1
Characteristics of modern inflation targeting
See previous lectures on monetary policy, Part II (April 29 2005) in particular.
Theme 5: Macroeconomic policy.
Part 2: Monetary policy (IV)
1. A floating exchange rate regime
2. The target of monetary policy is low and stable inflation
3. The operational target is the forecasted rate of inflation (1, 2 or 3 years
ahead)
RNy
May 12, 2005
4. The instrument is the interest rate that the Central Bank sets as the loan
rate in the domestic short-term money market. The interest rates offered
to the public are higher but they are highly correlated with the CB’s sight
deposit rate (’foliorente’).
5. The CB’s interest rate setting is forward looking. There are two reasons
given
2
1
(a) Signaling, and building up of credibility: By acting on the macroeconomic prospects (in practice the CB’s own forecasts) rather than observed realities, monetary authority can signal a commitment to the
target of low and stable inflation. The CB hopes that this will influence inflation anticipations among households and firms, which will in
turn make goal achievement easier (Think of π̄ in the B&W Phillips
curve)
Deviation
INF
WINF
.000
.000
-.001
-.001
-.002
-.002
-.003
-.003
-.004
-.004
-.005
-.005
PBGR
.000
-.002
-.004
-.006
-.008
1998
1999
2000
2001
2002
2003
-.010
-.012
1998
1999
LOGCPIVAL
2000
2001
2002
2003
1998
1999
2000
LOGCREX
.00
2001
2002
2003
2001
2002
2003
2002
2003
RL
.00
.011
.010
-.01
-.01
.009
-.02
-.02
.008
-.03
.007
-.03
(b) The transmission mechanism is dynamic: For it takes time before a
change in the instrument affects the rate of inflation. Hence by acting
“now” the costs of achieving the target is less than by waiting until a
too high/low inflation rate becomes a reality.
-.04
.006
-.04
-.05
.005
-.05
-.06
1998
1999
2000
2001
2002
2003
.004
1998
1999
LOGCR
2000
2001
2002
2003
1998
1999
LOGYF
.01
2000
UR2
.000
.0032
.00
.0028
-.004
-.01
.0024
-.02
.0020
-.008
-.03
.0016
-.04
-.012
.0012
-.05
-.06
.0008
-.016
.0004
-.07
-.020
-.08
1998
1999
2000
2001
2002
2003
.0000
1998
1999
2000
2001
2002
2003
1998
1999
2000
2001
6. Inflation targeting is flexible when the target horizon is long, so that interest
rate adjustments can be gradual.
3
Figure 1: The response to a permanent increase in the money market interest
rate by 1 percentage point. Interim multipliers, together with 95% confidence
intervals (marked by dashed lines).
4
2
A model of inflation targeting
Inflation targeting: the operational target variable is the forecasted rate of
inflation, π̂T +h|T .
A favourable situation occurs when it can be asserted that the bank’s forecasting model is a reasonably correct representation of the true inflation process
of the economy. In this case, forecast uncertainty can be represented by conventional forecast confidence intervals, or by the fan-charts preferred by best
practice inflation targeters.
Interest rate set so that it bring the forecasted inflation rate in line with target,
π∗
However an assumption of model correctness is not a practical basis for economic forecasting, as proven by the high incidence of forecasts failures.
Flexibility: related to the length of the forecasting horizon, h (as well as of
other aspects of the “utility function”).
However, a inflation forecast is uncertain, and might induce wrong use of policy.
Hence, a broad set of issues related to inflation forecasting is of interest for
those concerned with the operation and assessment of monetary policy.
A characteristic of a forecast failure is that forecast errors turn out to be
larger, and more systematic, than what is allowed if the model is correct in
the first place. In other words, realizations which the forecasts depict as highly
unlikely (e.g., outside the confidence interval computed from the uncertainties
due to parameter estimation and lack of fit) have a tendency to materialize too
frequently.
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6
As stated: forecast properties are closely linked to the assumptions we make
about the forecasting situation. One possible classification, is:
A The forecast model coincides with actual inflation in the econometric sense.
The parameters of the model are known and true constants over the forecasting period.
B As under A, but the parameters have to be estimated.
C As under B, but we cannot expect the parameters to remain constant over
the forecasting period–structural changes are likely to occur somewhere
in the .system.
D We do not know how well the forecasting model corresponds to the inflation
mechanism in the forecast period.
A is a very idealized description of the assumptions of macroeconomic forecasting. Nevertheless, there is still the incumbency of inherent uncertainty–even
under A.
7
Situation B represents the situation most econometric textbooks conjures up,
The properties of situation A will still hold–even though the inherent uncertainty will increase. The theory of inflation targeting also seems stuck with
B.
In real life we of course do not know what kind of shocks that will hit the
economy, or the policy makers during, the forecasting period, which is the focus
of situation C. Structural breaks and regime changes are the most important
source of forecast failure.
Situation D finally leads us to a realistic situation, namely one of uncertainty
and professional discord regarding what kind of model best representing reality.
This opens up the whole field of model building as well as the controversies
regarding econometric specification, so we will leave that subject here.
8
A forecast failure effectively invalidates any claim about a “correct” forecasting
mechanism (Situation A or B).
Upon finding a forecast failure, the issue is whether the misspecification was
detectable or not, at the time of preparing the forecast.
Given that regime shifts occur frequently in economics, and since there is no
way of anticipating them, it is unavoidable that after forecast structural breaks
damage forecasts from time to time. The task is then to be able to detect the
nature of the regime shift as quickly as possible.
Hence in there is a premium on adaptation in the forecasting process, in order
to avoid sequences of forecast failure.
Relevance for inflation targeting?
Forecast quality per se becomes of interest in this policy regime.
The rate of inflation, being a nominal growth rate, is particularly susceptible to
forecast failure (shifts in means of nominal variables in particular are notorious).
If central bank’s do as they claim, and set interest rates to affect the inflation
forecast, then regime shifts will not only damage the inflation forecasts, but
will also interest rate setting.
But in which way (with what consequences) depends on the operational aspects
of inflation targeting.
Lack of adaptation will make the forecast susceptible also to before forecast
structural break leading to unnecessary forecast failure.
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10
As an illustration, suppose that the following reduced form model—derived from
a structural model (AD-AS for example)– is used for forecasting
πt = δ + απt−1 + β1it + β2it−1 + εt, t = 1, 2, 3..., T,
(1)
−1 < α < 1, β1 + β2 < 0,
πt is the rate of inflation, and it is the interest rate.
Suppose, for simplicity, that the central bank have chosen a 2 period horizon.
The forecasts are prepared conditional on period T information, so
π̂T +1|T = δ + απT + β1iT +1|T + β2iT |T
(2)
2
π̂T +2|T = δ(1 + α) + α πT + αβ1iT +1|T + αβ2iT |T + β1iT +2|T + β2iT +1|T
(3)
For simplicity, set iT +1|T and iT |T to some autonomous level, represented by
0 (hence let it be a deviation from its mean, the period 1 interest rate is equal
to the mean interest rate). Hence, the interest rate path in this case is
iT |T = 0
iT +1|T = 0
o
1 n
−(1 − α2)µ − α2πT + π ∗
iT +2|T =
β1
o
1 n
=
−µ + α2(µ − πT ) + π ∗
β1
where µ denotes the long run mean of inflation.
There are 2 degrees of freedom if the bank chooses to attain the target π ∗ in
period 2 (inflation targeting is flexible), and iT +1|T and/or iT |T can be set to
(help) attain other priorities.
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12
In a constant parameter world, this path will secure that πT +2|T is equal to π ∗
on average.
The Norwegian Central Bank, in particular, has announced that interest rate
changes, will as a rule be gradual. We can model this by setting:
iT +j−1|T = γiT +j|T ,
But if µ increases in period T + 1 and T + 2, i.e,, a regime shift, both π̂T +1|T
and π̂T +2|T will be too low, possibly representing a forecast failure.
j = 1, 2, ...h, 0 ≤ γ < 1
which gives
o
1n
−µ + α2(µ − πT ) + π ∗
Bn
o
γ
iT +1|T =
−µ + α2(µ − πT ) + π ∗
B
o
γ2 n
iT |T =
−µ + α2(µ − πT ) + π ∗
B
where B < 0 is function of α, β1, β2 and γ. With gradual interest rate adjustment, regime-shifts and forecast failures are more serious, since interest rates
today are affected.
iT +2|T =
However, only iT +2|T is affected by the forecast failure, and can replaced by
iT +2|T +1 in the next forecast round.
With a different operational procedure, designed to move π̂T +1|T “in the direction” of the target, iT |T may be contaminated by regime shifts in the transmission mechanism.
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14
µ = E[πt] is the long-run mean of πt. As the forecast horizon increases, the
conditional forecast converges to the marginal expectation:
δ
= E[πt], when H → ∞, − 1 < α < 1.
1−α
which is also the (asymptotic) steady state solution based on (1).
π̂T +h|T →
∆4 p
Start of sample for estimation of mean
0.10
0.05
(4)
This always holds, even though the forecast for the first period ahead is very
model dependent, the long run forecast is more “objective”.
1965
1970
1975
1980
1985
1990
1995
2000
0.050
mean ∆ 4 p
0.025
0.000
-0.025
1993
Clearly, since any conditional forecast converge to the long run mean of inflation, and hence the equilibrium rate of inflation, it is quite helpful for the
legitimacy of inflation targeting that this equilibrium value is not too far from
the target.
15
1994
1995
1996
1997
1998
1999
2000
2001
2002
20
Figure 2: Actual inflation rate in Norway for the period 1966(1)-2002(2). Estimation of the univariate model of the rate of inflation is based on a sample that
starts in 1984(1). The lower part of the figure shows the estimated marginal
expectation of the inflation rate, i.e., the equilibrium rate of inflation.
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3
Norges Bank’s recent inflation forecasts
Inflation forecasts are published in the bank’s inflation reports, IRs.
The details of the process leading up to the published forecast is unknown to
the outsider, but the bank’s beliefs about the transmission mechanism between
policy instrument and inflation, represents a main premise for the forecasts,
and secures consistency in the communication of the forecasts from one round
of forecasting to the next.
A main feature of BM is that the joint contribution of all interest rate channels
secures a sufficiently strong and quick transmission of interest rate changes on
to inflation to justify a 2 year policy horizon.
This view of the transmission mechanism has left its mark on the published
inflation forecasts, which typically revert to the target of 2.5% within a 2-year
forecast horizon.
But in the summer of 2004, this view was changed.
For simplicity, we refer to the systematized set of beliefs about the transmission
mechanism as the Bank Model–BM for short.
18
17
0.0225
There is a trade-off between the wish to provide useful forecast, and the wish
to avoid forecast failure.
Forecasts with high information content come with narrow uncertainty bands.
Conversely, the wider the uncertainty bands are, the less information about
future outcome is communicated by the forecast. A simple indication of the
information content of the inflation forecast is therefore to compare the width
of the uncertainty bands with the variability of inflation itself (measured by the
standard deviation over, say the last 5 or 10 years). If the forecast confidence
region is narrow compared to the historical variability, the central bank forecasts
can be said to have a high intended information value, see figure 3.
0.0175
IR 1/02
0.0125
IR 1/04
IR 1/03
0.0075
0.0025
2002
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2003
2004
2005
2006
Figure 3: Uncertainty measures of Norges Bank’s inflation forecasts in Inflation
Reports 1/02, 1/03 and 1/04. The lines show the width of the the approximate
90% confidence region (the difference between the upper and lower 90% band
20
in the fan-charts), for the 12 month growth
rate of CPI-ATE.
Source: Internet versions of Inflation Reports 1/02 1/03 and 1/04
IR 1/02
IR 2/02
0.04
0.03
0.03
forecast
0.02
0.02
0.01
1. Norges Banks believes in low forecast uncertainty. High information content in forecast for the first couple of quarters.
0.01
actual
2001
2002
2003
2004
2005
2006
2007
2001
0.03
0.02
0.02
2003
2004
2005
2006
2007
2003
2004
2005
2006
2007
2003
2004
2005
2006
2007
0.01
0.01
2. Maximum uncertainty is reached fast- Hence Norges Bank acknowledges
that there is a strict limit to the predictability of inflation?
2002
IR 1/03
IR 3/02
0.03
2001
2002
2003
2004
2005
2006
2007
IR 2/03
2001
0.03
2002
IR 3/03
0.03
0.02
0.02
0.01
0.01
0.00
2001
3. Forecast uncertainty is increased in IR 1/04. Reflects how calculated uncertainty is based on part errors. A sign of adaptation. But enough?
2002
2003
2004
2005
2006
2007
2003
2004
2005
2006
2007
2001
2002
IR 1/04
0.04
0.03
0.02
0.01
0.00
2001
2002
Figure 4: Norges Bank’s inflation forecasts, 90% confidence regions and the
actual rate of inflation.
21
6 of 7 graphs show evidence of forecast failure.
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4
Econometric inflation forecasts
In the IR 2/02 forecasts the first four inflation outcomes are covered by the forecast confidence interval, but the continued fall in inflation in 2003 constitutes
a forecast failure.
As pointed out, poor forecasts due to after forecast structural breaks are unavoidable in economics.
Specifically, the forecast confidence interval of IR 3/03 doesn’t even cover the
actual inflation in the first forecast period.
Given that fact, there is a premium on having a robust and adaptable forecasting
process.
The 7th panel shows that the forecasted zero rate of inflation for 2004(1) in IR
1/04 turned out to be accurate. The forecasts have been substantially revised
from IR 3/04. Whether this will prove enough to end the sequence of poor
forecasts, remains to be seen.
Allowing relevant historical shocks to be reflected in forecast uncertainty calculations contributes to robustness in the forecasts, avoid too narrow forecast
confidence intervals.
The next section contains an evaluation by way of presenting ex post forecasts
based on information which were available to the forecasters at the time of
preparing the IR forecasts.
23
This may have some relevance for the recent forecasts, since the low and stable
inflation rates of the late 1990s may have lead some forecasters to down-play
uncertainty.
24
The forecast failures also give rise to the question whether the sequence of
poor forecasts was avoidable at the time of preparing the forecasts.
This is a complex issue which needs to be analyzed from several angles.
Yet, as any nominal variable, inflation mat be subject to frequent changes in
mean, exactly the type of shocks that will damage forecasts.
Adaptable forecasting mechanisms have the ability to adjust the forecasts when
a structural change is in the making, or at the latest, when a forecast failure
has manifested itself.
Here we follow an on-looker’s approach, and set up a forecasting mechanism
which features at least two elements which logically must be present in the
forecasting process in the bank:
1. All explanatory variables of inflation are themselves forecasted. Hence, our
ex-post forecasts do not condition on variables that could not have been
known also to the forecasters at the time of preparing the different inflation
reports.
2. Just like in a practical forecasting situation, the forecasts are updated:
model parameters are re-estimated as new periods are included in the historical sample, and, more importantly for the forecasts themselves, the
initial conditions are changed as we move forward in time.
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26
0.050
"IR 1/02"
"IR 2/02"
0.050
forecast
0.025
0.025
actual
0.000
0.000
Note that in our ex post forecasts, the up-dating of the forecasts is automatized.
In real life forecasting, the revision of the forecasts from one inflation report
to the next is done by experts. In comparison, our econometric forecasts are
naive. In general, naive econometric forecasts are not particularly adaptive, but
are prone to failures themselves.
2001
2002
2003
2004
2002
2003
2004
2002
2003
2004
2002
2003
2004
"IR 1/03"
0.04
0.02
0.02
0.00
0.00
2001
0.03
2002
2003
2004
2001
"IR 2/03"
"IR 3/03"
0.02
0.02
0.01
0.01
0.00
0.00
The set of forecasting equations was estimated on a quarterly data set which
starts in 1981(1). Figure 5 shows the sequence of model forecasts.
2001
"IR 3/02"
2001
0.02
2002
2003
2004
2002
2003
2004
2001
"IR 1/04"
0.01
0.00
2001
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Figure 5: Dynamic forecasts from an econometric model of inflation, where we
have emulated the (real time) forecast situation of the Norges Bank inflation
forecasts. The forecasted variable is the annual change in the logarithm of the
28are shown as bars.
CPI-ATE. Forecast confidence intervals
1. The confidence bands of the forecasts are wider in “IR 1/02”, both for the
one and eight quarter ahead forecasts.
5
2. Even though the second year forecasts in “IR 1/02” show too high inflation,
there is in fact a forecasted weak tendency towards lower inflation in 2003.
Although the comparison between the official and the econometric forecasts is
informal, the conclusion that presents itself is that the bank’s recent forecast
failure was to some extent avoidable.
3. Since the second year actual inflation rates are within the corresponding
confidence bars, these outcomes do not represent forecast failure in Figure
5, while they do in the Norges Bank forecast.
The forecasts of the econometric model are more robust, and show more adaptability to shocks than is the case of the recent official forecasts.
Discussion
5. The next three panels in Figure 5 show an even more market difference
from the Norges Bank forecasts.
Robustness comes in a form of confidence regions that are wide compared to
the IRs fan-charts. Being of a very simple forecasting system, and since no
judgement has been applied, the forecast confidence intervals of the econometric forecasts are probably too wide. This justifies the practice of shrinking
the forecast confidence region somewhat, and thus increase the information
content of the forecasts. However, care must be taken in order to avoid too
narrow bands which will create an illusion of high precision of the forecasts.
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30
4. In the panel, labeled “IR 3/02”, the impact of conditioning on 2002(2)
shows up in narrower confidence bands for 2003, which in fact almost
makes the realized inflation rate in 2003(4) a forecast failure.
A near to hand recommendation for improving the bank’s forecast performance,
is to anchor the fan-charts in an econometric model, and then account for the
amount of user-determined shrinkage of forecast uncertainty in the published
forecasts.
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