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Solving Heterogeneous-Agent Models by Projection and Perturbation

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Author Info
Michael Reiter
Abstract

The paper proposes a numerical solution method for general equilibrium models with a continuum of heterogeneous agents, which combines elements of projection and of perturbation methods. The basic idea is to solve first for the stationary solution of the model, without aggregate shocks but with fully specified idiosyncratic shocks. Afterwards one computes a first-order perturbation of the solution in the aggregate shocks. This approach allows to include a high-dimensional representation of the cross-sectional distribution in the state vector. The method is applied to a model of household saving with uninsurable income risk and liquidity constraints. The model includes not only productivity shocks, but also shocks to redistributive taxation, which cause substantial short-run variation in the cross-sectional distribution of wealth. If those shocks are operative, it is shown that a solution method based on very few statistics of the distribution is not suitable, while the proposed method can solve the model with high accuracy, at least for the case of small aggregate shocks. Techniques are discussed to reduce the dimension of the state space such that higher order perturbations are feasible. Matlab programs to solve the model can be downloaded.

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Paper provided by Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 972.

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Date of creation: Sep 2006
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Handle: RePEc:upf:upfgen:972

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Related research
Keywords: Heterogeneous agents; projection methods; perturbation methods;

Find related papers by JEL classification:
C63 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Computational Techniques
C68 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Computable General Equilibrium Models
E21 - Macroeconomics and Monetary Economics - - Macroeconomics: Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Bruce Preston & Mauro Roca, 2007. "Incomplete Markets, Heterogeneity and Macroeconomic Dynamics," NBER Working Papers 13260, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  2. Miao, Jianjun, 2006. "Competitive equilibria of economies with a continuum of consumers and aggregate shocks," Journal of Economic Theory, Elsevier, vol. 128(1), pages 274-298, May. [Downloadable!] (restricted)
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  3. Christopher D. Carroll, 2001. "A Theory of the Consumption Function, with and without Liquidity Constraints," Journal of Economic Perspectives, American Economic Association, vol. 15(3), pages 23-45, Summer. [Downloadable!] (restricted)
    Other versions:
  4. Yann Algan & Olivier Allais & Wouter J. Den Haan, 2006. "Solving heterogeneous-agent models with parameterized cross-sectional distributions," PSE Working Papers 2006-46, PSE (Ecole normale supérieure). [Downloadable!]
    Other versions:
  5. Christopher D. Carroll, 2004. "Theoretical Foundations of Buffer Stock Saving," Economics Working Paper Archive 517, The Johns Hopkins University,Department of Economics. [Downloadable!]
    Other versions:
  6. Henry Kim & Jinill Kim & Robert Kollmann, 2005. "Applying Perturbation Methods to Incomplete Market Models with Exogenous Borrowing Constraints," Discussion Papers Series, Department of Economics, Tufts University 0504, Department of Economics, Tufts University. [Downloadable!]
  7. Per Krusell & Anthony A. Smith & Jr., 1998. "Income and Wealth Heterogeneity in the Macroeconomy," Journal of Political Economy, University of Chicago Press, vol. 106(5), pages 867-896, October. [Downloadable!] (restricted)
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  8. 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 - Economic Institute, Prague. [Downloadable!]
  9. Saez, Emmanuel, 2001. "Using Elasticities to Derive Optimal Income Tax Rates," Review of Economic Studies, Blackwell Publishing, vol. 68(1), pages 205-29, January.
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Yann Algan & Olivier Allais & Wouter J. Den Haan, 2006. "Solving heterogeneous-agent models with parameterized cross-sectional distributions," PSE Working Papers 2006-46, PSE (Ecole normale supérieure). [Downloadable!]
    Other versions:
  2. Den Haan, Wouter, 2008. "Assessing the Accuracy of the Aggregate Law of Motion in Models with Heterogeneous Agents," CEPR Discussion Papers 6971, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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