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Economica (2004) 71, 209–221
Modelling Monetary Policy:
Inflation Targeting in Practice
By CHRISTOPHER MARTINw and COSTAS MILASz
wBrunel University
zCity University London
Final version received 9 December 2002.
This paper estimates a simple structural model of monetary policy in the UK focusing on the
policy of inflation targeting introduced in 1992. We find that: (i) the adoption of inflation
targeting led to significant changes in monetary policy; (ii) post-1992 monetary policy
is asymmetric as policy-makers respond more to upward deviation of inflation away from
the target; (iii) post-1992 policy-makers may be attempting to keep inflation within the
1.4%–2.6% range rather than pursuing a point target of 2.5% and (iv) the response of
monetary policy to inflation is nonlinear as interest rates respond more when inflation is
further from the target.
INTRODUCTION
In the decade since they were first introduced, inflation targets have proved to
be a valuable aspect of monetary policy and are now used in over 20 countries.
Developed countries with inflation targets have largely succeeded in maintaining low inflation while also experiencing less output volatility, an improved
sacrifice ratio and more predictable monetary policy. The verdict on inflation
targets has thus far been positive (see Bernanke et al. 1999; Mishkin and
Schmidt-Hebbel 2001; Corbo et al. 2001). To quote Mervyn King, ‘inflation
targets form a clear and transparent framework for monetary policyyI think
they are here to stay’ (King 1997).
This paper considers a number of issues related to inflation targeting. First,
has the adoption of inflation targets affected monetary policy? We might
expect an increased weight to be placed on inflation and a correspondingly
lower weight to be placed on output. Has this happened? Second, is the policy
symmetric, so that deviations of inflation above and below the target are seen
as equally bad? Third, do policy-makers attempt to hit the inflation target
precisely, or do they aim to keep inflation within a target range (see Mishkin
and Posen 1997; Bernanke et al. 1999)? Fourth, is monetary policy more
responsive to inflation when it is further from the target, or is the policy
response always linear?
We address these issues using a simple nonlinear structural framework to
analyse UK monetary policy between 1972 and 2000, focusing on the policy of
inflation targeting introduced in 1992. Our main conclusions are as follows. (i)
The adoption of inflation targets has led to significant changes in monetary
policy. Before 1992 the influence of output was stronger than that of inflation;
after 1992 we find that the influence of inflation is much increased while output
has no effect. (ii) Monetary policy since 1992 has been asymmetric as policymakers now respond more to an upward deviation of inflation away from the
target than to downward deviations. (iii) Since 1992 policy-makers may be
attempting to keep inflation within the range of 1.4%–2.6% rather than
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pursuing a point target of 2.5%. (iv) Monetary policy is more responsive to
inflation when it is further from the target.
The remainder of the paper is organised as follows. Section I presents our
model and explains how it can be used to address the issues raised above.
Section II presents our results and discusses the implications for these issues.
Section III summarises and concludes.
I. MODELLING MONETARY POLICY
Monetary policy in the UK since 1992
Since late 1992, the main aim of monetary policy in the UK has been to achieve
low and stable inflation (for details see Bernanke et al. 1999). The policy goal
announced in October 1992 was to keep inflation within target bands of 1%
and 4%, with the aim of achieving inflation below 2.5% within a time horizon
of five years. In 1995 an explicit medium-term target of 2.5% was introduced.
In May 1997 the Bank of England was given operational independence and the
target range was abolished, to be replaced by the sanction that the governor of
the Central Bank would have to write an explanatory letter if inflation rose
above 3.5% or fell below 1.5%.
In the light of this discussion, we model monetary policy in the period since
October 1992 as follows:
ð1Þ
it ¼ in þ yt MIt þ ð1 yt ÞMOt þ et ;
where
ð2Þ
MIt ¼ ai it 1 þ ap ðpetþ1 pT Þ þ ay ðy yn Þt 1 ;
ð3Þ
MOt ¼ bi it 1 þ bp ðpetþ1 pT Þ þ by ðy yn Þt 1
and
ð4Þ
yt ¼ prfpL 4petþ1 4pU g;
where i is the nominal interest rate, i n is a constant, MI is the ‘inner regime’,
MO is the ‘outer regime’, y is the relative weight on the inner regime, p is
inflation, pe is expected inflation, pT is the inflation target, y is output, yn is
trend output, t indexes time and e is a white noise error term.
Equation (1) is a nonlinear monetary policy rule that relates the interest
rate to a weighted average of MI and MO. Equations (2) and (3) describe MI
and MO as Taylor-like policy rules (Taylor 1993) that relate interest rates to
inflation relative to the inflation target (p – pT) and the output gap (y – yn).
Equation (4) equates the regime weight y to the probability that expected
inflation will lie between the bands pL and pU. To illustrate this, if it is known
with certainty that inflation will (resp. will not) be between the bands, then
policy is determined by MI (resp. MO). In general, the weight on MI is greater
the larger is the probability that expected inflation will lie between pL and pU. If
one regime is always dominant, our model simplifies to a familiar Taylor rule
model of monetary policy.
Both the Taylor-like rules in equations (2) and (3) and the equation for the
regime weights in (4) have expected inflation relative to the target as an
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MODELLING MONETARY POLICY
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argument. Our use of this forward-looking measure reflects the practice of the
Monetary Policy Committee of the Bank of England as revealed in the minutes
of their monthly meetings. It also reflects theoretical work that stresses the
importance of inflation forecasts for monetary policy (Svensson 1997a,b; Batini
and Haldane 1999; Rudebusch and Svensson 1999).1 In these models the
output gap measures the difference between the actual and the flex-price levels
of output. Our model is consistent with this if the flex-price output level can be
captured by a Hodrick–Prescott trend.
We model the regime weight using the quadratic logistic function
ð5aÞ
yt ¼ 1 f1 þ exp½ sðpetþ1 pL Þðpetþ1 pU Þ g 1 :
This function has the properties that (i) y becomes constant as s- 0 and (ii) as
s-N, y ¼ 0 if petþ1 opL or petþ1 4pU and y ¼ 1 if pL opetþ1 opU (see Jansen
and Teräsvirta 1996). We could use alternative functional forms; for example,
we could model y using the logistic function
ð5bÞ
yt ¼ 1 f1 þ exp½ sðpetþ1 pB Þ g 1
This assumes asymmetric adjustment to positive and negative deviations of
petþ1 relative to a single bound pB. We could also use the exponential function
ð5cÞ
yt ¼ exp½ sðpetþ1 pB Þ2 ;
which assumes asymmetric adjustment to small and large absolute values of
petþ1 . We prefer the quadratic logistic function to these alternatives as it allows
us to estimate separate upper and lower bands.2 We follow Granger and
Teräsvirta (1993) and Teräsvirta (1994) in making s dimension-free by dividing
it by the variance of petþ1 ..3 In addition, van Dijk et al. (2002) argue that the
likelihood function is very insensitive to s, suggesting that precise estimation of
this parameter is unlikely in our relatively short sample. For this reason, we do
not attempt to use estimates of s to test our model against the alternative of a
linear model.
Monetary policy before 1992
We use a similar approach in developing a model of monetary policy for the
period before inflation targets were introduced in October 1992. We specify our
model as
ð6Þ
0
it ¼ in þ y0t MIt0 þ ð1 y0t ÞMOt
þ et ;
where
ð7Þ
MIt0 ¼ a0i it 1 þ a0p petþ1 þ a0y ðy yn Þt 1 ;
ð8Þ
0
MOt
¼ b0i it 1 þ b0p petþ1 þ b0y ðy yn Þt 1
and
ð9Þ
0
0
y0t ¼ prfpL 4petþ1 4pU g:
The only substantive difference here is that the Taylor rules use inflation rather
than inflation relative to the target.
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There was considerable heterogeneity in policy over this period. As
discussed by Nelson (2000), monetary policy can be characterized as a sequence
of sub-periods in which the focus of monetary policy moved from the nominal
money supply to the value of the exchange rate relative to the Deutschmark
and then relative to ERM membership. It would not be feasible to model these
relatively short sub-periods using our nonlinear policy rule. (Nelson 2000
investigates changes in monetary policy over this period using Taylor rules.)
We therefore regard estimates of (6)–(9) as providing information on average
policy settings over the period to give a benchmark against which we can
compare monetary policy under inflation targeting.
Discussion
This model allows us to address the issues raised in the introduction. We can
investigate how the conduct of monetary policy has changed since the
introduction of inflation targets by considering differences in the estimated
parameters between regimes. If policy has altered since 1992 such that greater
importance is attached to inflation, we would expect the regime boundaries to
0
0
narrow, implying pL opL and pU 4pU. We would also expect changes within
each regime so that monetary policy became more responsive to inflation and
less responsive to output. This implies ap 4a0p ; bp 4b0p ; ay oa 0y and by ob0y .
If monetary policy were symmetric after 1992, we would expect
pT ¼ (pL þ pU)/2, implying that deviations of inflation from the target in either
direction are seen as equally bad. If pT4(pL þ pU)/2, then policy-makers will
be more sensitive to upward deviations of inflation from target, making the
policy asymmetric. If pL ¼ 0, there is no effective lower band for inflation and
the policy is one-sided. We can also compare the regime boundaries with the
bands within which inflation is permitted to fluctuate by testing whether
pL ¼ 1.5% and pU ¼ 3.5%.
We can examine whether policy-makers are pursuing a point target
or a target range. If they are attempting to keep inflation within the range of
pL – pU, then bp40 and ap ¼ 0, which implies that monetary policy responds
to inflation only when inflation lies outside the regime bands. If policy-makers are
aiming at a precise value of inflation, then bp40 and ap40, which implies that
monetary policy always strives to move inflation towards the target. Finally, we
can examine whether monetary policy responds more to expected inflation when
inflation is further away from the target by testing whether bp4ap.
Context
Nonlinear models of monetary policy can result from either nonlinear central
bank preferences (Dolado et al. 2000; Orphanides and Wieland 2000; Favero
et al. 2000; see also Nobay and Peel 1998) or a nonlinear macroeconomic
model (Schaling 1999; Dolado et al. 2002). Our nonlinear monetary policy rule
is a generalization of a Taylor rule for monetary policy (Taylor 1993). Taylor
rules have been widely used to analyse the actual behaviour of policy-makers in
recent years (e.g. Clarida et al. 1998, 2000), and our work is very much within that tradition. More controversially, Taylor rules have also been used
to analyse optimal monetary policy, that is, the values of monetary policy
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MODELLING MONETARY POLICY
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instruments that would best allow policy-makers to attain their policy goals.
Taylor rules are an example of what Svensson (2002, 2003) refers to as
‘instrument reaction functions’ for monetary policy. Svensson contrasts
instrument reaction functions with ‘targeting rules’ that analyse the implications of equality between the marginal rate of transformation and the marginal
rate of substitution in the policy-maker’s loss function and argues that
targeting rules are superior.
Some of the issues considered in this paper could be analysed in other ways.
The nonlinear monetary policy rule in (1) is a generalization of the more
familiar linear Taylor (1993) rule,
ð10Þ
it ¼ in þ oi it 1 þ op ðpetþ1 pT Þ þ oy ðy yn Þt 1 þ et :
Simple Taylor rules such as (10) can be used to investigate changes in monetary
policy over time (Nelson 2000). However, these Taylor rules cannot be used to
address the other issues considered in this paper. Asymmetry in monetary
policy might be analysed using an augmented Taylor rule of the form
ð11Þ
e
T þ
e
T
it ¼in þ oi it 1 þ oþ
p ðptþ1 p Þ þ oy ðptþ1 p Þ
þ oy ðy yn Þt 1 þ et ;
where ðpetþ1 pT Þþ ¼ ðpetþ1 pT Þ if ðpetþ1 pT ÞX0 and ðpetþ1 pT Þ is ðpetþ1
pT Þ if ðpetþ1 pT Þ40. This model includes inflation rates above and below the
inflation target as separate variables and so allows for differential responses
from policy-makers. This type of model has been used by Dolado et al. (2000)
to analyse monetary policy in Germany, France, Spain and the United States
in the period before monetary union (see also Gerlach 2000 and Surico 2002).
Although helpful and informative about asymmetry, this model cannot be used
to address any of the other issues. We might also use the augmented Taylor
rule
ð12Þ
it ¼ in þ oi it 1 þ op1 ðpetþ1 pT Þ þ op2 ðpetþ1 pT Þ2 þ oy ðy yn Þt 1 þ et
to analyse monetary policy where policy-makers are more responsive to
inflation when it is further from the inflation target. (Dolado et al. 2000 use a
similar model in a non-inflation targeting context.) However, there is no other
model that could be used to address the issue of whether policy-makers have a
point target or a target range; nor is there any other single model that can be
used to analyse all of the other issues. We will compare estimates of our model
to estimates of these alternative models, to investigate which is better able to
explain monetary policy.
Our model has similarities with Smooth Transition Auto-Regressive
(STAR) models (Granger and Teräsvirta 1993; van Dijk et al. 2002), in that
the endogenous variable is determined by a weighted average of regimes with
endogenous regime weights. Our approach differs from STAR models in using
a forward-looking variable to determine the regime weights. Bec et al. (2000)
use a STAR representation to model monetary policy in the United States,
France and Germany. They allow monetary policy to vary between periods of
‘boom’ and ‘slump’, modelling the regime weights using a function similar to
(5b) above but where the regime weight depends on the lagged output gap.
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Following previous work, our analysis is based on a single-equation setting.
Sims and Zha (2002) argue that single-equation models of monetary policy
are vulnerable to endogeneity bias. They propose an alternative methodology
based on a Markov regime switching structural Vector Autoregressive (VAR)
model. It would not be practical to use this approach here, given the limited
amount of data available since inflation targets were introduced in October
1992.
II. EMPIRICAL RESULTS AND DISCUSSION
Results
We use quarterly data for 1972(I)–2000(I). We use the three-month Treasury
bill rate as the nominal interest rate. (This has a close relationship with the
various interest rate instruments used over this periodFsee Nelson, 2000.)
Inflation is the annual change in the retail price index and output is measured
using the GDP deflator. We model the output gap as the difference between
output and a Hodrick–Prescott trend. In estimation, we replace expected future
inflation with actual future inflation and use lagged variables as instruments.
Preliminary unit root analysis (the results are not reported but are available on
request) showed that inflation and the output gap are stationary variables (see
also Nelson 2000; Driver et al. 2000; Hendry 2001). The order of integration of
the interest rate is more ambiguous, but we treat this variable as stationary.
(See also Fuhrer 1997, and Fuhrer and Moore 1995, for discussion of similar
issues.)
Because of the short sample size in the post-1992(III) period and our use
of a heavily parameterized nonlinear model, estimates of the full model were
poorly determined. When the least significant variables were removed, we
obtained a well determined simplified model. Our estimates are presented in
Table 1. Column (i) presents nonlinear least squares estimates, and column (ii)
presents corresponding nonlinear IV estimates. There is little difference
between nonlinear least squares and nonlinear IV estimates. Estimates of our
comparison model of monetary policy in the 1972–92 period are presented in
columns (iii) and (iv) of the table. Again, there is little difference between
nonlinear least squares and nonlinear IV estimates. The diagnostic tests show
no serious misspecification4 in Table 1.
There are four main findings. First, the adoption of inflation targets in
October 1992 led to significant changes in monetary policy. We estimate
0
pL ¼ 1.4% and pU ¼ 2.6%, pL ¼ 1.9% and pU ¼ 21.1% and cannot reject the
0
hypothesis that pL ¼ 0. It is clear from these estimates that monetary policy
became less tolerant of high inflation after 1992. We also find that bp 4b0p and
ay oa0y , and that ap ; a0p ; by and b0y are zero. These estimates confirm that
monetary policy became more responsive to inflation and less responsive to
output within each regime.5
Second, we find that monetary policy in the post-1992 period has been
asymmetric, suggesting that there may be an inflation bias. Our estimate of the
upper band is only 0.1% above the inflation target, implying that the outer
regime becomes important when expected inflation rises only slightly above the
target. By contrast, the lower band is 1.1% below the target. The null
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MODELLING MONETARY POLICY
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TABLE 1
Parameter Estimates a,b
(i)
Nonlinear least
squares estimates
(ii)
Nonlinear IV
estimates
(iii)
Nonlinear least
squares estimates
(iv)
Nonlinear IV
estimates
1992(IV)–2000(I) 1992(IV)–2000(I) 1972(I)–1992(III) 1972(I)–1992(III)
in
3.17 (0.34)
3.20 (0.36)
2.11 (0.67)
2.16 (0.67)
MI (or MI0 )
it 1
0.40 (0.06)
0.40 (0.07)
0.78 (0.06)
0.83 (0.07)
pet þ 1 pT
0.01 (0.19)
0.01 (0.18)
0.04 (0.04)
0.03 (0.05)
(y yn)t 1
–
–
0.19 (0.09)
0.24 (0.10)
MO (or MO0 )
it 1
0.47 (0.06)
0.45 (0.06)
–
–
pet þ 1 pT
0.58 (0.08)
0.67 (0.14)
0.35 (0.05)
0.41 (0.07)
(y yn)t 1
–
–
–
–
0
pL (or pL )
1.40 (0.04)
1.40 (0.04)
1.88 (1.12)
1.88 (1.12)
0
pU (or pU )
2.61 (0.01)
2.61 (0.01)
21.14 (1.22)
21.14 (1.22)
s
90.22 (616.52)
90.22 (616.52)
4.11 (6.75)
4.11 (6.75)
s.e.
0.24
0.24
1.42
1.44
RMSE
0.23
0.23
1.93
1.93
Symmetry
10.63 [0.00]
10.63 [0.00]
–
–
F ar
0.19 [0.96]
1.47 [0.91]
0.90 [0.49]
7.27 [0.20]
F arch
0.25 [0.91]
0.51 [0.73]
1.02 [0.40]
0.48 [0.75]
w2 nd
4.09 [0.13]
1.81 [0.40]
7.23 [0.03]
3.68 [0.16]
F het
0.26 [0.98]
0.64 [0.64]
1.09 [0.38]
2.31 [0.04]
F parameter
Constancy
0.89 [0.54]
0.89 [0.54]
1.54 [0.14]
1.54 [0.14]
a
1992(IV)–2000(I)
period:
it ¼ in þ yt MIt þ ð1 yt ÞMOt þ et ; MIt ¼ ai it 1 þ ap ðpetþ1 pT Þ þ
ay ðy yn Þt 1 ; MOt ¼ bi it 1 þ bp ðpetþ1 pT Þ þ by ðy yn Þt 1 and yt ¼ prfpL opetþ1 opU g 1972(I)–
0
0
þ et ; MIt0 ¼ a0i it 1 þ a0p petþ1 þ a0y ðy yn Þt 1 ; MOt
¼
1992(III) period: it ¼ in þ y0t MIt0 þ ð1 y0t ÞMOt
0
b0i it 1 þ b0p pet 1 þ b0y ðy yn Þt 1 and y0t ¼ prfpL opetþ1 opU g:
bNumbers in parentheses are the standard errors of the estimates. s is made dimension-free by
dividing it by the variance of petþ1 . Symmetry is a chi-square test of the hypothesis H0: (pL þ pU)/
2 ¼ 2.5; F ar is the Lagrange multiplier F-test for residual serial correlation of up to fifth order. F
arch is the fifth-order autoregressive conditional heteroscedasticity F-test. w2 nd is a chi-square test
for normality. F het is an F-test for heteroscedasticity. F parameter constancy is an F-test of
parameter stability (see Lin and Teräsvirta 1994; and Eitrheim and Teräsvirta 1996). Numbers in
square brackets are the probability values of the test statistics.
hypothesis of symmetric monetary policy, H0: (pL þ pU)/2 ¼ 2.5, is clearly
rejected (p-value ¼ 0.00). These results show that the inflation targeting regime
has been asymmetric, with greater priority attached to increases in inflation
above the target than to decreases below the target.
Third, we find that policy-makers may be attempting to keep inflation
within the 1.4%–2.6% range rather than pursuing a point target of 2.5%. The
estimate of bp is significantly greater than zero, so policy-makers adjust the
interest rate in the outer regime in order to move inflation towards the target.
However, we find that the estimate of ap is insignificant, suggesting that policymakers do not adjust interest rates to move inflation towards the target when in
the inner regime.6 We also note that the long-run response of interest rates to
inflation exceeds unity in the outer regime. This implies that policy-makers do
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FIGURE 1. Expected inflation and bounds, 1992(IV)–2000(I). F: expected inflation pte þ 1; – – – -:
lower bound pL ¼ 1.4%; F F F : upper bound pU ¼ 2.6%.
conform to the ‘Taylor principle’ that monetary policy should not accommodate inflation. Fourth, our estimates imply that inflation has a nonlinear
effect on monetary policy.
There are caveats to these findings. Our finding of asymmetry may be due
to the asymmetric nature of the inflation target over 1992–95, when the
medium-term aim was inflation of 2.5% or less. Similarly, our finding that
policy-makers act as if they have a target range rather than a point target may
again reflect the influence of the 1992–95 period, when it could be argued that
there was a target range rather than a precise target. We can investigate this
when sufficient data are available to estimate the model using data from 1995
onwards.
Figure 1 illustrates our results by plotting the estimated values of estimated
values of pL and pU and petþ1 . The outer regime has been dominant in several
periods since 1992, most notably 1994(IV)–1995(IV), 1996(IV)–1998(III) and
late 1999. The nonlinear impact of inflation on monetary policy is illustrated in
Figure 2, where we plot the impact of inflation on interest rates, calculated as
ð13Þ
rt ¼ yt ap þ ð1 yt Þbp :
We observe that, when expected inflation exceeds the upper bound of 2.6% in
1994(III)–1995(IV) and 1996(IV)–1998(II), r increases from zero to 0.67 as the
parameter on expected inflation switches from ap to bp. It is noteworthy that
interest rates rose in 1994(III), fell in 1995(IV), rose again in 1996(IV) and fell
again in 1998(II)–(III). We also observe that expected inflation fell below the
lower bound of 1.4% in 1993(I) and in 1999(I)–(II), and it is worth noting that
interest rates fell in both 1993(I) and 1999(I). Our model therefore seems to be
reasonably accurate in predicting changes in interest rates.
Sensitivity analysis
Table 2 presents estimates of other specifications of our model. (For
convenience we report only the regime bands; other estimates are available
from the authors on request.) First, we estimate a model that uses lagged
inflation (pt–1) rather than expected inflationðpetþ1 Þ. As can be seen from
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MODELLING MONETARY POLICY
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FIGURE 2. The impact of expected inflation on the interest rate, 1992(IV)–2000(I). F: rt ¼ yt
ap þ (1 yt) bp using the nonlinear IV estimates reported in Table 1. – – – -: interest rate it. LHS
axis: measurement units of rt. RHS axis: measurement units in %.
TABLE 2
Estimates of Alternative Specificationsa,b
pL
pU
(i)
Model with
lagged inflation
(ii)
Model with
forward-looking
output gap
(iii)
Inflation measured
by GDP deflator
(iv)
Interest rate
measured by
interbank rate
1.09 (16.27)
2.45 (451.08)
1.40 (0.04)
2.61 (0.01)
1.64 (0.40)
2.60 (0.14)
1.43 (0.10)
2.63 (0.23)
a
Sample period: 1992(IV)–2000(I).
See note b of Table 1.
b
column (i) of Table 2, the estimated bands are somewhat similar but poorly
determined. This supports our forward-looking specification. This is consistent
with Nelson (2000), who finds that a forward-looking Taylor rule outperforms
a backward-looking rule in 1992–97. We also estimated models that use
petþ2 ; petþ3 and petþ4 . The estimates using petþ2 are similar to estimates in column
(i) of Table 1, but much less precisely estimated. Estimates using petþ3 and petþ4
produce highly implausible estimated bands. (These estimates are not reported
but are available on request.)
Second, we examined whether the output gap is forward-looking by using
ðy yn Þetþ1 (replaced in estimation with the actual output gap and using the
lagged variable as an instrument) rather than the lagged output gap (see
column (ii) of Table 2). This makes little difference to the estimated bounds but
introduces autocorrelation and ARCH effects in the estimated model. Third,
we used an alternative measure of the inflation rate, the annual change in the
GDP price deflator. This makes little difference to our results. As can be seen
from column (iii) of Table 2, the estimated bands are very similar to those
reported in Table 1, as are estimates of the other parameters. Fourth, in
column (iv) of Table 2 we use an alternative measure of the interest rate,
namely the three-month interbank rate. This has little effect, as the bands are
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[MAY
ECONOMICA
estimated as 1.43% and 2.63%. We also used other measures of the output
gap, including deviations of real GDP from linear, quadratic and cubic trends.
Results (not reported here) are again similar to those in Table 1. We also
experimented with including various measures of the exchange rate as
additional arguments in (2), (3), (7) and (8) as some models of UK monetary
policy using Taylor rules find a role for these (c.f. Clarida et al. 1998; Nelson
2000). We did not find any significant effects.
Comparison with other methodologies
Estimates of the Taylor rule in (10) for 1972–92 and 1992–2000 are presented in
columns (i) and (ii) of Table 3. We find that the effect of inflation was small and
insignificant in the pre-1992 period but larger and significant post-1992. The
output gap is significant before 1992 but insignificant thereafter. These
estimates confirm our finding that the adoption of inflation targeting in 1992
led to an increased emphasis on inflation in monetary policy. We also note that
our nonlinear policy rule dominates a linear Taylor rule over the 1992–2000
period. It has a substantially lower standard error and a fitted value that is a
better predictor of the actual interest rate based on the root mean squared error
(RMSE). The Taylor rule also fails parameter stability tests. This means that
estimates of our nonlinear model are stable, whereas the stability of the
estimated simple Taylor rule is much more questionable. (See Bec et al. 2000,
for a discussion of the implications of this for the Lucas Critique.) In summary,
TABLE 3
Estimates of Taylor Rules (least squares estimates) a
in
it 1
petþ1
ðpetþ1 pT Þ
ðpetþ1 pT Þþ
ðpetþ1 pT Þ
ðpetþ1 pT Þ2
(y yn)t 1
s.e.
RMSE
w2 eqb
F ar
F arch
w2 nd
F het
F parameter constancy
1972–
1992(III)
(i)
1992(IV)–
2000(I)
(ii)
1992(IV)–
2000(I)
(iii)
1992(IV)–
2000(I)
(iv)
2.09 (0.65)
0.78 (0.06)
0.03 (0.03)
2.99 (0.39)
0.49 (0.06)
2.99 (0.37)
0.47 (0.06)
2.97 (0.38)
0.48 (0.06)
0.51 (0.10)
0.52 (0.10)
0.74 (0.17)
0.32 (0.15)
0.20 (0.09)
1.41
2.02
0.07 (0.08)
0.29
0.36
1.19 [0.32]
0.74 [0.57]
5.59 [0.06]
2.33 [0.04]
1.85 [0.08]
0.77 [0.58]
0.61 [0.65]
0.57 [0.75]
0.25 [0.95]
3.13 [0.02]
a
0.07 (0.07)
0.28
0.28
2.85 [0.09]
0.64 [0.67]
0.28 [0.88]
0.75 [0.68]
0.19 [0.98]
1.42 [0.26]
0.14 (0.09)
0.07 (0.08)
0.28
0.28
0.60 [0.70]
0.35 [0.84]
0.72 [0.69]
0.19 [0.98]
1.80 [0.15]
See the notes to Table 1.
w eq is a chi-square test of the hypothesis that the coefficients on ðpetþ1 pT Þþ and ðpetþ1 pT Þ
are equal.
b 2
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2004]
MODELLING MONETARY POLICY
219
our model appears to provide a better explanation of monetary policy in the
era of inflation targets. By contrast, the nonlinear policy rule does not
dominate the Taylor rule over the 1972–92 period as the two models have
similar standard errors and RMSEs. This is because estimates of our nonlinear
policy rule for 1972–92 reveal that the economy was in the inner regime in
every period save for 1974.
Column (iii) of Table 3 presents estimates of (11), where positive and negative deviations from the inflation target are entered as separate explanatory
variables. The point estimates suggest that monetary policy responds more
strongly when inflation is above the target. This is consistent with the estimates
in Table 1, suggesting an asymmetric policy regime where movements of
inflation above the target lead to a more vigorous policy response. However,
we cannot reject the hypothesis that the coefficients on ðpetþ1 pT Þþ and
ðpetþ1 pT Þ are the same. In addition, the standard error of the estimates is
only slightly lower than that of the simple Taylor rule in column (ii), so this
model is also dominated by our nonlinear monetary policy rule. Column (iv) of
Table 3 presents estimates of (12), where the Taylor rule is augmented to
include a quadratic inflation effect. The quadratic term is insignificant. Taking
these results together, our model appears to be better able to explain monetary
policy in the period after 1992 than do these alternative models.
III. CONCLUSIONS
We have estimated a simple structural model of monetary policy in the UK for
1972–2000, focusing on the policy of inflation targeting introduced in 1992. We
document the changes in monetary policy following the adoption of an
inflation targeting regime in 1992. We argue that inflation targeting in practice
has been asymmetric, we suggest that monetary policy throughout this period
has responded more to inflation when it is further from the target, and we
speculate that in the post-1992 period policy-makers may have been attempting
to keep inflation within the range of 1.4%–2.6% rather than pursuing a point
target of 2.5%. We have also shown how our model provides clearer answers to
these questions than the more familiar Taylor rules of monetary policy.
Our work can be extended in several ways. First, it would be interesting to
apply the model to other countries, as many of the issues considered in this
paper have relevance beyond the United Kingdom. Second, it would be
interesting to explore changes in monetary policy within the inflation targeting
regime after the adoption of a point target in 1995 and after the move to
operational independence of the central bank in 1997. We intend to explore
these issues in future work.
ACKNOWLEDGMENTS
We would like to thank two anonymous referees of this Journal and Carlo Favero for
their most helpful comments and suggestions on an earlier version of this paper. Any
remaining errors are ours.
NOTES
1. However, we should also note that the equilibrium may be indeterminate in forward-looking
models policy rules (Carlston and Fuerst 2001; Svensson 2001).
r The London School of Economics and Political Science 2004
220
ECONOMICA
[MAY
2. In addition, (5c) has the drawback that it becomes linear for extreme values of the s
parameter (van Dijk et al. 2002).
3. Based on this scaling, we use s ¼ 1 as a starting
value. Values of pet þ 1 close to its minimum
0
are used as starting values for the pL and pL parameters, whereas
values of pet þ 1 close to
U
U0
its maximum are used as starting values for the p and p parameters defined in the next
section.
4. There is a slight normality issue, due mainly to a large residual in 1985(I). This period saw a
large increase in the interest rate following rapid depreciation of the exchange rate and the
reactivation of the Minimum Lending Rate requirement at a higher level.
5. The lack of variation in inflation in the post-1992 period may affect the precision of our
estimates.
6. This could perhaps be interpreted in terms of flexible inflation targeting (see Bernanke et al.
1999; Svensson 2002, 2003).
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