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The Error Correction Model Economics Essay


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This chapter deals with the presentation, analysis and interpretation of results based on the objectives. The estimation results of the model are supported and further analyzed by using the relevant econometric techniques viz. Descriptive statistics, coefficient of determination, standard error, t- statistics etc. The study identified the following variables: trade openness (XM), inflation (INFLA), infrastructure (INFRA), government size (GS) and human capital (HUMCAP) these variables with FDI specified are analyzed in the equation and all the variables are used in their logarithm form.

4.2 Multicollinearity Test

The aim of the test is to ensure the explanatory variables are not correlated. Most often we have imperfect collinearity in economic data so there is a degree to which the variables are correlated. According to Ranjit Kumar Paul(), Complete elimination of multicollinearity is not possible but the degree of multicollinearity can be reduced by model specification eliminating a variable. However, it may not be adequate enough in providing satisfactory solution if the regressor dropped from the model have significant explanatory power to explain the dependent variable, that is eliminating regressor to reduce multicollinearity may damage the predictive power of the model. Precaution must be exercised in variables selection because many of the selection procedures are seriously distorted by the multicollinearity, and there is no assurance that the final model will exhibit any lesser degree of multicollinearity than was present in the original data.

There is a high degree of collinearity amongst the independent variables (see appendix 1), however we aim to reduce the degree of collinearity and by theoretical procedure, we determine to remove between the variable with the highest correlation that is INFRA and HUMCAP with a value of 0.921607, but the estimated results after the test were redundant leading to misleading inferences. Further estimates were carried out between the next highly correlated variables of GS and XM with a value of 0.912001 and the estimates gave a more significant result, hence we eliminate government size. To resolve this multicollinearlity problem we need to exclude one of the variables from the model, to decide this we regressed each of this variable on our dependent variable RGDP and the estimation results with the lower R-squared is excluded from the model. Therefore when both variables where regressed individually, GS had a lower R-squared of 0.679074 and XM had R-squared of 0.824690. So we exclude GS from our model and keep XM. Therefore our new model is given as:

RGDP = β0 + β1FDI + β2XM + β3INFL +β4INFRA + β5HUMCAP + U

4.2.1 Description of Statistics

The descriptive statistics of the variables used in the regression analysis is very important in statistical inference. The descriptive statistics of the variables in their logarithm form is presented in the table in appendix 2. The average value of Real gross Domestic Product within the period is 12.896 and it ranged from a maximum of 13.54330 to a minimum of 12.48891 and the standard deviation is 0.813. For Foreign Direct Investment the maximum was 2.116256 with an average of 1.244 and minimum value of 0.741937 and a standard deviation of 0.346276. Other descriptive statistics of the variables is shown in the table. Each variable had an equal number of observations. The test continues by testing unit root to check if the data are stationary.

4.3 Augmented Dickey‐Fuller (ADF) Test of Unit Roots

As a preliminary analysis, the Augmented Dickey‐Fuller (ADF) test is carried out to test for the presence of unit roots (ut is a white noise process, and the stationary condition is /Ø/ < 1) by suggesting an augmented version of the test that includes extra lagged terms of the dependent variables in other to eliminate autocorrelation. The lag length is determined by the Schwartz Bayesian Criterion (SBC) in the variables series. The ADF tests are conducted on the level and first differences and second differences of the variables by estimating the following models:

• Model (1): Constant and no trend model:

• Model (2): Constant and trend model:

Where is the first difference; , , and are the parameters to be estimated, and is a stochastic disturbance term This is necessary in order to determine if the relevant variables are stationary and find out their orders of integration.. The result of the test is presented in the table in appendix 3.

The unit-root test can be checked by comparing the observed values (in absolute terms) of the ADF test statistic with the critical values (also in absolute terms) of the test statistic at the 1%, 5% and 10% level of significance. The decision rule for confirming the presence of stationarity is to reject the null hypothesis if the calculated values of the test statistics are greater than the critical value of the test statistic whereas the decision rule for confirming the presence of non-stationarity is to accept the null hypothesis if the calculated value of the test statistics were lower than the critical value of the test statistic.

Based on the Augmented Dicker Fuller test, the assumptions of non-stationarity cannot be rejected for the levels of the variables at 5% significance level. That is, all variables were non-stationary at levels. However the non-stationarity variables; FDI, INFRA, XM became stationary at 1st differenced operation while RGDP and HUMCAP became Stationary at 2nd difference operation. The absolute values of the ADF statistics are higher than 5% level of Mackinnon critical value as provided by the results, which means we reject the null hypothesis of non-stationarity of variables. Order of integration is shown in table 4.1. Pesaran and Pesaran (1997) warn that where series has unit roots, the results may not be reliable. So we proceed to test for co- integration in the next section, since some of the time series are generated by random walk processes.

Table 4.1: Description of Integration in Annual Time Series Data






















Source: Computed by author

4.4 Test of Cointegration

Having confirmed that the variables included are stationary at their respective order of integration, we now test for the existence of a cointegrating relationship. However the Johansen cointegration test cannot be applied because the variables were stationary at different order. The aim of this test is find out if the regression residuals are stationary. So we shall apply the Engle-Granger Test.

Table 4.2 Engle-Granger Cointegration Results (Unit Root Test For Residuals)

Null hypothesis: u has a unit root.

t-statistics probability

Augmented Dickey-Fuller -5.209413 0.0027

At 1% -4.532598

At 5% -3.673616

At 10% -3.277364

Source: computed by author

From the above table the Engle-Granger 1%,5% and 10% critical values of the t-statistics are, respectively, -4.532598, -3.673616 and -3.277364 in absolute terms the estimated value of -5.209413, exceeds any of the critical value above, the conclusion would be that the estimated ut is stationary and therefore the variables despite being individually not stationary, are cointegrated. The results of the cointegration test suggest that RGDP, FDI, INFLA, INFRA, XM and HUMCAP have equilibrium condition which keeps them in proportion to each other in the long run.

4.5 Regression Results

We estimate the regression line of the equation to interpret all our coefficients

Table 4.3: Long run estimates



Std. Error



































Mean dependent var


Adjusted R-squared


S.D. dependent var


S.E of regression


Akaike info criterion


Sum squared resid


Schwarz criterion


Log likelihood


Hannan-Quinn criterion




Durbin-Watson stat


Prob(F- statistic)


4.5.1 Interpretation of Results

The regression result reveals that all the variables revealed their respective predicted signs. The coefficient of foreign direct investment was positive implying that there exists a positive relationship with real gross domestic product. In economic reasoning, holding other variables constant, it can be concluded that a 1% change in foreign direct investment would lead to a 2.4% rise in real gross domestic product while a percentage change in openness to trade would lead to a 16.56% rise in real gross domestic product. Still holding other variables constant, a percentage change in infrastructural development would lead to a 75.39% rise in gross domestic product. Also, a percentage change in human capital would lead to a more than unitary rise in real gross domestic product. The coefficient of Inflation was negative implying that the causal relationship with real gross domestic product was negative. In economic reasoning, holding other variables constant, it can be concluded that a 1% change in inflation would lead to 3.5% decrease in gross domestic product. The overall results showed that foreign direct investment added little to the real gross domestic product in the long run as compared to infrastructural development. This may be to the fact that foreign direct investment has a far better impact on real gross domestic product in the short run. In the test for hypothesis, the computed t-statistic foreign direct investment was 0.185231 which was lower than 2.62, 1.76 and 1.34 at 1%, 5% and 10% levels of significance so the null hypothesis (H0) was accepted and the alternative hypothesis (H1) was rejected in order to conclude that the foreign direct investment is not statistically significant and not relevant in explaining economic growth in Nigeria. The empirical findings do appear questionable.

The coefficient of determination that is R- squared explains how well the regression line fits the data in other to determine how well the results of the equation accounts for the behavior of the dependent variable economic growth (RGDP). R-squared is 0.863419 this indicates that 86.34% of the variation in economic growth is explained by all the regressor's. Therefore, the R-squared, close to one (1) indicates that the regressor's is good in predicting growth. We can imply that we do not need to include other variables to explain economic growth as the most important exogenous variables were captured by the model. The Adjusted R- square can be interpreted as our model being able to explain 81.78% of the variation in Real Gross Domestic Product in the Long run while the other 18.22% was unaccounted. The F- statistic shows that a joint or multiplicative relationship existed between all the variables. With the analysis of variance (ANOVA) that is F-test was used to test for joint significance of the regressors in impacting economic growth. The p- value of the F statistic was 0.000005, (or less than 5%) and this value suggests that all the explanatory variables are jointly significant to account for changes in real gross domestic product. The economic explanation of this is that foreign direct investment if regresses alone on real gross domestic product, is not responsible for changes in real gross domestic products, but it can jointly account for changes in real gross domestic product if incorporated alongside other significant variables.

According to Engle and Granger (1987), when variables are co-integrated there exist a valid error correction model describing their relationship, which includes residuals from the static cointegration regression between RGDP and the above-named variables as an explanatory variable called ECM.

4.6 The Error Correction Model (ECM)

The ECM corrects for disequilibrium, and the equation is given below:

∆yt = Ä…0 + þ1∆ xt- πÛt + Æ©βi∆yt-I + ut

This will now have the advantage of including both long run and short run information. In this model, þ1 is the impact multiplier (the short-run effect) that measures the immediate impact a change in xt will have on a change in yt. On the other hand, π is the feedback effect or the adjustment effect and shows how much of the disequilibrium is being corrected that is the extent to which any disequilibrium in the previous period affects any adjustment in yt. For our study, the model is represented below:

Table 4.4 ECM Results



t- statistic


D(RGDP, 1)




D(FDI, 1)






























Prob (F-statistic)


Durbin-Watson stat


The model provides estimates of short run estimates while the ECM coefficients show the speed with which the system converges to equilibrium. The Vector of interest in this study is the RGDP equation. The results show that the coefficient of the ECM (-1) is -0.047464. It is properly signed which means that all the variables are valid that is giving validity that the entire variable have a long run equilibrium relationship. The negative sign further indicates that the adjustment portrays the direction to restore the long run relationship. The magnitude of the ECM (-1) coefficient indicates that the speed of adjustment is quite low. However, we see that the p-value is 0.6478 which is not significant which means that there might be some variables which have been excluded from the model that could explain RGDP to a preferred extent. To certify this Angelos (1996) in his findings reported that when better predictors are included to explain the dependent variable then ECM will become significant. The R-squared for RGDP vector was good at 0.729, indicating that 73% of variations in RGDP have been explained by the variables in the model.

The estimates of the VECM show that in the short run inflation was not significant in explaining contemporaneous changes in RGDP (i.e. it was positively signed). Infrastructural development was significant at 5% and positively signed showing that a 1% increase in infrastructural development would lead to a 29.4% increase in economic growth. Also, foreign direct investment was seen to have a positive relationship with RGDP which is in line with our apriori expectation, but it showed a very minute impact on economic growth (i.e. 1.3%), which does not explain well enough the rate at which FDI is supposed to influence growth. As Foreign Direct Investment over the years accounts for a major increase in economic growth of a nation. Statistics is a technique in which we make certain assumptions regarding the behavior of variables and their causal relationship and in it is not a way to prove or disprove anything (Bhatia 2008). Openness to trade showed that there was a positive impact on economic growth and human capital had a more than unitary impact on economic growth of the nation.

The adequacy of the model must be checked by performing diagnostic test. On the positive side, the model passes the diagnostic test for serial correlation and autoregressive conditional heteroscedasticity (ARCH) in residuals. Where the p-value is 0.0004 and 0.0064 respectively was less than 5%.

4.7 Granger Causality Test`

The existence of relationships between variables does not prove causality or the direction of influence. However, causality test was conducted using the Pair-Wise Granger causality test. The model was estimated by lagging the explanatory variables by two periods as shown in appendix 4. Using the probability statistic for interpretation, the Granger-Causality results suggest that in testing the null hypothesis: FDI does not granger cause RGDP and RGDP does not granger cause FDI, as the null hypothesis is accepted for both hypotheses of 0.7406 and 0.7043 were lower than 5%, and this suggested independence among the variables say that the coefficients were not individually significant.

For, INFRA does not granger cause RGDP we accept the null as 0.2681 is greater than 5% and thus causality did not run from INFRA to RGDP. In reverse, the null hypothesis that RGDP does not granger cause INFRA was rejected; because p-value 0.0479 is less than 5% concluding that there is a unidirectional causality running RGDP to INFRA.

For, INFLA does not granger cause RGDP, we accepted the null hypothesis for both hypothesis because 0.5892 and 0.4723 are greater than 5% and this suggested independence among the variables means none of them causes the other.

For, XM does not granger cause RGDP, we accept it because 0.6529 is greater than 5%. However RGDP does not cause XM was rejected as 0.0007 is less than 0.5% meaning there is a unidirectional causality from RGDP to XM.

For, HUMCAP does not granger cause RGDP, we accepted the null hypothesis for both hypothesis because 0.4449 and 0.2524 are greater than 5% and this suggested independence among the variables means that none of them causes the other.

Causality results between two independent variables were not reported because they did not capture the scope of the research; however, only causality results between dependent and independent variables were reported.

To answer one of the objectives of the study, from the result we see clearly that FDI do not have a causal link with economic growth, but it has a positive relationship with economic growth. Among the sectors receiving FDI, service sector received the highest percentage of FDI particularly the telecommunication industry of nearly 41% inflows. Despite the inflow of FDI into this sector, there exist no causal link between FDI and growth in Nigeria. This reason might be that FDI in this sector was in the form of mergers and acquisitions which are not the most beneficial for the domestic economy. Also, it may be that service FDI does not provide access to export markets or linkages to local enterprises likewise advanced technologies, that manufacturing FDI would have provided. Finally, we see the concluding remarks of the whole study in the last chapter.

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