Evolution Equations of Discount Functions and Metrics of Dynamic Inconsistency

Abstract

This article considers continuous models of time discounting that evolve dynamically. While constant exponential discounting is the paradigmatic model for time discounting, many models which depart from exponential discounting have been proposed to attempt to more closely match the behavior of individuals, firms and markets. This article argues that it is the dynamic inconsistency of behavioral models that gives them their most salient features. The article then develops evolution equations for some of the most prominent continuous discounting models to more clearly consider their dynamic inconsistency. It then proposes metrics for the degree of dynamic inconsistency exhibited by discounting models allowing comparison of dynamic inconsistency both across and within models.