On the effect of weighting matrix in GMM specification test

• The effect of weighting matrix on the behavior of an over-identified restriction (OIR) test in GMM is investigated.
• The finite sample distribution of OIR test with centered weighting matrix is found to be close to F distribution.
• The finite sample distribution of OIR test with uncentered weighting matrix is found to be close to beta distribution.
• Two illustrations in the context of dynamic panel data and covariance structure models are provided.

In this paper, we study the finite sample behavior of an over-identifying restriction test, the JJ test, in generalized method of moments(GMM). We consider two variants of the JJ test, one with centered weighting matrix and the other with uncentered weighting matrix. We demonstrate that the finite sample distribution of JJ test with centered weighting matrix is close to FF distribution whereas that with uncentered weighting matrix is close to beta distribution and that both are far different from chi-square distribution. Using this, we demonstrate why competing simulation results relating to the size property is reported in the context of dynamic panel data and covariance structure models.