  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.
