Post on 09-Apr-2023
Empirical Investigation on the Relationship between Trade Openness and Gross
Domestic Product Growth Rate: The Case of South Africa (1980-2010)
Matsane S.H
Email: hemjum@gmail.com; shmatsane@hotmail.co.za
Tel: +27 79 045 0060
Abstract
The end of apartheid regime in the early 1990s radically expanded trade openness of South
Africa. This study conducted an investigation on trade openness and GDP growth in the South
African perspective. Trade openness has been measured in various ways in studies
investigating the matter. Ever since 1994, the South African economy has been through a
process of structural transformation. Hence, a significant increase in exports figures. However,
in comparison to international trends, the country’s exports are not growing fast enough. This
is due to the difficulty of measuring openness. A variety of studies have used different measures
to examine the effects of trade openness on GDP growth.
This study employed time series econometric techniques of cointegration and the Error
Correction Model to estimates a more precise relationship between GDP and its determinants
in South Africa.
The long run results conducted in this study shows that there is a positive relationship between
Exports and GDP Growth. Therefore, exports are found to be the main determinants of GDP
growth in the South African economy.
Keywords: Cointegration, Exports, Gross Capital Formation, GDP growth, Error Correction
Model, Imports and South Africa
1. Introduction
Trade openness has been measured in various ways in studies investigating the relationship
between trade openness and Gross domestic product (GDP) Growth Rate. Generally, trade is
expressed in terms of its share of GDP for a given country (Squalli & Wilson, 2006). The most
common and traditional measures are import and export ratios, and exports plus imports over
GDP. In 2000, trade openness in South Africa constituted about 16 percent of the GDP. The
total exports for 1994 were R92 million. This figure had increased to R396.5 million by 2006
(van der Walt, 2007). This shows a massive increase of more than 100 percent of the total
export for the past twelve years. The South Africa's economy is still largely reliant on the export
of primary and intermediate commodities to industrialised economies. In relation to the GDP,
exports increased from 18.7 percent of GDP in 1994 to 23 percent of GDP in 2006. This shows
a 4.3 percent in GDP for the past twelve years. It also provides evidence that South Africa's
trade and industrial policy is moving away from a highly protected inward looking economy
towards an internationally competitive economy. However, when compared to international
trends, the country’s exports are not growing fast enough. Srinivasan (2004) indicates that
China continues to outpace the world economy in trade openness. In 2002, China was the
world’s fifth largest exporter of merchandise with a share of 5 percent of the world exports. It
is clear that South Africa has much catching up to do to stimulate the growth rates of exports
in order to boost the GDP (Srinivasan, 2004).
2. Background
After the Apartheid regime, the South African economy has been through structural
transformation processes. Macroeconomic policies have been implemented which seek to
make the economy more outward orientated in order to promote domestic competitiveness,
growth and employment (Flatters & Stern, 2007). The country has embarked on a series of
trade negotiations such as Free Trade Agreement (FTA) (Andriamananjara & Hillberry, 2001).
Lewis (2001), and Andriamananjara and Hillberry (2001) indicated that FTA initiatives are
beneficial to South Africa and the region. In recent years, several emerging economies such as
India and Brazil in Latin America have experienced major macroeconomic and trade policy
reforms with emphasis on trade openness (Lewis, 2001).
Trade openness is often considered in the sense of an increase in the size of the country’s traded
sector in relation to total production. Hence, it is an acceptable proxy for trade liberalisation
(Yanikkaya, 2003). Actually, increasing trade openness often reflects the success of trade
liberalisation policies (Sarkar, 2007). Different studies have used different measures to
examine the effects of trade openness on economic growth. Emma and Samman (2005) argue
that reliance on the share of trade in GDP as an indicator of trade openness is highly misleading.
Despite the debate on what exactly are measures of trade openness, internationally the work of
Mbabazi, Milner and Morrissey (2004) indicates that trade openness is positively associated
with the growth of 44 developing countries over 1970-95. Moreover, Anderson (2007) states
that over the past 40 years since 1965, there is a one-on-one correlation between trade and GDP
growth in Asian countries. This in short, is export-led growth. International trade plays a
significant role in the Asians economies, while in South Africa, this is less so.
According to Rankin (2001), the trend GDP growth rate for South Africa’s real exports has
been increased by 5 percent in 1994. Although this is poor in comparison with countries such
as Malaysia and Indonesia. However, it is at least an improvement on the previous period. In
2001, the value of merchandise exports increased by 20.3 percent. The higher rand (ZAR) value
of merchandise exports in the first half of 2002 was related to the sharp depreciation of the
external value of the rand in the last quarter of 2001. Reports by the South African Reserve
Bank (SARB) (2008/09) indicates that the South Africa‘s exports increased by 8.1 percent in
2008 from 2007. Imports also increased by 7.1 percent in 2008 from US$ 81.9 billion in 2007
to US$ 87.7 billion in 2008. Total exports and imports of goods and services in 2007 amounted
to 31 percent and 35 percent of GDP, respectively.
South Africa’s real economic growth rate average was 3.1 percent during the period 1995 –
2004 (Du Plessis & Smit, 2007). This represented a substantial improvement in the economy.
Although it was a welcome improvement, South Africa’s growth performance remained
relatively low by world standards. According to SA Yearbook (2002/03), during 1997 and the
first half of 1998, the growth in total real GDP slowed down and subsequently turned negative
in the third quarter of 1998. It recovered again slightly in the fourth quarter of 1998 throughout
1999 and 2000. However, it is difficult to understand this performance with a change in the
long-run growth potential of the economy. In order to understand the nature of this
improvement in South Africa’s growth performance, the behaviour of trade openness may be
considered to determine whether it has an impact on the overall GDP growth.
The South African export sector has been characterised by low and fluctuating export growth
and exports earnings for the past years. Flatters and Stern (2007) indicate that a decade since
1994, South Africa’s average export growth fell marginally from 6.2 to 5.6 percent. On the
import side, Lewis (2001) states that during 1993 and 1997 Import penetration accounted
between -43 and -52 percent of the rise in GDP. He further indicates that relatively low import
penetration since 1993 suggests that trade openness has remained relatively resilient in the face
of domestic production. For this reason, this study intends to understand how South African
GDP growth has responded to trade openness.
3. Objectives
The main objective of this study was to investigate the causal relationship between trade
openness and GDP growth in the Republic of South Africa for the period 1980 to 2010. Specific
objectives were:
3.1. To evaluate the sensitivity of GDP growth to changes in trade openness.
3.2.To determine the degree of the relationship between GDP growth and trade openness.
3.3. To determine a long run relationship as well as a short run equilibrium model between
trade openness and GDP growth (a dynamic error correction model).
4. Methodology
The methodological and analytical basis for this study was drawn from the empirical literature
focusing on trade openness and GDP growth. To determine the relationship between trade
openness and GDP growth data was based on annual form from 1980-2010. The study used
secondary data collected from the South African Reserve Bank (SARB), an official statistical
and economic data provider. The sample period for the study was the period spanning from
1980-2010. The reason for this sample period is that South Africa embarked on market
restructuring as their economies changed from being apartheid planned with the state playing
a major role to market oriented economies dominated by the forces of the markets.
Following Jin (2003), various sets of measures of trade openness were employed in this study:
the first set consists of imports/GDP ratio, and the export/GDP ratio. The second set follows
Awokuse (2008) which consists of the absolute values of merchandise and service export, and
also merchandise and service import. The study employed a Granger causality test which was
developed by Granger (1969) where he defines the “arrow of time” to help in identifying the
difference between cause and effect. According to this approach, a variable Y is caused by X
if Y is better predicted from past values of Y and X together rather than from past values of Y
alone. Prior to estimation of the model adopted, an Augmented Dickey-Fuller (ADF) test was
employed to check for first order unit roots. A cointergration test was also applied to determine
whether the variables were cointergrated or not and an error correction model for short run
analysis. The study used computer programme Eviews version 7 for statistical data analysis.
4.1. Rational for choice of data
South Africa has undertaken market and trade reforms since the country’s independence in
1994. These reforms have resulted in the change of the trade patterns in South Africa and other
countries. Moreover, the agreement signed by South Africa in joining the World Trade
Organization (WTO) it is believed that it has improved trade openness in South Africa. It is,
therefore, of major interest to study the relationship between trade openness and GDP growth.
4.2. Model specification
From empirical literature and theoretical exposition, a number of possible proxies to measure
trade openness have been suggested. These include ratio of imports, ratio of exports, sum of
imports and exports over GDP, real exports of goods and services, and real imports of goods
and services.
To commence with variables that have been found to be considerable in the previous studies in
South Africa were chosen De Jager (2004) and Loots (2002). The two variables were exports
and exports ratio. The base model was then extended by adding other variables for which data
is available. This exercise yielded two possible models which produced results that are
economically meaningful. The reason for estimating two regression equations was to capture
various ways of explaining trade openness, and to avoid multi-collinearity since the measures
of trade openness are manipulated using export and import values.
GDPt = a0 + β1 Mt + β2 Xt + β3 Kinvt + µt…………..…............................... (41a)
GDPt = a0 + β1 Mrat + β2 Xrat + β3 Kinvt + µt………….............................. (4.1b)
where GDPt is Gross Domestic Product in levels, α and β are parameters to be estimated, Mt,
Xt, Kinvt, Mrat, Xrat and Kinvt which are defined as observable variables representing factors
affecting GDP in South Africa in year t, and µt is a random error term with a mean of zero,
representing measurement error and unmeasured and immeasurable factors.
4.2.1. Unit root test
Prior to estimation of the time series model, the first step was to check the stationarity of the
variables to be used as regressors in the model. The aim was to verify whether the series had a
stationary trend, and, if non-stationary, to establish orders of integration. To explain the
preceding statement, let Yt be a stochastic process of a time series variable as:
Yt = (t = 1, 2, 3…..)
for each Yt had its own mean, variance and covariance between different Yt then define such
time series as stationery if over time, its mean, variance and covariance remains constant that
is :
Mean: E (Yt) = constant
Variance: var (Yt) = constant
Covariance: cov (Yt, Yt + k) = constant
The problem with time series data is that independent variable can appear to be more significant
than they actually are if they have the same underlying trend as the dependent variable. This
causes the non-stationary variables to appear to be correlated even if they are not. Suppose
from both GDPt and OPENt are non-stationary to the same degree; that is, suppose that ∆GDPt
and ∆OPENt are both stationary. In such situation there is reasonable possibility that the non-
stationarity in the two variables will cancel each other out. Thus, the study needed to test for
stationarity conditions of variables in order to avoid spurious regression results.
The study first examined the stationarity in the time series by using graphical inspection on
series which were in their real values. Thereafter, all the variables were expressed in level form
to see whether after first differencing if the series exhibit non-stationarity. Scholars also argue
that although graphical evidence is useful as the first approximation to decide whether the
variables are non-stationary, most econometricians agree that this is clearly an unreliable
method to use to make inferences about unit roots. As a result, they advise the use of a formal
testing procedure in order to examine each of the variables under scrutiny (Medina-Smith,
2001).
To test the level of integration of the variables that were employed in the model, the study also
used the formal well known Augment Dickey-Fuller (ADF) test. The aim was to determine
whether the variables follow a non-stationary trend and were in fact of the order of 1 denoted
as I(1) or whether the series were stationary, i.e. of the order of 0 denoted as I(0). The
Augmented Dickey Fuller (ADF) tests were based on the estimation of the following
regression.
ΔXt = α0 + α1 + α2Xt-1 + Σ ΔXt-i + Фt …………………………..…… (4.2)
Where Δ is the first difference operator, t is a linear time trend and Фt is a normally distributed
error term. In (3), the null hypothesis that Ho: a2 = 0 against the alternative hypothesis H1: a2 ≠
0 is tested by comparing the calculated t- ratio of aX2 with Mackinnon critical values, which
are essentially adjusted t values. If the absolute value of the calculated t-ratio is greater than
the critical value, then the null hypothesis of a unit root (non-stationarity) is rejected, and the
time series Xt can be characterised as integrated of order zero, i.e. I(0), in levels.
However, first differencing was not an appropriate solution to the above problem and had a
major disadvantage: it prevented detection of the long-run relationship that may be present in
the data, i.e. the long-run information is lost, which was precisely the main question being
addressed (Gujarati, 1995).
The study also applied Phillips and Perron unit root test to verify ADF unit root results were
accurate. It was important to perform a second unit root test, which is the one developed by
Phillips and Perron (1988). This method utilises a nonparametric approach to control serial
correlation in the error term. Basically, the choices are the same as those explained in the ADF
test. Therefore, whichever assumption was used in the ADF test was also used for the P-P test.
The next section is the contegration test; here the study explains whether the series under
scrutiny were cointegrated.
4.2.2. Cointegration test
The study also followed the cointegration test as proposed by Engle and Granger (1987). The
question behind this test was to answer whether there was a long-run equilibrium relationship
between trade openness and GDP growth. A linear combination may exist between two or more
economic variables which converge to long-run equilibrium, even though the series tend to
move randomly over time. In other words, they are cointegrated when each individual variable
demonstrates stationarity only in first differences, but a linear combination of their levels may
result in stationarity.
Recent economic progress has made achievements in contegration methodology to examine
the long-run stable relationship between time series. Granger (1986); Engle and Granger (1987)
pioneered the area of cointegration tests. They proposed a two-step procedure to identify
cointegrating vectors. Firstly, this approach runs an ordinary least square (OLS) regression to
produce residuals. Secondly, it conducts a unit root test for the null hypothesis of no
cointegration relationship and against the alternative of a cointegration relationship between
them.
However, it is important to mention that Engle-Granger contegration procedure has a distinct
advantage and also that the test has several defects. This approach may suffer a bias since the
results are subject to arbitrary normalisation, and may also fail to distinguish the number of
cointegrating vectors. Moreover, literature holds that it is very important for empirical studies
to carry out several tests for cointegration instead of using one single procedure (Medina-
Smith, 2001). Alternatively, the study also applies the Johansen approach (1991). The
generalisation of the Johansen procedure is as follows:
∆yt = ΣΠi∆yt-1+ Πyt-n+εt…………………………………………..….… (4.3)
Where yt = (Kx1) vector of variables (β1yt-1, β1yt-2,…… βnyt-n), εt is independent and identically
distributed n-dimensional vector with mean zero and variance equal to matrix Σ ε,Π(αβ) is the
number of independent co-integration vectors, and Πyt-n is the error correction factor. The
Johansen procedure relies on the rank of Π and its characteristics roots. If rank (Π) =0, the
matrix is null (no cointegration) and equations in vector yt are a common VAR in first
differences. If Π has full rank (Π = k), the vector process is stationary and the equations in yt
are modeled in levels – I(0). If rank (Π)=1, there is evidence of a single cointegrating vectors
in Johansen’s cointegration procedure is applied to this study. These tests are:
Trace test
trace (r) = - T Σ In( 1- ) , and ……………………………………………….(4.4)
Maximum eigenvalue test
max (r,r + 1) = -T Σ In( 1- r+1) ,………………………………………………..(4.5)
Where r+1 ….,n are the (k-r) smallest estimated eigenvalues. In both tests, represents the
estimated values of the characteristics roots obtained from the estimated Π matrix, and T is the
number of observations. The trace test attempts to determine the number of cointegrating
vectors between the variables by testing the null hypothesis that r = 0 against the alternative
that r > 0 or r ≤ 1 (r equals the number of co-integrating vectors). The maximum eigenvalue
tests the null hypothesis that the number of co-integrating vectors is equal to r against the
alternative of r+1 co-integrating vectors. If the value of the likelihood ratio is greater than the
critical values, the null hypothesis of zero cointegrating vectors is rejected in favor of the
alternatives.
4.2.3. Error-correction Model (ECM)
An Error Correction Model (ECM) is an application of combining the long run, cointegrating
relationship between the levels variables and the short run relationship between the first
differences of the variables. It also has the advantage that other variables in the estimated
equation are stationary; hence there is no problem with spurious correlation. The error
correction model can be expressed as:
∆GDPt = a + ∑ α ∆GDPt-i + ∑ β ∆OPENt-j +Ω1ECTt-1+ µt…………………..... (4.6)
Where ∆ is the first difference operator, GDPt-I is lagged gross domestic product and OPENt-j
is lagged trade openness measures, respectively. The term ECTt-1 is all the residuals from the
spurious regressions estimated by OLS. This represents the short-term adjustment mechanism
from the equilibrium point, which is always significant regardless of the specifications
employed. The significance of the lagged residuals provides strong evidence of the adequacy
of an error correction framework.
4.2.4. Granger-Causality Tests
In examining the cause and effect on the variables, the study adopts the econometric
methodology followed by many time series studies such as Zestos and Tao (2002), and Beko
(2003). The study employs the granger causality test which has been developed by Granger
(1969) where he defines the “arrow of time” to help us identify between cause and effect.
According to this approach, a variable Y is caused by X if Y is better predicted from past values
of Y and X together rather than from past values of Y alone. For a simple bivariate model, the
pattern of causality can be identified by estimating regressions on Y and X using current and
past values of Y and X and by testing appropriate hypotheses. In using the following model,
causality between two variables will be tested.
GDPt = a + ∑ α GDPt-i + ∑ β OPENt-j + µt…………………………………………………………….. (4.7)
OPENt = a + ∑ α OPENt-i + ∑ β GDPt-j + έt ………..………………………...……………………… (4.8)
Where GDP is Gross domestic product and OPEN is all trade openness measures mentioned
above, µt and έt are serially uncorrelated white-noise residuals.
Ngozo (2006) explains that the test itself is just an F-test of the joint significance of the other
variable in a regression that includes lags of the dependent variable. The study tests whether
the null hypothesis trade openness does not causes GDP growth, where the alternative
hypothesis is that trade openness causes GDP growth. Given that the study has opted for α =
0.05 level of significance, the null hypothesis of no Granger causality must be rejected if the
p-value is smaller than the level of significance, that is, if (P > (F)) < 0.05. Otherwise, H0 cannot
be rejected.
5. Results and Discussions
5.1. Graphical inspection
The graphs below looked at the visual inspection of the graphs using raw data. After the visual
inspection of whether the graphs were stationary or non-stationary, correlation test was
employed to see if the prediction on visual inspection was true. The correlation table is found
in appendix A.
Figure 5.1: Graphical inspection
-20
-10
0
10
20
1980 1985 1990 1995 2000 2005 2010
X
-20
-10
0
10
20
30
1980 1985 1990 1995 2000 2005 2010
M
-4
-2
0
2
4
6
8
1980 1985 1990 1995 2000 2005 2010
GDP
12
16
20
24
28
1980 1985 1990 1995 2000 2005 2010
GCF
With the visual inspection on the above figure, X and GCF were seen non-stationary in level
form, meaning that their variances were not constant over time. GDP and M were non-
stationary in level form. Thus, correlation test for stationarity was employed. Appendix A
shows that GDP was the only variable that was non-stationary, and all other variables were
stationary. Meaning that the variance of GDP was not constant over time, it always changes.
5.2. Unit root results
Empirical literature suggests that the typical and well conventional method of detecting non-
stationary behaviour is to examine the tests for the existence of unit root (Sharma &
Panagiotidis, 2004). For this purpose, all the variables were examined through graphical check
of their time series plots. The variables were real gross domestic product (GDP), gross capital
formation (GCF), import ratio (M), and exports ratio (X).
Table 5.1: Unit root test
Variables Models ADF Lags PP Lags
GDP (Levels) Intercept -4.001705 0 -4.007703 1
trend and intercepts -5.018076 1 -4.544887 5
None -2.80377 0 -2.730896 2
M (Levels) intercept -4.950238 0 -4.938702 2
trend and intercepts -4.987907 0 -5.008933 4
None -4.494642 0 -4.480629 2
X (Levels) intercept -4.771585 0 -4.736737 3
trend and intercepts -4.687296 0 -4.646673 3
None -4.082808 0 -4.089778 2
GCF (Levels) intercept -3.097038 1 -1.832824 1
trend and intercepts -1.48184 2 -0.872475 5
None -1.209313 2 -1.150777 0
1st difference intercept -3.056603** 0 -3.159824** 2
trend and intercepts -4.310078** 1 -3.013424 10
None -2.998806** 0 -3.110413* 2 *; **; ***; level of the rejection at 1%, 5% and 10% respectively
The decision criterion when testing for stationary using ADF and P-P is to reject the null
hypothesis if the t-statistic is more negative than the critical values, or if the t-statistic is greater
than the critical values in absolute terms.
In the case of the above table, the variables: GDP, Exports, Imports were stationary at levels.
However the Gross capital formation appeared to have a unit root and had to be differenced
once to become stationary. With ADF the Gross capital formation was stationary after it had
been differences at 5 percent level of significance, and with P-P it was also stationary at 5
percent level of significance. This implies that Gross capital formation was integrated of order
one (I(1)), whereas other variables were integrated of order zero (I(0)).
5.3. Granger causality results
Since there was cointegration between trade openness and GDP growth, the next step was to
test for the direction of causality using a simple Granger causality test by estimating the
bivariate autoregressive processes for GDP and trade openness. The objective of this exercise
was to empirically test the trade openness led growth (TLG) hypothesis for South Africa. The
presence of a cointegrating vector allows for the use of a vector error correction model to test
causality. The results of the Granger causality test are presented in the following Table below.
Table 5.2: Granger causality test
Sample: 1980 - 2010
Null Hypothesis Lags Obs F-Statistic Prob.
X does not Granger Cause GDP 2 29 0.18413 0.833
GDP does not Granger Cause X 2 29 5.35056 0.012
From the table above, it is seen that the hypothesis that exports did not granger cause GDP was
accepted, whereas for the hypothesis that GDP did not granger cause exports were rejected and
conclude that GDP cause exports in South Africa. Therefore, there was unidirectional
causation. This indicates that causality runs from X to GDP in South Africa.
Table 5.3: Granger causality test
Null Hypothesis: Obs F-Statistic Prob.
M does not Granger Cause GDP 29 0.12300 0.8848
GDP does not Granger Cause M 1.45633 0.2530
X does not Granger Cause GDP 29 0.18413 0.8330
GDP does not Granger Cause X 5.35056 0.0120
GCF does not Granger Cause GDP 29 2.72706 0.0857
GDP does not Granger Cause GCF 8.65667 0.0015
X does not Granger Cause M 29 0.46856 0.6315
M does not Granger Cause X 2.64405 0.0917
GCF does not Granger Cause M 29 6.53784 0.0054
M does not Granger Cause GCF 3.73321 0.0388
GCF does not Granger Cause X 29 6.72369 0.0048
X does not Granger Cause GCF 0.64257 0.5347
In the table above, the hypothesis was accepted in that M did not granger cause GDP, and GDP
did not granger cause M, because the probability values 0.8848(88%) and 0.2530(25%) were
more than 10%. In this case, there was bidirectional causation. There was bidirectional
causality between GCF and GDP, and the null for both of them was rejected because the
probabilities were below 10%.
5.4. The Long run Cointegration results
Cointegration determines the long run relationship between GDP, exports in which the
economic theory predicts a positive relationship amongst them. It is acknowledged that
estimation of variables in levels may lead to spurious results. The estimation enables one to
find out if the residuals obtained from the co-integration regression is a white noise process.
It is extremely important to note that the customary diagnostic tests have not been reported.
Even though the coefficients reported in the spurious regression could be interpreted as
approximations of partial elasticities, they do not provide any kind of basis for sensible and
valid inferences at this stage. Furthermore, they cannot be used to draw any kind of inferences
without confirming in prior that the variables are in fact cointegrated.
Table 5.4: Cointegration
Cointegration
t-Statistic Prob.
Augmented Dickey-Fuller test statistic -4.137059 0.0002
Test critical values 1% level -2.644302
5% level -1.952473
10% level -1.610211
The results from the cointegration table shows that the ADF test on residuals with the model
of two variables, which were GDP and X(exports) were stationary and there was cointegration
between these two variables. The null hypothesis that residuals had a unit root was rejected and
the alternative that said the residuals did not have a unit root was accept.
5.5. Error correction model
Since the result shows that there was cointegration, then the next step was to test for the speed
of the adjustment that is displayed in the following table below.
Table 5.5: Error correction model Variable Coefficient Std. Error t-Statistic Prob.
RESID01(-1) -0.678881 0.168196 -4.036240 0.0004
D(X) 0.117481 0.050143 2.342923 0.0268
C -0.145550 0.394156 -0.369270 0.7148
R-squared 0.460607 Mean dependent var -0.123333
Adjusted R-squared 0.420652 S.D. dependent var 2.835816
S.E. of regression 2.158479 Akaike info criterion 4.471324
Sum squared residual 125.7938 Schwarz criterion 4.611444
Log likelihood -64.06986 Hannan-Quinn criter. 4.516149
F-statistic 11.52813 Durbin-Watson stat 2.077007
Probability (F-statistic) 0.000240
The result from the above table provides evidence for saying that there was cointegration
between GDP and X, because they had a positive relationship. The percentage change of D(x)
explains the variation of the dependent variable (GDP). This means that when D(X) increases
by 11%, GDP will increase by 1%. The R-squared which is the goodness of fit, in this case its
value was 0.460607, meaning that if there might be a shock in the process then GDP was going
to be able to recover with 46% per annum.
5.6. Engle and Granger cointegration test
Model specification for Engle and Granger is written on the equation below
GDPt = β0 + β1Xt + εt ……………………………………………………………………………… (4.7)
In the case of cointegration, two variables were tested, in the study it was for GDP as a
dependent variable and X as an independent variable from equation 4.7. The results on of PP
and ADF in table indicates that both of this variables were integrated of order zero I(0). The
null hypothesis was rejected if the probability value was less than 0.1 (10%). Similarly, the null
was rejected when the t-statistic value was more negative than the critical values. The results
obtained from the ADF test on residuals are shown on the table below.
Table 5.6: Engle and Granger cointegration ADF test results t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -4.137059 0.0002
Test critical values: 1% level -2.644302
5% level -1.952473
10% level -1.610211
*MacKinnon (1996) one-sided p-values.
The above table shows that, after applying the ADF test the residuals were stationary at all
levels of significance. Therefore, the null hypothesis of non-stationary was rejected and the
alternative of stationary was accepted and these results were because the probability was far
below 10%.
5.7. Johansen cointergration
The Johansen procedure was employed to examine the question of cointegration and provided
not only an estimation methodology but also explicit procedures for testing for the number of
cointegrating vectors as well as for restrictions suggested by economic theory in a multivariate
settings. The following table presents the results of Johansen cointegration.
Table 5.7.1: Unrestricted Cointegration Rank Test (Trace)
Hypothesized Trace 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob.**
None * 0.717869 72.02070 47.85613 0.0001
At most 1 * 0.567627 36.58998 29.79707 0.0071
At most 2 0.259391 13.11290 15.49471 0.1107
At most 3 * 0.154676 4.704990 3.841466 0.0301
Trace test indicates 2 cointegratingeqn(s) at the 0.05 level
* denotes rejection of the hypothesis at the 0.05 level
**MacKinnon-Haug-Michelis (1999) p-values
The above table states shows the rejection of the null hypothesis of cointegration and no
cointegrating vectors under both trace and eigenvalue form test. In the case of trace test, the
null hypothesis of no cointegrating vectors was rejected at 5 percent since the trace statistic of
72 was greater than the critical value of 47, this implies that cointegration exists at none.
Moving on to the test, the null of the at most 1 cointegration vectors, the trace statistic of 36
was greater than the critical value of 29, then this indicated the presence of cointegration. The
null of no cointegrating vectors was not rejected at most 2, the trace statistics of 13 was now
below the critical value of 15 at 5 percent indicating that the null should not be rejected. This
implies that the variables included in this study under trace statistics were cointegrated at none,
at most 1, and at most 3. Therefore, a unique long run relationship was expected to exist
between GDP and its variables.
Table 5.7.2: Unrestricted Cointegration Rank Test (Maximum Eigenvalue)
The Johansen test statistic for Maximum Eigenvalue in the table above shows that at none the
value of Max-Eigen Statistic 35 was greater than the critical value of 27. At most 1, and at most
3 there was cointegration since the Max-Eigen statistics were greater than the critical values at
5 percent, this means that the null hypothesis was reject. At most 2 Max-Eigen statistic was 8
which was well below the 5 percent critical value of 14, indicating that the null hypothesis of
no cointegartion vector was not rejected.
5.8. Diagnostic Test
The table below shows the results on residual diagnostic test which provides the tests for
heteroskedasticity, normality and serial correlation from the estimated equation and the
stability diagnostic by making use of the Ramsey reset test to check the model mis-
specification.
Table 5.8: Diagnostic summary and stability test
Table 4.8 diagnostic summary and stability test
Tests H0 Probability Diagnostic Test Conclusion
Breusch-Pagan
Godfrey
No
Heteroskedasticity
Prob.
F(3,27)
0.3562 Heteroskedasticity
There is no
heteroskedasticity
Jarque-Bera
Probability
Normal
Distribution 0.300391
Normality
Distribution
Normally
Distributed
BG Serial
Correlation LM
Test
No serial
correlation
Prob.
F(7,20)
0.1431 Serial Correlation
There is no serial
correlation
Ramsey reset
test
Normal
distribution ε ̴ N
(0,σ2I) 0.8688
Model Mis-
Specification
The model is
normally
distributed
Hypothesized Max-Eigen 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob.**
None * 0.717869 35.43072 27.58434 0.0040
At most 1 * 0.567627 23.47708 21.13162 0.0230
At most 2 0.259391 8.407912 14.26460 0.3387
At most 3 * 0.154676 4.704990 3.841466 0.0301
Max-eigenvalue test indicates 2 cointegratingeqn(s) at the 0.05 level
* denotes rejection of the hypothesis at the 0.05 level
**MacKinnon-Haug-Michelis (1999) p-values
The result from the above table shows that the model of this study meets the requirements of
the assumption of the Classical Linear Regression Model (CLRM). This implies that the model
was homoscedastic and linear.
6. Conclusion and Recommendation
The results shows that in estimating equation (3.1a), the long-run equilibrium relationship
shows that variables such as exports, imports and gross fixed capital formation were positively
correlated with GDP growth. These results were expected from economic theory that an
increase in exports leads to an increase in GDP. The causal relationship between trade openness
and GDP growth was examined using Granger-causality tests. When testing Granger causality,
the study used exports as the main variable that affect GDP growth. It was found that GDP
granger cause exports.
The study has also utilised the concept of impulse response functions in order to investigate
how the system responds to a macroeconomic shock. This approach allows the simulation of
the effect of a given (predetermined) shock on the economic system. The response shocks show
no evidence of causality between trade openness and GDP growth. The only exception that can
be made is the shock made by GDP growth on imports but the shock does not last for a long
period. Finally, the results of the diagnostic tests employed in equation (4.1a) were satisfactory,
with no heteroskedasticity, and residuals were normally distributed with no problem of serial
correlation in residuals. This implies that the South African government should continue
improving the policy regarding trade openness and GDP growth.
The findings of the study show a smaller than expected effects of trade openness on the GDP
growth process in South Africa. This is mostly because the South African exports are more raw
resource based. Therefore, to promote openness, the South African government should
encourage exporters to improve their competitive advantage and change their trade pattern
from raw material based to more technological and human capital intensive goods.
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Appendix A: Correlograms
GDP Growth Date: 10/22/12 Time: 22:26
Sample: 1980 2010
Included observations: 31
Autocorrelation Partial Correlation AC PAC Q-Stat Prob
. |******| . |******| 1 0.885 0.885 26.725 0.000
. |***** | ***| . | 2 0.686 -0.452 43.323 0.000
. |**** | . | . | 3 0.487 0.034 52.000 0.000
. |**. | . | . | 4 0.324 0.001 55.981 0.000
. |* . | . | . | 5 0.206 0.016 57.655 0.000
. |* . | . | . | 6 0.118 -0.057 58.226 0.000
. | . | . |* . | 7 0.069 0.092 58.428 0.000
. | . | . *| . | 8 0.024 -0.152 58.454 0.000
. | . | .**| . | 9 -0.059 -0.224 58.616 0.000
Gross Capital Formation
Date: 10/22/12 Time: 22:27
Sample: 1980 2010
Included observations: 31
Autocorrelation Partial Correlation AC PAC Q-Stat Prob
. |**. | . |**. | 1 0.323 0.323 3.5670 0.059
. | . | . *| . | 2 -0.052 -0.175 3.6629 0.160
. | . | . |* . | 3 -0.010 0.076 3.6669 0.300
. | . | . | . | 4 0.013 -0.021 3.6732 0.452
. *| . | . *| . | 5 -0.075 -0.082 3.8931 0.565
. | . | . |* . | 6 0.064 0.145 4.0619 0.668
. |* . | . | . | 7 0.154 0.069 5.0676 0.652
. |* . | . | . | 8 0.116 0.064 5.6614 0.685
. | . | . | . | 9 -0.006 -0.044 5.6629 0.773
Imports Date: 10/22/12 Time: 22:27
Sample: 1980 2010
Included observations: 31
Autocorrelation Partial Correlation AC PAC Q-Stat Prob
. |* . | . |* . | 1 0.093 0.093 0.2974 0.586
. *| . | . *| . | 2 -0.185 -0.196 1.5096 0.470
. *| . | . | . | 3 -0.082 -0.045 1.7555 0.625
. | . | . | . | 4 0.046 0.025 1.8370 0.766
.**| . | ***| . | 5 -0.342 -0.392 6.4292 0.267
. *| . | . *| . | 6 -0.174 -0.108 7.6732 0.263
. |* . | . | . | 7 0.098 -0.009 8.0866 0.325
. |* . | . | . | 8 0.160 0.025 9.2195 0.324
. | . | . | . | 9 -0.008 -0.003 9.2224 0.417
Exports Date: 10/22/12 Time: 22:28
Sample: 1980 2010
Included observations: 31
Autocorrelation Partial Correlation AC PAC Q-Stat Prob
. |* . | . |* . | 1 0.104 0.104 0.3713 0.542
. | . | . | . | 2 -0.050 -0.062 0.4610 0.794
. *| . | . | . | 3 -0.075 -0.064 0.6675 0.881
. *| . | . *| . | 4 -0.133 -0.124 1.3398 0.855
. |* . | . |* . | 5 0.088 0.111 1.6439 0.896
. | . | . *| . | 6 -0.040 -0.083 1.7093 0.944
. | . | . | . | 7 0.030 0.041 1.7482 0.972
. |* . | . |* . | 8 0.128 0.113 2.4738 0.963
. *| . | . *| . | 9 -0.105 -0.117 2.9817 0.965