Additional Moment Condition Tests ∗

The primary focus of this article is the provision of tests for additional conditional moment constraints in cross-section or short panel data contexts. The principal contribution is the explicit incorporation of conditional moment restrictions defining the maintained hypothesis in the formulation of the test statistics thus mirroring that of the classical parametric likelihood setting by defining restricted tests in contradistinction to standard unrestricted tests that ignore the maintained moment condition information. The framework is quite general allowing the parameters defining the additional and maintained conditional moment restrictions to differ and permitting the conditioning variates to differ likewise. GMM and generalized empirical likelihood test statistics are suggested. The asymptotic properties of the statistics are described under both null hypothesis and a suitable sequence of local alternatives. An extensive set of simulation experiments explores the relative practical efficacy of the various test statistics in terms of empirical size and size-adjusted power. JEL Classification: C12, C14, C30 Key-words: GMM; Generalized Empirical Likelihood; Series Approximations; Restricted Tests; Unrestricted Tests; Local Power. ∗The authors are grateful for comments on versions of this paper by participants at the CEMFI-UC3M Econometrics Seminar and the Universities of Cambridge and Surrey.