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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.

Suggested Citation

  • Radim Bohacek & Michal Kejak, 2005. "Projection Methods for Economies with Heterogeneous Agents," CERGE-EI Working Papers wp258, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
  • Handle: RePEc:cer:papers:wp258
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    References listed on IDEAS

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    1. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, January.
    2. Hansen, Gary D & Imrohoroglu, Ayse, 1992. "The Role of Unemployment Insurance in an Economy with Liquidity Constraints and Moral Hazard," Journal of Political Economy, University of Chicago Press, vol. 100(1), pages 118-142, February.
    3. S. Rao Aiyagari, 1994. "Uninsured Idiosyncratic Risk and Aggregate Saving," The Quarterly Journal of Economics, Oxford University Press, vol. 109(3), pages 659-684.
    4. Fernando Alvarez & Marcelo Veracierto, 2000. "Labor-Market Policies in an Equilibrium Search Model," NBER Chapters,in: NBER Macroeconomics Annual 1999, Volume 14, pages 265-316 National Bureau of Economic Research, Inc.
    5. 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.
    6. 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.
    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. 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.
    9. Lucas, Robert E, Jr, 1980. "Equilibrium in a Pure Currency Economy," Economic Inquiry, Western Economic Association International, vol. 18(2), pages 203-220, April.
    10. 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.
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    Cited by:

    1. Radim Bohacek & Michal Kejak, 2005. "Optimal Government Policies in Models with Heterogeneous Agents," CERGE-EI Working Papers wp272, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    2. Reiter, Michael, 2009. "Solving heterogeneous-agent models by projection and perturbation," Journal of Economic Dynamics and Control, 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.

    More about this item

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
    • D30 - Microeconomics - - Distribution - - - General
    • D58 - Microeconomics - - General Equilibrium and Disequilibrium - - - Computable and Other Applied General Equilibrium Models

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