A Test for Endogeneity in Conditional Quantiles
In this paper, we develop a test to detect the presence of endogeneity in conditional quantiles. Our test is a Hausman-type test based on the distance between two estimators, of which one is consistent only under no endogeneity while the other is consistent regardless of the presence of endogeneity in conditional quantile models. We derive the asymptotic distribution of the test statistic under the null hypothesis of no endogeneity. The finite sample properties of the test are investigated through Monte Carlo simulations, and it is found that the test shows good size and power properties in finite samples. As opposed to the test based on the IVQR estimator of Chernozhukov and Hansen (2006) in the case of more than a couple of variables, our approach does not imply an infeasible computation time. Finally, we apply our approach to test for endogeneity in conditional quantile models for estimating Engel curves using UK consumption and expenditure data. The pattern of endogeneity in the Engel curve is found to vary substantially across quantiles
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