A test for endogeneity in conditional quantile models

In this paper we develop a test to detect the presence of endogeneity in conditional quantile models. The proposed test is a Hausman-type test in that it is based on the distance between two estimators in which one is consistent only under no endogeneity while the other estimator 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 is investigated by Monte Carlo simulations and it is found that the test shows reasonably good size and power properties in finite samples. Finally, we apply our approach to test for endogeneity in a conditional quantile model for estimating Engel curves using the UK consumption and expenditure data. It is revealed that the pattern of endogeneity found in the Engel curve varies across different quantiles.