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Calculating and Using Second Order Accurate Solution of Discrete Time Dynamic Equilibrium Models

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  • Christopher A. Sims
  • Jinill Kim
  • Sunghyun Kim

Abstract

It is now widely understood how to obtain first-order accurate approximations to the solution to a dynamic, stochastic general equilibrium model (DSGE model). Such solutions are fairly easy to construct and useful for a wide variety of purposes. They are likely to be accurate enough to be a basis for fitting the models to data, for example. However, for some purposes first-order accuracy is not enough. This is true in particular for comparing welfare across policies that do not have first-order effects on the model's deterministic steady state, for example. It is also true for attempts to study asset pricing in the context of DSGE models. This paper describes the algorithm for computing a second order approximation and shows how to apply it to calculating forecasts and impulse responses in dynamic models and to evaluating welfare in DSGE models. It points out some necessary regularity conditions for application of the method and discusses the sense in which the approximate solutions are locally accurate

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Bibliographic Info

Paper provided by Econometric Society in its series Econometric Society 2004 North American Winter Meetings with number 411.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:nawm04:411

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Keywords: Second Order Solution; Perturbation Method; Welfare Calculation;

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  1. Den Haan, Wouter J & Marcet, Albert, 1994. "Accuracy in Simulations," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 61(1), pages 3-17, January.
  2. Kollmann, Robert, 2002. "Monetary policy rules in the open economy: effects on welfare and business cycles," Journal of Monetary Economics, Elsevier, Elsevier, vol. 49(5), pages 989-1015, July.
  3. Kim, Jinill & Kim, Sunghyun Henry, 2003. "Spurious welfare reversals in international business cycle models," Journal of International Economics, Elsevier, Elsevier, vol. 60(2), pages 471-500, August.
  4. Richard Clarida & Jordi Gali & Mark Gertler, 1999. "The Science of Monetary Policy: A New Keynesian Perspective," NBER Working Papers 7147, National Bureau of Economic Research, Inc.
  5. Alan Sutherland, 2002. "A Simple Second-Order Solution Method for Dynamic General Equilibrium Models," Discussion Paper Series, Department of Economics, Department of Economics, University of St. Andrews 200211, Department of Economics, University of St. Andrews.
  6. Ivan Tchakarov & Paul Bergin, 2003. "Does Exchange Rate Risk Matter for Welfare?," Computing in Economics and Finance 2003, Society for Computational Economics 61, Society for Computational Economics.
  7. King, Robert G & Watson, Mark W, 1998. "The Solution of Singular Linear Difference Systems under Rational Expectations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 1015-26, November.
  8. Gaspar, Jess & L. Judd, Kenneth, 1997. "Solving Large-Scale Rational-Expectations Models," Macroeconomic Dynamics, Cambridge University Press, Cambridge University Press, vol. 1(01), pages 45-75, January.
  9. Klein, Paul, 2000. "Using the generalized Schur form to solve a multivariate linear rational expectations model," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 24(10), pages 1405-1423, September.
  10. Marc P. Giannoni & Michael Woodford, 2003. "Optimal Interest-Rate Rules: I. General Theory," Levine's Bibliography 506439000000000384, UCLA Department of Economics.
  11. 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.
  12. 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.
  13. Woodford Michael, 2002. "Inflation Stabilization and Welfare," The B.E. Journal of Macroeconomics, De Gruyter, De Gruyter, vol. 2(1), pages 1-53, February.
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