Abstract
This paper studies panel quantile regression models with individual fixed effects. We formally establish sufficient conditions for consistency and asymptotic normality of the quantile regression estimator when the number of individuals, n, and the number of time periods, T, jointly go to infinity. The estimator is shown to be consistent under similar conditions to those found in the nonlinear panel data literature. Nevertheless, due to the non-smoothness of the objective function, we had to impose a more restrictive condition on T to prove asymptotic normality than that usually found in the literature. The finite sample performance of the estimator is evaluated by Monte Carlo simulations.
Highlights
Quantile regression (QR) for panel data has attracted considerable interest in both the theoretical and applied literatures
It should be pointed out that the above rate of the remainder term is the best one that we could achieve, there might be a room for improvement on the rate, which means that our condition for the asymptotic normality is only a sufficient one
We have studied the asymptotic properties of the fixed effects quantile regression (FE-QR) estimator
Summary
Quantile regression (QR) for panel data has attracted considerable interest in both the theoretical and applied literatures. It is important to note that, in contrast to mean regression, to our knowledge, there is no general transformation that can suitably eliminate the individual effects in the QR model Given these difficulties, in the QR panel data literature, it is usual to allow T to increase to infinity to achieve asymptotically unbiased estimators. Among them, Hahn and Newey (2004) studied the maximum likelihood estimation of a general nonlinear panel data model with individual effects They showed that the maximum likelihood estimator (MLE) has a limiting normal distribution with a bias in the mean when n and T grow at the same rate, and proposed several bias correction methods to the MLE.
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