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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. 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.
    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. 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.
    4. Bruce Preston & Mauro Roca, 2007. "Incomplete Markets, Heterogeneity and Macroeconomic Dynamics," NBER Working Papers 13260, National Bureau of Economic Research, Inc.
    5. 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.
    6. 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.
    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.
    8. 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.
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    Citations

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    Cited by:

    1. Mordecai Kurz & Maurizio Motolese & Giulia Piccillo & Howei Wu, 2015. "Monetary Policy with Diverse Private Expectations," Discussion Papers 15-004, Stanford Institute for Economic Policy Research.
    2. Fatih Guvenen, 2011. "Macroeconomics with hetereogeneity : a practical guide," Economic Quarterly, Federal Reserve Bank of Richmond, issue 3Q, pages 255-326.
    3. 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.
    4. Carvalho, Vasco M & Grassi, Basile, 2015. "Large Firm Dynamics and the Business Cycle," CEPR Discussion Papers 10587, C.E.P.R. Discussion Papers.
    5. Michael C. Hatcher & Eric M. Scheffel, 2016. "Solving the Incomplete Markets Model in Parallel Using GPU Computing and the Krusell–Smith Algorithm," Computational Economics, Springer;Society for Computational Economics, vol. 48(4), pages 569-591, December.
    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. Tobias Grasl, 2013. "Solving Incomplete Markets Models by Derivative Aggregation," Birkbeck Working Papers in Economics and Finance 1302, Birkbeck, Department of Economics, Mathematics & Statistics.
    8. Den Haan, Wouter & Rendahl, Pontus & Riegler, Markus, 2015. "Unemployment (Fears) and Deflationary Spirals," CEPR Discussion Papers 10814, C.E.P.R. Discussion Papers.
    9. Den Haan, Wouter J. & Rendahl, Pontus & Riegler, Markus, 2015. "Unemployment (fears) and deflationary spirals," LSE Research Online Documents on Economics 86288, London School of Economics and Political Science, LSE Library.
    10. Wouter J. DEN HAAN, 2009. "Solving Dynamic Models with Heterogeneous Agents and Aggregate Uncertainty with Dynare or Dynare++," 2009 Meeting Papers 776, Society for Economic Dynamics.
    11. repec:fip:fedreq:y:2011:i:3q:p:255-326:n:vol.97no.3 is not listed on IDEAS
    12. Masayuki Inui & Sohei Kaihatsu, 2016. "The Power of Unconventional Monetary Policy in a Liquidity Trap," Bank of Japan Working Paper Series 16-E-16, Bank of Japan.
    13. 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.
    14. Hull, Isaiah, 2015. "Approximate dynamic programming with post-decision states as a solution method for dynamic economic models," Journal of Economic Dynamics and Control, Elsevier, vol. 55(C), pages 57-70.
    15. 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.
    16. Reiter, Michael, 2010. "Approximate and Almost-Exact Aggregation in Dynamic Stochastic Heterogeneous-Agent Models," Economics Series 258, Institute for Advanced Studies.
    17. Giusto, Andrea, 2014. "Adaptive learning and distributional dynamics in an incomplete markets model," Journal of Economic Dynamics and Control, Elsevier, vol. 40(C), pages 317-333.
    18. Grey Gordon, 2011. "Computing Dynamic Heterogeneous-Agent Economies: Tracking the Distribution," PIER Working Paper Archive 11-018, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.

    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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