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Solving heterogeneous-agent models by projection and perturbation

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  • 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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Bibliographic Info

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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Web page: http://www.econ.upf.edu/

Related research

Keywords: Heterogeneous agents; projection methods; perturbation methods;

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References

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  1. Bruce Preston & Mauro Roca, 2007. "Incomplete Markets, Heterogeneity and Macroeconomic Dynamics," NBER Working Papers 13260, National Bureau of Economic Research, Inc.
  2. Christopher D. Carroll, 2001. "A Theory of the Consumption Function, With and Without Liquidity Constraints (Expanded Version)," NBER Working Papers 8387, National Bureau of Economic Research, Inc.
  3. repec:bla:restud:v:74:y:2007:i:4:p:1195-1227 is not listed on IDEAS
  4. Christopher D. Carroll, 2009. "Theoretical Foundations of Buffer Stock Saving," 2009 Meeting Papers 210, Society for Economic Dynamics.
  5. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711.
  6. Jianjun Miao, 2004. "Competitive Equilibria of Economies with a Continuum of Consumers and Aggregate Shocks," CEMA Working Papers 460, China Economics and Management Academy, Central University of Finance and Economics.
  7. 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.
  8. Jeffrey Campbell, 1998. "Entry, Exit, Embodied Technology, and Business Cycles," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 1(2), pages 371-408, April.
  9. Michael Reiter, 2001. "Recursive Solution Of Heterogeneous Agent Models," Computing in Economics and Finance 2001 167, Society for Computational Economics.
  10. Per Krusell & Anthony A. Smith, Jr., . "Income and Wealth Heterogeneity in the Macroeconomy," GSIA Working Papers 1997-37, Carnegie Mellon University, Tepper School of Business.
  11. Algan, Yann & Allais, Olivier & Den Haan, Wouter J., 2008. "Solving heterogeneous-agent models with parameterized cross-sectional distributions," Journal of Economic Dynamics and Control, Elsevier, vol. 32(3), pages 875-908, March.
  12. Emmanuel Saez, 2000. "Using Elasticities to Derive Optimal Income Tax Rates," NBER Working Papers 7628, National Bureau of Economic Research, Inc.
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Citations

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Cited by:
  1. Bruce Preston & Mauro Roca, 2007. "Incomplete Markets, Heterogeneity and Macroeconomic Dynamics," NBER Working Papers 13260, National Bureau of Economic Research, Inc.
  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.
  3. James Costain & Antón Nákov, 2009. "Dynamics of the price distribution in a general model of state-dependent pricing," Banco de España Working Papers 0831, Banco de España.
  4. James Costain & Anton Nakov, 2011. "Distributional dynamics under smoothly state-dependent pricing," Finance and Economics Discussion Series 2011-50, Board of Governors of the Federal Reserve System (U.S.).
  5. Algan, Yann & Allais, Olivier & Den Haan, Wouter, 2007. "Solving Heterogeneous-Agent Models with Parameterized Cross-Sectional Distributions," CEPR Discussion Papers 6062, C.E.P.R. Discussion Papers.
  6. Haefke, Christian & Reiter, Michael, 2012. "What Do Participation Fluctuations Tell Us About Labor Supply Elasticities?," Annual Conference 2012 (Goettingen): New Approaches and Challenges for the Labor Market of the 21st Century 62055, Verein für Socialpolitik / German Economic Association.
  7. Yann Algan & Olivier Allais & Wouter J. Den Haan, 2006. "Solving heterogeneous-agent models with parameterized cross-sectional distributions," Working Papers halshs-00589129, HAL.
  8. Pichler, Paul, 2011. "Solving the multi-country Real Business Cycle model using a monomial rule Galerkin method," Journal of Economic Dynamics and Control, Elsevier, vol. 35(2), pages 240-251, February.
  9. 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.
  10. Kim, Sunghyun Henry & Kollmann, Robert & Kim, Jinill, 2010. "Solving the incomplete market model with aggregate uncertainty using a perturbation method," Journal of Economic Dynamics and Control, Elsevier, vol. 34(1), pages 50-58, January.
  11. Anton Nakov & James Costain, 2010. "Precautionary price stickiness," 2010 Meeting Papers 774, Society for Economic Dynamics.
  12. Muffasir Badshah & Paul Beaumont & Anuj Srivastava, 2011. "Computing Equilibrium Wealth Distributions in Models with Heterogeneous-Agents, Incomplete Markets and Idiosyncratic Risk," Working Papers wp2011_08_02, Department of Economics, Florida State University.
  13. Regassa Senbeta S., 2011. "How applicable are the New Keynesian DSGE models to a typical Low-Income Economy?," Working Papers 2011016, University of Antwerp, Faculty of Applied Economics.
  14. Edward S. Knotek II & Stephen Terry, 2008. "Alternative methods of solving state-dependent pricing models," Research Working Paper RWP 08-10, Federal Reserve Bank of Kansas City.

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