Measuring heterogeneity with fixed effect quantile regression: Long panels and short panels

Abstract

The desire to capture heterogeneity in the response of the dependent variable to covariates often forces empiricists to employ panel data quantile regression models. Very often practitioners forget the limitations of their datasets in terms of the sample size n and the length of panel T. Yet, quantile regression requires large samples, long panels and small value of the ratio n/T. So the estimator in quantile regression with short panels is biased. The paper reviews the approaches for estimating longitudinal models for quantile regression. We highlight the fact that a method of smoothed quantile regression may be viewed as a remedy for reducing the asymptotic bias of the estimator in short panels, both in case of quantile-dependent and quantile-independent fixed effect specifications.