Journal of Macroeconomics 33 (2011) 644–655

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Journal of Macroeconomics

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Formal targets, central bank independence and inflation dynamicsin the UK: A Markov-Switching approach

William Miles ⇑, Chu-Ping Vijverberg 1

Department of Economics, Wichita State University, 1845 Fairmount, Wichita, KS 67260-0078, USA

a r t i c l e i n f o a b s t r a c t

Article history:Received 20 January 2010Accepted 19 April 2011Available online 19 May 2011

JEL classification:E31E52E58

Keywords:Central banks and their policiesInflationMonetary policy

0164-0704/$ - see front matter � 2011 Elsevier Incdoi:10.1016/j.jmacro.2011.04.003

⇑ Corresponding author. Tel.: +1 316 978 7085; faE-mail addresses: william.miles@wichita.edu (W

1 Tel.: +1 316 978 7093; fax: +1 316 978 3308.

We examine inflation and uncertainty in the UK with a version of the Markov Switchingmodel, which allows for changes in the variance as well as in the mean and persistenceof a series. We find that the UK’s attempts at exchange rate pegs in the form of shadowingthe deutschmark and entering the ERM were ineffective, and in the latter case counterpro-ductive in lowering inflation uncertainty. The 1981 budget, however, greatly lowereduncertainty, and the adoption of a formal inflation target also had a palpable, negativeimpact on inflation uncertainty. As a suggestive exercise, we examine inflation uncertaintyin the US, and find that, over 2005–2008, in the absence of an inflation target, uncertaintyrose in the US, while uncertainty remained low in the UK over this period of rising com-modity prices and financial turmoil.

� 2011 Elsevier Inc. All rights reserved.

1. Introduction

Low inflation is a major policy goal for both developed and many developing countries. Sadly, in the post-World War IIera, the inflation rate in the UK has at times been much higher than hoped for (see Benati, 2008a, for a detailed analysis ofinflation in the UK over the ‘‘Great Inflation’’ and ‘‘Great Moderation’’ periods). Moderate inflation in and of itself may beneutral for long run income. However, inflation has been shown to increase inflation uncertainty (Friedman, 1977; Ball,1992), and uncertainty over inflation has been shown theoretically and empirically to lower investment and real output.

Accordingly, the UK has tried a number of policies designed to lower inflation and its accompanying uncertainty. TheBank of England was given operational independence in 1997. Prior to this, there were several attempts to peg the exchangevalue of the pound, first by ‘‘shadowing’’ the deutschmark, and then by entering the Exchange Rate Mechanism (ERM) as apossible precursor to Euro adoption. Finally, after leaving the ERM in 1992, the Bank of England adopted a formal inflationtarget. Inflation targets have also since been adopted by most other industrialized nations.

The purpose of this paper is to examine the UK inflation dynamics with the Markov Switching (MS) technique and, at thesame time, to investigate the impacts of these various polices on UK inflation uncertainty. This differs from other papers thatuse regression or GARCH models to evaluate inflation mean/shock persistence/inflation uncertainty. The MS technique uti-lized here is based on an error correction model in which the mean, shock persistence and uncertainty in two different re-gimes can be evaluated. Thus, rather than examining changes in the mean, persistence and uncertainty of UK inflationseparately or jointly (i.e., any two of the three), we investigate all three issues simultaneously. Furthermore, due to the

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x: +1 316 978 3308.. Miles), chuping.vijverberg@wichita.edu (C.-P. Vijverberg).

W. Miles, C.-P. Vijverberg / Journal of Macroeconomics 33 (2011) 644–655 645

special characteristics of the MS model, we are able to obtain the probability of the economy being in the high inflationuncertainty regime. Given the probability derived from the MS model, a probit model is incorporated to assess the impactsof UK’s various policies on inflation uncertainty.

We find that the exchange rate pegs, e.g., shadowing the deutschmark and the ERM, were ineffective in decreasing uncer-tainty. In the case of the ERM, it actually increased uncertainty over the future path of prices. On the other hand, the 1981budget lowered inflation uncertainty. Moreover, the adoption of the formal inflation target had a decidedly negative impacton inflation uncertainty. The inflation target did seem to foster clear communication and transparency, thus palpablydecreasing the uncertainty over the future path of prices. While inflation rose above its 2% target, prompting a mandatoryexplanatory letter from the Bank of England’s governor Mervyn King to the Exchequer starting in April 2007, it is notable thatin our sample, which runs through May of 2008, uncertainty did not pick up at the end. This indicates that, despite the breachof the target, the public, at least for a year, invested the Bank of England with much credibility.

We investigate this issue further with a comparative exercise. While noting that the effect of inflation targeting in the UKmay not be replicated in other countries, it is of interest to contrast the UK’s experience with that of the US, as the US is thelargest industrialized country without a formal target, over the last several years of rising commodity prices and financialshocks. We find that over the 2005–2008 period, while uncertainty in the UK remained low, in the US, without a formal tar-get, uncertainty rose. While one cannot be too bold in drawing clear causal inference from this comparison, it does bolsterthe case that in the UK inflation targeting did decrease the public’s uncertainty of the future path of prices in the face of eco-nomic and financial disturbances.

This paper proceeds as follows. The next section describes the previous literature on inflation, uncertainty and policiesdesigned to decrease both. The third section describes the MS methodology to be employed. The fourth section describesour results, while the fifth section discusses our results in light of previous findings. The sixth section concludes.

2. Previous literature

Inflation has been a source of concern for policymakers in the UK, as elsewhere, due to the potential real economic coststhat a rising price level extracts. While the direct impact on long run output of low or moderate inflation may be negligible,uncertainty about the future price path may be costly. Friedman (1977) posits that the negative real effects of inflation arisemainly from inflation uncertainty. Uncertainty about the future price path lowers the information content of prices, there-fore making long term contracting difficult. This could lead to lower investment and long run growth (Cukierman et al.,1993). Grier and Perry (2000) and Grier et al. (2004) provide empirical evidence that inflation uncertainty decreases outputgrowth.

Policymakers thus desire, all else constant, a low rate of inflation and an accompanying low level of inflation uncertainty.Additionally, most central bankers find it desirable to have a low persistence of inflation shocks. If shocks to the price level donot have a significant long-lasting effect on the future path of prices, the central bank can maintain low inflation in the faceof disturbances. For instance, a spike in commodity prices need not require a severe monetary tightening, if the persistenceof shocks is low. Achieving low persistence may necessitate a high level of credibility for the central bank (Cecchetti andDebelle, 2006; see also Benati 2008b for a discussion of secular changes in UK inflation persistence).

While low inflation, persistence and uncertainty are desirable, the existence of nominal rigidities makes obtaining andsustaining a stable price level potentially costly in terms of short run output and employment. This is especially the case,if, as in the Barro–Gordon framework, the public mistrusts the central bank’s commitment to low inflation and thus main-tains expectations of higher inflation. This leads to higher-than-optimal inflation in equilibrium.

A possible way out of the Barro–Gordon conundrum is a commitment mechanism in the form of a formal target, or quan-titative goal (the exchange rate, money supply, or inflation). Another possible commitment mechanism is to give the centralbank a high degree of independence, so that its decisions are insulated from political pressure for short run monetary stim-ulation (Cukierman, 1992). There is a large literature, both theoretical and empirical, on the impact of exchange rate targetson monetary outcomes. Britain may yet go as far as possible in terms of exchange rate targeting by eliminating its currencyand joining the Euro. Even without doing so, its ‘‘shadowing’’ of the Deutschmark in the 1980s and entrance to the ERM inthe 1990s were variants of exchange rate targets. The desirability of currency targets is still debated. Some nations, especiallyin Eastern Europe, still endeavor to join the Euro, while other emerging markets in Asia and Latin America have had devas-tating balance of payments crises which some economists attribute to inappropriate currency pegs. To anticipate our results,we find that Britain’s recent exchange rate targets were ineffective in generating desired monetary results.

Another goal is a money supply target, which the UK has also employed in the past. The inability to hit such targets in theUK and elsewhere has led to a wide decrease in popularity (although the European Central bank still maintains a monetarytarget as one of its ‘‘twin pillars’’ of inflation and money supply targets). Finally, the difficulties of exchange rate and moneysupply targets have paved the way for inflation targets (IT). An IT is a formal announcement by the central bank of a targetedrate or range of inflation over a coming period. In the wake of the ERM crisis, the Bank of England adopted a formal inflationtarget in 1992. The UK thus stands with most industrialized (and many emerging market) nations in having an IT, although afew countries, most notably the United States, have no IT or any formal goal.2

2 Beginning in February 2009, the US Federal Reserve announced that it will publish long-term forecasts of inflation, which some interpret as a de factoinflation target. However, there is still no formal inflation or any other target for the US central bank.

646 W. Miles, C.-P. Vijverberg / Journal of Macroeconomics 33 (2011) 644–655

Empirically, there are conflicting results concerning the impact of targets. Ghosh et al. (1997) find that exchange raterigidity typically lowers the level of inflation, while Bleaney and Francisco (2005) find that only the ‘‘hardest’’ pegs (currencyboards and unions) have any palpable impact. Fatas et al. (2007) find that having any of the three formal targets lowers infla-tion, and that inflation targets have the greatest negative effect on price increases. On the other hand, Ball and Sheridan(2005) find that IT has no significant effect on the level or the variability of inflation.

As for central bank independence, empirical results support the notion that such monetary policy independence lowersthe level of inflation (Cukierman, 1992; Alesina and Summers, 1993). The latter paper also finds that independence of themonetary authority decreases the variability of inflation as well.

The above-cited papers are all based on cross-country regressions, and thus may not be reliable for inference regardingthe impact of a given policy or institutional change in a particular country (see Rodrik, 2005 for a discussion of the pitfalls ofcross-country studies of the impact of policies). Our goal in this paper is to examine inflation dynamics in the UK in the post-war years and to determine whether and what policies had an impact. In order to do so, we must formulate an empiricalstrategy that addresses several important issues.

First, to examine the impact on the level of inflation, we must control for potential changes in the persistence of inflationand vice-versa. Cecchetti and Debelle (2006) point out that studies which examine either changes in the mean or persistencebut which fail to control for potential changes in both are likely to lead to erroneous inference. Additionally, given that themain source of the output costs of inflation are through uncertainty, we seek to model this uncertainty and determinewhether it has been significantly changed through particular policies.

For the mean and persistence of inflation, an ARMA model should suffice, as we can test the intercept and slope coef-ficients for changes. Modeling uncertainty is not as clear-cut. Traditionally, the unconditional variance of inflation hasbeen employed as a proxy for uncertainty, as in Fischer (1981). However, if the determinants of inflation are variable,but predictable, a high unconditional variance of inflation will not be a good proxy for uncertainty (Grier and Grier,2006).

Since the development of ARCH and GARCH models (Engle, 1982; Bollerslev, 1986) the conditional GARCH variance ofthe residuals of an estimated ARMA inflation specification have been employed as a proxy for uncertainty. Grier andPerry (1998) for instance, examine inflation in the UK, as well as other G-7 countries with GARCH specifications. Inthe mean time, MS models were developed to capture the changing variances under different regimes (Hamilton,1989; Kim, 1993; Kim and Nelson, 1999a,b). Note that the changing variances of a GARCH model depend on the previousinnovation within a given structure. It differs from the MS model where changing variances are due to regime changesin the variance structure. This paper will incorporate changes in the mean, persistence and variance of inflation simul-taneously in a MS model. We believe that this MS technique can provide different perspectives and/or robust verifica-tions about the UK inflation behavior.

3. Methodology

To investigate the inflation dynamics, we can start with an AR(p) model,

3 WeMarkov

pt ¼ a0 þ b1pt�1 þ b2pt�2 þ b3pt�3 þ � � � þ bppt�p þ ut ð1Þ

where pt and pt�i are the inflation rates at time t and t � i, and then transform it by arranging the terms and get the errorcorrection format,

Dpt ¼ a0 þ ðq� 1Þpt�1 þ c1Dpt�1 þ c2Dpt�2 þ � � � þ cp�1Dpt�pþ1 þ ut : ð2Þ

where q ¼Pp

i¼1bi and q is a measure of persistence and c1 = �b2 �b3; c2 = �b3 for an AR(3) model.Now to examine the changes in the dynamics of the inflation process, including uncertainty, we use a MS3 model that

can simultaneously handle changes in the mean, persistence and variance of inflation. The previous model can thus be ex-pressed as

Dpt ¼ ða0 þ a1StÞ þ ð/0 þ /1StÞpt�1 þ c1Dpt�1 þ c2Dpt�2 þ � � � þ cp�1Dpt�pþ1 þ ut;St ð3Þ

where St is the state variable that denotes the state of the series at time t and /0 + /1St = q � 1. In this specification, wehave two different regimes: regime 0 (i.e., St = 0) and regime 1 (i.e., St = 1). A two-state Markov process has the followingtransition probabilities: PrðSt ¼ 0jSt�1 ¼ 0Þ ¼ ~q and PrðSt ¼ 1jSt�1 ¼ 1Þ ¼ ~p: The uncertainty in each regime is representedby the variance: Varðut;St Þ ¼ h2

0 when St = 0 and Varðut;St Þ ¼ ðh0 þ h1Þ2 when St = 1. The parameters a1, /1 and h1 capturethe changes in the mean of inflation, the persistence of a shock to inflation and the variance during regime 1 relative

have benefitted from the Gauss programs provided in the book of Kim and Nelson (1999) regarding the Markov-Switching model. However, all the-Switching programs used in this paper are coded in S+ and R.

W. Miles, C.-P. Vijverberg / Journal of Macroeconomics 33 (2011) 644–655 647

to regime 0. If h1 is positive (negative), it implies that regime 1 has a higher (lower) inflation uncertainty than that ofregime 0.4 In this paper, we will use p = 3.5

The parameters of the model are thus ða0; a1; /0; /1; c1; c2; h0; h1; ~p; ~qÞ. MLE is implemented to estimate the parame-ters. The log-likelihood function is the following:

4 In o5 Due

As the lthe equ

an 8 �

respect6 G i

f ðDpt ; S7 Dat8 The

i.e., wepercentnoisy inused in

9 It isbetweechangesai;/; cj

hi > 0 anaccordireduce(a1, a2,adjuste(a1, a2,pij � Bet

lnL ¼XT

t¼3

lnX1

St¼0

X1

St�1¼0

X1

St�2¼0

f ðDpt; jSt; St�1; St�2;Ut�1Þ � PrðSt; St�1; St�2j;Ut�1Þ( )

ð4Þ

where

f ðDptjSt ; St�1; St�2;Ut�1Þ ¼1ffiffiffiffiffiffiffiffiffiffiffiffiffi

2pr2st

p exp�ðDpt � ða0 þ a1StÞ � ð/0 þ /1StÞpt�1 � c1Dpt�1 � c2Dpt�2Þ2

2r2st

( )ð5Þ

and

PrðSt ¼ j; St�1 ¼ i; St�2 ¼ kjUt�1Þ ¼ PrðSt ¼ jjSt�1 ¼ i; St�2 ¼ kjUt�1Þ � ðSt�1 ¼ i; St�2 ¼ kjUt�1Þ ð6Þ

where Ut�1 denotes past information, r2

St¼ ðh0 þ h1StÞ2, and PrðSt ¼ jjSt�1 ¼ i; St�2 ¼ k;Ut�1Þ ¼ PrðSt ¼ jjSt�1 ¼ iÞ is the tran-

sition probability for i, j, k = 0, 1. Note that once the MLE estimates are obtained, we are able to calculate the probabilityof St = 1 or St = 0 for each time period6

4. Results

Monthly data of the UK long-term indicator of prices of consumer goods and services are used. The data are available from1947:6 to 2008:5.7 The inflation rate is calculated as the percentage change of the price index a year ago.8 The average inflationrate of this data set is 5.796%. The five number summary of the data (i.e., minimum, first quartile, median, third quartile, andmaximum) is the following: �0.818, 2.755, 4.193, 7.420, and 26.867.

We use Brock, Dechert, and Scheinkman (BDS) test to evaluate non-linearity. BDS is a popular test because of its poweragainst a variety of nonlinear time series models. For any two m-dimensional points, where m = 2 and 3, we find that the nullhypothesis of data being iid is rejected. This suggests that UK inflation data are not really a candidate for linear modeling.

One may contend that a two-regime MS model may not be optimal. One way to deal with this contention is to implementthree, four and higher regime MS models and to compare their likelihood values. We did not get too far with this techniquebecause of the difficulties in getting convergence in MLE in higher-regime models. An alternative to MLE is the Bayesiantechnique that treats both parameters and the state variables as random variables. Higher regime MS models may be imple-mented through the Gibbs sampling simulation tool, and one may use the marginal data density criteria to find the appro-priate number of regimes. Table 1 shows the results of marginal data density tests of two different priors.9 A four-regimemodel is better than one with two regimes under prior I while two regimes are better than four regimes under prior II. Thus,it is a choice between two and four regimes. As we examined the posterior means and standard deviations of all the parametersin the four-regime model for both priors, the means and variances of the original inflation model in both regimes three and fourhave the ratios of posterior mean/ standard deviation much less than 2. This indicates the imprecise estimates of both posterior

ur model, we do impose the restriction that h2 > 0 in our computer program. Thus, St = 1 is the higher volatility regime.to the programming complexity in dealing with various state variable statuses at different time points, it is not trivial to have a model with a long lag.

ag length of the model increases, the time-dimension of the state variable increases substantially. For example, if the lag length is l (=p � 1 as shown ination above), the time-dimension of the state variable is a 2l+1 � l + 1 matrix. Thus, for a lag length of l = 2, the time-dimension of the state variable G is

3 matrix, i.e., Gt ¼0 0 0 0 1 1 1 10 0 1 1 0 0 1 10 1 0 1 0 1 0 1

24

35 where the three columns of G represent the statuses of the state variable at t � 2, t � 1, and t

ively. Then for l = 3, G is a 16 � 4 matrix; for l = 4, G is a 32 � 5 matrixv e n

P1St¼0

P1St�1¼0

P1St�2¼0f ðDpt ; St ; St�1; St�2jUt�1Þ ¼ f ðDpt jUt�1Þ, w e c a n u p d a t e t h e p r o b a b i l i t y b y

t ; St�1; St�2jUt�1=fDpt jUt�1Þ ¼ f ðSt ; St�1; S�2jDpt ;Ut�1Þ ¼ f ðSt ; St�1; St�2jUtÞ. Then integrate out St�1 and St�2, we can get P(St = 1|Ut).a were downloaded from http://www.statistics.gov.uk/statbase on June 2008.inflation rates calculated by month to month change of the price index are very noisy. The MS model has difficulties in identifying the regime switch,could not get any converged results from using this noisy inflation data. The noise was reduced substantially as we calculated inflation rates as theage change of the price index a year ago. This is the main reason for using these monthly inflation rates. A further justification is the following. If theflation rates are decomposed into seasonal, trend and noise components, the trend component of the noisy inflation rates is very similar to the datathis paper. For details, see the attached appendix for referees. Readers may request the detailed illustration from the authors.known that the marginal data density results may be affected by the prior. Different priors were set to run for this test. The main competition is

n 2 and 4 regime models. Table 1 presents two sets of priors. Note that in the Bayesian model, we allow the means and variances to change as the regime; we did not let the persistence vary with the regimes. We follow Albert and Chib (1993) and Kim and Nelson (1999a,b) by assuming Normal priors forwhere i = 1, 2, . . ., 6 and j = 1, 2. For the variance parameters, r2

1 has an inverted gamma prior distributions and r2i ¼ r2

i�1ð1þ hiÞ where i = 2, 3, . . . ,6,d 1 + hi has an inverted gamma prior distribution. The evaluation of the posterior density evaluated at the posterior mean in Table 1 is calculated

ng to Chib (1995). All inferences are based on 20,000 Gibbs simulations, after discarding the initial 4000 Gibbs simulations, (these are discarded tothe impact of initial values. Prior 1: we specify for 6 regimes here and the lower regimes are specified similarly.

. . ., a6) � N((0, 0.1, 0.2, 0.1, 0.2, .2), 5 I6), / � N((�0.5, 1/25), (c1, c2) � N((0, 0), 5I2), r2i � inverted Gamma(1, 1), pii � Beta(0, 1, 0.1) for all i and the

d pij � Beta(0.1, 0.1) for all the relevant i and j. Prior 2: we specify for 6 regimes here and the lower regimes are specified similarly.. . ., a6) � N((0, 0.1, 0.2, 0.1, 0.2, .2), 2I6), U � N((�0.5, 1/25), (c1, c2) �N((0, 0), 2I2), r2

i � inverted Gamma(1, 10), pii � Beta(1, 10) for all i and the adjusteda(1, 10) for all the relevant i and j (see Kim and Nelson 1999b)

Table 1Marginal data density test results.

Number ofregimes

Likelihood (i) prior I/prior II

Prior (ii) prior I/prior II

Posterior (iii) prior I/prior II

Total marginal data density: (i) + (ii) � (iii) prior I/prior II

S = 1 �683.15/�683.44 �2.40/�14.00 13.36/13.33 �698.91/�710.77S = 2 �614.17/�614.71 �13.80/�55.72 22.52/19.87 �650.49/�690.30S = 3 �619.28/�616.70 �23.03/�56.86 10.40/22.67 �652.71/�696.23S = 4 �627.19/�628.66 �21.14/�61.50 �6.30/18.19 �642.03/�708.35S = 5 �687.45/�659.52 �49.16/�140.21 �57.44/35.60 �679.17/�835.33S = 6 �696.39/�681.27 �47.21/�57.36 �30.94/28.90 �712.66/�767.53

Table 2Parameter estimates of Markov –Switching models.a

Parameter estimates UK 1948:1–2008:5 US 1948:1–2008:5

Without restrictions With restrictedb /0 and h1 Without restrictions With restricted h1

a0 0.088 (0.011) 0.467 (0.000) 0.014 (0.559) 0.046 (0.047)a1 0.001 (0.990) �0.168 (0.069) 0.089 (0.351) 1.930 (0.000)/0 �0.019 (0.017) �0.019 0.0001 (0.988) �0.017 (0.001)/1 0.005 (0.696) �0.075 (0.000) �0.028 (0.058) �0.054 (0.327)c1 0.230 (0.000) 0.121 (0.001) 0.184 (0.000) 0.237 (0.000)c2 0.155 (0.011) 0.107 (0.004) 0.139 (0.000) 0.115 (0.000)h0 0.346 (0.000) 0.565 (0.000) 0.295 (0.000) 0.380 (0.000)h1 0.582 (0.000) 0 0.384 (0.000) 0~p 0.980 (0.114) 0.976 (0.021) 0.975 (0.098) 0.160 (0.000)~q 0.988 (0.069) 0.928 (0.005) 0.992 (0.057) 0.992 (0.028)

Nobc 719 719 719 719Log-like �546.61 �655.87 �293.47 �355.76

a Numbers in the parentheses are the p-values.b A simple restriction of h1 = 0 could not yield a valid hessian matrix. Thus, an additional restriction is imposed on /0.c Nob: number of observations.

648 W. Miles, C.-P. Vijverberg / Journal of Macroeconomics 33 (2011) 644–655

means and variances in the original inflation model. Furthermore, an extension of the model from two to four regimes intro-duces 14 additional parameters.10 Based on these results, and in the light of the model parsimony principle, a two-regime modelwould not be an inappropriate choice. Finally, the best marginal data density value11 does not clearly select between a two-re-gime model and a four-regime model while the best likelihood value in Table 1 sticks with the two-regime model consistentlyeven when the prior changes. Thus, after this examination of the appropriate number of regimes, we will focus on a two-regimeMLE model.

Columns 2 and 3 of Table 2 provide the numerical estimates of the Markov-Switching model of UK inflation. We will firstfocus on the model that imposes no restrictions on the parameter values. Based on the results shown on Column 2 of Table 2,the expected duration of the low uncertainty regime 0 is 83.3 months (i.e., 1=ð1� ~qÞ) while the expected duration of the highuncertainty regime 1 is 50 months (i.e., 1=ð1� ~pÞ). The estimate of a0 implies that the expected average inflation rate in re-gime 0 is 4.631% (=a0=ð1� qÞ where q ¼ ð1þ /0Þ). The estimate of a1 signals a shift in the mean inflation as St varies from 0to 1. The expected average inflation rate in regime 1 is 6.357% (=ða0 þ a1Þ=ð1� qÞ where q ¼ ð1þ /0 þ /1Þ). Though both a1

and /1 are not statistically significant, regime 1 shows a higher average inflation rate. Since it is important to know whetherthere is indeed a significant difference in the average inflation rate, a Wald test is implemented.12 The observed Wald teststatistic is 0.1113 and the p-value for the null hypothesis of no difference in the average inflation rates between two regimesis 0.739. Thus, the average inflation rates are basically the same in both regimes. As for inflation shock persistence,q ¼ 1þ /0 þ /1St . For the UK, the estimate of /0 is �0.019, indicating the value of q being 0.981, which is a highly persistentnumber for regime 0. Since the U.K. estimate of /1 is 0.005, the shock persistence measure in regime 1 is 0.986, which impliesthat shock persistence is slightly higher in regime 1. However, the p-value of the estimate of /1 is 0.696. Thus, the persistence ofshocks is approximately the same in both regimes. Finally, for inflation uncertainty, the estimate of h1 indicates the change instandard deviation (or uncertainty) when the regime changes. The UK estimate of h1 is 0.582 with a p-value less than 0.001.Comparing with regime 0 where the variance is 0.120 (i.e., Varðut;St Þ ¼ h2

0 when St ¼ 0), the measure of inflation uncertaintyin regime 1 is 0.861 (i.e., Varðut;St Þ ¼ ðh0 þ h1Þ2 when St ¼ 1). The increase in inflation uncertainty from regime 0 to regime 1is significant.

10 The transition matrix goes from two by two to four by four. Furthermore, there are other additional parameters.11 The marginal data density value is calculated according to Chib (1995) and Kim and Nelson (1999a).12 The null hypothesis is H0 : a0

/0¼ a0þa1

/0þ/1. Rearranging the terms, we obtain H0 : a1/0 � a0/1 ¼ 0. Let gðbÞ ¼ a1/0 � a0/1 and gðbÞ ¼ c. Using the delta method

(Greene, 2008: pp. 1055–1056), we are able to get the Wald test statistic W ¼ c2=VarðcÞ � v2ð1Þ.

W. Miles, C.-P. Vijverberg / Journal of Macroeconomics 33 (2011) 644–655 649

The MS two-regime model thus shows that, compared to regime 0, regime 1 has similar mean inflation and shock per-sistence, and much higher inflation uncertainty. Note that St = 1 means the economy is in regime 1. To have a better graspof the MS results, Fig. 1a shows the actual UK inflation rate (the solid line) and the probability that St = 1 (the dashed line) forthe period of 1948:6–2008:5.13 The left vertical axis denotes the inflation rate while the right vertical axis indicates the prob-ability. The probability of the economy in St = 1 is considered as ‘‘high’’ if the value is greater than 0.75. For the UK, the periods ofhigh probability of being in St = 1 occur in most of the 1950s, the early 1960s, 1974:1–1978:6, 1979:7–1981:5, and 1990:4–1991:11.

It is important to note, and bears repeating that the findings of statistically insignificant a1 and /1 do not imply that therehas been no secular, structural change in the mean or persistence of UK inflation over the post-war years. It simply indicatesthat the high uncertainty state is not significantly associated with a high mean level of inflation. There is strong evidence thatthere have been significant breaks in mean UK inflation over the last several decades. Indeed, a number of papers have care-fully documented secular structural breaks in both the mean and persistence of inflation for the UK (see Benati, 2008a,2008b; Cogley et al., 2003; Groen and Mumtaz, 2008; Rapach and Wohar, 2005).14 Again, our finding does not contradict theseresults in any way; instead, our MS model captures cyclical regimes changes, and what we have found is that the high uncer-tainty regime is not robustly associated with a high level of mean inflation.

There are two points to note on our finding that high uncertainty is not significantly correlated with mean inflation. First,this lack of association is both theoretically plausible and consistent with previous empirical findings.15 Secondly, the at-tempt to capture three inflation characteristics simultaneously in two different regimes may lead to competition among thesethree elements, i.e., a dominant element may drive the regime change and diminish the regime differentials in the other twoelements. Thus, to examine whether volatility dominates the other two in the regime switch, we impose the restriction of h1

being zero in the model, i.e., assuming the same volatility in both regimes. Due to the difficulty16 of getting a valid t-valuefor the estimate of /0, we also impose the restriction of /0 ¼ �0:019 in this case. Our results, shown in the third column ofTable 2, indicate that the estimate of /1 is significantly different from zero and the p-value of the estimate of a1 is drasticallyreduced. In this case, the expected duration of regime 0 is 13.9 months (i.e., 1/(1 � 0.928)) while the expected duration ofregime 1 is 41.7 months (i.e., 1/(1 � 0.976)). The expected average inflation rate in regime 0 is 24.578% while the expected

13 We lose 12 data points because of converting the price index into inflation.14 Recently some researchers used BVAR or BSVAR to examine the structural break and/or persistence in inflation. Even though the structural break issue is

not the focus of this paper, we did have the following observations. First, as mentioned in Table 1, the model with four regimes is optimal under prior I, eventhough it is not optimal under prior II. A model with one state variable (i.e., St) with four regimes is similar to, but more general than, a model with two statevariables (i.e., St and Dt) with each state variable having two regimes. For example, compare the model of S = 4, where St = 1, 2, 3, 4, and the model of S = 2 andD = 2 where the four regimes are S1D1, S1D2, S2D1 and S2D2A. A standard way to deal with structural breaks is to treat Dt as one that either stays at the currentregime or jumps to the next regime (Chib, 1998; Kim and Nelson, 1999a; Barnett et al., 2010). Thus, the transition matrix of Dt is restricted if one intends to useDt to indicate structural breaks. A model with one state variable (i.e., St) with four regimes is an un-restricted case because the model does not imposerestrictions on its transition matrix. We did the case for St and Dt with each state variable having two regimes and the transition matrix of Dt being

q11 1� q110 1

� �. When we incorporated Dt, we only controlled for the change in the means for Dt, i.e., if Dt moves to a higher regime, both means in either St = 1

or St = 2 will switch to a different level. Under prior I in Table 1, the marginal data density value of the S = 2 and D = 2 model is �646.53, which is lower than thevalue of �642.03 (the case of S = 4 and D = 1) Thus, the optimal choice in Table 1 under prior I remains valid, i.e., the model of S = 4 is better than the model ofS = 2 and D = 2. Second, even though S = 2 and D = 2 is not the optimal model, we would look at its results to find the implications for the structural break andpersistence. As we examined the results of the S = 2 and D = 2 model, the only significant ai (i.e., the ratio of the posterior mean/standard deviation issubstantially greater than 2) is the mean at D = 1 and S = 1; all the other ais are not significant. The implication is that we could not identify a significant changein mean inflation when D = 1 is moved to D = 2. Thus, we cannot find sufficient support of a structural break in inflation. Again, the culprit is probably in thevolatility, which takes away the ability to detect the change in mean inflation rates. This may also due to the fact that we are dealing with a single equationmodel and other researchers use BVAR models, which have multiple equations. Third, the posterior mean of the persistence parameter U is �.0077 in S2D2model while it is �0.0083 in S4D1 model. Thus, even when we control the change in the mean for possible structural breaks, the persistence of the inflationremains high.

15 Friedman (1977) and Ball (1992) posit a positive and causal relationship from the level of inflation to uncertainty, as higher inflation should theoreticallylead to higher uncertainty. However, Ungar and Zilberfarb (1993) note that the effect of inflation on uncertainty is ambiguous; if the cost of forecasting inflationis less than the cost of uncertainty, an increase in inflation will lead to better forecasts, and actually reduce uncertainty. Moreover, the causality in the otherdirection-from higher uncertainty to inflation, is also theoretically ambiguous. Cukierman (1992) presents a model in which higher uncertainty raises theoptimal rate of inflation, thus predicting a positive relationship. However, Holland (1995) points out that, if a central bank is aware of the negative effects ofuncertainty, it will seek to counter any increase in uncertainty by lowering the rate of inflation. This would suggest a negative causal relationship. Empirically,when ARCH and GARCH modeling began, Engle (1983) and Bollerslev (1986) employed ARCH and GARCH variances as proxies for uncertainty, and found that,for the US, there was no robust relationship between the mean of inflation and uncertainty (see Grier and Perry, 1998, p. 684 for a discussion). Grier and Perry,employing GARCH models and testing formally for the impact of inflation on uncertainty and vice-versa, find that inflation does increase uncertainty in the UK.However, the authors find uncertainty in the UK has a negative effect on inflation. Thus it is unsurprising that when employing the MS technique we find thatthe relationship between inflation and uncertainty is not significant. These findings are even less surprising, to anticipate further results, given that the entryinto the ERM raised uncertainty. This joining of the precursor to the Euro occurred during a time of low inflation, but the unpredictable nature of the policy (inthe end, of course, Britain dropped out) raised inflation uncertainty.

16 Due to the difficulty in deriving the analytical gradient and Hessian of the likelihood function, two optimization routines are used in the likelihoodmaximization procedure concurrently: nlminb in S+ and nlm in R. In S+, nlminb allows parameter restrictions but it does not provide a numerical gradient andHessian. In R, nlm provides numerical gradient and Hessian but it does not allow parameter restrictions automatically, i.e., we have to program the restrictions.In the case of setting h1 = 0, the optimal estimate of /0 is near zero in S+. As we program the restriction of /0 being between 0 and �1 by using the logisticfunction (�ex/(1 + ex)) in R, the Hessian matrix fails to be positive definite (in the minimization of –ln L) at the point of supposed convergence, probably due tooverflow and/or underflow problems and the ensuing numerical inaccuracies. Since our goal here is to check if /1 and a1 become significant estimates asvolatility is restricted, we also fix the number of /0 at �0.019, which is the optimal estimate in the unrestricted case.

Solid line: inflation rate (12 month ago); Dashed line: Pr(St=1)

05

1015

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09/01/1948 09/01/1959 09/01/1970 09/01/1981 09/01/1992 09/01/2003

0.0

0.2

0.4

0.6

0.8

1.0

Fig. 1a. UK inflation and the probability of being in St = 1

650 W. Miles, C.-P. Vijverberg / Journal of Macroeconomics 33 (2011) 644–655

average inflation rate in regime 1 is 3.180%. The measures of inflation shock persistence in regime 0 and regime 1 are 0.981 and0.906 respectively. Thus, when the volatility is restricted to be the same in both regimes, regime 0, comparing with regime 1,has a shorter expected duration with a much higher expected average inflation rate and slightly stronger shock persistence.Though the ordering of the regime is different, the significant switch in shock persistence and a sharp change in average infla-tion rates between regime 0 and regime 1 are results drastically different from the case where no restrictions are imposed.Fig. 1b shows the restricted case of the probability of the UK economy in regime 0, which is the regime with a higher averageinflation rate, comparing to regime 1. It is noticeable that, as we hold the variance constant in both regimes, the high averageinflation periods in the restricted case are very similar to the high inflation volatility periods in the un-restricted case (i.e.,Fig. 1a). This shows that, as we model mean, persistence and volatility together in the un-restricted case, it is volatility thatdrives the regime change and diminishes the differentials in mean and persistence in the regime switch.

What then is the choice between the un-restricted and the restricted cases? We implement the likelihood ratio test be-tween these two cases and find that the p-value of the observed test statistic is 0.000. Thus, the null hypothesis of h1 ¼ 0 and/0 ¼ �0:019 is rejected. We will thus from now on focus on the un-restricted case.

As mentioned, the intention of this paper is to evaluate the impact of IT and other policies on UK inflation dynamics. Aspecial characteristic of the MS model is that we are able to calculate the probability of the economy in St = 1 for each timeperiod. Based on these probability values, we will assess the impacts of different polices on inflation uncertainty.

In order to assess the effect of changes in monetary policy, we must first identify those major actions by the Bank of Eng-land that were most likely to have an impact on the level, persistence, and uncertainty of inflation. Like other industrializedcountries, Britain’s inflation rate appeared to be high in the 1970s. While informal (and, starting in 1977, formal) money sup-ply targets were implemented in an attempt to lower inflation, the targets were missed. Thus prices unsurprisingly contin-ued to rise.

Margaret Thatcher’s government came to power in May 1979, with a perceived commitment to lower inflation. However,for nearly 2 years, money supply targets continued to be overshot. These overshoots were allowed because of recessionaryconcerns at the time (Cobham, 2002, p. 17). Then, in March 1981, the Thatcher administration passed an annual budget thatadjusted the targets to take account of previous overshoots. This was described as a ‘‘turning point’’ in UK monetary policy.

While inflation proceeded to fall through the mid-1980s, money supply targets were still overshot. Thus in March 1987the Bank of England, under Chancellor Lawson, abandoned money supply targets and began shadowing the Deutschmark.Informally adopting an exchange-rate target was thought to give a better framework for monetary policy than the discred-ited money supply targets.

The third major policy action is the entry into the ERM in October 1990. This now gave the Bank of England a formal ex-change rate target. Although England would famously leave the ERM during the crisis of 1992, the ERM was clearly a cur-rency peg and led, for most of its member countries, to the adoption of the Euro. The fourth major change in policy wasthe adoption of the inflation target in October 1992. As noted, the impact of inflation targeting on monetary outcomeshas been the source of much inconclusive research. The last policy change we will investigate was in May of 1997, in whicha new Monetary Policy Committee of the Bank of England was given sole authority to conduct monetary policy and was nolonger beholden to the Exchequer. This amounts to central bank independence, which has been found, in cross-country stud-ies, to affect monetary outcomes (Cukierman, 1992; Alesina and Summers, 1993).

Solid line: inflation rate (12 month ago); Dashed line: Pr(St=0)

05

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0.0

0.2

0.4

0.6

0.8

1.0

Fig. 1b. The restricted case: UK inflation and the probability of being in St = 0

W. Miles, C.-P. Vijverberg / Journal of Macroeconomics 33 (2011) 644–655 651

We thus implement the following Probit model:

F�1ðPS1Þ ¼ s0 þ s1D81 þ s2D87 þ s3D90 þ s4D92 þ s5D97 þ et

where F�1 is the inverse of the normal CDF, PS1 is the probability of being in the state of St ¼ 1, D81, D87, D90, D92, D97 are thedummy variables for the 1981 budget, Deutschmark shadowing, ERM, IT and Bank of England independence. D81 equals 1 forthe periods of 1981:3–2008:5 and D81 is 0 for all the other time periods. Similarly, D87 (D90, D92, D97) equals 1 for the periodsof 1987:3–2008:5 (1990:10–2008:5; 1992:10–2008:5; 1997:5–2008:5) and D87 (D90, D92, D97) is 0 for all the other time peri-ods. Using PS1 derived from the Markov-Switching model in 1948:9–2008:5, we obtained the following regression results:

F�1ðPS1Þ ¼ 0:434� 1:949D81 � 0:210D87 þ 1:734D90 � 2:183D92 � 0:088D97

ðp�Þð0:000Þð0:000Þð0:240Þð0:000Þð0:000Þð0:016Þ

The numbers in the parentheses are the p-values calculated from robust standard errors. All parameter estimates, exceptthat of D87, are significantly different from zero at the 5% significance level. Again note that the state of St ¼ 1 is the regime ofhigher inflation uncertainty. Thus, the 1981 budget, IT and Bank of England Independence did have significantly negativeimpacts to the probability of the economy being in the state of high inflation uncertainty. Of these three polices that reduceinflation uncertainty in the economy, IT has the largest estimate (i.e., the estimate is �2.183). The estimate of the deutsch-mark shadowing policy is negative but insignificant. This policy thus has no impact on reducing inflation uncertainty. Nota-bly, as previously mentioned, the estimate of ERM membership is positive, implying that the ERM actually increased inflationuncertainty.

Another way to evaluate the impacts of the policies on the inflation dynamics is to inspect the changes in probability di-rectly. Table 3 shows the impacts of each policy on the probability of being in regime 1. By looking at the third column ofTable 3, it is obvious that 1981 budget has the greatest and the 1992 IT has the second greatest impact in reducing the prob-ability of being in a high inflation uncertainty regime. Bank independence actually does not have much impact and 1990ERM actually increases the probability of being in a high inflation uncertainty regime substantially.

5. Discussion

The finding that exchange rate rigidity has no (or, in the case of the ERM, actually a positive) effect on uncertainty must beinterpreted carefully. It bears repeating that the impact is on uncertainty, rather than mean inflation. There is a large liter-ature on the impact of fixed exchange rates on the level of inflation. Ghosh et al. (1997) for instance find a palpable impact,while Bleaney and Francisco (2005) found that, once the endogeneity of the exchange rate regime was controlled for, onlyhard pegs (currency boards and currency unions) had a significant, negative effect on price level changes. Examining fourindustrialized nations, Mumtaz and Sunder-Plassman (2010) find that real exchange rate shocks have less importance forinflation since the 1980s than previously. Again, while there have been papers which have shown a link between the mean

Table 3Impacts of policies on the probability of being in regime 1.

z-Value P(St = 1) DP(St = 1)

1948:6–1981:2 0.434 0.668 –1981:3–1987:2 �1.515 0.065 �0.6031987:3–1990:9 �1.725 0.042 �0.0231990:10–1992:9 0.009 0.504 +0.4621992:10–1997:4 �2.192 0.014 �0.4901997:5–2008:5 �2.280 0.011 �0.003

Solid line: inflation rate (12 month ago); Dashed line: Pr(St=1)

05

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0.0

0.2

0.4

0.6

0.8

1.0

Fig. 2a. US inflation and the probability of being in St = 1

652 W. Miles, C.-P. Vijverberg / Journal of Macroeconomics 33 (2011) 644–655

of inflation and uncertainty, our results only suggest that exchange rate rigidity has been ineffective in lowering uncertainty,and does not have such implications for average inflation.

In contrast to the ineffectiveness of exchange rate rigidity, independence for the Bank of England did lower uncertainty.This is in keeping with the findings of Alesina and Summers (1993). These authors found, in a cross-country study, that cen-tral bank independence lowered the variability of inflation. While this latter metric is a far cruder measure of uncertaintythan that employed in this paper, it does make sense that once monetary policy is insulated from political pressure, pricestability will be given greater weight, lessening the uncertainty the public has about inflation.

At the time of independence, the ‘‘great inflation’’ had been long over, so the impact, while negative and significant, wasfairly small in magnitude. The 1981 budget, in contrast, came on the heels of previous failed attempts to hit money supplytargets and lower inflation. Thus it is not surprising that this policy change had an effect that was quite large in magnitude.

The adoption of IT had a strong negative impact on inflation uncertainty. Fatas et al. (2007), while not examining uncer-tainty, found in a cross-sectional study that IT was more effective in lowering mean inflation than exchange rate targets. Asfor uncertainty, our results suggest that the transparency and communication with the public that IT entails clear up muchuncertainty about the path of inflation.

While it is important to keep in mind that the UK’s experience with IT does not necessarily mean that other countries willhave similar results, it is still interesting to contrast the UK’s performance in terms of inflation uncertainty with that of theUS, the largest economy without a formal target. IT has been a controversial issue for the US Federal Reserve chair Ben Ber-nanke is a well-known advocate of IT adoption for the US. Other members of the Federal Reserve Board, such as Donald Kohn,are on record opposed to IT adoption. The financial turmoil that began in July of 2007 has pushed the issue of a formal targettemporarily out of public view, as some fear that IT could lead to excessive tightening and hamper the central bank’s effortsto deal with the fallout of the subprime mess. On the other hand, the Fed announced in February 2009 that it would publishlong-run inflation and economic forecasts, which may be close to a de facto IT. Moreover, some economists, such as FredericMishkin, remain forceful advocates for de jure IT adoption in the US. The issue will thus be revisited in the future, so we willcontrast uncertainty in the US and UK since the UK adopted IT.

Solid line: inflation rate (12 month ago); Dashed line: Pr(St=1)

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0.0

0.2

0.4

0.6

0.8

1.0

Fig. 2b. The restricted case: US inflation and the probability of being in St = 1

Fig. A1. Classical decomposition of monthly UK inflation rates

W. Miles, C.-P. Vijverberg / Journal of Macroeconomics 33 (2011) 644–655 653

The US data set during the same time period (i.e., 1947:6–2008:5) is the monthly consumer price index for all urban con-sumers in the US The data are obtained from the FREDS website of the St. Louis Federal Reserve Bank. We run the same MS

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time

infla

tion

rate

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++++ : xm12 inflation data

solid line : decomposed xm1 inflation data

Fig. A2. Comparison of decomposed trend data and (X(t) � X(t � 12))/X(t � 12) inflation data

654 W. Miles, C.-P. Vijverberg / Journal of Macroeconomics 33 (2011) 644–655

model with changing mean, persistence and variance. The US estimates are presented in Table 1. By comparing the estimatesof a1, /1, and h1, we cannot see much differentiation between these two countries. However, as we calculate the probabilityof the economy being in St = 1, i.e., the high variance regime, there is a sharp contrast between two countries. As mentionedearlier, for the UK, the periods of high probability of being in St = 1 occur in most of the 1950s, the early 1960s, 1974:1–1978:6, 1979:7–1981:5, and 1990:4–1991:11. It is notable that there has not been a period of high variability in the UK sincethe adoption of IT. In contrast, for US, shown in Fig. 2a (the restricted case, shown in Fig. 2b),17 the periods of high probabilityof being in St = 1 occur in most of the early 1950s, 1973:8–1975:12, 1981:7–1983:7, and 2005:9–2008:1. Thus the US has suf-fered from a period of high uncertainty in the wake of recent shocks, while the UK has managed to avoid such uncertainty.While these results are not a formal test and are only suggestive, they are evidence that ought to be weighed as the US contem-plates adopting an inflation target.

6. Conclusion

To repeat, it is of course the case that results for the UK may not have direct policy implications for other countries. Still,the finding that intermediate steps toward currency union were ineffective, if not actually harmful in countering inflationuncertainty is something that eastern European and other euro-zone aspirants should keep in mind as they embark on targetzones and other ‘‘soft pegs’’ as first steps on the road to euro adoption.

The strong effect of IT on uncertainty does bolster the case that IT provides a clear, observable target and, in the case of theUK, the Bank of England has been credible in its commitment to IT. The first 16 years of IT are of course no guarantee of fu-ture success. This may especially be the case since the Bank of England has missed the formal target and had to send explan-atory letters to the Chancellor of the Exchequer starting in April of 2007. At the same time, our analysis indicates that, morethan a year after Governor Mervyn King first admitted missing the target of 2%, uncertainty did not yet significantly rise inthe UK, while the US with no target, has suffered from rising uncertainty over the path of future monetary policy andinflation.

Appendix A

The UK monthly inflation rates calculated by (X(t) � X(t � 1))/X(t � 1) is shown in the first panel of Fig. A1. Fig. A1 showsthat the actual monthly inflation rates may be decomposed into trend, seasonal and random parts. The method used is clas-sical seasonal decomposition by moving averages. Fig. A2 shows that the decomposed time trend data with a lag of 5 (shownwith solid line) match very closely with the (X(t) � X(t � 12))/X(t � 12) inflation data set (shown with ‘‘+’’). However, with

17 Note that when we restrict the volatility to be the same in both regimes for the US (i.e. the model only allows the level and persistence of inflation to varybetween regimes) we obtain the results shown in the last column of Table 1. Regime 1 has the higher average inflation rate. Fig. 2b shows the probability of USinflation being in regime 1, where the period of 2005–2008 is obviously in a low average inflation regime. The LR test results indicate, however, that theunrestricted case is the better model.

W. Miles, C.-P. Vijverberg / Journal of Macroeconomics 33 (2011) 644–655 655

the decomposed time trend data, we lose the first 6 and the last 6 observations of the original data set while with the(X(t) � X(t � 12))/X(t � 12) calculation, we lose the first 12 observation of the original data set.

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