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Capital Income Risk and the Dynamics of the Wealth Distribution

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  • Hoang Khieu
  • Klaus Wälde

Abstract

Labour income follows a deterministic growth trend and fluctuates between two values. Interest rates are drawn initially, fluctuate between two values and can differ in their arrival rates. Low interest rates imply a stationary long-run wealth distribution, high interest rates imply exploding wealth dynamics. When matching the NLSY 79 evolution of the wealth distribution from 1986 to 2008, we obtain a fit of 96:1%: With a more flexible interest rate distribution, employing “superstar states”, the fit can increase to 96:7%. For the fit of 96:1%, the standard deviation of model returns is much lower than the empirical standard deviation.

Suggested Citation

  • Hoang Khieu & Klaus Wälde, 2019. "Capital Income Risk and the Dynamics of the Wealth Distribution," CESifo Working Paper Series 7970, CESifo.
    • Handle: RePEc:ces:ceswps:_7970
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    1. 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.
    2. De Nardi, Mariacristina & Yang, Fang, 2016. "Wealth inequality, family background, and estate taxation," Journal of Monetary Economics, Elsevier, vol. 77(C), pages 130-145.
    3. 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.
    4. Achdou, Yves & Han, Jiequn & Lasry, Jean Michel & Lions, Pierre Louis & Moll, Ben, 2022. "Income and wealth distribution in macroeconomics: a continuous-time approach," LSE Research Online Documents on Economics 107422, London School of Economics and Political Science, LSE Library.
    5. Jess Benhabib & Alberto Bisin, 2018. "Skewed Wealth Distributions: Theory and Empirics," Journal of Economic Literature, American Economic Association, vol. 56(4), pages 1261-1291, December.
    6. Xavier Gabaix & Jean‐Michel Lasry & Pierre‐Louis Lions & Benjamin Moll, 2016. "The Dynamics of Inequality," Econometrica, Econometric Society, vol. 84, pages 2071-2111, November.
    7. A. B. Atkinson, 2017. "Pareto and the Upper Tail of the Income Distribution in the UK: 1799 to the Present," Economica, London School of Economics and Political Science, vol. 84(334), pages 129-156, April.
    8. Angeletos, George-Marios & Calvet, Laurent-Emmanuel, 2005. "Incomplete-market dynamics in a neoclassical production economy," Journal of Mathematical Economics, Elsevier, vol. 41(4-5), pages 407-438, August.
    9. SeHyoun Ahn & Greg Kaplan & Benjamin Moll & Thomas Winberry & Christian Wolf, 2018. "When Inequality Matters for Macro and Macro Matters for Inequality," NBER Macroeconomics Annual, University of Chicago Press, vol. 32(1), pages 1-75.
    10. Thomas Piketty, 2015. "Putting Distribution Back at the Center of Economics: Reflections on Capital in the Twenty-First Century," Journal of Economic Perspectives, American Economic Association, vol. 29(1), pages 67-88, Winter.
    11. Greg Kaplan & Benjamin Moll & Giovanni L. Violante, 2018. "Monetary Policy According to HANK," American Economic Review, American Economic Association, vol. 108(3), pages 697-743, March.
    12. Yves Achdou & Jiequn Han & Jean-Michel Lasry & Pierre-Louis Lionse & Benjamin Moll, 2022. "Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach [On the Existence and Uniqueness of Stationary Equilibrium in Bewley Economies with Production]," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(1), pages 45-86.
    13. Hoang Khieu, 2022. "Rising wealth inequality: when r − g matters [The rise and decline of general laws of capitalism]," Oxford Economic Papers, Oxford University Press, vol. 74(2), pages 333-358.
    14. Simon H. Boserup & Wojciech Kopczuk & Claus T. Kreiner, 2016. "The Role of Bequests in Shaping Wealth Inequality: Evidence from Danish Wealth Records," American Economic Review, American Economic Association, vol. 106(5), pages 656-661, May.
    15. Sennewald, Ken, 2007. "Controlled stochastic differential equations under Poisson uncertainty and with unbounded utility," Journal of Economic Dynamics and Control, Elsevier, vol. 31(4), pages 1106-1131, April.
    16. N. Gregory Mankiw, 2015. "Yes, r > g. So What?," American Economic Review, American Economic Association, vol. 105(5), pages 43-47, May.
    17. Yves Achdou & Jiequn Han & Jean-Michel Lasry & Pierre-Louis Lions & Benjamin Moll, 2017. "Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach," NBER Working Papers 23732, National Bureau of Economic Research, Inc.
    18. Jess Benhabib & Alberto Bisin & Mi Luo, 2019. "Wealth Distribution and Social Mobility in the US: A Quantitative Approach," American Economic Review, American Economic Association, vol. 109(5), pages 1623-1647, May.
    19. Laurent Bach & Laurent E. Calvet & Paolo Sodini, 2015. "Rich Pickings? Risk, Return, and Skill in the Portfolios of the Wealthy," Working Papers hal-02002692, HAL.
    20. Jeremy Lise, 2013. "On-the-Job Search and Precautionary Savings," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 80(3), pages 1086-1113.
    21. Emmanuel Saez & Gabriel Zucman, 2016. "Editor's Choice Wealth Inequality in the United States since 1913: Evidence from Capitalized Income Tax Data," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 131(2), pages 519-578.
    22. 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.
    23. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    24. Robert E. Hall & Paul R. Milgrom, 2008. "The Limited Influence of Unemployment on the Wage Bargain," American Economic Review, American Economic Association, vol. 98(4), pages 1653-1674, September.
    25. 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.
    26. 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.
    27. Juan Carlos Parra-Alvarez & Olaf Posch & Mu-Chun Wang, 2017. "Estimation of Heterogeneous Agent Models: A Likelihood Approach," CESifo Working Paper Series 6717, CESifo.
    28. Christian BAYER & Klaus WALDE, 2010. "Matching and Saving in Continuous Time: Proofs," LIDAM Discussion Papers IRES 2010014, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    29. 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.
    30. Blundell, Richard & Graber, Michael & Mogstad, Magne, 2015. "Labor income dynamics and the insurance from taxes, transfers, and the family," Journal of Public Economics, Elsevier, vol. 127(C), pages 58-73.
    31. 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.
    32. Piketty, Thomas & Zucman, Gabriel, 2014. "Wealth and Inheritance in the Long Run," CEPR Discussion Papers 10072, C.E.P.R. Discussion Papers.
    33. Mortensen, Dale T, 1982. "Property Rights and Efficiency in Mating, Racing, and Related Games," American Economic Review, American Economic Association, vol. 72(5), pages 968-979, December.
    34. 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.
    35. Diamond, Peter A, 1982. "Aggregate Demand Management in Search Equilibrium," Journal of Political Economy, University of Chicago Press, vol. 90(5), pages 881-894, October.
    36. Thomas Piketty, 2015. "About Capital in the Twenty-First Century," American Economic Review, American Economic Association, vol. 105(5), pages 48-53, May.
    37. Kasa, Kenneth & Lei, Xiaowen, 2018. "Risk, uncertainty, and the dynamics of inequality," Journal of Monetary Economics, Elsevier, vol. 94(C), pages 60-78.
    38. Yuan, Chenggui & Mao, Xuerong, 2003. "Asymptotic stability in distribution of stochastic differential equations with Markovian switching," Stochastic Processes and their Applications, Elsevier, vol. 103(2), pages 277-291, February.
    39. Per Krusell & Anthony A. Smith & Jr., 1998. "Income and Wealth Heterogeneity in the Macroeconomy," Journal of Political Economy, University of Chicago Press, vol. 106(5), pages 867-896, October.
    40. Marjorie Flavin & Takashi Yamashita, 2002. "Owner-Occupied Housing and the Composition of the Household Portfolio," American Economic Review, American Economic Association, vol. 92(1), pages 345-362, March.
    41. 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.
    42. Berisha, Edmond & Meszaros, John, 2020. "Macroeconomic determinants of wealth inequality dynamics," Economic Modelling, Elsevier, vol. 89(C), pages 153-165.
    43. George-Marios Angeletos, 2007. "Uninsured Idiosyncratic Investment Risk and Aggregate Saving," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 10(1), pages 1-30, January.
    44. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, May.
    45. Pissarides, Christopher A, 1985. "Short-run Equilibrium Dynamics of Unemployment Vacancies, and Real Wages," American Economic Review, American Economic Association, vol. 75(4), pages 676-690, September.
    46. Christian BAYER & Klaus WALDE, 2010. "Matching and Saving in Continuous Time: Proofs," LIDAM Discussion Papers IRES 2010014, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    47. Kaymak, Barış & Poschke, Markus, 2016. "The evolution of wealth inequality over half a century: The role of taxes, transfers and technology," Journal of Monetary Economics, Elsevier, vol. 77(C), pages 1-25.
    48. Aban, Inmaculada B. & Meerschaert, Mark M. & Panorska, Anna K., 2006. "Parameter Estimation for the Truncated Pareto Distribution," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 270-277, March.
    49. 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.
    50. Galo Nuno & Benjamin Moll, 2018. "Social Optima in Economies with Heterogeneous Agents," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 28, pages 150-180, April.
    51. Jess Benhabib & Alberto Bisin & Mi Luo, 2017. "Earnings Inequality and Other Determinants of Wealth Inequality," American Economic Review, American Economic Association, vol. 107(5), pages 593-597, May.
    52. Christian Bayer & Klaus Wälde, 2010. "Matching and Saving in Continuous Time: Theory," Working Papers 1004, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz, revised 13 Jan 2010.
    53. Ana Castaneda & Javier Diaz-Gimenez & Jose-Victor Rios-Rull, 2003. "Accounting for the U.S. Earnings and Wealth Inequality," Journal of Political Economy, University of Chicago Press, vol. 111(4), pages 818-857, August.
    54. He, Wei & Sun, Xiang & Sun, Yeneng, 2017. "Modeling infinitely many agents," Theoretical Economics, Econometric Society, vol. 12(2), May.
    55. Juan Carlos Parra-Alvarez & Olaf Posch & Mu-Chun Wang, 2017. "Identification and estimation of heterogeneous agent models: A likelihood approach," CREATES Research Papers 2017-35, Department of Economics and Business Economics, Aarhus University.
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    Cited by:

    1. 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.
    2. Donsimoni Jean Roch & Wälde Klaus & Glawion René & Plachter Bodo, 2020. "Projecting the spread of COVID-19 for Germany," German Economic Review, De Gruyter, vol. 21(2), pages 181-216, June.
    3. Juan Carlos Parra-Alvarez & Olaf Posch & Mu-Chun Wang, 2017. "Estimation of Heterogeneous Agent Models: A Likelihood Approach," CESifo Working Paper Series 6717, CESifo.
    4. Glawion, Rene & Puche, Marc & Haller, Frédéric, 2020. "A General Equilibrium Model of Earnings, Income, and Wealth," VfS Annual Conference 2020 (Virtual Conference): Gender Economics 224580, Verein für Socialpolitik / German Economic Association.

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    More about this item

    Keywords

    dynamics of wealth distributions; NLSY 1979 cohort; capital income risk; Fokker-Planck equations;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • D30 - Microeconomics - - Distribution - - - General
    • E20 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - General (includes Measurement and Data)

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