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Open-Economy Inflation-Forecast Targeting

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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 Ta ylorprinciple, as a sufficiently long horizon may not providea adequately strong interest rate response to the determinants of future inflation. Along horizon causes the short-term real interest rate and the exchange rate to fluctuate persistently, producing inflation and especially traded sector output volatility.
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Open-Economy Inflation-Forecast Targeting∗
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

t
=
AhXt,
(9)

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

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