Errors in the Dependent Variable of Quantile Regression Models
The popular quantile regression estimator of Koenker and Bassett (1978) is biased if there is an additive error term. Approaching this problem as an errors-in-variables problem where the dependent variable suffers from classical measurement error, we present a sieve maximum-likelihood approach that is robust to left-hand side measurement error. After providing sufficient conditions for identification, we demonstrate that when the number of knots in the quantile grid is chosen to grow at an adequate speed, the sieve maximum-likelihood estimator is consistent and asymptotically normal, permitting inference via bootstrapping. We verify our theoretical results with Monte Carlo simulations and illustrate our estimator with an application to the returns to education highlighting changes over time in the returns to education that have previously been masked by measurement-error bias.
We thank Isaiah Andrews, Colin Cameron, Victor Chernozhukov, Denis Chetverikov, Kirill Evdokimov, Hank Farber, Brigham Frandsen, Larry Katz, Brad Larsen, Rosa Matzkin, James McDonald, Ulrich Muller, Shu Shen, and Steven A. Snell for helpful feedback and discussions, as well as seminar participants at Cornell, Harvard, MIT, Princeton, UC Davis, UCL, and UCLA. Lei Ma, Yuqi Song, and Jacob Ornelas provided outstanding research assistance. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research, the Federal Reserve Bank of New York or the Federal Reserve System.