Testing for a Functional Form of Mean Regression in a Fully Parametric Environment

Abstract We develop a test for a restricted functional form of a mean regression when a complex distributional model for all variables is estimated. The test statistic is an average squared deviation from the estimated hypothesized function of the form implied by the estimated parametric model, and is asymptotically distributed as a mixture of χ2 distributions. The test is easy to implement using numerical derivatives, and it performs well in samples of typical size. We illustrate the test using data on labor market characteristics of US young men.