On the Unbiased Asymptotic Normality of Quantile Regression with Fixed Effects

TL;DR

This paper proves that quantile regression with fixed effects in panel data models is asymptotically unbiased and normally distributed under conditions similar to other nonlinear models, bridging a theoretical gap.

Contribution

It establishes the asymptotic unbiased normality of quantile regression with fixed effects under standard conditions, improving existing theoretical understanding.

Findings

Quantile regression with fixed effects is asymptotically normal.

Results hold under conditions similar to other nonlinear panel models.

Numerical experiments confirm theoretical results.

Abstract

Nonlinear panel data models with fixed individual effects provide an important set of tools for describing microeconometric data. In a large class of such models (including probit, proportional hazard and quantile regression to name just a few) it is impossible to difference out individual effects, and inference is usually justified in a `large n large T' asymptotic framework. However, there is a considerable gap in the type of assumptions that are currently imposed in models with smooth score functions (such as probit, and proportional hazard) and quantile regression. In the present paper we show that this gap can be bridged and establish asymptotic unbiased normality for quantile regression panels under conditions on n,T that are very close to what is typically assumed in standard nonlinear panels. Our results considerably improve upon existing theory and show that quantile regression is applicable to the same type of panel data (in terms of n,T) as other commonly used nonlinear panel data models. Thorough numerical experiments confirm our theoretical findings.