can central banks monetary policy be described by a linear taylor

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Journal of Financial Stability 7 (2011) 228–246

Contents lists available at ScienceDirect

Journal of Financial Stability

journal homepage: www.elsevier.com/locate/jfstabil

an central banks’ monetary policy be described by a linear (augmented) Taylorule or by a nonlinear rule?�

ítor Castroa,b,∗

Faculty of Economics, University of Coimbra, Av. Dias da Silva 165, 3004-512 Coimbra, PortugalUniversity of Warwick (UK) and NIPE, Portugal

r t i c l e i n f o

rticle history:eceived 20 August 2009eceived in revised form 14 May 2010ccepted 10 June 2010vailable online 30 June 2010

EL classification:434452

a b s t r a c t

The original Taylor rule establishes a simple linear relation between the interest rate, inflation and theoutput gap. An important extension to this rule is the assumption of a forward-looking behaviour ofcentral banks. Now they are assumed to target expected inflation and output gap instead of current val-ues of these variables. Using a forward-looking monetary policy reaction function, this paper analyseswhether central banks’ monetary policy can indeed be described by a linear Taylor rule or, instead, bya nonlinear rule. It also analyses whether that rule can be augmented with a financial conditions indexcontaining information from some asset prices and financial variables. The results indicate that the mon-etary behaviour of the European Central Bank and Bank of England is best described by a nonlinear rule,but the behaviour of the Federal Reserve of the United States can be well described by a linear Taylor rule.

58

eywords:onetary policyonlinear Taylor ruleinancial conditions index

Our evidence also suggests that only the European Central Bank is reacting to financial conditions.© 2010 Elsevier B.V. All rights reserved.

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mooth transition regression model

. Introduction

Since the establishment, by Taylor (1993), of the linear alge-raic interest rate rule that specifies how the Federal Reserve (Fed)f the United States (US) adjusts its Federal Funds target rate tourrent inflation and output gap, several papers have emerged toest the validity of that rule for other countries and time peri-ds.

An important extension was provided by Clarida et al. (1998,000), who suggested the use of a forward-looking version of theaylor rule where central banks target expected inflation and out-

� The author acknowledges helpful comments and suggestions from two anony-ous referees, Jennifer Smith, Natalie Chen, Francisco Veiga, Peter Claeys, Ricardo

ousa, the participants at the 10th INFER Annual Conference, Évora, Portugal, 19–21eptember 2008, and the participants at the Macroeconomics Workshop, Univer-ity of Warwick, UK, 30 September 2008. The author also wishes to express hisratitude for the financial support from the Portuguese Foundation for Science andechnology under Scholarship SFRH/BD/21500/2005. The usual disclaimer applies.∗ Correspondence address: Faculty of Economics, University of Coimbra, Av. Diasa Silva 165, 3004-512 Coimbra, Portugal. Tel.: +351 239 790 526;ax: +351 239 790 514.

E-mail address: [email protected].

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572-3089/$ – see front matter © 2010 Elsevier B.V. All rights reserved.oi:10.1016/j.jfs.2010.06.002

ut gap instead of past or current values of these variables. Thatractice allows the central bank to take various relevant variables

nto account when forming its forecasts.More recently, some studies have extended the forward-looking

aylor rule by considering the effect of other variables in the con-uct of monetary policy. One important extension is related to the

nclusion of asset prices and financial variables in the rule.1 Thisssue has caused a huge discussion in the literature: while someuthors consider it important that central banks target asset prices,thers disagree. To contribute to this discussion, we ask whetherhe basic Taylor rule could instead be augmented with an alter-ative variable that collects and synthesises the information fromhe asset and financial markets, i.e. whether central banks are tar-eting the relevant economic information contained in a group ofnancial variables and not simply targeting each financial variableer se. Thus, the first aim of this paper is to estimate a linear Tay-
or rule for the Eurozone, US and United Kingdom (UK) augmented
ith a financial conditions index that captures the relevant eco-omic information contained in some financial variables. Instead

1 See, for example, Bernanke and Gertler (1999, 2001), Cecchetti et al. (2000),hadha et al. (2004) and Driffill et al. (2006).

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dx.doi.org/10.1016/j.jfs.2010.06.002

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bof a linear reaction function. They find evidence supporting theinclusion of futures prices in the central bank’s reaction functionas a proxy for financial stability. Moreover, Kajuth (forthcoming)shows that monetary policy should also react to house prices due

V. Castro / Journal of Finan

f relying on particular asset prices or financial variables, like othertudies do, the index built in this paper synthesises the relevantnformation provided by those variables in a single variable wherehe weight of each asset and financial variable is allowed to varyver time. The central bank may not be targeting a particular assetr financial variable all the time, but it is possible that it may targett in some occasions, i.e. when, by some reason, it acquires partic-lar economic relevance. Thus, synthesising the information fromeveral assets and financial variables in a weighted index will per-it to extract the particular economic relevance of each variable at

ach point in time and, therefore, put together an amount of infor-ation that is more likely to be targeted by the central bank at any

ime.The results from the estimation of a linear forward-looking Tay-

or rule indicate that the European Central Bank (ECB) reacts to thenformation contained in the financial conditions index developedn this study, but the Fed and Bank of England (BOE) do not react tohis information; they only take into account one or two financialariables and clearly do not target asset prices.

The traditional Taylor rule is a policy rule that is derived from theinimization of a symmetric quadratic central bank’s loss function

ssuming that the aggregate supply function is linear. However, ineality, this may not be the case and the central bank can havesymmetric preferences, i.e. it might assign different weights toxpected negative and positive inflation and output gaps in its lossunction. In that case, they will be following not a linear but a non-inear forward-looking Taylor rule. Only very recently some studiestarted to consider these asymmetries or nonlinearities in the anal-sis of monetary policy.2 This paper extends the analysis into tworeas not yet explored by those studies. First, it applies, for therst time, a nonlinear model to the study of the ECB’s monetaryolicy, where the presence of asymmetries is taken into accountirectly in the structure of the model. This procedure will permitn answer to the following questions: Can the ECB’s monetary pol-cy be characterized by a nonlinear Taylor rule, or more precisely, ishe ECB reacting differently to levels of inflation above and belowhe target? Does the ECB attempt to hit the inflation target pre-isely or keep inflation within a certain range? Second, this studylso extends the nonlinear specification of the Taylor rule with thenancial index used in the linear estimations to check whether,fter controlling for nonlinearities, the ECB and the other two cen-ral banks are still (or not) reacting to the information contained inhat index.

The results of the estimation of the nonlinear smooth transi-ion regression model are very interesting. First, they show that theCB’s monetary policy is better described by a nonlinear monetaryule than by a linear Taylor rule: it only reacts actively to inflationhen it is above 2.5%; and it only starts to react to the business

ycle when inflation is stabilised, i.e. well below 2.5%. Althoughhis estimated threshold is slightly higher than the official target of%, this is an empirical result that confirms quite remarkably theain principles of the ECB’s monetary policy. Second, the results

lso show that the ECB – contrary to the other central banks – con-inues to consider the information contained in the financial indexven after nonlinearities are controlled for. Third, we find weakvidence to reject the linear model for the US but not for the UK,here the BOE seems to be pursuing a target range of 1.8–2.4% for

nflation rather than the current official point target of 2%.
The remainder of this paper is organized as follows: Section 2
resents a brief review of the literature on the Taylor rule. Thepecification used to estimate the linear Taylor rule is described

2 See Martin and Milas (2004), Taylor and Davradakis (2006), Surico (2007a,007b) and Petersen (2007).

ii

pil

ability 7 (2011) 228–246 229

n Section 3; this section also presents the data and analyses thempirical results of the estimation of that specification. The modelsed to estimate the nonlinear Taylor rule is presented and anal-sed in Section 4, as well as the results of its estimation. Section 5mphasises the main findings of this paper and concludes.

. A brief review of the literature on the Taylor rule

This section intends to provide a brief review of the literature onhe Taylor rule, emphasizing the main contributions that motivatehe analysis presented in this paper.

In its original form, the Taylor rule assumes that central banksse past or current values of inflation and output gap to set up the

nterest rate. However, in practice, they tend to rely on all avail-ble information – concerning the expected evolution of prices –hen defining the interest rate. For that reason, Clarida et al. (1998,

000) suggest the use of a forward-looking version of the Tay-or rule where central banks target expected inflation and outputap instead of past or current values of these variables. That prac-ice allows the central bank to take various relevant variables intoccount when forming its forecasts.3 They prove its advantages inhe analysis of the policy behaviour of the Fed and other influentialentral banks. Fourcans and Vranceanu (2004) and Sauer and Sturm2007) also stress the importance of considering a forward-lookingaylor rule in the analysis of the ECB’s monetary policy.

Some studies extend this linear rule by considering the effectf other variables in the conduct of monetary policy. For example,ourcans and Vranceanu (2004) present some evidence of an ECBesponse to the exchange rate deviations from its average. A similaresult is found by Chadha et al. (2004) for the Fed, Bank of Englandnd Bank of Japan and by Lubik and Schorfheide (2007) for theentral banks of Canada and England. Considering the role of moneyupply in the ECB reaction function, Fendel and Frenkel (2006) andurico (2007b) conclude that it does not affect the ECB’s behaviourirectly but it is a good instrument to predict future inflation.

The role of asset prices is an important issue considered inome studies. However, no consensus was reached about whetherhe central bank should or should not target this kind of vari-bles. Cecchetti et al. (2000), Borio and Lowe (2002), Goodhart andofmann (2002), Sack and Rigobon (2003), Chadha et al. (2004)nd Rotondi and Vaciago (2005) consider it important that cen-ral banks target asset prices. They also provide strong support andvidence in that direction. On the contrary, Bernanke and Gertler1999, 2001) and Bullard and Schaling (2002) do not agree with anx-ante control over asset prices. They consider that once the pre-ictive content of asset prices for inflation has been accounted for,onetary authorities should not respond to movements in assets

rices. Instead, central banks should act only if it is expected thathey affect inflation forecast or after the burst of a financial bubblen order to avoid damages to the real economy.4

On the other hand, Driffill et al. (2006) analyse the interactionsetween monetary policy and the futures market in the context

3 Clarida et al. (1998, 2000) also suggest the inclusion of an interest rate smoothingn the estimation of the Taylor rule. The reasons for its inclusion are discussed belown the description of the model.

4 Disyatat (2010) examines how an appropriate monetary policy reaction to assetrices could be operationalized when a concern for financial stability is explicitly

ncluded in the central bank loss function. On a different level, von Peter (2009)ooks at a model where asset prices affect banks’ balance sheets.

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ocetsaing to Clarida et al. (1998, 2000), the central bank’s desired levelfor interest rate (i*) depends on the deviation of expected infla-

30 V. Castro / Journal of Finan

o their effects on consumption. The issue of financial stability islso investigated by Montagnoli and Napolitano (2005). They buildnd use a financial conditional indicator that includes the exchangeate, share prices and house prices in the estimation of a Taylor ruleor some central banks. Their results show that this indicator can beelpful in modelling the conduct of monetary policy. Consideringhese developments, our first aim is simply to estimate a linearaylor rule for the Eurozone, US and UK, where the informationrom some financial variables is accounted for to shed some moreight on its (un)importance.

In all the studies mentioned so far, the Taylor rule is consid-red a simple linear interest rate rule that represents an optimalolicy-rule under the condition that the central bank is minimisingsymmetric quadratic loss function and that the aggregate supply

unction is linear. However, in reality, this may not be the case andhe central bank can have asymmetric preferences and, therefore,ollow a nonlinear Taylor rule. If the central bank is indeed assigningifferent weights to negative and positive inflation and output gaps

n its loss function, then a nonlinear Taylor rule seems to be moredequate to explain the behaviour of monetary policy. However,nly recently the literature has started to consider nonlinear mod-ls or asymmetries in the analysis of monetary policy. Asymmetriesn monetary policy can result from a nonlinear macroeconomic

odel (Dolado et al., 2005), nonlinear central bank preferencesDolado et al., 2000; Nobay and Peel, 2003; Ruge-Murcia, 2003nd Surico, 2007a) or both (Surico, 2007b). In particular, Surico2007b) studies the presence of nonlinearities in the ECB monetaryolicy for the period January 1999–December 2004 estimating a

inear GMM model resulting from the derivation of a loss functionith asymmetric preferences and considering a convex aggregate

upply curve. He finds that output contractions imply larger mon-tary policy responses than output expansions of the same size,ut no asymmetric response is found for inflation. With more datavailable and using a different model – more precisely, a nonlin-ar model (with forward-looking expectations) – we expect to findvidence of an asymmetric response of the ECB to inflation as well.

The forward-looking nonlinear monetary policy rule used in ournalysis takes into account the asymmetries in the macroeconomicodel and in the central bank preferences implicitly and general-

zes the Taylor rule in the tradition of Clarida et al. (1998, 2000).nstead of simply relying on a linear model, à la Surico (2007b),

here the asymmetries are accounted for by using products andross products of inflation and the output gap or by a separate anal-sis for inflation above or below the target, this paper estimates aonlinear model for monetary policy where the presence of asym-etries is taken into account directly in the structure of the model.oreover, this procedure will also give an answer to the question

f whether a central bank follows a point target or a target rangeor inflation.

Two studies deserve our attention in what concerns to the appli-ation of nonlinear models to the analysis of Central Banks’ policyehaviour: Martin and Milas (2004) and Petersen (2007). Martinnd Milas (2004) apply a nonlinear quadratic logistic smooth tran-ition model to the BOE’s monetary policy. They concentrate theirnalysis on the policy of inflation targeting set up in 1992 and find
vidence of nonlinearities in the conduct of monetary policy overhe period 1992–2000.5 They show that the UK monetary authori-ies attempt to keep inflation within a range rather than pursuing
5 Using a simple threshold autoregressive model, i.e. without allowing a smoothransition between high and low inflation regimes, Taylor and Davradakis (2006)lso find evidence of nonlinearities in the conduct of monetary policy by the BOEver the period 1992–2003. In particular, they find that UK monetary authoritiesend to react more actively to inflation when it is above target.

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ability 7 (2011) 228–246

point target and tend to react more actively to upward than toownward deviations of inflation away from the target range. Thenly shortcoming of the paper is not providing a test for the ade-uacy of the model, i.e. the authors do not test the validity of theironlinear model against a linear one or against other nonlinearlternatives. This is a key issue that we will cover in this study.

More recently, Petersen (2007) applies a simple logistic smoothransition regression model to the monetary policy of the Fedver the period 1985–2005 using a basic Taylor rule and findshe presence of nonlinearities: once inflation approaches a certainhreshold, the Fed begins to respond more forcefully to inflation.owever, Petersen (2007) does not take into account the degreef interest rate smoothing or the possibility of the Taylor ruleeing forward-looking. Therefore, a nonlinear analysis consider-

ng those aspects in the Fed behaviour is needed.6 We will providehat analysis and extend the nonlinear monetary rule with otherariables that provide information on the financial conditions. Fur-hermore, using data for the Eurozone, this study will be the first,o our knowledge, to apply a nonlinear model with smooth regimeransition to the study of the ECB’s monetary policy.

. Specification and estimation of the linear Taylor rule

A basic linear Taylor rule is specified and estimated in this sec-ion. We start by describing the rule in its contemporaneous andorward-looking versions. Then we proceed with its estimation forhe Eurozone, US and UK. In Section 4 we will consider the case ofnonlinear rule.

.1. The linear Taylor rule

The following rule was proposed by Taylor (1993) to character-ze the monetary policy in the US over the period 1987–1992:

∗t = r + �∗ + ˇ(�t − �∗) + �(yt − y∗

t ). (1)

This rule regards the nominal short-term interest rate (i*) ashe monetary policy instrument and assumes that it should rise ifnflation (�) rises above its target (�*) or if output (y) increasesbove its trend or potential value (y*). Therefore, ˇ indicates theensitivity of interest rate policy to deviations in inflation from thearget and � indicates the sensitivity of interest rate to the outputap. In equilibrium, the deviation of inflation and output from theirarget values is zero and, therefore, the desired interest rate (i*) ishe sum of the equilibrium real rate (r) plus the target value ofnflation.7

Taylor’s (1993) original rule considers the deviation of inflationver the last four quarters from its target. However, in practice,entral banks do not tend to target past or current inflation butxpected inflation. For that reason, Clarida et al. (1998) suggesthe use of a forward-looking version of the Taylor rule. That ver-ion allows the central bank to take various relevant variables intoccount when forming its inflation forecasts. Therefore, accord-

ion k periods ahead (in annual rates) from its target value and the

6 Qin and Enders (2008) also consider such a model among the several (linear)odels that they estimate for the Fed and where they allow for interest rate smooth-

ng and forward-looking behaviour. Their aim is simply to examine the in-samplend out-of-sample properties of linear and nonlinear Taylor rules for the US econ-my. However, unlike Petersen (2007), they did not find evidence of significantonlinearities in the Fed’s behaviour during the period 1987–2005.7 According to the literature, both the equilibrium real rate and the inflation target

re assumed to be constant (see, for example, Clarida et al., 1998, 2000).

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xpected output gap p periods ahead, which yields the followingorward-looking Taylor rule:

∗t = r + �∗ + ˇ[Et(�t+k|˝t) − �∗] + �Et[(yt+p − y∗

t+p)|˝t], (2)

here E is the expectations operator and ˝t is a vector includingll the available information for the central bank at the time it setshe interest rate.

According to the ‘Taylor principle’, for the monetary policy toe stabilizing the coefficient on the inflation gap (ˇ) should exceednity and the coefficient on the output gap (�) should be posi-ive. A coefficient greater than unity on the inflation gap meanshat the central bank increases the real rate in response to highernflation, which exerts a stabilizing effect on inflation; on the otherand, ˇ < 1 indicates an accommodative behaviour of interest rateso inflation, which may generate self-fulfilling bursts of inflationnd output. A positive coefficient on the output gap means thatn situations in which output is below its potential a decreasen the interest rate will have a stabilizing effect on the econ-my.

A common procedure when estimating monetary policy reac-ion functions is to control for the observed autocorrelation innterest rates. This is usually done by assuming that the centralank does not adjust the interest rate immediately to its desired

evel but is concerned about interest rate smoothing. Several theo-etical justifications are advanced in the literature for the inclusionf interest rate smoothing in the Taylor rule, like the fear of disrup-ions in the financial markets, the existence of transaction frictions,he existence of a zero nominal interest rate lower bound or evenncertainty about the effects of economic shocks. Thus, if the cen-ral bank adjusts interest rates gradually towards the desired level,he dynamics of adjustment of the current level of the interest rateo its target is generically given by:

t =

⎛⎝1 −

n∑j=1

�j

⎞⎠ i∗t +

n∑j=1

�jit−j with 0<n∑j=1

�j < 1, (3)

here the sum of �j captures the degree of interest rate smooth-ng and j represents the number of lags. The number of lags in thisquation is generally chosen on empirical grounds so that autocor-elation in the residuals is absent.

Defining ˛ = r − (ˇ − 1)�∗, yt+p = yt+p − y∗t+p and inserting Eq.

3) into (2) assuming that the central bank is able to control inter-st rates only up to an independent and identically distributedtochastic error (u) yields the following equation:

t =

⎛⎝1 −

n∑j=1

�j

⎞⎠ [˛+ ˇEt(�t+k|˝t) + �Et(yt+p|˝t)]

+n∑j=1

�jit−j + ut, (4)

hich is the specification that is usually estimated in the literature.his rule can be easily extended to include an additional vector ofther m explanatory variables (x) that may potentially influencenterest rate setting. To do that we just need to add �′Et(xt+q|˝t)o the terms in square brackets in (4), where � is a vector of coef-cients associated with the additional variables.8 Eliminating the
nobserved forecast variables from this equation, the policy rule
8 Note that q can be zero, positive or negative depending on the kind of additionalariable(s) considered.

f

ability 7 (2011) 228–246 231

an be rewritten in terms of realized variables:

t =

⎛⎝1 −

n∑j=1

�j

⎞⎠ [˛+ ˇ�t+k + �yt+p + �′xt+q)]

+n∑j=1

�jit−j + εt, (5)

here the error term εt is a linear combination of the forecast errorsf inflation, output, the vector of additional exogenous variablesnd the disturbance ut.9

Eq. (5) will be estimated by the generalized method of momentsGMM). According to Clarida et al. (1998, 2000), this method is welluited for the econometric analysis of interest rate rules when theegressions are made on variables that are not known by the centralank at the decision-making moment. To implement this method,he following set of orthogonality conditions is imposed:

t

{it −

(1 −

n∑j=1

�j

)[˛+ ˇ�t+k + �yt+p + �′xt+q] +

n∑i=1

�jit−j |vt

}= 0, (6)

here vt is a vector of (instrumental) variables within the centralank’s information set at the time it chooses the interest rate andhat are orthogonal with regard to εt. Among them we may haveset of lagged variables that help to predict inflation, the output

ap and the additional exogenous variables, together with otherontemporary variables that should not be correlated to the cur-ent disturbance ut. An optimal weighting matrix that accounts forossible heteroscedasticity and serial correlation in εt is used inhe estimation. Considering that the dimension of the instrumentector vt exceeds the number of parameters being estimated, someveridentifying restrictions must be tested in order to assess thealidity of the specification and the set of instruments used. In thatontext, Hansen’s (1982) overidentification test is implemented:nder the null hypothesis the set of instruments is considered valid;he rejection of orthogonality implies that the central bank doesot adjust its behaviour to the information about future inflationnd output contained in the instrumental variables. Since in thatase some instruments are correlated with vt, the set of orthogo-ality conditions will be violated, which leads to the rejection ofhe model.

In practice, to proceed with the estimation of Eq. (5), we considerhe following reduced form:

t = �0 + �1�t+k + �2yt+p + ϕ′xt+q +n∑i=1

�jit−j + εt, (7)

here the new vector of parameters is related to the former as fol-ows: (�0, �1, �2, ϕ)′ = (1 −

∑ni=1�j)(˛,ˇ, �, �)′. Therefore, given

he estimates of the parameters obtained from (7), we can recoverhe implied estimates of ˛, ˇ, � , and � and the respective standardrrors by using the delta method. Following Clarida et al. (1998),e consider the average of the observed real interest rate over theeriod in analysis as the equilibrium real interest rate. Hence, wean obtain an estimate of the implicit inflation target pursued byhe central bank as follows: �∗ = (r − ˆ )/( ˆ − 1).

.2. Data, variables and additional hypotheses to test

The data used in this study are monthly and mostly obtainedrom the statistics published by the three central banks analysed

9 For further details, see Clarida et al. (1998, 2000).

232 V. Castro / Journal of Financial Stability 7 (2011) 228–246

Fig. 1. Evolution of the main variables used in the estimation of the monetary rule: Eurozone (January 1999–December 2007).

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Fig. 2. Evolution of the main variables used in the estima

ere: ECB Statistics, Fred II for the Fed and BOE Statistics. Otherources are used, especially for data on the additional exogenous
ariables that we will consider here. A detailed description of allariables used in this study and respective sources is provided innnex. Figs. 1–3 show the evolution of the main variables consid-
1t

Fig. 3. Evolution of the main variables used in the estimation o

f the monetary rule: US (October 1982–December 2007).

red in the analysis of the monetary policy followed by each centralank.

The sample covers the following periods: January999–December 2007 for the Eurozone, which correspondso the period during which the ECB has been operating; October

f the monetary rule: UK (October 1992–December 2007).

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wvrespectively : the real exchange rate (REER gap), where the for-eign currency is in the denominator; real stock prices (RStock gap);real house prices (RHPI gap); the credit spread (CredSprd), com-puted as the spread between the 10-year government benchmark


982–December 2007 for the US, a period that starts after whats considered in the literature as the ‘Volcker’s disinflation’; andctober 1992–December 2007 for the UK, the period during which

he BOE has been operating under inflation targeting.We consider several measures of interest rates and inflation.

owever, in the estimations we decided to choose the ones thatave been followed more closely by each central bank and thatermit an easy comparison of the estimation results between thehree economies. For the Eurozone we use the Euro overnight indexverage lending rate (Eonia) as the policy instrument, which is thenterest rate more directly related to the key interest rate (KeyIR)nd that does not suffer from discrete oscillations observed in theater (see Fig. 1). The inflation rate is the annual rate of change ofhe harmonized index of consumer prices (Inflation), which is the

ain reference for the ECB monetary policy. The effective Federaleserve funds rate (FedRate) is used in the estimation of the Tay-

or rule for the US. The inflation variable is the core inflation rateCoreInfl), which excludes food and energy and that is considered aefinition of inflation that the Fed has been following closely (seeetersen, 2007). For the UK we use the three-month Treasury billate (TreasRate) as the nominal interest rate, which according toartin and Milas (2004) and Fig. 3 has a close relationship with the

various) official interest rate instruments used in the period anal-sed. The inflation rate variable is the annual rate of change of theonsumer price index (CPI), which is the main current referenceor the BOE’s monetary policy.10 Independently of the measuressed for the interest rate or inflation, Figs. 1–3 show that bothariables have remained relatively stable and at low levels duringlmost all the period considered for each of the three economiesnalysed in this study. In all the three cases, the output gap (Outp-ap) is constructed by calculating the percentage deviation of the

log) industrial production index from its Hodrick–Prescott trend.igs. 1–3 also illustrate its evolution over time.

For the estimation of the ECB monetary rule, we also considerhe role of money supply. The primary objective of the ECB is pricetability or, more precisely, to keep inflation below but close 2%ver the medium term. However, its strategy is also based on annalytical framework based on two pillars: economic analysis andonetary analysis. The output gap is used in our model to capture

he behaviour of the economy; to control for the role of money wenclude in the model the growth rate of the monetary aggregate

3 (M3). In theory, we expect the ECB to increase the interest ratehen M3 is higher than the 4.5% target defined by this institution

or the growth of money. Whether this variable has been indeedargeted by the ECB is not entirely clear and has been a matter ofuge discussion to which this analysis tries to contribute.11

Financial variables and asset prices represent another group ofariables that have recently been considered in the specification ofhe Taylor rule for the analysis of the behaviour of central banks.n this study we consider the effects of those variables not per seut including them in an index in which each of them will havedifferent weight. The weight depends on the relative economic

mportance of each variable at each particular moment in time.hus, the next step is devoted to the construction of a financial
onditions index (FCI) designed to capture misalignments in thenancial markets. Some monetary and financial indices have beensed in the literature as a measure of the stance of monetary policy
10 The former measure of inflation targeted by the BOE, i.e. the inflation rateomputed from the retail price index excluding mortgage interest payments (RPIXnflation), will also be considered in the robustness analysis for the BOE’s monetaryolicy.11 On this discussion see, for example, Fendel and Frenkel (2006) and Surico2007b).

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n

ability 7 (2011) 228–246 233

nd aggregate demand conditions. Therefore, it is expected thatuch indices can be able to capture current developments of thenancial markets and give a good indication of future economicctivity. Those indices may also contain some useful informationbout future inflationary pressures, which can then be taken intoccount by central banks in their reaction functions. Usually, the FCIs obtained from the weighted average of short-term real interestate, real effective exchange rate, real share prices and real propertyrices.12 The first two variables measure the effects of changes inhe monetary policy stance on domestic and external demand con-itions, whilst the other two collect wealth effects on aggregateemand.

In this analysis, besides computing the FCI we also constructnew and extended FCI (EFCI) from the weighted average of the

eal effective exchange rate, real share prices and real propertyrices plus credit spread and futures interest rate spread.13 Fol-

owing Montagnoli and Napolitano (2005), we use a Kalman Filterlgorithm to determine the weight of each asset. This procedurellows those weights to vary over time. Goodhart and Hofmann2001) propose other methodologies to compute financial indiceslike the estimation of a structural VAR system or the simple esti-ation of a reduced-form aggregate demand equation – in which

hey assume that the weight associated with each variable is fixed.owever, in reality, it is more likely that the economic agents’ port-

olios change with the business cycles. Hence, this study relaxes thessumption of fixed weights and allows for the possibility of struc-ural changes over time. Moreover, we extend the FCI proposed inhose two studies by considering the two additional financial vari-bles indicated above. From the central bank’s point of view, thoseariables may contain further relevant information regarding mar-ets stability and expectations. The credit spread is considered aood leading indicator of the business cycle and of financial stress;nd the changes in futures interest rate spread provide an indi-ation of the degree of volatility in economic agents’ expectationshat the central bank aims to reduce.14

To consider the importance of financial variables in the conductf monetary policy, we extend Rudebusch and Svensson’s (1999)odel by adding those variables to the IS equation.15 The result

s a simple backward-looking version of the model in which theconomy is defined by the following Phillips and IS curves:

t = a0 +m1∑i=1

a1,i�t−i +m2∑j=1

a2,jyt−j +st, (8)

˜t = b0 +p∑k=1

bkyt−k +q∑l=1

blrirt−l +5∑i=1

ni∑j=1

bijxi,t−j +dt , (9)

here rir is the de-trended real interest rate16 and the financialariables (x) are the deviation from the long run equilibrium of,

17

12 See Goodhart and Hofmann (2001).13 As the real interest rate is already incorporated in the monetary rule discussedbove, it is not included in the construction of our EFCI.14 See Driffill et al. (2006) for the use of these two variables in the estimation of aaylor rule for the US.15 For further details, see Goodhart and Hofmann (2001) and Montagnoli andapolitano (2005).

16 The real interest rate is obtained by subtracting the inflation rate from theominal short-term interest rate.17 The long run equilibrium values are computed using the Hodrick–Prescott filter.

2 cial St

bct(part

tcf

wnVtotlmrr

ˇ

w

HogUtaˇtoa

eaawatcwtdifveft

wmm

v

sriseqlnttaoBqive

3

tsactabtvciac

s(oiatpEU

zTrpstc(of the central bank or interest rate smoothing. Despite the estimatesfor OutpGap and�* being reasonable, results indicate that this sim-ple model is unable to capture the reaction of the ECB to inflation


ond yield (Yield10yr) and the interest rate return on commercialorporate bonds; and the change in the spread (FutSprd) betweenhe 3-month interest rate futures contracts in the previous quarterFutIR) and the current short-term interest rate. All these variablesroduce valuable financial information that can be compressed intosimple indicator and then included in the central banks’ monetary

ule to test whether and how they react to this information whenhey are setting up the interest rate.18

Allowing for the possibility of the parameters evolving overime, this means that an unobservable change in any coefficient bijtan be estimated employing the Kalman filter over the state-spaceorm of Eq. (9):

yt = Xˇt +t (measurement equation)ˇt = Fˇt−1 +ωt (transition equation),

(10)

here the error terms are assumed to be independent whiteoises with variance-covariance matrices given by Var(t) = Q andar(ωt) = R, and with Var(tωs) = 0, for all t and s. X is the matrix ofhe explanatory variables plus a constant; all variables are laggedne period. The state vector ˇt contains all the slope coefficientshat are now varying over time. As it is assumed that they fol-ow a random walk process, the matrix F is equal to the identity

atrix. The Kalman filter allows us to recover the dynamic of theelation between the output gap and its explanatory variables. Thisecursive algorithm estimates the state vector ˇt as follows:

t|t = Fˇt|t−1 +Ht−1X(X ′Ht−1X + Q )−1(yt−1 − X ′Fˇt−1|t−1), (11)

here Ht−1 = FPt−1|t−1F′ + R, Pt|t = Ht−1 −t−1X(X ′Ht−1X + Q )−1ZHt−1 (which is the mean square errorf ˇt) and ˇt|t−1 is the forecast of the state vector at period t,iven the information available at the previous period (t − 1).sing this filter we can now recover the unobservable vector of

ime-varying coefficients. The weights attached to each variablere then obtained as follows: wxi,t = |ˇxi,t |/

∑5k=1|ˇxk,t |, where

xi,t is the estimated coefficient of variable xi in period t. Hence,he EFCI time t is computed as the internal product of the vectorf weights and the vector of the five financial variables describedbove, i.e. EFCIt = w′

xt · xt.The EFCI is then included in the monetary rule defined for

ach central bank. As this variable contains valuable informationbout the financial health of the economy, as well as informationbout future economic activity and future inflationary pressures,e expect a reaction of the central bank to changes in this vari-

ble. In particular, we expect an increase of interest rates whenhis indicator improves; on the contrary, more restrictive financialonditions would require an interest rate cut. Using such an indexe are avoiding the critique formulated by some authors that cen-

ral banks should not target asset prices. Central banks may noto that directly and at all the time for each asset, but this study

ntends to show that they can extract some additional informationrom the evolution of those assets, as well as from other financialariables, when setting interest rates. Finally, as the economic rel-vance of these variables changes over time, we are also allowingor the possibility of central banks giving different importance tohem over time.19

A final note regarding the data goes to the kind of data used:e use ex-post revised data. Orphanides (2001) claims that esti-ated policy reactions based on ex-post revised data can provideisleading descriptions of the monetary policy. For that reason, he

18 Unit root and stationarity tests reported below in Table 1 show that all theseariables are stationary, as required, for the three economies.19 For a picture of the evolution of the FCI and EFCI over time, see Figs. 1–3.

r

t

raP

ability 7 (2011) 228–246

uggests the use of real-time data in the analysis of monetary policyules, i.e. data that are available at the time the central bank takests decision on the interest rate. However, Sauer and Sturm (2007)how that the use of real-time data for the Eurozone instead ofx-post data does not lead to substantially different results. As theuality of predictions for output and inflation has increased in the

ast years, those differences are less significant and less problematicowadays, especially in the case of the Eurozone, which representshe main object of study in this paper. For that reason we rely essen-ially on ex-post data in this analysis. However, in the robustnessnalysis we will provide some results with real-time inflation andutput gap data for the Eurozone obtained from the ECB Monthlyulletins.20 As industrial production is the variable that is more fre-uently revised, we also try to overcome the revised-data problem

n the three economies by including in the model an alternativeariable to collect relevant information regarding the state of theconomic activity: the unemployment rate (UR).

.3. Empirical results

Before proceeding with the estimation of the model it is impor-ant to consider some issues. First, the sample period must beufficiently long to contain enough variation in inflation, outputnd EFCI to identify the slope coefficients. Analysing Figs. 1–3, weonclude that the output gap presents sufficient volatility in thehree economies, but the low volatility of inflation for the Eurozonend UK suggests that the interest rate response to inflation muste carefully analysed since it may only represent the behaviour ofhe ECB and BOE in a period of relative inflation stability. The lowolatility of EFCI in those three economies also requires that weonsider the results for this variable with a grain of salt. Second,t is necessary that the variables included in the estimated modelre stationary. Unit root and stationarity tests for the variablesonsidered in this study are presented in Table 1.

Due to the low power and poor performance of these tests inmall samples, we report the results of two different unit root testsDickey and Fuller, 1979 and Ng and Perron, 2001) and the resultsf the KPSS (1992) stationarity test to see whether the power is anssue. For the Eurozone, the power of unit root tests seems to ben issue. Due to the small sample period, they are unable to rejecthe unit root in some variables. However, the KPSS test is able torovide evidence of stationarity for all variables (except M3) for theurozone. Most variables have also proved to be stationary for theK and US.21

The results of the estimation of the Taylor rule for the Euro-one for the period January 1999–December 2007 are reported inable 2. The t-statistics are presented in parentheses and for eachegression we compute the estimate of the implicit inflation targetursued by the ECB (�*). The adjusted R2, Durbin–Watson (DW)tatistic for autocorrelation and the Schwartz Bayesian Informa-ion Criterion (SBIC) are also reported for each regression. The firstolumn presents the results of a Taylor rule in the spirit of Taylor1993), i.e. without allowing for either a forward-looking behaviour

ate. This means that the ECB’s monetary policy is not characterized

20 See Sauer and Sturm (2007) for details on the construction of real-time data forhe Eurozone.21 The evidence is very weak to support the stationarity hypothesis for the interestate and inflation for the US. Nevertheless, considering a longer time period we areble to find evidence of stationarity for those two variables. On this issue, see alsoetersen (2007).

V. Castro / Journal of Financial Stability 7 (2011) 228–246 235

Table 1Unit root and stationarity tests.

Eurozone United States United Kingdom

DF NP KPSS DF NP KPSS DF NP KPSS

Eonia −0.604 −1.425 0.321+

Euribor3m 0.215 −0.868 0.295+

FedRate −1.887 −0.547 1.450TreasRate −4.425* −0.864 0.730+

Inflation −2.723* 0.117 0.432+ −2.718* −1.246 0.482+

CoreInfl −2.277 −0.250 1.990OutpGap −4.881* −3.869* 0.095+ −3.599* −1.141 0.035+ −6.210* −5.136* 0.044+

M3 1.593 0.529 0.927FCI −4.236* −3.512* 0.160+ −4.711* −1.640* 0.043+ −4.430* −3.346* 0.109+

EFCI −4.754* −2.700* 0.048+ −5.346* −1.876* 0.033+ −4.923* −4.141* 0.214+

REER gap −2.901* −1.439 0.142+ −4.509* −2.429* 0.032+ −3.579* −2.006* 0.156+

RStock gap −2.219 −2.457* 0.156+ −4.791* −2.460* 0.038+ −3.989* −3.305* 0.071+

RHPI gap −2.368 −1.992* 0.087+ −2.822* −1.877* 0.031+ −2.959* −2.441* 0.050+

CredSprd −1.452 −1.175 0.157+ −2.808* −0.800 0.187+ −1.227 −1.204 0.169+

FutSprd −7.352* −4.707* 0.229+ −14.22* −1.159 0.165+ −9.625* −0.812 0.195+

UR gap −1.425 −2.301* 0.093+ −5.470* −3.152* 0.076+ −4.107* −2.575* 0.087+

RT Inflation −2.647* −0.264 0.208+

RT OutpGap −3.951* −2.475* 0.076+

1% crit.value −3.507 −2.580 0.739 −3.456 −2.580 0.739 −3.482 −2.580 0.7395% crit.value −2.889 −1.980 0.463 −2.878 −1.980 0.463 −2.884 −1.980 0.46310%crit.value −2.579 −1.620 0.347 −2.570 −1.620 0.347 −2.574 −1.620 0.347

Sources: See Annex.Notes: DF = Dickey-Fuller (1979) unit root test; NP = Ng-Perron (2001) unit root MZt test (the MZa, MSB and MPT tests yield similar results); KPSS = Kwiatkowski-Phillips-Schmidt-Shin (1992) stationarity test. The automatic Newey-West bandwidth selection procedure is used in the NP and KPSS tests and, in both cases, the autocovariancesa

brcf

tsazrwd

av(raat

ipEtr

z

traiai

eibi

cspo(ttcbfle

tibdThis result confirms the evidence provided by Fendel and Frenkel(2006) and Surico (2007b) that the monetary aggregate is indeed

re weighted by the Bartlett kernel.* Unit root is rejected at a significance level of 10% = stationarity.+ Stationarity is not rejected at a significance level of 10%.

y a basic linear Taylor rule. But it can be described by a monetaryule that takes into account future expectations – besides past andurrent information. Hence, we proceed with the estimation of aorward-looking Taylor rule for the Eurozone.

A generalized method of moments (GMM) estimator is usedo estimate the forward-looking Taylor rule with interest ratemoothing. One lag of the interest rate is sufficient to eliminateny serial correlation in the error term (see DW statistic). The hori-ons of the inflation forecast and output gap were chosen to be,espectively, one year (k = 12) and 3 months (p = 3). These horizonsere selected using the SBIC and they seem to represent a sensibleescription of the actual way the ECB operates.22

The set of instruments includes a constant and lags 1–6, 9nd 12 of Inflation, OutpGap, Yield10yr and M3.23 To infer thealidity of the instruments, we report the results from Hansen’s1982) overidentification test, i.e. the Hansen’s J-statistic and theespective p-value. The validity of the instruments is confirmed inny of the regressions shown in Table 2. Heteroscedasticity andutocorrelation-consistent standard errors are used in all estima-ions.

Results for the baseline forward-looking estimation presentedn column 2 show a significant reaction of the ECB to inflation: a oneercentage point (p.p.) rise in expected annual inflation induces the
CB to raise the interest rate by more than one p.p. Therefore, ashe coefficient on inflation is greater than unity, the real interestate increases as well in response to higher inflation and this will
22 Results were not substantially different when other (shorter and longer) hori-ons were used.23 We will see below that our results reject the hypothesis of M3 being targeted byhe ECB, but it has proved to be a good instrument for the forward-looking monetaryule for the ECB. In fact, movements in the monetary aggregates can be informativebout future changes in prices, although their stabilization may not represent anndependent policy goal. The 10-year government benchmark bond yield (Yield10yr)lso contains good and useful past information about the future evolution of thenterest rate to be included in the set of instruments.

n

ttrttd

enr

xert the desired stabilizing effect on inflation. Independently ofts main concern about inflation, the ECB is also responding to theusiness cycle: a one p.p. increase in the output gap generates an

nterest rate increase of about two p.p.We also obtain an interesting estimate of �* = 2.32, which indi-

ates that the ECB’s implicit target for inflation is in practice onlylightly higher than the 2% target announced in its definition ofrice stability. In fact, the data shown in Fig. 1 for the evolutionf inflation rate is consistent with this result: inflation is belowbut close) to 2.3–2.4% for most of the time, but generally abovehe 2% formal target. This means that the ECB was tough in settinghe formal target for inflation to transmit the idea that it is highlyoncerned in controlling inflation (as the former German Bundes-ank). But despite this toughness, its policy has allowed for someexibility which permits to accommodate differences among theconomies that constitute the Eurozone.24

Next we extend the baseline model considering other factorshat the central bank can take into account when defining thenterest rate. According to the monetary pillar, the ECB shoulde targeting the growth of M3. However, no significant effect isetected from the inclusion of M3 in the model (see column 3).25

ot targeted by the ECB and should be excluded from the equation.

24 Alternatively, if we assume that the target is really 2%, we can use it to estimatehe equilibrium real rate. Our experiments provided estimates of around 0.5% forhe regressions presented here, which can be considered a low value for the equilib-ium real rate (see, for example, Fendel and Frenkel, 2006). This evidence reinforceshe idea that the ECB may in fact be targeting a slightly higher value for infla-ion to accommodate asymmetric shocks that may affect the Eurozone countriesifferently.25 In this case we are including in the estimation the variable M3 minus the ref-rence value of 4.5%, which is defined as the target for M3 by the ECB. Results didot change even when we included in the regression the difference of (log) of M3elative to its Hodrick–Prescott trend instead of M3-4.5%.


Table 2Results from the estimation of the linear monetary rule: Eurozone (January 1999–December 2007).

Main estimation results

1 2 3 4 5 6 7

Inflation −0.045 (−0.19) 2.774*** (2.85) 2.624*** (2.76) 2.322*** (3.37) 2.430*** (3.37) 1.179*** (4.58) 2.598*** (3.89)OutpGap 0.541*** (6.03) 1.991*** (5.84) 1.860*** (5.32) 1.717*** (6.92) 1.798*** (7.34) 1.153*** (9.01) 1.074*** (3.78)Eonia(-1) 0.948*** (101.3) 0.944*** (87.7) 0.947*** (125.0) 0.939*** (101.6) 0.953*** (175.5) 0.958*** (141.6)Euribor3m(-1)M3 −0.083 (−0.93)FCI 0.534*** (3.73)EFCI 0.706** (2.44) 1.561*** (4.55)REER gap 0.122*** (3.37)RStock gap 0.041*** (3.88)RHPI gap 1.096*** (4.86)CredSprd −0.271 (−1.27)FutSprd 3.186*** (4.15)US OutpGap 1.161*** (4.59)UR gapRT InflationRT OutpGap�* 2.05*** (16.7) 2.32*** (23.5) 2.22*** (17.5) 2.32*** (20.9) 2.42*** (18.6) 4.41 (1.35) 2.45*** (17.6)

Hansen J-stat. 17.5 [0.953] 17.6 [0.935] 16.5 [0.985] 18.2 [0.956] 22.1 [0.999] 19.6 [0.983]Adj. R2 0.347 0.977 0.977 0.979 0.978 0.981 0.983DW 0.37 2.21 2.20 2.34 2.32 2.51 2.57SBIC 447.8 70.54 74.8 68.2 69.0 70.9 49.4

Robustness checks and sensitivity analysis

8 9 10 11 12 13 14

1.337*** (2.92) 1.425*** (2.69) 1.733** (2.29) 2.501*** (4.16) 1.857*** (4.09)1.099*** (8.79) 1.880*** (8.32) 1.936*** (8.05)

0.904*** (69.2) 0.926*** (72.9) 0.950*** (84.3) 0.958*** (127.1) 0.944*** (121.3) 0.949*** (128.3)0.947*** (116.5)

0.506*** (3.65)1.222*** (5.44) 0.774*** (2.97) 1.758*** (4.31) 0.746*** (2.73) 0.778*** (3.89)

0.648*** (3.67) 1.230*** (4.14)−0.055*** (−9.44) −0.056*** (−5.52)

3.005*** (3.17) 2.018*** (4.64)1.319*** (5.82) 0.632*** (3.34)

2.68** (3.80) 2.96*** (3.11) 2.50*** (6.66) 2.35*** (26.4) 2.62*** (11.6) 2.50*** (21.6) 2.60*** (10.2)

19.8 [0.987] 18.1 [0.956] 18.1 [0.957] 17.7 [0.951] 20.3 [0.978] 16.7 [0.967] 20.1 [0.989]0.985 0.976 0.977 0.977 0.982 0.978 0.9791.50 1.72 1.83 2.10 2.51 2.34 2.39

33.7 76.3 77.9 70.4 52.3 67.7 64.0

Notes: See Annex for sources. Column 1 presents the least square estimates of the following basic Taylor rule: Eoniat =˛+ˇ*Inflationt−1 +�*OutpGapt−1 + ut . A GMM estimatoris used in the other regressions, where the horizons of the inflation and output gap forecasts are, respectively, 12 and 3 months (even when real-time data is used); theother variables (except US OutpGap) are all lagged one period to avoid simultaneity problems, i.e. Eoniat = (1 −�)*[˛+ˇ*Inflationt+12 +�*OutpGapt+3 + �′xt−1] +�*Eoniat−1 + εt ,where ˛, ˇ, � , and the vector � represent the estimated parameters; the respective standard errors are recovered from the estimated reduced form using the delta method.The set of instruments includes always a constant, 1–6, 9, 12 lagged values of the Inflation, OutpGap, Yield10yr and M3; identical lags of the other exogenous variables arealso used when those variables are added to the equation. In regression 13 the lags of Eonia (2–6, 9, 12) are used instead of Yield10yr and in regression 14 are used both.Robust standard errors (heteroscedasticity and autocorrelation-consistent) with Newey-West/Bartlett window and 3 lags were computed and the respective t-statistics arepresented in parentheses; significance level at which the null hypothesis is rejected: ***, 1%; **, 5%; and *, 10%. The estimate of �* (=(r −˛)/(ˇ− 1)) assumes that the long-rune alue oB here ks

Bfe

mtdtTa

u–imai

quilibrium real interest rate is equal to its sample average (here, r = 1.02). The p-vayesian Information Criterion is computed as follows: SBIC = N*ln(RSS) + k*ln(N), wum of squares. DW is the Durbin-Watson statistic.

ut as this variable traditionally provides valuable information toorecast inflation, it constitutes an important variable to be consid-red in the set of instruments.

The inclusion of the financial conditions indices in the ECB’sonetary rule provides a remarkable outcome: results indicate

hat the ECB is targeting not only inflation and the economic con-
itions but it is also reacting to financial conditions when defininghe interest rate. The evidence provided in columns 4 and 5 ofable 2 shows that expansive financial conditions in the Eurozonere stabilized by an increase in the interest rate. For example, a
fiTis

f the Hansen’s overidentification test is reported in square brackets. The Schwartzis the number of regressors, N is the number of observations and RSS is the residual

nitary increase in the financial indicator developed in this studyEFCI – leads to an increase of about three quarters of a p.p. in the

nterest rate. As this index contains additional and valuable infor-ation concerning the evolution of future economic activity and

bout future inflationary pressures, reacting to financial conditionss a way of the ECB also targeting inflation indirectly and avoiding
nancial imbalances that can be prejudicial for economic stability.his is a striking result and represents the first analysis provid-ng evidence that the ECB is not only trying to promote monetarytability but, in doing so, it is also trying to promote the required

cial St

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nancial stability. This means that the ECB monetary policy cane explained by a Taylor rule augmented with information fromnancial conditions.

As mentioned in Section 2, there is a huge discussion in the liter-ture about whether central banks should target financial variablesnd, in particular, asset prices. This paper provides some evidenceavouring the inclusion of the information contained in those vari-bles in the monetary rule.26 In general, existing studies deal withhis issue by including each single asset price or financial variablendependently in the model without taking into account the rel-tive importance of each one at each particular moment in time.ith the index used in this study, we overcome that problem and

oncentrate the information provided by those variables in a singlendicator. This also avoids possible multicollinearity problems that

ay result from the inclusion of all those variables at the same timen a single regression. Nevertheless, to permit a direct comparison

ith other studies, column 6 provides the results of a regressionhat includes the components of EFCI. With the exception of theredSprd, they all present a coefficient with the expected sign andre statistically significant.27 However, the implicit target for infla-ion is very high and not significant, which can be the consequencef a multicollinearity problem.

Another interesting issue raised by this study is whether,esides the ECB is reacting to the Eurozone economic cycle, it is alsoesponding to international economic conditions. To capture thisffect, the US output gap is used as a proxy for the world economicycle. Results indicate that the ECB takes into consideration the cur-ent state of the global economy when deciding on interest rates.n an open global economy, fears of imported inflation (or reces-ion) resulting from a higher (lower) global economic growth abovebelow) the trend are counteracted by a higher (lower) interest raten the Eurozone.

The next group of regressions was devised to analyse the robust-ess of the results presented so far. The first robustness test iselated to the definition of the interest rate. We have consideredhe Eonia as the policy instrument, but the main results are notubstantially affected when we use the 3-months Euribor insteadsee column 8). Only the implicit inflation target is higher than thexpected, which confirms the use of Eonia as a sensible choice.

As industrial production is quite volatile and a variable thatsually suffers revisions, we include an alternative variable in theodel to capture the reaction of the ECB to the economic condi-

ions: the unemployment rate gap (UR gap).28 This variable hasotential to provide relevant information regarding the state ofhe economy at the time the central bank takes its decision onhe interest rate.29 Results are presented in column 9 of Table 2nd show that the coefficient on this variable is positive and highlyignificant, as expected, and the other results are not substantiallyffected. In particular, when the unemployment rate is above its
natural” or long-run level, the ECB tends to decrease the inter-st rate. This important result indicates that the ECB is not simplyargeting economic growth when taking policy decisions, but it is
26 This evidence is in line with other works in the field, like Cecchetti et al. (2000),orio and Lowe (2002), Goodhart and Hofmann (2002), Chadha et al. (2004), Rotondind Vaciago (2005), Driffill et al. (2006) and Kajuth (forthcoming), for which assetrices and indicators of financial stress should be targeted by central banks.27 Note that a depreciation of the Euro above its trend, an increase in share andouse prices above their trends and a higher departure of futures interest rate fromhe current interest rate all contribute to a significant reaction of the ECB to anncrease in the interest rate.28 The variable UR gap is computed from the UR in the same way as we computehe output gap from the industrial production. While UR has a unit root, UR gap istationary, as required.29 The author expresses his gratitude to one of the anonymous referees for bringinghis point to his attention.

fOc

npucbpr

io

ability 7 (2011) 228–246 237

lso quite concerned with unemployment. Moreover, no major dif-erences are obtained even when we use FCI instead of EFCI (seeolumn 10). Results confirm that financial and general economiconditions are taken into account by the ECB when it takes policyctions.

In columns 11 and 12 we use real-time data for inflation andutput gap instead of ex-post revised data. However, as alreadyhown by Sauer and Sturm (2007), the use of real-time data for theurozone, instead of ex-post data, does not lead to substantiallyifferent results.

Finally, in the last two columns we provide a sensitivity analysiso the choice of the set of instruments, in particular in what con-erns to the interest rate instruments. As mentioned above, lagsf the 10-year government benchmark bond yield (Yield10yr) aresed in the set of instruments because they contain good and use-ul past information about the future evolution of the interest rate,

aking the long-term interest rate more (forward-looking) infor-ative as instrument than the short-term interest rate. However,

n the literature lags of the short-term interest rate are quite oftenncluded in the set of instruments.30 To check whether that canffect the results, we decided to use, in regression 13, the lags 2–6,and 12 of the short-term interest rate (Eonia) in the set of instru-ents instead of the lags of Yield10yr; moreover, in regression 14,e included the lags of both variables in the set of instruments. The

esults show that linear estimations are not substantially sensitiveo the use of the short-term instead of long-term interest rate (oroth). Therefore, we proceed by using the long-term interest rate

n the set of instruments given the advantage mentioned above.31

In the next table (Table 3) we reproduce some of the main resultsbtained for the other two economies: US and UK. The sequence inhich the results are presented is quite similar to the one used

or the Eurozone. The estimates in columns US1 and UK1 werebtained from a basic Taylor rule. Such a rule produces quite goodesults for the US but not so impressive for the UK. While the coeffi-ient on inflation is higher than 1 for the US, as expected, it is lowerhan 1 for the UK. However, note that both regressions suffer from aroblem of autocorrelation (see DW). Moreover, it is expected thathese central banks also tend to rely on all available information,hich requires a GMM estimation of a forward-looking Taylor ruleith interest rate smoothing.

The results presented in Table 3 show that two lags of the inter-st rate are required to eliminate any serial correlation in the errorerm in the regressions for the US and UK (see DW). The horizonsf the inflation and output gap forecasts for the US were chosen toe the same as the ones used for the Eurozone; for the UK, we havehe contemporaneous value of the output gap and lead 6 of infla-ion. As in the estimations for the Eurozone, these horizons wereelected using the SBIC. The set of instruments for the US includes aonstant and lags 1–6, 9 and 12 of CoreInfl, OutpGap and Yield10yr;
or the UK, it includes a constant and lags 1–6, 9 and 12 of RPI Infl,utpGap, Yield10yr and FCI.32 The validity of these instruments isonfirmed by the Hansen’s J-test in any of the GMM estimations.
30 See, for example, Clarida et al. (1998, 2000).31 The preference for the long-term interest rate is also practical, given that in theon-linear estimations it is very difficult to find initial values that make convergenceossible when lags of the short-term interest rate (Eonia, FedRate, TreasRate) aresed as instruments instead of (or with) Yield10yr. Even when they are found andonvergence is achieved, results tend to be unreasonable. This might be the caseecause those are lags of the dependent variable, which make the optimizationrocedure more complex. Therefore, given this practical reason and the theoreticaleason mentioned above, the lags of Yield10yr are used as instrument.32 The main conclusions remain unchanged when lags of the respective short term-nterest rates (FedRate or TreasRate) are included in the set of instruments insteadf the lags of Yield10yr (results are not reported here).


Table 3Results from the estimation of the linear monetary rule: US and UK.

United States (October 1982–December 2007)US1 US2 US3 US4 US5 US6 US7 US8

InflationCoreInfl 1.632*** (11.5) 1.530*** (5.18) 1.462*** (4.71) 1.542*** (5.53) 1.556*** (5.80) 1.185** (2.09) 1.588*** (2.73) 2.759*** (3.00)OutpGap 0.356*** (2.59) 1.404*** (2.77) 1.314*** (2.61) 1.039*** (2.71) 1.203*** (2.96) 1.168** (2.50) 0.967** (2.15)FedRate(-1) 1.430*** (14.2) 1.448*** (14.9) 1.471*** (13.4) 1.291*** (13.1) 1.744*** (18.2) 1.696*** (16.8) 1.755*** (21.7)FedRate(-2) −0.467*** (−4.73) −0.484*** (−5.09) −0.508*** (−4.73) −0.325*** (−3.37) −0.765*** (−8.46) −0.713*** (−7.10) −0.776*** (−10.1)TreasRate(-1)TreasRate(-2)FCI 0.125 (0.56)EFCI 1.658 (1.29) 1.864 (1.36)CredSprd 1.242** (2.56)FutSprd 4.734** (2.14)US OutpGapUR gap −0.038* (1.68)�* 3.23*** (11.9) 3.52*** (6.18) 3.54*** (5.29) 3.56*** (6.26) −1.36 (−0.44) 4.29 (0.952) 2.22*** (2.74) 2.11*** (10.5)Hansen J-stat. 20.3 [0.441] 21.6 [0.485] 21.9 [0.407] 24.9 [0.635] 21.4 [0.376] 19.5 [0.551] 13.2 [0.868]Adj. R2 0.603 0.993 0.993 0.993 0.993 0.992 0.994 0.995DW 0.06 2.18 2.22 2.29 2.18 2.57 2.32 2.48SBIC 2010.5 754.0 759.2 745.9 753.7 808.3 431.1 66.6

United Kingdom (October 1992–December 2007)UK1 UK2 UK3 UK4 UK5 UK6 UK7 UK8 UK9

0.532*** (3.27) 1.872*** (4.89) 1.971*** (4.59) 1.791*** (4.02) 1.377*** (3.60) 1.563*** (6.62) 1.240 (1.32) 2.971*** (2.73) 0.610 (1.43)

0.264*** (2.85) 0.912*** (2.80) 0.839** (2.43) 0.882** (2.10) 0.865*** (2.94) 0.648*** (3.01) 1.727*** (2.97) 0.725*** (3.02)

1.388*** (13.9) 1.396*** (13.3) 1.447*** (15.5) 1.456*** (19.5) 1.377*** (19.4) 1.703*** (27.3) 1.349*** (13.6) 1.577*** (36.4)−0.433*** (−4.78) −0.440*** (−4.69) −0.484*** (−5.75) −0.492*** (−6.96) −0.433*** (−6.95) −0.718*** (−11.9) −0.383*** (−4.03) −0.605*** (−15.3)

0.089 (0.63)0.160 (0.39)

1.878*** (3.57)

0.135* (1.82)0.037 (0.81)

1.80*** (6.48) 1.93*** (7.80) 1.93*** (8.17) 1.97*** (6.31) −2.69 (−0.64) 1.99*** (8.82) 1.52 (0.83) 2.60*** (23.4) 2.05** (2.29)22.2 [0.771] 21.6 [0.710] 22.4 [0.664] 26.5 [0.739] 32.2 [0.951] 27.4 [0.499] 21.1 [0.822] 18.6 [0.910]

0.142 0.979 0.979 0.980 0.982 0.979 0.981 0.980 0.9780.10 1.73 1.73 1.91 2.11 1.68 2.41 1.87 2.31927.4 234.7 238.9 228.2 213.0 241.4 214.8 226.6 28.8

Notes: See Annex for sources. Columns US1 and UK1 present the least square estimates of a basic Taylor rule identical to the one estimated for the Eurozone. A GMM estimatoris used in the other regressions; the horizons of the inflation and output gap forecasts for the US (UK) are, respectively, 12 (6) and 3 (0) months (these leads were chosenaccording to the SBIC); the other variables (except US OutpGap) are all lagged one period to avoid simultaneously problems. The set of instruments for the US includesa constant, 1–6, 9, 12 lagged values of the CoreInfl, OutpGap and Yield10yr; the set of instruments for the UK includes a constant, 1–6, 9, 12 lagged values of the RPI Infl,OutpGap, Yield10yr and FCI; identical lags of the other exogenous variables are also used when those variables are added to the equation. In these two cases, a second-orderpartial adjustment model fits the data better than the first-order model used for the Eurozone. Robust standard errors (heteroscedasticity and autocorrelation-consistent)with Newey-West/Bartlett window and 3 lags were computed and the respective t-statistics are presented in parentheses. The estimate of �* assumes that the long-runequilibrium real interest rate is equal to its sample average (r = 2.27 for the US and r = 3.41 for the UK). The p-value of the Hansen’s overidentification test is reported in squareb regret and Ur

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wiried about the financial conditions and let the financial markets,in particular the asset markets, act free from any direct control.The result of this different behaviour seems to be well evident in

rackets. The variable for inflation used in regression UK8 is the RPIX inflation. Thehe chairman at the Fed (August 1987–January 2006). Regressions in columns US8= 1.41 for US and r = 3.13 for the UK). For further details see Table 2.

Results are consistent with the Taylor rule for both countries:he coefficients on inflation are consistently higher than unity andtatistically significant, as required; and the coefficients on theutput gap are positive and statistically significant, as expected.esults also indicate that the Fed has been following an averagearget for inflation of about 3.5% from October 1982 to December007, while the BOE has been following an inflation target of about% in the period October 1992–December 2007, which is in lineith the current target defined by this central bank for its monetaryolicy.

Contrary to the ECB, these two central banks do not appear toeact to financial conditions, as it is shown by the insignificant coef-cients on FCI and EFCI in both cases. However, some componentsf the extended index seem to be considered by those central banks.s pointed out by Driffill et al. (2006), this work confirms that theed reacts to the expected future evolution of interest rates. Results
how that it also reacts to the information provided by the creditpread variable. On one hand, the Fed aims to reduce the volatilityf the spread between the futures and current interest rates, whichnduces it to follow the pace of the futures market. On the other
it

ssion in column US7 was estimated over the period in which Alan Greenspan wasK9 were estimated over the period January 1999–December 2007 (for this period

and, when the long-term government bond yield rate is above theorporate bond yield rate – which means an expected improvementf the economic conditions and consequent inflationary pressuresn the future – the Fed reacts increasing the interest rate. The sec-nd effect is also found for the BOE, but not the first. Moreover, weound no evidence that these two central banks are targeting thevolution of the exchange rate or asset prices,33 a result that is inine with the arguments advanced by Bernanke and Gertler (1999,001) and Bullard and Schaling (2002) on this matter.

These results bring about an important conclusion of this study:hile the ECB is reacting to financial conditions to avoid imbalances

n the asset and financial markets, the Fed and BOE are not so wor-

33 As the coefficients on these variables have not proved to be statistically signif-cant – either when included individually or in group – they were not included inhe estimations reported here.

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he recent credit crunch that arose in the US housing market andhat quickly spread to the UK. Due to the integration of global mar-ets, indirect repercussions are also felt in the Eurozone, but itssset markets (and the economy, in general) have shown more ini-ial resistance to the credit crisis than their counterparts in the USnd even in the UK. Thus, targeting financial conditions might besolution to avoid imbalances in the financial and asset markets

nd, consequently, to avoid a sharp economic slowdown.Results from column UK6 indicate that, as in the Eurozone, the

nternational economic conditions (proxied by the US output gap)eem to be taken into account in the monetary rule for the BOE asell. However, in this case the statistical evidence is much weaker.e also include the UR gap instead of OutpGap in the regressions

S6 and UK7, however, results are not so impressive as in thease of the ECB. The evidence indicates that, contrary to the ECB,he Fed and BOE are not concerned with unemployment. Overall,hese two central banks seem to pay more attention to economicrowth than unemployment in what concerns to the economic con-itions. The results presented in column UK8 were obtained usingdifferent variable for inflation, which is computed from the retailrices index excluding mortgage interest payments (RPIX). Resultsemain consistent relatively to the Taylor principle and the esti-ated target for (RPIX) inflation is now 2.6%, which is remarkably

lose to the official target of 2.5% that had been defined for RPIXnflation.34

According to Sack and Rigobon (2003), we could expect a signif-cant response of the Fed to financial conditions, especially duringhe period in which Alan Greenspan was the Chairman at the Fed.his might be the case because he has suggested that policy-makershould respond to asset prices according to their influence on theutlook for output and inflation (Sack and Rigobon, 2003).35 Toheck this conjecture, we estimate a regression over Greenspan’serm (August 1987–January 2006), but results are not substantiallyifferent from the ones we have obtained for the whole period (seeolumn US7). In particular, the magnitude of the coefficient on EFCIs higher, indeed, but it remains statistically insignificant.

Finally, to compare the monetary policy of the three centralanks analysed here in the same time period, we estimate aegression for the US and UK using data for the period January999–December 2007 (see columns US8 and UK9).36 The estimatedarget for the US inflation is now 2.1%, which indicates a strongeroncern by the Fed in keeping inflation low during this period. Ineneral, the results for the US are quite similar to the ones obtainedor the Eurozone and respect the Taylor principle. However, thestimated model for the UK – despite presenting reasonable esti-ates for the implicit inflation target (2.05%) and for the coefficient

n the output gap – does not show a stabilizing reaction of the BOEo the inflation rate: the coefficient on inflation does not respecthe Taylor principle and it is not statistically significant. One reason

ight be the fact that inflation has remained below the inflationarget defined by the BOE for most of the time during the period

34 RPIX inflation was the measure of inflation targeted by the BOE before changingo the CPI inflation in 2003. But, as the time-span used in this study goes beyond003 and as results using CPI inflation have shown more robust to the inclusion ofdditional regressors, the CPI is preferred to the RPIX.35 The author expresses his gratitude to one of the anonymous referees for bringinghis point to his attention.36 Note that as operational independence was granted to the BOE in May 1997,his time-span also covers most of the period during which it has operated inde-endently of the government control.

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ability 7 (2011) 228–246 239

999–2007 (see Fig. 3), which makes it difficult to detect a signifi-ant reaction of the BOE to this variable.37

In sum, after analysing the results from the estimation of theinear Taylor rule for the ECB, Fed and BOE, we conclude thathe monetary policy followed by these three central banks cane described by a forward-looking linear Taylor rule, which in thease of the Eurozone is clearly augmented by a composite indicatorf financial variables. However, an important question remains: ishe monetary policy of these central banks indeed described by ainear Taylor rule or can their behaviour be instead characterizedy a more complex nonlinear monetary rule? The next section isevoted to answering this question.

. Specification and estimation of the nonlinear Taylor rule

A forward-looking nonlinear Taylor rule is specified and esti-ated in this section. We start by presenting the nonlinear model

nd a test to detect the presence of nonlinearities. For cases inhich the nonlinearity is not rejected, we proceed with the esti-ation of the respective nonlinear specifications.

.1. The nonlinear Taylor rule

The Taylor rule presented and estimated above is a simple linearnterest rate rule that represents a policy-rule under the condi-ion that the central bank is minimising a symmetric quadratic lossunction and that the aggregate supply function is linear. However,n reality, this may not be the case and the central bank can beesponding differently to deviations of aggregates from their tar-ets. If the central bank is indeed assigning different weights toegative and positive inflation and output gaps in its loss function,hen a nonlinear Taylor rule seems to be more adequate to explainhe behaviour of monetary policy.38 Moreover, inflation and theutput gap tend to show an asymmetric adjustment to the busi-ess cycle: output tends to exhibit short and sharp recessions overhe business cycle, but long and smooth recoveries; inflation alsoncreases more rapidly over the business cycle than it decreases.39

nder these circumstances it is natural that the central bank has toespond differently to levels of inflation and output above, belowr around the required targets. These arguments emphasize themportance of considering a nonlinear Taylor rule in the analysis ofhe central bank’s behaviour.

To explain this nonlinear behaviour, we employ a smooth tran-ition regression (STR) model. As this model allows for smoothndogenous regime switches, it is able to explain when the centralank changes its policy rule. Although two versions of this modelave been applied to the study of the behaviour of some relevantentral banks by Martin and Milas (2004) and Petersen (2007), notudy has yet applied such a model to the analysis of the policyehaviour of the ECB.40 This paper intends to do so providing, at the
ame time, a comparative analysis between the monetary policyollowed by the ECB and the monetary policy followed by the Fednd the BOE. Additionally, this paper extends the existing studiesn nonlinear Taylor rules by controlling for financial conditions.
37 Moreover, no further significant evidence was found from the inclusion of theFCI or its components in some experimental regressions (not reported here) forhe US and UK for this shorter time period.38 See Nobay and Peel (2003), Ruge-Murcia (2003), Dolado et al. (2005) and Surico2007a,b).39 See, for example, Hamilton (1989) and Neftci (2001).40 The presence of nonlinearities in the ECB monetary policy was studied by Surico2007b), but without estimating a nonlinear model.

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Inflation is chosen to be the threshold variable because ofthe important weight central banks put on this variable and alsobecause this variable has provided the lowest p-value for the rejec-tion of the linear model.45 The tests for the choice of the transition


A standard STR model for a nonlinear Taylor rule can be defineds follows:41

t = ′zt +ω′ztG(�, c, st) + εt, t = 1, . . . , T (12)

here zt = (1, it−1, . . . , it−n;�t, yt; x1,t, . . . , xm,t)′ is the vector

f the explanatory variables, with h = n + 2 + m. The parameters= ( 0, 1, . . ., h)′ andω = (ω0,ω1, . . .,ωh)′ represent ((h + 1) × 1)

arameter vectors in the linear and nonlinear parts of the model,espectively.42 The disturbance term is assumed to be independentnd identically distributed with zero mean and constant variance,t ∼ iid(0, 2). The transition function G(�,c,st) is assumed to beontinuous and bounded between zero and one in the transitionariable st. As st → −∞, G(�,c,st) → 0 and as st → +∞, G(�,c,st) → 1.he transition variable, st, can be an element or a linear combinationf zt or even a deterministic trend.

A few definitions have been suggested for the transition func-ion in the literature. We start by considering G(�,c,st) as a logisticunction of order one:

(�, c, st) = [1 + exp{−�(st − c)}]−1, � > 0. (13)

This kind of STR model is called a logistic STR model or an LSTR1odel. This transition function is an increasing function of st, where

he slope parameter � indicates the smoothness of the transitionrom one regime to another, i.e. how rapid the transition from zeroo unity is, as a function of st. Finally, the location parameter cetermines where the transition occurs.

Considering this framework, the LSTR1 model can describeelationships that change according to the level of the thresh-ld variable. Assuming that the transition variable is the level ofnflation (st =�t), then the LSTR1 model is able to describe an asym-

etric reaction of the central bank to a high and to a low inflationegime. Given the important weight that the central banks analysedn this study put on inflation, we expect to find significant differ-nces in the behaviour of these banks when (expected) inflation iseviating considerably from a certain threshold.

The STR model is equivalent to a linear model with stochasticallyime-varying coefficients and, as so, it can be rewritten as:

t = [ ′ +ω′G(�, c, st)]zt + εt ⇔ it = �′zt + εt, t = 1, . . . , T. (14)

Given that G(�,c,st) is continuous and bounded between zerond one, the combined parameters, �, will fluctuate between and+ω and change monotonically as a function of st. The more the

ransition variable moves beyond the threshold, the closer G(�,c,st)ill be to one, and closer the parameters�will be to +ω; similarly,

he further st approaches the threshold, c, the closer the transitionunction will be to zero and closer the parameters � will be to .

As a monotonic transition may not be a satisfactory alternative,his study will also consider (and test for) the presence of a non-

onotonic transition function, in line with the work of Martin andilas (2004). In fact, central banks may consider not a simple point

arget for inflation but a band or an inner inflation regime, wherenflation is considered under control and, consequently, the reac-ion of the monetary authorities will be different from a situationhere inflation is outside that regime.

The non-monotonic alternative function to consider is the fol-owing logistic function of order two:

−1
(�, c, st) = [1 + exp{−�(st − c1)(st − c2)}] , (15)
here �> 0, c = {c1,c2} and c1 ≤ c2. This transition function is sym-etric around (c1 + c2)/2 and asymmetric otherwise, and the model

41 For further details, see Granger and Teräsvirta (1993), Teräsvirta (1998) and vanijk et al. (2002).

42 Some of these parameters may be zero a priori.

t

ao

ability 7 (2011) 228–246

ecomes linear when�→ 0. If�→ ∞ and c1 /= c2, G(�,c,st) becomesqual to zero for c1 ≤ st ≤ c2 and equal to 1 for other values; andhen st → ±∞, G(�,c,st) → 1. To distinguish this STR model from the

ne specified above, we call this the quadratic logistic STR modelr LSTR2 model. Considering inflation as a transition variable, thisodel allows us to estimate separate lower and upper bands for the

nflation instead of a simple target value (which in practice may note easy to reach every time).

.2. Linearity versus nonlinearity

In the estimation of the nonlinear model, it is important to testhether the behaviour of monetary policy in a particular coun-

ry can be really described by a nonlinear Taylor rule. This impliesesting linearity against the STR model.43 The null hypothesis ofinearity is H0: �= 0 against H1: �> 0. However, neither the LSTR1

odel nor the LSTR2 model are defined under this null hypothesis;hey are only defined under the alternative. Teräsvirta (1998) andan Dijk et al. (2002) show that this identification problem can beolved by approximating the transition function with a third-orderaylor-series expansion around the null hypothesis. This approxi-ation yields, after some simplifications and re-parameterisations,

he following auxiliary regression:

t = ˇ′0zt + ˇ′

1zt st + ˇ′2zt s

2t + ˇ′

3zt s3t + ε∗

t , t = 1, . . . , T, (16)

here ε∗t = εt +ω′ztR(�, c, st), with the remainder R(�,c,st), and

t = (1, z′t)′ where zt is a (h × 1) vector of explanatory variables.

oreover, ˇj = � ˜j , where ˜

j is a function of ω and c. The nullypothesis of linearity becomes H01: ˇ1 =ˇ2 =ˇ3 = 0, against thelternative H11: “at least one ˇj /= 0, j = 1, 2, 3”. An LM-test can besed to investigate this hypothesis because under the null, ε∗

t = εt .he resulting asymptotic distribution is �2 with 3 h degrees ofreedom under the null.44 If linearity is rejected, we can proceedith the estimation of the nonlinear model. But, which transi-

ion function should be employed? The decision between an LSTR1nd an LSTR2 model can be made from the following sequence ofull hypotheses based on the auxiliary regression (16): H02:ˇ3 = 0;03:ˇ2 = 0|ˇ3 = 0; and H04:ˇ1 = 0|ˇ3 =ˇ2 = 0. Granger and Teräsvirta

1993) show that the decision rule works as follows: if the p-valuerom the rejection of H03 is the lowest one, choose an LSTR2 model;therwise, select an LSTR1.

.3. Empirical results

The empirical work presented in this section provides clear evi-ence that the monetary policy followed by the ECB and by theOE can be described by a nonlinear Taylor rule, but the evidence

s not so clear regarding the behaviour of the Fed. The results ofhe linearity tests provided in the bottom of Table 4 (see line H01)where (expected) inflation is the threshold variable – show thate can reject the linearity hypothesis at a level of significance of

% for the ECB and BOE, but only at 10% for the preferred model forhe Fed.

43 These tests require that the errors are uncorrelated with zt and st , and that allhe variables are stationary. Stationarity tests are provided in Table 1.44 See Teräsvirta (1998).45 Teräsvirta (1998) argues that if there is no reason to choose one variable overny other to be the threshold variable, and if nonlinearity is rejected for more thatne transition variable, the variable presenting the lowest p-value for the rejection

V.Castro

/JournalofFinancialStability7

(2011)228–246

241

Table 4Results from the estimation of the nonlinear monetary rule.

Eurozone United States United Kingdom

EZ1 EZ2 EZ3 EZ4 US1 US2 UK1 UK2 UK3

0 3.156*** (19.9) −0.397 (−0.12) 2.636*** (14.9) 2.820*** (12.4) 4.806*** (14.9) −1.712** (−2.03) 5.536*** (11.0) 2.063* (1.71) 3.357*** (2.92) � 1.353 (0.87) y 0.347*** (3.56) 2.091*** (4.36) 1.979*** (4.67) 3.091*** (3.63) 0.303** (2.24) 0.555* (1.77) 0.257*** (2.62) 1.301** (2.30) 1.136*** (3.59) efci 0.092** (2.34) 0.537* (1.71) cs 1.031* (1.72)� 0.963*** (112.6) 0.960*** (110.8) 0.974*** (130.9)�1 1.500*** (11.6) 1.258*** (11.6) 1.267*** (14.4)�2 −0.561*** (−4.37) −0.295*** (−2.80) −0.289*** (−3.54)ω0 −2.784*** (−3.08) −6.117*** (−9.51) −1.388** (−2.28)ω� 1.139*** (2.88) 1.164* (1.83) 1.190** (2.38) 1.169*** (2.59) 1.974*** (13.5) 2.537*** (7.52) 0.541** (3.28) 2.356** (2.52) 2.415*** (2.82)ωy 0.321** (2.45) −2.483* (−1.82) −1.639 (−1.47)� 21.19 {29.26} 95.04 {651.3} 98.60 {353.0} 15.9 {23.47} 7.22 {7.00} 8.55 {7.01} 64.33 {1490.1} 5.61 {6.64} 2.79 {3.13}c 1.99*** (45.0) 2.47*** (190.3) 2.47*** (197.7) 2.41*** [72.4]c1 2.04*** (20.0) 3.10*** (13.3) 1.61*** (9.96) 1.79*** (9.67) 1.75*** (5.53)c2 3.67*** (10.0) 3.68*** (12.2) 1.99*** (9.87) 2.35*** (22.4) 2.37*** (21.4) �+ω� 2.517* (1.78) y +ωy 0.668*** (7.30) −0.392 (−0.31) 0.340 (0.33)

Hansen J-stat. 16.4 [0.927] 16.3 [0.947] 17.5 [0.983] 18.9 [0.331] 18.8 [0.804] 24.3 [0.912]Adj. R2 0.407 0.978 0.978 0.978 0.632 0.992 0.145 0.977 0.980DW 0.54 2.27 2.36 2.30 0.09 1.98 0.15 1.50 1.60SBIC 452.0 83.7 77.3 72.6 2006.2 817.0 942.5 262.0 247.0

H01 0.000 0.037 0.037 0.000 0.000 0.092 0.001 0.075 0.023H02 0.053 0.004 0.004 0.003 0.274 0.646 0.187 0.224 0.016H03 0.045 0.300 0.300 0.121 0.061 0.054 0.055 0.095 0.005H04 0.014 0.180 0.180 0.019 0.117 0.042 0.562 0.424 0.017

Notes: See Annex for sources. Column EZ1, US1 and UK1 present the (Gauss-Newton) nonlinear Least Square (LS) estimates of the following basic nonlinear Taylor rule:IRt = 0 + �*Inflationt−1 + y*OutpGapt−1 + (ω0 +ω�*Inflationt-1 +ωy*OutpGapt−1) *G(�,c,Inflationt−1) + ut , where IR is the respective interest rate considered for each country and G(�,c,Inflationt−1) = [1 + exp(−�(Inflationt−1 − c))]−1, when the LSTR1 is the chosen model, or G(�,c,Inflationt−1) = [1 + exp(−�(Inflationt−1 − c1)*(Inflationt−1 − c2))]−1, when an LSTR2 is preferred instead. H02 to H04 report the p-value of the testsused to choose the preferred model; H01 reports the p-value of the linearity test. A nonlinear Instrumental Variables (IV) estimator is used in the other regressions, where the horizons of the inflation and out-put gap forecasts are, respectively, 12 and 3 months for the Eurozone and the US, and 6 and 0 months for the UK. Considering the case of the Eurozone, the equation can be written generically as follows:Eoniat = (1 −�)*( 0 + �*Inflationt+12 + y*OutpGapt+3 + efci*EFCIt−1) +�*Eoniat−1 + (1 −�)*(ω0 +ω�*Inflationt+12 +ωy*OutpGapt+3 +ωefci*EFCIt−1)*G(�,c,Inflationt+12) + εt . A similar equation is considered for the US and UK,however, in these cases, a second-order partial adjustment model fits the data better than the first-order model used for the Eurozone; moreover, EFCI is replaced by CredSprd in regression 3 for the UK; both variables arelagged one period to avoid simultaneity problems. The best fitting model is found by sequentially eliminating insignificant regressors by using the SBIC measure of fit. The set of instruments includes: a constant, 1–6, 9, 12lagged values of the Inflation, OutpGap, Yield10yr and M3, and the second and third lags of EFCI for the Eurozone; a constant, 1-6, 9, 12 lagged values of the CoreInfl, OutpGap and Yield10yr for the US; and a constant, 1–6, 9,12 lagged values of the RPI Infl, OutpGap, Yield10yr and FCI for the UK. Following Granger and Teräsvirta (1993) and Teräsvirta (1998), � is made dimension free by dividing it by the standard deviation (LSTR1) or variance(LSTR2) of the inflation variable; since � is not defined at zero, the respective standard error is reported (in brackets) instead of the t-statistic; � presents high standard deviations because relative few observations are locatedaround the threshold. Robust standard errors (heteroscedasticity and autocorrelation-consistent) with Newey-West/Bartlett window and 3 lags were computed and the respective t-statistics are presented in parentheses;significance level at which the null hypothesis is rejected: ***, 1%; **, 5%; and *, 10%. The delta method is used to compute the standard errors of � +ω� and y +ωy . The p-value of the Hansen’s overidentification test isreported in square brackets. The time periods considered for each country are the same as in the linear estimations. For further details see Tables 2 and 3.

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tateapa strong reaction of the BOE to inflation when expected infla-tion is outside the 1.8–2.4% range. As soon as inflation is in thisrange, it only reacts to the business cycle and, to a lesser degree,

48 Note that according to the ECB: “The contribution of monetary policy consistsin maintaining price stability and establishing confidence in the continuation of itsefforts, thereby creating the conditions necessary for the sustained, non-inflationary


unction are also presented in the bottom of Table 4 (see lines H02,03 and H04) and indicate that an LSTR1 fits better to the Eurozone,hile an LSTR2 model is more adequate for the UK (and the US).

his means that the ECB is pursuing a point target, while the BOEand perhaps the Fed) are attempting to keep inflation within aertain range.

The first results presented in Table 4 (EZ1, US1 and UK1) werebtained from the nonlinear least squares estimation of a sim-le nonlinear Taylor rule without allowing for a forward-lookingehaviour or interest rate smoothing (see notes in Table 4). Theest fitting model is found by sequentially eliminating insignificantegressors by using the SBIC measure of fit. The results indicate thathe ECB is reacting to inflation – according to the Taylor principle,� > 1 – only when it reaches values above 2%, which remarkably

oincides with the ECB’s target for inflation and with the implicitarget for inflation estimated in the linear version.46 When inflations well below 2%, the ECB does not react to inflation directly, buteacts to the inflationary pressures that may arise through the eco-omic cycle. In this case, the ECB’s reaction to the output gap seemso become stronger when inflation grows above the 2% target.47

Instead of pursuing a point target (of 2%) for inflation like theCB, the Fed and BOE try to keep inflation within, respectively, the.04–3.67% and 1.61–1.99% ranges, according to this basic nonlin-ar Taylor rule. Results show that when inflation is inside theseanges, these two central banks only react to the output; and theynly react to inflation when it is outside these ranges. However, theeaction of the BOE does not obey to the Taylor principle (note that� < 1).

In general the results seem quite reasonable, but the auto-orrelation problems presented by these estimations suggest thate should allow for interest rate smoothing. Moreover, as central

anks are taking into account not only present and past informationut also future inflation expectations, a forward-looking version ofhe nonlinear model should be considered. Thus, a nonlinear instru-

ental variables (IV) estimator is used to estimate the nonlinearule, where the horizons of the inflation and output gap forecastsnd the set of instruments are the same as we considered in thestimation of the linear model. The validity of the instruments isonfirmed by the Hansen’s J-test in any of the IV estimations. Het-roscedasticity and autocorrelation-consistent standard errors aresed in all the estimations.

Considering the Eurozone first, we start by estimating a moreeneral version of the model where inflation and the output gapre included in the linear and nonlinear parts of the model. Givenhe relevance demonstrated by the EFCI variable in the linear

odel, we extend the forward-looking nonlinear model with theag of this variable. The results are presented in columns EZ2 andZ3 and confirm the significant nonlinear reaction of the ECB toxpected inflation: the ECB only starts to react actively to inflation
hen expected inflation is above 2.5%, a value that is very close
o the implicit inflation target estimated in the linear model andnly slightly higher than the official inflation target announced by

f linearity should be chosen to be the transition variable. In this study, we also triedhe output gap and the EFCI as transition variables but the p-value for the rejectionf the linear model was higher than for inflation and, in most of those cases, theinearity hypothesis was not rejected.46 Note that when inflation is above 2%, for each percentage point increase innflation, the ECB will react by increasing the nominal interest rate by about 1.14ercentage points. As the coefficient on inflation is higher than one that implies thathe real interest rate will increase as well, which means that the monetary behaviourf the ECB will exert the required and desired stabilizing effect over inflation.47 Note that one additional advantage of using this nonlinear model is that weo not need to make any assumption about the equilibrium real interest rate tostimate the (implicit) target for inflation.

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ability 7 (2011) 228–246

he ECB; moreover, the ECB only reacts to the output gap whenxpected inflation is well below 2.5% ( y +ωy is not significant).hese are very important results: first, they confirm the main aimf the ECB of keeping inflation low; second, once this objectives achieved, they also support the expressed ECB’s intention ofromoting a sustainable growth.48 This means that the nonlin-ar Taylor rule estimated in this section presents a quite accurateescription of the way the ECB conducts its monetary policy – evenhough its implicit inflation target has proved to be slightly higherhan the announced target of 2%.49 Moreover, the nonlinear modellso provides some evidence that the ECB is considering the infor-ation contained in some financial variables in its decisions on the

nterest rate.50 Therefore, this study concludes that this augmentedonlinear Taylor rule is the policy rule that best describes the ECB’sehaviour.51

The forward-looking Taylor rule with interest rate smooth-ng estimated for the US (see column US2) does not present anyignificant differences in comparison with the results presentedn column US1. Nevertheless, it is important to emphasize thathe forward-looking linear model for the US is only rejected at aevel of significance of 10%, which means that the Fed monetaryehaviour can be well explained by a forward-looking linear Tay-

or rule. Therefore, this study shows that the evidence found byetersen (2007) that the Fed follows a nonlinear Taylor rule is onlyalid when we consider a basic nonlinear Taylor rule. As soon ase depart from this assumption and consider a more complete

ramework – where the forward-looking behaviour of the Fed andnterest rate smoothing are controlled for – the conclusion mayot be the same.52 In fact, additional linearity tests (not presentedere) have shown that linearity is not rejected when two relevantariables such as CredSprd andFutSprd are included in the nonlin-ar model. The same result was obtained when we tried to includeFCI.

Finally, the results obtained for the UK are quite similar tohe ones obtained for the Eurozone (see columns UK2 and UK3)nd update the evidence provided by Martin and Milas (2004)hat the BOE’s monetary policy can be described by a nonlin-ar Taylor rule and that the BOE tries to keep inflation withinrange – of 1.8–2.4%, according to our evidence – rather than

ursuing the current official point target of 2%. Results indicate

rowth of output and employment.” Cf. ECB (1999, p. 10).49 Instead of estimating c, we also tried to set c = 2% and then estimate the model,ut it did not converge to reasonable values. Only for values of c around 2.5%, weere able to find robust results. This is the case because, as shown in Fig. 1, inflationas remained well above 2% for most of the time period analysed here for the Euro-one. Nevertheless, we think it is preferable to estimate c than to impose a valuehat, in practice, may not fit well to the available data. When a larger time-period isvailable – and more time the ECB is in activity – maybe we can find a value closero the official target of 2%. For the moment, our results show that the ECB is oper-ting with a slightly higher target, which can be seen as a way of accommodatingrevailing economic disparities between the countries that form the Eurozone andway of accommodating asymmetric shocks that may affect them differently.

50 Despite US OutpGap proving significant in the linear model, it is not includedn the nonlinear regressions because due to the complexity of the model it was notossible to achieve convergence after trying several combinations of initial values.51 The results of a nonlinear Taylor rule without EFCI are presented in columnZ4 to permit a direct comparison with the main results obtained for the otherconomies.52 The recent evidence provided by Qin and Enders (2008) for the Fed also pointsn that direction.

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Appendix A. ANNEX


o the additional economic information contained in the CredSprdariable.53

. Conclusions

This paper discusses two important issues. First, it asks whetherentral banks, besides targeting inflation and the output gap, arelso reacting to the information contained in the asset prices andnancial variables. Second, it analyses whether central banks’ mon-tary policy can be described by a linear forward-looking Taylorule or, instead, by a nonlinear rule. Related to this second point,his study also considers whether they are pursuing a point targetr a target range for inflation. The central banks considered in thisnalysis are the ECB, Fed and BOE.

To answer the first question we built a financial conditions indexrom the weighted average of a group of asset prices and financialariables and included it, first, in the linear Taylor rule. The resultsndicate that while the ECB is reacting to the information containedn this index in order to avoid inflationary pressures from imbal-nces in the asset and financial markets, the Fed and BOE do notespond to changes or developments in these markets. In our opin-on, this different behaviour might be one of the causes for theecent credit crunch to have arisen in the US (and UK) housingnd financial markets and not in the Eurozone – even though itsepercussions have spread to all developed markets and to the realconomy. Thus, the first main conclusion of this study is that react-ng to financial conditions might be a solution to avoid imbalancesn the financial and asset markets and, consequently, it may helpo avoid sharp economic slowdowns.

The results mentioned above were obtained using a forward-ooking linear Taylor rule. However, considering that the centralanks might be responding differently to deviations of inflationbove or below from their targets, we decided to test for the pres-nce of nonlinearities in the rule and to estimate a forward-lookingonlinear model, in case they are present. The linearity tests indi-ate that the monetary policy followed by the ECB and by the BOEan be described by a nonlinear Taylor rule, but the evidence is notnough to clearly reject the linear Taylor rule for the Fed.

The estimation of the nonlinear forward-looking Taylor rulesing a smooth transition regression model provides interestingesults. First, they show that the ECB pursuits a point target of about
.5% for inflation. Second, the ECB only reacts actively to expected
nflation when it is above that target and it only starts to react to theusiness cycle when inflation is stabilised well below 2.5%. Thus,nother important conclusion of this study is that the nonlinear

53 Like in the linear model, no other significant results were obtained with thenclusion of other variables.

ability 7 (2011) 228–246 243

aylor rule estimated in this paper encompasses quite remark-bly the principles of the ECB monetary policy: (i) promoting pricetability above everything; (ii) when that is achieved, promoteonditions for a sustainable growth. The fact that the estimatednflation threshold is slightly higher than the 2% reference valuennounced by the ECB may mean that the ECB is in reality allowingor some monetary flexibility to accommodate the economic dif-erences among the countries that constitute the Eurozone and toccommodate asymmetric shocks that may affect them differently.

Even after the nonlinearities are controlled for, the ECB contin-es to consider the information contained in financial variables,hich reinforces the first main conclusion of this study and allowss to say that the nonlinear Taylor rule, augmented with the finan-ial conditions index developed in this study, is the policy rule thatest describes the monetary behaviour of the ECB.

Finally, the nonlinear Taylor rule estimated for the BOE indicateshat this central bank is pursuing a target range of 1.8–2.4% fornflation rather than the official point target of 2%. The BOE reactsctively to inflation when it is outside that range, but, once inside,t only reacts to the business cycle and to the economic informationrovided by the credit spread variable.

Besides extending this study to other central banks, anothermportant extension would be to understand whether and hownancial sector regulation and commercial banks’ off-balance sheetntities are taken into account in the central banks’ reaction func-ion. We believe that such an analysis could contribute a little moreo the understanding of the reasons for the recent credit crunch. Ourntention is to proceed with this analysis in future work, as soon as

ore data become available.Another important point that deserves to be analysed in more

etail is the one related with the replacement of industrial pro-uction with the unemployment rate. The robustness analysisrovided by this paper has shown that the ECB seems to be moreoncerned with unemployment than the Fed or the BoE. Why is thathe case? Can really the unemployment rate be used instead of eco-omic growth in the Taylor rule? Or, are both equally important forentral Banks’ policy decisions? As these questions are beyond thecope of this paper, we leave it to be explored in a future paper.

Description of the variables and respective sources.

2 cial Stability 7 (2011) 228–246

nited States (October982–December 2007)

United Kingdom (October 1992–December2007)

ffective Federal Reserve funds interestate (monthly average).-Month (Libor) Interbank US Dollarnding rate (monthly average)

3-Month (Libor) Interbank Sterling lendingrate (monthly average)3-Month Treasury bill discount rate(monthly average)Official Central Bank interest rate (end ofthe month)

flation rate computed as the annualate of change of the consumer pricesdex (CPI, base year: 1982–84 = 100)

or all urban consumers and all items,easonally adjusted

Inflation rate computed as the annual rateof change of the CPI (base year:2005 = 100), seasonally adjusted. Note: Theofficial CPI starts in 1996 but historicalestimates back to 1988 were calculated bythe UK Office for National Statistics basedon archived RPI data

ore inflation rate computed as thennual rate of change of the consumerrice index (CPI, base year982–84 = 100) for all urbanonsumers and all items less food andnergy, seasonally adjusted

Retail price index (RPI) inflation ratecomputed as the annual change of the RPIall items (January 1987 = 100)RPI excluding mortgage interest payments(January 1987 = 100)

utput gap computed as theercentage deviation of the (log)dustrial production index (totaldustry, seasonally adjusted) from itsodrick–Prescott trend

Output gap computed as the percentagedeviation of the (log) industrial productionindex (total industry, seasonally adjusted)from its Hodrick–Prescott trend

inancial conditions index computeds the weighted average of the realffective exchange rate, real sharerices and real property prices

Financial conditions index computed asthe weighted average of the real effectiveexchange rate, real share prices and realproperty prices

xtended financial conditions indexomputed from the weighted averagef the real effective exchange rate, realhare prices and real property priceslus credit spread and futures interestate spread

Extended financial conditions indexcomputed from the weighted average ofthe real effective exchange rate, real shareprices and real property prices plus creditspread and futures interest rate spread

eal effective exchange rate of the USollar against the currencies of a groupf 26 major US trading partners (CPIeflated); a depreciation of the USollar corresponds to an increase inEER

Real effective exchange rate of the UKPound against the currencies of the majorUK trading partners (CPI deflated); adepreciation of the UK Pound correspondsto and increase in REER

eal share price index computed as theonthly average of the Dow Jonesilshire 5000 composite share pricedex (CPI deflated)

Real share price index computed as themonthly average of the FTSE 100 shareprice index (CPI deflated)

eal house price index obtained fromhe linear interpolation of theuarterly data for the US residentialroperty price index (1980Q1 = 100;PI deflated)

Real house price index obtained from theNationwide monthly house price index(1993Q1 = 100; CPI deflated and seasonallyadjusted)

0-Year US Treasury benchmark bondield (government constant maturityate, monthly average)

10-Year monthly average yield fromBritish Government Securities

UK corporate bond Yield, i.e. interest ratereturns on commercial corporate bonds(monthly average)


Eurozone (January 1999–December 2007) U1

Eonia Euro Overnight Index Average (Eonia) lendinginterest rate in the Eurozone money market(monthly average)

Euribor3m 3-Month (Euribor) Euro Interbank Offered Rate(monthly average)

KeyIR Key ECB interest rate of the main refinancingoperations; minimum bid rate (end of the month)

FedRate Er

Libor3m 3le

TreasRate

OfficRate

Inflation Inflation rate computed as the annual rate ofchange of the harmonized index of consumerprices (HICP, base year: 2005 = 100), seasonallyadjusted

Inrinfs

CoreInfl Cap1ce

RPI Infl

RPIX

OutpGap Output gap computed as the percentage deviationof the (log) industrial production index (totalindustry, seasonally adjusted) from itsHodrick–Prescott trend

OpininH

M3 Annual growth rate of the monetary aggregate M3(seasonally adjusted, 3-month moving average)

FCI Financial conditions index computed as theweighted average of the real effective exchangerate, real share prices and real property prices

Faep

EFCI Extended financial conditions index computedfrom the weighted average of the real effectiveexchange rate, real share prices and real propertyprices plus credit spread and futures interest ratespread

Ecospr

REER Real effective exchange rate of the Euro against agroup of 24 currencies (CPI deflated); adepreciation of the Euro corresponds to anincrease in REER

RDodDR

RStock Real share price index computed as the monthlyaverage of the Dow Jones Euro STOXX price index(HICP deflated)

RmWin

RHPI Real house price index obtained by linearinterpolation of half yearly data for the Eurozoneresidential property price index (period 1995–07;2004 = 100; HICP deflated)

RtqpC

Yield10yr 10-Year Eurozone government benchmark bondyield (monthly average).

1yr

CorpBond Eurozone corporate bond yield, i.e. interest ratereturns on commercial corporate bonds (monthlyaverage)

BAAYield MoodyYield (m

FutIR 3-Month Euribor interest rate futures contracts(monthly average)

3-Monfutures

’s Seasoned BAA Corporate Bondonthly average)

th Eurodollar interest ratecontracts (monthly average)

3-Month Sterling interest rate futurescontracts (monthly average)

cial Stability 7 (2011) 228–246 245

nited States (October982–December 2007)

United Kingdom (October 1992–December2007)

ifference between Yield10yr andAAYield

Difference between Yield10yr andCorpBond.

onthly change of the differenceetween FutIR in the previous quarternd the current FedRate

Monthly change of the difference betweenFutIR in the previous quarter and thecurrent TreasRate

nemployment rate gap computed ashe percentage deviation of thenemployment rate from itsodrick–Prescott trend

Unemployment rate gap computed as thepercentage deviation of the unemploymentrate from its Hodrick–Prescott trend

ederal Reserve Bank of St. Louisconomic Data – FredIIhttp://research.stlouisfed.org/fred2/);CB Statistics for Libor3m; Datastreamr REER, RStock and FutIRffice of Federal Housing Enterpriseversight

http://www.ofheo.gov/hpi download.spx) for RHPI.

Bank of England Statistics(http://www.bankofengland.co.uk/statistics/index.htm); UK Office for NationalStatistics (http://www.statistics.gov.uk/);OECD, Main Economic Indicators for REER,RStock and EcoSent; Nationwide BuildingSociety for RHPI

R

B

B

B

B

C

C

C

C

D

D

D

D

D

F

F

G

G

G

H

H

K

K

L

M

M

N

N

N

O

P

Q

R

R

R

S

S

S


Eurozone (January 1999–December 2007) U1

CredSprd Difference between Yield10yr and CorpBond DB

FutSprd Monthly change of the difference between FutIR inthe previous quarter and the current Euribor3m

Mba

UR gap Unemployment rate gap computed as thepercentage deviation of the unemployment ratefrom its Hodrick–Prescott trend

UtuH

RT Inflation Real-time inflation rate obtained from the inflationestimates reported in the Euro Area Statistics ofthe ECB Monthly Bulletins for each month

RT OutpGap Real-time output gap computed as the ex-postOutpGap, but from the most recent values for theindustrial production published in each ECBMonthly Bulletin

Sources European Central Bank Statistics and MonthlyBulletins(http://www.ecb.int/stats/html/index.en.html);Datastream for CorpBond and FutIR

FE(EfoOO(a

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