Abstract
In this paper, we study the finite sample behavior of an over-identifying restriction test, the J test, in generalized method of moments(GMM). We consider two variants of the J test, one with centered weighting matrix and the other with uncentered weighting matrix. We demonstrate that the finite sample distribution of J test with centered weighting matrix is close to F 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.
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