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

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 optimizing 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 rate, and it offers interesting insights for the calibration of discount rates in computational models.