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Non-stationary additive utility and time consistency

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  • Nicolas Drouhin

    (CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - CNRS - Centre National de la Recherche Scientifique)

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 pro le" of naive, time-inconsistent agents.
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  • Nicolas Drouhin, 2020. "Non-stationary additive utility and time consistency," Post-Print halshs-02363089, HAL.
    • Handle: RePEc:hal:journl:halshs-02363089
    DOI: 10.1016/j.jmateco.2019.10.005
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