Statistical Properties of Social Discount Rate Paths in a Heterogeneous Dynamic Stochastic Model

A thorough evaluation of public projects impacting society and the environment must account for the statistical dynamics of social discount rates (SDRs) derived from heterogeneous and evolving populations. This study examines the dynamic statistical properties of Weitzman’s gamma discounting model (Weitzman 2001), incorporating changes in individual discount-rate opinions over time. We introduce a fully dynamic stochastic (FDS) framework that captures agent heterogeneity and analyze the evolving distribution of individual discount rates using the Fokker-Planck equation, from which we derive the statistical properties of the SDR. Our model extends Weitzman’s framework by accounting for temporal shifts in the heterogeneity of discount-rate distributions. Through both closed-form solutions and numerical analyses, we show that although Weitzman’s SDR captures short-term statistical dynamics, it fails to reflect important long-term trends driven by evolving distributions. We further demonstrate how initial heterogeneity and stochastic shocks shape the statistical trajectories of both social discount factors (SDFs) and SDRs. These findings underscore the importance of dynamic, stochastic, and heterogeneous discounting models in informing long-term policy assessments.Keywords: Heterogeneity, Dynamic Stochastic Shocks, Gamma Discounting, Fokker-Planck Equation, Statistical Properties, Social Discount Rate, Climate Change, Public PoliciesJEL Classification: D90, E47, C00, H43, Q28