Is Discounting Hyperbolic? Experimental Evidence

A vast empirical evidence in experimental psychology on time discounting has documented various behavioral anomalies which cast doubts on the empirical support for exponential discounting, to date the most widely used assumption on time preference in economic theory. The most important of such anomalies, called ''reversal of preferences,'' has been interpreted to suggest that agents have a preference, a bias in fact, for present consumption which cannot be rationalized by preferences with exponential discounting. Psychologists (e.g., Herrnstein, 1961, de Villiers-Herrnstein, 1976, Ainsle-Herrnstein, 1981; see also Ainsle, 1992, 2001) and, most recently, behavioral economists (e.g., Elster, 1979, Laibson, 1996, O'Donoghue-Rabin, 1999) have noted that the evidence is consistent with a declining rate of time preference, and have suggested various specification of discounting which give rise to declining discount rates over time, hyperbolic discounting, and quasi-hyperbolic discounting. Such specifications of discounting would introduce a fundamental paradigm change in economic theory: preferences with hyperbolic (or quasi-hyperbolic) discounting in fact, as opposed to preferences with exponential discounting, lack time-consistency. While experimental psychologists have collected an impressive amount of data on time preference in support of declining discount rates, in fact, most of this data is not without problems: often experiments have been conducted with hypothetical rewards, or with "points" redeemable at the end of the experiments (thereby eliminating any rationale for time preference); often the design of the experiments gives rise to issues of strategic manipulability, or of framing effects. Rarely have the data been analyzed with proper econometric instruments; in particular, the hypothesis of hyperbolic discounting has never been tested statistically against the alternative of exponential discounting. This is the objective of the present paper.