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Inaccuracy of Loglinear Approximation in Welfare Calculations: the Case of International Risk Sharing

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  • Jinill Kim

    ()
    (University of Virginia)

  • Sunghyun Henry Kim

    ()
    (Brandeis University)

Abstract

This paper investigates the accuracy of the log-linear approximation method in welfare calculations, especially in measuring welfare gains of international risk sharing. We derive closed-form solutions for a two-country complete market economy using log-linearization and a nonlinear solution method and compare risk-sharing gains over financial autarky. We document that the loglinearized model underestimates risk-sharing gains by up to 20% of world consumption under certain parameter values with endogenous labor supply. While the nonlinear solution generates 4% risk-sharing gains, the loglinear approximation results in a loss of 16%. Loglinear approximation errors are large enough to generate welfare reversal between autarky and complete market economies, a violation of the first welfare theorem. This result can be crucial because a large number of papers adopt loglinearization method in calculating welfare.

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Bibliographic Info

Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 1999 with number 251.

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Date of creation: 01 Mar 1999
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Handle: RePEc:sce:scecf9:251

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  1. Cole, Harold L. & Obstfeld, Maurice, 1991. "Commodity trade and international risk sharing : How much do financial markets matter?," Journal of Monetary Economics, Elsevier, vol. 28(1), pages 3-24, August.
  2. Gaspar, Jess & L. Judd, Kenneth, 1997. "Solving Large-Scale Rational-Expectations Models," Macroeconomic Dynamics, Cambridge University Press, vol. 1(01), pages 45-75, January.
  3. Cho, Jang-Ok & Cooley, Thomas F & Phaneuf, Louis, 1997. "The Welfare Cost of Nominal Wage Contracting," Review of Economic Studies, Wiley Blackwell, vol. 64(3), pages 465-84, July.
  4. Christopher Otrok, 2000. "On Measuring the Welfare Cost of Business Cycles," Econometric Society World Congress 2000 Contributed Papers 1094, Econometric Society.
  5. Dale Henderson & Jinill Kim, 1999. "Exact Utilities under Alternative Monetary Rules in a Simple Macro Model with Optimizing Agents," International Tax and Public Finance, Springer, vol. 6(4), pages 507-535, November.
  6. David K. Backus & Patrick J. Kehoe & Finn E. Kydland, 1987. "International real business cycles," Working Papers 426, Federal Reserve Bank of Minneapolis.
  7. Christopher J. Erceg & Dale W. Henderson & Andrew T. Levin, 1999. "Optimal monetary policy with staggered wage and price contracts," International Finance Discussion Papers 640, Board of Governors of the Federal Reserve System (U.S.).
  8. Mendoza, Enrique G, 1995. "The Terms of Trade, the Real Exchange Rate, and Economic Fluctuations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 36(1), pages 101-37, February.
  9. Collard, Fabrice & Juillard, Michel, 2001. "Accuracy of stochastic perturbation methods: The case of asset pricing models," Journal of Economic Dynamics and Control, Elsevier, vol. 25(6-7), pages 979-999, June.
  10. Den Haan, Wouter J & Marcet, Albert, 1994. "Accuracy in Simulations," Review of Economic Studies, Wiley Blackwell, vol. 61(1), pages 3-17, January.
  11. Taylor, John B & Uhlig, Harald, 1990. "Solving Nonlinear Stochastic Growth Models: A Comparison of Alternative Solution Methods," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 1-17, January.
  12. Devereux, Michael B. & Saito, Makoto, 1997. "Growth and risk-sharing with incomplete international assets markets," Journal of International Economics, Elsevier, vol. 42(3-4), pages 453-481, May.
  13. Julio Rotemberg & Michael Woodford, 1997. "An Optimization-Based Econometric Framework for the Evaluation of Monetary Policy," NBER Chapters, in: NBER Macroeconomics Annual 1997, Volume 12, pages 297-361 National Bureau of Economic Research, Inc.
  14. Obstfeld, M., 1998. "Risk and Exchange Rate," Papers 193, Princeton, Woodrow Wilson School - Public and International Affairs.
  15. Tesar, Linda L., 1995. "Evaluating the gains from international risksharing," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 42(1), pages 95-143, June.
  16. Mark Bils & Yongsung Chang, 1999. "Wages and the Allocation of Hours and Effort," NBER Working Papers 7309, National Bureau of Economic Research, Inc.
  17. Benigno, Gianluca & Benigno, Pierpaolo, 2001. "Monetary Policy Rules and the Exchange Rate," CEPR Discussion Papers 2807, C.E.P.R. Discussion Papers.
  18. Ireland, Peter N., 1997. "A small, structural, quarterly model for monetary policy evaluation," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 47(1), pages 83-108, December.
  19. repec:cup:macdyn:v:1:y:1997:i:1:p:45-75 is not listed on IDEAS
  20. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-70, November.
  21. Michael Woodford, 2001. "Inflation Stabilization and Welfare," NBER Working Papers 8071, National Bureau of Economic Research, Inc.
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Cited by:
  1. Stephanie Schmitt-Grohe & Martin Uribe, 2002. "Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function," NBER Technical Working Papers 0282, National Bureau of Economic Research, Inc.
  2. Stephanie Schmitt-Grohe & Martin Uribe, 2000. "Stabilization Policy and the Costs of Dollarization," Departmental Working Papers 200006, Rutgers University, Department of Economics.
  3. Henning Bohn, 2004. "Intergenerational Risk Sharing and Fiscal Policy," 2004 Meeting Papers 22, Society for Economic Dynamics.

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