Errors in the Dependent Variable of Quantile Regression Models
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10.3982-ECTA14667.pdf
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703.18 KB
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Author(s)
Hausman, Jerry
Liu, Haoyang
Luo, Ye
Palmer, Christopher
Date Issued
March 2021
Journal
Econometrica
Publisher
The Econometric Society
Citation
Hausman, Jerry, Liu, Haoyang, Luo, Ye and Palmer, Christopher. 2021. "Errors in the Dependent Variable of Quantile Regression Models." Econometrica, 89 (2).
Version
Author's final manuscript
Abstract
We study the consequences of measurement error in the dependent variable of random‐coefficients models, focusing on the particular case of quantile regression. 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. Monte Carlo evidence verifies our method outperforms quantile regression in mean bias and MSE. Finally, we 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.
MIT Department
Sloan School of Management
Massachusetts Institute of Technology. Department of Economics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.3982/ecta14667
