The Distribution of Wealth and Fiscal Policy in Economies with Finitely Lived Agents

We study the dynamics of the distribution of wealth in an overlapping generation economy with finitely lived agents and intergenerational transmission of wealth. Financial markets are incomplete, exposing agents to both labor and capital income risk. We show that the stationary wealth distribution is a Pareto distribution in the right tail and that it is capital income risk, rather than labor income, that drives the properties of the right tail of the wealth distribution. We also study analytically the dependence of the distribution of wealth—of wealth inequality in particular—on various fiscal policy instruments like capital income taxes and estate taxes, and on different degrees of social mobility. We show that capital income and estate taxes can significantly reduce wealth inequality, as do institutions favoring social mobility. Finally, we calibrate the economy to match the Lorenz curve of the wealth distribution of the U.S. economy.

[1]  J. Poterba,et al.  The Income and Tax Share of Very High Income Households, 1960-1995 , 2000 .

[2]  E. Wolff.  Changes in Household Wealth in the 1980s and 1990s in the U.S , 2004 .

[3]  Mariacristina De Nardi,et al.  Entrepreneurship, Frictions, and Wealth , 2006, Journal of Political Economy.

[4]  Vilfredo Pareto.  Un’applicazione di teorie sociologiche , 1980 .

[5]  George Tauchen,et al.  Finite state markov-chain approximations to univariate and vector autoregressions , 1986 .

[6]  Feller William,et al.  An Introduction To Probability Theory And Its Applications , 1950 .

[7]  P. Whittle,et al.  A Model Explaining the Pareto Distribution of Wealth , 1957 .

[8]  M. Cagetti,et al.  WEALTH INEQUALITY: DATA AND MODELS , 2005, Macroeconomic Dynamics.

[9]  Benoite de Saporta,et al.  Tail of the stationary solution of the stochastic equation Y(n+1)=a(n)Y(n)+b(n) with Markovian coefficients , 2002 .

[10]  Vasia Panousi.  Capital Taxation with Entrepreneurial Risk , 2007 .

[11]  José-Víctor Ríos-Rull,et al.  Accounting for the U.S. Earnings and Wealth Inequality , 2003, Journal of Political Economy.

[12]  Charles Gide,et al.  Cours d'économie politique , 1911 .

[13]  Tobias J. Moskowitz,et al.  Testing Agency Theory with Entrepreneur Effort and Wealth , 2005 .

[14]  Jess Benhabib,et al.  Age, Luck, and Inheritance , 2008 .

[15]  Martin Flodén,et al.  A note on the accuracy of Markov-chain approximations to highly persistent AR(1) processes , 2008 .

[16]  X. Gabaix.  Zipf's Law for Cities: An Explanation , 1999 .

[17]  A. Atkinson.  Top Incomes in the United Kingdom Over the Twentieth Century , 2002 .

[18]  Per Krusell,et al.  Income and Wealth Heterogeneity in the Macroeconomy , 1998, Journal of Political Economy.

[19]  Mark Huggett,et al.  The risk-free rate in heterogeneous-agent incomplete-insurance economies , 1993 .

[20]  Wataru Souma,et al.  A Two Factor Model of Income Distribution Dynamics , 2007 .

[21]  Emmanuel Saez,et al.  Income inequality in the United States , 2003 .

[22]  Martha A. Starr,et al.  Household Portfolios in the United States , 2000 .

[23]  Edward N. Wolff,et al.  Estimates of Household Wealth Inequality in the U.S., 1962-1983 , 1987 .

[24]  D. Sornette.  Critical Phenomena in Natural Sciences: Chaos, Fractals, Selforganization and Disorder: Concepts and Tools , 2000 .

[25]  Emmanuel Saez,et al.  The Evolution of Income Concentration in Japan, 1886-2002: Evidence from Income Tax Statistics , 2006 .

[26]  D. Champernowne.  A Model of Income Distribution , 1953 .

[27]  Michel Loève,et al.  Probability Theory I , 1977 .

[28]  Ming-Deh A. Huang,et al.  Proof of proposition 2 , 1992 .

[29]  José-Víctor Ríos-Rull,et al.  Dimensions of inequality: facts on the U.S. distributions of earnings, income, and wealth , 1997 .

[30]  Jess Benhabib,et al.  The distribution of wealth and redistributive policies , 2006 .

[31]  George Tauchen,et al.  Quadrature-Based Methods for Obtaining Approximate Solutions to Nonlinear Asset Pricing Models , 1991 .

[32]  Chris I. Telmer,et al.  Consumption and Risk Sharing Over the Life Cycle , 2000 .

[33]  Mauro Gallegati,et al.  Power law tails in the Italian personal income distribution , 2004, cond-mat/0408067.

[34]  M. Huggett.  Wealth distribution in life-cycle economies , 1996 .

[35]  Rosario N. Mantegna,et al.  An Introduction to Econophysics: Contents , 1999 .

[36]  J. Scheinkman,et al.  Federal Reserve Bank of Minneapolis Research Department Staff Report 314 Wealth Inequality and Intergenerational Links , 2022 .

[37]  A. Shorrocks,et al.  The Measurement of Mobility , 1978 .

[38]  R. Lampman.  The Share of Top Wealth-Holders in National Wealth 1922-56 , 1962 .

[39]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[40]  Laurence J. Kotlikoff,et al.  The Role of Intergenerational Transfers in Aggregate Capital Accumulation , 1980, Journal of Political Economy.

[41]  Richard L. Tweedie,et al.  Markov Chains and Stochastic Stability , 1993, Communications and Control Engineering Series.

[42]  H. Kesten.  Random difference equations and Renewal theory for products of random matrices , 1973 .

[43]  Laurent E. Calvet,et al.  Idiosyncratic Production Risk, Growth, and the Business Cycle , 2003 .

[44]  K. Taira.  Proof of Theorem 1.3 , 2004 .

[45]  J. Scholz,et al.  Intergenerational Transfers and the Accumulation of Wealth , 1994 .

[46]  Olivier J. Blanchard,et al.  Debt, Deficits, and Finite Horizons , 1984, Journal of Political Economy.

[47]  C. Carroll,et al.  Buffer-Stock Saving and the Life Cycle/Permanent Income Hypothesis , 1996 .

[48]  R. Rutherford,et al.  Income Distributions: A New Model , 1955 .

[49]  M. Levy,et al.  POWER LAWS ARE LOGARITHMIC BOLTZMANN LAWS , 1996, adap-org/9607001.

[50]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1951 .

[51]  V. Pareto,et al.  The Rise and Fall of Elites: An Application of Theoretical Sociology , 1992 .

[52]  Alexander Roitershtein,et al.  One-dimensional linear recursions with Markov-dependent coefficients , 2004, math/0409335.

[53]  T. Piketty,et al.  Income Inequality in France, 1901–1998 , 2001, Journal of Political Economy.

[54]  M. Cagetti,et al.  Entrepreneurship, Frictions, and Wealth , 2005, Journal of Political Economy.

[55]  S. Solomon,et al.  The Forbes 400, the Pareto power-law and efficient markets , 2007 .

[56]  J. Dagsvik,et al.  Is the Distribution of Income Compatible with a Stable Distribution , 1999 .

[57]  Paul M. Sommers,et al.  Eigenvalue immobility measures for Markov chains 1 , 1979 .

[58]  George-Marios Angeletos,et al.  Uninsured Idiosyncratic Investment Risk and Aggregate Saving , 2005 .

[59]  C. Goldie.  IMPLICIT RENEWAL THEORY AND TAILS OF SOLUTIONS OF RANDOM EQUATIONS , 1991 .

[60]  Emmanuel Saez,et al.  Income inequality in the United States , 2003 .

[61]  R. Jagannathan,et al.  Uninsured Idiosyncratic Risk and Aggregate Saving , 1994 .

[62]  M. Cagetti,et al.  Estate Taxation, Entrepreneurship, and Wealth , 2007 .

[63]  Jose V Rios-Rul,et al.  Updated Facts on the U.S. Distributions of Earnings, Income and Wealth , 2002 .

[64]  Leonard M. Adleman,et al.  Proof of proposition 3 , 1992 .

[65]  Owner-Occupied Housing and the Composition of the Household Portfolio , 2002 .

[66]  Vincenzo Quadrini,et al.  Entrepreneurship, saving and social mobility , 2000 .

[67]  Vincenzo Quadrini,et al.  THE IMPORTANCE OF ENTREPRENEURSHIP FOR WEALTH CONCENTRATION AND MOBILITY , 1999 .

[68]  Fatih Guvenen,et al.  Learning Your Earning: Are Labor Income Shocks Really Very Persistent? , 2007 .

[69]  Gary S. Becker,et al.  An Equilibrium Theory of the Distribution of Income and Intergenerational Mobility , 1979, Journal of Political Economy.

[70]  J. Heathcote.  Discussion of “Heterogeneous life-cycle profiles, income risk and consumption inequality” by Giorgio Primiceri and Thijs van Rens☆ , 2009 .

[71]  Giorgio E. Primiceri,et al.  Marriage, partnership and sexual orientation: a study of British university academics and administrators , 2008, The Journal of Human Resources.

[72]  Richard L. Tweedie,et al.  Drift conditions and invariant measures for Markov chains , 2001 .

[73]  V. Burris.  The myth of old money liberalism: the politics of the Forbes 400 richest Americans , 2000 .

[74]  Incomplete Market Dynamics in a Neoclassical Production Economy , 2004 .

[75]  Benoîte de Saporta,et al.  Tail of the stationary solution of the stochastic equation Yn+1=anYn+bn with Markovian coefficients , 2004 .

[76]  W. Arthur,et al.  The Economy as an Evolving Complex System II , 1988 .

[77]  L. Dworsky.  An Introduction to Probability , 2008 .

[78]  Giorgio E. Primiceri,et al.  Heterogeneous Life-Cycle Profiles, Income Risk and Consumption Inequality , 2006 .

[79]  A. Brandt.  The stochastic equation Yn+1=AnYn+Bn with stationary coefficients , 1986 .

[80]  J. Chipman.  The Paretian heritage , 1976 .

[81]  Benoîte de Saporta,et al.  Etude de la solution stationnaire de l'équation Y(n+1)=a(n)Y(n)+b(n) à coefficients aléatoires , 2004 .

[82]  Valentino Dardanoni,et al.  Measuring Social Mobility , 1993 .

[83]  M. Yaari,et al.  Uncertain lifetime, life insurance, and the theory of the consumer , 1965 .

[84]  Kazuo Nishimura,et al.  Stability of stochastic optimal growth models: a new approach , 2005, J. Econ. Theory.

[85]  Moshe Levy,et al.  Market Efficiency, the Pareto Wealth Distribution, and the Lévy Distribution of Stock Returns , 2005 .

[86]  R. Shiller,et al.  The Efficiency of the Market for Single-Family Homes , 1988 .

[87]  Sheng Zhu.  Wealth Distribution under Idiosyncratic Investment Risk , 2010 .

[88]  The Role of Intergenerational Transfers in Aggregate Capital Accumulation , 1981 .

[89]  K. Arrow.  The Demand for Information and the Distribution of Income , 1987, Probability in the Engineering and Informational Sciences.