Testing a parametric quantile-regression model with an endogenous explanatory variable against a nonparametric alternative

Abstract

This paper is concerned with inference about a function g that is identified by a conditional quantile restriction involving instrumental variables. The paper presents a test of the hypothesis that g belongs to a finite-dimensional parametric family against a nonparametric alternative. The test is not subject to the ill-posed inverse problem of nonparametric instrumental variables estimation. Under mild conditions, the test is consistent against any alternative model. In large samples, its power is arbitrarily close to 1 uniformly over a class of alternatives whose distance from the null hypothesis is O n −1/2 , where n is the sample size. Monte Carlo simulations illustrate the finitesample performance of the test.