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Projection Methods for Economies with Heterogeneous Agents

  • Radim Bohacek
  • Michal Kejak

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 - Economics 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. Fernando Alvarez & Marcelo Veracierto, 1999. "Labor market policies in an equilibrium search model," Working Paper Series WP-99-10, Federal Reserve Bank of Chicago.
  2. Michal Kejak, 2000. "Minimum Weighted Residual Methods in Endogeneous Growth Models," CERGE-EI Working Papers wp155, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
  3. Gary D. Hansen & Ayse Imrohoroglu, 1990. "The Role of Unemployment Insurance in an Economy with Liquidity Constraints and Moral Hazard," UCLA Economics Working Papers 583, UCLA Department of Economics.
  4. Huggett, Mark, 1997. "The one-sector growth model with idiosyncratic shocks: Steady states and dynamics," Journal of Monetary Economics, Elsevier, vol. 39(3), pages 385-403, August.
  5. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, June.
  6. Huggett, Mark, 1993. "The risk-free rate in heterogeneous-agent incomplete-insurance economies," Journal of Economic Dynamics and Control, Elsevier, vol. 17(5-6), pages 953-969.
  7. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
  8. Lucas, Robert E, Jr, 1980. "Equilibrium in a Pure Currency Economy," Economic Inquiry, Western Economic Association International, vol. 18(2), pages 203-20, April.
  9. Krusell, Per & Quadrini, Vincenzo & Rios-Rull, Jose-Victor, 1997. "Politico-economic equilibrium and economic growth," Journal of Economic Dynamics and Control, Elsevier, vol. 21(1), pages 243-272, January.
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