Estimation Procedures

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the long-run coefficients to be equal across groups, thus combining the features of MG and FE estimators.

However, given the nature of data requirement in employing the MG and PMG estimators³⁶, only DFE estimator is employed to explore the heterogeneity across the pooled countries and test for the existence of long run and the speed of adjustment in the short run.

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for which the time series and cross-sectional dimensions grew large at the same rate. They considered the case in which both dimensions grew large independently and derived asymptotic distributions for panel unit root tests that allowed for heterogeneous intercepts and trends across individual members. Im, Pesaran, and Shin (2003) developed a panel unit root estimator based on a group mean approach (See: Pedroni, 2004; Levin, Lin, and Chu, 2002; Im, Persaran and Shin, 2003).

As a general rule, non-stationary time series should not be used in regression models in order to avoid the problem of spurious regression. Engle and Granger (1987) pointed out that a linear combination of two non-stationary series may be stationary. The existence of a stationary linear combination of the non-stationary time series is referred to as cointegration and it can be interpreted as a long-run equilibrium relationship among the variables. Given this consideration, the Kao Residual Cointegration test was first conducted testing the null hypothesis of existence of ―no cointegration‖. Kao (Engle-Granger based) Cointegration test follows the same basic approach as the Pedroni tests, but specifies cross- section specific intercepts and homogeneous coefficients on the first-stage regressors. The test was based on the assumption of no deterministic trend.

Probing further on the existence of cointegration among the current account balance and its determinants, residual based panel cointegration test developed by Pedroni (1999, 2004) was employed³⁷. Pedroni proposed several tests for cointegration that allow for heterogeneous slope coefficients across cross-sections. The tests are Panel v-Statistic, Panel rho-Statistic, Panel PP-Statistic, Panel ADF-Statistic, Group rho-Statistic, Group PP- Statistic and Group ADF-Statistic. In the alternative hypothesis, the residual is nonstationary which literally implies that there is no cointegrating relationship. In the alternative hypothesis, the residuals are stationary (i.e. there is a cointegrating relationship).

In addition, Pedroni’s test of cointegration assumed that the residuals of the alternative hypothesis have common autoregressive (AR) coefficients for the first four tests; namely, Panel v-Statistic, Panel rho-Statistic, Panel PP-Statistic and Panel ADF-Statistic; and individual AR coefficients for the last three tests which are Group rho-Statistic, Group PP-

37 The maximum numbers of variables that can be tested at a time with the available software for Pedroni are seven. Two of the variables introduced through investment (TOT and SAV) were dropped.

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Statistic and Group ADF-Statistic. Four of the tests, namely Panel PP-Statistic, Panel ADF- Statistic, Group rho-Statistic, and Group ADF-Statistic, were carried out and their results were reported accordingly.

In order to establish the impact (both in the short run and long run) of government expenditure and other control variables employed in the current account balance in SSA, DFE estimator was employed to estimate the models specified in equation (4.37). Five versions of the DFE results were derived from five sub-groups of the sampled countries.

The first version results are obtained from pooled data from all the selected 34 SSA countries, while the remaining four versions were estimated by re-grouping the sampled countries in line with the IMF classification, which is oil-exporting countries, middle- income countries, low-income excluding fragile countries and fragile countries³⁸.

Furthermore, in estimating the dynamic panel model of the current account balance specified in equation (4.26), several estimation procedures are explored to establish the robustness of the relationship. This approach helps to answer the question of the extent of the impact of the current account determinants on the current account balance. It helps to quantify the extent of the impact exerted by government expenditure and other control variables on the current account balance. The two-step GMM system estimator is employed because of its several abilities. Several specifications and diagnostic tests are undertaken to authenticate the results and establish their robustness. The first is a Hansen test of over-identifying restrictions, which test the overall validity of the instruments by analysing the sample analogue of the moment conditions used in the estimation process.

Failure to reject the null hypothesis gives support to the model. The second test examines the hypothesis that the error term is first- or second order serially correlated. First-order serial correlation of this error term is expected, while the second-order serial correlation of the differenced residual indicates that the original error term is serially correlated and follows a moving average process at least of order one. Failure to reject the null hypothesis of absence of second-order serial correlation implies that the original error term is serially

38 Out of the thirty four (34) selected countries, five (5) are from oil-exporting countries, eleven (11) are from middle-income countries, fourteen (14) are from low-income and fragile countries and twelve (12) are from fragile countries. See Appendix D2 for the list of various countries that fall into each group.

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uncorrelated and uses the corresponding moment conditions specified in equations (4.31), (4.32), (4.33) and (4.34).

In order to analyse the dynamic impact of fiscal policy changes in the current account balance, PVAR was carried out. PVAR results are presented in the form of the dynamic impulse response and variance decomposition of the current account balance to the Cholesky One Standard Deviation innovations from fiscal policy. However, the lag order selection of the VAR model, which is critical to its analysis, was first carried out. This is because VAR are generally sensitive to lag length. Kilian (2001) as well as Hamilton and Herrera (2004) argued that different lag orders can significantly affect the substantive interpretation of VAR estimates, especially, when those differences are large enough. As pointed out by Kireyev (2000), few lags do not adequately capture the dynamics of the system and lead to omitted variable bias while too many lags lead to loss of too much information, thus appropriate lag length matters.

The selection of the optimum lag length was guided by some pre-specified criterion, basically 5 in this study. They are Sequential Modified Likelihood Ratio (LR) test, Final Prediction Error, Akaike Information Criterion (AIC), the Schwarz Information Criterion (SIC) and the Hannan Quinn Criterion (HQC). The literature suggested that these criteria may draw different conclusions on the lag order. However, Ivanov and Kilian (2005) argued that the SIC is the most accurate criterion for all realistic sample sizes.

Furthermore, in ensuring that the selected lag lengths were appropriate, a multivariate diagnostic test, Portmanteau Tests for Autocorrelations, was applied to test the null hypothesis that ―there is no residual autocorrelations up to lag h‖.

The reactions of other variables to the shock from government expenditure are assumed (Response to Cholesky One S.D. Innovation from government expenditure). The differences in dynamic responses of variables to government expenditure shocks are evaluated by comparing aggregate impulse response functions and variance decompositions over 12 years. The impulse response functions will trace out the time path of variable response to shocks in the error terms for several periods in the future and show the sign and time trajectory of the impact. Variance decomposition describes the percentage of the

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variation in other variables, at the same time pointing out the current account balance, in this case, among others, since it is the variable of interest as explained by the fiscal policy measure, which is government expenditure. As suggested by Ramey and Francis (2009), the panel VAR is estimated in level to ensure that relevant information are lost, since over- differencing may remove important information.