Time is Money: Arithmetic Discounting Outperforms Hyperbolic and Exponential Discounting
29 Pages Posted: 17 May 2010
Date Written: May 17, 2010
Hyperbolic discounting (H) is currently the dominant behavioral model of intertemporal choice, since it better explains how people behave than the normatively correct exponential discounting model (E). This paper promotes an arithmetic discounting model (A) which challenges H. First, A is more behaviorally plausible than H or E because it is underpinned by the analogical model, cost of time, which is more familiar and therefore accessible to lay-people than the analogical model investment growth, which underpins H and E. Also, it is much simpler for people to compute in A than in H or E: the calculations in A are the same as the accountant’s straight-line “depreciation” of future values to present values. Second, and most importantly, A gives better fits than H or E to actual choice behavior, both (i) when the past data from other researchers’ studies are reanalyzed at an aggregate level; and (ii) in two new studies analyzed at aggregate and individual levels. The superiority of A over H and E is robust, even when subjective time and money are modeled using Stevens power laws. However, the small gains from using exponents for time and money, and the uncertainty in estimating optimal exponents, suggest no compelling reason yet to abandon simple linear scaling (exponents = 1). Despite the superiority of A to H and E, all three models give highly concordant assessments of individuals’ impatience to receive smaller rewards now rather than larger ones later. Consequently, adopting arithmetic discounting as the most accurate model of human behavior should have few retrospective implications for past studies whose focus was between-group differences in impatience.
Keywords: delay discounting, intertemporal choice, exponential, hyperbolic, cost of time
JEL Classification: D9, D91, M3, M31
Suggested Citation: Suggested Citation