Errors in the Dependent Variable of Quantile Regression Models
研究因变量存在经典测量误差时，分位数回归估计量会有偏，提出一种筛子极大似然估计方法，能纠正偏差，在蒙特卡洛模拟中表现优于传统分位数回归，并应用于教育回报率分析。
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.