Testing exogeneity in nonparametric instrumental variables identified by conditional quantile restrictions

Jia-Young Michael Fu, Joel L. Horowitz () and Matthias Parey
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Jia-Young Michael Fu: Institute for Fiscal Studies
Joel L. Horowitz: Institute for Fiscal Studies and Northwestern University

No CWP68/15, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

Abstract: 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 the structural function belongs to a known finite-dimensional parametric family and does not require nonparametric estimation of this function. The latter property is important because, owing to the ill-posed inverse problem, a test based on a nonparametric estimator of the structural function has low power. The test presented here is consistent whenever the structural function differs from the conditional quantile function on a set of non-zero probability. The test has non-trivial 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 illustrate the usefulness of the test.

Date: 2015-10-21
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Working Paper: Testing exogeneity in nonparametric instrumental variables identified by conditional quantile restrictions (2015)
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