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Risk Aversion and Precautionary Savings in Dynamic Settings

Author

Listed:
  • Antoine Bommier

    (Department of Management, Technology and Economics, ETH Zurich, 8092 Zurich, Switzerland)

  • François Le Grand

    (emlyon Business School, 69130 Écully, France; ETH Zurich, 8092 Zurich, Switzerland)

Abstract

We study the saving behavior of infinitely long-lived agents who face income uncertainty and deterministic interest rates. Using monotone recursive preferences, we prove that risk aversion unambiguously increases savings. The result accounts for possibly binding borrowing constraints and holds for very general specification of income uncertainty, which can follow any kind of stochastically monotone process.

Suggested Citation

  • Antoine Bommier & François Le Grand, 2019. "Risk Aversion and Precautionary Savings in Dynamic Settings," Management Science, INFORMS, vol. 65(3), pages 1386-1397, March.
    • Handle: RePEc:inm:ormnsc:v:65:y:2019:i:3:p:1386-1397
    DOI: 10.1287/mnsc.2017.2959
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    as
    1. Araujo, A, 1991. "The Once but Not Twice Differentiability of the Policy Function," Econometrica, Econometric Society, vol. 59(5), pages 1383-1393, September.
    2. Ashoka Mody & Franziska Ohnsorge & Damiano Sandri, 2012. "Precautionary Savings in the Great Recession," IMF Economic Review, Palgrave Macmillan;International Monetary Fund, vol. 60(1), pages 114-138, April.
    3. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    4. 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.
    5. Jouini, Elyès & Napp, Clotilde & Nocetti, Diego, 2013. "On multivariate prudence," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1255-1267.
    6. Benveniste, L M & Scheinkman, J A, 1979. "On the Differentiability of the Value Function in Dynamic Models of Economics," Econometrica, Econometric Society, vol. 47(3), pages 727-732, May.
    7. Miles Kimball & Philippe Weil, 2009. "Precautionary Saving and Consumption Smoothing across Time and Possibilities," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 41(2‐3), pages 245-284, March.
    8. Han Bleichrodt & Louis Eeckhoudt, 2005. "Saving under rank-dependent utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(2), pages 505-511, February.
    9. Edouard Challe & Xavier Ragot, 2016. "Precautionary Saving Over the Business Cycle," Economic Journal, Royal Economic Society, vol. 126(590), pages 135-164, February.
    10. Denuit, M. & Eeckhoudt L., 2010. "A general index of absolute risk attitude," LIDAM Discussion Papers ISBA 2010013, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    11. Bommier, Antoine & Chassagnon, Arnold & Le Grand, François, 2012. "Comparative risk aversion: A formal approach with applications to saving behavior," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1614-1641.
    12. Santos, Manuel S, 1991. "Smoothness of the Policy Function in Discrete Time Economic Models," Econometrica, Econometric Society, vol. 59(5), pages 1365-1382, September.
    13. repec:dau:papers:123456789/7344 is not listed on IDEAS
    14. Thomas W. Bates & Kathleen M. Kahle & René M. Stulz, 2009. "Why Do U.S. Firms Hold So Much More Cash than They Used To?," Journal of Finance, American Finance Association, vol. 64(5), pages 1985-2021, October.
    15. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Control and Model Misspecification," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 6, pages 155-216, World Scientific Publishing Co. Pte. Ltd..
    16. Kihlstrom, Richard E. & Mirman, Leonard J., 1974. "Risk aversion with many commodities," Journal of Economic Theory, Elsevier, vol. 8(3), pages 361-388, July.
    17. Eeckhoudt, Louis & Schlesinger, Harris, 2008. "Changes in risk and the demand for saving," Journal of Monetary Economics, Elsevier, vol. 55(7), pages 1329-1336, October.
    18. Pye, Gordon, 1973. "Lifetime Portfolio Selection in Continuous Time for a Multiplicative Class of Utility Functions," American Economic Review, American Economic Association, vol. 63(5), pages 1013-1016, December.
    19. 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.
    20. Christophe Courbage & Béatrice Rey, 2007. "Precautionary saving in the presence of other risks," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 32(2), pages 417-424, August.
    21. Philippe Weil, 1990. "Nonexpected Utility in Macroeconomics," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 105(1), pages 29-42.
    22. Tauchen, George, 1986. "Finite state markov-chain approximations to univariate and vector autoregressions," Economics Letters, Elsevier, vol. 20(2), pages 177-181.
    23. Miller, Bruce L., 1976. "The effect on optimal consumption of increased uncertainty in labor income in the multiperiod case," Journal of Economic Theory, Elsevier, vol. 13(1), pages 154-167, August.
    24. Frederick van der Ploeg, 1993. "A Closed-form Solution for a Model of Precautionary Saving," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(2), pages 385-395.
    25. Ran Duchin, 2010. "Cash Holdings and Corporate Diversification," Journal of Finance, American Finance Association, vol. 65(3), pages 955-992, June.
    26. Santos, Manuel S. & Vila, Jean-Luc, 1991. "Smoothness of the policy function in continuous-time economic models : The one-dimensional case," Journal of Economic Dynamics and Control, Elsevier, vol. 15(4), pages 741-753, October.
    27. Murillo Campello & Erasmo Giambona & John R. Graham & Campbell R. Harvey, 2011. "Liquidity Management and Corporate Investment During a Financial Crisis," The Review of Financial Studies, Society for Financial Studies, vol. 24(6), pages 1944-1979.
    28. Christophe Courbage & Béatrice Rey, 2007. "Precautionary saving in the presence of other risks," Post-Print halshs-03353387, HAL.
    29. Larry G. Epstein & Stanley E. Zin, 2013. "Substitution, risk aversion and the temporal behavior of consumption and asset returns: A theoretical framework," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 12, pages 207-239, World Scientific Publishing Co. Pte. Ltd..
    30. A. Sandmo, 1970. "The Effect of Uncertainty on Saving Decisions," Review of Economic Studies, Oxford University Press, vol. 37(3), pages 353-360.
    31. W. Henry Chiu, 2005. "Skewness Preference, Risk Aversion, and the Precedence Relations on Stochastic Changes," Management Science, INFORMS, vol. 51(12), pages 1816-1828, December.
    32. Sebastian Ebert & Daniel Wiesen, 2011. "Testing for Prudence and Skewness Seeking," Management Science, INFORMS, vol. 57(7), pages 1334-1349, July.
    33. Christopher D. Carroll, 1997. "Buffer-Stock Saving and the Life Cycle/Permanent Income Hypothesis," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(1), pages 1-55.
    34. Menezes, C & Geiss, C & Tressler, J, 1980. "Increasing Downside Risk," American Economic Review, American Economic Association, vol. 70(5), pages 921-932, December.
    35. Yaari, Menahem E., 1969. "Some remarks on measures of risk aversion and on their uses," Journal of Economic Theory, Elsevier, vol. 1(3), pages 315-329, October.
    36. Diego C. Nocetti, 2016. "Robust Comparative Statics of Risk Changes," Management Science, INFORMS, vol. 62(5), pages 1381-1392, May.
    37. Michel M. Denuit & Louis Eeckhoudt, 2010. "A General Index of Absolute Risk Attitude," Management Science, INFORMS, vol. 56(4), pages 712-715, April.
    38. Campello, Murillo & Graham, John R. & Harvey, Campbell R., 2010. "The real effects of financial constraints: Evidence from a financial crisis," Journal of Financial Economics, Elsevier, vol. 97(3), pages 470-487, September.
    39. Philippe Weil, 1993. "Precautionary Savings and the Permanent Income Hypothesis," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(2), pages 367-383.
    40. Antoine Bommier & Asen Kochov & François Le Grand, 2017. "On Monotone Recursive Preferences," Econometrica, Econometric Society, vol. 85, pages 1433-1466, September.
    41. Scott F. Richard, 1975. "Multivariate Risk Aversion, Utility Independence and Separable Utility Functions," Management Science, INFORMS, vol. 22(1), pages 12-21, September.
    42. TallariniJr., Thomas D., 2000. "Risk-sensitive real business cycles," Journal of Monetary Economics, Elsevier, vol. 45(3), pages 507-532, June.
    43. Antoine Bommier, 2013. "Life-Cycle Preferences Revisited," Journal of the European Economic Association, European Economic Association, vol. 11(6), pages 1290-1319, December.
    44. Duchin, Ran & Ozbas, Oguzhan & Sensoy, Berk A., 2010. "Costly external finance, corporate investment, and the subprime mortgage credit crisis," Journal of Financial Economics, Elsevier, vol. 97(3), pages 418-435, September.
    45. Hayne E. Leland, 1968. "Saving and Uncertainty: The Precautionary Demand for Saving," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 82(3), pages 465-473.
    46. Dreze, Jacques H. & Modigliani, Franco, 1972. "Consumption decisions under uncertainty," Journal of Economic Theory, Elsevier, vol. 5(3), pages 308-335, December.
    47. Antoine Bommier & Arnold Chassagnon & François Le Grand, 2012. "Comparative risk aversion: A formal approach with applications to saving behavior," PSE-Ecole d'économie de Paris (Postprint) halshs-00754583, HAL.
    48. Ahn, Chang Mo, 1989. " The Effect of Temporal Risk Aversion on Optimal Consumption, the Equity Premium, and the Equilibrium Interest Rate," Journal of Finance, American Finance Association, vol. 44(5), pages 1411-1420, December.
    49. Antoine Bommier & Arnold Chassagnon & François Le Grand, 2012. "Comparative risk aversion: A formal approach with applications to saving behavior," Post-Print halshs-00754583, HAL.
    50. Duncan, George T, 1977. "A Matrix Measure of Multivariate Local Risk Aversion," Econometrica, Econometric Society, vol. 45(4), pages 895-903, May.
    51. Karni, Edi, 1979. "On Multivariate Risk Aversion," Econometrica, Econometric Society, vol. 47(6), pages 1391-1401, November.
    52. Denuit, M. & Eeckhoudt, L., 2010. "A General Index of Absolute Risk Attitude," LIDAM Reprints ISBA 2010026, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    53. repec:hal:spmain:info:hdl:2441/54k1p7hdq38odb1k39k1rdm8di is not listed on IDEAS
    54. Lins, Karl V. & Servaes, Henri & Tufano, Peter, 2010. "What drives corporate liquidity? An international survey of cash holdings and lines of credit," Journal of Financial Economics, Elsevier, vol. 98(1), pages 160-176, October.
    55. Antoine Bommier & Arnold Chassagnon & François Le Grand, 2012. "Comparative risk aversion : A formal approach with applications to saving behavior," Post-Print hal-02312602, HAL.
    56. Kreps, David M & Porteus, Evan L, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Econometrica, Econometric Society, vol. 46(1), pages 185-200, January.
    57. repec:dau:papers:123456789/4434 is not listed on IDEAS
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