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---

### Alternative Measures of Core Inflation (median and trimmed-mean PCE)
- Robustness check: median PCE and trimmed mean PCE yield results similar to median CPI.
- Phillips curve estimates — Median PCE (monthly, 1985-2022; Table 1A column 4):
  - V/U: 6.931***; (V/U)‑squared: -8.208***; (V/U)‑cubed: 3.559***
  - H: 0.158; H‑squared: 0.171***; H‑cubed: 0.048*
  - Observations: 452
  - R‑squared: 0.435; Rbar‑squared: 0.428
- Phillips curve estimates — Trimmed mean PCE (monthly, 1985-2022; Table 1B column 4):
  - V/U: 5.396***; (V/U)‑squared: -5.659**; (V/U)‑cubed: 2.167***
  - Headline‑inflation shock: 0.320***; Headline‑shock‑squared: 0.122***; Headline‑shock‑cubed: 0.002
  - Observations: 452
  - R‑squared: 0.388; Rbar‑squared: 0.379
- Figures:
  - Figure 6A/6B: fitted inflation gaps vs V/U and vs headline shocks with 95 percent confidence bands.
  - Figure 7A/7B: model predictions for 2020–2022 using full-sample and pre-pandemic estimates.

### Measuring Inflation Expectations with Michigan 5-year-ahead Forecasts
- Replacing SPF 10‑year-ahead expectations with Michigan 5‑year-ahead expectations yields similar results.
- Figure 2C: Michigan 5‑year-ahead CPI inflation expectations and median CPI inflation, 2000‑2022.
- Phillips curve estimates — Median CPI with Michigan 5‑year-ahead (monthly, 1985-2022; Table 1C column 4):
  - V/U: 10.806***; (V/U)‑squared: -12.428***; (V/U)‑cubed: 5.048***
  - H: 0.033; H‑squared: 0.061***; H‑cubed: 0.031***
  - Observations: 453

### Measuring Labor Market Conditions: U‑U* versus V/U
- Using unemployment gap (U−U*, CBO natural rate) yields somewhat worse fit than V/U:
  - Pre‑pandemic monthly Rbar‑squared: V/U = 0.27; U gap = 0.25.
  - Full sample through 2022 monthly Rbar‑squared: V/U = 0.51; U gap = 0.46.
- Horse‑race results:
  - Both U gap and V/U are statistically significant when included together.
  - Incremental fit gains:
    - Including U gap after V/U raises Rbar‑squared by 0.005 (monthly, full sample).
    - Including V/U after U gap raises Rbar‑squared by 0.055 (monthly, full sample).
- Table 1D reports detailed coefficient estimates for U−U*, its powers, H terms, and V/U terms across samples.

### Contemporaneous V/U (vs. 4‑quarter or 12‑month averages)
- Scatter plots: strong positive relationship between contemporaneous V/U and the inflation gap; recent observations are more outlying.
- Phillips curve with contemporaneous V/U: coefficients similar but lower fit.
  - Monthly, full sample (1985‑2022; Table 1E column 4):
    - V/U: 6.434***; (V/U)‑squared: -6.181**; (V/U)‑cubed: 2.306***
    - H: 0.135; H‑squared: 0.080***; H‑cubed: -0.006
    - Observations: 453
    - R‑squared: 0.500; Rbar‑squared: 0.493
  - Rbar‑squared comparison: contemporaneous monthly full‑sample Rbar‑squared = 0.473 versus 0.514 for 12‑month average reported in Text Table 1 Column 4.

### Headline Shocks Averaged over Shorter Periods
- Experiment: headline‑inflation shocks averaged over 1, 3, 6 months instead of 12 months.
- Finding: shorter averages explain core (median) inflation less well than 12‑month averages.
- Selected fit statistics (Table 1F):
  - 1‑month H (columns 1–2): R‑squared: 0.255 (1985‑2019), 0.505 (1985‑2022); Rbar‑squared: 0.244, 0.498
  - 3‑months H (columns 3–4): R‑squared: 0.271, 0.515; Rbar‑squared: 0.260, 0.509
  - 6‑months H (columns 5–6): R‑squared: 0.269, 0.529; Rbar‑squared: 0.258, 0.522
  - 12‑months H (columns 7–8): R‑squared: 0.284, 0.575; Rbar‑squared: 0.274, 0.569
- Conclusion: 12‑month headline‑inflation shocks provide better explanatory power for core (median) inflation.

### Core Inflation Measured by CPI Excluding Food and Energy (XFE)
- Using CPI XFE as core yields different results: no evidence of pass‑through from past headline shocks into core inflation.
- Headline shocks (deviations of headline inflation from XFE) are jointly insignificant in all specifications with XFE core.
- CPI XFE core specification fails to predict pandemic-era rise in inflation, unlike median/weighted‑median core measures.
- Phillips curve estimates — CPI XFE (monthly, 1985-2022; Table 1G column 4):
  - V/U: 7.946**; (V/U)‑squared: -9.000*; (V/U)‑cubed: 3.680*
  - H: 0.229; H‑squared: 0.059; H‑cubed: -0.010
  - Observations: 453
  - R‑squared: 0.180; Rbar‑squared: 0.169
- Figure 7D: model fitted values (full sample and pre‑pandemic) show lack of predicted rise in CPI XFE gap during 2020–2022.

### Wage Phillips Curve
- Appendix provides wage Phillips curve estimates used for Figure 10.
- Specification notes:
  - “V/U” denotes ratio of vacancies to unemployed (4‑quarter average).
  - “H” denotes headline‑inflation shock (4‑quarter average).
  - Trend productivity growth: output per hour in the non‑farm business sector smoothed with Hodrick‑Prescott filter with λ = 16,000.
- Given lack of evidence for nonlinearity in V/U for wages, a specification with linear V/U is also considered.

### Model comparison: Predictions for Median CPI Inflation Gap During the Pandemic
- Preferred core‑inflation equation performs best, exhibiting the highest adjusted R‑squared.
- The equation with only a linear unemployment term performs poorly, with "8 percentage points lower adjusted R‑squared compared to our preferred model."
- Each modification—measure of slack, non‑linearity, and the pass‑through variable—contributes materially to the fit.
- Key statistics from Table 13A (monthly equations estimated for 1985-2019; Newey‑West standard errors with 12 lags):
  - Column (1) (U‐U* only):
    - U‐U*: ‐0.249*** (0.066)
    - Constant: 0.122* (0.067)
    - Observations: 420
    - R‐squared: 0.193; Rbar‑squared: 0.191
  - Column (2) (V/U and polynomials):
    - V/U: 1.669*** (0.316)
    - V/U‑squared: ‐8.572 (6.795)
    - V/U‑cubed: 3.382 (3.089)
    - H: 0.105* (0.053)
    - Constant: ‐1.045*** (0.218)
    - Observations: 420
    - R‐squared: 0.211; Rbar‑squared: 0.209
  - Column (3):
    - V/U: 7.966* (4.616)
    - V/U‑squared: ‐11.324* (6.409)
    - V/U‑cubed: 4.683 (2.945)
    - H: 0.010 (0.073)
    - Constant: ‐2.346** (0.972)
    - Observations: 420
    - R‐squared: 0.239; Rbar‑squared: 0.233
  - Column (4):
    - V/U: 9.747** (4.293)
    - V/U‑squared: ‐10.879* (6.435)
    - V/U‑cubed: 4.439 (2.958)
    - H‑squared: 0.128*** (0.035)
    - H‑cubed: 0.053*** (0.017)
    - Constant: ‐2.667*** (0.889)
    - Observations: 420
    - R‑squared: 0.253; Rbar‑squared: 0.246
  - Column (5):
    - V/U: 9.553** (4.297)
    - V/U‑squared: ‐10.879* (6.435)
    - H‑squared: 0.128*** (0.035)
    - H‑cubed: 0.053*** (0.017)
    - Constant: ‐2.759*** (0.879)
    - Observations: 420
    - R‑squared: 0.284; Rbar‑squared: 0.274
- Notes:
  - "U-U*" = gap between unemployment rate and CBO estimate of natural rate (4‑quarter or 12‑month average).
  - "V/U" = ratio of vacancies to unemployed (12‑month average).
  - "H" = headline‑inflation shock (12‑month average).
  - ***, **, * denote significance at 1, 5, 10 percent, respectively.

### Model comparison: Predictions for Median PCE Inflation Gap During the Pandemic
- Results for median PCE similar to median CPI:
  - Traditional equation fails to predict significant rise in inflation.
  - Preferred specification predicts most of observed rise (some under‑prediction since May 2022).
  - Measure of slack, non‑linearity, and pass‑through variable are important.
- Key statistics from Table 13B (monthly equations estimated for 1985-2019; Newey‑West standard errors with 12 lags):
  - Column (1) (U‐U* only):
    - U‐U*: ‐0.187*** (0.043)
    - Constant: 0.198*** (0.067)
    - Observations: 420
    - R‐squared: 0.139; Rbar‑squared: 0.137
  - Column (2):
    - V/U: 1.190*** (0.234)
    - V/U‑squared: ‐4.006 (5.669)
    - V/U‑cubed: 1.402 (2.634)
    - H: 0.059 (0.065)
    - Constant: ‐0.641*** (0.169)
    - Observations: 420
    - R‑squared: 0.136; Rbar‑squared: 0.134
  - Column (3):
    - V/U: 4.373 (3.687)
    - V/U‑squared: ‐5.079 (5.896)
    - V/U‑cubed: 1.886 (2.732)
    - H: 0.090 (0.127)
    - Constant: ‐1.336* (0.701)
    - Observations: 420
    - R‑squared: 0.150; Rbar‑squared: 0.144
  - Column (4):
    - V/U: 5.113 (3.833)
    - V/U‑squared: ‐5.719 (6.010)
    - V/U‑cubed: 2.192 (2.789)
    - H‑squared: 0.145* (0.084)
    - H‑cubed: 0.049 (0.033)
    - Constant: ‐1.458** (0.708)
    - Observations: 420
    - R‑squared: 0.154; Rbar‑squared: 0.145
  - Column (5):
    - V/U: 5.530 (3.918)
    - V/U‑squared: ‐5.719 (6.010)
    - V/U‑cubed: 2.192 (2.789)
    - H‑squared: 0.145* (0.084)
    - Constant: ‐1.590** (0.715)
    - Observations: 420
    - R‑squared: 0.162; Rbar‑squared: 0.149

### Drivers of headline‑inflation shocks before 2020 (Table 2A)
- Objective: estimate drivers of headline‑inflation shocks in pre‑pandemic period (dependent variable: Headline – Median CPI monthly annualized inflation).
- Energy‑price, food‑price, and auto‑price variables help explain headline shocks before the pandemic; backlogs do not. Food‑price inflation is significant pre‑pandemic but not during the pandemic.
- Selected coefficients and statistics (bivariate and selected multivariate regressions; robust standard errors):
  - Energy price inflation:
    - Coefficient: 0.068*** (0.007)
    - Observations: 720
    - Start of sample: 1960m1
    - R‑squared: 0.503; Rbar‑squared: 0.502
  - Food price inflation:
    - Coefficient: 0.189*** (0.011) in bivariate; 0.186*** (0.009) in multivariate
    - Observations: 720
    - Start of sample: 1960m1
    - R‑squared (bivariate): 0.170; Rbar‑squared (bivariate): 0.169
  - Harper Charter Rate:
    - Coefficient: 0.001** (0.001)
    - Observations: 228
    - Start of sample: 2001m1
    - R‑squared: 0.026; Rbar‑squared: 0.0221
  - Baltic Dry:
    - Coefficient: 0.000*** (0.000)
    - Observations: 410
    - Start of sample: 1985m1
    - R‑squared: 0.041; Rbar‑squared: 0.0391
  - FRBNY Supply Chain Index:
    - Coefficient: 0.151* (0.091)
    - Observations: 152
    - Start of sample: 2007m5
    - R‑squared: 0.020; Rbar‑squared: 0.0134
  - Backlogs of work:
    - Coefficient: 1.603*** (0.510)
    - Observations: 264
    - Start of sample: 1998m1
    - R‑squared: 0.061; Rbar‑squared: 0.0571
  - Durable goods share of real consumption:
    - Coefficient: 0.061 (0.121)
    - Observations: 123
    - Start of sample: 2009m10
    - R‑squared: 0.001; Rbar‑squared: ‑0.00694
  - Weighted average of car inflation rates:
    - Coefficient: 0.159*** (0.041) in bivariate; 0.089*** (0.020) in multivariate
    - Observations: 720 (bivariate) and 263 (multivariate)
    - Start of sample: 1960m1 (bivariate) and 1998m2 (multivariate)
    - R‑squared (multivariate): 0.794; Rbar‑squared (multivariate): 0.792
- Notes:
  - Relative energy, food, and auto‑related price inflation variables are created by subtracting median inflation from each respective series; monthly annualized terms.
  - Backlogs of work variable from IHS Markit Economics.

### Simulations of core (median) PCE inflation and scenario outputs
- Simulations use Phillips curve for median PCE inflation (Table 1A column 4) and same equations for Beveridge curve and inflation expectations as in the text.
- Results (Figures 17A and 19A) correspond to and are similar to those for median CPI in the main text.

- Figure 17A: Scenarios for Core (Median) PCE Inflation Conditional on September 2022 FOMC Unemployment Forecasts (12‑month; percent)
  - Unemployment forecast: Summary of Economic Projections of the FOMC published in September 2022 (fourth quarters of 2022, 2023, 2024, and 2025). Forecasts assigned to November of each year and a monthly unemployment series interpolated starting from actual value of 3.5 percent in September 2022.
  - Vertical line: September 2022.
  - Core inflation denotes PCE median inflation.
  - Horizontal dashes: assumed 2.4 percent target for median PCE inflation (based on 2 percent PCE target and 0.4 percentage point gap between the median PCE inflation and PCE inflation excluding food and energy).
  - Scenario marker values shown in figure: 6.01 and 2.58.

- Figure 19A: Scenarios for Core (Median) PCE Inflation Conditional on Alternative Unemployment Paths (12‑month; percent)
  - Vertical line: September 2022.
  - Panel A: Conditional on IMF staff unemployment path
    - IMF staff forecast underlying the October 2022 IMF World Economic Outlook Report; quarterly forecasts allocated to the second month of each quarter and interpolated to monthly.
    - Scenario marker values: 4.53 and 2.43.
  - Panel B: Conditional on Higher Unemployment Path
    - "Higher unemployment" path assumes 7.5 percent unemployment during 2023 and 2024 as suggested by Summers (2022b).
    - Unemployment rises linearly from its September 2022 level to 7.5 percent in January 2023 and remains at that level through December 2024.
    - Scenario marker values: 3.12 and 1.91.
  - Horizontal dashes: assumed 2.4 percent target for median PCE inflation (same basis as Figure 17A).

*Source: IMF Working Paper Appendix (WP/22/208), "Understanding U.S. Inflation During the COVID Era" — Appendix, authors Laurence Ball, Daniel Leigh, and Prachi Mishra.*

### Section 1

### Appendix: Section 1 (wpiea2022208app-print-pdf)

### Alternative Measures of Core Inflation (median and trimmed-mean PCE)
- Robustness check: median PCE and trimmed mean PCE yield results similar to median CPI.
- Phillips curve estimates — Median PCE (monthly, 1985-2022; Table 1A column 4):
  - V/U: 6.931*** (V/U)‑squared: -8.208*** (V/U)‑cubed: 3.559***
  - H: 0.158; H‑squared: 0.171***; H‑cubed: 0.048*
  - Observations: 452
  - R‑squared: 0.435; Rbar‑squared: 0.428
- Phillips curve estimates — Trimmed mean PCE (monthly, 1985-2022; Table 1B column 4):
  - V/U: 5.396*** (V/U)‑squared: -5.659** (V/U)‑cubed: 2.167***
  - Headline‑inflation shock: 0.320***; Headline‑shock‑squared: 0.122***; Headline‑shock‑cubed: 0.002
  - Observations: 452
  - R‑squared: 0.388; Rbar‑squared: 0.379
- Figures:
  - Figure 6A/6B show fitted inflation gaps vs V/U and vs headline shocks with 95 percent confidence bands.
  - Figure 7A/7B report model predictions for 2020–2022 using full-sample and pre-pandemic estimates.

### Measuring Inflation Expectations with Michigan 5-year-ahead Forecasts
- Replacing SPF 10‑year-ahead expectations with Michigan 5‑year-ahead expectations yields similar results.
- Figure 2C: plots Michigan 5‑year-ahead CPI inflation expectations and median CPI inflation, 2000‑2022.
- Phillips curve estimates — Median CPI with Michigan 5‑year-ahead (monthly, 1985-2022; Table 1C column 4):
  - V/U: 10.806*** (V/U)‑squared: -12.428*** (V/U)‑cubed: 5.048***
  - H: 0.033; H‑squared: 0.061***; H‑cubed: 0.031***
  - Observations: 453

### Measuring Labor Market Conditions: U‑U* versus V/U
- Using unemployment gap (U−U*, CBO natural rate) yields somewhat worse fit than V/U.
  - Pre-pandemic monthly Rbar‑squared: V/U = 0.27; U gap = 0.25.
  - Full sample through 2022 monthly Rbar‑squared: V/U = 0.51; U gap = 0.46.
- Horse-race results:
  - Both U gap and V/U are statistically significant when included together.
  - Incremental fit gains: including U gap after V/U raises Rbar‑squared by 0.005 (monthly, full sample).
  - Including V/U after U gap raises Rbar‑squared by 0.055 (monthly, full sample).
- Table 1D (quarterly and monthly) reports detailed coefficient estimates for U−U*, its powers, H terms, and V/U terms across samples.

### Contemporaneous V/U (vs. 4‑quarter or 12‑month averages)
- Scatter plots show a strong positive relationship between contemporaneous V/U and the inflation gap, with recent observations more outlying.
- Phillips curve with contemporaneous V/U: coefficients similar but lower fit.
  - Monthly, full sample (1985‑2022; Table 1E column 4):
    - V/U: 6.434*** (V/U)‑squared: -6.181** (V/U)‑cubed: 2.306***
    - H: 0.135; H‑squared: 0.080***; H‑cubed: -0.006
    - Observations: 453
    - R‑squared: 0.500; Rbar‑squared: 0.493
  - Rbar‑squared comparison: contemporaneous monthly full-sample Rbar‑squared = 0.473 versus 0.514 for 12‑month average reported in Text Table 1 Column 4.

### Headline Shocks Averaged over Shorter Periods
- Experiment: headline‑inflation shocks averaged over 1, 3, 6 months instead of 12 months.
- Finding: shorter averages explain core (median) inflation less well than 12‑month averages.
- Selected fit statistics (Table 1F):
  - 1‑month H (columns 1–2): R‑squared: 0.255 (1985‑2019), 0.505 (1985‑2022); Rbar‑squared: 0.244, 0.498
  - 3‑months H (columns 3–4): R‑squared: 0.271, 0.515; Rbar‑squared: 0.260, 0.509
  - 6‑months H (columns 5–6): R‑squared: 0.269, 0.529; Rbar‑squared: 0.258, 0.522
  - 12‑months H (columns 7–8): R‑squared: 0.284, 0.575; Rbar‑squared: 0.274, 0.569
- Conclusion: 12‑month headline‑inflation shocks provide better explanatory power for core (median) inflation.

### Core Inflation Measured by CPI Excluding Food and Energy (XFE)
- Using CPI XFE as core yields different results: no evidence of pass‑through from past headline shocks into core inflation.
- Headline shocks (deviations of headline inflation from XFE) are jointly insignificant in all specifications with XFE core.
- The CPI XFE core specification fails to predict the pandemic-era rise in inflation, unlike median/weighted‑median core measures.
- Phillips curve estimates — CPI XFE (monthly, 1985-2022; Table 1G column 4):
  - V/U: 7.946** (V/U)‑squared: -9.000* (V/U)‑cubed: 3.680*
  - H: 0.229; H‑squared: 0.059; H‑cubed: -0.010
  - Observations: 453
  - R‑squared: 0.180; Rbar‑squared: 0.169
- Figure 7D: model fitted values (full sample and pre‑pandemic) show lack of predicted rise in CPI XFE gap during 2020–2022.

### Wage Phillips Curve
- Appendix provides wage Phillips curve estimates used for Figure 10 in the text.
- Specification notes:
  - “V/U” denotes ratio of vacancies to unemployed (4‑quarter average).
  - “H” denotes headline‑inflation shock (4‑quarter average).
  - Trend productivity growth measured using output per hour in the non‑farm business sector smoothed with the Hodrick‑Prescott filter with λ = 16,000.
- Given lack of evidence for nonlinearity in V/U for wages, a specification with linear V/U is also considered.

*Source: IMF Working Paper Appendix (WP/22/208), "Understanding U.S. Inflation During the COVID Era" — Appendix, authors Laurence Ball, Daniel Leigh, and Prachi Mishra.*

### Section 2

### wpiea2022208app-print-pdf - Section 2

### Model comparison: Predictions for Median CPI Inflation Gap During the Pandemic
- Preferred core-inflation equation performs best, exhibiting the highest adjusted R-squared.
- The equation with only a linear unemployment term performs poorly, with "8 percentage points lower adjusted R-squared compared to our preferred model."
- Each modification to the traditional specification—measure of slack, non-linearity, and the pass-through variable—contributes materially to the fit.

Key statistics from Table 13A (monthly equations estimated for 1985-2019; Newey-West standard errors with 12 lags):
- Column (1) (U‐U* only)
  - U‐U*: ‐0.249*** (0.066)
  - Constant: 0.122* (0.067)
  - Observations: 420
  - R‐squared: 0.193
  - Rbar‐squared: 0.191
- Column (2) (V/U and polynomials)
  - V/U: 1.669*** (0.316)
  - V/U‐squared: ‐8.572 (6.795)
  - V/U‐cubed: 3.382 (3.089)
  - H: 0.105* (0.053)
  - Constant: ‐1.045*** (0.218)
  - Observations: 420
  - R‐squared: 0.211
  - Rbar‐squared: 0.209
- Column (3)
  - V/U: 7.966* (4.616)
  - V/U‐squared: ‐11.324* (6.409)
  - V/U‐cubed: 4.683 (2.945)
  - H: 0.010 (0.073)
  - Constant: ‐2.346** (0.972)
  - Observations: 420
  - R‐squared: 0.239
  - Rbar‐squared: 0.233
- Column (4)
  - V/U: 9.747** (4.293)
  - V/U‐squared: ‐10.879* (6.435)
  - V/U‐cubed: 4.439 (2.958)
  - H‐squared: 0.128*** (0.035)
  - H‐cubed: 0.053*** (0.017)
  - Constant: ‐2.667*** (0.889)
  - Observations: 420
  - R‐squared: 0.253
  - Rbar‐squared: 0.246
- Column (5)
  - V/U: 9.553** (4.297)
  - V/U‐squared: ‐10.879* (6.435) [note: same coefficient labeling pattern as column (4)]
  - H‐squared: 0.128*** (0.035)
  - H‐cubed: 0.053*** (0.017)
  - Constant: ‐2.759*** (0.879)
  - Observations: 420
  - R‐squared: 0.284
  - Rbar‐squared: 0.274

Notes:
- "U-U*" denotes gap between unemployment rate and Congressional Budget Office estimate of natural rate (4-quarter or 12-month average).
- "V/U" denotes ratio of vacancies to unemployed (12-month average).
- "H" denotes headline-inflation shock (12-month average).
- ***, **, and * denote statistical significance at the 1,5, and 10 percent level, respectively.

### Model comparison: Predictions for Median PCE Inflation Gap During the Pandemic
- Results for median PCE are similar to median CPI:
  - The traditional equation fails to predict a significant rise in inflation.
  - Preferred specification predicts most of the observed rise (some under-prediction since May 2022).
  - Measure of slack, non-linearity, and pass-through variable are important.

Key statistics from Table 13B (monthly equations estimated for 1985-2019; Newey-West standard errors with 12 lags):
- Column (1) (U‐U* only)
  - U‐U*: ‐0.187*** (0.043)
  - Constant: 0.198*** (0.067)
  - Observations: 420
  - R‐squared: 0.139
  - Rbar‐squared: 0.137
- Column (2)
  - V/U: 1.190*** (0.234)
  - V/U‐squared: ‐4.006 (5.669)
  - V/U‐cubed: 1.402 (2.634)
  - H: 0.059 (0.065)
  - Constant: ‐0.641*** (0.169)
  - Observations: 420
  - R‐squared: 0.136
  - Rbar‐squared: 0.134
- Column (3)
  - V/U: 4.373 (3.687)
  - V/U‐squared: ‐5.079 (5.896)
  - V/U‐cubed: 1.886 (2.732)
  - H: 0.090 (0.127)
  - Constant: ‐1.336* (0.701)
  - Observations: 420
  - R‐squared: 0.150
  - Rbar‐squared: 0.144
- Column (4)
  - V/U: 5.113 (3.833)
  - V/U‐squared: ‐5.719 (6.010)
  - V/U‐cubed: 2.192 (2.789)
  - H‐squared: 0.145* (0.084)
  - H‐cubed: 0.049 (0.033)
  - Constant: ‐1.458** (0.708)
  - Observations: 420
  - R‐squared: 0.154
  - Rbar‐squared: 0.145
- Column (5)
  - V/U: 5.530 (3.918)
  - V/U‐squared: ‐5.719 (6.010)
  - V/U‐cubed: 2.192 (2.789)
  - H‐squared: 0.145* (0.084)
  - Constant: ‐1.590** (0.715)
  - Observations: 420
  - R‐squared: 0.162
  - Rbar‐squared: 0.149

### Drivers of headline-inflation shocks before 2020 (Table 2A)
- Objective: estimate drivers of headline-inflation shocks in the pre-pandemic period (dependent variable: Headline – Median CPI monthly annualized inflation).
- Energy-price, food-price, and auto-price variables help explain headline shocks before the pandemic; backlogs do not.
- Food-price inflation is significant before the pandemic but not during the pandemic.

Selected coefficients and statistics (Bivariate and selected multivariate regressions; robust standard errors in parentheses; ***, **, and * denote significance at 1, 5, and 10 percent):
- Energy price inflation
  - Coefficient: 0.068*** (0.007)
  - Observations: 720
  - Start of sample: 1960m1
  - R‐squared: 0.503
  - Rbar‐squared: 0.502
- Food price inflation
  - Coefficient: 0.189*** (0.011) in bivariate; 0.186*** (0.009) in multivariate specification
  - Observations: 720
  - Start of sample: 1960m1
  - R‐squared (bivariate): 0.170
  - Rbar‐squared (bivariate): 0.169
- Harper Charter Rate
  - Coefficient: 0.001** (0.001)
  - Observations: 228
  - Start of sample: 2001m1
  - R‐squared: 0.026
  - Rbar‐squared: 0.0221
- Baltic Dry
  - Coefficient: 0.000*** (0.000)
  - Observations: 410
  - Start of sample: 1985m1
  - R‐squared: 0.041
  - Rbar‐squared: 0.0391
- FRBNY Supply Chain Index
  - Coefficient: 0.151* (0.091) [sign indicated as 0.151* in the table layout]
  - Observations: 152
  - Start of sample: 2007m5
  - R‐squared: 0.020
  - Rbar‐squared: 0.0134
- Backlogs of work
  - Coefficient: 1.603*** (0.510)
  - Observations: 264
  - Start of sample: 1998m1
  - R‐squared: 0.061
  - Rbar‐squared: 0.0571
- Durable goods share of real consumption
  - Coefficient: 0.061 (0.121)
  - Observations: 123
  - Start of sample: 2009m10
  - R‐squared: 0.001
  - Rbar‐squared: ‐0.00694
- Weighted average of car inflation rates
  - Coefficient: 0.159*** (0.041) in bivariate; 0.089*** (0.020) in multivariate
  - Observations: 720 (bivariate) and 263 (multivariate)
  - Start of sample: 1960m1 (bivariate) and 1998m2 (multivariate)
  - R‐squared (multivariate): 0.794
  - Rbar‐squared (multivariate): 0.792

Notes:
- Relative energy, food, and auto-related price inflation variables are created by subtracting median inflation from energy, food, and auto-related price inflation respectively, and these are in monthly annualized terms.
- Backlogs of work variable is taken from IHS Markit Economics.

### Simulations of core (median) PCE inflation and scenario outputs
- Simulations use: Phillips curve for median PCE inflation (Table 1A column 4) and same equations for Beveridge curve and inflation expectations as in the text.
- Results (Figures 17A and 19A) correspond to and are similar to those obtained for median CPI in the main text.

Figure 17A: Scenarios for Core (Median) PCE Inflation Conditional on September 2022 FOMC Unemployment Forecasts (12-month; percent)
- Unemployment forecast: Summary of Economic Projections of the FOMC published in September 2022 (numbers for the fourth quarters of 2022, 2023, 2024, and 2025). Forecasts assigned to November of each year and a monthly unemployment series interpolated starting from actual value of 3.5 percent in September 2022.
- Vertical line indicates September 2022.
- Core inflation denotes PCE median inflation.
- Horizontal dashes indicate assumed 2.4 percent target for median PCE inflation based on 2 percent PCE target and 0.4 percentage point gap between the median PCE inflation and PCE inflation excluding food and energy.
- Scenario marker values shown in figure: 6.01 and 2.58 (plotted points in the scenario figure).

Figure 19A: Scenarios for Core (Median) PCE Inflation Conditional on Alternative Unemployment Paths (12-month; percent)
- Vertical line indicates September 2022.
- Panel A: Conditional on IMF staff unemployment path
  - IMF staff forecast underlying the October 2022 IMF World Economic Outlook Report; quarterly forecasts allocated to the second month of each quarter and interpolated to monthly.
  - Scenario marker values shown in figure: 4.53 and 2.43 (plotted points in panel A).
- Panel B: Conditional on Higher Unemployment Path
  - "Higher unemployment" path assumes 7.5 percent unemployment during 2023 and 2024 as suggested by Summers (2022b).
  - Unemployment rate rises linearly from its September 2022 level to 7.5 percent in January 2023 and remains at that level through December 2024.
  - Scenario marker values shown in figure: 3.12 and 1.91 (plotted points in panel B).
- Horizontal dashes indicate assumed 2.4 percent target for median PCE inflation (same basis as Figure 17A).

*Understanding U.S. Inflation During the COVID Era – Appendix, Working Paper No. WP/2022/208*

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_Source: https://www.imf.org/-/media/files/publications/wp/2022/english/wpiea2022208app-print-pdf.pdf_