IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v79y2015icp83-95.html
   My bibliography  Save this article

Coexistence of equilibria in a New Keynesian model with heterogeneous beliefs

Author

Listed:
  • Agliari, Anna
  • Pecora, Nicolò
  • Spelta, Alessandro

Abstract

The recent macroeconomic literature has been stressing the importance of considering heterogeneous expectations while addressing monetary policy. In this paper we consider a standard New Keynesian model, described by a two-dimensional nonlinear map, to analyze the bifurcation structure when agents have heterogeneous expectations and update their beliefs based on past performance. Depending on the degree of reactivity of the monetary policy to inflation and output deviations from the target equilibrium, different kind of dynamics may occur. We find that multiple equilibria and complicated dynamics, associated to codimension-2 bifurcations, may arise even if the monetary policy is set to respond more than point for point to inflation, as the Taylor principle prescribes. We show that if the monetary policy accommodates for a sufficient degree of output stabilization, complicated dynamics can be avoided and the number of coexisting equilibria reduces.

Suggested Citation

  • Agliari, Anna & Pecora, Nicolò & Spelta, Alessandro, 2015. "Coexistence of equilibria in a New Keynesian model with heterogeneous beliefs," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 83-95.
    • Handle: RePEc:eee:chsofr:v:79:y:2015:i:c:p:83-95
    DOI: 10.1016/j.chaos.2015.05.016
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077915001526
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2015.05.016?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Pierpaolo Benigno & Michael Woodford, 2005. "Inflation Stabilization And Welfare: The Case Of A Distorted Steady State," Journal of the European Economic Association, MIT Press, vol. 3(6), pages 1185-1236, December.
    2. George W. Evans & Seppo Honkapohja, 2003. "Adaptive learning and monetary policy design," Proceedings, Federal Reserve Bank of Cleveland, pages 1045-1084.
    3. N. Gregory Mankiw & Ricardo Reis & Justin Wolfers, 2004. "Disagreement about Inflation Expectations," NBER Chapters, in: NBER Macroeconomics Annual 2003, Volume 18, pages 209-270, National Bureau of Economic Research, Inc.
    4. Mordecai Kurz & Maurizio Motolese, 2011. "Diverse beliefs and time variability of risk premia," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 47(2), pages 293-335, June.
    5. 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.
    6. George W. Evans & Seppo Honkapohja, 2003. "Expectations and the Stability Problem for Optimal Monetary Policies," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(4), pages 807-824.
    7. William A. Brock & Cars H. Hommes, 2001. "A Rational Route to Randomness," Chapters, in: W. D. Dechert (ed.), Growth Theory, Nonlinear Dynamics and Economic Modelling, chapter 16, pages 402-438, Edward Elgar Publishing.
    8. Benhabib, Jess & Eusepi, Stefano, 2005. "The design of monetary and fiscal policy: A global perspective," Journal of Economic Theory, Elsevier, vol. 123(1), pages 40-73, July.
    9. Gaunersdorfer, Andrea & Hommes, Cars H. & Wagener, Florian O.O., 2008. "Bifurcation routes to volatility clustering under evolutionary learning," Journal of Economic Behavior & Organization, Elsevier, vol. 67(1), pages 27-47, July.
    10. Lars E. O. Svensson & Michael Woodford, 2004. "Implementing Optimal Policy through Inflation-Forecast Targeting," NBER Chapters, in: The Inflation-Targeting Debate, National Bureau of Economic Research, Inc.
    11. Bullard, James & Mitra, Kaushik, 2002. "Learning about monetary policy rules," Journal of Monetary Economics, Elsevier, vol. 49(6), pages 1105-1129, September.
    12. Paul De Grauwe & Marianna Grimaldi, 2014. "Exchange Rate Puzzles: A Tale of Switching Attractors," World Scientific Book Chapters, in: Exchange Rates and Global Financial Policies, chapter 3, pages 71-117, World Scientific Publishing Co. Pte. Ltd..
    13. Thomas Lux & Michele Marchesi, 2000. "Volatility Clustering In Financial Markets: A Microsimulation Of Interacting Agents," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(04), pages 675-702.
    14. Branch, William A. & McGough, Bruce, 2010. "Dynamic predictor selection in a new Keynesian model with heterogeneous expectations," Journal of Economic Dynamics and Control, Elsevier, vol. 34(8), pages 1492-1508, August.
    15. Charles T. Carlstrom & Timothy Fuerst, 2007. "Asset Prices, Nominal Rigidities, and Monetary Policy," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 10(2), pages 256-275, April.
    16. Bennett T. McCallum & Edward Nelson, 1999. "Performance of Operational Policy Rules in an Estimated Semiclassical Structural Model," NBER Chapters, in: Monetary Policy Rules, pages 15-56, National Bureau of Economic Research, Inc.
    17. Branch, William A. & Evans, George W., 2006. "Intrinsic heterogeneity in expectation formation," Journal of Economic Theory, Elsevier, vol. 127(1), pages 264-295, March.
    18. Christopher D. Carroll, 2003. "Macroeconomic Expectations of Households and Professional Forecasters," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 118(1), pages 269-298.
    19. William A. Branch, 2004. "The Theory of Rationally Heterogeneous Expectations: Evidence from Survey Data on Inflation Expectations," Economic Journal, Royal Economic Society, vol. 114(497), pages 592-621, July.
    20. Alex Brazier & Richard Harrison & Mervyn King & Tony Yates, 2008. "The Danger of Inflating Expectations of Macroeconomic Stability: Heuristic Switching in an Overlapping-Generations Monetary Model," International Journal of Central Banking, International Journal of Central Banking, vol. 4(2), pages 219-254, June.
    21. John B. Taylor, 1999. "A Historical Analysis of Monetary Policy Rules," NBER Chapters, in: Monetary Policy Rules, pages 319-348, National Bureau of Economic Research, Inc.
    22. John B. Taylor, 1999. "Monetary Policy Rules," NBER Books, National Bureau of Economic Research, Inc, number tayl99-1.
    23. Bernanke, Ben S & Woodford, Michael, 1997. "Inflation Forecasts and Monetary Policy," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 29(4), pages 653-684, November.
    24. Preston, Bruce, 2006. "Adaptive learning, forecast-based instrument rules and monetary policy," Journal of Monetary Economics, Elsevier, vol. 53(3), pages 507-535, April.
    25. Branch, William A. & McGough, Bruce, 2009. "A New Keynesian model with heterogeneous expectations," Journal of Economic Dynamics and Control, Elsevier, vol. 33(5), pages 1036-1051, May.
    26. Paul Grauwe, 2011. "Animal spirits and monetary policy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 47(2), pages 423-457, June.
    27. Lines, Marji & Westerhoff, Frank, 2010. "Inflation expectations and macroeconomic dynamics: The case of rational versus extrapolative expectations," Journal of Economic Dynamics and Control, Elsevier, vol. 34(2), pages 246-257, February.
    28. LeBaron, Blake, 2006. "Agent-based Computational Finance," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 24, pages 1187-1233, Elsevier.
    29. Stephanie Schmitt-Grohé & Martín Uribe, 2006. "Optimal Fiscal and Monetary Policy in a Medium-Scale Macroeconomic Model," NBER Chapters, in: NBER Macroeconomics Annual 2005, Volume 20, pages 383-462, National Bureau of Economic Research, Inc.
    30. Kurz, Mordecai & Piccillo, Giulia & Wu, Howei, 2013. "Modeling diverse expectations in an aggregated New Keynesian Model," Journal of Economic Dynamics and Control, Elsevier, vol. 37(8), pages 1403-1433.
    31. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
    32. Agliari, Anna, 2006. "Homoclinic connections and subcritical Neimark bifurcation in a duopoly model with adaptively adjusted productions," Chaos, Solitons & Fractals, Elsevier, vol. 29(3), pages 739-755.
    33. Anna Agliari & Gian-Italo Bischi & Laura Gardini, 2006. "Some Methods for the Global Analysis of Closed Invariant Curves in Two-Dimensional Maps," Springer Books, in: Tönu Puu & Iryna Sushko (ed.), Business Cycle Dynamics, chapter 1, pages 7-47, Springer.
    34. Anufriev, Mikhail & Assenza, Tiziana & Hommes, Cars & Massaro, Domenico, 2013. "Interest Rate Rules And Macroeconomic Stability Under Heterogeneous Expectations," Macroeconomic Dynamics, Cambridge University Press, vol. 17(8), pages 1574-1604, December.
    35. Agliari, Anna & Gardini, Laura & Puu, Tönu, 2005. "Some global bifurcations related to the appearance of closed invariant curves," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 68(3), pages 201-219.
    36. Hommes, Cars H., 2006. "Heterogeneous Agent Models in Economics and Finance," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 23, pages 1109-1186, Elsevier.
    37. Calvo, Guillermo A., 1983. "Staggered prices in a utility-maximizing framework," Journal of Monetary Economics, Elsevier, vol. 12(3), pages 383-398, September.
    38. Branch, William A., 2007. "Sticky information and model uncertainty in survey data on inflation expectations," Journal of Economic Dynamics and Control, Elsevier, vol. 31(1), pages 245-276, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Hommes, Cars & Lustenhouwer, Joep, 2019. "Inflation targeting and liquidity traps under endogenous credibility," Journal of Monetary Economics, Elsevier, vol. 107(C), pages 48-62.
    2. Pecora, Nicolò & Spelta, Alessandro, 2017. "Managing monetary policy in a New Keynesian model with many beliefs types," Economics Letters, Elsevier, vol. 150(C), pages 53-58.
    3. Anna Agliari & Domenico Massaro & Nicolò Pecora & Alessandro Spelta, 2017. "Inflation Targeting, Recursive Inattentiveness, and Heterogeneous Beliefs," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 49(7), pages 1587-1619, October.
    4. Argentiero, Amedeo & Bovi, Maurizio & Cerqueti, Roy, 2016. "Bayesian estimation and entropy for economic dynamic stochastic models: An exploration of overconsumption," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 143-157.
    5. Hommes, Cars & Lustenhouwer, Joep, 2019. "Managing unanchored, heterogeneous expectations and liquidity traps," Journal of Economic Dynamics and Control, Elsevier, vol. 101(C), pages 1-16.
    6. Pecora, Nicolò, 2018. "Analysis of 1:4 resonance in a monopoly model with memory," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 95-104.

    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. Branch, William A. & McGough, Bruce, 2010. "Dynamic predictor selection in a new Keynesian model with heterogeneous expectations," Journal of Economic Dynamics and Control, Elsevier, vol. 34(8), pages 1492-1508, August.
    2. Hommes, Cars & Lustenhouwer, Joep, 2019. "Inflation targeting and liquidity traps under endogenous credibility," Journal of Monetary Economics, Elsevier, vol. 107(C), pages 48-62.
    3. Annicchiarico, Barbara & Surricchio, Silvia & Waldmann, Robert J., 2019. "A behavioral model of the credit cycle," Journal of Economic Behavior & Organization, Elsevier, vol. 166(C), pages 53-83.
    4. George W. Evans & Seppo Honkapohja, 2009. "Expectations, Learning and Monetary Policy: An Overview of Recent Research," 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 2, pages 027-076, Central Bank of Chile.
    5. Branch, William A. & McGough, Bruce, 2009. "A New Keynesian model with heterogeneous expectations," Journal of Economic Dynamics and Control, Elsevier, vol. 33(5), pages 1036-1051, May.
    6. Gasteiger, Emanuel, 2018. "Do Heterogeneous Expectations Constitute A Challenge For Policy Interaction?," Macroeconomic Dynamics, Cambridge University Press, vol. 22(8), pages 2107-2140, December.
    7. George W. Evans & Seppo Honkapohja, 2009. "Expectations, Learning and Monetary Policy: An Overview of Recent Research," 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 2, pages 027-076, Central Bank of Chile.
    8. Anna Agliari & Domenico Massaro & Nicolò Pecora & Alessandro Spelta, 2017. "Inflation Targeting, Recursive Inattentiveness, and Heterogeneous Beliefs," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 49(7), pages 1587-1619, October.
    9. Hagenhoff, Tim, 2018. "An aggregate welfare optimizing interest rate rule under heterogeneous expectations," BERG Working Paper Series 139, Bamberg University, Bamberg Economic Research Group.
    10. repec:zbw:bofrdp:2007_032 is not listed on IDEAS
    11. Jump, Robert Calvert & Levine, Paul, 2019. "Behavioural New Keynesian models," Journal of Macroeconomics, Elsevier, vol. 59(C), pages 59-77.
    12. Tiziana Assenza & William A. Brock & Cars H. Hommes, 2017. "Animal Spirits, Heterogeneous Expectations, And The Amplification And Duration Of Crises," Economic Inquiry, Western Economic Association International, vol. 55(1), pages 542-564, January.
    13. Hommes, Cars & Massaro, Domenico & Weber, Matthias, 2019. "Monetary policy under behavioral expectations: Theory and experiment," European Economic Review, Elsevier, vol. 118(C), pages 193-212.
    14. Anufriev, Mikhail & Assenza, Tiziana & Hommes, Cars & Massaro, Domenico, 2013. "Interest Rate Rules And Macroeconomic Stability Under Heterogeneous Expectations," Macroeconomic Dynamics, Cambridge University Press, vol. 17(8), pages 1574-1604, December.
    15. Hommes, Cars, 2018. "Behavioral & experimental macroeconomics and policy analysis: a complex systems approach," Working Paper Series 2201, European Central Bank.
    16. Bofinger, Peter & Debes, Sebastian & Gareis, Johannes & Mayer, Eric, 2013. "Monetary policy transmission in a model with animal spirits and house price booms and busts," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2862-2881.
    17. Hommes, Cars & Lustenhouwer, Joep, 2019. "Managing unanchored, heterogeneous expectations and liquidity traps," Journal of Economic Dynamics and Control, Elsevier, vol. 101(C), pages 1-16.
    18. Adriana Cornea-Madeira & Cars Hommes & Domenico Massaro, 2019. "Behavioral Heterogeneity in U.S. Inflation Dynamics," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(2), pages 288-300, April.
    19. Lines Marji & Westerhoff Frank, 2012. "Effects of Inflation Expectations on Macroeconomic Dynamics: Extrapolative Versus Regressive Expectations," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 16(4), pages 1-30, October.
    20. William Branch & George Evans, 2011. "Monetary policy and heterogeneous expectations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 47(2), pages 365-393, June.
    21. Goy, Gavin & Hommes, Cars & Mavromatis, Kostas, 2022. "Forward guidance and the role of central bank credibility under heterogeneous beliefs," Journal of Economic Behavior & Organization, Elsevier, vol. 200(C), pages 1240-1274.

    More about this item

    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:chsofr:v:79:y:2015:i:c:p:83-95. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.