Computing Longitudinal Moments for Heterogeneous Agent Models

Abstract

Computing population moments for heterogeneous agent models is a necessary step for their estimation and evaluation. Computation based on Monte Carlo methods is time- and resource-consuming because it involves simulating a large sample of agents and tracking them over time. We formalize how an alternative non-stochastic method, widely used for computing cross-sectional moments, can be extended to also compute longitudinal moments. The method relies on following the distribution of populations of interest by iterating forward the Markov transition function that defines the evolution of the distribution of agents in the model. Approximations of this function are readily available from standard solution methods of dynamic programming problems. We document the performance of this method vis-a-vis standard Monte Carlo simulations when calculating longitudinal moments. The method provides precise estimates of moments like top-wealth shares, auto-correlations, transition rates, age-profiles, or coefficients of population regressions at lower time- and resource-costs compared to Monte Carlo based methods. The method is particularly useful for moments of small groups of agents or involving rare events, but implies increasing memory costs in models with a large state space.