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A theory of the saving rate of the rich

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  • Ma, Qingyin
  • Toda, Alexis Akira

Abstract

Empirical evidence suggests that the rich have higher propensity to save than do the poor. While this observation may appear to contradict the homotheticity of preferences, we theoretically show that that is not the case. Specifically, we consider an income fluctuation problem with homothetic preferences and general shocks and prove that consumption functions are asymptotically linear, with an exact analytical characterization of asymptotic marginal propensities to consume (MPC). We provide necessary and sufficient conditions for the asymptotic MPCs to be zero. We calibrate a model with standard constant relative risk aversion utility and show that zero asymptotic MPCs are empirically plausible, implying that our mechanism has the potential to accommodate a large saving rate of the rich and high wealth inequality (small Pareto exponent) as observed in the data.

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  • Ma, Qingyin & Toda, Alexis Akira, 2021. "A theory of the saving rate of the rich," Journal of Economic Theory, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:jetheo:v:192:y:2021:i:c:s0022053121000107
    DOI: 10.1016/j.jet.2021.105193
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    1. 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.
    2. Morand, Olivier F. & Reffett, Kevin L., 2003. "Existence and uniqueness of equilibrium in nonoptimal unbounded infinite horizon economies," Journal of Monetary Economics, Elsevier, vol. 50(6), pages 1351-1373, September.
    3. Ivo Welch & Amit Goyal, 2008. "A Comprehensive Look at The Empirical Performance of Equity Premium Prediction," Review of Financial Studies, Society for Financial Studies, vol. 21(4), pages 1455-1508, July.
    4. Carroll, Christopher D., 2009. "Precautionary saving and the marginal propensity to consume out of permanent income," Journal of Monetary Economics, Elsevier, vol. 56(6), pages 780-790, September.
    5. Datta, Manjira & Mirman, Leonard J. & Reffett, Kevin L., 2002. "Existence and Uniqueness of Equilibrium in Distorted Dynamic Economies with Capital and Labor," Journal of Economic Theory, Elsevier, vol. 103(2), pages 377-410, April.
    6. Jaroslav Borovička & John Stachurski, 2020. "Necessary and Sufficient Conditions for Existence and Uniqueness of Recursive Utilities," Journal of Finance, American Finance Association, vol. 75(3), pages 1457-1493, June.
    7. Gary Chamberlain & Charles A. Wilson, 2000. "Optimal Intertemporal Consumption Under Uncertainty," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(3), pages 365-395, July.
    8. Bar Light, 2018. "Precautionary Saving in a Markovian Earnings Environment," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 29, pages 138-147, July.
    9. 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.
    10. Tanaka, Ken'ichiro & Toda, Alexis Akira, 2015. "Discretizing Distributions with Exact Moments: Error Estimate and Convergence Analysis," University of California at San Diego, Economics Working Paper Series qt7g23r5kh, Department of Economics, UC San Diego.
    11. 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.
    12. Erzo G.J. Luttmer, 2010. "Models of Growth and Firm Heterogeneity," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 547-576, September.
    13. Tom Krebs, 2006. "Recursive equilibrium in endogenous growth models with incomplete markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(3), pages 505-523, November.
    14. Lehrer, Ehud & Light, Bar, 2018. "The effect of interest rates on consumption in an income fluctuation problem," Journal of Economic Dynamics and Control, Elsevier, vol. 94(C), pages 63-71.
    15. Carroll, Christopher D & Kimball, Miles S, 1996. "On the Concavity of the Consumption Function," Econometrica, Econometric Society, vol. 64(4), pages 981-992, July.
    16. Li, Huiyu & Stachurski, John, 2014. "Solving the income fluctuation problem with unbounded rewards," Journal of Economic Dynamics and Control, Elsevier, vol. 45(C), pages 353-365.
    17. Mariacristina De Nardi, 2004. "Wealth Inequality and Intergenerational Links," Review of Economic Studies, Oxford University Press, vol. 71(3), pages 743-768.
    18. Andreas Fagereng & Martin Blomhoff Holm & Benjamin Moll & Gisle Natvik, 2019. "Saving Behavior Across the Wealth Distribution: The Importance of Capital Gains," NBER Working Papers 26588, National Bureau of Economic Research, Inc.
    19. 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, Oxford University Press, vol. 131(2), pages 519-578.
    20. Leland E. Farmer & Alexis Akira Toda, 2017. "Discretizing nonlinear, non‐Gaussian Markov processes with exact conditional moments," Quantitative Economics, Econometric Society, vol. 8(2), pages 651-683, July.
    21. Tanaka, Ken’ichiro & Toda, Alexis Akira, 2013. "Discrete approximations of continuous distributions by maximum entropy," Economics Letters, Elsevier, vol. 118(3), pages 445-450.
    22. Karen E. Dynan & Jonathan Skinner & Stephen P. Zeldes, 2004. "Do the Rich Save More?," Journal of Political Economy, University of Chicago Press, vol. 112(2), pages 397-444, April.
    23. Friend, Irwin & Blume, Marshall E, 1975. "The Demand for Risky Assets," American Economic Review, American Economic Association, vol. 65(5), pages 900-922, December.
    24. Rabault, Guillaume, 2002. "When do borrowing constraints bind? Some new results on the income fluctuation problem," Journal of Economic Dynamics and Control, Elsevier, vol. 26(2), pages 217-245, February.
    25. Vincenzo Quadrini, 1999. "The Importance Of Entrepreneurship For Wealth Concentration And Mobility," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 45(1), pages 1-19, March.
    26. Coleman, Wilbur John, II, 1990. "Solving the Stochastic Growth Model by Policy-Function Iteration," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 27-29, January.
    27. Cao, Dan, 2020. "Recursive equilibrium in Krusell and Smith (1998)," Journal of Economic Theory, Elsevier, vol. 186(C).
    28. Moritz Kuhn, 2013. "Recursive Equilibria In An Aiyagari‐Style Economy With Permanent Income Shocks," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 54, pages 807-835, August.
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    Cited by:

    1. Marcello D'Amato & Christian Di Pietro & Marco M. Sorge, 2023. "Left and Right: A Tale of Two Tails of the Wealth Distribution," CSEF Working Papers 691, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    2. Yang, C.C. & Zhao, Xueya & Zhu, Shenghao, 2023. "Tax progressivity and the Pareto tail of income distributions," Economics Letters, Elsevier, vol. 231(C).
    3. Tjeerd de Vries & Alexis Akira Toda, 2022. "Capital and Labor Income Pareto Exponents Across Time and Space," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 68(4), pages 1058-1078, December.
    4. Alexis Akira Toda, 2023. "Unbounded Markov Dynamic Programming with Weighted Supremum Norm Perov Contractions," Papers 2310.04593, arXiv.org.
    5. Tomohiro HIRANO & Ryo Jinnai & Alexis Akira Toda, 2023. "Necessity of Rational Asset Price Bubbles in Two Sector Growth Economies," CIGS Working Paper Series 23-002E, The Canon Institute for Global Studies.
    6. Ma, Qingyin & Toda, Alexis Akira, 2022. "Asymptotic linearity of consumption functions and computational efficiency," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    7. Ma, Qingyin & Stachurski, John & Toda, Alexis Akira, 2022. "Unbounded dynamic programming via the Q-transform," Journal of Mathematical Economics, Elsevier, vol. 100(C).
    8. 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.
    9. Lee, Byoungchan, 2023. "Wealth Inequality and Endogenous Growth," Journal of Monetary Economics, Elsevier, vol. 133(C), pages 132-148.
    10. Tomohiro Hirano & Alexis Akira Toda, 2023. "Bubble Necessity Theorem," CIGS Working Paper Series 23-011E, The Canon Institute for Global Studies.
    11. Thomas J. Sargent & John Stachurski, 2024. "Dynamic Programming: Finite States," Papers 2401.10473, arXiv.org.

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    More about this item

    Keywords

    Asymptotic linearity; Income fluctuation problem; Monotone convex map; Saving rate;
    All these keywords.

    JEL classification:

    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • D15 - Microeconomics - - Household Behavior - - - Intertemporal Household Choice; Life Cycle Models and Saving
    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth

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