FRBNY Economic Policy Review / December 2007 19
A Comparison of Measures
of Core Inflation
1. Introduction
entral banks differ in their specific inflation objectives
and conduct of policy. However, they typically confront
the common problem of identifying which price changes are
permanent and which are transitory. Because of the lagged
effects of monetary policy, mistaking the nature of price
changes can be extremely costly. For example, the failure
to detect the onset of inflationary pressures may lead to a
sustained rise in inflation and ultimately require a more
prolonged period of policy tightening. Then again, an
overreaction to a temporary increase in inflation may result in
an unwarranted slowing, and possible decline, in economic
activity. Thus, the ability of central banks to differentiate
between permanent and transitory price movements is critical
for determining the appropriate prescription for monetary
policy.
The importance of gauging the persistence of price changes
in a timely manner has led to the development of schemes to
filter incoming data on aggregate prices. The filtering schemes
are designed to remove transitory price movements and
thereby produce a measure of underlying, or “core,” inflation.
The most common measure of core inflation is aggregate
household inflation excluding the contribution of price
Robert Rich is a research officer and Charles Steindel a senior vice president
at the Federal Reserve Bank of New York.
<robert.rich@ny.frb.org>
<charles.steindel@ny.frb.org>
The authors have benefited from the suggestions of attendees at the Bank for
International Settlements conference on the Evolving Inflation Process and the
Federal Reserve Bank of Cleveland–Federal Reserve Bank of Dallas conference
on Price Measurement for Monetary Policy. They thank Adam Ashcraft, Steve
Cecchetti, Tim Cogley, and two anonymous referees for valuable comments,
and are grateful to Steven Reed of the Bureau of Labor Statistics for supplying
detailed methodologically consistent CPI data. They also thank David Bedoll,
Michael Strain, and Evan LeFlore for research assistance. The views expressed
are those of the authors and do not necessarily reflect the position of the
Federal Reserve Bank of New York or the Federal Reserve System.
• Designed to remove transitory changes from
aggregate price data, measures of underlying,
or “core,” inflation are important tools in the
monetary policymaking process.
• Somewhat surprisingly, little consensus
has been reached on a preferred measure
of U.S. core inflation.
• An evaluation of several proposed measures
of U.S. core inflation, including the popular
ex food and energy series, finds that no
measure consistently dominates the others.
• There is arguably too much variability in
the nature and sources of transitory price
movements to be captured effectively through
the design of any individual measure.
• The general practice of focusing on a measure
of core inflation that excludes food and energy
does not seem to be justified by the analysis.
Robert Rich and Charles Steindel
C
20 A Comparison of Measures of Core Inflation
changes from food and energy. However, alternative core
inflation measures have been proposed. Some of these
candidate series include ex energy measures (Clark 2001),
weighted median measures (Bryan and Cecchetti 1994), and
exponentially smoothed measures (Cogley 2002), with
proponents citing the superior properties and performance
of the respective series across various dimensions.
The lack of consensus on a preferred measure of core
inflation might seem surprising given the importance of this
information to policymakers. However, a closer examination
of the evidence reveals little uniformity across the dimensions
used to compare the proposed measures. These dimensions
include statistical metrics, such as within-sample regression fit
and out-of-sample forecast performance as well as more basic
considerations relating to the selection of the sample period for
the analysis; the data frequency of the price changes (that is,
monthly versus quarterly observations); and even the choice of
the price measure used to calibrate the core inflation series.
Consequently, it is unclear whether the conflicting evidence in
support of various measures of core inflation reflects inherent
differences in performance capabilities or a lack of
standardization in the evaluation process.
This article provides a systematic evaluation of several
proposed measures of U.S. core inflation: the popular ex food
and energy series, an ex energy series, a weighted median series,
and an exponentially smoothed series. To inform the current
debate on this issue, we adopt a general framework for the
analysis. Regarding the choice of aggregate price indexes, we
focus on inflation measures that are likely goals for U.S.
monetary policy, namely the consumer price index (CPI) and
the personal consumption expenditure (PCE) index. To
evaluate the core measures of inflation, we select criteria that
have been used in previous studies: ease of design, a similar
mean to the goal inflation series, and an ability to track the
trend in the goal inflation series.
We also include the explanatory and forecasting capabilities
of the core measures of inflation as criteria, but recognize that
the need to specify an econometric model introduces some
discretion into the analysis. In an attempt to mitigate this
concern, we adopt a benchmark model that relates future
changes in inflation to the transitory component of price
changes identified by the candidate series. This specification
has the advantage of being not only simple to interpret in this
context, but also flexible enough to allow us to incorporate
alternative horizons into the analysis. As a further check for
robustness, we also examine results over different subsamples.
Taken together, we find that no core measure of inflation
consistently dominates the others. Further, the performance
of the candidate series differs markedly across the aggregate
inflation measures, criteria, and sample periods. This
conclusion is unaffected by the addition of simple measures
of economic slack to the benchmark model. Therefore, we
contend that the specifics of the criteria and methods used
likely do not account for the differences in performance
capabilities of the candidate series. Rather, we suggest that
this conflicting evidence reflects the lack of a consistent pattern
in transitory price movements. Namely, there is too much
variability in the nature and sources of transitory price
movements to be captured effectively through the design of
the individual core inflation measures. We argue that this
interpretation is consistent with the diversity of previous
findings using U.S. data and with the work of Hogan, Johnson,
and Laflèche (2001) in the Canadian context and Mankikar and
Paisley (2002) in the U.K. context. Both studies similarly
conclude that there is no single core inflation measure that
performs well across-the-board.
Our inability to identify a clear “best” or “worst” measure of
either core CPI or core PCE inflation also has implications for
some aspects of policy formulation and discussion. While it
would be desirable to rely on a single measure of core inflation
to perform a multitude of tasks, the evidence does not offer
support for this scenario. Consequently, we cannot identify
a compelling analytical reason, on either an ex ante or ex post
basis, to concentrate attention on a measure of inflation that
excludes food and energy prices.
2. Motivation and Concepts
Almost all central banks are concerned with, and have some
mandate to achieve, price stability. Even when ongoing changes
in the aggregate price level are anticipated, however, the
changes impose costs on economies. These costs need not be
directly related to movements in any type of household price
measure; they could stem from systematic changes in the prices
of all goods and services produced or purchased, including
items bought by businesses and governments.
The lack of consensus on a preferred
measure of core inflation might seem
surprising given the importance of this
information to policymakers. However, a
closer examination of the evidence reveals
little uniformity across the dimensions
used to compare the proposed measures.
FRBNY Economic Policy Review / December 2007 21
As a practical matter, inflation goals are often linked to
movements in a price measure for goods and services
purchased by consumers. One reason for this linkage is that
the prices for many capital goods purchased by businesses are
extremely difficult to measure,
1
as are those for many products
provided by governments (such as public education).
Moreover, a broad measure of consumer prices should be
reasonably successful in capturing the component of aggregate
price movements that may affect economic efficiency.
Another reason why a central bank would be concerned with
movements in a household or consumer price measure is that
many formal escalation arrangements, notably for wages as well
as taxes and government benefits, are connected to indexes of
consumer prices.
2
These arrangements could lead to household
price movements affecting the distribution of income as well as
government revenues and expenditures. In turn, these shifts
could influence employment, investment, and basic fiscal policy
decisions, and thereby affect the macroeconomic environment
faced by monetary policymakers. Thus, there are pragmatic
reasons for central banks to concentrate their attention on the
consumer component of inflation.
Given a concern with longer term movements in household
price inflation, central banks and private agents need some
means by which to gauge current performance vis-à-vis a price
inflation objective.
3
The main reason to focus on the behavior
of a core price measure is the belief that there is a significant
amount of transitory noise in the movement of aggregate
consumer prices. Filtering out the transitory noise gives a better
sense of the underlying trend in prices, and thus a better sense
of how a measure of current price changes compares with an
explicit or inferred longer term goal.
4
Accordingly, the role of a
core price measure lends itself to being interpreted as a means
to an end, with low and stable growth of a core price measure
serving as an “intermediate target” of policy rather than as
a direct “goal.”
5
This interpretation might also make clear that
a central bank’s decision to downplay certain price changes in
the conduct and communication of monetary policy does not
1
One could argue that the ideal aggregate inflation index would not include the
acquisition prices of capital goods, but rather would include the current “user
cost” of existing capital. Nonetheless, as is the case for capital goods acquisition
prices, it is difficult to measure these user costs accurately.
2
For instance, increases in the U.S. CPI automatically increase federal income
tax brackets and some deductions and exemptions as well as trigger boosts in
social security benefits, federal employee pensions, and interest payments on
inflation-protected securities.
3
The issue of whether or not a price inflation objective should be stated as a
numerical inflation target is not relevant to our analysis. Our focus is the
construction of a measure of underlying inflation that both satisfies some given
criteria and is useful for policymakers and private agents concerned with the
ongoing path of price changes.
4
As in Mankikar and Paisley (2002) and Brischetto and Richards (2006), one can
alternatively describe the role of a core price measure in terms of distinguishing
between relative price movements and changes in underlying inflation.
indicate a lack of concern for the impact of these price changes
on current movements in the cost of living.
6
The development of the core inflation concept appears to
have begun in the early 1970s. An early (and likely initial)
construction, associated with the late Otto Eckstein, was
a weighted growth of unit labor and capital costs for the
economy as a whole (Eckstein 1981). The more familiar
measure of core inflation as aggregate price growth excluding
food and energy appears to have been analyzed first in a
systematic fashion in a paper by Gordon (1975b). Gordon’s
aggregate “‘core’ price equation” was estimated for final sales
prices excluding food and energy.
7
The name “core inflation” then began to be attached to the
growth of price measures excluding food and energy. In 1978,
the Bureau of Labor Statistics began to report monthly growth
of both the CPI and the producer price index excluding food
and energy. The Bureau of Economic Analysis also releases data
on the monthly growth of the PCE index excluding food and
energy as well as the “market-based” PCE index excluding food
and energy. An important point concerning the development
of these “core inflation” measures is that little or no specific
consideration was given for their future use in the formulation
of monetary policy.
5
Some researchers (Aoki 2001; Benigno 2004; Goodfriend and King 1997)
have argued that the appropriate goal for monetary policy should be set in
terms of a measure of “core” inflation. However, these authors are
referring to a measure that comprises “sticky” prices—those prices that change
at fixed intervals—and excludes “flexible” prices that may change at any time.
The authors’ use of this terminology may stem from the view that their goal
inflation series is somewhat comparable to the aggregate index less food and
energy, since food and energy prices may be much more flexible than others.
Nevertheless, it is important to note that the models underlying this argument
are highly stylized. Moreover, while the argument that policy should be
concerned primarily with changes in “sticky” prices to offset the resulting
inefficiencies may have merits, there is the more overriding concern that it is
very difficult to develop an index of “stickiness” to evaluate candidate core
inflation measures.
6
That is, this treatment may alleviate the apparent disconnect and occasional
sharp deviation between changes in a cost-of-living index and in the inflation
measure(s) that may be the focus of central bank discussion.
7
In a slightly earlier piece, Gordon (1975a) refers to 1973-74 inflation as comprising
several components, including “underlying ‘hard-core’ inflation” (p. 184).
The main reason to focus on the behavior
of a core price measure is the belief that
there is a significant amount of transitory
noise in the movement of aggregate
consumer prices.
22 A Comparison of Measures of Core Inflation
3. Core Inflation: Proposed
Measures and Evaluation
3.1 Candidate Core Inflation Measures
Although the term “core inflation” has long meant an
inflation series excluding food and energy price changes,
alternative measures of core inflation have been proposed.
This development likely reflects the lack of a widely accepted
definition of core inflation. These alternative measures of
core inflation are derived using one of two approaches.
Borrowing the terminology of Mankikar and Paisley (2002),
we refer to these methods as the “statistical approach” and
the “model-based approach.”
The statistical approach derives measures of core inflation
by performing a predetermined operation on an aggregate
price index. The operation may involve excluding certain items
from the price index, re-weighting the components of the price
index, or smoothing time-series movements in the price index.
Alternatively, the model-based approach typically derives
measures of core inflation by imposing restrictions from
economic theory within the context of a multivariate
econometric analysis. This approach leads to estimates of core
inflation that may be associated with dynamic factor models
or defined as a component of measured inflation possessing
particular interactive effects with other variables.
8
For this study, we restrict our attention to measures of core
inflation associated with the statistical approach. We do this
for several reasons. One is that the statistical approach yields
core inflation measures that are more widely used by central
banks and are more familiar to the public. Measures of this
type often appear in central bank discussions of monetary
policy or in the media. Another reason is that there is little
consensus about the specification and identification schemes
of model-based measures of core inflation. Last, there is a
marked difference between the two approaches in terms of
complexity. Model-based core inflation measures could
remain problematic to policymakers and the public because
the concepts underlying their design can be abstract and their
construction computationally demanding. On the contrary,
while there is a variety of core inflation measures associated
with the statistical approach, each measure is relatively easy to
understand and compute.
Within the statistical approach, the core inflation measures
reflect very different characterizations of transitory price
8
As examples, Velde (2006) defines core inflation as the (unobserved)
component common to a large number of individual price series, while Quah
and Vahey (1995) define core inflation as the component of measured inflation
that is uncorrelated with output at medium- to long-run horizons.
movements. Some of these measures associate the bulk of
transitory price fluctuations with specific components, thereby
prompting their exclusion from an aggregate price index. We
consider two examples of this type of core inflation measure.
One is based on the conventional practice of excluding food
and energy price changes from movements in an aggregate
series. The other has been proposed by Clark (2001), who
argues for a core measure of inflation that removes only energy
price changes from movements in an aggregate series. His
motivation is that food prices, at least at the consumer level,
likely react to many of the same forces that influence other
retail prices, whereas energy price changes are dominated by
transitory commodity price shifts.
As an alternative to core inflation measures that remove
some prespecified item(s) in every period, Bryan and Cecchetti
(1994) advance a measure that involves re-weighting all the
components in the price index. Specifically, their proposed
core inflation measure is the weighted median price change in
a period, which is defined as the price change in the period for
that product such that half the expenditure is for items whose
prices are rising just as, or more, rapidly, and half is for items
whose price changes are rising just as, or more, slowly. The
weighted median is related to the “trimmed mean” concept of
core inflation (Dolmas 2005).
9
Bryan and Cecchetti’s argument
for focusing on measures constructed along these lines is that
9
The trimmed mean is the average price change computed when omitting a
specified percentage of the highest and lowest price changes of products
(weighted by their expenditure share) for a period. While our analysis does not
include the trimmed mean measure among the candidate series, we believe that
some caution needs to be exercised in evaluating this measure. Specifically,
researchers typically use full-sample estimation techniques to determine how
much the distribution of price changes should be trimmed. However, the use
of a criterion function to optimally select the amount of trimming could
favorably bias the performance of this measure within a particular period
of interest. In our view, any evaluation of a trimmed mean measure
should be undertaken using recursive estimation so that the trimmed mean is
constructed sequentially. This method would circumvent any difficulties that
arise from allowing the future history of the data to impact the construct
of the series during an earlier time period.
Although the term “core inflation” has
long meant an inflation series excluding
food and energy price changes,
alternative measures of core inflation have
been proposed. This development likely
reflects the lack of a widely accepted
definition of core inflation.
FRBNY Economic Policy Review / December 2007 23
the tails of the price distribution are mainly associated with
temporary price level effects; thus, systematically eliminating
their influence should yield a more robust measure of the
persistent component of inflation.
In contrast to the weighted median that smoothes the cross-
section of price changes, Cogley (2002) develops a core
measure of inflation that down-weights past changes in the
price index. His proposed core inflation measure involves the
exponential smoothing of current and past aggregate price
changes. The motivation for this measure is the idea that the
government and private sector use adaptive methods to learn
about a world in which there are occasional regime shifts in
mean inflation.
For the analysis, we examine the following four candidate
core inflation measures noted above:
10
• the aggregate inflation series excluding food and energy,
• the aggregate inflation series excluding energy proposed
by Clark (2001),
• the weighted median measure of the aggregate inflation
series proposed by Bryan and Cecchetti (1994),
11
and
• the exponentially smoothed version of the aggregate
inflation series proposed by Cogley (2002).
Cogley’s formulation is given as:
(1) ,
where denotes the relevant aggregate inflation measure.
Equation 1 defines the core measure as a one-sided geometric
distributed lag of current and past inflation. We follow Cogley
and set the gain parameter
.
3.2 Performance Criteria
Previously, we argued that core inflation should be viewed as
an intermediate target for an aggregate inflation goal. Using
this proposition as a guide, we evaluate the candidate core
measures of inflation based on criteria comparable to those
discussed in Wynne (1999):
12
1. Transparency of construction. It may be helpful to build a
core price measure in a straightforward, relatively easy
10
In addition to these four series, Rich and Steindel (2005) examine
exponentially smoothed versions of the ex food and energy, ex energy, and
weighted median series as candidate core inflation measures.
11
The Federal Reserve Bank of Cleveland issues monthly estimates of the
change in the weighted median CPI. The Bank has recently announced changes
in the procedures used to construct this measure (Bryan and Meyer 2007)
based on the work of Brischetto and Richards (2006). Our computations are
based on the older procedure.
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fashion. This criterion facilitates the communication of
the concept in the policy dialogue.
2. Similarity of means. A core measure should have a mean
comparable to the goal inflation series over a long period
of time.
3. Tracking the trend rate of inflation. A core measure should
display a close coherence to the underlying trend in the
goal inflation series.
4. Explanatory content. A core measure should explain past
movements in the goal inflation series as well as provide
information about potential future developments.
It is important to note, however, that in the literature there
has been little uniformity in the criteria used to evaluate core
measures of inflation. For example, Cogley (2002) focuses on
the within-sample regression fit of core inflation measures
(part of criterion 4). Bryan and Cecchetti (1994) examine the
marginal within-sample predictive content of core inflation
measures as well as their out-of-sample forecast performance
(criterion 4). Clark (2001) judges core inflation measures based
on their complexity, similarity of means, ability to track a
measure of the trend rate of inflation, and within-sample
predictive content (criteria 1, 2, 3, and part of criterion 4).
Consequently, our set of criteria listed above is not only
consistent with the attributes considered in other studies, but
also broader in scope.
Given the lack of a common set of performance criteria for
core inflation measures in the literature, a similar issue arises
concerning the choice of the goal inflation series. Bryan and
Cecchetti (1994), Clark (2001), Cogley (2002), and Blinder and
Reis (2005) examine the (standard published) CPI, whereas
Dolmas (2005) and Smith (2006) examine the PCE deflator,
and Smith (2004) and Khettry and Mester (2006) examine both
12
Silver (2006) also discusses a wide range of comparable criteria for judging the
relative merits of proposed core inflation measures. Wynne (1999), like Bryan
and Cecchetti (1994), notes that at times the rationale for the construction of a
core price index has been to identify the common component of price changes
attributable to monetary policy. If such is the purpose of a core price index,
however, then it is not altogether clear why one would confine the measure to
elements of household price indexes. The difficulty is that monetary policy
affects the demand for all types of products in complex ways. These demand
effects are not necessarily similar for household and nonhousehold prices, nor is
there any strong reason to assume that the distribution of monetary policy effects
between household and other prices will be stable over time.
It is important to note . . . that in the
literature there has been little uniformity
in the criteria used to evaluate core
measures of inflation.