Abstract
Abstract The celebrated Taylor rule provides a simple formula that aims to capture how the central bank interest rate is adjusted as a linear function of inflation and output gap. However, the rule does not take explicitly into account the zero lower bound on the interest rate. Prior studies on interest rate selection subject to the zero lower bound have not produced derivations of explicit formulas. In this work, Taylor-like rules for central bank interest rates bounded below by zero are derived rigorously using a multi-parametric model predictive control framework. This framework is used to derive rules with or without inertia. The proposed approach is illustrated through simulations. Application of the approach to US economy data demonstrates its relevance and provides insight into the objectives underlying central bank interest rate decisions. A number of issues for future study are proposed.
Highlights
The main issue addressed in this work is the effect of zero lower bound on the optimal interest rate determined by a central bank
We address this issue in a multi-parametric model predictive control framework, which allows the derivation of explicit feedback rules even when inequality constraints are present
Application of this framework to a simple model of the US economy produced a number of Taylor-like rules, depending on the form and parameter values in the objective function employed by model predictive control (MPC)
Summary
The general form of the celebrated Taylor rule suggests that the short-term interest rate it applied by the central bank at time t can be set according to the simple formula i=t φy ( yt − y*) + φπ (πt − π *) + r * +π *. While the initial inspiration for the Taylor rule was based on fitting actual historical data, the rule, and a number of related variants, can be derived as a commitment policy through application of optimal control theory on a (quadratic) objective function, subject to the output gap, y , and inflation, π , responding to the interest rate i according to a simple dynamic model of the economy (Ball, 1999; Orphanides and Wieland, 2000; Giannoni and Woodford, 2002; Orphanides, 2003) Such derivations have mainly focused on how various forms of the objective function in the optimal control problem may result in corresponding Taylor-like rules, and have provided considerable insight into the underlying intents for interest rate decisions.
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