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Cognition and Wealth: The Importance of Probabilistic Thinking


  • Lee Lillard
  • Robert J. Willis

    (University of Michigan)


This paper utilizes a large set of subjective probability questions from the Health and Retirement Survey to construct an index measuring the precision of probabilistic beliefs (PPB) and relates this index to household choices about the riskiness of their portfolios and the rate of growth of their net worth. A theory of uncertainty aversion based on repeated sampling is proposed that resolves the Ellsberg Paradox within a conventional expected utility model. In this theory, uncertainty aversion is implied by risk aversion. This theory is then used to propose a link between an individual’s degree of uncertainty and his propensity to give “focal” answers of “0”, “50_50” or “100” or “exact” answers to survey questions and the validity of this interpretation is tested empirically. Finally, an index of the precision of probabilistic thinking is constructed by calculating the fraction of probability questions to which each HRS respondent gives a non-focal answer. This index is shown to have a statistically and economically significant positive effect on the fraction of risky assets in household portfolios and on the rate of growth of these assets longitudinally. These results suggest that there is systematic variation in the competence of individuals to manage investment accounts that should be considered in designing policies to create individual retirement accounts in the Social Security system.

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  • Lee Lillard & Robert J. Willis, 2001. "Cognition and Wealth: The Importance of Probabilistic Thinking," Working Papers wp007, University of Michigan, Michigan Retirement Research Center.
  • Handle: RePEc:mrr:papers:wp007

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    References listed on IDEAS

    1. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
    2. Lillard, Lee A & Willis, Robert J, 1978. "Dynamic Aspects of Earning Mobility," Econometrica, Econometric Society, vol. 46(5), pages 985-1012, September.
    3. Michael D. Hurd & Kathleen McGarry, 1995. "Evaluation of the Subjective Probabilities of Survival in the Health and Retirement Study," Journal of Human Resources, University of Wisconsin Press, vol. 30, pages s268-s292.
    4. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    5. Smith, J-P, 1997. "Inheritances and Bequests," Papers 97-04, RAND - Labor and Population Program.
    6. Chris Starmer, 2000. "Developments in Non-expected Utility Theory: The Hunt for a Descriptive Theory of Choice under Risk," Journal of Economic Literature, American Economic Association, vol. 38(2), pages 332-382, June.
    7. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, Oxford University Press, vol. 75(4), pages 643-669.
    8. James M. Poterba & David A. Wise, 1998. "Individual Financial Decisions in Retirement Saving Plans and the Provision of Resources for Retirement," NBER Chapters,in: Privatizing Social Security, pages 363-401 National Bureau of Economic Research, Inc.
    9. F. Thomas Juster & Richard Suzman, 1995. " An Overview of the Health and Retirement Study," Journal of Human Resources, University of Wisconsin Press, vol. 30, pages s7-s56.
    10. Heckman, James J & Willis, Robert J, 1977. "A Beta-logistic Model for the Analysis of Sequential Labor Force Participation by Married Women," Journal of Political Economy, University of Chicago Press, vol. 85(1), pages 27-58, February.
    11. Arulampalam, W. & Robin A. Naylor & Jeremy P. Smith, 2002. "University of Warwick," Royal Economic Society Annual Conference 2002 9, Royal Economic Society.
    12. Michael D. Hurd & Daniel L. McFadden & Li Gan, 1998. "Subjective Survival Curves and Life Cycle Behavior," NBER Chapters,in: Inquiries in the Economics of Aging, pages 259-309 National Bureau of Economic Research, Inc.
    13. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    14. William R. Johnson, 1978. "A Theory of Job Shopping," The Quarterly Journal of Economics, Oxford University Press, vol. 92(2), pages 261-277.
    15. Willis, Robert J., 1999. "Theory confronts data: how the HRS is shaped by the economics of aging and how the economics of aging will be shaped by the HRS," Labour Economics, Elsevier, vol. 6(2), pages 119-145, June.
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    Cited by:

    1. Thomas Dohmen & Armin Falk & David Huffman & Uwe Sunde, 2010. "Are Risk Aversion and Impatience Related to Cognitive Ability?," American Economic Review, American Economic Association, vol. 100(3), pages 1238-1260, June.
    2. Aylit Tina Romm, 2012. "Retirement Date Effects on Pre-Retirement Wealth Accumulation: An Analysis of US Households," Working Papers 266, Economic Research Southern Africa.
    3. John Ameriks & Andrew Caplin & Steven Laufer & Stijn Van Nieuwerburgh, 2007. "The Joy of Giving or Assisted Living? Using Strategic Surveys to Separate Bequest and Precautionary Motives," NBER Working Papers 13105, National Bureau of Economic Research, Inc.
    4. Wändi Bruine de Bruin & Andrew Parker & Jürgen Maurer, 2011. "Assessing small non-zero perceptions of chance: The case of H1N1 (swine) flu risks," Journal of Risk and Uncertainty, Springer, vol. 42(2), pages 145-159, April.
    5. Adeline Delavande & Hans-Peter Kohler, 2009. "Subjective expectations in the context of HIV/AIDS in Malawi," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 20(31), pages 817-875, June.
    6. Daniel J. Benjamin & Sebastian A. Brown & Jesse M. Shapiro, 2013. "Who Is ‘Behavioral’? Cognitive Ability And Anomalous Preferences," Journal of the European Economic Association, European Economic Association, vol. 11(6), pages 1231-1255, December.
    7. Claudia R. Sahm, 2007. "Stability of risk preference," Finance and Economics Discussion Series 2007-66, Board of Governors of the Federal Reserve System (U.S.).
    8. repec:wsi:qjfxxx:v:02:y:2012:i:04:n:s2010139212500206 is not listed on IDEAS
    9. Aylit Romm, 2015. "The Effect of Retirement Date Expectations on Pre-retirement Wealth Accumulation: The Role of Gender and Bargaining Power in Married US Households," Journal of Family and Economic Issues, Springer, vol. 36(4), pages 593-605, December.
    10. Andrew M. Parker & Leandro S. Carvalho & Susann Rohwedder, 2013. "Cognitive Ability, Expectations, and Beliefs about the Future: Psychological Influences on Retirement Decisions," Working Papers wp298, University of Michigan, Michigan Retirement Research Center.
    11. Aylit Tina Romm, 2014. "An interpretation of focal point responses as non-additive beliefs," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 9(5), pages 387-402, September.
    12. Steven Haider & Mel StephensJr., 2006. "How Accurate are Expected Retirement Savings?," Working Papers wp128, University of Michigan, Michigan Retirement Research Center.
    13. Post, Thomas & Hanewald, Katja, 2013. "Longevity risk, subjective survival expectations, and individual saving behavior," Journal of Economic Behavior & Organization, Elsevier, vol. 86(C), pages 200-220.
    14. Olympia Bover, 2015. "Measuring expectations from household surveys: new results on subjective probabilities of future house prices," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 6(4), pages 361-405, November.
    15. Adeline Delavande & Susann Rohwedder, 2008. "Differential Mortality in Europe and the U.S. Estimates Based on Subjective Probabilities of Survival," Working Papers 613, RAND Corporation.
    16. Adeline Delavande & Susann Rohwedder, 2008. "Eliciting Subjective Expectations in Internet Surveys," Working Papers 589, RAND Corporation.
    17. Todd Elder, 2007. "Subjective Survival Probabilities in the Health and Retirement Study: Systematic Biases and Predictive Validity," Working Papers wp159, University of Michigan, Michigan Retirement Research Center.
    18. repec:eee:moneco:v:90:y:2017:i:c:p:1-12 is not listed on IDEAS
    19. Gábor Kézdi & Robert J. Willis, 2003. "Who Becomes a Stockholder? Expectations, SUbjective Uncertainty, and Asset Allocation," Working Papers wp039, University of Michigan, Michigan Retirement Research Center.
    20. Julia P. Prims & Don A. Moore, 2017. "Overconfidence over the lifespan," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 12(1), pages 29-41, January.

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