Consistent Specification Tests for Regression Models

Chunrong Ai

This paper presents three procedures for testing specifications of regression models. The first procedure is parametric and it tests the specification of an unconditional moment restriction model against a nonnested unconditional moment restriction model. The second procedure is nonparametric and it tests the specification of a conditional moment restriction model against a nonnested conditional moment restriction model. The third procedure also is nonparametric but it tests the specification of a conditional moment restriction model against all alternative specifications. All procedures permit heteroskedasticity of unknown form and are shown to be consistent. The test statistics of the first two procedures are simply the t-ratios of a 2SLS estimator while that of the third procedure is computable from LS output via auxiliary LS
regressions.