Zipf's Law, Pareto's Law, and the Evolution of Top Incomes in the U.S.

Aoki, Shuhei and Nirei, Makoto (2016): Zipf's Law, Pareto's Law, and the Evolution of Top Incomes in the U.S.

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 U.S. The model matches the decline in the Pareto exponent of the income distribution and the trend of the top 1% income share in recent decades.

• Item Type: MPRA Paper
• Language: English
• Keywords: income distribution; wealth distribution; Pareto exponent; top income share; firm size distribution; Zipf's law
• Subjects: D - Microeconomics > D3 - Distribution > D31 - Personal Income, Wealth, and Their Distributions; L - Industrial Organization > L1 - Market Structure, Firm Strategy, and Market Performance > L11 - Production, Pricing, and Market Structure ; Size Distribution of Firms; O - Economic Development, Innovation, Technological Change, and Growth > O4 - Economic Growth and Aggregate Productivity > O40 - General

References

Alvaredo, Facundo, Anthony B. Atkinson, Thomas Piketty, and Emmanuel Saez (2013) ``The World Top Incomes Database,'' http://topincomes.g-mond.parisschoolofeconomics.eu/. Data are extracted at 25/11/2013.

Atkinson, Anthony B., Thomas Piketty, and Emmanuel Saez (2011) ``Top Incomes in the Long Run of History,'' Journal of Economic Literature, Vol.49, No. 1, pp. 3-71.

Bakija, Jon, Adam Cole, and Bradley T. Heim (2012) ``Jobs and Income Growth of Top Earners and the Causes of Changing Income Inequality: Evidence from U.S. Tax Return Data,'' mimeo.

Benhabib, Jess, Alberto Bisin, and Shenghao Zhu (2011) ``The Distribution of Wealth and Fiscal Policy in Economies with Finitely Lived Agents,'' Econometrica, Vol. 79, No. 1, pp. 123-157.

Benhabib, Jess, Alberto Bisin, and Shenghao Zhu (2015) ``The Wealth Distribution in Bewley Economies with Capital Income Risk,'' Journal of Economic Theory, Vol. 159, Part A, pp. 489-515.

Benhabib, Jess, Alberto Bisin, and Shenghao Zhu (2016) ``The Distribution of Wealth in the Blanchard-Yaari Model,'' Macroeconomic Dynamics, Vol. 20, No. 2, pp. 466-481.

Bitler, Marianne P., Tobias J. Moskowitz, and Annette Vissing-Jorgensen (2005) ``Testing Agency Theory with Entrepreneur Effort and Wealth,'' Journal of Finance, Vol. 60, No. 2, pp. 539-576.

Blanchard, Olivier J. (1985) ``Debt, Deficits, and Finite Horizons,'' Journal of Political Economy, Vol. 93, No. 2, pp. 223-247.

Calvet, Laurent E., John Y. Campbell, and Paolo Sodini (2007) ``Down or Out: Assessing the Welfare Costs of Household Investment Mistakes,'' Journal of Political Economy, Vol. 115, No. 5, pp. 707-747.

Campbell, John Y. and Luis M. Viceira (2002) Strategic Asset Allocation: Portfolio Choice for Long-Term Investors, Oxford University Press.

Champernowne, D.G. (1953) ``A Model of Income Distribution,'' Economic Journal, Vol. 63, No. 250, pp. 318-351.

Clementi, Gian Luca and Thomas F. Cooley (2009) ``Executive Compensation: Facts,'' NBER Working Papers 15426, National Bureau of Economic Research, Inc.

Davis, Steven J., John Haltiwanger, Ron Jarmin, and Javier Miranda (2007) ``Volatility and Dispersion in Business Growth Rates: Publicly Traded versus Privately Held Firms,'' in NBER Macroeconomics Annual 2006, Vol. 21, National Bureau of Economic Research, Inc., pp. 107-180.

Dutta, Jayasri and Philippe Michel (1998) ``The Distribution of Wealth with Imperfect Altruism,'' Journal of Economic Theory, Vol. 82, No. 2, pp. 379-404.

Edmans, Alex, Xavier Gabaix, and Augustin Landier (2009) ``A Multiplicative Model of Optimal CEO Incentives in Market Equilibrium,'' Review of Financial Studies, Vol. 22, No. 12, pp. 4881-4917.

Edmans, Alex, Xavier Gabaix, Tomasz Sadzik, and Yuliy Sannikov (2012) ``Dynamic CEO Compensation,'' Journal of Finance, Vol. 67, No. 5, pp. 1603-1647.

Fagereng, Andreas, Luigi Guiso, Davide Malacrino, and Luigi Pistaferri (2016) ``Heterogeneity and Persistence in Returns to Wealth,'' mimeo.

Flavin, Marjorie and Takashi Yamashita (2002) ``Owner-Occupied Housing and the Composition of the Household Portfolio,'' American Economic Review, Vol. 92, No. 1, pp. 345-362.

Frydman, Carola and Dirk Jenter (2010) ``CEO Compensation,'' Annual Review of Financial Economics, Vol. 2, No. 1, pp. 75-102.

Frydman, Carola and Raven E. Saks (2010) ``Executive Compensation: A New View from a Long-Term Perspective, 1936-2005,'' Review of Financial Studies, Vol. 23, No. 5, pp. 2099-2138.

Gabaix, Xavier (2009) ``Power Laws in Economics and Finance,'' Annual Review of Economics, Vol. 1, No. 1, pp. 255-294.

Gabaix, Xavier and Augustin Landier (2008) ``Why Has CEO Pay Increased So Much?'' Quarterly Journal of Economics, Vol. 123, No. 1, pp. 49-100.

Gabaix, Xavier, Benjamin Moll, Jean-Michel Lasry, and Pierre-Louis Lions (2015) ``The Dynamics of Inequality,'' mimeo.

Hacker, Jacob S. and Paul Pierson (2010) Winner-Take-All Politics: How Washington Made the Rich Richer and Turned Its Back on the Middle Class, Simon and Schuster.

Jones, Charles I. (2015) ``Pareto and Piketty: The Macroeconomics of Top Income and Wealth Inequality,'' Journal of Economic Perspectives, Vol. 29, No. 1, pp. 29-46.

Jones, Charles I. and Jihee Kim (2014) ``A Schumpeterian Model of Top Income Inequality,'' mimeo.

Kaplan, Steven N. and Joshua Rauh (2013) ``It's the Market: The Broad-Based Rise in the Return to Top Talent,'' Journal of Economic Perspectives, Vol. 27, No. 3, pp. 35-56.

Katz, Lawrence F. and Kevin M. Murphy (1992) ``Changes in Relative Wages, 1963-1987: Supply and Demand Factors,'' Quarterly Journal of Economics, Vol. 107, No. 1, pp. 35-78.

Kim, Jihee (2013) ``The Effect of the Top Marginal Tax Rate on Top Income Inequality,'' mimeo.

Klette, Tor Jakob and Samuel Kortum (2004) ``Innovating Firms and Aggregate Innovation,'' Journal of Political Economy, Vol. 112, No. 5, pp. 986-1018.

Luttmer, Erzo G.J. (2007) ``Selection, Growth, and the Size Distribution of Firms,'' Quarterly Journal of Economics, Vol. 122, No. 3, pp. 1103-1144.

Luttmer, Erzo G.J. (2010) ``Models of Growth and Firm Heterogeneity,'' Annual Review of Economics, Vol. 2, No. 1, pp. 547-576.

Luttmer, Erzo G.J. (2011) ``On the Mechanics of Firm Growth,'' Review of Economic Studies, Vol. 78, No. 3, pp. 1042-1068.

McGrattan, Ellen R. and Edward C. Prescott (2005) ``Taxes, Regulations, and the Value of U.S. and U.K. Corporations,'' Review of Economic Studies, Vol. 72, No. 3, pp. 767-796.

Merton, Robert C. (1969) ``Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case,'' Review of Economics and Statistics, Vol. 51, No. 3, pp. 247-57.

Merton, Robert C. (1971) ``Optimum Consumption and Portfolio Rules in a Continuous-time Model,'' Journal of Economic Theory, Vol. 3, No. 4, pp. 373-413.

Mizuno, Takayuki, Atushi Ishikawa, Shouji Fujimoto, and Tsutomu Watanabe (2012) ``Power Laws in Firm Productivity,'' Progress of Theoretical Physics Supplement, Vol. 194, pp. 122-134.

Moskowitz, Tobias J. and Annette Vissing-Jorgensen (2002) ``The Returns to Entrepreneurial Investment: A Private Equity Premium Puzzle?'' American Economic Review, Vol. 92, No. 4, pp. 745-778.

Nirei, Makoto and Shuhei Aoki (2016) ``Pareto Distribution of Income in Neoclassical Growth Models,'' Review of Economic Dynamics, Vol. 20, pp. 25-42.

Nirei, Makoto and Wataru Souma (2007) ``A Two Factor Model of Income Distribution Dynamics,'' Review of Income and Wealth, Vol. 53, No. 3, pp. 440-459.

Piketty, Thomas and Emmanuel Saez (2003) ``Income Inequality in the United States, 1913-1998,'' Quarterly Journal of Economics, Vol. 118, No. 1, pp. 1-39.

Piketty, Thomas, Emmanuel Saez, and Stefanie Stantcheva (2011) ``Optimal Taxation of Top Labor Incomes: A Tale of Three Elasticities,'' NBER Working Papers 17616, National Bureau of Economic Research, Inc.

Reed, William J. (2001) ``The Pareto, Zipf and Other Power Laws,'' Economics Letters, Vol. 74, No. 1, pp. 15-19.

Rossi-Hansberg, Esteban and Mark L.J. Wright (2007) ``Establishment Size Dynamics in the Aggregate Economy,'' American Economic Review, Vol. 97, No. 5, pp. 1639-1666.

Saez, Emmanuel, Joel Slemrod, and Seth H. Giertz (2012) ``The Elasticity of Taxable Income with Respect to Marginal Tax Rates: A Critical Review,'' Journal of Economic Literature, Vol. 50, No. 1, pp. 3-50.

Sinn, Hans-Werner (1991) ``Taxation and the Cost of Capital: The `Old' View, the `New' View, and Another View,'' in Tax Policy and the Economy, Vol. 5, National Bureau of Economic Research, Inc., pp. 25-54.

Toda, Alexis Akira (2014) ``Incomplete Market Dynamics and Cross-sectional Distributions,'' Journal of Economic Theory, Vol. 154, pp. 310-348.

Wold, H.O.A. and P. Whittle (1957) ``A Model Explaining the Pareto Distribution of Wealth,'' Econometrica, Vol. 25, No. 4, pp. 591-595.