Nonparametric Quantile Regressions for Panel Data Models with Large T

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