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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", 10-11 December 2004, Frankfurt and the CFS International Macroeconomics Summer

School, 24-30 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 (e-mail: maarten.dossche@nbb.be) and SHERPPA, Ghent University

(www.sherppa.be).

SHERPPA, Ghent University (e-mail: gerdie.everaert@UGent.be) – (www.sherppa.be). (**)

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NBB WORKING PAPER No. 70 - JUNE 2005

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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 time-varying 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 cost-push shock to several years for a shock to

long-run inflation expectations or the output gap.

JEL-code : 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

inflation-generating 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 long-run

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 post-WW 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 post-WW 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 stability-oriented central bank can learn from them.

The data-generating 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 wage-setting

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 non-stationary 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 post-WW 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. Half-life 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 post-WW 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 non-stationary 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 expectations-based 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 price-setting 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.

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troduces backward-lookingness 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 Dickey-Fuller unit root test is biased towards non-rejection 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 sub-samples.

By lowering the sub-sample 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 1984Q1-2003Q4. Once a structural

break is allowed for, persistence drops to 0.36. Third, Cogley and Sargent (2001, 2003), and

Benati (2004) estimate time-varying AR coefficients conditional on a time-varying 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

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should be stressed. First, rolling regressions do not entirely rule out the possibility that a

shift occurred in a specific sub-sample, 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 time-varying 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 expectations-based persistence in response to shocks to the inflation target.

Expectations-based 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 (1970Q2-1998Q4), 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.

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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. Expectations-based

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) expectations-based

persistence, (iii) intrinsic persistence and (iv) extrinsic persistence. The model is identified

both in a univariate and a multivariate set-up. 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

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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 long-run 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 signal-to-noise 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

long-run inflation expectations of private agents (for evidence see Castelnuovo et al., 2003).

This might be due to costs of acquiring information and/or re-optimisation (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 sticky-information 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.

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Consequently, δ measures the speed at which changes in the central bank’s inflation target

affect long-run inflation expectations of private agents, i.e. δ measures expectations-based

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 sticky-information model of Mankiw and Reis (2002), δ decreases in the cost of

acquiring information and/or the cost of re-optimising 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 signal-to-noise 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 short-run 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 long-run impact on πP, i.e. πTis the long-run equilibrium inflation

rate. This is consistent with the generally accepted feature that long-run 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 medium-run inflation anchor. Both business cycle shocks, reflected

in the output gap zt−1, as well as cost-push shocks, measured by ε1t, hitting inflation induce

temporary deviations of πtfrom πP

t. The sluggish adjustment of πtin response to cost-push

shocks ε1tis measured by the sum of the AR coefficients,Pq

persistence is likely to be related to price- and wage-setting 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