Uncertainty and Hyperbolic Discounting

Empirical studies in economics and behavioral ecology suggest that, ceteris paribus, animals and humans appear to place less weight on the future than on the present, i.e., they act as though they discount future payoffs. Furthermore (and more interestingly), they do so with discount rates that increase as the time before those payoffs are realized grows shorter. In other words, subjects act as though they become less patient when payoffs are more imminent. An anecdotal (human) example is offered by Ted O’Donoghue and Matthew Rabin (1999): when offered the choice in February between a painful seven-hour task (e.g., preparing a tax return) on April 1 and a painful eight-hour task on April 15, most of us, they suggest, will opt for the earlier date. But as April 1 approaches, we are apt to change our minds, if we can, and postpone the pain to April 15, even though it will then be greater. Thus, we behave as though we discount the later pain more as time grows short. Robert H. Strotz (1956) discusses a similar phenomenon involving positive payoffs. Early in the calendar year, he notes, many people attempt to lay money aside for Christmas. As time goes by, however, they may find themselves spending the money on summer vacations or back-to-school clothes. It is as though they have become more impatient than they were in January. Both the O’Donoghue-Rabin and Strotz examples accord with “hyperbolic discounting,” which has attracted considerable interest among economists because it appears to shed light on important economic phenomena such as household saving behavior (see David Laibson, 1997; B. Douglas Bernheim et al., 2001; Christopher Harris and Laibson, 2003). One might ask whether there is some reason for such behavior. The point of view that we take is that, to a considerable extent, animal and human behavior is shaped by preferences that are the outcome of evolutionary forces. That is, cravings, urges, or instincts—the operational manifestations of preferences—induce the animal or human to make the right choice in the “average” situation that it, he, or she is likely to face, where the “right” choice means the one that maximizes survival (and, therefore, the opportunity to reproduce). We show that if the “average” situation entails some uncertainty about when payoffs are realized, the corresponding preferences may well entail hyperbolic discounting, giving rise to preference reversals. To get a rough understanding of this result, imagine that a decision maker (DM) is offered the choice between a small (positive) payoff relatively soon (prospect P) or a big payoff relatively late (prospect P ). Furthermore, suppose that, for either P or P , there is a small but * Dasgupta: Faculty of Economics, University of Cambridge, Sidgwick Avenue, Cambridge CB3 9DD, United Kingdom (e-mail: [email protected]); Maskin: Institute of Advanced Study, Einstein Drive, Princeton, NJ 08540 (e-mail: [email protected]). We are grateful to the Beijer International Institute of Ecological Economics, Stockholm, and the National Science Foundation (Grant SES-0318103) for research support. For comments on earlier versions of this paper, we thank Roland Bénabou, Douglas Bernheim, David Colander, Nick Davies, Eddie Dekel, Avinash Dixit, Ernst Fehr, Christopher Harris, Alex Kacelnik, John Kagel, Adi Livnat, François Maniquet, Ariel Rubinstein, Larry Samuelson, Peter Sozou, and three referees. This paper was previously entitled “Uncertainty, Waiting Costs, and Hyperbolic Discounting.” 1 The empirical literature on birds (particularly pigeons and starlings) is summarized in James E. Mazur (1987) and Leonard Green and Joel Myerson (1996); that on humans in George Ainslie (1992). 2 Strictly speaking, hyperbolic discounting requires that the discount rate vary inversely with the time to payoffs. But the term has come to be applied more generally to any manifestation of increasing impatience as time horizons shrink. See Ariel Rubinstein (2001), who cautions that many observed behaviors are consistent with a variety of preferences in addition to those involving hyperbolic discounting. 3 In this respect, our approach is similar to that of Larry Samuelson and Jeroen Swinkels (2004), who—although their approach is otherwise quite different from ours—share our view that an animal’s urges are evolutionarily determined substitutes for full information about the choices it faces.