A TEST FOR FUNCTIONAL FORM AGAINST NONPARAMETRIC ALTERNATIVES

A test for neglected nonlinearities in regression models is proposed. The test is of the Davidson-MacKinnon type against an increasingly rich set of nonnested alternatives, and is based on sieve estimation of the alternative model. For the case of a linear parametric model, the test statistic is shown to be asymptotically standard normal under the null, while rejecting with probability going to one if the linear model is misspecified. A small simulation study suggests that the test has adequate finite sample properties, but one must guard against overfitting the nonparametric alternative.