Non stationary additive utility and time consistency

Nicolas Drouhin (1)

1 ENS Paris Saclay - Ecole Normale Supérieure Paris-Saclay

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 prole" of naive, time-inconsistent agents.

Mots clés: exponential discounting; time invariance; hyperbolic discounting; aging; time consistency; stationarity of preferences; life cycle theory of consumption and savings; time discounting; anomalies in intertemporal choice

Domaines: Economies et finances; Psychologie

Nicolas Drouhin. Non stationary additive utility and time consistency. 2019. ⟨halshs-01238584v5⟩