Criterion-based inference for GMM in autoregressive panel data models

In this paper we examine the properties of a simple criterion-based, likelihood ratio type test of parameter restrictions for standard GMM estimators in autoregressive panel data models. A comparison is made with recent test proposals based on the continuously-updated GMM criterion [Journal of Business & Economic Statistics 14 (1996) 262] or exponential tilting parameters [Econometrica 66 (1998) 333]. The likelihood ratio type statistic is computed simply as the difference between the standard GMM tests of overidentifying restrictions in the restricted and unrestricted models. In Monte Carlo simulations we find this test has similar properties to the two criterion-based alternatives, whilst being much simpler to compute. All three criterion-based tests outperform conventional Wald tests in this context.