Taylor Rules and Interest Rate Smoothing
in the Euro Area
University of Padua
Conventional wisdom suggests that Central Banks implement mon-
etary policy in a gradual fashion. Some researchers claim that this
gradualism is due to ’optimal cautiousness’; by contrast, Rudebusch
(2002) states that the observed policy-rate sluggishness is mainly due
to serially correlated exogenous shocks. In this paper we employ mod-
els in first-differences to assess the ’endogenous’ vs. ’exogenous’ grad-
ualism hypothesis for the Euro Area. Our results offer support to the
former one, so highlighting the importance to model the systematic
policy inertia when tracking the Euro Area monetary policy conduct.
JEL classification system: E4, E5.
Keywords: Taylor rules, interest rate smoothing, Euro Area, serial
correlation, omitted variables.
∗First draft: December 2002. We are grateful to Keith Blackburn (the Editor) and
two anonymous referees for helpful comments and suggestions. We also thank Marie-
Luce Bianne, Antonello D’Agostino, Carlo Favero, Marzio Galeotti, Dieter Gerdesmeier,
Petra Gerlach-Kristen, Victor Lopez, Roberto Motto, Sergio Nicoletti-Altimari, Jorge Ro-
drigues, Barbara Roffia, Massimo Rostagno, Frank Smets, Paul Söderlind, Paolo Surico,
Astrid Van Landschoot, and the participants at the ECB/Monetary Policy Strategy Di-
vision Seminar for insightful discussions. All remaining errors are ours. The hospitality
of the European Central Bank, where much of this work was developed, is gratefully ac-
knowledged. Author’s details: Efrem Castelnuovo, Department of Economics, University
of Padua, Via del Santo 33, I-35123 Padua (PD). Phone: +39 049 827 4257, Fax: +39
049 827 4211. E-mail: email@example.com.
The Taylor (1993) rule has captured the attention of researchers involved in
monetary policy analyses for more than a decade now. One of the reasons of
its success is that, in spite of its simplicity, this rule (which links the inflation
rate and a measure of the output gap to the monetary policy rate) provides
a good ex-post description of the monetary policy implemented by various
Central Banks all over the world. Interestingly, when estimating Taylor-type
rules econometricians typically find that the fit of such rules remarkably
improves when the lagged policy rate is included among the regressors. The
significance and high magnitude of the lagged interest rate has stimulated
several scholars in this field to investigate the rationale behind this apparent
gradualism in the conduct of monetary policy, gradualism often labelled as
’interest rate smoothing’, or ’monetary policy inertia’.1
Such a policy inertia may be rationalized in different ways. Mishkin
(1999) argues that monetary authorities are very averse to reversing the pol-
icy rate course too frequently because of credibility problems, i.e. sudden,
large reversals might lead agents in the economy to reduce their confidence
in the Central Bank (CB henceforth)’s competence. Goodfriend (1991) dis-
cusses how a too volatile policy rate might induce financial instability be-
cause of the likely over-reaction of the markets (e.g. drastic portfolio reallo-
cations, sharp modifications in the cost of loans for firms) that could lead to
disastrous economic feedbacks. Amato and Laubach (1999) and Woodford
(1999, 2001) demonstrate that a smooth policy rate path can be seen as an
optimal choice when the CB is not endowed with any commitment technol-
ogy. In fact, an inertial rate, perceived as such by forward-looking private
agents, may contribute to the reduction of the inflation bias arising under
discretion. Following the intuition provided by Brainard (1967), Söderström
1Clarida, Galí, and Gertler (2000) estimate such a partial adjustment degree with var-
ious specifications of the Taylor rule with US data, finding a magnitude ' 0.8. Approxi-
mately the same magnitude is found by Kozicki (1999), Amato and Laubach (1999), and
Domenéch, Ledo, and Taguas (2002). Estimates for some other industrialized countries
are present in Henderson and McKibbin (1993) and Clarida, Galí, and Gertler (1998),
while for the Euro area there exist contributions by e.g. Peersman and Smets (1999),
Taylor (1999), Gerlach and Schnabel (2000), Domenéch, Ledo, and Taguas (2002), Surico
(2003), Sauer and Sturm (2003), Hayo and Hofmann (2003), and Gerlach-Kristen (2003).
(1999) and Sack (2000) show that parameter uncertainty may be another
element suggesting gradualism to a monetary authority whose knowledge of
the monetary transmission dynamics is limited. Positive exercises conducted
by Favero and Milani (2001) and Castelnuovo and Surico (2004) suggest that
model uncertainty is likely to have been a very important issue for the Fed.
Finally, Orphanides (2003) argues that monetary authorities respond mod-
erately to perceived shocks because it is mindful not to respond to noise in
Interestingly enough, Rudebusch (2002) goes against the conventional
wisdom and claims that the interest rate smoothing at quarterly frequencies
is just an illusion. In a nutshell, his reasoning is the following.If the
partial adjustment strategy had such a high importance in the policy rate
setting, then rational agents should be capable to predict future values of
the quarterly rate with a high degree of precision. On the contrary, standard
term structure regressions show how unpredictable the policy rate is over
one quarter. Rudebusch takes this evidence as convincing to claim that the
quarterly interest rate smoothing is just negligible, and that the persistency
of the observed policy rate is probably due to serially correlated deviations
from the Taylor rate, due e.g. to commodity price scares, credit crunches,
Indeed, the issue of dynamics is important from a policy perspective.
In fact, in the last two decades we have observed an improvement of the
inflation-output gap trade-off in many industrialized countries. Part of this
improvement is surely attributable to better monetary-policy management,
as remarked by Cecchetti, Flores-Lagunes, and Krause (2001) and Favero
and Rovelli (2003).4In general, it is necessary to understand the determi-
2Discussions concerning the interest rate smoothing issue may be found in Lowe and
Ellis (1998), Goodhart (1999), Sack and Wieland (2000), Cecchetti (2000), and Srour
3Moreover, Rudebusch (2002) claims that there might be an omitted variable problem
in standard Taylor rules; a similar opinion is expressed by Söderlind, Söderström, and
Vredin (2004). Indeed, if the Taylor model is misspecified and missing an important
serially correlated regressor, then the importance of the lagged interest rate might be just
spurious. We deal with this relevant issue later in the paper.
4Both Cecchetti et al (2001) and Favero and Rovelli (2003) acknowledge that the
improved inflation-output gap trade-off has probably not been uniquely caused by a better
nants of this successful management, in order to possibly replicate this suc-
cess in presence of similar macroeconomic conditions. Then, is the observed
gradualism endogenous, i.e. stemming from the systematic component of the
monetary policy under analysis, or exogenous, i.e. due to serially correlated
While the discussion has been quite lively as far as the U.S. case is con-
cerned [Rudebusch (2002), English, Nelson, and Sack (2003, ENS hereafter),
Castelnuovo (2003a)], to our knowledge the literature is still silent with re-
gard to the Euro Area case. In fact, although several contributions about
the ’counterfactual’ as well as the true European Central Bank have already
focussed their attention on Taylor-type rules,5none of them has deepened
the important issue of dynamics discussed above.
In this paper we employ models in first differences to assess the impor-
tance of the interest rate smoothing argument vs. that of serially correlated
policy shocks in the Euro Area context. This strategy is followed to overcome
Rudebusch (2002)’s criticism on the mis-specification of the tests performed
with models in levels. In doing so, we take into account several definitions of
the Taylor rate, in order to control for possible omitted variables problems
as done by Clarida, Galí, and Gertler (1998, CGG henceforth), Gerlach and
Schnabel (2000), Surico (2003), and Gerdesmeier and Roffia (2004a). Our
results indicates that also European data supports the partial adjustment
In performing this exercise, we have to keep in mind some important
caveats. First, this is an ex-post analysis mostly referring to a counterfactual
monetary policy conduct. In fact, the European Central Bank began to
manage the Euro Area monetary policy in 1999, while the sample we employ
starts much earlier, i.e. at the beginning of the year 1980. Second, we deal
with a dataset created by computing weighted-averages for the relevant data
for different, potentially ’heterogeneous’ countries such as those belonging
monetary policy management. In fact, there is evidence of a change in monetary policy
preferences, and of more favourable sequences of supply shocks. Still, better monetary
policy management seems to have been quite significant for the last two decades now. For
a contribution focussing on the measurement of policy-makers’ preferences over inflation
and the output gap volatilities, see Cecchetti et al (2002).
5A nice survey of such contributions is offered by Sauer and Sturm (2003).
to the Euro Area. Third, we deal with revised-data, while a CB operates in
Nevertheless, although some breaks may be clearly identified in this pat-
tern (e.g. ERM crisis in 1992), a common effort to bring down inflation to
more sustainable levels has been implemented by several European countries
since the early ’80s, and continued under the monetary policy management
by the European Central Bank [Gerdesmeier and Roffia (2004a)]. Moreover,
the use of synthetic European data is fairly widespread among researchers
[e.g. Peersman and Smets (1999), Taylor (1999), Gerlach and Schnabel
(2000), Doménech et al (2002), Gerdesmeier and Roffia (2004a,b), Surico
(2003), Sauer and Sturm (2003)]. Therefore, we think that our exercise can
be considered as a fairly good first approximation of the track followed by
the ’average’ monetary policy conduct in the Euro Area during the last two
decades. Last but not least in terms of importance, given what written
above we obviously refrain from attaching any normative evaluation to our
estimated simple Taylor rules.7
The structure of the paper reads as follows. Section 2 explains the ad-
vantage of employing models in first differences when dealing with the iden-
tification issue affecting models in levels. In Section 3 we present and discuss
our findings. Section 4 concludes. A description of the dataset employed in
this paper is offered to the reader, and References follow.
2 A direct test for partial adjustment versus serial
Thinking of models in levels, an econometrician can easily build up two
frameworks for representing the partial adjustment (PA) vs. the serial cor-
relation (SC) hypothesis. In particular, the former may be captured by the
6Gerdesmeier and Roffia (2004b) show that Orphanides (2001)’s intuition on the im-
portance of dealing with the real-time data issue applies to the Euro Area as well. By
contrast, Sauer and Sturm (2003) demonstrate that the use of real-time industrial pro-
duction data does not seem to play a very significant role for the point estimates of the
Taylor rules they focus on. We leave the assessment of the impact of the data-revision
issue on the results presented in this study to future research.
7For a critical assessment of Taylor-type rules in such a context, see European Central
it= (1 − ρ)eit+ ρit−1+ ηt
where itis the short-term policy rate managed by the CB in order to
influence the inflation rate and the business-cycle,eitis the target rate (i.e.
tive, and ηtis a white noise policy shock. Alternatively, a process relating
the serially correlated policy shock to the policy rate with no-endogenous
Taylor rate), ρ measures the importance of the interest rate smoothing mo-
persistence may be shaped as follows:
it=eit+ εt, εt= ρεεt−1+ ηt
where εtis an AR(1) process with root ρε.8
Once defined the PA model (1) and the SC model (2), a structure nesting
the two reads as follows:
it= (1 − ρ)eit+ ρit−1+ εt, εt= ρεεt−1+ ηt
Unfortunately, an identification problem arises with such a model [Rude-
busch (2002), Castelnuovo (2003b)]. In fact, both (1) and (2) tend to pro-
duce a persistent policy rate, then it is not very wise to rely upon models
in levels like (3) for scrutinizing the two hypothesis under investigation. By
contrast, it is much more useful to manipulate the model in levels in order
to work with their first-differences counterparts [ENS (2003)]. Once done
so, we are left with the following equations for the PA vs. SC hypothesis:
∆it= (1 − ρ)∆eit+ (1 − ρ)(eit−1− it−1) + ηt
∆it= ∆eit+ (1 − ρε)(eit−1− it−1) + ηt
8We performed some econometric exercises in order to measure which is the serial cor-
relation order featuring the residuals of simple backward and forward looking Taylor rules
without smoothing. Our findings suggest that an AR(1) process is a good approximation
of the errors. These findings - not included in the paper for sake of brevity - are available
The latter equation sheds some light on the implications of the SC engine.
Here, variations of the Taylor-rate cause an immediate and full reaction of
the policy rate change; in fact, there is no inertial adjustment, which is
by contrast present in equation (4) via the coefficient (1 − ρ). Then, it is
possible to build up a direct test on the PA vs. SC hypotheses by exploiting
the empirical model
∆it= γ2∆eit+ γ3(eit−1− it−1) + ηt
and testing the null hypothesis
H0SC: γ2= 1 (7)
Under the null (7), the SC specification holds true. By contrast, a re-
jection of the null hypothesis has clear implications for the dynamics of the
policy rate, which must be at that point influenced also by its lag, if not nec-
essarily just by its lag, the latter case corresponding to the pure PA model.
Actually, there is no reason to believe that only one of the two hypotheses
holds. However, the rejection of the null (7) would imply that the lagged
policy rate enters the Taylor-type rule in its own right, and would support
the endogenous gradualism hypothesis typically discussed in the literature.
Taylor-rate definitions employed in our study
As far as the Taylor rateeitis concerned, it is natural to concentrate on
rate, which reads as follows:
some popular definitions of it. Our benchmark is the original Taylor (1993)
eit= c + bππHICP
= year-on-year HICP inflation rate, and yt
where c is a constant, πHICP
= the output gap.9,10A different specification of the Taylor rate has been
9For a description of the dataset employed in our study, as well as the construction of
the variables involved in our regressions, see the Data description at the end of the paper.
The dataset we used is available upon request.
10In Taylor (1993), the policy rule reads as follows: it = πt+0.5yt+0.5(πt−π∗)+r∗,
with π∗= r∗= 2%. Then, the constant c in the various Taylor rates is a linear convolution
of the inflation target π∗and the real interest rate of equilibrium r∗, i.e. r∗−bππ∗. Neither
popularized by CGG (1998, 2000). These authors have underlined the im-
portance for the CB to adjust the policy rate with respect to future, forecast
movements of both inflation and output gap. Their idea finds its rationale
in the lags affecting the monetary policy transmission. Their definition of
the Taylor rate can be captured by the following modelization:11
eit= c + bπEt−1πHICP
However, as already mentioned above, Rudebusch (2002) calls for omit-
ted serially correlated variables as potential cause of the estimated high
degree of PA. To check also for this, we enrich the original specification (8)
by adding a third regressor, as follows:
eit= c + bππHICP
+ byyt+ bzzt
In our exercise, the regressor ztplays different roles. A variable that we
want to control for is a quadratic transformation of the output gap level,
i.e. zt= y2
t. In doing so we feel inspired by recent works on CBs’ asym-
metric preferences, which imply a non-quadratic representation of their loss
Many normative analyses conducted so far have relied on a
quadratic formalization of the CB’s penalty function. Indeed, apart from
analytical tractability, there does not seem to be an obvious reason why a
CB should symmetrically target the output gap measure [Blinder (1997),
Goodhart (1999), Mayer (2002)]. With our simple modeling strategy we
try to capture possibly asymmetric reactions by the CB to business-cycle
Moreover, we also aim at investigating the CB’s possible responses to
movements in variables such as money (M3) growth and the nominal effec-
tive exchange rate, on the lines of contributions such as CGG (1998), Gerlach
in Rudebusch (2002)’s nor in our study the focus is the one of assessing these elements; for
investigations concentrating on these components, see Judd and Rudebusch (1998) and
Domenéch, Ledo, and Taguas (2002).
11Sauer and Sturm (2003) underline the importance of considering a forward-looking
Taylor rule when describing the monetary policy implemented in the Euro Area.
12Researchers such as Gerlach (2003), Surico (2002, 2003), and Cukierman and Mus-
catelli (2003) have performed empirical endeavours along this avenue. See also the refer-
ences quoted in those papers.
and Schnabel (2000), and Gerdesmeier and Roffia (2004a). The first element
was important for the Bundesbank (CGG, 1998) and it has still a prominent
status within the ECB’s monetary policy strategy [European Central Bank
(2003)]; by contrast, the latter component is meant to capture possible ’ex-
ternal pressures’ affecting Euroland. Given that a CB reacts to deviations of
the relevant aggregates from their long-run equilibrium values or reference
values, we estimate our policy rules by taking the nominal effective exchange
rate in deviations with respect to its sample mean, while the M3 growth rate
is considered in deviations with respect to its reference value, i.e. 4.5%.
The time-span we consider in our analysis is 1980Q1-2003Q4. We adopt
a Nonlinear Least Square estimator for models without expectations (i.e.
when either (8) or (10) is considered), while we employ a 2-Stage Nonlinear
Least Square procedure when (9) is taken into account.13
In the next Section we present and comment our findings.
Our estimates for the Euro area confirm the importance of the PA mech-
anism in explaining the dynamics of the short-term policy rate. This is
understandable when looking at Table 1, that displays the results stemming
from the implementation of the ENS test. Notably, the null (7) is strongly
rejected with all the different specifications of the Taylor rate considered.
Interestingly enough, almost all the point estimates of the inflation coef-
ficient bπ suggest that a fairly tight monetary policy was implemented in
Europe in the ’80s and ’90s.14Indeed, all these simple feedback rules find
13The initial conditions for the NLS/2SNLS are provided by LS/2SLS regressions. The
instruments used for our 2SLS regressions are a constant and 5 lags of the HICP inflation
rate, of the output gap, and of the short-term nominal interest rate. Such number of lags
was selected by running an unrestricted VAR(n) with HICP inflation and the output gap
as endogenous variables, and the policy rate (lags from 1 to n) as exogenous variable, and
by checking the indications stemming from standard lag-length criteria. Likelihood-ratio,
Final prediction error, Akaike, and Hannan-Quinn criteria all suggested a number of lags
equal to 5.
14According to the standard New-Keynesian model a la Clarida et al (1999), the nec-
essary and sufficient condition for having a unique and stable equilibrium in an economic
system populated by rational agents is (approximately) bπ > 1. Interestingly, with the
estimates at hand we can never statistically reject the null hypothesis of unique and stable
in the output gap measure a significant regressor, so confirming also for the
Euro Area the goodness of Taylor (1993)’s descriptive scheme.15
[insert Table 1 about here]
Notably, all the additional regressors considered here do not show any
statistical relevance at the standard confidence levels. This result is in line
with those found by Peersman and Smets (1999) and Gerlach and Schnabel
Table 2 shows the outcome of a stability analysis performed by exploiting
two very popular stability tests: The Chow-breakpoint test and the Chow-
As a break-date we chose 1999Q1, i.e. the beginning of
Stage Three of EMU, a very important date for the Euro Area from an
economic perspective. Overall, our estimates turn out to be fairly stable.
In particular, the only doubts regarding the stability of our coefficients are
15The figures displayed in Table 1 refer to Taylor rules estimated with an output gap
measured as log-deviation of the real GDP with respect to a linear trend (with constant),
i.e. our benchmark case. Our results in terms of statistical importance of the output
gap in such regressions turns out to be robust when an HP-filter measure of the potential
output is employed, as well as when the output gap provided in the Area-Wide Model
database is taken into account. The figures of the latter two cases are available upon
16Instead, these findings seem to be at odds with those in CGG (1998), whose investi-
gated sample spans from 1979 up to 1993. One reason for this different findings may rely
on the different data at hand: National in CGG (1998)’s case, aggregate in ours. More-
over, a plausible explanation for this contrasting result may be the fact that the Maastricht
Treaty, signed up in 1992, forced all the signatory countries to implement tight monetary
and fiscal policies in order to quickly converge toward the Maastricht criteria. Then, al-
though important, external pressures might have been replaced by domestic concerns fully
captured by our sample choice, while only partially by CGG’s.
17The idea of the Chow-breakpoint test is to fit the equation at hand separately for each
subsample to see whether there are significant differences in the estimated equations. A
significant difference indicates a structural change in the relationship. Instead, the Chow-
forecast test first estimates the model for a subsample comprised of the first observations,
then exploits such estimated model to predict the values of the dependent variable in the
remaining data points. A large difference between the actual and predicted values casts
doubt on the stability of the estimated relation over the two subsamples. The distributions
of these two tests are presented in Table 2. For more information about these tests, see
Greene (1997), chapter 7.
cast on the Forward-looking model and on the M3 growth rate gap model.
Nevertheless, the rejection of the stability of the estimated coefficients is not
clearcut, given the different and conflicting indications coming from the two
tests we employed.
In this paper we focussed our attention on the interest rate smoothing ar-
gument in Taylor-type schemes. In a recent contribution, Rudebusch (2002)
challenges the conventional wisdom, and states that the interest rate smooth-
ing at quarterly frequencies is just an illusion. As an indirect proof, he claims
that if this were not the case, then rational agents should be capable to pre-
dict future movements of the policy rate. Indeed, it does not seem to be
true in the real world.
Following English, Nelson, and Sack (2003), we implemented a direct
test for the interest rate smoothing hypothesis in the Euro Area case. Our
estimates turn out to be in favor of the modelization of an ’endogenous
persistence’ mechanisms when fitting Taylor rules for the Euro Area. This
finding, robust across different specifications of the Taylor rate, tends to
underline the importance of undertaking research oriented towards a better
understanding of the monetary policy endogenous gradualism.
5 Data description
For our study we employed the ’Area Wide Model’ dataset. This dataset
collects seasonally adjusted series (except for the HICP index) built up with
the ’Index aggregation method’, i.e. the log-level index for any series is
constructed as a weighted average of the log-level country-specific indexes
of the 12 countries belonging to the Euro Area. A standard adjustment
for seasonality - i.e.the ’Ratio to moving average (multiplicative)’ was
applied to the HICP index, and it revealed there was no need of perform-
ing any seasonal-adjustment for such series. The series employed in this
studies are the following (labels as in Fagan et al, 2005): ’HICP’= harmo-
nized index of consumer prices, ’YER’ = real GDP, ’STN’ = short-term
nominal interest rate, ’EEN’ = effective nominal exchange rate, ’YGA’ =
the output gap. The year-on-year HICP inflation rate was computed as
= 100[log(HICPt/HICPt−4)]. Our benchmark measure of the out-
put gap was computed by applying a linear trend (with constant) to the
log of real GDP. As alternatives, we computed the potential output i) by
employing a standard HP-filter approach with smoothing parameter = 1600,
and ii) by employing the output gap measured by Fagan et al (2005), i.e.
by considering a potential output costructed with the production function
approach. The nominal exchange rate employed in our regressions was de-
meaned by considering the in-sample mean for 1980Q1-2003Q4. For a better
description of the above mentioned time-series, see Fagan et al (2005).
The annual growth rate of the money stock ’M3’ was downloaded from
the European Central Bank’s web-site (http://www.ecb.int, under ’Key indi-
cators’), and it refers to a seasonally-adjusted measure of M3. We performed
a ’monthly-to-quarterly’ frequency transformation by taking simple averages
of monthly observations. The M3 growth rate employed in our regressions
was considered in deviations with respect to the 4.5% reference value.
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H0: γ2= 1
(Wald test, p−value)
Point estimates [Newey-West corrected standard errors in squared brackets].
∗=90%/∗∗=95%/∗∗∗=99% stat. confid. for the rej. of H0: insign. coefficient. Model in diff:
in the others. zt= y2
t; or zt=nominal exchange rate in deviations from its sample mean;
or zt=nominal M3 growth rate. Estimates performed via 2SLS for the forward-looking rule;
NLS for the backward ones. Instruments empl.: [c,πHICP
A constant and a spike dummy for 1992Q3 were also included in the estimated model.
,f(yt)=Et−1ytin the ’Forw.-look.’ case; f(πHICP
Table 1: Endogenous (PA) vs. Exogenous (SC) persistence: Test based on
Models in First-Differences.
Taylor rate Download full-text
Chow − breakpoint
Chow − forecast
∗=90%/∗∗=95%/∗∗∗=99% stat. confid. for the rej. of H0: estimated parameters’ stability.
Breakpoint: 1999Q1. Distributions of the tests (’1’ stands for the sub-sample 1980Q1-1998Q2,
’2’ for the sub-sample 1999Q1-2003Q4, ’12’ for the whole sample, Ti= # obs.i, k = # param.):
Chow breakpoint test, F-stat: F(k,T − 2k) =[u0
Chow forecast test, F-stat: F(T2,T1− k) =(u0
Table 2: Estimated Models in First-Differences: Stability tests.