[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/a/eee/jeborg/v84y2012i1p364-381.html
   My bibliography  Save this article

The double power law in income distribution: Explanations and evidence

Author

Listed:
  • Toda, Alexis Akira
Abstract
Conditional on education and experience, the distribution of personal labor income appears to be double Pareto, a distribution that obeys the power law in both the upper and lower tails. In particular, the error term of the classical Mincer equation appears to be Laplace, or double exponential. This “double power law” is not rejected by goodness-of-fit tests. I compare two diffusion processes (one mean-reverting, the other unit root) with a stationary double Pareto distribution as a model of income dynamics. The data favors the mean-reverting process for modeling income dynamics over the unit root process.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jeborg:v:84:y:2012:i:1:p:364-381
    DOI: 10.1016/j.jebo.2012.04.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167268112000923
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jebo.2012.04.012?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. Lillard, Lee A & Willis, Robert J, 1978. "Dynamic Aspects of Earning Mobility," Econometrica, Econometric Society, vol. 46(5), pages 985-1012, September.
    3. Martin Browning & Mette Ejrnæs & Javier Alvarez, 2010. "Modelling Income Processes with Lots of Heterogeneity," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(4), pages 1353-1381.
    4. Foley Duncan K., 1994. "A Statistical Equilibrium Theory of Markets," Journal of Economic Theory, Elsevier, vol. 62(2), pages 321-345, April.
    5. Jacob A. Mincer, 1974. "Introduction to "Schooling, Experience, and Earnings"," NBER Chapters, in: Schooling, Experience, and Earnings, pages 1-4, National Bureau of Economic Research, Inc.
    6. Hodrick, Robert J & Prescott, Edward C, 1997. "Postwar U.S. Business Cycles: An Empirical Investigation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 29(1), pages 1-16, February.
    7. Majumder, Amita & Chakravarty, Satya Ranjan, 1990. "Distribution of Personal Income: Development of a New Model and Its Application to U.S. Income Data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 189-196, April-Jun.
    8. Salem, A B Z & Mount, T D, 1974. "A Convenient Descriptive Model of Income Distribution: The Gamma Density," Econometrica, Econometric Society, vol. 42(6), pages 1115-1127, November.
    9. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, May.
    10. Jacob A. Mincer, 1974. "Schooling, Experience, and Earnings," NBER Books, National Bureau of Economic Research, Inc, number minc74-1.
    11. 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.
    12. Dagum, Camilo, 1980. "Inequality Measures between Income Distributions with Applications," Econometrica, Econometric Society, vol. 48(7), pages 1791-1803, November.
    13. Costas Meghir & Luigi Pistaferri, 2004. "Income Variance Dynamics and Heterogeneity," Econometrica, Econometric Society, vol. 72(1), pages 1-32, January.
    14. Silver, Jonathan & Slud, Eric & Takamoto, Keiji, 2002. "Statistical Equilibrium Wealth Distributions in an Exchange Economy with Stochastic Preferences," Journal of Economic Theory, Elsevier, vol. 106(2), pages 417-435, October.
    15. Singh, S K & Maddala, G S, 1976. "A Function for Size Distribution of Incomes," Econometrica, Econometric Society, vol. 44(5), pages 963-970, September.
    16. Milton Friedman, 1953. "Choice, Chance, and the Personal Distribution of Income," Journal of Political Economy, University of Chicago Press, vol. 61(4), pages 277-277.
    17. Jacob A. Mincer, 1974. "Schooling and Earnings," NBER Chapters, in: Schooling, Experience, and Earnings, pages 41-63, National Bureau of Economic Research, Inc.
    18. A. Drăgulescu & V.M. Yakovenko, 2001. "Evidence for the exponential distribution of income in the USA," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 20(4), pages 585-589, April.
    19. Shoshana Grossbard (ed.), 2006. "Jacob Mincer A Pioneer of Modern Labor Economics," Springer Books, Springer, number 978-0-387-29175-8, December.
    20. James B. McDonald, 2008. "Some Generalized Functions for the Size Distribution of Income," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 3, pages 37-55, Springer.
    21. Reed, William J., 2001. "The Pareto, Zipf and other power laws," Economics Letters, Elsevier, vol. 74(1), pages 15-19, December.
    22. 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.
    23. William J. Reed & Fan Wu, 2008. "New Four- and Five-Parameter Models for Income Distributions," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 11, pages 211-223, Springer.
    24. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    25. Lillard, Lee A & Weiss, Yoram, 1979. "Components of Variation in Panel Earnings Data: American Scientists, 1960-70," Econometrica, Econometric Society, vol. 47(2), pages 437-454, March.
    26. MaCurdy, Thomas E., 1982. "The use of time series processes to model the error structure of earnings in a longitudinal data analysis," Journal of Econometrics, Elsevier, vol. 18(1), pages 83-114, January.
    27. Benoit Mandelbrot, 1963. "New Methods in Statistical Economics," Journal of Political Economy, University of Chicago Press, vol. 71(5), pages 421-421.
    28. 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.
    29. Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(3), pages 739-767.
    30. Alfarano, Simone & Milaković, Mishael & Irle, Albrecht & Kauschke, Jonas, 2012. "A statistical equilibrium model of competitive firms," Journal of Economic Dynamics and Control, Elsevier, vol. 36(1), pages 136-149.
    31. Neal, Derek & Rosen, Sherwin, 2000. "Theories of the distribution of earnings," Handbook of Income Distribution, in: A.B. Atkinson & F. Bourguignon (ed.), Handbook of Income Distribution, edition 1, volume 1, chapter 7, pages 379-427, Elsevier.
    32. Alexis Toda, 2010. "Existence of a statistical equilibrium for an economy with endogenous offer sets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(3), pages 379-415, December.
    33. Jacob Mincer, 1958. "Investment in Human Capital and Personal Income Distribution," Journal of Political Economy, University of Chicago Press, vol. 66(4), pages 281-281.
    Full references (including those not matched with items on IDEAS)

    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. Magnac, Thierry & Pistolesi, Nicolas & Roux, Sébastien, 2013. "Post schooling human capital investments and the life cycle variance of earnings," IDEI Working Papers 765, Institut d'Économie Industrielle (IDEI), Toulouse.
    2. Vladimir Hlasny, 2021. "Parametric representation of the top of income distributions: Options, historical evidence, and model selection," Journal of Economic Surveys, Wiley Blackwell, vol. 35(4), pages 1217-1256, September.
    3. Paul Bingley & Lorenzo Cappellari & Niels Westergård‐Nielsen, 2013. "Unemployment Insurance, Wage Dynamics and Inequality Over the Life Cycle," Economic Journal, Royal Economic Society, vol. 0, pages 341-372, May.
    4. Ramos, Arturo & Sanz-Gracia, Fernando & González-Val, Rafael, 2013. "A new framework for the US city size distribution: Empirical evidence and theory," MPRA Paper 52190, University Library of Munich, Germany.
    5. Mirko Felchner, 2015. "Einkommensdynamik bei Selbständigen als Freie Berufe und abhängig Beschäftigte Eine dynamische Paneldatenschätzung mit Daten des Sozio-oekonomischen Panels," FFB-Discussionpaper 101, Research Institute on Professions (Forschungsinstitut Freie Berufe (FFB)), LEUPHANA University Lüneburg.
    6. Seik Kim, 2010. "Uncertainty in Human Capital Investment and Earnings Dynamics," Journal of Human Capital, University of Chicago Press, vol. 4(1), pages 62-83.
    7. Huggett, Mark & Ventura, Gustavo & Yaron, Amir, 2006. "Human capital and earnings distribution dynamics," Journal of Monetary Economics, Elsevier, vol. 53(2), pages 265-290, March.
    8. Toda, Alexis Akira, 2017. "A Note On The Size Distribution Of Consumption: More Double Pareto Than Lognormal," Macroeconomic Dynamics, Cambridge University Press, vol. 21(6), pages 1508-1518, September.
    9. Gustavsson, Magnus & Österholm, Pär, 2014. "Does the labor-income process contain a unit root? Evidence from individual-specific time series," Journal of Economic Dynamics and Control, Elsevier, vol. 47(C), pages 152-167.
    10. Jesper Bagger & Fran?ois Fontaine & Fabien Postel-Vinay & Jean-Marc Robin, 2014. "Tenure, Experience, Human Capital, and Wages: A Tractable Equilibrium Search Model of Wage Dynamics," American Economic Review, American Economic Association, vol. 104(6), pages 1551-1596, June.
    11. Bayer, Christian & Kuhn, Moritz, 2018. "Which Ladder to Climb? Wages of Workers by Job, Plant, and Education," IZA Discussion Papers 11827, Institute of Labor Economics (IZA).
    12. 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.
    13. Bayer, Christian & Kuhn, Moritz, 2018. "Which Ladder to Climb? Decomposing Life Cycle Wage Dynamics," CEPR Discussion Papers 13158, C.E.P.R. Discussion Papers.
    14. Denisa Maria Sologon & Cathal O'Donoghue, 2009. "Earnings Dynamics and Inequality in EU, 1994-2001," SOEPpapers on Multidisciplinary Panel Data Research 184, DIW Berlin, The German Socio-Economic Panel (SOEP).
    15. Behzod B. Ahundjanov & Sherzod B. Akhundjanov & Botir B. Okhunjanov, 2022. "Power law in COVID‐19 cases in China," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(2), pages 699-719, April.
    16. Jin Seo Cho & Peter C. B. Phillips & Juwon Seo, 2022. "Parametric Conditional Mean Inference With Functional Data Applied To Lifetime Income Curves," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(1), pages 391-456, February.
    17. Sologon, Denisa Maria & O'Donoghue, Cathal, 2009. "Earnings Dynamics and Inequality among Men across 14 EU Countries, 1994-2001: Evidence from ECHP," IZA Discussion Papers 4012, Institute of Labor Economics (IZA).
    18. Jean-Marc Fournier & Isabell Koske, 2012. "The determinants of earnings inequality: evidence from quantile regressions," OECD Journal: Economic Studies, OECD Publishing, vol. 2012(1), pages 7-36.
    19. Fortin, Bernard & Ragued, Safa, 2017. "Does temporary interruption in postsecondary education induce a wage penalty? Evidence from Canada," Economics of Education Review, Elsevier, vol. 58(C), pages 108-122.
    20. Jesper Bagger & Francois Fontaine & Fabien Postel-Vinay & Jean-Marc Robin, 2014. "Tenure, Experience, Human Capital, and Wages," Post-Print hal-01301431, HAL.

    More about this item

    Keywords

    Anderson–Darling test; Diffusion processes; Fokker–Planck equation; Kolmogorov–Smirnov test; Laplace distribution; Mincer equation; Power law;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • J3 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs

    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:eee:jeborg:v:84:y:2012:i:1:p:364-381. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jebo .

    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.