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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
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Handle: RePEc:cpr:ceprdp:9464
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  1. Eric M. Leeper & Tao Zha, 2003. "Modest policy interventions," Working Paper 2003-24, Federal Reserve Bank of Atlanta.
  2. 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.
  3. Lombardo, Giovanni, 2010. "On approximating DSGE models by series expansions," Working Paper Series 1264, European Central Bank.
  4. Jesús Fernández-Villaverde & Pablo Guerrón-Quintana & Juan Rubio-Ramirez, 2013. "Estimating Dynamic Equilibrium Models with Stochastic Volatility," Working Papers 2013-23, FEDEA.
  5. Farmer, Roger E.A. & Waggoner, Daniel F. & Zha, Tao, 2009. "Understanding Markov-switching rational expectations models," Journal of Economic Theory, Elsevier, vol. 144(5), pages 1849-1867, September.
  6. Manuel S. Santos & Adrian Peralta-Alva, 2003. "Accuracy Of Simulations For Stochastic Dynamic Models," Economics Working Papers we034615, Universidad Carlos III, Departamento de Economía.
  7. Troy Davig & Taeyoung Doh, 2008. "Monetary policy regime shifts and inflation persistence," Research Working Paper RWP 08-16, Federal Reserve Bank of Kansas City.
  8. Francesco Bianchi & Leonardo Melosi, 2012. "Modeling the Evolution of Expectations and Uncertainty in General Equilibrium," PIER Working Paper Archive 13-042, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  9. Fernández-Villaverde, Jesús & Rubio-Ramírez, Juan Francisco, 2006. "Estimating Macroeconomic Models: A Likelihood Approach," CEPR Discussion Papers 5513, C.E.P.R. Discussion Papers.
  10. Richard Clarida & Jordi Galí & Mark Gertler, 2000. "Monetary Policy Rules And Macroeconomic Stability: Evidence And Some Theory," The Quarterly Journal of Economics, MIT Press, vol. 115(1), pages 147-180, February.
  11. 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.
  12. Frank Smets & Raf Wouters, 2007. "Shocks and Frictions in US Business Cycles : a Bayesian DSGE Approach," Working Paper Research 109, National Bank of Belgium.
  13. 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.
  14. Pablo A. Guerron-Quintana & Martin Uribe & Juan Rubio-Ramirez & Jesús Fernández-Villaverde, 2009. "Risk Matters: The Real E¤ects of Volatility Shocks," 2009 Meeting Papers 237, Society for Economic Dynamics.
  15. Farmer, Roger E.A. & Waggoner, Daniel F. & Zha, Tao, 2011. "Minimal state variable solutions to Markov-switching rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 35(12), pages 2150-2166.
  16. 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.
  17. 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.
  18. Amisano, Gianni & Tristani, Oreste, 2011. "Exact likelihood computation for nonlinear DSGE models with heteroskedastic innovations," Journal of Economic Dynamics and Control, Elsevier, vol. 35(12), pages 2167-2185.
  19. Thomas Lubik & Frank Schorfheide, 2002. "Testing for Indeterminacy:An Application to U.S. Monetary Policy," Economics Working Paper Archive 480, The Johns Hopkins University,Department of Economics, revised Jun 2003.
  20. Rudebusch, Glenn D. & Swanson, Eric T., 2008. "Examining the bond premium puzzle with a DSGE model," Journal of Monetary Economics, Elsevier, vol. 55(Supplemen), pages S111-S126, October.
  21. Martin M. Andreasen & Jesús Fernández-Villaverde & Juan Rubio-Ramírez, 2013. "The Pruned State-Space System for Non-Linear DSGE Models: Theory and Empirical Applications," NBER Working Papers 18983, National Bureau of Economic Research, Inc.
  22. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, June.
  23. 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.
  24. 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.
  25. Christopher A. Sims & Tao Zha, 2004. "Were there regime switches in U.S. monetary policy?," Working Paper 2004-14, Federal Reserve Bank of Atlanta.
  26. Francesco Bianchi, 2010. "Regime Switches, Agents' Beliefs, and Post-World War II U.S. Macroeconomic Dynamics," Working Papers 10-39, Duke University, Department of Economics.
  27. Frank Schorfheide, 2005. "Learning and Monetary Policy Shifts," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 8(2), pages 392-419, April.
  28. S. Boragan Aruoba & Jesus Fernandez-Villaverde & Juan Francisco Rubio-Ramirez, 2003. "Comparing solution methods for dynamic equilibrium economies," Working Paper 2003-27, Federal Reserve Bank of Atlanta.
  29. Tauchen, George, 1986. "Finite state markov-chain approximations to univariate and vector autoregressions," Economics Letters, Elsevier, vol. 20(2), pages 177-181.
  30. Nicholas Bloom, 2009. "The Impact of Uncertainty Shocks," Econometrica, Econometric Society, vol. 77(3), pages 623-685, 05.
  31. Lars Svensson & Noah Williams, 2005. "Monetary Policy with Model Uncertainty: Distribution Forecast Targeting," NBER Working Papers 11733, National Bureau of Economic Research, Inc.
  32. Aldrich, Eric M. & Fernández-Villaverde, Jesús & Ronald Gallant, A. & Rubio-Ramírez, Juan F., 2011. "Tapping the supercomputer under your desk: Solving dynamic equilibrium models with graphics processors," Journal of Economic Dynamics and Control, Elsevier, vol. 35(3), pages 386-393, March.
  33. 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.
  34. Ruchira Datta, 2010. "Finding all Nash equilibria of a finite game using polynomial algebra," Economic Theory, Springer, vol. 42(1), pages 55-96, January.
  35. 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.
  36. Kubler, Felix & Schmedders, Karl, 2010. "Competitive equilibria in semi-algebraic economies," Journal of Economic Theory, Elsevier, vol. 145(1), pages 301-330, January.
  37. 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.
  38. Paul Gomme & Paul Klein, 2009. "Second-order approximation of dynamic models without the use of tensors," Working Papers 09004, Concordia University, Department of Economics, revised 28 Apr 2010.
  39. Huixin Bi & Nora Traum, 2012. "Estimating Sovereign Default Risk," American Economic Review, American Economic Association, vol. 102(3), pages 161-66, May.
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