Estimation and inference about tail features with tail censored data

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