## wpiea2022260-print-pdf — EXECUTIVE SUMMARY

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---

### I. Purpose and methodological approach
- Develop a bottom-up model of euro area inflation using augmented Phillips curve models for seven core HICP sub-components and auxiliary regressions for two non-core items.
- Rationale:
  - Exploit heterogeneous data generation processes of HICP sub-components to improve forecasting accuracy and to better understand inflation drivers and transmission channels to core and headline inflation.
- Model structure:
  - Core sub-components (each estimated with an augmented reduced-form Phillips curve): processed food; durable goods; semi- and non-durable goods; housing services; recreation services (excl package holidays and accommodation); transport services; other services.
  - Non-core: energy (disaggregated into fuels, gas, electricity) and unprocessed food modeled via auxiliary regressions focused on international commodity prices and persistence.
  - Auxiliary regressions and projections for exogenous variables (e.g., vacancy-to-unemployment rate, non-energy manufacturing import prices, Chinese and US PPIs, house price growth, manufacturing inventories) are estimated for out-of-sample projections.

### II. Main empirical findings and forecasting performance
- Forecast accuracy:
  - Bottom-up framework improves overall forecast accuracy versus a canonical top-down Phillips curve model and simple autoregressive processes in pseudo out-of-sample evaluations.
  - Outperformance strongest for headline inflation where the energy model adds significant value; headline bottom-up outperformance increases over the 2020-2022 period due to sectoral shocks.
- Decomposition of the surge in inflation (early 2021 to Q2 2022):
  - Commodity prices drove three-quarters of the surge in headline inflation.
  - Declining slack and rising inflation expectations explain a further 10 percent of the headline surge.
  - For core inflation: international energy and food prices explain around 30 percent; slack and inflation expectations account for around 20 percent; other model variables (non-energy manufactured import prices or house prices) explain another 20 percent.
  - Unexplained forecast errors account for around one third — or around 1 percentage point — of the increase in core inflation, and also around 1 percentage point of the increase in headline inflation.
- Forecast errors and uncertainty:
  - RMSEs increased over time, largest errors during 2022.
  - Confidence band around end-2024 core inflation projection is as wide as 4 percentage points and even wider for headline inflation.

### III. Drivers of model miss and limitations
- Four salient contributors to large unexplained forecast errors and deteriorated recent forecast performance:
  - (i) Challenges in measuring economic slack.
  - (ii) Policy changes, such as measures to limit passthrough of energy price increases.
  - (iii) Non-linearities in energy pass-through amid an historic natural gas price shock.
  - (iv) Role of supply-side disruptions.
- Modeling and practical constraints:
  - No constant in Phillips curve models for core components (equilibrium assumption of zero slack and anchored expectations); constants included in non-core and auxiliary equations.
  - Vacancy-to-unemployment (V/U) rate performs best in recent years as a slack measure and is preferred despite data and projection limitations; WEO-based unemployment gap and output gap used in robustness checks.
  - Sectoral slack measures explored but coefficients tend not to be significant when included.
  - Out-of-sample projections require exogenous projections of all explanatory variables; some series require auxiliary regressions because not available in GAS/WEO.

### IV. Key model augmentations by sub-component
- Processed food: add first lag of YoY IMF international food price index (in Euro) and lagged electricity inflation; drop non-energy manufacturing import price.
- Durable goods: add banks’ self-reported change in lending standards (past three months), lagged electricity inflation, and firms’ inventories survey responses.
- Semi- and non-durable goods: benchmark Phillips variables plus lag of electricity price inflation.
- Housing services: headline HICP inflation (previous year) to capture indexation, and house price growth.
- Recreation services (excl. package holidays and accommodation): lagged electricity inflation and YoY growth (and one lag) of IMF international food price index (in Euro).
- Transport services: YoY growth (and one lag) of Brent crude oil price (in Euro).
- Other services: lagged electricity price inflation and correction for package holiday series anomaly with a dummy.
- Energy subcomponents:
  - Fuel: YoY inflation of Brent oil in USD and EUR-USD exchange rate.
  - Electricity: lagged TTF natural gas prices (in Euro).
  - Natural gas: lagged wholesale natural gas.
- Unprocessed food: YoY growth (and lag) of IMF international food price index (in Euro) and lag of natural gas inflation.

### V. Data composition and selected statistics (preserved sample-period figures)
- HICP component weights (averages since early 2000s): core components overall account for slightly below 85 percent of the HICP basket, energy about 10 percent, unprocessed food around 7 percent.
- Selected component average weights: semi- and non-durable goods 19 percent; processed food 13 percent; transport services 7 percent.
- Energy composition (within energy): fuels for personal transport equipment 40%; electricity 30%; natural gas 20%.
- Summary statistics (YoY inflation, 2000Q1-2019Q4 vs 2020Q1-2022Q2):
  - Processed food mean: 2.3; Std. Dev.: 1.4 → Mean: 2.4; Std. Dev.: 1.7
  - Durables mean: -0.1; Std. Dev.: 0.4 → Mean: 1.8; Std. Dev.: 1.8
  - Semi- and non-durables mean: 0.9; Std. Dev.: 0.5 → Mean: 1.1; Std. Dev.: 1.0
  - Housing mean: 1.9; Std. Dev.: 0.5 → Mean: 1.5; Std. Dev.: 0.3
  - Recreation mean: 2.3; Std. Dev.: 0.7 → Mean: 2.2; Std. Dev.: 0.9
  - Transport mean: 2.5; Std. Dev.: 0.8 → Mean: 1.8; Std. Dev.: 1.6
  - Other services mean: 1.3; Std. Dev.: 0.8 → Mean: 1.1; Std. Dev.: 1.1
  - Unprocessed food mean: 2.2; Std. Dev.: 2.0 → Mean: 3.9; Std. Dev.: 2.8
  - Energy mean: 3.6; Std. Dev.: 6.5 → Mean: 10.0; Std. Dev.: 17.6
- Five out of nine categories hit their maximum inflation rate since 2002 in Q2 2022; three others were 0.1 percentage point off their maximum.

### VI. Selected regression coefficients and model summary (baseline bottom-up, 2006Q1-2022Q2; observations: 66)
- Processed Food:
  - Lagged dependent variable: 0.781*** (0.0498)
  - V/U rel. to trend: 0.0411** (0.0161)
  - LT Inflation Expectations: 0.150** (0.0742)
  - HICP electricity price growth, lag: 0.0392** (0.0179)
  - Dummy for 2015: 1.062*** (0.241)
  - R-squared: 0.953
- Durables:
  - Lagged dependent variable: 0.959*** (0.0527)
  - V/U rel. to trend: 0.00594 (0.00709)
  - LT Inflation Expectations: -0.0752*** (0.0270)
  - Non-energy manufacturing import price growth: 0.0503*** (0.00851)
  - Manufacturing stocks growth: -0.0242*** (0.00457)
  - R-squared: 0.946
- Semi- and Nondurables:
  - Lagged dependent variable: 0.462*** (0.0924)
  - V/U rel. to trend: 0.0117 (0.00820)
  - LT Inflation Expectations: 0.141*** (0.0414)
  - Food price index growth, lag: 0.0189*** (0.00704)
  - R-squared: 0.928
- Housing services:
  - Lagged dependent variable: 0.905*** (0.0255)
  - V/U rel. to trend: 0.00731** (0.00330)
  - LT Inflation Expectations: 0.0599** (0.0290)
  - House price index growth: 0.00748* (0.00438)
  - Rent indexator: 0.0185 (0.0129)
  - HICP electricity price growth, lag: 0.0152* (0.00902)
  - R-squared: 0.997
- Recreation excl. package holidays:
  - Lagged dependent variable: 0.838*** (0.0365)
  - V/U rel. to trend: 0.0206*** (0.00450)
  - LT Inflation Expectations: 0.140*** (0.0420)
  - HICP electricity price growth, lag: 0.0499*** (0.0116)
  - R-squared: 0.996
- Transport services:
  - Lagged dependent variable: 0.716*** (0.0567)
  - V/U rel. to trend: 0.0257** (0.0122)
  - LT Inflation Expectations: 0.313*** (0.0741)
  - Brent crude oil (in Euros) growth, lag: 0.00750*** (0.00229)
  - R-squared: 0.967
- Other services:
  - Lagged dependent variable: 0.314*** (0.0947)
  - V/U rel. to trend: 0.0568*** (0.0139)
  - LT Inflation Expectations: 0.358*** (0.0657)
  - R-squared: 0.869

### VII. Weighted-average (bottom-up) Phillips curve coefficients and parameter stability
- Weighted-average coefficients:
  - Slack coefficient (V/U deviation from trend): 0.024.
  - Coefficient on long-term inflation expectations: 0.16.
  - Coefficient on lagged dependent variable (persistence): 0.7.
- Using unemployment gap as measure of slack gives Phillips curve coefficient of around -0.075.
- Rolling regressions (adding one quarter at a time from an initial window until 2014):
  - Slack coefficient oscillates between 0.02 and 0.026.
  - Coefficient on long-term inflation expectations ranges between 0.12 and 0.18.
  - Persistence coefficient ranges between 0.67 and 0.73.
  - Including the pandemic period changes parameters modestly; no dramatic movements.

### VIII. Non-core components and auxiliary regressions (selected)
- Energy components strongly correlated with international commodity prices; model fit for energy inflation significantly better than for unprocessed food.
- Selected non-core coefficients (2006Q1-2022Q2; observations: 66):
  - Fuels: Lagged dependent variable 0.432*** (0.0304); Brent crude oil growth 0.239*** (0.0104); R-squared: 0.961.
  - Electricity: Lagged dependent variable 0.654*** (0.0574); Dutch TTF natural gas price growth, lag: 0.0251*** (0.00244); R-squared: 0.921.
  - Natural gas: Lagged dependent variable 0.743*** (0.0559); Dutch TTF natural gas price growth, lag: 0.0398*** (0.00454); R-squared: 0.905.
  - Unprocessed food: Lagged dependent variable 0.450*** (0.0999); Food price index growth, lag: 0.0380** (0.0169); R-squared: 0.486.
- Top-down comparisons (observations: 66; R-squared: Headline 0.981; Core 0.985):
  - Headline lagged dependent variable: 0.663*** (0.0672)
  - Core lagged dependent variable: 0.832*** (0.0891)
  - V/U rel. to trend: Headline 0.0303** (0.0130); Core 0.0228*** (0.00692)
  - LT Inflation Expectations: Headline 0.206*** (0.0591); Core 0.0906 (0.0683)
  - Brent crude oil (in Euros) growth: Headline 0.0131*** (0.00201); Core 0.00142 (0.000933)

### IX. Forecasting performance details and component-level results
- Pseudo-out-of-sample evaluation: rolling 4-quarter ahead forecasts from an initial estimation window ending in 2014 through final forecast window 2021q3-2022q2 (26 partially overlapping projection windows).
- Overall: bottom-up performs best for core and headline; AR(1) performs worst; difference between bottom-up and top-down not statistically significant for core but large for headline.
- Component performance categories:
  - Satisfactory: processed food, semi- and nondurable goods, housing services, recreation services; fuel and electricity models (large absolute RMSEs but favorable NRMSE and relative performance).
  - Broadly satisfactory: remaining core components and natural gas model; transport, other services, durable goods outperform AR(1) despite worse RMSEs.
  - Poor: unprocessed food model (poor NRMSE and RMSE-to-AR(1) ratio).
- Pre-pandemic vs 2020-2022:
  - Bottom-up outperforms top-down especially since 2021 for headline inflation.
  - Bottom-up missed headline inflation by 1.4 percentage points in Q2 2022 for model estimated through Q4 2021 (two-quarter-ahead).
  - Housing services: only component not to see deterioration since 2020.
  - Natural gas, fuels, and durable goods: largest deterioration in RMSE (natural gas fourfold increase).

### X. Causes of worsened forecast performance (summarized)
- Measurement difficulties: diverging slack signals during the pandemic; V/U gap performs best recently; recommendation to use alternative slack measures as cross checks and apply forecaster judgment.
- Policy changes: temporary VAT cut in Germany H2 2020 (crude counterfactual VAT impact estimated at 0.4 p.p.); measures to limit passthrough of wholesale gas and electricity since mid-2021; indirect tax changes subtracted as much as 10 percentage points from electricity inflation in Q2 2022 (Eurostat constant tax comparison).
- Energy pass-through and structural break: oil increase Q1 2021–Q2 2022 was a one standard deviation event; natural gas increase was a five standard deviation shock; evidence of changed coefficients in electricity and natural gas equations when extending sample through the shock; recommended re-estimation at constant tax rates and apply judgment for future policy changes.
- Supply disruptions and durable goods: manufacturing stocks included but insufficient to capture bottlenecks; supply disruptions may have increased core inflation by 0.3-0.4pp (Celasun et. al (2022) estimate); recommend ex post adjustments to durable goods model if bottlenecks unwind.

### XI. Drivers of inflation — standardized shocks and decomposition
- Impact of one standard deviation inflationary shocks on core inflation (selected):
  - Economic slack: peaks at over 0.15 percentage points after three quarters.
  - EUR-USD exchange rate (one standard deviation ≈ 10 percent depreciation): about 0.15 percentage point increase after 4 quarters.
  - Natural gas prices: large delayed impact, peaking after 7 quarters at about 0.25 percentage points.
  - Food price and crude oil increases: slightly smaller impact than gas.
  - Inflation expectations and Chinese PPI: smallest impacts.
- Decomposition of recent surge (average of pseudo out-of-sample projections over 2021q3-2022q2 and 2020q1-2022q2):
  - Commodity prices (energy and food, including exchange rate) account for 75 percent of headline inflation increase in Q2 2022.
  - Commodity prices account for roughly 30 percent of core inflation increase.
  - Reduction in slack and increase in inflation expectations account for 10 percent of higher headline inflation and 20 percent of higher core inflation.
  - Other model variables account for close to 20 percent of core inflation.
  - Unexplained component: around one-third of core inflation increase (~1 percentage point); slightly over 10 percent of headline inflation (~close to 1 percentage point).

### XII. Projecting inflation — uncertainty and scenarios
- Stylized "neutral" economy assumptions from Q4 2022: no slack as of Q4 2022; long-term expectations at target; no year-on-year change in commodity prices or exchange rate.
- Confidence intervals:
  - By end-2024, 95 percent confidence interval considering parameter and residual uncertainty: core inflation spans from around 2 to 6 percent; headline inflation spans from around 1 to 8 percent.
- Scenarios (midpoint projections):
  1. October 2022 WEO:
     - Brent crude around 90 USD/bbl during 2023.
     - Natural gas slightly above first half 2022 levels.
     - International food prices drop slightly.
     - Long-term inflation expectations: 2.1 percent.
     - Ex-post adjustment to durable goods model for unwinding of bottlenecks.
  2. Demand reduction:
     - US growth marginally negative on annual basis in 2023.
     - Euro Area unemployment rate increases by 3 p.p.
     - Output gap worsens by 2p.p.
     - Oil prices drop to 70 bbl/USD in 2023.
     - Gas prices stabilize at 2021Q4–2022Q1 levels.
     - Food prices drop five percentage points.
     - Euro appreciates 10 percent.
     - Inflation expectations anchored at 2 percent.
     - Ex-post durable goods adjustment for unwinding bottlenecks.
  3. Stagflation:
     - TTF natural gas returns to Q3 2022 record levels and stabilizes.
     - Oil prices climb to 100 USD/bbl.
     - Euro Area unemployment and output gap weaken by 2p.p. each.
     - Long-term inflation expectations move up to 3 percent.
- Scenario outcomes:
  - By early-2023 inflation expected to be on a downward trajectory but significantly above target in all scenarios.
  - Demand reduction: disinflation in 2023 nearly as steep as the 2022 spike.
  - Stagflation: core and headline remain substantially above target at end-2024.
  - Processed food expected to remain persistent and stay above 5 percent in all scenarios.
  - Durable goods dynamics depend critically on assumptions about supply bottlenecks and any ex-post adjustments.

### XIII. Conclusion and policy implications
- Bottom-up Phillips curve relationships (inflation vs. slack; inflation vs. expectations) do not appear to have changed dramatically in this framework.
- Several supply-side shocks—most prominently the increase in European gas prices—were unprecedented and likely changed passthrough to specific consumer prices.
- Rotation in demand between services and goods produced unusual sectoral imbalances.
- Bottom-up modeling improves forecast accuracy and is particularly relevant given current dislocations, but model outputs require careful ex post adjustments and forecaster judgment given policy interventions, structural breaks, and large shocks.

*Source: IMF Working Paper — Executive Summary (wpiea2022260-print-pdf)*

### EXECUTIVE SUMMARY ___________________________________________________________________________ 3

### wpiea2022260-print-pdf - EXECUTIVE SUMMARY

### I. INTRODUCTION
- Title listed: "I. INTRODUCTION"

### II. METHODOLOGY
- Title listed: "II. METHODOLOGY"
- Subsections:
  - A. The Harmonized Index of Consumer Prices (HICP) Basket
  - B. The Canonical Phillips Curve
  - C. An Important Aside on Economic Slack
  - D. Baseline Bottom-Up Model Specification

### III. REGRESSION RESULTS
- Title listed: "III. REGRESSION RESULTS"

### IV. FORECASTING PERFORMANCE
- Title listed: "IV. FORECASTING PERFORMANCE"
- Subsections and practical breakdown:
  - A. Practical Considerations
  - A. Overall
  - B. Pre-Pandemic Period vs 2020-2022
  - C. What explains the increase in forecast errors?

### V. THE DRIVERS OF INFLATION
- Title listed: "V. THE DRIVERS OF INFLATION"
- Subsections:
  - A. Impact of Standardized Changes in Explanatory Variables
  - B. Decomposing the Drivers of the Recent Inflation Surge

### VI. PROJECTING INFLATION
- Title listed: "VI. PROJECTING INFLATION"
- Subsections:
  - A. The role of model uncertainty
  - B. Scenario Analysis

### VII. CONCLUSION
- Title listed: "VII. CONCLUSION"

### ANNEX I.
- Title listed: "ANNEX I."

### REFERENCES
- Title listed: "REFERENCES"

*Source: wpiea2022260-print-pdf - EXECUTIVE SUMMARY*

### Executive Summary

### wpiea2022260-print-pdf - Executive Summary

### Purpose and methodological approach
- Develop a bottom-up model of inflation in the euro area based on augmented Phillips curve models for seven core sub-components and auxiliary regressions for two non-core items.
- Rationale:
  - Exploit heterogeneous data generation processes of HICP sub-components to improve forecasting accuracy.
  - Better understand inflation drivers and transmission channels to core and headline inflation.
- Model structure:
  - Core: seven sub-components — processed food; durable goods; semi- and non-durable goods; housing services; recreation services (excl package holidays and accommodation); transport services; other services — each estimated with an augmented reduced-form Phillips curve of the form in equation [1].
  - Non-core: energy (disaggregated into fuels, gas, electricity) and unprocessed food modeled via auxiliary regressions focused on international commodity prices and persistence rather than slack or expectations.
  - Auxiliary regressions and projections for exogenous variables (e.g., vacancy-to-unemployment rate, non-energy manufacturing import prices, Chinese and US PPIs, house price growth, manufacturing inventories) are estimated to enable out-of-sample projections.

### Main empirical findings and forecast performance
- Forecast accuracy:
  - The bottom-up framework improves overall forecast accuracy relative to a canonical top-down Phillips curve model and simple autoregressive processes in pseudo out-of-sample evaluations.
  - Outperformance is particularly strong for headline inflation, where the energy model adds significant value; the headline bottom-up outperformance increases over the 2020-2022 period due to prevalent sectoral shocks.
- Decomposition of the surge in inflation (early 2021 to Q2 2022):
  - Three-quarters of the surge in headline inflation was driven by rising commodity prices.
  - Declining slack and increasing inflation expectations explain a further 10 percent of the headline inflation surge.
  - For core inflation:
    - International energy and food prices explain around 30 percent of the increase.
    - Slack and inflation expectations account for around 20 percent.
    - Other model variables (non-energy manufactured import prices or house prices) explain another 20 percent.
    - Unexplained forecast errors account for around one third — or around 1 percentage point — of the increase in core inflation, and also around 1 percentage point of the increase in headline inflation.
- Forecast errors and uncertainty:
  - The model’s RMSEs increased over time, with the largest errors during 2022.
  - Uncertainty around scenarios is large and increasing: the confidence band around the end-2024 core inflation projection is as wide as 4 percentage points and even wider for headline inflation.

### Drivers of model miss and limitations
- Four salient contributors to large unexplained forecast errors and deteriorated recent forecast performance:
  - (i) Challenges in measuring economic slack.
  - (ii) Policy changes, such as measures to limit the passthrough of energy price increases.
  - (iii) Non-linearities in energy pass-through amid an historic natural gas price shock.
  - (iv) The role of supply-side disruptions.
- Modeling choices and practical constraints:
  - No constant included in Phillips curve models for core components (equilibrium assumption of zero slack and anchored expectations); constants included in non-core and auxiliary equations.
  - Slack measurement matters since 2020; vacancy-to-unemployment (V/U) rate performs best in recent years and is preferred despite data and projection limitations. WEO-based unemployment gap and output gap are used in robustness checks.
  - Sectoral slack measures were explored but sectoral slack coefficients tend not to be significant when included; focus remains on aggregate slack measures.
  - For out-of-sample projections, all explanatory variables must be projected exogenously; some series required auxiliary regressions because they are not available in GAS/WEO.

### Key model augmentations by sub-component (high-level)
- Processed food: add first lag of YoY IMF international food price index (in Euro) and lagged electricity inflation; drop non-energy manufacturing import price.
- Durable goods: add banks’ self-reported change in lending standards (past three months), lagged electricity inflation, and firms’ inventories survey responses.
- Semi- and non-durable goods: benchmark Phillips variables plus lag of electricity price inflation.
- Housing services: headline HICP inflation (previous year) to capture indexation, and house price growth.
- Recreation services (excl. package holidays and accommodation): lagged electricity inflation and YoY growth (and one lag) of IMF international food price index (in Euro).
- Transport services: YoY growth (and one lag) of Brent crude oil price (in Euro).
- Other services: lagged electricity price inflation and correction for package holiday series anomaly with a dummy.
- Energy subcomponents:
  - Fuel: YoY inflation of Brent oil in USD and EUR-USD exchange rate.
  - Electricity: lagged TTF natural gas prices (in Euro).
  - Natural gas: lagged wholesale natural gas.
- Unprocessed food: YoY growth (and lag) of IMF international food price index (in Euro) and lag of natural gas inflation.

### Data composition and selected statistics preserved from sample periods
- HICP component weights (averages since early 2000s): core components overall account for slightly below 85 percent of the HICP basket, energy about 10 percent, unprocessed food around 7 percent.
- Selected component average weights noted: semi- and non-durable goods 19 percent; processed food 13 percent; transport services 7 percent (smallest core component).
- Energy composition (within energy): fuels for personal transport equipment 40%, electricity 30%, natural gas 20%, remainder small categories.
- Summary statistics (YoY inflation, 2000Q1-2019Q4 vs 2020Q1-2022Q2):
  - Processed food mean: 2.3; Std. Dev.: 1.4 (pre-pandemic) → Mean: 2.4; Std. Dev.: 1.7 (2020Q1-2022Q2)
  - Durables mean: -0.1; Std. Dev.: 0.4 → Mean: 1.8; Std. Dev.: 1.8
  - Semi- and non-durables mean: 0.9; Std. Dev.: 0.5 → Mean: 1.1; Std. Dev.: 1.0
  - Housing mean: 1.9; Std. Dev.: 0.5 → Mean: 1.5; Std. Dev.: 0.3
  - Recreation mean: 2.3; Std. Dev.: 0.7 → Mean: 2.2; Std. Dev.: 0.9
  - Transport mean: 2.5; Std. Dev.: 0.8 → Mean: 1.8; Std. Dev.: 1.6
  - Other services mean: 1.3; Std. Dev.: 0.8 → Mean: 1.1; Std. Dev.: 1.1
  - Unprocessed food mean: 2.2; Std. Dev.: 2.0 → Mean: 3.9; Std. Dev.: 2.8
  - Energy mean: 3.6; Std. Dev.: 6.5 → Mean: 10.0; Std. Dev.: 17.6
- Five out of nine categories hit their maximum inflation rate since 2002 in Q2 2022; three others were 0.1 percentage point off their maximum (two of those then exceeded the previous maximum in Q3 2022).

### Scenarios and projections
- The model is used to explore several scenarios for euro area inflation over the coming two years.
- Uncertainty is large and increases over time: the confidence band around end-2024 core inflation is as wide as 4 percentage points; headline inflation uncertainty is even larger.

*Source: IMF Working Paper — Executive Summary (wpiea2022260-print-pdf)*

### Appendix shows the main regression table when using the unemployment gap as the slack measure as a

### wpiea2022260-print-pdf - Appendix shows the main regression table when using the unemployment gap as the slack measure as a

### Robustness checks and slack measures
- Appendix: main regression table using the unemployment gap as the slack measure as a robustness check; coefficients are similar in most cases; deviations are flagged in discussion.
- Table A2 (appendix): coefficients when using vacancy to unemployment rate as the measure of slack as a further robustness check, with regression ending in 2019q4.

### Core sub-component Phillips curve findings
- Strong positive relationship between inflation rate and deviation of the vacancy to unemployment rate from trend for most core sub-components; exception:
  - Non-energy industrial goods: coefficient not statistically different from zero.
- Long-term inflation expectations:
  - Enter with a positive coefficient and are significant in all models except durable goods and housing services (insignificant in housing services; counterintuitive sign in durable goods).
- House price growth:
  - Contributes significantly to housing inflation.
- Indexation variable:
  - Not significant when using vacancy to unemployment rate to measure slack.
  - Highly significant when using the unemployment gap.
- International commodity price series:
  - Significant (either contemporaneous or lagged) in all models where included.
- Durable goods:
  - Manufacturing inventory growth variable enters with a negative and significant coefficient.
- Electricity prices:
  - Lagged electricity price coefficient is highly significant with a positive sign where included except for other services.
- Persistence (AR terms) across sub-components:
  - Range from 0.3 for other services inflation to over 0.9 for durable goods inflation.

### Baseline bottom-up regression exact coefficients (selected from Table 2)
- Regression period: 2006Q1-2022Q2. Observations: 66 for each equation. R-squared values listed below are adjusted R-squared.
- Processed Food (column 1):
  - Lagged dependent variable: 0.781*** (0.0498)
  - V/U rel. to trend: 0.0411** (0.0161)
  - LT Inflation Expectations: 0.150** (0.0742)
  - HICP electricity price growth, lag: 0.0392** (0.0179)
  - Dummy for 2015: 1.062*** (0.241)
  - R-squared: 0.953
- Durables (column 2):
  - Lagged dependent variable: 0.959*** (0.0527)
  - V/U rel. to trend: 0.00594 (0.00709)
  - LT Inflation Expectations: -0.0752*** (0.0270)
  - Non-energy manufacturing import price growth: 0.0503*** (0.00851)
  - Manufacturing stocks growth: -0.0242*** (0.00457)
  - R-squared: 0.946
- Semi- and Nondurables (column 3):
  - Lagged dependent variable: 0.462*** (0.0924)
  - V/U rel. to trend: 0.0117 (0.00820)
  - LT Inflation Expectations: 0.141*** (0.0414)
  - Food price index growth, lag: 0.0189*** (0.00704)
  - R-squared: 0.928
- Housing services (column 4):
  - Lagged dependent variable: 0.905*** (0.0255)
  - V/U rel. to trend: 0.00731** (0.00330)
  - LT Inflation Expectations: 0.0599** (0.0290)
  - House price index growth: 0.00748* (0.00438)
  - Rent indexator: 0.0185 (0.0129)
  - HICP electricity price growth, lag: 0.0152* (0.00902)
  - R-squared: 0.997
- Recreation excl. package holidays (column 5):
  - Lagged dependent variable: 0.838*** (0.0365)
  - V/U rel. to trend: 0.0206*** (0.00450)
  - LT Inflation Expectations: 0.140*** (0.0420)
  - HICP electricity price growth, lag: 0.0499*** (0.0116)
  - R-squared: 0.996
- Transport services (column 6):
  - Lagged dependent variable: 0.716*** (0.0567)
  - V/U rel. to trend: 0.0257** (0.0122)
  - LT Inflation Expectations: 0.313*** (0.0741)
  - Brent crude oil (in Euros) growth, lag: 0.00750*** (0.00229)
  - R-squared: 0.967
- Other services (column 7):
  - Lagged dependent variable: 0.314*** (0.0947)
  - V/U rel. to trend: 0.0568*** (0.0139)
  - LT Inflation Expectations: 0.358*** (0.0657)
  - R-squared: 0.869

Notes: Standard errors in parentheses. Significance: *** p<0.01, ** p<0.05, * p<0.1.

### Weighted-average (bottom-up) Phillips curve coefficients
- Slack coefficient for deviation of vacancy to unemployment rate from trend: 0.024.
- Coefficient on long-term inflation expectations: 0.16.
- Coefficient on lagged dependent variable (persistence): 0.7.
- Using unemployment gap as measure of slack gives Phillips curve coefficient of around -0.075.
- Interpretation: overall relatively flat Phillips curve, broadly in line with standard reduced-form Phillips curve coefficients from top-down exercises.

### Parameter stability (Figure 5 results)
- Rolling regression exercise: initial regression window until 2014, then add one quarter at a time.
- Slack coefficient oscillates between 0.02 and 0.026.
- Coefficient on long-term inflation expectations ranges between 0.12 and 0.18.
- Persistence coefficient ranges between 0.67 and 0.73.
- Including the pandemic period changes parameters modestly but no dramatic movements.
- Note on rolling windows: observation for 2021q3 is the final one as the four quarter window 2021q3-2022q2 is the final projection window used for rolling average coefficient graphs.

### Non-core inflation components (Table 3) and top-down (Table 4)
- Energy components (fuels, electricity, natural gas) and unprocessed food prices:
  - Strongly correlated with international commodity prices.
  - Model fit for energy inflation significantly better than for unprocessed food.
- Table 4 (Top-down regressions) highlights:
  - Contemporaneous crude oil price movements important for headline inflation.
  - Food prices important for core inflation (processed food included in core definition).
- Selected coefficients from Table 3 (non-core, regression period 2006Q1-2022Q2; observations 66):
  - Fuels:
    - Lagged dependent variable: 0.432*** (0.0304)
    - Brent crude oil growth: 0.239*** (0.0104)
    - R-squared: 0.961
  - Electricity:
    - Lagged dependent variable: 0.654*** (0.0574)
    - Dutch TTF natural gas price growth, lag: 0.0251*** (0.00244)
    - R-squared: 0.921
  - Natural gas:
    - Lagged dependent variable: 0.743*** (0.0559)
    - Dutch TTF natural gas price growth, lag: 0.0398*** (0.00454)
    - R-squared: 0.905
  - Unprocessed food:
    - Lagged dependent variable: 0.450*** (0.0999)
    - Food price index growth, lag: 0.0380** (0.0169)
    - R-squared: 0.486
- Top-down energy and core/headline comparisons (selected):
  - Headline lagged dependent variable: 0.663*** (0.0672)
  - Core lagged dependent variable: 0.832*** (0.0891)
  - V/U rel. to trend: Headline 0.0303** (0.0130); Core 0.0228*** (0.00692)
  - LT Inflation Expectations: Headline 0.206*** (0.0591); Core 0.0906 (0.0683)
  - Brent crude oil (in Euros) growth: Headline 0.0131*** (0.00201); Core 0.00142 (0.000933)
  - Observations: 66 for both headline and core. R-squared: Headline 0.981; Core 0.985.

### Auxiliary regressions (Table 5) — explanatory variables not in IMF GAS or WEO
- Regression period: 2006Q1-2022Q2. Robust standard errors reported. Selected findings:
  - Sum of lagged dependent variables significant across equations (e.g., 0.626***, 0.803***, 0.683***, 0.938***, 0.568***, 0.651***).
  - Oil price growth significant positive contemporaneous effects (0.0678***, 0.0698***); negative significant lagged effects (-0.0292***, -0.0454***).
  - PPI China growth: 0.338*** (0.0918) with a lag coefficient of -0.236** (0.117) in one specification.
  - EUR-USD exchange rate change: 0.318*** (0.0210) with lag -0.197*** (0.0380) in one specification.
  - Credit standards change: -0.0217*** (0.00793).
  - Output Gap: 0.330*** (0.127).
  - Unemployment Gap: -0.812*** (0.265).
  - Dummy for 2022: 7.984*** (1.089).
  - Observations vary by equation (e.g., 81, 81, 81, 78, 81, 65). R-squared values reported (e.g., 0.955, 0.936, 0.951, 0.972, 0.801, 0.932).

### Forecasting performance — methodology (Section IV)
- Evaluation: pseudo-out-of-sample projection exercise comparing bottom-up model to (1) top-down PC model and (2) simple AR process.
- Rolling 4-quarter ahead forecast steps:
  1. Initial estimation window ending in 2014.
  2. Compute 4-quarter ahead forecast and RMSE for that horizon (initial forecast: regression ends 2014q4, forecast for four quarters of 2015).
  3. Calculate (i) average RMSEs, (ii) average normalized RMSE (NRMSE) normalized by standard deviation of inflation over full estimation and projection window, and (iii) ratio of RMSE of full model relative to simple AR(1).
  4. Roll estimation and 4-quarter projection window forward by 1 quarter.
  5. Repeat steps 2-4 until final forecast window 2021q3-2022q2, yielding 26 partially overlapping projection windows.
- Also tested five non-overlapping windows (four quarters of 2015, 2016, 2017, 2018, 2019); results quantitatively unchanged.

### Forecasting performance — overall results (Section IV.A)
- Over full period:
  - Bottom-up model performs best for both core and headline inflation.
  - Autoregressive model performs worst.
  - Difference between bottom-up and top-down not statistically significant for core inflation; difference large for headline inflation.
  - Modeling energy inflation separately is advantageous.
- Performance categories for individual bottom-up component models:
  - Satisfactory forecasting performance:
    - Core: processed food, semi- and nondurable goods, housing services, recreation services — low RMSEs and NRMSEs and outperform AR(1).
    - Non-core: fuel and electricity models — large absolute RMSEs due to volatility but favorable NRMSE and relative performance; fuel model best performer across both criteria.
  - Broadly satisfactory:
    - Remaining core components and natural gas model.
    - Transport, other services, durable goods: worse RMSEs and NRMSEs than other core models but outperform AR(1).
    - Durable goods: worst fit among core; low pre-pandemic volatility followed by sharp post-2020 increase not adequately captured.
    - Natural gas: very large RMSEs, but NRMSE less dramatic once adjusted for volatility.
  - Poor performance:
    - Unprocessed food model: poor NRMSE and RMSE-to-AR(1) ratio; attempted alternatives unsuccessful due to erratic series. Retained lags of international food prices and natural gas prices given statistical significance and intuitive appeal.

### Pre-pandemic vs 2020-2022 forecasting performance (Section IV.B)
- Inflation dynamics since 2020:
  - Core goods inflation (processed food, durable goods, semi- and non-durables) diverged from pre-pandemic behavior: fell into negative territory during pandemic, then rose sharply from start of 2021 driven by energy and core goods inflation.
  - Services: nuanced pattern; unusual negative print early in pandemic for two of four components; Q2 2022 saw unusually high prints for all services components except housing.
  - Services remain the smallest contributor to surge in inflation relative to pre-pandemic contributions.
  - Energy surge stands out for non-core items.
- Rolling 4-quarter projection performance over 2020Q1-2022Q2:
  - Bottom-up model tends to outperform top-down model, especially since 2021 for headline inflation.
  - Bottom-up model missed headline inflation by 1.4 percentage points in Q2 2022 for the model estimated through Q4 2021 (two-quarter-ahead projection).
  - Pre-pandemic period: no difference between bottom-up and top-down for core inflation.
  - Since 2020: bottom-up outperforms top-down for core inflation; bottom-up outperforms top-down for headline inflation in all periods.
  - All models: worsening forecast errors in recent quarters, particularly large during 2022.
  - Component-level deterioration (2020-2022 vs pre-2020):
    - Housing services: only component not to see deterioration since 2020.
    - Natural gas, fuels, and durable goods: largest deterioration in RMSE (natural gas fourfold increase).
- Visuals referenced: Figures 6, 7, 8 (RMSE comparisons, component contributions, and projections). Figure A.3 (appendix) shows bottom-up, top-down, and AR(1) projections for core and headline over 2020q1-2022q2.

### What explains the increase in forecast errors? (intro)
- Model forecast performance deteriorated significantly since 2020; several important contributing factors are discussed (section truncated in source).

*Source: wpiea2022260-print-pdf - Appendix shows the main regression table when using the unemployment gap as the slack measure as a*

### 1. Measurement difficulties: Measuring economic slack became particularly difficult during the Covid-19

### 1. Measurement difficulties: Measuring economic slack became particularly difficult during the Covid-19

### Diverging slack signals and forecast implications
- Different slack variables showed strongly diverging patterns during the pandemic, making it hard to discern the true level of slack as relevant for inflation pressures.
- The V/U gap, which shows a very tight labor market in recent quarters, does the best job at forecasting inflation over the past quarters, and this could point towards an overall assessment of a tight labor market.
- The fundamental issue of diverging signals from different slack variables reduces confidence in the assessment of demand side pressures on inflation and could be contributing to worse forecast performance.
- Recommendation: Use alternative measures of slack as a cross check and apply forecaster judgment to adjust pure model-based projections.

### Key numeric observations
- One standard deviation increase in economic slack has the largest impact on core inflation, peaking at over 0.15 percentage points after three quarters (Figure 11).

---

### 2. Policy changes

### Identified policy interventions affecting inflation dynamics
- Temporary VAT cut in Germany in H2 2020.
- Various policy interventions to limit passthrough of wholesale natural gas and electricity prices introduced since mid-2021.

### Quantitative adjustments and model performance
- The crude counterfactual adjustment for the German VAT change yields an estimated VAT impact of 0.4 p.p., close to an assessment by the ECB.
- Incorporating the VAT counterfactual substantially improves 8-quarter ahead model forecast performance; model performance against this counterfactual is nearly as good as the pre-pandemic one.
- Indirect tax changes subtracted as much as 10 percentage points from electricity inflation in Q2 2022 (Eurostat constant tax comparison).
- Note: Calculations do not cover additional, non-tax measures governments have taken to limit passthrough.

---

### 3. Energy pass-through, especially from the European natural gas shock

### Unprecedented energy movements and structural break evidence
- The increase in oil prices between Q1 2021 and Q2 2022 was a one standard deviation event; the increase in natural gas prices was a five standard deviation shock.
- Comparing coefficients estimated through Q2 2022 with those estimated until Q4 2019 shows generally limited changes except:
  - Coefficient on TTF wholesale natural gas price in the electricity regression is somewhat larger when extending the sample through the recent energy shock.
  - The coefficient in the natural gas equation is 70 percent smaller when extending the sample through the recent energy shock.
- Using the Q4 2019 coefficient to project natural gas inflation over Q1 2020–Q2 2022 yields significant overestimation (natural gas inflation peak close to 100 percent vs 60 percent observed).
- Using the smaller coefficient underestimates natural gas inflation in Q2 2022.
- Interpretation: Possible structural break in the energy inflation relationship due to policy interventions, very large shock magnitude, greater share of LNG purchased at spot prices, and country institutional differences in passthrough.

### Implications and recommended approach
- Re-run natural gas and electricity models for inflation series at constant tax rates to recover closer-to-non-policy-distorted passthrough coefficients.
- Use recovered coefficients in out-of-sample projections and apply judgement to add/subtract future policy changes.

---

### 4. Supply disruptions and durable goods forecasting

### Evidence and model shortcomings
- Sharp deterioration in the durable goods model performance; manufacturing stocks included but insufficient to capture full supply bottlenecks story.
- Celasun et. al (2022) estimate supply disruptions might have increased core inflation by 0.3-0.4pp.
- Large forecast errors for durable goods indicate the model’s high persistence assumption may not capture unwinding of bottlenecks.

### Recommended adjustments
- Forecaster may consider explicit ex post adjustments to the durable goods model if information suggests the model’s persistence is inappropriate as bottlenecks unwind.

---

### 5. The drivers of inflation

### A. Impact of standardized changes in explanatory variables (one standard deviation inflationary shocks)
- Variables analyzed: EUR-USD exchange rate, crude oil prices, food prices, vacancy-to-unemployment rate, long-term inflation expectations, Chinese PPI inflation, natural gas prices.
- Core inflation impacts:
  - Economic slack: peaks at over 0.15 percentage points after three quarters.
  - Exchange rate: similar impact to slack (one standard deviation ~10 percent depreciation → 0.15 percentage point increase in core inflation after 4 quarters).
  - Natural gas prices: large and delayed impact, peaking after 7 quarters at about 0.25 percentage points.
  - Food price and crude oil price increases: slightly smaller impact than gas.
  - Inflation expectations and Chinese PPI: smallest impacts.
- Headline inflation impacts:
  - Oil price shocks have large, but transitory, effects (unwind almost fully after 5 quarters).
  - Natural gas shocks: large, delayed, and persistent impact.
  - Exchange rate and economic slack: meaningful and persistent effects.

### B. Decomposing the recent inflation surge (average of pseudo out-of-sample projections over 2021q3-2022q2 and 2020q1-2022q2)
- Commodity prices (energy and food, including exchange rate component) account for 75 percent of the increase in headline inflation in Q2 2022 (relative to Q2 2021 and Q4 2019).
- Commodity prices account for roughly 30 percent of the increase in core inflation.
- Reduction in slack and increase in inflation expectations account for:
  - 10 percent of higher headline inflation.
  - 20 percent of higher core inflation.
- Other model variables (house price growth, manufacturing stocks, imported manufacturing prices) account for close to 20 percent of core inflation.
- Unexplained component:
  - Around one-third of the increase in core inflation—1 percentage point—remains unexplained by the model.
  - Slightly over 10 percent of headline inflation—close to 1 percentage point—remains unexplained by the model.

---

### 6. Projecting inflation

### A. Model uncertainty and stylized neutral economy projection
- Stylized “neutral” economy assumptions starting Q4 2022:
  - No slack as of Q4 2022.
  - Long-term expectations at target.
  - No year-on-year change in commodity prices or exchange rate.
- Confidence intervals:
  - 95 percent confidence interval considering only parameter uncertainty (darker band); wider band including residual uncertainty (lighter band).
  - By end-2024, the confidence band for core inflation spans from around 2 to 6 percent.
  - By end-2024, the confidence band for headline inflation spans from around 1 to 8 percent.
- Implication: High uncertainty even from Q4 2022 onward.

### B. Scenario analysis (midpoint projections for each scenario)
- Scenarios studied:
  1. October 2022 WEO scenario
     - Brent crude around 90 USD/bbl during 2023.
     - Natural gas prices slightly above levels seen in first half of 2022.
     - International food prices expected to drop slightly from elevated levels.
     - Long-term inflation expectations: 2.1 percent (professional forecasters).
     - Ex-post adjustment to durable goods model to allow for unwinding of supply bottlenecks.
  2. Demand reduction scenario
     - US growth turns marginally negative on an annual basis in 2023.
     - Euro Area unemployment rate gradually increases by 3 p.p.
     - Output gap shows significant slack as of 2023 with a worsening of 2p.p.
     - Oil prices drop to 70 bbl/USD in 2023 and stabilize in 2024.
     - Gas prices stabilize at the level observed in 2021Q4 and 2022Q1.
     - Food prices drop five percentage points.
     - Euro appreciated 10 percent.
     - Inflation expectations anchored at 2 percent.
     - Ex-post adjustment to durable goods model to allow for unwinding of supply bottlenecks.
  3. Stagflation scenario
     - TTF natural gas prices return to record levels observed in Q3 2022 and stabilize there.
     - Oil prices climb to 100 USD/bbl.
     - US growth broadly unchanged.
     - Euro Area unemployment and output gap weaken by 2p.p. each.
     - Long-term inflation expectations move up to 3 percent.

### Scenario outcomes and component effects
- By early-2023 the model expects inflation to be on a downward trajectory but significantly above target in all scenarios; speed of decline differs by scenario.
- Demand reduction scenario: disinflation in 2023 nearly as steep as the 2022 inflationary spike.
- Stagflation scenario: core and headline remain substantially above target even at end-2024.
- Component-level insights:
  - Fuel inflation sensitive to Brent crude level; Brent at 70 USD/bbl leads to large negative fuel inflation in 2023 and supports rapid drop in transport services inflation.
  - Gas price assumptions drive large level differences in natural gas and electricity inflation across scenarios; retail gas and electricity inflation projected to remain high but drop in both scenarios (assuming measures to limit passthrough are maintained).
  - Services categories sensitive to economic slack show similar dynamics across demand reduction and stagflation scenarios due to labor market worsening; level differences at end-2024 driven partly by higher inflation expectations in stagflation and higher electricity prices.
  - Processed food expected to remain persistent, staying above 5 percent in all scenarios.
  - Durable goods dynamics depend critically on assumptions about supply bottlenecks and any ex-post adjustments.

---

### 7. Conclusion

- Bottom-up Phillips curve relationships (inflation vs. economic slack; inflation vs. inflation expectations) do not seem to have changed dramatically when examined in this framework.
- Several supply-side shocks—most prominently the increase in European gas prices—have been unprecedented and likely changed passthrough to specific consumer prices relative to previous periods.
- Rotation in demand between services and goods has produced unusual sectoral demand-supply imbalances.
- Bottom-up modeling improves forecast accuracy and is particularly pertinent given current dislocations, but model outputs require careful ex post adjustments and forecaster judgment given policy interventions, structural breaks, and large shocks.

*IMF Working Paper: A Bottom-Up Phillips Curve for the Euro Area (excerpts from chapter “1. Measurement difficulties: Measuring economic slack became particularly difficult during the Covid-19”)*

### Annex I.

### Annex I. Additional Figures

### Figures (visual summary)
- Figure A.1. Contribution to Year-on-Year Inflation Subindices
  - Subindices shown: Goods, Core goods, Core services, Non-core items.
  - Sources: Eurostat; Authors’ calculations.
- Figure A.2. HICP Weights (2002-2022)
  - Sources: Eurostat; Authors’ calculations.
- Figure A.3. 9-Quarter Ahead Pseudo out of Sample Projections During the Pandemic
  - Series shown: Core, Headline.
  - Sources: Eurostat; Authors’ calculations.

### Table A1. Bottom-Up Phillips Curve Regressions with the Unemployment Gap as the Measure of Slack
- Estimation details:
  - Bottom-up models using unemployment gap as slack measure.
  - Estimated by system of seemingly unrelated regressions (SUR) where the errors are assumed to be correlated across equations.
  - Regression period is 2002Q2-2022Q2.
  - R-squared refers to adjusted R-squared.
- Panel summary by equation (columns (1)–(11)):
  - Observations: 81 (for each equation).
  - R-squared by column:
    - (1) 0.959
    - (2) 0.945
    - (3) 0.923
    - (4) 0.997
    - (5) 0.995
    - (6) 0.972
    - (7) 0.886
    - (8) 0.953
    - (9) 0.919
    - (10) 0.897
    - (11) 0.471
  - Lagged dependent variable coefficients (with standard errors in parentheses):
    - (1) 0.763*** (0.0463)
    - (2) 0.969*** (0.0453)
    - (3) 0.606*** (0.0705)
    - (4) 0.917*** (0.0230)
    - (5) 0.877*** (0.0323)
    - (6) 0.727*** (0.0505)
    - (7) 0.608*** (0.0694)
    - (8) 0.425*** (0.0299)
    - (9) 0.658*** (0.0524)
    - (10) 0.749*** (0.0534)
    - (11) 0.440*** (0.0832)
  - Slack coefficient (unemployment gap) where reported:
    - (1) -0.191*** (0.0596)
    - (2) -0.0254 (0.0251)
    - (3) -0.0552* (0.0326)
    - (4) 0.00233 (0.0120)
    - (5) -0.0697*** (0.0212)
    - (6) -0.105** (0.0477)
    - (7) -0.171*** (0.0591)
  - LT Inflation Expectations coefficients where reported:
    - (1) 0.239*** (0.0786)
    - (2) -0.0531** (0.0226)
    - (3) 0.133*** (0.0408)
    - (4) 0.0187 (0.0253)
    - (5) 0.116*** (0.0451)
    - (6) 0.355*** (0.0753)
    - (7) 0.313*** (0.0721)
  - Selected additional coefficients reported in table (examples):
    - Non-energy manufacturing import price growth: 0.0454*** (0.00686) in one equation; 0.00754 (0.00959) in another.
    - Manufacturing stocks growth: -0.0211*** (0.00428).
    - Food price index (in Euros) growth, lag: 0.0153** (0.00600); 0.00384 (0.00282); 0.0337** (0.0147) across different equations.
    - House price index growth: 0.0154*** (0.00317).
    - Rent indexator: 0.0382*** (0.0113).
    - Brent crude oil (in Euros) growth, lag: 0.00679*** (0.00204).
    - HICP electricity price growth, lag: 0.0613*** (0.0146); 0.0162** (0.00786); 0.0409*** (0.00987); 0.0239*** (0.00462); 0.00767 (0.0118).
    - Dummy for 2015: 0.673*** (0.243).
    - Brent crude oil growth: 0.229*** (0.00970).
    - Euro-USD exchange rate change: 0.269*** (0.0310).
    - Dutch TTF natural gas price growth, lag: 0.0250*** (0.00221); 0.0401*** (0.00437).
    - HICP natural gas price growth, lag: 0.0706*** (0.0188).
  - Constants reported in selected equations:
    - (1) -0.1150. (0.282)
    - (2) 0.968*** (0.233)
    - (3) 0.3810. (0.385)
    - (4) 0.827*** (0.219)

### Table A2. Bottom-Up Phillips Curve Regressions with V/U relative to Trend as Slack Measure (estimated until 2019Q4)
- Estimation details:
  - Bottom-up models using V/U relative to trend as slack measure.
  - Estimated by system of seemingly unrelated regressions (SUR) where the errors are assumed to be correlated across equations.
  - Regression period is 2006Q1-2019Q4.
  - R-squared refers to adjusted R-squared.
- Panel summary by equation (columns (1)–(11)):
  - Observations: 56 (for each equation).
  - R-squared by column:
    - (1) 0.951
    - (2) 0.861
    - (3) 0.938
    - (4) 0.998
    - (5) 0.996
    - (6) 0.983
    - (7) 0.891
    - (8) 0.965
    - (9) 0.758
    - (10) 0.789
    - (11) 0.420
  - Lagged dependent variable coefficients (with standard errors in parentheses):
    - (1) 0.761*** (0.0636)
    - (2) 0.828*** (0.0498)
    - (3) 0.490*** (0.0918)
    - (4) 0.937*** (0.0272)
    - (5) 0.867*** (0.0383)
    - (6) 0.819*** (0.0530)
    - (7) 0.333*** (0.103)
    - (8) 0.358*** (0.0271)
    - (9) 0.700*** (0.0634)
    - (10) 0.427*** (0.0900)
    - (11) 0.529*** (0.101)
  - Slack coefficient (V/U relative to trend) where reported:
    - (1) 0.0543*** (0.0185)
    - (2) 0.00315 (0.00515)
    - (3) 0.00738 (0.00711)
    - (4) 0.000977 (0.00408)
    - (5) 0.0178*** (0.00463)
    - (6) 0.0208** (0.0101)
    - (7) 0.0562*** (0.0141)
  - LT Inflation Expectations coefficients where reported:
    - (1) 0.236*** (0.0862)
    - (2) -0.0455 (0.0280)
    - (3) 0.0598 (0.0434)
    - (4) 0.0136 (0.0320)
    - (5) 0.145*** (0.0405)
    - (6) 0.210*** (0.0704)
    - (7) 0.377*** (0.0799)
  - Selected additional coefficients reported in table (examples):
    - Non-energy manufacturing import price growth: 0.0400*** (0.00690); 0.0146 (0.00991).
    - Manufacturing stocks growth: -0.0121*** (0.00402).
    - Food price index (in Euros) growth, lag: 0.0188** (0.00769); 0.00814*** (0.00262); 0.0153 (0.0160).
    - House price index growth: 0.0119** (0.00495).
    - Rent indexator: 0.0288* (0.0159).
    - Brent crude oil (in Euros) growth, lag: 0.00403** (0.00204).
    - HICP electricity price growth, lag: 0.00908 (0.0410); -0.007440 (0.0115); 0.0814*** (0.0188); -0.00438 (0.00873); -0.00703 (0.0261).
    - Dummy for 2015: 1.019*** (0.240).
    - Brent crude oil growth: 0.258*** (0.0104).
    - Euro-USD exchange rate change: 0.300*** (0.0320).
    - Dutch TTF natural gas price growth, lag: 0.0199*** (0.00391); 0.108*** (0.0185).
    - HICP natural gas price growth, lag: 0.0212 (0.0229).
  - Constants reported in selected equations:
    - (1) -0.3750. (0.256)
    - (2) 0.874*** (0.260)
    - (3) 0.6310. (0.486)
    - (4) 0.815*** (0.238)

### Analytical implications (as presented in the annex)
- The bottom-up Phillips curve framework is estimated across disaggregated HICP components with different measures of slack (unemployment gap; V/U relative to trend), producing heterogeneous coefficients across sectors.
- Lagged inflation dynamics are strongly persistent across most components (lagged dependent variable coefficients typically significant and between 0.333*** and 0.969*** across tables).
- Slack measures exhibit both negative and positive coefficients depending on specification and component:
  - Using the unemployment gap, several components show negative slack coefficients (e.g., -0.191***, -0.0697***, -0.105**, -0.171*** in Table A1).
  - Using V/U relative to trend, several components show positive slack coefficients (e.g., 0.0543***, 0.0178***, 0.0208**, 0.0562*** in Table A2).
- Long-term inflation expectations enter positively and significantly in several component equations (examples: 0.239***, 0.116***, 0.355*** in Table A1; 0.236***, 0.145***, 0.210***, 0.377*** in Table A2).
- Energy and commodity-related variables (Brent crude oil growth, Dutch TTF natural gas price growth, HICP electricity price growth) frequently appear as significant explanatory variables for energy-related HICP components.
- Model fit varies substantially across components, with adjusted R-squared ranging from 0.420 to 0.998 across the reported specifications.

*Sources: Eurostat; Authors’ calculations; Tables and figures as presented in Annex I.*

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_Source: https://www.imf.org/-/media/files/publications/wp/2022/english/wpiea2022260-print-pdf.pdf_