Constructing and evaluating core inflation measures from component‐level inflation data

• Published date: 01 December 2019
• Date: 01 December 2019
• DOI: http://doi.org/10.1002/for.2595
• Author: Julie K. Smith,Edward N. Gamber

RESEARCH ARTICLE

Constructing and evaluating core inflation measures from

component‐level inflation data

Edward N. Gamber

1

| Julie K. Smith

2,3

1

Congressional Budget Office,

Washington, District of Columbia

2

Department of Economics, Lafayette

College, Easton, Pennsylvania

3

Research Program on Forecasting Center

of Economic Research, Department of

Economics, The George Washington

University, Washington, District of

Columbia

Correspondence

Julie K Smith, Department of Economics,

Lafayette College, Easton, PA 18042

Email: smithjk@lafayette.edu

Abstract

This paper undertakes a comprehensive examination of 10 measures of core

inflation and evaluates which measure produces the best forecast of headline

inflation out‐of‐sample. We use the Personal Consumption Expenditure Price

Index as our measure of inflation. We use two sets of components (17 and

50) of the Personal Consumption Expenditure Price Index to construct these

core inflation measures and evaluate these measures at the three time horizons

(6, 12 and 24 months) most relevant for monetary policy decisions. The best

measure of core inflation for both sets of components and over all time hori-

zons uses weights based on the first principal component of the disaggregated

(component‐level) prices. Interestingly, the results vary by the number of com-

ponents used; when more components are used the weights based on the per-

sistence of each component is statistically equivalent to the weights generated

by the first principal component. However, those forecasts using the persis-

tence of 50 components are statistically worse than those generated using the

first principal component of 17 components. The statistical superiority of the

principal component method is due to the fact that it extracts (in the first prin-

cipal component) the common source of variation in the component level

prices that accurately describes trend inflation over the next 6–24 months.

KEYWORDS

core, inflation, disaggregated components, forecasting, inflation, principal components

1|INTRODUCTION

Core inflation measures are essentially a re‐weighting of

the growth in component‐level prices to construct an

aggregate measure of inflation that achieves some objec-

tive such as maximizing the correlation of (the alterna-

tively weighted) inflation with money growth (Bryan &

Cecchetti, 1994), maximizing economic stability in an

inflation‐targeting regime (Mankiw & Reis, 2003) or min-

imizing the out‐of‐sample forecast error over some

forecast horizon (Smith, 2004). Researchers differ in their

approaches to constructing the weights. Some approaches

place zero weight on certain volatile components whereas

others replace the budget share weights with weights cho-

sen to achieve one of the aforementioned objectives.

Our objective is to identify the weighting method that

produces the most accurate out‐of‐sample forecasts of the

growth in the Personal Consumption Expenditures Price

Index (PCEPI) over 6‐,12‐, and 24‐month horizons. We

investigate three methods that place zero weight on cer-

tain components. Those methods are the weighted

median, the trimmed mean, and the “less food and

energy”measures of core inflation. We also investigate

*The views and analysis in this paper are the author's and should not be

interpreted as the Congressional Budget Office's.

Received: 6 February 2018 Revised: 4 December 2018 Accepted: 13 March 2019

DOI: 10.1002/for.2595

Journal of Forecasting. 2019;38:833–852. © 2019 John Wiley & Sons, Ltd.wileyonlinelibrary.com/journal/for 833

three methods that are based on a re‐weighting of all the

component‐level inflation data. The first method is based

on weights that measure the persistence of each of the

component‐level inflation rates. The second method is

based on weights estimated from a linear regression of

headline inflation (at some future date) on the full set

of component‐level inflation series. The third method

uses the weights estimated from the first principal com-

ponent of the component‐level data. Besides identifying

the weighting procedure that results in the most accurate

out‐of‐sample forecasts, we investigate whether the num-

ber of components or the level of disaggregation used

matters in creating good forecasts. We test two sets of

components

1

or levels of disaggregation and compare

forecasts not only within sets of components but also

the best forecasts from each set.

Previous work has evaluated the accuracy of each of

these measures of core inflation individually and relative

to a handful of benchmark inflation forecasts. Our paper

fills a gap in the literature by performing a comprehen-

sive evaluation of the accuracy of all these measures.

2

Because we compare the accuracy of a large set of possi-

ble core inflation measures, our findings provide valuable

guidance to policymakers interested in forecasting infla-

tion. Additionally, the deteriorating performance of

Phillips‐curve‐based inflation forecasting models since

the mid‐1980s (Stock & Watson, 2007) highlights the

need for an assessment of the forecast performance of

the various concepts of core inflation examined here.

3

We find that core inflation constructed using weights

based on the first principal component factor loadings

of 17 components is statistically better than the other

methods that use either 17 or 50 components. These

results reinforce findings by Crone et al. (2013) that the

trimmed mean inflation rate is not the best forecaster of

headline inflation and contradict those by Hendry and

Hubrich (2006), who find that for the USA using sectoral

(component) level data aggregated using regression

weights provides a good forecast of aggregate headline

inflation.

The rest of this paper is outlined as follows. In Section

2, we describes previous research on core inflation. Sec-

tion 3 describes the data. The empirical models and

results are examined in Sections 4 and 5. Section 6

concludes.

2|PREVIOUS RESEARCH ON

MEASURING CORE INFLATION

Headline inflation is constructed from individual

component‐level price changes using budget shares as

weights. While budget shares might be useful when com-

paring the cost of living over two historical time periods,

they are not necessarily the optimal weights from a fore-

casting perspective. For example, components that are

subject to frequent tax changes, weather or supply‐related

disturbances might affect headline inflation from period

to period because of their relatively large budget share

but have little effect on overall trend inflation.

Researchers have investigated several alternatives to bud-

get shares in an effort to dampen the effect of these tran-

sient movements in prices.

The weighted median and trimmed mean measures of

core inflation have been researched extensively.

4

Bryan

and Cecchetti's (1994) idea of using disaggregated infor-

mation on prices to obtain core inflation sparked great

interest. With the trimmed mean and weighted median,

which exploits the cross‐section information in the com-

ponents, core inflation is constructed period by period.

Each component can have a different weight every

period. Specifically, in the case of the weighted median

a component can have a zero weight (not the median ele-

ment) in period 1 and then in period 2 have a weight of

one (the median element); therefore, the lack of smooth-

ness of weights across time may disregard some informa-

tion relevant to future inflation (the correlation of prices

over time, for example) which may lead to inefficient

forecasts.

In addition to the weighted median, the trimmed

mean (and closely related) less food and energy measures

of core inflation (all of which impose zero restrictions on

some of the component‐level prices), researchers have

1

We use the 17 components suggested by Stock and Watson (2016) and

the 50 suggested by Bermingham and D'Agostino (2014).

2

Stock and Watson (2016) compare forecasts from an unobserved com-

ponents measure of core inflation to forecasts produced by six bench-

mark methods. However, the six benchmark methods do not include

the limited influence measures (such as the trimmed mean) that we

examine here and that are widely followed by economic forecasters

and policymakers. Previous research has found mixed results as to

whether these limited‐influence estimators are good forecasters (Crone,

Khettry, Mester, & Novak, 2013; Smith, 2004). In addition, the Federal

Reserve Bank of Cleveland produces a monthly weighted median infla-

tion rate of the consumer price index, and the Federal Reserve Bank of

Dallas produces a monthly trimmed mean inflation rate of the personal

consumption expenditure deflator, indicating that policymakers are

interested in the information contained in these measures. Therefore,

we conduct a horse race with the other measures suggested by the

literature.

3

An exception to this general finding in the literature is Ball and

Mazumder (2011), who present a modified Phillips curve that captures

movements in inflation for the entire period since 1960, up to and

including the Great Recession.

4

See Bryan and Cecchetti (1994), Alvarez and de los Llano Matea (1999),

Apel and Jansson (1999), Cockerell (1999), Johnson (1999), Le Bihan

and Sedillot (2002), and Smith (2004).

GAMBER AND SMITH

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