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Income disaster model with optimal consumption

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  • Seyoung Park

    (University of Nottingham)

Abstract

We propose a continuous-time income disaster model with optimal consumption. We endogenously determine the stochastic discount factor (SDF) in an incomplete market caused by income disaster. We then derive optimal consumption decisions for two types of agents, one who is exposed to income disaster and another who is not. We find a large incomplete-markets precautionary savings term between the two agents, which pushes the interest rate down and helps to resolve the risk-free rate puzzle. Interestingly, with income disaster the equilibrium interest rate is a decreasing function of risk aversion while the equity premium is an increasing function. Finally, our model can better match empirical marginal propensities to consume numbers and explain the low-consumption-high-savings puzzle.

Suggested Citation

  • Seyoung Park, 2025. "Income disaster model with optimal consumption," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 80(1), pages 241-320, August.
    • Handle: RePEc:spr:joecth:v:80:y:2025:i:1:d:10.1007_s00199-024-01629-x
    DOI: 10.1007/s00199-024-01629-x
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    1. Fatih Guvenen & Fatih Karahan & Serdar Ozkan & Jae Song, 2015. "What Do Data on Millions of U.S. Workers Reveal about Life-Cycle Earnings Risk?," NBER Working Papers 20913, National Bureau of Economic Research, Inc.
    2. Caballero, Ricardo J., 1990. "Consumption puzzles and precautionary savings," Journal of Monetary Economics, Elsevier, vol. 25(1), pages 113-136, January.
    3. Elmendorf, Douglas W & Kimball, Miles S, 2000. "Taxation of Labor Income and the Demand for Risky Assets," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(3), pages 801-833, August.
    4. Campbell, John Y, 1987. "Does Saving Anticipate Declining Labor Income? An Alternative Test of the Permanent Income Hypothesis," Econometrica, Econometric Society, vol. 55(6), pages 1249-1273, November.
    5. Constantinides, George M & Duffie, Darrell, 1996. "Asset Pricing with Heterogeneous Consumers," Journal of Political Economy, University of Chicago Press, vol. 104(2), pages 219-240, April.
    6. Jun Liu, 2005. "An Equilibrium Model of Rare-Event Premia and Its Implication for Option Smirks," The Review of Financial Studies, Society for Financial Studies, vol. 18(1), pages 131-164.
    7. Wang, Chong & Wang, Neng & Yang, Jinqiang, 2016. "Optimal consumption and savings with stochastic income and recursive utility," Journal of Economic Theory, Elsevier, vol. 165(C), pages 292-331.
    8. Christopher D. Carroll & Karen E. Dynan & Spencer D. Krane, 2003. "Unemployment Risk and Precautionary Wealth: Evidence from Households' Balance Sheets," The Review of Economics and Statistics, MIT Press, vol. 85(3), pages 586-604, August.
    9. Franco Modigliani & Shi Larry Cao, 2004. "The Chinese Saving Puzzle and the Life-Cycle Hypothesis," Journal of Economic Literature, American Economic Association, vol. 42(1), pages 145-170, March.
    10. Christensen, Peter Ove & Larsen, Kasper & Munk, Claus, 2012. "Equilibrium in securities markets with heterogeneous investors and unspanned income risk," Journal of Economic Theory, Elsevier, vol. 147(3), pages 1035-1063.
    11. Krueger, Dirk & Lustig, Hanno, 2010. "When is market incompleteness irrelevant for the price of aggregate risk (and when is it not)?," Journal of Economic Theory, Elsevier, vol. 145(1), pages 1-41, January.
    12. Weil, Philippe, 1989. "The equity premium puzzle and the risk-free rate puzzle," Journal of Monetary Economics, Elsevier, vol. 24(3), pages 401-421, November.
    13. Xavier Gabaix, 2008. "Variable Rare Disasters: A Tractable Theory of Ten Puzzles in Macro-finance," American Economic Review, American Economic Association, vol. 98(2), pages 64-67, May.
    14. John Campbell & Angus Deaton, 1989. "Why is Consumption So Smooth?," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 56(3), pages 357-373.
    15. Xing Jin & Allen X. Zhang, 2012. "Decomposition of Optimal Portfolio Weight in a Jump-Diffusion Model and Its Applications," The Review of Financial Studies, Society for Financial Studies, vol. 25(9), pages 2877-2919.
    16. Lucas, Deborah J., 1994. "Asset pricing with undiversifiable income risk and short sales constraints: Deepening the equity premium puzzle," Journal of Monetary Economics, Elsevier, vol. 34(3), pages 325-341, December.
    17. Hamish Low & Costas Meghir & Luigi Pistaferri, 2010. "Wage Risk and Employment Risk over the Life Cycle," American Economic Review, American Economic Association, vol. 100(4), pages 1432-1467, September.
    18. Ehling, Paul & Gallmeyer, Michael & Heyerdahl-Larsen, Christian & Illeditsch, Philipp, 2018. "Disagreement about inflation and the yield curve," Journal of Financial Economics, Elsevier, vol. 127(3), pages 459-484.
    19. Bernard Dumas & Karen K. Lewis & Emilio Osambela, 2017. "Differences of Opinion and International Equity Markets," The Review of Financial Studies, Society for Financial Studies, vol. 30(3), pages 750-800.
    20. Nicolae Gârleanu & Stavros Panageas, 2015. "Young, Old, Conservative, and Bold: The Implications of Heterogeneity and Finite Lives for Asset Pricing," Journal of Political Economy, University of Chicago Press, vol. 123(3), pages 670-685.
    21. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
    22. Robert J. Barro, 2006. "Rare Disasters and Asset Markets in the Twentieth Century," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 121(3), pages 823-866.
    23. Hyeng Keun Koo, 1998. "Consumption and Portfolio Selection with Labor Income: A Continuous Time Approach," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 49-65, January.
    24. Neng Wang, 2003. "Caballero Meets Bewley: The Permanent-Income Hypothesis in General Equilibrium," American Economic Review, American Economic Association, vol. 93(3), pages 927-936, June.
    25. Jessica A. Wachter, 2013. "Can Time-Varying Risk of Rare Disasters Explain Aggregate Stock Market Volatility?," Journal of Finance, American Finance Association, vol. 68(3), pages 987-1035, June.
    26. Bewley, Truman, 1977. "The permanent income hypothesis: A theoretical formulation," Journal of Economic Theory, Elsevier, vol. 16(2), pages 252-292, December.
    27. repec:bla:jfinan:v:59:y:2004:i:4:p:1481-1509 is not listed on IDEAS
    28. Robert S. Pindyck & Neng Wang, 2013. "The Economic and Policy Consequences of Catastrophes," American Economic Journal: Economic Policy, American Economic Association, vol. 5(4), pages 306-339, November.
    29. Harrison Hong & Neng Wang & Jinqiang Yang, 2023. "Mitigating Disaster Risks in the Age of Climate Change," Econometrica, Econometric Society, vol. 91(5), pages 1763-1802, September.
    30. Ball, R & Brown, P, 1968. "Empirical Evaluation Of Accounting Income Numbers," Journal of Accounting Research, John Wiley & Sons, Ltd., vol. 6(2), pages 159-178.
    31. repec:spo:wpmain:info:hdl:2441/8686 is not listed on IDEAS
    32. Yiqing Lin & Zhenjie Ren & Nizar Touzi & Junjian Yang, 2020. "Random horizon principal-agent problems," Papers 2002.10982, arXiv.org, revised Feb 2022.
    33. Martin L. Weitzman, 2007. "Subjective Expectations and Asset-Return Puzzles," American Economic Review, American Economic Association, vol. 97(4), pages 1102-1130, September.
    34. Fisher, Jonathan D. & Johnson, David S. & Smeeding, Timothy M. & Thompson, Jeffrey P., 2020. "Estimating the marginal propensity to consume using the distributions of income, consumption, and wealth," Journal of Macroeconomics, Elsevier, vol. 65(C).
    35. Painter, Gary & Yang, Xi & Zhong, Ninghua, 2022. "Housing Wealth as Precautionary Saving: Evidence from Urban China," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 57(2), pages 761-789, March.
    36. Fatih Guvenen & Fatih Karahan & Serdar Ozkan & Jae Song, 2021. "What Do Data on Millions of U.S. Workers Reveal About Lifecycle Earnings Dynamics?," Econometrica, Econometric Society, vol. 89(5), pages 2303-2339, September.
    37. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    38. Bernard Dumas & Alexander Kurshev & Raman Uppal, 2009. "Equilibrium Portfolio Strategies in the Presence of Sentiment Risk and Excess Volatility," Journal of Finance, American Finance Association, vol. 64(2), pages 579-629, April.
    39. Xavier Gabaix, 2012. "Variable Rare Disasters: An Exactly Solved Framework for Ten Puzzles in Macro-Finance," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 127(2), pages 645-700.
    40. Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October.
    41. Emmanuel Farhi & Xavier Gabaix, 2016. "Editor's Choice Rare Disasters and Exchange Rates," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 131(1), pages 1-52.
    42. Rietz, Thomas A., 1988. "The equity risk premium a solution," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 117-131, July.
    43. Frey, Carl Benedikt & Osborne, Michael A., 2017. "The future of employment: How susceptible are jobs to computerisation?," Technological Forecasting and Social Change, Elsevier, vol. 114(C), pages 254-280.
    44. Pierre Collin-Dufresne & Michael Johannes & Lars A. Lochstoer, 2016. "Parameter Learning in General Equilibrium: The Asset Pricing Implications," American Economic Review, American Economic Association, vol. 106(3), pages 664-698, March.
    45. Hengjie Ai & Anmol Bhandari, 2021. "Asset Pricing With Endogenously Uninsurable Tail Risk," Econometrica, Econometric Society, vol. 89(3), pages 1471-1505, May.
    46. Jang, Bong-Gyu & Park, Seyoung & Rhee, Yuna, 2013. "Optimal retirement with unemployment risks," Journal of Banking & Finance, Elsevier, vol. 37(9), pages 3585-3604.
    47. Ray Ball & Gil Sadka & Ronnie Sadka, 2009. "Aggregate Earnings and Asset Prices," Journal of Accounting Research, John Wiley & Sons, Ltd., vol. 47(5), pages 1097-1133, December.
    48. Rafael Azevedo & Luis Bettoni & Marcelo Santos, 2024. "Severance savings accounts and life-cycle savings," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 78(4), pages 1275-1331, December.
    49. He, Hui & Huang, Feng & Liu, Zheng & Zhu, Dongming, 2018. "Breaking the “iron rice bowl:” Evidence of precautionary savings from the chinese state-owned enterprises reform," Journal of Monetary Economics, Elsevier, vol. 94(C), pages 94-113.
    50. George M. Constantinides & Anisha Ghosh, 2017. "Asset Pricing with Countercyclical Household Consumption Risk," Journal of Finance, American Finance Association, vol. 72(1), pages 415-460, February.
    51. Blanchet-Scalliet, Christophette & El Karoui, Nicole & Martellini, Lionel, 2005. "Dynamic asset pricing theory with uncertain time-horizon," Journal of Economic Dynamics and Control, Elsevier, vol. 29(10), pages 1737-1764, October.
    52. Flavin, Marjorie A, 1981. "The Adjustment of Consumption to Changing Expectations about Future Income," Journal of Political Economy, University of Chicago Press, vol. 89(5), pages 974-1009, October.
    53. Baker, Steven D. & Hollifield, Burton & Osambela, Emilio, 2016. "Disagreement, speculation, and aggregate investment," Journal of Financial Economics, Elsevier, vol. 119(1), pages 210-225.
    54. Jang, Bong-Gyu & Koo, Hyeng Keun & Park, Seyoung, 2019. "Optimal consumption and investment with insurer default risk," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 44-56.
    55. Alain Bensoussan & Bong-Gyu Jang & Seyoung Park, 2016. "Unemployment Risks and Optimal Retirement in an Incomplete Market," Operations Research, INFORMS, vol. 64(4), pages 1015-1032, August.
    56. Liya Liu & Yingjie Niu & Yuanping Wang & Jinqiang Yang, 2020. "Optimal consumption with time-inconsistent preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(3), pages 785-815, October.
    57. Gormley, Todd & Liu, Hong & Zhou, Guofu, 2010. "Limited participation and consumption-saving puzzles: A simple explanation and the role of insurance," Journal of Financial Economics, Elsevier, vol. 96(2), pages 331-344, May.
    58. Hong Liu & Mark Loewenstein, 2002. "Optimal Portfolio Selection with Transaction Costs and Finite Horizons," The Review of Financial Studies, Society for Financial Studies, vol. 15(3), pages 805-835.
    59. repec:hal:spmain:info:hdl:2441/8686 is not listed on IDEAS
    60. Lorenzo Garlappi & Georgios Skoulakis, 2010. "Solving Consumption and Portfolio Choice Problems: The State Variable Decomposition Method," The Review of Financial Studies, Society for Financial Studies, vol. 23(9), pages 3346-3400.
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    JEL classification:

    • D15 - Microeconomics - - Household Behavior - - - Intertemporal Household Choice; Life Cycle Models and Saving
    • D58 - Microeconomics - - General Equilibrium and Disequilibrium - - - Computable and Other Applied General Equilibrium Models
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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