Mohamed R. Abonazel

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.

In dynamic panel data (DPD) models, the generalized method of moments (GMM) estimation gives efficient estimators. However, this efficiency is affected by the choice of the initial weighting matrix. In practice, the inverse of the moment matrix of the instruments has been used as an initial weighting matrix which led to a loss of efficiency. Therefore, we will present new GMM estimators based on optimal or suboptimal weighting matrices in GMM estimation. Monte Carlo study indicates that the potential efficiency gain by using these matrices. Moreover, the bias and efficiency of the new GMM estimators are more reliable than any other conventional GMM estimators.

This thesis considers estimation of dynamic panel data models under different assumptions, and we focus on explore the bias properties of the different estimation methods. And, we focus on GMM estimation because of it has been used in many applications and it gives efficient estimators. This efficiency is affected by the choice of the initial weighting matrix. It is common practice to use the inverse of the moment matrix of the instruments as an initial weighting matrix. However, an initial optimal weighting matrix is not known, especially in the system GMM estimation procedure.Therefore, the main objective of this thesis is to improve the efficiency of GMM estimators.
To achieve this objective we proposed new approach to improve the efficiency of GMM estimators. Our approach based on finding and using the optimal weighting matrices to obtain more efficient estimators.

A particularly useful approach for analyzing pooled cross sectional and time series data is Swamy's random coefficient panel data (RCPD) model. This paper examines the performance of Swamy's estimators and tests associated with this model by using Monte Carlo simulation. The Monte Carlo study shed some light into how well the Swamy's estimate perform in small, medium, and large samples, in cases when the regression coefficients are fixed, random, and mixed. The Monte Carlo simulation results suggest that the Swamy's estimate perform well in small samples if the coefficients are random and but it does not when regression coefficients are fixed or mixed. But if the samples sizes are medium or large, the Swamy's estimate performs well when the regression coefficients are fixed, random, or mixed.

This paper examines the panel data models when the regression coefficients are fixed, random, and mixed, and proposed the different estimators for this model. We used the Mote Carlo simulation for making comparisons between the behavior of several estimation methods, such as Random Coefficient Regression (RCR), Classical Pooling (CP), and Mean Group (MG) estimators, in the three cases for regression coefficients. The Monte Carlo simulation results suggest that the RCR estimators perform well in small samples if the coefficients are random. While CP estimators perform well in the case of fixed model only. But the MG estimators perform well if the coefficients are random or fixed.