Abstract
In recent macro models with staggered price and wage settings, the presence of variables such as relative price and wage dispersion is prevalent, which leads to the source of bifurcations. In this paper, we illustrate how to detect the existence of a bifurcation in stylized macroeconomic models with Calvo (J Monet Econ 12(3):383–398, 1983) pricing. Following the general approach of Judd (Numerical methods in economics, 1998), we employ l’Hospital’s rule to characterize the first-order dynamics of relative price distortion in terms of its higher-order derivatives. We also show that, as in the usual practice in the literature, the bifurcation can be eliminated through renormalization of model variables. Furthermore, we demonstrate that the second-order approximate solutions under this renormalization and under bifurcations can differ significantly.
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References
Benhabib J., Nishimura K. (1979) The hopf bifurcation and the existence and stability of closed orbits in multisector models of optimal economic growth. Journal of Economic Theory 21(3): 421–444
Benigno P., Woodford M. (2005) Inflation stabilization and welfare: The case of a distorted steady state. Journal of the European Economic Association 3(6): 1185–1236
Calvo G. (1983) Staggered prices in a utility maximizing framework. Journal of Monetary Economics 12(3): 383–398
Judd K. (1998) Numerical methods in economics. MIT Press, London
Judd K., Guu S.-M. (2001) Asymptotic methods for asset market equilibrium analysis. Economic Theory 1(18): 127–157
Levin A., Onatski A., Williams J., Williams N. (2006) Monetary policy under uncertainty in micro-founded macroeconometric models. In: Gertler M., Rogoff K. (eds) NBER macroeconomics annual 2005. MIT Press, Cambridge
Levine P., Pearlman J., Pierse R. (2008) Linear-quadratic approximation, external habit and targeting rules. Journal of Economic Dynamics and Control 32(10): 3315–3349
Schmitt-Grohé S., Uribe M. (2007) Optimal simple and implementable monetary and fiscal rules. Journal of Monetary Economics 54(6): 1702–1725
Woodford M. (2003) Interest and prices: Foundations of theory of monetary policy. Princeton University Press, Princeton
Yun T. (2005) Optimal monetary policy with relative price distortions. American Economomic Review 95(1): 89–109
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Kim, J., Levin, A.T. & Yun, T. Bifurcation in Perturbation Analysis:Calvo Pricing Examples. Comput Econ 37, 221–236 (2011). https://doi.org/10.1007/s10614-010-9251-x
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DOI: https://doi.org/10.1007/s10614-010-9251-x