Bias Correction and Inference for Panel Quantile Regression

Abstract

We develop a large-$n$, large-$T$ theory for the unsmoothed fixed-effects quantile regression estimator, paralleling Hahn and Newey (2004) for smooth nonlinear panel models. An exact rank-score identity for the profiled criterion, with a convexity argument, delivers the leading incidental parameter bias of the slope estimator, of order $T^{-1}$, in closed form. When $n$ and $T$ grow at the same rate, the estimator is asymptotically normal but in general not centred, and conventional intervals are invalid. Admissible growth of $n$ relative to $T$, up to $n=o(T^3)$, depends on the regularity of the conditional error densities. A split-panel jackknife removes the leading bias throughout this range and yields valid inference. In serially dependent panels whose dependence decays geometrically or polynomially, the bias acquires a term from the dependence between regressors and errors of different periods, the jackknife remains valid with contiguous but not with interleaved half-panels, and clustered standard errors are valid.