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Diagnosing and treating bifurcations in perturbation analysis of dynamic macro models

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Author Info

  • Jinill Kim
  • Andrew T. Levin
  • Tack Yun

Abstract

In perturbation analysis of nonlinear dynamic systems, the presence of a bifurcation implies that the first-order behavior of the economy cannot be characterized solely in terms of the first-order derivatives of the model equations. In this paper, we use two simple examples to illustrate how to detect the existence of a bifurcation. Following the general approach of Judd (1998), we then show how to apply l'Hospital's rule to characterize the solution of each model in terms of its higher-order derivatives. We also show that in some cases the bifurcation can be eliminated through renormalization of model variables; furthermore, renormalization may yield a more accurate first-order solution than applying l'Hospital's rule to the original formulation.

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Bibliographic Info

Paper provided by Board of Governors of the Federal Reserve System (U.S.) in its series Finance and Economics Discussion Series with number 2007-14.

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Date of creation: 2007
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Handle: RePEc:fip:fedgfe:2007-14

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Keywords: Bifurcation theory ; Perturbation (Mathematics);

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  1. Pierpaolo Benigno & Michael Woodford, 2005. "Inflation Stabilization And Welfare: The Case Of A Distorted Steady State," Journal of the European Economic Association, MIT Press, vol. 3(6), pages 1185-1236, December.
  2. Kenneth L. Judd & Sy-Ming Guu, 2001. "Asymptotic Methods for Asset Market Equilibrium Analysis," NBER Working Papers 8135, National Bureau of Economic Research, Inc.
  3. Tack Yun, 2005. "Optimal Monetary Policy with Relative Price Distortions," American Economic Review, American Economic Association, vol. 95(1), pages 89-109, March.
  4. Stephanie Schmitt-Grohé & Martín Uribe, 2007. "Optimal simple and implementable monetary and fiscal rules," Working Paper 2007-24, Federal Reserve Bank of Atlanta.
  5. 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.
  6. Levine, Paul & Pearlman, Joseph G. & Pierse, Richard, 2007. "Linear-quadratic approximation, external habit and targeting rules," Working Paper Series 0759, European Central Bank.
  7. Calvo, Guillermo A., 1983. "Staggered prices in a utility-maximizing framework," Journal of Monetary Economics, Elsevier, vol. 12(3), pages 383-398, September.
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