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Applying Perturbation Methods to Incomplete Market Models with Exogenous Borrowing Constraints

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  • 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.

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Bibliographic Info

Paper provided by Department of Economics, Tufts University in its series Discussion Papers Series, Department of Economics, Tufts University with number 0504.

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Date of creation: 2005
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Handle: RePEc:tuf:tuftec:0504

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

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References

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  1. Krusell, P & Smith Jr, A-A, 1995. "Income and Wealth Heterogeneity in the Macroeconomic," RCER Working Papers 399, University of Rochester - Center for Economic Research (RCER).
  2. Felix Kubler & Karl Schmedders, 2000. "Incomplete Markets, Transitory Shocks and Welfare," Levine's Working Paper Archive 2133, David K. Levine.
  3. David K. Levine & William Zame, 2001. "Does Market Incompleteness Matter," Levine's Working Paper Archive 78, David K. Levine.
  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. 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 821-54, November.
  6. 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.
  7. Patrick J. Kehoe & Fabrizio Perri, 2000. "International Business Cycles with Endogenous Incomplete Markets," NBER Working Papers 7870, National Bureau of Economic Research, Inc.
  8. Stephanie Schmitt-Grohe & Martin Uribe, 2001. "Closing Small Open Economy Models," Departmental Working Papers 200115, Rutgers University, Department of Economics.
  9. Fernando Alvarez & Urban J. Jermann, 1999. "Quantitative Asset Pricing Implications of Endogenous Solvency Constraints," NBER Working Papers 6953, National Bureau of Economic Research, Inc.
  10. 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.
  11. Jinill Kim and Sunghyun Henry Kim, 2001. "Spurious Welfare Reversals in International Business Cycle Models," Computing in Economics and Finance 2001 3, Society for Computational Economics.
  12. 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.
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Cited by:
  1. Darlene C. Chisholm & Margaret S. McMillan & George Norman, 2005. "Product Differentiation and Film Programming Choice: Do First-Run Movie Theatres Show the Same Films?," Discussion Papers Series, Department of Economics, Tufts University 0523, Department of Economics, Tufts University.
  2. 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.
  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. Gilbert Metcalf & Jongsang Park, 2007. "A comment on the role of prices for excludable public goods," International Tax and Public Finance, Springer, vol. 14(6), pages 685-698, December.
  5. Yannis M. Ioannides & Adriaan R. Soetevent, 2005. "Social Networking and Individual Outcomes Beyond the Mean Field Case," Discussion Papers Series, Department of Economics, Tufts University 0521, Department of Economics, Tufts University.
  6. Bulut Levent, 2011. "External Debts and Current Account Adjustments," The B.E. Journal of Macroeconomics, De Gruyter, vol. 11(1), pages 1-53, December.
  7. Mauro Roca, 2009. "Search in the Labor Market Under Imperfectly Insurable Income Risk," IMF Working Papers 09/188, International Monetary Fund.
  8. 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.
  9. Bruce Preston & Mauro Roca, 2007. "Incomplete Markets, Heterogeneity and Macroeconomic Dynamics," NBER Working Papers 13260, National Bureau of Economic Research, Inc.
  10. 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.
  11. 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.

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