Working Paper Series: Special Edition of 2016 to 2018 Interns

Estimating the long-run relationship Using static approaches such as ordinary least squares (OLS) methodology to estimate cointegrated relationships have great consequences such as biased estimator of the parameters. Alternative approaches for panel cointegration estimation are the fully modified ordinary least square (FMOLS) proposed by Pedroni (2000) and the dynamic ordinary least squares (DOLS) offered by Stock and Watson (1993). Both the FMOLS and the DOLS are found to provide consistent estimates more appropriate for inference purposes and have normal limiting properties. In light of the short times series dimension, the study opted to use the DOLS since it is superior to the FMOLS in short samples. Most importantly, the DOLS corrects for the statistical issue of endogeneity and serial correlation, issues that need to be adequately addressed. VECM model If the variables of the model, at least two, are cointegrated then the Granger representation theorem holds. It posits that a valid error correction model holds which utilizes an error correction term to correct for any short-run deviation in the variables. The VECM advances on the cointegration analysis to explore the existence of causality between the variables as well. In addition, Maddala & Kim (1998) explains that the pure VAR produces erratic estimates due to high multicollinearity among the explanatory variables. Alternatively, ECMs were established to remedy the issues of the pure VAR, determine whether or not there are any long run relationships and capture the dynamic behaviour of current variables as well. The VECM was estimated using generalized method of moments (GMM) using lagged values of the regressors as instruments. Panel Granger Causality The last step is the Granger Causality. In statistical terms, the concept posits that given a time series containing and , Granger causes if the inclusion of leads to a better prediction of than if was excluded. Further, causality can be unidirectional, running from to or vice versa; or bidirectional, running both directions. In addition, if cointegration is found between the variables then the Granger Representation Theorem holds, which indicates that Granger causality exists in at least one direction.

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