## Annex Table 2.1.2. (ch2onlineannex)

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### Data sources and measurement
- Main defense spending source: Stockholm International Peace Research Institute (SIPRI), covering 164 countries during 1948–2024. SIPRI coverage includes personnel costs, operations and maintenance, procurement, military R&D, military aid, paramilitary forces, military space activities, and military pensions.
- SIPRI figures are typically cash-based and may include off-budget items; equipment expenditures are recorded at the time of payment rather than delivery, which can generate timing discrepancies relative to GDP measurement.
- Missing defense spending values supplemented with Gethin (2024b) for 175 countries since 1980 and the World Human Capital Expenditure (WHCE) dataset for 48 countries since 1800 (created by Bharti and others 2026).
- Disaggregated military spending subcomponents sourced from Becker and others (2024) for a subsample of 35 NATO and EU member countries during 1965–2020.
- Other data sources: SIPRI Arms Transfers Database; Correlates of War (COW) Project Arms Technology version 1.0 and COW National Material Capabilities version 6.0; Uppsala Conflict Data Program (UCDP/PRIO Armed Conflict Dataset version 25.1) and COW war datasets; Public Finances in Modern History (PFMH) dataset; Global Macro Database (GMD); IMF World Economic Outlook (WEO); World Bank World Development Indicators; World Bank World Integrated Trade Solution (WITS).
- Measurement limitations: SIPRI gathers extra-budgetary and off-budget military spending when possible and makes estimates using country-tailored methodology, but confidentiality and exclusion of domestic security/paramilitary spending can cause measurement errors.

### Definitions and counts of defense spending booms
- Baseline definition: periods during which the 2-year moving average of defense spending as a share of GDP rises by at least 1 percentage point, continuing for as long as defense spending does not decline.
- Alternative definitions:
  - Alternative I: same as baseline but threshold lowered to 0.5 percentage point of GDP.
  - Alternative II (Marzian and Trebesch, 2025—MT): boom begins when the 2-year moving average growth rate of defense spending as a share of GDP exceeds the in-sample standard deviation of the growth rate (10.5 percent) for two consecutive years, and ends when the growth rate falls below 0 for two consecutive years.
- Baseline counts and characteristics:
  - Number of booms (Baseline): 215 total; AEs: 26; EMDEs: 189; Wartime: 99; Peacetime: 116.
  - Alternative I (0.5 percentage point threshold): 403 total; AEs: 49; EMDEs: 354; Wartime: 163; Peacetime: 240.
  - Alternative II (MT definition): 329 total; AEs: 36; EMDEs: 293; Wartime: 111; Peacetime: 218.
- Average size and duration (Baseline):
  - Average size: 2.7 (percent of GDP); AEs: 2.4; EMDEs: 2.7; Wartime: 2.5; Peacetime: 2.7.
  - Average duration: 2.7 (years); AEs: 2.5; EMDEs: 2.7; Wartime: 2.8; Peacetime: 2.5.
- Permanent versus temporary booms (Baseline):
  - Count: Permanent: 112; Temporary: 103.
  - Permanent average size: 3.0; AEs: 2.7; EMDEs: 3.0; Wartime: 3.9; Peacetime: 2.2.
  - Permanent average duration: 3.1 years; AEs: 2.8; EMDEs: 3.2; Wartime: 3.2; Peacetime: 3.0.
  - Temporary average size: 2.3; AEs: 2.1; EMDEs: 2.4; Wartime: 2.8; Peacetime: 1.9.
  - Temporary average duration: 2.2 years; AEs: 2.3; EMDEs: 2.2; Wartime: 2.4; Peacetime: 2.0.

### Narrative identification of exogenous (peacetime) booms
- Narrative subset identifies peacetime booms plausibly exogenous (driven by external geopolitical factors or alliances and largely unrelated to domestic macro-fiscal conditions).
- Exclusions: booms associated with domestic security concerns, onsite conflicts, economic crises, and commodity price booms.
- Result: 59 narrative boom episodes identified in the post-World War II period.
- Classification procedure:
  - Each of the 116 peacetime boom episodes described and classified via a structured prompt to GPT-5 and then manually checked into categories:
    1. Exogenous-geopolitical
    2. Exogenous-alliance-driven
    3. Endogenous-macrofiscal
    4. Endogenous-security-domestic
    5. Ambiguous
  - Example: United States booms starting in 1949, 1965, and 1980 identified as exogenous and consistent with narrative episodes in Ramey (2011).

### Financing of defense spending booms
- Main finding: defense spending booms are mostly deficit financed; robust across alternative boom definitions.
- Average financing decomposition:
  - Increase of the deficit is the main financing source, especially in the first years of the boom.
  - Nondefense spending reprioritization and revenue mobilization are limited on average and tend to appear in later years.
- Heterogeneity across booms:
  - Permanent booms: first three years register an increase in the primary deficit and tax revenues, with limited role for defense reprioritization.
  - Temporary booms: mostly deficit financed.
- Financing decomposition calculation note: Nondefense spending reprioritization is computed residually from Change in Deficit = Change in Defense Spending + Change in Nondefense Spending - Change in Revenues.

### Temporary versus permanent booms (classification and stylized facts)
- Classification rule: booms are temporary if defense spending (as a share of GDP) returns to pre-boom levels within 10 years; otherwise permanent.
- Stylized facts:
  - Permanent booms are, on average, larger and last longer than temporary ones.
  - Permanent and temporary booms are evenly split across EMDEs and AEs, and between wartime and peacetime.

### Endogeneity, anticipation, and identification caveats
- Identification requirements for estimating macro effects: (i) unanticipated changes in defense spending; (ii) changes plausibly unrelated to the business cycle (exogenous).
- Challenges:
  - Anticipation effects: military spending increases may be announced before actual spending occurs; annual data mitigates but does not eliminate this concern.
  - Implementation over long periods can bias estimated effects downward.
  - Full resolution of endogeneity requires procurement-level data or large-scale news-based measures of defense spending announcements.
- Mitigations:
  - Focus on peacetime booms (excluding wartime booms defined as those that immediately follow a conflict or culminate in an onsite conflict within three years).
  - Exclude fragile/conflict-affected states and EMDE commodity exporters in some analyses.

### Predictability and determinants of defense spending (panel OLS and boom-prediction)
- Predictors (examples from panel OLS):
  - Armed onsite conflict (one-year lag): coefficients include 6.650***, 6.909***, 5.593***, 6.015***, 5.031**, 5.185** (standard errors (1.651), (1.565), (1.823), (1.712), (2.187), (2.018)).
  - Government revenue over GDP (one-year lag): coefficients include 0.195***, 0.210***, 0.184**, 0.196**, 0.135, 0.150* (standard errors (0.067), (0.066), (0.078), (0.076), (0.090), (0.088)).
  - GDP growth (one-year lag): coefficients generally small and not consistently significant (examples: 0.061, 0.057, 0.065, 0.082, 0.074, 0.080 with standard errors (0.061), (0.076), (0.067), (0.091), (0.080), (0.101)).
- Boom-prediction regressions (dummy for boom start):
  - Armed onsite conflict (one-year lag) coefficients examples: 3.061***, 2.958***, 2.650***, 2.435***, 2.389***, 2.347***, 3.029***, 1.624** (standard errors (0.469), (0.540), (0.561), (0.643), (0.637), (0.742), (0.976), (0.758)).
  - Government revenue sometimes positive and marginally significant (examples: 0.046* (0.027); 0.045* (0.025); 0.068** (0.030)).
  - R-squared values for boom-prediction regressions are low (examples): 0.025, 0.021, 0.023, 0.022, 0.027, 0.028.
- Interpretation:
  - Defense spending cannot be assumed exogenous to local economic conditions in the full chapter sample.
  - Excluding fragile/conflict-affected states and commodity-exporting EMDEs reduces endogeneity: boom start dates are predicted by armed conflicts but not by GDP growth, government revenues, or recessions.

### Macroeconomic dynamics following booms (local projections results)
- Estimation framework:
  - Local projections with OLS estimate cumulative changes over a 5-year window.
  - Dependent variables: GDP and subcomponents (government consumption, private consumption, investment, imports, exports), factors of production (capital stock, employment, TFP), fiscal indicators (defense and nondefense spending, overall balance, debt, social spending), and CPI.
  - Key regressor: dummy denoting start of defense spending boom (Boom_i,t). Controls include lagged dependent variable, 4 lags of the boom variable, country and year fixed effects; standard errors clustered at country level.
- Robustness: results similar using Alternative I (0.5 threshold) and OLS using defense spending as share of potential GDP; robust to excluding Russia and post-Soviet states.

### Output and components — Peacetime booms (excluding FCS and commodity-exporting EMDEs)
- Baseline finding: peacetime defense spending booms are followed, on average, by a 3 percent increase in GDP over five years.
- TFP:
  - TFP increases three years after boom onset.
  - When adjusting for capacity utilization, short-term TFP coefficient is muted; coefficient increases over time and becomes significant 10 years after the start of the boom.
- Components (three-year-ahead, real percent change): government consumption, private consumption, GFCF, imports, exports show heterogeneous responses; significance indicated in figures (darker-colored bars denote significance at the 10 percent level).
- Factors of production three-year-ahead: capital stock, employment, and TFP responses are mixed in magnitude and significance.

### Temporary vs permanent booms — differential macro effects
- Permanent booms (definition: defense spending increase sustained for next 10 years):
  - Baseline 3 percent five-year GDP increase is driven by booms that lead to a permanent increase in the defense spending–to–GDP ratio.
  - Permanent booms trigger durable increases in military procurement and encourage firms to expand capacity and invest in specialized capital (production lines, R&D, supplier networks).
  - Permanent booms tend to crowd in private investment and employment rather than merely time-shifting activity; induce stronger labor supply responses as households anticipate persistently higher taxes.
  - Real GDP increase associated with permanent booms is sustained and reaches over 6 percent by year 5.
  - Average size of permanent booms is 3 percent of GDP; implied multiplier is about 2.
- Temporary booms:
  - Followed by a temporary increase in GDP that peaks in year three before fading away.

### Fiscal consequences and social spending
- Defense spending booms lead to a significant rise in the fiscal deficit on average.
- Government debt-to-GDP:
  - Does not rise on average across all booms because wartime booms raise debt while peacetime booms show an opposite decline in debt.
- Nondefense spending as share of GDP:
  - Declines in wartime booms but moderately increases in peacetime booms.
- Debt decomposition (subset ≈ one third of episodes due to data availability):
  - Rise in debt driven roughly equally by the primary deficit and interest on past debt.
  - GDP growth and the stock-flow adjustment contribute negatively to the change in debt.
- Social spending:
  - For booms financed by spending reprioritization, reductions in social spending observed (declines in social protection, health, education three years ahead).

### Robustness to additional controls
- Effect on real GDP under baseline specification is similar when using expanded controls (4 lags of dependent and shock variables, nondefense government spending and government revenue as share of potential GDP, and a contemporaneous war dummy).

### Firm-level analysis (Online Annex 2.4): data, design, and key findings
- Sample: over 4.6 million private non-financial firms in 41 countries between 1995 and 2023 (Orbis).
- Sample restrictions: firms with at least 5 observations; non-financial private sector firms in manufacturing and trade; countries with at least 5,000 observations over the sample period.
- Empirical objective: test whether investment-to-cash flow sensitivity differs during defense spending booms, separately for booms associated or not with an increase in public debt-to-GDP.
- Baseline regression (Huang, Panizza, and Varghese (2018) style):
  - Dependent variable: I/A (investment scaled by assets).
  - Key regressor: (CF/A) × DS_Boom, where DS_Boom indicator values: (i) not in a boom, (ii) boom not associated with increasing public debt, (iii) boom associated with increasing public debt.
  - Controls: firm fixed effects (휗i), sector-year fixed effects (휇s,t), country-year fixed effects (훿c,t); winsorization at 2.5 and 97.5 percentiles; assets winsorized at 97.5 percentile; standard errors clustered at firm level.
  - Defense-related sectors identified at NACE Rev.2 4-digit including NACE 25.40, 30.30, 30.40, 26.30, 26.51, 26.70, 20.51, and 30.11.
- Key empirical results:
  - Baseline: positive coefficient β1 indicates investment is sensitive to internal cash flow absent booms.
  - When boom not associated with rising public debt: sensitivity of investment to cash flow declines, suggesting positive demand effects ease financing constraints.
  - In defense-related sectors: coefficient not statistically different from zero in that subsample.
  - When boom associated with rising public debt: investment–cash flow sensitivity is higher than when there is no boom, consistent with crowding out from rising public debt increasing firms’ financing constraints.
  - Arms importers subsample (average defense imports-to-defense spending ratio above sample median): investment–cash flow sensitivity does not vary with the presence or not of a defense spending boom (large import leakages attenuate domestic demand effects).
- Selected regression magnitudes and diagnostics (Online Annex Table 2.4.1):
  - Number of observations: 44,119,720; 44,119,343; 152,879; 3,025,050 across columns (1)–(4).
  - R2: 0.21; 0.30; 0.27; 0.45 across columns (1)–(4).
  - Lagged (I/A)i,s,c,t-1 coefficients: -0.0419*** (0.000), -0.0617*** (0.000), -0.0137*** (0.004), -0.1053*** (0.001).
  - (S/A)i,s,c,t coefficients: -0.0054*** (0.000), -0.0093*** (0.000), -0.0129*** (0.001), -0.0093*** (0.000).
  - (CF/A) × (DS Boom = 0): 0.0237*** (0.000), 0.0207*** (0.000), 0.0589*** (0.003) in relevant columns.
  - (CF/A) × (DS Boom = 1, without Rising Debt): -0.0087*** (0.001), 0.0126*** (0.002), 0.0042 (0.044).
  - (CF/A) × (DS Boom = 1, with Rising Debt): 0.0025 (0.007), 0.0270*** (0.007), 0.0818* (0.047).
  - (CF/A) × (DS Boom = 0) in column (4): 0.0384*** (0.001); (CF/A) × (DS Boom = 1) in column (4): 0.0381*** (0.003).
  - Significance notation: *** p<0.01; ** p<0.05; * p<0.1.

### Fiscal multipliers: empirical estimates and heterogeneity (Online Annex 2.5)
- Sample and method:
  - Panel of 138 countries over 1946–2024.
  - Panel local projection methods following Ramey and Zubairy (2018).
  - Cumulative output ∑_{j=0}^h Y_{i,t+j} regressed on cumulative defense spending ∑_{j=0}^h D_{i,t+j} plus controls; both normalized by potential GDP.
  - Controls: 1–4 year lags of GDP, defense spending, non-defense spending as share of potential GDP; contemporaneous war dummy; country and year fixed effects; standard errors clustered at country level.
- Heterogeneity dimensions: AEs vs EMDEs; wartime vs peacetime; temporary vs permanent buildups; arms importers vs exporters; financing source (deficit-financed vs other); current vs capital spending; exchange rate regime; public investment efficiency; post-World War II vs post-Cold War.
- Selected cumulative multiplier results (horizons 0–5):
  - Horizon 0: AEs 0.432***; EMDEs 1.842***; Peace 1.935***; War 0.959; Temporary 1.196***; Permanent 2.273***.
  - Horizon 1: AEs 0.596***; EMDEs 2.186***; Peace 2.031***; War 1.634***; Temporary 1.510***; Permanent 2.580***.
  - Horizon 2: AEs 0.726***; EMDEs 2.422***; Peace 2.126***; War 1.926***; Temporary 1.717***; Permanent 2.638***.
  - Horizon 3: AEs 0.825***; EMDEs 2.540***; Peace 2.245***; War 1.896***; Temporary 1.859***; Permanent 2.613***.
  - Horizon 4: AEs 0.823***; EMDEs 2.477***; Peace 2.268***; War 1.620***; Temporary 1.896***; Permanent 2.403***.
  - Horizon 5: AEs 0.828***; EMDEs 2.359***; Peace 2.166***; War 1.462***; Temporary 1.906***; Permanent 2.137***.
- Arms importer vs exporter and current vs capital spending (selected horizon values):
  - Horizon 0: Importer 0.671**; Exporter 3.073***; No (deficit-financed = No) 1.077***; Yes (deficit-financed = Yes) 1.009*; Current 1.722***; Capital 0.994.
  - Horizon 1: Importer 1.101***; Exporter 3.143***; No 1.189***; Yes 1.725***; Current 2.031***; Capital 1.348**.
  - Horizon 2: Importer 1.403***; Exporter 3.119***; No 1.271***; Yes 2.118***; Current 2.245***; Capital 1.291*.
  - Horizon 3: Importer 1.607***; Exporter 3.134***; No 1.33***; Yes 2.244***; Current 2.352***; Capital 1.198.
  - Horizon 4: Importer 1.684***; Exporter 2.983***; No 1.294***; Yes 2.26***; Current 2.284***; Capital 1.205.
  - Horizon 5: Importer 1.713***; Exporter 2.775***; No 1.254***; Yes 2.203***; Current 2.173***; Capital 1.094.
- Significance notation preserved: *** p<0.01; ** p<0.05; * p<0.1.

### Strategies to mitigate endogeneity and IV diagnostics
- Two approaches move multipliers closer to unity:
  1. Narrative approach:
     - Uses subset of narrative defense spending booms as instrument for defense spending.
     - Narrative booms produce strong first-stage results; IV first-stage coefficients (Post-WWII) horizons 0–5 = 0.01***; 0.03***; 0.05***; 0.07***; 0.08***; 0.10***.
     - Weak IV F-statistics (Post-WWII) for horizons 0–5: 161.0; 196.4; 118.4; 92.3; 77.8; 74.6.
     - Weak IV F-statistics (Post-Cold War) for horizons 0–5: 154.4; 87.3; 37.8; 22.6; 15.5; 14.4.
  2. Defense alliances approach:
     - Subsamples where exogeneity more plausible: members of NATO and IMCTC (post-Cold War).
     - For alliance sample, defense spending booms are not anticipated by conflicts or local economic conditions.
     - Controlling for geopolitical risk index (subset of 42 countries) yields defense multipliers even closer to unity.
- Alliance sample notes:
  - NATO includes 32 member countries; IMCTC includes 41 countries; contemporaneous membership treated as proxy for cooperation going back in time.
  - Fragile and conflict states excluded from alliance sample.

### IV specification controlling for geopolitical risk
- IV specification controls for historical geopolitical risk index (Caldara and Iacoviello 2022) for subset of 42 countries.
- Plots show solid lines = point estimates and shaded area = 90 percent confidence interval; years after onset of defense spending boom on horizontal axis.

### Literature review and historical extension
- Literature summary (selected study findings preserved exactly):
  - Barro and Redlick (US, 1947–2007, VAR): "1.5 cumulative over 20 months".
  - Ramey (US, 1930–2006, OLS panel): "0.4 to 0.5 on impact and 0.6 to 0.7 over 2 years".
  - Nakamura and Steinsson (US, 1939–2008, VAR): "0.6 to 1.2 for peak and cumulative multipliers".
  - Kollias and Paleologou (US - State-level, 1966–2006, IV panel with State-level variation in defense contracts): "1.5 over 2 years".
  - Ben Zeev and Pappa (EU, 1961–2014, VAR): "Zero".
  - Dupor and Guerrero (US, 1947–2007, VAR): "1.3 or 2.14 cumulative multiplier, depensing on shock idenitification strategy".
  - Ramey and Zubairy (US - State-level, 1951–2014, GMM panel with State-level variation in defense contracts): "Between zero and 0.5 cumulative multipliers over 2 to 4 years".
  - Olejnik (US, 1889–2015, LP): "Around 0.7".
  - Olejnik (Short-run military expenditures in NATO's Eastern Flank, 1999–2021, LP): "0.6 on impact and 1.5-1.6 at year 2 and 3".
  - Antolin-Diaz and Surico (Central and Eastern European countries, 1999–2021, LP): "0.6 on impact and 1.5-1.6 at year 2 and 3".
  - Ben Zeev, Pappa, and Scola Gagliardi (US, 1890–2015, VAR): "Below or around 1 at business cycle frequencies, rising to exceed 1 at long horizons".
  - García, Sarasa-Flores, and Ulloa (European countries, 1960–2024, VAR): "2 on impact, falling to 0.92 after 10 years".
  - Furceri et al. (EU, 1995–2023, LP, IMF Working Paper 2026): "1.4 on impact with a peak at 1.6 at year 2".
  - Furceri et al. (EU, 1989–2023, LP): "1.3 on impact rising to 1.9 after 2 years" and "1.5 to 1.9 over 3 years using procurement data".
- Historical extension to 1800:
  - Using standard OLS yields defense spending multipliers above 2.
  - Using narrative booms as instruments yields multipliers closer to 1.
- Methodological labels preserved exactly: "GMM = generalized methods of moments; LP = local-projections; OLS = ordinary least squares; VAR = vector autoregression."

### Fiscal multipliers: modeling simulations (Online Annex 2.6) and scenario with higher risk premia
- Model: Flexible System of Global Models (FSGM), semi-structural combining micro-founded and reduced-form formulations (see Andrle and other (2015) for model description).
- FSGM used for model-based simulations of defense spending shocks; EUROMOD module is an "annual, multi-region, general equilibrium model of the global economy" with blocs for major euro area countries and stand-alone blocs including China, India, Japan, Switzerland, Sweden, United Kingdom, and United States.
- Higher risk premia scenario:
  - Assumes "a one-off increase in risk premia by 50 basis points" to model "possible implications of rising spreads in response to higher spending, especially in countries with limited fiscal space, lacking any coordination."
  - Exact phrasing: "The higher risk premia scenario (blue lines) assumes a 50 basis points increase in terms premia in 2026."
  - Qualitative outcome: more muted output and price response, and a larger increase in public debt relative to baseline.
- Variables plotted in annex figures (labels preserved): "1. GDP Path of the Shock and Real GDP (Percent difference)"; "2. Real Consumption (Percent difference)"; "3. Real Investment (Percent difference)"; "4. Core CPI Inflation"; "5. Long-Term Interest Rate"; "6. Government Deficit/GDP"; "7. Government Debt/GDP"; "8. Current Account/GDP".

*Source: IMF staff compilation (Annex Table 2.1.2., Online Annex Tables and Figures as provided in the source content).*

### Annex Table 2.1.2.

### Annex Table 2.1.2.

### Data sources and measurement
- Main defense spending source: Stockholm International Peace Research Institute (SIPRI), covering 164 countries during 1948–2024. SIPRI’s coverage includes personnel costs, operations and maintenance, procurement, military R&D, military aid, paramilitary forces, military space activities, and military pensions.
- SIPRI figures are typically cash-based and may include off-budget items; equipment expenditures are recorded at the time of payment rather than delivery, which can generate timing discrepancies relative to GDP measurement.
- Missing defense spending values are supplemented with Gethin (2024b) for 175 countries since 1980 and the World Human Capital Expenditure (WHCE) dataset for 48 countries since 1800 (created by Bharti and others 2026).
- Disaggregated military spending subcomponents (equipment, personnel, infrastructure, operating expenses) sourced from Becker and others (2024) for a subsample of 35 NATO and EU member countries during 1965–2020.
- Other data sources referenced: SIPRI Arms Transfers Database; Correlates of War (COW) Project Arms Technology version 1.0 and COW National Material Capabilities version 6.0; Uppsala Conflict Data Program (UCDP/PRIO Armed Conflict Dataset version 25.1) and COW war datasets; Public Finances in Modern History (PFMH) dataset; Global Macro Database (GMD); IMF World Economic Outlook (WEO); World Bank World Development Indicators; World Bank World Integrated Trade Solution (WITS).
- Note on measurement limitations: SIPRI gathers extra-budgetary and off-budget military spending when possible and makes estimates using country-tailored methodology, but confidentiality and exclusion of domestic security/paramilitary spending can cause measurement errors.

### Definitions and identification of defense spending booms
- Baseline definition: defense spending booms are periods during which the 2-year moving average of defense spending as a share of GDP rises by at least 1 percentage point, continuing for as long as defense spending does not decline.
- Alternative definitions:
  - Alternative I: same definition but with threshold lowered to 0.5 percentage point of GDP.
  - Alternative II (Marzian and Trebesch, 2025—MT): boom begins when the 2-year moving average growth rate of defense spending as a share of GDP exceeds the in-sample standard deviation of the growth rate (10.5 percent) for two consecutive years, and ends when the growth rate falls below 0 for two consecutive years.
- Baseline counts and characteristics (Online Annex Table 2.2.1):
  - Number of booms (Baseline): 215 total; AEs: 26; EMDEs: 189; Wartime: 99; Peacetime: 116.
  - Alternative I (0.5 percentage point threshold): 403 total; AEs: 49; EMDEs: 354; Wartime: 163; Peacetime: 240.
  - Alternative II (MT definition): 329 total; AEs: 36; EMDEs: 293; Wartime: 111; Peacetime: 218.
- Average size and duration (as reported in Online Annex Table 2.2.1 and Table 2.2.2):
  - Baseline average size: 2.7 (percent of GDP); AEs: 2.4; EMDEs: 2.7; Wartime: 2.5; Peacetime: 2.7.
  - Baseline average duration: 2.7 (years); AEs: 2.5; EMDEs: 2.7; Wartime: 2.8; Peacetime: 2.5.
  - Permanent versus temporary booms (Baseline):
    - Count: Permanent: 112; Temporary: 103.
    - Permanent average size: 3.0; AEs: 2.7; EMDEs: 3.0; Wartime: 3.9; Peacetime: 2.2.
    - Permanent average duration: 3.1 years; AEs: 2.8; EMDEs: 3.2; Wartime: 3.2; Peacetime: 3.0.
    - Temporary average size: 2.3; AEs: 2.1; EMDEs: 2.4; Wartime: 2.8; Peacetime: 1.9.
    - Temporary average duration: 2.2 years; AEs: 2.3; EMDEs: 2.2; Wartime: 2.4; Peacetime: 2.0.

### Narrative identification of exogenous booms
- A narrative approach identifies a subset of peacetime booms plausibly exogenous (driven by external geopolitical factors or alliances and largely unrelated to domestic macro-fiscal conditions).
- The narrative subset excludes booms associated with domestic security concerns, onsite conflicts, economic crises, and commodity price booms.
- Result: 59 narrative boom episodes identified in the post-World War II period.
- Manual validation: each of the 116 peacetime boom episodes was described and classified via a structured prompt to GPT-5 and then manually checked for correct classification into categories:
  1. Exogenous-geopolitical
  2. Exogenous-alliance-driven
  3. Endogenous-macrofiscal
  4. Endogenous-security-domestic
  5. Ambiguous
- Example classification outcome: United States booms starting in 1949, 1965, and 1980 identified as exogenous and consistent with narrative episodes in Ramey (2011).

### Financing of defense spending booms
- Main finding: defense spending booms are mostly deficit financed; this result is robust across alternative boom definitions.
- Average financing decomposition (presented in Online Annex Figure 2.2.3 and Figure 2.2.5):
  - Increase of the deficit is the main financing source, especially in the first years of the boom.
  - Role of nondefense spending reprioritization and revenue mobilization is limited on average and tends to appear in later years.
- Heterogeneity across booms:
  - Considerable heterogeneity exists across booms in how they are financed (Online Annex Figure 2.2.4).
  - Permanent booms: first three years register an increase in the primary deficit and tax revenues, with limited role for defense reprioritization.
  - Temporary booms: mostly deficit financed.
- Financing decomposition calculation note: Nondefense spending reprioritization is computed residually from Change in Deficit = Change in Defense Spending + Change in Nondefense Spending - Change in Revenues.

### Temporary versus permanent booms
- Classification rule: booms are temporary if defense spending (as a share of GDP) returns to pre-boom levels within 10 years; otherwise classified as permanent.
- Key stylized facts:
  - Permanent booms are, on average, larger and last longer than temporary ones.
  - Permanent and temporary booms are evenly split across emerging market and developing economies and advanced economies, and between wartime and peacetime.

### Endogeneity, anticipation, and identification caveats
- Two identification requirements for estimating macroeconomic effects: (i) unanticipated changes in defense spending; (ii) changes plausibly unrelated to the business cycle (exogenous).
- Challenges:
  - Anticipation effects: military spending increases may be announced before actual spending occurs; annual data mitigates but does not eliminate this concern.
  - Implementation over long periods can bias estimated effects downward.
  - Difficulty of fully addressing endogeneity without procurement-level data or large-scale news-based measures of defense spending announcements.
- Mitigations:
  - Analysis focuses in part on peacetime booms (excluding wartime booms defined as those that immediately follow a conflict or culminate in an onsite conflict within three years), and excludes fragile/conflict-affected states and EMDE commodity exporters in some analyses to avoid confounding from domestic conflicts and commodity price cycles.

*Source: IMF staff compilation (Annex Table 2.1.2., Online Annex Tables and Figures as provided in the source content).*

### 1. Permanent Defense Spending Booms (Average)

### 1. Permanent Defense Spending Booms (Average)

### Predictability and Endogeneity of Defense Spending
- Panel OLS regressions show defense spending is predictable by:
  - Armed onsite conflict (one-year lag) with coefficients: 6.650***, 6.909***, 5.593***, 6.015***, 5.031**, 5.185** (standard errors in parentheses: (1.651), (1.565), (1.823), (1.712), (2.187), (2.018)).
  - Government revenue over GDP (one-year lag) with coefficients: 0.195***, 0.210***, 0.184**, 0.196**, 0.135, 0.150* ((0.067), (0.066), (0.078), (0.076), (0.090), (0.088)).
  - GDP growth (one-year lag) coefficients are generally small and not consistently significant (examples: 0.061, 0.057, 0.065, 0.082, 0.074, 0.080 with standard errors (0.061), (0.076), (0.067), (0.091), (0.080), (0.101)).
- Subsample regressions (post-World War II and post-Cold War panels, and exclusions of FCS and commodity-exporting EMDEs) show similar predictive power of armed conflict and revenues; R-squared values across specifications range (examples): 0.179, 0.164, 0.186, 0.161, 0.211, 0.205.
- Interpretation:
  - In the chapter sample, defense spending cannot be assumed exogenous to local economic conditions.
  - Defense spending increases after onsite conflicts and in periods of higher GDP growth or rising government revenue (e.g., windfall commodity revenues).
  - Excluding fragile and conflict-affected states (FCS) and commodity-exporting EMDEs reduces some endogeneity: boom start dates are predicted by armed conflicts but not by GDP growth, government revenues, or recessions, implying peacetime booms (excluding conflict-related booms) can be considered largely exogenous.

### Predictors of Defense Spending Booms (Alternative Definitions)
- Regressions of a dummy for defense spending booms on lagged variables show:
  - Armed onsite conflict (one-year lag) coefficients (examples across columns): 3.061***, 2.958***, 2.650***, 2.435***, 2.389***, 2.347***, 3.029***, 1.624** (standard errors: (0.469), (0.540), (0.561), (0.643), (0.637), (0.742), (0.976), (0.758)).
  - Government revenue over GDP (one-year lag) sometimes positive and marginally significant (example: 0.046* with (0.027); 0.045* with (0.025); 0.068** with (0.030)).
  - GDP growth (one-year lag) coefficients mostly not significant (examples: -0.023, -0.044, -0.047, -0.058).
- R-squared values for boom-prediction regressions are low (examples): 0.025, 0.021, 0.023, 0.022, 0.027, 0.028.
- Alternative boom definitions (including Alternative I with 0.5 percentage point threshold and Alternative II following Marzian and Trebesch (2025)) yield similar conclusions: armed conflicts predict boom starts; peacetime booms are less predictable by domestic macroeconomic variables.

### Macroeconomic Dynamics Following Booms (Local Projections Framework)
- Main specification:
  - Local projections estimated with OLS regress cumulative changes over a 5-year window.
  - Dependent variables include GDP and subcomponents (government consumption, private consumption, investment, imports, exports), factors of production (capital stock, employment, TFP), fiscal indicators (defense and nondefense spending, overall balance, debt, social spending), and CPI.
  - Key explanatory variable: dummy denoting start of defense spending boom (Boom_i,t).
  - Controls: lagged dependent variable and 4 lags of the boom variable; country and year fixed effects; standard errors clustered at country level.
- Robustness:
  - Alternative boom definition (0.5 threshold, Alternative I) and OLS using defense spending as share of potential GDP produce broadly similar patterns.
  - Results are robust to excluding Russia and post-Soviet states.

### Effects on Output and Components (Peacetime Booms, Excluding FCS and Commodity-Exporting EMDEs)
- Defense spending booms are sizable and persistent on average (Online Annex Figure 2.3.1).
- Baseline finding: peacetime defense spending booms are followed, on average, by a 3 percent increase in GDP over five years.
- Long-run TFP:
  - Peacetime defense spending booms are followed by an increase in total factor productivity (TFP) three years after the boom onset.
  - When adjusting for capacity utilization, the short-term TFP coefficient is muted; the coefficient increases over time and becomes significant 10 years after the start of the boom.
- Components (three-year-ahead, real percent change):
  - Government consumption, private consumption, GFCF, imports, exports show heterogeneous responses across specifications; darker-colored bars in figures denote coefficients significant at the 10 percent level.
  - Factors of production three-year-ahead include capital stock, employment, and TFP responses (figures indicate mixed magnitudes and significance).

### Temporary vs Permanent Booms
- Distinction:
  - A boom is defined as permanent if the direction of change in defense spending over GDP in year t is the same as in the following 10 years; otherwise temporary.
- Findings:
  - The baseline 3 percent five-year GDP increase is driven by booms that lead to a permanent increase in the defense spending–to–GDP ratio.
  - Permanent booms:
    - Trigger durable increases in military procurement, encourage firms to expand capacity and invest in specialized capital (production lines, R&D, supplier networks).
    - Tend to crowd in private investment and employment rather than merely time-shifting activity.
    - Induce stronger labor supply responses as households anticipate persistently higher taxes.
    - Real GDP increase associated with permanent booms is sustained and reaches over 6 percent by year 5.
    - Average size of permanent booms is 3 percent of GDP; implied multiplier is about 2.
  - Temporary booms:
    - Followed by a temporary increase in GDP that peaks in year three before fading away (Online Annex Figure 2.3.5).

### Fiscal Consequences and Costs
- Defense spending booms lead to a significant rise in the fiscal deficit on average.
- Government debt-to-GDP ratio:
  - Does not rise on average across all booms because wartime booms raise debt while peacetime booms show an opposite decline in debt.
- Nondefense spending as a share of GDP:
  - Declines in wartime booms but moderately increases in peacetime booms (Online Annex Figure 2.3.7, panel 1).
- Debt decomposition (subset of burst episodes, ≈ one third of episodes due to data availability):
  - The rise in debt is driven roughly equally by the primary deficit and interest on past debt.
  - GDP growth and the stock-flow adjustment contribute negatively to the change in debt.
- Social spending:
  - For booms financed by spending reprioritization, reductions in social spending are observed (panels indicate declines in social protection, health, education three years ahead; magnitudes shown in figures).

### Robustness to Additional Controls
- Effect of defense spending booms on real GDP under baseline specification is similar when using an expanded set of controls (includes 4 lags of dependent and shock variables, nondefense government spending and government revenue as share of potential GDP, and a contemporaneous war dummy).
- Figures plot baseline vs additional-controls estimates showing similar cumulative responses for peacetime booms.

*Source: IMF staff calculations (from Online Annex, CHAPTER 2: DEFENSE SPENDING: MACROECONOMIC CONSEQUENCES AND TRADE-OFFS).*

### 2024. Solid lines denote point estimates, and shaded

### ch2onlineannex - 2024. Solid lines denote point estimates, and shaded

### Online Annex 2.4 — Firm-level Analysis: data and research design
- Sample: over 4.6 million private non-financial firms in 41 countries between 1995 and 2023.
- Data source: Orbis dataset; cleaning procedure follows Kalemli-Özcan and others (2024), and Díez, Fan, and Villegas-Sanchez (2021).
- Sample restrictions:
  - Drops firms with less than 5 observations.
  - Includes non-financial private sector firms in manufacturing and trade.
  - Restricted to countries with at least 5,000 observations over the sample period.
- Empirical objective: test whether sensitivity of investment to internal funds (investment-to-cash flow sensitivity) differs during defense spending booms, separately for booms associated or not with an increase in public debt-to-GDP ratio.
- Baseline regression specification (Huang, Panizza, and Varghese (2018) style):
  - Dependent variable: I/A (investment scaled by assets).
  - Key regressor: CF/A × DS_Boom (cash flow scaled by assets interacted with defense spending boom indicator).
  - Defense spending boom indicator takes three values: (i) not in a boom, (ii) boom not associated with increasing public debt, (iii) boom associated with increasing public debt.
  - Controls: firm fixed effects (휗i), sector-year fixed effects (휇s,t), country-year fixed effects (훿c,t).
  - Variables winsorized at the 2.5 and 97.5 percentiles; assets A winsorized at the 97.5 percentile.
  - Standard errors clustered at the firm level.
- Defense-related sectors identification: NACE Rev.2 at the 4-digit level including NACE 25.40, 30.30, 30.40, 26.30, 26.51, 26.70, 20.51, and 30.11.

### Online Annex 2.4 — Firm-level Analysis: key empirical results
- Baseline finding: positive coefficient β1 indicates firm investment is sensitive to availability of internal cash flow even absent defense spending booms.
- Effects when boom is not associated with rising public debt:
  - Sensitivity of investment to cash flow declines, suggesting positive demand effects from increased defense spending ease firms’ financing constraints.
  - Stronger evidence when restricting the sample to defense-related sectors: coefficient is not statistically different from zero in that subsample.
- Effects when boom is associated with rising public debt:
  - Investment–cash flow sensitivity is higher than when there is no boom, consistent with crowding out from rising public debt increasing firms’ financing constraints and borrowing costs.
- Arms importers subsample (defined as average defense imports-to-defense spending ratio above the sample median):
  - Investment–cash flow sensitivity does not vary with the presence or not of a defense spending boom (regardless of financing), consistent with large import leakages attenuating positive domestic demand effects.
  - Reduced sample size prevented separating booms with or without rising public debt for this subsample.
- Selected regression magnitudes and diagnostics (from Online Annex Table 2.4.1; all numeric values preserved):
  - Number of observations: 44,119,720; 44,119,343; 152,879; 3,025,050 across columns (1)–(4).
  - R2: 0.21; 0.30; 0.27; 0.45 across columns (1)–(4).
  - Lagged (I/A)i,s,c,t-1 coefficients: -0.0419*** (0.000), -0.0617*** (0.000), -0.0137*** (0.004), -0.1053*** (0.001).
  - (S/A)i,s,c,t coefficients: -0.0054*** (0.000), -0.0093*** (0.000), -0.0129*** (0.001), -0.0093*** (0.000).
  - (CF/A) × (DS Boom = 0): 0.0237*** (0.000), 0.0207*** (0.000), 0.0589*** (0.003) in relevant columns.
  - (CF/A) × (DS Boom = 1, without Rising Debt): -0.0087*** (0.001), 0.0126*** (0.002), 0.0042 (0.044).
  - (CF/A) × (DS Boom = 1, with Rising Debt): 0.0025 (0.007), 0.0270*** (0.007), 0.0818* (0.047).
  - (CF/A) × (DS Boom = 0) in column (4): 0.0384*** (0.001); (CF/A) × (DS Boom = 1) in column (4): 0.0381*** (0.003).
  - Significance notation: *** p<0.01; ** p<0.05; * p<0.1.

### Online Annex 2.5 — Fiscal multipliers: empirical estimates — main specification
- Sample: panel of 138 countries over 1946–2024.
- Methodology: panel local projection methods following Ramey and Zubairy (2018).
- Estimation equation:
  - Cumulative output ∑_{j=0}^h Y_{i,t+j} regressed on cumulative defense spending ∑_{j=0}^h D_{i,t+j} plus controls.
  - Both output and defense spending normalized by potential GDP (potential GDP estimated by detrending GDP by a sixth-order time polynomial; robustness to linear, quadratic, and fourth-order polynomials reported).
  - Controls: vector X (1-4 year lags of GDP, defense spending, non-defense spending as share of potential GDP), contemporaneous war dummy, country and year fixed effects.
  - Standard errors clustered at the country level.

### Online Annex 2.5 — Heterogeneous multipliers and definitions
- Heterogeneity dimensions: income group (AEs vs EMDEs), wartime versus peacetime, temporary versus permanent defense buildups, arms importers versus exporters, financing source (deficit-financed vs other), current versus capital spending, exchange rate regime, public investment efficiency, post-World War II versus post-Cold War periods.
- Definitions:
  - Temporary defense change: direction of change in defense spending as a share of GDP relative to the previous period is the same for the next ten years.
  - Importer (exporter): average share of arms exports in arms trade is below (above) the median.
  - Deficit-financed: annual change in defense spending mostly driven by change in the deficit rather than revenues or nondefense spending.
  - Current spending: personnel and operating expenses; capital spending: equipment and infrastructure.
  - Exchange rate regime classification: fixed versus flexible based on Ilzetzki and others (2019, 2021); fixed if coarse classification code is below 2, flexible if equal or larger than 2.
  - Public investment efficiency: high (low) if the country’s average investment efficiency score (October 2025 Fiscal Monitor) is above (below) the median.

### Online Annex 2.5 — Heterogeneous multiplier results (selected values)
- Table/exhibit of cumulative multipliers horizons 0–5 (AEs vs EMDEs; Peace vs War; Temporary vs Permanent) — selected numeric entries preserved below:
  - Horizon 0: AEs 0.432***; EMDEs 1.842***; Peace 1.935***; War 0.959; Temporary 1.196***; Permanent 2.273***.
  - Horizon 1: AEs 0.596***; EMDEs 2.186***; Peace 2.031***; War 1.634***; Temporary 1.510***; Permanent 2.580***.
  - Horizon 2: AEs 0.726***; EMDEs 2.422***; Peace 2.126***; War 1.926***; Temporary 1.717***; Permanent 2.638***.
  - Horizon 3: AEs 0.825***; EMDEs 2.540***; Peace 2.245***; War 1.896***; Temporary 1.859***; Permanent 2.613***.
  - Horizon 4: AEs 0.823***; EMDEs 2.477***; Peace 2.268***; War 1.620***; Temporary 1.896***; Permanent 2.403***.
  - Horizon 5: AEs 0.828***; EMDEs 2.359***; Peace 2.166***; War 1.462***; Temporary 1.906***; Permanent 2.137***.
- Arms importer vs exporter, and current vs capital spending (selected horizon values preserved):
  - Horizon 0: Importer 0.671**; Exporter 3.073***; No (deficit-financed = No) 1.077***; Yes (deficit-financed = Yes) 1.009*; Current 1.722***; Capital 0.994.
  - Horizon 1: Importer 1.101***; Exporter 3.143***; No 1.189***; Yes 1.725***; Current 2.031***; Capital 1.348**.
  - Horizon 2: Importer 1.403***; Exporter 3.119***; No 1.271***; Yes 2.118***; Current 2.245***; Capital 1.291*.
  - Horizon 3: Importer 1.607***; Exporter 3.134***; No 1.33***; Yes 2.244***; Current 2.352***; Capital 1.198.
  - Horizon 4: Importer 1.684***; Exporter 2.983***; No 1.294***; Yes 2.26***; Current 2.284***; Capital 1.205.
  - Horizon 5: Importer 1.713***; Exporter 2.775***; No 1.254***; Yes 2.203***; Current 2.173***; Capital 1.094.
- Note: significance notation preserved: *** p<0.01; ** p<0.05; * p<0.1. AEs = advanced economies; EMDEs = emerging markets and developing economies.

### Online Annex 2.5 — Additional results and robustness
- Post-Cold War results: defense spending multipliers are higher under fixed exchange rate regimes and when public investment efficiency is high.
- Charted finding: higher multipliers for advanced economies than for EMDEs in post-Cold War sample (a reversal when sample extended to 1946).
- European Union OLS multipliers (separate panels for post-World War II and post-Cold War periods):
  - For post-Cold War period, defense spending multipliers in Europe seem to be greater than one.

### Online Annex 2.5 — Empirical strategies to mitigate endogeneity and diagnostics
- Two main approaches to mitigate endogeneity, yielding multipliers closer to unity:
  1. Narrative approach:
     - Uses subset of narrative defense spending booms as instrument for defense spending (plausible exogeneity and strong instrument).
     - Online Annex Table 2.5.3: narrative booms cause defense spending to rise significantly and yield first-stage weak-instrument F-statistics exceeding rule-of-thumb value of 10 at all forecast horizons.
     - IV first-stage diagnostics (selected values preserved):
       - IV Coefficient (Post-WWII): horizons 0–5 = 0.01***; 0.03***; 0.05***; 0.07***; 0.08***; 0.10***.
       - IV Coefficient (Post-Cold War): horizons 0–5 = 0.01***; 0.03***; 0.05***; 0.06***; 0.08***; 0.08***.
       - Weak IV F-statistics (Post-WWII): 161.0; 196.4; 118.4; 92.3; 77.8; 74.6 for horizons 0–5 respectively.
       - Weak IV F-statistics (Post-Cold War): 154.4; 87.3; 37.8; 22.6; 15.5; 14.4 for horizons 0–5 respectively.
  2. Defense alliances approach:
     - Subsamples of countries where exogeneity of defense spending is more plausible: members of NATO and IMCTC, focusing on post-Cold War period.
     - For that sample, defense spending booms are not anticipated by conflicts or local economic conditions (Online Annex Table 2.5.4).
     - Controlling for countries’ geopolitical risk index (subset of 42 countries) yields defense multipliers even closer to unity (Online Annex Figure 2.5.3).
- Alliance sample details:
  - NATO includes 32 member countries; IMCTC includes 41 countries; contemporaneous membership treated as proxy for cooperation going back in time.
  - Fragile and conflict states excluded from the alliance sample.
- Exogeneity regression (Online Annex Table 2.5.4) — selected numeric entries preserved:
  - Number of observations in columns: 1,055; 1,055; 1,020; 1,055; 1,020; 888; 888; 888; 888; 888.
  - R2 values: 0.209; 0.186; 0.199; 0.186; 0.226; 0.257; 0.257; 0.266; 0.257; 0.267.
  - Number of countries: NATO columns use 32; IMCTC columns use 27 where indicated.
  - Lagged armed on-site conflict coefficients examples: 12.333 (8.979), 12.720 (9.398), -0.670 (2.607), -0.763 (2.393) — standard errors in parentheses.
  - Other covariates include GDP Growth_{i,t-1}, Government Revenue over GDP_{i,t-1}, Recession_{i,t-1} with reported coefficients and standard errors in table.

### Online Annex 2.5 — IV defense spending multiplier controlling for geopolitical risk
- IV specification controls for historical geopolitical risk index (Caldara and Iacoviello 2022) for subset of 42 countries.
- Plot description: solid lines denote point estimates, shaded area denotes 90 percent confidence interval.
- Years after onset of defense spending boom used on horizontal axis in plotted cumulative responses.

### Online Annex 2.5 — Literature review and historical results
- Summary: estimates of defense spending multipliers vary substantially across studies.
  - Foundational estimates by Hall (2009) and Barro and Redlick (2011) reported multipliers below unity.
  - Later research adjusted estimates upwards toward values near 1.5.
  - More recent studies indicate defense multipliers ranging from 1.3 to 2 among European countries after the Cold War.
  - Majority of analyses focus on advanced economies; limited estimates for EMDEs.
- Historical extension to 1800:
  - Using standard OLS yields defense spending multipliers above 2.
  - Using narrative booms as instruments yields multipliers closer to 1 (Online Annex Figure 2.5.4).

### Online Annex 2.6 — Fiscal multipliers: modeling simulations
- Model: Flexible System of Global Models (FSGM), semi-structural combining micro-founded and reduced-form formulations (see Andrle and other (2015) for model description).
- FSGM used to conduct model-based simulations of defense spending shocks (text indicates additional model details are provided in referenced literature).

*Source: IMF staff calculations (ch2onlineannex).*

### 1.5 cumulative over 20 months

### 1.5 cumulative over 20 months

### Empirical evidence on defense spending multipliers
- Barro and Redlick (US, 1947–2007, VAR): "1.5 cumulative over 20 months".
- Ramey (US, 1930–2006, OLS panel): "0.4 to 0.5 on impact and 0.6 to 0.7 over 2 years".
- Nakamura and Steinsson (US, 1939–2008, VAR): "0.6 to 1.2 for peak and cumulative multipliers".
- Kollias and Paleologou (US - State-level, 1966–2006, IV panel with State-level variation in defense contracts): "1.5 over 2 years".
- Ben Zeev and Pappa (EU, 1961–2014, VAR): "Zero".
- Dupor and Guerrero (US, 1947–2007, VAR): "1.3 or 2.14 cumulative multiplier, depensing on shock idenitification strategy".
- Ramey and Zubairy (US - State-level, 1951–2014, GMM panel with State-level variation in defense contracts): "Between zero and 0.5 cumulative multipliers over 2 to 4 years".
- Olejnik (US, 1889–2015, LP): "Around 0.7".
- Olejnik (Short-run military expenditures in NATO's Eastern Flank, 1999–2021, LP): "0.6 on impact and 1.5-1.6 at year 2 and 3".
- Antolin-Diaz and Surico (Central and Eastern European countries, 1999–2021, LP): "0.6 on impact and 1.5-1.6 at year 2 and 3".
- Ben Zeev, Pappa, and Scola Gagliardi (US, 1890–2015, VAR): "Below or around 1 at business cycle frequencies, rising to exceed 1 at long horizons".
- García, Sarasa-Flores, and Ulloa (European countries, 1960–2024, VAR): "2 on impact, falling to 0.92 after 10 years".
- Furceri et al. (EU, 1995–2023, LP, IMF Working Paper 2026): "1.4 on impact with a peak at 1.6 at year 2".
- Furceri et al. (EU, 1989–2023, LP): "1.3 on impact rising to 1.9 after 2 years" and "1.5 to 1.9 over 3 years using procurement data".
- Source summary: "Source: IMF staff compilation." Note: methodological labels preserved exactly: "GMM = generalized methods of moments; LP = local-projections; OLS = ordinary least squares; VAR = vector autoregression."

### Model framework and scenario analysis (FSGM / EUROMOD)
- Model structure:
  - "annual, multi-region, general equilibrium model of the global economy."
  - EUROMOD module of FSGM used; includes "a bloc for each of the 11 major euro area countries plus 13 other blocs", covering stand-alone blocs: "China, India, Japan, Switzerland, Sweden, United Kingdom, and United States" and six other regions.
- Alternative scenario: higher risk premia
  - Assumes "a one-off increase in risk premia by 50 basis points" to model "possible implications of rising spreads in response to higher spending, especially in countries with limited fiscal space, lacking any coordination."
  - Scenario outcomes (qualitative summary from text): "more muted output and price response, and a larger increase in public debt."
  - Figure labeling and interpretation preserved: "Online Annex Figure 2.6.1. Higher Risk Premia" and "The higher risk premia scenario (blue lines) assumes a 50 basis points increase in terms premia in 2026."
- Model variables plotted in annex figures (labels preserved):
  - "1. GDP Path of the Shock and Real GDP (Percent difference)"
  - "2. Real Consumption (Percent difference)"
  - "3. Real Investment (Percent difference)"
  - "4. Core CPI Inflation"
  - "5. Long-Term Interest Rate"
  - "6. Government Deficit/GDP"
  - "7. Government Debt/GDP"
  - "8. Current Account/GDP"
  - Baseline and Higher risk premia lines shown in figures.

### Historical multipliers visualization and estimation notes
- "Online Annex Figure 2.5.4. Defense Multipliers, since 1800 (Cumulative multipliers)" presents:
  - Panel 1: "OLS Estimates"
  - Panel 2: "IV Estimates"
  - Note: "The panels plot local-projection estimates of cumulative responses of output to defense spending. Solid lines denote point estimates, and shaded areas denote 90 percent confidence intervals. IV = instrumental variable; OLS = ordinary least squares."

### Key quantitative points and methodological terms (exact phrasing preserved)
- Exact shock assumption in alternative scenario: "one-off increase in risk premia by 50 basis points".
- Exact year cited for the premia change: "in 2026."
- Confidence interval notation preserved for figures: "90 percent confidence intervals."
- Exact methodological abbreviations preserved: "GMM", "LP", "OLS", "VAR", "IV".

*Source: ch2onlineannex - 1.5 cumulative over 20 months (IMF staff compilation, Online annex material from Chapter 2).*

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_Source: https://www.imf.org/-/media/files/publications/weo/2026/april/english/ch2onlineannex.pdf_