On the estimation of the Dynamic Panel Model in the presence of heteroscedasticity

Dynamic panel (DP) modeling is crucial in econometric analysis for addressing endogeneity, serial correlation, and unobserved heterogeneity. However, the comparative efficiency of different estimators under varying sample dimensions and data conditions remains inconclusive. This study evaluates four DP estimators, namely the Generalized Method of Moments (GMM), Instrumental Variable (IV), Least Squares Dummy Variable (LSDV), and Weighted Least Squares (WLS), using both theoretical and empirical approaches. Simulations were performed for three sample sizes (N=5, T=10; N=20, T=15; N=50, T=50), deliberately violating the homoscedasticity assumption of the error covariance matrix to assess robustness under heteroscedasticity. The results indicate that LSDV achieved the lowest AIC, BIC, and RMSE in small to medium samples. Conversely, GMM demonstrated superior performance in larger samples, exhibiting greater consistency and robustness in handling autocorrelation and endogeneity, as confirmed by the non-significance of the AR(2) and Sargan test statistics. In contrast, IV and WLS estimators were found to be inconsistent under heteroscedasticity, with higher error variances. Empirical application using macroeconomic data on inflation and economic growth for 40 sub-Saharan African countries over 31 years further validated a significant positive relationship for both GMM (β = 26.0318, p < 0.001) and LSDV (β = 22.3896, p < 0.001). Overall, while LSDV performs efficiently in small samples, GMM remains the most valid and consistent estimator for large dynamic panels characterized by heteroscedasticity and endogeneity.