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On the Super-Additivity and Estimation Biases of Quantile Contributions

Author

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  • Nassim Nicholas Taleb

    (NYU Polytechnic School of Engineering)

  • Raphaël Douady

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, Riskdata - Financial Risk Management Software)

Abstract

Sample measures of top centile contributions to the total (concentration) are downward biased, unstable estimators, extremely sensitive to sample size and concave in accounting for large deviations. It makes them particularly unfit in domains with power law tails, especially for low values of the exponent. These estimators can vary over time and increase with the population size, as shown in this article, thus providing the illusion of structural changes in concentration. They are also inconsistent under aggregation and mixing distributions, as the weighted average of concentration measures for A and B will tend to be lower than that from A ∪ B. In addition, it can be shown that under such fat tails, increases in the total sum need to be accompanied by increased sample size of the concentration measurement. We examine the estimation superadditivity and bias under homogeneous and mixed distributions.

Suggested Citation

  • Nassim Nicholas Taleb & Raphaël Douady, 2014. "On the Super-Additivity and Estimation Biases of Quantile Contributions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01149834, HAL.
    • Handle: RePEc:hal:cesptp:hal-01149834
    Note: View the original document on HAL open archive server: https://hal.science/hal-01149834
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    References listed on IDEAS

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    1. Thomas Piketty & Emmanuel Saez, 2006. "The Evolution of Top Incomes: A Historical and International Perspective," American Economic Review, American Economic Association, vol. 96(2), pages 200-205, May.
    2. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, May.
    3. Singh, S K & Maddala, G S, 1978. "A Function for Size Distribution of Incomes: Reply," Econometrica, Econometric Society, vol. 46(2), pages 461-461, March.
    4. Dagum, Camilo, 1980. "Inequality Measures between Income Distributions with Applications," Econometrica, Econometric Society, vol. 48(7), pages 1791-1803, November.
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    Cited by:

    1. Thomas Blanchet & Lucas Chancel & Amory Gethin, 2019. "How Unequal is Europe? Evidence from Distributional National Accounts, 1980-2017," World Inequality Lab Working Papers hal-02877000, HAL.
    2. Demetrio Guzzardi & Elisa Palagi & Andrea Roventini & Alessandro Santoro, 2022. "Reconstructing Income Inequality in Italy: New Evidence and Tax Policy Implications from Distributional National Accounts," World Inequality Lab Working Papers halshs-03693201, HAL.
    3. Thomas Blanchet & Juliette Fournier & Thomas Piketty, 2022. "Generalized Pareto Curves: Theory and Applications," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 68(1), pages 263-288, March.
    4. Thomas Blanchet & Lucas Chancel & Amory Gethin, 2022. "Why Is Europe More Equal than the United States?," American Economic Journal: Applied Economics, American Economic Association, vol. 14(4), pages 480-518, October.
    5. Maia, Adriano & Matsushita, Raul & Da Silva, Sergio, 2020. "Earnings distributions of scalable vs. non-scalable occupations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 560(C).
    6. Fontanari, Andrea & Taleb, Nassim Nicholas & Cirillo, Pasquale, 2018. "Gini estimation under infinite variance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 256-269.
    7. Thomas Blanchet & Ignacio Flores & Marc Morgan, 2022. "The weight of the rich: improving surveys using tax data," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 20(1), pages 119-150, March.
    8. Pablo Gutiérrez Cubillos, 2022. "Gini and undercoverage at the upper tail: a simple approximation," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 29(2), pages 443-471, April.
    9. Carranza, Rafael & De Rosa, Mauricio & Flores, Ignacio, 2023. "Wealth inequality in Latin America," LSE Research Online Documents on Economics 119426, London School of Economics and Political Science, LSE Library.
    10. Andrea Fontanari & Nassim Nicholas Taleb & Pasquale Cirillo, 2017. "Gini estimation under infinite variance," Papers 1707.01370, arXiv.org, revised Dec 2017.
    11. Nassim Nicholas Taleb, 2015. "How to (Not) Estimate Gini Coefficients for Fat Tailed Variables," Papers 1510.04841, arXiv.org.
    12. Ignacio Flores, 2021. "The capital share and income inequality: Increasing gaps between micro and macro-data," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 19(4), pages 685-706, December.

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    More about this item

    Keywords

    law of large numbers; fat tails; quantile contribution; Gini coefficient;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions

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