Efficiency Comparisons for a System GMM Estimator in Dynamic Panel Data Models

Abstract

The system GMM estimator in dynamic panel data models combines moment conditions for the differenced equation with moment conditions for the model in levels. An initial optimal weight matrix under homoskedasticity and non-serial correlation is not known for this estimation procedure. It is common practice to use the inverse of the moment matrix of the instruments as the initial weight matrix. This paper assesses the potential efficiency loss from the use of this weight matrix using the efficiency bounds as derived by Liu and Neudecker (1997). A standard practice to estimate the parameters in dynamic panel data models is to take first differences to eliminate the correlated individual specific effects , and estimate the differenced model by generalised method of moments (GMM) using appropriately lagged level variables as instruments. As the information of the instruments for the differenced model decreases as the series become more persistent, Arellano and Bover (1995) and Blundell and Bond (1998) have proposed use of a system GMM estimator that combines the differ-enced equation with the level equation. The instruments for the level equation are lagged differences of the variables, which are valid when these differences are uncorrelated with the individual effects. Blundell and Bond (1998) show that the system estimator has superior properties in terms of small sample bias and RMSE, especially for persistent series. The GMM estimator is a two-step estimator. In the first step, an initial positive semidefinite weight matrix is used to obtain consistent estimates of the parameters. Given these consistent estimates, a weight matrix can be constructed that is consistent for the efficient weight matrix, and this weight matrix 1 I would like to thank Steve Bond for helpful comments. The usual disclaimer applies.