Inflation targeting (part 2)
The Regime III (inflation targeting) system of equations:
Lecture 15: Macro dynamics of the open
f
yt = β0 + β1ert − β2rt + β3gt + β4yt
e
rt = it − πt+1
economy (cont)
f
πt − πt + ert−1
πt = πte + γ(yt − ȳ) + st
f
it = it + ee + αe(∆et + et−1) αe < 0
f
it = it + h(πt − π̄ f )
Ragnar Nymoen
Department of Economics, University of Oslo
mt − pt = m0 − m1it + m2yt, mi > 0, i = 1, 2
(1)
(2)
(3)
(4)
(5)
(6)
Note αe = −θ in IAM.
May 9, 2006
mt is endogenous in the short-run model. Together with yt
1
2
The short-run analysis (R-III, inflation targeting)
hence the model becomes
½
¾
1
f
f ) − ee) − e
r
yt = β0 + β1
(h(π
−
π̄
+
π
−
π
+
e
t
t
t−1
t−1
t
αe
n
o
f
f
− β2 it + h(πt − π̄ f ) − π̄ f + β3gt + β4yt
From (4):
∆et =
1
f
(it − it − ee) − et−1
αe
and
substitution of it from (5)
−1 f
1 f
∆et = e (it + ee) − et−1 + e (it + h(πt − π̄ f ))
α
α
1
= e (h(πt − π̄ f ) − ee) − et−1
α
We therefore obtain the short-run AD schedule from
½
¾
1
f
f ) − ee) − e
r
yt = β0 + β1
(h(π
−
π̄
+
π
−
π
+
e
t
t
t−1
t−1
t
αe
n
o
f
f
f
e
− β2 it + h(πt − π̄ ) − πt+1 + β3gt + β4yt
We adopt IAM’s assumptions about inflation expectations:
(9)
πt = π̄ f + γ(yt − ȳ) + st
(10)
Differentiate (9) to obtain the slope of the R-III short-run AD-curve:
(7)
(8)
¯
∂πt ¯¯
−1
=
<0
¯
β1
∂yt ¯AD,rIII
β1 + h(β2 − α
e)
consistent with β̂1in eq. (15) on page 776 in IAM.
¯
¯
∂πt ¯¯
∂πt ¯¯
−
>−
, when αe < 0
¯
¯
∂yt ¯AD,rV I
∂yt ¯AD,rIII
e
πt+1
= πte = π ∗ = π̄ f
hence the short-run AD schedule is flatter in R-III (inflation targeting) than in
R-VI.
3
4
Interpretation of slope-difference
inflation
The interpretation of the difference has to do with how the interest rate is
determined in the two regimes: When πt increases, y-demand is reduced in
both regimes through the real exchange rate, er . But there are additional
effects in R-III: The interest rate is increased (monetary policy response) which
leads to further reduction in yt.
f
R-III
Hence regime III is different from the fixed exchange rate VI, but also from the
floating exchange rate regime I (money as the target) where lower demand for
money reduces the interest rate in the domestic money market.
R-VI
R-I
y
y
We have generalized figure 25.3: AD(flex) represent only one sub-category of
floating exchange rate regimes.
6
5
Short-run effect of a supply-shock
Long-run effects of a supply-shock
Consider a positive aggregate supply shock in period t = 1, s1 < 0 (s0 = 0)
If the reduction in s is temporary: no long run effects. π − π̄ f = 0 from AS
(the Phillips curve). Then er = er0 from definition of real-exchange rate.
The impact multipliers:
GDP: largest for R-III, smallest for R-I.
Inflation: Largest reduction for R-I, smallest reduction for R-III.
The fixed exchange rate regime (R-VI) is an intermediate case.
If h → ∞ R-III multipliers approach R-VI multipliers (not R-I).
7
If a permanent reduction of s, then π − π̄ f = s1 < 0 from the AS. In this case
e
the assumption of: πt+1
= πte = π ∗ = π̄ f is no longer meaningful. Replace by
e
e
f
πt+1 = πt = π̄ + s1 for example? Might mean a higher long-run real interest
e ) in which case er would need to be increased.
rate (since r = it − πt+1
ȳ = β0 + β1er − β2r + β3g + β4y f
Not clear whether this can be reconciled with the assumed constant inflation
target.
8
Short-run effects of a demand shock
However, note that for a given π:
¯
dyt ¯¯
= β3
¯
dgt ¯πt=π̄,rIII
Use fiscal policy again to represent a demand shock.
We already know that R-I and R-VI can be compared by (identical) vertical
shifts of the AD curve:
However, from (9)
¯
¯
dπt ¯¯
dπt ¯¯
β
=
= 3>0
¯
¯
dgt ¯yt=ȳ,rI
dgt ¯yt=ȳ,rI
β1
½
1
f
yt = β0 + β1
(h(πt − π̄ f ) − ee) − et−1 + πt − πt + ert−1
e
α
n
o
f
f
− β2 it + h(πt − π̄ f ) − π̄ f + β3gt + β4yt
we see that
¾
¯
dπt ¯¯
β3
=
¯
β1
dgt ¯yt=ȳ,rIII
β1 + h(β2 − α
e)
so (unless the trivial case of h = 0) a vertical shift are not comparable (IAM p
782)
since there are no indirect demand side effects of a change in y in this regime
(yt is not included in the policy response function). The same is true in R-VI
where the interest rate is determined on the FEX marked. Hence, from
n
f
yt = β0 + β1 πt − πt + ert−1
n
f
o
o
f
e
− β2 it + ee + αe(∆et + et−1) − πt+1
+ β3gt + β4yt
we have
¯
dπt ¯¯
= β3
¯
dgt ¯πt=π̄,rV I
hence, we can make a comparison of regime III and VI with the aid of a
horizontal shift of the AD schedule.
See IAM p 782 for the algebraic analysis.
10
9
Operational inflation targeting (Case of Norway)
The impact multipliers (of a change in gt):
Charateristics of the regime
GDP: larger for R-VI than for R-III.
1. A floating exchange rate regime
Inflation: larger for R-VI than for R-III.
2. The target of monetary policy is low and stable inflation
Hence there is no clear cut answer to which monetary policy regime give most
automatic stabilization to shocks.
Relative frequency of demand and supply shocks is one aspect.
This theme is developed further in IAM ch 26.1-26.2, in different directions,
which we leave for self-study.
3. The operational target is the forecasted rate of inflation (1, 2 or 3 years
ahead)
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
11
12
(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
(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.
A premise is of course the interest rate has an effect on the rate of inflation.
What does the evidence say?
Consider the Norwegian Aggregate Model for example.
6. Inflation targeting is flexible when the target horizon is long, so that interest
rate adjustments can be gradual.
13
14
Deviation
INF
WINF
.000
.000
-.001
-.001
-.002
-.002
-.003
-.003
-.004
-.004
-.005
-.005
The implications from this set of multipliers are:
PBGR
.000
-.002
-.004
-.006
1. The interest rate affects inflation through a complicated causal chain.
-.008
1998
1999
2000
2001
2002
2003
-.010
-.012
1998
1999
LOGCPIVAL
2000
2001
2002
2003
1998
1999
2000
LOGCREX
.00
2001
2002
2003
RL
.00
.011
2. Small and temporary interest rate changes will work no wonders for the
rate of inflation
.010
-.01
-.01
.009
-.02
-.02
.008
-.03
.007
-.03
-.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
2001
2002
2003
UR2
.000
3. The most lasting, and over time strongest, influece is through demand.
.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
2002
2003
Figure 1: The response to a permanent increase in the money market interest
rate by 1 percentage point. Interim multipliers of Norwegian Aggregate Model,
together with 95% confidence intervals
15(marked by dashed lines).
4. Flip of the coin of 3. is that i adjusments are best suited to offset demand
shocks. Large supply shocks represent a challenge.
16
Inflation forecasting and targeting
Inflation targeting: the operational target variable is the forecasted rate of
inflation, π̂T +H|T .
Interest rate set so that it bring the forecasted inflation rate in line with target,
π∗
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.
17
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.
19
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.
However an assumption of model correctness is not a practical basis for economic forecasting, as proven by the high incidence of forecasts failures.
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.
18
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.
20
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.
21
22
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,
(11)
−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
(12)
2
π̂T +2|T = δ(1 + α) + α πT + αβ1iT +1|T + αβ2iT |T + β1iT +2|T + β2iT +1|T
(13)
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
−μ + α2(μ − πT ) + π ∗
iT +2|T =
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.
23
24
(14)
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.
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.
25
j = 1, 2, ...H, 0 ≤ γ < 1
which gives
o
γ2 n
−μ + α2(μ − πT ) + π ∗
Bn
o
γ
iT +1|T =
−μ + α2(μ − πT ) + π ∗
(15)
B
n
o
1
iT +2|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 |T =
26
Norges Bank’s recent inflation forecasts
Inflation forecasts are published in the bank’s inflation reports, IRs.
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.
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.
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.
27
28
0.030
0.025
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 2.
29
Inflation
0.020
0.015
IR 1/02
IR 1/04
IR 1/05
IR 1/03
0.010
0.005
2002
2003
2004
2005
2006
2007
Figure 2: 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
30
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
0.04
IR 1/02
IR 2/02
0.04
forecast
forecast
0.02
0.02
actual
actual
0.00
0.00
1. Norges Banks believes in low forecast uncertainty. High information content in forecast for the first couple of quarters.
2001
0.04
2002
2003
2004
2005
2006
2007
IR 3/02
2001
forecast
2002
2003
2004
2007
actual
0.00
2001
2002
IR 2/03
2003
2004
2005
2006
2007
0.04
2001
2002
2003
2004
2005
2006
2007
2006
2007
2006
2007
IR 3/03
0.04
forecast
forecast
0.02
0.02
actual
actual
0.00
0.00
2001
0.04
2006
forecast
0.02
actual
0.00
3. Forecast uncertainty is increased in IR 1/04. Reflects how calculated uncertainty is based on part errors. A sign of adaptation. But enough?
2005
IR 1/03
0.04
0.02
2. Maximum uncertainty is reached fast- Hence Norges Bank acknowledges
that there is a strict limit to the predictability of inflation?
2008
Time
2002
2003
2004
2005
2006
2007
IR 1/04
2001
0.04
2002
2005
forecast
0.02
0.00
0.00
2001
2004
actual
forecast
actual
0.02
2003
IR 2/04
2002
2003
2004
2005
2006
2007
2001
2002
2003
2004
2005
Figure 3: Norges Bank’s inflation forecasts, 90% confidence regions and the
actual rate of inflation.
31
32
6 of 8 graphs show clear evidence of forecast failure.
How avoidable was the forecast failure?
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.
33
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.
34
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.
35
36
0.04
AIR 1/02
0.04
0.02
0.02
0.00
0.00
2001
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.
0.04
2002
2003
2004
2005
AIR 3/02
2002
2003
2004
2005
AIR 2/03
0.02
2004
2005
2002
2003
2004
2005
2002
2003
2004
2005
2002
2003
2004
2005
AIR 3/03
0.02
0.00
2001
2002
2003
2004
2005
AIR 1/04
2001
2001
0.04
AIR 2/04
0.02
0.00
1. The confidence bands of the forecasts are wider in “IR 1/02”, both for the
one and eight quarter ahead forecasts.
2001
0.04
0.02
37
2003
0.00
2001
0.04
2002
AIR 1/03
0.02
0.00
0.00
The set of forecasting equations was estimated on a quarterly data set which
starts in 1981(1). Figure 4 shows the sequence of model forecasts.
2001
0.04
0.02
0.04
AIR 2/02
0.00
2002
2003
2004
2005
2001
Figure 4: 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
38are shown as bars.
CPI-ATE. Forecast confidence intervals
A subjective assessment
In the period 2001-2005 monetary policy in Norway has been hampered by
several problems and mistakes
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.
3. Since the second year actual inflation rates are within the corresponding
confidence bars, these outcomes do not represent forecast failure in Figure
4, while they do in the Norges Bank forecast.
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.
5. The next three panels in Figure 4 show an even more market difference
from the Norges Bank forecasts.
39
1. Overestimation of the effect of the interest rate on inflation (the interim
multipliers) by Norges Bank.
2. Underestimation of the period of adjustment and of the forecast uncertainty.
3. Very slow identification of the nature of the drop in the rate of inflation
that started in 2003 (relative weight on supply and demand factors, an on
domestic and foreign).
4. Exceptionally slow adaptation of the forecasts.
40
5. Interest rate decisions might have suffered.
Time will show if these are still only teething problems.
41