An Improved Nonparametric Test for Misspecification of Functional Form

Ralph Bradley and Robert McClelland


In this paper, we develop a two-stage test for misspecification of a conditional mean that is similar to one recently developed by Bierens (1990). Our test uses the idea that in misspecified models the explanatory variables, X, better predict the residuals, uhat, than their mean. Thus, an appealing function that detects misspecification is E(uhat|X). We estimate this with a kernel regression which is then a component of the second stage which tests for the nonzero correlation of uhat and the kernel estimate. By directly estimating the misspecification our approach should have good power while making fewer a priori restrictions than Bierens, while also helping researchers better understand the nature of any misspecification.