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Evaluating linear approximations in a two-country model with occasionally binding borrowing constraints

Author

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  • Anagnostopoulos Alexis

    (Stony Brook University – Economics, Stony Brook, NY, USA)

  • Tang Xin

    (Stony Brook University – Economics, Stony Brook, NY, USA)

Abstract
Under a linear approximation, a standard two-country business cycles model with incomplete markets delivers consumption and debt dynamics that are non-stationary (unit root) and a bond price that is independent of the wealth distribution. We argue that these two features are due to the local nature of the approximation and we show that they survive even when second or third order local approximations are used. However, these features disappear when debt limits and the associated precautionary motives are taken into account by a standard, global solution method. We subsequently investigate whether this qualitative difference has significant quantitative implications regarding the linear solution as an approximation to the model’s equilibrium dynamics. Policy function differences between the local and global solutions can be large and remain significant even in the case of debt limits as loose as the natural debt limit. These differences can lead to significant discrepancies in implied simulated second moments. In a benchmark calibration, the cross-country correlation of consumption is 0.61 under linearization, but only 0.38 when a policy iteration algorithm is used.

Suggested Citation

  • Anagnostopoulos Alexis & Tang Xin, 2015. "Evaluating linear approximations in a two-country model with occasionally binding borrowing constraints," The B.E. Journal of Macroeconomics, De Gruyter, vol. 15(1), pages 43-91, January.
    • Handle: RePEc:bpj:bejmac:v:15:y:2015:i:1:p:49:n:4
    DOI: 10.1515/bejm-2013-0175
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    1. Den Haan, Wouter J., 2001. "The importance of the number of different agents in a heterogeneous asset-pricing model," Journal of Economic Dynamics and Control, Elsevier, vol. 25(5), pages 721-746, May.
    2. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    3. Christiano, Lawrence J, 2002. "Solving Dynamic Equilibrium Models by a Method of Undetermined Coefficients," Computational Economics, Springer;Society for Computational Economics, vol. 20(1-2), pages 21-55, October.
    4. Schmitt-Grohe, Stephanie & Uribe, Martin, 2003. "Closing small open economy models," Journal of International Economics, Elsevier, vol. 61(1), pages 163-185, October.
    5. Tauchen, George & Hussey, Robert, 1991. "Quadrature-Based Methods for Obtaining Approximate Solutions to Nonlinear Asset Pricing Models," Econometrica, Econometric Society, vol. 59(2), pages 371-396, March.
    6. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
    7. Schmitt-Grohe, Stephanie & Uribe, Martin, 2004. "Solving dynamic general equilibrium models using a second-order approximation to the policy function," Journal of Economic Dynamics and Control, Elsevier, vol. 28(4), pages 755-775, January.
    8. McGrattan, Ellen R, 1990. "Solving the Stochastic Growth Model by Linear-Quadratic Approximation," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 41-44, January.
    9. Heaton, John & Lucas, Deborah J, 1996. "Evaluating the Effects of Incomplete Markets on Risk Sharing and Asset Pricing," Journal of Political Economy, University of Chicago Press, vol. 104(3), pages 443-487, June.
    10. Marcet, Albert & Singleton, Kenneth J., 1999. "Equilibrium Asset Prices And Savings Of Heterogeneous Agents In The Presence Of Incomplete Markets And Portfolio Constraints," Macroeconomic Dynamics, Cambridge University Press, vol. 3(2), pages 243-277, June.
    11. Tauchen, George, 1986. "Finite state markov-chain approximations to univariate and vector autoregressions," Economics Letters, Elsevier, vol. 20(2), pages 177-181.
    12. Lars Ljungqvist & Thomas J. Sargent, 2004. "Recursive Macroeconomic Theory, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 026212274x, December.
    13. Lane, Philip R. & Milesi-Ferretti, Gian Maria, 2007. "The external wealth of nations mark II: Revised and extended estimates of foreign assets and liabilities, 1970-2004," Journal of International Economics, Elsevier, vol. 73(2), pages 223-250, November.
    14. Levine, David K. & Zame, William R., 1996. "Debt constraints and equilibrium in infinite horizon economies with incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 26(1), pages 103-131.
    15. Marcet, Albert & Scott, Andrew, 2009. "Debt and deficit fluctuations and the structure of bond markets," Journal of Economic Theory, Elsevier, vol. 144(2), pages 473-501, March.
    16. S. Rao Aiyagari, 1994. "Uninsured Idiosyncratic Risk and Aggregate Saving," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 109(3), pages 659-684.
    17. Pontus Rendahl, 2015. "Inequality Constraints and Euler Equation‐based Solution Methods," Economic Journal, Royal Economic Society, vol. 125(585), pages 1110-1135, June.
    18. Xu, Xiaonian, 1995. "Precautionary Savings under Liquidity Constraints: A Decomposition," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 36(3), pages 675-690, August.
    19. Lane, Philip & Milesi-Ferretti, Gian Maria, "undated". "External Wealth of Nations," Instructional Stata datasets for econometrics extwealth, Boston College Department of Economics.
    20. Granger, Clive W. J. & Swanson, Norman R., 1997. "An introduction to stochastic unit-root processes," Journal of Econometrics, Elsevier, vol. 80(1), pages 35-62, September.
    21. 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.
    22. Flodén, Martin, 2008. "A note on the accuracy of Markov-chain approximations to highly persistent AR(1) processes," Economics Letters, Elsevier, vol. 99(3), pages 516-520, June.
    23. G. M. Grossman & K. Rogoff (ed.), 1995. "Handbook of International Economics," Handbook of International Economics, Elsevier, edition 1, volume 3, number 3.
    24. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
    25. Coleman, Wilbur John, II, 1990. "Solving the Stochastic Growth Model by Policy-Function Iteration," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 27-29, January.
    26. Christiano, Lawrence J, 1990. "Solving the Stochastic Growth Model by Linear-Quadratic Approximation and by Value-Function Iteration," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 23-26, January.
    27. 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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    Keywords

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    JEL classification:

    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth
    • F44 - International Economics - - Macroeconomic Aspects of International Trade and Finance - - - International Business Cycles
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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