# Inflation Targeting under Imperfect Knowledge

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**Finance and Economics Discussion Series**

**Divisions of Research & Statistics and Monetary Affairs**

**Federal Reserve Board, Washington, D.C.**

**Inflation Targeting under Imperfect Knowledge**

**Athanasios Orphanides and John C. Williams**

**2006-20**

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.

Inﬂation Targeting under Imperfect Knowledge∗

Athanasios Orphanides

Board of Governors of the Federal Reserve System

and

John C. Williams

Federal Reserve Bank of San Francisco

April 2006

Abstract

A central tenet of inﬂation targeting is that establishing and maintaining well-anchored

inﬂation expectations are essential. In this paper, we reexamine the role of key elements

of the inﬂation targeting framework towards this end, in the context of an economy where

economic agents have an imperfect understanding of the macroeconomic landscape within

which the public forms expectations and policymakers must formulate and implement mon-

etary policy. Using an estimated model of the U.S. economy, we show that monetary policy

rules that would perform well under the assumption of rational expectations can perform

very poorly when we introduce imperfect knowledge. We then examine the performance

of an easily implemented policy rule that incorporates three key characteristics of inﬂation

targeting: transparency, commitment to maintaining price stability, and close monitoring of

inﬂation expectations, and ﬁnd that all three play an important role in assuring its success.

Our analysis suggests that simple diﬀerence rules in the spirit of Knut Wicksell excel at

tethering inﬂation expectations to the central bank’s goal and in so doing achieve superior

stabilization of inﬂation and economic activity in an environment of imperfect knowledge.

Keywords: Learning, Natural rate of interest, natural rate of unemployment, rational

expectations, monetary policy rules, uncertainty, bond prices.

JEL Classiﬁcation: D83, D84, E52, E58.

∗We would like to thank Richard Dennis, Bill English, Ali Hakan Kara, Thomas Laubach, Nissan

Liviatan, John Murray, Rodrigo Vergara, and participants of presentations at the Federal Reserve

Board, the Bundesbank, the Federal Reserve Banks of Chicago and New York, the American Univer-

sity, the conference on “Monetary Policy under Inﬂation Targeting,” Santiago, October 20–21, 2005,

the conference in honor of Alex Cukierman on “New Developments in the Analysis of Monetary

Policy and Institutions,” Tel Aviv, December 15–16, 2005, and the British Columbia Macro/Bank

of Canada conference, Vancouver, April 7-8, 2006, for useful comments. The opinions expressed are

those of the authors and do not necessarily reﬂect the views of the Board of Governors of the Federal

Reserve System or the management of the Federal Reserve Bank of San Francisco.

Correspondence: Orphanides: Federal Reserve Board, Washington, D.C. 20551, Tel.: (202) 452-2654,

e-mail: [email protected] Williams: Federal Reserve Bank of San Francisco, 101

Market Street, San Francisco, CA 94105, Tel.: (415) 974-2240, e-mail: [email protected]

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Introduction

A central tenet of inﬂation targeting is that establishing and maintaining well-anchored

inﬂation expectations are essential. Well-anchored expectations enables inﬂation-targeting

central banks to achieve greater stability of output and employment in the short-run, while

ensuring price stability in the long-run. Three elements of inﬂation targeting have been crit-

ically important for the successful implementation of this framework.1 First and foremost

is the announcement of an explicit quantitative inﬂation target and the acknowledgment

that low and stable inﬂation is the primary objective and responsibility of the central bank.

Second is the clear communication of the central bank’s policy strategy and the rationale

for its decisions, which enhances the predictability of the central bank’s actions and its

accountability to the public. Third is a forward-looking policy orientation, characterized by

the vigilant monitoring of inﬂation expectations at both short-term and longer-term hori-

zons. Together, these elements provide a focal point for inﬂation, facilitate the formation of

the public’s inﬂation expectations, and provide guidance as to actions that may be needed

to foster price stability.

Although inﬂation-targeting (IT) central banks have stressed these key elements, the

literature that has studied inﬂation targeting in the context of formal models has largely

described inﬂation targeting in terms of the solution to an optimization problem within the

conﬁnes of a linear rational expectations model. This approach is limited in its appreci-

ation of the special features of the inﬂation-targeting framework, as emphasized by Faust

and Henderson (2004), and strips from IT its raison d’ˆetre. In an environment of rational

expectations with perfect knowledge, for instance, inﬂation expectations are anchored as

long as policy satisﬁes a minimum test of stability. Furthermore, with the possible excep-

tion of a one-time statement of the central bank’s objectives, central bank communication

loses any independent role because the public already knows all it needs in order to form

expectations relevant for its decisions. In such an environment, the public’s expectations of

inﬂation and other variables are characterized by a linear combination of lags of observed

macroeconomic variables and, as such, they do not merit special monitoring by the central

1A number of studies have examined in detail the deﬁning characteristics of inﬂation targeting. See

Leiderman and Svensson (1995), Bernanke and Mishkin (1997), Bernanke et al (1999), Goodfriend (2004),

and citations therein.

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bank or provide useful information to the policymaker for guiding policy decisions.

In this paper, we argue that in order to understand the attraction of IT to central

bankers and its eﬀectiveness relative to other monetary policy strategies, it is essential

to recognize economic agents’ imperfect understanding of the macroeconomic landscape

within which the public forms expectations and policymakers must formulate and implement

monetary policy. To this end, we consider two modest deviations from the perfect knowledge

rational expectations benchmark, and reexamine the role of the key elements of the inﬂation

targeting framework in the context of an economy with imperfect knowledge. We ﬁnd

that including these modiﬁcations provides a rich framework in which to analyze inﬂation

targeting strategies and their implementation.

The ﬁrst relaxation of perfect knowledge that we incorporate is to recognize that policy-

makers face uncertainty regarding the evolution of key natural rates. In the United States,

for example, estimates of the natural rates of interest and unemployment are remarkably

imprecise.2 Indeed, this problem is arguably even more dramatic for small open economies

and transitional economies that have tended to adopt IT. As is well known, policymaker

misperceptions regarding the evolution of natural rates can result in persistent policy errors,

hindering successful stabilization policy.3

The second modiﬁcation that we allow for is the presence of imperfections in expecta-

tions formation that arise when economic agents have incomplete knowledge of the econ-

omy’s structure. We assume that agents rely on an adaptive learning technology to update

their beliefs and form expectations based on incoming data. Recent research has high-

lighted the ways in which imperfect knowledge can act as a propagation mechanism for

macroeconomic disturbances in terms of ampliﬁcation and persistence that have ﬁrst-order

implications for monetary policy.4 Agents may rely on a learning technology to guard

against numerous potential sources of uncertainty. One source could be the evolution of

natural rates in the economy, paralleling the uncertainty faced by policymakers. But an-

2For discussion and documentation of this imprecision see Orphanides and Williams (2002), Laubach and

Williams (2003), Clark and Kozicki (2005) and references therein. See also Orphanides and van Norden

(2002) for the related unreliability regarding the measurement of the natural rate of output and implied

output gap.

3For analyses of the implications of misperceptions for policy design see Orphanides and Williams (2002);

Orphanides (2003a); Cukierman and Lippi (2005); and references therein.

4See Orphanides and Williams (2004, 2005a,b,c); Gaspar and Smets (2002); Gaspar, Smets and Vestin

(2005); Milani 2005; and references in these papers.

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other might be uncertainty regarding the policymaker’s understanding of the economy, and

likely response to economic developments, and perhaps the precise quantiﬁcation of policy

objectives. Recognition of this latter element in the economy highlights a role for central

bank communications, including that of an explicit quantitative inﬂation target, that would

be absent in an environment of perfect knowledge.

We investigate the role of inﬂation targeting in an environment of imperfect knowledge

using an estimated quarterly model of the U.S. economy. Speciﬁcally, we compare the per-

formance of the economy subject to shocks with characteristics similar to those observed in

the data over the past four decades under alternative informational assumptions and policy

strategies. Following McCallum (1988) and Taylor (1993), we focus our attention on imple-

mentable policy rules that, nonetheless, capture the key characteristics of IT. Our analysis

shows that some monetary policy rules that would perform well under the assumption of

rational expectations with perfect knowledge can perform very poorly when we introduce

imperfect knowledge. In particular, rules that rely on estimates of natural rates for the set-

ting of policy are susceptible to making persistent errors. Under certain conditions, these

errors can give rise to endogenous “inﬂation scares” whereby inﬂation expectations become

unmoored from the central bank’s desired anchor. These results illustrate the potential

shortcomings of such standard policy rules and the desirability of identifying an alternative

monetary policy framework when knowledge is imperfect.

We then examine the performance of an easily implemented policy rule that incorporates

the three key characteristics of inﬂation targeting highlighted above in an economy with

imperfect knowledge, and ﬁnd that all three play an important role in assuring its success.

First, central bank transparency, including explicit communication of the inﬂation target,

can lessen the burden placed on agents to infer central bank intentions and can thereby

improve macroeconomic performance. Second, policies that do not rely on estimates of nat-

ural rates are easier to communicate and better designed to ensuring medium-run inﬂation

control when natural rates are highly uncertain. Finally, policies that respond to the pub-

lic’s near-term inﬂation expectations help the central bank avoid falling “behind the curve”

in terms of controlling inﬂation, and result in better stabilization outcomes than policies

that rely only on past realizations of data and ignore information contained in private agent

expectations.

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A reassuring aspect of our analysis is that despite the environment of imperfect knowl-

edge and the associated complexity of the economic environment, successful policy can be

remarkably simple to implement and communicate. We ﬁnd that simple “diﬀerence” rules

that do not require any knowledge of the economy’s natural rates are particularly well suited

to assure medium-run inﬂation control when natural rates are highly uncertain. These rules

share commonalities with the simple robust strategy ﬁrst proposed by Wicksell (1898), who,

after deﬁning the natural rate of interest, also pointed out that precise knowledge about

it, though desirable, was neither feasible nor necessary for policy implementation aimed

towards maintaining price stability.

“This does not mean that the bank ought actually to ascertain the natural rate

before ﬁxing their own rates of interest. That would, of course, be impractica-

ble, and would also be quite unnecessary. For the current level of commodity

prices provides a reliable test of the agreement or diversion of the two rates.

The procedure should rather be simply as follows: So long as prices remain

unchanged, the bank’s rate of interest is to remain unaltered. If prices rise, the

rate of interest is to be raised; and if prices fall, the rate of interest is to be

lowered; and the rate of interest is henceforth to be maintained at its new level

until a further movement in prices calls for a further change in one direction or

the other. ...

In my opinion, the main cause of the instability of prices resides in the instability

of the banks to follow this rule.”

Wicksell (1898, 1936), p. 189 (emphasis in original)

Our analysis conﬁrms that simple diﬀerence rules that implicitly target the price level in

the spirit of Wicksell excel at tethering inﬂation expectations to the central bank’s goal and

in so doing achieve superior stabilization of inﬂation and economic activity.

The remainder of the paper is organized as follows. Section II describes the estimated

model of the economy. Section III lays out the model of perpetual learning and its cal-

ibration. Section IV analyzes key features of the model under rational expectations and

imperfect knowledge. Section V examines the performance of alternative monetary policy

strategies, including our implementation of inﬂation targeting. Section VI concludes.

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2

A Simple Estimated Model of the U.S. Economy

We use a simple estimated quarterly model of the U.S. economy from Orphanides and

Williams (2002), the core of which consists of the following two equations:

πt = φππet+1 + (1 − φπ)πt−1 + απ(uet − u∗t) + eπ,t, eπ ∼ iid(0, σ2e ),

(1)

π

ut = φuuet+1 + χ1ut−1 + χ2ut−2 + χ3u∗t + αu (rat−1 − r∗t) + eu,t, eu ∼ iid(0, σ2e ).

(2)

u

Here π denotes the annualized percent change in the aggregate output price deﬂator, u

denotes the unemployment rate, u∗ denotes the (true) natural rate of unemployment, ra

denotes the (ex ante) real interest rate with one year maturity, and r∗ the (true) natural

real rate of interest. The superscript e denotes the public’s expectations formed during

t − 1. This model combines forward-looking elements of the New Synthesis model studied

by Goodfriend and King (1997), Rotemberg and Woodford (1999), Clarida, Gal´ı and Gertler

(1999), and McCallum and Nelson (1999), with intrinsic inﬂation and unemployment inertia

as in Fuhrer and Moore (1995a), Batini and Haldane (1999), Smets (2003), and Woodford

(2003).

The “Phillips curve” in this model (1) relates inﬂation during quarter t to lagged in-

ﬂation, expected future inﬂation, and expectations of the unemployment gap during the

quarter, using retrospective estimates of the natural rate discussed below. The estimated

parameter φπ measures the importance of expected inﬂation for the determination of in-

ﬂation. The unemployment equation (2) relates unemployment during quarter t to the

expected future unemployment rate, two lags of the unemployment rate, the natural rate

of unemployment, and the lagged real interest rate gap. Here, two elements importantly

reﬂect forward-looking behavior. The ﬁrst element is the estimated parameter φu, which

measures the importance of expected unemployment, and the second is the duration of the

real interest rate, which serves as a summary of the inﬂuence of interest rates of various

maturities on economic activity. We restrict the coeﬃcient χ3 to equal 1 − φu − χ1 − χ2 so

that the equation can be equivalently written in terms of the unemployment gap.

In estimating this model, we are confronted with the diﬃculty that expected inﬂation

and unemployment are not directly observed. Instrumental variable and full-information

maximum likelihood methods impose the restriction that the behavior of monetary policy

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and the formation of expectations be constant over time, neither of which appears tenable

over the sample period that we consider (1969–2002). Instead, we follow the approach

of Roberts (1997) and use survey data as proxies for expectations. (See also Rudebusch

(2002) and Orphanides and Williams (2005b).) In particular, we use the median forecasts

from the Survey of Professional Forecasters from the prior quarter as the expectations

relevant for the determination of inﬂation and unemployment in period t; that is, we assume

expectations are based on information available at time t − 1. In addition, to match the

inﬂation and unemployment data as well as possible with the forecasts, we employ ﬁrst-

announced estimates of these series in our estimation. Our primary sources for these data

are the Real-Time Dataset for Macroeconomists and the Survey of Professional Forecasters,

both currently maintained by the Federal Reserve Bank of Philadelphia (Zarnowitz and

Braun (1993), Croushore (1993), and Croushore and Stark (2001)). Using least squares

over the sample 1969:1 to 2002:2, we obtain the following estimates:

πt = 0.540 πet+1 +0.460 πt−1 − 0.341 (uet − u∗t) + eπ,t,

(3)

(0.086)

(−−)

(0.099)

SER = 1.38, DW = 2.09,

ut = 0.257 uet+1 + 1.170 ut−1 − 0.459 ut−2 − 0.032 u∗t + 0.043 (rat−1 − r∗t) + eu,t, (4)

(0.084)

(0.107)

(0.071)

(−−)

(0.013)

SER = 0.30, DW = 2.08,

The numbers in parentheses are the estimated standard errors of the corresponding re-

gression coeﬃcients. (Dashes are shown under the restricted parameters.) The estimated

unemployment equation also includes a constant term (not shown) that captures the aver-

age premium of the one-year Treasury bill rate we use for estimation over the average of the

federal funds rate, which corresponds to the natural rate of interest estimates we employ in

the model. For simplicity, we make no attempt to model the evolution of risk premia. In

the model simulations, we impose the expectations theory of the term structure whereby

the one-year rate equals the expected average of the federal funds rate over four quarters.

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2.1

Natural Rates

We assume that the true processes governing natural rates in the economy follow highly

persistent autoregressions. Speciﬁcally, we posit that the natural rates follow:

u∗t = 0.01¯u∗ + 0.99 u∗t−1 + eu∗,t,

r∗t = 0.01¯r∗ + 0.99 r∗t−1 + er∗,t,

where ¯

u∗ and ¯

r∗ denote the unconditional means of the natural rates of unemployment and

interest, respectively. The assumption that these processes are stationary is justiﬁed by the

ﬁnding based on a standard ADF test that one can reject the null of nonstationarity of

both the unemployment rate and the ex post real federal funds rate over 1950–2003 at the

5 percent level. To capture the assumed high persistence of these series, we set the AR(1)

coeﬃcient to 0.99 and and then calibrate the innovation variances to be consistent with

estimates of time variation in the natural rates in postwar U.S. data.

As discussed in Orphanides and Williams (2002), there exists a wide range of estimates

of the variances of the innovations to the natural rates. Indeed, owing to the imprecision in

estimates of these variances, the postwar U.S. data do not provide clear guidance regarding

these parameters. Therefore, we consider three alternative calibrations of these variances,

which we index by s. The case of s = 0 corresponds to constant and known natural rates,

where σe

= σ

= 0. For the case of s = 1, we assume σ

= 0.070 and σ

= 0.085.

u∗

er∗

eu∗

er∗

These values imply an unconditional standard deviation of the natural rate of unemployment

(interest) of 0.50 (0.60), in the low end of the range of standard deviations of smoothed

estimates of these natural rates suggested by various estimation methods (see Orphanides

and Williams 2002 for details). Finally, the case of s = 2 corresponds to the high end of

the range of estimates, for which case we assume σe

= 0.140 and σ

= 0.170. Arguably,

u∗

er∗

given the stability of the post-war U.S. economy relative to many small open economies

and transitional economies, for those countries the relevant values of s may be higher than

those based on U.S. data.

2.2

Monetary Policy

We consider two classes of simple monetary policy rules. First, we analyze versions of the

“Taylor Rule” (Taylor 1993), where the level of the nominal interest rate is determined by

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the perceived natural rate of interest, ˆ

r∗t, the inﬂation rate, and a measure of the level of

the perceived unemployment gap, the diﬀerence between the unemployment rate and the

perceived natural rate of unemployment, ˆ

u∗t,

it = ˆr∗t + ¯πet+j + θπ(¯πet+j − π∗) + θu(uet+k − ˆu∗t),

(5)

where ¯

π denotes the four-quarter average of the inﬂation rate, π∗ is the central bank’s

inﬂation objective, j is the forecast horizon of inﬂation, and k is the forecast horizon of

the unemployment rate forecast. We consider a range of values for the forecast horizons

from −1, in which case policy responds to the latest observed data (for quarter t − 1), to

a forecast horizon up to three years into the future. When policy is based on forecasts, we

assume that the central bank uses the same forecasts of inﬂation and unemployment rate

as available to private agents.

We refer to this class of rules as “level rules” because they relate the level of the interest

rate to the level of the unemployment gap. Rules of this type have been found to perform

quite well in terms of stabilizing economic ﬂuctuations, at least when the natural rates of

interest and unemployment are accurately measured. Note that here we consider a variant

of the Taylor rule that responds to the unemployment gap instead of the output gap for our

analysis, recognizing that the two are related by Okun’s (1962) law. In his 1993 exposition,

Taylor examined response parameters equal to 1/2 for the inﬂation gap and the output gap,

which, using an Okun’s coeﬃcient of 2, corresponds to setting θπ = 0.5 and θu = −1.0.

If policy follows a level rule given by equation (5), then the “policy error” introduced

in period t by natural rate misperceptions is given by

(ˆ

r∗t − r∗t) − θu(ˆu∗t − u∗t).

Although unintentional, these errors could subsequently induce undesirable ﬂuctuations

in the economy, worsening stabilization performance. The extent to which misperceptions

regarding the natural rates translate into policy induced ﬂuctuations depends on the param-

eters of the policy rule. As is evident from the expression above, policies that are relatively

unresponsive to real-time assessments of the unemployment gap, that is, those with small

θu, minimize the impact of misperceptions regarding the natural rate of unemployment.

As discussed in Orphanides and Williams (2002), one policy rule that is immune to

natural rate mismeasurement of the kind considered here is a “diﬀerence” rule where the

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