# Open-Economy Inflation-Forecast Targeting

### Text-only Preview

Kai Leitemo

Monetary Policy Strategy Unit, Research Department

Norges Bank

May 2002

Abstract

This paper extends previous research on simple inﬂation-forecast targeting by considering

its eﬀect in the open economy. It discusses the eﬀect of the forecast-targeting horizon on

interest rates and the exchange rate, and moreover what role it plays in determining the

rational expectations equilibrium. Inﬂation-forecast targeting may not comply with the

Taylor principle, as a suﬃciently long horizon may not provide a adequately strong interest

rate response to the determinants of future inﬂation. A long horizon causes the short-term

real interest rate and the exchange rate to ﬂuctuate persistently, producing inﬂation and

especially traded sector output volatility.

Keywords: Inﬂation targeting, forecast targeting, monetary policy, small open economy.

JEL codes: E52, E47, E43.

∗Comments and suggestions from Steinar Holden and Lars E.O. Svensson have been particularly useful.

Comments from Larry Ball, Alex Cuikerman, Petra Geraats, Henrik Jensen, Marianne Ness´

en, Simon Price,

Øistein Røisland, Frank Smets, Ingvild Svendsen, Ulf S¨

oderstr¨

om, Bent Vale, Anders Vredin and participants in

seminars at the University of Oslo, Norwegian School of Management BI, the CEPR/ESI conference “Old Age,

New Economy and Central Banking” and the ECB workshop on “The Role of Policy Rules in the Conduct of

Monetary Policy” are gratefully acknowledged. I thank Gunnar B˚

ardsen, Ragnar Nymoen and Kenneth Wallis

for making data available and Janet Aagenæs for editorial assistance. This paper has made use of modiﬁed

computer algorithms originally created by Paul S¨

oderlind. Any remaining errors are entirely my own. The views

expressed in this paper are those of the author and not necessarily those of Norges Bank (the Central Bank

of Norway). Address of the author: Research Department, Norges Bank, PO Box 1179 Sentrum, 0107 OSLO,

Norway. Tel/Fax: +47 22 31 69 58. E-mail: kai.leitemo@norges-bank.no

1. Introduction

A large number of countries have either formally or more informally adopted inﬂation targeting

as a framework for monetary policy throughout the 1990s. Following the idea that inﬂation

targeting implies using all available information eﬃciently in minimizing the variance of inﬂation

around a target level1 (possibly by stabilizing other variables as well), the implementation is left

to the discretion of the analysts and policymakers in the respective central banks. Due to the

traditional arguments of lags in the monetary policy transmission mechanism, e.g. as modeled

in the inﬂuential article by Svensson (1997), the inﬂation forecast plays an important role in the

conduct of monetary policy. The argument is that since the monetary policymaker’s instrument

has its strongest impact on its goal variables several quarters ahead, optimal monetary policy

is forward looking and the instrument should respond to the determinants of future inﬂation

(i.e. the forecast) and possibly other target variables. Since in most models, nominal inertia

implies a trade-oﬀ between nominal and real variability, the inﬂation targeting central bank

should aim to bring inﬂation in line with target over time. Short-sightedness should be avoided,

since such a policy could produce high output and interest rate volatility. In the open economy,

the exchange rate channel opens the possibility of stabilizing inﬂation at a very short horizon,

leading to high real variability (Svensson, 2000).

This paper extends previous research on the implications of a simple inﬂation-forecast target-

ing strategy where the central bank sets an interest rate level which, if kept constant throughout

the forecast-targeting horizon, produces a conditional inﬂation forecast equal to the inﬂation

target level.2 This rule has seemingly strong intuitive appeal: the monetary policy stance is

set in such a way that if the economy evolves as expected, policy is in line with achieving the

inﬂation target at some horizon. Rudebusch and Svensson (1999) discuss this strategy within a

backward-looking, closed-economy model of the US economy. This paper extends the analysis

of the properties of inﬂation-forecast targeting by considering its open-economy implications.

Particular emphasis is put on describing how the forecast targeting horizon eﬀects the traded

and non-traded sectors through implied exchange-rate and interest rate dynamics and what

role the choice of horizon plays in determining the rational expectations equilibrium. Moreover,

the paper also discusses what role the inﬂation target plays in pinning down long-run inﬂation

expectations under inﬂation-forecast targeting.

1Lars Svensson has suggested this deﬁnition of inﬂation targeting in several papers, for instance (Svensson,

1999b, 2000).

2This policy should be contrasted to optimal inﬂation-forecast targeting, explored in Svensson and Woodford

(1999) and Svensson (2001), where the forecasts of the target variables satisfy the ﬁrst-order conditions of optimal

inﬂation targeting, i.e. a situation in which the policymaker minimizes a quadratic loss function.

2

Inﬂation-forecast targeting requires strong movements in the interest rate when the forecast-

targeting horizon is relatively short. If a shock hits the economy, the policymaker needs to

stabilize the inﬂationary impulses quickly which requires strong interest rate responses to the

factors determining future inﬂation. With a longer forecast-targeting horizon, there is less need

for strong interest rate responses since the policy multiplier increases with the forecast-targeting

horizon. In models that respect the long-run superneutrality of monetary policy, an equilibrium

rate of inﬂation is achieved without monetary policy following a state-contingent rule, but

rather satisﬁes conditions for having the equilibrium inﬂation rate equal to target. Extending

the forecast-targeting horizon brings it closer to the time it takes for the nominal inertia to

have worked itself out and the equilibrium rate of inﬂation achieved. Hence, a longer forecast-

targeting horizon implies a greater degree of interest rate stabilization around its equilibrium

rate.

In order to address the open-economy implications, we develop a New Keynesian, small open-

economy macroeconomic model similar to the one-sector model developed by Batini and Haldane

(1999) and used as a policy model at the Bank of England.3 Our model is, however, extended

in several respects. Recently, Ball (2000) has argued that analysis should be carried out within

multi-sector models in order to shed light on the role and sectoral inﬂuence of the exchange

rate in monetary policymaking. In this respect, we add a competitive, traded sector to the

model in order to reﬁne the view of how monetary policy inﬂuences the real economy. We show

that the nominal interest rate stabilization implied by a long forecast-targeting horizon implies

that inﬂation will ﬂuctuate more, causing the short real interest rate and the real exchange rate

to ﬂuctuate persistently. As the real exchange rate aﬀects the traded sector relatively more

than it does the non-traded sector, we show that if the inﬂation-forecast targeting central bank

chooses a long forecast-targeting horizon, the traded sector will be relatively more exposed to

ﬂuctuations than the non-traded sector. Thus, merely extending the forecast-targeting horizon

does not necessarily provide more real stability. Inﬂation variability will, however, increase.

The paper is organized as follows. Section 2 starts by deﬁning what we mean by inﬂation-

forecast targeting in this context and discusses the simple intuition behind it. In the ﬁnal

part of Section 2, we derive the policy rule implied by inﬂation-forecast targeting and discuss

some model-independent features of such a rule. Section 3 introduces open-economy elements by

considering a model in the New Keynesian, open-economy model. Section 4 ﬁrst discusses issues

of rational expectations determinacy and the so-called Taylor principle with respect to inﬂation-

forecast targeting within the model and then goes on to discuss its stabilizing properties. Finally,

3See Bank of England (1999).

3

Section 5 concludes.

2. Inﬂation-forecast targeting

Goodhart (1999) suggests that the instrument should be adjusted so as to stabilize the forecast

of inﬂation at some appropriate horizon at the target level. Formally, such a policy target can

be denoted by

¯

πt+h|t = π∗,

(1)

where h is the inﬂation-forecast targeting horizon; ¯

πt+h|t is the central bank’s forecast of the

four-quarter inﬂation rate at time t + h made at time t; and π∗ is the inﬂation target level. If h

is set equal to the shortest lag at which the instrument of the central bank aﬀects inﬂation (the

inﬂation control lag), (1) is equivalent to strict inﬂation targeting, in Svensson’s terminology,

as this policy would imply a use of the instrument that would minimize the variance of inﬂation

(and inﬂation only) around the target level. If, however, h is a number greater than the length of

the inﬂation control lag, equation (1) does not fully determine policy. There is then an inﬁnity

of instrument paths that are consistent with this formulation. For concreteness, assume that

the forecast-targeting horizon is three periods and the inﬂation control lag is two, and that the

prevailing inﬂation rate is above target. The policymaker can now either choose to follow a lax

policy in the ﬁrst period and a more contractionary policy in the second period or do this in

the reverse order; in either case the target can be reached at the speciﬁed horizon.

In order to pin down policy, we need to place additional restrictions on policy. One common

restriction is that the interest rate is constant within the forecast-targeting horizon. Let a policy

of setting the instrument so as to have the constant-interest-rate forecast of inﬂation at a given

horizon on target be denoted by

¯

πt+h|t(i) = π∗,

(2)

where policy is well-deﬁned in a mathematical sense. The interest rate is now set at the rate

which, on the assumption that it is kept constant throughout the forecast-targeting horizon,

will ensure that the inﬂation forecast is on target. If the forecast of inﬂation at the forecast-

targeting horizon is not on target given the prevailing interest rate level, the interest rate is

exactly adjusted to correct for this.4 This is the deﬁnition of inﬂation-forecast targeting used

in this paper.5

4Smets (2000) discusses a similar targeting procedure, where the central bank minimizes a loss function subject

to inﬂation being back on target within a speciﬁed time.

5Our deﬁnition of (simple) inﬂation-forecast targeting is distinct from optimal inﬂation-forecast targeting,

as pointed out in footnote 3. Simple and optimal inﬂation-forecast targeting will, however, coincide when the

forecast-targeting horizon is equal to the inﬂation control lag and inﬂation is the only argument in the loss

4

Several central banks provide constant-interest-rate projections of inﬂation in their inﬂation

reports and discuss their policy stance in relation to these projections. The reason is that these

projections show the most likely outcome of inﬂation if the policy stance is kept unchanged,

thereby providing a helpful benchmark to guide the policy assessment (See, e.g. Bank of England,

2001, p.58). Some researchers have even claimed that inﬂation-forecast targeting comes very

close to describing the actual policy procedure at some central banks.6 Considering the intuitive

and simple appeal of inﬂation-forecast targeting, together with the claimed empricial relevance,

make it altogether an interesting strategy to analyze.

2.1. Time inconsistency, inﬂation dynamics and credibility

It is important to note that forecast targeting does not necessarily imply that inﬂation will be

back on target at the end of the h-period forecast-targeting horizon, if h is a number greater

than the shortest lag at which the monetary policy instrument aﬀects inﬂation. Under forecast

targeting, the chosen interest rate will attain the inﬂation target (in expectations) provided

that the interest rate is kept constant within the forecast-targeting horizon. If the central bank,

however, follows inﬂation-forecast targeting also in subsequent periods, the condition of interest

rate constancy will in general not be valid. The reason for this is that as time passes, the end

of the forecast-targeting horizon moves forward and the relevant forecast changes which may

necessitate a change in the interest rate. For these reasons inﬂation-forecast targeting is time

inconsistent. This time inconsistency will, however, disappear if the forecast-targeting horizon

exceeds the inﬂation control lag. Time inconsistency implies that the forecast-targeting horizon

is not equal to the expected time at which inﬂation will have returned to its target level.7

This form of time inconsistency may not be as harmless as it may seem at ﬁrst sight.

As a constant-interest-rate inﬂation forecast potentially deviates considerably from the rational

expectations path, it may contain limited information for agents who strive to base their nominal

contracts on the most likely future development of inﬂation. For agents who do not understand

the time-inconsistency implications of inﬂation-forecast targeting, the updating of policy each

period which creates the “postponement” of the time at which inﬂation should attain its target

function.

6Goodhart (2000), former member of the UK Monetary Policy Committee, states: “When I was a member of

the MPC I thought that I was trying, at each forecast round, to set the level of interest rates, on each occasion,

so that without the need for future rate changes prospective inﬂation would on average equal the target at the

policy horizon. That was, I thought, what the exercise was supposed to be.” Svensson (2001) asks whether “[it

is] possible to provide more optimal, but still operational, targeting rules than the Bank of Englands and the

Riksbanks ‘the constant-interest-rate inﬂation forecast about two years ahead should equal the inﬂation target?’

”. 7It should be noted that the forecast-targeting horizon, as deﬁned in this paper, is distinct from the forecast-

feedback horizon, as discussed in Batini and Nelson (2001). The latter concept refers to the forecast-lead of

inﬂation when used as an argument in an interest rate reaction function.

5

level, may be interpreted as the central bank not being fully committed to its stated inﬂation

target. Such beliefs would possibly induce a loss of credibility for the central bank and be a

problem for reasons outlined in Svensson (1999a). If private agents do not believe inﬂation

will quickly stabilize around the announced inﬂation target, the informational content of the

target is reduced and agents will undertake the costs of forming expectations based upon other

indicators with larger informational content. This may reduce the central bank’s ability to

stabilize inﬂation without causing large output movements, i.e., increase the sacriﬁce ratio.

In order to understand what inﬂation dynamics inﬂation-forecast targeting may induce,

it is useful to study some stylized examples. Figure 1 shows three possible developments of

inﬂation under two-period inﬂation-forecast targeting within diﬀerent model settings where the

interest rate aﬀects inﬂation with a one-period lag. The solid line in each panel shows the

expected evolution of the inﬂation rate after a shock to inﬂation. The dashed lines show the

constant-interest-rate forecasts made in each period for two and three periods ahead. Note that

the two-period forecasts are on target, while the three-period forecasts in general deviate from

the target value. The constant-interest-rate forecasts coincide with the expected development

during the ﬁrst period, but then deviate as policy is updated to conform to the new forecast

horizon.

Panel A illustrates a state of the economy and a model in which the three-period inﬂation

forecast undershoots the target level. As time passes, and assuming no new information arrives,

the previous three-period forecast becomes the two-period forecast at the prevailing interest

rate, and due to the undershooting, the interest rate is lowered accordingly. In this situation,

forecast-targeting induces a monotonic convergence of inﬂation toward the target level. In the

situation illustrated by Panel B, the three-period inﬂation forecast overshoots the target level.

As time passes, the overshooting requires a tightening of monetary policy and the interest

rate is raised accordingly, causing a further decline in the inﬂation rate. Inﬂation converges

non-monotonically toward the target level, but monetary policy does cause inﬂation to deviate

persistently from the target level. Panel C shows that forecast-targeting may induce oscillations

in the inﬂation process. If the model implies that the assumption of a constant interest rate

induces the two-period and three-period forecasts to move in the opposite directions, inﬂation-

forecast targeting may produce erratic movements in the interest rate and hence possibly in the

inﬂation rate.

Although the intuition behind forecast targeting may be quite seductive, these simple ex-

amples show that time-inconsistency makes this intuition somewhat deceptive. This intensiﬁes

the need for analyzing inﬂation-forecast targeting in models we have conﬁdence in, as most of

6

P a n e l A

M o n o t o n i c c o n v e r g i n g p r o c e s s

P a n e l B

O v e r - o r u n d e r s h o o t i n g c o n v e r g i n g p r o c e s s

P a n e l C

O s c i l l a t i n g c o n v e r g i n g p r o c e s s

Figure 1

Constant-interest-rate forecast targeting illustration.

its properties are likely to be highly model dependent.

2.2. Deriving the policy implications

An inﬂation-forecast targeting central bank is concerned with choosing an interest rate each

period that minimizes its loss function given by

L

1

t =

θ ¯π

2

t+h|t i − π∗ 2 + (1 − θ) yt+h|t(i) − y∗ 2 ,

(3)

where ¯

πt+h|t i and yt+h|t(i) are the constant-interest-rate forecasts of four-quarter inﬂation

and output respectively, and y∗ is the output target, assumed to be equal to the natural rate.

For the remainder of the paper, the inﬂation target (π∗) and the natural rate (y∗) are both

normalized to zero. According to (3), the central bank is concerned about both having the

7

forecast of inﬂation close to its target and the forecast of output not deviating too far from

its natural rate. θ ∈ [.5, 1] is a parameter reﬂecting the central bank preference for inﬂation

forecast stabilization relative to output stabilization.8 A lower value reﬂects a central bank that

is relatively more concerned about stabilizing the output forecast, denoted a ﬂexible inﬂation-

forecast targeter. The ﬁrst order condition of (3) is

∂¯π

∂y

θ

t+h|t i

t+h|t(i) y

∂i

¯

πt+h|t i + (1 − θ)

∂i

t+h|t(i) = 0.

(4)

According to (4), the central bank targets a weighted average of the inﬂation and output

forecasts. The weights are partly determined by the preferences of the central bank, but also by

the policy multipliers, i.e. the eﬀect a change in the interest rate has on the respective forecasts.

An inﬂation-forecast targeting central bank with preferences for output forecast targeting, i.e.

θ < 1, accepts over- or undershooting of the target in accordance with the distance of the

forecast of output from the natural rate. This can easily be seen by rearranging (4) as

∂yt+h|t(i)

¯

π

∂i

t+h|t i = − (1 − θ)

y

θ

∂¯π

t+h|t(i),

(5)

t+h|t(i)

∂i

which implies a conditional inﬂation target. If the output forecast is well below the natural

rate, the inﬂation target rises above its normal rate, e.g. to the upper level of the target band.

Equation (2) is equivalent to equation (5) when θ = 1, that is, under strict inﬂation-forecast

targeting.

In order to derive the policy implications, i.e. the interest rate reaction function, under this

procedure, consider a general backward-looking model in state space form

Xt+1 = AXt + Bit + t+1,

(6)

where X is a vector of state variables; i is the policy instrument, i.e. the short nominal interest

rate within this framework, and

is a vector of disturbance terms with zero expectations and

ﬁnite variance. A is the transition matrix of the model and B is the vector of parameters

describing the direct eﬀects of the interest rate. By subsequent substitutions, the h-period-

8It seems appropriate to restrict θ downwards to a value of .5, as a smaller number would be more in line with

output-forecast targeting than inﬂation-forecast targeting.

8

ahead forecast is written as

h−1

Xt+h|t = AhXt +

AjBit+h−1−j|t,

(7)

j=0

where the forecast of the state variables is a function of the state of the economy at the time

of the forecast, the policy assumptions in the forecast period and the economic model being

analyzed. Under the assumption that the interest rate is kept constant in the forecast period,

it+j|t(¯ı) = it for h > j ≥ 0, we can write the constant-interest-rate forecast of the state variables

as

h−1

Xt+h|t(¯ı) = AhXt +

AjBit.

(8)

j=0

We may also write the target variables as functions of the state variables

¯

πt = KπXt,

yt = KyXt,

where Kπ and Ky are vectors that relate inﬂation and output to the state vector.

Correspondingly, the constant-interest-rate forecasts of the target variables are then given

by ¯

πt+h|t i = KπXt+h|t(i) and yt+h|t(i) = KyXt+h|t(i). Using (2.5) we can write these forecasts

as functions of the interest rate and the current state,

h−1

¯

πt+h|t i = KπAhXt + Kπ

AjBit,

j=0

h−1

yt+h|t(i) = KyAhXt + Ky

AjBit,

j=0

where the policy multipliers associated with the inﬂation and output forecasts are

∂¯π

h−1

t+h|t i

AjB,

∂i

= Kπ

j=0

∂y

h−1

t+h|t(i)

AjB.

∂i

= Ky

j=0

9

Substituting the expressions for the forecasts and the policy multipliers into (4) gives

h−1

h−1

h−1

h−1

θKπ

AjB KπAhXt + Kπ

AjBit + (1 − θ)Ky

AjB KyAhXt + Ky

AjBit = 0,

j=0

j=0

j=0

j=0

which may be expressed in terms of the interest rate as

i

Ω

t

=

AhXt,

(9)

Ω

h−1

j=0 AjB

= FcirXt,

where Ω =

−θK

h−1

h−1

π

j=0 AjBKπ + (1 − θ)Ky

j=0 AjBKy . Equation (9) denotes the CIR

targeting central bank’s reaction function and yields the following proposition.

Proposition 1

Given that A is positive semi-deﬁnite and has eigenvalues within the unit circle, extending the

length of the forecast-targeting horizon reduces the absolute value of the coeﬃcients in the

reaction function (9).

There are two independent eﬀects that produce this outcome. The ﬁrst, which refers to

h−1

j=0 AjB in the denominator of (9), is the eﬀect of the interest rate level on the forecast when

extending the inﬂation-forecast targeting horizon. A given constant interest rate level is more

eﬀective in inﬂuencing the determinants of the forecasts if it remains in place for a longer period

of time. Thus, the reaction to the underlying determinants does not have to be as strong as

under a shorter forecast-targeting horizon. The second eﬀect refers to the inherent properties

of the forecasting model and its transition matrix, A. If A is ‘stable’, that is, has all eigenvalues

within the unit circle,9 the state variables in the model will approach their equilibrium values

even without any response from policy since Ah → 0 as h → ∞. In the case of a long forecast-

targeting horizon, the inﬂation targeting central bank will exploit these eﬀects to a greater

degree than a central bank with a shorter horizon. The result is less need for monetary policy

to respond to disequilibrium conditions, but rather instead satisfy the equilibrium conditions

for having inﬂation equal the target level.

9For an important class of models, this conditions will fail to hold. If the backward-looking model includes

an accellerationist Phillips curve, there is a unit root in the A matrix, and the model is not self-stabilizing with

respect to the inﬂation rate. The ﬁrst eﬀect will still ensure that a long forecast-targeting horizon will imply

more interest rate stability.

10