1

The Impacts of Market Capitalization, Interest Spread and Foreign Reserves on Velocity of

Money in the Nigerian Economy

Oluwafemi. O. Bamikole1

August, 2014

Abstract

The paper examines the stability of two functions, interest rate and foreign reserves,

using the Autoregressive Distributed Lag Model of Pesaran et al (2001). More importantly, we

analyze quantitatively and the qualitatively the influence of foreign reserves and interest spread

on the velocity of money in Nigeria from 1980 to 2013. Multiple long run relationships between

the variables are established in the model, however only the velocity of money has stable long

and short run relationships with market capitalization and reserves. The policy implication of this

result is that the Federal Government of Nigeria needs to stabilize the lending, time deposit rates

and foreign reserves in order to improve the velocity of money and market capitalization in the

stock market.

Keywords: ARDL, Velocity of Money, Foreign Reserves, Interest Spread, Nigeria

JEL Classification Codes: C32, E41, E44

1 E mail: oluwafemi.bamikole@hotmail.com. All errors are mine.

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Section 1: Introduction

The secondary market (money market) and the primary market (capital market) are two

separate institutions that make savings, lending and investing possible, however they are linked

by an underlying variable, the interest rate. If there should be a major shock to the primary

market, the secondary market might not feel the effect of such shock (negative or positive)

immediately but there is bound to be a long-run impact on the secondary market and the rest of

the economy. For example, the stock market crash that occurred in the United States in 1929 led

to the collapse of major financial intermediaries and institutions and subsequently to the decline

of the purchasing power of US citizens since there was lack of effective aggregate demand. The

stock market crash in the US not only impacted domestic residents, it also impacted

neighbouring European countries such as Britain, France, Germany and the list goes on. This

clearly attests to the fact that both the primary and the secondary markets have strong linkages.

The financial crisis of 2008/2009 also provides further evidence of the tight relationship

between the money market and the capital market. Several homes witnessed foreclosures, jobs

were lost and world economic growth and output fell; the negative effect of the crisis could also

not be avoided by major commercial banks, building societies, investment banks and foreign

exchange traders as loan portfolios and other investment activities declined.

In Nigeria, much has been done to raise the banking standards and the capital base of

major commercial banks such as First Bank, Oceanic Bank, Standard Trust Bank and others; this

has helped to stabilize lending rates, deposit rates, velocity of money and consequently, the

Nigerian economy has been performing well, in the first quarter of 2014, the economy recorded a

growth rate of 7% and got a major boost from Foreign Direct Investments. The stock market has

also greatly improved and companies have witnessed over-subscription of shares and new

companies have also been listed on the stock exchange. This has undoubtedly assisted in the

diversification of the investment portfolios of entrepreneurs, Nigerian consumers and foreign

investors.

This study is deemed necessary in order to further study the stability between the certain

monetary variables such as the interest spread, velocity, foreign reserves and the stock market

using market capitalization as a proxy. The study is divided into five sections. Section 1 does a

brief introduction to the study, section 2 deals with the literature review and the theoretical

framework, section 3 discusses the econometric tests carried out and data sources, section four

takes care of the interpretation of model results and section five concludes the study with certain

recommendations for future studies. Line and scatter plots graphs are shown in the appendix.

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Section 2a: A Brief Literature Review

Ologunde, et al (2006) examine the relationships between stock market capitalization rate

and interest rate in Nigeria. Using simple Ordinary Least Squares, they find that prevailing

interest rate exerts positive influence on stock market capitalization rate. Rurchera (2006)

suggests that stock market capitalization rate is significantly influenced by the macroeconomic

environment factors such as GDP, exchange rate, interest rates, current account and money

supply. Hsing (2004) finds an inverse relationship between stock prices and interest rates.

Campbell (1987) considers the relationship between the yield spread and stock market returns.

Campbell shows that an evidence of effectiveness of the term structure of interest rates in

predicting excess returns on the US market is supported. Jeroh (2012) asserts that variations in

interest rate affect the level of stock market capitalization, as such serious attention has to be

paid to policies geared towards lending rate in any country.

Akingunola, et al (2012) affirm using a multiple regression analysis that interest rates have

adverse effect on capital market growth in Nigeria. Their analyses point out that a 1% increase in

interest rate will lead to a 44% decrease in all share price index; inflation and exchange rate in

their model are not however statistically significant. Akingunola et al further posit that the stock

market provides an engine that spurs liquidity in the capital market, and without it, the capital

market would be very illiquid and could not provide the investment that makes growth possible.

Large stock market lowers the cost of mobilizing savings thereby facilitating investments in the

most productive technologies. Omotor (2012) also finds that the empirical relationship between

stock market returns and inflation is positive and statistically significant; the author uses co-

integration analyses to construct his model and posit that the Fisher’s hypothesis regarding

inflation and stock prices holds in the Nigeria

Section 2b: Theoretical Framework

The quantity theory of money put forward by the classicists provides a link between total money

supply(M) and total amount of spending on final goods and services (PY) produced in a given

peiod.P represents price level. The velocity of money as defined by the classical economists is

the average number of times per year that a dollar is spent in purchasing goods and services. The

following equations explain the interactions between the aforementioned variables:

𝑀𝑉 = 𝑃𝑌, 𝑡ℎ𝑖𝑠 𝑖𝑚𝑝𝑙𝑖𝑒𝑠 𝑡ℎ𝑎𝑡 𝑉 =𝑃𝑌

𝑀− − − − − − − −1

𝑖𝑛 𝑒𝑞𝑢𝑖𝑙𝑖𝑏𝑟𝑖𝑢𝑚 𝑀𝐷 = 𝑀𝑆 − − − − − − − − − −2

Equation 2 states that money demand is equal to money supply. Thus equation 2 can be modified

slightly as 𝑀𝐷 =𝑃𝑌

𝑉− − − − − 3. Equation 3 implies that money demand is proportional to

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money income and since the velocity is constant, interest rates have no effect on the demand for

money.

Keynes later challenged the proponents of the quantity theory of money theory and

posited the liquidity preference theory. There are three motives for demanding for money, these

include, transactionary, precautionary and speculative motives. Transactionary and precautionary

motives depend on income while speculative motive depends on interest rate because people are

hedging against the fall in the returns of other assets such as bonds and stocks. The famous

Keynes’ equation is as follows:

𝑀𝐷

𝑃= 𝑓(𝑌, 𝑖), 𝑡ℎ𝑖𝑠 𝑖𝑚𝑝𝑙𝑖𝑒𝑠 𝑡ℎ𝑎𝑡 𝑀𝐷 = 𝑃𝑓(𝑌, 𝑖) − − − − − −4

If we assume that money demand and money supply are equal then equation 4 translates to the

following:

𝑉 =𝑃𝑌

𝑀=

𝑌

𝑓(𝑌, 𝑖)= 𝑣 − − − − − − − 5

Therefore equation 5 implies that as interest rate rises, the velocity of money also increases

implying that a procyclical relationship exists between interest rate and velocity, this important

relationship exists in our model.

Baumol and Tobin modify Keynes’ liquidity preference theory by stating that

transactionary and precautionary motives are also functions of interest rate because people use

credit cards from time to time to transact business and goods that are bought today may incur

interest charges that have to be settled for a certain period of time. Friedman believes that money

is neutral and consequently it has no effect on real economic variables, as such monetary policy

and real fundamentals (consumer preferences, technology, resource endowments) are

independent factors influencing the economy. Friedman further states that in the long run, faster

(slower) money growth may not cause faster (slower) inflation and real fundamentals determine

the real economic variables in the long run. The following equation demonstrates this:

𝑉 =𝑌

𝑀− − − − − − − −6

Equation 6 shows that the velocity of money is indeed the ratio of two nominal variables,

money supply and national income and thus velocity of money must be a real variable.

As it has been rightly pointed out in the introduction of this paper, the interest rate as

commonly bandied by the media, has a wide and varied impact on the economy. When it is

raised, the general effect is a lessening of the amount of money in circulation which helps to

keep inflation low . An increase in the interest rate also makes borrowing expensive, which

affects how consumers and businesses spend their money; this increases expenses for companies,

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lowering earnings and profits for those with debt to pay. Finally, such an increase tends to make

the stock market less predictable.

Khrawish, et al (2010) affirms that stock market capitalization is measured by the total

value of companies outstanding shares. To find the market capitalization of a company, one

needs to multiply the market price of the stock by the number of outstanding shares. The stock

market price is described by the following equation:

𝑃0 = ∑ 𝐸(𝐷𝑡

∞

𝑡=0

)1

(1 + 𝑟)𝑡− − − − − 7

In the equation above, D is the expected cash flow, r is the required rate of return, t indexes time

series. Stock market capitalization rate is simply the inverse of the price-earnings ratio. The

price-earnings ratio is the market value per share divided by earnings per share. The participants

at the Nigerian Stock Exchange include discount houses, development banks, investment banks,

building societies, stock-broking firms, insurance and pension organizations, quoted companies,

government and individuals.

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Section 3: Data Sources, Description of Data, ARDL model properties and Econometric

Assumptions

Data Sources and Description of Data

The Data used are derived from index mundi website and Central Bank of Nigeria Statistical

Bulletin, 2013. The data span from 1980-2013. The variables used include interest spread,

foreign reserves, exchange rate, velocity of money (the difference between the gross domestic

product at current basic prices (billion naira) and broad money M2 (billion naira) at current price,

inflation rate and market capitalization.

Table 1: Descriptive Statistics of Data

Variable Mean Median Maximum Minimum Standard

Deviation

IntSpread 12.410 15.100 26.040 2.250 6.932

LReserves 22.475 22.266 24.705 20.654 1.312

LmakCap 25.786 26.294 30.210 20.723 2.857

Excr 59.174 21.90 154.74 0.620 59.835

Velocity 1.827 1.828 2.456 0.968 0.320

Ifr 21.155 13.720 72.80 5.400 17.950

Observations 31 31 31 31 31

Velocity has a minimum value of 0.968, a maximum value of 2.456 and a mean of 1.827.

In addition, the interest spread has been low over the years. The spread has a minimum value of

2.25%, a maximum value of 26.04% and a mean of 12.14%. This modest spread value has

undoubtedly provided incentives for lenders to borrow without any significant negative impact

on the participation constraint of savers. Reserves and market capitalization have been log-

linearized in order to aid effective comparisons. Reserves and market capitalization both have

respectively maximum values of 24.705 and 30.210, minimum values of 22.266 and 26.294 and

mean of 22.475 and 25.786. Inflation rate has a maximum value of 72.80%, a minimum of 5.4%,

a mean of 21.55% and a standard deviation of 17.95%. Moreover, the exchange rate shows a

maximum value of US$154.74, a minimum value of US$0.62 recorded right before the adoption

of the Structural Adjustment Programme and a mean of US$59.174

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The Autoregressive Distributed Lag Model and its Properties

The ARDL is a model that has the framework of simultaneous equations’ modeling. It

shows the feedbacks between variables and assumes that there exist bi-directional relationships,

this gives this modeling approach a special flavour. First, the existence of long run relationships

is examined between variables by regressing the differenced variables on its own level lags,

lagged differences and the lags and lagged differences of the other independent variables and

then a Wald-test of joint significance of the level variables is performed. The values of the F-

Statistic from the regressions are now compared with the upper and lower bounds at a certain

significance level. If the F-Statistic falls below the lower bound, no co-integration exists between

the variables, if it falls between the two bounds, the result is inconclusive. If the F-Statistic,

however, is above the upper bound, co-integration exists. The ARDL model has as one of its

assumptions that variables that are integrated of order one, zero or fractionally integrated can still

be combined to produce results that yield stable long and short run relationships; this is a major

innovation in time-series analyses.

The ARDL Model2 used in this paper is specified as follows:

𝑽𝒆𝒍𝒐𝒄𝒊𝒕𝒚 = 𝒇(𝑰𝒏𝒕𝑺𝒑𝒓𝒆𝒂𝒅, 𝑹𝒆𝒔𝒆𝒓𝒗𝒆𝒔, 𝑰𝒏𝒇𝒍𝒂𝒕𝒊𝒐𝒏 𝑹𝒂𝒕𝒆, 𝑬𝒙𝒄𝒉𝒂𝒏𝒈𝒆 𝑹𝒂𝒕𝒆, 𝑴𝒂𝒌𝑪𝒂𝒑)

𝐷(𝑙𝑛(𝑅𝑒𝑠𝑡) = 𝛼01 + 𝛽11𝑅𝑒𝑠𝑡−1 + 𝛽21𝑖𝑛𝑡𝑆𝑡−1 + 𝛽31𝑉𝑒𝑙𝑡−1 + 𝛽41𝑖𝑓𝑟𝑡−1 + 𝛽51𝑒𝑥𝑟𝑡−1

+ 𝑏61(𝑙𝑚𝑎𝑘𝑐𝑎𝑝𝑡−1) + ∑ 𝑎1𝑖

𝑝

𝑖=1

𝐷(𝑙𝑛(𝑅𝑒𝑠𝑡−𝑖) + ∑ 𝑎2𝑖

𝑞

𝑖=1

𝐷(𝐼𝑛𝑡𝑆𝑡−𝑖) + ∑ 𝑎3𝑖

𝑞

𝑖=1

𝐷(𝑉𝑒𝑙𝑡−𝑖)

+ ∑ 𝑎4𝑖

𝑞

𝑖=1

𝐷(𝑖𝑓𝑟𝑡−𝑖) + ∑ 𝑎5𝑖

𝑞

𝑖=1

𝐷(𝑒𝑥𝑟𝑡−𝑖) + ∑ 𝑎6𝑖

𝑞

𝑖=1

𝐷(𝑙𝑛(𝑚𝑎𝑘𝑐𝑎𝑝𝑡−𝑖) + 𝜀1𝑡 − − − −(1)

𝐷(𝐼𝑛𝑡𝑆𝑡) = 𝛼02 + 𝛽12𝑅𝑒𝑠𝑡−1 + 𝛽22𝑖𝑛𝑡𝑆𝑡−1 + 𝛽32𝑉𝑒𝑙𝑡−1 + 𝛽42𝑖𝑓𝑟𝑡−1 + 𝛽52𝑒𝑥𝑟𝑡−1 + 𝑏62(𝑙𝑚𝑎𝑘𝑐𝑎𝑝𝑡−1)

+ ∑ 𝑎1𝑖

𝑝

𝑖=1

𝐷(𝑙𝑛(𝑅𝑒𝑠𝑡−𝑖) + ∑ 𝑎2𝑖

𝑞

𝑖=1

𝐷(𝐼𝑛𝑡𝑆𝑡−𝑖) + ∑ 𝑎3𝑖

𝑞

𝑖=1

𝐷(𝑉𝑒𝑙𝑡−𝑖) + ∑ 𝑎4𝑖

𝑞

𝑖=1

𝐷(𝑖𝑓𝑟𝑡−𝑖)

+ ∑ 𝑎5𝑖

𝑞

𝑖=1

𝐷(𝑒𝑥𝑟𝑡−𝑖) + ∑ 𝑎6𝑖

𝑞

𝑖=1

𝐷(𝑙𝑛(𝑚𝑎𝑘𝑐𝑎𝑝𝑡−𝑖) + 𝜀2𝑡 − − − −(2)

2 One lag is chosen using the SIC (Schwarz Information Criterion) and two lags are chosen by the AIC (Akaike

Information Criterion). In the ARDL setup above each differenced variable is regressed on its own level lags, level lags of the independent variables, its own lagged differences and the lagged differences of the independent variables. We make use of two lags for the differenced variables on the right hand side of the ARDL equations above. Also, all the equations are made robust applying White heteroskedasticity option.

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𝐷(𝑉𝑒𝑙𝑡) = 𝛼03 + 𝛽13𝑅𝑒𝑠𝑡−1 + 𝛽23𝑖𝑛𝑡𝑆𝑡−1 + 𝛽33𝑉𝑒𝑙𝑡−1 + 𝛽43𝑖𝑓𝑟𝑡−1 + 𝛽53𝑒𝑥𝑟𝑡−1 + 𝑏63(𝑙𝑚𝑎𝑘𝑐𝑎𝑝𝑡−1)

+ ∑ 𝑎1𝑖

𝑝

𝑖=1

𝐷(𝑙𝑛(𝑅𝑒𝑠𝑡−𝑖) + ∑ 𝑎2𝑖

𝑞

𝑖=1

𝐷(𝐼𝑛𝑡𝑆𝑡−𝑖) + ∑ 𝑎3𝑖

𝑞

𝑖=1

𝐷(𝑉𝑒𝑙𝑡−𝑖) + ∑ 𝑎4𝑖

𝑞

𝑖=1

𝐷(𝑖𝑓𝑟𝑡−𝑖)

+ ∑ 𝑎5𝑖

𝑞

𝑖=1

𝐷(𝑒𝑥𝑟𝑡−𝑖) + ∑ 𝑎6𝑖

𝑞

𝑖=1

𝐷(𝑙𝑛(𝑚𝑎𝑘𝑐𝑎𝑝𝑡−𝑖) + 𝜀3𝑡 − − − −(3)

𝐷(𝑖𝑓𝑟𝑡) = 𝛼04 + 𝛽14𝑅𝑒𝑠𝑡−1 + 𝛽24𝑖𝑛𝑡𝑆𝑡−1 + 𝛽34𝑉𝑒𝑙𝑡−1 + 𝛽44𝑖𝑓𝑟𝑡−1 + 𝛽54𝑒𝑥𝑟𝑡−1 + 𝑏64(𝑙𝑚𝑎𝑘𝑐𝑎𝑝𝑡−1)

+ ∑ 𝑎1𝑖

𝑝

𝑖=1

𝐷(𝑙𝑛(𝑅𝑒𝑠𝑡−𝑖) + ∑ 𝑎2𝑖

𝑞

𝑖=1

𝐷(𝐼𝑛𝑡𝑆𝑡−𝑖) + ∑ 𝑎3𝑖

𝑞

𝑖=1

𝐷(𝑉𝑒𝑙𝑡−𝑖) + ∑ 𝑎4𝑖

𝑞

𝑖=1

𝐷(𝑖𝑓𝑟𝑡−𝑖)

+ ∑ 𝑎5𝑖

𝑞

𝑖=1

𝐷(𝑒𝑥𝑟𝑡−𝑖) + ∑ 𝑎6𝑖

𝑞

𝑖=1

𝐷(𝑙𝑛(𝑚𝑎𝑘𝑐𝑎𝑝𝑡−𝑖) + 𝜀4𝑡 − − − −(4)

𝐷(𝑒𝑥𝑟𝑡) = 𝛼05 + 𝛽15𝑅𝑒𝑠𝑡−1 + 𝛽25𝑖𝑛𝑡𝑆𝑡−1 + 𝛽35𝑉𝑒𝑙𝑡−1 + 𝛽45𝑖𝑓𝑟𝑡−1 + 𝛽55𝑒𝑥𝑟𝑡−1 + 𝑏65(𝑙𝑚𝑎𝑘𝑐𝑎𝑝𝑡−1)

+ ∑ 𝑎1𝑖

𝑝

𝑖=1

𝐷(𝑙𝑛(𝑅𝑒𝑠𝑡−𝑖) + ∑ 𝑎2𝑖

𝑞

𝑖=1

𝐷(𝐼𝑛𝑡𝑆𝑡−𝑖) + ∑ 𝑎3𝑖

𝑞

𝑖=1

𝐷(𝑉𝑒𝑙𝑡−𝑖) + ∑ 𝑎4𝑖

𝑞

𝑖=1

𝐷(𝑖𝑓𝑟𝑡−𝑖)

+ ∑ 𝑎5𝑖

𝑞

𝑖=1

𝐷(𝑒𝑥𝑟𝑡−𝑖) + ∑ 𝑎6𝑖

𝑞

𝑖=1

𝐷(𝑙𝑛(𝑚𝑎𝑘𝑐𝑎𝑝𝑡−𝑖) + 𝜀5𝑡 − − − −(5)

𝐷(𝑙𝑚𝑎𝑘𝑐𝑎𝑝𝑡) = 𝛼06 + 𝛽16𝑅𝑒𝑠𝑡−1 + 𝛽26𝑖𝑛𝑡𝑆𝑡−1 + 𝛽36𝑉𝑒𝑙𝑡−1 + 𝛽46𝑖𝑓𝑟𝑡−1 + 𝛽56𝑒𝑥𝑟𝑡−1

+ 𝑏66(𝑙𝑚𝑎𝑘𝑐𝑎𝑝𝑡−1) + ∑ 𝑎1𝑖

𝑝

𝑖=1

𝐷(𝑙𝑛(𝑅𝑒𝑠𝑡−𝑖) + ∑ 𝑎2𝑖

𝑞

𝑖=1

𝐷(𝐼𝑛𝑡𝑆𝑡−𝑖) + ∑ 𝑎3𝑖

𝑞

𝑖=1

𝐷(𝑉𝑒𝑙𝑡−𝑖)

+ ∑ 𝑎4𝑖

𝑞

𝑖=1

𝐷(𝑖𝑓𝑟𝑡−𝑖) + ∑ 𝑎5𝑖

𝑞

𝑖=1

𝐷(𝑒𝑥𝑟𝑡−𝑖) + ∑ 𝑎6𝑖

𝑞

𝑖=1

𝐷(𝑙𝑛(𝑚𝑎𝑘𝑐𝑎𝑝𝑡−𝑖) + 𝜀6𝑡 − − − −(6)

The long and short run velocity equilibrium functions are singled out in a series of simultaneous

equations because they pass the test of short run dynamic stability while the other functions fail

that test; however all the equations above are estimated nevertheless . We will also concentrate

solely on the long run and short run dynamics of velocity function with the aim of empirically

analyzing the relationships velocity of money has with the other variables.

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Table 2: Results from Bounds Testing3

Dependent Variable4 AIC and SIC lag F-Stat Decision

𝐹𝑅𝐸𝑆(𝑅𝐸𝑆/𝑥𝑖) 2 1.101 No Cointegration

𝐹𝑖𝑛𝑡𝑆(𝐼𝑛𝑡𝑆/𝑧𝑖) 2 1.193 No Cointegration

𝐹𝑉𝑒𝑙(𝑉𝑒𝑙/𝑗𝑖) 2 5.576 Cointegration

𝐹𝐼𝑓𝑟(𝐼𝑓𝑟/𝑠𝑖) 2 0.823 No Cointegration

𝐹𝐸𝑥𝑟(𝐸𝑥𝑟/𝑐𝑖) 2 2.435 No Cointegration

𝐹𝑚𝑎𝑘𝑐𝑎𝑝(𝑚𝑎𝑘𝑐𝑎𝑝/𝑏𝑖) 2 3.132 No Cointegration

Lower-bound crit value 5%, k=6

2.27

Upper-bound crit value 5%, k=6

3.28

Long Run and Short run Granger Causality Tests

Estimated long and short run coefficients using the ARDL (𝑝, 𝑞1, 𝑞2, 𝑞3, 𝑞4 , 𝑞5) long run model

for velocity is as follows:

𝑉𝑒𝑙 = 𝛼0 + ∑ 𝑎1𝑖ln (𝑅𝐸𝑆𝑡−𝑖

𝑃

𝐼=1

) + ∑ 𝑎2𝑖ln (𝑚𝑎𝑘𝑐𝑎𝑝𝑡−𝑖

𝑃

𝐼=1

) + ∑ 𝑎3𝑖𝐼𝑓𝑟𝑡−𝑖

𝑃

𝐼=1

+ ∑ 𝑎4𝑖𝐸𝑥𝑟𝑡−𝑖

𝑃

𝐼=1

+ ∑ 𝑎5𝑖𝑉𝑒𝑙𝑡−𝑖

𝑃

𝐼=1

+ ∑ 𝑎6𝑖𝑖𝑛𝑡𝑆𝑡−𝑖

𝑃

𝐼=1

+ 𝜖1𝑡 − − − − − − − − − −7

𝐷(𝑉𝑒𝑙𝑡) = 𝛼0 + ∑ 𝑎1𝑖

𝑝

𝑖=1

𝐷(𝑙𝑛(𝑅𝑒𝑠𝑡−𝑖) + ∑ 𝑎2𝑖

𝑞

𝑖=1

𝐷(𝐼𝑛𝑡𝑆𝑡−𝑖) + ∑ 𝑎3𝑖

𝑞

𝑖=1

𝐷(𝑉𝑒𝑙𝑡−𝑖) + ∑ 𝑎4𝑖

𝑞

𝑖=1

𝐷(𝑖𝑓𝑟𝑡−𝑖)

+ ∑ 𝑎5𝑖

𝑞

𝑖=1

𝐷(𝑒𝑥𝑟𝑡−𝑖) + ∑ 𝑎6𝑖

𝑞

𝑖=1

𝐷(𝑙𝑛(𝑚𝑎𝑘𝑐𝑎𝑝𝑡−𝑖) + 𝑒𝑐𝑚𝑡−1 − − − −(8)

3 The independent variables have been normalized on the right hand side of the equations to ensure that the

exogeneity assumption holds 4 𝑥𝑖 𝑧𝑖𝑗𝑖𝑐𝑖𝑠𝑖𝑏𝑖 𝑖𝑛𝑑𝑒𝑥 𝑡ℎ𝑒 𝑖𝑛𝑑𝑒𝑝𝑒𝑛𝑑𝑒𝑛𝑡 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒𝑠 𝑎𝑠 𝑡ℎ𝑒𝑦 𝑒𝑛𝑡𝑒𝑟 𝑡ℎ𝑒 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛𝑠, 𝑖 𝑏𝑒𝑖𝑛𝑔 𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑎𝑡𝑖𝑣𝑒 𝑜𝑓

𝑒𝑎𝑐ℎ 𝑖𝑛𝑑𝑒𝑝𝑒𝑛𝑑𝑒𝑛𝑡 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒 .

10

Econometric Assumptions and Validity Tests

All the variables in the model satisfy the vector autoregression or unrestricted VAR

stability test because no root of the characteristic polynomial lies outside the AR graph. This

indicates that there is indeed a good short run relationship between the variables. Also the

residuals obtained in the long run model specified for velocity are normal. The Jarque Bera

value for the long run model is 3.987 with a probability of 0.136. In addition, the residuals from

the long run model estimated are stationary in levels; this is the first sign of co-integration.

Strong exogeneity assumption is violated as there are lags of the dependent variable on the right

hand side of the velocity short and long run equilibrium functions however, the block exogeneity

test shows that this violation of one of the classical linear regression assumption is not a problem

as there are joint significances between the bi-directional relationships in equations (1) to (7)

above.

In addition, low correlation coefficients between the variables as shown in table 2

indicate that the ARDL models specified do not suffer from the multi-collinearity problem.

Regarding the a-priori expectations, it is expected that velocity should be positively impacted by

reserves, inflation rate, market capitalization and interest rate while there should be a negative

relationship between exchange rate and the dependent variable in both the long and the short run.

The normality test is passed for the short run specifications with a Jarque Bera statistics of 0.136

and a probability value of 0.558.

11

Section Four: Presentation of Results

Table 3: Correlation Matrix5

Variables D(velocity) D(lreserves) D(lmakcap) D(Excr) D(ifr) D(IntSpread)

D(Velocity) 1.000 0.017 0.272 -0.107 -0.158 0.052

D(lreserves) 0.017 1.000 0.398 -0.186 -0.478 -0.172

D(lmakcap) 0.272 0.398 1.000 -0.051 -0.189 0.069

D(Excr) -0.107 -0.186 -0.051 1.000 0.093 0.284

D(ifr) -0.158 -0.478 -0.189 0.093 1.000 0.012

D(IntSpread) 0.052 -0.172 0.069 0.284 0.012 1.000

5 D(exr), D(lmakcap), D(intspread), D(lreserves) and D(ifr) are respectively the first differences of exchange rate,

market capitalization, interest spread, foreign reserves (including gold) and inflation rate. While vel indexes the velocity of circulation which is the MV=PY equation (Money Supply multiplied by Velocity of Circulation must be equal to the Total Expenditure) if we divide both sides of this equation by M we would obtain the velocity of money value).

12

Table 4: Unit root test ( Levels)

Augmented Dickey-Fuller6 (ADF)

Dickey-Fuller GLS7 (DF-GLS)

Phillips-Perron8 (PP)

Variables SIC lag

T-stat Critical Values 5%

SIC Critical Values

t-stat Critical Values

T-stat Remarks9

Interest Spread 0 -0.184 -1.952 0 -1.952 -1.512 -3.558 -3.90 I(0)

Exchange Rate 0 1.399 -1.952 1 -1.952 0.337 -3.558 -2.094 I(1)

Log of GDP 0 6.301 -1.952 1 -1.952 0.371 -3.558 -2.292 I(1)

Log of M2 (Broad Money)

1 2.688 -1.952 1 -1.952 -0.428 -3.563 -2.854 I(1)

Log of Reserves 0 0.383 -1.952 0 -1.952 -0.797 --3.563 -4.778 I(0)

Log of Market Capitalization

0 2.163 -1.952 1 -1.952 0.500 -3.558 -3.544 I(0)

Velocity (Log of GDP minus log of M2)

0 -0.474 -1.952 0 -1.952 -1.793 -3.558 -2.209 I(1)

Inflation Rate 0 -1.786 -1.952 0 -1.952 -2.832 -3.553 -2.898 I(0) and I(1)

6 No constant, no trend

7 A constant and no trend

8 A trend and a constant

9 Interest spread is stationary in levels using the Phillips Perron test, however the DF-GLS and ADF-tests show that

the series is stationary bat first difference. Also the PP-test shows that the logarithms of foreign reserves and market capitalization are stationary in levels while the other tests show that the variables are stationary at first difference. In addition, the ADF test confirms that the velocity of circulation is stationary in levels, this is however disproved by the DF-GLS and PP-tests.

13

Table 5: Unit Root test ( First Difference)

Augmented Dickey-Fuller10 (ADF)

Dickey-Fuller GLS11 (DF-GLS)

Phillips-Perron12 (PP)

Variables SIC lag

T-stat Critical Values 5%

SIC Critical Values

t-stat Critical Values

T-stat Remarks13

Interest Spread 0 -7.271 -1.952 0 -7.441 -1.512 -3.563 -16.424 I(1)

Exchange Rate 0 -5.304 -1.952 1 -5.296 0.337 -3.563 -5.314 I(1)

Log of GDP 0 -2.818 -1.952 1 -1.952 -4.976 -3.563 -5.202 I(1)

Log of M2 (Broad Money)

0 -1.254 -1.952 1 -1.952 -2.797 -2.960 -3.201 I(1)

Log of Reserves 0 -4.648 -1.952 0 -3.504 -0.797 -3.568 -6.441 I(0) and I(1)

Log of Market Capitalization

0 -6.497 -1.952 1 -7.763 0.500 -3.563 -8.254 I(1)

Velocity (Log of GDP minus log of M2)

0 -5.107 -1.952 1 -0.972 -5.111 -3.563 -5.085 I(1)

Inflation Rate 1 -5.681 -1.952 0 -5.360 -2.832 -3.558 -11.223 I(1)

10

No constant, no trend 11

A constant and no trend 12

A trend and a constant 13

Interest spread is stationary in levels using the Phillips Perron test; however the DF-GLS and ADF-tests show that the series is stationary at first difference. Also the PP-test shows that the logarithms of foreign reserves and market capitalization are stationary in levels while the other tests show that the variables are stationary at first difference. In addition, the ADF test confirms that the velocity of circulation is stationary in levels, this is however disproved by the DF-GLS and PP-tests.

14

Table 6: Long-Run Relationship for equation 7:

Dependent Variable: Velocity

Variable Coefficient T-Stat Prob

Constant 4.160 2.442 0.022

𝑖𝑛𝑡𝑠𝑝𝑟𝑒𝑎𝑑𝑡−1 0.007 0.452 0.655

𝐸𝑥𝑐𝑟𝑡−1 -0.003 -1.900 0.069

𝑙𝑚𝑎𝑘𝑐𝑎𝑝𝑡−1 0.06 1.134 0.267

𝑙𝑟𝑒𝑠𝑒𝑟𝑣𝑒𝑠𝑡−1 -0.173 -1.917 0.067

𝑖𝑓𝑟𝑡−1 0.002 0.815 0.423

𝑅2 0.58

F Stat 6.934

Standard Error of

Regression

0.228

Residuals Series -4.009 0.03

Table 5 above shows that long run relationships exist between the dependent and independent

variables, the lag of the dependent has been normalized to combat the problem of weak

exogeneity in the model, this greatly improves the explanatory power of the model. As expected ,

the interest rate, inflation, exchange rate are correctly signed. However, the lagged value of

reserves with respect to velocity is negative. 58% of the variation in the dependent variable is

explained by the independent variables and the residuals of this model are also invariant with

time.

15

Table 7: Short run dynamics coefficient estimates for equation 8.

Dependent Variable: D(Velocity)

Variable Coefficient T-Stat Prob

𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 -0.061 -1.761 0.097

𝐷(𝑉𝑒𝑙)𝑡−1 0.718 5.109 0.000

𝐷(𝐸𝑥𝑐𝑟)𝑡−1 -0.004 -2.489 0.024

𝐷(𝐸𝑥𝑐𝑟)𝑡−2 0.006 3.059 0.008

𝐷(𝐼𝑛𝑡𝑆𝑝𝑟𝑒𝑎𝑑)𝑡 0.009 1.563 0.138

𝐷(𝐼𝑛𝑡𝑆𝑝𝑟𝑒𝑎𝑑)𝑡−1 -0.003 -0.334 0.743

𝐷(𝑙𝑟𝑒𝑠)𝑡−1 0.052 0.944 0.359

𝐷(𝑙𝑟𝑒𝑠𝑒𝑟𝑣𝑒𝑠)𝑡 -0.154 -2.434 0.027

𝐷(𝑖𝑓𝑟)𝑡−2 -0.003 -2.081 0.054

𝐷(𝑖𝑓𝑟)𝑡−1 0.002 1.212 0.2430

𝐷(𝑙𝑚𝑎𝑘𝑐𝑎𝑝)𝑡 0.148 2.933 0.010

𝐷(𝑙𝑚𝑎𝑘𝑐𝑎𝑝)𝑡−1 0.048 1.165 0.261

𝑒𝑐𝑚𝑡−1 -0.79 -4.230 0.000

𝑅2 0.81

Standard Error of

Regression

0.119

Durbin Watson 1.630

Jarque-Bera 1.165 0.558

Breusch-Godfrey

Serial Correlation

Test

0.864 0.393

Breusch-Pagan

Godfrey

Heteroskedacticity

Test

14.729 0.257

As can be seen from table 5 above, the error correction coefficient is indeed negative and

statistically significant. It shows that almost 80% of the previous year’s shocks converge back to

long run equilibrium in the current year. Also, some of the short run parameters show

actualization of a-priori formations a 1% increase in the market capitalization rate raises the

growth rate of velocity by 15% in the current period.

16

Figure 1: CUSUM Test of Stability of short run parameters

Figure 2: CUSUM Test of Squares

Figures 1 and 2 show that the residuals of the short run function stay within the band indicating

the stability of the short run relationship between velocity and the independent variables.

-12

-8

-4

0

4

8

12

96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11

CUSUM 5% Significance

-0.4

0.0

0.4

0.8

1.2

1.6

96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11

CUSUM of Squares 5% Significance

17

Figure 3: AR Graph

Figure 3 above shows that all the inverse roots of the autoregression polynomial are all within

the circle, this is the sign of stability of the short run relationships between the variables.

Table 8: Results of Granger Causality Test

Dependent

Variable

D(Vel) D(lmakcap) D(IntSpread) D(excr) D(ifr) D(lreserves)

D(Vel) - 0.001 0.157 2.412 4.363* 4.845*

D(lmakcap) 2.850** - 0.297

D(IntSp) 1.319 1.114 -

D(Excr) 1.818 0.099 1.172 - 0.031 0.984

D(Ifr) 3.369** 0.809 0.061 0.152 0.998

D(lreserves) 1.539 0.003 0.420 0.001 2.287 -

*5% significance level, ** 10% significance level

Table 7 shows that there are one-way relationships between market capitalization, inflation rate

and velocity. Also, the velocity of money has a unidirectional granger causality flowing to

inflation rate and reserves. Moreover, inflation rate also a unidirectional relationship with

velocity. These linkages have indeed been well documented in the literature given the close

relationship between money and inflation.

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

Inverse Roots of AR Characteristic Polynomial

18

Section Five: Conclusions and Recommendations

This study has shown that velocity of money has an important role to play in both the

money and capital markets. The Central Bank of Nigeria has to pay close attention to the

variables that transmit news from the money market to the capital market especially interest rate

since it tells bondholders or stockbrokers the relative returns to their investments in comparison

with the risk free rate. For future studies, a dynamic stochastic general equilibrium model that

links velocity to the capital markets could be used to further study the asymmetric nature of

information availability between the money market and the capital market.

19

References

Akingunola, R. et al (2012). Impact of Interest Rate on Capital Market Growth ( A Case

Study of Nigeria). Universal Journal of Management and Social Sciences, Vol.2, no.11.

Hsing, Y. (2004). Impact of Fiscal Policy, Monetary Policy and Exchange Rate Policy on Real

GDP in Brazil: A VAR Model”, Brazillian Electronic Journal of Economics, Vol. 6, no.1

Jeroh, E. (2012) Interest Rate Variations and Stock Market Capitalization in Nigeria:

An Empirical Analysis. AUDCE, Vol. 8, no.5, pp5-14

Khrawish, H, A, et al (2010) Interest Rate Variations and Stock Market Capitalization in Nigeria:

An Empirical Analysis. AUDCE, Vol. 8, no.5, pp5-14

Ologunde, A, et al (2006) “Stock Market Capitalization and Interest Rate in Nigeria: A Time

Series Analysis” International Research Journal of Finance and Economics, Issue 4,

Pp. 154-67.

Omotor, D.G. (2012) The Relationship Between Inflation and Stock Market Returns: Evidence

from Nigeria. Journal of Applied Statistics, Vol. 1, No.1

Pesaran M. H, et al (2001)” Bounds Testing Approaches to the Analysis of Level Relationships”,

Journal of Applied Econometrics, 16, 289-326

20

Appendix

Table I: Line Graphs

Figure II: Scatter plots

0.8

1.2

1.6

2.0

2.4

2.8

1980 1985 1990 1995 2000 2005 2010

VELOCITY

20

21

22

23

24

25

1980 1985 1990 1995 2000 2005 2010

LRESERVES

0

5

10

15

20

25

30

1980 1985 1990 1995 2000 2005 2010

INTSPREAD

0

20

40

60

80

1980 1985 1990 1995 2000 2005 2010

IFR

0

40

80

120

160

1980 1985 1990 1995 2000 2005 2010

EXCR

20

22

24

26

28

30

32

1980 1985 1990 1995 2000 2005 2010

LMAKCAP

21

The scatter plot graph above shows that the independent variables are exogenous since they do

not correlate perfectly with the dependent variable

0

20

40

60

80

100

120

140

160

0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6

VELOCITY

LRESERVES

LMAKCAP

EXCR

IFR

INTSPREAD