This paper presents a test for exogeneity of explanatory variables in a nonparametric instrumental variables (IV) model whose structural function is identified through a conditional quantile restriction. Quantile regression models are increasingly important in applied econometrics. As with mean-regression models, an erroneous assumption that the explanatory variables in a quantile regression model are exogenous can lead to highly misleading results. In addition, a test of exogeneity based on an incorrectly specified parametric model can produce misleading results. This paper presents a test of exogeneity that does not assume that the structural function belongs to a known finite-dimensional parametric family and does not require estimation of this function. The latter property is important because nonparametric estimates of the structural function are unavoidably imprecise. The test presented here is consistent whenever the structural function differs from the conditional quantile function on a set of nonzero probability. The test has nontrivial power uniformly over a large class of structural functions that differ from the conditional quantile function by |$O({n^{ - 1/2}})$|⁠. The results of Monte Carlo experiments and an empirical application illustrate the performance of the test.

中文翻译：

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在由条件分位数限制确定的非参数工具变量模型中测试外生性

本文针对非参数工具变量（IV）模型中的解释变量的外生性进行了测试，该模型的结构功能是通过条件分位数限制来确定的。在应用计量经济学中，分位数回归模型越来越重要。与均值回归模型一样，分位数回归模型中的解释变量是外生的错误假设可能导致极具误导性的结果。此外，基于错误指定的参数模型进行的外生性测试可能会产生误导性的结果。本文提出了一种外生性检验，该检验不假定结构功能属于已知的有限维参数族，并且不需要对此功能进行估计。后一种特性很重要，因为结构函数的非参数估计不可避免地不精确。只要结构函数与条件分位数函数在一组非零概率上有所不同，此处提供的检验就是一致的。该测试在与条件分位数函数不同的一大类结构函数上均匀地具有非平凡幂| $ O（{n ^ {-1/2}}）$ |⁠。蒙特卡洛实验的结果和经验应用说明了该测试的性能。