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Time and risk

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Abstract

Intertemporal choice has obvious similarities with choice under uncertainty. However, because of technical difficulties in mapping results between the two domains, theoretical analysis of these topics has proceeded independently. In this article, we show that, using Rank Dependent Expected Utility rather than Expected Utility as the basic uncertain choice model, numerous analogies between the two fields may be identified and exploited. The key result is the derivation of a natural analogy between risk-aversion and impatience. This permits the reinterpretation of well-known results on stochastic dominance and comparative risk-aversion in the context of intertemporal choice. It is also possible to reinterpret results on intertemporal optimization in order to derive new results for portfolio choice problems under uncertainty.

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References

  • Allais, Maurice. (1988). “The General Theory of Random Choices in Relation to the Invariant Cardinal Utility Function and the Specific Probability Function.” In B. Munier (ed.),Risk, Decision and Rationality. Dordrecht, Reidel.

    Google Scholar 

  • Allais, Maurice. (1953). “Le Comportement de l'homme rationel devant le risque: critique des axioms et postulates de l'école Americaine.”Econometrica 21, 503–46.

    Google Scholar 

  • Bawa, V. (1975). “Optimal Rules for Ordering Uncertain Prospects.”Journal of Financial Economics 2, 95–121.

    Google Scholar 

  • Brown, D. (1981). “Myopic Economic Agents.”Econometrica 49, 359–368.

    Google Scholar 

  • Camerer, Colin. (1991). “Recent Tests of Generalized Utility Theories.” In W. Edwards (ed.),Utility: Measurement, Theory and Applications. Amsterdam, Kluwer, Nijhoff.

    Google Scholar 

  • Chateauneuf, Alain, and Michele Cohen. (1991). “Risk-seeking with Diminishing Marginal Utility in a Nonexpected Utility Model.” Working Paper, Université de Paris.

  • Chew, Soo-Hoong. (1989). “An Axiomatic Generalization of the Quasilinear Mean and Gini Mean with Application to Decision Theory.” Unpublished paper, Johns Hopkins University.

  • Chew, Soo-Hoong. (1983). “A Generalization of the Quasilinear Mean with Applications to the Measurement of Income Inequality and Decision Theory Resolving the Allais Paradox.”Econometrica 51, 1065–92.

    Google Scholar 

  • Chew, Soo-Hoong, and Larry Epstein. (1990). “Nonexpected Utility Preferences in a Temporal Framework with an Application to Consumption-Savings Behavior.”Journal of Economic Theory 50, 54–81.

    Google Scholar 

  • Chew, Soo-Hoong, Edi Karni, and Zvi Safra. (1987). “Risk Aversion in the Theory of Expected Utility with Rank-dependent Preferences.”Journal of Economic Theory 42, 370–81.

    Google Scholar 

  • Diamond, P. (1965). “The Evaluation of Infinite Utility Streams.”Econometrica 33, 170–177.

    Google Scholar 

  • Edwards, Ward. (1954). “Probability Preferences among Bets with Differing Expected Values,”American Journal of Psychology 67, 56–67.

    Google Scholar 

  • Edwards, Ward. (1962). “Subjective Probabilities Inferred from Decisions,”Psychological Review 69, 109–35.

    Google Scholar 

  • Ellsberg, Daniel. (1961). “Risk, Ambiguity and the Savage Axioms,”Quarterly Journal of Economics 75, 643–69.

    Google Scholar 

  • Epstein, L., and A. Hynes. (1983). “The Rate of Time Preference and Dynamic Economic Analysis,”Journal of Political Economy 91, 611–635.

    Google Scholar 

  • Epstein, Larry. (1983). “Stationary Cardinal Utility and Optimal Growth under Uncertainty,”Journal of Economic Theory 31, 133–152.

    Google Scholar 

  • Fishburn, Peter C., and A. Rubinstein. (1982). “Time Preference,”International Economic Review 23, 677–694.

    Google Scholar 

  • Gilboa, Itzhak. (1989). “Expectation and Variation in Multi-period Decisions,”Econometrica 57, 1153–69.

    Google Scholar 

  • Green, Jerry. (1987). “‘Making Book Against Oneself, The Independence Axiom and Non-linear Utility Theory,”Quarterly Journal of Economics 102, 785–796.

    Google Scholar 

  • Green, Jerry, and Bruno Jullien. (1988). “Ordinal Independence in Non-linear Utility Theory,”Journal of Risk and Uncertainty 1, 355–88.

    Google Scholar 

  • Hadar, Joseph, and William Russell. (1969). “Rules for Ordering Uncertain Prospects,”American Economic Review 59, 25–34.

    Google Scholar 

  • Horowitz, John. (1992). “Comparative Impatience,”Economics Letters, forthcoming.

  • Kahneman, Daniel, and Amos Tversky. (1979). “Prospect Theory: an Analysis of Decision under Risk,”Econometrica 47, 263–91.

    Google Scholar 

  • Koopmans, T. (1960). “Stationary Ordinal Utility and Impatience,”Econometrica 28, 287–309.

    Google Scholar 

  • Koopmans, T., P. Diamond, and R. Williamson. (1964). “Stationary Utility and Time Perspective,”Econometrica 32, 82–100.

    Google Scholar 

  • Lawrance, Emily. (1991). “Poverty and the Rate of Time Preference: Evidence from Panel Data,”Journal of Political Economy 99, 54–77.

    Google Scholar 

  • Lichtenstein, Sarah, and Paul Slovic. (1973). “Response-induced Reversals of Preferences in Gambling: An Extended Replication in Las Vegas,”Journal of Experimental Psychology 101, 16–20.

    Google Scholar 

  • Loewenstein, G. (1987). “Anticipation and the Valuation of Delayed Consumption,”Economic Journal 97, 666–684.

    Google Scholar 

  • Loewenstein, G., and R. Thaler. (1989). “Anomalies in Intertemporal Choice,”Journal of Economic Perspectives 3, 181–193.

    Google Scholar 

  • Loewenstein, George, and Drazen Prelec. (1993). “Preferences for Sequences of Outcomes,”Psychological Review 100, 91–108.

    Google Scholar 

  • Loomes, Graham, and Robert Sugden. (1982). “Regret Theory: An Alternative Theory of Rational Choice under Uncertainty,”Economic Journal 92, 805–24.

    Google Scholar 

  • Machina, Mark. (1989). “Dynamic Consistency and Non-expected Utility Models of Choice under Uncertainty,”Journal of Economic Literature 27, 1622–1688.

    Google Scholar 

  • Machina, Mark. (1982). “ 'Expected Utility' Analysis without the Independence Axiom,”Econometrica 50, 277–323.

    Google Scholar 

  • Machina, Mark. (1982). “A Stronger Characterisation of Declining Risk Aversion,”Econometrica 50, 1069–79.

    Google Scholar 

  • Machina, Mark. (1984). “Temporal Risk and the Nature of Induced Preferences,”Journal of Economic Theory 33, 199–231.

    Google Scholar 

  • Meyer, Jack. (1977). “Choice among Distributions,”Journal of Economic Theory 14, 326–36.

    Google Scholar 

  • Meyer, Jack, and Michael Ormiston. (1989). “Deterministic Transformation of Random Variables and the Comparative Statics of Risk,”Journal of Risk and Uncertainty 2, 179–88.

    Google Scholar 

  • Meyer, R. (1976). “Preferences over Time.” In R. Keeney and L. Raiffa (eds.),Decisions with Multiple Objectives: Preferences and Value Tradeoffs. New York: Wiley.

    Google Scholar 

  • Olson, M., and M. Bailey. (1981). “Positive Time Preference,”Journal of Political Economy 89, 1–25.

    Google Scholar 

  • Pratt, John. (1988). “Aversion to One Risk in the Presence of Others,”Journal of Risk and Uncertainty 1, 395–414.

    Google Scholar 

  • Prelec, Drazen, and George Loewenstein. (1991). “Decision-making over Time and under Uncertainty: A Common Approach,”Management Science 37, 770–786.

    Google Scholar 

  • Prescott, E., and Lucas R. (1972). “A Note on Price Systems in Infinite Dimensional Space,”International Economic Review 13, 416–422.

    Google Scholar 

  • Quiggin, John. (1991). “Comparative Statics for Rank-Dependent Expected Utility Theory,”Journal of Risk and Uncertainty 4, 339–50.

    Google Scholar 

  • Quiggin, John. (1992). “Efficient Sets with and Without the Expected Utility Hypothesis-A Generalization,”Journal of Mathematical Economics 21, 395–99.

    Google Scholar 

  • Quiggin, John. (1991). “Increasing Risk: Another Definition.” In Attila Chikan (ed.),Progress in Decision, Utility and Risk Theory. Amsterdam: Kluwer.

    Google Scholar 

  • Quiggin, John. (1982). “A Theory of Anticipated Utility,”Journal of Economic Behavior and Organisation 3, 323–43.

    Google Scholar 

  • Quirk, James, and R. Saposnik. (1962). “Admissibility and Measurable Utility Functions,”Review of Economic Studies 29, 140–46.

    Google Scholar 

  • Rader, T. (1981). “Utility over Time: The Homothetic Case,”Journal of Economic Theory 25, 219–236.

    Google Scholar 

  • Ross, Stephen. (1981). “Some Stronger Measures of Risk Aversion in the Small and in the Large with Applications,”Econometrica 49, 621–38.

    Google Scholar 

  • Rothschild, Michael, and Joseph Stiglitz. (1970). “Increasing Risk: I. A Definition,”Journal of Economic Theory 2, 225–243.

    Google Scholar 

  • Rothschild, Michael, and Joseph Stiglitz. (1971). “Increasing Risk: II. Its Economic Consequences,”Journal of Economic Theory 3, 66–84.

    Google Scholar 

  • Ryder, H., and G. Heal. (1973). “Optimal Growth with Intertemporally Dependent Preferences,”Review of Economic Studies 40, 1–31.

    Google Scholar 

  • Safra, Zvi, and Itzhak Zilcha. (1989). “Efficient Sets with and without the Expected Utility Hypothesis,”Journal of Mathematical Economics 17, 369–84.

    Google Scholar 

  • Savage, L. J. (1951). “The Theory of Statistical Decision,”Journal of the American Statistical Association 46, 55–67.

    Google Scholar 

  • Schmeidler, David. (1989). “Subjective Probability and Expected Utility without Additivity,”Econometrica 57, 571–87.

    Google Scholar 

  • Strotz, R. (1956). “Myopia and Inconsistency in Dynamic Utility Maximization,Review of Economic Studies 23, 165–180.

    Google Scholar 

  • Thaler, R. (1990). “Anomalies: Saving, Fungibility, and Mental Accounts,”Journal of Economic Perspectives 4, 193–205.

    Google Scholar 

  • von Neumann, John and O. Morgenstern. (1944).Theory of Games and Economic Behavior. Princeton University Press.

  • Wakker, Peter. (1990). “Under Stochastic Dominance Choquet-expected Utility and Anticipated Utility are Identical,”Theory and Decision 29, 119–132.

    Google Scholar 

  • Wang, Tan. (1991). “Lp Frechet Differentiable Preference and ‘Local Utility’ Analysis.” Working Paper, University of Toronto.

  • Whitmore, G. (1970). “Third Order Stochastic Dominance,”American Economic Review 50, 457–59.

    Google Scholar 

  • Yaari, Menahem. (1987). “The Dual Theory of Choice under Risk,”Econometrica 55, 95–115.

    Google Scholar 

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Authors and Affiliations

  1. Department of Economics, Research School of Social Sciences, Australian National University, 0200, Australia

    John Quiggin

  2. Department of Agricultural and Resource Economics, University of Maryland College Park, 20742, College Park, MD

    John Horowitz

Authors
  1. John Quiggin
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  2. John Horowitz
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Quiggin, J., Horowitz, J. Time and risk. J Risk Uncertainty 10, 37–55 (1995). https://doi.org/10.1007/BF01211527

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