A Simple Estimator for Quantile Panel Data Models Using Smoothed Quantile Regressions

TL;DR

This paper revisits Canay's simple two-step estimator for quantile panel data models, identifies bias issues in its asymptotic analysis, and proposes a bias-corrected estimator using smoothed quantile regressions with validated finite sample performance.

Contribution

It introduces a bias-corrected estimator for quantile panel data models based on smoothed regressions, improving inference accuracy over Canay's original method.

Findings

The new estimator has an explicit asymptotic distribution.

Bias correction methods improve inference validity.

Finite sample simulations confirm the effectiveness of bias correction.

Abstract

Canay (2011)'s two-step estimator of quantile panel data models, due to its simple intuition and low computational cost, has been widely used in empirical studies in recent years. In this paper, we revisit the estimator of Canay (2011) and point out that in his asymptotic analysis the bias of his estimator due to the estimation of the fixed effects is mistakenly omitted, and that such omission will lead to invalid inference on the coefficients. To solve this problem, we propose a similar easy-to-implement estimator based on smoothed quantile regressions. The asymptotic distribution of the new estimator is established and the analytical expression of its asymptotic bias is derived. Based on these results, we show how to make asymptotically valid inference based on both analytical and split-panel jackknife bias corrections. Finally, finite sample simulations are used to support our theoretical analysis and to illustrate the importance of bias correction in quantile regressions for panel data.