Hopf Bifurcation from new-Keynesian Taylor rule to Ramsey Optimal Policy

Jean-Bernard Chatelain (1) , Kirsten Ralf (2)

1 PSE - Paris School of Economics
2 Ecole Supérieure du Commerce Extérieur - ESCE

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. For new-Keynesian Taylor rule, this Hopf bifurcation implies a lack of robustness and multiple equilibria if public debt is not set to zero for all observation.

Mots clés: Bifurcations; Taylor rule; Taylor principle; new-Keynesian model; Ramsey optimal policy; Finite horizon commitment

Domaines: Economies et finances

Jean-Bernard Chatelain, Kirsten Ralf. Hopf Bifurcation from new-Keynesian Taylor rule to Ramsey Optimal Policy. 2017. ⟨hal-01527872v1⟩