Alternative Over-identifying Restriction Tests in the GMM Estimation of Panel Data Models

Abstract

A new over-identifying restriction test in the generalized method of moments (GMM) estimation of panel data models is proposed. In contrast to the conventional over-identifying restriction test, where the sample covariance matrix of the moment conditions is used in the weighting matrix, the proposed test uses a block diagonal weighting matrix constructed from the efficient optimal weighting matrix. It is shown that the proposed test statistic asymptotically follows the weighted sum of the chi-square distribution with one degree of freedom. A detailed local power analysis is provided for dynamic panel data models, and it is demonstrated that the new test has a comparable power to the conventional J test in many cases. The Monte Carlo simulations reveal that the proposed test has a substantially better size property than the conventional test does.

Keywords: panel data; GMM; over-identification test; system of equations