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 conditional moment test and nonparametric estimation techniques. Using degenerate and nondegenerate U-statistic theories, the test statistic is shown to be asymptotically distributed standard normal under the null hypothesis 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 deviations from the parametric model. The test is robust to heteroskedasticity. A version of the test can be constructed which will have asymptotic power equal to 1 against any local alternatives approaching the null at rates slower than the parametric rate 1/√n. A simulation study reveals that the test has good finite-sample properties.