A test statistic equation for obtaining alternative Wald and score statistics in the generalized method of moments framework

In this article we derive a test statistic generating equation (TSGE) from which several statistics suitable for testing parametric restrictions in models estimated by the generalized method of moments (GMM) may be obtained. This statistic presents three main features: it is valid for producing statistics appropriate for testing constraints expressed in very general forms, which may involve not only the parameters of interest but also a vector of nuisance parameters; some of the tests proposed in the GMM literature are special cases of the TSGE; it can be evaluated at any consistent and asymptotically normal estimator.