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Projection Methods for Economies with Heterogeneous Agents

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  • Radim Bohacek
  • Michal Kejak

Abstract

In this paper we develop a general methodology for solving models with heterogeneous agents by projection methods. Our approach is solely based on the functional forms of agents’ optimal policy rules and on a functional condition on the endogenous stationary distribution. Solving simultaneously the optimal policy rules and the distribution, this paper provides a new methodology for computing equilibria in which the distribution of wealth and income is a part of a social planner’s optimization problem. We do not impose any additional restrictions or assumptions on the equilibrium allocations. Compared to other computational methods, it does not suffer from the curse of dimensionality and provides an efficient tool for computing models of economies with a continuum of heterogeneous agents with several endogenous and exogenous state variables. We illustrate the algorithm on a standard model with uninsurable idiosyncratic risk from labor income. The approximate solution is highly accurate, especially for the distribution function. This method can be used to compute equilibria in economies with heterogeneous agents in which the distribution of wealth and income is a part of a government’s optimization problem.

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Paper provided by The Center for Economic Research and Graduate Education - Economic Institute, Prague in its series CERGE-EI Working Papers with number wp258.

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Date of creation: May 2005
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Handle: RePEc:cer:papers:wp258

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  1. Huggett, Mark, 1997. "The one-sector growth model with idiosyncratic shocks: Steady states and dynamics," Journal of Monetary Economics, Elsevier, Elsevier, vol. 39(3), pages 385-403, August.
  2. Fernando Alvarez & Marcelo Veracierto, 2000. "Labor-Market Policies in an Equilibrium Search Model," NBER Chapters, National Bureau of Economic Research, Inc, in: NBER Macroeconomics Annual 1999, Volume 14, pages 265-316 National Bureau of Economic Research, Inc.
  3. Krusell, Per & Quadrini, Vincenzo & Rios-Rull, Jose-Victor, 1997. "Politico-economic equilibrium and economic growth," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 21(1), pages 243-272, January.
  4. Michal Kejak, 2001. "Minimum Weighted Residual Methods in Endogeneous Growth Models," Development and Comp Systems 0012013, EconWPA.
  5. Hansen, G.D. & Imrohoroglu, A., 1990. "The Role Of Unemployment Insurance In An Economy With Liquidity Constraints And Moral Hazard," Papers, California Los Angeles - Applied Econometrics 21, California Los Angeles - Applied Econometrics.
  6. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, Elsevier, vol. 58(2), pages 410-452, December.
  7. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, The MIT Press, edition 1, volume 1, number 0262100711, December.
  8. Huggett, Mark, 1993. "The risk-free rate in heterogeneous-agent incomplete-insurance economies," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 17(5-6), pages 953-969.
  9. Lucas, Robert E, Jr, 1980. "Equilibrium in a Pure Currency Economy," Economic Inquiry, Western Economic Association International, Western Economic Association International, vol. 18(2), pages 203-20, April.
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Cited by:
  1. Radim Bohacek & Michal Kejak, 2005. "Optimal Government Policies in Models with Heterogeneous Agents," CERGE-EI Working Papers, The Center for Economic Research and Graduate Education - Economic Institute, Prague wp272, The Center for Economic Research and Graduate Education - Economic Institute, Prague.
  2. Reiter, Michael, 2009. "Solving heterogeneous-agent models by projection and perturbation," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 33(3), pages 649-665, March.
  3. Paul Pichler, 2007. "On the accuracy of low-order projection methods," Economics Bulletin, AccessEcon, vol. 3(50), pages 1-8.

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