2.2 Generalized Methods of Moments (GMM)

In the present study, the dynamic panel data model is estimated. To evaluate the significant impact of the concerned explanatory variables on the environmental quality, we use the Blundell and Bond system GMM methodology. The GMM is the most popular estimation technique if time span (T) is less than cross-sections (N) Arellano and Bond [44]. The choice of system GMM is justified on the basis that if the dependent variable is persistent to a random walk then difference GMM performs poorly, as past values are vague about future changes. So, higher-order lags of the regressors are weak instruments for the differenced variables [45]. In such case, system GMM is the best choice Blundell and Bond [46]. Secondly, fixed effects estimator is biased in the presence of the lagged dependent variable and it also accounts for possible endogeneity issues. Moreover, if the difference GMM estimates lie below or close to fixed effects, this will be biased downward, and consequently, system GMM would be efficient. Additionally, GMM estimator, in the absence of MLE, can be used as an alternative to other methods. The beauty of both difference and system GMM methods are the use of the instruments which are valid based on the assumption that the disturbance terms are truly independent and are serially uncorrelated. Therefore, the Arellano-Bond test, checks for serial correlation in the residuals by testing the residuals in the differenced equations for serial correlation. However, the first-order serial correlation is to be expected and therefore the key test is to check for second-order serial correlation which should not be rejected the null hypothesis of no second-order serial correlation. Moreover, the joint validity of the instruments can be verified by running the Sargan/Hansen test.