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An Alternative Measure of Core Inflation:
The Trimmed Persistence PCE Price Index
WP 23-10
John O'Trakoun
Federal Reserve Bank of Richmond
An Alternative Measure of Core Inflation:
The Trimmed Persistence PCE Price Index
John O'Trakoun 1
October 20, 2023
ABSTRACT
I introduce the "trimmed persistence PCE," a new measure of core inflation in which component prices
are weighted according to the time-varying persistence of their price changes. The components of
trimmed persistence personal consumption expenditures (PCE) display less tendency to mechanically
pass-through the level of the prior period's inflation to the current period; thus, the impact of the
current stance of monetary policy and real economic factors are more likely to be visible in recent
trimmed persistence inflation compared to headline inflation. Trimmed persistence inflation performs
comparably to existing popular measures of core inflation in terms of volatility and relationship with
economic slack. Model selection procedures confirm trimmed persistence PCE contributes additional
information to inflation forecasting models when stacked against other popular measures of core
inflation. Applying the new index in a Taylor rule analysis suggests the Fed's aggressive path of federal
funds rate hikes during the pandemic may have achieved appropriately restrictive levels by the fourth
quarter of 2022, clearing the way for more measured policy adjustment thereafter as risks of policy
overshooting became more salient.
Keywords: inflation, core inflation, inflation persistence, time-varying, inflation dynamics
JEL Classification Numbers: C22, E31, E37, E52
I.
Introduction
Following the shock of the COVID-19 pandemic and the subsequent fiscal and monetary policy response,
inflation in the United States reached multidecade highs. As shown in Figure 1, inflation as measured by
year-over-year growth in the personal consumption expenditures (PCE) price index rose to 7.12 percent
in June 2022, which was the highest rate since December 1981.
Federal Reserve Bank of Richmond, PO Box 27622, Richmond, VA 23261. Email: John.OTrakoun@rich.frb.org. The
views and opinions expressed in this article belong to the author and do not reflect those of the Federal Reserve
Bank of Richmond or the Federal Reserve System.
1
1
14%
12%
10%
8%
6%
4%
2%
-2%
Jan-60
Jan-62
Jan-64
Jan-66
Jan-68
Jan-70
Jan-72
Jan-74
Jan-76
Jan-78
Jan-80
Jan-82
Jan-84
Jan-86
Jan-88
Jan-90
Jan-92
Jan-94
Jan-96
Jan-98
Jan-00
Jan-02
Jan-04
Jan-06
Jan-08
Jan-10
Jan-12
Jan-14
Jan-16
Jan-18
Jan-20
Jan-22
0%
-4%
Figure 1 Personal consumption expenditure (PCE) price inflation, 1:1960-5:2023. Gray shading indicates recessions.
Interpreting the rise in inflation was a major challenge for policymakers on the Federal Open Market
Committee (FOMC), who referred to a number of different inflation metrics when they communicated
to the public.
In parsing the inflation data during the pandemic, one challenge that became particularly salient was
judging the extent to which disaggregated pricing data contained useful information about the
trajectory of future inflation. As shown in Figure 2, the period of elevated inflation in PCE ex food and
energy (PCExFE) prices beginning in 2021 initially manifested as an outsized contribution of used vehicle
prices to month-over-month growth rates, before broadening in scope. In early diagnoses of rising
inflation in 2021, policymakers and academics debated whether the used vehicle price increase
represented a transitory relative price change or the initial manifestation of inflation resulting from a
broader imbalance between aggregate supply and demand. 2
As an example of one such public debate, Nobel laureate Paul Krugman stated on Twitter, "Inflation [is]
somewhat higher than expected, but I don't think we should get too worked up about the prices of used cars."
(https://twitter.com/paulkrugman/status/1392458554578247685, 12 May 2021, accessed 14 Dec. 2022). Former
Council of Economic Advisers chair Jason Furman expressed a contrary view, stating, "You want to be cautious
about taking different sectors out of your price basket in assessing inflation trends ... If people have a lot more
money to spend and car prices did not go up then maybe they would have spent even more on other stuff and
inflation would have been similar in aggregate, just spread out differently."
(https://twitter.com/jasonfurman/status/1458886069093556229, 11 Nov. 2021, accessed 14 Dec. 2022).
2
2
Month-Over-Month Core PCE Growth (Annualized)
10
8
6
4
2
Jul-22
Aug-22
Jun-22
Apr-22
May-22
Mar-22
Jan-22
Feb-22
Dec-21
Nov-21
Oct-21
Sep-21
Aug-21
Jul-21
Jun-21
Apr-21
May-21
Mar-21
Jan-21
Feb-21
Dec-20
Oct-20
Nov-20
Sep-20
Jul-20
Aug-20
Jun-20
May-20
Apr-20
Feb-20
-4
Mar-20
-2
Jan-20
0
-6
-8
New vehicles
Rent+OER
Used vehicles
Bars and restaurants
Hotels and Motels
Air transportation
Admissions
Everything else
Core PCE inflation (mom % ann.)
Figure 2 PCExFE inflation by selected expenditure categories, 2020-2022
The resulting debate renewed public interest in measuring inflation and in the differences between
popular price indices. The Economist calculated an alternative core price index, commenting on the
popular PCExFE and trimmed mean PCE inflation measures that "both of these methods have flaws.
Changes in food and energy prices are not necessarily unusually large or short-lived. And trimmed
means' weighting schemes are plagued by abrupt cliffs." (The Economist, 2021)
Leigh et al. (2021) distinguish core price indices according to "fixed-exclusion" and "outlier-exclusion"
categories based on whether the indices exclude signals from fixed categories of consumer expenditure
(i.e., food and energy, or “sticky price” categories), or whether large price changes are dropped from the
index. During the COVID-19 pandemic, they find PCExFE performed poorly for most of 2020-2021
because large industry price changes occurred outside of the food and energy sectors. Other fixedexclusion measures such as the Atlanta Fed sticky consumer price index (CPI) omitted more industries
and fared better than PCExFE during the pandemic. However, outlier-exclusion measures such as the
trimmed mean and median PCE inflation measures displayed superior performance on the basis of
volatility and negative comovement with economic slack.
In this article, I propose an alternate measure of core inflation called the “trimmed persistence PCE.”
The trimmed persistence PCE price index is neither a fixed-exclusion measure, as it does not omit
changes in a pre-specified group of expenditure components, nor an outlier-exclusion measure, as it
3
does not necessarily omit all large component-level price changes. Similar to the popular trimmed mean
and median measures of PCE inflation, trimmed persistence PCE takes inflation signals from a subset of
the PCE expenditure basket. But in contrast to existing measures which exclude expenditure categories
based on realized monthly price changes, trimmed persistence inflation excludes price categories based
on the time-varying persistence of price changes in each category. Large price changes for a spending
category are omitted from the trimmed persistence PCE index only when they cause the category's
estimated time-varying persistence coefficient to cross an optimal inclusion threshold. Trimming the
relatively persistent components, which are more variable, reduces the volatility of trimmed persistence
inflation compared to headline PCE inflation. In addition, the trimming process results in an inflation
measure that is less prone to mechanically inheriting the prior period's level of inflation and is arguably
more responsive to real-time changes in real economic and monetary policy factors determining
inflation.
During the post-COVID-19 recession inflationary episode, trimmed persistence PCE displayed less
volatility than headline PCE inflation with a standard deviation of monthly annualized inflation prints
falling between those of median PCE and PCExFE. However, over a longer sample beginning in 1988,
trimmed persistence was more volatile than trimmed mean and median PCE. Nevertheless, the benefit
of this approach is that it preserves potentially useful signals about changes in inflation dynamics which
might have been dropped from the trimmed mean and median PCE. For example, in times of
accelerating inflation, it may be particularly important to retain such signals from outlying relative price
changes if a high-inflation regime initially manifests as large price changes in a smaller number of
categories before becoming more broad-based across multiple categories. Trimmed persistence
inflation also performs comparably to other core inflation measures in displaying a negative relationship
with economic slack, with a correlation coefficient falling between that of PCExFE and median PCE
inflation following the pandemic recession.
Despite the visual similarity between twelve-month changes in trimmed persistence PCE and PCExFE, as
well as the similarity of the two measures in terms of the volatility of monthly annualized inflation and
inverse comovement with resource slack, trimmed persistence PCE contributes a distinct perspective
about the trajectory of inflation and implications for policy. Model selection procedures applied to
statistical inflation forecasting models that pit trimmed persistence inflation against other core inflation
measures show evidence that trimmed persistence inflation contributes to improved forecast accuracy
for inflation at horizons up to three years ahead.
The remainder of the paper proceeds as follows. Section II discusses how this article fits into the existing
literature on inflation. Section III discusses the basic intuition and motivation behind the trimmed
persistence PCE. Section IV describes the methodology underlying the construction of the index, along
with data sources. Section V examines the behavior of trimmed persistence PCE inflation during the
pandemic with an application to policy, and Section VI offers concluding thoughts.
4
II.
Literature Review
This paper is related to studies exploring time-variation in inflation dynamics. In an early contribution,
Barsky (1987) presents evidence that inflation persistence evolved from a white noise process in the
pre-World War I years to a highly persistent, nonstationary ARIMA process after 1960. Cogley and
Sargent (2002) use a time-varying parameter Bayesian vector autoregression (TVP-VAR) model to
characterize inflation as weakly persistent in the 1960s and strongly persistent in the 1970s, with
persistence declining again in the 1990s. Williams (2006) studies time variation in inflation persistence
by estimating Phillips curves over different samples of historical data, finding some evidence that
inflation has become less persistent since the 1990s. Stock and Watson (2007) fit an unobserved
components model with stochastic volatility on inflation data finding further evidence of time variation
in inflation persistence. Beechey and Österholm (2012) find that inflation persistence declined rapidly
during the Volcker and Greenspan tenures compared to the experience of the 1970s. In contrast, Pivetta
and Reis (2007) find very wide Bayesian credible sets associated with estimated persistence coefficients
and conclude that inflation persistence has essentially been unchanged between 1965 and 2001. Cogley
et al. (2010) document inflation persistence increasing during the Great Inflation and falling after the
Volcker disinflation. In this article—unlike these studies which focus on aggregate inflation measures—I
study time-varying dynamics of the price indices of disaggregated expenditure categories.
This article is most closely related to those which focus on extracting core inflation from disaggregated
inflation data. Bryan and Pike (1991) examine the CPI, finding that median price changes give a superior
signal of underlying inflation compared to headline CPI because the median purges noise from transitory
relative price movements. Bryan et al. (1997) introduce a version of the trimmed mean CPI. In a crosscountry study, Brischetto and Richards (2006) find that trimmed mean CPI inflation outperforms
headline and exclusion-based core CPI inflation (such as CPIxFE inflation) at separating inflation signals
from noise, and in terms of near-term predictive ability. Bryan and Meyer (2010) group CPI components
into sticky and flexible categories based on the speed at which prices adjust, calculating a sticky-price
CPI which displays superior inflation forecasting performance relative to the headline CPI measure.
Meyer et al. (2013) and Meyer and Venkatu (2014) find that the median CPI outperforms other trimmed
mean inflation measures in predicting CPI inflation, and that it also outperforms PCExFE in predicting
PCE inflation.
Other contributions, including this paper, focus on the PCE price index which is the Fed's preferred
measure of consumer prices. Dolmas (2005) introduces the trimmed mean PCE measure, which strips
out expenditure components associated with the largest absolute monthly price changes. In a related
study, Dolmas and Koenig (2019) explain that while trimmed mean PCE does not dominate PCExFE in
terms of forecasting, it is more successful at filtering out transitory variation from the headline PCE
inflation number. Carroll and Verbrugge (2019) calculate median PCE inflation rates and find that these
measures perform comparably to other trend inflation estimators such as trimmed mean PCE. Mahedy
and Shapiro (2017) sort PCE spending categories into procyclical and acyclical groups according to their
sensitivity to the unemployment gap, developing alternative measures of cyclical and acyclical core
inflation. Stock and Watson (2019) introduce a similar measure of cyclically sensitive inflation, which reweights seventeen broad components of PCE inflation according to their correlation with a broad
5
measure of economic slack estimated during the 1984-2019 period. Shapiro (2022) classifies PCE
components into supply- and demand-driven groups based on the comovement of price and quantities
of each component in response to unexpected shocks.
The motivation of the trimmed persistence PCE index is similar to that of Stock and Watson (2016) who
use disaggregated data on sectoral inflation to construct indices of core inflation that feature timevarying sectoral weights. These authors use a multivariate unobserved-components stochastic volatility
model to recover common volatilities and trends, sector-specific volatilities and trends, sector-specific
factor loadings, common and sector-specific outlier factors, and the aggregate inflation trend from
quarterly inflation series of seventeen components of the PCE price index. The model is computationally
intensive, and the authors note that extending the approach to more finely disaggregated data presents
substantial challenges due to instability in measurement. In a more recent contribution, Almuzara and
Sbordone (2022) introduce the Multivariate Core Trend, extending the Stock and Watson (2016)
approach to monthly data from seventeen sectors, although their MCT index ultimately excludes the
food and energy sectors. In contrast to these authors, I use a simpler approach on even more granular
monthly data, using 180 components of PCE. My approach allows a more disaggregated level analysis of
the contributors to core inflation while preserving the use of monthly data to provide higher-frequency
information to policymakers making decisions in real time.
As mentioned in the previous section and shown in Table 1, these alternative measures of core inflation
can largely be classified into fixed-exclusion and outlier-exclusion categories. In contrast, the trimmed
persistence PCE measure introduced in the next section is neither a fixed- nor outlier-exclusion measure.
Fixed-exclusion
CPIbased
CPI ex food and energy, Atlanta Fed Sticky
CPI
PCEbased
PCE ex food and energy, San Francisco Fed
cyclical and acyclical core PCE, San
Franscisco Fed supply- and demand-driven
PCE, Stock and Watson (2019) cyclically
sensitive inflation, Almuzara and Sbordone
(2022) Multivariate Core Trend
Outlier-exclusion
Cleveland Fed 16
percent trimmed
mean CPI,
Cleveland Fed
median CPI
Dallas Fed
trimmed mean
PCE, Cleveland
Fed median PCE
Neither fixed- nor outlierexclusion
Stock and Watson (2016)
unobserved components
stochastic volatility trend
inflation, Trimmed
persistence PCE
Table 1 Classification of core inflation measures
III.
Motivation
How is time-varying inflation persistence related to identifying underlying “core” inflation? To motivate
the basic intuition behind the trimmed persistence PCE index, consider the AR(1) process:
𝜋𝜋𝑡𝑡 = 𝛼𝛼(1 − 𝜌𝜌) + 𝜌𝜌𝜋𝜋𝑡𝑡−1 + 𝜖𝜖𝑡𝑡 ,
(1)
6
where ϵt ∼ IID(0, σ2𝜖𝜖 ). We assume that the random variable 𝜋𝜋𝑡𝑡 has some degree of persistence, so that
0 ≤ 𝜌𝜌 ≤ 1. 𝜋𝜋𝑡𝑡 is covariance-stationary if 𝜌𝜌 < 1, which then implies 𝐸𝐸(𝜋𝜋𝑡𝑡 ) = 𝛼𝛼. Importantly, the
variance of 𝜋𝜋𝑡𝑡 is 𝜎𝜎𝜋𝜋2 =
𝜎𝜎𝜖𝜖2
,
1−𝜌𝜌2
which is increasing in 𝜌𝜌.
If 𝜌𝜌 = 1, then setting 𝛼𝛼 = 0 to prevent 𝜋𝜋𝑡𝑡 from trending, 𝜋𝜋𝑡𝑡 follows the driftless random walk
process:
𝜋𝜋𝑡𝑡 = 𝜋𝜋𝑡𝑡−1 + 𝜖𝜖𝑡𝑡 .
(2)
𝜋𝜋𝑡𝑡 = 𝜋𝜋0 + ∑𝑡𝑡−1
𝑗𝑗=0 𝜖𝜖𝑡𝑡−𝑗𝑗 .
(3)
Given initial condition 𝜋𝜋0 , by repeated substitution of lagged values into (2) it can be shown that 𝜋𝜋𝑡𝑡
follows the moving average representation:
Thus, if 𝜋𝜋𝑡𝑡 follows a random walk, 𝜖𝜖𝑡𝑡−𝑗𝑗 shocks have a permanent effect on 𝜋𝜋𝑡𝑡 . Furthermore, the
variance of 𝜋𝜋𝑡𝑡 does not exist: initializing 𝜋𝜋0 = 0, 𝜋𝜋𝑡𝑡 = 𝜖𝜖𝑡𝑡 + 𝜖𝜖𝑡𝑡−1 + ⋯ + 𝜖𝜖1 ∼ 𝐼𝐼𝐼𝐼𝐼𝐼(0, 𝑡𝑡𝜎𝜎𝜖𝜖2 ). In other
words, the variance of 𝜋𝜋𝑡𝑡 grows linearly with 𝑡𝑡, and as 𝑡𝑡 increases without bound, so too will the
variance of 𝜋𝜋𝑡𝑡 .
This has implications for building a price index. Suppose our goal is to construct a price index that
smooths out the impact of its most volatile underlying components. If we can estimate an AR(1) process
for the price index of each component 𝑖𝑖, we can assess its volatility 𝜎𝜎𝜋𝜋2𝑖𝑖 by judging how far 𝜌𝜌𝑖𝑖 is from 1:
in other words, how far away the price index for 𝑖𝑖 is from being a random walk. Giving greater weight to
components with lower estimated persistence would reduce the variance of the aggregated index
compared to headline PCE which is essentially weighted by expenditure shares. An index constructed in
this manner would arguably better reflect changes in present conditions versus echoes of the past,
compared to the headline index. The higher 𝜌𝜌𝑖𝑖 , the more that current inflation 𝜋𝜋𝑖𝑖𝑖𝑖 will mechanically
inherit its level from the prior period 𝜋𝜋𝑖𝑖𝑖𝑖−1 , and the less visible that current period changes in other
determinants of inflation, such as cumulative policy effects and real economic activity as of date 𝑡𝑡, will
be.
As a further refinement to the index, we can take into account evidence of time-varying inflation
dynamics discussed in the prior section by allowing 𝜌𝜌 and 𝛼𝛼 to vary over time. This entails estimating a
time-varying parameter version of Equation (1) as follows:
𝜋𝜋𝑡𝑡 = 𝛼𝛼𝑡𝑡 (1 − 𝜌𝜌𝑡𝑡 ) + 𝜌𝜌𝑡𝑡 𝜋𝜋𝑡𝑡−1 + 𝜖𝜖𝑡𝑡 .
The basic idea that the variance of 𝜋𝜋𝑡𝑡 is increasing in 𝜌𝜌𝑡𝑡 continues to hold with some slight
modifications.
(4)
7
A.
Determining inclusion criteria
Having established that the AR(1) persistence coefficient is a potentially useful criterion for including
category-level prices in a trimmed persistence core PCE price index, the question remains: how
persistent is too persistent? In other words, at what levels of |𝜌𝜌𝑖𝑖𝑖𝑖 | should we discount the signals from
𝜋𝜋𝑖𝑖𝑖𝑖 ?
I draw on Dolmas (2005), who outlines a trimming process that minimizes the discrepancy between the
inflation rate captured by a newly constructed price index and three proxies for core inflation. The first
proxy of core inflation is a centered thirty-six-month moving average of monthly inflation rates, first
proposed by Bryan et al. (1997). The second proxy is obtained by applying a Christiano-Fitzgerald
bandpass filter to monthly headline inflation; Dolmas (2005) describes this measure, which discards
high-frequency movements in PCE inflation lasting less than thirty-nine months, as the inflation rate that
the FOMC appears to have responded to in setting monetary policy. The last proxy represents an
inflation signal that contains information about future inflation and is calculated as a moving average of
inflation in the current month and twenty-four coming months.
B.
The optimal trimming problem
The optimal trimming problem chooses the threshold 𝜌𝜌∗ to minimize the root mean square deviation
𝑇𝑇
���}
between trimmed persistence inflation and the proxy of core inflation. Letting { 𝜋𝜋
𝑡𝑡 𝑡𝑡=1 denote the proxy
∗
of core inflation, the optimal threshold 𝜌𝜌 solves:
∗)
(𝜌𝜌
𝑚𝑚𝑚𝑚𝑛𝑛𝜌𝜌∗ �𝑇𝑇 −1 ∑𝑇𝑇𝑡𝑡=1 �𝜋𝜋𝑡𝑡
2
− ����
𝜋𝜋𝑡𝑡 .
(5)
Table 2 shows the optimal trim for each core proxy. The selection process chooses an optimal threshold
value of 𝜌𝜌∗ = 0.23 for all three proxies.
Core proxy
36-month centered moving average
Trend correlated with Fed Funds Rate
Forward-looking moving average
Average across alternative proxies
Table 2 Optimal trimming for various core proxies
IV.
Optimal threshold ρ*
0.23
0.23
0.23
0.23
Data and methodology
A.
Data
Data on the underlying components of the PCE price index are retrieved from the Bureau of Economic
Analysis (BEA) and accessed via Haver Analytics. The data are also publicly available on the BEA's
website in the Underlying Detail tables 2.4.4U and 2.4.5U for chain-type price indices and nominal
8
personal consumption expenditures (used to calculate monthly PCE shares) by detailed type of product,
respectively.
When choosing the degree of disaggregation, there is a trade-off between sample length and finer
granularity. For the purposes of this study, I include 180 subcategories of PCE consumption whose
expenditure weights add up to 100 percent of the PCE consumption basket. This level of aggregation is
very similar to that used in the trimmed mean PCE index. While the many component price indices have
data starting as early as January 1959, the price indices for digital videos, personal computers and
tablets, and computer software are only available post-1977. Furthermore, the price indices for personal
computers and computer software were constant from January 1977-March 1979; this further restricts
the sample for estimating time-varying persistence and delays the starting date for the trimmed
persistence PCE until 1979. Further information on the components is presented in Appendix Table 1.
B.
Estimating time-varying persistence
For each of the 180 components of the PCE consumption basket, I fit a time-varying AR(1) model to the
month-over-month annualized change in the component's corresponding price index similar to Equation
(4):
𝜋𝜋𝑖𝑖𝑖𝑖 = 𝛼𝛼�𝚤𝚤𝚤𝚤 + 𝜌𝜌𝑖𝑖𝑖𝑖 𝜋𝜋𝑖𝑖𝑖𝑖−1 + 𝜖𝜖𝑖𝑖𝑖𝑖 ,
(6)
where 𝑖𝑖 is the index for component 𝑖𝑖 and 𝛼𝛼�𝚤𝚤𝚤𝚤 ≡ 𝛼𝛼𝑖𝑖𝑖𝑖 (1 − 𝜌𝜌𝑖𝑖𝑖𝑖 ) is the time-varying intercept term. Our
main object of interest is the 𝑇𝑇 × 𝑖𝑖 matrix 𝒫𝒫 of time-varying AR1 persistence parameters 𝜌𝜌𝑖𝑖𝑖𝑖 .
Equation (6) is estimated via a generalized additive model approach (Hastie & Tibshirani, 1986; Hastie &
Tibshirani, Generalized Additive Models, 1990; Wood, 2017), which models price growth as a sum of
smooth basis functions of covariates (i.e., time and lagged price changes). For the underlying basis
functions, I use twenty thin plate regression splines, an approximation of optimal thin plate spline
smoothers which, unlike some other basis function alternatives, allow bases to represent smooths of
multiple predictor variables and avoid subjectivity in choosing knot locations.
The assumption that changes in the dynamics of inflation happen smoothly over time, rather than
suddenly and abruptly, is key to the construction of the trimmed persistence PCE index and is built into
the methodology. It allows for large relative price changes to potentially be retained in the computation
of the index, so long as these changes do not push the estimated AR(1) coefficient in the current period
above the optimal inclusion threshold. As discussed in Wood (2017), the prior belief that the “truth” is
more likely to be smooth rather than volatile and wiggly can also be formalized through a Bayesian
interpretation of the smoothing penalty. However, there may exist real-world scenarios where inflation
dynamics are highly unstable, such as in episodes of hyperinflation observed in some emerging markets,
where this underlying assumption of the methodology is invalid.
9
To illustrate an application of this methodology, Figure 3 plots estimates of 𝛼𝛼�𝑡𝑡 ≡ 𝛼𝛼𝑡𝑡 (1 − 𝜌𝜌𝑡𝑡 ) and 𝜌𝜌𝑡𝑡
when Equation (4) is fitted to monthly annualized PCE inflation from January 1959 through August
2023; the shaded gray region indicates the 95 percent Bayesian credible sets associated with each
estimate. As shown in the first panel, during the COVID-19-related inflationary episode, the estimated
time-varying intercept sharply increased, while the second panel suggests a decline in the persistence of
headline PCE inflation after 2020.
(a) Time-varying intercept 𝛼𝛼
�𝑡𝑡
10
(b) Time-varying AR1 coefficient 𝜌𝜌𝑡𝑡
Figure 3 Time-varying coefficient estimates of fitted AR(1) model of month-over-month annualized headline PCE inflation,
January 1959-August 2023
C.
Building the index
Following Wolman and Ding (2005), I construct the trimmed persistence PCE price index as an
expenditure-share weighted average of the rates of change of component price indices.
𝑁𝑁
Specifically, let �𝑃𝑃𝑖𝑖,𝑡𝑡 , 𝑄𝑄𝑖𝑖,𝑡𝑡 �𝑖𝑖=1 denote a set of prices and real quantities for 𝑁𝑁 expenditure categories that
make up the PCE price index at time 𝑡𝑡. The growth rate of the PCE price index 𝑝𝑝𝑡𝑡 between 𝑡𝑡 + 1 and 𝑡𝑡 is
given by the Fisher ideal index formula:
𝜋𝜋𝑡𝑡 =
𝑝𝑝𝑡𝑡+1
𝑝𝑝𝑡𝑡
∑𝑖𝑖 𝑄𝑄𝑖𝑖,𝑡𝑡 𝑃𝑃𝑖𝑖,𝑡𝑡+1 ∑𝑖𝑖 𝑄𝑄𝑖𝑖,𝑡𝑡+1 𝑃𝑃𝑖𝑖,𝑡𝑡+1
.
∑𝑖𝑖 𝑄𝑄𝑖𝑖,𝑡𝑡 𝑃𝑃𝑖𝑖,𝑡𝑡
∑𝑖𝑖 𝑄𝑄𝑖𝑖,𝑡𝑡+1 𝑃𝑃𝑖𝑖,𝑡𝑡
= �
(7)
This can be rewritten as:
11
𝑁𝑁
𝜋𝜋𝑡𝑡 = ��∑𝑁𝑁
𝑖𝑖=1 𝜔𝜔𝑖𝑖,𝑡𝑡−1 𝜋𝜋𝑖𝑖,𝑡𝑡 ��∑𝑖𝑖=1 𝜃𝜃𝑖𝑖,𝑡𝑡 𝜋𝜋𝑖𝑖,𝑡𝑡 �,
(8)
where 𝜋𝜋𝑖𝑖,𝑡𝑡 is the rate of price change for category 𝑖𝑖 from period 𝑡𝑡 − 1 to period 𝑡𝑡, and
𝜔𝜔𝑖𝑖,𝑡𝑡 ≡
𝜃𝜃𝑖𝑖,𝑡𝑡 ≡
𝑥𝑥𝑖𝑖,𝑡𝑡
𝑁𝑁
∑𝑗𝑗=1 𝑥𝑥𝑗𝑗,𝑡𝑡
𝑥𝑥𝑖𝑖,𝑡𝑡 ⁄𝜋𝜋𝑖𝑖,𝑡𝑡
∑𝑁𝑁
𝑗𝑗=1(𝑥𝑥𝑗𝑗,𝑡𝑡 ⁄𝜋𝜋𝑗𝑗,𝑡𝑡 )
(9)
(10)
for 𝑖𝑖 = 1, … , 𝑁𝑁, with 𝑥𝑥𝑖𝑖,𝑡𝑡 ≡ 𝑃𝑃𝑖𝑖,𝑡𝑡 × 𝑄𝑄𝑖𝑖,𝑡𝑡 referring to period 𝑡𝑡 dollar expenditures on category 𝑖𝑖.
In equation (8), both objects in square brackets are weighted averages of the rates of price change for
each expenditure category. The weights 𝜔𝜔𝑖𝑖,𝑡𝑡−1 are expenditure weights for category 𝑖𝑖 in period 𝑡𝑡 − 1,
while the weights 𝜃𝜃𝑖𝑖,𝑡𝑡 are hypothetical expenditure shares that combine period 𝑡𝑡 real quantities with
period 𝑡𝑡 − 1 prices. PCE inflation 𝜋𝜋𝑡𝑡 is the geometric average of the two weighted averages.
From here, I employ a further approximation that aggregates prices for each expenditure category using
a Divisia index. As described in Ding and Wolman (2005), the Divisia index is a simpler calculation that
gives a good approximation of the true PCE inflation rate, and it is obtained by using the expenditure
share of component 𝑖𝑖 at time 𝑡𝑡, 𝜔𝜔𝑖𝑖,𝑡𝑡 , as the weight for the price change of component 𝑖𝑖 between 𝑡𝑡 and
𝑡𝑡 + 1:
𝐷𝐷
𝜋𝜋𝑡𝑡+1
= ∑𝑖𝑖 𝜔𝜔𝑖𝑖,𝑡𝑡 𝜋𝜋𝑖𝑖,𝑡𝑡+1 .
(11)
As described in Section III.B, only a subset of PCE expenditure components whose estimated AR(1)
coefficients 𝜌𝜌𝑖𝑖𝑖𝑖 fall below the optimal inclusion threshold 𝜌𝜌∗ will be included in the trimmed persistence
PCE at time 𝑡𝑡. The weight for component 𝑖𝑖 in the trimmed persistence PCE is:
𝑇𝑇𝑇𝑇
𝜔𝜔𝑖𝑖,𝑡𝑡
=
𝐼𝐼(𝜌𝜌𝑖𝑖𝑖𝑖 ≤𝜌𝜌∗ )𝜔𝜔𝑖𝑖,𝑡𝑡
𝑁𝑁
∑𝑖𝑖=1 𝐼𝐼(𝜌𝜌𝑖𝑖𝑖𝑖 ≤𝜌𝜌∗ )𝜔𝜔𝑖𝑖,𝑡𝑡
,
(12)
where 𝐼𝐼(⋅) is equal to one if the argument in parentheses is true, and zero otherwise. Month-overmonth changes in the trimmed persistence PCE are calculated as:
𝑇𝑇𝑇𝑇
𝑇𝑇𝑇𝑇
𝜋𝜋𝑡𝑡+1
= � 𝜔𝜔𝑖𝑖,𝑡𝑡
𝜋𝜋𝑖𝑖,𝑡𝑡+1 .
𝑖𝑖
(13)
12
The level of the trimmed persistence PCE, which is used to calculate year-over-year inflation rates, is
computed by setting the period preceding the first 𝜋𝜋𝑡𝑡𝑇𝑇𝑇𝑇 equal to 100, and cumulatively applying the
month-over-month growth rates.
The composition of the trimmed persistence PCE index thus changes over time as shown in Figure 4.
During the COVID-19 inflation episode, the number of expenditure components included in the index
declined from 128 in December 2019 to 98 as of August 2023, as the estimated persistence of many
inflation components rose above the inclusion threshold. The share of PCE expenditure included in the
index, plotted on the right axis, declined from 60.1 percent in December 2019 to 51.1 percent in August
2023.
Components Included in Trimmed Persistence PCE
150
0.8
0.75
140
0.7
130
0.65
0.6
120
0.55
110
0.5
100
98
0.45
0.4
Number of components included (left axis)
Jun-21
Dec-22
Jun-18
Dec-19
Dec-16
Jun-15
Dec-13
Jun-12
Jun-09
Dec-10
Jun-06
Dec-07
Jun-03
Dec-04
Dec-01
Jun-00
Dec-98
Jun-97
Jun-94
Dec-95
Jun-91
Dec-92
Dec-89
Jun-88
Dec-86
Jun-85
Jun-82
Dec-83
Jun-79
Dec-80
90
Expenditure share included (right axis)
Figure 4 Count and expenditure share of components included in trimmed persistence PCE
Figure 5 plots the final result. The first panel of Figure 5 compares month-over-month annualized
growth rates of the trimmed persistence PCE index to those of the headline PCE price index. The second
panel plots year-over-year inflation rates of the trimmed persistence PCE and headline PCE price indices.
13
-2
Trimmed Persistence PCE
Jul-23
Jan-22
Jul-20
Jan-19
Jul-17
Jan-16
Jul-14
Jan-13
Jul-11
Jan-10
Jul-08
Jan-07
Trimmed Persistence PCE
Jul-05
Jan-04
Jul-02
Jan-01
Jul-99
Jan-98
Jul-96
Jan-95
Jul-93
Jan-92
Jul-90
Jan-89
Jul-87
Jan-86
Jul-84
Jan-83
Month-over-month (% annualized)
Oct-22
Mar-21
Aug-19
Jan-18
Jun-16
Nov-14
Apr-13
Sep-11
Feb-10
Jul-08
Dec-06
May-05
Oct-03
Mar-02
Aug-00
Jan-99
Jun-97
Nov-95
Apr-94
Sep-92
Feb-91
Jul-89
Dec-87
May-86
Oct-84
Mar-83
Aug-81
Jan-80
-5
Jul-81
Jan-80
Year-over-year (%)
20
15
10
5
0
-10
-15
Headline PCE
Month-over-month annualized change in headline and trimmed persistence PCE price indices, January
1980-August 2023
14
12
10
8
6
4
2
0
-4
Headline PCE
Figure 5 Headline and trimmed persistence PCE inflation, January 1980-August 2023
Year-over-year headline and trimmed persistence PCE inflation rates, January 1980-August 2023
14
V.
The post-COVID-19 inflation
Figure 6 compares year-over-year trimmed persistence PCE inflation to year-over-year PCExFE, trimmed
mean PCE, median PCE, cyclical core PCE inflation, and multivariate core trend inflation. Year-over-year
trimmed persistence PCE inflation as of August 2023 was 3.1 percent—1.8 percentage points from its
February 2020 level. In comparison, year-over-year PCExFE inflation in August 2023 was 2.2 percentage
points from its February 2020 level, while trimmed mean and median inflation were both 1.9 percentage
points from their February 2020 reading.
9.00
8.00
Year-over-year (%)
7.00
6.00
5.00
4.00
3.00
2.00
1.00
PCExFE
Trimmed mean PCE
Median PCE
Cyclical Core PCE
Multivariate Core Trend
Trimmed Persistence PCE
Jan-21
May-22
Sep-19
Jan-17
May-18
Sep-15
May-14
Jan-13
Sep-11
Jan-09
May-10
Sep-07
May-06
Jan-05
Sep-03
Jan-01
May-02
Sep-99
May-98
Jan-97
Sep-95
Jan-93
May-94
Sep-91
May-90
Jan-89
Sep-87
Jan-85
May-86
0.00
Comparison of core inflation proxy measures, 1980-present
Figure 6 Trimmed persistence PCE inflation versus other core inflation measures
Typically, authors introducing new core inflation measures use their new index to perform some kind of
forecasting exercise. These exercises typically take the form of a horse race pitting the new core
inflation measure against other alternatives in a forecasting regression, or against some rule of thumb
such as a random walk forecast of inflation computed as the average of the previous four quarters of
inflation (Atkeson & Ohanian, 2001). I skip this step for two reasons.
15
First, previous authors have found that out-of-sample predictive power is similar across alternative
measures of core inflation: Dolmas and Koenig (2019) find that trimmed mean PCE does not dominate
PCExFE inflation in terms of forecast performance; Carroll and Verbrugge (2019) find that median PCE
inflation performs comparably to other trend inflation estimators such as trimmed mean PCE; and Bryan
and Meyer (2010) find similar out-of-sample forecasting accuracy of sticky CPI, core sticky CPI, and CPI
ex food and energy.
Second, sticking the trimmed persistence PCE in a forecasting model to generate unconditional forecasts
of inflation may not be the best use of this measure. If a central bank is credible in its ability to influence
the price level, then any forecast for inflation should be conditioned on the forecaster's assumptions
about the future path of monetary policy. As evident in the FOMC Summary of Economic Projections
from March 2022 (see Figure 7), intelligent people armed with the same information on realized
inflation, economic fundamentals, and even inside knowledge of FOMC deliberations might still disagree
on the path of inflation if their views of the appropriate future path of policy differ.
Figure 7 Distribution of FOMC projections for 2022 full-year core PCE inflation, March 2022
Source: Board of Governors, 16 March 2022.
https://www.federalreserve.gov/monetarypolicy/files/fomcprojtabl20220316.pdf}. Accessed 17 Dec. 2022.
Instead, the best use of the trimmed persistence PCE may be to serve as an additional signal about
underlying inflationary pressures when incoming inflation readings are mixed. The COVID-19-era
inflation spotlighted a number of challenges identifying and interpreting inflation data in an
environment of mixed shocks to aggregate demand and supply. Ball et al. (2022) show that narratives
explaining the trajectory of underlying inflation can be sensitive to the choice of core inflation metric
used. Schmitt-Grohé and Uribe (2022) find that narratives explaining the rise in inflation during the
pandemic can also be sensitive to the length of the historical sample used in the supporting empirical
analysis. As discussed in Section I, Leigh et al. (2021) find that fixed-exclusion and outlier-exclusion
measures of inflation can offer different perspectives on the trajectory of inflation.
16
The trimmed persistence PCE is neither a fixed-exclusion measure, as it does not omit changes in a fixed
group of components, nor an outlier-exclusion measure, as it does not necessarily omit all large
component-level price changes. This is clearly seen in Table 3, which lists the first ten items of all 180
PCE expenditure categories, sorted in ascending order by month-over-month price change for
September 2022. Focusing on these ten categories with the largest monthly annualized price decreases
reveals that some of the categories in the top ten, such as window coverings and spectator sports, are
retained in the trimmed persistence PCE index whereas they would be excluded from trimmed mean
and median PCE. Additionally, the price index for eggs is retained in the index in that month’s trimmed
persistence PCE reading, in contrast to PCExFE.
1
2
3
4
5
6
7
8
9
10
Category
Gasoline & Other Motor Fuel
Eggs
Window Coverings
Calculators/Typewriters/Other Info Processing Eqpt
Telephone and Related Communication Equipment
Spectator Sports
Fuel Oil
Other Recreational Vehicles
Bicycles & Accessories
Pleasure Boats
Price change
(% MoM
ann.)
-49.92
-42.55
-41.31
-37.49
-37.48
-34.69
-32.34
-30.7
-30.69
-30.69
AR1
coefficient Included?
0.25
No
0.22
Yes
-0.17
Yes
0.33
No
0.33
No
0.17
Yes
0.3
No
-0.29
No
-0.11
Yes
-0.29
No
Table 3 Top 10 PCE price changes and inclusion in trimmed persistence PCE, in ascending order (Sep. 2022)
Because it retains information from a subset of components with large relative price changes, the
trimmed persistence PCE displays higher month-to-month volatility compared to other measures of core
inflation. From January 1988 through July 2023, the standard deviation of month-over-month
annualized changes in trimmed persistence PCE was 1.7, compared to 1.6 for PCE ex food and energy,
1.1 for median PCE, and 1.0 for trimmed mean PCE.
However, the relative performance of core inflation measures in terms of volatility can vary depending
on the sample window. Figure 8 shows the standard deviation of monthly annualized inflation across
various measures of inflation following the pandemic recession (May 2020-July 2023). Over this period,
volatility of the trimmed persistence PCE has fallen between that of median PCE and PCExFE, suggesting
that trimmed persistence inflation has performed comparably to other measures of core inflation during
a period of elevated inflation and uncertainty.
17
Standard Deviation of Monthly Annualized Inflation
(May 2020-July 2023)
3
2.5
2
1.5
1
0.5
0
Headline PCE Cyclical core
PCE
Median PCE
Trimmed
persistence
PCE
PCExFE
PCE core
services
excluding
housing
Trimmed
mean PCE
Multivariate
core trend
Figure 8 Volatility of monthly annualized inflation, May 2020-July 2023 (standard deviation, percentage points)
In terms of the relationship between inflation and economic slack, the trimmed persistence PCE
compares favorably against the alternative core inflation measures examined in this article. I follow
Leigh et al. (2021), who assess comovement between inflation measures and economic slack as
measured by the twelve-month average gap between the unemployment rate and the Congressional
Budget Office's estimate of the natural rate.
Figure 9 shows the estimated coefficient in a regression of twelve-month inflation against the average
unemployment gap following the pandemic recession, with larger absolute magnitudes indicating a
greater degree of negative comovement between inflation and slack. Based on this measure, the
trimmed persistence PCE displays a similar degree of comovement with slack as median PCE, performing
favorably in comparison to trimmed mean and multivariate core trend inflation.
18
Comovement of Inflation and Unemployment Gap
(May 2020-July 2023)
-0.68
Headline PCE
Cyclical core
PCE
PCExFE
Trimmed
persistence PCE
Median PCE
Trimmed mean
PCE
Mulitvariate
core trend
-0.66
-0.64
-0.62
-0.60
-0.58
-0.56
-0.54
Figure 9 Comovement of inflation and unemployment gap (May 2020-May 2023)
Given the comparability of trimmed persistence inflation to other core inflation proxies in terms of
volatility and correlation with economic slack, it would be reasonable to question whether the trimmed
persistence PCE contributes any additional information to a forecaster's information set over preexisting core inflation measures. I allow the data to decide, estimating inflation forecasting regression
equations of the form:
(ℎ)
π({𝑡𝑡+ℎ},{𝑡𝑡+ℎ}−12) = α + βπ𝑐𝑐(𝑡𝑡,𝑡𝑡−12) + ϵ𝑡𝑡 ,
(14)
where π({𝑡𝑡+ℎ},{𝑡𝑡+ℎ}−12) represents ℎ-month ahead, year-over-year headline PCE inflation, and π𝑐𝑐(𝑡𝑡,𝑡𝑡−12)
represents a vector of core inflation proxies measured as year-over-year inflation rates at month 𝑡𝑡. I
look at horizons of ℎ ∈ {6, 12, 18, 24, 30, 36} months ahead. π𝑐𝑐 contains some subset of the core
inflation proxies displayed in Figure 9 .
I use statistical variable selection procedures to let the data decide which subset of the core inflation
measures to retain in equation (14). These are tools designed to simplify models and tackle issues of
collinearity that can arise when correlations between regressor variables (i.e., multicollinearity) are high.
I consider three such procedures:
1. Forward stepwise regression, which starts from a model with no variables and individually tests
each candidate variable according to a model fit criterion, selecting the best variable and
repeating the process until no remaining variable results in an improvement in the fit;
19
2. Backward stepwise regression, which starts from a model that contains all candidate predictor
variables and tests the deletion of each variable using a model fit criterion, removing the
variable that results in the best improvement in the fit criterion and repeating the process until
no variable can be deleted without a deterioration in model fit; and
3. LASSO (least absolute shrinkage and selection operator) regression, which selects a subset of
known covariates in a model by shrinking coefficients toward and setting some coefficients
equal to zero.
For the two stepwise regressions, I use the standard choice of Akaike's information criterion (AIC) as a
measure of model fit.
Results for the model selection procedure are presented in Table 4. Trimmed persistence PCE is retained
as a predictor variable in forecasting headline inflation at every horizon across all three model selection
algorithms, with the exception of the six-month ahead inflation forecasting model selected via backward
stepwise selection. Notably, trimmed persistence inflation is retained under every model selected via
LASSO regression, which has been found to outperform stepwise selection procedures in out-of-sample
forecast accuracy.
20
Forward
stepwise
selection
Backward
stepwise
selection
LASSO
Forecast
Horizon
Multivariate core
PCE, Median PCE,
Headline PCE,
Trimmed
persistence PCE,
Cyclical core PCE,
PCExFE, Trimmed
mean PCE
Multivariate core
PCE, Trimmed mean
PCE, Headline PCE,
PCExFE, Trimmed
persistence PCE
Multivariate core
PCE, PCExFE,
Trimmed mean PCE,
Median PCE,
Trimmed
persistence PCE
Multivariate core
PCE, PCExFE,
Headline PCE,
Trimmed
persistence PCE,
Median PCE
Multivariate core
PCE, Trimmed
persistence PCE,
Median PCE,
Headline PCE,
Cyclical core PCE
Cyclical core PCE,
Multivariate core
PCE, Trimmed
persistence PCE,
Trimmed mean PCE,
PCExFE
Headline PCE,
PCExFE, Trimmed
mean PCE, Cyclical
core PCE,
Multivariate core
PCE
Headline PCE,
PCExFE, Trimmed
mean PCE,
Multivariate core
PCE, Trimmed
persistence PCE
PCExFE, Trimmed
mean PCE, Median
PCE, Multivariate
core PCE, Trimmed
persistence PCE
Headline PCE,
PCExFE, Median
PCE, Multivariate
core PCE, Trimmed
persistence PCE
Headline PCE,
Trimmed mean PCE,
Multivariate core
PCE, Trimmed
persistence PCE
PCExFE, Trimmed
mean PCE, Cyclical
core PCE,
Multivariate core
PCE, Trimmed
persistence PCE
Headline PCE,
PCExFE, Trimmed
mean PCE, Median
PCE, Cyclical core
PCE, Multivariate
core PCE, Trimmed
persistence PCE
Headline PCE,
PCExFE, Trimmed
mean PCE, Median
PCE, Cyclical core
PCE, Multivariate
core PCE, Trimmed
persistence PCE
Headline PCE,
PCExFE, Trimmed
mean PCE, Median
PCE, Cyclical core
PCE, Multivariate
core PCE, Trimmed
persistence PCE
Headline PCE,
PCExFE, Trimmed
mean PCE, Median
PCE, Cyclical core
PCE, Multivariate
core PCE, Trimmed
persistence PCE
Headline PCE,
PCExFE, Trimmed
mean PCE, Median
PCE, Cyclical core
PCE, Multivariate
core PCE, Trimmed
persistence PCE
Headline PCE,
PCExFE, Trimmed
mean PCE, Cyclical
core PCE,
Multivariate core
PCE, Trimmed
persistence PCE
6
12
18
24
30
36
Table 4 Inflation forecasting at various horizons: Model selection results
21
The alternative signal about true core inflation provided by the trimmed persistence PCE may be useful
to monetary policymakers assessing the appropriate level of the policy rate through the framework of
policy rules such as the Taylor (1993) rule. For example, former Richmond Fed president Jeffrey Lacker
and Philadelphia Fed president Charles Plosser argued in 2022 that the Fed should routinely make
reference to the implications of systematic monetary policy rules when discussing the likely future path
of interest rates (Lacker & Plosser, 2022). The policy prescriptions of such rules can be sensitive to the
choice of inflation metric used in the calculation (Dhawan & Jeske, 2007; Mehra & Sawhney, 2010;
Garciga, Knotek, & Verbrugge, 2016). During the pandemic inflation, St. Louis Fed president James
Bullard suggested using different measures of core inflation, including trimmed mean PCE and PCExFE,
along with different calibrations of a Taylor-type rule to derive upper and lower bounds for the
recommended level of the federal funds rate (Bullard, 2022).
To illustrate this application of the trimmed persistence PCE, I compare policy rule prescriptions
obtained from using different measures of inflation in a generalized version of the Taylor rule, described
�𝑡𝑡 given by the
in the Atlanta Fed's online Taylor Rule Utility (Higgins, 2016). The policy prescription 𝐹𝐹𝐹𝐹𝑅𝑅
rule is calculated via the formula:
�𝑡𝑡 = ρ𝐹𝐹𝐹𝐹𝑅𝑅𝑡𝑡−1 + (1 − ρ)[(𝑟𝑟𝑡𝑡∗ + π∗𝑡𝑡 ) + 1.5(π𝑡𝑡 − π∗𝑡𝑡 ) + β𝑔𝑔𝑔𝑔𝑝𝑝𝑡𝑡 ],
𝐹𝐹𝐹𝐹𝑅𝑅
(15)
where 𝐹𝐹𝐹𝐹𝑅𝑅𝑡𝑡 denotes the fed funds target rate at the end of month 𝑡𝑡, π𝑡𝑡 denotes inflation, π∗𝑡𝑡 denotes
the inflation target (set to 2.0 percent), 𝑟𝑟𝑡𝑡∗ denotes the natural (real) interest rate (set to 1.0 percent),
and 𝑔𝑔𝑔𝑔𝑝𝑝𝑡𝑡 is a measure of resource gap in the economy. Various measures of the resource gap are
commonly used, but here I use a measure based on the difference between the unemployment rate in
month 𝑡𝑡 and the Congressional Budget Office's estimate of the natural rate of unemployment for the
corresponding period. ρ in Equation (15) refers to the interest-rate smoothing parameter, which I set to
0.85 in line with the inertial Taylor rule in the Federal Reserve Board's FRB/US model of the U.S.
economy, and β refers to the weight on the resource gap which is set to 0.5.
Table 5 shows that as of July 2023, the actual federal funds rate (FFR) of 5.375 was within the range of
prescribed values obtained by incorporating various core inflation measures into the Taylor rule
described in equation (15). However, the Taylor rule prescription under trimmed persistence PCE
inflation was on the lower end of the range of prescriptions, suggesting the FFR setting may have been
more restrictive than suggested by formulations of the policy rule using other inflation metrics.
22
Inflation Measure
Headline PCE
PCExFE
Trimmed Mean PCE
Median PCE
Cyclical Core PCE
Multivariate Core Trend
Trimmed Persistence PCE
Actual Fed Funds Rate
Taylor Rule Prescription
5.25
5.44
5.43
5.59
6.12
5.12
5.21
5.38
Table 5 Taylor rule prescriptions for fed funds rate (July 2023)
Figure 10 plots the actual FFR versus the prescribed rate from the trimmed persistence PCE-based Taylor
rule. The gray shaded region indicates the range of rate prescriptions obtained from incorporating the
alternative inflation measures listed in Table 5 into the specified rule. The figure shows that prior to the
pandemic recession, the trimmed persistence PCE-based rule characterized the FOMC's setting for the
FFR reasonably well, despite a notable period from 2009-2013 when the effective lower bound (ELB)
was a binding constraint, with the rule recommending levels at or below zero.
During the early phase of the pandemic, the ELB once again became binding as the Taylor rule
recommended negative rates from April through October 2020. The situation quickly reversed when
inflation began to rise in March 2021; the rule-prescribed FFR was over 100 basis points higher than the
actual FFR by the end of 2021.
With historically rapid policy tightening beginning in March 2022, including a string of four consecutive
75 basis point hikes, the gap between the actual FFR and the prescribed value narrowed rapidly. While
the prescribed rate remained above the actual FFR through the first ten months of 2022, the gap
between the two series was eliminated with a large 75 basis point FFR hike in November 2022, bringing
the funds rate to 3.875 versus the rule-based prescription of 3.76. Thus, from the perspective of this
particular specification of the Taylor rule, steep rate hikes by the FOMC were successful in bringing
policy close to “appropriate” levels as quickly as the fourth quarter of 2022—though the rule-based
prescription continued to rise in following months with ongoing elevated inflation, indicating further
adjustment remained necessary. Still, taken as a whole, aggressive FFR normalization may have
contributed to signs of progress for overall PCE inflation in the fourth quarter of 2022. This in turn may
have allowed the FOMC to slow the pace of its rate hikes beginning in December 2022 as policy
overshooting risks became more relevant.
23
7
6
5
4
3
2
1
May-23
Oct-22
Mar-22
Aug-21
Jan-21
Jun-20
Nov-19
Apr-19
Sep-18
Feb-18
Jul-17
Dec-16
May-16
Oct-15
Mar-15
Aug-14
Jan-14
Jun-13
Nov-12
Apr-12
Sep-11
Feb-11
Jul-10
Dec-09
May-09
Oct-08
Mar-08
Aug-07
-1
Jan-07
0
-2
Taylor Rule Prescription
Actual FFR
Figure 10 Fed funds rate versus prescription of trimmed persistence PCE-based Taylor rule, 2007-present
VI.
Conclusion
I introduced an alternative measure of core inflation called the trimmed persistence PCE in which
expenditure categories are weighted according to the time-varying persistence of their corresponding
price changes. Excluding categories associated with more persistent price changes yields an inflation
measure that is less volatile than headline PCE inflation. Additionally, because the underlying
components of trimmed persistence inflation display less tendency to mechanically pass-through the
prior period's level to the current period, the contemporaneous influence of fundamental drivers of
inflation such as real supply and demand effects and the cumulative impact of monetary policy actions
are likely to be more visible in recent trimmed persistence PCE inflation compared to the headline
measure.
In contrast to other popular measures of core inflation, the trimmed persistence PCE is neither a fixedexclusion measure omitting pre-specified expenditure categories such as food, energy, or “sticky price”
categories, nor is it an outlier-exclusion measure that automatically strips out expenditure categories
that experience outsized monthly price changes. Because it retains some information from expenditure
categories with large price changes, the trimmed persistence PCE can be a more volatile measure of
24
core inflation than trimmed mean or median PCE. However, following the pandemic recession, the
trimmed persistence PCE performed favorably versus other measures of core inflation, with a standard
deviation of monthly annualized inflation falling between that of median PCE and PCExFE.
Additionally, the trimmed persistence PCE performs comparably to other core inflation proxies in terms
of relationship with economic slack. In the aftermath of the COVID-19 recession, trimmed persistence
PCE displayed a stronger negative relationship with the unemployment gap than trimmed mean and
multivariate core inflation, with the degree of comovement with slack similar to median PCE. In variable
selection procedures pitting trimmed persistence PCE against other inflation measures, trimmed
persistence PCE is shown to contribute to the predictive fit of regression-based inflation forecasting
models for horizons up to three years ahead.
The trimmed persistence PCE can provide a helpful alternative signal of underlying inflation pressure. By
relying on alternative weighting and exclusion criteria compared to other core inflation proxies, it
contributes to policy debates about how, if at all, to take signals about aggregate inflation from
disaggregated, expenditure category-level data. Additionally, for policymakers and economic forecasters
judging the appropriate level of the benchmark policy rate through the framework of Taylor-type rules,
incorporating trimmed persistence PCE inflation into such rules may provide additional context about
the possible range of appropriate settings for the FFR. Using trimmed persistence PCE inflation in a
Taylor-type rule calibrated to fit data observed prior to the pandemic shows a considerable deviation
between the actual FFR and levels prescribed by the rule at the end of 2021, while aggressive rate hiking
in 2022 may have returned policy to appropriate levels—as indicated by the rule—by the fourth quarter
of that year.
This study also opens further avenues for additional research. For example, I estimated a simple timevarying AR(1) process for component-level price indices; further research could explore whether having
richer specifications that include more autoregressive lags, or allowing for moving-average terms could
improve the performance of the index. Another simplifying step used in this paper was a Divisia
approximation to construct the trimmed persistence price index; further work could be done to move
toward the Fisher ideal index construction. Additionally, I use a simple rule to determine whether an
expenditure component is included at any given period; further work could explore alternative inclusion
criteria relating each components' weight in the aggregate index to their estimated persistence
coefficient. Future research could also explore whether other methods of estimating time-varying
inflation dynamics, different from the generalized additive approach used in this paper, might yield
superior results.
VII. Appendices
A.
Component
1
2
3
4
Appendix 1: List of PCE components used in calculation
Description
Start Date
New Domestic Autos
New Foreign Autos
New Light Trucks
Used Autos
1959-01-31
1959-01-31
1959-01-31
1959-01-31
25
Component
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
Description
Used Light Trucks
Tires
Accessories & Parts
Furniture
Clock/Lamp/Lighting Fixture/Other HH Decorative Item
Carpets & Other Floor Coverings
Window Coverings
Major Household Appliances
Small Elec Household Appliances
Dishes and Flatware
Nonelectric Cookware & Tableware
Tools, Hardware & Supplies
Outdoor Equipment & Supplies
Televisions
Other Video Equip
Audio Equipment
Audio Discs/Tapes/Vinyl/Permanent Digital Downloads
Video Discs, Tapes & Permanent Digital Downloads
Photographic Equip
Personal Computers/Tablets & Peripheral Equipment
Computer Software & Accessories
Calculators/Typewriters/Other Info Processing Eqpt
Sporting Equip, Supplies, Guns & Ammunition
Motorcycles
Bicycles & Accessories
Pleasure Boats
Pleasure Aircraft
Other Recreational Vehicles
Recreational Books
Musical Instruments
Jewelry
Watches
Therapeutic Medical Equip
Corrective Eyeglasses & Contact Lenses
Educational Books
Luggage & Similar Personal Items
Telephone and Related Communication Equipment
Cereals
Bakery Products
Beef and Veal
Pork
Other Meats
Poultry
Start Date
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1977-01-31
1959-01-31
1977-01-31
1977-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
26
Component
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
Description
Fish and Seafood
Fresh Milk
Processed Dairy Products
Eggs
Fats and Oils
Fresh Fruit
Fresh Vegetables
Processed Fruits & Vegetables
Sugar and Sweets
Food Products, Not Elsewhere Classified
Coffee, Tea & Other Beverage Mtls
Mineral Waters, Soft Drinks & Vegetable Juices
Spirits
Wine
Beer
Food Produced & Consumed on Farms
Women's & Girls' Clothing
Men's & Boys' Clothing
Children's & Infants' Clothing
Clothing Materials
Standard Clothing Issued to Military Personnel
Shoes & Other Footwear
Gasoline & Other Motor Fuel
Lubricants & Fluids
Fuel Oil
Other Fuels
Prescription Drugs
Nonprescription Drugs
Other Medical Products
Games, Toys & Hobbies
Pets & Related Products
Flowers, Seeds & Potted Plants
Film & Photographic Supplies
Household Cleaning Products
Household Paper Products
Household Linens
Sewing Items
Misc Household Products
Hair/Dental/Shave/Misc Pers Care Prods ex Elec Prod
Cosmetic/Perfumes/Bath/Nail Preparatns & Implements
Elec Appliances for Personal Care
Tobacco
Newspapers & Periodicals
Start Date
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
27
Component
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
Description
Stationery & Misc Printed Materials
Expenditures Abroad by U.S. Residents
Less: Personal Remittances in Kind to Nonresidents
Rental of Tenant-Occupied Nonfarm Housing
Owner-Occupied Mobile Homes
Owner-Occupied Stationary Homes
Rental Value of Farm Dwellings
Group Housing
Water Supply & Sewage Maintenance
Garbage & Trash Collection
Electricity
Natural Gas
Physician Services
Dental Services
Paramedical Services
Nonprofit Hospitals' Services to HHs
Proprietary Hospitals
Govt Hospitals
Nursing Homes
Motor Vehicle Maintenance & Repair
Motor Vehicle Leasing
Motor Vehicle Rental
Parking Fees & Tolls
Railway Transportation
Intercity Buses
Taxicabs and Ride Sharing Services
Intracity Mass Transit
Other Road Transportation Service
Air Transportation
Water Transportation
Membership Clubs/Participant Sports Centers
Amusement Parks/Campgrounds/Rel Recral Svcs
Motion Picture Theaters
Live Entertainment, ex Sports
Spectator Sports
Museums & Libraries
Audio-Video, Photographic/Info Process Svcs
Casino Gambling
Lotteries
Pari-Mutuel Net Receipts
Veterinary & Other Services for Pets
Package Tours
Maint/Repair of Rec Vehicles/Sports Eqpt
Start Date
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1973-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
28
Component
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
Description
Elementary & Secondary School Lunches
Higher Education School Lunches
Other Purchased Meals
Alcohol in Purchased Meals
Food Supplied to Civilians
Food Supplied to Military
Hotels and Motels
Housing at Schools
Commercial Banks
Other Dep Instns/Regulated Invest Companies
Pension Funds
Financial Service Charges, Fees/Commissions
Life Insurance
Net Household Insurance
Net Health Insurance
Net Motor Vehicle/Oth Transportation Insur
Communication
Proprietary & Public Higher Education
Nonprofit Pvt Higher Education Svcs to HHs
Elementary & Secondary Schools
Day Care & Nursery Schools
Commercial & Vocational Schools
Legal Services
Tax Preparation & Other Rel Services
Employment Agcy Services
Other HH Business Services
Labor Organization Dues
Prof Assn Dues
Funeral & Burial Services
Hairdressing Salons & HH Grooming Establishments
Misc HH Care Services
Laundry & Dry Cleaning Services
Clothing Repair, Rental & Alterations
Repair & Hire of Footwear
Child Care
Social Assistance
Social Advocacy/Civic/Social Organizations
Religious Organizations' Services to HHs
Sales Receipts: Foundatns/Grant Making/Giving Svcs to HH
Domestic Services
Moving, Storage & Freight Services
Repair of Furn, Furnishings/Floor Coverings
Repair of HH Appliances
Start Date
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
1959-01-31
29
Component
177
178
179
180
Description
Other Household Services
Foreign Travel by U.S. Residents
Less: Exps in the US by Nonresidents
Final Consumptn Exps of Nonprofit Instns Serving HH
Start Date
1959-01-31
1959-01-31
1959-01-31
1959-01-31
Appendix Table 1 PCE components used in calculating trimmed persistence PCE
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