# The Error Correction Model Economics Essay

This chapter deals with the presentation, analysis and reading of consequences based on the aims. The appraisal consequences of the theoretical account are supported and further analyzed by utilizing the relevant econometric techniques viz. Descriptive statistics, coefficient of finding, standard mistake, t- statistics etc. The survey identified the undermentioned variables: trade openness ( XM ) , rising prices ( INFLA ) , substructure ( INFRA ) , authorities 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 signifier.

## 4.2 Multicollinearity Test

The purpose of the trial is to guarantee the explanatory variables are non correlated. Most frequently we have imperfect collinearity in economic informations so there is a grade to which the variables are correlated. Harmonizing to Ranjit Kumar Paul ( ) , Complete riddance of multicollinearity is non possible but the grade of multicollinearity can be reduced by theoretical account specification extinguishing a variable.

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However, it may non be equal plenty in supplying satisfactory solution if the regressor dropped from the theoretical account have important explanatory power to explicate the dependant variable, that is extinguishing regressor to cut down multicollinearity may damage the prognostic power of the theoretical account. Precaution must be exercised in variables choice because many of the choice processs are earnestly distorted by the multicollinearity, and there is no confidence that the concluding theoretical account will exhibit any lesser grade of multicollinearity than was present in the original informations.There is a high grade of collinearity amongst the independent variables ( see appendix 1 ) , nevertheless we aim to cut down the grade of collinearity and by theoretical process, we determine to take between the variable with the highest correlativity that is INFRA and HUMCAP with a value of 0.

921607, but the estimated consequences after the trial were excess taking to deceptive illations. Further estimations were carried out between the following extremely correlative variables of GS and XM with a value of 0.912001 and the estimations gave a more important consequence, hence we eliminate authorities size. To decide this multicollinearlity job we need to except one of the variables from the theoretical account, to make up one’s mind this we regressed each of this variable on our dependant variable RGDP and the appraisal consequences with the lower R-squared is excluded from the theoretical account. Therefore when both variables where regressed separately, GS had a lower R-squared of 0.

679074 and XM had R-squared of 0.824690. So we exclude GS from our theoretical account and maintain XM. Therefore our new theoretical account is given as:

## 4.2.1 Description of Statisticss

The descriptive statistics of the variables used in the arrested development analysis is really of import in statistical illation. The descriptive statistics of the variables in their logarithm signifier is presented in the tabular array in appendix 2.

The mean value of Real gross Domestic Product within the period is 12.896 and it ranged from a upper limit of 13.54330 to a lower limit of 12.48891 and the standard divergence is 0.813. For Foreign Direct Investment the upper limit was 2.116256 with an norm of 1.

244 and minimal value of 0.741937 and a standard divergence of 0.346276. Other descriptive statistics of the variables is shown in the tabular array. Each variable had an equal figure of observations.

The trial continues by proving unit root to look into if the informations are stationary.

## 4.3 Augmented Dickeyaˆ?Fuller ( ADF ) Test of Unit Roots

As a preliminary analysis, the Augmented Dickeyaˆ?Fuller ( ADF ) trial is carried out to prove for the presence of unit roots ( Greenwich Mean Time is a white noise procedure, and the stationary status is / & A ; Oslash ; / & A ; lt ; 1 ) by proposing an augmented version of the trial that includes excess lagged footings of the dependent variables in other to extinguish autocorrelation. The slowdown length is determined by the Schwartz Bayesian Criterion ( SBC ) in the variables series.

The ADF trials are conducted on the degree and first differences and 2nd differences of the variables by gauging the undermentioned theoretical accounts:• Model ( 1 ) : Changeless and no tendency theoretical account:• Model ( 2 ) : Changeless and tendency theoretical account:Where is the first difference ; , , and are the parametric quantities to be estimated, and is a stochastic perturbation term This is necessary in order to find if the relevant variables are stationary and happen out their orders of integration.. The consequence of the trial is presented in the tabular array in appendix 3.The unit-root trial can be checked by comparing the ascertained values ( in absolute footings ) of the ADF trial statistic with the critical values ( besides in absolute footings ) of the trial statistic at the 1 % , 5 % and 10 % degree of significance.

The determination regulation for corroborating the presence of stationarity is to reject the void hypothesis if the deliberate values of the trial statistics are greater than the critical value of the trial statistic whereas the determination regulation for corroborating the presence of non-stationarity is to accept the void hypothesis if the deliberate value of the trial statistics were lower than the critical value of the trial statistic.Based on the Augmented Dicker Fuller trial, the premises of non-stationarity can non be rejected for the degrees of the variables at 5 % significance degree. That is, all variables were non-stationary at degrees. 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 % degree of Mackinnon critical value as provided by the consequences, which means we reject the void hypothesis of non-stationarity of variables. Order of integrating is shown in table 4.

1. Pesaran and Pesaran ( 1997 ) warn that where series has unit roots, the consequences may non be dependable. So we proceed to prove for co- integrating in the following subdivision, since some of the clip series are generated by random walk processes.

## Table 4.1: Description of Integration in Annual Time Series Data

VariableOrder OF INTEGRATIONDESCRIPTION OF SERIESRGDPI ( 2 )StationaryFDII ( 1 )StationaryINFLAI ( 1 )StationaryINFRAI ( 1 )StationaryXMI ( 1 )StationaryHUMCAPI ( 2 )Stationary

## 4.4 Test of Cointegration

Having confirmed that the variables included are stationary at their several order of integrating, we now test for the being of a cointegrating relationship.

However the Johansen cointegration trial can non be applied because the variables were stationary at different order. The purpose of this trial is find out if the arrested development remainders are stationary. So we shall use 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 chanceAugmented Dickey-Fuller -5.209413 0.0027At 1 % -4.532598At 5 % -3.673616At 10 % -3.277364

## Beginning: computed by writer

From the above tabular array the Engle-Granger 1 % ,5 % and 10 % critical values of the t-statistics are, severally, -4.532598, -3.

673616 and -3.277364 in absolute footings the estimated value of -5.209413, exceeds any of the critical value above, the decision would be that the estimated Greenwich Mean Time is stationary and hence the variables despite being separately non stationary, are cointegrated. The consequences of the cointegration trial suggest that RGDP, FDI, INFLA, INFRA, XM and HUMCAP have equilibrium status which keeps them in proportion to each other in the long tally.

## 4.5 Arrested development Consequences

We estimate the arrested development line of the equation to construe all our coefficients

## Table 4.3: Long tally estimations

VariableCoefficientStd. Mistaket-statisticProbabilityFDI0.

0249900.1349140.1852310.

8555XM0.1656110.0536693.0857710.0075INFRA0.7539930.

5536111.3619550.1933INFLA-0.

0360090.060053-0.5996200.5577HUMCAP3.03650610.

286240.2952010.7719C-19.4757352.98244-0.

3675880.7183R-squared0.863419Average dependant volt-ampere12.89614Adjusted R-squared0.817892S.D. dependant volt-ampere0.371483S.

E of arrested development0.158527Akaike info standard-0.610827Sum squared resid0.376962Schwarz standard-0.312392Log likeliness12.

41368Hannan-Quinn standard-0.546059F-statistic18.96499Durbin-Watson stat0.314810Prob ( F- statistic )0.000005

## 4.5.1 Interpretation of Consequences

The arrested development consequence reveals that all the variables revealed their several predicted marks. The coefficient of foreign direct investing was positive implying that there exists a positive relationship with existent gross domestic merchandise. In economic logical thinking, keeping other variables changeless, it can be concluded that a 1 % alteration in foreign direct investing would take to a 2.4 % rise in existent gross domestic merchandise while a per centum alteration in openness to merchandise would take to a 16.56 % rise in existent gross domestic merchandise. Still keeping other variables changeless, a per centum alteration in infrastructural development would take to a 75.39 % rise in gross domestic merchandise.

Besides, a per centum alteration in human capital would take to a more than unitary rise in existent gross domestic merchandise. The coefficient of Inflation was negative implying that the causal relationship with existent gross domestic merchandise was negative. In economic logical thinking, keeping other variables changeless, it can be concluded that a 1 % alteration in rising prices would take to 3.5 % lessening in gross domestic merchandise. The overall consequences showed that foreign direct investing added small to the existent gross domestic merchandise in the long tally every bit compared to infrastructural development. This may be to the fact that foreign direct investing has a far better impact on existent gross domestic merchandise in the short tally.

In the trial for hypothesis, the computed t-statistic foreign direct investing was 0.185231 which was lower than 2.62, 1.

76 and 1.34 at 1 % , 5 % and 10 % degrees of significance so the void hypothesis ( H0 ) was accepted and the alternate hypothesis ( H1 ) was rejected in order to reason that the foreign direct investing is non statistically important and non relevant in explicating economic growing in Nigeria. The empirical findings do look questionable.The coefficient of finding that is R- squared explains how good the arrested development line fits the informations in other to find how good the consequences of the equation histories for the behaviour of the dependant variable economic growing ( RGDP ) . R-squared is 0.863419 this indicates that 86.34 % of the fluctuation in economic growing is explained by all the regressor ‘s.

Therefore, the R-squared, near to one ( 1 ) indicates that the regressor ‘s is good in foretelling growing. We can connote that we do non necessitate to include other variables to explicate economic growing as the most of import exogenic variables were captured by the theoretical account. The Adjusted R- square can be interpreted as our theoretical account being able to explicate 81.78 % of the fluctuation in Real Gross Domestic Product in the Long tally 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 discrepancy ( ANOVA ) that is F-test was used to prove for joint significance of the regressors in impacting economic growing.

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 important to account for alterations in existent gross domestic merchandise. The economic account of this is that foreign direct investing if regresses entirely on existent gross domestic merchandise, is non responsible for alterations in existent gross domestic merchandises, but it can jointly account for alterations in existent gross domestic merchandise if incorporated alongside other important variables.Harmonizing to Engle and Granger ( 1987 ) , when variables are co-integrated there exist a valid mistake rectification theoretical account depicting their relationship, which includes remainders from the inactive cointegration arrested development between RGDP and the above-mentioned 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:a?†yt = A…0 + & A ; thorn ; 1a?† xt- ? & A ; Ucirc ; t + ?©?ia?†yt-I + Greenwich Mean TimeThis will now hold the advantage of including both long tally and short tally information. In this theoretical account, & A ; thorn ; 1 is the impact multiplier ( the short-term consequence ) that measures the immediate impact a alteration in crosstalk will hold on a alteration in yt. On the other manus, ? is the feedback consequence or the adjustment consequence and shows how much of the disequilibrium is being corrected that is the extent to which any disequilibrium in the old period affects any accommodation in yt.

For our survey, the theoretical account is represented below:

## Table 4.4 ECM Consequences

VariablesCoefficientt- statisticProbabilityD ( RGDP, 1 )0.6096833.

3919790.0069D ( FDI, 1 )0.0135050.

4842960.6386D ( XM )0.0013700.0566900.9559D ( INFRA )0.2945623.

4405790.0063D ( INFLA )0.0102060.6357940.5392D ( HUMCAP, 2 )3.3852400.

8563040.4119C0.0237671.77096601070Electronic countermeasures-0.047464-0.4708650.6478R-squared0.729031Prob ( F-statistic )0.

027236Durbin-Watson stat1.852050The theoretical account provides estimations of short tally estimations while the ECM coefficients show the velocity with which the system converges to equilibrium. The Vector of involvement in this survey is the RGDP equation. The consequences show that the coefficient of the ECM ( -1 ) is -0.047464.

It is decently signed which means that all the variables are valid that is giving cogency that the full variable have a long tally equilibrium relationship. The negative mark further indicates that the accommodation portrays the way to reconstruct the long tally relationship. The magnitude of the ECM ( -1 ) coefficient indicates that the velocity of accommodation is rather low. However, we see that the p-value is 0.6478 which is non important which means that there might be some variables which have been excluded from the theoretical account that could explicate RGDP to a preferable extent.

To attest this Angelos ( 1996 ) in his findings reported that when better forecasters are included to explicate the dependant variable so ECM will go important. The R-squared for RGDP vector was good at 0.729, bespeaking that 73 % of fluctuations in RGDP have been explained by the variables in the theoretical account.

The estimations of the VECM show that in the short tally rising prices was non important in explicating contemporary alterations in RGDP ( i.e. it was positively signed ) . Infrastructural development was important at 5 % and positively signed demoing that a 1 % addition in infrastructural development would take to a 29.4 % addition in economic growing.

Besides, foreign direct investing was seen to hold a positive relationship with RGDP which is in line with our apriori outlook, but it showed a really infinitesimal impact on economic growing ( i.e. 1.3 % ) , which does non explicate good plenty the rate at which FDI is supposed to act upon growing. As Foreign Direct Investment over the old ages histories for a major addition in economic growing of a state.

Statistics is a technique in which we make certain premises sing the behaviour of variables and their causal relationship and in it is non a manner to turn out or confute anything ( Bhatia 2008 ) . Openness to merchandise showed that there was a positive impact on economic growing and human capital had a more than unitary impact on economic growing of the state.The adequateness of the theoretical account must be checked by executing diagnostic trial. On the positive side, the theoretical account passes the diagnostic trial for consecutive correlativity and autoregressive conditional heteroscedasticity ( ARCH ) in remainders.

Where the p-value is 0.0004 and 0.0064 severally was less than 5 % .

## 4.7 Granger Causality Test`

The being of relationships between variables does non turn out causality or the way of influence. However, causality trial was conducted utilizing the Pair-Wise Granger causality trial. The theoretical account was estimated by dawdling the explanatory variables by two periods as shown in appendix 4.

Using the chance statistic for reading, the Granger-Causality consequences suggest that in proving the void hypothesis: FDI does non granger cause RGDP and RGDP does non granger cause FDI, as the void hypothesis is accepted for both hypotheses of 0.7406 and 0.7043 were lower than 5 % , and this suggested independency among the variables say that the coefficients were non separately important.For, INFRA does non granger cause RGDP we accept the nothing as 0.2681 is greater than 5 % and therefore causality did non run from INFRA to RGDP. In contrary, the void hypothesis that RGDP does non granger cause INFRA was rejected ; because p-value 0.0479 is less than 5 % reasoning that there is a unidirectional causality running RGDP to INFRA.

For, INFLA does non granger cause RGDP, we accepted the void hypothesis for both hypothesis because 0.5892 and 0.4723 are greater than 5 % and this suggested independency among the variables means none of them causes the other.For, XM does non granger cause RGDP, we accept it because 0.

6529 is greater than 5 % . However RGDP does non do XM was rejected as 0.0007 is less than 0.5 % significance there is a unidirectional causality from RGDP to XM.For, HUMCAP does non granger cause RGDP, we accepted the void hypothesis for both hypothesis because 0.

4449 and 0.2524 are greater than 5 % and this suggested independency among the variables means that none of them causes the other.Causality consequences between two independent variables were non reported because they did non capture the range of the research ; nevertheless, merely causality consequences between dependent and independent variables were reported.To reply one of the aims of the survey, from the consequence we see clearly that FDI do non hold a causal nexus with economic growing, but it has a positive relationship with economic growing.

Among the sectors having FDI, service sector received the highest per centum of FDI peculiarly the telecommunication industry of about 41 % influxs. Despite the influx of FDI into this sector, there exist no causal link between FDI and growing in Nigeria. This ground might be that FDI in this sector was in the signifier of amalgamations and acquisitions which are non the most good for the domestic economic system. Besides, it may be that service FDI does non supply entree to export markets or linkages to local endeavors similarly advanced engineerings, that fabricating FDI would hold provided. Finally, we see the reasoning comments of the whole survey in the last chapter.

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