NATIONAL BUREAU OF ECONOMIC RESEARCH
NATIONAL BUREAU OF ECONOMIC RESEARCH
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Errors in the Dependent Variable of Quantile Regression Models

Jerry A. Hausman, Haoyang Liu, Ye Luo, Christopher Palmer

NBER Working Paper No. 25819
Issued in May 2019
NBER Program(s):Economics of Education Program, Labor Studies Program, Public Economics Program, Technical Working Papers

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.

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Document Object Identifier (DOI): 10.3386/w25819

 
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