Computing Dynamic Heterogeneous-Agent Economies: Tracking the Distribution

23 Pages Posted: 27 Jun 2011 Last revised: 25 Jan 2013

See all articles by Grey Gordon

Grey Gordon

Federal Reserve Banks - Federal Reserve Bank of Richmond

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Date Written: June 24, 2011

Abstract

Theoretical formulations of dynamic heterogeneous-agent economies typically include a distribution as an aggregate state variable. This paper introduces a method for computing equilibrium of these models by including a distribution directly as a state variable if it is finite-dimensional or a fine approximation of it if infinite-dimensional. The method accurately computes equilibrium in an extreme calibration of Huffman's (1987) overlapping-generations economy where quasi-aggregation, the accurate forecasting of prices using a small state space, fails to obtain. The method also accurately solves for equilibrium in a version of Krusell and Smith's (1998) economy wherein quasi-aggregation obtains but households face occasionally binding constraints. The method is demonstrated to be not only accurate but also feasible with equilibria for both economies being computed in under ten minutes in Matlab. Feasibility is achieved by using Smolyak's (1963) sparse-grid interpolation algorithm to limit the necessary number of gridpoints by many orders of magnitude relative to linear interpolation. Accuracy is achieved by using Smolyak's algorithm, which relies on smoothness, only for representing the distribution and not for other state variables such as individual asset holdings.

Keywords: Numerical Solutions, Heterogeneous Agents, Projection Methods

JEL Classification: C63, C68, E21

Suggested Citation

Gordon, Grey, Computing Dynamic Heterogeneous-Agent Economies: Tracking the Distribution (June 24, 2011). PIER Working Paper No. 11-018, Available at SSRN: https://ssrn.com/abstract=1873357 or http://dx.doi.org/10.2139/ssrn.1873357

Grey Gordon (Contact Author)

Federal Reserve Banks - Federal Reserve Bank of Richmond ( email )

P.O. Box 27622
Richmond, VA 23261
United States

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