86
E. N. Udemba
4.2 Unit Root/Stationarity Test
In every time series study, it is very essential to account for stationarity of the data. It
is expected that the data are impacted by the structural events in the economy within
the chosen period of research, and for this reason, stochastic trends are unavoidable
in the history of the data which are likely to affect the outcome of the study if not
accounted for. For this, unit root was tested in this study to ascertain the stationarity
of the data and the order of integration. Author employed [6, 22]; KwiatkowskiPhilips-Schmidt-Shin [16] for effective estimation of the unit root, and unit root with
mixed order of integration were found. Also, Chow test was applied for a robust
check of the stationarity test. Most times, conventional tests are found to be weak in
face of structural break caused by some natural or economic shocks (e.g., recession,
pandemic, or epidemic) which always create a permanent shock to an economy
capable of affecting the stationarity of data for the period of occurrence. With the aid
of Chow tests, a structural break was identified in the year 2008, and dummy variable
was created to correct the impact on the data. The outcomes of both the conventional
tests Augmented Dickey Fuller [6]; Philip [22]; Kwiatkowski-Philips-Schmidt-Shin,
Kwiatkowski et al. [16] (ADF, PP, and KPS) and the Chow tests are presented on
Tables 3 and 4.
4.3 Test for Cointegration (Both the Short and Long Run)
and Diagnostic Tests
ARDL-bound testing and other diagnostic tests were applied in this research for
purpose of identifying the existence of cointegration (i.e., long-run relationship
between the variables) and for confirming the stability, reliability, and fitting of
the model. Bound testing has advantages over other methods of testing cointegration
such as Engle and Granger [7] and Johansen [12]. Bound testing can be applied even
when the series are integrated of mixed order or on the same order, and also, it can
be applied when the sample is small. The result of the cointegration (short-run and
long-run relationships that exist between the selected variables) estimation and the
diagnostic tests are presented in Table 5. The outputs on the table are explained as
follows: The goodness of fit which showed the part of dependent variable (lnEFP)
that are explained by the independent variables (lnEU, lnGDP, lnGDP
2 , lnAG, and
lnPOP) is represented with R
2
= 0.999635 and adjusted R
2
= 0.999327 while the
remaining part of dependent variable is explained by residual (error term = μ). Autocorrelation and serial correlation are tested with Durbin Watson and Breuch–Godfrey
serial correlation LM tests. From the outputs of both tests absence of autocorrelation
or serial correlation is confirmed with the values of Durbin Watson (2.22) and serial
correlation LM tests (F-stats = 0.5734 and Chi-square = 0.4117). Among the results
displayed on the table is the cointegration from bound testing. With the values of Fstats (6.320642) and critical values of both lower (4.045) and upper (5.898) bounds,
E. N. Udemba
4.2 Unit Root/Stationarity Test
In every time series study, it is very essential to account for stationarity of the data. It
is expected that the data are impacted by the structural events in the economy within
the chosen period of research, and for this reason, stochastic trends are unavoidable
in the history of the data which are likely to affect the outcome of the study if not
accounted for. For this, unit root was tested in this study to ascertain the stationarity
of the data and the order of integration. Author employed [6, 22]; KwiatkowskiPhilips-Schmidt-Shin [16] for effective estimation of the unit root, and unit root with
mixed order of integration were found. Also, Chow test was applied for a robust
check of the stationarity test. Most times, conventional tests are found to be weak in
face of structural break caused by some natural or economic shocks (e.g., recession,
pandemic, or epidemic) which always create a permanent shock to an economy
capable of affecting the stationarity of data for the period of occurrence. With the aid
of Chow tests, a structural break was identified in the year 2008, and dummy variable
was created to correct the impact on the data. The outcomes of both the conventional
tests Augmented Dickey Fuller [6]; Philip [22]; Kwiatkowski-Philips-Schmidt-Shin,
Kwiatkowski et al. [16] (ADF, PP, and KPS) and the Chow tests are presented on
Tables 3 and 4.
4.3 Test for Cointegration (Both the Short and Long Run)
and Diagnostic Tests
ARDL-bound testing and other diagnostic tests were applied in this research for
purpose of identifying the existence of cointegration (i.e., long-run relationship
between the variables) and for confirming the stability, reliability, and fitting of
the model. Bound testing has advantages over other methods of testing cointegration
such as Engle and Granger [7] and Johansen [12]. Bound testing can be applied even
when the series are integrated of mixed order or on the same order, and also, it can
be applied when the sample is small. The result of the cointegration (short-run and
long-run relationships that exist between the selected variables) estimation and the
diagnostic tests are presented in Table 5. The outputs on the table are explained as
follows: The goodness of fit which showed the part of dependent variable (lnEFP)
that are explained by the independent variables (lnEU, lnGDP, lnGDP
2 , lnAG, and
lnPOP) is represented with R
2
= 0.999635 and adjusted R
2
= 0.999327 while the
remaining part of dependent variable is explained by residual (error term = μ). Autocorrelation and serial correlation are tested with Durbin Watson and Breuch–Godfrey
serial correlation LM tests. From the outputs of both tests absence of autocorrelation
or serial correlation is confirmed with the values of Durbin Watson (2.22) and serial
correlation LM tests (F-stats = 0.5734 and Chi-square = 0.4117). Among the results
displayed on the table is the cointegration from bound testing. With the values of Fstats (6.320642) and critical values of both lower (4.045) and upper (5.898) bounds,