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Solving General Incomplete Market Models with Substantial Heterogeneity

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  • Thomas Mertens

    (New York University)

Abstract

We propose a simple but general solution method for models with incomplete markets and finitely but arbitrarily many heterogeneous agents. Our method can handle many state and choice variables for each agent and thus an extremely high-dimensional state space. The solution technique is based on perturbation methods that build an approximation around a point at which the solution is known. At this point, agents are either identical or their policy functions are known. The novel idea is to exploit the symmetry of the problem to avoid the curse of dimensionality. Our method underlies an approximation theory that specifies the speed and radius of convergence as well as the class of models to which our method applies. As a result, we study the interaction between uninsurable idiosyncratic labor income risk and asset price dynamics within a standard macroeconomic model. We show that not only the variability of individual wealth but also its comovement with other agentsâ wealth plays an important role.

Suggested Citation

  • Thomas Mertens, 2012. "Solving General Incomplete Market Models with Substantial Heterogeneity," 2012 Meeting Papers 1173, Society for Economic Dynamics.
  • Handle: RePEc:red:sed012:1173
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    File URL: https://economicdynamics.org/meetpapers/2012/paper_1173.pdf
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    References listed on IDEAS

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    1. YiLi Chien & Hanno Lustig, 2010. "The Market Price of Aggregate Risk and the Wealth Distribution," Review of Financial Studies, Society for Financial Studies, vol. 23(4), pages 1596-1650, April.
    2. Zhigang Feng & Jianjun Miao & Adrian Peralta‐Alva & Manuel S. Santos, 2014. "Numerical Simulation Of Nonoptimal Dynamic Equilibrium Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55, pages 83-110, February.
    3. 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.
    4. Tarek A. Hassan & Thomas M. Mertens, 2017. "The Social Cost of Near-Rational Investment," American Economic Review, American Economic Association, vol. 107(4), pages 1059-1103, April.
    5. Kenneth Judd & Lilia Maliar & Serguei Maliar, 2009. "Numerically Stable Stochastic Simulation Approaches for Solving Dynamic Economic Models," NBER Working Papers 15296, National Bureau of Economic Research, Inc.
    6. Bruce Preston & Mauro Roca, 2007. "Incomplete Markets, Heterogeneity and Macroeconomic Dynamics," NBER Working Papers 13260, National Bureau of Economic Research, Inc.
    7. Eric T. Swanson & Gary S. Anderson & Andrew T. Levin, 2006. "Higher-order perturbation solutions to dynamic, discrete-time rational expectations models," Working Paper Series 2006-01, Federal Reserve Bank of San Francisco.
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