Measurement Errors in Quantile Regression Models∗

This paper develops estimation and inference for quantile regression models with measurement errors. We propose an easily-implementable semiparametric two-step estimator when we have repeated measures for the covariates. Building on recent theory on Z-estimation with infinite-dimensional parameters, consistency and asymptotic normality of the proposed estimator are established. We also develop statistical inference procedures and show the validity of a bootstrap approach to implement the methods in practice. Monte Carlo simulations assess the finite sample performance of the proposed methods. We apply our methods to the well-known example of returns to education on earnings using a data set on female monozygotic twins in the U.K. We document strong heterogeneity in returns to education along the conditional distribution of earnings. In addition, the returns are relatively larger at the lower part of the distribution, providing evidence that a potential economic redistributive policy should focus on such quantiles.