Hopf Bifurcation from new-Keynesian Taylor rule to Ramsey Optimal Policy
Jean-Bernard Chatelain  2, 1@  , Kirsten Ralf  3, *@  
2 : Paris School of Economics, Université Paris 1 Panthéon Sorbonne  (PSE)  -  Site web
Université Paris 1 Panthéon Sorbonne, Paris School of Economics, PARIS SCHOOL OF ECONOMICS
48 Boulevard Jourdan 75014 Paris -  France
1 : Paris School of Economics
Université Paris I Panthéon Sorbonne
3 : ESCE International Business School, 10 rue Sextius Michel, 75015 Paris
* : Auteur correspondant

This paper shows that a shift from Ramsey optimal policy under short term commitment (based on a negative-feedback mechanism) to a Taylor rule (based on positive-feedback mechanism) in the new-Keynesian model is in fact a Hopf bifurcation, with opposite policy advice. The number of stable eigenvalues corresponds to the number of predetermined variables including the interest rate and its lag as policy instruments for Ramsey optimal policy. With a new-Keynesian Taylor rule, however, these policy instruments are arbitrarily assumed to be forward-looking variables when policy targets (inflation and output gap) are forward-looking variables.

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