Yulong Wang, Zhijie Xiao
arXiv 23 Feb 2020 · Econometrics
arXiv:2002.09982 · PDF · Extracted main text
This paper considers estimation and inference about tail features when the observations beyond some threshold are censored. We first show that ignoring such tail censoring could lead to substantial bias and size distortion, even if the censored probability is tiny. Second, we propose a new maximum likelihood estimator (MLE) based on the Pareto tail approximation and derive its asymptotic properties. Third, we provide a small sample modification to the MLE by resorting to Extreme Value theory. The MLE with this modification delivers excellent small sample performance, as shown by Monte Carlo simulations. We illustrate its empirical relevance by estimating (i) the tail index and the extreme quantiles of the US individual earnings with the Current Population Survey dataset and (ii) the tail index of the distribution of macroeconomic disasters and the coefficient of risk aversion using the dataset collected by Barro and Urs{\'u}a (2008). Our new empirical findings are substantially different from the existing literature.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Barro and Jin (2011) On the Size Distribution of Macroeconomic Disasters | 0.874 | 10 | 2 | 100% |
| 2 | Barro and Ursúa (2008) Macroeconomic Crisis Since 1870 | 0.843 | 3 | 3 | 100% |
| 3 | de Haan and Ferreira (2007) Extreme Value Theory: An Introduction | 0.794 | 10 | 5 | 50% |
| 4 | Gabaix and Ibragimov (2011) Rank-1/2: A Simple Way to Improve the OLS Estimation of Tail Exponents | 0.737 | 3 | 2 | 100% |
| 5 | Elliott, Müller, and Watson (2015) Nearly Optimal Tests When a Nuisance Parameter is Present under the Null Hypothesis | 0.644 | 3 | 2 | 67% |
| 6 | Hall (1982) On Some Simple Estimates of an Exponent of Regular Variation | 0.644 | 2 | 2 | 100% |
| 7 | Hill (1975) A Simple General Approach to Inference about the Tail of a Distribution | 0.644 | 2 | 2 | 100% |
| 8 | Müller and Wang (2017) Fixed-k Asymptotic Inference about Tail Properties | 0.644 | 2 | 2 | 100% |
| 9 | Smith (1987) Estimating Tails of Probability Distributions | 0.606 | 6 | 2 | 33% |
| 10 | Goldie and Smith (1987) Slow Variation with Remainder: Theory and Applications | 0.511 | 2 | 2 | 50% |
Showing the top 10 of 37 scored citations.