A Model of Intertemporal Choice with Rank-Dependent Discounted Utility

Abstract

Intertemporal choice is intuitively analogous to choice under risk/uncertainty when outcomes are viewed as consequences received in an uncertain future. Discounted incremental (DIU) model of intertemporal choice parallels expected utility representation of risk preferences. DIU coincides with Samuelson’s discounted utility (constant/exponential discounting) when utility function is linear. DIU has several advantages over discounted utility (and its generalizations — quasi-hyperbolic and generalized hyperbolic discounting): a) time preferences are continuous; b) utility does not increase when a larger payoff is split into two smaller payoffs, one of which is slightly delayed in time; c) utility is not separable across time periods, i.e. the model allows for intertemporal wealth, complementarity and substitution effects. DIU is generalized to rank-dependent discounted utility (RDDU), which is analogous to rank-dependent utility in choice under risk/uncertainty. RDDU with a concave utility and inverse S-shaped weighting function can rationalize several behavioral regularities such as a greater impatience for immediate outcomes. An application of RDDU to intertemporal consumption/saving reveals that consumers with an inverse S-shaped weighting function exhibit dynamic inconsistency. Initially, they commit to saving for future consumption but, as time passes, they prefer to renegotiate such a contract for an advance payment. Behavioral characterization/axiomatization of RDDU is presented.