## wpiea2021291-print-pdf

## Source details

**Canonical URL:** [wpiea2021291-print-pdf](https://www.imf.org/-/media/files/publications/wp/2021/english/wpiea2021291-print-pdf.pdf)

## Other formats

- [Markdown version](/-/media/files/publications/wp/2021/english/wpiea2021291-print-pdf.pdf.md)
- [Structured JSON version](/-/media/files/publications/wp/2021/english/wpiea2021291-print-pdf.pdf.json)

---

### Introduction
- COVID-19 era (2020-2021) produced high volatility in headline inflation and renewed debate on measuring underlying or “core” inflation.
- Traditional core measure: inflation excluding food and energy (XFE inflation), historically motivated by 1970s energy shocks.
- Alternative classes of core measures:
  - Fixed-exclusion measures: exclude a pre-specified set of industries (e.g., Atlanta Fed sticky-price inflation).
  - Outlier-exclusion measures: exclude outliers in the monthly distribution of industry price changes (e.g., Cleveland Fed weighted median, Dallas Fed trimmed mean).

### Pre-Pandemic Evidence on Alternative Core Measures (1985–2019)
- Volatility (standard deviations reported exactly as in source):
  - CPI: Median 1.05; Trimmed 1.18; XFE 1.42; Headline 3.06.
  - PCE: Trimmed 0.93; Median 0.96; XFE 1.45; Headline 2.28.
- Relation to slack (Phillips curve estimates, quarterly 1985–2019; equation and sample as specified in source):
  - CPI: Headline R-squared 0.014; XFE R-squared 0.161; Trimmed R-squared 0.186; Median R-squared 0.376.
  - CPI estimated β (unemployment-gap slope): Headline -0.174**(0.087); XFE -0.170***(0.035); Trimmed -0.183***(0.039); Median -0.254***(0.036). N = 140 for each row.
  - PCE: Headline R-squared -0.002; XFE R-squared 0.010; Trimmed R-squared 0.206; Median R-squared 0.279.
  - PCE estimated β: Headline -0.068(0.066); XFE -0.054*(0.031); Trimmed -0.149***(0.025); Median -0.190***(0.025). N = 140 for each row.
- Forecasting: mixed evidence in literature; forecasting performance depends on period and specification. This paper does not address forecasting for 2020-2021.

### Comparison of Fixed-Exclusion and Outlier-Exclusion Core Measures During the Pandemic (January 2020–Nov 2021 for CPI; through Oct 2021 for PCE)
- Representative measures compared:
  - Outlier-exclusion: Cleveland Fed weighted median CPI and PCE; Dallas Fed trimmed mean PCE.
  - Fixed-exclusion: XFE; Atlanta Fed sticky-price CPI; San Francisco Fed COVID-insensitive PCE.
- Key empirical observations (all numbers preserved as reported):
  - CPI monthly standard deviations during 2020–21: Median 1.51; Sticky 1.77; XFE 3.86; Headline 4.71.
  - PCE monthly standard deviations during 2020–21: Median 1.10; Insensitive 2.72; XFE 2.84; Headline 3.40.
  - XFE underperformed in 2020–2021:
    - XFE CPI monthly standard deviation = 3.9 compared to headline = 4.7 (values reported in text).
    - 12-month XFE CPI: pre-COVID 2015–2019 range 1.6 to 2.4 percent; fell to 1.2 in June 2020; rose to 5.0 in November 2021 (highest in 30 years).
  - Weighted median inflation:
    - Ratio of standard deviations of median to headline is less than a third and lower than the 1985–2019 ratio.
    - Median drifted down modestly in 2020 and rose over 2021 as the economy strengthened.
  - Atlanta sticky-price CPI: intermediate behavior—muted following of headline/XFE.
  - San Francisco COVID-insensitive PCE: volatility similar to XFE and follows many headline/XFE fluctuations with idiosyncratic spike in March 2021.

### Which Industries and Distributional Features Explain Differences
- Distributional shifts and skewness in industry price changes created extreme headline values:
  - April 2020 weighted skewness = –3.8 (left tail with large price decreases).
  - April 2021 weighted skewness = 4.1 (right tail with large price increases).
- Median is robust to skewness and remains moderate in both months; XFE failed to filter many extreme industry shocks because food and energy were near the middle of the distribution.
- Examples of extreme annualized industry moves (CPI context, numbers preserved):
  - April 2020 largest annualized price falls among industries not excluded from XFE: Car and truck rental (–88.2 percent); Used autos (–78.3 percent); Air transportation (–78.3 percent); Hotels and motels (–58.1 percent); Financial service charges, fees, and commissions (–57.8 percent).
  - April 2021 largest annualized price increases among industries not excluded from XFE: Infants' and toddlers' apparel (44.9 percent); Public transportation (97.5 percent); Lodging away from home (142.1 percent); Used cars and trucks (215.1 percent); Car and truck rental (505.7 percent).
  - Because food and energy prices were stable relative to these outliers, XFE inflation spiked to 11.6 percent in April 2021 versus headline inflation at 9.6 percent.
- Analogous large moves for PCE XFE reported in source (April 2020 falls and April 2021 increases with preserved figures, including Motor vehicle rental –88.2 percent; Used autos –78.3 percent; Air transportation 189.5 percent; Motor vehicle rental 505.6 percent; etc.).

### Performance Across Outlier-Exclusion Measures and Trimming Depth
- Trimming depth matters; performance similar across outlier-exclusion measures if trimming is substantial:
  - Recommended trimming: “at least 25-30 percent from each side of the weighted distribution of prices.”
  - Dallas Fed trimmed mean PCE trims bottom 24 percent and top 31 percent (total 55 percent asymmetrically trimmed); its volatility and relation to slack are similar to the Cleveland Fed weighted median.
  - Cleveland Fed symmetric trim of 8 percent (total 16 percent) is too narrow and less effective at filtering headline volatility.
- Trimmed-mean and median numeric comparisons (2020–2021, preserved):
  - PCE: Dallas trimmed mean is on average 0.40 percentage points below the median throughout 2020-2021; standard deviation trimmed mean 0.95 vs. median 1.10 (12-month series).
  - CPI: Cleveland trimmed mean standard deviation 2.10 vs. median 1.51 (12-month series); Cleveland trimmed mean reached annualized 4.5 percent in April 2021 while median CPI inflation was 2.9 percent.
- Sensitivity to total trimming percentage (as reported):
  - Volatility of trimmed mean falls as trimming rises from 0 percent to about 25–30 percent on each side (50–60 percent total). Beyond that point little additional effect on volatility.
  - Choice of symmetry vs. asymmetry affects average level but has essentially no effect on volatility for a given total amount of trimming.
- Comovement with slack:
  - Median and heavily trimmed mean (e.g., Dallas Fed) show similar comovement with the unemployment gap over the pandemic era.
  - Light trims (e.g., Cleveland’s 8 percent each side) produce a core measure that is more volatile and less closely related to slack.

### Relation of Core Measures to Economic Slack (2020–2021)
- Slack measure: gap between unemployment and its natural rate as measured by the Congressional Budget Office (CBO), using 12-month averages where specified.
- Observed relationships (preserved qualitative and numeric descriptions):
  - XFE: sometimes moves in same direction as slack (example April–September 2020 for PCE deflator); starting April 2021 XFE remained consistently much higher despite similar ranges of unemployment gaps.
  - Weighted median: displays a negative relationship between 12-month median inflation and the 12-month unemployment gap; median drifts down from January 2020 through February 2021 as unemployment gap rises, then rises after February 2021 as unemployment falls. An anomaly in September–November 2021 where inflation rises faster than the unemployment gap is noted.
  - Atlanta sticky-price and San Francisco COVID-insensitive measures: negative relationship with slack but less tight than the median.
  - Stock-Watson cyclically-sensitive measure: performs less well—rises in early pandemic despite growing slack and shows pronounced anomalous increases at end of sample.

### Policy Implications and Recommendations
- Overall ranking during COVID-19 stress test (2020–2021):
  - Outlier-exclusion measures (weighted median, heavily trimmed means) performed best at filtering transitory sectoral shocks and comoving with slack.
  - Fixed-exclusion measures that exclude a broader fixed set of industries can improve on XFE but generally do not match outlier-exclusion performance.
  - Traditional XFE performed poorly during 2020–2021 and was almost as volatile as headline inflation because many large industry price changes occurred outside food and energy.
- Policy recommendation highlighted in source:
  - The case for the Federal Reserve to move away from focusing solely on XFE in policy communication and analysis has strengthened over 2020-2021, given superior performance of outlier-exclusion measures in this period.
- Suggested trimming practice based on pandemic evidence:
  - Trim at least 25-30 percent from each side of the industry price-change distribution; increasing trimming from that level up to 50 percent (the median) matters little for volatility.
- Recommended areas for future research (preserved from source):
  - Explore the anomaly in September-November 2021 where inflation rises faster than implied by the unemployment gap.
  - Examine whether the trimming and median findings hold over longer time periods.

*Measuring U.S. Core Inflation: The Stress Test of COVID-19 — Working Paper No. WP/21/291*

### References .............................................................................................................

### wpiea2021291-print-pdf - References

### Introduction
- The COVID-19 era (2020-2021) produced high volatility in headline inflation and prompted renewed debate on measuring underlying or “core” inflation.
- Traditional core measure: inflation excluding food and energy (XFE inflation), historically motivated by 1970s energy shocks.
- Alternative classes:
  - Fixed-exclusion measures: exclude a pre-specified set of industries (e.g., Atlanta Fed sticky-price inflation).
  - Outlier-exclusion measures: exclude outliers in the monthly distribution of industry price changes (e.g., Cleveland Fed weighted median, Dallas Fed trimmed mean).

### Pre-Pandemic Evidence on Alternative Core Measures
- Volatility (1985–2019):
  - XFE filters out a substantial share of headline fluctuations: standard deviation ratios cited as 1.42/3.06 for the CPI and 1.45/2.28 for the PCE.
  - Weighted median standard deviations: 1.05/3.06 for the CPI and 0.96/2.28 for the PCE, indicating medians are even less volatile than XFE.
  - Trimmed means are also less volatile than XFE.
- Relation to slack (Phillips curve):
  - Simple Phillips curve estimated for quarterly data, 1985–2019, using 10-year-ahead inflation expectations and a 4-quarter average unemployment gap.
  - Estimated unemployment-gap slopes for the median: –0.25 for CPI and –0.19 for PCE.
  - For headline and XFE inflation, the fit is poor; for PCE the adjusted R-squared statistics are near zero.
  - Median and trimmed-mean measures generally show stronger comovement with slack than headline or XFE inflation.
- Forecasting:
  - Evidence is mixed: some studies find median inflation better than XFE for forecasting; others find contrary results.
  - Forecasting performance depends on time period and specification; this paper does not address forecasting for 2020-2021.

### Comparison of Fixed-Exclusion and Outlier-Exclusion Core Measures During the Pandemic
- Data scope: January 2020 through November 2021 for CPI, and through October 2021 for PCE (latest data available as paper completed).
- Representative measures compared:
  - Outlier-exclusion: weighted median CPI and weighted median PCE (Cleveland Fed); Dallas Fed trimmed mean PCE.
  - Fixed-exclusion: XFE; Atlanta Fed sticky-price CPI; San Francisco Fed COVID-insensitive PCE.
- Key empirical observations:
  - XFE underperformed during 2020-2021:
    - Monthly standard deviation: XFE = 3.9 compared to headline = 4.7 for the CPI.
    - XFE followed erratic headline spikes: plunges and sharp rises (e.g., spikes below zero, around 10 percent for CPI in April–June 2021, then to 1 percent in August, then rises in October).
    - 12-month XFE CPI: pre-COVID narrow range 1.6 to 2.4 percent (2015–2019); fell to 1.2 in June 2020 and rose to 5.0 in November 2021—the highest level in 30 years.
  - Weighted median inflation:
    - Fairly stable over the COVID-19 era; ratio of standard deviations of median to headline is less than a third and lower than the 1985–2019 ratio.
    - Median inflation drifted down modestly in 2020 and rose over 2021 as the economy strengthened.
  - Atlanta Fed sticky-price CPI: intermediate behavior between XFE and weighted median, follows headline/XFE in a muted way.
  - San Francisco Fed COVID-insensitive PCE: volatility similar to XFE and follows many headline/XFE fluctuations, with its own idiosyncratic spike in March 2021.

### Which Industries and Distributional Features Explain Differences
- Histograms of industry inflation rates (April 2020 and April 2021, CPI) reveal:
  - Skewed distributions generate extreme headline values:
    - April 2020 weighted skewness = –3.8 (left tail with large price decreases).
    - April 2021 weighted skewness = 4.1 (right tail with large price increases).
  - Median is robust to skewness and remains moderate in both months.
  - XFE fails to filter many extreme industry shocks because in these months food and energy prices were mostly near the middle of the distribution; most tail industries were not excluded by XFE.
  - Example extreme annualized price falls in April 2020 not excluded from XFE include Car and truck rental (–88.6 percent), Public transportation (–69.3 percent), and Motor vehicle insurance (–... [text truncated at source]).

### Performance Across Outlier-Exclusion Measures and Trimming Depth
- Trimming depth matters:
  - Performance is similar across outlier-exclusion measures so long as trimming is substantial, “at least 25-30 percent from each side of the weighted distribution of prices.”
  - Dallas Fed trimmed mean PCE trims bottom 24 percent and top 31 percent; its volatility and relation to slack are similar to the Cleveland Fed weighted median.
  - Less heavily trimmed measures (for example, Cleveland Fed measure trimming top and bottom 8 percent) are less effective at filtering headline volatility.

### Implications and Policy-Relevant Conclusions
- Overall ranking during the COVID-19 stress test (2020–2021):
  - Outlier-exclusion measures (weighted median, heavily trimmed means) performed best at filtering transitory sectoral shocks and comoving with slack.
  - Fixed-exclusion measures that exclude a broader fixed set of industries can improve on XFE but generally do not match outlier-exclusion performance.
  - The traditional XFE measure performed poorly during 2020–2021 and was almost as volatile as headline inflation because many large industry price changes occurred outside food and energy.
- Policy implication highlighted in the source:
  - The case for the Federal Reserve to move away from focusing solely on XFE in policy communication and analysis has strengthened over 2020-2021, given the superior performance of outlier-exclusion measures in this period.

*International Monetary Fund — Measuring U.S. Core Inflation: The Stress Test of COVID-19 (excerpts from the References/figures section and main text).*

### 59.4 percent); Lodging away from home (–58.6 percent); and Women’s and girls’ apparel (–48.9 percent).

### Measuring U.S. Core Inflation: The Stress Test of COVID-19

### Outlier movements and spikes in core measures
- In April 2020 (CPI context), among industries not excluded from XFE inflation, the largest 5 annualized price falls included:
  - Car and truck rental (–88.2 percent)
  - Used autos (–78.3 percent)
  - Air transportation (–78.3 percent)
  - Hotels and motels (–58.1 percent)
  - Financial service charges, fees, and commissions (–57.8 percent)
- In April 2021 (CPI context), among industries not excluded from XFE inflation, the largest 5 annualized price increases included:
  - Infants' and toddlers' apparel (44.9 percent)
  - Public transportation (97.5 percent)
  - Lodging away from home (142.1 percent)
  - Used cars and trucks (215.1 percent)
  - Car and truck rental (505.7 percent)
- Because food and energy prices were stable relative to these outliers, XFE inflation spiked to 11.6 percent in April 2021 versus headline inflation at 9.6 percent.
- For PCE XFE inflation the analogous large moves noted in the footnote include:
  - April 2020 largest 5 annualized price falls: Motor vehicle rental (–88.2 percent); Used autos (–78.3 percent); Air transportation (–78.3 percent); Hotels and motels (–58.1 percent); Financial service charges, fees, and commissions (–57.8 percent).
  - April 2021 largest 5 annualized price increases: Air transportation (189.5 percent); Used light trucks (206.8 percent); Used autos (216.6 percent); Spectator sports (216.7 percent); Motor vehicle rental (505.6 percent); followed by Hotels and motels (174.7 percent).

### Performance of fixed-exclusion measures (Atlanta sticky-price, COVID-insensitive)
- Atlanta sticky-price measure:
  - Excludes many industries near the middle of the distribution; mixed success in excluding outliers.
  - Example: In April 2020 it excluded Car and truck rental (largest XFE industry price fall) but failed to exclude Public transportation and Motor vehicle insurance.
  - Result: less volatile than XFE inflation but more volatile than the weighted median.
- COVID-insensitive inflation (PCE only):
  - Filters out some but not all large price changes in April 2020 and April 2021.
  - Example: March 2021 spike to 7.9 percent; an important outlier not excluded was Financial service charges, fees, and commissions with an annualized rise of 95.7 percent.
  - The COVID-insensitive index excludes more than 60 percent of the weighted industries in the PCE basket, leaving a small remaining basket that is highly responsive to large price changes.

### Relation of core measures to economic slack
- Slack measure used: the gap between unemployment and its natural rate as measured by the Congressional Budget Office (CBO).
- XFE inflation:
  - Shows a negative result for stable Phillips curve relationship; XFE inflation sometimes moves in the same direction as slack (e.g., April-September 2020 for the PCE deflator).
  - Starting in April 2021, XFE inflation remained consistently much higher despite similar ranges of unemployment gaps.
- Weighted median:
  - Performs better: displays a negative relationship between median inflation (12-month) and the 12-month unemployment gap.
  - For both CPI and PCE deflator the 12-month median drifts down from January 2020 through February 2021 as the unemployment gap rises, then rises after February 2021 as unemployment falls.
  - The unemployment-inflation tradeoff slope seems fairly stable from January 2020 through August 2021; anomaly in September-November 2021 where inflation rises faster than the unemployment gap suggests.
- Atlanta sticky-price and San Francisco COVID-insensitive measures:
  - Appear to have a negative relationship with slack but less tight than the median.
- San Francisco cyclical PCE and Stock-Watson cyclically-sensitive measures:
  - San Francisco measure: similar middling performance.
  - Stock-Watson measure: performs less well—rises in early pandemic despite growing slack and shows pronounced anomalous increases at end of sample.

### Trimmed means versus weighted median: volatility and slack comovement
- Fed trimmed-mean specifications:
  - Dallas Fed trimmed PCE: removes industries with total weights of 31 percent from the top and 24 percent from the bottom (total 55 percent asymmetrically trimmed).
  - Cleveland Fed trimmed CPI: symmetrically trims 8 percent of the weights from both top and bottom (total 16 percent trimmed).
- Key empirical findings over 2020-2021:
  - Trimmed means and weighted medians both filter out most monthly headline fluctuations and are more stable than fixed-exclusion measures.
  - PCE results:
    - The Dallas trimmed mean is somewhat below the median throughout 2020-2021; the difference averages 0.40 percentage points.
    - Standard deviation: trimmed mean 0.95 vs. median 1.10 (12-month series).
  - CPI results:
    - Cleveland trimmed mean is not systematically higher or lower than the median but is substantially more volatile: standard deviation 2.10 percentage points vs. 1.51 for the median.
    - Cleveland’s 8 percent trims are too narrow to exclude many large price-change industries. Example: April 2021 headline CPI spike to 9.6 percent (monthly annualized) — Cleveland trimmed mean failed to exclude Processed fruits and vegetables (15.8 percent), Recreation (11.6 percent), and Household furnishings and operations (11.1 percent); trimmed mean reached annualized 4.5 percent while median CPI inflation was 2.9 percent.
- Sensitivity to trimming amounts:
  - Constructed symmetric trims from 0 percent to 50 percent on each side.
  - Volatility of the trimmed mean falls as trimming rises from 0 percent to about 25-30 percent on each side (50-60 percent total). Beyond that point little additional effect on volatility.
  - Cleveland Fed’s total trim of 16 percent is not optimal for reducing volatility.
  - Dallas Fed’s total trim of 55 percent yields volatility similar to the weighted median.
  - Choice of symmetry vs. asymmetry affects average level but has essentially no effect on volatility for a given total amount of trimming.
- Comovement with slack:
  - The choice between median and a heavily trimmed mean (e.g., Dallas Fed) does not matter materially for comovement with the unemployment gap over the pandemic era.
  - A light trim (e.g., Cleveland’s) produces a core measure that is more volatile and less closely related to slack.

### Policy implications and recommendations
- The pandemic experience strengthens the case for the Federal Reserve to revise its measurement of core inflation away from XFE-type measures.
- Outlier-exclusion measures (weighted medians and heavily trimmed means) outperform XFE and many fixed-exclusion measures by the criteria of lower volatility and stronger relation to economic slack.
- For the pandemic period, trimming at least 25-30 percent from each side of the industry price-change distribution appears best; increasing trimming from that level to 50 percent (the median) matters little for volatility.
- Future research should:
  - Explore the anomaly in September-November 2021 where inflation rises faster than implied by the unemployment gap.
  - Examine whether the trimming and median findings hold over longer time periods.

*IMF WORKING PAPERS Measuring U.S. Core Inflation: The Stress Test of COVID-19 — INTERNATIONAL MONETARY FUND*

### References

### References

### Bibliographic citations
- Ball, Laurence, and Sandeep Mazumder, 2020, “The Nonpuzzling Behavior of Median Inflation,” in Changing Inflation Dynamics, Evolving Monetary Policy, ed. by Gonzalo Castex, Jordi Galí, and Diego Saravia. Edition 1. Vol. 27, Chapter 3, pp. 49–70 (Central Bank of Chile).
- Ball, Laurence, and Sandeep Mazumder, 2011, “Inflation Dynamics and the Great Recession,” Brookings Papers on Economic Activity, Brookings Institution, Vol. 42 (Spring), pp. 337–405.
- Bank of Canada, 2016, “Renewal of the Inflation-Control Target—Background Information,” October (Ottawa: Bank of Canada).
- Bryan, Michael F., and Stephen G. Cecchetti, 1994, “Measuring Core Inflation,” in Monetary Policy, ed. by N. Gregory Mankiw (Chicago: University of Chicago Press).
- Bryan, Michael F., and Christopher J. Pike, 1991, “Median Price Changes: An Alternative Approach to Measuring Current Monetary Inflation,” Economic Commentary (Federal Reserve Bank of Cleveland).
- Crone, Theodore M., N. Neil K. Khettry, Loretta J. Mester, and Jason A. Novak, 2013, “Core Measures of Inflation as Predictors of Total Inflation,” Journal of Money, Credit and Banking, Vol. 45, pp. 505–19.
- Dolmas, Jim, and Evan F. Koenig, 2019, “Two Measures of Core Inflation: A Comparison,” Federal Reserve Bank of St. Louis Review, Fourth Quarter 2019, 101(4), pp. 245-58.
- Dolmas, Jim, 2005, “Trimmed Mean PCE Inflation,” Federal Reserve Bank of Dallas Research Department Working Paper No. 0506.
- Gordon, Robert J, 1975, “The Impact of Aggregate Demand on Prices,” Brookings Papers on Economic Activity: 2, Brookings Institution, pp. 613–62.
- Hazell, Jonathon, Juan Herreno, Emi Nakamura, and Jón Steinsson, 2020, “The Slope of the Phillips Curve: Evidence from U.S. States,” NBER Working Paper No. 28005 (Cambridge, Massachusetts: National Bureau for Economic Research).
- Krugman, Paul, 2021, “Wonking Out: I'm Still on Team Transitory,” New York Times, September 10.
- Macklem, Tiff, 2001, “A New Measure of Core Inflation,” Bank of Canada Review, Vol. 2001 (Autumn), pp. 3–12 (Ontario: Bank of Canada).
- Mahedy, Tim, and Adam Shapiro, 2017, “What’s Down with Inflation?” FRBSF Economic Letter 2017–35 (November), Research from Federal Reserve Bank of San Francisco.
- Miller, Rich, 2021, “Summers Slams Woke Fed for Risking Losing Control of Inflation,” Bloomberg, October 13.
- Mishkin, 2007, “Headline versus Core Inflation in the Conduct of Monetary Policy,” Speech at the Business Cycles, International Transmission and Macroeconomic Policies Conference, HEC Montréal (Montréal: Canada).
- Schembri, Lawrence, 2017, “Getting to the Core of Inflation,” Remarks at the Department of Economics, Western University (London: Ontario, Canada).
- Shapiro, Adam Hale, 2020, “A Simple Framework to Monitor Inflation,” Federal Reserve Bank of San Francisco Working Paper 2020–29.
- Smith, Julie K, 2004, “Weighted Median Inflation: Is This Core Inflation?” Journal of Money, Credit and Banking, Vol 36, No. 2, pp. 253–63.
- Stock, James H., and Mark W. Watson, 2019, “Slack and Cyclically Sensitive Inflation,” NBER Working Paper No. 25987 (Cambridge, Massachusetts: National Bureau for Economic Research).
- Verbrugge, Randal, 2021, “Is It Time to Reassess the Focal Role of Core PCE Inflation?” Federal Reserve Bank of Cleveland Working Paper No. 21–10.
- Verbrugge, Randal, 2019, “Behavior of a New Median PCE Measure: A Tale of Tails” Federal Reserve Bank of Cleveland Working Paper No. 2019–10.
- Yellen, Janet, 2016, “Macroeconomic Research After the Crisis,” Speech at 60th Annual Economic Conference “The Elusive ‘Great’ Recovery: Causes and Implications for Future Business.”

### Table and figure notes (content and exact numeric values as presented)
- Table 1. Phillips Curve Estimates for Selected Inflation Measures, 1985–2019
  - Note description: “XFE” denotes inflation measure excluding food and energy. “Median” denotes weighted median series produced by the Federal Reserve Bank of Cleveland staff. “Trimmed” denotes the trimmed mean series prepared by the Federal Reserve Bank of Cleveland staff and Federal Reserve Bank of Dallas staff for the CPI and PCE, respectively. Equation estimated: 휋௧ െ 휋௧௘ = 훼 + 훽푢෤௧ + 휀௧ where 휋௧ = quarterly seasonally adjusted annualized inflation; 휋௧௘ = 10-year-ahead Survey of Professional Forecasters inflation expectations; and 푢෤௧ = trailing 4-quarter average gap between unemployment and its CBO natural rate. Table reports adjusted R-squared statistics; point estimates; robust standard errors (s.e.) in parentheses; and number of observations (N). *, **, and *** denote statistical significance at the 10, 5, and 1 percent level, respectively.
  - CPI Inflation rows:
    - Headline: R-squared 0.014; β(s.e.) -0.174**(0.087); α(s.e.) -0.154(0.160); N 140
    - XFE: R-squared 0.161; β(s.e.) -0.170***(0.035); α(s.e.) -0.118**(0.053); N 140
    - Trimmed: R-squared 0.186; β(s.e.) -0.183***(0.039); α(s.e.) -0.153***(0.051); N 140
    - Median: R-squared 0.376; β(s.e.) -0.254***(0.036); α(s.e.) 0.130***(0.043); N 140
  - PCE Inflation rows:
    - Headline: R-squared -0.002; β(s.e.) -0.068(0.066); α(s.e.) -0.410***(0.124); N 140
    - XFE: R-squared 0.010; β(s.e.) -0.054*(0.031); α(s.e.) -0.411***(0.059); N 140
    - Trimmed: R-squared 0.206; β(s.e.) -0.149***(0.025); α(s.e.) -0.210***(0.041); N 140
    - Median: R-squared 0.279; β(s.e.) -0.190***(0.025); α(s.e.) 0.204***(0.041); N 140

- Figure 1. Pre-pandemic Volatility of Monthly Annualized Inflation, 1985–2019 (Standard deviation; percentage points)
  - CPI Inflation numeric sequence as presented: 1.05 1.18 1.42 3.06 0 1 2 3 Median Trimmed XFE Headline CPI Inflation
  - PCE Inflation numeric sequence as presented: 0.93 0.96 1.45 2.28 0.5 1.5 2.2 2.5 Trimmed Median XFE Headline PCE Inflation

- Figure 2. Inflation Since COVID-19, 2020–2021 (percent)
  - CPI panels: axis ticks and labels shown as -10 -5 0 5 10 (monthly annualized) and 0 2 4 6 8 (12-month); series labels: Headline, XFE, Median, Sticky; years indicated 2020 2021.
  - PCE panels: axis ticks and labels shown as -10 -5 0 5 10 and 0 1 2 3 4 5; series labels: Headline, XFE, Median, Insensitive; years indicated 2020 2021.

- Figure 3. Volatility of Monthly Annualized Inflation During 2020–21 (Standard deviation; percentage points)
  - CPI Inflation numeric sequence as presented: 1.51 1.77 3.86 4.71 0 1 2 3 4 5 Median Sticky XFE Headline CPI Inflation
  - PCE Inflation numeric sequence as presented: 1.10 2.72 2.84 3.40 0 1 2 3 4 Median Insensitive XFE Headline PCE Inflation

- Figure 4. April 2020 and April 2021: Histogram of Changes in the Prices of CPI Categories (Monthly, not annualized, percent)
  - Note: Figure reports non-annualized inflation rates. Vertical axis cut off at 15. Weights computed following Dolmas (2005).
  - Axis ticks and labels presented: 0 5 10 15 (Sum of weights of components) and -25 -20 -15 -10 -5 0 5 (Price change (%)). Multiple panels labeled: Excluded: Food and Energy / Non-Food and Energy; Excluding Food and Energy; Excluded: Flexible Prices / Sticky Prices; Excluding Flexible Prices; and analogous panels for April 2021 with axis ticks -5 0 5 10 15 and -5 0 5 10 15 price change (%).

- Figure 5. March 2021: Histogram of Changes in the Prices of PCE Categories (Monthly, not annualized, percent)
  - Note: Figure reports non-annualized inflation rates. Vertical axis cut off at 15. Weights computed following Dolmas (2005).
  - Axis ticks and labels presented: 0 5 10 15 (Sum of weights of components) and -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 (Price change (%)). Panel labels: Excluded: Sensitive / Insensitive; Excluding COVID-19 Sensitive Items.

- Figure 6. CPI Inflation: Relation with Unemployment Gap, 2020–2021 (12-month rates)
  - Note: Blue points indicate 2020. Red dots indicate 2021. Unemployment gap indicates 12-month average of unemployment rate minus Congressional Budget Office (CBO) estimate of natural rate. Note: “XFE” denotes inflation measure excluding food and energy. “Median” denotes weighted median series produced by the Federal Reserve Bank of Cleveland staff. “Sticky” denotes series produced by the Federal Reserve Bank of Atlanta staff based on a subset of CPI components assessed as slow to change due to the low frequency of price adjustment.
  - Axis and labels as presented: time markers 2020m1 through 2021m11; inflation ticks 1 2 3 4 5; unemployment gap ticks -10 1 2 3 4.

- Figure 7. PCE Inflation: Relation with Unemployment Gap, 2020–2021 (12-month rates)
  - Note: Blue points indicate 2020. Red dots indicate 2021. Unemployment gap indicates 12-month average of unemployment rate minus Congressional Budget Office (CBO) estimate of natural rate. “XFE” denotes inflation measure excluding food and energy. “Median” denotes weighted median series produced by the Federal Reserve Bank of Cleveland staff. “Insensitive” denotes series produced by Federal Reserve Bank of San Francisco staff (Shapiro 2020) that excludes food and energy as well as additional PCE components for which either prices or quantities moved in a statistically significant manner at the onset of the COVID-19 pandemic, between February and April 2020. “Cyclical” denotes measure produced by Federal Reserve Bank of San Francisco staff (Mahedy and Shapiro 2017) that excludes food and energy and also excludes additional items assessed as being acyclical. “StockWatson” denotes cyclically sensitive inflation measure of Stock and Watson (2019) published on Federal Reserve Bank of Atlanta Underlying Inflation Dashboard.
  - Axis and labels as presented: time markers 2020m1 through 2021m10; inflation ticks 1 2 3 4 5; unemployment gap ticks -10 1 2 3 4.

- Figure 8. Median and Trimmed-Mean Inflation, 2020–2021 (percent)
  - Note: “Median” denotes weighted median series produced by the Federal Reserve Bank of Cleveland staff. “Trimmed” denotes the trimmed mean series prepared by the Federal Reserve Bank of Cleveland staff and Federal Reserve Bank of Dallas staff for the CPI and PCE, respectively.
  - CPI panels axis ticks and labels presented: -10 -5 0 5 10 (monthly annualized) and 0 2 4 6 8 (12-month). PCE panels axis ticks and labels presented: -5 0 5 10 (monthly annualized) and 0 1 2 3 4 5 (12-month). Series labeled Median, Trimmed Mean, Headline; years 2020 2021.

- Figure 9. Volatility of Median and Trimmed-Mean Monthly Annualized Inflation During 2020–2021 (Standard deviation; percentage points)
  - Note: “Median” denotes weighted median series produced by the Federal Reserve Bank of Cleveland staff. “Trimmed” denotes the trimmed mean series prepared by the Federal Reserve Bank of Cleveland staff and Federal Reserve Bank of Dallas staff for the CPI and PCE, respectively.
  - CPI numeric sequence as presented: 2.10 1.51 0.51 1.52 Trimmed Median CPI Inflation
  - PCE numeric sequence as presented: 0.95 1.10 0.51 Trimmed Median PCE Inflation

- Figure 10. Trimmed-Mean Inflation Volatility vs. Total Trimming Percentage, 2020–2021 (Standard deviation of monthly annualized inflation; percentage points)
  - Note: Total trimming percentage indicates sum of the proportion of price changes trimmed from upper and from lower end of the weighted distribution of monthly price changes.
  - Series/annotations as presented: Cleveland Fed 16 percent trimmed mean; Symmetric 55 percent trimmed mean; Asymmetric (Dallas Fed) 55 percent trimmed mean. Axes ticks shown 0 1 2 3 4 5 (Standard deviation) and 0 20 40 60 80 100 (Total trimming percentage) for CPI and PCE panels.

*Measuring Core Inflation: The Stress Test of COVID-19 — Working Paper No. WP/21/291*

---


_Source: https://www.imf.org/-/media/files/publications/wp/2021/english/wpiea2021291-print-pdf.pdf_