Haoyang Liu

Federal Reserve Bank of New York

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Institutional Affiliation: Federal Reserve Bank of New York

NBER Working Papers and Publications

May 2019Errors in the Dependent Variable of Quantile Regression Models
with Jerry A. Hausman, Ye Luo, Christopher Palmer: w25819
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 tim...

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