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

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  • 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
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    References listed on IDEAS

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    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. Hoang Van Khieu & Roberto Leon-Gonzalez, 2024. "The distributions of annual earnings and interest rates in a continuous time Markov chain economy," Economics Bulletin, AccessEcon, vol. 44(3), pages 1096-1108.
    10. Tetsugen HARUYAMA, 2021. "A Schumpeterian Exploration of Gini and Top/Bottom Income Shares," Discussion Papers 2125, Graduate School of Economics, Kobe University.
    11. 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.
    12. 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.
    13. Makoto NIREI & Koki OIKAWA & Masahiro OROKU, 2024. "Economic Growth through Basic Research by Firms: A science linkage approach," Discussion papers 24013, Research Institute of Economy, Trade and Industry (RIETI).
    14. 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.
    15. 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.
    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. 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.
    18. 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.
    19. 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.
    20. 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.

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    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

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