Errors in the Dependent Variable of Quantile Regression Models

We study the consequences of measurement error in dependent variable random‐coefficients models, focusing on particular case quantile regression. The popular regression estimator Koenker and Bassett (1978) is biased if there an additive term. Approaching this problem as errors‐in‐variables where suffers from classical error, we present a sieve maximum likelihood approach that robust to left‐hand‐side error. After providing sufficient conditions for identification, demonstrate when number knots grid chosen grow at adequate speed, sieve‐maximum‐likelihood consistent asymptotically normal, permitting inference via bootstrapping. Monte Carlo evidence verifies our method outperforms mean bias MSE. Finally, illustrate with application returns education highlighting changes over time have previously been masked by measurement‐error bias.