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Economica (2004) 71, 209â€“221

Modelling Monetary Policy:

Inï¬‚ation 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 inï¬‚ation targeting introduced in 1992. We ï¬nd that: (i) the adoption of inï¬‚ation

targeting led to signiï¬cant changes in monetary policy; (ii) post-1992 monetary policy

is asymmetric as policy-makers respond more to upward deviation of inï¬‚ation away from

the target; (iii) post-1992 policy-makers may be attempting to keep inï¬‚ation within the

1.4%â€“2.6% range rather than pursuing a point target of 2.5% and (iv) the response of

monetary policy to inï¬‚ation is nonlinear as interest rates respond more when inï¬‚ation is

further from the target.

INTRODUCTION

In the decade since they were ï¬rst introduced, inï¬‚ation targets have proved to

be a valuable aspect of monetary policy and are now used in over 20 countries.

Developed countries with inï¬‚ation targets have largely succeeded in maintaining low inï¬‚ation while also experiencing less output volatility, an improved

sacriï¬ce ratio and more predictable monetary policy. The verdict on inï¬‚ation

targets has thus far been positive (see Bernanke et al. 1999; Mishkin and

Schmidt-Hebbel 2001; Corbo et al. 2001). To quote Mervyn King, â€˜inï¬‚ation

targets form a clear and transparent framework for monetary policyyI think

they are here to stayâ€™ (King 1997).

This paper considers a number of issues related to inï¬‚ation targeting. First,

has the adoption of inï¬‚ation targets affected monetary policy? We might

expect an increased weight to be placed on inï¬‚ation and a correspondingly

lower weight to be placed on output. Has this happened? Second, is the policy

symmetric, so that deviations of inï¬‚ation above and below the target are seen

as equally bad? Third, do policy-makers attempt to hit the inï¬‚ation target

precisely, or do they aim to keep inï¬‚ation within a target range (see Mishkin

and Posen 1997; Bernanke et al. 1999)? Fourth, is monetary policy more

responsive to inï¬‚ation 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

inï¬‚ation targeting introduced in 1992. Our main conclusions are as follows. (i)

The adoption of inï¬‚ation targets has led to signiï¬cant changes in monetary

policy. Before 1992 the inï¬‚uence of output was stronger than that of inï¬‚ation;

after 1992 we ï¬nd that the inï¬‚uence of inï¬‚ation 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 inï¬‚ation away from the

target than to downward deviations. (iii) Since 1992 policy-makers may be

attempting to keep inï¬‚ation within the range of 1.4%â€“2.6% rather than

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pursuing a point target of 2.5%. (iv) Monetary policy is more responsive to

inï¬‚ation 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 inï¬‚ation (for details see Bernanke et al. 1999). The policy goal

announced in October 1992 was to keep inï¬‚ation within target bands of 1%

and 4%, with the aim of achieving inï¬‚ation below 2.5% within a time horizon

of ï¬ve 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 inï¬‚ation 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:

Ã°1Ãž

it Â¼ in Ã¾ yt MIt Ã¾ Ã°1 yt ÃžMOt Ã¾ et ;

where

Ã°2Ãž

MIt Â¼ ai it 1 Ã¾ ap Ã°petÃ¾1 pT Ãž Ã¾ ay Ã°y yn Ãžt 1 ;

Ã°3Ãž

MOt Â¼ bi it 1 Ã¾ bp Ã°petÃ¾1 pT Ãž Ã¾ by Ã°y yn Ãžt 1

and

Ã°4Ãž

yt Â¼ prfpL 4petÃ¾1 4pU g;

where i is the nominal interest rate, i n is a constant, MI is the â€˜inner regimeâ€™,

MO is the â€˜outer regimeâ€™, y is the relative weight on the inner regime, p is

inï¬‚ation, pe is expected inï¬‚ation, pT is the inï¬‚ation 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

inï¬‚ation relative to the inï¬‚ation target (p â€“ pT) and the output gap (y â€“ yn).

Equation (4) equates the regime weight y to the probability that expected

inï¬‚ation will lie between the bands pL and pU. To illustrate this, if it is known

with certainty that inï¬‚ation 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 inï¬‚ation will lie between pL and pU. If

one regime is always dominant, our model simpliï¬es 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 inï¬‚ation 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 reï¬‚ects the practice of the

Monetary Policy Committee of the Bank of England as revealed in the minutes

of their monthly meetings. It also reï¬‚ects theoretical work that stresses the

importance of inï¬‚ation 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 ï¬‚ex-price levels

of output. Our model is consistent with this if the ï¬‚ex-price output level can be

captured by a Hodrickâ€“Prescott trend.

We model the regime weight using the quadratic logistic function

Ã°5aÃž

yt Â¼ 1 f1 Ã¾ expÂ½ sÃ°petÃ¾1 pL ÃžÃ°petÃ¾1 pU Ãž g 1 :

This function has the properties that (i) y becomes constant as s- 0 and (ii) as

s-N, y Â¼ 0 if petÃ¾1 opL or petÃ¾1 4pU and y Â¼ 1 if pL opetÃ¾1 opU (see Jansen

and TeraÌˆsvirta 1996). We could use alternative functional forms; for example,

we could model y using the logistic function

Ã°5bÃž

yt Â¼ 1 f1 Ã¾ expÂ½ sÃ°petÃ¾1 pB Ãž g 1

This assumes asymmetric adjustment to positive and negative deviations of

petÃ¾1 relative to a single bound pB. We could also use the exponential function

Ã°5cÃž

yt Â¼ expÂ½ sÃ°petÃ¾1 pB Ãž2 ;

which assumes asymmetric adjustment to small and large absolute values of

petÃ¾1 . 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

TeraÌˆsvirta (1993) and TeraÌˆsvirta (1994) in making s dimension-free by dividing

it by the variance of petÃ¾1 ..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 inï¬‚ation targets were introduced in October 1992. We specify our

model as

Ã°6Ãž

0

it Â¼ in Ã¾ y0t MIt0 Ã¾ Ã°1 y0t ÃžMOt

Ã¾ et ;

where

Ã°7Ãž

MIt0 Â¼ a0i it 1 Ã¾ a0p petÃ¾1 Ã¾ a0y Ã°y yn Ãžt 1 ;

Ã°8Ãž

0

MOt

Â¼ b0i it 1 Ã¾ b0p petÃ¾1 Ã¾ b0y Ã°y yn Ãžt 1

and

Ã°9Ãž

0

0

y0t Â¼ prfpL 4petÃ¾1 4pU g:

The only substantive difference here is that the Taylor rules use inï¬‚ation rather

than inï¬‚ation relative to the target.

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ECONOMICA

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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)â€“(9) as providing information on average

policy settings over the period to give a benchmark against which we can

compare monetary policy under inï¬‚ation 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 inï¬‚ation targets by considering differences in the estimated

parameters between regimes. If policy has altered since 1992 such that greater

importance is attached to inï¬‚ation, 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 inï¬‚ation 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 Â¼ (pL Ã¾ pU)/2, implying that deviations of inï¬‚ation from the target in either

direction are seen as equally bad. If pT4(pL Ã¾ pU)/2, then policy-makers will

be more sensitive to upward deviations of inï¬‚ation from target, making the

policy asymmetric. If pL Â¼ 0, there is no effective lower band for inï¬‚ation and

the policy is one-sided. We can also compare the regime boundaries with the

bands within which inï¬‚ation is permitted to ï¬‚uctuate by testing whether

pL Â¼ 1.5% and pU Â¼ 3.5%.

We can examine whether policy-makers are pursuing a point target

or a target range. If they are attempting to keep inï¬‚ation within the range of

pL â€“ pU, then bp40 and ap Â¼ 0, which implies that monetary policy responds

to inï¬‚ation only when inï¬‚ation lies outside the regime bands. If policy-makers are

aiming at a precise value of inï¬‚ation, then bp40 and ap40, which implies that

monetary policy always strives to move inï¬‚ation towards the target. Finally, we

can examine whether monetary policy responds more to expected inï¬‚ation when

inï¬‚ation 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

213

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

â€˜instrument reaction functionsâ€™ for monetary policy. Svensson contrasts

instrument reaction functions with â€˜targeting rulesâ€™ that analyse the implications of equality between the marginal rate of transformation and the marginal

rate of substitution in the policy-makerâ€™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,

Ã°10Ãž

it Â¼ in Ã¾ oi it 1 Ã¾ op Ã°petÃ¾1 pT Ãž Ã¾ oy Ã°y yn Ãžt 1 Ã¾ 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

Ã°11Ãž

e

T Ã¾

e

T

it Â¼in Ã¾ oi it 1 Ã¾ oÃ¾

p Ã°ptÃ¾1 p Ãž Ã¾ oy Ã°ptÃ¾1 p Ãž

Ã¾ oy Ã°y yn Ãžt 1 Ã¾ et ;

where Ã°petÃ¾1 pT ÃžÃ¾ Â¼ Ã°petÃ¾1 pT Ãž if Ã°petÃ¾1 pT ÃžX0 and Ã°petÃ¾1 pT Ãž is Ã°petÃ¾1

pT Ãž if Ã°petÃ¾1 pT Ãž40. This model includes inï¬‚ation rates above and below the

inï¬‚ation 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

Ã°12Ãž

it Â¼ in Ã¾ oi it 1 Ã¾ op1 Ã°petÃ¾1 pT Ãž Ã¾ op2 Ã°petÃ¾1 pT Ãž2 Ã¾ oy Ã°y yn Ãžt 1 Ã¾ et

to analyse monetary policy where policy-makers are more responsive to

inï¬‚ation when it is further from the inï¬‚ation target. (Dolado et al. 2000 use a

similar model in a non-inï¬‚ation 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 TeraÌˆsvirta 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

â€˜boomâ€™ and â€˜slumpâ€™, 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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ECONOMICA

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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 inï¬‚ation targets were introduced in October

1992.

II. EMPIRICAL RESULTS AND DISCUSSION

Results

We use quarterly data for 1972(I)â€“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.)

Inï¬‚ation is the annual change in the retail price index and output is measured

using the GDP deï¬‚ator. We model the output gap as the difference between

output and a Hodrickâ€“Prescott trend. In estimation, we replace expected future

inï¬‚ation with actual future inï¬‚ation and use lagged variables as instruments.

Preliminary unit root analysis (the results are not reported but are available on

request) showed that inï¬‚ation 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 signiï¬cant variables were removed, we

obtained a well determined simpliï¬ed 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 1972â€“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 misspeciï¬cation4 in Table 1.

There are four main ï¬ndings. First, the adoption of inï¬‚ation targets in

October 1992 led to signiï¬cant changes in monetary policy. We estimate

0

pL Â¼ 1.4% and pU Â¼ 2.6%, pL Â¼ 1.9% and pU Â¼ 21.1% and cannot reject the

0

hypothesis that pL Â¼ 0. It is clear from these estimates that monetary policy

became less tolerant of high inï¬‚ation after 1992. We also ï¬nd that bp 4b0p and

ay oa0y , and that ap ; a0p ; by and b0y are zero. These estimates conï¬rm that

monetary policy became more responsive to inï¬‚ation and less responsive to

output within each regime.5

Second, we ï¬nd that monetary policy in the post-1992 period has been

asymmetric, suggesting that there may be an inï¬‚ation bias. Our estimate of the

upper band is only 0.1% above the inï¬‚ation target, implying that the outer

regime becomes important when expected inï¬‚ation 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)â€“2000(I) 1992(IV)â€“2000(I) 1972(I)â€“1992(III) 1972(I)â€“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 Ã¾ 1 pT

0.01 (0.19)

0.01 (0.18)

0.04 (0.04)

0.03 (0.05)

(y yn)t 1

â€“

â€“

0.19 (0.09)

0.24 (0.10)

MO (or MO0 )

it 1

0.47 (0.06)

0.45 (0.06)

â€“

â€“

pet Ã¾ 1 pT

0.58 (0.08)

0.67 (0.14)

0.35 (0.05)

0.41 (0.07)

(y yn)t 1

â€“

â€“

â€“

â€“

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]

â€“

â€“

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)â€“2000(I)

period:

it Â¼ in Ã¾ yt MIt Ã¾ Ã°1 yt ÃžMOt Ã¾ et ; MIt Â¼ ai it 1 Ã¾ ap Ã°petÃ¾1 pT Ãž Ã¾

ay Ã°y yn Ãžt 1 ; MOt Â¼ bi it 1 Ã¾ bp Ã°petÃ¾1 pT Ãž Ã¾ by Ã°y yn Ãžt 1 and yt Â¼ prfpL opetÃ¾1 opU g 1972(I)â€“

0

0

Ã¾ et ; MIt0 Â¼ a0i it 1 Ã¾ a0p petÃ¾1 Ã¾ a0y Ã°y yn Ãžt 1 ; MOt

Â¼

1992(III) period: it Â¼ in Ã¾ y0t MIt0 Ã¾ Ã°1 y0t ÃžMOt

0

b0i it 1 Ã¾ b0p pet 1 Ã¾ b0y Ã°y yn Ãžt 1 and y0t Â¼ prfpL opetÃ¾1 opU g:

bNumbers in parentheses are the standard errors of the estimates. s is made dimension-free by

dividing it by the variance of petÃ¾1 . Symmetry is a chi-square test of the hypothesis H0: (pL Ã¾ pU)/

2 Â¼ 2.5; F ar is the Lagrange multiplier F-test for residual serial correlation of up to ï¬fth order. F

arch is the ï¬fth-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 TeraÌˆsvirta 1994; and Eitrheim and TeraÌˆsvirta 1996). Numbers in

square brackets are the probability values of the test statistics.

hypothesis of symmetric monetary policy, H0: (pL Ã¾ pU)/2 Â¼ 2.5, is clearly

rejected (p-value Â¼ 0.00). These results show that the inï¬‚ation targeting regime

has been asymmetric, with greater priority attached to increases in inï¬‚ation

above the target than to decreases below the target.

Third, we ï¬nd that policy-makers may be attempting to keep inï¬‚ation

within the 1.4%â€“2.6% range rather than pursuing a point target of 2.5%. The

estimate of bp is signiï¬cantly greater than zero, so policy-makers adjust the

interest rate in the outer regime in order to move inï¬‚ation towards the target.

However, we ï¬nd that the estimate of ap is insigniï¬cant, suggesting that policymakers do not adjust interest rates to move inï¬‚ation towards the target when in

the inner regime.6 We also note that the long-run response of interest rates to

inï¬‚ation exceeds unity in the outer regime. This implies that policy-makers do

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ECONOMICA

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FIGURE 1. Expected inï¬‚ation and bounds, 1992(IV)â€“2000(I). F: expected inï¬‚ation pte Ã¾ 1; – – – -:

lower bound pL Â¼ 1.4%; F F F : upper bound pU Â¼ 2.6%.

conform to the â€˜Taylor principleâ€™ that monetary policy should not accommodate inï¬‚ation. Fourth, our estimates imply that inï¬‚ation has a nonlinear

effect on monetary policy.

There are caveats to these ï¬ndings. Our ï¬nding of asymmetry may be due

to the asymmetric nature of the inï¬‚ation target over 1992â€“95, when the

medium-term aim was inï¬‚ation of 2.5% or less. Similarly, our ï¬nding that

policy-makers act as if they have a target range rather than a point target may

again reï¬‚ect the inï¬‚uence of the 1992â€“95 period, when it could be argued that

there was a target range rather than a precise target. We can investigate this

when sufï¬cient 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 petÃ¾1 . The outer regime has been dominant in several

periods since 1992, most notably 1994(IV)â€“1995(IV), 1996(IV)â€“1998(III) and

late 1999. The nonlinear impact of inï¬‚ation on monetary policy is illustrated in

Figure 2, where we plot the impact of inï¬‚ation on interest rates, calculated as

Ã°13Ãž

rt Â¼ yt ap Ã¾ Ã°1 yt Ãžbp :

We observe that, when expected inï¬‚ation exceeds the upper bound of 2.6% in

1994(III)â€“1995(IV) and 1996(IV)â€“1998(II), r increases from zero to 0.67 as the

parameter on expected inï¬‚ation 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)â€“(III). We also observe that expected inï¬‚ation fell below the

lower bound of 1.4% in 1993(I) and in 1999(I)â€“(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 speciï¬cations 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

inï¬‚ation (ptâ€“1) rather than expected inï¬‚ationÃ°petÃ¾1 Ãž. As can be seen from

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MODELLING MONETARY POLICY

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FIGURE 2. The impact of expected inï¬‚ation on the interest rate, 1992(IV)â€“2000(I). F: rt Â¼ yt

ap Ã¾ (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 inï¬‚ation

(ii)

Model with

forward-looking

output gap

(iii)

Inï¬‚ation measured

by GDP deï¬‚ator

(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)â€“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 speciï¬cation. This is consistent

with Nelson (2000), who ï¬nds that a forward-looking Taylor rule outperforms

a backward-looking rule in 1992â€“97. We also estimated models that use

petÃ¾2 ; petÃ¾3 and petÃ¾4 . The estimates using petÃ¾2 are similar to estimates in column

(i) of Table 1, but much less precisely estimated. Estimates using petÃ¾3 and petÃ¾4

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

Ã°y yn ÃžetÃ¾1 (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 inï¬‚ation rate, the annual change in the

GDP price deï¬‚ator. 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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218

[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 ï¬nd a role for these (c.f. Clarida et al. 1998; Nelson

2000). We did not ï¬nd any signiï¬cant effects.

Comparison with other methodologies

Estimates of the Taylor rule in (10) for 1972â€“92 and 1992â€“2000 are presented in

columns (i) and (ii) of Table 3. We ï¬nd that the effect of inï¬‚ation was small and

insigniï¬cant in the pre-1992 period but larger and signiï¬cant post-1992. The

output gap is signiï¬cant before 1992 but insigniï¬cant thereafter. These

estimates conï¬rm our ï¬nding that the adoption of inï¬‚ation targeting in 1992

led to an increased emphasis on inï¬‚ation in monetary policy. We also note that

our nonlinear policy rule dominates a linear Taylor rule over the 1992â€“2000

period. It has a substantially lower standard error and a ï¬tted 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

petÃ¾1

Ã°petÃ¾1 pT Ãž

Ã°petÃ¾1 pT ÃžÃ¾

Ã°petÃ¾1 pT Ãž

Ã°petÃ¾1 pT Ãž2

(y yn)t 1

s.e.

RMSE

w2 eqb

F ar

F arch

w2 nd

F het

F parameter constancy

1972â€“

1992(III)

(i)

1992(IV)â€“

2000(I)

(ii)

1992(IV)â€“

2000(I)

(iii)

1992(IV)â€“

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 coefï¬cients on Ã°petÃ¾1 pT ÃžÃ¾ and Ã°petÃ¾1 pT Ãž

are equal.

b 2

r The London School of Economics and Political Science 2004

2004]

MODELLING MONETARY POLICY

219

our model appears to provide a better explanation of monetary policy in the

era of inï¬‚ation targets. By contrast, the nonlinear policy rule does not

dominate the Taylor rule over the 1972â€“92 period as the two models have

similar standard errors and RMSEs. This is because estimates of our nonlinear

policy rule for 1972â€“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 inï¬‚ation target are entered as separate explanatory

variables. The point estimates suggest that monetary policy responds more

strongly when inï¬‚ation is above the target. This is consistent with the estimates

in Table 1, suggesting an asymmetric policy regime where movements of

inï¬‚ation above the target lead to a more vigorous policy response. However,

we cannot reject the hypothesis that the coefï¬cients on Ã°petÃ¾1 pT ÃžÃ¾ and

Ã°petÃ¾1 pT Ãž 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 inï¬‚ation effect. The quadratic term is insigniï¬cant. 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

1972â€“2000, focusing on the policy of inï¬‚ation targeting introduced in 1992. We

document the changes in monetary policy following the adoption of an

inï¬‚ation targeting regime in 1992. We argue that inï¬‚ation targeting in practice

has been asymmetric, we suggest that monetary policy throughout this period

has responded more to inï¬‚ation when it is further from the target, and we

speculate that in the post-1992 period policy-makers may have been attempting

to keep inï¬‚ation within the range of 1.4%â€“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 inï¬‚ation 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).

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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 Â¼ 1 as a starting

value. Values of pet Ã¾ 1 close to its minimum

0

are used as starting values for the pL and pL parameters, whereas

values of pet Ã¾ 1 close to

U

U0

its maximum are used as starting values for the p and p parameters deï¬ned 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 inï¬‚ation in the post-1992 period may affect the precision of our

estimates.

6. This could perhaps be interpreted in terms of ï¬‚exible inï¬‚ation targeting (see Bernanke et al.

1999; Svensson 2002, 2003).

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