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Solving endogenous regime switching models

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  • Barthélemy, Jean
  • Marx, Magali

Abstract

This paper solves rational expectations models in which structural parameters switch across multiple regimes according to state-dependent (endogenous) transition probabilities. Assuming small shocks and smooth transition probabilities, we apply a perturbation approach. We first provide for conditions under which a unique bounded equilibrium exists. We then compute first- and second-order approximations. In a new-Keynesian model with monetary policy switching, we document new effects of monetary policy switching when transition probabilities depend on inflation.

Suggested Citation

  • Barthélemy, Jean & Marx, Magali, 2017. "Solving endogenous regime switching models," Journal of Economic Dynamics and Control, Elsevier, vol. 77(C), pages 1-25.
  • Handle: RePEc:eee:dyncon:v:77:y:2017:i:c:p:1-25
    DOI: 10.1016/j.jedc.2017.01.011
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    1. Leeper, Eric M. & Zha, Tao, 2003. "Modest policy interventions," Journal of Monetary Economics, Elsevier, vol. 50(8), pages 1673-1700, November.
    2. 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.
    3. Coe, Patrick J, 2002. "Financial Crisis and the Great Depression: A Regime Switching Approach," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 34(1), pages 76-93, February.
    4. 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.
    5. Nicolas Coeurdacier & Helene Rey & Pablo Winant, 2011. "The Risky Steady State," American Economic Review, American Economic Association, vol. 101(3), pages 398-401, May.
    6. Alejandro Justiniano & Giorgio E. Primiceri, 2008. "The Time-Varying Volatility of Macroeconomic Fluctuations," American Economic Review, American Economic Association, vol. 98(3), pages 604-641, June.
    7. John H. Cochrane, 2011. "Determinacy and Identification with Taylor Rules," Journal of Political Economy, University of Chicago Press, vol. 119(3), pages 565-615.
    8. Lars E.O. Svensson & Noah Williams, 2009. "Optimal Monetary Policy under Uncertainty in DSGE Models: A Markov Jump-Linear-Quadratic Approach," Central Banking, Analysis, and Economic Policies Book Series, in: Klaus Schmidt-Hebbel & Carl E. Walsh & Norman Loayza (Series Editor) & Klaus Schmidt-Hebbel (Series (ed.),Monetary Policy under Uncertainty and Learning, edition 1, volume 13, chapter 3, pages 077-114, Central Bank of Chile.
    9. Junior Maih, 2014. "Efficient Perturbation Methods for Solving Regime-Switching DSGE Models," Working Papers No 10/2014, Centre for Applied Macro- and Petroleum economics (CAMP), BI Norwegian Business School.
    10. 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.
    11. Foerster, Andrew & Rubio-Ramírez, Juan Francisco & Waggoner, Daniel F & Zha, Tao, 2013. "Perturbation Methods for Markov-Switching DSGE Models," CEPR Discussion Papers 9464, C.E.P.R. Discussion Papers.
    12. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-1311, July.
    13. Enrique G. Mendoza & Vivian Z. Yue, 2012. "A General Equilibrium Model of Sovereign Default and Business Cycles," The Quarterly Journal of Economics, Oxford University Press, vol. 127(2), pages 889-946.
    14. 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.
    15. Filardo, Andrew J, 1994. "Business-Cycle Phases and Their Transitional Dynamics," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 299-308, July.
    16. Troy Davig & Eric M. Leeper, 2008. "Endogenous Monetary Policy Regime Change," NBER Chapters, in: NBER International Seminar on Macroeconomics 2006, pages 345-391, National Bureau of Economic Research, Inc.
    17. repec:hal:spmain:info:hdl:2441/3bvs8clr5k9dqqcbq7j5ul2o65 is not listed on IDEAS
    18. Jean Barthélemy & Magali Marx, 2012. "Generalizing the Taylor Principle: New Comment," Working Papers hal-03461113, HAL.
    19. Troy Davig & Eric M. Leeper, 2007. "Generalizing the Taylor Principle," American Economic Review, American Economic Association, vol. 97(3), pages 607-635, June.
    20. 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.
    21. 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.
    22. 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.
    23. 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.
    24. Filardo, Andrew J. & Gordon, Stephen F., 1998. "Business cycle durations," Journal of Econometrics, Elsevier, vol. 85(1), pages 99-123, July.
    25. Roger E. A. Farmer & Daniel F. Waggoner & Tao Zha, 2007. "Understanding the New Keynesian model when monetary policy switches regimes," FRB Atlanta Working Paper 2007-12, Federal Reserve Bank of Atlanta.
    26. Christopher A. Sims, 1982. "Policy Analysis with Econometric Models," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 13(1), pages 107-164.
    27. Friedman, Milton, 1976. "Inflation and Unemployment," Nobel Prize in Economics documents 1976-1, Nobel Prize Committee.
    28. James Tobin, 1980. "Stabilization Policy Ten Years After," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 11(1, Tenth ), pages 19-90.
    29. 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.
    30. Guillermo A. Calvo, 1998. "Capital Flows and Capital-Market Crises: The Simple Economics of Sudden Stops," Journal of Applied Economics, Universidad del CEMA, vol. 1, pages 35-54, November.
    31. Michael Woodford, 2014. "Stochastic Choice: An Optimizing Neuroeconomic Model," American Economic Review, American Economic Association, vol. 104(5), pages 495-500, May.
    32. Michael Woodford, 2012. "Inflation Targeting and Financial Stability," NBER Working Papers 17967, National Bureau of Economic Research, Inc.
    33. 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.
    34. 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.
    35. Troy Davig & Eric M Leeper, 2011. "Temporarily Unstable Government Debt and Inflation," IMF Economic Review, Palgrave Macmillan;International Monetary Fund, vol. 59(2), pages 233-270, June.
    36. Seonghoon Cho, 2016. "Sufficient Conditions for Determinacy in a Class of Markov-Switching Rational Expectations Models," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 21, pages 182-200, July.
    37. Rotemberg, Julio J, 1982. "Sticky Prices in the United States," Journal of Political Economy, University of Chicago Press, vol. 90(6), pages 1187-1211, December.
    38. Roger E. A. Farmer & Daniel F. Waggoner & Tao Zha, 2009. "Indeterminacy in a forward‐looking regime switching model," International Journal of Economic Theory, The International Society for Economic Theory, vol. 5(1), pages 69-84, March.
    39. Blake, Andrew P. & Zampolli, Fabrizio, 2011. "Optimal policy in Markov-switching rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 35(10), pages 1626-1651, October.
    40. repec:hal:wpspec:info:hdl:2441/c8dmi8nm4pdjkuc9g704ld0h3 is not listed on IDEAS
    41. Francesco Bianchi, 2012. "Evolving Monetary/Fiscal Policy Mix in the United States," American Economic Review, American Economic Association, vol. 102(3), pages 167-172, May.
    42. repec:hal:spmain:info:hdl:2441/c8dmi8nm4pdjkuc9g704ld0h3 is not listed on IDEAS
    43. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
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    2. Cho, Seonghoon, 2021. "Determinacy and classification of Markov-switching rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 127(C).
    3. Julien Albertini & Stéphane Moyen, 2020. "A General and Efficient Method for Solving Regime-Switching DSGE Models," Working Papers halshs-03067554, HAL.
    4. Chang, Yoosoon & Maih, Junior & Tan, Fei, 2021. "Origins of monetary policy shifts: A New approach to regime switching in DSGE models," Journal of Economic Dynamics and Control, Elsevier, vol. 133(C).
    5. Julien Albertini & Valentin Jouvanceau & Stéphane Moyen, 2022. "State-Contingent Forward Guidance," Working Papers 2205, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
    6. Andrei A. Sirchenko, 2017. "An endogenous regime-switching model of ordered choice with an application to federal funds rate target," 2017 Papers psi424, Job Market Papers.
    7. Christopher Otrok & Andrew Foerster & Alessandro Rebucci & Gianluca Benigno, 2017. "Estimating Macroeconomic Models of Financial Crises: An Endogenous Regime Switching Approach," 2017 Meeting Papers 572, Society for Economic Dynamics.
    8. Chang, Yoosoon & Kwak, Boreum, 2017. "U.S. monetary-fiscal regime changes in the presence of endogenous feedback in policy rules," IWH Discussion Papers 15/2017, Halle Institute for Economic Research (IWH).
    9. Tolga Özden, 2021. "Heterogeneous Expectations and the Business Cycle at the Effective Lower Bound," Working Papers 714, DNB.
    10. Yoosoon Chang & Junior Maih & Fei Tan, 2018. "State Space Models with Endogenous Regime Switching," Working Papers No 9/2018, Centre for Applied Macro- and Petroleum economics (CAMP), BI Norwegian Business School.
    11. Zakipour-Saber, Shayan, 2019. "State-dependent Monetary Policy Regimes," Research Technical Papers 4/RT/19, Central Bank of Ireland.
    12. Roberto M. Billi & Jordi Galí & Anton Nakov, 2022. "Optimal Monetary Policy with r," Working Papers 1333, Barcelona School of Economics.
    13. Holden, Thomas, 2016. "Existence and uniqueness of solutions to dynamic models with occasionally binding constraints," EconStor Preprints 130142, ZBW - Leibniz Information Centre for Economics.
    14. Binning, Andrew & Bjørnland, Hilde C. & Maih, Junior, 2019. "Is monetary policy always effective? Incomplete interest rate pass-through in a DSGE model," Working Paper 2019/22, Norges Bank.
    15. Chang, Yoosoon & Kwak, Boreum & Qiu, Shi, 2021. "U.S. monetary and fiscal policy regime changes and their interactions," IWH Discussion Papers 12/2021, Halle Institute for Economic Research (IWH).
    16. Shayan Zakipour-Saber, 2019. "Monetary policy regimes and inflation persistence in the United Kingdom," Working Papers 895, Queen Mary University of London, School of Economics and Finance.
    17. Xin Wei, 2020. "Dynamic Expectations Formation and U.S. Monetary Policy Regime Change," CAEPR Working Papers 2020-007, Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington.
    18. Le Bihan Hervé, & Marx Magali, & Matheron Julien., 2021. "Inflation tolerance ranges in the New Keynesian model," Working papers 820, Banque de France.
    19. Neusser, Klaus, 2019. "Time–varying rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 107(C), pages 1-1.
    20. Yoosoon Chang & Fei Tan & Xin Wei, 2018. "State Space Models with Endogenous Regime Switching," CAEPR Working Papers 2018-012, Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington.
    21. Ruoyun Mao & Wenyi Shen & Shu-Chun S. Yang, 2022. "Uncertain Policy Regimes and Government Spending Effects," IEAS Working Paper : academic research 22-A004, Institute of Economics, Academia Sinica, Taipei, Taiwan.
    22. Andrew Foerster & Christian Matthes, 2022. "Learning About Regime Change," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(4), pages 1829-1859, November.
    23. Eduardo C. Castro, 2020. "RegGae: a toolkit for macroprudential policy with DSGEs," Working Papers Series 526, Central Bank of Brazil, Research Department.
    24. Roulleau-Pasdeloup, Jordan, 2020. "Optimal monetary policy and determinacy under active/passive regimes," European Economic Review, Elsevier, vol. 130(C).

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    More about this item

    Keywords

    Regime switching; Rational expectations models; Indeterminacy; Perturbation methods;
    All these keywords.

    JEL classification:

    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects

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