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

The paper discusses two errors in the approach proposed in Canay (2011) for constructing a computationally simple two-step estimator in a quantile regression model with quantile-independent fixed effects. Firstly, we show that Canay's assumption about n/T^s --> 0 for some s>1 is not strong enough and can entail severe bias or even non-existence of the limiting distribution for the estimator of the vector of coefficients. The condition n/T --> 0 appears to be closer to the required set of restrictions. These problems are likely to cause incorrect inference in applied papers with large n/T, but the impact is less in applications with small n/T. In an attempt to improve Canay's estimator, we propose a simple correction which may reduce the bias. The second error concerns incorrect asymptotic standard error of the estimator of the constant term. We show that contrary to Canay's assumption, the within estimator has an influence function that is not i.i.d. and this affects inference. Moreover, the constant term is unlikely to be estimable at rate sqrt{nT}, so a different estimator may not be available. However, the issue concerning the constant term does not have an effect on slope coefficients. Finally, we give recommendations to practitioners and conduct a meta-review of applied papers that use Canay's estimator.