Revisiting the determinacy on New Keynesian Models: A survey

TL;DR

This paper reviews analytic techniques, including the Budan-Fourier Theorem, to analyze determinacy in New Keynesian models, emphasizing that multiple monetary policy rules can ensure equilibrium uniqueness.

Contribution

It reorganizes and emphasizes existing methods for analyzing determinacy in New Keynesian models, highlighting the role of various policy rules beyond Taylor-like rules.

Findings

Multiple policy rules can guarantee equilibrium determinacy.

The Budan-Fourier Theorem is a useful analytical tool.

Existing ideas are reorganized with new emphasis.

Abstract

The goal of this paper is to review some analytic techniques that are potentially useful to shed light on the determinacy question that arises in New Keynesian models as result of a combination of several monetary policy rules; in these models, we provide conditions to guarantee existence and uniqueness of equilibrium by means of results that are obtained from theoretical analysis. In particular, these methods confirm the well known fact that Taylor--like rules in interest rate setting are not the only way to reach determinacy of the rational expectations equilibrium in the New Keynesian setting. The key technical tool we use for that purposes is the so--called Budan--Fourier Theorem, that we review along the paper. All the ideas and techniques presented have been already used, our contribution that might be original here are the organization and emphasis.