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 restristions for standard GMM estimators in autoregressive panel data models. A comparison is made with recent test proposals based in the continuously-updated GMM criterion (Hansen, Heaton and Yaron, 1996) or exponential tilting parameters (Imbens, Spady and Johnson, 1998). 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 thsi test had similar properties to the criterion-based alternatives, whilst being much simpler to compute. All three criterion-based tests outperform conventional Wald tests in this context.