Advanced Search
MyIDEAS: Login to save this article or follow this journal

Empirical assessment of bifurcation regions within New Keynesian models

Contents:

Author Info

  • William Barnett

    ()

  • Evgeniya Duzhak

    ()

Abstract

As is well known in systems theory, the parameter space of most dynamic models is stratified into subsets, each of which supports a different kind of dynamic solution. Since we do not know the parameters with certainty, knowledge of the location of the bifurcation boundaries is of fundamental importance. Without knowledge of the location of such boundaries, there is no way to know whether the confidence region about the parameters’ point estimates might be crossed by one or more such boundaries. If there are intersections between bifurcation boundaries and a confidence region, the resulting stratification of the confidence region damages inference robustness about dynamics, when such dynamical inferences are produced by the usual simulations at the point estimates only. Recently, interest in policy in some circles has moved to New Keynesian models, which have become common in monetary policy formulations. As a result, we explore bifurcations within the class of New Keynesian models. We study different specifications of monetary policy rules within the New Keynesian functional structure. In initial research in this area, Barnett and Duzhak (2008) found a New Keynesian Hopf bifurcation boundary, with the setting of the policy parameters influencing the existence and location of the bifurcation boundary. Hopf bifurcation is the most commonly encountered type of bifurcation boundary found among economic models, since the existence of a Hopf bifurcation boundary is accompanied by regular oscillations within a neighborhood of the bifurcation boundary. Now, following a more extensive and systematic search of the parameter space, we also find the existence of Period Doubling (flip) bifurcation boundaries in the class of models. Central results in this research are our theorems on the existence and location of Hopf bifurcation boundaries in each of the considered cases. We also solve numerically for the location and properties of the Period Doubling bifurcation boundaries an

(This abstract was borrowed from another version of this item.)

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://hdl.handle.net/10.1007/s00199-008-0430-0
Download Restriction: Access to full text is restricted to subscribers.

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Bibliographic Info

Article provided by Springer in its journal Economic Theory.

Volume (Year): 45 (2010)
Issue (Month): 1 (October)
Pages: 99-128

as in new window
Handle: RePEc:spr:joecth:v:45:y:2010:i:1:p:99-128

Contact details of provider:
Web page: http://link.springer.de/link/service/journals/00199/index.htm

Order Information:
Web: http://link.springer.de/orders.htm

Related research

Keywords: Bifurcation; Dynamic general equilibrium; Hopf bifurcation; Flip bifurcation; Period doubling bifurcation; Robustness; New Keynesian macroeconometrics; Taylor rule; Inflation targeting; C10; C30; C52; E32; E37; E60;

Other versions of this item:

Find related papers by JEL classification:

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. Calvo, Guillermo A., 1983. "Staggered prices in a utility-maximizing framework," Journal of Monetary Economics, Elsevier, Elsevier, vol. 12(3), pages 383-398, September.
  2. S. Rao Aiyagari, 1988. "Can there be short-period deterministic cycles when people are long lived?," Staff Report, Federal Reserve Bank of Minneapolis 114, Federal Reserve Bank of Minneapolis.
  3. William T. Gavin, 2003. "Inflation targeting: why it works and how to make it work better," Working Papers 2003-027, Federal Reserve Bank of St. Louis.
  4. Day, Richard H. & Shafer, Wayne, 1987. "Ergodic fluctuations in deterministic economic models," Journal of Economic Behavior & Organization, Elsevier, vol. 8(3), pages 339-361, September.
  5. Barnett William A. & He Yijun, 1999. "Stability Analysis of Continuous-Time Macroeconometric Systems," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 3(4), pages 1-22, January.
  6. Stefano Eusepi, 2005. "Comparing forecast-based and backward-looking Taylor rules: a "global" analysis," Staff Reports 198, Federal Reserve Bank of New York.
  7. 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.
  8. Clarida, R. & Gali, J. & Gertler, M., 1999. "The Science of Monetary Policy: A New Keynesian Perspective," Working Papers, C.V. Starr Center for Applied Economics, New York University 99-13, C.V. Starr Center for Applied Economics, New York University.
  9. Bennett T. McCallum, 1997. "Issues in the Design of Monetary Policy Rules," NBER Working Papers 6016, National Bureau of Economic Research, Inc.
  10. Adam Hale Shapiro, 2008. "Estimating the New Keynesian Phillips Curve: A Vertical Production Chain Approach," Journal of Money, Credit and Banking, Blackwell Publishing, Blackwell Publishing, vol. 40(4), pages 627-666, 06.
  11. Richard Clarida & Jordi Gali & Mark Gertler, 1997. "Monetary Policy Rules in Practice: Some International Evidence," NBER Working Papers 6254, National Bureau of Economic Research, Inc.
  12. Bergstrom,Albert Rex & Nowman,Khalid Ben, 2007. "A Continuous Time Econometric Model of the United Kingdom with Stochastic Trends," Cambridge Books, Cambridge University Press, number 9780521875493, 9.
  13. Svensson, Lars E. O., 1998. "Inflation targeting as a monetary policy rule," CFS Working Paper Series 1998/16, Center for Financial Studies (CFS).
  14. He, Yijun & Barnett, William A., 2006. "Singularity bifurcations," Journal of Macroeconomics, Elsevier, Elsevier, vol. 28(1), pages 5-22, March.
  15. Torre, V, 1977. "Existence of Limit Cycles and Control in Complete Keynesian System by Theory of Bifurcations," Econometrica, Econometric Society, Econometric Society, vol. 45(6), pages 1457-66, September.
  16. Jess Benhabib & Aldo Rustichini, 1990. "Vintage Capital, Investment and Growth," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 886, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  17. Barnett, William A. & He, Yijun, 2002. "Stabilization Policy As Bifurcation Selection: Would Stabilization Policy Work If The Economy Really Were Unstable?," Macroeconomic Dynamics, Cambridge University Press, Cambridge University Press, vol. 6(05), pages 713-747, November.
  18. Benhabib, Jess & Nishimura, Kazuo, 1979. "The hopf bifurcation and the existence and stability of closed orbits in multisector models of optimal economic growth," Journal of Economic Theory, Elsevier, vol. 21(3), pages 421-444, December.
  19. Barnett, William A. & Duzhak, Evgeniya, 2006. "Non-Robust Dynamic Inferences from Macroeconometric Models: Bifurcation Stratification of Confidence Regions," MPRA Paper 402, University Library of Munich, Germany.
  20. Charles T. Carlstrom & Timothy S. Fuerst, 2000. "Forward-looking versus backward-looking Taylor rules," Working Paper 0009, Federal Reserve Bank of Cleveland.
  21. 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.
  22. Gale, David, 1973. "Pure exchange equilibrium of dynamic economic models," Journal of Economic Theory, Elsevier, vol. 6(1), pages 12-36, February.
  23. Frederic S. Mishkin & Adam S. Posen, 1997. "Inflation targeting: lessons from four countries," Economic Policy Review, Federal Reserve Bank of New York, Federal Reserve Bank of New York, issue Aug, pages 9-110.
  24. 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, Elsevier, vol. 18(3-4), pages 731-761.
  25. Benhabib, Jess & Day, Richard H., 1982. "A characterization of erratic dynamics in, the overlapping generations model," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 4(1), pages 37-55, November.
  26. William A. Barnett & Yijun He, 2002. "Bifurcations in Macroeconomic Models," Macroeconomics, EconWPA 0210006, EconWPA.
  27. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, Econometric Society, vol. 48(5), pages 1305-11, July.
  28. Jordi Gali & Mark Gertler, 2000. "Inflation Dynamics: A Structural Econometric Analysis," NBER Working Papers 7551, National Bureau of Economic Research, Inc.
  29. Roberts, John M, 1995. "New Keynesian Economics and the Phillips Curve," Journal of Money, Credit and Banking, Blackwell Publishing, Blackwell Publishing, vol. 27(4), pages 975-84, November.
  30. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, Econometric Society, vol. 53(5), pages 995-1045, September.
  31. Dixit, Avinash K & Stiglitz, Joseph E, 1977. "Monopolistic Competition and Optimum Product Diversity," American Economic Review, American Economic Association, vol. 67(3), pages 297-308, June.
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 in new window

Cited by:
  1. Barnett, William A. & Ghosh, Taniya, 2013. "Stability analysis of Uzawa-Lucas endogenous growth model," MPRA Paper 47231, University Library of Munich, Germany.
  2. William Barnett & Unal Eryilmaz, 2012. "An Analytical and Numerical Search for Bifurcations in Open Economy New Keynesian Models," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201210, University of Kansas, Department of Economics, revised Aug 2012.
  3. Fabrizio Orrego, 2014. "Habit formation and indeterminacy in overlapping generations models," Economic Theory, Springer, Springer, vol. 55(1), pages 225-241, January.
  4. Jacques K Ngoie & Arnold Zellner, 2012. "Evaluation of the Effects of Reduced Personal and Corporate Tax Rates on the Growth Rates of the U.S. Economy," Working Papers 280, Economic Research Southern Africa.
  5. Barnett, William A. & Eryilmaz, Unal, 2013. "Hopf bifurcation in the Clarida, Gali, and Gertler model," Economic Modelling, Elsevier, vol. 31(C), pages 401-404.
  6. Sanjibani Banerjee & William Barnett & Evgeniya Duzhak & Ramu Gopalan, 2011. "Bifurcation Analysis of Zellner's Marshallian Macroeconomic Model," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201102, University of Kansas, Department of Economics, revised Apr 2011.
  7. Cornaro, Alessandra & Agliari, Anna, 2011. "Global and local determinacy in a one-step forward looking New Keynesian model," Economic Modelling, Elsevier, vol. 28(3), pages 1354-1362, May.
  8. Barnett, William A. & He, Susan, 2009. "Existence of Singularity Bifurcation in an Euler-Equations Model of the United States Economy: Grandmont was Right," MPRA Paper 12803, University Library of Munich, Germany.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:spr:joecth:v:45:y:2010:i:1:p:99-128. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Guenther Eichhorn) or (Christopher F Baum).

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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