## Econometrics; Panel Data Models; GMM Estimators

Abonazel, M. R., International Journal of Applied Mathematical Research, vol. 6, issue 2, pp. 58-66, 2017. Abstractijamr-7774.pdf

This paper considers the estimation methods for dynamic panel data (DPD) models with fixed effects which suggested in econometric literature, such as least squares (LS) and generalized method of moments (GMM). These methods obtain biased estimators for DPD models. The LS estimator is inconsistent when the time dimension (T) is short regardless of the cross sectional dimension (N). Although consistent estimates can be obtained by GMM procedures, the inconsistent LS estimator has a relatively low variance and hence can lead to an estimator with lower root mean square error after the bias is removed. Therefore, we discuss in this paper the different methods to correct the bias of LS and GMM estimations. The analytical expressions for the asymptotic biases of the LS and GMM estimators have been presented for large N and finite T. Finally, we display new estimators that presented by Youssef and Abonazel [40] as more efficient estimators than the con-ventional estimators.

Youssef, A. H., A. A. Elshekh, and M. R. Abonazel, Far East Journal of Theoretical Statistics, vol. 47, issue 2, pp. 171-189, 2014. Abstractimprove_the_efficiency_of_gmm_estimators_for_dynamic_panel_models.pdfWebsite

In dynamic panel models, the generalized method of moments (GMM) has been used in many applications since it gives efficient estimators. This efficiency is affected by the choice of the initial weighted matrix. It is common practice to use the inverse of the moment matrix of the instruments as an initial weighted matrix. However, an initial optimal weighted matrix is not known, especially in the system GMM estimation procedure. Therefore, we present the optimal weighted matrix for level GMM estimator, and suboptimal weighted matrices for system GMM estimator, and use these matrices to increase the efficiency of GMM estimator. By using the Kantorovich inequality (KI), we find that the potential efficiency gain becomes large when the variance of individual effects increases compared with the variance of the errors.

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