## 1. Gas shortages if Gas is Shut Off on June 1, 2022

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### Executive findings and headline projections
- Complete and permanent shutoff of Russian natural gas supplies to Europe starting June 1, 2022 could produce gas shortages of:
  - 9 percent of national consumption in the second half of 2022
  - 10 percent in 2023
  - 4 percent in 2024
- Shortages would likely fall on firms, given legal protections on households.
- Combined channels of impact reduce German GDP relative to baseline by:
  - about 1.5 percent in 2022
  - 2.7 percent in 2023
  - 0.4 percent in 2024
- Associated rise in wholesale gas prices could increase inflation by about 2 percentage points on average in 2022 and 2023.
- No output “catch-up” gains are projected in subsequent years from deferred economic activity.

### Germany’s exposure and recent supply developments
- Gas shares and imports:
  - Gas accounts for just over a quarter of Germany’s energy use; almost all is imported.
  - As of end-April 2022, about 35 percent of Germany’s natural gas imports (33 billion cubic meters (bcm) a year) came from Russia.
- June 2022 flow reductions:
  - Russia reduced flows through Nord Stream 1 by around 60 percent.
  - Russian gas flows into Germany at Waidhaus on the Czech border fell some 69 percent.
  - If these cuts persist, they amount to 56 bcm a year.
- Sanctions and supplier disruptions:
  - Russia sanctioned Gazprom Germania on May 11, 2022; its imports were about 4 percent of German gas imports (media reports).
  - Shell’s German subsidiary reportedly denied further gas supplies in May, amounting to some 1 percent of all German gas imports.
- Wholesale gas prices in 2022Q2 ranged from US$ 16.7 per MWh in Louisiana, USA to US$110 per MWh in the Netherlands.

### Policy responses and infrastructure actions under way
- Government target: reduce the share of gas imported from Russia to 10 percent by mid-2024.
- Storage and procurement:
  - Operators required to fill leased storage space up to 90 percent of capacity by November 1, 2022, or risk forfeiture to the government.
  - Government bought 1 bcm of gas in March 2022.
  - Credit lines to the market area manager (THE) through KfW to finance further purchases.
- Import diversification and infrastructure:
  - Record-high imports through neighboring countries using reverse pipeline flows and other measures.
  - Leased four FSRUs; planned domestic LNG terminals with capacities:
    - Wilhelmshaven: 7.5 bcm per year (first terminal expected operational by end of the year)
    - Brunsbüttel: 5 bcm per year (expected operational in early 2023)
    - Two remaining FSRUs each with capacities of 5 bcm per year expected operational by 2024.
- Other measures:
  - Proposed laws to enable reactivation of coal-fired power plants until March 2024 to save gas.
  - Proposed legal amendments to allow government control of critical energy infrastructure and to authorize gas suppliers to pass on higher prices to customers on fixed-price contracts.
  - Government assessment that nuclear power cannot help offset gas shortages.

### Range of estimates from recent studies and drivers of differences
- Recent study headline comparisons:
  - ECB (2022): gas loss 10 → GDP loss 0.7 percent
  - OECD (2022): gas loss 20 → GDP loss 0.9 percent
  - Bachmann et al. (2022): GDP losses ranging from 0.2–2.2 percent depending on model specification
  - Schnittker et al. (2022): gas loss 9 → GDP loss 1.5 percent; gas loss 36 → GDP loss 3.4 percent
  - German Council of Economic Experts (March 2022): gas loss 30 → GDP loss 2.0 percent
  - Bundesbank (April 2022): scenarios include 40 → 5.0 percent in their April presentation
  - Bundesbank (June 2022): scenarios include 31 in winter '22/'23 → 1.5 in '22, 6.75 in '23; 11 in winter '23/'24 → 4.5 in '24 (as stated in source table)
  - Di Bella et al. (2022): with frictions 3 → 0.4 percent; without frictions 3 → (value indicated as 3 in table)
- Key drivers of cross-study differences:
  - inclusion/exclusion of demand-side amplification (sticky prices, unemployment)
  - shock size, composition and duration assumptions
  - assumptions on replacement and inventories
  - approach to rationing across households, power sector, and firms
  - substitutability of gas with other inputs (elasticities)

### Methodology and scenario design
- Projection period: monthly gas flows between June 1, 2022 and end-2027, using information as of June 22, 2022.
- Two scenarios:
  - Baseline: flows continue at current pace and inventories are accumulated in advance of winter 2022/2023.
  - Adverse: flows from Russia to the European Union stop on June 1.
- Modeled variables: German gas consumption, gas inventories, and net gas imports from Russia and non-Russian sources.
- Core assumptions (selected):
  - Baseline: Russian imports account for 35 percent of German consumption in April and May 2022.
  - To capture June curtailment through Nord Stream 1 and Waidhaus, Russian import quantities are scaled down by 45 percent in June and by 60 percent thereafter.
  - Baseline: Germany slowly reduces its Russian import share to zero by end-2024.
  - Net non-Russian gas imports are 5.1 bcm a month.
  - Baseline average daily wholesale natural gas prices in Germany: US$ 104 a MWh in 2022, US$ 83 in 2023, US$ 64 in 2024 and US$ 49 in 2025.
  - Infrastructure expansion (FSRUs) come online in December 2022 (7.5 bcm/year), February 2023 (5 bcm/year), September 2023 (5 bcm/year) and February 2024 (5 bcm/year).
  - Gas-to-coal switching: assumed substitution around 5 GW of power capacity, or 4.5 bcm of gas a year; government extension assumed from March 2024 to March 2027 in the baseline.
  - Baseline gas consumption follows the last five years (90.5 bcm over 2017-2021), adjusted down by about 1.8 bcm a year to reflect 2022 import price increases.
  - Germany has about 24.8 bcm of gas storage capacity, just over two months’ winter consumption (22 bcm).
  - Adverse inventories: drawn down with perfect foresight and always maintain 10 percent of capacity as ‘base’ gas.
  - Renewables increase equivalent to about 2.7 bcm a year; phasing out of nuclear reactors equivalent to about 3.5 bcm a year.

### Adverse scenario: estimated gas shortages (Russian gas shutoff on June 1, 2022)
- Projected shortages (bcm):
  - Between June and December 2022: 3.9 bcm
  - 2023: 8.9 bcm
  - 2024: 3.4 bcm
  - 2025: 0.9 bcm
  - 2026: 0.4 bcm
  - 2027: 0.6 bcm
- Shortage as percent of national consumption in period:
  - Jun-Dec 2022: 9
  - 2023: 10
  - 2024: 4
  - 2025: 1.0
  - 2026: 0.5
  - 2027: 0.7
- Replacement ratio: 44 for Jun-Dec 2022, and "< 0" for subsequent periods shown.
- National consumption reductions relative to baseline:
  - June–December 2022: some 9 percent
  - Jan–Dec 2023: 10 percent
  - Jan–Dec 2024: 4 percent
- Monthly winter contractions (concentrated in winters) with inventories smoothing:
  - National consumption would have to contract by 10-20 percent each month between November 2022 and March 2023, and similar contractions in winter 2023/24.
- Demand compression by protection regime (percent of non-protected consumption in period):
  - If only households (HHs) are protected:
    - Jun-Dec 2022: 13
    - 2023: 14
    - 2024: 6
    - 2025: 1.5
    - 2026: 0.7
    - 2027: 1.0
  - If HHs and energy transformation are protected:
    - Jun-Dec 2022: 19
    - 2023: 22
    - 2024: 8
    - 2025: 2.3
    - 2026: 1.1
    - 2027: 1.6
- Cumulative demand compression (% of cumulative non-protected consumption) from Jun '22 until Dec of successive years:
  - If only HHs are protected: Dec 2022: 13; Dec 2023: 14; Dec 2024: 11; Dec 2025: 8; Dec 2026: 6; Dec 2027: 5
  - If HHs and energy transformation are protected: Dec 2022: 19; Dec 2023: 21; Dec 2024: 16; Dec 2025: 12; Dec 2026: 10; Dec 2027: 8

### Reasons why these shortage estimates may be smaller than other studies
- Germany reduced dependence on Russian gas over time.
- Differences with other analyses:
  - Similar to Bundesbank (2022b) for winter 2022/23.
  - Larger than Bundesbank for winter 2023/24 in this analysis (~20 percent of unprotected sectors vs. Bundesbank 11 percent).
  - Smaller than Bundesbank (2022a) and GCEE (2022) because this analysis starts from a lower and more recent share of Russian gas and allows for release of gas reserves.
  - Monthly shortages here do not exceed 21 percent of consumption in any one month, while Joint Economic Forecast (2022) median reaches 60 percent in October 2022.

### Uncertainty and upside risks to shortages
- Infrastructure constraints and cross-border bottlenecks could increase shortages (ENTSOG (2022) notes significant bottlenecks).
- Germany may need to supply neighbors in need; winter shortage in neighboring countries could amount to 9 bcm under cited estimates.
- Colder or longer winters could increase consumption by up to 3.1 bcm a year.
- If shutoff leads to further increases in imported and retail gas prices, households might reduce demand by up to 0.8 bcm a year more than assumed.
- Shortages may occur through price-induced demand compression or through non-clearing markets caused by infrastructure bottlenecks; both included in analysis.

### Approach to estimating GDP impacts
- Three mechanisms captured:
  - Production cuts due to lack of gas (direct impacts).
  - Downstream amplification through intermediate products (second-round effects).
  - Increases in uncertainty leading to broader economic contraction.
- Two-model approach:
  - Model 1: sectoral firm production model with 17 sectors, representative firm per sector, constant returns to scale, nested production function (Cobb–Douglas combining energy and intermediate inputs; CES combining gas, oil, coal, renewables into energy). Includes input–output links to capture one round of downstream amplification.
  - Model 2: summarized effect of higher uncertainty on economic activity based on historical relationships.
- Elasticity of substitution between gas and other energy:
  - June–December 2022 period: elasticity = 0.1
  - June 2022–December 2027 period: elasticity = 0.4
- Second-round impacts assumed to materialize 6 months after direct impact.
- Model is static and applied over different scenario horizons.

### Estimated GDP impacts: direct, second-round, uncertainty, and combined
- Direct and second-round effects examples:
  - 19 percent contraction in firms’ gas consumption between June and December 2022 directly reduces GDP by 0.9 percent relative to baseline in this period.
  - Second-round effects from Jun–Dec 2022 reduce GDP by a further 0.9 percent (felt Dec 2022–Jun 2023).
- Annualized direct + second-round impacts:
  - GDP lower than baseline by 0.7 percent in 2022, 1.8 percent in 2023, and 0.4 percent in 2024.
- Uncertainty channel:
  - One-standard-deviation increase in uncertainty could lower GDP by about 1 percent relative to trend up to two years after the shock.
  - Assumed uncertainty shock reduces GDP by 0.8 percent in 2022, 0.9 percent in 2023 and 0.1 percent in 2024.
- Combined effects:
  - GDP reduced by 1.5 percent in 2022, 2.7 percent in 2023 and 0.4 percent in 2024.
  - Cumulative GDP loss between 2022 and 2024 is 4.8 percent of 2020 GDP.
- Alternate scenario where energy transformation activities help bear shortages:
  - GDP would be 1.2 percent lower than baseline in 2022, 1.9 percent lower in 2023, and 0.4 percent lower in 2024.

### Table 3 selected numeric findings (expanded windows and yearly effects)
- Expanding windows, required demand compression (percent of consumption) if only households protected: 13, 14, 11, 8, 6, 5 (Dec '22, Dec '23, Dec '24, Dec '25, Dec '26, Dec '27).
- Expanding windows, required demand compression (percent) if households and transformation protected: 19, 21, 16, 12, 10, 8.
- Elasticity of substitution across horizons: 0.10, 0.12, 0.16, 0.20, 0.30, 0.40.
- First-round impact on cumulative GDP (percent deviation from baseline) if households and transformation protected: -0.9, -0.9, -0.4, -0.2, -0.1, -0.1 (to Dec '22, Dec '23, Dec '24, Dec '25, Dec '26, Dec '27).
- Second-round impact on GDP in 6 months' time (percent deviation) if households and transformation protected: -0.9, -0.9, -0.4, -0.2, -0.1, -0.1.
- Yearly combined impacts (Real GDP level percent deviation from baseline) if households and transformation protected:
  - 2021 0.0; 2022 -1.5; 2023 -2.7; 2024 -0.4; 2025 0.0; 2026 0.0; 2027 0.0.

### The importance of rationing design and distributional choices
- Rationing choices crucially affect economic impacts:
  - Protecting households and power sector reduces immediate hardship but increases production losses and downstream propagation.
  - Sharing shortages with households could reduce GDP losses but implies direct household welfare costs.
- Rationing experiments (June–Dec 2022; households and energy protected baseline: 19 percent cut in unprotected sectors):
  - "Naïve" rationing (equal 19 percent cuts): direct impact 0.88; second-round impact 0.88.
  - "GDP-loss minimizing" (households and energy protected): direct impact 0.31; second-round impact 0.32.
  - Allowing households to share burden (households’ gas consumption cut by 10 percent) reduces direct GDP losses from 0.31 to 0.21 and second-round losses from 0.32 to 0.20.
- Sectors prioritized for rationing in GDP-minimizing solutions include: non-metallic minerals; iron, steel and non-ferrous metals; paper, pulp and printing; chemicals and petrochemicals; food, beverages and tobacco.
- Assumptions in rationing experiments: no sector cut by more than 50 percent; results use 2021 OECD Inter-Country Input—Output Table.

### International price and inflation effects
- International price shocks:
  - Albrizio et al. (forthcoming) estimate Netherlands TTF 2022 average could be 110 to 370 percent higher than 2022:Q1 depending on demand elasticities and LNG rerouting feasibility.
  - Netherlands TTF more than doubled right after February 24; at end of May remained about 15 percent higher than February.
- Empirical passthrough findings (sample 1996Q1 to 2022Q1):
  - Passthrough from international to domestic gas prices averages around 0.02 over 2-3 quarters in normal times, rising to 0.1 following large increases (fivefold).
  - Contemporaneous passthrough of international oil price averages 0.2 in normal times and jumps to 0.3 in a price surge.
  - Passthrough from HICP energy inflation to core inflation negligible in normal times, reaching 0.05 contemporaneously following large energy price jumps.
  - Gas pass-through to consumer prices is more lagged (about 12 months) due to contract structures.
- Inflation projections under gas shutoff scenarios (deviation from baseline annual inflation):
  - If international gas prices rise by 110 percent and last 12 months:
    - German inflation about ¾ of a percentage point higher in 2022.
    - German inflation about 1¼ percentage points higher in 2023.
  - If international gas prices rise by 370 percent and last 12 months:
    - Inflation could be about 2 percentage points higher in 2022.
    - Inflation could be about 3.5 percentage points higher in 2023.
  - If government permits contemporaneous passthrough and international gas prices rise by 370 percent:
    - Inflation could be 3¼ percentage points higher than without the shutoff in both 2022 and 2023.
- Caveat: international gas price increases considered have no precedent prior to 2021; passthrough and consumer inflation rates could be greater than these estimates.

### Policy implications and recommended measures
- Enhance energy security:
  - Diversify suppliers and expand LNG import capacity (FSRUs and domestic terminals).
  - Explore additional gas from the United States, Norway and Qatar.
  - Cooperate with EU and neighbors; REPowerEU noted as important.
- Storage, procurement and supply resilience:
  - Fill gas storage facilities (government target: 90 percent of leased capacity by Nov 1, 2022).
  - Auction mechanism to compensate firms for reducing gas consumption to help fill storages.
  - Monitor financial health of energy companies; provide liquidity support (KfW loans, loan guarantees).
- Short-term supply adjustments and generation:
  - Reactivate coal-fired power plants temporarily to spare gas for non-electricity uses.
  - Ensure gas-fired plants cut gas consumption if competing with coal plants.
- Demand-side policies and welfare support:
  - Energy-saving campaigns for households, firms, public sector and non-profits.
  - Programs to exchange gas heaters for heat pumps.
  - Targeted income support or one-off energy relief payments for vulnerable households if prices rise.
  - Consider rebates or discounts on gas bills to incentivize household gas savings.
- Infrastructure and information:
  - Publish clear diagnosis of infrastructure gaps under a full shutoff; address odorization differences and consider financing deodorization plant.
  - Improve consumer access to up-to-date online gas usage statistics; wider deployment of smart meters.
  - Federal Network Agency could act as central authority to manage day-to-day rationing policy; publish regular gas projections and dashboards.
- Rationing policy design:
  - Prioritize rationing schemes that minimize overall output losses, consider sharing some burden with households and targeting cuts toward more gas-intensive and downstream firms.
  - Balance economic analysis with social, environmental, health, technical and legal considerations.
- Renewable acceleration:
  - “Easter package” aims to raise target to 80 percent of electricity demand met with renewables by 2030 (from 42 percent in 2021).
  - Measures include establishing overriding public interest in renewables, increase public tenders to 22 GW solar and 10 GW onshore wind a year.

### Production model and aggregation mechanics (selected technical points)
- Representative firm production function: Yk = Zk Ek^αE k Π_{j=1}^J X_{jk}^{α_{jk}}, with energy aggregated via CES:
  - Ek = (ω egas_k^{(ε−1)/ε} + (1−ω) eoth_k^{(ε−1)/ε})^{ε/(ε−1)}.
- Second-order approximation yields dlnEk ≈ ω dln egas_k + 1/2 (1−1/ε) ω(1−ω) (dln egas_k)^2.
- Cobb-Douglas property implies sectoral expenditure share on intermediate goods invariant; dlnXjk = dlnYj.
- Input-output linkage aggregation uses Leontief inverse L = (I − A)−1; second-round impacts computed as (I − A′)−1 αE dlnE.
- Aggregation to GDP uses value-added shares λk with dlnGDPd = Σ λk dlnYkd and dlnGDPs = Σ λk dlnYks.

*International Monetary Fund, "THE ECONOMIC IMPACTS ON GERMANY OF A POTENTIAL RUSSIAN GAS SHUTOFF", June 30, 2022.*

### 1. Gas shortages if Gas is Shut Off on June 1, 2022 ______________________________________________ 10

### 1. Gas shortages if Gas is Shut Off on June 1, 2022

### Executive findings and headline projections
- A complete and permanent shutoff of Russian natural gas supplies to Europe, starting on June 1, 2022, could produce gas shortages of:
  - 9 percent of national consumption in the second half of 2022
  - 10 percent in 2023
  - 4 percent in 2024
- These shortages would likely fall on firms, given legal protections on households.
- Combined channels of impact (reduced gas on production, reduced supply of intermediate goods and services to downstream firms, and reduced economic activity due to rising uncertainty) reduce German GDP relative to baseline by:
  - about 1.5 percent in 2022
  - 2.7 percent in 2023
  - 0.4 percent in 2024
- The associated rise in wholesale gas prices could increase inflation by about 2 percentage points on average in 2022 and 2023.
- No output “catch-up” gains are projected in subsequent years from deferred economic activity.

### Germany’s exposure and recent supply developments
- Gas accounts for just over a quarter of Germany’s energy use; almost all is imported.
- As of end-April 2022, about 35 percent of Germany’s natural gas imports (33 billion cubic meters (bcm) a year) came from Russia.
- In June 2022 Russia reduced flows through Nord Stream 1 by around 60 percent, and Russian gas flows into Germany at Waidhaus on the Czech border fell some 69 percent. If these cuts persist, they will amount to 56 bcm a year.
- Russia sanctioned Gazprom Germania on May 11, 2022; its imports were about 4 percent of German gas imports (media reports). Shell’s German subsidiary was reportedly denied further gas supplies in May, amounting to some 1 percent of all German gas imports.
- In 2022Q2 wholesale gas prices ranged from US$ 16.7 per MWh in Louisiana, USA to US$110 per MWh in the Netherlands.

### Policy responses and infrastructure actions under way
- Government target: reduce the share of gas imported from Russia to 10 percent by mid-2024.
- Storage and procurement measures:
  - Operators required to fill leased storage space up to 90 percent of capacity by November 1, 2022, or risk forfeiture to the government, which would fill it by tendering.
  - Government bought 1 bcm of gas in March 2022.
  - Credit lines to the market area manager (THE) through KfW to finance further purchases.
- Import diversification and infrastructure:
  - Record-high imports through neighboring countries (Belgium, the Netherlands) using reverse pipeline flows and other measures that do not require new infrastructure.
  - Leased four FSRUs; first domestic LNG terminals planned. Planned terminal capacities:
    - Wilhelmshaven: 7.5 bcm per year (first terminal expected operational by end of the year)
    - Brunsbüttel: 5 bcm per year (expected operational in early 2023)
    - Two remaining FSRUs each with capacities of 5 bcm per year expected operational by 2024.
- Other measures:
  - Proposed laws to enable reactivation of coal-fired power plants until March 2024 to save gas used in electricity generation.
  - Proposed legal amendments to allow government control of critical energy infrastructure and to authorize gas suppliers to pass on higher prices to customers on fixed-price contracts to ensure supplier solvency.
  - Government assessment that nuclear power cannot help offset gas shortages.

### Range of estimates from recent studies and drivers of differences
- Recent studies estimate wide-ranging economic impacts for Germany:
  - Impacts in 2022 of up to 5 percent of GDP in the first year, and up to 2.6 percentage points’ higher inflation in the same year.
- Key factors explaining differences across studies:
  - Comprehensiveness of transmission channels (supply-side only vs. inclusion of demand-side amplification such as sticky prices and unemployment).
  - Shock size, composition and duration (different assumed shares of Russian dependence, whether disruption affects pipelines or all exports, whether disruption is limited to gas or includes other trade).
  - Assumptions on replacement and inventories (some studies assume no replacement, others that a share can be replaced or that shortages only emerge after inventories are exhausted).
  - Approach to rationing across households, the power sector, and other firms (many studies assume households are protected and firms bear full quantity rationing; some studies consider more targeted rationing to limit output losses).
  - Substitutability of gas with other inputs (higher substitutability reduces output losses; short-term analyses that assume low substitutability find larger impacts).
- Examples and model comparisons (selected results reported in source):
  - ECB (2022): gas loss 10 → GDP loss 0.7 percent
  - OECD (2022): gas loss 20 → GDP loss 0.9 percent
  - Bachmann et al. (2022): various model approaches with GDP losses ranging from 0.2–2.2 percent depending on model specification
  - Schnittker et al. (2022): gas loss 9 → GDP loss 1.5 percent; gas loss 36 → GDP loss 3.4 percent
  - German Council of Economic Experts (March 2022): gas loss 30 → GDP loss 2.0 percent
  - Bundesbank (April 2022): various scenarios reported (e.g., 40 → 5.0 percent in their April presentation)
  - Bundesbank (June 2022): scenarios including 31 in winter '22/'23 → 1.5 in '22, 6.75 in '23; 11 in winter '23/'24 → 4.5 in '24 (as stated in source table)
  - Di Bella et al. (2022): with frictions 3 → 0.4 percent; without frictions 3 → (value indicated as 3 in table but context denotes methodological differences)
- Staff finding on inflation pass-through: oil prices typically pass through to German consumer prices within the year, while longer contracts mean gas prices take about 12 months to do so. However, rationing would prevent energy prices from matching supply with demand and could break usual pass-through patterns.

### Rationing, distributional choices, and policy tradeoffs
- Rationing decisions crucially affect economic impacts:
  - The national plan for a gas emergency and several studies assume household protection from quantity rationing, concentrating the burden on firms.
  - Targeted rationing that places stricter cuts on more gas-intensive sectors (e.g., steel and chemicals) and milder rationing elsewhere could save some economic output.
  - Protection of the power generation sector from rationing depends on power generators’ ability to switch fuels and on the country’s ability to reduce electricity or heat demand.
- Tradeoffs:
  - Protecting households and the power sector reduces immediate hardship but increases production losses and downstream propagation through input–output linkages.
  - Sharing shortages with households could reduce GDP losses but implies direct welfare costs to households.

### Policy implications emphasized
- The sizable economic impacts underscore the need to enhance German energy security.
- Important policy responses include:
  - Diversifying suppliers and expanding LNG import capacity (FSRUs and domestic terminals).
  - Filling storage facilities (90 percent by November 1, 2022 target for leased space).
  - Expanding crisis management tools, including legal powers over critical infrastructure and mechanisms to preserve supplier solvency.
  - Using alternative electricity generation (e.g., temporary reactivation of coal-fired plants) to spare gas for non-electricity uses.
  - Prioritizing rationing schemes that minimize overall output losses, including consideration of sharing some burden with households and targeting cuts toward more gas-intensive and downstream firms.

*International Monetary Fund, "THE ECONOMIC IMPACTS ON GERMANY OF A POTENTIAL RUSSIAN GAS SHUTOFF", June 30, 2022.*

### 6. We calculate the shortages due to the shutoff of Russian gas supplies as the

### 6. We calculate the shortages due to the shutoff of Russian gas supplies as the

### Methodology and scenario design
- Projection period: monthly gas flows between June 1, 2022 and end-2027, using information as of June 22, 2022.
- Two scenarios:
  - Baseline: flows continue at their current pace and inventories are accumulated in advance of the winter 2022/2023.
  - Adverse: flows from Russia to the European Union stop on June 1.
- Modeled variables: German gas consumption, gas inventories, and net gas imports from Russia and non-Russian sources.
- Net (not gross) gas imports are modeled for parsimony.

### Core assumptions
- LNG and Russian imports:
  - Baseline: Russian imports account for 35 percent of German consumption in April and May 2022.
  - To capture June 2022 curtailment through Nord Stream 1 and Waidhaus, Russian import quantities are scaled down by 45 percent in June and by 60 percent thereafter.
  - Baseline: Germany slowly reduces its Russian import share to zero by end-2024.
  - Net non-Russian gas imports are 5.1 bcm a month (difference between observed net gas imports 8.1 bcm a month and estimated Russia portion 3 bcm between January and May 2022).
  - Baseline average daily wholesale natural gas prices in Germany: US$ 104 a MWh in 2022, US$ 83 in 2023, US$ 64 in 2024 and US$ 49 in 2025.
- Infrastructure expansion (FSRUs):
  - Come online in December 2022 (7.5 bcm/year), February 2023 (5 bcm/year), September 2023 (5 bcm/year) and February 2024 (5 bcm/year).
- Gas-to-coal switching:
  - Baseline: whole grid and capacity reserves of coal-fired power stations activated from July 2022.
  - Assumed substitution: around 5 GW of power capacity, or 4.5 bcm of gas a year.
  - Government extension assumed from March 2024 to March 2027 in the baseline to prevent gas shortages.
  - Adverse scenario makes same assumptions for coal-fired power generation as baseline.
- Gas consumption:
  - Baseline follows average levels and seasonal pattern of the last five years (90.5 bcm over 2017-2021), adjusted down by about 1.8 bcm a year to reflect 2022 import price increases.
  - Temperatures assumed in line with their recent averages.
  - In the adverse scenario, consumption is calculated as a residual.
- Inventories:
  - Germany has about 24.8 bcm of gas storage capacity, just over two months’ winter consumption (22 bcm).
  - Baseline: inventories accumulate in summers and are drawn down in winters.
  - Adverse scenario: government removes all requirements to fill gas storage facilities; inventories drawn down with perfect foresight and always maintain 10 percent of capacity as ‘base’ gas.
- Renewables and nuclear:
  - Renewable increase equivalent to about 2.7 bcm a year; phasing out of nuclear reactors equivalent to about 3.5 bcm a year.
  - These affect both baseline and adverse equally and are not adjusted further because shortages are measured as deviations of adverse from baseline.

### Baseline scenario results and vulnerability
- To avoid shortages in the winter of the baseline scenario:
  - Gas-to-coal switching must be extended to March 2027.
  - Intermediate storage filling targets for August 1 and October 1 can be met, but storage levels only around 80 percent of capacity by November 1 (government target: 90 percent).
- Calculations indicate dangerously low gas inventory levels (just above 10 percent of capacity) in all future winters out to winter 2026/2027, risking intra-month, inter-region, or national shortages if temperatures are colder than expected.

### Adverse scenario: estimated gas shortages (Russian gas shutoff on June 1, 2022)
- Projected shortages (bcm):
  - Between June and December 2022: 3.9 bcm
  - 2023: 8.9 bcm
  - 2024: 3.4 bcm
  - 2025: 0.9 bcm
  - 2026: 0.4 bcm
  - 2027: 0.6 bcm
- Shortage as percent of national consumption in period:
  - Jun-Dec 2022: 9
  - 2023: 10
  - 2024: 4
  - 2025: 1.0
  - 2026: 0.5
  - 2027: 0.7
- Replacement ratio (=((Net release of inventories)+(Inventories not built up due to shutoff))/(Russian supplies lost) x100): 44 for Jun-Dec 2022, and "< 0" for subsequent periods shown.
- National consumption reductions relative to baseline:
  - June–December 2022: some 9 percent
  - Jan–Dec 2023: 10 percent
  - Jan–Dec 2024: 4 percent
- Monthly winter contractions (concentrated in winters) with inventories smoothing:
  - National consumption would have to contract by 10-20 percent each month between November 2022 and March 2023, and similar contractions in winter 2023/24.
- Demand compression by protection regime (percent of non-protected consumption in period):
  - If only households (HHs) are protected:
    - Jun-Dec 2022: 13
    - 2023: 14
    - 2024: 6
    - 2025: 1.5
    - 2026: 0.7
    - 2027: 1.0
  - If HHs and energy transformation are protected:
    - Jun-Dec 2022: 19
    - 2023: 22
    - 2024: 8
    - 2025: 2.3
    - 2026: 1.1
    - 2027: 1.6
- Cumulative demand compression (% of cumulative non-protected consumption) from Jun '22 until Dec of successive years:
  - If only HHs are protected: Dec 2022: 13; Dec 2023: 14; Dec 2024: 11; Dec 2025: 8; Dec 2026: 6; Dec 2027: 5
  - If HHs and energy transformation are protected: Dec 2022: 19; Dec 2023: 21; Dec 2024: 16; Dec 2025: 12; Dec 2026: 10; Dec 2027: 8

### Reasons why these shortage estimates may be smaller than other studies
- Germany has reduced its dependence on Russian gas over time.
- Similarities and differences with other analyses:
  - Similar to Bundesbank (2022b) for winter 2022/23 (they have 31 percent of unprotected sectors’ consumption).
  - Larger than Bundesbank for winter 2023/24 (they have 11 percent of unprotected sectors’ consumption vs. this analysis ~20 percent).
  - Estimates here are smaller than Bundesbank (2022a) and GCEE (2022) because this analysis starts from a lower and more recent share of Russian gas and allows for release of gas reserves.
  - Monthly gas shortages in this analysis do not exceed 21 percent of consumption in any one month, while the median scenario in Joint Economic Forecast (2022) reaches 60 percent in October 2022.

### Uncertainty and upside risks to shortages
- Infrastructure constraints and cross-border bottlenecks could increase shortages (ENTSOG (2022) notes significant bottlenecks).
- Germany may be required to supply neighbors in need (e.g., Austria, Czech Republic, Hungary, Slovakia) — winter shortage in these countries could amount to 9 bcm under estimates cited.
- Colder or longer winters could increase consumption by up to 3.1 bcm a year.
- If the gas shutoff leads to further increases in imported and retail gas prices, households might reduce demand by up to 0.8 bcm a year more than assumed.
- Shortages may occur through price-induced demand compression or through non-clearing markets caused by infrastructure bottlenecks; both are included in the analysis.

### Approach to estimating GDP impacts
- Three mechanisms captured:
  - Production cuts due to lack of gas (direct impacts).
  - Downstream amplification through intermediate products (second-round effects).
  - Increases in uncertainty leading to broader economic contraction.
- Two-model approach:
  - Model 1: sectoral firm production model with 17 sectors, representative firm per sector, constant returns to scale, nested production function (Cobb–Douglas combining energy and intermediate inputs; CES combining gas, oil, coal, renewables into energy). Includes input–output links to capture one round of downstream amplification.
  - Model 2: summarized effect of higher uncertainty on economic activity based on historical relationships.
- Elasticity of substitution between gas and other energy:
  - June–December 2022 period: elasticity = 0.1
  - June 2022–December 2027 period: elasticity = 0.4
- Second-round impacts assumed to materialize 6 months after direct impact (e.g., direct impacts in June 2022; second-round effects start in December 2022 and mostly felt in 2023).
- The model is static and applied over different scenario horizons to estimate GDP impacts over time.
- The model generalizes the ‘simplest’ production function approach and can replicate a 2.2 percent decline in GDP shown in Bachmann et al. (2022) Table 2. Only one round of downstream propagation is analyzed.

*Source: IMF staff calculations; information as of June 22, 2022.*

### 13.    There are three reasons why we focus on the gas shortage scenario where energy

### 13.    There are three reasons why we focus on the gas shortage scenario where energy

### Rationale for focusing on the scenario protecting energy transformation activity
- Three reasons are given for focusing on the gas shortage scenario where energy transformation activity is protected from gas rationing, in addition to protections on households’ gas consumption:
  - Gas-to-coal switching is already factored into the estimation of gas shortages; further gas supply cuts to energy transformation could significantly affect the provision of electricity, and even heating, with potentially serious non-economic welfare effects.
  - The model does not describe the energy sector in detail and could underestimate the economic effects of cutting gas supplies to energy transformation activities by relying on their small share of the economy and high gas intensity of production.
  - Protecting energy transformation activity imposes a larger contraction on the gas consumption of productive industries, indirectly capturing extra burdens on such industries that could result from protections on other users (e.g., hospitals and social services).

### Model limitations: exports, imports, and sector detail
- Explicitly modelling exports and imports could reduce estimated economic effects because:
  - German domestic demand could fall by more than foreign demand, so separating domestic and export demand would make overall demand fall by less.
  - Firms might substitute imports for domestically sourced inputs in response to the shock.
- The model does not differentiate production consumed domestically from production exported, nor domestic versus imported inputs.
- The energy sector is not modeled in detail; input–output linkages across sectors are not explicitly captured in the simplest aggregate specifications.

### Estimation of the relationship between uncertainty and output
- Two uncertainty measures are used:
  - number of occurrences of the word “uncertainty” in Economist Intelligence Unit reports about Germany (Ahir et al., 2022)
  - dispersion of economic forecasts (Jurado et al., 2015; Grimme and Stöckli, 2018)
- Regression specification (local projections) for each horizon h:
  - g_{t+h} = α + β u_t + η u_{t−1} + λ g̃_{t−1} + Σ_k Γ_k X_{t−k} + ε_{t+h}
  - where g_{t+h} denotes the deviation of GDP from its (Hamilton (2018) filter) trend in quarter t+h, and u_t denotes the uncertainty measure.
  - Controls include lags of growth, uncertainty, inflation, ECB monetary policy stance, and DAX stock market returns.
  - Sample runs from 1991Q2 to 2019Q3 based on availability of uncertainty measures.
- Parameter of interest is β, measuring the impact of uncertainty on growth at horizon h.

### Estimated GDP impacts: direct, second-round, and uncertainty channels
- Direct and second-round (downstream) effects tend to diminish over longer horizons.
- Direct impact examples:
  - The 19 percent contraction in firms’ gas consumption between June and December 2022 directly reduces GDP by 0.9 percent relative to baseline in this period.
  - The direct impact on GDP is 0.9 percent between June 2022 and December 2023 for a larger shock to gas consumption (21 vs. 19 percent) with higher elasticity (0.12 vs 0.1).
  - Between June 2022 and December 2027, gas consumption is reduced by 8 percent and the direct effect reduces GDP by less than 0.05 percent.
- Second-round effects:
  - Gas shortages between June and December 2022 generate second-round effects that reduce GDP by a further 0.9 percent, assessed to be felt 6 months later between December 2022 and June 2023.
  - Second-round effects are roughly the same size as direct impacts and diminish over expanding scenario horizons.
- Annualized direct + second-round impacts (converting expanding windows to annual basis):
  - GDP lower than baseline by 0.7 percent in 2022, 1.8 percent in 2023, and 0.4 percent in 2024.
  - Note: these are percentage deviations from baseline GDP levels, not percentage growth rates year-to-year.
- Uncertainty channel:
  - Estimated β (averaged across the two uncertainty measures) implies a one-standard-deviation increase in uncertainty could lower GDP by about 1 percent relative to trend up to two years after the shock, with statistically unclear effects thereafter.
  - Assumed shock: uncertainty rises to the 95th percentile of its historical distribution in 2022Q2 and then decays by half from 2022Q3 to 2023Q1.
  - This uncertainty shock reduces GDP by 0.8 percent in 2022, 0.9 percent in 2023 and 0.1 percent in 2024; no clear effect thereafter.

### Combined impacts and cumulative losses
- Combining direct, second-round and uncertainty effects yields:
  - GDP reduced by 1.5 percent in 2022, 2.7 percent in 2023 and 0.4 percent in 2024.
  - These losses are permanent in the sense that they are not “caught up” by deferring production, consumption, or investment to subsequent years.
  - Cumulative GDP loss between 2022 and 2024 is 4.8 percent of 2020 GDP.
- Alternate scenario where energy transformation activities help bear some shortages:
  - GDP would be 1.2 percent lower than baseline in 2022, 1.9 percent lower in 2023, and 0.4 percent lower in 2024, with no catch-up effects.

### Comparison with other studies
- The estimated impact of 1.5 percent in 2022 matches Bundesbank (2022b) but is smaller than Bundesbank (2022a) which estimates 5 percent, due to narrower scope and smaller energy shortages in this analysis.
- Over twelve months, GDP losses are similar to the 2-3 percent impact in Di Bella et al. (forthcoming) with adjustment frictions.
- Over two years, the estimated cumulative loss of 4.3 percent of 2021 GDP for 2022–2023 is smaller than the Joint Economic Forecast (2022) reported cumulative loss of 6.5 percent (in some base year), likely due to stricter substitution assumptions and additional channels in that forecast.
- The larger impact in 2023 than 2022 in this study owes more to delayed second-round effects than to depletion of gas reserves in 2022.

### Table 3 (selected numeric findings reproduced)
- Panel (a): Expanding windows, direct and second-round effects (From May '22 until:)
  - Required demand compression (percent of consumption):
    - If only households are protected: 13, 14, 11, 8, 6, 5 (for Dec '22, Dec '23, Dec '24, Dec '25, Dec '26, Dec '27 respectively)
    - If households and transformation are protected: 19, 21, 16, 12, 10, 8
  - Elasticity of substitution: 0.10, 0.12, 0.16, 0.20, 0.30, 0.40
  - Implied change in expenditure share /1: 2.0, 1.8, 1.0, 0.5, 0.3, 0.1
  - First-round impact on cumulative GDP (percent deviation from baseline):
    - If only households are protected: -0.5, -0.5, -0.2, -0.1, -0.1, 0.0
    - If households and transformation are protected: -0.9, -0.9, -0.4, -0.2, -0.1, -0.1
  - Second-round impact on GDP in 6 months' time (percent deviation from baseline):
    - If only households are protected: -0.6, -0.6, -0.3, -0.2, -0.1, -0.1
    - If households and transformation are protected: -0.9, -0.9, -0.4, -0.2, -0.1, -0.1
- Panel (b): Yearly direct, second-round and uncertainty effects (Real GDP level percent deviation from baseline):
  - If only households are protected: 2021 0.0; 2022 -1.2; 2023 -1.9; 2024 -0.4; 2025 -0.1; 2026 0.0; 2027 0.0
  - If households and transformation are protected: 2021 0.0; 2022 -1.5; 2023 -2.7; 2024 -0.4; 2025 0.0; 2026 0.0; 2027 0.0
- /1 Formula note: Based on the formula 100(1−1/σ)α(1−α) log(1−z/100), where z is the required demand compression in percent with households and energy transformation protected, σ is the elasticity of substitution, and α=0.025 is the national expenditure share on gas.

### The importance of how gas is rationed
- Allocation of scarce gas supplies across economic activities substantially affects GDP loss estimates.
- Baseline implicit assumption: gas supplies to unprotected sectors are cut in proportion to their gas consumption (e.g., with households and energy transformation protected, each remaining unprotected sector faces the same 19 percent cut between June and December 2022).
- In the medium term, technical constraints may be overcome and some sectors could face deeper cuts than others while still achieving the same national-level reduction.

### Findings from rationing-scheme experiments (summary)
- Cutting gas supplies more to gas-intensive and downstream industries can substantially reduce GDP loss.
- Table 4 shows four illustrative rationing schemes:
  - “Naïve” rationing: equal 19 percent cuts in every unprotected sector (direct and second-round impacts each 0.88 percent).
  - Three “GDP-loss minimizing” schemes solve linear programming problems minimizing direct and/or second-round impacts subject to constraints (e.g., no sector cut more than 50 percent).
- Numerical outcomes (between June and December 2022):
  - Direct impact on output:
    - "Naïve" Rationing (households and energy sectors protected): 0.88
    - "GDP Loss-Minimizing" given households and energy sectors protected: 0.31
    - Given households rationed by 10% and energy sector protected: 0.21
    - Given households and energy sectors rationed by 10%: 0.12
  - Second-round impact on output:
    - "Naïve": 0.88
    - GDP-loss minimizing (households & energy protected): 0.32
    - Given households rationed by 10%: 0.20
    - Given households and energy sectors rationed by 10%: 0.16
- Sectors identified by the rationing algorithm (in various orders/combinations) for rationing include:
  - non-metallic minerals; iron, steel and non-ferrous metals; paper, pulp and printing; chemicals and petrochemicals; food, beverages and tobacco.
- Allowing households to share in the burden (households’ gas consumption cut by 10 percent) can reduce direct GDP losses by one-third (from 0.31 to 0.21 percent) and second-round losses by over one-third (from 0.32 to 0.20 percent).
  - A 10 percent reduction in households’ gas consumption is equivalent to reducing heating temperature by about 2 degrees over the heating period (BDEW, 2022).

### Notes and methodological points
- Rationing algorithms balance gas-intensity and downstreamness of sectors; the GDP-minimization results use the 2021 edition of the OECD Inter-Country Input—Output Table.
- Assumption in rationing experiments: no sector can have its gas consumption cut by more than 50 percent.
- Operational/technical constraints: with available short-notice data, individual orders to cut gas supply for specific end-consumers are only possible in exceptional cases (Federal Network Agency, 2022b).
- Policy levers: households’ purchasing power could be supported via income transfers or other policy measures if prices rise; laws exist allowing pass-through of wholesale price increases in a gas emergency to preserve supplier solvency.

*Source: IMF staff analysis as presented in the provided content unit.*

### 24.    International gas prices could rise substantially with a shutoff of Russian gas. The gas

### 24.    International gas prices could rise substantially with a shutoff of Russian gas. The gas

### Estimated international price increases and scenarios
- Albrizio et al. (forthcoming) estimate that a shutoff could make the average Netherlands TTF gas price in 2022 between 110 to 370 percent higher than 2022:Q1, depending on the demand elasticity of natural gas and the feasibility of rerouting LNG from Asia to Europe.
  - Worst-case scenario assumes no LNG supplies are rerouted from Asia.
- For reference, the Netherlands TTF natural gas price more than doubled right after the invasion of Ukraine on February 24 and at the end of May remained about 15 percent higher than February.
- As of June 2, part of these price increases has already been seen in 2022 and are factored into the baseline.

### Passthrough to domestic inflation: empirical findings
- Historical evidence:
  - International oil and gas prices affect inflation directly (household prices for refined oil and gas products) and indirectly (higher production costs for other goods and services).
  - Literature documents significant passthrough from international energy prices to headline inflation, with magnitudes depending on monetary policy conduct, trade openness, and energy intensity (e.g., Chen, 2009; Choi et al., 2018; Habermeier et al., 2009).
- Estimated passthrough magnitudes (sample 1996Q1 to 2022Q1; Brent crude and Netherlands TTF used as international oil and gas prices; HICP oil includes solid and fluid fuels and fuels and lubricants for vehicles; HICP gas includes natural gas, electricity, and heating):
  - Passthrough from international to domestic gas prices averages around 0.02 over 2-3 quarters in normal times, but rises to 0.1 following large increases in international gas prices (fivefold increase).
  - Contemporaneous passthrough of international oil price averages 0.2 in normal times and jumps to 0.3 in the case of a price surge.
  - Passthrough of international gas price is more lagged than oil due to typical 12-month fixed contracts for gas and electricity.
  - Passthrough from HICP energy inflation to core inflation is negligible in normal times, but reaches 0.05 contemporaneously following large energy price jumps.
- Estimation approach:
  - Local projection specification with state-dependent passthrough for each horizon h, allowing larger international energy price shocks to have larger effects on German inflation.
  - Large increase defined (following Hamilton, 2003) as π̃tE* = max(0, p̃t / p̃t3yr − 1), where p̃t is international energy price in quarter t and p̃t3yr is the maximum price during the most recent 3 years up to quarter t−1.
  - Regression controls for four lags of HICP and international energy price inflation; estimated by OLS with Newey–West standard errors.
  - Also estimate passthrough from HICP energy inflation to core inflation using a forward-looking Phillips curve specification that adds five-year consensus inflation expectation and output gap.

### Inflation projections under gas shutoff scenarios
- Assumptions:
  - International gas prices rise in 2022Q2 by 110, 221 or 367 percent and last for 12 months.
  - GDP impact from uncertainties will widen the output gap.
- Estimated impacts relative to baseline (deviation from baseline annual inflation):
  - If international gas prices rise by 110 percent (scenario where Asia shares the Russian supply shock with Europe in equal proportions):
    - German inflation would be about ¾ of a percentage point higher in 2022 than without the shutoff.
    - German inflation would be about 1¼ percentage points higher in 2023 than without the shutoff.
  - If international gas prices rise by 370 percent (scenario in which Asian LNG supplies are not rerouted to Europe):
    - Inflation could be higher by about 2 percentage points in 2022 than without the shutoff.
    - Inflation could be higher by about 3.5 percentage points in 2023 than without the shutoff.
  - If the government activates powers to permit firms to pass on price increases to consumers regardless of existing contracts (leading to contemporaneous passthrough), and international gas prices rise by 370 percent:
    - Inflation could be 3¼ percentage points higher than without the shutoff in both 2022 and 2023.
- Comparison to other estimates:
  - These estimates are larger than Bundesbank (2022b) which reports 0.5 in 2022, 1.5 in 2023 and 0.25 in 2024 (in percentage points). Possible reasons: (i) Bundesbank’s demand-side analysis contains more deflationary forces; (ii) the IMF model is nonlinear, so larger price shocks have larger effects.
- Caveat:
  - International gas price increases considered are without precedent prior to 2021; passthrough and consumer price inflation rates could be greater than these estimates.

### Policy discussion — measures to enhance energy security and mitigate impacts
- Build resilience and secure new gas supplies:
  - Explore additional gas from the United States, Norway and Qatar.
  - Germany is establishing terminals to import more LNG.
- Energy storage and efficiency:
  - Fill gas storage facilities before winter.
  - Enhance energy efficiency and accelerate renewable energy development.
- Protecting energy company solvency:
  - Monitor financial health of energy companies (regular calls or surveys).
  - Recent legal amendments allowing more flexibility in retail prices could help solvency but may need accompanying targeted income support for vulnerable households (one-off energy relief payments or housing benefits).
  - Government plans to support firms’ liquidity with loans through KfW, extension of pandemic-era loan guarantee programs, and loans to energy producers to post margins on hedging contracts.
- Demand-side measures and incentives:
  - Energy-saving campaigns for households, firms, public sector agencies and non-profits (analogue to Japan’s setsuden).
  - Programs to exchange gas heaters for heat pumps.
  - Auction mechanism to compensate firms for reducing gas consumption to help fill storages; policy should replace temporary targeted subsidies for firms’ increased gas costs given urgency to accumulate reserves.
  - Consider a similar gas-saving program for households using rebates or discounts on gas bills, depending on technical feasibility.
  - Improve consumer access to up-to-date online gas usage statistics; smart meters not widely available.
- Short-term supply adjustments:
  - Reactivation of coal-fired power plants to save gas for electricity generation, while ensuring gas-fired plants cut gas consumption if competing with coal plants.
  - Federal Network Agency’s daily dashboard provides transparent overview of current supply situation; regular publication of gas projections (like June 23, 2022) would encourage energy saving.
- Infrastructure and international cooperation:
  - Publish a clear diagnosis of infrastructure gaps under a full shutoff scenario; ENTSOG (2022) identifies several gaps including within Germany.
  - Network development plan consultation document was postponed on May 2, 2022; a diagnosis could be published earlier given urgency.
  - Cooperation with EU and neighboring countries is key; REPowerEU is an important step.
  - Address ‘odorization’ differences with France (potential financing of deodorization plant), consider additional flows from Dunkirk LNG terminal and planned FSRU at Eemshaven.
  - Germany has signed solidarity agreements under EU Regulation 2017/1938 with Denmark and Austria; further agreements possible.
- Rationing policy:
  - Further elaboration needed; economic analysis should be balanced with social, environmental, health, technical and legal considerations.
  - Involve households in voluntary or price-based burden sharing; apply stricter rationing to more gas-intensive and downstream firms.
  - Major rationing decisions require political participation; Federal Network Agency has collected information on firms’ gas usage and could act as central authority to manage day-to-day rationing policy.
- Renewable energy acceleration:
  - “Easter package” (announced April 2022) aims to raise target to 80 percent of electricity demand met with renewables by 2030 (from 42 percent observed in 2021).
  - Measures in the package:
    - Establish overriding public interest in renewables development in law to speed up investment processes.
    - Increase public tenders for solar and onshore wind power to 22 and 10 GW a year, respectively.

### Production model appendix — role of gas in sectoral output
- Representative firm production function (constant returns to scale):
  - Yk = Zk Ek^αE k Π_{j=1}^J X_{jk}^{α_{jk}}, where αE>0 captures importance of energy input; X_{jk} are intermediate inputs; Ek aggregates gas and other energy inputs.
- Energy aggregation (CES form):
  - Ek = (ω egas_k^{(ε−1)/ε} + (1−ω) eoth_k^{(ε−1)/ε})^{ε/(ε−1)}, where ω>0 captures importance of gas in total energy inputs and ε is elasticity of substitution between gas and other energy inputs.
- Second-order approximation and log-differentiation yield:
  - dlnEk ≈ ω dln egas_k + 1/2 (1−1/ε) ω(1−ω) (dln egas_k)^2.
  - dlnYk ≈ αE k dlnEk + Σ α_{jk} dln X_{jk}.
  - Direct impact of gas shocks on gross output (approximated):
    - dlnYk_d ≈ p_gas e_gas_k / Pk Yk dln egas_k + 1/2 Δ p_gas e_gas_k / Pk Yk (dln egas_k)^2,
    - where Δ p_gas e_gas_k / Pk Yk = αE (1−1/ε) ω(1−ω) dln egas_k.
- Interpretation:
  - αE and ω calibrate to energy expenditure share and gas share in energy inputs respectively.
  - Higher ε (greater substitutability) implies firms can switch away from gas more easily, implying smaller changes in gas expenditure shares for a given price increase.

*Source: IMF staff calculations and text as provided in the content unit.*

### 6. The production function equation (1) formalized the idea that firms in industry 푘 will need

### 6. The production function equation (1) formalized the idea that firms in industry 푘 will need

### Second-round effects and Cobb-Douglas property
- The Cobb-Douglas production function implies sectoral expenditure share on intermediate goods is unchanged and invariant to the realization of supply shocks.
- Changes in intermediate inputs from sector 푗 in production of sector 푘 are equal to the changes in output of sector 푗:
  - 푑ln푋푗푘 = 푑ln푌푗.
- Using this property, equation (5) can be rewritten as:
  - 푑ln푌푘 ≈ 훼퐸푘 푑ln퐸푘 + ∑ 훼푗푘푗 푑ln푌푗.
- Note: these are log changes, rather than percentage changes; as percentage change approaches −100%, the log change approaches −∞.

### Input-output linkages and Leontief inverse
- Define input-output matrix 퐴 = [푎푗푘], where 훼푗푘 summarizes inputs from sector 푗 required for one unit of output 푘 (equivalent to sector 푘’s expenditure share on inputs from sector 푗).
- The Leontief inverse matrix is denoted as 퐿 = (퐼 − 퐴)−1 = ∑퐴푖∞푖=0.
- Relationship between sectoral direct and second-round effects:
  - 푑ln푌⃗𝑠 = (퐼 − 퐴′)−1 훼퐸 푑ln퐸⃗ = (퐼 − 퐴′)−1 푑ln푌𝑑⃗ .
- The (푗,푘) element of the Leontief inverse 푙푗푘 = 푎푗푘 + ∑푎푗푟푎푟푘 + ⋯ .

### Sectoral second-round impacts of a gas shock
- Sectoral second-round impacts of gas shock on sector k can be written:
  - 푑ln푌푘𝑠 = ∑푙푗푘 푗 푑ln푌푗𝑑 = ∑(푎푗푘 + ∑푎푗푟 푎푟푘 + ⋯ 푟 ) 푑ln푌푗𝑑푗.
- The second-round impact of the gas shock on sector 푘 propagates:
  - directly from input suppliers (first-order input linkages), and
  - indirectly through downstream suppliers (higher-order linkages).
- Analysis focuses on the second-round impact captured by ∑푎푗푘 푑ln푌푗𝑑푗 because higher-order effects take time to materialize.
- Over time, intermediate inputs become more substitutable and the supply bottleneck from the gas shock eases; hence higher-order propagation through input-output linkages becomes less critical.

### Aggregation to GDP
- Given 푑ln𝐺𝐷𝑃 = ∑ 푑ln𝑉𝐴𝑘 and assuming changes in value added equal changes in output at sectoral level, aggregate direct and second-round impacts are:
  - 푑ln𝐺𝐷𝑃𝑑 = ∑ 휆𝑘 푑ln𝑌𝑘𝑑
  - 푑ln𝐺𝐷𝑃𝑠 = ∑ 휆𝑘 푑ln𝑌𝑘𝑠
- Where 휆𝑘 = 푉𝑘 / ∑ 푉𝑘 is the value-added share of sector 푘, calibrated from the input-output table.
- Footnote: the assumption that changes in value added equal changes in output implicitly assumes sectoral labor and capital shares are invariant to the gas shocks, consistent with the Cobb-Douglas specification; factor inputs (labor and capital) are not explicitly specified.

*International Monetary Fund — extracted section content*

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_Source: https://www.imf.org/-/media/files/publications/cr/2022/english/1deuea2022002.pdf_