PCCI, data-rich measure of underlying inflation in the euro area.
Date: 2021-08-05
Institutions: European Central Bank
Subjects: consumption, economic model, economic statistics, euro area, financial statistics, inflation, price fluctuation

Statistics Paper Series 

Marta Bańbura 
Elena Bobeica 

PCCI – a data-rich measure of 
underlying inflation in the euro area 

No 38 / October 2020 

Disclaimer: This paper should not be reported as representing the views of the European Central Bank (ECB). 
The views expressed are those of the authors and do not necessarily reflect those of the ECB. This 
methodological description does not impact the ongoing ECB strategy review. 

 
Contents 

Abstract 

Non-technical summary 

1 

2 

3 

Introduction 

Methodology 

The PCCI – why is it useful? 

3.1  Ability to track more lasting inflationary developments 

3.2 

3.3 

Leading properties of the PCCI 

Stability of the estimated underlying inflation to new observations 

3.4  Degree of commonality across all inflation rates 

4 

Conclusions 

References 

Annex: Sensitivity to some parameter choices 

Abbreviations 

2 

3 

5 

8 

12 

12 

13 

15 

16 

18 

19 

22 

23 

ECB Statistics Paper Series No 38 / October 2020 

1 

Abstract 

This paper details the rationale and methodology behind the construction of the 
Persistent and Common Component of Inflation (PCCI), a measure of underlying 
inflation in the euro area. The PCCI reflects the view that underlying inflation captures 
widespread developments across the Harmonised Index of Consumer Prices (HICP) 
basket and that it is the persistent component of inflation. Methodologically, it relies on 
a generalised dynamic factor model estimated on a large set of disaggregated HICP 
inflation rates for 12 euro area countries. For each individual inflation rate, we estimate 
a low-frequency common component, i.e. a component driven by shocks or factors 
that are relevant for all inflation series and capturing cycles longer than three years. 
The PCCI is a weighted average of these common components. It is an alternative to 
the typical exclusion-based measures used to gauge underlying inflation (e.g. HICP 
excluding food and energy), as it does not a priori exclude any HICP items. It exhibits 
a set of desirable properties as a measure of underlying inflation, and it is a good 
tracker of more lasting inflationary developments (judging by smoothness and bias). 
Furthermore, it is timely and signals turning points with some lead, while acting as an 
attractor for headline inflation. 

Keywords: Underlying (core) inflation, dynamic factor model, frequency domain 

JEL Codes: C32, E31, E32, E52 

ECB Statistics Paper Series No 38 / October 2020 

2 

Non-technical summary 

This paper describes the methodology behind the Persistent and Common 
Component of Inflation (PCCI), which is one of the measures of underlying inflation 
that is monitored by the European Central Bank (ECB). The paper also discusses why 
the PCCI is a useful indicator as part of the ECB’s toolkit for assessing past and future 
inflationary pressures. Timely estimates of PCCI are published in the ECB Statistical 
Data Warehouse. 

Conceptually, the PCCI reflects the view that underlying inflation captures widespread 
or generalised developments across consumer prices for different items, and that it is 
the persistent part of inflation. Methodologically, it relies on the generalised dynamic 
factor model proposed by Forni et al. (2000, 2005) and adopted for underlying inflation 
by Cristadoro et al. (2005). 

The model explores the rich dataset in the Harmonised Index of Consumer Prices 
(HICP), covering the four-digit ECOICOP (European Classification of Individual 
Consumption according to Purpose) classes for 12 euro area countries and amounting 
to around 1,000 monthly time series in total. It incorporates approximately 97% of the 
euro area HICP basket. In contrast to Cristadoro et al. (2005) we rely only on the 
information contained in the HICP and we use country as opposed to aggregate euro 
area data. The goal of this indicator is thus to capture the underlying inflationary 
pressures that are common across euro area countries. This is particularly 
policy-relevant given the special architecture of the euro area, in which the single one 
monetary policy should be fit for many participating countries. 

The main idea behind the model is that the inflation rate of each item can be 
decomposed into two orthogonal components: a common one, driven by shocks 
relevant for all inflation series and capturing the bulk of cross-sectional correlation; 
and an idiosyncratic one, driven by measurement errors and sector and 
country-specific items. The PCCI is defined as a weighted average of common 
components of a large set of inflation rates. This is different from the approach of 
Cristadoro et al. (2005) and facilitates, among other things, an understanding of the 
drivers of the PCCI, and the derivation of low-frequency common components for 
sub-aggregates such as HICP excluding energy and food. Apart from commonality, 
the model also imposes persistence, as it excludes high-frequency fluctuations from 
the common components (defined as cycles shorter than three years). As a result, the 
PCCI should be free from idiosyncratic and transient elements. 

Estimation is based on dynamic and generalised principal components. In order to 
hedge against the uncertainty related to the number of (dynamic and static) factors, 
the PCCI is calculated as the average of estimates based on a range of values. The 
methodology makes it possible to simultaneously combine both the information from 
the cross-sectional distribution of prices and their time series properties in a unified 
framework. Therefore, in contrast to univariate filtering techniques, it can exploit 
leading properties of certain (sectoral price) indices in the panel and produce a timely 
estimate of more lasting developments in inflation, as well as its turning points. 

ECB Statistics Paper Series No 38 / October 2020 

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The PCCI proves to be a valuable complementary tool to understand past inflation 
developments and assess future inflationary pressures. It fares well as a measure of 
underlying inflation, in particular by comparison with exclusion-based measures, such 
as HICP excluding energy (and food). The PCCI is also a good tracker of more lasting 
inflationary developments (judging by smoothness and bias), and it is timely, signalling 
turning points in annual headline inflation with some lead, while acting as an attractor 
for headline inflation. 

ECB Statistics Paper Series No 38 / October 2020 

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1 

Introduction 

The prolonged period of low inflation in the euro area in the aftermath of the Great 
Recession calls for an in-depth examination as to whether these developments reflect 
a secular trend or are mostly a result of transitory shocks, likely to fade away in the 
near future. Information on more lasting inflation developments is a crucial input into 
monetary policy decision-making, as policymakers need to see through transitory 
shocks and concentrate on medium and long-term inflation trends. This is also due to 
the fact that monetary policy affects economic variables such as inflation only with a 
considerable delay. It was reflected, for instance, in the introductory statement of 
former ECB President Mario Draghi to the ECB’s press conference of 15 April 2015: 
“When carrying out its assessment, the Governing Council will follow its monetary 
policy strategy and concentrate on trends in inflation, looking through unexpected 
outcomes in measured inflation in either direction if judged to be transient and to have 
no implication for the medium-term outlook for price stability” (see Draghi, 2015). For 
these reasons, measures of underlying inflation, which are ideally free from the 
transient shocks reflected in headline inflation, are often constructed and used by 
central banks. 

This paper details the rationale and methodology behind the construction of one of the 
underlying inflation measures monitored by the ECB, namely the Persistent and 
Common Component of Inflation (PCCI). The PCCI is a measure based on a dynamic 
factor model, exploiting disaggregated information from the HICP for a wide range of 
items from a large set of euro area countries. Real-time estimates of the PCCI are 
published in the ECB Statistical Data Warehouse.1 

As important as it is, underlying inflation is an unobservable variable that is hard to 
grasp. While it is generally believed that it should capture the persistent component of 
inflation and provide timely signals for future inflation developments, there is neither a 
unanimously accepted definition of underlying or core inflation, nor a set of criteria it 
should satisfy (see, for example, Clark, 2001; Rich and Steindel, 2007; Wynne, 2008). 
Consequently, even with the benefit of hindsight, the decomposition of inflation into 
persistent and transitory developments is model-specific and surrounded by 
considerable uncertainty. 

In order to ensure a robust assessment, a wide range of underlying inflation measures 
are often considered, including at the ECB (see, for instance, ECB, 2001, 2013; 
Ehrmann et al., 2018; Nickel and O’Brien, 2018). The ECB’s Economic Bulletin 
routinely shows the path of the monitored measures of underlying inflation, and the 
President’s introductory statement to the press conference regularly makes 
references to them.2  Perhaps the most popular underlying inflation measures are the 
permanent exclusion-based measures. Such measures are derived by excluding a 
certain fixed set of items, considered as volatile and noisy, from the overall consumer 

1    The PCCI series can be found in the Statistical Data Warehouse with the code 

ICP.M.U2.N.PCCI00.3.3MM. 

2    See for instance ECB (2020) and Lagarde (2020), respectively. 

ECB Statistics Paper Series No 38 / October 2020 

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price index. The most prominent indicators monitored by the ECB in this category 
include: HICP excluding energy; HICP excluding energy and unprocessed food; HICP 
excluding energy and food; and HICP excluding energy, food, travel-related items and 
clothing. Temporary exclusion-based measures also form part of the ECB toolkit. In 
this case, the items to be excluded are selected at a given point in time depending on 
their relative volatility. These measures offer more flexibility than the permanent 
exclusion-based measures, as they can also abstract from large one-off price changes 
in items that are typically less volatile. The examples include the 10% trimmed mean, 
the 30% trimmed mean or the weighted median of the HICP inflation items. 

The main drawback of all exclusion-based measures is that the resulting indicators 
may still not be free of temporary shocks that have no implication for price stability 
over the medium term (e.g. temporary movements in commodity prices, changes in 
administered prices and indirect taxes, and calendar effects).3  Also, the components 
considered to be volatile and thus excluded, such as energy and food, can exhibit very 
persistent movements that have implications for price stability in the medium term. 
This is also because they may trigger second-round effects, which will only show up 
with a delay in the exclusion-based measure. Moreover, in the euro area, 
exclusion-based measures can reflect idiosyncratic developments in a particular 
(large) member state, with limited relevance for the single monetary policy. This is why 
central banks complement exclusion-based measures with those based on more 
sophisticated statistical techniques, among which factor models feature prominently 
(see, for example, Kirker, 2010; Machado et al., 2001; Amstad et al., 2014). The PCCI, 
constructed at the ECB, is one such measure.4 

Conceptually, the PCCI reflects the view that underlying inflation captures widespread 
or generalised developments across consumer prices of different items – as 
supported by Bryan and Cecchetti, 1993 – and that it is the persistent part of inflation 
(Eckstein, 1981; Blinder, 1997). Methodologically, it relies on the generalised dynamic 
factor model proposed by Forni et al. (2000, 2005) and adopted for underlying inflation 
by Cristadoro et al. (2005). A common component is estimated for all inflation series, 
reflecting the shocks or factors relevant across the items in the HICP basket. The 
PCCI is the weighted average across these common components, and reflects, apart 
from commonality, medium and long-run movements in inflation as it excludes 
high-frequency fluctuations from the common components (cycles shorter than three 
years). As a result, PCCI should be free – up to the estimation error – from 
idiosyncratic (e.g. sector or country-specific) and transient elements. The 
methodology makes it possible to simultaneously combine both the information from 
the cross-sectional distribution of prices and their time series properties in a unified 
framework. Therefore, in contrast to univariate filtering techniques, it can exploit 
leading properties of certain (sectoral price) indices in the panel and produce a timely 
estimate of more lasting headline inflation dynamics and its turning points.5 

3    Measures of inflation that exclude the impact of changes in taxes on products (e.g. value added tax, 

excise duties) are also assessed by the ECB. See, for example, ECB (2007). 

4    The ECB also monitors the so-called Supercore measure, which is based on those items in the HICP 

excluding energy and food that co-move with the business cycle, in a similar vein to Stock and Watson 
(2019a). 

5    Univariate low-pass filters typically introduce a phase shift, meaning that turning points in the filtered 

series occur at a later point than in the original series. 

ECB Statistics Paper Series No 38 / October 2020 

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In contrast to Cristadoro et al. (2005) we rely only on the information contained in the 
HICP6  and we use country as opposed to aggregate euro area data. Another 
difference is that Cristadoro et al. (2005) define core inflation directly as the common 
component of euro area headline HICP, whereas we derive it from the common 
components of country and sector HICP inflation rates. Our approach is motivated by 
a number of considerations. First, it allows us to better disentangle aggregate euro 
area from country-specific developments. Second, we can obtain insights into whether 
the trends at the aggregate level are shared across countries or hide highly 
heterogeneous country developments. Furthermore, it also allows us to pinpoint which 
countries, and also which items, account for the deviation of euro area headline 
inflation from its underlying level. 

The PCCI fares well in satisfying some criteria for a desirable measure of underlying 
inflation. It is a good tracker of more lasting inflationary developments (judging by 
smoothness and bias), it is timely, signalling turning points in annual headline inflation 
with some lead, and it acts as an attractor for headline inflation, indicating the direction 
in which headline inflation will head. 

It is important to stress that the model underlying the PCCI relies on the stationarity of 
inflation rates. One element of such an assumption is that the long-term averages 
(unconditional means) of inflation rates do not change over time. Consequently, even 
if it can be persistent, the deviation of the PCCI from the long-term average of headline 
inflation is by construction temporary. This is conceptually different from some recent 
models, which allow trend or core inflation to be driven by shocks of a permanent 
nature.7  Some of these models further incorporate survey-based inflation 
expectations as potential proxies for the degree of anchoring of inflation expectations 
and credibility of monetary policy. This is in order to pin down the unobserved inflation 
trend. While we find them insightful, we do not explore these avenues in this paper. 

The rest of the paper is organised as follows: Section 2 provides the methodological 
details on the estimation of the PCCI and the data used, Section 3 explains why this 
indicator is useful, and Section 4 presents the conclusion. 

6    Stock and Watson (2019b) extend the multivariate unobserved component models with the stochastic 
volatility of Stock and Watson (2016) to estimate euro area trend inflation based on 13 sectoral price 
indices only. Approaches that also consider other economic variables, with the aim of relating shifts in 
inflation to the evolution of real activity or monetary policy, include Cogley and Sargent (2005) and Cogley 
et al. (2010), who define trend inflation as the time-varying steady-state level of inflation in a small VAR 
model, or Andrle et al. (2013) who construct a trimmed mean measure of underlying inflation using the 
correlation with output at business cycle frequencies as a criterion. Extensions of our model considering 
a vast set of real, financial and external variables have been explored, but the results are similar overall to 
the results obtained using price data only. 

7    See, for example, Garnier et al. (2015), Mertens (2016) and Chan et al. (2018), where inflation trends 

evolve as random walks. The changes in trend (steady-state) inflation are also permanent in the models 
of Cogley and Sargent (2005) and Cogley et al. (2010). 

ECB Statistics Paper Series No 38 / October 2020 

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2 

Methodology 

The methodology closely follows Cristadoro et al. (2005) with some differences in the 
implementation, which will be described in detail later in the text. It relies on the 
generalised dynamic factor model proposed by Forni et al. (2000), with (one-sided) 
estimation based on generalised principal components, as detailed in Forni et al. 
(2005). 

The econometric model 

The model rests on the assumption that the inflation rate of each item in the HICP 
basket can be decomposed into two orthogonal components: a common one, driven 
by shocks relevant for all inflation series and capturing the bulk of cross-sectional 
correlation, and an idiosyncratic one, driven by measurement errors and sector and 
country-specific shocks. For each item 
inflation rate at time 
unobserved components, namely the common component 
component 

  can be decomposed into two stationary and orthogonal 
𝑗

  and an idiosyncratic 

, it is assumed that the monthly 

  and country 

 𝑥𝑖𝑗,𝑡

: 

𝑡

𝑖

,

𝜒𝑖𝑗,𝑡

𝜉𝑖𝑗,𝑡

𝑥𝑖𝑗,𝑡 = 𝜒𝑖𝑗,𝑡 + 𝜉𝑖𝑗,𝑡
Furthermore, it is assumed that the common component is a linear combination of 
current and past values of 

  dynamic factors, 

: 

𝑞𝑞

, 

𝑓𝑡

𝜒𝑖𝑗,𝑡 = 𝜆𝑖𝑗,1(𝐿)𝑓1,𝑡 + ⋯ + 𝜆𝑖𝑗,𝑞(𝐿)𝑓𝑞,𝑡
which are driven by 

  common shocks, 

: 

,           

𝑞𝑞

𝑢𝑡

𝐴(𝐿)𝑓𝑡 = 𝑢𝑡
𝑓𝑡 = (𝑓1,𝑡, ⋯ , 𝑓𝑞,𝑡)
see Forni et al. (2005) for details. 

′

,

We are interested in the part of the common component that abstracts from 
high-frequency fluctuations in order to distil the medium and long-term movements in 
inflation. Using spectral domain techniques, the common component can be 
decomposed into low and high-frequency parts: 

𝐹
+ 𝜒𝑖𝑗,𝑡
  would capture the commonalities with frequencies below a certain 

𝐿
𝜒𝑖𝑗,𝑡 = 𝜒𝑖𝑗,𝑡
where 
threshold (or, equivalently, periodicities/cycles above a certain threshold).8 

𝐿
𝜒𝑖𝑗,𝑡

8    Spectral domain techniques rely on the fact that a stationary time series is an aggregation (over 

frequencies) of waves with random amplitudes. 

ECB Statistics Paper Series No 38 / October 2020 

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Definition of PCCI 

We define the PCCI as the weighted average of the low-frequency common 
components of the individual sectoral and country inflation rates: 

𝐿
𝑃𝐶𝐶𝐼𝑡 = � 𝑤𝑗,𝑡 � 𝜔𝑖𝑗,𝑡𝜒𝑖𝑗,𝑡
where 

𝑗

𝑖

  refers to the weight of country 

  in the euro area (HICP) and 

  is the 

𝑤𝑗,𝑡

  in the consumption basket of country 

weight of item 
𝑗
weights is equal to one; the original weights have been adjusted to account for the fact 
that, for reasons of data availability, not all the countries and not all the items are 
included. For more information, see the “Data” subsection. 

). The sum of the 
𝜔𝑖𝑗,𝑡

  (at time 

𝑡

𝑗

𝑖

Note that our approach is somewhat different from that of Cristadoro et al. (2005) who 
define the core measure as the (low-frequency) common component of the headline 
inflation rate.9  With our bottom-up approach it is straightforward to derive 
low-frequency common components for euro area or country sub-aggregates, such as 
HICP excluding energy and food, which are consistent with exclusion-based 
measures of underlying inflation monitored by the ECB. This can be done by applying 
the above formula to a subset of items and adjusting the weights. In the same way, we 
can decompose the difference between the headline inflation and the underlying 
inflation measure into contributions of individual items, and therefore gain insights into 
which countries or items account for the deviation. Finally, we want to avoid a 
disproportionate contribution from items with a low weight in the euro area headline 
inflation. 

Estimation 

As explained in Forni et al. (2005) and Cristadoro et al. (2005), the low-frequency 
common components can be estimated by projecting 
  on the 

space spanned by the common shocks/factors. 

𝐿
𝜒𝑡

𝐿

= (𝜒11,𝑡

𝐿
, ⋯ , 𝜒𝐼𝐽,𝑡

)

′

    to be the estimate of 

In what follows, we denote   
It can be shown (see Forni et 
al., 2005) that the projection, and thus the estimate of the low-frequency component, is 
the product of the estimates of the projection coefficients and of the common factors 
as follows: 

𝑥.  

𝑥�

. 

′

𝐿

𝐿
𝜒̂𝑡
= Γ�
  and 

𝑍̂

′

−1

𝐿

′

′

−1

(𝑍̂𝑥𝑡)
(𝑍̂𝛤�𝑍̂
  denote the covariance matrices of the vector of inflation rates, 

𝐹�𝑡 = 𝛤�

(𝑍̂𝛤�𝑍̂

𝑍̂

)

)

𝐿

, and of 
Γ
Γ
the dynamic principal components.10 
(𝑥11,𝑡, ⋯ , 𝑥𝐼𝐽,𝑡)

𝐿
𝜒𝑡

′

, respectively. The latter covariance matrix is estimated using 

  static factors, collecting the 

𝑥𝑡 =

  is a vector of 

𝐹𝑡

𝑟

9    They include the headline inflation rate in the dataset. 
10    Dynamic principal components operate on spectral densities (in the frequency domain). The covariance 
matrices of the common components are estimated by aggregating the “common” part of the spectral 
densities (which are restricted to having a rank 
, reflecting the assumed number of dynamic factors) 
over frequencies. For the covariance matrix of the low-frequency common component, only the 
𝑞𝑞
frequencies below a certain threshold are included in the aggregation. 

ECB Statistics Paper Series No 38 / October 2020 

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contemporaneous and lagged dynamic factors, 
principal components: 

, where 

. It is estimated via the generalised 

𝐹�𝑡 = 𝑍̂𝑥𝑡
′

𝜉

𝜒

′

  and 

)′

′
𝑍̂ = (𝑍̂1
𝜉

𝑓𝑡
′
, ⋯ , 𝑍̂𝑟
′
𝑍̂𝑚

𝑍̂𝑗 = arg max𝑎 𝑎 𝛤�

𝑎

   𝑠. 𝑡.   𝑎𝛤�

𝑎

= 1   𝑎𝑛𝑑   𝑎𝛤�

= 0,   1 ≤ 𝑚 ≤ 𝑗 − 1,   𝑗 = 1, ⋯ , 𝑟. 

and 

  denote the covariance matrices of the common and idiosyncratic 

𝜉

Γ

𝜒
components respectively. The maximisation searches for linear combinations that 
Γ
give a large weight to series with a high percentage of variance explained by common 
sources of fluctuations, subject to orthogonality constraints. See Forni et al. (2005) 
and Cristadoro et al. (2005) for a detailed explanation. 

Data 

The model explores a rich dataset of inflation rates from 12 euro area countries, as 
shown in Table 1. The data covers the ECOICOP four-digit classes, approximately 
1,000 monthly time series in total.11  The precise number of series can change, 
reflecting data availability at the country level for a given update. Series which are not 
available for the full period are eliminated and the weights are readjusted accordingly. 
This still ensures that for virtually every included country, almost all of the consumption 
basket is accounted for. In terms of coverage at the euro area level, the dataset 
incorporates 97% of the euro area HICP basket. 

The inflation rates are expressed as annualised monthly inflation rates to ensure 
stationarity and are seasonally adjusted using the Census X-12-ARIMA method. 
Outliers are also removed prior to estimation. Owing to the data availability at this very 
disaggregated level, the sample starts in April 2001. The end date of the sample for 
the analysis in this paper is December 2018. 

Table 1 
Data coverage per country 

(number, percentage) 

Country   

BE    DE 

IE 

GR 

ES 

FR 

IT 

LU 

NL 

AT 

PT 

FI 

Total 

Number of inflation rates   

83 

92 

87 

88 

86 

89 

85 

89 

85 

90 

84 

86 

1,044 

Weight in the national basket    98.3 

99.9 

99.9 

96.1 

99.9 

96.1 

99.6 

99.4 

99.7 

100 

98.5 

99.9 

- 

Weight in the euro area basket  3.7 

28.0 

1.5 

2.1 

11.5 

19.4 

17.3 

0.3 

5.1 

3.4 

2.2 

1.9 

97 

Implementation details 

In order to estimate the common components, we need to select the number of static 
and dynamic factors, 
values. However, no single choice was found to be superior to another according to all 
possible criteria, which we set out below. To hedge against the uncertainty related to 

  respectively. We have experimented with a range of 

  and 

𝑞𝑞

𝑟

11    See the Eurostat’s website for more information on the ECOICOP classification. The dataset does not 

include the methodological changes implemented by Eurostat on 22 January 2019. 

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this choice, the PCCI is the average of estimates based on two to eight dynamic 
factors and four to 16 static factors (under the restriction that the latter has to be larger 
or equal to the former) – 81 specifications in total.12  It turns out that the estimates are 
relatively similar for a wide range of values for the number of factors, with a slight 
increase in uncertainty during the global financial crisis (see Chart A in the Annex). 

Turning to the frequency threshold for the low-frequency common component, we 
keep the cycles with periodicities equal to or above three years and discard the others. 
Given the forecast horizon and the transmission lags of monetary policy, we deem this 
choice reasonable. We have also considered thresholds of two and six years. This is 
illustrated in Chart B in the Annex, which shows that the longer the considered cut-off 
periodicity, the smoother the estimated underlying inflation indicator. However, the 
results are qualitatively similar, for instance in terms of turning points. 

An additional smoothing of the estimated component is performed ex post by taking 
the three-month moving average of the model output. This choice helps to achieve a 
satisfactory degree of smoothing which would otherwise not be obtained by exploiting 
the multivariate information, with a cost in terms of timeliness of the indicator.13 

To sum up, the PCCI is estimated by means of a weighted average of the 
disaggregated inflation data. The weights attach more importance to series driven by 
common – as opposed to idiosyncratic – sources of fluctuations. Moreover, by 
exploiting the low-frequency covariance matrices, only more persistent movements of 
HICP inflation rates are retained. This permits the aggregation of all potentially 
leading, coincident and lagging information contained in the panel. Thus a measure is 
constructed that is coincident with month-on-month HICP inflation but is at least as 
smooth as year-on-year inflation without requiring, unlike centred moving averages, 
knowledge of unavailable future inflation rates. 

12    Automatic selection criteria for the number of common factors have also been applied, such as those 

proposed by Bai and Ng (2002), who argue that the optimum number of factors can be determined in a 
usual model selection framework, where there is a trade-off between good fit and parsimony. However, 
this procedure did not yield estimates of the common component that were superior in terms of 
smoothness, leading power for inflation or stability in the face of revisions. 

13    This helps to smooth out several spikes that “leak” through the cross-sectional filter. 

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3 

The PCCI – why is it useful? 

Chart 1 shows the estimated PCCI and the annual and annualised monthly headline 
inflation rates for the euro area. The annual headline inflation rate is much smoother 
than the annualised monthly rate, but it is lagging. This is because it is essentially the 
result of a one-sided filter over 12 months. By contrast, the PCCI mainly relies on a 
“cross-sectional” filter and reduces the volatility of the annualised monthly inflation 
while not losing the timeliness. Overall, it appears to be a timely and smooth measure 
of more lasting inflationary developments. The next subsections evaluate these 
features more formally, also comparing them with the performance of the HICP 
excluding energy and the HICP excluding energy and food, which are frequently used 
to assess more persistent inflation developments (see, for example, ECB, 2013; 
Ehrmann et al., 2018). 

Chart 1 
The PCCI and headline HICP inflation in the euro area 

(annualised monthly percentage changes, annual percentage changes) 

HICP month-on-month
HICP year-on-year
PCCI

8

6

4

2

0

-2

-4

-6

2001

2003

2005

2007

2009

2011

2013

2015

2017

Notes: HICP month-on-month is the annualised monthly headline HICP inflation rate, seasonally and working day-adjusted; its unit of 
measure is annualised monthly percentage changes. HICP year-on-year is the annual headline HICP inflation rate; its unit of measure is 
annual percentage changes, the same as for the PCCI. 

3.1 

Ability to track more lasting inflationary developments 

In this subsection we present a number of statistics evaluating how well three 
measures of underlying inflation (the PCCI, the HICP excluding energy and the HICP 
excluding energy and food) perform in tracking low-frequency developments in 
headline inflation. We look at their volatility, long-term mean and closeness to a proxy 
for more lasting inflationary developments (see Table 2).14  The latter is obtained as a 
three-year centred moving average of headline inflation and is therefore not a useful 
“real-time” measure, as it is not available for the most recent months. 

14    The statistics presented in Tables 1 and 2 are discussed in more detail in Clark (2001) and ECB (2013). 

ECB Statistics Paper Series No 38 / October 2020 

12 

 
 
 
                                                                    
The PCCI fares well across these statistics when compared with the exclusion-based 
measures. First, it provides a less biased estimate of underlying inflation 
developments, as the long-term average of headline inflation is closer to the mean of 
the PCCI than to that of HICP inflation excluding energy and food or HICP inflation 
excluding energy. Second, the PCCI is a more precise real-time indicator of the more 
lasting developments in headline inflation, as its root mean squared error (RMSE) with 
respect to the centred moving average is smaller than that of the exclusion-based 
measures. Finally, it is less volatile than the exclusion-based measures and much less 
than annual headline HICP inflation. 

Table 2 
Volatility and ability to track more lasting headline inflation developments 

Tracking of more lasting inflation 
developments 

Volatility 

Average inflation rate 
(percentage) 

RMSE vis-à-vis the 
three-year centred 
moving average of 
headline inflation 

Standard 
deviation 

Coefficient of 
variation 

Mean absolute 
change 

Headline HICP 

HICP excluding 
energy and 
food 

HICP excluding 
energy 

PCCI 

Three-year 
centred moving 
average 

1.74   

1.40   

1.59 

1.63 

1.73 

0.63 

0.54 

0.47 

0.41 

- 

0.96 

0.45 

0.58 

0.46 

0.65 

0.55 

0.32 

0.36 

0.28 

0.37 

0.20   

0.12 

0.12 

0.06 

0.03 

Notes: Based on monthly year-on-year growth rates; sample 2001-18. The coefficient of variation is the standard deviation divided by the 
mean. The mean absolute change is the average of the absolute value of the first difference of each inflation measure. The RMSE is the 
square root of the average squared difference between each underlying inflation measure and the three-year centred moving average of 
headline inflation, which is the proxy chosen for more lasting headline inflation developments. 

3.2 

Leading properties of the PCCI 

The PCCI outperforms exclusion-based measures of underlying inflation in terms of 
leading properties with respect to headline inflation. It is highly correlated with annual 
headline inflation and tends to lead it by two months. Whereas the absolute correlation 
of the PCCI with headline inflation is highest at a two-month lead, that of HICP inflation 
excluding energy and food is highest at a six-month lag, and that of HICP inflation 
excluding energy is highest at a two-month lag (see Table 3). The PCCI also has a 
lower RMSE for headline inflation for various near-term forecast horizons than the 
exclusion-based measures. 

All considered measures of underlying inflation exhibit “attractor” properties for 
headline inflation, i.e. when there is a gap between the headline rate and an 
underlying inflation measure, headline inflation is more likely to converge towards the 
underlying measure than vice versa. Moreover, on the basis of 
amount of variation of future changes in headline inflation is explained by this 
reversion process, and more with the PCCI than when an exclusion-based measure of 
underlying inflation is used. 

, a significant 

𝑅

2

ECB Statistics Paper Series No 38 / October 2020 

13 

 
 
 
 
 
 
 
Table 3 
Leading properties with respect to headline inflation 

(based on monthly year-on-year growth rates) 

Inflation measure 

Correlation 

RMSE vis-à-vis future headline inflation   

Attractor properties 

HICP excluding energy 
and food 

HICP excluding energy   

PCCI 

Maximum  Lead 

Three months 
ahead 

Six months 
ahead 

12 months 
ahead 

0.65 

-6 

0.89 

0.91 

0.95 

Intercept  Slope 

𝟐
𝑹𝑹
0.38 

0.25*** 

0.92 

0.77 

0.85 

-2 

2 

0.77 

0.70 

0.85 

0.71 

1.01 

0.90 

0.24 

0.08 

0.90 

0.47 

0.06 

1.26*** 

Notes: “Lead” refers to a shift in months at which the correlation with headline inflation is the highest. A positive number means that the 
measure leads the headline rate. The RMSE is the square root of the average squared difference vis-à-vis the future headline rate. 
“Intercept” and “slope” refer to α and β from the regression respectively: 
headline and underlying inflation rates and 
  stands for 12 months. Asterisks denote a significant difference from 0 for the intercept and 
− 𝜋𝜋𝑡) + 𝜀𝜀𝑡+ℎ
from 1 for the slope, with 3, 2 and 1 asterisk(s) denoting the 1%, 5% and 10% confidence levels respectively; the lack of asterisk shows 
that the null hypothesis of the intercept being equal to 0 or the slope being equal to 1 cannot be rejected. 

𝑢
𝜋𝜋𝑡+ℎ − 𝜋𝜋𝑡 = 𝛼𝛼 + 𝛽𝛽(𝜋𝜋𝑡

  refer to 

, where 

  and 

𝑢
𝜋𝜋𝑡

𝜋𝜋𝑡

ℎ

Finally, the PCCI can provide early signals on the turning points in annual headline 
HICP. The turning points identified over the historical sample typically occur a couple 
of months earlier in the case of the PCCI than in the case of the headline HICP. Chart 
2 illustrates this point by applying the Bry and Boschan (1971) algorithm to identify the 
turning points in the PCCI and headline inflation. This statistical univariate procedure 
also identifies some local troughs and peaks with little economic relevance, for 
example, the February 2004 trough in headline inflation. However, when it comes to 
the big turning points in inflation, such as those in July 2008, July 2009 and November 
2011,15  the PCCI seems to have led inflation by even more than two months, as 
indicated by the lead/lag correlation analysis. Nevertheless, the latter is an average of 
the entire sample and if we look at specific episodes, there might be some deviations 
from this average. Overall, different measures of the leading properties yield different 
results, but what is consistent is that there appears to be some leading power in the 
PCCI. 

15    These big turning points are also in line with the estimates of de Bondt et al. (2018), who present an 

estimated euro area headline inflation cycle using data over a long period of time. 

ECB Statistics Paper Series No 38 / October 2020 

14 

 
 
 
 
                                                                    
Chart 2 
Turning points 

(annual percentage changes) 

HICP
PCCI

HICP turning points
PCCI turning points

5

4

3

2

1

0

-1

2001

2003

2005

2007

2009

2011

2013

2015

2017

Note: The identification of the turning points is based on Bry and Boschan (1971). 

3.3 

Stability of the estimated underlying inflation to new 
observations 

The PCCI, as any estimated variable, is subject to revisions when a new observation 
is added to the dataset. This is also common to other unobservable economic 
variables, such as the output gap or the non-accelerating inflation rate of 
unemployment. 16 

The PCCI is, overall, robust to new observations added to the sample, as shown in 
Chart 3. The chart presents the sequence of PCCIs estimated recursively over an 
expanding window (45 samples in total). Even when compared with an estimate based 
on a much shorter sample not covering the Great Recession period, the PCCI does 
not exhibit major revisions. The turning points in the underlying inflation measure are 
also estimated robustly, a necessary condition for ascertaining the ability of the PCCI 
to lead headline inflation. However, a sequence of downward revisions over recent 
years can be noted and potential structural breaks in inflation rates (e.g. in long-term 
averages) could be investigated. 

16   Recent analysis at the ECB of these unobservable variables can be found in ECB (2017) and Andersson 

et al. (2018). 

ECB Statistics Paper Series No 38 / October 2020 

15 

 
 
 
                                                                    
Chart 3 
Estimates of PCCI over different samples 

(annual percentage changes) 

PCCI
HICP

5

4

3

2

1

0

-1

2001

2003

2005

2007

2009

2011

2013

2015

2017

Notes: Recursive estimates of the PCCI based on 45 expanding samples. The first sample starts in February 2001 and ends before the 
Great Recession in December 2007. The length of each subsequent sample increases by 3 months, with the 45th sample covering 
February 2001 to December 2018. 

3.4 

Degree of commonality across all inflation rates 

The common shocks/factors account on average for almost 40% of the variability in 
the euro area inflation rates. Chart 4 shows the share of variance explained by the 
factors for different periodicities.17  The share of the variability explained increases for 
higher periodicities (lower frequencies). This perhaps unsurprisingly suggests that the 
co-movement in inflation rates across items and countries increases after transitory 
shocks are removed. 

It would be desirable for the common component as depicted by the PCCI to explain 
the bulk of the variability of inflation rates across items. The quite considerable share 
of the variability in the data that is not explained (by the common factors) suggests that 
there are sizeable idiosyncratic factors affecting the inflation rates of individual items. 
In other words, it appears that when it comes to the most disaggregated inflation data 
for the euro area, namely over 1,000 inflation series for 12 euro area countries, the 
degree of “commonality” is not extremely high; high-frequency and local/idiosyncratic 
noise characterise the data.18  The PCCI does extract what is common from the 
cross-sectional information, but the considerable unexplained variability in the data 
might point to a limitation in this measure. 

17    Specifically, the degree of commonality is assessed by the ratio of the sum of the largest 

  dynamic 
eigenvalues (2 to 8, depending on the specification) of the spectral density matrix over the sum of all 
eigenvalues, in absolute terms. For instance, this share for periods of less than two years is computed by 
averaging the shares for the spectral density matrices over the frequencies corresponding to these 
periods. 

𝑞𝑞

18    Using a similar model for the United States, Luciani (2020) finds that most of the fluctuations in core 

personal consumption expenditure prices observed since the Great Recession have been idiosyncratic in 
nature. 

ECB Statistics Paper Series No 38 / October 2020 

16 

 
 
 
                                                                    
Chart 4 
Share of variance explained by the common shocks 

(percentage) 

70

60

50

40

30

20

10

0

<2 years

2 - 4 years

4 - 6 years

>6 years

Average

Notes: The share of variance is measures as the ratio of the sum of the largest 
eigenvalues. The average value of the statistics for 
for all frequencies. 

𝑞𝑞

  between 2 and 8 is reported. “Average” refers to the average variability explained 

  dynamic eigenvalues to the sum of all (dynamic) 

𝑞𝑞

ECB Statistics Paper Series No 38 / October 2020 

17 

 
 
 
4 

Conclusions 

The model-based measure of underlying inflation described in this paper reflects the 
view that underlying inflation is the persistent part of inflation and that it captures 
widespread developments across HICP items. The PCCI captures commonalities 
among disaggregated HICP items in 12 euro area countries and abstracts from cycles 
shorter than three years. Exploiting lead-lag relationships among the HICP items, the 
PCCI is a timely and relatively smooth tracker of more lasting headline inflation 
developments. 

For a judicious reading of the PCCI, the following considerations are noteworthy. 

• 

• 

• 

• 

• 

• 

It is derived on the basis of a fairly complicated model and the result depends on 
the choice of several parameters (e.g. the number of static and dynamic factors, 
the frequency of cycles to be eliminated, the lags and frequency grid for 
computing the covariance matrices, the number of months for the ex post 
computation of the moving average.). 

The degree of commonality explained is not overwhelming, suggesting a high 
degree of heterogeneity in the underlying data. 

The measure is subject to revisions when new observations are added to the 
sample. 

Its ability to forecast year-on-year inflation stems mainly from its exploitation of 
the lead-lag relationships of individual inflation rates, whereas a proper 
forecasting model would take into account a much wider dataset than only price 
series, thus incorporating more leading information. 19 

Potential structural breaks (e.g. in long-term averages of inflation rates) are not 
accounted for in the estimation. 

The PCCI is only one of the measures of underlying inflation monitored by the 
ECB and, like others, has its own advantages and drawbacks. This justifies the 
current practice of monitoring a larger set of measures and, importantly, 
complementing the analysis with more structural examinations of the inflation 
drivers in order to better grasp (future) inflationary developments. 

19    See, for example, Peach et al. (2013). 

ECB Statistics Paper Series No 38 / October 2020 

18 

 
 
                                                                    
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ECB Statistics Paper Series No 38 / October 2020 

21 

 
 
Annex: Sensitivity to some parameter 
choices 

Chart A 
Sensitivity to the choice of the number of factors 

(annual percentage changes) 

HICP
PCCI (average)

5

4

3

2

1

0

-1

2001

2003

2005

2007

2009

2011

2013

2015

2017

Note: The shaded area indicates the range of estimates based on two to eight dynamic factors and four to 16 static factors (under the 
restriction that the latter has to be larger or equal to the former) – 81 specifications in total. 

Chart B 
Sensitivity to the choice of the threshold cycle length 

(annual percentage changes) 

HICP
PCCI (3 years)

2 years
6 years

5

4

3

2

1

0

-1

2001

2003

2005

2007

2009

2011

2013

2015

2017

Note: The last two lines are based on common components for which the cycles shorter than two and six years respectively have been 
filtered out. 

ECB Statistics Paper Series No 38 / October 2020 

22 

 
 
 
 
 
 
Abbreviations 

Countries 

BE 
DE 
IE 
GR 
ES 

Belgium 
Germany 
Ireland 
Greece 
Spain 

FR 
IT 
LU 
NL 
AT 

France 

Italy 
Luxembourg 
Netherlands 
Austria 

PT 
FI 

Portugal 
Finland 

In accordance with EU practice, the euro area Member States are listed in this report using the alphabetical order of the country names in 
the national languages. 

 
 
 
 
 
 
Acknowledgements 
We would like to thank Marco Bazzi and Carlos Montes-Galdon for their valuable input and to Chiara Osbat for her guidance. We would 
also like to thank the Editorial Board of the ECB Statistics Paper Series for their useful comments, and in particular we thank Per 
Nymand-Andersen. 

Marta Bańbura 
European Central Bank; email: Marta.Banbura@ecb.europa.eu 

Elena Bobeica 
European Central Bank; email: Elena.Bobeica@ecb.europa.eu 

© European Central Bank, 2020 

Postal address 
Telephone 
Website 

60640 Frankfurt am Main, Germany 
+49 69 1344 0
www.ecb.europa.eu

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This paper can be downloaded without charge from the ECB website or from RePEc: Research Papers in Economics. Information on all of 
the papers published in the ECB Statistics Paper Series can be found on the ECB’s website. 

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ISBN 978-92-899-4416-8, ISSN 2314-9248, doi:10.2866/02690, QB-BF-20-006-EN-N