Censored panel quantile regression with fixed effects via an asymmetric link function

In this study, we consider 2- and 3-step estimators for censored quantile regression models with fixed effects. In the first step of these estimators, the informative subset is determined through the estimation of censoring probability. While previous studies often employ symmetric link functions for estimating the censoring probability, these may not accurately identify the best subset when the distribution of the censoring probability is skewed. Given the prevalence of asymmetrically censored data in empirical analyses, we propose using an asymmetric link function for more accurate subset determination. We conduct Monte Carlo simulations and empirical analysis to assess our proposed methods. Our Monte Carlo simulations and empirical analysis confirm that an asymmetric link function offers a better fit for asymmetrically censored data. For symmetrically censored data, the symmetric link function performs better in moderate and large samples, while the asymmetric link function performs slightly better in small samples. These findings underscore the importance of considering both the censoring probability distribution and sample size in panel quantile regression.