On the Effect of Weighting Matrix in GMM Specification Test

Abstract

In this paper, we study the finite sample behavior of over-identifying restriction test, J test, in GMM. We consider two variants of J test, one with centered weighting matrix and the other is with uncentered weighting matrix. We demonstrate that the finite sample distribution of J test with centered weighting matrix is close to F distribution while that with uncentered weighting matrix is close to a beta distribution, and both are far different from chi-square distribution. This fact can then be used to demonstrate why competing simulation results with regard to the size property is reported in the context of dynamic panel data models and covariance structure models.