Diagnosing and treating bifurcations in perturbation analysis of dynamic macro models
AbstractIn 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 InfoPaper provided by Board of Governors of the Federal Reserve System (U.S.) in its series Finance and Economics Discussion Series with number 2007-14.
Date of creation: 2007
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- Pierpaolo Benigno & Michael Woodford, 2004.
"Inflation stabilization and welfare: The case of a distorted steady state,"
0405-04, Columbia University, Department of Economics.
- 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.
- Michael Woodford & Pierpaolo Benigno, 2004. "Inflation Stabilization and Welfare: The Case of a Distorted Steady State," 2004 Meeting Papers 481, Society for Economic Dynamics.
- Pierpaolo Benigno & Michael Woodford, 2004. "Inflation Stabilization and Welfare: The Case of a Distorted Steady State," NBER Working Papers 10838, National Bureau of Economic Research, Inc.
- 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.
- Levine, Paul & Pearlman, Joseph & Pierse, Richard, 2008.
"Linear-quadratic approximation, external habit and targeting rules,"
Journal of Economic Dynamics and Control,
Elsevier, vol. 32(10), pages 3315-3349, October.
- Levine, Paul & Pearlman, Joseph G. & Pierse, Richard, 2007. "Linear-quadratic approximation, external habit and targeting rules," Working Paper Series 0759, European Central Bank.
- Schmitt-Grohe, Stephanie & Uribe, Martin, 2007.
"Optimal simple and implementable monetary and fiscal rules,"
Journal of Monetary Economics,
Elsevier, vol. 54(6), pages 1702-1725, September.
- Stephanie Schmitt-Grohe & Martin Uribe, 2004. "Optimal Simple and Implementable Monetary and Fiscal Rules," NBER Working Papers 10253, National Bureau of Economic Research, Inc.
- Schmitt-Grohé, Stephanie & Uribe, Martín, 2004. "Optimal Simple and Implementable Monetary and Fiscal Rules," CEPR Discussion Papers 4334, C.E.P.R. Discussion Papers.
- Stephanie Schmitt-Grohé & Martín Uribe, 2007. "Optimal simple and implementable monetary and fiscal rules," Working Paper 2007-24, Federal Reserve Bank of Atlanta.
- Tack Yun, 2005. "Optimal Monetary Policy with Relative Price Distortions," American Economic Review, American Economic Association, vol. 95(1), pages 89-109, March.
- Sy-Ming Guu & Kenneth L. Judd, 2001.
"Asymptotic methods for asset market equilibrium analysis,"
Springer, vol. 18(1), pages 127-157.
- Kenneth L. Judd & Sy-Ming Guu, 2001. "Asymptotic Methods for Asset Market Equilibrium Analysis," NBER Working Papers 8135, National Bureau of Economic Research, Inc.
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