## wpiea2025091-print-pdf

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---

### 2.1 Aggregate Data
- Data sources and construction:
  - Quarterly data on CPI inflation and GDP growth from the IMF WEO database.
  - Output gaps estimated using a univariate HP-filter.
  - Oil, gas, and coal prices from the IMF’s Primary Commodities database.
    - Global oil and gas prices use respective global indices aggregating underlying indices: oil (Brent, Dubai Fateh, WTI) and gas (American, European, Japanese).
  - Nominal effective exchange rates and energy inflation from Haver Analytics.
  - Country-level energy inflation measured using Haver Analytics’ quarterly seasonally adjusted energy HICP index.

### 2.2 Sectoral Data
- Sectoral sources and transformations:
  - Sectoral nominal and real value added for 11 sectors per country from the OECD Value Added by Activity database.
    - Supplemented with sectoral BEA data for the US and Haver Analytics data for Brazil.
  - Sectoral value added deflators constructed as the difference between quarterly nominal and real value-added growth rates.
  - Annual international input-output linkages from the OECD’s ICIO data covering 45 sectors across 76 individual countries from 1995 to 2020; remainder summarized as “rest of the world”.
  - Use of international input-output tables to capture imported energy inputs and avoid understating sectoral energy dependence.

- Technical definitions and matrices:
  - International input-output matrix denoted by Ω with elements Ωi,j indicating amount of input sector j sources from sector i.
  - Let I be total number of sectors and N number of countries; Ω has size IN x IN.
  - Technical matrix ̃Ω obtained by dividing each column of Ω by sectoral gross output Yi:
    - ̃Ω = (Y−1 1 ,....,Y−1 i ,...,Y−1 I )′ Ω where Y−1 i is a column vector with each entry equal to Y−1 i.
  - Sectoral gross output Yi computed as sum of all intermediates sector i uses plus sectoral value-added plus taxes less subsidies from ICIO tables.

- Energy dependence measures:
  - Two measures constructed:
    - Direct energy dependence: total input share of energy in sectoral gross output.
    - Total energy dependence: direct plus indirect energy dependence measured by Leontief-inverse weighted energy dependence of suppliers (captures all indirect input-output linkages).
  - Notation:
    - Let ei denote an IN x 1 vector of zeros with a one for sector i among the IN sector-country pairs.
    - Let eenergy denote an IN x 1 vector of zeros with ones for all sector-country pairs that include the energy sector.
  - Formulas:
    - γdirect i = e′energy ̃Ω ei  (1)
    - γtotal i = e′energy (I − ̃Ω)−1 ei  (2)
  - Two definitions of the energy sector used:
    - Narrow: ICIO sector C19 (coke and refined petroleum products).
    - Broad: ICIO sector C19 and sector D (utilities, technically “electricity, gas, steam, and air conditioning supply”).
  - Aggregation: sectoral energy dependence measures aggregated from 45 OECD ICIO sectors (NACE classification) to 11 sectors using the average across sectors in the sectoral mapping.
  - Missing sectoral energy dependence in recent years imputed with the most recent available value.

- Empirical correlations and operational choice:
  - Correlations of direct and total sectoral energy dependence at country-sector level in 2019:
    - Narrow energy definition: .8 (Panel a).
    - Broad energy definition: .83 (Panel b).
  - Example sector averages:
    - “manufacturing, utilities and water supply”: average total energy dependence is .34 (.05 using the narrow definition).
    - finance and insurance: average total energy dependence is .03 (.01 using the narrow definition).
  - Primary operational choice: rely primarily on total energy dependence under the broad definition unless otherwise noted.

- Sectoral price flexibility:
  - Sectoral price flexibility data from Rubbo (2023), based on firm-level BLS data feeding into the US PPI, constructing sectoral price adjustment probabilities δi.
  - Assumption: US sectoral price stickiness captures sectoral price stickiness of same sectors in other countries.

- Sample, winsorization, and summary statistics:
  - Final sample: unbalanced panel of 33 countries with country-level and sectoral price data plus sectoral energy dependence data.
    - Sample composition: 25 advanced economies and 8 emerging markets (Brazil, Bulgaria, Chile, Colombia, Costa Rica, Hungary, Poland, Romania) with data starting in 1981.
  - For most regressions, data starting in 2010 to focus on recent period.
  - Winsorization: outcomes winsorized at the 2 and 98 percentile period-by-period to mitigate large outliers.

- Table 1: Sectoral Summary Statistics (sample 2010-2024)
  - N Mean Std
  - Gross Value Added (in million USD) 19,790 17247.77 34569.61
  - Sectoral Value-Added Deflator (yoy) 20,468 3.72 14.60
  - Sectoral PPI Inflation (yoy) 8,533 3.27 13.22
  - Direct Energy Dependence 21,830 .0346 .0532
  - Indirect Energy Dependence 21,830 .0927 .0971
  - Sectoral Price Flexibility 21,830 .2566 .1492

### 3 Descriptive Statistics and Stylized Facts of the 2021-2023 Inflation Episode
- Macro-level developments:
  - Global energy prices doubled relative to 2019 during 2021 and 2022 (Figure 2 Panel B).
  - Median global energy price increase of more than 50 percent (Figure 2 Panel A).
  - Distributional features (country-level quarterly energy inflation since 1992, Haver HICP energy index, annualized rates):
    - Cross-country quarterly energy price inflation displayed much thicker tails and much lower kurtosis in 2020-2023 than previous decades.
    - Energy price inflation surged in 2021 and 2022 driving the right tail; widespread decline in inflation in 2023 contributed to thick left-tail.
  - Across energy sources:
    - 2020-2023 price movements particularly large for gas in historical comparison.
    - Distribution of oil price changes broadly in line with previous episodes; quarterly oil price surges > 100 percent (annualized) had occurred in prior decades.
    - Gas price distribution in 2020-2023 had extremely low kurtosis and thick tail; quarterly gas price changes in excess of 200 percent (annualized) occurred in 2022 after Russia’s invasion of Ukraine — unprecedented since at least early 1990s.
    - These 2022 gas price surges followed historically low gas price inflation from 2010-2019.

- Sectoral developments:
  - Heterogeneous sectoral effects driven by sectoral energy dependence and price flexibility.
  - Sectors with higher energy dependence (e.g., agriculture, manufacturing, construction) saw a surge in sectoral inflation beginning in 2021 and accelerating after Russia’s invasion of Ukraine; inflation in energy-dependent sectors peaked towards late 2022 and then declined rapidly.
  - Less-energy dependent sectors (several services) experienced more gradual but more persistent inflation with a later peak; by early 2024, sectoral inflation in less-energy intensive sectors remained elevated on average 1-2 percentage points higher than in more energy dependent sectors.
  - Patterns robust when using broader energy dependence definition including utilities and after controlling for country-time variation and country-sector time-invariant heterogeneity.

- Role of price flexibility (Figure 6 findings):
  - Sectors split by median energy dependence and within those by median price flexibility (Rubbo (2023) measure).
  - Rapid surge in sectoral inflation was considerably driven by sectors with higher energy input reliance, irrespective of price flexibility.
  - Differences in inflation between high and low price flexibility groups exist, but magnitude of energy shocks induced contemporaneous inflation increases across both groups.
  - Inflation surged more moderately but persisted longer in less price flexible sectors.

### 4 Three Key Facts on the passthrough of Energy Shocks into Inflation

- Empirical framework used across facts:
  - Local projections (Jordà, 2005) up to 12 quarters ahead with standard errors double-clustered by country and time.
  - Controls typically include two lags of inflation, output gap, change in nominal effective exchange rate, and policy rate.
  - Post-Covid dummy equals one for 2020 onward in many specifications.
  - Robustness includes two-stage IV using Känzig (2021) oil supply news shock aggregated to quarterly frequency.

#### 4.1 Fact 1: Stability of passthrough amid historical energy shocks
- Estimation equation (local projections):
  - πi,t+h = αh i + βh πenergy,i,t + γh πenergy,i,t Post t + νh Post t + θh Xi,t−1 + εi,t+h  for h = 0,1,2,3,...,12  (3)
- Identification and robustness notes:
  - Concern about simultaneous determination of energy prices and inflation via aggregate demand shocks; addressed with IV using oil supply news shocks (Känzig (2021)).
  - Output gap included to control for fiscal stimulus and energy price support influences; paper notes limitation in not providing in-depth assessment of energy support measures during the pandemic.
- Main empirical findings (country-level CPI and PPI passthrough):
  - For Advanced Economies (AEs), passthrough coefficients indicate that a 1 percentage point increase in energy inflation has a passthrough of about .05 - .07 percentage point into CPI inflation over six quarters.
  - Empirical estimates in literature oscillate between a passthrough of .02 and .08 for different periods, samples, and energy definitions.
  - Differences in passthrough over time (pre- vs post-Covid) are not statistically significant for both advanced economies and emerging and developing economies (EMDEs).
  - IV robustness: results robust in instrumental variable regressions with Känzig (2021) oil supply news shock as instrument (Figure B.8).
  - Passthrough into producer prices (PPI) is larger than for CPI, but the passthrough from energy price increases into PPI inflation has not changed significantly during the pandemic period.
- Interpretation:
  - Findings consistent with models predicting comparable energy price passthrough over time conditional on shock size (e.g., menu cost models).
  - Broadly unchanged passthrough suggests general equilibrium feedback loops (e.g., wage-price spirals) were overall not stronger or weaker than during previous episodes.
  - This does not imply passthrough from other supply shocks was comparable; supply disruptions beyond food and energy likely contributed to Covid-period inflation dynamics.

#### 4.2 Fact 2: Stable Non-linear Effects
- Theoretical motivation:
  - Models with costly price adjustment (e.g., (s,S) frameworks) imply potential non-linearities: firms may not adjust prices when shocks are small but will when shocks are large.
- Empirical specification:
  - π_CPI_{i,t+h} = α^h_i + β^h_1 π^e_{i,t−1} + β^h_2 π^{2,e}_{i,t−1} + β^h_3 π^{3,e}_{i,t−1} + γ_1 π^e_{i,t−1} × Post_t + γ_2 π^{2,e}_{i,t−1} × Post_t + γ_3 π^{3,e}_{i,t−1} × Post_t + φ^h Post_t + θ^h X_{i,t−1} + ε_{i,t+h} ∀h = 0,1,2,...,12
  - Marginal effects computed for three levels of energy price inflation:
    - i) 1 percent
    - ii) pre-Covid standard deviation of 11 percent
    - iii) 2020-2023 standard deviation of 20 percent
  - Sample starts in 2010. Post-Covid period is 2020 onward. Standard errors double clustered by country and time.
- Main empirical findings on non-linearities:
  - Advanced Economies (AEs):
    - Evidence of non-linearities in the pre-COVID period.
    - When energy inflation is 1 percent, a marginal increase in energy inflation has a passthrough into CPI inflation of about 5 percent after 4-6 quarters.
    - When energy inflation is 20 percent, a marginal increase in energy inflation is associated with a close to 10 percent passthrough.
    - At higher levels of energy inflation, inflationary effects onto CPI inflation are more persistent.
  - Emerging and Developing Economies (EMDEs):
    - No clear evidence for non-linearities in the more limited EMDEs sample.
    - The marginal effect of higher energy inflation remains relatively constant when going from 1 to 20 percent energy inflation.
  - Stability over time:
    - Little evidence for systematic strengthening of these non-linear effects in the post-COVID period.
    - Coefficients on the change post-Covid are statistically and economically insignificant.
    - Non-linearities in AEs were already present pre-Covid and did not strengthen significantly after 2020.
    - For EMDEs, no clear evidence for non-linearities in the baseline nor in the post 2020 sample.
- Additional estimation and robustness notes:
  - Individual coefficient estimates on the quadratic and cubic terms are reported in Figure B.4.
  - Figures report marginal effects for 1%, 11%, and 20% energy inflation levels with 95 % confidence bands.
  - Regressions control for Post-Covid changes and include country-time clustering; standard errors double clustered by country and time.

- Overall conclusion from Facts 1 and 2:
  - Passthrough of energy shocks into CPI and PPI inflation has been stable across pre- and post-Covid periods for AEs and EMDEs in aggregate evidence, with non-linearities present in AEs but not systematically stronger after 2020.

*Source: wpiea2025091-print-pdf*

### 2.1    Aggregate Data

### 2.1    Aggregate Data

### Aggregate data sources and construction
- Quarterly data on CPI inflation and GDP growth from the IMF WEO database.
- Output gaps estimated using a univariate HP-filter.
- Oil, gas, and coal prices from the IMF’s Primary Commodities database.
  - Global oil and gas prices use respective global indices aggregating underlying indices: oil (Brent, Dubai Fateh, WTI) and gas (American, European, Japanese).
- Nominal effective exchange rates and energy inflation from Haver Analytics.
- Country-level energy inflation measured using Haver Analytics’ quarterly seasonally adjusted energy HICP index.

---

### 2.2    Sectoral Data

### Sectoral data sources and transformations
- Sectoral nominal and real value added for 11 sectors per country from the OECD Value Added by Activity database.
  - Supplemented with sectoral BEA data for the US and Haver Analytics data for Brazil.
- Sectoral value added deflators constructed as the difference between quarterly nominal and real value-added growth rates.
- Annual international input-output linkages from the OECD’s ICIO data covering 45 sectors across 76 individual countries from 1995 to 2020; remainder summarized as “rest of the world”.
- Use of international input-output tables to capture imported energy inputs and avoid understating sectoral energy dependence.

### Technical definitions and matrices
- International input-output matrix denoted by Ω with elements Ωi,j indicating amount of input sector j sources from sector i.
- Let I be total number of sectors and N number of countries; Ω has size IN x IN.
- Technical matrix ̃Ω obtained by dividing each column of Ω by sectoral gross output Yi:
  - ̃Ω = (Y−1 1 ,....,Y−1 i ,...,Y−1 I )′ Ω where Y−1 i is a column vector with each entry equal to Y−1 i.
- Sectoral gross output Yi computed as sum of all intermediates sector i uses plus sectoral value-added plus taxes less subsidies from ICIO tables.

### Energy dependence measures
- Two measures constructed:
  - Direct energy dependence: total input share of energy in sectoral gross output.
  - Total energy dependence: direct plus indirect energy dependence measured by Leontief-inverse weighted energy dependence of suppliers (captures all indirect input-output linkages).
- Notation:
  - Let ei denote an IN x 1 vector of zeros with a one for sector i among the IN sector-country pairs.
  - Let eenergy denote an IN x 1 vector of zeros with ones for all sector-country pairs that include the energy sector.
- Formulas:
  - γdirect i = e′energy ̃Ω ei  (1)
  - γtotal i = e′energy (I − ̃Ω)−1 ei  (2)
- Two definitions of the energy sector used:
  - Narrow: ICIO sector C19 (coke and refined petroleum products).
  - Broad: ICIO sector C19 and sector D (utilities, technically “electricity, gas, steam, and air conditioning supply”).
- Aggregation: sectoral energy dependence measures aggregated from 45 OECD ICIO sectors (NACE classification) to 11 sectors using the average across sectors in the sectoral mapping.
- Missing sectoral energy dependence in recent years imputed with the most recent available value.

### Empirical correlations and choice
- Correlations of direct and total sectoral energy dependence at country-sector level in 2019:
  - Narrow energy definition: .8 (Panel a).
  - Broad energy definition: .83 (Panel b).
- Example sector averages:
  - For “manufacturing, utilities and water supply”: average total energy dependence is .34 (.05 using the narrow definition).
  - For finance and insurance: average total energy dependence is .03 (.01 using the narrow definition).
- Primary operational choice: rely primarily on total energy dependence under the broad definition unless otherwise noted.

### Sectoral price flexibility
- Sectoral price flexibility data from Rubbo (2023), based on firm-level BLS data feeding into the US PPI, constructing sectoral price adjustment probabilities δi.
- Assumption: US sectoral price stickiness captures sectoral price stickiness of same sectors in other countries.

### Sample, winsorization, and summary statistics
- Final sample: unbalanced panel of 33 countries with country-level and sectoral price data plus sectoral energy dependence data.
  - Sample composition: 25 advanced economies and 8 emerging markets (Brazil, Bulgaria, Chile, Colombia, Costa Rica, Hungary, Poland, Romania) with data starting in 1981.
- For most regressions, data starting in 2010 to focus on recent period.
- Winsorization: outcomes winsorized at the 2 and 98 percentile period-by-period to mitigate large outliers.

- Table 1: Sectoral Summary Statistics (sample 2010-2024)
  - N Mean Std
  - Gross Value Added (in million USD) 19,790 17247.77 34569.61
  - Sectoral Value-Added Deflator (yoy) 20,468 3.72 14.60
  - Sectoral PPI Inflation (yoy) 8,533 3.27 13.22
  - Direct Energy Dependence 21,830 .0346 .0532
  - Indirect Energy Dependence 21,830 .0927 .0971
  - Sectoral Price Flexibility 21,830 .2566 .1492

---

### 3    Descriptive Statistics and Stylized Facts of the 2021-2023 Inflation Episode

### 3.1    Macro-level developments
- Global energy prices doubled relative to 2019 during 2021 and 2022 (Figure 2 Panel B).
- Median global energy price increase of more than 50 percent (Figure 2 Panel A).
- Distributional features (country-level quarterly energy inflation since 1992, Haver HICP energy index, annualized rates):
  - Cross-country quarterly energy price inflation displayed much thicker tails and much lower kurtosis in 2020-2023 than previous decades.
  - Energy price inflation surged in 2021 and 2022 driving the right tail; widespread decline in inflation in 2023 contributed to thick left-tail.

- Across energy sources:
  - 2020-2023 price movements particularly large for gas in historical comparison.
  - Distribution of oil price changes broadly in line with previous episodes; quarterly oil price surges > 100 percent (annualized) had occurred in prior decades.
  - Gas price distribution in 2020-2023 had extremely low kurtosis and thick tail; quarterly gas price changes in excess of 200 percent (annualized) occurred in 2022 after Russia’s invasion of Ukraine — unprecedented since at least early 1990s.
  - These 2022 gas price surges followed historically low gas price inflation from 2010-2019.

### 3.2    Sectoral developments
- Heterogeneous sectoral effects driven by sectoral energy dependence and price flexibility.
- Sectors with higher energy dependence (e.g., agriculture, manufacturing, construction) saw a surge in sectoral inflation beginning in 2021 and accelerating after Russia’s invasion of Ukraine; inflation in energy-dependent sectors peaked towards late 2022 and then declined rapidly.
- Less-energy dependent sectors (several services) experienced more gradual but more persistent inflation with a later peak; by early 2024, sectoral inflation in less-energy intensive sectors remained elevated on average 1-2 percentage points higher than in more energy dependent sectors.
- Patterns robust when using broader energy dependence definition including utilities and after controlling for country-time variation and country-sector time-invariant heterogeneity.

- Role of price flexibility (Figure 6 findings):
  - Sectors split by median energy dependence and within those by median price flexibility (Rubbo (2023) measure).
  - Rapid surge in sectoral inflation was considerably driven by sectors with higher energy input reliance, irrespective of price flexibility.
  - Differences in inflation between high and low price flexibility groups exist, but magnitude of energy shocks induced contemporaneous inflation increases across both groups.
  - Inflation surged more moderately but persisted longer in less price flexible sectors.

---

### 4    Three Key Facts on the passthrough of Energy Shocks into Inflation

### 4.1    Fact 1: Stability of passthrough amid historical energy shocks
- Empirical approach:
  - Local projections (Jordà, 2005) estimating:
    πi,t+h = αh i + βh πenergy,i,t + γh πenergy,i,t Post t + νh Post t + θh Xi,t−1 + εi,t+h  for h = 0,1,2,3,...,12  (3)
  - πi,t+h: quarterly country-level inflation measure (CPI inflation, median inflation, PPI inflation).
  - Xi,t−1: macro controls — two lags of inflation, output gap, change in nominal effective exchange rate, and policy rate.
  - Local projections up to 12 quarters ahead; standard errors double-clustered by country and time.
  - Post-Covid dummy equals one for 2020 onward (used to capture post-Covid differences via γh).
  - Sample restricted to period since 2010 for comparability across time.
- Identification and robustness:
  - Concern: simultaneous determination of energy prices and inflation via aggregate demand shocks.
  - Robustness: two-stage instrumental variables estimation using Känzig (2021) oil supply news shock derived from high-frequency oil futures price movements (details in B.5).
  - Concern: fiscal stimulus and sectoral energy price support could bias passthrough estimates; output gap included as control; IV strategy mitigates concerns.
  - Limitation: paper does not provide in-depth assessment of energy support measures during the pandemic.
- Key empirical findings (country-level CPI and PPI passthrough):
  - For Advanced Economies (AEs), passthrough coefficients indicate that a 1 percentage point increase in energy inflation has a passthrough of about .05 - .07 percentage point into CPI inflation over six quarters.
  - Empirical estimates in literature oscillate between a passthrough of .02 and .08 for different periods, samples, and energy definitions.
  - Differences in passthrough over time (pre- vs post-Covid) are not statistically significant for both advanced economies and emerging and developing economies (EMDEs).
  - IV robustness: results robust in instrumental variable regressions with Känzig (2021) oil supply news shock as instrument (Figure B.8).
  - Passthrough into producer prices (PPI) is larger than for CPI, but the passthrough from energy price increases into PPI inflation has not changed significantly during the pandemic period.
- Interpretation:
  - Findings consistent with models predicting comparable energy price passthrough over time conditional on shock size (e.g., menu cost models).
  - Broadly unchanged passthrough suggests general equilibrium feedback loops (e.g., wage-price spirals) were overall not stronger or weaker than during previous episodes.
  - This does not imply passthrough from other supply shocks was comparable; supply disruptions beyond food and energy likely contributed to Covid-period inflation dynamics.

*Source: wpiea2025091-print-pdf - 2.1    Aggregate Data*

### 4.2    Fact 2: Stable Non-linear Effects

### 4.2    Fact 2: Stable Non-linear Effects

### Literature and theoretical motivation
- Several papers highlight the importance of non-linearities during the recent inflationary episode (e.g.  Cavallo et al. (2024), Dao et al. (2024), Gagliardone et al. (2023), Karadi et al. (2023)).
- Models incorporating costly price adjustment, such as (s,S) models (Alvarez and Neumeyer (2020), Caballero and Engel (2007), Cavallo et al. (2023), Karadi and Reiff (2019)), imply potential non-linearities in the passthrough of energy shocks into inflation.
- Theoretical mechanism: firms may not adjust prices when shocks are small due to price adjustment frictions, but may adjust when larger shocks occur.

### Empirical specification
- Estimated equation (with quadratic and cubic terms for changes in energy prices):
  - π_CPI_{i,t+h} = α^h_i + β^h_1 π^e_{i,t−1} + β^h_2 π^{2,e}_{i,t−1} + β^h_3 π^{3,e}_{i,t−1} + γ_1 π^e_{i,t−1} × Post_t + γ_2 π^{2,e}_{i,t−1} × Post_t + γ_3 π^{3,e}_{i,t−1} × Post_t + φ^h Post_t + θ^h X_{i,t−1} + ε_{i,t+h} ∀h = 0,1,2,...,12
- Marginal effects computed for three levels of energy price inflation:
  - i) 1 percent
  - ii) pre-Covid standard deviation of 11 percent
  - iii) 2020-2023 standard deviation of 20 percent
- Sample starts in 2010. Post-Covid period is 2020 onward. Standard errors are double clustered by country and time.

### Main empirical findings on non-linearities
- Advanced Economies (AEs):
  - Evidence of non-linearities in the pre-COVID period.
  - When energy inflation is 1 percent, a marginal increase in energy inflation has a passthrough into CPI inflation of about 5 percent after 4-6 quarters.
  - When energy inflation is 20 percent, a marginal increase in energy inflation is associated with a close to 10 percent passthrough.
  - At higher levels of energy inflation, inflationary effects onto CPI inflation are more persistent.
- Emerging and Developing Economies (EMDEs):
  - No clear evidence for non-linearities in the more limited EMDEs sample.
  - The marginal effect of higher energy inflation remains relatively constant when going from 1 to 20 percent energy inflation.
- Stability over time:
  - Little evidence for systematic strengthening of these non-linear effects in the post-COVID period.
  - Coefficients on the change post-Covid (blue lines) are statistically and economically insignificant.
  - Non-linearities in AEs were already present pre-Covid and did not strengthen significantly after 2020.
  - For EMDEs, no clear evidence for non-linearities in the baseline nor in the post 2020 sample.
- Overall conclusion for Fact 2:
  - Confirms stable inflation passthrough both in the pre- and post-Covid period.

### Additional notes on estimation and robustness
- Individual coefficient estimates on the quadratic and cubic terms are reported in Figure B.4.
- Figures report marginal effects for 1%, 11%, and 20% energy inflation levels with 95 % confidence bands.
- Regressions control for Post-Covid changes and include country-time clustering; standard errors are double clustered by country and time.

*Source: wpiea2025091-print-pdf - 4.2    Fact 2: Stable Non-linear Effects*

### References

### References

### Key literature themes
- Extensive literature on energy price pass-through, inflation dynamics, and production networks covering:
  - How changes in retail energy prices affect inflation (Abdallah and Kpodar (2023)).
  - The impact of the war in Ukraine on euro area energy markets and gas price shocks (Adolfsen et al. (2022); Adolfsen et al. (2024)).
  - Inflation and GDP dynamics in production networks and relative-price changes as aggregate supply shocks (Afrouzi and Bhattarai (2023); Afrouzi, Bhattarai, and Wu (2024)).
  - Sectoral shocks, market integration, and the role of natural gas (Albrizio et al. (2023); Alessandri and Gazzani (2025)).
  - Pass-through of oil and energy prices to inflation across advanced and developing economies (Choi et al. (2018); Clark and Terry (2010); Casoli, Manera, and Valenti (2024)).
  - Price setting, menu costs, and sectoral price rigidity (Golosov and Lucas Jr (2007); Karadi et al. (2023); Karadi and Reiff (2019); Pasten, Schoenle, and Weber (2024); Rubbo (2023)).
  - Monetary policy lags, wage–price spirals, and inflation expectation channels (Aruoba and Drechsel (2024); Alvarez et al. (2024); Boeck, Zörner, and Nationalbank (2025); Patzelt and Reis (2024)).
  - Identification of exogenous oil supply shocks using high-frequency oil futures around OPEC announcements (Kränzig (K̈anzig) (2021)).
- Empirical and methodological sources cited include NBER Working Papers, IMF Working Papers, BIS Working Papers, ECB Occasional Papers, Brookings Papers, American Economic Review, Econometrica, Journal of Monetary Economics, Journal of International Money and Finance, Journal of Political Economy, and others.

### Data (Annex A)
- Aggregate data:
  - GDP and CPI inflation sourced from the World Economic Outlook (WEO) database.
  - Output gap constructed using a univariate HP filter.
  - Commodity price indices obtained from the IMF Primary Commodity Prices System Database; indices are weighted averages of select commodity price indices based on benchmark prices.
  - Central bank policy rates from the Bank for International Settlements (BIS); end-of-period monthly rates selected (for the first quarter, the March observation is used) and converted into quarterly data.
- Sectoral data:
  - Uses the OECD 11-sector classification as the primary sector classification, integrating Gross Value Added (GVA) data from the OECD.
  - Classification adheres to ISIC Rev. 4 and is mapped to NACE Rev.2 at the section level.
  - Producer Price Index (PPI) data incorporated from Eurostat.
  - For Brazil and the US (missing in OECD data), merged data from Haver Analytics (Brazil) and BEA (US); BEA sectors manually mapped and aggregated into OECD categories to incorporate US value added data from BEA.

### Robustness Checks (Annex B)
- Sectoral energy dependence measures (B.1):
  - Measures of direct and total sectoral energy dependence remain highly correlated using the full 1995-2020 sample.
  - Sectoral energy dependence measures are residualized on country and time fixed effects; correlation remains high despite expectation that fixed effects should reduce correlation.
  - Energy sector definitions used: Panel a) ICIO sector C19; Panel b) ICIO sectors C19 and D. Data covers 1995-2020.
- Sectoral energy inflation trends (B.2):
  - Patterns in Figure 5 are robust when expanding energy definition to include sector D - utilities.
  - Inflation in more energy dependent sectors rose significantly faster than in less energy dependent sectors; passthrough into less energy dependent sectors occurred gradually; sectoral inflation was more persistent in less energy dependent sectors.
  - Data: median quarterly inflation by sector using sectoral value-added deflators for a panel of 36 countries and 11 sectors per country.
- Role of energy dependence vs. price flexibility (B.2, Figure B.3):
  - Sectoral splits by median energy dependence and median price flexibility show higher inflation for high energy dependence sectors and heterogeneity based on price flexibility measure from Rubbo (2023).
  - Dashed line indicates 2021Q4, the last quarter before the Russian invasion of Ukraine. Quarterly sectoral inflation reported in annualized rates and collapsed using median across sectors.
- Country-level local projection regressions (B.3):
  - Non-linearities (B.3.1): In Advanced Economies (AEs), the quadratic term on energy inflation is consistently positive and statistically significant; in EMDEs there is no clear evidence for non-linearities with wide confidence bands and small point estimates. Sample starts in 2010. Standard errors double clustered by country and time.
  - Median inflation (B.3.2): Median CPI inflation used as dependent variable for 18 countries (median CPI inflation available for 18 countries). No clear evidence for systematic strengthening of passthrough into median CPI inflation; smaller sample implies less precise estimates and wider confidence bands. Regressions use sample from 2010 onward; Post-Covid dummy equals one for 2020 onward. Controls include two lags of median CPI inflation, output gap, change in nominal effective exchange rate, and policy rate. Standard errors double clustered by time and country.
- Sectoral local projection regressions (B.4):
  - Robust to coarser energy definition using only ICIO sector "C19 - coke and refined petroleum products"; estimated coefficients larger due to smaller mean of interaction variable but marginal effects comparable. Regressions include country-sector and country-time fixed effects. Sample starts in 2010. Standard errors double-clustered by country-sector and time.
  - Triple interactions with median splits on energy dependence and price flexibility show sectors with higher energy dependence have higher passthrough if also higher price flexibility, and vice versa.
- Local Projections using Instrumental Variables (B.5):
  - Instruments: oil supply news shocks from K̈anzig (2021) aggregated to quarterly frequency by taking unweighted quarterly averages.
  - Aggregate regressions (B.5.1): LP-IV passthrough of energy inflation into CPI inflation is remarkably similar across pre-Covid (2010-2019) and post-Covid (2020 - 2023) periods, confirming main findings. Regressions include country-sector fixed effects. Sample starts in 2010. Standard errors double-clustered by country-sector and time.
  - Sectoral regressions (B.5.2): Instruments are strong with Kleibergen and Paap (2006) test statistics consistently above 10 (typically between 10 and 50). LP-IV confirms that more energy dependent sectors have greater inflation passthrough. Regressions include country-sector fixed effects; sample starts in 2010. Standard errors double-clustered by country-sector and time.
  - Additional LP-IV results: Sectors with greater sectoral price flexibility have greater passthrough; passthrough larger for overall energy prices than oil prices only, implying importance of considering energy beyond oil. Triple-interaction IVs show higher energy dependence and higher price flexibility linked to higher passthrough but without statistical significance for energy overall in some specifications.

### Sectoral Passthrough of Oil Prices (Annex C)
- Heterogeneity in sectoral passthrough of oil price changes (Figure C.12):
  - Local projection double interaction coefficients on oil inflation with sectoral oil dependence are statistically and economically significant.
  - Oil dependence measured as direct input share of oil (sector C19) in Panel a) and total input share of oil based on Leontief inverse in Panel b).
  - Regressions include country-sector and country-time fixed effects. Sample starts in 2010. Standard errors double-clustered by country-sector and time.
- Key comparative finding:
  - The impact of oil price changes onto sectoral inflation is similar for the direct input share, suggesting comparable passthrough to energy inflation.
  - There is much less network amplification for oil: estimated coefficients in Panel b) are substantially smaller for oil price changes compared to total energy price changes. This aligns with Miranda-Pinto et al. (2024) showing oil is used relatively downstream in production networks, limiting network amplification.

### Energy Dependence Event Studies (Annex D)
- Event study specification (equation (8)):
  - π_{i,j,t} = α_{i,j} + α_{i,t} + Σ_{τ=2018Q1; τ≠2020Q3}^{2023Q3} β_{τ} s_{i,j} + ε_{i,j,t}
  - Dependent variable: sectoral inflation in sector j in country i in quarter t, measured as sectoral value-added deflator (also PPI in robustness checks).
  - α_{i,j} are country-sector fixed effects; α_{i,t} are country-time fixed effects.
  - s_{i,j} is a dummy measuring sectoral energy dependence or sectoral price flexibility.
  - Sample for event studies starts in 2018Q1; coefficient in 2020Q3 normalized to zero.
- Event study results (D.1):
  - Energy dependence (D.1.1): No notable pre-Covid differences, but more energy-dependent sectors started surging in 2021 relative to less energy-dependent sectors. As energy shocks moderated, differences narrowed; by 2023 sectoral inflation in more energy-dependent sectors was lower than in less energy-dependent sectors. Standard errors double clustered by time and country-sector.
  - Price flexibility (D.1.2): Comparable pattern when splitting sectors by sectoral price flexibility; sectoral price flexibility and energy dependence were not perfect proxies during the recent inflation period.
- Robustness checks (D.2):
  - Event studies re-estimated using Eurostat PPI data (covers 8/11 sectors; missing sectors: "Financial and insurance activities", "education and related services", and "Other service activities"). Figures D.15 and D.16 confirm previous evidence from value-added deflators.
  - Results are consistent across value-added deflators and Eurostat PPI where available.

*The Energy Origins of the Global Inflation Surge Working Paper No. WP/2025/091*

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_Source: https://www.imf.org/-/media/files/publications/wp/2025/english/wpiea2025091-print-pdf.pdf_