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Applying Perturbation Methods to Incomplete Market Models with Exogenous Borrowing Constraints

Author

Listed:
  • Henry Kim
  • Jinill Kim
  • Robert Kollmann

Abstract

This paper solves an incomplete market model with infinite number of agents and exogenous borrowing constraints described in den Haan, Judd and Juillard (2004). We apply the idea of “barrier methods” to convert optimization problem with borrowing constraints as inequalities into a problem with equality constraints, and the converted model is solved by a second-order perturbation method. The simulation results of impulse responses and second moments match the standardized features of incomplete market models. Accuracy of the solution is in a reasonable range but significantly decreases when the economy is near the borrowing limit or moves away from the steady state.

Suggested Citation

  • 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.
  • Handle: RePEc:tuf:tuftec:0504
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    File URL: http://ase.tufts.edu/econ/papers/200504.pdf
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    References listed on IDEAS

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    1. Schmitt-Grohe, Stephanie & Uribe, Martin, 2003. "Closing small open economy models," Journal of International Economics, Elsevier, vol. 61(1), pages 163-185, October.
    2. Baxter, Marianne & Crucini, Mario J, 1995. "Business Cycles and the Asset Structure of Foreign Trade," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 36(4), pages 821-854, November.
    3. Kim, Jinill & Kim, Sunghyun Henry, 2003. "Spurious welfare reversals in international business cycle models," Journal of International Economics, Elsevier, vol. 60(2), pages 471-500, August.
    4. Felix Kubler & Karl Schmedders, 2001. "Incomplete Markets, Transitory Shocks, and Welfare," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 4(4), pages 747-766, October.
    5. Alvarez, Fernando & Jermann, Urban J, 2001. "Quantitative Asset Pricing Implications of Endogenous Solvency Constraints," Review of Financial Studies, Society for Financial Studies, vol. 14(4), pages 1117-1151.
    6. David K. Levine & William R. Zame, 2002. "Does Market Incompleteness Matter?," Econometrica, Econometric Society, vol. 70(5), pages 1805-1839, September.
    7. 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.
    8. Kim, Sunghyun Henry & Kose, M. Ayhan, 2003. "Dynamics Of Open-Economy Business-Cycle Models: Role Of The Discount Factor," Macroeconomic Dynamics, Cambridge University Press, vol. 7(02), pages 263-290, April.
    9. Patrick J. Kehoe & Fabrizio Perri, 2002. "International Business Cycles with Endogenous Incomplete Markets," Econometrica, Econometric Society, vol. 70(3), pages 907-928, May.
    10. 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.
    11. Mendoza, Enrique G, 1991. "Real Business Cycles in a Small Open Economy," American Economic Review, American Economic Association, vol. 81(4), pages 797-818, September.
    12. 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.
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    Citations

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    Cited by:

    1. Mauro F Roca, 2009. "Search in the Labor Market under Imperfectly Insurable Income Risk," IMF Working Papers 09/188, International Monetary Fund.
    2. Bingbing Dong, 2014. "Asset Pricing and Monetary Policy," 2014 Meeting Papers 881, Society for Economic Dynamics.
    3. Darlene Chisholm & Margaret McMillan & George Norman, 2010. "Product differentiation and film-programming choice: do first-run movie theatres show the same films?," Journal of Cultural Economics, Springer;The Association for Cultural Economics International, vol. 34(2), pages 131-145, May.
    4. Ioannides, Yannis M. & Soetevent, Adriaan R., 2007. "Social networking and individual outcomes beyond the mean field case," Journal of Economic Behavior & Organization, Elsevier, vol. 64(3-4), pages 369-390.
    5. Gilbert Metcalf & Jongsang Park, 2007. "A comment on the role of prices for excludable public goods," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 14(6), pages 685-698, December.
    6. Antoni Calvo-Armengol & Yannis M. Ioannides, 2005. "Social Networks in Labor Markets," Discussion Papers Series, Department of Economics, Tufts University 0517, Department of Economics, Tufts University.
    7. Andrea Pescatori, 2007. "Incomplete markets and households’ exposure to interest rate and inflation risk: implications for the monetary policy maker," Working Paper 0709, Federal Reserve Bank of Cleveland.
    8. 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.
    9. 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.
    10. Bulut Levent, 2011. "External Debts and Current Account Adjustments," The B.E. Journal of Macroeconomics, De Gruyter, vol. 11(1), pages 1-53, December.
    11. Bruce Preston & Mauro Roca, 2007. "Incomplete Markets, Heterogeneity and Macroeconomic Dynamics," NBER Working Papers 13260, National Bureau of Economic Research, Inc.
    12. Darlene C. Chisholm & George Norman, 2006. "When to Exit a Product: Evidence from the U. S. Motion-Picture Exhibition Market," American Economic Review, American Economic Association, vol. 96(2), pages 57-61, May.

    More about this item

    Keywords

    perturbation; barrier method; borrowing constraint; incomplete market; accuracy.;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
    • C88 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Other Computer Software
    • F41 - International Economics - - Macroeconomic Aspects of International Trade and Finance - - - Open Economy Macroeconomics

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