Reconsideration of a simple approach to quantile regression for panel data: a comment on the Canay (2011) fixed effects estimator

Estimation of individual effects in quantile regression can be difficult in large panel datasets, but a solution is apparently offered by a computationally simple estimator by Ivan Canay (2011, The Econometrics Journal) for quantile-independent individual effects. The Canay estimator is widely used by practitioners and is often cited in the theoretical literature. However, our paper discusses two fallacies in Canay's approach. We formally prove that Canay's assumptions can entail severe bias or even non-existence of the limiting distribution for the estimator of the vector of coefficients, leading to incorrect inference. A second problem is incorrect asymptotic standard error of the estimator of the constant term. In an attempt to improve Canay's estimator, we propose a simple correction which may reduce the bias. Regarding the constant term, we focus on the fact that finding a sqrt(nT) consistent first step estimator may be problematic. Finally, we give recommendations to practitioners in terms of different values of n=T, and conduct a meta-review of applied papers, which use Canay's estimator.