Nonparametric Tests for the Independence of Regressors and Disturbances as Specification Tests

We adapt techniques from the literature on chaos and nonlinear dynamics to detect misspecification in models of serially independent data by checking for dependence between the regressors and disturbances. Our tests are nonparametric in that they determine whether the distribution of the disturbances depends on the regressors without identifying a model of dependence or the distribution of the disturbances. In Monte Carlo simulations we find that these tests have good power against dependence caused by omitted variables, incorrect functional form, heteroskedasticity, and similar problems.We also apply our tests to detect misspecification in models of income imputation.