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Optimal Reference Points and Anticipation

  • Todd Sarver

This paper considers a model of reference-dependent utility in which the individual makes a conscious choice of her reference point for future consumption. The model incorporates the combination of loss aversion and anticipatory utility as competing forces in the determination of the optimal reference point: anticipating better outcomes boosts current utility but also raises the reference level for future consumption, making the individual more susceptible to losses. A central focus of the paper is on the implications of this model of Optimal Anticipation for attitudes toward risk in dynamic environments. The main representation is formulated in an infinite-horizon framework, and axiomatic foundations are provided. I also describe special cases and show in particular that recursive expected utility in the sense of Epstein and Zin (1989) and Kreps and Porteus (1978) can be reinterpreted in terms of optimal anticipation and loss aversion. Finally, I describe a homogeneous version of the model and apply it to a portfolio choice problem. I show that asset pricing for the Optimal Anticipation model is based on simple modifications of standard Euler equations. While maintaining tractability, this model is rich enough to permit first-order risk aversion and can overcome several deficits of standard expected utility, such as the equity premium puzzle and Rabin's paradox. JEL Classification: D03, D81, G12

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Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1566.

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Date of creation: 18 Jun 2012
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Handle: RePEc:nwu:cmsems:1566
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  1. Larry G. Epstein, 2007. "Living with risk," RCER Working Papers 534, University of Rochester - Center for Economic Research (RCER).
  2. Chew, Soo Hong, 1983. "A Generalization of the Quasilinear Mean with Applications to the Measurement of Income Inequality and Decision Theory Resolving the Allais Paradox," Econometrica, Econometric Society, vol. 51(4), pages 1065-92, July.
  3. Sanford J. Grossman & Guy Laroque, 1987. "Asset Pricing and Optimal Portfolio Choice in the Presence of Illiquid Durable Consumption Goods," NBER Working Papers 2369, National Bureau of Economic Research, Inc.
  4. Machina, Mark J, 1982. ""Expected Utility" Analysis without the Independence Axiom," Econometrica, Econometric Society, vol. 50(2), pages 277-323, March.
  5. Haluk Ergin & Todd Sarver, 2012. "Hidden Actions and Preferences for Timing of Resolution of Uncertainty," Discussion Papers 1567, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. Weil, Philippe, 1990. "Nonexpected Utility in Macroeconomics," The Quarterly Journal of Economics, MIT Press, vol. 105(1), pages 29-42, February.
  7. Lars Peter Hansen & Ravi Jagannathan, 1990. "Implications of security market data for models of dynamic economies," Discussion Paper / Institute for Empirical Macroeconomics 29, Federal Reserve Bank of Minneapolis.
  8. Machina, Mark J., 1984. "Temporal risk and the nature of induced preferences," Journal of Economic Theory, Elsevier, vol. 33(2), pages 199-231, August.
  9. Pascal J. Maenhout, 2004. "Robust Portfolio Rules and Asset Pricing," Review of Financial Studies, Society for Financial Studies, vol. 17(4), pages 951-983.
  10. Kocherlakota, N., 1995. "The Equity Premium: It's Still a Puzzle," Working Papers 95-05, University of Iowa, Department of Economics.
  11. Epstein, Larry G. & Zin, Stanley E., 2001. "The independence axiom and asset returns," Journal of Empirical Finance, Elsevier, vol. 8(5), pages 537-572, December.
  12. Epstein, Larry G & Zin, Stanley E, 1991. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: An Empirical Analysis," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 263-86, April.
  13. R. Mehra & E. Prescott, 2010. "The equity premium: a puzzle," Levine's Working Paper Archive 1401, David K. Levine.
  14. Faruk Gul & Wolfgang Pesendorfer, 2004. "Self-Control and the Theory of Consumption," Econometrica, Econometric Society, vol. 72(1), pages 119-158, 01.
  15. Epstein, Larry G. & Zin, Stanley E., 1990. "'First-order' risk aversion and the equity premium puzzle," Journal of Monetary Economics, Elsevier, vol. 26(3), pages 387-407, December.
  16. Andrew Caplin & John Leahy, 2001. "Psychological Expected Utility Theory And Anticipatory Feelings," The Quarterly Journal of Economics, MIT Press, vol. 116(1), pages 55-79, February.
  17. Shlomo Benartzi & Richard H. Thaler, 1993. "Myopic Loss Aversion and the Equity Premium Puzzle," NBER Working Papers 4369, National Bureau of Economic Research, Inc.
  18. Barillas, Francisco & Hansen, Lars Peter & Sargent, Thomas J., 2009. "Doubts or variability?," Journal of Economic Theory, Elsevier, vol. 144(6), pages 2388-2418, November.
  19. Thomas Tallarini, . "Risk-Sensitive Real Business Cycles," GSIA Working Papers 1997-35, Carnegie Mellon University, Tepper School of Business.
  20. Bekaert, Geert & Hodrick, Robert J. & Marshall, David A., 1997. "The implications of first-order risk aversion for asset market risk premiums," Journal of Monetary Economics, Elsevier, vol. 40(1), pages 3-39, September.
  21. Bryan R. Routledge & Stanley E. Zin, 2010. "Generalized Disappointment Aversion and Asset Prices," Journal of Finance, American Finance Association, vol. 65(4), pages 1303-1332, 08.
  22. Rabin, Matthew, 2000. "Risk Aversion and Expected-Utility Theory: A Calibration Theorem," Department of Economics, Working Paper Series qt731230f8, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
  23. Harry Markowitz, 1952. "The Utility of Wealth," Journal of Political Economy, University of Chicago Press, vol. 60, pages 151.
  24. Marinacci, Massimo & Montrucchio, Luigi, 2010. "Unique solutions for stochastic recursive utilities," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1776-1804, September.
  25. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-91, March.
  26. Xavier Gabaix & David Laibson, 2002. "The 6D Bias and the Equity-Premium Puzzle," NBER Chapters, in: NBER Macroeconomics Annual 2001, Volume 16, pages 257-330 National Bureau of Economic Research, Inc.
  27. Kreps, David M. & Porteus, Evan L., 1979. "Temporal von neumann-morgenstern and induced preferences," Journal of Economic Theory, Elsevier, vol. 20(1), pages 81-109, February.
  28. Dekel, Eddie, 1986. "An axiomatic characterization of preferences under uncertainty: Weakening the independence axiom," Journal of Economic Theory, Elsevier, vol. 40(2), pages 304-318, December.
  29. Nicholas Barberis & Ming Huang & Tano Santos, 2001. "Prospect Theory And Asset Prices," The Quarterly Journal of Economics, MIT Press, vol. 116(1), pages 1-53, February.
  30. Epstein, Larry G & Zin, Stanley E, 1989. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework," Econometrica, Econometric Society, vol. 57(4), pages 937-69, July.
  31. Weil, Philippe, 1989. "The equity premium puzzle and the risk-free rate puzzle," Journal of Monetary Economics, Elsevier, vol. 24(3), pages 401-421, November.
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