Measuring inflation persistence: a structural time series approach. NBB Working Paper Nr.70, June 2005
ABSTRACT Time series estimates of inflation persistence incur an upward bias if shifts in the inflation target of the central bank remain unaccounted for. Using a structural time series approach we measure different sorts of inflation persistence allowing for an unobserved timevarying inflation target.
Unobserved components are identified using Kalman filtering and smoothing techniques. Posterior densities of the model parameters and the unobserved components are obtained in a Bayesian framework based on importance sampling. We find that inflation persistence, expressed by the halflife of a shock, can range from 1 quarter in case of a costpush shock to several years for a shock to
longrun inflation expectations or the output gap.
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Working paper research
n° 70
June 2005
Measuring infl ation persistence :
a structural time series approach
Maarten Dossche Gerdie Everaert
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NBB WORKING PAPER No. 70  JUNE 2005
NATIONAL BANK OF BELGIUM
WORKING PAPERS  RESEARCH SERIES
Measuring inflation persistence:
a structural time series approach
___________________
Maarten Dossche (*)
Gerdie Everaert (**)
This study was developed in the context of the "Eurosystem Inflation Persistence Network". We are
grateful for helpful comments of participants of the ECB Conference on "Inflation Persistence in the
Euro Area", 1011 December 2004, Frankfurt and the CFS International Macroeconomics Summer
School, 2430 August 2004, Eltville. We particularly thank Luc Aucremanne, Reinout De Bock,
Freddy Heylen, Andrew Levin, Philippe Moës, Benoît Mojon, Gert Peersman, Raf Wouters and an
anonymous referee for useful comments and suggestions. The views expressed in this paper are
those of the authors and do not necessarily reflect the views of the National Bank of Belgium. We
acknowledge support from the Interuniversity Attraction Poles Program  Belgian Science Policy,
contract no. P5/21. All remaining errors are the authors'.
__________________________________
(*) NBB, Research Department (email: maarten.dossche@nbb.be) and SHERPPA, Ghent University
(www.sherppa.be).
SHERPPA, Ghent University (email: gerdie.everaert@UGent.be) – (www.sherppa.be). (**)
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NBB WORKING PAPER No. 70  JUNE 2005
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ISSN: 1375680X
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NBB WORKING PAPER No. 70  JUNE 2005
Abstract
Time series estimates of inflation persistence incur an upward bias if shifts in the inflation target of
the central bank remain unaccounted for. Using a structural time series approach we measure
different sorts of inflation persistence allowing for an unobserved timevarying inflation target.
Unobserved components are identified using Kalman filtering and smoothing techniques. Posterior
densities of the model parameters and the unobserved components are obtained in a Bayesian
framework based on importance sampling. We find that inflation persistence, expressed by the half
life of a shock, can range from 1 quarter in case of a costpush shock to several years for a shock to
longrun inflation expectations or the output gap.
JELcode : C11, C13, C22, C32, E31
Keywords: Inflation persistence, inflation target, Kalman filter, Bayesian analysis.
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NBB WORKING PAPER No. 70  JUNE 2005
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NBB WORKING PAPER No. 70  JUNE 2005
Non technical summary
The Working Paper "Measuring inflation persistence: a structural time series approach", which is
also published in the ECB Working Paper Series, has been developed within the scope of the
"Eurosystem Inflation Persistence Network", a research network consisting of the euro area's
12 national central banks, the ECB and the academic world. This network examines the size,
causes and consequences of inflation persistence. The paper measures various kinds of inflation
persistence.
It is generally accepted that  over the medium to long run  inflation is a monetary phenomenon, i.e.
entirely determined by monetary policy. Over shorter horizons, however, various macroeconomic
shocks, including variations in economic activity or production costs, will temporarily move inflation
away from the central bank’s inflation objective. Therefore, a profound understanding of the
inflationgenerating process, in particular the speed of inflation adjustment in response to such
shocks, is of crucial importance for a central bank whose policy is oriented towards price stability.
Inflation persistence then refers to the tendency of inflation to converge slowly towards its longrun
value in response to these shocks.
When it comes to measuring historical inflation persistence, a common practice in empirical
research is to estimate univariate autoregressive (AR) time series models and to measure
persistence as the sum of the estimated AR coefficients. In most of these studies, inflation is found
to exhibit high to very high persistence over the postWW II period, i.e. persistence is found to be
close to that of a random walk. This suggests that a central bank's task of pursuing price stability
might be more complicated than if persistence were low. The main point highlighted in this paper is
that unconditional estimates of high postWW II inflation persistence are hard to interpret. The
extent to which the estimates are affected by historical changes in the policy objective blurs the
lesson that a stabilityoriented central bank can learn from them.
The datagenerating process of inflation can be broken down into a number of distinct components,
each of them exhibiting its own degree of persistence. First, shifts in the central bank’s inflation
objective can induce permanent shifts in the mean inflation rate. Second, imperfect or sticky
information implies that private agents have to learn about the central bank’s true inflation objective.
As such, the inflation objective perceived by private agents can persistently differ from the central
bank’s true inflation objective. Third, persistence in the drivers of inflation also introduces
persistence in the observed inflation rate. Finally, there is intrinsic inflation persistence in response
to shocks hitting inflation directly. The latter is likely to be related to price and wagesetting
mechanisms, e.g. price and wage indexation.
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NBB WORKING PAPER No. 70  JUNE 2005
We measure the persistence in the change of the euro area and United States GDP deflator, using
a structural time series model which explicitly models the various components driving inflation. We
pursue both a univariate and a multivariate approach. By extracting information from the central
bank’s key interest rate, we find confirmation that shifts in the central bank’s inflation objective
induce a nonstationary component in the inflation rate. Moreover, the slow adjustment of inflation
expectations in response to changes in the central bank’s inflation objective delays the adjustment
towards the new inflation objective. Both components explain a large fraction of the high degree of
persistence observed in the postWW II inflation rate. Persistence in the drivers of inflation is also
an important factor determining the observed inflation persistence. Taking these components into
account, intrinsic inflation persistence in both the euro area and the United States is found to be
significantly lower than the persistence of a random walk.
The implications for monetary policy are the following. Our evidence indicates that in a stable
inflation regime, where the central bank’s inflation objective does not change and where the public
perception about this inflation objective is well anchored, inflation persistence is relatively low. The
results also imply that in case monetary policy would again give rise to unstable inflation, it would
afterwards be very hard to disinflate due to the slow adjustment of inflation expectations in response
to changes in the inflation objective.
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NBB WORKING PAPER No. 70  JUNE 2005
TABLE OF CONTENTS
1. Introduction............................................................................................................................... 1
2. A structural time series approach .......................................................................................... 4
2.1. Baseline structural model ........................................................................................................... 4
2.2. Univariate identification............................................................................................................... 7
2.3. Multivariate identification ............................................................................................................ 7
3. Estimation methodology........................................................................................................ 11
3.1. State space representation....................................................................................................... 11
3.2. Kalman filter and smoother....................................................................................................... 12
3.3. Bayesian analysis ..................................................................................................................... 13
4. Estimation results................................................................................................................... 14
4.1. Prior information........................................................................................................................ 15
4.2. Posterior distribution................................................................................................................. 16
4.2.1. Posterior distribution of the parameters .............................................................................. 17
4.2.2. Posterior distribution of the states....................................................................................... 19
4.2.3. Halflife and impulse response analysis.............................................................................. 23
5. Conclusions ............................................................................................................................ 25
References ....................................................................................................................................... 27
Appendix 1........................................................................................................................................ 31
Appendix 2........................................................................................................................................ 34
Appendix 3........................................................................................................................................ 35
National Bank of Belgium working paper series............................................................................... 37
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1Introduction
It is generally accepted that over the medium to long run inflation is a monetary phenom
enon, i.e. entirely determined by monetary policy. Over shorter horizons, though, various
macroeconomic shocks, including variations in economic activity or production costs, will
temporarily move inflation away from the central bank’s inflation target. Therefore, a pro
found understanding of the process generating inflation, in particular the speed of inflation
adjustment in response to such shocks is of crucial importance for an inflation targeting cen
tral bank. Inflation persistence then refers to the tendency of inflation to converge slowly
towards the central bank’s inflation target in response to these shocks.
With respect to measuring historical inflation persistence, a common practice in empir
ical research is to estimate univariate autoregressive (AR) time series models and measure
persistence as the sum of the estimated AR coefficients (Nelson and Plosser, 1982; Fuhrer
and Moore, 1995; Pivetta and Reis, 2004). In most of these studies, inflation is found to
exhibit high to very high persistence over the postWW II period, i.e. persistence is found
to be close to that of a random walk. This suggests that, in order to bring inflation back to
its target level, a central bank should react more vigorously than if persistence were low.
Important to note, though, is that this estimated high persistence should be interpreted
as a measure of unconditional inflation persistence as this literature does not take into ac
count that the data generating process of inflation is composed of a number of distinct
components, each of them exhibiting its own level of persistence. As such, there are var
ious factors underlying measured historical inflation persistence. First, over the last four
decades large changes in the monetary policy strategy of industrialised economies have oc
curred. This has lead to shifts in the inflation target1of central banks, which introduces
a nonstationary component in the observed inflation series. Second, due to asymmetric
information, sticky information or imperfect credibility, private agents’ perceptions about
the central bank’s inflation target can differ from the true inflation target. The persis
tence of such deviations can be called expectationsbased persistence (see Angeloni et al.,
2004). Third, the sluggish response of inflation to various macroeconomic shocks is likely
to be related to the wage and pricesetting mechanism. If wages and prices are adjusted
infrequently, they will only gradually incorporate the effects of these shocks and therefore
deviations of the observed inflation rate from the perceived inflation target will persist dur
ing several consecutive periods. This kind of inflation persistence can be called intrinsic
inflation persistence (see Angeloni et al., 2004). Also price and wage indexation, which in
1Although inflation targeting is a monetary policy strategy that only emerged in the 1990s, we will still
use this framework for the 1970s and 1980s. It enables us to identify the implicit inflation target of central
banks from their policy choices as well as subsequent economic outcomes.
1
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troduces backwardlookingness into inflation, add to intrinsic inflation persistence. Fourth,
inflation persistence is determined by the persistence of the various macroeconomic shocks
hitting inflation, e.g. persistent deviations of output from its potential level. This type of
inflation persistence can be called extrinsic inflation persistence (see Angeloni et al., 2004).
In order to get a reliable estimate of the various types of inflation persistence, each of the
above mentioned components should be taken into account explicitly when constructing the
data generating process of inflation. First, permanent shifts in the central bank’s inflation
target lead to permanent changes in inflation. As standard AR models assume that inflation
has a stable mean, these shifts induce an upward bias on measured inflation persistence
(Levin and Piger, 2004). In fact, this argument goes back to Perron (1990) who pointed
out that the standard DickeyFuller unit root test is biased towards nonrejection of the
unit root hypothesis if the true data generating process includes breaks in its deterministic
components. Taking historical changes in the central bank’s inflation target into account
might not be straightforward, though. Contrary to the current conduct of monetary policy,
most countries typically did not directly communicate their inflation target to the public.
Second, if the central bank’s inflation target is not known to private agents or if it is not
fully credible, the inflation target perceived by economic agents might differ from the central
bank’s inflation target. In this case intrinsic and extrinsic inflation persistence should be
measured as the persistence in the deviations of the actual inflation rate from the perceived
inflation target rather than from the central bank’s inflation target. Third, in order to
disentangle intrinsic and extrinsic persistence, the persistence in macroeconomic shocks
hitting inflation should be modelled as well.
In the recent literature, shifts in the central bank’s inflation target are accounted for in
three different ways. First, O’Reilly and Whelan (2004) and Pivetta and Reis (2004) use
rolling regressions to allow for shifts in the mean of inflation over different subsamples.
By lowering the subsample size, the number of breaks that can occur is reduced. Still,
the authors cannot reject the hypothesis that the sum of the AR coefficients equals 1.
Second, Levin and Piger (2004), Gadzinski and Orlandi (2004) and Bilke (2004) estimate
an AR process allowing for discrete breaks in the mean of the inflation process. Without
accounting for possible shifts, Levin and Piger (2004) report a persistence parameter for
the United States GDP deflator of 0.92 over the period 1984Q12003Q4. Once a structural
break is allowed for, persistence drops to 0.36. Third, Cogley and Sargent (2001, 2003), and
Benati (2004) estimate timevarying AR coefficients conditional on a timevarying mean,
which is specified as a random walk process. They find evidence that the AR coefficients of
inflation have dropped considerably over the last decade.
With respect to these recent contributions to the literature, the following drawbacks
2
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should be stressed. First, rolling regressions do not entirely rule out the possibility that a
shift occurred in a specific subsample, especially when shifts are frequent. Moreover, this
approach has limits in terms of degrees of freedom. Second, capturing shifts in monetary
policy by allowing for a timevarying mean inflation rate, either by adding discrete breaks
or a random walk process to the AR model, is inappropriate if the perceived inflation target
differs from the central bank’s inflation target. As this difference is not accounted for in
these models, the persistence in the deviation of the perceived inflation target from the
central bank’s inflation target is implicitly restricted to equal the average of intrinsic and
extrinsic inflation persistence.
This paper uses a structural time series approach to model the data generating process
of inflation in the euro area2and the United States. Given the various sources of inflation
persistence, structural time series models are particularly suited as in these models a time
series can be decomposed into a number of distinct components, each of them being modelled
explicitly. We pursue both a univariate and a multivariate approach. In both approaches,
intrinsic and extrinsic inflation persistence are measured as the persistence of the devia
tions of inflation from the perceived inflation target. In contrast to the current literature,
this allows for expectationsbased persistence in response to shocks to the inflation target.
Expectationsbased persistence is incorporated by modelling the perceived inflation target
as an AR process around the central bank’s inflation target, the latter being modelled as a
random walk. Kozicki and Tinsley (2003) use a similar model to disentangle permanent and
transitory monetary policy shifts. Contrary to these authors, in the multivariate model we
explicitly decompose output into potential output and a business cycle component. In this
way we can consistently disentangle intrinsic and extrinsic inflation persistence in response
to shocks to the business cycle.
As the univariate and the multivariate model both include a number of unobserved
components, they are cast in a linear Gaussian state space representation. This enables the
identification of the unobserved components from the observed data using Kalman filtering
and smoothing techniques. The unknown parameters are estimated in a Bayesian framework,
exploiting information both from the sample data and from previous studies estimating
similar models. Posterior densities of the model parameters and the unobserved components
are obtained using importance sampling.
The results indicate that intrinsic inflation persistence is not close to that of a random
walk, i.e. the sum of the AR coefficients ranges from 0.45 in the euro area to 0.80 in the
United States. Considerable extrinsic persistence explains why inflation deviates from the
2Although the euro area did not exist for the larger part of our data sample (1970Q21998Q4), we use
synthetic data aggregating the respective national data (Fagan et al, 2005). We thus implicitly assume that
the euro area was an economy with a homogeneous monetary policy over the entire sample.
3
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perceived inflation target during several consecutive periods. This source of persistence
corresponds to the persistence in the output gap that drives inflation. Expectationsbased
persistence is estimated to be at least as high as intrinsic persistence, indicating that the
dissipation of changes in the policy target is typically slower than in case of temporary
shocks. Next to permanent changes in the central bank’s inflation target, this explains the
observed high degree of aggregate post war inflation persistence.
The implications for monetary policy are as follows. Our evidence indicates that in a
stable inflation regime, where the central bank’s inflation target does not change and where
the public perception about this inflation target is well anchored, inflation persistence is
relatively lower. The results also imply that in the case monetary policy would again give
rise to unstable inflation, it would afterwards be very hard to disinflate due to the slow
adjustment of inflation expectations in response to changes in the inflation target. In the
case of natural rate misperceptions (Orphanides and Williams, 2004) this might however
not be straightforward to avoid.
2A structural time series approach
In this section, we present a structural time series model for inflation which takes into
account (i) possible shifts in the central bank’s inflation target, (ii) expectationsbased
persistence, (iii) intrinsic persistence and (iv) extrinsic persistence. The model is identified
both in a univariate and a multivariate setup. The univariate approach relies on time series
data for inflation only. In the multivariate model, we add information contained in real
output and the central bank’s key interest rate. Using a variant of the macroeconomic model
of Rudebusch and Svensson (1999), this allows us to impose more economic structure on the
identification process. The advantage of the univariate over the multivariate model is that
its relative simplicity reduces the risk of specification errors. The state space representation
of both models is given in section 3.
2.1Baseline structural model
The baseline structural model is given by:
πT
t+1
=πT
t+ η1t, (1)
πP
t+1
=Et+1πT
t+1,
Xq
(2)
πt
= (1 −
i=1ϕi)πP
t+
Xq
i=1ϕiLiπt+ β1zt−1+ ε1t,
Xq
i=1ϕi< 1, (3)
where πT
tis the central bank’s inflation target, πP
tis the perceived inflation target, πtis the
observed inflation rate and ztis the output gap, i.e. the percentage deviation of real output
4
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from potential output. L is the lag operator so that Liπt= πt−i. ε1tand η1tare mutually
independent zero mean white noise processes.
Equation (1) specifies πT
tas a random walk process, i.e. shifts in the central bank’s infla
tion target are assumed to be permanent. These shifts can be thought of as representing (i)
changes in the central bank’s preferences over alternative inflation outcomes (see Andolfatto
et al., 2002) or (ii) an implicit change in the inflation target of the central bank created by
misperceptions about the natural rate of different real variables (Orphanides and Williams,
2004)
Shifts in πT
tare unlikely to be passed on to inflation expectations immediately. Castel
nuovo et al. (2003) present data on longrun inflation expectations. These suggest that in
the aftermath of shifts in monetary policy, convergence towards the new equilibrium evolves
smoothly over time. In the literature, this is often attributed to asymmetric information
and signal extraction, sticky information or imperfect credibility. The source of asymmetric
information on behalf of the private agents can be due to a lack of knowledge about the
central bank’s inflation target (Kozicki and Tinsley, 2003) or uncertainty about the central
bank’s preferences of inflation over real activity (Cukierman and Meltzer, 1986; Tetlow and
von zur Muehlen, 2001). If private agents have to extract information about the central
bank’s inflation target from a monetary policy rule, the signaltonoise ratio of this policy
rule determines the uncertainty faced by private agents in disentangling transitory and per
manent policy shocks and therefore also the speed at which they recognise permanent policy
shocks (Erceg and Levin, 2003). Further, even if the central bank clearly announces a new
inflation target, it can take quite some time before the new policy target is incorporated into
longrun inflation expectations of private agents (for evidence see Castelnuovo et al., 2003).
This might be due to costs of acquiring information and/or reoptimisation (Mankiw and
Reis, 2002). Summing up, private agents must form expectations about the inflation target
πT
t. Therefore, equation (2) introduces the perceived inflation target πP
t, which captures
the private agents’ beliefs about the central bank’s inflation target πT
t.
The expectations operator in equation (2) is operationalised by modelling πP
t+1as a
weighted average of πP
tand πT
t+1,
πP
t+1= (1 − δ)πP
t+ δπT
t+1+ η2t,0 < δ ≤ 1,(4)
where η2tis a zero mean white noise process. The weighting parameter δ can be interpreted
as being the information updating parameter λ in a variant of the stickyinformation model
of Mankiw and Reis (2002) or as being proportional to the Kalman gain parameter kg in
the signal extraction problem of Erceg and Levin (2003) and Andolfatto et al. (2002).3
3See appendix 1 for more details on how equation (4) can be derived from these two models.
5
Page 15
Consequently, δ measures the speed at which changes in the central bank’s inflation target
affect longrun inflation expectations of private agents, i.e. δ measures expectationsbased
persistence. If δ is one, a shift in the central bank’s inflation target is immediately and
completely passed on to inflation expectations. This would be the case if the central bank’s
inflation target is perfectly known to all private agents and immediately credible. The
smaller δ, the slower expectations respond to a shift in the central bank’s inflation target.4
In the stickyinformation model of Mankiw and Reis (2002), δ decreases in the cost of
acquiring information and/or the cost of reoptimising prices in response to a shift in the
central bank’s inflation target. In the signal extraction problem of Erceg and Levin (2003)
and Andolfatto et al. (2002), δ increases in the signaltonoise ratio of the monetary policy
rule, i.e. the lower the uncertainty about whether monetary policy signals reflect transitory
rather than permanent policy changes, the faster private agents will react to these signals
by updating their inflation expectations.5
Note that shocks to the perceived inflation target, η2, only have a shortrun impact
on πP. These shocks should be interpreted as misperceptions of private agents about the
central bank’s inflation target, due to for instance noise in the signal extraction problem of
Erceg and Levin (2003) and Andolfatto et al. (2002). Shocks to the central bank’s inflation
target, η1, have a unit longrun impact on πP, i.e. πTis the longrun equilibrium inflation
rate. This is consistent with the generally accepted feature that longrun inflation is a purely
monetary phenomenon.
Equation (3) is a Phillips curve, relating the observed inflation rate πtto the perceived
inflation target πP
t, q lags of inflation and the lagged output gap zt−1. The perceived inflation
t is the inflation rate consistent with the private agents’ inflation expectations.
target πP
Therefore, it serves as the mediumrun inflation anchor. Both business cycle shocks, reflected
in the output gap zt−1, as well as costpush shocks, measured by ε1t, hitting inflation induce
temporary deviations of πtfrom πP
t. The sluggish adjustment of πtin response to costpush
shocks ε1tis measured by the sum of the AR coefficients,Pq
persistence is likely to be related to price and wagesetting mechanisms, e.g. price and
i=1ϕi. This intrinsic inflation
wage indexation. The sluggish adjustment of πt in response to business cycle shocks is
determined, besides the intrinsic inflation persistence, by the persistence of the output gap
zt in response to business cycle shocks. The latter source of inflation persistence can be
called extrinsic inflation persistence.
Note that equation (3) does not impose that the observed inflation series is additively
4We do not allow δ to take a value of 0, as in this case πP
monetary policy is not credible. Note that this restriction does not imply that all monetary policy actions
are fully credible. Rather, only credible shifts in the central bank’s inflation target are included in η1t.
5Equation (4) does not distinguish between these two theories, neither excludes that δ is a weighted
average of kg and λ, which could be the case if reality is a mixture of both theories.
tdoes not react to monetary policy shocks, i.e.
6
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