Geometric Discounting in Discrete, Infinite-Horizon Choice Problems

The rate of time preference is traditionally defined as the marginal rate of substitution between current and future consumption. This definition is not applicable when outcomes are indivisible. Such is the case in all discrete-choice dynamic problems which arise, for example, in modeling housing or occupational decisions. Assuming an infinite horizon and a standard time-additive utility representation, this note shows that the discount factor can be uniquely recovered from the underlying preference order, provided that the decision-maker is sufficiently patient. Under the same conditions, the utility index over outcomes is cardinally unique. Finally, an algorithm for approximating the discount factor is provided which, at each stage, uses only finite-horizon data.