Some Further Results on Tests for Model Specification in the Presence of Alternative Hypotheses

Davidson and MacKinnon (1981) proposed a simple procedure for testing the specification of a non-linear regression model against the evidence provided by a non-nested alternative. We extend their results in several directions. First, we relax a number of assumptions of the previous paper: We admit the possibility that the nonlinear regression functions may depend on lagged dependent variables, and we do not require that the error terms be normally distributed. Second, we show how the earlier procedure may straightforwardly be generalized to the case where the two non-nested models involve different transformations of the dependent variable. Finally, we propose a simple procedure for testing non-nested linear regression models which have endogenous variables on the right-hand side, and have therefore been estimated by two-stage least squares.