# Wealth Inequality and the Ergodic Hypothesis: Evidence from the United States

## DOI:

https://doi.org/10.25071/1874-6322.40455## Keywords:

Wealth inequality, Wealth dynamics, Ergodic hypothesis, Stochastic processes## Abstract

Many studies of wealth inequality make the ergodic hypothesis that rescaled wealth converges rapidly to a stationary distribution. Under this assumption, changes in distribution are expressed as changes in model parameters, reflecting shocks in economic conditions, with rapid equilibration thereafter. Here we test the ergodic hypothesis in an established model of wealth in a growing and reallocating economy. We fit model parameters to historical data from the United States. In recent decades, we find negative reallocation, from poorer to richer, for which no stationary distribution exists. When we find positive reallocation, convergence to the stationary distribution is slow. Our analysis does not support using the ergodic hypothesis in this model for these data. It suggests that inequality evolves because the distribution is inherently unstable on relevant timescales, regardless of shocks. Studies of other models and data, in which the ergodic hypothesis is made, would benefit from similar tests.

## References

Adamou, Alexander and Ole Peters (2016) “Dynamics of Inequality”, Significance 13(3), 32-35.

Atkinson, Anthony B. (1969) “The Timescale of Economic Models: How Long is the Long Run?”, Review of Economic Studies 36(2), 137-152.

Bach, Laurent, Laurent E. Calvet, and Paolo Sodini (2020) “Rich Pickings? Risk, Return, and Skill in Household Wealth”, American Economic Review 110(9), 2703-2747.

Benhabib, Jess, Alberto Bisin, and Mi Luo (2017) “Earnings Inequality and Other Determinants of Wealth Inequality”, American Economic Review 107(5), 593-597.

Benhabib, Jess, Alberto Bisin, and Mi Luo (2019) “Wealth Distribution and Social Mobility in the US, A Quantitative Approach”, American Economic Review, 109(5), 1623-1647.

———–, Alberto Bisin, and Shenghao Zhu (2011) “The Distribution of Wealth and Fiscal Policy in Economies with Finitely Lived Agents”, Econometrica 79(1), 123-157.

Berman, Yonatan (2019) “On the Link Between Intergenerational Mobility and Inequality: Are They Truly Distinct?”, Mimeo.

———–, and Yoash Shapira (2017) “Revisiting r>g − The Asymptotic Dynamics of Wealth Inequality”, Physica A 467, 562-572.

———–, Eshel Ben-Jacob, and Yoash Shapira (2016) “The Dynamics of Wealth Inequality and the Effect of Income Distribution”, PLOS ONE11(6): e0199999.

Bewley, Truman (1977) “The Permanent Income Hypothesis: A Theoretical Formulation”, Journal of Economic Theory 16(2), 252-292.

Bouchaud, Jean-Philippe (2015a) “Note on Mean-Field Wealth Models and the Random Energy Model”, Mimeo.

———– (2015b) “On Growth-Optimal Tax Rates and the Issue of Wealth Inequalities” arXiv: 1508.00275.

———–, and Marc Mézard (2000) “Wealth Condensation in a Simple Model of Economy“, Physica A 282(4), 536-545.

Bricker, Jesse, Alice Henriques, Jacob Krimmel, and John Sabelhaus (2016) “Measuring Income and Wealth at the Top Using Administrative and Survey Data“, Brookings Papers on Economic Activity, 261-331.

Brzeziski, Michat (2014) “Do Wealth Distributions Follow Power Laws? Evidence from ’Rich Lists’ ”, Physica A 406, 155-162.

Champernowne, David G. (1953) “A Model of Income Distribution”, The Economic Journal 63(250), 318-351.

Corak, Miles (2013) “Income Inequality, Equality of Opportunity, and Intergenerational Mobility”, Journal of Economic Perspectives 27(3), 79-102.

Cowell, Frank A. (2014) “Piketty in the Long Run”, The British Journal of Sociology 65(4), 708-720.

De Nardi, Mariacristina (2015) “Quantitative Models of Wealth Inequality: A Survey”, Working Paper 21106, NBER.

———–, Giulio Fella, and Fang Yang (2015) “Piketty’s Book and Macro Models of Wealth Inequality”, Working Paper 21730, NBER.

Fagereng, Andreas, Luigi Guiso, Davide Malacrino, and Luigi Pistaferri (2020) “Heterogeneity and Persistence in Returns to Wealth”, Econometrica 88(1), 115-170.

Gabaix, Xavier (2009) “Power Laws in Economics and Finance”, Annual Review of Economics 1(1), 255-294.

———–, Jean-Michel Lasry, Pierre-Louis Lions, and Benjamin Moll (2016) “The Dynamics of Inequality”, Econometrica, 84(6), 2071-2111.

Hubmer, Joachim, Per Krusell, and Anthony A. Smith Jr. (2019) “Sources of U.S. Wealth Inequality: Past, Present, and Future”, Mimeo.

Jones, Charles I (2015) “Pareto and Piketty: The Macroeconomics of Top Income and Wealth Inequality”, Journal of Economic Perspectives 29(1), 29-46.

Kaymak, Bars, and Markus Poschke (2016) “The Evolution of Wealth Inequality Over Half a Century: The Role of Taxes, Transfers and Technology”, Journal of Monetary Economics 77, 1-25.

Klass, Oren S., Ofer Biham, Moshe Levy, Ofer Malcai, and Sorin Solomon (2006) “The Forbes 400 and the Pareto Wealth Distribution”, Economics Letters 90(2), 290-295.

Kopczuk, Wojciech (2015) “What Do We Know about the Evolution of Top Wealth Shares in the United States?”, Journal of Economic Perspectives 29(1), 47-66 .

———–, and Emmanuel Saez (2004) “Top Wealth Shares in the United States, 1916-2000: Evidence from Estate Tax Returns”, National Tax Journal 57(2), 445- 487.

Krueger, Alan (2012) “The Rise and Consequences of Inequality”, Presentation Made to the Center for American Progress, January 12th.

Liu, Kang, Nicholas Lubbers, William Klein, Jan Tobochnik, Bruce Boghosian, and Harvey Gould (2013) “The Effect of Growth on Equality in Models of the Economy”, arXivil 305.0794.

Liu, Z., and Rostislav A. Serota (2017) “Correlation and Relaxation Times for a Stochastic Process with a Fat-tailed Steady-state Distribution”, Physica A 474, 301-311.

Marsili, Matteo, Sergei Maslov, and Yi-Cheng Zhang (1998) “Dynamical Optimization Theory of a Diversified Portfolio”, Physica A 253, 403-418.

Meade, James E. (1964) Efficiency, Equality and The Ownership of Property London, UK: Allen & Unwin.

Nelder, John A., and Roger Mead (1965) “A Simplex Method for Function Minimization”, The Computer Journal 7(4), 308-313.

Pareto, Vilfredo (1897) Cours d’Économie Politique Lausanne, Switzerland: F. Rouge.

Peters, Ole (2019) “The Ergodicity Problem in Economics”, Nature Physics 15, 1216-1221.

———–, and Alexander Adamou (2018) “The Sum of Log-Normal Variates in Geometric Brownian Motion”, arXiv: 1802.02939.

———–, and Murray Gell-Mann (2016) “Evaluating Gambles using Dynamics”, Chaos 26, 23103.

———–, and William Klein (2013) “Ergodicity Breaking in Geometric Brownian Motion”, Physical Review Letters, 110(10), 100603.

Piketty, Thomas (2014) Capital in the Twenty-First Century Cambridge, MA: Harvard University Press.

———–, and Emmanuel Saez (2013) “A Theory of Optimal Inheritance Taxation”, Econometrica 81(5), 1851-1886.

———–, and Gabriel Zucman (2014) “Capital is Back: Wealth-Income Ratios in Rich Countries,1700-2010”, Quarterly Journal of Economics 129(3), 1255-1310.

————, and Gabriel Zucman (2015) “Wealth and Inheritance in the Long Run”, In Handbook of Income Distribution, ed. Anthony B. Atkinson and François Bourguignon Amsterdam: Elsevier, pp. 1303-1368.

Pinkovskiy, Maxim, and Xavier Sala-i-Martin (2009) “Parametric Estimations of the World Distribution of Income”, Working Paper 15433, NBER.

Quandl (2016) “Dow Jones Industrial Average”, Accessed, 04/19/2016.

Rios-Rull, Jose-Victor, and Moritz Kuhn (2016) “2013 Update on the U.S. Earnings, Income, and Wealth Distributional Facts: A View from Macroeconomics”, Quarterly Review 1-75.

Saez, Emmanuel, and Gabriel Zucman (2016) “Wealth Inequality in the United States since 1913: Evidence from Capitalized Income Tax Data”, Quarterly Journal of Economics 131(2), 519-578.

———–, and Gabriel Zucman (2019) “Progressive Wealth Taxation”, Brookings Papers on Economic Activity.

Samuelson, Paul A. (1968) “What Classical and Neoclassical Monetary Theory Really Was”, The Canadian Journal of Economics 1(1), 1-15

Stiglitz, Joseph E. (1969) “Distribution of Income and Wealth Among Individuals”, Econometrica 37(3), 382-397.

The World Inequality Database (2016) “USA Top 10% and 1% and Bottom 50% Wealth Shares,1913-2014”,http://wid.world/data/, Accessed: 12/26/2016.

Toda, Alexis A., and Kieran Walsh (2015) “The Double Power Law in Consumption and Implications for Testing Euler Equations”, Journal of Political Economy 123(5), 1177-1200.

Uhlenbeck, George E., and Leonard S. Ornstein (1930) “On the Theory of the Brownian Motion”, Physical Review 36(5), 823-841.

Vasicek, Oldrich (1977) “An Equilibrium Characterization of the Term Structure”, Journal of Financial Economics 5(2), 177-188.

Vermeulen, Philip (2018) “How Fat is the Top Tail of the Wealth Distribution?”, Review of Incomeand Wealth 64(2), 357-387.

Wolff, Edward N (2014) “Household Wealth Trends in the United States, 1983-2010”, Oxford Review of Economic Policy 30(1), 21-43.

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*Journal of Income Distribution®*,

*1*. https://doi.org/10.25071/1874-6322.40455