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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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Paper provided by FEDEA in its series Working Papers with number 2013-22.

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Date of creation: Dec 2013
Date of revision:
Handle: RePEc:fda:fdaddt:2013-22
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  1. Jesús Fernández-Villaverde & Pablo Guerrón-Quintana & Juan F. Rubio-Ramírez, 2013. "Estimating dynamic equilibrium models with stochastic volatility," Working Papers 13-19, Federal Reserve Bank of Philadelphia.
  2. Bianchi, Francesco & Melosi, Leonardo, 2013. "Modeling the Evolution of Expectations and Uncertainty in General Equilibrium," Working Paper Series WP-2013-12, Federal Reserve Bank of Chicago.
  3. 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.
  4. Roger E.A. Farmer & Tao Zha & Daniel F. Waggoner, 2009. "Understanding Markov-Switching Rational Expectations Models," NBER Working Papers 14710, National Bureau of Economic Research, Inc.
  5. 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.
  6. 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.
  7. 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.
  8. Lombardo, Giovanni, 2010. "On approximating DSGE models by series expansions," Working Paper Series 1264, European Central Bank.
  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. S. Boragan Aruoba & Jesus Fernandez-Villaverde & Juan F. Rubio-Ramirez, 2003. "Comparing Solution Methods for Dynamic Equilibrium Economies," PIER Working Paper Archive 04-003, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  11. Amisano, Gianni & Tristani, Oreste, 2011. "Exact likelihood computation for nonlinear DSGE models with heteroskedastic innovations," Working Paper Series 1341, European Central Bank.
  12. Eric M. Leeper & Tao Zha, 2002. "Modest Policy Interventions," NBER Working Papers 9192, National Bureau of Economic Research, Inc.
  13. 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.
  14. 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.
  15. 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.
  16. Eric M. Aldrich & Jesús Fernández-Villaverde & A. Ronald Gallant & Juan F. Rubio-Ramírez, 2010. "Tapping the Supercomputer Under Your Desk: Solving Dynamic Equilibrium Models with Graphics Processors," NBER Working Papers 15909, National Bureau of Economic Research, Inc.
  17. repec:tpr:qjecon:v:115:y:2000:i:1:p:147-180 is not listed on IDEAS
  18. Lars Svensson & Noah Williams, 2005. "Monetary Policy with Model Uncertainty: Distribution Forecast Targeting," NBER Working Papers 11733, National Bureau of Economic Research, Inc.
  19. 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.
  20. Manuel S. Santos & Adrian Peralta-Alva, 2003. "Accuracy of Simulations for Stochastic Dynamic Models," Levine's Bibliography 666156000000000264, UCLA Department of Economics.
  21. Smets, Frank & Wouters, Rafael, 2007. "Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach," CEPR Discussion Papers 6112, C.E.P.R. Discussion Papers.
  22. 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.
  23. 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.
  24. Troy Davig & Eric M. Leeper & Todd B. Walker, 2010. "Inflation and the Fiscal Limit," NBER Working Papers 16495, National Bureau of Economic Research, Inc.
  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. 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.
  27. Troy A. 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.
  28. Tauchen, George, 1986. "Finite state markov-chain approximations to univariate and vector autoregressions," Economics Letters, Elsevier, vol. 20(2), pages 177-181.
  29. 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.
  30. 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.
  31. 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.
  32. Troy A. Davig & Eric M. Leeper, 2005. "Generalizing the Taylor principle," Research Working Paper RWP 05-13, Federal Reserve Bank of Kansas City.
  33. Ruchira Datta, 2010. "Finding all Nash equilibria of a finite game using polynomial algebra," Economic Theory, Springer, vol. 42(1), pages 55-96, January.
  34. Nicholas Bloom, 2007. "The Impact of Uncertainty Shocks," NBER Working Papers 13385, National Bureau of Economic Research, Inc.
  35. Kubler, Felix & Schmedders, Karl, 2010. "Competitive equilibria in semi-algebraic economies," Journal of Economic Theory, Elsevier, vol. 145(1), pages 301-330, January.
  36. 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.
  37. 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.
  38. Frank Schorfheide, 2003. "Learning and monetary policy shifts," FRB Atlanta Working Paper 2003-23, Federal Reserve Bank of Atlanta.
  39. Huixin Bi & Nora Traum, 2012. "Estimating Sovereign Default Risk," American Economic Review, American Economic Association, vol. 102(3), pages 161-66, May.
  40. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, June.
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