Criterion-Based Inference for GMM in Linear Dynamic Panel Data Models

In this paper we consider the properties of a simple test of parameter restrictions based on standard two-step efficient GMM estimators. The test is computed simply as the difference between the minimised values of the GMM criterion function in the restricted and unrestricted models. We compare this to criterion-based tests of parameter restrictions based on the continuously-updated GMM estimator of Hansen, Heaton and Yaron (1996) and the exponential tilting proposal of Imbens, Spady and Johnson (1998), as well as to standard asymptotic Wald tests, and to the LM test statistic which is easily computed in the case of moment conditions that are linear in the parameters. We investigate the properties of these tests using Monte Carlo experiments in the context of simple parameter restrictions in linear dynamic panel data models. Our main finding is that the test based on the standard GMM criterion function has very similar size and power properties as the computationally more burdensome alternatives. In future research we will investigate whether this finding holds in more general settings, for example in the context of non-linear restrictions and non-linear models.