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This paper considers panel data models where the conditional quantiles of thedependent variables are additively separable as unknown functions of theregressors and the individual effects. We propose two estimators of thequantile partial effects while controlling for the individual heterogeneity.The first estimator is based on local linear quantile regressions, and thesecond is based on local linear smoothed quantile regressions, both of whichare easy to compute in practice. Within the large T framework, we providesufficient conditions under which the two estimators are shown to beasymptotically normally distributed. In particular, for the first estimator, itis shown that $N<<T^{2/(d+4)}$ is needed to ignore the incidental parameterbiases, where $d$ is the dimension of the regressors. For the second estimator,we are able to derive the analytical expression of the asymptotic biases underthe assumption that $N\approx Th^{d}$, where $h$ is the bandwidth parameter inlocal linear approximations. Our theoretical results provide the basis of usingsplit-panel jackknife for bias corrections. A Monte Carlo simulation shows thatthe proposed estimators and the bias-correction method perform well in finitesamples.

Nonparametric Quantile Regressions for Panel Data Models with Large T