Time-Inconsistent Preferences in Adam Smith and David Hume

Recent research in economics and psychology reveals that people and animals may evaluate choices inconsistently at certain times or in some areas of their lives. This inconsistency is often characterized, for example, by choosing the smaller and earlier of two alternative cash prizes when both are near, but changing to the larger, later prize as they draw more distant. The persistence and robustness of such observations have led some economists and psychologists to think “that the problem may not come from some extraordinary condition that impairs the normal operation of intentionality, but rather from the process by which all people, perhaps all organisms, evaluate future goals” (Ainslie and Haslam 1992, 58).

Evidence supports the postulate that the basic temporal discount function of human beings and some animals is such that preference reversals may naturally arise unless some actions are taken to avoid them. Preference reversals have been explained by the tendency for discounting to increase as the time delay diminishes. Indeed, several experiments and real-life experiences indicate that a discount curve more concave than an exponential curve may govern the subjects' choices in the situations studied. Discount functions may thus be approximated by a hyperbola; that is, rewards t periods in the future are discounted by 1 / (k₁ + k₂ · t), where the k_i's are constants.¹ A function more concave than the usual exponential curve b^t produces intertemporal conflict, causing preferences to change between a given pair of alternatives as time elapses. This is because such a function discounts more heavily than the exponential function for events in the near future, but less heavily for events in the distant future. Therefore, preferences of decision makers with hyperbolic discount functions are dynamically inconsistent.

Over the last few years a large literature has developed that studies various “behavioral anomalies.” In particular, there is a growing body of literature that studies the behavior of economic agents with hyperbolic discount functions, as well as the implications of such behavior.² In fact, some economists and psychologists argue that hyperbolic discounting may explain some of the behavioral anomalies that have been documented during the last decades.³

However, despite the apparent novelty and sense of discovery with which this behavior is treated in the literature, the analysis of dynamically inconsistent behavior is not new. This behavior was analyzed by Hume ([1739] 1978) and Smith ([1759] 1976), and later by Malthus ([1826] 1986), Jevons (1871), Böhm-Bawerk ([1891] 1971), Marshall ([1890] 1920), and Pareto (1909) in their discussion of intertemporal trade-offs. Although foreseeable changes of preferences were not formalized analytically until Strotz (1956), and later further developed in the articles of the psychologist Ainslie (1975, 1986, 1992), the pervasiveness of this behavior was studied in previous centuries. The purpose of this article is to examine the insights established by Adam Smith and David Hume within the context of dynamically inconsistent behavior. In particular, it shows how their analyses of this behavior remain novel, despite much progress in the literature during the last decade. The essay also provides a formal assessment of their contributions.

The implications of a hyperbolic discount function are important for economics as well as for all other social sciences. One of the main implications is that it implies an overvaluation of an imminent reward relative to a larger, later reward. Consequently, in order to attain their long-range goals, individuals prefer to compensate for their inconsistencies by restricting in part their own current and future choices. The most apparent way for an individual to forestall his change in optimal choices or preferences is to adopt some type of commitment device: “He may ‘precommit' his future behavior by precluding future options so that it will conform to his present desire as to what it should be. Or, alternatively, he may modify his chosen plan to take account of future disobedience, realizing that the possibility of disobedience...