IDEAS home Printed from https://ideas.repec.org/a/eee/dyncon/v77y2017icp1-25.html
   My bibliography  Save this article

Solving endogenous regime switching models

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165188917300192
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jedc.2017.01.011?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    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, President and Fellows of Harvard College, 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. repec:spo:wpmain:info:hdl:2441/c8dmi8nm4pdjkuc9g704ld0h3 is not listed on IDEAS
    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. Nicolas Coeurdacier & Helene Rey & Pablo Winant, 2011. "The Risky Steady State," American Economic Review, American Economic Association, vol. 101(3), pages 398-401, May.
    9. 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.
    10. 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.
    11. Francesco Bianchi, 2013. "Regime Switches, Agents' Beliefs, and Post-World War II U.S. Macroeconomic Dynamics," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 80(2), pages 463-490.
    12. Zha, Tao & Rubio-Ramírez, Juan Francisco & , & Foerster, Andrew, 2013. "Perturbation Methods for Markov-Switching DSGE Models," CEPR Discussion Papers 9464, C.E.P.R. Discussion Papers.
    13. 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.
    14. repec:spo:wpecon:info:hdl:2441/c8dmi8nm4pdjkuc9g704ld0h3 is not listed on IDEAS
    15. Enrique G. Mendoza & Vivian Z. Yue, 2012. "A General Equilibrium Model of Sovereign Default and Business Cycles," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 127(2), pages 889-946.
    16. 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.
    17. 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.
    18. 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.
    19. repec:hal:spmain:info:hdl:2441/3bvs8clr5k9dqqcbq7j5ul2o65 is not listed on IDEAS
    20. repec:spo:wpmain:info:hdl:2441/3bvs8clr5k9dqqcbq7j5ul2o65 is not listed on IDEAS
    21. Troy Davig & Eric M. Leeper, 2007. "Generalizing the Taylor Principle," American Economic Review, American Economic Association, vol. 97(3), pages 607-635, June.
    22. 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.
    23. 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.
    24. Jean Barthélemy & Magali Marx, 2012. "Generalizing the Taylor Principle: New Comment," SciencePo Working papers Main hal-03461113, HAL.
    25. 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.
    26. 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.
    27. Filardo, Andrew J. & Gordon, Stephen F., 1998. "Business cycle durations," Journal of Econometrics, Elsevier, vol. 85(1), pages 99-123, July.
    28. 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.
    29. 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.
    30. Friedman, Milton, 1976. "Inflation and Unemployment," Nobel Prize in Economics documents 1976-1, Nobel Prize Committee.
    31. 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.
    32. 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.
    33. 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.
    34. Michael Woodford, 2014. "Stochastic Choice: An Optimizing Neuroeconomic Model," American Economic Review, American Economic Association, vol. 104(5), pages 495-500, May.
    35. Michael Woodford, 2012. "Inflation Targeting and Financial Stability," NBER Working Papers 17967, National Bureau of Economic Research, Inc.
    36. 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.
    37. 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.
    38. 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.
    39. 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.
    40. 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.
    41. 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.
    42. 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.
    43. repec:hal:wpspec:info:hdl:2441/c8dmi8nm4pdjkuc9g704ld0h3 is not listed on IDEAS
    44. 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.
    45. repec:hal:spmain:info:hdl:2441/c8dmi8nm4pdjkuc9g704ld0h3 is not listed on IDEAS
    46. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zakipour-Saber, Shayan, 2019. "State-dependent Monetary Policy Regimes," Research Technical Papers 4/RT/19, Central Bank of Ireland.
    2. repec:hal:spmain:info:hdl:2441/644vfdaim38frrvbit4u0bh0ha is not listed on IDEAS
    3. repec:spo:wpmain:info:hdl:2441/644vfdaim38frrvbit4u0bh0ha is not listed on IDEAS
    4. 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.
    5. Jean Barthélemy & Magali Marx, 2011. "State-Dependent Probability Distributions in Non Linear Rational Expectations Models," Working Papers hal-03461407, HAL.
    6. Jean Barthélemy & Magali Marx, 2016. "Solving Endogenous Regime Switching Models," SciencePo Working papers hal-03393181, HAL.
    7. repec:hal:spmain:info:hdl:2441/7l23tbn4rd9539sljmp8of2hcb is not listed on IDEAS
    8. repec:spo:wpmain:info:hdl:2441/7l23tbn4rd9539sljmp8of2hcb is not listed on IDEAS
    9. Cho, Seonghoon, 2021. "Determinacy and classification of Markov-switching rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 127(C).
    10. 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.
    11. 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.
    12. Andrew T. Foerster, 2016. "Monetary Policy Regime Switches And Macroeconomic Dynamics," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 57(1), pages 211-230, February.
    13. Francesco Bianchi & Cosmin Ilut, 2017. "Monetary/Fiscal Policy Mix and Agent's Beliefs," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 26, pages 113-139, October.
    14. 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).
    15. Jean Barthelemy & Seonghoon Cho & Magali Marx, 2024. "A Unified Approach to Determinacy Conditions with Regime Switching," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 54, October.
    16. Francesco Bianchi & Leonardo Melosi, 2018. "Constrained Discretion and Central Bank Transparency," The Review of Economics and Statistics, MIT Press, vol. 100(1), pages 187-202, March.
    17. McClung, Nigel, 2020. "E-stability vis-à-vis determinacy in regime-switching models," Journal of Economic Dynamics and Control, Elsevier, vol. 121(C).
    18. 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.
    19. Bianchi, Francesco, 2016. "Methods for measuring expectations and uncertainty in Markov-switching models," Journal of Econometrics, Elsevier, vol. 190(1), pages 79-99.
    20. Guido Ascari & Anna Florio & Alessandro Gobbi, 2020. "Controlling Inflation With Timid Monetary–Fiscal Regime Changes," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 61(2), pages 1001-1024, May.
    21. 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.
    22. Francesco Bianchi & Leonardo Melosi, 2014. "Dormant Shocks and Fiscal Virtue," NBER Macroeconomics Annual, University of Chicago Press, vol. 28(1), pages 1-46.
    23. Francesco Bianchi & Cosmin L. Ilut & Martin Schneider, 2018. "Uncertainty Shocks, Asset Supply and Pricing over the Business Cycle," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(2), pages 810-854.
    24. Mehmet Balcilar & Rangan Gupta & Kevin Kotzé, 2017. "Forecasting South African macroeconomic variables with a Markov-switching small open-economy dynamic stochastic general equilibrium model," Empirical Economics, Springer, vol. 53(1), pages 117-135, August.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:dyncon:v:77:y:2017:i:c:p:1-25. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jedc .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.