Descriptive Models of Intertemporal Choice Part 1: Anomalies in Choices Between Less Sooner and More Later

Abstract

Two comparative models of intertemporal choice have recently been proposed as an alternative to the hyperbolic discounting model. One, the interval discounting model, retains the notion that intertemporal choice is governed by discounting, but proposes that discounting involves direct comparisons between the options along the time attribute. The other, the tradeoff model, discards the notion of discounting, and proposes that intertemporal choice is governed by direct comparisons along both the time attribute and the outcome attribute. These comparative models predict a wider range of phenomena than the hyperbolic discounting model, but it is yet to be shown how much more accurate they are in quantitative analyses, and whether one is more accurate than the other. We parameterize all three models, and apply them to three data sets containing five core anomalies in choices between a smaller-sooner and a larger-later outcome. A sixth anomaly, the delay-speedup asymmetry, raises additional, both theoretical and methodological, issues, and is therefore left for the second part of our report. In this first part, we reach the conclusion that, in terms of practical applicability and predictive accuracy, the tradeoff model is the best tool for the modeling of choices between a smaller-sooner and a larger-later outcome. Although we cannot generalize beyond the specific parameterizations of the three competing models, the parameterizations are those that we can justify theoretically and estimate empirically.