Models of intertemporal choice draw on three evaluation rules, which we compare in the restricted domain of choices between smaller sooner and larger later monetary outcomes. The hyperbolic discounting model proposes an alternative-based rule, in which options are evaluated separately. The interval discounting model proposes a hybrid rule, in which the outcomes are evaluated separately, but the delays to those outcomes are evaluated in comparison with one another. The tradeoff model proposes an attribute-based rule, in which both outcomes and delays (...) are evaluated in comparison with one another: People consider both the intervals between the outcomes and the compensations received or paid over those intervals. We compare highly general parametric functional forms of these models by means of a Bayesian analysis, a method of analysis not previously used in intertemporal choice. We find that the hyperbolic discounting model is outperformed by the interval discounting model, which, in turn, is outperformed by the tradeoff model. Our cognitive modeling is among the first to offer quantitative evidence against the conventional view that people make intertemporal choices by discounting the value of future outcomes, and in favor of the view that they directly compare options along the time and outcome attributes. (shrink)

The problem of intertemporal choice arises when outcomes are received in different moments of time. This paper presents an axiomatic model of intertemporal choice when consumption in the previous moment of time contributes to utility evaluation of consumption in the current moment. This model generalizes classic discounted utility theory (also known as constant or exponential discounting) in two ways. First, in every moment of time, a decision maker derives utility not only from current consumption but also from “residual” consumption in (...) the previous moment of time. Second, these utilities are discounted with weights that are essentially a quasi-hyperbolic discounting function. The paper presents an application of the proposed model to the problem of optimal consumption and savings given a fixed income (wealth). When a decision maker derives satisfaction from both instantaneous consumption as well as a share of consumption in the previous moment of time, optimal consumption path is cyclic—periods of relatively high consumption are interchanged with periods of relatively low consumption. These cycles decay over time. Asymptotically, the consumption path exhibits conventional properties (constant, increasing or decreasing over time when a gross interest rate multiplied by discount factor is correspondingly equal to, greater than, or less than one). (shrink)