IDEAS home Printed from https://ideas.repec.org/a/now/fnteco/0800000026.html
   My bibliography  Save this article

Bifurcation of Macroeconometric Models and Robustness of Dynamical Inferences

Author

Listed:
  • Barnett, William A.
  • Chen, Guo

Abstract

In systems theory, it is well known that the parameter spaces of dynamical systems are stratified into bifurcation regions, with each supporting a different dynamical solution regime. Some can be stable, with different characteristics, such as monotonic stability, periodic damped stability, or multiperiodic damped stability, and some can be unstable, with different characteristics, such as periodic, multiperiodic, or chaotic unstable dynamics. But in general the existence of bifurcation boundaries is normal and should be expected from most dynamical systems, whether linear or nonlinear. Bifurcation boundaries in parameter space are not evidence of model defect. While existence of such bifurcation boundaries is well known in economic theory, econometricians using macroeconometric models rarely take bifurcation into consideration, when producing policy simulations from macroeconometrics models. Such models are routinely simulated only at the point estimates of the models' parameters.

Suggested Citation

  • Barnett, William A. & Chen, Guo, 2015. "Bifurcation of Macroeconometric Models and Robustness of Dynamical Inferences," Foundations and Trends(R) in Econometrics, now publishers, vol. 8(1-2), pages 1-144, September.
  • Handle: RePEc:now:fnteco:0800000026
    DOI: 10.1561/0800000026
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1561/0800000026
    Download Restriction: no

    File URL: https://libkey.io/10.1561/0800000026?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
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Campbell Leith & Ioana Moldovan & Raffaele Rossi, 2012. "Optimal Monetary Policy in a New Keynesian Model with Habits in Consumption," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 15(3), pages 416-435, July.
    2. Benhabib Jess & Perli Roberto, 1994. "Uniqueness and Indeterminacy: On the Dynamics of Endogenous Growth," Journal of Economic Theory, Elsevier, vol. 63(1), pages 113-142, June.
    3. 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.
    4. John B. Taylor, 1999. "Introduction to "Monetary Policy Rules"," NBER Chapters, in: Monetary Policy Rules, pages 1-14, National Bureau of Economic Research, Inc.
    5. Bullard, James & Mitra, Kaushik, 2002. "Learning about monetary policy rules," Journal of Monetary Economics, Elsevier, vol. 49(6), pages 1105-1129, September.
    6. Kim, Jinill, 2000. "Constructing and estimating a realistic optimizing model of monetary policy," Journal of Monetary Economics, Elsevier, vol. 45(2), pages 329-359, April.
    7. Barnett, William A. & Eryilmaz, Unal, 2013. "Hopf bifurcation in the Clarida, Gali, and Gertler model," Economic Modelling, Elsevier, vol. 31(C), pages 401-404.
    8. Mark Gertler & Jordi Gali & Richard Clarida, 1999. "The Science of Monetary Policy: A New Keynesian Perspective," Journal of Economic Literature, American Economic Association, vol. 37(4), pages 1661-1707, December.
    9. Carl E. Walsh, 2003. "Monetary Theory and Policy, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232316, April.
    10. Clarida, Richard & Gali, Jordi & Gertler, Mark, 2002. "A simple framework for international monetary policy analysis," Journal of Monetary Economics, Elsevier, vol. 49(5), pages 879-904, July.
    11. Mondal, Debasis, 2008. "Stability analysis of the Grossman-Helpman model of endogenous product cycles," Journal of Macroeconomics, Elsevier, vol. 30(3), pages 1302-1322, September.
    12. Barnett, William A. & Ghosh, Taniya, 2013. "Bifurcation analysis of an endogenous growth model," The Journal of Economic Asymmetries, Elsevier, vol. 10(1), pages 53-64.
    13. Brunner, Karl & Meltzer, Allan H., 1976. "The Phillips curve," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 1(1), pages 1-18, January.
    14. 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.
    15. 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.
    16. Jean-Michel Grandmont, 1998. "Expectations Formation and Stability of Large Socioeconomic Systems," Econometrica, Econometric Society, vol. 66(4), pages 741-782, July.
    17. Barnett, William A. & Duzhak, Evgeniya Aleksandrovna, 2008. "Non-robust dynamic inferences from macroeconometric models: Bifurcation stratification of confidence regions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3817-3825.
    18. Calvo, Guillermo A., 1983. "Staggered prices in a utility-maximizing framework," Journal of Monetary Economics, Elsevier, vol. 12(3), pages 383-398, September.
    19. Boldrin, Michele & Woodford, Michael, 1990. "Equilibrium models displaying endogenous fluctuations and chaos : A survey," Journal of Monetary Economics, Elsevier, vol. 25(2), pages 189-222, March.
    20. Medio,Alfredo & Gallo,Giampaolo, 1995. "Chaotic Dynamics," Cambridge Books, Cambridge University Press, number 9780521484619, September.
    21. Groen, Jan J J & Mumtaz, Haroon, 2008. "Investigating the structural stability of the Phillips curve relationship," Bank of England working papers 350, Bank of England.
    22. Mark Gertler & Jordi Gali & Richard Clarida, 1999. "The Science of Monetary Policy: A New Keynesian Perspective," Journal of Economic Literature, American Economic Association, vol. 37(4), pages 1661-1707, December.
    23. Jess Benhabib & Kazuo Nishimura, 2012. "The Hopf Bifurcation and Existence and Stability of Closed Orbits in Multisector Models of Optimal Economic Growth," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 51-73, Springer.
    24. Bergstrom, A. R. & Nowman, K. B. & Wymer, C. R., 1992. "Gaussian estimation of a second order continuous time macroeconometric model of the UK," Economic Modelling, Elsevier, vol. 9(4), pages 313-351, October.
    25. William A. Barnett & Taniya Ghosh, 2014. "Stability analysis of Uzawa–Lucas endogenous growth model," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(1), pages 33-44, April.
    26. Binder, Michael & Pesaran, M Hashem, 1999. "Stochastic Growth Models and Their Econometric Implications," Journal of Economic Growth, Springer, vol. 4(2), pages 139-183, June.
    27. Warne, Anders, 2000. "Causality and Regime Inference in a Markov Switching VAR," Working Paper Series 118, Sveriges Riksbank (Central Bank of Sweden).
    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. Clarida, Richard & Gali, Jordi & Gertler, Mark, 1998. "Monetary policy rules in practice Some international evidence," European Economic Review, Elsevier, vol. 42(6), pages 1033-1067, June.
    30. Jordi Galí & Tommaso Monacelli, 2005. "Monetary Policy and Exchange Rate Volatility in a Small Open Economy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(3), pages 707-734.
    31. Veloce, William & Zellner, Arnold, 1985. "Entry and empirical demand and supply analysis for competitive industries," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 459-471.
    32. Ronald Schettkat & Rongrong Sun, 2009. "Monetary policy and European unemployment," Oxford Review of Economic Policy, Oxford University Press and Oxford Review of Economic Policy Limited, vol. 25(1), pages 94-108, Spring.
    33. Arnold, Lutz G., 2000. "Stability of the Market Equilibrium in Romer's Model of Endogenous Technological Change: A Complete Characterization," Journal of Macroeconomics, Elsevier, vol. 22(1), pages 69-84, January.
    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. William A. Barnett & Yijun He, 2002. "Bifurcations in Macroeconomic Models," Macroeconomics 0210006, University Library of Munich, Germany.
    36. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    37. Wymer, Clifford R., 1997. "Structural Nonlinear Continuous-Time Models In Econometrics," Macroeconomic Dynamics, Cambridge University Press, vol. 1(2), pages 518-548, June.
    38. Hansen, Bruce E., 1992. "Testing for parameter instability in linear models," Journal of Policy Modeling, Elsevier, vol. 14(4), pages 517-533, August.
    39. George Evans, 1985. "Expectational Stability and the Multiple Equilibria Problem in Linear Rational Expectations Models," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 100(4), pages 1217-1233.
    40. Bucci, Alberto, 2008. "Population growth in a model of economic growth with human capital accumulation and horizontal R&D," Journal of Macroeconomics, Elsevier, vol. 30(3), pages 1124-1147, September.
    41. Engelbert Dockner & Gustav Feichtinger, 1991. "On the optimality of limit cycles in dynamic economic systems," Journal of Economics, Springer, vol. 53(1), pages 31-50, February.
    42. Jones, Charles I, 1995. "R&D-Based Models of Economic Growth," Journal of Political Economy, University of Chicago Press, vol. 103(4), pages 759-784, August.
    43. Jordi Gali & Tommaso Monacelli, 1999. "Optimal Monetary Policy and Exchange Rate Volatility in a Small Open Economy," Boston College Working Papers in Economics 438, Boston College Department of Economics, revised 15 Nov 1999.
    44. John B. Taylor, 1999. "Monetary Policy Rules," NBER Books, National Bureau of Economic Research, Inc, number tayl99-1.
    45. Luenberger, David G & Arbel, Ami, 1977. "Singular Dynamic Leontief Systems," Econometrica, Econometric Society, vol. 45(4), pages 991-995, May.
    46. Bergstrom, A. R. & Nowman, K. B. & Wandasiewicz, S., 1994. "Monetary and fiscal policy in a second-order continuous time macroeconometric model of the United Kingdom," Journal of Economic Dynamics and Control, Elsevier, vol. 18(3-4), pages 731-761.
    47. Torre, V, 1977. "Existence of Limit Cycles and Control in Complete Keynesian System by Theory of Bifurcations," Econometrica, Econometric Society, vol. 45(6), pages 1457-1466, September.
    48. Lucas, Robert Jr, 1976. "Econometric policy evaluation: A critique," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 1(1), pages 19-46, January.
    49. Demirel, Ufuk Devrim, 2010. "Macroeconomic stabilization in developing economies: Are optimal policies procyclical?," European Economic Review, Elsevier, vol. 54(3), pages 409-428, April.
    50. Dowrick,Steve & Pitchford,Rohan & Turnovsky,Stephen J. (ed.), 2004. "Economic Growth and Macroeconomic Dynamics," Cambridge Books, Cambridge University Press, number 9780521835619, September.
    51. Michael Woodford, 1990. "Equilibrium Models of Endogenous Fluctuations: an Introduction," NBER Working Papers 3360, National Bureau of Economic Research, Inc.
    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. Barnett, William A. & Bella, Giovanni & Ghosh, Taniya & Mattana, Paolo & Venturi, Beatrice, 2022. "Shilnikov chaos, low interest rates, and New Keynesian macroeconomics," Journal of Economic Dynamics and Control, Elsevier, vol. 134(C).
    2. Chatelain, Jean-Bernard & Ralf, Kirsten, 2020. "Hopf Bifurcation from New-Keynesian Taylor Rule to Ramsey Optimal Policy," EconStor Open Access Articles, ZBW - Leibniz Information Centre for Economics.
    3. Chatelain, Jean-Bernard & Ralf, Kirsten, 2021. "Hopf Bifurcation From New-Keynesian Taylor Rule To Ramsey Optimal Policy," Macroeconomic Dynamics, Cambridge University Press, vol. 25(8), pages 2204-2236, December.
    4. Chatelain, Jean-Bernard & Ralf, Kirsten, 2022. "Ramsey Optimal Policy In The New-Keynesian Model With Public Debt," Macroeconomic Dynamics, Cambridge University Press, vol. 26(6), pages 1588-1614, September.
    5. Barnett, William A. & Hu, Mingzhi & Wang, Xue, 2019. "Does the utilization of information communication technology promote entrepreneurship: Evidence from rural China," Technological Forecasting and Social Change, Elsevier, vol. 141(C), pages 12-21.
    6. Barnett William A. & Jawadi Fredj & Ftiti Zied, 2020. "Causal relationships between inflation and inflation uncertainty," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 24(5), pages 1-26, December.
    7. Meir Russ, 2017. "The Trifurcation of the Labor Markets in the Networked, Knowledge-Driven, Global Economy," Journal of the Knowledge Economy, Springer;Portland International Center for Management of Engineering and Technology (PICMET), vol. 8(2), pages 672-703, June.
    8. William A. Barnett & Unal Eryilmaz, 2022. "Monetary Policy and Determinacy: An Inquiry in Open Economy New Keynesian Framework," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202203, University of Kansas, Department of Economics.
    9. William, Barnett & Hu, Jingxian, 2017. "Capital Control, Exchange Rate Regime, and Monetary Policy: Indeterminacy and Bifurcation," MPRA Paper 81450, University Library of Munich, Germany.
    10. Maxime MENUET & Alexandru MINEA & Patrick VILLIEU & Anastasios XEPAPADEAS, 2021. "Growth, Endogenous Environmental Cycles, and Indeterminacy," LEO Working Papers / DR LEO 2889, Orleans Economics Laboratory / Laboratoire d'Economie d'Orleans (LEO), University of Orleans.
    11. William A. Barnett & Unal Eryilmaz, 2023. "Monetary Policy and Determinacy: An Inquiry into Open Economy New Keynesian Macrodynamics," Open Economies Review, Springer, vol. 34(2), pages 217-253, April.
    12. Maxime Menuet & Alexandru Minea & Patrick Villieu & Anastasios Xepapadeas, 2020. "Economic Growth and the Environment: A Theoretical Reappraisal," DEOS Working Papers 2031, Athens University of Economics and Business.

    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. Barnett, William A. & Duzhak, Evgeniya A., 2019. "Structural Stability Of The Generalized Taylor Rule," Macroeconomic Dynamics, Cambridge University Press, vol. 23(4), pages 1664-1678, June.
    2. William Barnett & Evgeniya Duzhak, 2010. "Empirical assessment of bifurcation regions within New Keynesian models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(1), pages 99-128, October.
    3. Barnett, William A. & He, Susan, 2010. "Existence of singularity bifurcation in an Euler-equations model of the United States economy: Grandmont was right," Economic Modelling, Elsevier, vol. 27(6), pages 1345-1354, November.
    4. Barnett, William A. & Duzhak, Evgeniya Aleksandrovna, 2008. "Non-robust dynamic inferences from macroeconometric models: Bifurcation stratification of confidence regions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3817-3825.
    5. William A. Barnett & Unal Eryilmaz, 2023. "Monetary Policy and Determinacy: An Inquiry into Open Economy New Keynesian Macrodynamics," Open Economies Review, Springer, vol. 34(2), pages 217-253, April.
    6. Philip Arestis & Alexander Mihailov, 2011. "Classifying Monetary Economics: Fields And Methods From Past To Future," Journal of Economic Surveys, Wiley Blackwell, vol. 25(4), pages 769-800, September.
    7. Jordi Galí & J. David López-Salido, 2003. "Rule-of-Thumb Consumers and the Design of Interest Rate Rules," Working Papers 104, Barcelona School of Economics.
    8. Adnan Haider & Musleh ud Din & Ejaz Ghani, 2012. "Monetary Policy, Informality and Business Cycle Fluctuations in a Developing Economy Vulnerable to External Shocks," The Pakistan Development Review, Pakistan Institute of Development Economics, vol. 51(4), pages 609-681.
    9. Jensen Henrik, 2011. "Estimated Interest Rate Rules: Do they Determine Determinacy Properties?," The B.E. Journal of Macroeconomics, De Gruyter, vol. 11(1), pages 1-22, May.
    10. 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.
    11. repec:spo:wpecon:info:hdl:2441/f4rshpf3v1umfa09lat09b1bg is not listed on IDEAS
    12. Yüksel, Ebru & Metin-Ozcan, Kivilcim & Hatipoglu, Ozan, 2013. "A survey on time-varying parameter Taylor rule: A model modified with interest rate pass-through," Economic Systems, Elsevier, vol. 37(1), pages 122-134.
    13. repec:hal:wpspec:info:hdl:2441/f4rshpf3v1umfa09lat09b1bg is not listed on IDEAS
    14. Michael Paetz, 2007. "Robust Control and Persistence in the New Keynesian Economy," Quantitative Macroeconomics Working Papers 20711, Hamburg University, Department of Economics.
    15. repec:hal:spmain:info:hdl:2441/f4rshpf3v1umfa09lat09b1bg is not listed on IDEAS
    16. repec:spo:wpmain:info:hdl:2441/f4rshpf3v1umfa09lat09b1bg is not listed on IDEAS
    17. repec:zbw:bofrdp:2007_032 is not listed on IDEAS
    18. He, Yijun & Barnett, William A., 2006. "Existence of bifurcation in macroeconomic dynamics: Grandmont was right," MPRA Paper 756, University Library of Munich, Germany.
    19. Annicchiarico, Barbara & Giammarioli, Nicola & Piergallini, Alessandro, 2012. "Budgetary policies in a DSGE model with finite horizons," Research in Economics, Elsevier, vol. 66(2), pages 111-130.
    20. Galí, Jordi, 2002. "New Perspectives on Monetary Policy, Inflation and the Business Cycle," CEPR Discussion Papers 3210, C.E.P.R. Discussion Papers.
    21. Wieland, Volker & Cwik, Tobias & Müller, Gernot J. & Schmidt, Sebastian & Wolters, Maik, 2012. "A new comparative approach to macroeconomic modeling and policy analysis," Journal of Economic Behavior & Organization, Elsevier, vol. 83(3), pages 523-541.
    22. Bask, Mikael, 2009. "Instrument rules in monetary policy under heterogeneity in currency trade," Journal of Economics and Business, Elsevier, vol. 61(2), pages 97-111.
    23. Fair, Ray C., 2007. "Evaluating Inflation Targeting Using a Macroeconometric Model," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 1, pages 1-52.
    24. 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.
    25. Olivier Coibion & Yuriy Gorodnichenko, 2011. "Monetary Policy, Trend Inflation, and the Great Moderation: An Alternative Interpretation," American Economic Review, American Economic Association, vol. 101(1), pages 341-370, February.

    More about this item

    Keywords

    Bifurcation; Dynamical systems; Systems theory; Hopf; Robustness; Dynamical inference; Policy simulations; Econometrics; Macroeconomics;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C54 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Quantitative Policy Modeling
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • E60 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - General

    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:now:fnteco:0800000026. 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: Lucy Wiseman (email available below). General contact details of provider: http://www.nowpublishers.com/ .

    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.