Estimation and inference about tail features with tail censored data

This paper considers estimation and inference about tail features such as tail index and extreme quantile when the observations beyond some threshold are censored. Ignoring such tail censoring could lead to substantial bias and size distortion, even if the censored probability is tiny. We first propose a new maximum likelihood estimator (MLE) based on the Pareto tail approximation and derive its asymptotic properties. Then, we propose an alternative method of constructing confidence intervals by resorting to extreme value theory. The MLE and the confidence intervals deliver excellent small sample performance, as shown by Monte Carlo simulations. Finally, we apply the proposed methods to estimate and construct confidence intervals for the tail index of the distribution of macroeconomic disasters and the coefficient of risk aversion using the dataset collected by Barro and Ursúa (2008). Our empirical findings are substantially different from those obtained from the existing methods.