A CONSISTENT TEST OF FUNCTIONAL FORM VIA NONPARAMETRIC-ESTIMATION TECHNIQUES

This paper presents a consistent test of functional form of nonlinear regression models. The test combines the methodology of the conditiona l moment test and nonparametric estimation techniques. Using degenerat e and nondegenerate U-statistic theories, the test statistic is shown to be asymptotically distributed standard normal under the null hypoth esis that the parametric model is correct, while diverging to infinity at a rate arbitrarily close to n, the sample size, if the parametric model is misspecified. Therefore, the test is consistent against all d eviations from the parametric model. The test is robust to heteroskeda sticity. A version of the test can be constructed which will have asym ptotic power equal to 1 against any local alternatives approaching the null at rates slower than the parametric rate 1/root n. A simulation study reveals that the test has good finite-sample properties.