This technique postulates the long-run relationship among a group of time series variables.
Variables are said to be cointegrated if they are affected by the same long-run influences. Non-stationary variables may drift apart in the short-run but eventually converge towards equilibrium in the long-run. Cointegration is a powerful and recent econometrie technique that allows the econometrician to separate long-run equilibrium relationship postulated by economie theory in general, from their short-run dynamics. The adoption of this technique was a timely and appropriate response to rescue researchers many of whom, if not all, hitherto assumed that time series data were all stationary. This unfortunately is not the case.
43
From the end of the Second World War until the economie cnses of the early 1970s, the macroeconomie environment of most countries, developing and industrialized countries alike, was relatively stationary. World inflation was low and stable, while income growth, savings, investment and even comrnodity priees fluctuated only marginally. In such a world, the costs of treating non-stationary series as if they were stationary were not great. However, after the mid 1970s, it became increasingly clear that the economie world was not as stationary as researchers thought and these found expression in large fluctuations in macroeconomie aggregates. Thus, inevitably, the costs ofinappropriate time-series analyses becarne more pronounced.
It was largely for this reason that many hitherto well-established econometrie relationships began to break down, to the disappointrnent and concem of many researchers. The estimated models failed to predict outcomes accurately. In response to this, a more comprehensive treatrnent of the time-series characteristics into econometrie modeling was found-the notion of cointegration (see Hendry (1986) and Granger (1986) for an elaboration on the technique). The above explains why non-stationarity has been a phenomenon of the 1980s and 1990s and any time-series econometrie study 1 investigation in 1999 that fails to take it into account would definitely suffer a major defect.
Time-series, as stated above, are said to be stationary when they have a constant mean, constant variance and covariance, all of which are independent of time. This can be established by a unit root test and was done in our study using the Augrnented Dickey-Fuller (ADF) test. It is recognized that even if a set of variables is non-stationary, there may exist a linear combination of the set that is stationary. Such a set would be cointegrated. There is cointegration when,
although a set of variables might vary with time, they move together over time and require the same level of differencing to achieve stationarity. For a bivariate case, there is cointegration when the Ordinary Least Squares (OLS) estimator yields an estimate of the slope coefficient that is a consistent estimator of the long-mn relationship between levels in the two variables, with no need to resort to either lagging or differencing. In the multivariate case, which is our main concem, the residuaVerror term from the regression in the levels of the variables should be stationary. Such a regression equation would then form a cointegrating equation and valid inferences about the long-run can be drawn from its estimation (Worrell and Scantlebury-Maynard, pp.233). The short-mn dynamics would have to be determined otherwise, however.
All the equations in this study were mn using Ordinary Least Squares (OLS). For each of the functions we estimated three equations as follows: one for unit root using Augmented Dickey-Fuller test, another for the cointegration model using Ordinary Least Squares and yet another for the error correction model to obtain the dynamic equation over the period. The error correction rnodel enables us to capture both the short-mn and the long-mn dynamics. The Engle-Granger Representation Theo rem establishes that if a set of variables is cointegrated, it will have an error correction mechanism that will ensure an adjustrnent process in which the errors in the long-mn relationship do not grow over time. In other words, the short-mn dynamic relationship will converge with tl;le long-mn relationship.
3.2 Specification of the Fun etions
The real demand for money function is specified as follows:
REALM2 = f (RDPR, RGNP, IRA TE, INFL DMMY) (-) (+) (+) (-)
+/-45
where
REALM2= real demand for money broadly defined RDPR =real deposit rate
RGNP = real gross national product IRA TE = Investment rate
INFL = Inflation rate
DMMY = Dummy variable representing the overall structural adjustment programme.
For the pre-adjustment period (1970-1984), dummy is zero whereas from 1985-1997, dummy is equal to one.
The above relation can be rewritten in a logarithmic formas follows:
Log(RealM2)= C + a1log(RGNP) + a 2log(IRATE) + a3RDPR + a4log(INFL)+ as DMMY + Ut ... (1)
Similarly, the real gross domestic savings function is defined as follows:
GDSRATE = f(DPNR, RDPR, FSRATE, GRATE, DMMY),
where,
(-) (+) (-) (+)
+/-GDSRATE =gross domestic savings rate RDPR =real deposit rate
FSRATE =real foreign savings rate (net foreign capital inflows) GRA TE = GDP growth rate
DPNR = Dependency ratio
DMMY= Dummy variable representing the overall adjustment programme with values as defined above.
The above can also be represented in the form of an equation in logarithmic form:
Log(GDSRATE) = C + a1log(GRATE) + u2log(FSRATE) + u3log(RDPR) + a4log(DPNR) + a5DMMY +Ut. ... (2)
3.3. Sorne Theo retie al Considerations for the Choice of Regressors
The a priori signs are based on theoretical expectations and these may or may not be supported by country realities. Sorne of the theoretical justifications for the expected signs are discussed below.
The Dependency Ratio (DPNR): In many LDCs, the population structure has been seen as an influencing factor in mobilizing domestic savings. In the life-cycle model, the age composition of the population is postulated to have a significant impact on household savings. While the youth and the elderly have low incomes and low savings, those in the middle age have higher incomes and save more to repay past obligations and to finance their retirement. Rapid population growth will increase the proportion of the youth and may adversely affect savings unless an increase in income or a reduction in consumption by the working population offsets it.
The postulated inverse relationship between domestic savings and the dependency ratio means that rapidly growing populations are characterized by high dependants in relation to the working population who, because they contribute to consumption and not production, impose a severe
47
constraint on society' s potential for saving. The life-cycle model as a result predicts an inverse relationship between domestic savings and the dependency ratio.
The GDP Growth Rate (GRATE): The inclusion of the income variable is based a priori on
' '
Keynes' ab solute income hypothesis which states that there should be a positive relationship between savings and income and hence the expected positive sign on this variable. The permanent income hypothesis also postulates that savings are a function of permanent income, which can be proxied by weighted averages of past levels of in come, or growth in income.
The Real Deposit Rate (RDPR): The inclusion of the real interest rate in the domestic savings function and the expected positive sign is based on the financial repression theory that is due to Mckinnon and Shaw (1973). The Mckinnon and Shaw doctrine argued that in countries characterized by " financial repression", raising interest rates relative to inflation would increase savings and the supply of investable resources in an economy. According to these two authors, financial repression arises mostly when a country imposes ceilings on nominal deposit and lending rates at low levels relative to inflation. The low or negative real interest rates that results discourage savings mobilization and the channeling of mobilized savings through the financial system. This has a negative impact on the quality and quantity of investment and hence on economie growth.
Despite the above conclusions there are still sorne unresolved theoretical questions as far as the impact of the real interest rate on household savings is concemed. In economie theory, the influence of the real interest rate on savings depends on the relative strength of the offsetting
substitution and income effects. Higher interest rates increase the opportunity cast of consumption, hence households will increase their savings as future consumption becomes cheaper relative to current consumption (substitution effect). At the same time, higher interest rates increase the wealth of positive sa vers, hence their consumption increases thereby reducing the savings necessary to purchase a given amount of future consumption (incarne effect). The Mckinnon and Shaw doctrine therefore postulates that under conditions of financial repression, the substitution effect dominates the incarne effect, whereas in financial liberalisation the opposite holds thus resulting in increased savings. The impact of the real deposit rate on the demand for money is expected to be positive by the financialliberalization theorists because according to them, real money balances serve as a repository of savings. On the other hand Keynesians postulate a negative relationship.
The Foreign Saving Rate (FSRATE): The foreign saving rate was included in arder to test the hypothesis that foreign savings crowd out domestic savings and hence the expected negative sign. Developrn:ent economists such as Holis Chenery, writing in the context of the "two-gap"
madel of economie development ascertain that foreign assistance was essen ti al if !east developed countries (LDCs) were to close the savings gap and achieve sorne meaningful progress. But the experience of many LDCs in the last three decades has, however, brought the view of the complementarity and the essential role of foreign capital under severe scrutiny. In developing countries, unlike developed countries, where consumption is a very high proportion of GDP, foreign savings may not be positively correlated with domestic savings. While foreign savings have traditionally been regarded as complementary there is now a contention that they may partially or fully crowd-out domestic savings. This implies that foreign savings will on average act as a substitute to domestic savings by easing liquidity constraints. This argument is valid for
49
a country where foreign borrowing, instead of financing investment, finances consumption, which imply lower domestic savings. This explains the expected negative sign, although the contention is controversial and can only be resolved empirically.
Inflation Rate (INFL): The impact of the inflation rate is expected to be negative on the demand for money. During inflationary periods people will not hold money or other liquid assets such as bank deposits ~ecause doing so makes them lose due to the inflation tax. Instead they would prefer to hold other real assets and this explains the theorized negative sign on the demand for real money balances.
The Investment Rate (IRA TE): The inclusion of the investment rate was to test Mckinnon's complementarity hypothesis between real money demand and investment. The hypothesis contends that there should be a positive relationship between the investment rate and the demand formoney.
The Real Income (RGNPMl): The real incarne variable (RGNPM1) is consistent with any standard demand for money function which posits a positive relationship between incarne levels (disposable incarne, permanent incarne, current incarne etc.) and the demand for money. A priori as incarnes increase, the demand to hold money also increase.
3.4 Sources of Data, Scope of the Study and Clarifications
The study will co ver the period 1973 to 1997 using secondary data from the World Bank W orld Tables, African Development Indicators, International Financial Statistics of the IMF,
publications from the Central Statistics Department of The Gambia (Statistical Abstract-various years); Central Bank of The Gambia Annual and Quarterly Publications.
The GDP growth rate, real GDP, nominal GDP, real GNP and foreign savings rate are derived from the World Tables. It should be noted that foreign savings in this study is the negative of the current account balance and we deflated it by GDP in order to obtain our variable of interest-the foreign saving rate. The nominal deposit rate and the discount rate are obtained from the International Financial Statistics Yearbook and to obtain the real deposit and real discount rates we adjusted these for inflation. The age dependency variable is calculated from country data using 1973, 1983 and 1993 census data and intercensal growth rates of the various age groups concerned. This is the surnmation of 0-14 and 65+ age groups divided by the active population (15-64) years. The domestic savings rate and the investrnent rate are derived from the African Development Indicators. The M1 and M2 definitions of money are obtained from the International Financial Statistics Y earbook, all deflated by the consumer priee index and the latter used as a proxy for the demand for real money balances in the economy. A limitation of the use of this variable, which is in fact the actual supply ofmoney, is recognized and we rely on the assumption of monetary equilibrium in which case the amount of money demanded is assumed equal to the amount supplied.
A financial deepening indicator was also calculated as the ratio of broad mo ney to GNP in order to investigate the relationship between financialliberalization and financial development in The Gambia over the period of the study. In addition, a proxy for financial savings in the banking sector was also calculated as the difference between real money balances broadly defined (Mz) and real money_balances stricto sensu (M1). The difference between M2 and M1 was deflated by
GDP to determine the evolution of financial savings rate in the banking sector over the period of the study. The inflation rate represents the percentage change in the consumer priee index and was obtained from the International Financial Statistics Y earbook.
CHAPTER FOUR
EMPIRICAL ANALYSES
4.0 Introduction
From theoretical propositions, we move to empirical analyses to examine empirically to what extent these variables contribute to explaining the observed performance of domestic savings rate and the demand for money in the context of a small open Sub-Saharan African country: The Gambia.
In this empirical chapter, analyses of the secondary data are made using the Ordinary Least Squares over the period 1973-1997. The use of OLS is justified even though sorne of the explanatory variables might be endogenous following theoretical postulates of Granger (1986) and more recently by Jeroen and Timothy. They stated this explicit conclusion« ... the exchange rate is an endogenous variable, so that the static equation does not satisfy the assumptions of the general linear regression model ;however, as discussed by Granger(1986), OLS estimatio:O: yields consistent estimates of a cointegrating relationship among a set of non-stationary 1(1) variables, even if sorne ofthese variables are endogenous. »9
9 IMF StaffPaper, Vol. 37, no. 4, Dec. 1990, P.273
We begin with stationarity testing using the Augmented Dickey-Fuller test to determine the arder of integration of the series. This was followed by a regression on the levels of the series and a test on the residuals from the resulting equations for stationarity in arder to be able to determine the presence of a cointegrating relationship between the variables. The short-mn dynamics of the two functions was also determined by running regressions on the error-correction madel i.e.on the differenced terms including the lags of the residuals from the levels regressions as explanatory variables. To do all these, the study made use of the Eviews Programme (Version 2.0) developed in 1995.
4.1 Stationarity Tests
The first step in any application of the cointegration technique is to establish the arder of integration of the variables concemed. This step assumes that all the variables have been tested on the levels to show that they are not stationary and this first step gives an insight into the arder integration.
The stationarity of each series was tested using the Augmented Dickey- Fuller (ADF) test instead of the Dickey-Fuller (DF) class of unit root tests. This is because of the assumption by the DF test that the structure of the long-mn relationship is first-order auto-regressive (AR (1 )). If this is not the case (a real possibility), then autocorrelation in the residuall error term will bias the test. To circumvent this shortcoming as stated, the study, in line with Adams (1992) and S.S. Ali and A.H. Khan (1997), used the Augmented Dickey-Fuller test. Basically, the ADF test consists in running a regression of the first difference of the series against the series lagged once, lagged
difference terms, and optionally, a constant and a time trend. With two lagged difference terms, a constant term and a time trend, the regression can be presented as follows:
/j,yt= aiYt-1 + a2~Yt-1+ a3~Yt-2+ '4 +ast. .... 0 0 0 0 .. . . . · o o 0 0 . . (3)
All the terms are as defined above respectively. There are three choices that can be made in running the ADF test as follows: whether to include a constant term, a linear time trend and a constant, or none; and lastly how many lagged differences to be included in the regression. In each case the test for a unit root is a test on the coefficient of y1_1 in the regression. The null hypothesis of non-stationarity is rejected if the computed ADF statistic is greater in absolute terms than the reported Mackinnon critical values. Otherwise the alternative hypothesis of the presence of a unit root cannot be rejected at the conventionallevels of significance. A summary of the output from the ADF test for the dependent and explanatory variables used in the two equations are presented in the tables to be presented in the next two pages.
To begin with stationarity tests were conducted on the levels of all the series used (in the money demand and domestic savings functions) to demonstrate that they were all non-stationary except GRATE. In all the series (on the levels) the Mackinnon critical values were higher in absolute terms suggesting that they are non-stationary as shown in table in the next page. GRA TE as noted is stationary at the level of the series (ADF value higher than Mackinnon critical value in absolute terms).
Table 4.1: ADF Tests on the levels of the series
Variables ADF Statistics Mackinnon Critical Values
LOG(REALM2) -1.84 -3.67
LOG(REALMl) -1.94 -3.02
LOG(RGNPMl) -1.82 -3.67
LOG(INFL) -1.31 -3.60
DCRATE -2.74 -3.59
LOG(IRATE) -1.76 -3.59
RDPR -2.31 -3.51
LOG(GDSRATE) -2.69 -3.05
LOG(FSRATE2) -1.79 -3.63
LOG(DPNR) -2.42 -3.59
GRATE -5.67 -4.35
The above results necessitate further tests on the differenced terms of the series characterized by the presence of a unit root to determine the order of integration of the series that we want to model. Differencing the series further and testing for stationarity show that all the non-stationary series are I(l) except log(dpm) and log(fsrate) which became stationary only at second difference. This is elaborated in table .4.1 a in page 57.
Table 4.1a: ADF Tests for the Order oflntegration
Variables ADF Statistics Mackinnon Order of Integration Critical Values difference of the series and D(x, 2) represents second-order difference.
The results as shown in the above table demonstrate that all the variables in the money demand function are integrated of order one and require to be first-order differenced to attain stationarity.
As shown in each case, the ab~olute ADF values are higher than the corresponding Mackinnon
absolute terms than their corresponding Mackinnon critical values The other variables like most '
series, are integrated of arder one except the growth rate which is an 1(0) variable. Being an 1(0) variable, GRA TE requires no differencing since differencing a stationary series would still yield
an 1(0) series. In other words, the level of the GDP growth rate is stationary. It should be noted that the presence of the 1(0) variable or 1(2) variables does not pose any practical problem for cointegration theory for as demonstrated in Johanson (1985), it is not necessary that ali the
an 1(0) series. In other words, the level of the GDP growth rate is stationary. It should be noted that the presence of the 1(0) variable or 1(2) variables does not pose any practical problem for cointegration theory for as demonstrated in Johanson (1985), it is not necessary that ali the