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Perturbation Methods for Markov-Switching DSGE Models

  • Foerster, Andrew
  • Rubio-Ramírez, Juan Francisco
  • Waggoner, Daniel F
  • Zha, Tao

This paper develops a general perturbation methodology for constructing high-order approximations to the solutions of Markov-switching DSGE models. We introduce an important and practical idea of partitioning the Markov-switching parameter space so that a steady state is well defined. With this definition, we show that the problem of definding an approximation of any order can be reduced to solving a system of quadratic equations. We propose using the theory of Grobner bases in searching all the solutions to the quadratic system. This approach allows us to obtain all the approximations and ascertain how many of them are stable. Our methodology is applied to three models to illustrate its feasibility and practicality.

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Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 9464.

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Date of creation: May 2013
Date of revision:
Handle: RePEc:cpr:ceprdp:9464
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  1. Frank Smets & Rafael Wouters, 2007. "Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach," American Economic Review, American Economic Association, vol. 97(3), pages 586-606, June.
  2. Aruoba, S. Boragan & Fernandez-Villaverde, Jesus & Rubio-Ramirez, Juan F., 2006. "Comparing solution methods for dynamic equilibrium economies," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2477-2508, December.
  3. Eric M. Aldrich & Jesus Fernandez-Villaverde & A. Ronald Gallant & Juan F. Rubio-Ramirez, 2010. "Tapping the Supercomputer Under Your Desk: Solving Dynamic Equilibrium Models with Graphics Processors," Working Papers 10-89, Duke University, Department of Economics.
  4. Roger E. A. Farmer & Daniel F. Waggoner & Tao Zha, 2009. "Understanding Markov-switching rational expectations models," FRB Atlanta Working Paper 2009-05, Federal Reserve Bank of Atlanta.
  5. Roger E. A. Farmer & Daniel F. Waggoner & Tao Zha, 2010. "Minimal State Variable Solutions to Markov-switching Rational Expectations Models," Emory Economics 1003, Department of Economics, Emory University (Atlanta).
  6. Kubler, Felix & Schmedders, Karl, 2010. "Competitive equilibria in semi-algebraic economies," Journal of Economic Theory, Elsevier, vol. 145(1), pages 301-330, January.
  7. Jesús Fernández-Villaverde & Pablo A. Guerrón-Quintana & Juan Rubio-Ramírez & Martín Uribe, 2009. "Risk Matters: The Real Effects of Volatility Shocks," NBER Working Papers 14875, National Bureau of Economic Research, Inc.
  8. Troy Davig & Eric M. Leeper & Todd B. Walker, 2010. ""Unfunded Liabilities" and Uncertain Fiscal Financing," NBER Working Papers 15782, National Bureau of Economic Research, Inc.
  9. Eric M. Leeper & Tao Zha, 2002. "Modest policy interventions," FRB Atlanta Working Paper 2002-19, Federal Reserve Bank of Atlanta.
  10. Jes�s Fern�ndez-Villaverde & Juan F. Rubio-Ram�rez, 2007. "Estimating Macroeconomic Models: A Likelihood Approach," Review of Economic Studies, Oxford University Press, vol. 74(4), pages 1059-1087.
  11. Huixin Bi & Nora Traum, 2012. "Estimating Sovereign Default Risk," American Economic Review, American Economic Association, vol. 102(3), pages 161-66, May.
  12. Francesco Bianchi & Leonardo Melosi, 2013. "Modeling the Evolution of Expectations and Uncertainty in General Equilibrium," Working Papers 13-14, Duke University, Department of Economics.
  13. Fernández-Villaverde, Jesús & Guerron-Quintana, Pablo A. & Rubio-Ramírez, Juan Francisco, 2012. "Estimating Dynamic Equilibrium Models with Stochastic Volatility," CEPR Discussion Papers 9130, C.E.P.R. Discussion Papers.
  14. Andreasen, Martin M. & Fernández-Villaverde, Jesús & Rubio-Ramírez, Juan Francisco, 2013. "The Pruned State-Space System for Non-Linear DSGE Models: Theory and Empirical Applications," CEPR Discussion Papers 9442, C.E.P.R. Discussion Papers.
  15. Davig, Troy & Leeper, Eric M. & Walker, Todd B., 2011. "Inflation and the fiscal limit," European Economic Review, Elsevier, vol. 55(1), pages 31-47, January.
  16. Ruchira Datta, 2010. "Finding all Nash equilibria of a finite game using polynomial algebra," Economic Theory, Springer, vol. 42(1), pages 55-96, January.
  17. Thomas A. Lubik & Frank Schorfheide, 2004. "Testing for Indeterminacy: An Application to U.S. Monetary Policy," American Economic Review, American Economic Association, vol. 94(1), pages 190-217, March.
  18. Zheng Liu & Daniel F. Waggoner & Tao Zha, 2011. "Sources of macroeconomic fluctuations: A regime‐switching DSGE approach," Quantitative Economics, Econometric Society, vol. 2(2), pages 251-301, 07.
  19. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, June.
  20. 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.
  21. Gomme, Paul & Klein, Paul, 2011. "Second-order approximation of dynamic models without the use of tensors," Journal of Economic Dynamics and Control, Elsevier, vol. 35(4), pages 604-615, April.
  22. Frank Schorfheide, 2003. "Learning and monetary policy shifts," FRB Atlanta Working Paper 2003-23, Federal Reserve Bank of Atlanta.
  23. Christopher A. Sims & Tao Zha, 2005. "Were There Regime Switches in U.S. Monetary Policy?," Working Papers 92, Princeton University, Department of Economics, Center for Economic Policy Studies..
  24. Nicholas Bloom, 2009. "The Impact of Uncertainty Shocks," Econometrica, Econometric Society, vol. 77(3), pages 623-685, 05.
  25. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-84, March.
  26. Troy A. Davig & Taeyoung Doh, 2008. "Monetary policy regime shifts and inflation persistence," Research Working Paper RWP 08-16, Federal Reserve Bank of Kansas City.
  27. Clarida, Richard & Galí, Jordi & Gertler, Mark, 1998. "Monetary Policy Rules and Macroeconomic Stability: Evidence and Some Theory," CEPR Discussion Papers 1908, C.E.P.R. Discussion Papers.
  28. Troy Davig & Eric M. Leeper, 2006. "Generalizing the Taylor Principle," Caepr Working Papers 2006-001, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington.
  29. Svensson, Lars E O & Williams, Noah, 2007. "Monetary Policy with Model Uncertainty: Distribution Forecast Targeting," CEPR Discussion Papers 6331, C.E.P.R. Discussion Papers.
  30. Glenn D. Rudebusch & Eric T. Swanson, 2008. "Examining the bond premium puzzle with a DSGE model," Working Paper Series 2007-25, Federal Reserve Bank of San Francisco.
  31. Ralph S.J. Koijen & Jules H. van Binsbergen & Juan F. Rubio-Ramírez & Jesus Fernandez-Villaverde, 2008. "Likelihood Estimation of DSGE Models with Epstein-Zin Preferences," 2008 Meeting Papers 1099, Society for Economic Dynamics.
  32. Manuel S. Santos & Adrian Peralta-Alva, 2003. "Accuracy of Simulations for Stochastic Dynamic Models," Levine's Bibliography 666156000000000264, UCLA Department of Economics.
  33. Amisano, Gianni & Tristani, Oreste, 2011. "Exact likelihood computation for nonlinear DSGE models with heteroskedastic innovations," Working Paper Series 1341, European Central Bank.
  34. 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.
  35. Tauchen, George, 1986. "Finite state markov-chain approximations to univariate and vector autoregressions," Economics Letters, Elsevier, vol. 20(2), pages 177-181.
  36. Jesus Fernández-Villaverde & Pablo Guerrón-Quintana & Juan F. Rubio-Ramírez, 2010. "Fortune or virtue: time-variant volatilities versus parameter drifting," Working Papers 10-14, Federal Reserve Bank of Philadelphia.
  37. Francesco Bianchi, 2009. "Regime Switches, Agents’ Beliefs, and Post-World War II U.S. Macroeconomic Dynamics," 2009 Meeting Papers 198, Society for Economic Dynamics.
  38. Andrew P Blake & Fabrizio Zampolli, 2006. "Optimal monetary policy in Markov-switching models with rational expectations agents," Bank of England working papers 298, Bank of England.
  39. Lombardo, Giovanni, 2010. "On approximating DSGE models by series expansions," Working Paper Series 1264, European Central Bank.
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