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Perturbation Methods for Markov-Switching DSGE Models

  • Andrew Foerster
  • Juan Rubio-Ramirez
  • Dan Waggoner
  • Ta Zha

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 de?ned. With this de?nition, we show that the problem of ?nding an approximation of any order can be reduced to solving a system of quadratic equations. We propose using the theory of Gröbner 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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File URL: http://documentos.fedea.net/pubs/dt/2013/dt-2013-22.pdf
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Paper provided by FEDEA in its series Working Papers with number 2013-22.

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Date of creation: Dec 2013
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Handle: RePEc:fda:fdaddt:2013-22
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  1. S. B. Aruoba & Jesús Fernández-Villaverde & Juan F. Rubio-Ramirez, 2005. "Comparing Solution Methods for Dynamic Equilibrium Economies," Levine's Bibliography 122247000000000855, UCLA Department of Economics.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. Richard Clarida & Jordi Gali & Mark Gertler, 1998. "Monetary Policy Rules and Macroeconomic Stability: Evidence and Some Theory," NBER Working Papers 6442, National Bureau of Economic Research, Inc.
  7. Svensson, Lars E. O. & Williams, Noah, 2005. "Monetary policy with model uncertainty: distribution forecast targeting," Discussion Paper Series 1: Economic Studies 2005,35, Deutsche Bundesbank, Research Centre.
  8. Jesús Fernández-Villaverde & Pablo Guerrón-Quintana & Juan Rubio-Ramirez, 2013. "Estimating Dynamic Equilibrium Models with Stochastic Volatility," Working Papers 2013-23, FEDEA.
  9. 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.
  10. Francesco Bianchi, 2009. "Regime Switches, Agents’ Beliefs, and Post-World War II U.S. Macroeconomic Dynamics," 2009 Meeting Papers 198, Society for Economic Dynamics.
  11. 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.
  12. 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.
  13. 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.
  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. 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.
  16. 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.
  17. Ruchira Datta, 2010. "Finding all Nash equilibria of a finite game using polynomial algebra," Economic Theory, Springer, vol. 42(1), pages 55-96, January.
  18. Huixin Bi & Nora Traum, 2012. "Estimating Sovereign Default Risk," American Economic Review, American Economic Association, vol. 102(3), pages 161-66, May.
  19. Roger E.A. Farmer & Daniel F. Waggoner & Tao Zha, 2009. "Understanding Markov-switching rational expectations models," Working Paper 2009-05, Federal Reserve Bank of Atlanta.
  20. Troy Davig & Taeyoung Doh, 2008. "Monetary policy regime shifts and inflation persistence," Research Working Paper RWP 08-16, Federal Reserve Bank of Kansas City.
  21. 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.
  22. Lombardo, Giovanni, 2010. "On approximating DSGE models by series expansions," Working Paper Series 1264, European Central Bank.
  23. 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.
  24. 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.
  25. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, June.
  26. Nicholas Bloom, 2007. "The Impact of Uncertainty Shocks," NBER Working Papers 13385, National Bureau of Economic Research, Inc.
  27. Kubler, Felix & Schmedders, Karl, 2010. "Competitive equilibria in semi-algebraic economies," Journal of Economic Theory, Elsevier, vol. 145(1), pages 301-330, January.
  28. Christopher A. Sims & Tao Zha, 2006. "Were There Regime Switches in U.S. Monetary Policy?," American Economic Review, American Economic Association, vol. 96(1), pages 54-81, March.
  29. Leeper, Eric M. & Zha, Tao, 2003. "Modest policy interventions," Journal of Monetary Economics, Elsevier, vol. 50(8), pages 1673-1700, November.
  30. Troy Davig & Eric M. Leeper & Todd B. Walker, 2010. ""Unfunded liabilities" and uncertain fiscal financing," Research Working Paper RWP 10-09, Federal Reserve Bank of Kansas City.
  31. Troy Davig & Eric M. Leeper, 2005. "Generalizing the Taylor Principle," NBER Working Papers 11874, National Bureau of Economic Research, Inc.
  32. 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.
  33. Tauchen, George, 1986. "Finite state markov-chain approximations to univariate and vector autoregressions," Economics Letters, Elsevier, vol. 20(2), pages 177-181.
  34. Frank Schorfheide, 2003. "Learning and monetary policy shifts," Working Paper 2003-23, Federal Reserve Bank of Atlanta.
  35. Todd Walker & Eric Leeper & Troy Davig, 2010. "Inflation and the Fiscal Limit," 2010 Meeting Papers 837, Society for Economic Dynamics.
  36. Amisano, Gianni & Tristani, Oreste, 2011. "Exact likelihood computation for nonlinear DSGE models with heteroskedastic innovations," Working Paper Series 1341, European Central Bank.
  37. 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.
  38. Manuel S. Santos & Adrian Peralta-Alva, 2005. "Accuracy of Simulations for Stochastic Dynamic Models," Econometrica, Econometric Society, vol. 73(6), pages 1939-1976, November.
  39. 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.
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