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

Authors: Joel L. Horowitz and Sokbae Lee
Date: 01 February 2007
Type: cemmap Working Paper, CWP02/07
DOI: 10.1920/wp.cem.2007.0207

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 (n1/2), where n is the sample size. Monte Carlo simulations illustrate the finite-sample performance of the test.

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