Kernel-weighted specification testing under general distributions

TL;DR

This paper develops the limit theory for kernel-based specification tests in complex distributional settings, including non-absolutely continuous distributions with singular components, impacting inference in various econometric models.

Contribution

It introduces a new limit theory for kernel-weighted tests under general distributions, extending their applicability beyond traditional assumptions.

Findings

Distribution of conditioning variables affects test power

Limit theory applies to non-absolutely continuous distributions

Simulations demonstrate impact on test performance

Abstract

Kernel-weighted test statistics have been widely used in a variety of settings including non-stationary regression, inference on propensity score and panel data models. We develop the limit theory for a kernel-based specification test of a parametric conditional mean when the law of the regressors may not be absolutely continuous to the Lebesgue measure and is contaminated with singular components. This result is of independent interest and may be useful in other applications that utilize kernel smoothed U-statistics. Simulations illustrate the non-trivial impact of the distribution of the conditioning variables on the power properties of the test statistic.