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Authorized for public release by the FOMC Secretariat on 1/12/2024
Comparing Two Measures of Core Inflation: Some Additional Perspective
Evan F. Koenig1
Federal Reserve Bank of Dallas
September 14, 2018
Executive Summary: Trimmed-mean PCE inflation does not clearly dominate ex-food-and-energy “core”
PCE inflation in real-time forecasting of headline PCE inflation. However, trimmed-mean inflation is a
superior communications tool. That is because trimmed-mean inflation more successfully filters out
headline inflation’s transitory variation, leaving only cyclical and trend components. A corollary is that
armed with a trusted measure of longer-run trend inflation, it is relatively easy to use the behavior of
trimmed-mean inflation to draw inferences about slack. (Alternatively, armed with a trusted measure of
slack, it is relatively easy to use the behavior of trimmed-mean inflation to draw inferences about
inflation’s longer-run trend.) Finally, over periods where we have relevant data, real-time trimmedmean inflation has been a less-biased estimator of “true” (i.e., revised) headline inflation.
● Comparing mean values of latest-vintage data across headline and core PCE inflation measures is of
limited interest unless one is contemplating switching from a long-run target for headline PCE inflation
to a long-run target for core PCE inflation. Taking as given the FOMC’s decision to specify a long-run
target for headline inflation, of greater interest are the average deviations of first-release trimmedmean and ex-food-and-energy inflation from latest-vintage headline inflation. It is, after all, first-release
core inflation data that you will be watching and reacting to in real time, while it is the latest-vintage
headline numbers that are relevant to an ex post assessment of inflation-control performance. We have
real-time trimmed-mean data starting in 2005:Q2 and real-time ex-food-and-energy PCE inflation
starting in 1996:Q1. Table 1 shows mean and median values of the relevant alternative inflation
measures over sample periods that begin on those dates.
Table 1. Mean and Median Inflation Rates
_______________________________________________________________
Mean Inflation
Headline*
Ex F&E**
Trimmed Mean**
2005:2 - 2018:Q2
1.77
1.61
1.78
1996:1 - 2018:Q2
1.81
1.60
1.90
Median Inflation
Headline*
Ex F&E**
Trimmed Mean**
2005:2 - 2018:Q2
1.95
1.52
1.79
1996:1 - 2018:Q2
1.96
1.60
1.95
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*Latest-available (September 11, 2018) vintage.
** First release or as close as possible to first release. (The earliest-available vintage of trimmed-mean
inflation is 2005:Q2.)
This memo benefitted greatly from research assistance provided by Emil Mihaylov, and from the comments of
Jim Dolmas.
1
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Conclusion: Early-release trimmed-mean PCE inflation is, on average, a more accurate gauge of
headline inflation than is early-release ex-food-and-energy PCE inflation. If you want a sense of
whether trend headline inflation is at, above, or below the FOMC’s 2-percent longer-run target, you
will likely want to pay more attention to trimmed-mean inflation releases than to ex-food-and-energy
inflation releases.
● Analysts sometimes use inflation data to draw inferences about slack. (For example, the
Congressional Budget Office historically has made revisions to its estimates of the natural rate of
unemployment based on the behavior of inflation.) The strength and robustness of the relationship
between early-release estimates of an inflation measure and latest-vintage slack is important for
assessing the usefulness of that measure as a rule-of-thumb indicator of resource utilization. 2 We
regressed early-release estimates of inflation (de-trended using SPF long-run inflation expectations) on a
constant and latest-vintage CBO estimates of the unemployment gap. Results suggest that trimmedmean inflation is more strongly and more reliably related to labor-market slack than is either headline
inflation or ex-food-and-energy inflation. See Table 2 and Figures 1, 2, and 3.
Table 2. Which Inflation Measure is Most Closely, and Reliably, Related to Slack?
_____________________________________________________________________________________
Inflation Measure
Constant (S.E)
U – U* (S.E.)
Adj. R2
2005:2 – 2018:2
Headline – SPF
Ex F&E – SPF
Trimmed Mean – SPF
- 0.146 (0.315)
- 0.241 (0.070)
0.035 (0.079)
- 0.124 (0.104)
- 0.136 (0.031)
- 0.197 (0.039)
0.033
0.487
0.651
1996:1 – 2018:2
Headline – SPF
Ex F&E – SPF
Trimmed Mean – SPF
- 0.367 (0.170)
- 0.531 (0.073)
- 0.120 (0.065)
- 0.048 (0.067)
- 0.049 (0.031)
- 0.152 (0.033)
- 0.001
0.051
0.432
1981:4 – 2018:2
Headline – SPF
- 0.173 (0.170)
- 0.047 (0.077)
- 0.001
Ex F&E – SPF
- 0.139 (0.145)
- 0.069 (0.065)
0.017
Trimmed Mean – SPF - 0.124 (0.061)
- 0.198 (0.037)
0.442
_____________________________________________________________________________________
Notes:
• First-release inflation data were used whenever possible. When first-release inflation was unavailable (before
2005:Q2 for trimmed-mean inflation and before 1996:Q1 for conventional-core inflation) the earliest-available
vintage was used instead.
• “SPF” denotes 10-year inflation expectations, from the Survey of Professional Forecasters. The unemployment
gap is lagged 4 quarters, but results were qualitatively similar with a 1-quarter lag.
• Coefficients that are statistically significant at the 1-percent level are bolded.
2
Alternatively, the analyst armed with a real-time slack measure in which she has confidence might hope to use
the behavior of inflation to draw inferences about longer-run inflation expectations. Then it will be useful for early
releases of the inflation measure to be strongly and robustly related to longer-run expectations, without having to
control for a wide range of influences other than slack.
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Conclusion: Deviations of trimmed-mean inflation from SPF long-run inflation expectations are a
better indicator of whether slack remains in the labor market (as gauged, ex post, by the CBO) than
are deviations of either headline or ex-food-and-energy inflation. Put another way, trimmed-mean
inflation is more successful at filtering out transitory inflation variation than is ex-food-and-energy
inflation: The deviation of trimmed-mean inflation from trend inflation (as captured by SPF long-run
expectations) better approximates inflation’s cyclical component.
● Which core inflation measure is most useful for predicting future headline inflation? You can’t
accurately answer that question without thinking carefully about how best to go about estimating
forecasting equations in real time. Koenig, Dolmas, and Piger ("The Use and Abuse of ‘Real-Time’ Data
in Economic Forecasting," Review of Economics and Statistics, 85, 2003) show that if you are going to be
forecasting using first-release data, then you should estimate your forecasting equation with firstrelease data on its right-hand side. Analysts often, instead, use end-of-sample-vintage real-time data
(the most up-to-date vintage available in real time) on the right-hand side of their real-time forecasting
equations. For the left-hand-side variable, the obvious choice is end-of-sample data. However, there
are potential gains in coefficient precision (hence, forecast accuracy) from stripping unforecastable
noise from the left-hand-side variable before estimation. Gains will be most evident in smaller samples.
When forecasting inflation, depending on the forecast horizon, stripping out unforecastable noise could
mean using trimmed-mean or ex-food-and-energy inflation as the dependent variable, even if it is
headline inflation that you are ultimately interested in forecasting (Koenig and Atkinson, Federal
Reserve Bank of Dallas Staff Papers, Issue 16, 2012). 3 Lacking time for a complete analysis of real-time
inflation forecasting, we undertook two very simple exercises, described below.
Rule-of-Thumb Forecasting
A simple rule of thumb is to set your forecast of inflation over the next four quarters equal to observed
inflation over the most recent 4-quarter period. There’s no estimation, here. The relevant “observed
inflation” is first release. The variable being forecasted is latest-vintage headline inflation. Results are
shown in Table 3A.
Table 3A. Rule-of-Thumb Inflation Forecasting
______________________________________________________________________________
RMSE
Rule-of-Thumb Forecast
2006:2–2018:2
1996:1–2018:2
1981:4–2018:2
Lagged Headline
1.472
1.229
1.411
Lagged Ex Food & Energy
1.060
0.998
1.218
Lagged Trimmed Mean
1.134
0.985
0.923
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Note: When first-release inflation was unavailable (before 2005:Q2 for trimmed-mean inflation and
before 1996:Q1 for conventional-core inflation) the earliest-available vintage was used instead.
Depending on the data-revision process, it might also mean using early-release data on the left-hand-side of the
forecasting equation. See, again, Koenig, Dolmas, and Piger ("The Use and Abuse of ‘Real-Time’ Data in Economic
Forecasting," Review of Economics and Statistics, 85, 2003).
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The above results may be distorted by the aftermath of the financial crisis, which brought about a sharp
decline in inflation. It is highly unlikely that anyone would have relied on a rule-of-thumb inflation
forecast during that period. Excluding 2009:Q1 – 2009:Q4 from the calculations yields the results
displayed in Table 3B.
Table 3B. Rule-of-Thumb Inflation Forecasting (excluding 2009)
______________________________________________________________________________
RMSE
Rule-of-Thumb Forecast
2006:2–2018:2
1996:1–2018:2
1981:4–2018:2
Lagged Headline
1.021
0.945
1.274
Lagged Ex Food & Energy
0.823
0.870
1.162
Lagged Trimmed Mean
0.840
0.807
0.807
______________________________________________________________________________
Note: When first-release inflation was unavailable (before 2005:Q2 for trimmed-mean inflation and
before 1996:Q1 for conventional-core inflation) the earliest-available vintage was used instead.
Conclusion: Over the periods for which we have real-time trimmed-mean and ex-food-and-energy
inflation, these two series perform about equally well as rule-of-thumb predictors of headline
inflation. Both core inflation series perform notably better than lagged headline inflation.
Recursive Real-Time Forecasts of Headline Inflation
We also recursively estimate an inflation-forecasting equation of the form
π(t) = α + β1π(t – 4) + β2πc(t – 4) + β3πe(t – 4) + γu(t – 4),
where u is the unemployment rate, π is 4-quarter headline inflation, πc is either ex-food-and-energy or
trimmed-mean inflation, and πe is SPF long-run inflation expectations. End-of-sample-vintage data are
used on the equation’s left-hand side and first-release (or as close to first release as possible) data are
used on the right-hand side. The first forecast is for 2006:Q2, using first-release data for 2005:Q2. The
final forecast is for 2018:Q2, using first-release data for 2017:Q2. We use two different sample starting
points: 1996:Q1 and 1982:Q4. The real-time forecasts are compared with latest-vintage headline PCE
inflation. The 4-quarter period immediately following the financial crisis (2009:Q1 – 2009:Q4) is
excluded from both estimation and forecast evaluation. Results are shown in Table 4A.
Table 4A. Real-time Forecasts of Headline Inflation
______________________________________________________________
RMSE: 2006:Q2 – 2018:Q2 (ex 2009)
Start of Sample
πc = ex-food-and-energy
πc = trimmed-mean
1996:Q1
1.21
1.12
1982:Q4
0.86
0.89
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When the sample period used for estimation is short, forecast performance is slightly better using the
trimmed mean to measure core inflation. That advantage disappears (and forecast performance
improves) when the sample period is extended back into the 1980s.
As noted above, more-precise coefficient estimates (and, so, better forecasts) can sometimes be
obtained by stripping noise from the dependent variable. That fact suggests there could be an
advantage to replacing π(t) on the left-hand side of the above equation with πc(t). Again, left-hand-side
data are end-of-sample vintage, and forecasts are compared with latest-vintage headline PCE inflation
data. Results are displayed in Table 4B.
Table 4B. Real-time Core Inflation Forecasts as Predictors of Headline Inflation
__________________________________________________________________
RMSE: 2006:Q2 – 2018:Q2 (ex 2009)
Start of Sample
πc = ex-food-and-energy
πc = trimmed-mean
1996:Q1
0.87
0.83
1982:Q4
0.88
0.88
__________________________________________________________________
Forecast performance with a short sample is much improved, regardless of which core inflation measure
is used, but there is no change in forecast performance when the estimation period is extended back to
the 1980s. Interestingly, the root-mean-square forecast errors reported in Table 4B are no better than
those obtained from simple rule-of-thumb forecasting based on lagged core inflation. (Compare the
RMSEs reported in Table 4B with the left-column entries in Table 3B.)
Conclusion: At a 4-quarter horizon, evidently, real-time forecasts of core inflation usefully serve, also,
as forecasts of headline inflation. It makes relatively little difference whether the core measure is exfood-and-energy inflation or trimmed-mean inflation.
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Figure 1. De-trended headline inflation is only loosely related to labor-market slack
1st-release Headline - long-run expectations
4
2005:Q2 - Present
2009
3
1981:Q4-2005:Q1
Linear trend (full sample)
2
1
0
-1
-2
-3
-2
-1
0
1
2
3
4
Unemployment gap (lagged four quarters)
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Authorized for public release by the FOMC Secretariat on 1/12/2024
Figure 2. De-trended ex-food-and-energy inflation is only loosely related to labor-market slack
1st-release Ex F&E - long-run expectations
4
2005:Q2Present
2009
3
1981:Q42005:Q1
2
1
0
-1
-2
-3
-2
-1
0
1
2
3
4
Unemployment gap (lagged four quarters)
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Authorized for public release by the FOMC Secretariat on 1/12/2024
Figure 3. De-trended trimmed-mean inflation shows a fairly strong connection to labor-market slack
1st-release Trimmed mean - long-run expectations
4
2005:Q2Present
2009
3
1981:Q42005:Q1
2
1
0
-1
-2
-3
-2
-1
0
1
2
3
4
Unemployment gap (lagged four quarters)
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@FedFRASER