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Perturbation methods for Markov‐switching dynamic stochastic general equilibrium models

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  • Andrew Foerster
  • Juan F. Rubio‐Ramírez
  • Daniel F. Waggoner
  • Tao Zha

Abstract

Markov‐switching dynamic stochastic general equilibrium (MSDSGE) modeling has become a growing body of literature on economic and policy issues related to structural shifts. This paper develops a general perturbation methodology for constructing high‐order approximations to the solutions of MSDSGE models. Our new method—“the partition perturbation method”—partitions the Markov‐switching parameter space to keep a maximum number of time‐varying parameters from perturbation. For this method to work in practice, we show how to reduce the potentially intractable problem of solving MSDSGE models to the manageable problem of solving a system of quadratic polynomial equations. This approach allows us to first obtain all the solutions and then determine how many of them are stable. We illustrate the tractability of our methodology through two revealing examples.

Suggested Citation

  • Andrew Foerster & Juan F. Rubio‐Ramírez & Daniel F. Waggoner & Tao Zha, 2016. "Perturbation methods for Markov‐switching dynamic stochastic general equilibrium models," Quantitative Economics, Econometric Society, vol. 7(2), pages 637-669, July.
  • Handle: RePEc:wly:quante:v:7:y:2016:i:2:p:637-669
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    1. Jesús Fernández-Villaverde & Juan F. Rubio-Ramírez, 2007. "Estimating Macroeconomic Models: A Likelihood Approach," Review of Economic Studies, Oxford University Press, vol. 74(4), pages 1059-1087.
    2. Leeper, Eric M. & Zha, Tao, 2003. "Modest policy interventions," Journal of Monetary Economics, Elsevier, vol. 50(8), pages 1673-1700, November.
    3. Richard Clarida & Jordi Galí & Mark Gertler, 2000. "Monetary Policy Rules and Macroeconomic Stability: Evidence and Some Theory," The Quarterly Journal of Economics, Oxford University Press, vol. 115(1), pages 147-180.
    4. Francesco Bianchi & Leonardo Melosi, 2016. "Modeling The Evolution Of Expectations And Uncertainty In General Equilibrium," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 57(2), pages 717-756, May.
    5. Huixin Bi & Nora Traum, 2012. "Estimating Sovereign Default Risk," American Economic Review, American Economic Association, vol. 102(3), pages 161-166, May.
    6. Fernández-Villaverde, Jesús & Guerrón-Quintana, Pablo & Rubio-Ramírez, Juan F., 2015. "Estimating dynamic equilibrium models with stochastic volatility," Journal of Econometrics, Elsevier, vol. 185(1), pages 216-229.
    7. Noah Williams & Lars E.O. Svensson, 2005. "Monetary Policy with Model Uncertainty: Distribution Forecast Targeting," Computing in Economics and Finance 2005 108, Society for Computational Economics.
    8. 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 2530-2561, October.
    9. 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.
    10. Martin M Andreasen & Jesús Fernández-Villaverde & Juan F Rubio-Ramírez, 2018. "The Pruned State-Space System for Non-Linear DSGE Models: Theory and Empirical Applications," Review of Economic Studies, Oxford University Press, vol. 85(1), pages 1-49.
    11. Kubler, Felix & Schmedders, Karl, 2010. "Competitive equilibria in semi-algebraic economies," Journal of Economic Theory, Elsevier, vol. 145(1), pages 301-330, January.
    12. Tauchen, George, 1986. "Finite state markov-chain approximations to univariate and vector autoregressions," Economics Letters, Elsevier, vol. 20(2), pages 177-181.
    13. 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.
    14. 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.
    15. Davig, Troy & Leeper, Eric M. & Walker, Todd B., 2010. ""Unfunded liabilities" and uncertain fiscal financing," Journal of Monetary Economics, Elsevier, vol. 57(5), pages 600-619, July.
    16. 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.
    17. Francesco Bianchi, 2013. "Regime Switches, Agents' Beliefs, and Post-World War II U.S. Macroeconomic Dynamics," Review of Economic Studies, Oxford University Press, vol. 80(2), pages 463-490.
    18. 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.
    19. Lawrence J. Christiano & Martin Eichenbaum & Charles L. Evans, 2005. "Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy," Journal of Political Economy, University of Chicago Press, vol. 113(1), pages 1-45, February.
    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 111-126, October.
    21. 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 357-384, March.
    22. Manuel S. Santos & Adrian Peralta-Alva, 2005. "Accuracy of Simulations for Stochastic Dynamic Models," Econometrica, Econometric Society, vol. 73(6), pages 1939-1976, November.
    23. 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.
    24. 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.
    25. Troy Davig & Eric M. Leeper, 2007. "Generalizing the Taylor Principle," American Economic Review, American Economic Association, vol. 97(3), pages 607-635, June.
    26. 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.
    27. 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.
    28. 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.
    29. 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.
    30. Ruchira Datta, 2010. "Finding all Nash equilibria of a finite game using polynomial algebra," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 55-96, January.
    31. 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.
    32. 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.
    33. Marimon, Ramon & Scott, Andrew (ed.), 1999. "Computational Methods for the Study of Dynamic Economies," OUP Catalogue, Oxford University Press, number 9780198294979.
    34. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711.
    35. 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.
    36. 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.
    37. Lombardo, Giovanni, 2010. "On approximating DSGE models by series expansions," Working Paper Series 1264, European Central Bank.
    38. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    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.
    40. Jesús Fernández-Villaverde & Pablo Guerrón-Quintana & Juan F. Rubio-Ramirez, 2010. "Fortune or virtue: time-variant volatilities versus parameter drifting," Working Papers 10-14, Federal Reserve Bank of Philadelphia.
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    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • E3 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles
    • G1 - Financial Economics - - General Financial Markets

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