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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. Francesco Bianchi, 2009. "Regime Switches, Agents’ Beliefs, and Post-World War II U.S. Macroeconomic Dynamics," 2009 Meeting Papers 198, Society for Economic Dynamics.
  2. 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.
  3. 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.
  4. Troy Davig & Taeyoung Doh, 2014. "Monetary Policy Regime Shifts and Inflation Persistence," The Review of Economics and Statistics, MIT Press, vol. 96(5), pages 862-875, December.
  5. 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.
  6. Frank Smets & Raf Wouters, 2007. "Shocks and Frictions in US Business Cycles : a Bayesian DSGE Approach," Working Paper Research 109, National Bank of Belgium.
  7. Ruchira Datta, 2010. "Finding all Nash equilibria of a finite game using polynomial algebra," Economic Theory, Springer, vol. 42(1), pages 55-96, January.
  8. 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.
  9. Eric M. Leeper & Tao Zha, 2003. "Modest policy interventions," Working Paper 2003-24, Federal Reserve Bank of Atlanta.
  10. Huixin Bi & Nora Traum, 2012. "Estimating Sovereign Default Risk," American Economic Review, American Economic Association, vol. 102(3), pages 161-66, May.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. 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.
  17. 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.
  18. Nicholas Bloom, 2007. "The Impact of Uncertainty Shocks," NBER Working Papers 13385, National Bureau of Economic Research, Inc.
  19. Jesus Fernandez-Villaverde & Pablo Guerron-Quintana & Juan F. Rubio-Ramírez & Martin Uribe, 2009. "Risk Matters: The Real Effects of Volatility Shocks," PIER Working Paper Archive 09-013, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  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. 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..
  22. 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.
  23. 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.
  24. Kubler, Felix & Schmedders, Karl, 2010. "Competitive equilibria in semi-algebraic economies," Journal of Economic Theory, Elsevier, vol. 145(1), pages 301-330, January.
  25. 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.
  26. Troy Davig & Eric M. Leeper, 2007. "Generalizing the Taylor Principle," American Economic Review, American Economic Association, vol. 97(3), pages 607-635, June.
  27. Amisano, Gianni & Tristani, Oreste, 2011. "Exact likelihood computation for nonlinear DSGE models with heteroskedastic innovations," Working Paper Series 1341, European Central Bank.
  28. 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.
  29. Manuel S. Santos & Adrian Peralta-Alva, 2005. "Accuracy of Simulations for Stochastic Dynamic Models," Econometrica, Econometric Society, vol. 73(6), pages 1939-1976, November.
  30. 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).
  31. 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.
  32. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, June.
  33. Troy Davig & Eric M. Leeper & Todd B. Walker, 2010. "Inflation and the Fiscal Limit," NBER Working Papers 16495, National Bureau of Economic Research, Inc.
  34. 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.
  35. Lombardo, Giovanni, 2010. "On approximating DSGE models by series expansions," Working Paper Series 1264, European Central Bank.
  36. Tauchen, George, 1986. "Finite state markov-chain approximations to univariate and vector autoregressions," Economics Letters, Elsevier, vol. 20(2), pages 177-181.
  37. 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.
  38. 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.
  39. 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.
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