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Solving the incomplete market model with aggregate uncertainty using a perturbation method

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  • Kim, Sunghyun Henry
  • Kollmann, Robert
  • Kim, Jinill

Abstract

We use a perturbation method to solve the incomplete markets model with aggregate uncertainty described in den Haan et al. [Computational suite of models with heterogeneous agents: incomplete markets and model uncertainty. Journal of Economic Dynamics & Control, this issue]. To apply that method, we use a "barrier method" to replace the original problem with occasionally binding inequality constraints by one with only equality constraints. We replace the structure with a continuum of agents by a setting in which a single infinitesimal agent faces prices generated by a representative-agent economy. We also solve a model variant with a large (but finite) number of agents. Our perturbation-based method is much simpler and faster than other methods.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:dyncon:v:34:y:2010:i:1:p:50-58
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    1. Den Haan, Wouter J, 1996. "Heterogeneity, Aggregate Uncertainty, and the Short-Term Interest Rate," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 399-411, October.
    2. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, September.
    3. 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.
    4. Christopher A. Sims & Jinill Kim & Sunghyun Kim, 2003. "Calculating and Using Second Order Accurate Solution of Discrete Time Dynamic Equilibrium Models," Computing in Economics and Finance 2003 162, Society for Computational Economics.
    5. 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.
    6. Bruce Preston & Mauro Roca, 2007. "Incomplete Markets, Heterogeneity and Macroeconomic Dynamics," NBER Working Papers 13260, National Bureau of Economic Research, Inc.
    7. Den Haan, Wouter J., 1997. "Solving Dynamic Models With Aggregate Shocks And Heterogeneous Agents," Macroeconomic Dynamics, Cambridge University Press, vol. 1(2), pages 355-386, June.
    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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    Cited by:

    1. Kollmann, Robert & Kim, Jinill & Kim, Sunghyun H., 2011. "Solving the multi-country Real Business Cycle model using a perturbation method," Journal of Economic Dynamics and Control, Elsevier, vol. 35(2), pages 203-206, February.
    2. Brzoza-Brzezina, Michał & Kolasa, Marcin & Makarski, Krzysztof, 2015. "A penalty function approach to occasionally binding credit constraints," Economic Modelling, Elsevier, vol. 51(C), pages 315-327.
    3. Lambertini, Luisa & Mendicino, Caterina & Teresa Punzi, Maria, 2013. "Leaning against boom–bust cycles in credit and housing prices," Journal of Economic Dynamics and Control, Elsevier, vol. 37(8), pages 1500-1522.
    4. Benigno, Gianluca & Chen, Huigang & Otrok, Christopher & Rebucci, Alessandro & Young, Eric R., 2016. "Optimal capital controls and real exchange rate policies: A pecuniary externality perspective," Journal of Monetary Economics, Elsevier, vol. 84(C), pages 147-165.
    5. Benigno, Gianluca & Chen, Huigang & Otrok, Christopher & Rebucci, Alessandro & Young, Eric R, 2012. "Optimal Policy for Macro-Financial Stability," CEPR Discussion Papers 9223, C.E.P.R. Discussion Papers.
    6. Rabitsch, Katrin & Stepanchuk, Serhiy & Tsyrennikov, Viktor, 2015. "International portfolios: A comparison of solution methods," Journal of International Economics, Elsevier, vol. 97(2), pages 404-422.
    7. Mendicino, Caterina, 2012. "On the amplification role of collateral constraints," Economics Letters, Elsevier, vol. 117(2), pages 429-435.
    8. Martin D. D. Evans, 2017. "Exchange-Rate Dark Matter," World Scientific Book Chapters, in: Studies in Foreign Exchange Economics, chapter 4, pages 101-185, World Scientific Publishing Co. Pte. Ltd..
    9. Mertens, Thomas M. & Judd, Kenneth L., 2018. "Solving an incomplete markets model with a large cross-section of agents," Journal of Economic Dynamics and Control, Elsevier, vol. 91(C), pages 349-368.
    10. Gauti B. Eggertsson & Sergey K. Egiev & Alessandro Lin & Josef Platzer & Luca Riva, 2020. "A Toolkit for Solving Models with a Lower Bound on Interest Rates of Stochastic Duration," NBER Working Papers 27878, National Bureau of Economic Research, Inc.
    11. Piergiorgio Alessandri & Haroon Mumtaz, 2017. "Financial conditions and density forecasts for US output and inflation," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 24, pages 66-78, March.
    12. Karmakar, Sudipto, 2016. "Macroprudential regulation and macroeconomic activity," Journal of Financial Stability, Elsevier, vol. 25(C), pages 166-178.
    13. Laséen, Stefan & Pescatori, Andrea & Turunen, Jarkko, 2017. "Systemic risk: A new trade-off for monetary policy?," Journal of Financial Stability, Elsevier, vol. 32(C), pages 70-85.
    14. Piergiorgio Alessandri & Haroon Mumtaz, 2014. "Financial indicators and density forecasts for US output and inflation," Temi di discussione (Economic working papers) 977, Bank of Italy, Economic Research and International Relations Area.
    15. 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.
    16. Bulut Levent, 2011. "External Debts and Current Account Adjustments," The B.E. Journal of Macroeconomics, De Gruyter, vol. 11(1), pages 1-53, December.
    17. Andrei Jirnyi & Vadym Lepetyuk, 2011. "A reinforcement learning approach to solving incomplete market models with aggregate uncertainty," Working Papers. Serie AD 2011-21, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    18. Xavier Ragot & Francois Le Grand, 2017. "Optimal Fiscal Policy with Heterogeneous Agents and Aggregate Shocks," 2017 Meeting Papers 969, Society for Economic Dynamics.
    19. Guerrieri, Luca & Iacoviello, Matteo, 2015. "OccBin: A toolkit for solving dynamic models with occasionally binding constraints easily," Journal of Monetary Economics, Elsevier, vol. 70(C), pages 22-38.
    20. Caterina Mendicino, 2012. "Collateral Requirements: Macroeconomic Fluctuations and Macro-Prudential Policy," Working Papers w201211, Banco de Portugal, Economics and Research Department.
    21. Christophe Gouel, 2013. "Comparing Numerical Methods for Solving the Competitive Storage Model," Computational Economics, Springer;Society for Computational Economics, vol. 41(2), pages 267-295, February.
    22. Thomas Mertens, 2012. "Solving General Incomplete Market Models with Substantial Heterogeneity," 2012 Meeting Papers 1173, Society for Economic Dynamics.
    23. Karsten O. Chipeniuk, 2020. "Optimal Grid Selection for the Numerical Solution of Dynamic Stochastic Optimization Problems," Computational Economics, Springer;Society for Computational Economics, vol. 56(4), pages 883-928, December.
    24. 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.
    25. Martin D Evans, 2012. "Exchange-Rate Dark Matter," IMF Working Papers 2012/066, International Monetary Fund.

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