How Long does a Generation Last? Assessing the Relationship Between Infinite and Finite Horizon Dynamic Models*

Abstract

This note aims at assessing the temporal relationship that exists between the time reference of dynamic models with infinite and finite horizon. Specifically, comparing the optimal inter-temporal plans arising from an infinite horizon model and a 2-period overlapping generations model in their stationary equilibria, I suggest way to assess the number of time periods of the former that form a time unit of the latter. Relying on an argument grounded on consumption smoothing, I show that the theoretical length of a generation is an increasing function of the discount factor of the optimising agent. Moreover, from an empirical point of view, I give evidence that this analysis corroborates the well-documented nexus that links demographic developments and the path of interest rates, and it offers interesting insights for the calibration of discount rates in computational models.