Left with Bias? Quantile Regression with Measurement Error in Left Hand Side Variables

This paper examines the effect of measurement error in the dependent variable on quantile regression, because unlike OLS regression, even classical measurement error can generate bias. I examine the pattern and size of the bias using both simulation and an empirical example. The simulations indicate that classical error can cause bias and that non-classical measurement error, particularly heteroskedastic measurement error, has the potential to produce substantial bias. Also, the size and direction of the bias depends on the amount of heterogeneity in the effects across quantiles and the regression error distribution. Using restricted access Health and Retirement Study data containing matched IRS W-2 earnings records, I examine whether estimates of the returns to education statistically differ using a precisely measured and mismeasured earnings variable. I find that returns to education are over-stated by roughly 1 percentage point at the median and 75th percentile using earnings reported by survey respondents.