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

<p><p>This paper is concerned with inference about a function <i>g</i> that is identified by a conditional quantile restriction involving instrumental variables. The paper presents a test of the hypothesis that <i>g</i> 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 (<i>n</i>^1/2), where <i>n</i> is the sample size. Monte Carlo simulations illustrate the finite-sample performance of the test.</p></p>