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Solving the Incomplete Markets Model with Aggregate Uncertainty using Explicit Aggregation

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  • Den Haan, Wouter
  • Rendahl, Pontus

Abstract

We construct a method to solve models with heterogeneous agents and aggregate uncertainty that is simpler than existing algorithms; the aggregate law of motion is obtained neither by simulation nor by parameterization of the cross-sectional distribution, but by explicitly aggregating the individual policy rule. This establishes a link between the individual policy rule and the set of necessary aggregate state variables. In particular, the cross-sectional average of each basis function in the individual policy rule is a state variable. That is, if the individual capital stock, k, (or k²) enters the policy function then the mean of k (or the mean of k²) is a state variable. The laws of motions for these aggregate state variables are obtained by explicit aggregation of separate individual policy functions for the different elements.

Suggested Citation

  • Den Haan, Wouter & Rendahl, Pontus, 2008. "Solving the Incomplete Markets Model with Aggregate Uncertainty using Explicit Aggregation," CEPR Discussion Papers 6963, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:6963
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    References listed on IDEAS

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    1. Carroll, Christopher D., 2006. "The method of endogenous gridpoints for solving dynamic stochastic optimization problems," Economics Letters, Elsevier, vol. 91(3), pages 312-320, June.
    2. 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.
    3. Bruce Preston & Mauro Roca, 2007. "Incomplete Markets, Heterogeneity and Macroeconomic Dynamics," NBER Working Papers 13260, National Bureau of Economic Research, Inc.
    4. Den Haan, Wouter J., 2010. "Assessing the accuracy of the aggregate law of motion in models with heterogeneous agents," Journal of Economic Dynamics and Control, Elsevier, vol. 34(1), pages 79-99, January.
    5. repec:hal:spmain:info:hdl:2441/41rhqgovpp8hnq9i7ndtl26ltm is not listed on IDEAS
    6. Algan, Yann & Allais, Olivier & Den Haan, Wouter J., 2010. "Solving the incomplete markets model with aggregate uncertainty using parameterized cross-sectional distributions," Journal of Economic Dynamics and Control, Elsevier, vol. 34(1), pages 59-68, January.
    7. Reiter, Michael, 2010. "Solving the incomplete markets model with aggregate uncertainty by backward induction," Journal of Economic Dynamics and Control, Elsevier, vol. 34(1), pages 28-35, 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.
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    More about this item

    Keywords

    Numerical solutions; Projection methods;

    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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