Advanced Search
MyIDEAS: Login to save this paper or follow this series

Empirical assessment of bifurcation regions within new Keynesian models

Contents:

Author Info

  • Barnett, William A.
  • Duzhak, Evgeniya A.

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 and their dependence upon policy-rule parameter settings.

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://mpra.ub.uni-muenchen.de/11249/
File Function: original version
Download Restriction: no

Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 11249.

as in new window
Length:
Date of creation: 23 Oct 2008
Date of revision:
Handle: RePEc:pra:mprapa:11249

Contact details of provider:
Postal: Schackstr. 4, D-80539 Munich, Germany
Phone: +49-(0)89-2180-2219
Fax: +49-(0)89-2180-3900
Web page: http://mpra.ub.uni-muenchen.de
More information through EDIRC

Related research

Keywords: Bifurcation; dynamic general equilibrium; Hopf bifurcation; flip bifurcation; period doubling bifurcation; robustness; New Keynesian macroeconometrics; Taylor rule; inflation targeting;

Other versions of this item:

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

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. Gali, Jordi & Gertler, Mark, 1999. "Inflation dynamics: A structural econometric analysis," Journal of Monetary Economics, Elsevier, vol. 44(2), pages 195-222, October.
  2. Clarida, Richard & Galí, Jordi & Gertler, Mark, 1997. "Monetary Policy Rules in Practice: Some International Evidence," CEPR Discussion Papers 1750, C.E.P.R. Discussion Papers.
  3. Richard Clarida & Jordi Galí & Mark Gertler, 1997. "The science of monetary policy: A new Keynesian perspective," Economics Working Papers 356, Department of Economics and Business, Universitat Pompeu Fabra, revised Apr 1999.
  4. 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.
  5. Charles T. Carlstrom & Timothy S. Fuerst, 2000. "Forward-looking versus backward-looking Taylor rules," Working Paper 0009, Federal Reserve Bank of Cleveland.
  6. Gale, David, 1973. "Pure exchange equilibrium of dynamic economic models," Journal of Economic Theory, Elsevier, vol. 6(1), pages 12-36, February.
  7. Calvo, Guillermo A., 1983. "Staggered prices in a utility-maximizing framework," Journal of Monetary Economics, Elsevier, vol. 12(3), pages 383-398, September.
  8. Stefano Eusepi, 2005. "Comparing forecast-based and backward-looking Taylor rules: a "global" analysis," Staff Reports 198, Federal Reserve Bank of New York.
  9. Svensson, Lars E. O., 1998. "Inflation targeting as a monetary policy rule," CFS Working Paper Series 1998/16, Center for Financial Studies (CFS).
  10. Benhabib, Jess & Day, Richard H., 1982. "A characterization of erratic dynamics in, the overlapping generations model," Journal of Economic Dynamics and Control, Elsevier, vol. 4(1), pages 37-55, November.
  11. William Barnett & Evgeniya Aleksandrovna Duzhak, 2006. "Non-Robust Dynamic Inferences from Macroeconometric Models: Bifurcation Stratification of Confidence Regions," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200608, University of Kansas, Department of Economics.
  12. S. Rao Aiyagari, 1988. "Can there be short-period deterministic cycles when people are long lived?," Staff Report 114, Federal Reserve Bank of Minneapolis.
  13. Adam Hale Shapiro, 2006. "Estimating the New Keynesian Phillips curve: a vertical production chain approach," Working Papers 06-11, Federal Reserve Bank of Boston.
  14. Jess Benhabib & Aldo Rustichini, 1990. "Vintage Capital, Investment and Growth," Discussion Papers 886, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  15. 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.
  16. Dixit, Avinash K & Stiglitz, Joseph E, 1975. "Monopolistic Competition and Optimum Product Diversity," The Warwick Economics Research Paper Series (TWERPS) 64, University of Warwick, Department of Economics.
  17. 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.
  18. 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, April.
  19. He, Yijun & Barnett, William A., 2006. "Singularity bifurcations," Journal of Macroeconomics, Elsevier, vol. 28(1), pages 5-22, March.
  20. 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.
  21. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-11, July.
  22. Torre, V, 1977. "Existence of Limit Cycles and Control in Complete Keynesian System by Theory of Bifurcations," Econometrica, Econometric Society, vol. 45(6), pages 1457-66, September.
  23. 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.
  24. 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.
  25. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, vol. 53(5), pages 995-1045, September.
  26. William A. Barnett & Yijun He, 2002. "Bifurcations in Macroeconomic Models," Macroeconomics 0210006, EconWPA.
  27. Frederic S. Mishkin & Adam S. Posen, 1997. "Inflation targeting: lessons from four countries," Economic Policy Review, Federal Reserve Bank of New York, issue Aug, pages 9-110.
  28. Roberts, John M, 1995. "New Keynesian Economics and the Phillips Curve," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 27(4), pages 975-84, November.
  29. 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, vol. 6(05), pages 713-747, November.
  30. 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.
  31. Bennett T. McCallum, 1997. "Issues in the Design of Monetary Policy Rules," NBER Working Papers 6016, 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 in new window

Cited by:
  1. Barnett, William A. & Eryilmaz, Unal, 2012. "Hopf bifurcation in the Clarida, Gali, and Gertler model," MPRA Paper 40668, 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. 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.
  4. 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.
  5. Fabrizio Orrego, 2014. "Habit formation and indeterminacy in overlapping generations models," Economic Theory, Springer, vol. 55(1), pages 225-241, January.
  6. 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.
  7. William Barnett & Taniya Ghosh, 2013. "Stability Analysis of Uzawa-Lucas Endogenous Growth Model," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201304, University of Kansas, Department of Economics, revised May 2013.
  8. 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.

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:pra:mprapa:11249. 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: (Ekkehart Schlicht).

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.