IDEAS home Printed from https://ideas.repec.org/a/aea/aejmac/v9y2017i3p36-71.html
   My bibliography  Save this article

Zipf's Law, Pareto's Law, and the Evolution of Top Incomes in the United States

Author

Listed:
  • Shuhei Aoki
  • Makoto Nirei

Abstract

We construct a tractable neoclassical growth model that generates Pareto's law of income distribution and Zipf's law of the firm size distribution from idiosyncratic, firm-level productivity shocks. Executives and entrepreneurs invest in risk-free assets, as well as their own firms' risky stocks, through which their wealth and income depend on firm-level shocks. By using the model, we evaluate how changes in tax rates can account for the evolution of top incomes in the United States. The model matches the decline in the Pareto exponent of the income distribution and the trend of the top 1 percent income share in recent decades.

Suggested Citation

  • Shuhei Aoki & Makoto Nirei, 2017. "Zipf's Law, Pareto's Law, and the Evolution of Top Incomes in the United States," American Economic Journal: Macroeconomics, American Economic Association, vol. 9(3), pages 36-71, July.
    • Handle: RePEc:aea:aejmac:v:9:y:2017:i:3:p:36-71
    Note: DOI: 10.1257/mac.20150051
    as

    Download full text from publisher

    File URL: https://www.aeaweb.org/articles?id=10.1257/mac.20150051
    Download Restriction: no
    File URL: https://www.aeaweb.org/articles/attachments?retrieve=hkLfN6-h04ZLlRtJ6qAiDUvEZLn8c9GM
    Download Restriction: no
    File URL: https://www.aeaweb.org/articles/attachments?retrieve=NY2uHhgMJwikQtAtdrGvDord5tLBewy5
    Download Restriction: Access to full text is restricted to AEA members and institutional subscribers.
    ---><---

    References listed on IDEAS

    as
    1. Jess Benhabib & Alberto Bisin & Shenghao Zhu, 2011. "The Distribution of Wealth and Fiscal Policy in Economies With Finitely Lived Agents," Econometrica, Econometric Society, vol. 79(1), pages 123-157, January.
    2. Steven J. Davis & John Haltiwanger & Ron Jarmin & Javier Miranda, 2007. "Volatility and Dispersion in Business Growth Rates: Publicly Traded versus Privately Held Firms," NBER Chapters, in: NBER Macroeconomics Annual 2006, Volume 21, pages 107-180, National Bureau of Economic Research, Inc.
    3. Charles I. Jones, 2015. "Pareto and Piketty: The Macroeconomics of Top Income and Wealth Inequality," Journal of Economic Perspectives, American Economic Association, vol. 29(1), pages 29-46, Winter.
    4. Xavier Gabaix & Augustin Landier, 2008. "Why has CEO Pay Increased So Much?," The Quarterly Journal of Economics, Oxford University Press, vol. 123(1), pages 49-100.
    5. Laurent E. Calvet & John Y. Campbell & Paolo Sodini, 2007. "Down or Out: Assessing the Welfare Costs of Household Investment Mistakes," Journal of Political Economy, University of Chicago Press, vol. 115(5), pages 707-747, October.
    6. Emmanuel Saez & Joel Slemrod & Seth H. Giertz, 2012. "The Elasticity of Taxable Income with Respect to Marginal Tax Rates: A Critical Review," Journal of Economic Literature, American Economic Association, vol. 50(1), pages 3-50, March.
    7. Thomas Piketty & Emmanuel Saez & Stefanie Stantcheva, 2014. "Optimal Taxation of Top Labor Incomes: A Tale of Three Elasticities," American Economic Journal: Economic Policy, American Economic Association, vol. 6(1), pages 230-271, February.
    8. Carola Frydman & Raven E. Saks, 2010. "Executive Compensation: A New View from a Long-Term Perspective, 1936--2005," Review of Financial Studies, Society for Financial Studies, vol. 23(5), pages 2099-2138.
    9. Hans-Werner Sinn, 1991. "Taxation and the Cost of Capital: The "Old" View, the "New" View, and Another View," NBER Chapters, in: Tax Policy and the Economy, Volume 5, pages 25-54, National Bureau of Economic Research, Inc.
    10. 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.
    11. Toda, Alexis Akira, 2014. "Incomplete market dynamics and cross-sectional distributions," Journal of Economic Theory, Elsevier, vol. 154(C), pages 310-348.
    12. Andreas Fagereng & Luigi Guiso & Davide Malacrino & Luigi Pistaferri, 2020. "Heterogeneity and Persistence in Returns to Wealth," Econometrica, Econometric Society, vol. 88(1), pages 115-170, January.
    13. Shuhei Aoki & Makoto Nirei, 2016. "Pareto Distribution of Income in Neoclassical Growth Models," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 20, pages 25-42, April.
    14. Tobias J. Moskowitz & Annette Vissing-Jørgensen, 2002. "The Returns to Entrepreneurial Investment: A Private Equity Premium Puzzle?," American Economic Review, American Economic Association, vol. 92(4), pages 745-778, September.
    15. Benhabib, Jess & Bisin, Alberto & Zhu, Shenghao, 2015. "The wealth distribution in Bewley economies with capital income risk," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 489-515.
    16. Makoto Nirei & Wataru Souma, 2007. "A Two Factor Model Of Income Distribution Dynamics," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 53(3), pages 440-459, September.
    17. Campbell, John Y. & Viceira, Luis M., 2002. "Strategic Asset Allocation: Portfolio Choice for Long-Term Investors," OUP Catalogue, Oxford University Press, number 9780198296942, Decembrie.
    18. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    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. Andrew Atkeson & Magnus Irie, 2020. "Understanding 100 Years of the Evolution of Top Wealth Shares in the U.S.: What is the Role of Family Firms?," NBER Working Papers 27465, National Bureau of Economic Research, Inc.
    2. Toda, Alexis Akira, 2019. "Wealth distribution with random discount factors," Journal of Monetary Economics, Elsevier, vol. 104(C), pages 101-113.
    3. Axelle Ferriere & Philipp Grubener & Gaston Navarro & Oliko Vardishvili, 2021. "Larger transfers financed with more progressive taxes? On the optimal design of taxes and transfers," Working Papers halshs-03466762, HAL.
    4. Beare, Brendan K. & Seo, Won-Ki & Toda, Alexis Akira, 2022. "Tail Behavior Of Stopped Lévy Processes With Markov Modulation," Econometric Theory, Cambridge University Press, vol. 38(5), pages 986-1013, October.
    5. Stachurski, John & Toda, Alexis Akira, 2019. "An impossibility theorem for wealth in heterogeneous-agent models with limited heterogeneity," Journal of Economic Theory, Elsevier, vol. 182(C), pages 1-24.
    6. 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.
    7. Andreas Fagereng & Luigi Guiso & Davide Malacrino & Luigi Pistaferri, 2020. "Heterogeneity and Persistence in Returns to Wealth," Econometrica, Econometric Society, vol. 88(1), pages 115-170, January.
    8. Lei, Xiaowen, 2019. "Information and Inequality," Journal of Economic Theory, Elsevier, vol. 184(C).
    9. Tetsugen HARUYAMA, 2021. "A Schumpeterian Exploration of Gini and Top/Bottom Income Shares," Discussion Papers 2125, Graduate School of Economics, Kobe University.
    10. Petar Jolakoski & Arnab Pal & Trifce Sandev & Ljupco Kocarev & Ralf Metzler & Viktor Stojkoski, 2022. "The fate of the American dream: A first passage under resetting approach to income dynamics," Papers 2212.13176, arXiv.org.
    11. Bayer, Christian & Rendall, Alan D. & Wälde, Klaus, 2019. "The invariant distribution of wealth and employment status in a small open economy with precautionary savings," Journal of Mathematical Economics, Elsevier, vol. 85(C), pages 17-37.
    12. NIREI Makoto & OIKAWA Koki & OROKU Masahiro, 2024. "Economic Growth through Basic Research by Firms: A science linkage approach," Discussion papers 24013, Research Institute of Economy, Trade and Industry (RIETI).
    13. Shenghao Zhu, 2019. "A Becker–Tomes model with investment risk," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(4), pages 951-981, June.
    14. Corrado Di Guilmi & Yoshi Fujiwara, 2020. "Does the supply network shape the firm size distribution? The Japanese case," CAMA Working Papers 2020-66, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    15. Gouin-Bonenfant, Emilien & Toda, Alexis Akira, 2018. "Pareto Extrapolation: Bridging Theoretical and Quantitative Models of Wealth Inequality," University of California at San Diego, Economics Working Paper Series qt90n2h2bb, Department of Economics, UC San Diego.
    16. Ji Hyung Lee & Yuya Sasaki & Alexis Akira Toda & Yulong Wang, 2021. "Fixed-k Tail Regression: New Evidence on Tax and Wealth Inequality from Forbes 400," Papers 2105.10007, arXiv.org, revised Sep 2022.
    17. Viktor Stojkoski & Petar Jolakoski & Arnab Pal & Trifce Sandev & Ljupco Kocarev & Ralf Metzler, 2021. "Income inequality and mobility in geometric Brownian motion with stochastic resetting: theoretical results and empirical evidence of non-ergodicity," Papers 2109.01822, arXiv.org.
    18. Joachim Hubmer & Per Krusell & Anthony A. Smith Jr., 2020. "Sources of US Wealth Inequality: Past, Present, and Future," NBER Chapters, in: NBER Macroeconomics Annual 2020, volume 35, pages 391-455, National Bureau of Economic Research, Inc.
    19. Émilien Gouin‐Bonenfant & Alexis Akira Toda, 2023. "Pareto extrapolation: An analytical framework for studying tail inequality," Quantitative Economics, Econometric Society, vol. 14(1), pages 201-233, January.

    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. Shuhei Aoki & Makoto Nirei, 2014. "Zipf's Law, Pareto's Law, and the Evolution of Top Incomes in the U.S," Working Papers e074, Tokyo Center for Economic Research.
    2. Aoki, Shuhei & Nirei, Makoto, 2013. "Pareto Distributions and the Evolution of Top Incomes in the U.S," MPRA Paper 47967, University Library of Munich, Germany.
    3. Dan Cao & Wenlan Luo, 2017. "Persistent Heterogeneous Returns and Top End Wealth Inequality," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 26, pages 301-326, October.
    4. Xavier Gabaix & Jean‐Michel Lasry & Pierre‐Louis Lions & Benjamin Moll, 2016. "The Dynamics of Inequality," Econometrica, Econometric Society, vol. 84, pages 2071-2111, November.
    5. Toda, Alexis Akira, 2019. "Wealth distribution with random discount factors," Journal of Monetary Economics, Elsevier, vol. 104(C), pages 101-113.
    6. Khieu, Hoang & Wälde, Klaus, 2023. "Capital income risk and the dynamics of the wealth distribution," Economic Modelling, Elsevier, vol. 122(C).
    7. Shuhei Aoki & Makoto Nirei & Kazufumi Yamana, 2018. "Risk-Taking, Inequality and Output in the Long-Run," Bank of Japan Working Paper Series 18-E-4, Bank of Japan.
    8. Hubar, Sylwia & Koulovatianos, Christos & Li, Jian, 2020. "The role of labor-income risk in household risk-taking," European Economic Review, Elsevier, vol. 129(C).
    9. Kasa, Kenneth & Lei, Xiaowen, 2018. "Risk, uncertainty, and the dynamics of inequality," Journal of Monetary Economics, Elsevier, vol. 94(C), pages 60-78.
    10. Shuhei Aoki & Makoto Nirei, 2016. "Pareto Distribution of Income in Neoclassical Growth Models," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 20, pages 25-42, April.
    11. Jan Schulz & Mishael Milaković, 2023. "How Wealthy are the Rich?," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 69(1), pages 100-123, March.
    12. Mariacristina De Nardi & Fella Giulio & Fang Yang, 2016. "Piketty’s Book and Macro Models of Wealth Inequality," Chicago Fed Letter, Federal Reserve Bank of Chicago.
    13. Joachim Hubmer & Per Krusell & Anthony A. Smith Jr., 2020. "Sources of US Wealth Inequality: Past, Present, and Future," NBER Chapters, in: NBER Macroeconomics Annual 2020, volume 35, pages 391-455, National Bureau of Economic Research, Inc.
    14. Stachurski, John & Toda, Alexis Akira, 2019. "An impossibility theorem for wealth in heterogeneous-agent models with limited heterogeneity," Journal of Economic Theory, Elsevier, vol. 182(C), pages 1-24.
    15. Mariacristina De Nardi & Giulio Fella, 2017. "Saving and Wealth Inequality," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 26, pages 280-300, October.
    16. Gouin-Bonenfant, Emilien & Toda, Alexis Akira, 2018. "Pareto Extrapolation: Bridging Theoretical and Quantitative Models of Wealth Inequality," University of California at San Diego, Economics Working Paper Series qt90n2h2bb, Department of Economics, UC San Diego.
    17. Per Krusell & Anthony Smith & Joachim Hubmer, 2015. "The historical evolution of the wealth distribution: A quantitative-theoretic investigation," 2015 Meeting Papers 1406, Society for Economic Dynamics.
    18. Andreas Fagereng & Luigi Guiso & Davide Malacrino & Luigi Pistaferri, 2020. "Heterogeneity and Persistence in Returns to Wealth," Econometrica, Econometric Society, vol. 88(1), pages 115-170, January.
    19. Per Krusell & Anthony Smith & Joachim Hubmer, 2015. "The historical evolution of the wealth distribution: A quantitative-theoretic investigation," 2015 Meeting Papers 1406, Society for Economic Dynamics.
    20. Michael R. Veall, 2012. "Top income shares in Canada: recent trends and policy implications," Canadian Journal of Economics, Canadian Economics Association, vol. 45(4), pages 1247-1272, November.

    More about this item

    JEL classification:

    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • H24 - Public Economics - - Taxation, Subsidies, and Revenue - - - Personal Income and Other Nonbusiness Taxes and Subsidies
    • L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms

    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:aea:aejmac:v:9:y:2017:i:3:p:36-71. 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: Michael P. Albert (email available below). General contact details of provider: https://edirc.repec.org/data/aeaaaea.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.