Fixed Effects Quantile Regression via Deconvolutional Differencing in Short Panels

Abstract

This paper provides point identification results for a quantile regression model with distributional fixed effects. Instead of high-level assumptions typical of nonlinear measurement error models or covariates with dense or large support, I consider a low-level shape restriction: conditional symmetry. Conditional symmetry allows for covariate-heterogeneous quantile effects, arbitrary correlation between the fixed effects and the covariates, and asymmetric observed distributions. I show how “deconvolutional differencing” can be applied if at least two measurements are available. Under mild regularity conditions, computationally simple and numerically reliable plug-in estimators are sup-norm consistent and point-wise asymptotically normal as the sample size diverges. Monte Carlo simulations suggest excellent finite-sample performance. I apply the new method to measure the effect of smoking during pregnancy on birthweight.