1
Modern monetary policy: flexible exchange rate
targeting or inflation rate targeting.
Theme 5: Macroeconomic policy.
Part 2: Monetary policy, continued
As we have seen, increasing degree of capital mobility reduces the scope for
monetary policy in a fixed exchange rate regime. Highlighted by B&W use of
the term “impossible trilogy”.
At the same time, many governments experienced reduced fiscal independence.
Ragnar Nymoen
University of Oslo, Department of Economics
May 7, 2004
Other developments have also (as we have seen) reduced the belief in fiscal
policy.
Two (opposite) responses to this:
• Adopt floating exchange rate, in order to re-install monetary policy independence
• Adopt a so called “hard peg” to do away with all monetary policy.
2
1
1.1
Target choice: Consequence for output stability (OEM Ch
10.1)
Hard pegs:
— Monetary union;
— Adopt another countries currency, a currency board is an example of
formal arrangement of this type.
In the following, we discuss the choice of floating exchange rate with the whole
range of “fixed exchange rate regimes”, from hard pegs to flexible exchange
rate regimes with target zones.
A main issue is how a specific choice of monetary target affects the strive to
reach the ultimate targets of economic policy, for example output stabilization
(at a high level of employment).
In modern monetary policy the choice is between a price level or inflation target
(the two be not have very different in practical in times of moderate inflation,
see below) and a fixed exchange rate.
A first analysis of can be done is the AS/AD diagram, and the conclusions are:
• A price stability target, allowing the exchange rate to float freely, reduces
the impact of demand shocks
• An exchange rate stability target reduces the impact of supply side shock.
[Graph.]
3
4
A positive demand shock leads to i % and σ % in the case of a clean float.
Both effects reduce the expansionary effect relative to the fixed exchange rate
regime. Hence, even if a short run rise in π above the target is tolerated (flexible
inflation targeting, see below) the effect on Y is less with a price/inflation target
than with an exchange rate target.
A negative supply shock has a larger effect on Y with a fixed than with a
floating exchange rate. However, if there is a strict inflation target, then the
ADfloat curve contracts so much that the decline in Y is larger than in the
fixed exchange rate case.
The analysis shows that the choice of target/instrument presumes an analysis
of which shock is the important or typical one. Answer is likely to depend
on structure of the economy, whether it is in line with, or out of step with,
international business cycles etc.
However also conceivable that the reaction function, i.e., how the central bank
uses its instrument to attain its target, should depend on a wider analysis, and
on several variables, not only on the observed or forecasted deviation from a
single target.
Example: Suppose wage claims of are because of high electricity prices (living
costs). Increase interest rates despite loss of competitiveness in exposed sector?
5
1.2
6
FIX
FLOAT
Hard pegs
Strict monetary targets
Low target
Narrow band
Short horizon
Simple reaction function
Strict vs flexibile monetary policy
STRICT
Modern monetary policy can be characterized along several other dimensions
than the fix vs float distinction:
examples:
Monetary union
Currency board
• How simple/complex is the reaction function?
• How ambitious is the (central) target?
FLEXIBLE
• Is there a target zone? How wide is it?
“flexible fixed”
Wide target zone (> 4%)
Allow E outside zone
Reaction function:
- contingent
- multivariate
flexible inflation targeting
Wide band
π-forecast is target
2 − 3 year horizon
Reaction function
-multivariate
Table 2: A typology of monetary policy regimes
Depending on answer, monetary policy is more or less strict/flexible.
7
8
2
Flexible exchange rate targeting
[Graph, adapted from OEM].
Attributes
1. Wide target zone (> 4%)
2. Allow exchange rate E outside zone
3. Reaction function:
One motivation for a wide target zone is to “engineer” uncertainty about depreciation/appreciation within the zone. Conversely, if E changes too little and
too seldom, then the expected rate of depreciation may become uniformly zero
with the result that UIP holds with i = i∗. A wide target zone, if successful,
in a way serves the same purpose as a Tobin tax: it creates some room for
monetary policy manoeuvre, in spite of capital market deregulation.
Point of discussion: Many central banks intervene inside zone–hope to avoid
to rise the interest of “new investors”?
- contingent
- multivariate
Focus on domestic real economy when E inside zone. When outside priority
to E-target.
Instrument mix: Use reserves when E hits boundaries. Use interest rate when
outside. But then may need to build credibility slowly, not overnight.
Speculation: When is the degree of capital mobility highest, inside or outside
the target-zone?
This regime probably not an option for countries with high system risk.
10
9
Inflasjonsendring
3
Flexible inflation targeting
The defining dimension of flexibility in this case is forward looking interest rate
setting. The longer time horizon, the more flexible is interest rate targeting.
Appresiering av valutakurs
.0000
.000
-.0005
-.004
-.0010
-.008
-.0015
-.012
-.0020
-.016
-.0025
-.020
-.0030
-.024
0
5
10
15
20
25
0
5
Vekstrate i fastlandsBNP
In real economies, the first dynamic multipliers of inflation with the respect to
the rate of interest are low. Hence, with a short horizon, a certain change in π
can only be achieved with large interest rate movements.
15
20
25
.000
20
25
.004
-.001
.003
-.002
-.003
.002
-.004
.001
-.005
A longer time horizon allows instrument use to be based on to the larger interim
multipliers.
10
Endring i ledighetsrate
-.006
.000
-.007
-.001
-.008
0
5
10
15
20
25
0
5
10
15
The multipliers are necessary based on a model of the transmission mechanism
Figure 1: Norway: empirical multipliers of 1 pp interest rate increase on annual rate of inflation, nominal exchange rate, GDP growth rate, and rate of
unemployment.
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12
3.1
A is a very idealized description of the assumptions of macroeconomic forecasting. Nevertheless, there is still the incumbency of inherent uncertainty–even
under A.
Forecast based interest rate setting
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.
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.
D We do not know how well the forecasting model corresponds to the inflation
mechanism in the forecast period.
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.
13
14
A later section looks at the sources and implications of systematic forecast
errors.
and
In order to illustrate the principles, assume the following model of the transmission mechanism
Setting π̂T +2|T = π ∗ shows that at the time of preparing the forecast, the
period T + 1 interest rate is set to:
πt = δ + απt−1 + β∆it + εt, t = 1, 2, 3..., T,
−1 < α < 1, β < 0,
(1)
Think of the time period as one year. Over the sample period 1, 2, 3..., T
the model is econometrically well specified, and, since we are at level A, the
parameters δ, α and β are assumed to be known, thus neglecting estimation
uncertainty.
The forecast period is T + 1, T + 2, ..., T + H. An inflation targeting central
bank has its focus on the 2 periods ahead forecast, i.e., π̂T +2|T and sets the
interest rate in period T +1 in order to make that forecast equal to the inflation
target π ∗. For the subsequent periods the interest rate is kept constant, i.e.
iT +2|T = iT +3|T = .... = iT +1|T . Based on this, the two first forecasts are:
π̂T +1|T = δ + απT + β∆iT +1|T
15
π̂T +2|T = δ(1 + α) + α2πT + βα∆iT +1
δ(1 + α)
1
+
(π ∗ − α2πT ),
αβ
αβ
The resulting forecasts are given below,
iT +1|T = iT −
Instrument use:
∆iT +1|T
0
0
..
0
..
Inflation forecast:
−δ
1
π̂T +1|T =
+ π∗
α
α
π̂T +2|T = π ∗
π̂T +3|T = δ + E[πt] + α(π ∗ − E[πt])
π̂T +h|T = E[πt] =
where E denotes the mathematical expectation.
16
δ
1−α
(2)
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
(3)
1965
1970
1975
1980
1985
1990
1995
2000
0.050
This always holds, even though the forecast for the first period ahead is very
model dependent, the long run forecast is more “objective”.
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.
17
3.2
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.
18
Limits to inflation forecastability
Define the forecast errors (for the period T forecasting round) as eT +h|T =
πT +h − π̂T +h|T . It can be shown that
σ 2(1 − α2h)
,
(1 − α2)
−1 ≤ α < 1,
Var[eT +h|T ] =
h = 1, 2, ..., H
(4)
where α is 0.05, 0.01, etc. The value of Hα depends on the dynamics of the
forecasting system. Implicit in the choice of a 2-3 years horizon for inflation
targeting is that Hα < 2.5 say.
where σ 2 is the variance of εt. Hence for eT +2|T we have Var[eT +2|T ] =
σ2
σ 2(1 + α2) and for a sufficiently long horizon Var[eT +H|T ] ≈ (1−α
2 ) which is
the (marginal) variance of the rate of inflation.
Hence, despite forward looking interest rate setting, the forecast error variance
increases with the horizon, and the unconditional variance may be a useful
measure of the limit of forecastability. Hence, we define the ‘limit of inflation
forecastability horizon’ Hα as
Var[eT +Hα|T ] > (1 − α)Var[eT +H ]
19
(5)
20
3.3
Using the definition δ = δ̄ + (1 − α)µ, where µ is the long run mean of the
rate of inflation, and δ̄ is the growth rate, the expression for iT +1|T can be
re-expressed more conveniently:
Real world forecast uncertainty
So far we have assumed that forecasting and interest rate setting, thrived in
a situation like A and B, where there was no misspecification within sample.
and where the there were no regime shifts in the forecast period. In such a
situation, systematic forecast errors would never occur, and single incidents
of error larger than the 95% prediction interval would by definition be very
rare. By implications, there would be little chance of policy errors and serious
misjudgements in interest rate setting (rT +1|T above).
However, experience tells us that economics forecasts are often systematically
wrong, and that within sample model fit underestimates the true uncertainty
of the forecasts. Hence, a more realistic description of the situation is C or D
above.
The interest rate setting captured by (2) will only be correct if the parameters
α , δ and β remain stable in the forecast period.
21
Robust interest rate setting
The rationale for the current dictum of forward looking interest rate setting, is
that the targeting of the forecasted rate of inflation speeds up the adjustment
of actual inflation to the target, i.e., relative to having interest rates reacting
to current or lagged inflation. However, as we have seen, there is a cost
to this as the sources of forecast failure are transmitted directly into policy
decisions. Moreover, a simple way of avoiding the damaging consequences of
forecast failure for interest rate setting, is to let the interest rate react to lagged
inflation:
∆iT +1|T = λ(πT − π ∗), λ > 0,
∆iT +j|T = 0, j = 2, 3, ...
23
δ̄(1 + α) + (1 − α2)µ
1
+
(π ∗ − α2πT )
αβ
αβ
(6)
As an illustration, assume that µ = 0.028 (corresponding to figure 2 above),
and α = 0.8, β = −0.1. In this case a reduction in δ̄ by 0.0001 in the course
of the first two years of the forecast period means that the iT +1|T should be
1.4% lower than was determined in the forecasting round. Modest changes in
the equilibrium rate of inflation have a similar impact: Say that µ changes from
0.028 to 0.025: according to the (of course) stylized policy setting here this
would entail that interest rates are 1.35% higher than necessary to achieve the
target two years ahead. Changes in the long run mean of µ of this magnitude
hard to detect even within sample, e.g., the graph 95% confidence interval in
of µ̂ in figure 2.
22
The potential damage of deterministic shifts in the forecast period to interest
rate setting have been little discussed in the inflation targeting literature, but
represent a difficult challenge for inflation targets.
3.4
iT +1|T = iT −
(7)
(8)
With this simple rule, the conditional inflation forecast for period T + 1, T + 2
etc. will be influenced by the any large deviations from the target in period T ,
so qualitatively inflation is helped towards the target in the course of the first
few quarters, also with the backward looking “rule” (7). For longer horizons
π̂T +h|T converges on the long run mean µ, just as in the forward looking case.
Figure 3 illustrates by showing a sequence of dynamic forecasts for the annual
rate of inflation for the period 2002(4)-2005(2), i.e. 12 quarters. The last
observation of the rate of the rate of inflation is 2002(3), which is the initial
value for the forecast of 2002(4). The estimated equilibrium inflation rate of
inflation (the long run mean E[πt]), is 2.8%, which is well within a ±1 percent
interval of “tolerance” around the target of 2.5% inflation. Hence, it is not
surprising that in this example, the inflation target is reached within the eight
first quarters of the forecast horizon of 12 quarters. In line with the algebra, the
estimated uncertainty of the forecast increases with the length of the horizon,
as shown by the fan-chart of the distribution of the forecast errors.
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0.05
0.04
0.03
E[π t ]
0.02
0.01
0.00
2002
2003
2004
2005
2006
Figure 3: Example of dynamic forecasts of the annual rate of Norwegian inflation The first forecast period is 2002(4). The boundaries of the fan represent
the 95percent prediction intervals. The dashed horizontal lines are ±2 estimated standard errors of the rate of inflation.
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