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.

中文翻译：

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分位数回归模型因变量中的误差

我们研究了随机系数模型因变量中测量误差的后果，重点是分位数回归的特殊情况。如果存在一个加性误差项，Koenker和Bassett（1978）的流行的分位数回归估计量是有偏差的。将因变量作为经典测量误差的变量误差问题来解决这个问题，我们提出了一种筛查最大似然方法，该方法对左侧测量误差具有鲁棒性。用于识别提供足够的条件后，我们证明，当选择在网格位数结的数量在适当的速度增长，筛最大似然估计的一致性和渐近正常，通过自举允许推断。蒙特卡洛证据证明我们的方法在均值偏差和MSE方面优于分位数回归。最后，我们通过对教育收益的应用来说明我们的估算器，突出显示了过去因测量误差而被掩盖的教育收益随时间的变化。