Abstract

AbstractThis paper characterizes optimal commitment policy in the New Keynesian model using a recursive formulation of the central bank's infinite‐horizon optimization problem in which promised inflation and output gap – as opposed to lagged Lagrange multipliers – act as pseudo‐state variables. Our recursive formulation is motivated by (Kydland, F. and Prescott, E. C. (1980). Journal of Economic Dynamics and Control Vol. 2, pp. 79–91). Using three well‐known variants of the model – one featuring inflation bias, one featuring stabilization bias and one featuring a lower bound constraint on nominal interest rates – we show that the proposed formulation sheds new light on the nature of the intertemporal trade‐off facing the central bank.

Highlights

  • Optimal commitment policy is a widely adopted approach among economists and policymakers to studying the question of how to best conduct monetary policy

  • In many advanced economies where the policy rate was constrained at the effective lower bound (ELB), the insights from the optimal commitment policy in a stylized New Keynesian model have played a key role in the inquiry on how long the policy rate should be kept at the ELB (Bullard (2013), Evans (2013), Kocherlakota (2011), Plosser (2013), Woodford (2012))

  • We describe our recursive approach—which we will refer to as the promised value approach—in three variants of the New Keynesian model that have been widely studied in the literature: the model with inflation bias, the model with stabilization bias, and the model with an ELB constraint

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Summary

A Promised Value Approach to Optimal Monetary Policy

Please cite this paper as: Timothy S. “A Promised Value Approach to Optimal Monetary Policy,” Finance and Economics Discussion Series 2018-083. NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers

Introduction
Model with inflation bias
Promised value approach
Lagrange multiplier approach
Analysis of optimal policy
Model with stabilization bias
Model with the ELB
Conclusion
A Details of the promised value approach for the model with inflation bias
Recursive formulation
Computing Ω with the B operator
B Details of the promised value approach for the model with stabilization bias
C Details of the promised value approach for the model with ELB
Brute-force search algorithm
D Analytical results for the model with inflation bias
Summary of coefficients ay
Equivalence
Equivalence of time-one allocations
E Analytical results for the model with stabilization bias
Marcet and Marimon’s recursive formulation
G Additional results for the model with inflation bias
Markov perfect policy in the model with inflation bias
A value-maximizing pair of constant inflation and output gap
H Markov perfect policy in the model with stabilization bias
Findings
Markov perfect policy in the model with the ELB

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