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Computing Dynamic Heterogeneous-Agent Economies: Tracking the Distribution

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  • Grey Gordon

    ()
    (Department of Economics, University of Pennsylvania)

Abstract

Theoretical formulations of dynamic heterogeneous-agent economiestypically include a distribution as an aggregate state variable. This paperintroduces 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.

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Bibliographic Info

Paper provided by Penn Institute for Economic Research, Department of Economics, University of Pennsylvania in its series PIER Working Paper Archive with number 11-018.

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Length: 23 pages
Date of creation: 24 Jun 2011
Date of revision:
Handle: RePEc:pen:papers:11-018

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Keywords: Numerical Solutions; Heterogeneous Agents; Projection Methods;

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  1. Kenneth L. Judd & Lilia Maliar & Serguei Maliar, 2010. "A Cluster-Grid Projection Method: Solving Problems with High Dimensionality," NBER Working Papers 15965, National Bureau of Economic Research, Inc.
  2. Per Krusell & Jose-Victor Rios-Rull, 1997. "On the size of U.S. government: political economy in the neoclassical growth model," Staff Report 234, Federal Reserve Bank of Minneapolis.
  3. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
  4. Young, Eric R., 2010. "Solving the incomplete markets model with aggregate uncertainty using the Krusell-Smith algorithm and non-stochastic simulations," Journal of Economic Dynamics and Control, Elsevier, vol. 34(1), pages 36-41, January.
  5. YiLi Chien & Harold Cole & Hanno Lustig, 2007. "A Multiplier Approach to Understanding the Macro Implications of Household Finance," NBER Working Papers 13555, National Bureau of Economic Research, Inc.
  6. Judd, Kenneth L. & Guu, Sy-Ming, 1997. "Asymptotic methods for aggregate growth models," Journal of Economic Dynamics and Control, Elsevier, vol. 21(6), pages 1025-1042, June.
  7. Krusell, P & Smith Jr, A-A, 1995. "Income and Wealth Heterogeneity in the Macroeconomic," RCER Working Papers 399, University of Rochester - Center for Economic Research (RCER).
  8. Carroll, Christopher D., 2006. "The method of endogenous gridpoints for solving dynamic stochastic optimization problems," Economics Letters, Elsevier, vol. 91(3), pages 312-320, June.
  9. Per Krusell & Anthony A. Smith, Jr., . "Income and Wealth Heterogeneity, Portfolio Choice, and Equilibrium Asset Returns," GSIA Working Papers 1997-45, Carnegie Mellon University, Tepper School of Business.
  10. Aldrich, Eric M. & Fernández-Villaverde, Jesús & Ronald Gallant, A. & Rubio-Ramírez, Juan F., 2011. "Tapping the supercomputer under your desk: Solving dynamic equilibrium models with graphics processors," Journal of Economic Dynamics and Control, Elsevier, vol. 35(3), pages 386-393, March.
  11. Den Haan, Wouter & Rendahl, Pontus, 2008. "Solving the Incomplete Markets Model with Aggregate Uncertainty using Explicit Aggregation," CEPR Discussion Papers 6963, C.E.P.R. Discussion Papers.
  12. Krueger, Dirk & Kubler, Felix, 2004. "Computing equilibrium in OLG models with stochastic production," Journal of Economic Dynamics and Control, Elsevier, vol. 28(7), pages 1411-1436, April.
  13. Huffman, Gregory W, 1987. "A Dynamic Equilibrium Model of Asset Prices and Transaction Volume," Journal of Political Economy, University of Chicago Press, vol. 95(1), pages 138-59, February.
  14. Den Haan, Wouter J. & Judd, Kenneth L. & Juillard, Michel, 2010. "Computational suite of models with heterogeneous agents: Incomplete markets and aggregate uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 34(1), pages 1-3, January.
  15. Den Haan, Wouter, 2008. "Comparison of Solutions to the Incomplete Markets Model with Aggregate Uncertainty," CEPR Discussion Papers 7019, C.E.P.R. Discussion Papers.
  16. Marina Azzimonti & Eva de Francisco & Per Krusell, 2006. "Median-voter Equilibria in the Neoclassical Growth Model under Aggregation," Scandinavian Journal of Economics, Wiley Blackwell, vol. 108(4), pages 587-606, December.
  17. Benjamin Malin & Dirk Krueger & Felix Kubler, 2007. "Computing Stochastic Dynamic Economic Models with a Large Number of State Variables: A Description and Application of a Smolyak-Collocation Method," NBER Technical Working Papers 0345, National Bureau of Economic Research, Inc.
  18. S. Boragan Aruoba & Jesus Fernandez-Villaverde & Juan F. Rubio-Ramirez, 2003. "Comparing Solution Methods for Dynamic Equilibrium Economies," PIER Working Paper Archive 04-003, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  19. Reiter, Michael, 2010. "Solving the incomplete markets model with aggregate uncertainty by backward induction," Journal of Economic Dynamics and Control, Elsevier, vol. 34(1), pages 28-35, January.
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Blog mentions

As found by EconAcademics.org, the blog aggregator for Economics research:
  1. Computing Dynamic Heterogeneous-Agent Economies: Tracking the Distribution
    by Christian Zimmermann in NEP-DGE blog on 2011-07-22 13:21:27
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Cited by:
  1. Fernández-Villaverde, Jesús & Gordon, Grey & Guerron-Quintana, Pablo A. & Rubio-Ramírez, Juan Francisco, 2012. "Nonlinear Adventures at the Zero Lower Bound," CEPR Discussion Papers 8972, C.E.P.R. Discussion Papers.

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