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Existence of Singularity Bifurcation in an Euler-Equations Model of the United States Economy: Grandmont was Right

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  • Barnett, William A.
  • He, Susan

Abstract

Abstract: Grandmont (1985) found that the parameter space of the most classical dynamic general-equilibrium macroeconomic models are stratified into an infinite number of subsets supporting an infinite number of different kinds of dynamics, from monotonic stability at one extreme to chaos at the other extreme, and with all forms of multiperiodic dynamics between. But Grandmont provided his result with a model in which all policies are Ricardian equivalent, no frictions exist, employment is always full, competition is perfect, and all solutions are Pareto optimal. Hence he was not able to reach conclusions about the policy relevance of his dramatic discovery. As a result, Barnett and He (1999, 2001, 2002) investigated a Keynesian structural model, and found results supporting Grandmont’s conclusions within the parameter space of the Bergstrom-Wymer continuous-time dynamic macroeconometric model of the UK economy. That prototypical Keynesian model was produced from a system of second order differential equations. The model contains frictions through adjustment lags, displays reasonable dynamics fitting the UK economy’s data, and is clearly policy relevant. In addition, results by Barnett and Duzhak (2008,2009) demonstrate the existence of Hopf and flip (period doubling) bifurcation within the parameter space of recent New Keynesian models. Lucas-critique criticism of Keynesian structural models has motivated development of Euler equations models having policy-invariant deep parameters, which are invariant to policy rule changes. Hence, we continue the investigation of policy-relevant bifurcation by searching the parameter space of the best known of the Euler equations general-equilibrium macroeconometric models: the path-breaking Leeper and Sims (1994) model. We find the existence of singularity bifurcation boundaries within the parameter space. Although never before found in an economic model, singularity bifurcation may be a common property of Euler equations models, which often do not have closed form solutions. Our results further confirm Grandmont’s views. Beginning with Grandmont’s findings with a classical model, we continue to follow the path from the Bergstrom-Wymer policy-relevant Keynesian model, to New Keynesian models, and now to Euler equations macroeconomic models having deep parameters.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 12803.

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Date of creation: 16 Jan 2009
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Handle: RePEc:pra:mprapa:12803

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Keywords: Bifurcation; inference; dynamic general equilibrium; Pareto optimality; Hopf bifurcation; Euler equations; Leeper and Sims model; singularity bifurcation; stability;

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  1. Nieuwenhuis, Herman J. & Schoonbeek, Lambert, 1997. "Stability and the structure of continuous-time economic models," Economic Modelling, Elsevier, vol. 14(3), pages 311-340, July.
  2. 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.
  3. Barnett, William A. & Duzhak, Evgeniya A., 2008. "Empirical assessment of bifurcation regions within new Keynesian models," MPRA Paper 11249, University Library of Munich, Germany.
  4. Eric M. Leeper & Christopher A. Sims, 1994. "Toward a Modern Macroeconomic Model Usable for Policy Analysis," NBER Chapters, in: NBER Macroeconomics Annual 1994, Volume 9, pages 81-140 National Bureau of Economic Research, Inc.
  5. 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.
  6. 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.
  7. 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.
  8. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, vol. 53(5), pages 995-1045, September.
  9. He, Yijun & Barnett, William A., 2006. "Singularity bifurcations," Journal of Macroeconomics, Elsevier, vol. 28(1), pages 5-22, March.
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  11. Jean-Michel Grandmont, 1998. "Expectations Formation and Stability of Large Socioeconomic Systems," Econometrica, Econometric Society, vol. 66(4), pages 741-782, July.
  12. 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.
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  14. Lucas, Robert Jr, 1976. "Econometric policy evaluation: A critique," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 1(1), pages 19-46, January.
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  16. Wymer, Clifford R., 1997. "Structural Nonlinear Continuous-Time Models In Econometrics," Macroeconomic Dynamics, Cambridge University Press, vol. 1(02), pages 518-548, June.
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  18. Swamy, P.A.V.B. & Tavlas, George S. & Chang, I-Lok, 2005. "How stable are monetary policy rules: estimating the time-varying coefficients in monetary policy reaction function for the US," Computational Statistics & Data Analysis, Elsevier, vol. 49(2), pages 575-590, April.
  19. 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.
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Cited by:
  1. William Barnett & Apostolos Serletis & Demitre Serletis, 2012. "Nonlinear and Complex Dynamics in Economics," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201238, University of Kansas, Department of Economics, revised Sep 2012.
  2. Banerjee, Sanjibani & A. Barnett, William & A. Duzhak, Evgeniya & Gopalan, Ramu, 2011. "Bifurcation analysis of Zellner's Marshallian Macroeconomic Model," Journal of Economic Dynamics and Control, Elsevier, vol. 35(9), pages 1577-1585, September.

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