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Computing Equilibrium Wealth Distributions in Models with Heterogeneous-Agents, Incomplete Markets and Idiosyncratic Risk

Author

Listed:
  • Muffasir Badshah

    () (Department of Finance and Economcis, Qatar University, Doha Qatar)

  • Paul Beaumont

    () (Department of Economics, Florida State University)

  • Anuj Srivastava

    () (Department of Statistics, Florida State University)

Abstract

This paper describes an accurate, fast and robust fixed point method for computing the stationary wealth distributions in macroeconomic models with a continuum of infinitely-lived households who face idiosyncratic shocks with aggregate certainty. The household wealth evolution is modeled as a mixture Markov process and the stationary wealth distributions are obtained using eigen structures of transition matrices by enforcing the conditions for the Perron-Frobenius theorem by adding a perturbation constant to the Markov transition matrix. This step is utilized repeatedly within a binary search algorithm to find the equilibrium state of the system. The algorithm suggests an efficient and reliable framework for studying dynamic stochastic general equilibrium models with heterogeneous agents.

Suggested Citation

  • 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.
  • Handle: RePEc:fsu:wpaper:wp2011_08_02
    as

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    References listed on IDEAS

    as
    1. 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.
    2. S. Rao Aiyagari, 1994. "Uninsured Idiosyncratic Risk and Aggregate Saving," The Quarterly Journal of Economics, Oxford University Press, vol. 109(3), pages 659-684.
    3. Aiyagari, S Rao, 1995. "Optimal Capital Income Taxation with Incomplete Markets, Borrowing Constraints, and Constant Discounting," Journal of Political Economy, University of Chicago Press, vol. 103(6), pages 1158-1175, December.
    4. 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.
    5. Maliar, Lilia & Maliar, Serguei & Valli, Fernando, 2010. "Solving the incomplete markets model with aggregate uncertainty using the Krusell-Smith algorithm," Journal of Economic Dynamics and Control, Elsevier, vol. 34(1), pages 42-49, January.
    6. Den Haan, Wouter J., 2010. "Comparison of solutions to the incomplete markets model with aggregate uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 34(1), pages 4-27, January.
    7. Den Haan, Wouter J. & Judd, Kenneth L. & Juillard, Michel, 2010. "Computational suite of models with heterogeneous agents: Incomplete markets and aggregate uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 34(1), pages 1-3, January.
    8. 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.
    9. Young, Eric R., 2010. "Solving the incomplete markets model with aggregate uncertainty using the Krusell-Smith algorithm and non-stochastic simulations," Journal of Economic Dynamics and Control, Elsevier, vol. 34(1), pages 36-41, January.
    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.
    11. Marimon, Ramon & Scott, Andrew (ed.), 1999. "Computational Methods for the Study of Dynamic Economies," OUP Catalogue, Oxford University Press, number 9780198294979.
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    More about this item

    Keywords

    Numerical solutions; Wealth distributions; Stationary equilibria; DSGE models;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets

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