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The theory of precautionary saving: an overview of recent developments

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  • Donatella Baiardi

    (University of Parma)

  • Marco Magnani

    (University of Parma)

  • Mario Menegatti

    (University of Parma)

Abstract

This work reviews recent developments in the literature analyzing precautionary saving. After a description of traditional precautionary saving theory, which considers labor income risk and interest rate risk, we present different research lines which introduce a wide range of extensions and generalizations of the classical model: the contemporaneous presence of multiple risks, changes in risks of different types, multiple variables affecting household utility, preferences non-featuring risk aversion and joint decisions on many choice variables. For each of these issues, we provide specific highlights which summarize the main results obtained in the literature. Lastly, we briefly discuss the analyzes beyond the classical model.

Suggested Citation

  • Donatella Baiardi & Marco Magnani & Mario Menegatti, 2020. "The theory of precautionary saving: an overview of recent developments," Review of Economics of the Household, Springer, vol. 18(2), pages 513-542, June.
    • Handle: RePEc:kap:reveho:v:18:y:2020:i:2:d:10.1007_s11150-019-09460-3
    DOI: 10.1007/s11150-019-09460-3
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    1. Sebastian Ebert & Diego C. Nocetti & Harris Schlesinger, 2018. "Greater Mutual Aggravation," Management Science, INFORMS, vol. 64(6), pages 2809-2811, June.
    2. repec:dau:papers:123456789/12392 is not listed on IDEAS
    3. Donatella Baiardi & Marco Magnani & Mario Menegatti, 2014. "Precautionary saving under many risks," Journal of Economics, Springer, vol. 113(3), pages 211-228, November.
    4. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
    5. Thomas Eichner & Andreas Wagener, 2004. "Relative risk aversion, relative prudence and comparative statics under uncertainty: The case of (μ, σ)‐preferences," Bulletin of Economic Research, Wiley Blackwell, vol. 56(2), pages 159-170, April.
    6. Dionne, Georges & Eeckhoudt, Louis, 1984. "Insurance and saving: some further results," Insurance: Mathematics and Economics, Elsevier, vol. 3(2), pages 101-110, April.
    7. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    8. Mario Menegatti, 2009. "Optimal saving in the presence of two risks," Journal of Economics, Springer, vol. 96(3), pages 277-288, April.
    9. Eeckhoudt, Louis & Etner, Johanna & Schroyen, Fred, 2009. "The values of relative risk aversion and prudence: A context-free interpretation," Mathematical Social Sciences, Elsevier, vol. 58(1), pages 1-7, July.
    10. Aizenman, Joshua, 1998. "Buffer stocks and precautionary savings with loss aversion," Journal of International Money and Finance, Elsevier, vol. 17(6), pages 931-947, December.
    11. Elyès Jouini & Clotilde Napp & Diego Nocetti, 2013. "Economic consequences of Nth-degree risk increases and Nth-degree risk attitudes," Journal of Risk and Uncertainty, Springer, vol. 47(2), pages 199-224, October.
    12. Desu Liu & Mario Menegatti, 2019. "Precautionary Investment in Wealth and Health," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 86(1), pages 237-255, March.
    13. 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.
    14. Baiardi, Donatella & De Donno, Marzia & Magnani, Marco & Menegatti, Mario, 2015. "New results on precautionary saving under two risks," Economics Letters, Elsevier, vol. 130(C), pages 17-20.
    15. Bowman, David & Minehart, Deborah & Rabin, Matthew, 1999. "Loss aversion in a consumption-savings model," Journal of Economic Behavior & Organization, Elsevier, vol. 38(2), pages 155-178, February.
    16. Annamaria Lusardi & Olivia S. Mitchell, 2014. "The Economic Importance of Financial Literacy: Theory and Evidence," Journal of Economic Literature, American Economic Association, vol. 52(1), pages 5-44, March.
    17. John Beshears & James J. Choi & David Laibson & Brigitte C. Madrian, 2018. "Behavioral Household Finance," NBER Working Papers 24854, National Bureau of Economic Research, Inc.
    18. Hamish Low, 2005. "Self-Insurance in a Life-Cycle Model of Labor Supply and Savings," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 8(4), pages 945-975, October.
    19. Eeckhoudt, Louis & Schlesinger, Harris & Tsetlin, Ilia, 2009. "Apportioning of risks via stochastic dominance," Journal of Economic Theory, Elsevier, vol. 144(3), pages 994-1003, May.
    20. Eeckhoudt, Louis & Gollier, Christian & Schlesinger, Harris, 1996. "Changes in Background Risk and Risk-Taking Behavior," Econometrica, Econometric Society, vol. 64(3), pages 683-689, May.
    21. Kimball, Miles S, 1993. "Standard Risk Aversion," Econometrica, Econometric Society, vol. 61(3), pages 589-611, May.
    22. Gunning, Jan Willem, 2010. "Risk and savings: A taxonomy," Economics Letters, Elsevier, vol. 107(1), pages 39-41, April.
    23. 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.
    24. Dreze, Jacques H. & Modigliani, Franco, 1972. "Consumption decisions under uncertainty," Journal of Economic Theory, Elsevier, vol. 5(3), pages 308-335, December.
    25. Desu Liu & Mario Menegatti, 2019. "Optimal saving and health prevention," Journal of Economics, Springer, vol. 128(2), pages 177-191, October.
    26. 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..
    27. Jingyuan Li, 2012. "Precautionary saving in the presence of labor income and interest rate risks," Journal of Economics, Springer, vol. 106(3), pages 251-266, July.
    28. Alba Lugilde & Roberto Bande & Dolores Riveiro, 2019. "Precautionary Saving: A Review Of The Empirical Literature," Journal of Economic Surveys, Wiley Blackwell, vol. 33(2), pages 481-515, April.
    29. M. Menegatti, 2007. "A new interpretation for the precautionary saving motive: a note," Journal of Economics, Springer, vol. 92(3), pages 275-280, December.
    30. Liu, Liqun, 2014. "Precautionary saving in the large: nth degree deteriorations in future income," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 169-172.
    31. Seth Neumuller & Casey Rothschild, 2017. "Financial Sophistication and Portfolio Choice over the Life Cycle," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 26, pages 243-262, October.
    32. Peter, Richard, 2019. "Revisiting precautionary saving under ambiguity," Economics Letters, Elsevier, vol. 174(C), pages 123-127.
    33. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    34. 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.
    35. Diego Nocetti & William T. Smith, 2011. "Precautionary Saving and Endogenous Labor Supply with and without Intertemporal Expected Utility," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 43(7), pages 1475-1504, October.
    36. W. Chiu & Louis Eeckhoudt & Beatrice Rey, 2012. "On relative and partial risk attitudes: theory and implications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(1), pages 151-167, May.
    37. Laibson, David, 1998. "Life-cycle consumption and hyperbolic discount functions," European Economic Review, Elsevier, vol. 42(3-5), pages 861-871, May.
    38. Bertoni, Marco & Brunello, Giorgio & Mazzarella, Gianluca, 2018. "Does postponing minimum retirement age improve healthy behaviors before retirement? Evidence from middle-aged Italian workers," Journal of Health Economics, Elsevier, vol. 58(C), pages 215-227.
    39. Menegatti, Mario, 2015. "New results on high-order risk changes," European Journal of Operational Research, Elsevier, vol. 243(2), pages 678-681.
    40. Milton Friedman, 1957. "Introduction to "A Theory of the Consumption Function"," NBER Chapters, in: A Theory of the Consumption Function, pages 1-6, National Bureau of Economic Research, Inc.
    41. Louis Eeckhoudt & Harris Schlesinger, 2006. "Putting Risk in Its Proper Place," American Economic Review, American Economic Association, vol. 96(1), pages 280-289, March.
    42. Berger, Loïc, 2014. "Precautionary saving and the notion of ambiguity prudence," Economics Letters, Elsevier, vol. 123(2), pages 248-251.
    43. 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.
    44. 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.
    45. 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.
    46. Michel Denuit & Louis Eeckhoudt & Mario Menegatti, 2011. "Correlated risks, bivariate utility and optimal choices," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(1), pages 39-54, January.
    47. Michel Denuit & Béatrice Rey, 2014. "Benchmark values for higher order coefficients of relative risk aversion," Post-Print halshs-03353452, HAL.
    48. Denuit, Michel & Rey, Beatrice, 2014. "Benchmark values for higher order coefficients of relative risk aversion," LIDAM Reprints ISBA 2014001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    49. 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.
    50. Louis Eeckhoudt & Béatrice Rey & Harris Schlesinger, 2007. "A Good Sign for Multivariate Risk Taking," Management Science, INFORMS, vol. 53(1), pages 117-124, January.
    51. 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.
    52. Milton Friedman, 1957. "A Theory of the Consumption Function," NBER Books, National Bureau of Economic Research, Inc, number frie57-1, February.
    53. Michel Denuit & Béatrice Rey, 2014. "Benchmark values for higher order coefficients of relative risk aversion," Theory and Decision, Springer, vol. 76(1), pages 81-94, January.
    54. Christophe Courbage & Béatrice Rey, 2007. "Precautionary saving in the presence of other risks," Post-Print halshs-03353387, HAL.
    55. Choi, Gyemyung & Kim, Iltae & Snow, Arthur, 2001. "Comparative Statics Predictions for Changes in Uncertainty in the Portfolio and Savings Problems," Bulletin of Economic Research, Wiley Blackwell, vol. 53(1), pages 61-72, January.
    56. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    57. Mackowiak, Bartosz & Wiederholt, Mirko, 2011. "Inattention to Rare Events," CEPR Discussion Papers 8626, C.E.P.R. Discussion Papers.
    58. Eisenhauer, Joseph G., 2006. "Risk aversion and prudence in the large," Research in Economics, Elsevier, vol. 60(4), pages 179-187, December.
    59. A. Sandmo, 1970. "The Effect of Uncertainty on Saving Decisions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 37(3), pages 353-360.
    60. Selden, Larry, 1978. "A New Representation of Preferences over "Certain A Uncertain" Consumption Pairs: The "Ordinal Certainty Equivalent" Hypothesis," Econometrica, Econometric Society, vol. 46(5), pages 1045-1060, September.
    61. Moffet, Denis, 1975. "Risk-Bearing And Consumption Theory," ASTIN Bulletin, Cambridge University Press, vol. 8(3), pages 342-358, September.
    62. Eeckhoudt, Louis & Gollier, Christian & Schneider, Thierry, 1995. "Risk-aversion, prudence and temperance: A unified approach," Economics Letters, Elsevier, vol. 48(3-4), pages 331-336, June.
    63. Peter, Richard, 2017. "Optimal self-protection in two periods: On the role of endogenous saving," Journal of Economic Behavior & Organization, Elsevier, vol. 137(C), pages 19-36.
    64. Ekern, Steinar, 1980. "Increasing Nth degree risk," Economics Letters, Elsevier, vol. 6(4), pages 329-333.
    65. Milton Friedman & L. J. Savage, 1948. "The Utility Analysis of Choices Involving Risk," Journal of Political Economy, University of Chicago Press, vol. 56(4), pages 279-279.
    66. Annamaria Lusardi & Pierre-Carl Michaud & Olivia S. Mitchell, 2017. "Optimal Financial Knowledge and Wealth Inequality," Journal of Political Economy, University of Chicago Press, vol. 125(2), pages 431-477.
    67. Menegatti, Mario & Rebessi, Filippo, 2011. "On the substitution between saving and prevention," Mathematical Social Sciences, Elsevier, vol. 62(3), pages 176-182.
    68. Menegatti, Mario, 2001. "On the Conditions for Precautionary Saving," Journal of Economic Theory, Elsevier, vol. 98(1), pages 189-193, May.
    69. Patrick L. Brockett & Linda L. Golden, 1987. "A Class of Utility Functions Containing all the Common Utility Functions," Management Science, INFORMS, vol. 33(8), pages 955-964, August.
    70. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    71. Menezes, C & Geiss, C & Tressler, J, 1980. "Increasing Downside Risk," American Economic Review, American Economic Association, vol. 70(5), pages 921-932, December.
    72. Marco Magnani, 2017. "A new interpretation of the condition for precautionary saving in the presence of an interest-rate risk," Journal of Economics, Springer, vol. 120(1), pages 79-87, January.
    73. Rothschild, Michael & Stiglitz, Joseph E., 1971. "Increasing risk II: Its economic consequences," Journal of Economic Theory, Elsevier, vol. 3(1), pages 66-84, March.
    74. David Crainich & Louis Eeckhoudt & Alain Trannoy, 2013. "Even (Mixed) Risk Lovers Are Prudent," American Economic Review, American Economic Association, vol. 103(4), pages 1529-1535, June.
    75. 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.
    76. Diego C. Nocetti, 2016. "Robust Comparative Statics of Risk Changes," Management Science, INFORMS, vol. 62(5), pages 1381-1392, May.
    77. Steinorth, Petra, 2011. "Impact of health savings accounts on precautionary savings, demand for health insurance and prevention effort," Journal of Health Economics, Elsevier, vol. 30(2), pages 458-465, March.
    78. Hubbard, R Glenn & Judd, Kenneth L, 1987. "Social Security and Individual Welfare: Precautionary Saving, Borrowing Constraints, and the Payroll Tax," American Economic Review, American Economic Association, vol. 77(4), pages 630-646, September.
    79. Gollier, Christian & Pratt, John W, 1996. "Risk Vulnerability and the Tempering Effect of Background Risk," Econometrica, Econometric Society, vol. 64(5), pages 1109-1123, September.
    80. Kit Pong Wong, 2019. "An interpretation of the condition for precautionary saving: the case of greater higher-order interest rate risk," Journal of Economics, Springer, vol. 126(3), pages 275-286, April.
    81. Peter C. Fishburn & R. Burr Porter, 1976. "Optimal Portfolios with One Safe and One Risky Asset: Effects of Changes in Rate of Return and Risk," Management Science, INFORMS, vol. 22(10), pages 1064-1073, June.
    82. 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.
    83. Mario Menegatti, 2009. "Precautionary saving in the presence of other risks: a comment," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 39(3), pages 473-476, June.
    84. Sebastian Ebert, 2013. "Even (Mixed) Risk Lovers Are Prudent: Comment," American Economic Review, American Economic Association, vol. 103(4), pages 1536-1537, June.
    85. L. Eeckhoudt & H. Bleichrodt, 2005. "Saving under rank-dependent expected utility," Post-Print hal-00326118, HAL.
    86. Vergara, Marcos, 2017. "Precautionary saving: A taxonomy of prudence," Economics Letters, Elsevier, vol. 150(C), pages 18-20.
    87. Engen, Eric M. & Gruber, Jonathan, 2001. "Unemployment insurance and precautionary saving," Journal of Monetary Economics, Elsevier, vol. 47(3), pages 545-579, June.
    88. Abel, Andrew B, 1985. "Precautionary Saving and Accidental Bequests," American Economic Review, American Economic Association, vol. 75(4), pages 777-791, September.
    89. Wang, Hongxia & Wang, Jianli & Li, Jingyuan & Xia, Xinping, 2015. "Precautionary paying for stochastic improvements under background risks," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 180-185.
    90. Annette Hofmann & Richard Peter, 2016. "Self-Insurance, Self-Protection, and Saving: On Consumption Smoothing and Risk Management," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 83(3), pages 719-734, September.
    91. Menegatti, Mario, 2014. "New results on the relationship among risk aversion, prudence and temperance," European Journal of Operational Research, Elsevier, vol. 232(3), pages 613-617.
    92. Lajeri-Chaherli, Fatma, 2004. "Proper prudence, standard prudence and precautionary vulnerability," Economics Letters, Elsevier, vol. 82(1), pages 29-34, January.
    93. Aurélien Baillon, 2017. "Prudence With Respect To Ambiguity," Economic Journal, Royal Economic Society, vol. 127(604), pages 1731-1755, September.
    94. Aurélien Baillon, 2017. "Prudence With Respect To Ambiguity," Economic Journal, Royal Economic Society, vol. 127(604), pages 1731-1755, September.
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