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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. Wymer, Clifford R., 1997. "Structural Nonlinear Continuous-Time Models In Econometrics," Macroeconomic Dynamics, Cambridge University Press, vol. 1(02), pages 518-548, June.
  2. Jean-Michel Grandmont, 1997. "Expectations Formation and Stability of Large Socioeconomic Systems," Working Papers 97-27, Centre de Recherche en Economie et Statistique.
  3. 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.
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Cited by:
  1. 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.
  2. William Barnett & Alfredo Medio & Apostolos Serletis, 2012. "Nonlinear And Complex Dynamics In Economics," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201223, University of Kansas, Department of Economics, revised Sep 2012.

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