Monetary Policy and Inflation

Inflation Targets, Credibility, and Persistence

In a Simple Sticky-Price Framework

Jeremy Rudd

Federal Reserve Board

Karl Whelan

Central Bank of Ireland

July 23, 2003

Abstract

This paper presents a re-formulated version of a canonical sticky-price model that has

been extended to account for variations over time in the central bank's inflation tar-

get. We derive a closed-form solution for the model, and analyze its properties under

various parameter values. The model is used to explore topics relating to the eects of

disinflationary monetary policies and inflation persistence. In particular, we employ the

model to illustrate and assess the critique that standard sticky-price models generate

counterfactual predictions for the eects of monetary policy.

Corresponding author. Mailing address: Mail Stop 80, 20th and C Streets NW, Washington, DC 20551.

E-mail: jeremy.b.rudd@frb.gov.

E-mail: karl.whelan@centralbank.ie. We thank Gregory Mankiw and Olivier Blanchard for useful dis-

cussions on several of the topics considered here. The views expressed in this paper are our own, and do

not necessarily reflect the views of the Board of Governors, the sta of the Federal Reserve System, or the

Central Bank of Ireland.

1 Introduction

An important trend in macroeconomic research in recent years involves the increased use

of optimization-based sticky-price models to analyze how monetary policy aects the econ-

omy and how optimal policy should be designed. Much of this analysis employs a simple

baseline model that features a new-Keynesian" Phillips curve to characterize inflation, an

expectational IS curve" to determine output growth, and a policy rule that describes how

the central bank sets short-term interest rates; representative examples of studies that use

this framework include Clarida, Gal, and Gertler (1999), McCallum (2001), and Wood-

ford (2003).

One limitation of existing work in this area is that applications of the baseline model

have typically been restricted to contexts in which the central bank maintains a xed infla-

tion target, with particular attention being paid to the eects of the type of monetary policy

shock" that is usually analyzed in the empirical VAR literature (namely, a temporary de-

viation from a stable policy rule). In this paper, we present a re-formulated version of the

baseline sticky-price model that has been extended to account for variations over time in

the central bank's inflation target. We derive a fully specied closed-form solution for the

model in which output and inflation are related both to policy shocks (as usually dened)

and to expected future changes in the inflation target. The model provides a simple but

flexible framework for understanding a number of issues that have previously been dealt

with using a range of dierent specications. In particular, the model sheds light on some

important existing critiques regarding the general ability of sticky-price models to capture

the eects of disinflationary monetary policies.

One such critique that we consider stems from Laurence Ball's (1994) well-known ex-

ample of a sticky-price economy in which an announcement of a gradual reduction in the

rate of growth of the money supply results in a boom in output. This has commonly

been seen as an important counterfactual prediction of these models in light of the large

observed costs of disinflation; moreover, Ball's result appears at odds with the position of

Woodford (2003) and others that these models adequately capture the eect of a monetary

tightening on output. We use our framework to demonstrate how these apparently con-

tradictory results can be reconciled by noting that they reflect the eects of two dierent

types of shocks in our model. Specically, in the more general framework that we derive

here, Ball's example of a gradual disinflation that is achieved through a deceleration in the

money supply is equivalent to an example where the central bank's target inflation rate is

1

gradually reduced. In our framework, a credible announcement of future reductions in the

inflation target will indeed result in increased output today (at least for most parameter

values). However, we also demonstrate that another aspect of Ball's result|specically,

that inflation can be reduced without output's ever declining below its baseline level|

relies on a highly restrictive assumption about pricing behavior (namely, that rms do not

discount their future prots).

We then use an extended version of our basic framework in order to assess the idea|

rst proposed by Ball (1995)|that allowing for imperfect