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Calculating and using second order accurate solutions of discrete time dynamic equilibrium models

  • Jinill Kim
  • Sunghyun Kim
  • Ernst Schaumburg
  • Christopher A. Sims

We describe an algorithm for calculating second order approximations to the solutions to nonlinear stochastic rational expectation models. The paper also explains methods for using such an approximate solution to generate forecasts, simulated time paths for the model, and evaluations of expected welfare differences across different versions of a model. The paper gives conditions for local validity of the approximation that allow for disturbance distributions with unbounded support and allow for non-stationarity of the solution process.

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Paper provided by Board of Governors of the Federal Reserve System (U.S.) in its series Finance and Economics Discussion Series with number 2003-61.

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Date of creation: 2003
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Handle: RePEc:fip:fedgfe:2003-61
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  1. Kollmann, Robert, 2002. "Monetary policy rules in the open economy: effects on welfare and business cycles," Journal of Monetary Economics, Elsevier, vol. 49(5), pages 989-1015, July.
  2. 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.
  3. Alan Sutherland, 2002. "A Simple Second-Order Solution Method for Dynamic General Equilibrium Models," Discussion Paper Series, Department of Economics 200211, Department of Economics, University of St. Andrews.
  4. Wouter J. den Haan & Albert Marcet, 1993. "Accuracy in simulations," Economics Working Papers 42, Department of Economics and Business, Universitat Pompeu Fabra.
  5. Stephanie Schmitt-Grohe & Martin Uribe, 2001. "Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function," Departmental Working Papers 200106, Rutgers University, Department of Economics.
  6. Clarida, Richard & Galí, Jordi & Gertler, Mark, 1999. "The Science of Monetary Policy: A New Keynesian Perspective," CEPR Discussion Papers 2139, C.E.P.R. Discussion Papers.
  7. 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.
  8. Klein, Paul, 2000. "Using the generalized Schur form to solve a multivariate linear rational expectations model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(10), pages 1405-1423, September.
  9. Marc P. Giannoni & Michael Woodford, 2003. "Optimal Interest-Rate Rules: I. General Theory," Levine's Bibliography 506439000000000384, UCLA Department of Economics.
  10. 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, vol. 39(4), pages 1015-26, November.
  11. Paul R. Bergin & Ivan Tchakarov, 2003. "Does Exchange Rate Risk Matter for Welfare?," NBER Working Papers 9900, National Bureau of Economic Research, Inc.
  12. Gaspar, Jess & L. Judd, Kenneth, 1997. "Solving Large-Scale Rational-Expectations Models," Macroeconomic Dynamics, Cambridge University Press, vol. 1(01), pages 45-75, January.
  13. Michael Woodford, 2001. "Inflation Stabilization and Welfare," NBER Working Papers 8071, National Bureau of Economic Research, Inc.
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