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Estimation and Inference about Tail Features with Tail Censored Data

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  • Yulong Wang

    (Syracuse University)

  • Zhijie Xiao

    (Boston College)

Abstract

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 Ursúa (2008). Our new empirical findings are substantially different from the existing literature.

Suggested Citation

  • Yulong Wang & Zhijie Xiao, 2020. "Estimation and Inference about Tail Features with Tail Censored Data," Boston College Working Papers in Economics 994, Boston College Department of Economics.
    • Handle: RePEc:boc:bocoec:994
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    References listed on IDEAS

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    1. Graham Elliott & Ulrich K. Müller & Mark W. Watson, 2015. "Nearly Optimal Tests When a Nuisance Parameter Is Present Under the Null Hypothesis," Econometrica, Econometric Society, vol. 83, pages 771-811, March.
    2. Robert J. Barro & Tao Jin, 2011. "On the Size Distribution of Macroeconomic Disasters," Econometrica, Econometric Society, vol. 79(5), pages 1567-1589, September.
    3. Han Hong & Elie Tamer, 2003. "Inference in Censored Models with Endogenous Regressors," Econometrica, Econometric Society, vol. 71(3), pages 905-932, May.
    4. Victor Chernozhukov & Iván Fernández-Val, 2011. "Inference for Extremal Conditional Quantile Models, with an Application to Market and Birthweight Risks," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(2), pages 559-589.
    5. Lasse Eika & Magne Mogstad & Basit Zafar, 2019. "Educational Assortative Mating and Household Income Inequality," Journal of Political Economy, University of Chicago Press, vol. 127(6), pages 2795-2835.
    6. Giesen, Kristian & Zimmermann, Arndt & Suedekum, Jens, 2010. "The size distribution across all cities - Double Pareto lognormal strikes," Journal of Urban Economics, Elsevier, vol. 68(2), pages 129-137, September.
    7. Portnoy S., 2003. "Censored Regression Quantiles," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 1001-1012, January.
    8. Alexis Akira Toda & Yulong Wang, 2021. "Efficient minimum distance estimation of Pareto exponent from top income shares," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(2), pages 228-243, March.
    9. Aban, Inmaculada B. & Meerschaert, Mark M. & Panorska, Anna K., 2006. "Parameter Estimation for the Truncated Pareto Distribution," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 270-277, March.
    10. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
    11. Powell, James L., 1986. "Censored regression quantiles," Journal of Econometrics, Elsevier, vol. 32(1), pages 143-155, June.
    12. Brzezinski, Michal, 2013. "Asymptotic and bootstrap inference for top income shares," Economics Letters, Elsevier, vol. 120(1), pages 10-13.
    13. Ulrich K. Müller & Yulong Wang, 2017. "Fixed- Asymptotic Inference About Tail Properties," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1334-1343, July.
    14. Xavier Gabaix & Rustam Ibragimov, 2011. "Rank - 1 / 2: A Simple Way to Improve the OLS Estimation of Tail Exponents," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(1), pages 24-39, January.
    15. Reed, William J., 2003. "The Pareto law of incomes—an explanation and an extension," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 319(C), pages 469-486.
    16. Philip Armour & Richard V. Burkhauser & Jeff Larrimore, 2013. "Deconstructing Income and Income Inequality Measures: A Crosswalk from Market Income to Comprehensive Income," American Economic Review, American Economic Association, vol. 103(3), pages 173-177, May.
    17. Toda, Alexis Akira, 2012. "The double power law in income distribution: Explanations and evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 84(1), pages 364-381.
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    More about this item

    Keywords

    Extreme Value theory; power law; extreme quantile; tail index;
    All these keywords.

    JEL classification:

    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics

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