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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. 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.
  2. Troy Davig & Eric M. Leeper, 2005. "Generalizing the Taylor Principle," NBER Working Papers 11874, National Bureau of Economic Research, Inc.
  3. Christopher A. Sims & Tao Zha, 2004. "Were there regime switches in U.S. monetary policy?," Working Paper 2004-14, Federal Reserve Bank of Atlanta.
  4. Taeyoung Doh & Troy Davig, 2009. "Monetary Policy Regime Shifts and Inflation Persistence," 2009 Meeting Papers 182, Society for Economic Dynamics.
  5. 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.
  6. 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.
  7. Roger E.A. Farmer & Daniel F. Waggoner & Tao Zha, 2008. "Minimal state variable solutions to Markov-switching rational expectations models," Working Paper 2008-23, Federal Reserve Bank of Atlanta.
  8. Jesus Fernandez-Villaverde & Pablo Guerron-Quintana & Juan F. Rubio-Ramirez, 2014. "Estimating Dynamic Equilibrium Models with Stochastic Volatility," Working Papers 1424, BBVA Bank, Economic Research Department.
  9. 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.
  10. Tauchen, George, 1986. "Finite state markov-chain approximations to univariate and vector autoregressions," Economics Letters, Elsevier, vol. 20(2), pages 177-181.
  11. 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.
  12. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, June.
  13. Francesco Bianchi & Leonardo Melosi, 2013. "Modeling the Evolution of Expectations and Uncertainty in General Equilibrium," Working Papers 13-14, Duke University, Department of Economics.
  14. Martin M. Andreasen & Jesús Fernández-Villaverde & Juan F. Rubio-Ramírez, 2013. "The Pruned State-Space System for Non-Linear DSGE Models: Theory and Empirical Applications," CREATES Research Papers 2013-12, School of Economics and Management, University of Aarhus.
  15. 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.
  16. 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.
  17. Eric M. Aldrich & Jesús Fernández-Villaverde & Ronald Gallant & Juan F. Rubio-Ramírez, 2010. "Tapping the Supercomputer Under Your Desk: Solving Dynamic Equilibrium Models with Graphics Processors," PIER Working Paper Archive 10-014, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  18. Leeper, Eric M. & Zha, Tao, 2003. "Modest policy interventions," Journal of Monetary Economics, Elsevier, vol. 50(8), pages 1673-1700, November.
  19. Jesus Fernandez-Villaverde & Pablo Guerron-Quintana & Juan F. Rubio-Ramirez & Martin Uribe, 2011. "Risk Matters: The Real Effects of Volatility Shocks," American Economic Review, American Economic Association, vol. 101(6), pages 2530-61, October.
  20. 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.
  21. 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.
  22. 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.
  23. 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.
  24. Manuel S. Santos & Adrian Peralta-Alva, 2003. "Accuracy Of Simulations For Stochastic Dynamic Models," Economics Working Papers we034615, Universidad Carlos III, Departamento de Economía.
  25. 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.
  26. Francesco Bianchi, 2009. "Regime Switches, Agents’ Beliefs, and Post-World War II U.S. Macroeconomic Dynamics," 2009 Meeting Papers 198, Society for Economic Dynamics.
  27. 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.
  28. Zheng Liu & Daniel F. Waggoner & Tao Zha, 2010. "Sources of Macroeconomic Fluctuations: A Regime-switching DSGE Approach," Emory Economics 1002, Department of Economics, Emory University (Atlanta).
  29. Felix Kuber & Karl Schmedders, 2007. "Competitive Equilibria in Semi-Algebraic Economies," PIER Working Paper Archive 07-013, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  30. Amisano, Gianni & Tristani, Oreste, 2011. "Exact likelihood computation for nonlinear DSGE models with heteroskedastic innovations," Working Paper Series 1341, European Central Bank.
  31. 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.
  32. 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.
  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. Huixin Bi & Nora Traum, 2012. "Estimating Sovereign Default Risk," American Economic Review, American Economic Association, vol. 102(3), pages 161-66, May.
  35. Nicholas Bloom, 2009. "The Impact of Uncertainty Shocks," Econometrica, Econometric Society, vol. 77(3), pages 623-685, 05.
  36. Ruchira Datta, 2010. "Finding all Nash equilibria of a finite game using polynomial algebra," Economic Theory, Springer, vol. 42(1), pages 55-96, January.
  37. 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.
  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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