IV Quantile Regression for Group-Level Treatments, with an Application to the Effects of Trade on the Distribution of Wages

We present a methodology for estimating the distributional effects of an endogenous treatment that varies at the group level when there are group-level unobservables, a quantile extension of Hausman and Taylor (1981). Standard quantile regression techniques are inconsistent in this setting, even if the treatment is exogenous. Using the Bahadur representation of quantile estimators, we derive weak conditions on the growth of the number of observations per group that are sufficient for consistency and asymptotic normality. Simulations confirm the superiority of this grouped instrumental variables quantile regression estimator to standard quantile regression. An empirical application finds that low-wage earners in the U.S. from 1990-2007 were significantly more affected by increased Chinese import competition than high-wage earners. We also illustrate the usefulness of the estimation approach with additional empirical examples from urban economics, labor, regulation, and empirical auctions