Consistent model specification testing

Abstract

This paper proposes a consistent model specfication test that can be applied to a wide class of models and estimators, including all variants of quasi-maximum likelihood and generalized method of moments. Our framework is independent of the form of the model and generalizes Bierens (1982, 1990) approach. It has particular applications in new cases such as heteroskedastic errors, discrete data models, but the chief appeal of our approach is that it provides a "one size fits all" test. We specify a test based on a linear combination of individual components of the indicator vector that can be computed routinely, does not need to be tailored to the particular model, and is expected to have power against a wide class of alternatives. Although primarily envisaged as a test of functional form, this type of moment test can also be extended to testing for omitted variables.