IDEAS home Printed from https://ideas.repec.org/p/mse/cesdoc/14090.html
   My bibliography  Save this paper

On the Super-Additivity and Estimation Biases of Quantile Contributions

Author

Listed:

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," Documents de travail du Centre d'Economie de la Sorbonne 14090, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:14090
    as

    Download full text from publisher

    File URL: ftp://mse.univ-paris1.fr/pub/mse/CES2014/14090.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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).
    8. Andrea Fontanari & Nassim Nicholas Taleb & Pasquale Cirillo, 2017. "Gini estimation under infinite variance," Papers 1707.01370, arXiv.org, revised Dec 2017.
    9. Nassim Nicholas Taleb, 2015. "How to (Not) Estimate Gini Coefficients for Fat Tailed Variables," Papers 1510.04841, arXiv.org.
    10. 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.
    11. 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.
    12. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Foellmi, Reto & Martínez, Isabel Z., 2014. "Volatile Top Income Shares in Switzerland? Reassessing the Evolution Between 1981 and 2009," CEPR Discussion Papers 10006, C.E.P.R. Discussion Papers.
    2. Anthony B. Atkinson & Thomas Piketty & Emmanuel Saez, 2011. "Top Incomes in the Long Run of History," Journal of Economic Literature, American Economic Association, vol. 49(1), pages 3-71, March.
    3. Nassim Nicholas Taleb, 2018. "How Much Data Do You Need? An Operational, Pre-Asymptotic Metric for Fat-tailedness," Papers 1802.05495, arXiv.org, revised Nov 2018.
    4. Taleb, Nassim Nicholas, 2019. "How much data do you need? An operational, pre-asymptotic metric for fat-tailedness," International Journal of Forecasting, Elsevier, vol. 35(2), pages 677-686.
    5. Nicholas Rohde, 2016. "J-divergence measurements of economic inequality," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 179(3), pages 847-870, June.
    6. 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.
    7. von Fintel, Dieter & Orthofer, Anna, 2020. "Wealth inequality and financial inclusion: Evidence from South African tax and survey records," Economic Modelling, Elsevier, vol. 91(C), pages 568-578.
    8. Abduraimova, Kumushoy, 2022. "Contagion and tail risk in complex financial networks," Journal of Banking & Finance, Elsevier, vol. 143(C).
    9. SAITO Yukiko, 2013. "Role of Hub Firms in Geographical Transaction Network," Discussion papers 13080, Research Institute of Economy, Trade and Industry (RIETI).
    10. Alan J. Auerbach, 2006. "The Future of Capital Income Taxation," Fiscal Studies, Institute for Fiscal Studies, vol. 27(4), pages 399-420, December.
    11. Fabbri, Francesca & Marin, Dalia, 2012. "What explains the rise in CEO pay in Germany? A Panel Data Analysis for 1977-2009," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 374, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    12. Rey, Sergio, 2015. "Bells in Space: The Spatial Dynamics of US Interpersonal and Interregional Income Inequality," MPRA Paper 69482, University Library of Munich, Germany.
    13. Dominik Prochniewicz & Jacek Kudrys & Kamil Maciuk, 2022. "Noises in Double-Differenced GNSS Observations," Energies, MDPI, vol. 15(5), pages 1-18, February.
    14. Stefan Bach & Giacomo Corneo & Viktor Steiner, 2007. "From Bottom to Top: The Entire Distribution of Market Income in Germany, 1992-2001," SOEPpapers on Multidisciplinary Panel Data Research 51, DIW Berlin, The German Socio-Economic Panel (SOEP).
    15. Timm Bönke & Markus M. Grabka & Carsten Schröder & Edward N. Wolff & Lennard Zyska, 2019. "The Joint Distribution of Net Worth and Pension Wealth in Germany," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 65(4), pages 834-871, December.
    16. Nikos Koutsiaras, 2010. "How to Spend it: Putting a Labour Market Modernization Fund in Place of the European Globalization Adjustment Fund," Journal of Common Market Studies, Wiley Blackwell, vol. 48(3), pages 617-640, June.
    17. Ross Richardson & Matteo G. Richiardi & Michael Wolfson, 2015. "We ran one billion agents. Scaling in simulation models," LABORatorio R. Revelli Working Papers Series 142, LABORatorio R. Revelli, Centre for Employment Studies.
    18. Igor Fedotenkov, 2020. "A Review of More than One Hundred Pareto-Tail Index Estimators," Statistica, Department of Statistics, University of Bologna, vol. 80(3), pages 245-299.
    19. Harmenberg, Karl, 2020. "A Simple Theory of Pareto Earnings," Working Papers 21-2020, Copenhagen Business School, Department of Economics.
    20. Da Silva, Sergio, 2009. "Does Macroeconomics Need Microeconomic Foundations?," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 3, pages 1-11.

    More about this item

    Keywords

    Law of large numbers; fat tails; quantile contribution; Gini Coefficent;
    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:mse:cesdoc:14090. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Lucie Label (email available below). General contact details of provider: https://edirc.repec.org/data/cenp1fr.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.