Non-Stationary Additive Utility and Time Consistency

Abstract

Within a continuous time life cycle model of consumption and savings, I study the properties of the most general class of additive intertemporal utility functionals. They are not necessarily stationary, and do not necessarily multiplicatively separate a discount factor from "per-period utility". I prove rigorously that time consistency holds if and only if the per-period felicity function is multiplicatively separable in t, the date of decision and in s, the date of consumption, or equivalently, if the Fisherian instantaneous subjective discount rate does not depend on t. The model allows to explain "anomalies in intertemporal choice" and various empirical regularities, even when the agents are time consistent. On the other hand, the model allows to characterize mathematically the "effective consumption profile" of naive, time-inconsistent agents.Code JEL: D91, E21, E71

Hyperbolic discounting and the time‐consistent solution of three canonical environmental problems

“…Since the discount rate is independent from decision time, decisions are time‐consistent. The crucial feature that provides time‐consistency is that the discount factor is multiplicatively separable in decision time and calendar time (Burness, 1976; Drouhin, 2009, 2020).…”

“…The “if”‐clause, however, has sometimes been forgotten in the following literature such that the conventional wisdom evolved that nonexponential discounting necessarily entails time inconsistency. Here, I apply a form of hyperbolic discounting to which the theorem of multiplicative separability in decision time and payoff time applies (see Burness, 1976; Drouhin, 2009, 2020). As a result, decisions are time‐consistent.…”

Renewable Resource Use with Imperfect Self-Control

“…Angeletos et al, 2001), it is actually possible to propose empirically plausible forms of hyperbolic discounting that support time-consistent decisions by giving up the stationarity assumption (Halevy, 2015). Such preferences are characterized by a discount factor that is multiplicatively separable in planning time and payoff time (Burness, 1976;Drouhin, 2020). These preferences imply that individuals become more patient as they grow older, a feature which receives empirical support (Green et al, 1994;Bishai, 2004) and which is consistent with theoretical considerations on the evolution of time preference through natural selection (Rogers, 1994).…”