cause Edu10t 067481 [0009] 1 Reject H0
Eq (19) Edu1 does not Granger cause RPCt 005154 [0473] 1 Cannot reject H0
Edu2 does not Granger cause RPCt 011954 [0274] 1 Cannot reject H0
Edu3 does not Granger cause RPCt 162365 [0000] 1 Reject H0
Edu4 does not Granger cause RPCt 148964 [0000] 1 Reject H0
Edu5 does not Granger cause RPCt 243978 [0000] 1 Reject H0
Edu6 does not Granger cause RPCt 040262 [0045] 1 Reject H0
Edu7 does not Granger cause RPCt 035138 [0061] 1 Reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 333
able IV (Continued )
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Edu8 does not Granger cause RPCt 030100 [0083] 1 Reject H0
Edu9 does not Granger cause RPCt 462564 [0000] 1 Reject H0
Edu10 does not Granger cause RPCt 009580 [0328] 1 Cannot reject H0
Eq (19a) RGDPt does not Granger cause RPCt (Edu1t as a 3rd variable) 009936 [0319] 1 Cannot reject H0
RGDPt does not Granger cause RPCt (Edu2t as a 3rd variable) 039369 [0047] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu3t as a 3rd variable) 003822 [0536] 1 Cannot reject H0
RGDPt does not Granger cause RPCt (Edu4t as a 3rd variable) 028000 [0094] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu5t as a 3rd variable) 039910 [0046] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu6t as a 3rd variable) 033500 [0067] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu7t as a 3rd variable) 029924 [0084] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu8t as a 3rd variable) 002803 [0597] 1 Cannot Reject H0
RGDPt does not Granger cause RPCt (Edu9t as a 3rd variable) 011416 [0285] 1 Cannot reject H0
RGDPt does not Granger cause RPCt (Edu10t as a 3rd variable) 006944 [0405] 1 Cannot reject H0
Eq (20) Edu1t does not Granger cause LFt 015302 [0216] 1 Cannot reject H0
Edu2t does not Granger cause LFt 001053 [0746] 1 Cannot reject H0
Edu3t does not Granger cause LFt 080072 [0005] 1 Reject H0
Edu4t does not Granger cause LFt 143854 [0000] 1 Reject H0
Edu5t does not Granger cause LFt 061159 [0013] 1 Reject H0
Edu6t does not Granger cause LFt 003113 [0577] 1 Cannot reject H0
Edu7t does not Granger cause LFt 002394 [0625] 1 Cannot reject H0
Edu8t does not Granger cause LFt 196804 [0000] 1 Reject H0
Edu9t does not Granger cause LFt 046285 [0496] 1 Cannot reject H0
Edu10t does not Granger cause LFt 04161 1 [0041] 1 Reject H0
Eq (20a) RGDPt does not Granger cause LFt (Edu1t as a 3rd variable) 006872 [0407] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu2t as a 3rd variable) 018604 [0173] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu3t as a 3rd variable) 066905 [0010] 1 Reject H0
RGDPt does not Granger cause LFt (Edu4t as a 3rd variable) 023249 [0127] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu5t as a 3rd variable) 070835 [0008] 1 Reject H0
RGDPt does not Granger cause LFt (Edu6t as a 3rd variable) 016501 [0199] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu7t as a 3rd variable) 018532 [0173] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu8t as a 3rd variable) 003730 [0541] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu9t as a 3rd variable) 039255 [0048] 1 Reject H0
RGDPt does not Granger cause LFt (Edu10t as a 3rd variable) 055266 [0019] 1 Reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335334
T
References
Abbas Q amp Peck J F (2008) Human capital and economic growth Pakistan 1960ndash2003 The Lahore Journal of Economics 13(1) 1ndash28Ayara N A (2002) The paradox of education and economic growth in Nigeria Empirical evidence The Nigerian Economic Society (NES) Pt 2 371ndash393Babatunde M A amp Adefabi R A (2005) Long run relationship between education and economic growth in Nigeria Evidence from the Johansenrsquos cointegration
approach Paper presented at the regional conference on education in West Africa Constraints and Opportunities Dakar Senegal November 1stndash2nd 2005Cornell UniversityCREAMinisterede lrsquoEducation du Senegal
Baldacci E Clements B Cui Q amp Gupta S (2005) What does it take to help the poor Finance and Development The Quarterly Magazine of the IMF 42(2)Changzheng Z Zhijian H amp Huaizu L (2007) An empirical study on education equity in China 1978ndash2004 Frontier in Economics of China 2(4) 536ndash544Chaudhary A R Asim I amp Gillani S Y M (2009) The nexus between higher education and economic growth An empirical investigation for Pakistan Pakistan
Journal of Commerce and Social Sciences 3Chaudhry I S Malik S amp Ashraf M (2006) Rural poverty in Pakistan Some related concepts issues and empirical analysis Pakistan Economic and Social Review
44(2) 259ndash276Diebolt C amp Litago J (1997) Education and economic growth in Germany before the Second World War An econometric analysis of dynamic relations Historical
Social Research 2(22) 132ndash149Easterly W (2001) The middle class consensus and economic development Journal of Economic Growth 6(4) 317ndash335Engle R F amp Granger C W J (1987) Cointegration and error correction Representation estimation and testing Econometrica 55 251ndash276Fernandez E amp Mauro P (2000) The role of human capital in economic growth The case of Spain (IMF Working Paper) International Monetary FundFrancis B amp Iyare S (2006) Education and development in the Caribbean A cointegration and causality approach Economics Bulletin 15(2) 1ndash13Galor O amp Moav O (2000) Das human capital Retrieved from httpeconpstcn brownedufacultygalorindexhtmlGoode R B (1959) Adding to the stock of physical and human capital American Economic Review 49(2) 147Government of Pakistan (1970ndash2009) Pakistan economic survey various issues Finance Division Islamabad Economic Advisorrsquos WingGregory A W amp Hansen B E (1996) Residual-based tests for cointegration in models with regime shifts Journal of Econometrics 70 99ndash126Grossman G M amp Helpman E (1991) Innovation and growth in the global economy Cambridge MIT PressGylfason T amp Zoega G (2003) Education social equality and economic growth A view of the landscape CESifo Economic Studies 49(4) 557ndash579Hassan S amp Ahmed H (2008) Educationrsquos contribution to the economic growth of sub-Saharan Africa Southwestern Economic Review 1(32) 175ndash190Islam T S Wadud M A amp Islam Q B T (2007) Relationship between education and GDP growth A multivariate causality analysis for Bangladesh Economics
Bulletin 3(35) 1ndash7Jin J C (2009) Economic research and economic growth Evidence from East Asian Economies Journal of Asian Economics 20 150ndash155Johansen S (1988) Statistical analysis of cointegration vectors Journal of Economic Dynamics and Control 12 231ndash254Johansen S amp Juselius K (1990) Maximum likelihood estimation and inference on cointegration with applications to the demand for money Oxford Bulletin of
Economics and Statistics 52 169ndash210Katırcıoglu S T (2009) Investigating higher-education-led growth hypothesis in a small Island Time series evidence from Northern Cyprus Paper presented at
Econ Anadolu 2009 Anadolu International Conference in Economics June 17ndash19 2009 TurkeyKhorasgani M F (2008) Higher education development and economic growth in Iran Education Business and Society Contemporary Middle Eastern Issues 1
162ndash174
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 335
Kui L (2005) The interactive causality between education and economic growth in China Retrieved from httppapersssrncomsol3paperscfmAbstrac-tid=920624
Loening J L (2004) Time series evidence on education and growth The case of Guatemala 1951ndash2002 Revista de Analisis Economico 19(2) 3ndash40Lucas R E (1988) On the mechanics of economic development Journal of Monetary Economics 22 3ndash42Macerinskiene I amp Vaiksnoraite B (2006) The role of higher education to economic development VadybaManagement 2(11)Mankiw N G Romer D amp Weil D N (1992) A contribution to the empirics of economic growth Quarterly Journal of Economics 107 407ndash437Momete D C (2007) Analysis of the relationship between employment and economic growth in Romania Fascicle of Management and Technological Engineering
VI(XVI)Morote E S (2000) Higher education employment and economic growth Mexico and Peru Retrieved from httpwwwamericanprofessororgdocumentation
lasapa perdocNarayan P K (2005) The saving and investment nexus for China Evidence from cointegration tests Applied Economics 37 1979ndash1990Permani R (2008) Education as a determinant of economic growth in East Asia Historical trends and empirical evidences (1965ndash2000) Retrieved from http
wwwuoweduaucommerceeconehsanzpdfsPermani202008pdfPesaran M H amp Pesaran B (1997) Working with Microfit 40 Interactive econometric analysis Oxford Oxford University PressPesaran M H amp Shin Y (1999) An autoregressive distributed lag modeling approach to cointegration analysis In S Strom (Ed) Econometrics and economic theory
in the 20th century Cambridge Cambridge University PressPesaran M H Shin Y amp Smith R J (2001) Bounds testing approaches to the analysis of level relationships Journal of Applied Econometrics 16 289ndash326Pradhan R P (2009) Education and economic growth in India Using error correction modeling International Research Journal of Finance and Economics 25Pritchett L (2001) Where has all the education gone The World Bank Economic Review 15(3)Quah D amp Rauch J E (1990) Openness and the rate of economic growth Journal Development of Studies 2(49) 307ndash335Rivera-Batiz L A amp Romer P M (1991) Economic integration and endogenous growth Quarterly Journal of Economics 106 531ndash555Romer P M (1986) Increasing returns and long run growth Journal of Political Economy 6(90) 1002ndash1037Romer P M (1989) Human capital and growth Theory and evidence (NBER Working Papers 3173) National Bureau of Economic Research IncRomer P M (1990) Endogenous technological change Journal of Political Economy 5(98) 71ndash101Rondinelli D amp Montgomery J (1995) Great policies Strategic innovations in Asia and the Pacific Basin Westport Praeger PublishingSaikkonen P amp Lutkepohl H (2000) Testing for the cointegration rank of a VAR process with structural shifts Journal of Business and Economic Statistics 18(4)
451ndash464Schultz T W (1961) Investment in human capital American Economic Review 51(1) 1State Bank of Pakistan (1972ndash2009) Annual reports Karachi SBP PressStengos T amp Aurangzeb A (2008) An empirical investigation of the relationship between education and growth in pakistan International Economic Journal 3
345ndash359 Retrieved from httpwwwinformaworldcomsmpptitledb=allcontent=t713685453tab=issueslistbranches=22-v2222Toda H Y amp Yamamoto T (1995) Statistical inference in vector autoregressive with possible integrated processes Journal of Econometrics 66 225ndash250United Nations (1997) Human Development Report New York Oxford University Press
- Education and economic growth in Pakistan A cointegration and causality analysis
-
- Introduction
- Review of literature
- Method and procedure
- Empirical results
-
- Unit root results
- Cointegration
- Toda-Yamamoto Augmented Granger Causality (TYAGC) Test
- Bivariate TYAGC framework
- Trivariate TYAGC framework
- Tetravariate TYAGC framework
- Figures in parentheses are p-values
-
- Conclusions and recommendations
-
- References
-
Table III
Trivariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Trivariate-RGDPt LFt and Eduit
Eq (14) Edu1t does not Granger cause RGDPt 068472 [0009] 1 Reject H0
Edu2t does not Granger cause RGDPt 092326 [0002] 1 Reject H0
Edu3t does not Granger cause RGDPt 180477 [0000] 1 Reject H0
Edu4t does not Granger cause RGDPt 132070 [0000] 1 Reject H0
Edu5t does not Granger cause RGDPt 109716 [0001] 1 Reject H0
Edu6t does not Granger cause RGDPt 086017 [0003] 1 Reject H0
Edu7t does not Granger cause RGDPt 078604 [0005] 1 Reject H0
Edu8t does not Granger cause RGDPt 020470 [0153] 1 Cannot reject H0
Edu9t does not Granger cause RGDPt 293293 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 005754 [0448] 1 Cannot reject H0
Eq (14a) LFt does not Granger cause RGDPt (Edu1t as a 3rd variable) 409533 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu2t as a 3rd variable) 332636 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu3t as a 3rd variable) 701171 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu4t as a 3rd variable) 605496 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu5t as a 3rd variable) 240867 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu6t as a 3rd variable) 330495 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu7t as a 3rd variable) 332860 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu8t as a 3rd variable) 352003 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu9t as a 3rd variable) 573087 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edu10t as a 3rd variable) 343199 [0000] 1 Reject H0
Eq (15) RGDPt does not Granger cause Edu1t 134939 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 804323 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 109273 [0001] 1 Reject H0
RGDPt does not Granger cause Edu4t 278785 [0000] 1 Reject H0
RGDPt does not Granger cause Edu5t 050547 [0025] 1 Reject H0
RGDPt does not Granger cause Edu6t 790307 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 738342 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 043402 [0037] 1 Reject H0
RGDPt does not Granger cause Edu9t 175731 [0000] 1 Reject H0
RGDPt does not Granger cause Edu10t 061709 [0013] 1 Reject H0
Eq (15a) LFt does not Granger cause Edu1t 009324 [0334] 1 Cannot reject H0
LFt does not Granger cause Edu2t 377339 [0000] 1 Reject H0
LFt does not Granger cause Edu3t 176565 [0000] 1 Reject H0
LFt does not Granger cause Edu4t 180046 [0000] 1 Reject H0
LFt does not Granger cause Edu5t 091061 [0003] 1 Reject H0
LFt does not Granger cause Edu6t 355203 [0000] 1 Reject H0
LFt does not Granger cause Edu7t 327354 [0000] 1 Reject H0
LFt does not Granger cause Edu8t 053664 [0021] 1 Reject H0
LFt does not Granger cause Edu9t 251724 [0000] 1 Reject H0
LFt does not Granger cause Edu10t 060787 [0014] 1 Reject H0
Eq (16) Edu1t does not Granger cause LFt 036697 [0055] 1 Reject H0
Edu2t does not Granger cause LFt 004605 [0497] 1 Cannot reject H0
Edu3t does not Granger cause LFt 093988 [0002] 1 Reject H0
Edu4t does not Granger cause LFt 177287 [0000] 1 Reject H0
Edu5t does not Granger cause LFt 059203 [0015] 1 Reject H0
Edu6t does not Granger cause LFt 007202 [0396] 1 Cannot reject H0
Edu7t does not Granger cause LFt 005520 [0458] 1 Cannot reject H0
Edu8t does not Granger cause LFt 241662 [0000] 1 Reject H0
Edu9t does not Granger cause LFt 004009 [0527] 1 Cannot reject H0
Edu10t does not Granger cause LFt 058477 [0016] 1 Reject H0
Eq (16a) RGDPt does not Granger cause LFt (Edu1t as a 3rd variable) 002436 [0622] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu2t as a 3rd variable) 004276 [0513] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu3t as a 3rd variable) 047690 [0029] 1 Reject H0
RGDPt does not Granger cause LFt (Edu4t as a 3rd variable) 015207 [0218] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu5t as a 3rd variable) 040757 [0044] 1 Reject H0
RGDPt does not Granger cause LFt (Edu6t as a 3rd variable) 003392 [0560] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu7t as a 3rd variable) 004309 [0512] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu8t as a 3rd variable) 003145 [0575] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu9t as a 3rd variable) 017426 [0187] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu10t as a 3rd variable) 048448 [0028] 1 Reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335332
Table IV
Tetravariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Tetravariate-RGDPt RPCt LFt and Edut
Eq (17) Edu1t does not Granger cause RGDPt 029350 [0087] 1 Reject H0
Edu2t does not Granger cause RGDPt 065661 [0010] 1 Reject H0
Edu3t does not Granger cause RGDPt 097521 [0002] 1 Reject H0
Edu4t does not Granger cause RGDPt 071590 [0007] 1 Reject H0
Edu5t does not Granger cause RGDPt 116263 [0001] 1 Reject H0
Edu6t does not Granger cause RGDPt 059569 [0015] 1 Reject H0
Edu7t does not Granger cause RGDPt 054327 [0020] 1 Reject H0
Edu8t does not Granger cause RGDPt 040033 [0045] 1 Reject H0
Edu9t does not Granger cause RGDPt 195734 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 034374 [0064] 1 Reject H0
Eq (17a) LFt does not Granger cause RGDPt (Edut = Edu1) 251518 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu2) 165581 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu3) 316418 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu4) 289993 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu5) 109302 [0001] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu6) 165606 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu7) 168037 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu8) 176645 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu9) 247435 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu10) 146998 [0000] 1 Reject H0
Eq (17b) RPCt does not Granger cause RGDPt (Edut = Edu1) 042975 [0038] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu2) 039280 [0047] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu3) 034296 [0064] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu4) 027068 [0100] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu5) 062858 [0012] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu6) 039537 [0047] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu7) 040022 [0045] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu8) 045487 [0033] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu9) 068323 [0009] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu10) 083479 [0004] 1 Reject H0
Eq (18) RGDPt does not Granger cause Edu1t 150200 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 633103 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 045767 [0032] 1 Reject H0
RGDPt does not Granger cause Edu4t 122392 [0000] 1 Reject H0
RGDPt does not Granger cause Edu5t 004235 [0515] 1 Cannot reject H0
RGDPt does not Granger cause Edu6t 453644 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 418611 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 055973 [0454] 1 Cannot reject H0
RGDPt does not Granger cause Edu9t 053890 [0020] 1 Reject H0
RGDPt does not Granger cause Edu10t 011119 [0292] 1 Cannot reject H0
Eq (18a) LFt does not Granger cause Edu1t 006023 [0438] 1 Cannot reject H0
LFt does not Granger cause Edu2t 364559 [0000] 1 Reject H0
LFt does not Granger cause Edu3t 197423 [0000] 1 Reject H0
LFt does not Granger cause Edu4t 166511 [0000] 1 Reject H0
LFt does not Granger cause Edu5t 383886 [0000] 1 Reject H0
LFt does not Granger cause Edu6t 359377 [0000] 1 Reject H0
LFt does not Granger cause Edu7t 328249 [0000] 1 Reject H0
LFt does not Granger cause Edu8t 135310 [0000] 1 Reject H0
LFt does not Granger cause Edu9t 630068 [0000] 1 Reject H0
LFt does not Granger cause Edu01t 109365 [0001] 1 Reject H0
Eq (18b) RPCt does not Granger cause Edu1t 114248 [0001] 1 Reject H0
RPCt does not Granger cause Edu2t 036828 [0055] 1 Reject H0
RPCt does not Granger cause Edu3t 021023 [0147] 1 Cannot reject H0
RPCt does not Granger cause Edu4t 000484 [0826] 1 Cannot reject H0
RPCt does not Granger cause Edu5t 610934 [0000] 1 Reject H0
RPCt does not Granger cause Edu6t 070279 [0008] 1 Reject H0
RPCt does not Granger cause Edu7t 051166 [0024] 1 Reject H0
RPCt does not Granger cause Edu8t 167481 [0000] 1 Reject H0
RPCt does not Granger cause Edu9t 335271 [0000] 1 Reject H0
RPCt does not Granger cause Edu10t 067481 [0009] 1 Reject H0
Eq (19) Edu1 does not Granger cause RPCt 005154 [0473] 1 Cannot reject H0
Edu2 does not Granger cause RPCt 011954 [0274] 1 Cannot reject H0
Edu3 does not Granger cause RPCt 162365 [0000] 1 Reject H0
Edu4 does not Granger cause RPCt 148964 [0000] 1 Reject H0
Edu5 does not Granger cause RPCt 243978 [0000] 1 Reject H0
Edu6 does not Granger cause RPCt 040262 [0045] 1 Reject H0
Edu7 does not Granger cause RPCt 035138 [0061] 1 Reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 333
able IV (Continued )
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Edu8 does not Granger cause RPCt 030100 [0083] 1 Reject H0
Edu9 does not Granger cause RPCt 462564 [0000] 1 Reject H0
Edu10 does not Granger cause RPCt 009580 [0328] 1 Cannot reject H0
Eq (19a) RGDPt does not Granger cause RPCt (Edu1t as a 3rd variable) 009936 [0319] 1 Cannot reject H0
RGDPt does not Granger cause RPCt (Edu2t as a 3rd variable) 039369 [0047] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu3t as a 3rd variable) 003822 [0536] 1 Cannot reject H0
RGDPt does not Granger cause RPCt (Edu4t as a 3rd variable) 028000 [0094] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu5t as a 3rd variable) 039910 [0046] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu6t as a 3rd variable) 033500 [0067] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu7t as a 3rd variable) 029924 [0084] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu8t as a 3rd variable) 002803 [0597] 1 Cannot Reject H0
RGDPt does not Granger cause RPCt (Edu9t as a 3rd variable) 011416 [0285] 1 Cannot reject H0
RGDPt does not Granger cause RPCt (Edu10t as a 3rd variable) 006944 [0405] 1 Cannot reject H0
Eq (20) Edu1t does not Granger cause LFt 015302 [0216] 1 Cannot reject H0
Edu2t does not Granger cause LFt 001053 [0746] 1 Cannot reject H0
Edu3t does not Granger cause LFt 080072 [0005] 1 Reject H0
Edu4t does not Granger cause LFt 143854 [0000] 1 Reject H0
Edu5t does not Granger cause LFt 061159 [0013] 1 Reject H0
Edu6t does not Granger cause LFt 003113 [0577] 1 Cannot reject H0
Edu7t does not Granger cause LFt 002394 [0625] 1 Cannot reject H0
Edu8t does not Granger cause LFt 196804 [0000] 1 Reject H0
Edu9t does not Granger cause LFt 046285 [0496] 1 Cannot reject H0
Edu10t does not Granger cause LFt 04161 1 [0041] 1 Reject H0
Eq (20a) RGDPt does not Granger cause LFt (Edu1t as a 3rd variable) 006872 [0407] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu2t as a 3rd variable) 018604 [0173] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu3t as a 3rd variable) 066905 [0010] 1 Reject H0
RGDPt does not Granger cause LFt (Edu4t as a 3rd variable) 023249 [0127] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu5t as a 3rd variable) 070835 [0008] 1 Reject H0
RGDPt does not Granger cause LFt (Edu6t as a 3rd variable) 016501 [0199] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu7t as a 3rd variable) 018532 [0173] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu8t as a 3rd variable) 003730 [0541] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu9t as a 3rd variable) 039255 [0048] 1 Reject H0
RGDPt does not Granger cause LFt (Edu10t as a 3rd variable) 055266 [0019] 1 Reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335334
T
References
Abbas Q amp Peck J F (2008) Human capital and economic growth Pakistan 1960ndash2003 The Lahore Journal of Economics 13(1) 1ndash28Ayara N A (2002) The paradox of education and economic growth in Nigeria Empirical evidence The Nigerian Economic Society (NES) Pt 2 371ndash393Babatunde M A amp Adefabi R A (2005) Long run relationship between education and economic growth in Nigeria Evidence from the Johansenrsquos cointegration
approach Paper presented at the regional conference on education in West Africa Constraints and Opportunities Dakar Senegal November 1stndash2nd 2005Cornell UniversityCREAMinisterede lrsquoEducation du Senegal
Baldacci E Clements B Cui Q amp Gupta S (2005) What does it take to help the poor Finance and Development The Quarterly Magazine of the IMF 42(2)Changzheng Z Zhijian H amp Huaizu L (2007) An empirical study on education equity in China 1978ndash2004 Frontier in Economics of China 2(4) 536ndash544Chaudhary A R Asim I amp Gillani S Y M (2009) The nexus between higher education and economic growth An empirical investigation for Pakistan Pakistan
Journal of Commerce and Social Sciences 3Chaudhry I S Malik S amp Ashraf M (2006) Rural poverty in Pakistan Some related concepts issues and empirical analysis Pakistan Economic and Social Review
44(2) 259ndash276Diebolt C amp Litago J (1997) Education and economic growth in Germany before the Second World War An econometric analysis of dynamic relations Historical
Social Research 2(22) 132ndash149Easterly W (2001) The middle class consensus and economic development Journal of Economic Growth 6(4) 317ndash335Engle R F amp Granger C W J (1987) Cointegration and error correction Representation estimation and testing Econometrica 55 251ndash276Fernandez E amp Mauro P (2000) The role of human capital in economic growth The case of Spain (IMF Working Paper) International Monetary FundFrancis B amp Iyare S (2006) Education and development in the Caribbean A cointegration and causality approach Economics Bulletin 15(2) 1ndash13Galor O amp Moav O (2000) Das human capital Retrieved from httpeconpstcn brownedufacultygalorindexhtmlGoode R B (1959) Adding to the stock of physical and human capital American Economic Review 49(2) 147Government of Pakistan (1970ndash2009) Pakistan economic survey various issues Finance Division Islamabad Economic Advisorrsquos WingGregory A W amp Hansen B E (1996) Residual-based tests for cointegration in models with regime shifts Journal of Econometrics 70 99ndash126Grossman G M amp Helpman E (1991) Innovation and growth in the global economy Cambridge MIT PressGylfason T amp Zoega G (2003) Education social equality and economic growth A view of the landscape CESifo Economic Studies 49(4) 557ndash579Hassan S amp Ahmed H (2008) Educationrsquos contribution to the economic growth of sub-Saharan Africa Southwestern Economic Review 1(32) 175ndash190Islam T S Wadud M A amp Islam Q B T (2007) Relationship between education and GDP growth A multivariate causality analysis for Bangladesh Economics
Bulletin 3(35) 1ndash7Jin J C (2009) Economic research and economic growth Evidence from East Asian Economies Journal of Asian Economics 20 150ndash155Johansen S (1988) Statistical analysis of cointegration vectors Journal of Economic Dynamics and Control 12 231ndash254Johansen S amp Juselius K (1990) Maximum likelihood estimation and inference on cointegration with applications to the demand for money Oxford Bulletin of
Economics and Statistics 52 169ndash210Katırcıoglu S T (2009) Investigating higher-education-led growth hypothesis in a small Island Time series evidence from Northern Cyprus Paper presented at
Econ Anadolu 2009 Anadolu International Conference in Economics June 17ndash19 2009 TurkeyKhorasgani M F (2008) Higher education development and economic growth in Iran Education Business and Society Contemporary Middle Eastern Issues 1
162ndash174
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 335
Kui L (2005) The interactive causality between education and economic growth in China Retrieved from httppapersssrncomsol3paperscfmAbstrac-tid=920624
Loening J L (2004) Time series evidence on education and growth The case of Guatemala 1951ndash2002 Revista de Analisis Economico 19(2) 3ndash40Lucas R E (1988) On the mechanics of economic development Journal of Monetary Economics 22 3ndash42Macerinskiene I amp Vaiksnoraite B (2006) The role of higher education to economic development VadybaManagement 2(11)Mankiw N G Romer D amp Weil D N (1992) A contribution to the empirics of economic growth Quarterly Journal of Economics 107 407ndash437Momete D C (2007) Analysis of the relationship between employment and economic growth in Romania Fascicle of Management and Technological Engineering
VI(XVI)Morote E S (2000) Higher education employment and economic growth Mexico and Peru Retrieved from httpwwwamericanprofessororgdocumentation
lasapa perdocNarayan P K (2005) The saving and investment nexus for China Evidence from cointegration tests Applied Economics 37 1979ndash1990Permani R (2008) Education as a determinant of economic growth in East Asia Historical trends and empirical evidences (1965ndash2000) Retrieved from http
wwwuoweduaucommerceeconehsanzpdfsPermani202008pdfPesaran M H amp Pesaran B (1997) Working with Microfit 40 Interactive econometric analysis Oxford Oxford University PressPesaran M H amp Shin Y (1999) An autoregressive distributed lag modeling approach to cointegration analysis In S Strom (Ed) Econometrics and economic theory
in the 20th century Cambridge Cambridge University PressPesaran M H Shin Y amp Smith R J (2001) Bounds testing approaches to the analysis of level relationships Journal of Applied Econometrics 16 289ndash326Pradhan R P (2009) Education and economic growth in India Using error correction modeling International Research Journal of Finance and Economics 25Pritchett L (2001) Where has all the education gone The World Bank Economic Review 15(3)Quah D amp Rauch J E (1990) Openness and the rate of economic growth Journal Development of Studies 2(49) 307ndash335Rivera-Batiz L A amp Romer P M (1991) Economic integration and endogenous growth Quarterly Journal of Economics 106 531ndash555Romer P M (1986) Increasing returns and long run growth Journal of Political Economy 6(90) 1002ndash1037Romer P M (1989) Human capital and growth Theory and evidence (NBER Working Papers 3173) National Bureau of Economic Research IncRomer P M (1990) Endogenous technological change Journal of Political Economy 5(98) 71ndash101Rondinelli D amp Montgomery J (1995) Great policies Strategic innovations in Asia and the Pacific Basin Westport Praeger PublishingSaikkonen P amp Lutkepohl H (2000) Testing for the cointegration rank of a VAR process with structural shifts Journal of Business and Economic Statistics 18(4)
451ndash464Schultz T W (1961) Investment in human capital American Economic Review 51(1) 1State Bank of Pakistan (1972ndash2009) Annual reports Karachi SBP PressStengos T amp Aurangzeb A (2008) An empirical investigation of the relationship between education and growth in pakistan International Economic Journal 3
345ndash359 Retrieved from httpwwwinformaworldcomsmpptitledb=allcontent=t713685453tab=issueslistbranches=22-v2222Toda H Y amp Yamamoto T (1995) Statistical inference in vector autoregressive with possible integrated processes Journal of Econometrics 66 225ndash250United Nations (1997) Human Development Report New York Oxford University Press
- Education and economic growth in Pakistan A cointegration and causality analysis
-
- Introduction
- Review of literature
- Method and procedure
- Empirical results
-
- Unit root results
- Cointegration
- Toda-Yamamoto Augmented Granger Causality (TYAGC) Test
- Bivariate TYAGC framework
- Trivariate TYAGC framework
- Tetravariate TYAGC framework
- Figures in parentheses are p-values
-
- Conclusions and recommendations
-
- References
-
Table IV
Tetravariate TYAGC results
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Tetravariate-RGDPt RPCt LFt and Edut
Eq (17) Edu1t does not Granger cause RGDPt 029350 [0087] 1 Reject H0
Edu2t does not Granger cause RGDPt 065661 [0010] 1 Reject H0
Edu3t does not Granger cause RGDPt 097521 [0002] 1 Reject H0
Edu4t does not Granger cause RGDPt 071590 [0007] 1 Reject H0
Edu5t does not Granger cause RGDPt 116263 [0001] 1 Reject H0
Edu6t does not Granger cause RGDPt 059569 [0015] 1 Reject H0
Edu7t does not Granger cause RGDPt 054327 [0020] 1 Reject H0
Edu8t does not Granger cause RGDPt 040033 [0045] 1 Reject H0
Edu9t does not Granger cause RGDPt 195734 [0000] 1 Reject H0
Edu10t does not Granger cause RGDPt 034374 [0064] 1 Reject H0
Eq (17a) LFt does not Granger cause RGDPt (Edut = Edu1) 251518 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu2) 165581 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu3) 316418 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu4) 289993 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu5) 109302 [0001] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu6) 165606 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu7) 168037 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu8) 176645 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu9) 247435 [0000] 1 Reject H0
LFt does not Granger cause RGDPt (Edut = Edu10) 146998 [0000] 1 Reject H0
Eq (17b) RPCt does not Granger cause RGDPt (Edut = Edu1) 042975 [0038] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu2) 039280 [0047] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu3) 034296 [0064] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu4) 027068 [0100] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu5) 062858 [0012] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu6) 039537 [0047] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu7) 040022 [0045] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu8) 045487 [0033] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu9) 068323 [0009] 1 Reject H0
RPCt does not Granger cause RGDPt (Edut = Edu10) 083479 [0004] 1 Reject H0
Eq (18) RGDPt does not Granger cause Edu1t 150200 [0000] 1 Reject H0
RGDPt does not Granger cause Edu2t 633103 [0000] 1 Reject H0
RGDPt does not Granger cause Edu3t 045767 [0032] 1 Reject H0
RGDPt does not Granger cause Edu4t 122392 [0000] 1 Reject H0
RGDPt does not Granger cause Edu5t 004235 [0515] 1 Cannot reject H0
RGDPt does not Granger cause Edu6t 453644 [0000] 1 Reject H0
RGDPt does not Granger cause Edu7t 418611 [0000] 1 Reject H0
RGDPt does not Granger cause Edu8t 055973 [0454] 1 Cannot reject H0
RGDPt does not Granger cause Edu9t 053890 [0020] 1 Reject H0
RGDPt does not Granger cause Edu10t 011119 [0292] 1 Cannot reject H0
Eq (18a) LFt does not Granger cause Edu1t 006023 [0438] 1 Cannot reject H0
LFt does not Granger cause Edu2t 364559 [0000] 1 Reject H0
LFt does not Granger cause Edu3t 197423 [0000] 1 Reject H0
LFt does not Granger cause Edu4t 166511 [0000] 1 Reject H0
LFt does not Granger cause Edu5t 383886 [0000] 1 Reject H0
LFt does not Granger cause Edu6t 359377 [0000] 1 Reject H0
LFt does not Granger cause Edu7t 328249 [0000] 1 Reject H0
LFt does not Granger cause Edu8t 135310 [0000] 1 Reject H0
LFt does not Granger cause Edu9t 630068 [0000] 1 Reject H0
LFt does not Granger cause Edu01t 109365 [0001] 1 Reject H0
Eq (18b) RPCt does not Granger cause Edu1t 114248 [0001] 1 Reject H0
RPCt does not Granger cause Edu2t 036828 [0055] 1 Reject H0
RPCt does not Granger cause Edu3t 021023 [0147] 1 Cannot reject H0
RPCt does not Granger cause Edu4t 000484 [0826] 1 Cannot reject H0
RPCt does not Granger cause Edu5t 610934 [0000] 1 Reject H0
RPCt does not Granger cause Edu6t 070279 [0008] 1 Reject H0
RPCt does not Granger cause Edu7t 051166 [0024] 1 Reject H0
RPCt does not Granger cause Edu8t 167481 [0000] 1 Reject H0
RPCt does not Granger cause Edu9t 335271 [0000] 1 Reject H0
RPCt does not Granger cause Edu10t 067481 [0009] 1 Reject H0
Eq (19) Edu1 does not Granger cause RPCt 005154 [0473] 1 Cannot reject H0
Edu2 does not Granger cause RPCt 011954 [0274] 1 Cannot reject H0
Edu3 does not Granger cause RPCt 162365 [0000] 1 Reject H0
Edu4 does not Granger cause RPCt 148964 [0000] 1 Reject H0
Edu5 does not Granger cause RPCt 243978 [0000] 1 Reject H0
Edu6 does not Granger cause RPCt 040262 [0045] 1 Reject H0
Edu7 does not Granger cause RPCt 035138 [0061] 1 Reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 333
able IV (Continued )
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Edu8 does not Granger cause RPCt 030100 [0083] 1 Reject H0
Edu9 does not Granger cause RPCt 462564 [0000] 1 Reject H0
Edu10 does not Granger cause RPCt 009580 [0328] 1 Cannot reject H0
Eq (19a) RGDPt does not Granger cause RPCt (Edu1t as a 3rd variable) 009936 [0319] 1 Cannot reject H0
RGDPt does not Granger cause RPCt (Edu2t as a 3rd variable) 039369 [0047] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu3t as a 3rd variable) 003822 [0536] 1 Cannot reject H0
RGDPt does not Granger cause RPCt (Edu4t as a 3rd variable) 028000 [0094] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu5t as a 3rd variable) 039910 [0046] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu6t as a 3rd variable) 033500 [0067] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu7t as a 3rd variable) 029924 [0084] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu8t as a 3rd variable) 002803 [0597] 1 Cannot Reject H0
RGDPt does not Granger cause RPCt (Edu9t as a 3rd variable) 011416 [0285] 1 Cannot reject H0
RGDPt does not Granger cause RPCt (Edu10t as a 3rd variable) 006944 [0405] 1 Cannot reject H0
Eq (20) Edu1t does not Granger cause LFt 015302 [0216] 1 Cannot reject H0
Edu2t does not Granger cause LFt 001053 [0746] 1 Cannot reject H0
Edu3t does not Granger cause LFt 080072 [0005] 1 Reject H0
Edu4t does not Granger cause LFt 143854 [0000] 1 Reject H0
Edu5t does not Granger cause LFt 061159 [0013] 1 Reject H0
Edu6t does not Granger cause LFt 003113 [0577] 1 Cannot reject H0
Edu7t does not Granger cause LFt 002394 [0625] 1 Cannot reject H0
Edu8t does not Granger cause LFt 196804 [0000] 1 Reject H0
Edu9t does not Granger cause LFt 046285 [0496] 1 Cannot reject H0
Edu10t does not Granger cause LFt 04161 1 [0041] 1 Reject H0
Eq (20a) RGDPt does not Granger cause LFt (Edu1t as a 3rd variable) 006872 [0407] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu2t as a 3rd variable) 018604 [0173] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu3t as a 3rd variable) 066905 [0010] 1 Reject H0
RGDPt does not Granger cause LFt (Edu4t as a 3rd variable) 023249 [0127] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu5t as a 3rd variable) 070835 [0008] 1 Reject H0
RGDPt does not Granger cause LFt (Edu6t as a 3rd variable) 016501 [0199] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu7t as a 3rd variable) 018532 [0173] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu8t as a 3rd variable) 003730 [0541] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu9t as a 3rd variable) 039255 [0048] 1 Reject H0
RGDPt does not Granger cause LFt (Edu10t as a 3rd variable) 055266 [0019] 1 Reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335334
T
References
Abbas Q amp Peck J F (2008) Human capital and economic growth Pakistan 1960ndash2003 The Lahore Journal of Economics 13(1) 1ndash28Ayara N A (2002) The paradox of education and economic growth in Nigeria Empirical evidence The Nigerian Economic Society (NES) Pt 2 371ndash393Babatunde M A amp Adefabi R A (2005) Long run relationship between education and economic growth in Nigeria Evidence from the Johansenrsquos cointegration
approach Paper presented at the regional conference on education in West Africa Constraints and Opportunities Dakar Senegal November 1stndash2nd 2005Cornell UniversityCREAMinisterede lrsquoEducation du Senegal
Baldacci E Clements B Cui Q amp Gupta S (2005) What does it take to help the poor Finance and Development The Quarterly Magazine of the IMF 42(2)Changzheng Z Zhijian H amp Huaizu L (2007) An empirical study on education equity in China 1978ndash2004 Frontier in Economics of China 2(4) 536ndash544Chaudhary A R Asim I amp Gillani S Y M (2009) The nexus between higher education and economic growth An empirical investigation for Pakistan Pakistan
Journal of Commerce and Social Sciences 3Chaudhry I S Malik S amp Ashraf M (2006) Rural poverty in Pakistan Some related concepts issues and empirical analysis Pakistan Economic and Social Review
44(2) 259ndash276Diebolt C amp Litago J (1997) Education and economic growth in Germany before the Second World War An econometric analysis of dynamic relations Historical
Social Research 2(22) 132ndash149Easterly W (2001) The middle class consensus and economic development Journal of Economic Growth 6(4) 317ndash335Engle R F amp Granger C W J (1987) Cointegration and error correction Representation estimation and testing Econometrica 55 251ndash276Fernandez E amp Mauro P (2000) The role of human capital in economic growth The case of Spain (IMF Working Paper) International Monetary FundFrancis B amp Iyare S (2006) Education and development in the Caribbean A cointegration and causality approach Economics Bulletin 15(2) 1ndash13Galor O amp Moav O (2000) Das human capital Retrieved from httpeconpstcn brownedufacultygalorindexhtmlGoode R B (1959) Adding to the stock of physical and human capital American Economic Review 49(2) 147Government of Pakistan (1970ndash2009) Pakistan economic survey various issues Finance Division Islamabad Economic Advisorrsquos WingGregory A W amp Hansen B E (1996) Residual-based tests for cointegration in models with regime shifts Journal of Econometrics 70 99ndash126Grossman G M amp Helpman E (1991) Innovation and growth in the global economy Cambridge MIT PressGylfason T amp Zoega G (2003) Education social equality and economic growth A view of the landscape CESifo Economic Studies 49(4) 557ndash579Hassan S amp Ahmed H (2008) Educationrsquos contribution to the economic growth of sub-Saharan Africa Southwestern Economic Review 1(32) 175ndash190Islam T S Wadud M A amp Islam Q B T (2007) Relationship between education and GDP growth A multivariate causality analysis for Bangladesh Economics
Bulletin 3(35) 1ndash7Jin J C (2009) Economic research and economic growth Evidence from East Asian Economies Journal of Asian Economics 20 150ndash155Johansen S (1988) Statistical analysis of cointegration vectors Journal of Economic Dynamics and Control 12 231ndash254Johansen S amp Juselius K (1990) Maximum likelihood estimation and inference on cointegration with applications to the demand for money Oxford Bulletin of
Economics and Statistics 52 169ndash210Katırcıoglu S T (2009) Investigating higher-education-led growth hypothesis in a small Island Time series evidence from Northern Cyprus Paper presented at
Econ Anadolu 2009 Anadolu International Conference in Economics June 17ndash19 2009 TurkeyKhorasgani M F (2008) Higher education development and economic growth in Iran Education Business and Society Contemporary Middle Eastern Issues 1
162ndash174
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 335
Kui L (2005) The interactive causality between education and economic growth in China Retrieved from httppapersssrncomsol3paperscfmAbstrac-tid=920624
Loening J L (2004) Time series evidence on education and growth The case of Guatemala 1951ndash2002 Revista de Analisis Economico 19(2) 3ndash40Lucas R E (1988) On the mechanics of economic development Journal of Monetary Economics 22 3ndash42Macerinskiene I amp Vaiksnoraite B (2006) The role of higher education to economic development VadybaManagement 2(11)Mankiw N G Romer D amp Weil D N (1992) A contribution to the empirics of economic growth Quarterly Journal of Economics 107 407ndash437Momete D C (2007) Analysis of the relationship between employment and economic growth in Romania Fascicle of Management and Technological Engineering
VI(XVI)Morote E S (2000) Higher education employment and economic growth Mexico and Peru Retrieved from httpwwwamericanprofessororgdocumentation
lasapa perdocNarayan P K (2005) The saving and investment nexus for China Evidence from cointegration tests Applied Economics 37 1979ndash1990Permani R (2008) Education as a determinant of economic growth in East Asia Historical trends and empirical evidences (1965ndash2000) Retrieved from http
wwwuoweduaucommerceeconehsanzpdfsPermani202008pdfPesaran M H amp Pesaran B (1997) Working with Microfit 40 Interactive econometric analysis Oxford Oxford University PressPesaran M H amp Shin Y (1999) An autoregressive distributed lag modeling approach to cointegration analysis In S Strom (Ed) Econometrics and economic theory
in the 20th century Cambridge Cambridge University PressPesaran M H Shin Y amp Smith R J (2001) Bounds testing approaches to the analysis of level relationships Journal of Applied Econometrics 16 289ndash326Pradhan R P (2009) Education and economic growth in India Using error correction modeling International Research Journal of Finance and Economics 25Pritchett L (2001) Where has all the education gone The World Bank Economic Review 15(3)Quah D amp Rauch J E (1990) Openness and the rate of economic growth Journal Development of Studies 2(49) 307ndash335Rivera-Batiz L A amp Romer P M (1991) Economic integration and endogenous growth Quarterly Journal of Economics 106 531ndash555Romer P M (1986) Increasing returns and long run growth Journal of Political Economy 6(90) 1002ndash1037Romer P M (1989) Human capital and growth Theory and evidence (NBER Working Papers 3173) National Bureau of Economic Research IncRomer P M (1990) Endogenous technological change Journal of Political Economy 5(98) 71ndash101Rondinelli D amp Montgomery J (1995) Great policies Strategic innovations in Asia and the Pacific Basin Westport Praeger PublishingSaikkonen P amp Lutkepohl H (2000) Testing for the cointegration rank of a VAR process with structural shifts Journal of Business and Economic Statistics 18(4)
451ndash464Schultz T W (1961) Investment in human capital American Economic Review 51(1) 1State Bank of Pakistan (1972ndash2009) Annual reports Karachi SBP PressStengos T amp Aurangzeb A (2008) An empirical investigation of the relationship between education and growth in pakistan International Economic Journal 3
345ndash359 Retrieved from httpwwwinformaworldcomsmpptitledb=allcontent=t713685453tab=issueslistbranches=22-v2222Toda H Y amp Yamamoto T (1995) Statistical inference in vector autoregressive with possible integrated processes Journal of Econometrics 66 225ndash250United Nations (1997) Human Development Report New York Oxford University Press
- Education and economic growth in Pakistan A cointegration and causality analysis
-
- Introduction
- Review of literature
- Method and procedure
- Empirical results
-
- Unit root results
- Cointegration
- Toda-Yamamoto Augmented Granger Causality (TYAGC) Test
- Bivariate TYAGC framework
- Trivariate TYAGC framework
- Tetravariate TYAGC framework
- Figures in parentheses are p-values
-
- Conclusions and recommendations
-
- References
-
able IV (Continued )
Equations Null hypothesis Test statistic Wald test (x2-statistic)
Estimated value (p-value) df Decision
Edu8 does not Granger cause RPCt 030100 [0083] 1 Reject H0
Edu9 does not Granger cause RPCt 462564 [0000] 1 Reject H0
Edu10 does not Granger cause RPCt 009580 [0328] 1 Cannot reject H0
Eq (19a) RGDPt does not Granger cause RPCt (Edu1t as a 3rd variable) 009936 [0319] 1 Cannot reject H0
RGDPt does not Granger cause RPCt (Edu2t as a 3rd variable) 039369 [0047] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu3t as a 3rd variable) 003822 [0536] 1 Cannot reject H0
RGDPt does not Granger cause RPCt (Edu4t as a 3rd variable) 028000 [0094] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu5t as a 3rd variable) 039910 [0046] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu6t as a 3rd variable) 033500 [0067] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu7t as a 3rd variable) 029924 [0084] 1 Reject H0
RGDPt does not Granger cause RPCt (Edu8t as a 3rd variable) 002803 [0597] 1 Cannot Reject H0
RGDPt does not Granger cause RPCt (Edu9t as a 3rd variable) 011416 [0285] 1 Cannot reject H0
RGDPt does not Granger cause RPCt (Edu10t as a 3rd variable) 006944 [0405] 1 Cannot reject H0
Eq (20) Edu1t does not Granger cause LFt 015302 [0216] 1 Cannot reject H0
Edu2t does not Granger cause LFt 001053 [0746] 1 Cannot reject H0
Edu3t does not Granger cause LFt 080072 [0005] 1 Reject H0
Edu4t does not Granger cause LFt 143854 [0000] 1 Reject H0
Edu5t does not Granger cause LFt 061159 [0013] 1 Reject H0
Edu6t does not Granger cause LFt 003113 [0577] 1 Cannot reject H0
Edu7t does not Granger cause LFt 002394 [0625] 1 Cannot reject H0
Edu8t does not Granger cause LFt 196804 [0000] 1 Reject H0
Edu9t does not Granger cause LFt 046285 [0496] 1 Cannot reject H0
Edu10t does not Granger cause LFt 04161 1 [0041] 1 Reject H0
Eq (20a) RGDPt does not Granger cause LFt (Edu1t as a 3rd variable) 006872 [0407] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu2t as a 3rd variable) 018604 [0173] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu3t as a 3rd variable) 066905 [0010] 1 Reject H0
RGDPt does not Granger cause LFt (Edu4t as a 3rd variable) 023249 [0127] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu5t as a 3rd variable) 070835 [0008] 1 Reject H0
RGDPt does not Granger cause LFt (Edu6t as a 3rd variable) 016501 [0199] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu7t as a 3rd variable) 018532 [0173] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu8t as a 3rd variable) 003730 [0541] 1 Cannot reject H0
RGDPt does not Granger cause LFt (Edu9t as a 3rd variable) 039255 [0048] 1 Reject H0
RGDPt does not Granger cause LFt (Edu10t as a 3rd variable) 055266 [0019] 1 Reject H0
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335334
T
References
Abbas Q amp Peck J F (2008) Human capital and economic growth Pakistan 1960ndash2003 The Lahore Journal of Economics 13(1) 1ndash28Ayara N A (2002) The paradox of education and economic growth in Nigeria Empirical evidence The Nigerian Economic Society (NES) Pt 2 371ndash393Babatunde M A amp Adefabi R A (2005) Long run relationship between education and economic growth in Nigeria Evidence from the Johansenrsquos cointegration
approach Paper presented at the regional conference on education in West Africa Constraints and Opportunities Dakar Senegal November 1stndash2nd 2005Cornell UniversityCREAMinisterede lrsquoEducation du Senegal
Baldacci E Clements B Cui Q amp Gupta S (2005) What does it take to help the poor Finance and Development The Quarterly Magazine of the IMF 42(2)Changzheng Z Zhijian H amp Huaizu L (2007) An empirical study on education equity in China 1978ndash2004 Frontier in Economics of China 2(4) 536ndash544Chaudhary A R Asim I amp Gillani S Y M (2009) The nexus between higher education and economic growth An empirical investigation for Pakistan Pakistan
Journal of Commerce and Social Sciences 3Chaudhry I S Malik S amp Ashraf M (2006) Rural poverty in Pakistan Some related concepts issues and empirical analysis Pakistan Economic and Social Review
44(2) 259ndash276Diebolt C amp Litago J (1997) Education and economic growth in Germany before the Second World War An econometric analysis of dynamic relations Historical
Social Research 2(22) 132ndash149Easterly W (2001) The middle class consensus and economic development Journal of Economic Growth 6(4) 317ndash335Engle R F amp Granger C W J (1987) Cointegration and error correction Representation estimation and testing Econometrica 55 251ndash276Fernandez E amp Mauro P (2000) The role of human capital in economic growth The case of Spain (IMF Working Paper) International Monetary FundFrancis B amp Iyare S (2006) Education and development in the Caribbean A cointegration and causality approach Economics Bulletin 15(2) 1ndash13Galor O amp Moav O (2000) Das human capital Retrieved from httpeconpstcn brownedufacultygalorindexhtmlGoode R B (1959) Adding to the stock of physical and human capital American Economic Review 49(2) 147Government of Pakistan (1970ndash2009) Pakistan economic survey various issues Finance Division Islamabad Economic Advisorrsquos WingGregory A W amp Hansen B E (1996) Residual-based tests for cointegration in models with regime shifts Journal of Econometrics 70 99ndash126Grossman G M amp Helpman E (1991) Innovation and growth in the global economy Cambridge MIT PressGylfason T amp Zoega G (2003) Education social equality and economic growth A view of the landscape CESifo Economic Studies 49(4) 557ndash579Hassan S amp Ahmed H (2008) Educationrsquos contribution to the economic growth of sub-Saharan Africa Southwestern Economic Review 1(32) 175ndash190Islam T S Wadud M A amp Islam Q B T (2007) Relationship between education and GDP growth A multivariate causality analysis for Bangladesh Economics
Bulletin 3(35) 1ndash7Jin J C (2009) Economic research and economic growth Evidence from East Asian Economies Journal of Asian Economics 20 150ndash155Johansen S (1988) Statistical analysis of cointegration vectors Journal of Economic Dynamics and Control 12 231ndash254Johansen S amp Juselius K (1990) Maximum likelihood estimation and inference on cointegration with applications to the demand for money Oxford Bulletin of
Economics and Statistics 52 169ndash210Katırcıoglu S T (2009) Investigating higher-education-led growth hypothesis in a small Island Time series evidence from Northern Cyprus Paper presented at
Econ Anadolu 2009 Anadolu International Conference in Economics June 17ndash19 2009 TurkeyKhorasgani M F (2008) Higher education development and economic growth in Iran Education Business and Society Contemporary Middle Eastern Issues 1
162ndash174
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 335
Kui L (2005) The interactive causality between education and economic growth in China Retrieved from httppapersssrncomsol3paperscfmAbstrac-tid=920624
Loening J L (2004) Time series evidence on education and growth The case of Guatemala 1951ndash2002 Revista de Analisis Economico 19(2) 3ndash40Lucas R E (1988) On the mechanics of economic development Journal of Monetary Economics 22 3ndash42Macerinskiene I amp Vaiksnoraite B (2006) The role of higher education to economic development VadybaManagement 2(11)Mankiw N G Romer D amp Weil D N (1992) A contribution to the empirics of economic growth Quarterly Journal of Economics 107 407ndash437Momete D C (2007) Analysis of the relationship between employment and economic growth in Romania Fascicle of Management and Technological Engineering
VI(XVI)Morote E S (2000) Higher education employment and economic growth Mexico and Peru Retrieved from httpwwwamericanprofessororgdocumentation
lasapa perdocNarayan P K (2005) The saving and investment nexus for China Evidence from cointegration tests Applied Economics 37 1979ndash1990Permani R (2008) Education as a determinant of economic growth in East Asia Historical trends and empirical evidences (1965ndash2000) Retrieved from http
wwwuoweduaucommerceeconehsanzpdfsPermani202008pdfPesaran M H amp Pesaran B (1997) Working with Microfit 40 Interactive econometric analysis Oxford Oxford University PressPesaran M H amp Shin Y (1999) An autoregressive distributed lag modeling approach to cointegration analysis In S Strom (Ed) Econometrics and economic theory
in the 20th century Cambridge Cambridge University PressPesaran M H Shin Y amp Smith R J (2001) Bounds testing approaches to the analysis of level relationships Journal of Applied Econometrics 16 289ndash326Pradhan R P (2009) Education and economic growth in India Using error correction modeling International Research Journal of Finance and Economics 25Pritchett L (2001) Where has all the education gone The World Bank Economic Review 15(3)Quah D amp Rauch J E (1990) Openness and the rate of economic growth Journal Development of Studies 2(49) 307ndash335Rivera-Batiz L A amp Romer P M (1991) Economic integration and endogenous growth Quarterly Journal of Economics 106 531ndash555Romer P M (1986) Increasing returns and long run growth Journal of Political Economy 6(90) 1002ndash1037Romer P M (1989) Human capital and growth Theory and evidence (NBER Working Papers 3173) National Bureau of Economic Research IncRomer P M (1990) Endogenous technological change Journal of Political Economy 5(98) 71ndash101Rondinelli D amp Montgomery J (1995) Great policies Strategic innovations in Asia and the Pacific Basin Westport Praeger PublishingSaikkonen P amp Lutkepohl H (2000) Testing for the cointegration rank of a VAR process with structural shifts Journal of Business and Economic Statistics 18(4)
451ndash464Schultz T W (1961) Investment in human capital American Economic Review 51(1) 1State Bank of Pakistan (1972ndash2009) Annual reports Karachi SBP PressStengos T amp Aurangzeb A (2008) An empirical investigation of the relationship between education and growth in pakistan International Economic Journal 3
345ndash359 Retrieved from httpwwwinformaworldcomsmpptitledb=allcontent=t713685453tab=issueslistbranches=22-v2222Toda H Y amp Yamamoto T (1995) Statistical inference in vector autoregressive with possible integrated processes Journal of Econometrics 66 225ndash250United Nations (1997) Human Development Report New York Oxford University Press
- Education and economic growth in Pakistan A cointegration and causality analysis
-
- Introduction
- Review of literature
- Method and procedure
- Empirical results
-
- Unit root results
- Cointegration
- Toda-Yamamoto Augmented Granger Causality (TYAGC) Test
- Bivariate TYAGC framework
- Trivariate TYAGC framework
- Tetravariate TYAGC framework
- Figures in parentheses are p-values
-
- Conclusions and recommendations
-
- References
-
M Afzal et al International Journal of Educational Research 50 (2011) 321ndash335 335
Kui L (2005) The interactive causality between education and economic growth in China Retrieved from httppapersssrncomsol3paperscfmAbstrac-tid=920624
Loening J L (2004) Time series evidence on education and growth The case of Guatemala 1951ndash2002 Revista de Analisis Economico 19(2) 3ndash40Lucas R E (1988) On the mechanics of economic development Journal of Monetary Economics 22 3ndash42Macerinskiene I amp Vaiksnoraite B (2006) The role of higher education to economic development VadybaManagement 2(11)Mankiw N G Romer D amp Weil D N (1992) A contribution to the empirics of economic growth Quarterly Journal of Economics 107 407ndash437Momete D C (2007) Analysis of the relationship between employment and economic growth in Romania Fascicle of Management and Technological Engineering
VI(XVI)Morote E S (2000) Higher education employment and economic growth Mexico and Peru Retrieved from httpwwwamericanprofessororgdocumentation
lasapa perdocNarayan P K (2005) The saving and investment nexus for China Evidence from cointegration tests Applied Economics 37 1979ndash1990Permani R (2008) Education as a determinant of economic growth in East Asia Historical trends and empirical evidences (1965ndash2000) Retrieved from http
wwwuoweduaucommerceeconehsanzpdfsPermani202008pdfPesaran M H amp Pesaran B (1997) Working with Microfit 40 Interactive econometric analysis Oxford Oxford University PressPesaran M H amp Shin Y (1999) An autoregressive distributed lag modeling approach to cointegration analysis In S Strom (Ed) Econometrics and economic theory
in the 20th century Cambridge Cambridge University PressPesaran M H Shin Y amp Smith R J (2001) Bounds testing approaches to the analysis of level relationships Journal of Applied Econometrics 16 289ndash326Pradhan R P (2009) Education and economic growth in India Using error correction modeling International Research Journal of Finance and Economics 25Pritchett L (2001) Where has all the education gone The World Bank Economic Review 15(3)Quah D amp Rauch J E (1990) Openness and the rate of economic growth Journal Development of Studies 2(49) 307ndash335Rivera-Batiz L A amp Romer P M (1991) Economic integration and endogenous growth Quarterly Journal of Economics 106 531ndash555Romer P M (1986) Increasing returns and long run growth Journal of Political Economy 6(90) 1002ndash1037Romer P M (1989) Human capital and growth Theory and evidence (NBER Working Papers 3173) National Bureau of Economic Research IncRomer P M (1990) Endogenous technological change Journal of Political Economy 5(98) 71ndash101Rondinelli D amp Montgomery J (1995) Great policies Strategic innovations in Asia and the Pacific Basin Westport Praeger PublishingSaikkonen P amp Lutkepohl H (2000) Testing for the cointegration rank of a VAR process with structural shifts Journal of Business and Economic Statistics 18(4)
451ndash464Schultz T W (1961) Investment in human capital American Economic Review 51(1) 1State Bank of Pakistan (1972ndash2009) Annual reports Karachi SBP PressStengos T amp Aurangzeb A (2008) An empirical investigation of the relationship between education and growth in pakistan International Economic Journal 3
345ndash359 Retrieved from httpwwwinformaworldcomsmpptitledb=allcontent=t713685453tab=issueslistbranches=22-v2222Toda H Y amp Yamamoto T (1995) Statistical inference in vector autoregressive with possible integrated processes Journal of Econometrics 66 225ndash250United Nations (1997) Human Development Report New York Oxford University Press
- Education and economic growth in Pakistan A cointegration and causality analysis
-
- Introduction
- Review of literature
- Method and procedure
- Empirical results
-
- Unit root results
- Cointegration
- Toda-Yamamoto Augmented Granger Causality (TYAGC) Test
- Bivariate TYAGC framework
- Trivariate TYAGC framework
- Tetravariate TYAGC framework
- Figures in parentheses are p-values
-
- Conclusions and recommendations
-
- References
-
