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Risk, Delay, and Convex Self-Control Costs


  • Drew Fudenberg
  • David K. Levine


We develop a dual-self model of self-control that is compatible with modern dynamic macroeconomic theory and evidence. We show that a convex cost of self-control explains a wide range of behavioral anomalies concerning risk, including the Allais paradox, and also explains the observed interaction between risk and delay. We calibrate the model to obtain a quantitative fit. We find that most of the data can be explained with subjective interest rates in the range of 1-7 percent, short-run relative risk aversion of about two, and a time horizon of one day for the short-run self. (JEL D11, D44, D81)

Suggested Citation

  • Drew Fudenberg & David K. Levine, 2011. "Risk, Delay, and Convex Self-Control Costs," American Economic Journal: Microeconomics, American Economic Association, vol. 3(3), pages 34-68, August.
  • Handle: RePEc:aea:aejmic:v:3:y:2011:i:3:p:34-68 Note: DOI: 10.1257/mic.3.3.34

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    References listed on IDEAS

    1. Matthew Rabin, 2000. "Risk Aversion and Expected-Utility Theory: A Calibration Theorem," Econometrica, Econometric Society, vol. 68(5), pages 1281-1292, September.
    2. Andrew Postlewaite & Larry Samuelson & Dan Silverman, 2001. "Consumption Commitments and Preferences for Risk," PIER Working Paper Archive 04-021, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 18 May 2004.
    3. Isabelle Brocas & Juan D. Carrillo, 2008. "The Brain as a Hierarchical Organization," American Economic Review, American Economic Association, vol. 98(4), pages 1312-1346, September.
    4. Raj Chetty & Adam Szeidl, 2007. "Consumption Commitments and Risk Preferences," The Quarterly Journal of Economics, Oxford University Press, vol. 122(2), pages 831-877.
    5. David K. Levine & Drew Fudenberg, 2006. "A Dual-Self Model of Impulse Control," American Economic Review, American Economic Association, vol. 96(5), pages 1449-1476, December.
    6. Charles A. Holt & Susan K. Laury, 2002. "Risk Aversion and Incentive Effects," American Economic Review, American Economic Association, vol. 92(5), pages 1644-1655, December.
    7. Adrian Bruhin & Helga Fehr-Duda & Thomas Epper, 2010. "Risk and Rationality: Uncovering Heterogeneity in Probability Distortion," Econometrica, Econometric Society, vol. 78(4), pages 1375-1412, July.
    8. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-291, March.
    9. B. Douglas Bernheim & Antonio Rangel, 2004. "Addiction and Cue-Triggered Decision Processes," American Economic Review, American Economic Association, vol. 94(5), pages 1558-1590, December.
    10. Loewenstein, George & O'Donoghue, Ted, 2004. "Animal Spirits: Affective and Deliberative Processes in Economic Behavior," Working Papers 04-14, Cornell University, Center for Analytic Economics.
    11. Battalio, Raymond C & Kagel, John H & Jiranyakul, Komain, 1990. "Testing between Alternative Models of Choice under Uncertainty: Some Initial Results," Journal of Risk and Uncertainty, Springer, vol. 3(1), pages 25-50, March.
    12. 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.
    13. Manel Baucells & Franz Heukamp, 2010. "Common ratio using delay," Theory and Decision, Springer, vol. 68(1), pages 149-158, February.
    14. Benhabib, Jess & Bisin, Alberto, 2005. "Modeling internal commitment mechanisms and self-control: A neuroeconomics approach to consumption-saving decisions," Games and Economic Behavior, Elsevier, vol. 52(2), pages 460-492, August.
    15. Shiv, Baba & Fedorikhin, Alexander, 1999. " Heart and Mind in Conflict: The Interplay of Affect and Cognition in Consumer Decision Making," Journal of Consumer Research, Oxford University Press, vol. 26(3), pages 278-292, December.
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    Cited by:

    1. Isabelle Brocas & Juan D Carrillo, 2007. "Reason, Emotion, and Information Processing in the Brain," Levine's Working Paper Archive 122247000000001594, David K. Levine.
    2. Fudenberg, Drew & Levine, David K. & Maniadis, Zacharias, 2014. "An approximate dual-self model and paradoxes of choice under risk," Journal of Economic Psychology, Elsevier, vol. 41(C), pages 55-67.
    3. Alexandrer Groves, 2013. "Identifying What is Tempting," 2013 Papers pgr489, Job Market Papers.
    4. Drichoutis, Andreas C. & Nayga, Rodolfo M., 2013. "Eliciting risk and time preferences under induced mood states," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 45(C), pages 18-27.
    5. Koch, Alexander K. & Nafziger, Julia, 2016. "Goals and bracketing under mental accounting," Journal of Economic Theory, Elsevier, vol. 162(C), pages 305-351.
    6. Tim Friehe & Hannah Schildberg-Hörisch, 2014. "Crime and Self-Control Revisited: Disentangling the Effect of Self-Control on Risk and Social Preferences," CESifo Working Paper Series 4747, CESifo Group Munich.
    7. Dufwenberg, Martin & Servátka, Maroš & Vadovič, Radovan, 2017. "Honesty and informal agreements," Games and Economic Behavior, Elsevier, vol. 102(C), pages 269-285.
    8. S. Nageeb Ali, 2011. "Learning Self-Control," The Quarterly Journal of Economics, Oxford University Press, vol. 126(2), pages 857-893.
    9. repec:eee:eecrev:v:100:y:2017:i:c:p:463-487 is not listed on IDEAS
    10. repec:eee:gamebe:v:107:y:2018:i:c:p:329-344 is not listed on IDEAS
    11. Gerhardt, Holger & Schildberg-Hörisch, Hannah & Willrodt, Jana, 2017. "Does self-control depletion affect risk attitudes?," European Economic Review, Elsevier, vol. 100(C), pages 463-487.
    12. Friehe, Tim & Schildberg-Hörisch, Hannah, 2017. "Self-control and crime revisited: Disentangling the effect of self-control on risk taking and antisocial behavior," International Review of Law and Economics, Elsevier, vol. 49(C), pages 23-32.
    13. Mark Schneider, 2016. "Dual Process Utility Theory: A Model of Decisions Under Risk and Over Time," Working Papers 16-23, Chapman University, Economic Science Institute.
    14. Brocas, Isabelle & Carrillo, Juan D., 2014. "Dual-process theories of decision-making: A selective survey," Journal of Economic Psychology, Elsevier, vol. 41(C), pages 45-54.
    15. Alós-Ferrer, Carlos & Strack, Fritz, 2014. "From dual processes to multiple selves: Implications for economic behavior," Journal of Economic Psychology, Elsevier, vol. 41(C), pages 1-11.

    More about this item

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty


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