INTRODUCTION

Robert Strotz (1956) first suggested that people are more impatient when they make short-run trade-offs than when they make long-run trade-offs. Virtually every experimental study on time preference has supported Strotz's conjecture. When two rewards are both far away in time, decision-makers act relatively patiently (e.g., I prefer two apples in 101 days, rather than one apple in 100 days). But when both rewards are brought forward in time, preferences exhibit a reversal, reflecting more impatience (e.g., I prefer one apple right now, rather than two apples tomorrow).

Such reversals should be well understood by everyone who makes far-sighted New Year's resolutions and later backtracks.We promise ourselves to exercise, diet, and quit smoking, but often postpone those virtuous behaviors when the moment arrives to make the required sacrifices. Looking to the long run, we wish to act patiently, but the desire for instant gratification frequently overwhelms our good intentions.

The contrast between long-run patience and short-run impatience has been modeled with discount functions that take an approximately hyperbolic form (Ainslie, 1992, Loewenstein and Prelec 1992, Laibson, 1997a). Such preferences imply that the instantaneous discount rate declines as the horizon increases. This pattern of discounting sets up a conflict between today's preferences and the preferences that will be held in the future. From the perspective of period 0, the discount rate between two distant periods, t and t + 1, is a long-term low discount rate. However, from the perspective of period t, the discount rate between t and t + 1 is a short-term high discount rate.