Small Bandwidth Asymptotics for Density-Weighted Average Derivatives

Abstract

This paper proposes (apparently) novel standard error formulas for the density-weighted average derivative estimator of Powell, Stock, and Stoker (1989). Asymptotic validity of the standard errors developed in this paper does not require the use of higher-order kernels and the standard errors are "robust" in the sense that they accommodate (but do not require) bandwidths that are smaller than those for which conventional standard errors are valid. Moreover, the results of a Monte Carlo experiment suggest that the finite sample coverage rates of confidence intervals constructed using the standard errors developed in this paper coincide (approximately) with the nominal coverage rates across a nontrivial range of bandwidths.

Keywords: Semiparametric estimation, density-weighted average derivatives

JEL Classification: C14, C21