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.

本文考虑对超过某个阈值的观测值进行删失时对尾部特征（如尾部指数和极值分位数）的估计和推断。忽略这种尾部审查可能会导致严重的偏差和尺寸失真，即使审查的概率很小。我们首先提出了一种基于帕累托尾近似的新的最大似然估计器（MLE），并推导出其渐近特性。然后，我们提出了一种利用极值理论构建置信区间的替代方法。如蒙特卡罗模拟所示，MLE 和置信区间可提供出色的小样本性能。最后，我们使用 Barro 和 Ursúa（2008 年）收集的数据集应用所提出的方法来估计和构建宏观经济灾害分布的尾部指数和风险厌恶系数的置信区间。我们的实证结果与从现有方法中获得的结果大不相同。