On the Solution of High-Dimensional Macro Models with Distributional Channels

Abstract

Importance of distributional channels in macroeconomic dynamics has been the object of considerable attention in empirical studies. Despite significant amount of effort aimed at incorporating heterogeneity into macroeconomics, however, their explicit inclusion in the standard policy toolbox is far from widespread. A relevant obstacle, in such cases, is the computation of equilibria. I propose a global solution method for the computation of infinite-horizon, heterogeneous agent macroeconomic models with aggregate uncertainty. Details of the algorithm are illustrated by presenting its application to a an example model: in it, aggregate dynamics depends explicitly on firm entry and exit, and individual choices are often constrained by a form of market incompleteness. Existing computational strategies are either unfeasible or provide inaccurate solutions. Moreover, global solutions are computationally expensive because the minimal representation of the aggregate state space - and thus the aggregate law of motion - faces the curse of dimensionality. The proposed strategy thus combines adaptive sparse grids with a cross-sectional density approximation, and introduces a framework for solving the more general class of dynamic models with firm or household heterogeneity accurately.