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Who Saves More, the Naive or the Sophisticated Agent?

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  • Ludwig, Alexander
  • Groneck, Max
  • Zimper, Alexander

Abstract

We consider an additively time-separable life-cycle model for the family of power period utility functions u such that u'(c) = c^(-theta) for resistance to inter-temporal substitution of theta > 0. The utility maximization problem over life-time consumption is dynamically inconsistent for almost all specifications of effective discount factors. Pollak (1968) shows that the savings behavior of a sophisticated agent and her naive counterpart is always identical for a logarithmic utility function (i.e., for theta = 1). As an extension of Pollak's result we show that the sophisticated agent saves a greater (smaller) fraction of her wealth in every period than her naive counterpart whenever theta > 1 (theta

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  • Ludwig, Alexander & Groneck, Max & Zimper, Alexander, 2021. "Who Saves More, the Naive or the Sophisticated Agent?," CEPR Discussion Papers 16412, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:16412
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    as
    1. A. Ludwig & A. Zimper, 2013. "A parsimonious model of subjective life expectancy," Theory and Decision, Springer, vol. 75(4), pages 519-541, October.
    2. Lee M. Lockwood, 2018. "Incidental Bequests and the Choice to Self-Insure Late-Life Risks," American Economic Review, American Economic Association, vol. 108(9), pages 2513-2550, September.
    3. Itzhak Gilboa, 1988. "A Combination of Expected Utility and Maxmin Decision Criteria," Post-Print hal-00753244, HAL.
    4. R. A. Pollak, 1968. "Consistent Planning," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 35(2), pages 201-208.
    5. Chateauneuf, Alain & Eichberger, Jurgen & Grant, Simon, 2007. "Choice under uncertainty with the best and worst in mind: Neo-additive capacities," Journal of Economic Theory, Elsevier, vol. 137(1), pages 538-567, November.
    6. R. H. Strotz, 1955. "Myopia and Inconsistency in Dynamic Utility Maximization," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 23(3), pages 165-180.
    7. David I. Laibson & Andrea Repetto & Jeremy Tobacman, 1998. "Self-Control and Saving for Retirement," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 29(1), pages 91-196.
    8. Franco Peracchi & Valeria Perotti, 2010. "Subjective survival probabilities and life tables: Evidence from Europe," EIEF Working Papers Series 1016, Einaudi Institute for Economics and Finance (EIEF), revised Nov 2011.
    9. Laibson, David, 1998. "Life-cycle consumption and hyperbolic discount functions," European Economic Review, Elsevier, vol. 42(3-5), pages 861-871, May.
    10. Mohammed Abdellaoui & Aurelien Baillon & Laetitia Placido & Peter P. Wakker, 2011. "The Rich Domain of Uncertainty: Source Functions and Their Experimental Implementation," American Economic Review, American Economic Association, vol. 101(2), pages 695-723, April.
    11. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    12. Yoram Halevy, 2008. "Strotz Meets Allais: Diminishing Impatience and the Certainty Effect," American Economic Review, American Economic Association, vol. 98(3), pages 1145-1162, June.
    13. Hong, Chew Soo & Karni, Edi & Safra, Zvi, 1987. "Risk aversion in the theory of expected utility with rank dependent probabilities," Journal of Economic Theory, Elsevier, vol. 42(2), pages 370-381, August.
    14. Harris, Christopher & Laibson, David, 2001. "Dynamic Choices of Hyperbolic Consumers," Econometrica, Econometric Society, vol. 69(4), pages 935-957, July.
    15. Charles F. Manski, 2004. "Measuring Expectations," Econometrica, Econometric Society, vol. 72(5), pages 1329-1376, September.
    16. Drouhin, Nicolas, 2015. "A rank-dependent utility model of uncertain lifetime," Journal of Economic Dynamics and Control, Elsevier, vol. 53(C), pages 208-224.
    17. Mariacristina De Nardi & Eric French & John B. Jones, 2010. "Why Do the Elderly Save? The Role of Medical Expenses," Journal of Political Economy, University of Chicago Press, vol. 118(1), pages 39-75, February.
    18. Groneck, Max & Ludwig, Alexander & Zimper, Alexander, 2016. "A life-cycle model with ambiguous survival beliefs," Journal of Economic Theory, Elsevier, vol. 162(C), pages 137-180.
    19. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    20. Thomas Epper & Helga Fehr-Duda & Adrian Bruhin, 2011. "Viewing the future through a warped lens: Why uncertainty generates hyperbolic discounting," Journal of Risk and Uncertainty, Springer, vol. 43(3), pages 169-203, December.
    21. Todd Elder, 2013. "The Predictive Validity of Subjective Mortality Expectations: Evidence From the Health and Retirement Study," Demography, Springer;Population Association of America (PAA), vol. 50(2), pages 569-589, April.
    22. Loewenstein, George & Thaler, Richard H, 1989. "Intertemporal Choice," Journal of Economic Perspectives, American Economic Association, vol. 3(4), pages 181-193, Fall.
    23. E. S. Phelps & R. A. Pollak, 1968. "On Second-Best National Saving and Game-Equilibrium Growth," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 35(2), pages 185-199.
    24. 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..
    25. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
    26. Annamarie Lusardi & Olivia S. Mitchell, 2005. "Financial Literacy and Planning: Implications for Retirement Wellbeing," Working Papers wp108, University of Michigan, Michigan Retirement Research Center.
    27. Essid, Samir, 1997. "Choice under risk with certainty and potential effects: A general axiomatic model," Mathematical Social Sciences, Elsevier, vol. 34(3), pages 223-247, October.
    28. Li Gan & Michael D. Hurd & Daniel L. McFadden, 2005. "Individual Subjective Survival Curves," NBER Chapters, in: Analyses in the Economics of Aging, pages 377-412, National Bureau of Economic Research, Inc.
    29. Paul A. Samuelson, 2011. "Lifetime Portfolio Selection by Dynamic Stochastic Programming," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 31, pages 465-472, World Scientific Publishing Co. Pte. Ltd..
    30. George Wu & Richard Gonzalez, 1996. "Curvature of the Probability Weighting Function," Management Science, INFORMS, vol. 42(12), pages 1676-1690, December.
    31. Yoram Halevy, 2015. "Time Consistency: Stationarity and Time Invariance," Econometrica, Econometric Society, vol. 83, pages 335-352, January.
    32. Robert B. Barsky & F. Thomas Juster & Miles S. Kimball & Matthew D. Shapiro, 1997. "Preference Parameters and Behavioral Heterogeneity: An Experimental Approach in the Health and Retirement Study," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(2), pages 537-579.
    33. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    34. George-Marios Angeletos & David Laibson & Andrea Repetto & Jeremy Tobacman & Stephen Weinberg, 2001. "The Hyberbolic Consumption Model: Calibration, Simulation, and Empirical Evaluation," Journal of Economic Perspectives, American Economic Association, vol. 15(3), pages 47-68, Summer.
    35. Drouhin, Nicolas, 2015. "A rank-dependent utility model of uncertain lifetime," Journal of Economic Dynamics and Control, Elsevier, vol. 53(C), pages 208-224.
    36. Bleichrodt, Han & Eeckhoudt, Louis, 2006. "Survival risks, intertemporal consumption, and insurance: The case of distorted probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 335-346, April.
    37. David Laibson, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(2), pages 443-478.
    38. Paul A. Samuelson, 1937. "A Note on Measurement of Utility," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 4(2), pages 155-161.
    39. Mitchell, Olivia S. & Lusardi, Annamaria (ed.), 2011. "Financial Literacy: Implications for Retirement Security and the Financial Marketplace," OUP Catalogue, Oxford University Press, number 9780199696819.
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    2. Adeline Delavande & Jinkook Lee & Seetha Menon, 2017. "Eliciting Survival Expectations of the Elderly in Low-Income Countries: Evidence From India," Demography, Springer;Population Association of America (PAA), vol. 54(2), pages 673-699, April.

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    More about this item

    Keywords

    Life-cycle model; Discount functions; Dynamic inconsistency; Savings behavior; Naive agent; Sophisticated agent; Choquet expected utility preferences; Epstein-weil-zin preferences;
    All these keywords.

    JEL classification:

    • D15 - Microeconomics - - Household Behavior - - - Intertemporal Household Choice; Life Cycle Models and Saving
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth

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