## Playing with blocs: Quantifying Decoupling — selected chapters (Introduction; 3.1 Setup; 3.5 Robustness and sensitivity; References; Appendices)

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### Trade trends and basic facts
- After a long era of ever-increasing globalization, the past decade saw substantial headwinds to economic integration, including Brexit, the US-China trade war, and the rupture of economic relations between the West and Russia.
- World goods trade relative to economic activity did not fall between 2015 and 2023; the trade-GDP ratio remained resilient and partly reversed the downward trend that started in 2009.
- The trade-GDP ratio did not fall for the US, China, and the EU over 2015-2023.
- Even major parties to trade conflicts did not experience a discernible fall in total trade.

### Evidence on reallocation vs. deglobalization (selected figures)
- Table 1 (Change in trade (2015-2023)) — selected entries (percentage changes in the imports-GDP ratio from source to destination):
  - USA → USA: -0.275
  - USA → China: 0.262
  - USA → EU: 0.015
  - China → USA: -0.401
  - China → China: 0.237
  - China → EU: 0.137
  - EU → USA: 0.050
  - EU → China: -0.066
  - EU → EU: 0.148
  - ROW → USA: 0.012
  - ROW → China: 0.047
  - ROW → EU: 0.035
  - ROW → ROW: 0.105
  - Change in total imports-to-GDP: USA -0.070; China 0.005; EU 0.128; ROW 0.076
- Interpretation: trade between the US and China fell, but trade between those economies and the rest of the world increased — the world economy is experiencing decoupling rather than deglobalization.

### Measuring decoupling and classification into blocs
- Goal: measure decoupling and quantify its impact on real GDP and income across a large sample of countries.
- Data-driven classification approach:
  - Gravity framework: project log changes in bilateral goods trade over 2015-2023 on importer and exporter fixed effects; residuals reflect relative changes in bilateral trade barriers.
  - Transform residual ŵ_mn into change in bilateral trade costs via Δlnτ_mn = ŵ_mn/(1−γ).
  - Classification into 3 groups based on changes in trade costs with US and China:
    - US bloc: average import and export costs with respect to the US fell, and trade costs with respect to China rose.
    - China bloc: opposite pattern.
    - Unaligned: trade costs with the US and China changed in the same direction.
  - Sample classification results:
    - Full DOTS sample of 187 countries: 43 moved towards the US bloc, 46 moved towards the China bloc, and 98 were unaligned.
- Notes:
  - Classification based on changes in relative trade costs, not on initial bilateral trade levels.
  - Only trade linkages considered (not FDI, remittances, technology transfers, migration, etc.).

### Quantitative framework and identification strategy
- Model: multi-country, multi-sector international trade model (references to Huo, Levchenko, and Pandalai-Nayar (2025); Bonadio et al. (2021); Bonadio et al. (2025)).
- Data and calibration:
  - Bilateral trade flows up to 2023 from IMF Direction of Trade Statistics (DOTS), covering 187 countries.
  - Nominal GDP from IMF World Economic Outlook (WEO).
  - Quantitative model calibrated with OECD 2021 Inter-Country Input-Output (ICIO) tables; model sample reduced to 66 countries and aggregated to 22 sectors.
  - 2015 used as initial (pre-shock) period.
- Identification challenge and solution:
  - Gravity regressions identify relative trade cost changes only; domestic absorption for 2023 not available.
  - Scale gravity-implied bilateral trade cost changes by a common factor so model matches the 2015-23 change in the world trade-GDP ratio.
  - The uniform across-the-board decline in worldwide trade costs required to match the increase in world trade-GDP ratio is −0.3% (Δlnτ_base = −0.003).

### Key model setup elements (from section 3.1)
- Economy structure:
  - N countries, J sectors.
  - Households: Fréchet idiosyncratic labor productivity b_nj(ω) ∼ Fréchet(ξ_nj, μ).
  - Labor supply parameters: ψ (Frisch elasticity), μ (sectoral labor supply dispersion); regularity condition μ > ψ+1.
- Consumption and trade:
  - Final consumption CES across sectors with ρ = 1.
  - Sectoral Armington aggregates with trade-with-iceberg costs τ^f_mn j and τ^x_mi,nj for intermediates.
  - Trade elasticities: γ = 4 (final consumption), ν = 4 (intermediate inputs).
- Production:
  - Representative firm: Y_nj = Z_nj H_nj^{η_j} X_nj^{1−η_j}.
  - Intermediate aggregation elasticities: ε = 1 (cross-sector intermediates), ν = 4 (source substitution).
- Calibration parameters (summary):
  - ρ = 1; ε = 1; γ = 4; ν = 4.
  - ψ = 1; μ = 1.5.
  - η_j: ICIO value added share in gross output; π_f and π_x shares from ICIO.
- Aggregate outcomes reported:
  - Real GDP change (first-order approximation): d ln G_n = Σ_j η_j (P_nj,0 Y_nj,0 / G_n,0) d ln H_nj.
  - Real income defined as W_n / P_n (real wage).
- Solution method: exact-hat algebra (ˆX = X′/X) with iterative algorithm summarized in Appendix B.

### Baseline quantitative findings (2015–2023 factual simulation)
- Calibration target: world trade/GDP ratio from 21.8% in 2015 to 22.6% in 2023 (0.8 percentage point increase); implies Δlnτ_base = −0.003.
- Table 4 — Log change in average trade costs between blocs (weighted by 2015 bilateral trade flows), average Δlnτ_mn + Δlnτ_base:
  - Exporter↓ | Importer→ Bloc USA | Bloc CHN | Unaligned | Overall
  - Bloc USA: -0.046 0.040 0.004 -0.003
  - Bloc CHN: 0.114 -0.072 0.023 0.050
  - Unaligned: -0.033 -0.035 -0.008 -0.024
  - Overall: 0.002 -0.012 0.003 0.000
- Interpretation of trade-cost patterns:
  - Trade costs between the US and China blocs increased: China bloc → US bloc increased by 11.4% (0.114); US bloc → China bloc rose by 4.0% (0.040).
  - These cross-bloc increases were counteracted by reductions in within-bloc trade costs and reductions in import trade costs from unaligned countries.
  - Only the China bloc experiences an overall increase in export costs; none of the blocs see significant increases in overall import costs.
  - Conclusion: despite decoupling, overall trade costs have not increased.
- Baseline real outcomes (Table 5 — Baseline change in Real GDP and Real Income, Percentage Points, 2015-2023):
  - Overall — Real GDP: Median 0.588; p25 0.061; p75 1.297 — Real Income: Median 0.619; p25 0.059; p75 1.322
  - Bloc USA — Real GDP: Median 0.532; p25 0.125; p75 0.712 — Real Income: Median 0.536; p25 0.147; p75 0.699
  - Bloc CHN — Real GDP: Median 0.299; p25 -0.263; p75 0.773 — Real Income: Median 0.372; p25 -0.261; p75 0.780
  - Unaligned — Real GDP: Median 0.787; p25 0.034; p75 1.397 — Real Income: Median 0.755; p25 0.066; p75 1.432
- Distributional and notable country outcomes:
  - Median country experienced a 0.6% real GDP and real income increase from the rewiring of trade and inferred trade cost changes occurring from 2015 to 2023.
  - Result holds even when considering only the relative trade cost changes from the gravity regression (excluding the −0.3% worldwide uniform decrease).
  - Across the 66-country model sample, 51 out of 66 countries experienced real income increases from the observed trade cost changes.
  - Nonaligned countries on average experienced larger income changes (0.8%) than countries moving to the US or China blocs.
  - US and China experience changes close to zero.
  - Heterogeneity large: Vietnam gains 6.9%; Laos gains 3.5%; Baltic countries lose 3–5%.
- Decomposition (Table B2):
  - Real GDP — Overall: Total 0.637; Δlnτ_mn 0.574; Δlnτ_base 0.074.
  - Real Income — Overall: Total 0.690; Δlnτ_mn 0.610; Δlnτ_base 0.074.
  - Note: about 90% (≈0.574/0.637) of the total real income change is due to bilateral relative trade cost changes rather than the worldwide shift Δlnτ_base.

### Counterfactual bloc-assignment exercises and welfare implications
- Construction: for each country, replace factual trade-cost changes with bloc-level averages while preserving the country’s trade-weighted average change (see counterfactual formulas and adjustment factors in section 3.1 and Appendix B).
- Summary results (selected medians and percentiles reported in section 3.5 and Table 6 / Figure 5):
  - Moving to Bloc USA (Real GDP; Real Income) — Overall median: -0.445; -0.448; p25: -1.534; -1.512; p75: 0.969; 0.945.
  - Moving to Bloc CHN (Real GDP; Real Income) — Overall median: -0.269; -0.289; p25: -1.465; -1.430; p75: 0.740; 0.717.
  - Moving to Unaligned (Real GDP; Real Income) — Overall median: -0.593; -0.589; p25: -0.944; -0.967; p75: 1.203; 1.253.
- Bloc-specific median effects:
  - China-bloc countries moving to the US bloc: six out of ten would benefit; median real income benefit for these China-bloc countries: 0.66%.
  - US-bloc countries moving to the China bloc: eight out of fourteen US-bloc countries gain; median US-bloc country gains 0.2%.
  - Unaligned countries on average lose from joining either bloc.
  - On average, countries moving to the US (or China) bloc would have gained more by moving to the opposite bloc — suggests observed bloc alignment corresponds poorly to trade-related economic interests and that non-economic motives may drive bloc choices.
- Heterogeneity: substantial within-bloc variation — some countries would win and others would lose from switching blocs (examples: Saudi Arabia, Latvia, Lithuania could see GDP increases of over 2% by becoming unaligned).

### Robustness and sensitivity (section 3.5; selected checks)
- Observable tariffs:
  - Tariff data (UN-TRAINS) cover changes between 2015 and 2021.
  - Findings: large dispersion in effectively applied tariff changes; average applied tariff change close to 0; 39.5% of bilateral pairs experience tariff decreases.
- Alternative bloc assignment: Leiden community-detection algorithm
  - Procedure: apply Leiden algorithm to residualized trade growth; perform 100 draws; classify based on frequency of co-classification with US or China.
  - Comparison: baseline more conservative (classifies more countries as unaligned); two methods agree more than 70% of the time when both assign a country to either US or China bloc.
- Alternative start and end years:
  - Start year 2016: bloc assignment similar to baseline; model-sample classifications do not flip bloc membership relative to baseline.
  - Pre-Covid sample 2015-2019:
    - Trade-costs: cross-bloc increases already present; within-bloc decreases less pronounced.
    - Baseline real income median: −0.06% (2015-2019) vs +0.6% (2015-2023).
    - Interpretation: cross-bloc increases preceded within-bloc decreases; COVID-19 and other shocks may have influenced timing.
- Placebo: 2002–2007
  - No evidence of decoupling in 2002–2007; most bloc pairs experienced trade cost declines.
- Validation vs Head and Ries (HR) method:
  - Implement procedure on years with domestic absorption data and compare to HR.
  - Average difference at the mean: -0.9%; median difference: -0.03%; correlation: 0.79.
  - Table C11 (2002–2007 summary): Model implied average −0.105; HR average −0.096; Difference average −0.009; Median −0.0004.

### Key limitations and caveats (explicit from the paper)
- Simulations abstract from dynamic productivity and knowledge transfer effects, economies of scale, and frictions to reallocation (incomplete contracts, sunk costs, search costs).
- Gravity-residual measure of bilateral trade cost changes does not disentangle underlying sources (trade policy, preference shifts, bilateral markups, other bilateral shocks).
- World events in 2020-2022 (Covid-19 disruptions, Russia-Ukraine war, fiscal stimulus, high inflation) are not modeled explicitly and may be partially reflected in data-inferred trade cost changes; Appendix C.3 presents 2015-2019 results for comparison.

### Practical numeric highlights (preserved exactly)
- World trade/GDP ratio: 21.8% in 2015 → 22.6% in 2023 (0.8 percentage point increase).
- Calibrated common trade-cost shifter: Δlnτ_base = −0.003 (implying average decrease in trade costs of 0.3%).
- Trade-cost changes between blocs (Table 4, weighted averages):
  - Bloc CHN → Bloc USA: 0.114
  - Bloc USA → Bloc CHN: 0.040
  - Unaligned → Unaligned: -0.008
  - Overall row: 0.002 (to Bloc USA); -0.012 (to Bloc CHN); 0.003 (to Unaligned); Overall 0.000
- Baseline median real GDP change: 0.588 percentage points (Overall); median real income change: 0.619 percentage points (Overall).
- Decomposition (Table B2) — Real GDP Overall: Total 0.637; Δlnτ_mn 0.574; Δlnτ_base 0.074. Real Income Overall: Total 0.690; Δlnτ_mn 0.610; Δlnτ_base 0.074.
- Counterfactual medians (moving to blocs, section 3.5):
  - Moving to Bloc USA — Overall median Real GDP: -0.445; Real Income: -0.448.
  - Moving to Bloc CHN — Overall median Real GDP: -0.269; Real Income: -0.289.
  - Moving to Unaligned — Overall median Real GDP: -0.593; Real Income: -0.589.
- Tariff-change statistic: 39.5% of bilateral pairs experience tariff decreases (2015–2021 UN-TRAINS data).

*Source: wpiea2025263-source-pdf (IMF Working Paper — selected chapters and appendices).*

### 1. Introduction

### 1. Introduction

### Trade trends and basic facts
- After a long era of ever-increasing globalization, the past decade saw substantial headwinds to economic integration, including Brexit, the US-China trade war, and the rupture of economic relations between the West and Russia.
- World goods trade relative to economic activity did not fall between 2015 and 2023; the trade-GDP ratio remained resilient and partly reversed the downward trend that started in 2009 (Figure 1(a)); the vertical line in figures denotes 2015.
- The trade-GDP ratio did not fall for the US, China, and the EU over 2015-2023 (Figure 1 panels (b)-(d)).
- Even major parties to trade conflicts did not experience a discernible fall in total trade.

### Evidence on reallocation vs. deglobalization
- Proximate explanation: countries that disengaged from each other increased trade with other countries; bilateral reallocation offset declines between certain pairs.
- Table 1 (Change in trade (2015-2023)) reports percentage changes in the imports-GDP ratio from source economy (rows) to destination economy (columns). Selected entries:
  - USA → USA: -0.275
  - USA → China: 0.262
  - USA → EU: 0.015
  - China → USA: -0.401
  - China → China: 0.237
  - China → EU: 0.137
  - EU → USA: 0.050
  - EU → China: -0.066
  - EU → EU: 0.148
  - ROW → USA: 0.012
  - ROW → China: 0.047
  - ROW → EU: 0.035
  - ROW → ROW: 0.105
  - Change in total imports-to-GDP: USA -0.070; China 0.005; EU 0.128; ROW 0.076
- Interpretation: trade between the US and China fell, but trade between those economies and the rest of the world increased — the world economy is experiencing decoupling rather than deglobalization.

### Measuring decoupling and classification into blocs
- Goal: measure decoupling and quantify its impact on real GDP and income across a large sample of countries.
- Data-driven classification:
  - Use gravity framework: project log changes in bilateral goods trade over 2015-2023 on importer and exporter fixed effects (multilateral resistance). Residuals reflect relative changes in bilateral trade barriers between country pairs (includes bilateral policy shifts and bilateral shocks).
  - Transform estimated residual ŵ_mn into change in bilateral trade costs via Δlnτ_mn = ŵ_mn/(1−γ).
  - Classification into 3 groups based on changes in trade costs with US and China:
    - US bloc: average import and export costs with respect to the US fell, and trade costs with respect to China rose.
    - China bloc: opposite pattern.
    - Unaligned: trade costs with the US and China changed in the same direction.
  - Sample classification results:
    - Full DOTS sample of 187 countries: 43 moved towards the US bloc, 46 moved towards the China bloc, and 98 were unaligned.
  - Notes on interpretation:
    - Classification is based on changes in relative trade costs, not on initial bilateral trade levels.
    - Only trade linkages considered (not FDI, remittances, technology transfers, migration, etc.).

### Quantitative framework and identification strategy
- Use a multi-country, multi-sector international trade model (Huo, Levchenko, and Pandalai-Nayar (2025); Bonadio et al. (2021); Bonadio et al. (2025)) to compute general equilibrium changes in real GDP and real incomes.
- Implementation details and data:
  - Bilateral trade flows up to 2023 from IMF Direction of Trade Statistics (DOTS), covering 187 countries.
  - Nominal GDP from IMF World Economic Outlook (WEO).
  - Quantitative model calibrated with OECD 2021 Inter-Country Input-Output (ICIO) tables; model sample reduced to 66 countries (listed in Appendix Table A1) and aggregated to 22 sectors (Appendix Table A2).
  - 2015 used as initial (pre-shock) period.
- Identification challenge and solution:
  - Gravity regressions identify relative trade cost changes only and domestic absorption for 2023 is not available; cannot recover absolute level of trade costs by inversion.
  - Solve by scaling the gravity regression-implied bilateral trade cost changes by a common factor so that the model matches the 2015-23 change in the world trade-GDP ratio (Figure 1(a)).
  - The uniform across-the-board decline in worldwide trade costs required to match the increase in world trade-GDP ratio is −0.3%.

### Quantitative findings
- Baseline exercise: apply full set of inferred and scaled bilateral trade cost changes to the 2015 world economy.
- Counterfactual exercise: decompose real income changes arising purely from relative realignment towards/away from US and China blocs while holding worldwide shift in trade costs at zero.
- Key results:
  - Median country experienced a 0.6% real GDP and real income increase from the rewiring of trade and inferred trade cost changes occurring from 2015 to 2023.
  - This result holds even when considering only the relative trade cost changes from the gravity regression (i.e., leaving out the −0.3% worldwide uniform decrease in trade costs).
  - Across the sample, 51 out of 66 countries in the model experienced real income increases from the observed trade cost changes.
  - Nonaligned countries on average experienced larger income changes (0.8%) than countries moving to the US or China blocs.
  - Countries moving to the US and China blocs on average experienced marginal real income gains.
  - Conclusion: decoupling thus far has not reduced world GDP as a whole; global trade remained quite stable relative to global activity between 2015 and 2023, with reallocation offsetting bilateral declines.
- Bloc-alignment counterfactuals:
  - For each country, compute counterfactual changes in real GDP and income if it had belonged to a different bloc.
  - Finding: the bloc alignment uncovered in the data corresponds poorly to trade-related economic interests:
    - On average, countries moving to the US bloc would gain from moving to the China bloc.
    - On average, China bloc countries would gain from moving to the US bloc.
    - Unaligned countries would on average lose from joining either bloc.
  - Heterogeneity: substantial variation exists within blocs — some countries would win and others would lose from switching blocs, suggesting non-economic motives (likely geopolitical) may drive bloc choices.

### Connection to literature and positioning
- Contributions:
  - Complements literature documenting negative consequences of specific inward-oriented policies (e.g., US tariffs, Brexit) by providing a quantitative analysis of GDP impacts worldwide.
  - Corroborates heterogeneity in bilateral trade cost changes during US-China trade tensions: China decreased MFN tariffs on the rest of the world while raising them against the US.
  - Adds to debates on deglobalization by showing aggregate trade-to-GDP ratios do not support a deglobalization narrative; patterns are more consistent with fragmentation/decoupling.
  - Differs from prior work by:
    - Assigning countries to blocs using revealed trade cost changes across all country pairs (gravity framework) rather than pre-defined blocs or alternative indicators (e.g., UN votes).
    - Studying whether countries have optimally selected their blocs given the choices of the rest of the world.
- Relation to specific strands:
  - Slowdown in globalization after 2008: complements Antràs (2021); Goldberg and Reed (2023); Gopinath et al. (2025) who find no overall decline in trade flows and evidence of fragmentation.
  - Geoeconomics literature: relates to Aiyar, Presbitero, and Ruta (2023); Attinasi, Boeckelmann, and Meunier (2025); Bolhuis, Chen, and Kett (2023); Cerdeiro et al. (2021); Clayton, Maggiori, and Schreger (2023); Hakobyan, Meleshchuk, and Zymek (2023); Javorcik et al. (2024).
  - Methodological contrast: some papers use UN votes to assign blocs; revealed trade-cost blocs are correlated with UN votes but not perfectly.

### Scope, caveats, and organization
- Caveats:
  - Simulations abstract from dynamic productivity and knowledge transfer effects, economies of scale, and frictions to reallocation (e.g., incomplete contracts, sunk costs, search costs).
  - The gravity-residual measure of bilateral trade cost changes does not disentangle underlying sources (trade policy, preference shifts, bilateral markups, other bilateral shocks).
  - World events in 2020-2022 (Covid-19 disruptions, Russia-Ukraine war, fiscal stimulus, high inflation) are not modeled and may be partially reflected in data-inferred trade cost changes; Appendix C.3 presents results for 2015-2019 only.
- Paper organization:
  - Section 2: data and classification of countries into blocs.
  - Section 3: quantitative model and results.
  - Section 4: conclusion.
  - Appendices: further details on bloc classification, model solution, and alternative exercises.

*Source: wpiea2025263-source-pdf - 1. Introduction*

### 3.1  Setup

### 3.1  Setup

### Preliminaries
- There are 푁 countries indexed by 푛, 푚, and ℓ, and 퐽 sectors indexed by 푗, 푖, and 푘.
- Each country 푛 is populated by households that consume the final good available in country 푛 and supply labor to firms.

### Households
- Continuum of households indexed by 휔 maximize:
  - max ℱ푛(휔),퐻푛(휔) ℱ푛(휔) − 휒푛 [퐻푛(휔)]1+1/휓 /(1+1/휓) (equation 3.1)
  - subject to 푃푛ℱ푛 = 푊푛(휔)퐻푛(휔)
- Definitions:
  - ℱ푛(휔): consumption of final goods
  - 푃푛: price index of final good
  - 퐻푛(휔): hours supplied; wage received 푊푛(휔)
- Households can supply labor to any sector 푗 with household-specific productivity 푏푛푗(휔).
  - If household 휔 works in sector 푗, effective labor supplied is 푏푛푗(휔)퐻푛(휔) and labor income is 푊푛푗 푏푛푗(휔)퐻푛(휔).
- Idiosyncratic labor productivity: 푏푛푗(휔) ∼ Fréchet(휉푛푗,휇) with dispersion parameter 휇 and central tendency 휉푛푗.
- Aggregate/sectoral labor supply (up to normalization, with regularity condition 휇 > 휓+1):
  - Sectoral labor supply:
    - 퐻푛푗 = 휉푛푗 [1/휒푛 (푊푛/푃푛)]휓 [푊푛푗/푊푛]휇−1 (equation 3.2)
  - Economy-wide wage index:
    - 푊푛 ≡ (Σ푖 휉푛푖 푊푛푖^휇)^{1/휇}
  - Aggregate labor supply:
    - 퐻푛 = [푊푛/푃푛 1/휒푛]^{휓} (equation 3.3)
- Interpretation:
  - Aggregate labor supply coincides with the GHH utility formulation and is governed by Frisch elasticity 휓.
  - Conditional on aggregate labor, labor allocation across sectors is isoelastic with elasticity 휇−1 in relative wages (Roy-Fréchet).

### Final consumption and trade structure
- Final consumption bundle (CES across sectors):
  - ℱ푛 = [Σ푗 휁푛푗 ℱ푛푗^{휌−1/휌}]^{휌/(휌−1)} ; 푃푛 = [Σ푗 휁푛푗 (푃푓푛푗)^{1−휌}]^{1/(1−휌)}
  - ℱ푛푗: sector 푗 quantity consumed; 푃푓푛푗: its price
- Trade subject to iceberg costs 휏푓푚푛푗 shipping final good 푗 from source 푚 to destination 푛.
- Sectoral bundle is Armington aggregate over source countries:
  - ℱ푛푗 = [Σ푚 휇푚푛푗 ℱ푚푛푗^{훾−1/훾}]^{훾/(훾−1)}
  - 푃푓푛푗 = [Σ푚 휇푚푛푗 (휏푓푚푛푗 푃푚푗)^{1−훾}]^{1/(1−훾)}
- Expenditure shares:
  - Sector composite share in final expenditure:
    - 휋푓푛푗 = 휁푛푗 (푃푓푛푗)^{1−휌} / Σ푘 휁푛푘 (푃푓푛푘)^{1−휌}
  - Share of origin m in sector j expenditure:
    - 휋푓푚푛푗 = 휇푚푛푗 (휏푓푚푛푗 푃푚푗)^{1−훾} / Σℓ 휇ℓ푛푗 (휏푓ℓ푛푗 푃ℓ푗)^{1−훾}

### Firms and production
- Representative firm in sector 푗 in country 푛 has CRS production function:
  - 푌푛푗 = 푍푛푗 퐻푛푗^{휂푗} 푋푛푗^{1−휂푗} (equation 3.4)
  - 푍푛푗: total factor productivity; 퐻푛푗: equipped labor; 푋푛푗: aggregate intermediate inputs
- Intermediate input aggregate:
  - 푋푛푗 ≡ [Σ푖 휗푖,푛푗 푋푖,푛푗^{휀−1/휀}]^{휀/(휀−1)}
- Sector-i inputs are Armington aggregates across sources:
  - 푋푖,푛푗 ≡ [Σ푚 휇푚푖,푛푗 푋푚푖,푛푗^{휈−1/휈}]^{휈/(휈−1)}
  - 푃푋푖,푛푗 = [Σ푚 휇푚푖,푛푗 (휏푥푚푖,푛푗 푃푚푖)^{1−휈}]^{1/(1−휈)}
- Intermediate iceberg trade costs 휏푥푚푖,푛푗 may differ from final-goods iceberg costs 휏푓푚푛푖.
- Intermediate expenditure shares:
  - 휋푥푖,푛푗 = 휗푖,푛푗 (푃푋푖,푛푗)^{1−휀} / Σ푘 휗푘,푛푗 (푃푋푘,푛푗)^{1−휀}
  - 휋푥푚푖,푛푗 = 휇푚푖,푛푗 (휏푥푚푖,푛푗 푃푚푖)^{1−휈} / Σℓ 휇ℓ푖,푛푗 (휏푥ℓ푖,푛푗 푃ℓ푖)^{1−휈}
- Payments to factors and intermediates (cost minimization, marginal-cost pricing):
  - 푊푛푗 퐻푛푗 = 휂푗 푃푛푗 푌푛푗 (equation 3.5)
  - 푃푚푖,푛푗 푋푚푖,푛푗 = 휋푥푖,푛푗 휋푥푚푖,푛푗 (1−휂푗) 푃푛푗 푌푛푗 (equation 3.6)

### Equilibrium conditions
- An equilibrium is a set of goods and factor prices {푃푛푗, 푊푛푗}, allocations {퐻푛푗}, goods allocations {푌푛푗, ℱ푚푛푗, 푋푚푖,푛푗} such that:
  - (i) households maximize utility;
  - (ii) firms maximize profits;
  - (iii) all markets clear.
- Sectoral market clearing for each country n, sector j:
  - 푃푛푗 푌푛푗 = Σ푚 푃푚 ℱ푚 휋푓푚푗 휋푓푛푚푗 + Σ푚 Σ푖 (1−휂푖) 푃푚푖 푌푚푖 휋푥푗,푚푖 휋푥푛푗,푚푖 (equation 3.7)
- Trade balance / national accounts identity:
  - 푃푚 ℱ푚 = Σ푖 휂푖 푃푚푖 푌푚푖 (equation 3.8)

### Aggregate outcomes, changes, and solution method
- Simulations shock iceberg trade costs and compute changes relative to pre-shock equilibrium.
- Two aggregate outcomes reported:
  - Real GDP change (first-order approximation):
    - d ln 퐺푛 = Σ푗=1^퐽 휂푗 (푃푛푗,0 푌푛푗,0 / 퐺푛,0) d ln 퐻푛푗 (equation 3.9)
    - Subscript “0” denotes pre-shock/steady state values.
  - Real income defined as 푊푛 / 푃푛 (also referred to as real wage).
- Equilibrium in changes solved using exact-hat algebra: ˆ푋 = 푋′ / 푋.
- For given changes in trade costs ˆ휏푥푚푖,푛푗 and ˆ휏푓푚푛푗, changes in all endogenous variables are computed per formulas in Appendix B.

### Calibration (summary)
- Substitution elasticities:
  - 휌 = 1 (final cross-sector substitution elasticity)
  - 휀 = 1 (intermediate cross-sector substitution elasticity)
  - 훾 = 4 (trade elasticity in final consumption) — Broda and Weinstein (2006)
  - 휈 = 4 (trade elasticity in intermediate inputs) — Broda and Weinstein (2006)
- Labor supply and Fréchet parameters:
  - 휓 = 1 (Frisch elasticity of labor supply) — Chetty et al. (2011)
  - 휇 = 1.5 (sectoral labor supply elasticity parameter) — Galle, Rodríguez-Clare, and Yi (2023)
- Production and share parameters:
  - 휂푗: ICIO value added share in gross output
  - 휋푓푛푗, 휋푥푖,푛푗: ICIO sectoral consumption and intermediate shares
  - 휋푓푚푛푗, 휋푥푚푖,푛푗: ICIO final and intermediate trade shares
- Calibration starts from the 2015 equilibrium.

### Baseline trade cost change scenario (calibration to world trade/GDP)
- Gravity estimation identifies relative trade cost changes Δln휏푚푛; to pin down absolute changes add a common shift Δln휏푏푎푠푒:
  - For all exporting manufacturing sectors 푖 and all 푚 ≠ 푛:
    - ˆ휏푥푚푖,푛푗 = ˆ휏푓푚푛푖 = exp(Δln휏푚푛 + Δln휏푏푎푠푒) (equation 3.10)
- Target: match change in world trade to GDP ratio from 21.8% in 2015 to 22.6% in 2023 (0.8 percentage point increase).
- Calibrated common trade-cost shifter:
  - Δln휏푏푎푠푒 = −0.003 (implying an average decrease in trade costs of 0.3%).

### Baseline findings (selected quantitative results from the factual simulation)
- Table 4: Log change in average trade costs between blocs (2015-2023), average Δln휏푚푛 + Δln휏푏푎푠푒, weighted by 2015 bilateral trade flows:
  - Exporter↓ | Importer→ Bloc USA | Bloc CHN | Unaligned | Overall
  - Bloc USA: -0.046 0.040 0.004 -0.003
  - Bloc CHN: 0.114 -0.072 0.023 0.050
  - Unaligned: -0.033 -0.035 -0.008 -0.024
  - Overall: 0.002 -0.012 0.003 0.000
- Interpretation:
  - Trade costs between the US and China blocs have increased: from China bloc to US bloc increased by 11.4% (0.114), and the opposite direction rose by 4.0% (0.040).
  - These cross-bloc increases are counteracted by reductions in within-bloc trade costs and reductions in import trade costs from unaligned countries.
  - Only the China bloc experiences an overall increase in export costs; none of the blocs see significant increases in overall import costs.
  - Conclusion: despite decoupling, overall trade costs have not increased.
- Baseline real outcomes:
  - Figure 4 and Table 5 summarize changes in real GDP and real income (percentage points, baseline 2015-2023).
  - Table 5: Baseline change in Real GDP and Real Income, Percentage Points (2015-2023)
    - Bloc — Real GDP (Median p25 p75) — Real Income (Median p25 p75)
    - Overall: 0.588 0.061 1.297 — 0.619 0.059 1.322
    - Bloc USA: 0.532 0.125 0.712 — 0.536 0.147 0.699
    - Bloc CHN: 0.299 -0.263 0.773 — 0.372 -0.261 0.780
    - Unaligned: 0.787 0.034 1.397 — 0.755 0.066 1.432
  - Distributional findings:
    - Median country sees a 0.6% gain in real GDP.
    - Three-quarters of countries experience an increase in both real GDP and real incomes.
    - US and China experience changes close to zero.
    - Heterogeneity is large: e.g., Vietnam gains 6.9%, Laos gains 3.5%; Baltic countries lose 3–5%.
  - Decomposition note (Appendix): about 90% (≈0.574/0.637) of the total real income change is due to bilateral relative trade cost changes rather than the worldwide shift 휏푏푎푠푒.

### Counterfactual exercises (bloc reassignment)
- Objective: examine whether countries would benefit from switching blocs by replacing a country’s factual trade-cost changes with bloc-level averages while preserving the country’s trade-weighted average change.
- Construction:
  - For country m and bloc l:
    - Average export cost change from bloc to country m: d ln 휏_{l,m} = (1/N_l) Σ_{n ∈ l} d ln 휏_{n,m}
    - Average import cost change from m to bloc: d ln 휏_{m,l} = (1/N_l) Σ_{n ∈ l} d ln 휏_{m,n}
  - Adjustments:
    - Compute adjustment factors d ln 휏_{adj,l}^{n,imports} and d ln 휏_{adj,l}^{n,exports} so that the country’s trade-weighted average change equals the factual.
    - Counterfactual trade-cost changes when moving country n into bloc l:
      - d ln 휏_{CF:l}_{m,n} = d ln 휏_{m,l} + d ln 휏_{adj,l}^{n,imports}
      - d ln 휏_{CF:l}_{n,m} = d ln 휏_{l,m} + d ln 휏_{adj,l}^{n,exports}
  - Each country is moved one at a time; for each factual bloc membership there are two possible moves (to one of the other two blocs).
- Counterfactual results (summary):
  - Moving countries to the US bloc:
    - Six out of ten China-bloc countries would benefit from switching to the US bloc.
    - Median real income benefit for these China-bloc countries: 0.66%.
    - Unaligned countries on average lose from moving to the US bloc, but effects are heterogeneous.
  - Moving countries to the China bloc:
    - Countries in the US bloc would on average benefit from moving to the China bloc.
    - Eight out of fourteen US-bloc countries gain; median US-bloc country gains 0.2%.
  - Moving aligned countries to Unaligned:
    - On average moving countries from US and China blocs to Unaligned reduces real GDP and income, but some countries (e.g., Saudi Arabia, Latvia, Lithuania) could see GDP increases of over 2% by becoming unaligned.
  - Overall interpretation:
    - On average, countries in the US and China blocs appear to be in the “wrong” bloc relative to their welfare gains; however, averages mask wide within-group heterogeneity with both gains and losses across possible moves.

*Source: wpiea2025263-source-pdf — section 3.1 Setup.*

### 3.5  Robustness and sensitivity

### 3.5  Robustness and sensitivity

### Sensitivity checks using observable trade costs: tariffs
- The component of trade costs directly observable in the data (tariffs) is used to validate inferred trade cost changes.
- Tariff data coverage: most recent tariff data are for 2021; documented changes between 2015 and 2021. Source: UN-TRAINS.
- Findings from tariff histograms:
  - Large dispersion in effectively applied tariff changes.
  - The average applied tariff change is close to 0.
  - 39.5% of bilateral pairs experience tariff decreases.
  - MFN tariff changes (measured with less error) are reported separately and shown in the right-panel histogram.

### Bloc assignment robustness: Leiden algorithm
- Alternative classification method: Leiden algorithm (Traag, Waltman, and van Eck, 2019) applied to the same residualized trade growth between 2015 and 2023.
- Methodological note: The Leiden algorithm contains a random component; the authors perform many draws and assign countries to blocs based on the percentage of times they co-classify with the US or China.
- Comparison with baseline:
  - Appendix C.1 details the procedure; Table C1 summarizes overlap.
  - Overall, the baseline procedure is more conservative and classifies more countries as unaligned.
  - The two methods agree more than 70% of the time when both assign the country to either the US or China bloc.

### Alternative start and end years
- Baseline pre-period: 2015 (chosen because it precedes the Brexit referendum and the 2016 US presidential election).
- Alternative start date tested: 2016 (since US-China tariff increases began in 2017).
  - Tables C2 and C3: bloc assignment similar to baseline.
  - Some countries become unaligned, but no country in the quantitative model sample is classified in the opposite bloc relative to baseline.
  - Tables C4 and C5: summary statistics of trade cost and GDP changes are qualitatively the same as baseline: cross-bloc trade costs increase but are compensated by decreases within bloc and to/from the unaligned bloc.
- Pre-Covid sample (2015-2019), Appendix C.3:
  - Table C6: trade costs between blocs (moving-to-US and moving-to-China) already increase in this sample.
  - Decrease in within-bloc trade costs is less pronounced and almost null for the US bloc, so overall trade costs increase slightly.
  - Table C7: real income changes show a negligible negative change of −0.06% for the median country (compared to +0.6% in the 2015-2023 exercise), with more negative outcomes for US and China bloc countries.
  - Interpretation: timing suggests cross-bloc increases preceded within-bloc decreases; within-bloc reductions lagged the initial US-China decoupling shock. Alternative interpretation: COVID-19 pandemic, Russia’s 2022 invasion of Ukraine, and other shocks influenced bilateral trade barriers and timing.

### Placebo period (2002–2007)
- Procedure repeated for 2002–2007 (pre US-China trade tensions).
- Findings:
  - No evidence of decoupling in 2002–2007.
  - Table C8: bloc assignment vs baseline 2015-23 classification: only 3 countries assigned to the China bloc, including China.
  - More countries unaligned than in baseline (70% instead of 60%).
  - Table C9: change in trade costs across bloc pairs between 2002 and 2007 — most bloc pairs, including China bloc to US bloc, experience trade cost declines.
  - Using 2015-23 bloc partition applied to 2002–2007 data (Table C10): all cross-bloc pairs experience trade cost decreases, in the same order of magnitude as within-bloc pairs.

### Fit of trade costs and comparison to Head and Ries method
- Identification issue: domestic absorption data are not available for 2023, preventing use of Head and Ries (2001) HR method to identify trade cost levels.
- Authors match the global trade to GDP ratio to pin down trade cost change levels.
- Validation exercise: implement their procedure on years where domestic absorption data are available and compare to HR.
  - Use 8-year windows starting from 2000 until 2010.
  - On average, the authors’ procedure and the HR method produce similar trade cost changes:
    - Difference at the mean: -0.9%
    - Difference at the median: -0.03%
    - Correlation: 0.79
  - Appendix C.5 details the exercise.

### Counterfactual GDP and real income sensitivity (summary of Table 6 and Figure 5)
- Counterfactual changes in GDP and real income are reported in percentage points relative to baseline for the 2015-2023 period.
- Moving to Bloc USA (Real GDP; Real Income):
  - Overall median: -0.445; -0.448
  - Overall p25: -1.534; -1.512
  - Overall p75: 0.969; 0.945
  - Bloc CHN median effect: 0.658; 0.661
  - Unaligned median effect: -0.710; -0.762
- Moving to Bloc CHN (Real GDP; Real Income):
  - Overall median: -0.269; -0.289
  - Overall p25: -1.465; -1.430
  - Overall p75: 0.740; 0.717
  - Bloc USA median effect: 0.211; 0.238
  - Unaligned median effect: -0.501; -0.476
- Moving to Unaligned (Real GDP; Real Income):
  - Overall median: -0.593; -0.589
  - Overall p25: -0.944; -0.967
  - Overall p75: 1.203; 1.253
  - Bloc USA median effect: -0.622; -0.629
  - Bloc CHN median effect: -0.324; -0.328
- Figure 5 (panels a–c) shows percentage change in GDP for each country when moved to different blocs relative to factual outcomes.

Final source: _IMF Working Paper chapter titled "3.5  Robustness and sensitivity" (from the provided source PDF)._

### References

### References

### Bibliographic scope and key themes
- The references list covers literature on geo-economic fragmentation, global value chains, trade costs, trade policy shocks, supply-chain decoupling, friendshoring, and methods for measuring fragmentation and international comovement.
- Notable thematic concentrations in the cited works:
  - Geo-economic fragmentation and multilateralism: works by Aiyar et al. (2023), Aiyar, Presbitero, and Ruta (2023), Fernández-Villaverde et al. (2024).
  - Global value chains, reallocation, and comovement: Antràs (2021), Antràs and Chor (2022), Bonadio et al. (2021, 2023, 2025), Huo, Levchenko, and Pandalai-Nayar (2025).
  - Trade policy impacts and tariffs: Amiti, Redding, and Weinstein (2019); Grossman, Helpman, and Redding (2024); Fajgelbaum et al. (2024); Bown, Jung, and Zhang (2019).
  - Quantitative methods and network models: Bonadio et al. (User Manual, 2023), Bolhuis, Chen, and Kett (2023), Cerdeiro et al. (2021).
  - Empirical topics: effects of geopolitical conflict (Góes and Bekkers 2022), economic costs of friendshoring (Javorcik et al. 2024), measuring state preferences (Bailey et al. 2017).
- The references include working papers, journal articles, memos, and staff working papers across multiple organizations (IMF, NBER, CEPR, WTO, journals).

### Online appendix — Data and Bloc Assignment (Section A)
- Country coverage:
  - Table A1 lists the countries included in the quantitative model; the country list includes ISO-like codes paired with country names (examples: AUS Australia, ARG Argentina, AUT Austria, BEL Belgium, etc.).
- Sectoral classification and aggregation:
  - Table A2 maps ICIO codes to sector descriptions and to aggregated sector codes. Representative mappings include:
    - ICIO 01T02 / Sector code 1: "Agriculture, hunting, forestry and fishing"
    - ICIO 05T06 / Sector code 2: "Mining and quarrying, energy producing products"
    - ICIO 10T12 / Sector code 4: "Food products, beverages and tobacco"
    - ICIO 26 / Sector code 11: "Computer, electronic and optical equipment"
    - ICIO 64 / Sector code 21: "Financial, real estate, professional and administrative services"
    - ICIO 84 / Sector code 22: "Public administration, education and other services"
  - Other ICIO-to-sector mappings are listed in Table A2 across sector codes 1 through 22.
- Bloc assignment:
  - Table A3: "Bloc Assignment, 187 Countries (2015-2023)" enumerates country-to-bloc assignments with blocs labeled "USA", "CHN", and "Unaligned".
  - Assignment rule (verbatim):
    - “USA” bloc refers to the group of countries moving towards the US bloc, “CHN” refers to the group of countries moving towards the China bloc, and unaligned refers to the rest of the countries.
    - A country is assigned to the USA bloc if 푑ln휏푈푆퐴푖 < 0 and 푑ln휏퐶퐻푁푖 > 0.
    - Similarly, a country is assigned to the CHN bloc if 푑ln휏퐶퐻푁푖 < 0 and 푑ln휏푈푆퐴푖 > 0.
    - All other countries are assigned to the Unaligned bloc.

### Online appendix — Quantification and numerical solution (Section B)
- Purpose:
  - Presents how to solve for the equilibrium change following a change in exogenous trade costs ˆ휏푓푚푛푗 and ˆ휏푥푚푖,푛푗 and potential exogenous change in trade deficit ˆ퐷푛.
- Endogenous variables solved for (verbatim list of variables determined by the system):
  - output ˆ푌푛푗
  - prices ˆ푃푛푗
  - consumption sectoral shares ˆ휋푓푚푗
  - final trade shares ˆ휋푓푛푚푗
  - intermediate sectoral shares ˆ휋푥푗,푚푖
  - intermediate trade shares ˆ휋푥푛푗,푚푖
  - sectoral wages ˆ푊푛푗
- Structure of the equilibrium system:
  - The system equates vectors [ˆ푃푛푗 ˆ푌푛푗] to weighted sums over m and i involving ˆ푃푚푖, ˆ푌푚푖, sectoral shares, and ˆ퐷푚/퐷푚, and contains normalization and indexation through variables such as ˆ푃퐹푛푗, ˆ푃푋푖,푛푗, ˆ푍푛푗, ˆ퐾푛푗, ˆ푊푛, ˆ푃푛.
  - Definitions given (verbatim forms) for:
    - ˆ푃퐹푛푗 in terms of ∑푚 휋푓푚푛푗,푡, d휏푓푚푛푗, and ˆ푃푚푗.
    - ˆ휋푓푚푛푗,푡+1 and ˆ휋푥푖,푛푗,푡+1 in recursive forms involving trade-cost terms and price indexes.
    - ˆ푃푋푖,푛푗 as a composite of ˆ푃푚푖, sectoral trade shares, and ̃휏푥푚푖,푛푗.
    - ˆ푃푋푛푗 as an aggregation over i of ˆ푃푋푖,푛푗.
    - ˆ푃푛푗 as a function of ˆ푍푛푗, ˆ푊, sectoral parameters (훼푗, 휂푗), ˆ푃푋푛푗, and ˆ퐾푛푗.
    - ˆ푊푛푗 relative to aggregate ˆ푊푛 and ˆ푃푛 using parameters 휓 and 휇.
    - ˆ푊푛 and ˆ푃푛 in aggregate form (involving ∑푗 휋퐻푛푗 and ∑푗 휋푓푛푗,푡).
- Numerical algorithm (verbatim steps 1–5):
  1. Guess ˆ푃푛푗
  2. Solve for ˆ휋푓푛푗, ˆ휋푓푚푛푗, ˆ휋푥푖,푛푗, ˆ휋푥푚푖,푛푗 using:
     - ˆ휋푓푛푗 = (ˆ푃퐹푛푗)1−휌 / ∑푘 휋푓푛푘,푡 (ˆ푃퐹푛푘)1−휌
     - ˆ푃퐹푛푗 = [∑푚 휋푓푚푛푗,푡 (d휏푓푚푛푗 ˆ푃푚푗)1−훾]ˆ휋푓푚푛푗,푡+1 = [d휏푓푚푛푗 ˆ푃푚푗]1−훾 ∑푘 휋푓푘푛푗,푡 [d휏푓푘푛푗 ˆ푃푘푗]1−훾
     - ˆ휋푥푖,푛푗 = (ˆ푃푋푖,푛푗)1−휀 / ∑푘 휋푥푘,푛푗,푡 (ˆ푃푋푘,푛푗)1−휀
     - ˆ푃푋푖,푛푗 = {[∑푚 휋푥푚푖,푛푗,푡 (̃휏푥푚푖,푛푗 ˆ푃푚푖)1−휈]}1/(1−휈)
     - ˆ휋푥푚푖,푛푗 = [̃휏푥푚푖,푛푗 ˆ푃푚푗]1−휈 ∑푘 휋푥푘푖,푛푗,푡 [̃휏푥푘푖,푛푗 ˆ푃푘푗]1−휈
  3. Solve for ˆ푃푛푗 ˆ푌푛푗 using the new trade shares via the system:
     - [ˆ푃푛푗 ˆ푌푛푗] − (푃푛푗 푌푛푗) = ∑푚 ∑푖 휂푖 [ˆ푃푚푖 ˆ푌푚푖](푃푚푖 푌푚푖) + (ˆ퐷푚/퐷푚) ! 휋푓푚푗 ˆ휋푓푚푗 휋푓푛푚푗 ˆ휋푓푛푚푗 + ∑푚 ∑푖 (1−휂푖) [ˆ푃푚푖 ˆ푌푚푖](푃푚푖 푌푚푖) 휋푥푗,푚푖 ˆ휋푥푗,푚푖 ˆ휋푥푛푗,푚푖/휋푥푛푗,푚푖
  4. Solve for wages ˆ푊푛푗 using:
     - ˆ푊푛푗 [ (ˆ푊푛/ˆ푃푛) ]휓 (ˆ푊푛푗/ˆ푊푛)휇−1 = ˆ푃푛푗 ˆ푌푛푗
  5. Solve for prices ˆ푃푛푗 using:
     - ˆ푃푛푗/ˆ푃푛푗 = (ˆ푍푛푗)−1 ˆ푊 (1−훼푗)휂푗 푛푗 [ˆ푃푛푗 ˆ푌푛푗]훼푗/휂푗 [ˆ퐾푛푗]−훼푗/휂푗 [ˆ푃푋푛푗]1−휂푗
     - with ˆ푃푋푛푗 = [∑푖 휋푥푖,푛푗,푡 (ˆ푃푋푖,푛푗)1−휀]1/(1−휀)
- Algorithmic structure emphasizes iterative solution:
  - Initial guess for ˆ푃푛푗, recalculation of trade shares and aggregates, then updating outputs, wages, and prices until convergence.

*Source: wpiea2025263-source-pdf - References (PDF chapter/section).*

### 6. Go back to 1

### 6. Go back to 1

### Table B1 — Bloc Assignment, 66 Model Countries (2015-2023)
- Table lists 66 model countries and their bloc assignment when running the procedure described in section 2.2.
- Bloc definitions:
  - “USA” bloc: group of countries moving towards the US bloc.
  - “CHN” bloc: group of countries moving towards the China bloc.
  - “Unaligned”: the rest of the countries.
- Assignment rule (as stated):
  - Country assigned to the USA bloc if 푑ln휏_푈푆퐴_푖 < 0 and 푑ln휏_퐶퐻푁_푖 > 0.
  - Country assigned to the CHN bloc if 푑ln휏_퐶퐻푁_푖 < 0 and 푑ln휏_푈푆퐴_푖 > 0.
  - All other countries assigned to Unaligned.
- Example country-bloc mappings as shown (excerpted exactly as in source):
  - AUT USA ARG Unaligned NZL Unaligned
  - CYP USA AUS Unaligned PER Unaligned
  - DEU USA BEL Unaligned PHL Unaligned
  - DNK USA BGR Unaligned PRT Unaligned
  - GBR USA BRN Unaligned ROU Unaligned
  - HRV USA CAN Unaligned ROW Unaligned
  - IND USA CHE Unaligned SVK Unaligned
  - JPN USA CHL Unaligned SWE Unaligned
  - KOR USA CRI Unaligned THA Unaligned
  - LTU USA CZE Unaligned TUN Unaligned
  - LVA USA ESP Unaligned TUR Unaligned
  - MMR USA EST Unaligned VNM Unaligned
  - POL USA FIN Unaligned ZAF Unaligned
  - SGP USA FRA Unaligned
  - USA USA GRC Unaligned
  - HUN Unaligned
  - BRA CHN IRL Unaligned
  - CHN CHN ISL Unaligned
  - COL CHN ITA Unaligned
  - HKG CHN KAZ Unaligned
  - IDN CHN LAO Unaligned
  - ISR CHN LUX Unaligned
  - KHM CHN MAR Unaligned
  - MYS CHN MEX Unaligned
  - RUS CHN MLT Unaligned
  - SAU CHN NLD Unaligned
  - SVN CHN NOR Unaligned
- Notes: table displays country list in quantitative model and bloc assignment using the described procedure.

### Table B2 — Decomposition of baseline change in GDP and Real Income (2015-2023)
- Purpose: Decompose changes in GDP and real income into components from bilateral relative trade cost changes (Δln휏_푚푛) and overall average change (Δln휏_푏푎푠푒).
- Reported values (percentage changes):
  - Real GDP
    - Overall: Total 0.637; Δln휏_푚푛 0.574; Δln휏_푏푎푠푒 0.074
    - Bloc USA: Total 0.585; Δln휏_푚푛 0.533; Δln휏_푏푎푠푒 0.073
    - Bloc CHN: Total 0.418; Δln휏_푚푛 0.301; Δln휏_푏푎푠푒 0.072
    - Unaligned: Total 0.878; Δln휏_푚푛 0.788; Δln휏_푏푎푠푒 0.074
  - Real Income
    - Overall: Total 0.690; Δln휏_푚푛 0.610; Δln휏_푏푎푠푒 0.074
    - Bloc USA: Total 0.589; Δln휏_푚푛 0.537; Δln휏_푏푎푠푒 0.073
    - Bloc CHN: Total 0.459; Δln휏_푚푛 0.374; Δln휏_푏푎푠푒 0.071
    - Unaligned: Total 0.845; Δln휏_푚푛 0.756; Δln휏_푏푎푠푒 0.074
- Note: Total column does not exactly match Table 5 due to nonlinearities.

### Figure B1 — Counterfactual Real Income Changes (2015-2023)
- Each bar shows percentage change in real income for each country, relative to factual, when the country is moved to a different bloc.

### Section C — Additional exercises and robustness

#### C.1 Community detection algorithm (Leiden algorithm)
- Method:
  - Run regression Δln푥_2023−2015_푚푛 = 훼_푚 + 훼_푛 + 휀_푚푛, where Δln푥_2023−2015_푚푛 is the log-change in aggregate trade flows from source m to destination n between 2015 and 2023; 훼_푚 and 훼_푛 are source and destination fixed effects.
  - Recover predicted residual d휀_푚푛 and calculate undirected trade weight 푤_푚푛 = (d휀_푚푛 + d휀_푛푚) / 2 (notationally presented as d휀_푚푛 + d휀_푚푛 over 2 in source).
  - Drop repeated pairs since 푤_푚푛 = 푤_푛푚.
  - Run Leiden algorithm using 푤_푚푛 as inputs; perform 100 draws (random component).
  - Count percentage of draws each country belongs to same community as US (푝_푈푆퐴) and China (푝_퐶퐻푁).
  - Only count draws where (i) USA and China belong in different communities and (ii) there are 5 communities or less.
- Frequency-based classification:
  - Country belongs to US bloc if 푝_푈푆퐴 > 0.2 and 푝_푈푆퐴 > 푝_퐶퐻푁.
  - Country belongs to China bloc if 푝_퐶퐻푁 > 0.2 and 푝_퐶푯푁 > 푝_푈푆퐴.
  - Country is unaligned if 푝_푈푆퐴 < 0.2 and 푝_퐶퐻푁 < 0.2.
- Table C1 — Bloc comparison (Leiden vs baseline):
  - Baseline vs Community detection counts:
    - Baseline USA bloc vs Leiden USA bloc: 24
    - Baseline USA bloc vs Leiden CHN bloc: 10
    - Baseline USA bloc vs Leiden Unaligned: 32
    - Baseline CHN bloc vs Leiden USA bloc: 11
    - Baseline CHN bloc vs Leiden CHN bloc: 28
    - Baseline CHN bloc vs Leiden Unaligned: 57
    - Baseline Unaligned vs Leiden USA bloc: 7
    - Baseline Unaligned vs Leiden CHN bloc: 7
    - Baseline Unaligned vs Leiden Unaligned: 10
- Summary statement: Different classification method yields similar results; baseline is more conservative classifying more countries as unaligned. For 73 countries assigned by both procedures to either USA or CHN bloc, 52 (or 71%) are assigned to the same bloc.

#### C.2 Start year: 2016 (robustness)
- Table C2 — Bloc comparison Baseline 2015 vs Baseline 2016 (All Countries)
  - Baseline 2016 counts vs Baseline 2015:
    - USA bloc: 30 (Baseline 2016) vs 21 (Baseline 2015)
    - China bloc: 23 vs 7
    - Unaligned: 11 vs 71
  - Note: USA(CHN) bloc includes USA(CHN) itself.
- Table C3 — Bloc comparison (Model Countries)
  - Baseline 2016 vs Baseline 2015 (Model Countries):
    - USA bloc: 11 vs 05
    - China bloc: 0 vs 52
    - Unaligned: 35 vs 33
- Table C4 — Log Change in Average Trade Cost between Blocs (Model countries, 2016-2023)
  - Average Δln휏_푚푛 + Δln휏_푏푎푠푒, weighted by 2016 bilateral trade flows:
    - Exporter Bloc USA → Importer Bloc USA: -0.051
    - Exporter Bloc USA → Importer Bloc CHN: 0.040
    - Exporter Bloc USA → Importer Unaligned: -0.034
    - Exporter Bloc USA Overall: -0.027
    - Exporter Bloc CHN → Importer Bloc USA: 0.081
    - Exporter Bloc CHN → Importer Bloc CHN: -0.150
    - Exporter Bloc CHN → Importer Unaligned: -0.020
    - Exporter Bloc CHN Overall: 0.019
    - Exporter Unaligned → Importer Bloc USA: -0.053
    - Exporter Unaligned → Importer Bloc CHN: -0.059
    - Exporter Unaligned → Importer Unaligned: -0.050
    - Exporter Unaligned Overall: -0.053
    - Overall column: -0.020 (to Bloc USA), -0.027 (to Bloc CHN), -0.037 (to Unaligned), Overall -0.010
- Table C5 — Baseline Change in GDP and Real Income (2016-2023) (percentage changes)
  - Overall GDP: Median 1.262; p25 0.720; p75 1.868
  - Overall Real Income: Median 1.257; p25 0.748; p75 1.919
  - Bloc USA GDP: Median 0.774; p25 0.210; p75 1.135
  - Bloc USA Real Income: Median 0.815; p25 0.203; p75 1.137
  - Bloc CHN GDP: Median 1.672; p25 0.903; p75 2.554
  - Bloc CHN Real Income: Median 1.855; p25 0.895; p75 2.562
  - Unaligned GDP: Median 1.581; p25 0.839; p75 2.521
  - Unaligned Real Income: Median 1.607; p25 0.846; p75 2.519

#### C.3 Pre-Covid: 2015-2019
- Table C6 — Log Change in Average Trade Cost between Blocs (Model countries, 2015-2019)
  - Exporter Bloc USA → Importer Bloc USA: -0.001
  - Exporter Bloc USA → Importer Bloc CHN: 0.065
  - Exporter Bloc USA → Importer Unaligned: -0.006
  - Exporter Bloc USA Overall: 0.010
  - Exporter Bloc CHN → Importer Bloc USA: 0.051
  - Exporter Bloc CHN → Importer Bloc CHN: -0.038
  - Exporter Bloc CHN → Importer Unaligned: 0.004
  - Exporter Bloc CHN Overall: 0.016
  - Exporter Unaligned → Importer Bloc USA: 0.010
  - Exporter Unaligned → Importer Bloc CHN: 0.009
  - Exporter Unaligned → Importer Unaligned: -0.013
  - Exporter Unaligned Overall: 0.000
  - Overall column: 0.018 (to Bloc USA), 0.018 (to Bloc CHN), -0.007 (to Unaligned), Overall 0.003
- Table C7 — Baseline Change in GDP and Real Income (2015-2019) (percentage changes)
  - Overall GDP: Median -0.063; p25 -0.732; p75 0.696
  - Overall Real Income: Median -0.059; p25 -0.737; p75 0.691
  - Bloc USA GDP: Median -0.239; p25 -0.790; p75 0.111
  - Bloc USA Real Income: Median -0.211; p25 -0.818; p75 0.109
  - Bloc CHN GDP: Median -0.228; p25 -1.029; p75 0.567
  - Bloc CHN Real Income: Median -0.221; p25 -1.121; p75 0.582
  - Unaligned GDP: Median 0.373; p25 -0.648; p75 0.990
  - Unaligned Real Income: Median 0.358; p25 -0.661; p75 1.000

#### C.4 Placebo: 2002-2007
- Table C8 — Bloc comparison Baseline 2015 vs Baseline 2002 (Model Countries)
  - Counts:
    - Baseline 2002 USA bloc vs Baseline 2015 USA bloc: 4
    - Baseline 2002 USA bloc vs Baseline 2015 China bloc: 3
    - Baseline 2002 USA bloc vs Baseline 2015 Unaligned: 9
    - Baseline 2002 China bloc vs Baseline 2015 USA bloc: 1
    - Baseline 2002 China bloc vs Baseline 2015 China bloc: 1
    - Baseline 2002 China bloc vs Baseline 2015 Unaligned: 0
    - Baseline 2002 Unaligned vs Baseline 2015 USA bloc: 9
    - Baseline 2002 Unaligned vs Baseline 2015 China bloc: 6
    - Baseline 2002 Unaligned vs Baseline 2015 Unaligned: 31
- Table C9 — Log Change in Average Trade Cost between Blocs (Model countries, 2002-2007)
  - Exporter Bloc USA → Importer Bloc USA: -0.082
  - Exporter Bloc USA → Importer Bloc CHN: 0.081
  - Exporter Bloc USA → Importer Unaligned: -0.141
  - Exporter Bloc USA Overall: -0.102
  - Exporter Bloc CHN → Importer Bloc USA: -0.032
  - Exporter Bloc CHN → Importer Bloc CHN: -0.063
  - Exporter Bloc CHN → Importer Unaligned: -0.135
  - Exporter Bloc CHN Overall: -0.075
  - Exporter Unaligned → Importer Bloc USA: -0.159
  - Exporter Unaligned → Importer Bloc CHN: -0.085
  - Exporter Unaligned → Importer Unaligned: -0.197
  - Exporter Unaligned Overall: -0.177
  - Overall column: -0.123 (to Bloc USA), -0.009 (to Bloc CHN), -0.175 (to Unaligned), Overall -0.145
- Table C10 — Log Change in Average Trade Costs between 2015 Blocs (Model countries, 2002-2007)
  - Using 2015 blocs classification, weighted by 2002 trade flows:
    - Exporter Bloc USA → Importer Bloc USA: -0.145
    - Exporter Bloc USA → Importer Bloc CHN: -0.005
    - Exporter Bloc USA → Importer Unaligned: -0.139
    - Exporter Bloc USA Overall: -0.124
    - Exporter Bloc CHN → Importer Bloc USA: -0.119
    - Exporter Bloc CHN → Importer Bloc CHN: -0.015
    - Exporter Bloc CHN → Importer Unaligned: -0.172
    - Exporter Bloc CHN Overall: -0.127
    - Exporter Unaligned → Importer Bloc USA: -0.166
    - Exporter Unaligned → Importer Bloc CHN: -0.124
    - Exporter Unaligned → Importer Unaligned: -0.181
    - Exporter Unaligned Overall: -0.168
    - Overall column: -0.152 (to Bloc USA), -0.055 (to Bloc CHN), -0.161 (to Unaligned), Overall -0.145

#### C.5 Validation of the trade cost estimates
- Method: For each 8-year period since 2000 with ICIO data, compute Head and Ries ratio to back out trade cost change including own-trade data, starting from gravity equation in changes:
  - dlnX_푚푛 = 휂_푚 + 훾_푛 + (1−훾) dln휏_푚푛 (equation C.1)
  - Recover change in bilateral trade cost from:
    - ̃휏_퐻푅_푚푛 = Δ_{t,t−8} (ln휏_푚푛 + ln휏_푛푚) = 1/(1−훾) Δ_{t,t−8} ln( X_푚푛 X_푛푛^* X_푛푚 X_푚푚 ) (equation C.2)
- Comparison: Compute ̃휏_퐻푅_푚푛 from trade data and model-implied Δln휏_푚푛 + Δln휏_푛푚 from residual-based procedure targeting world trade to GDP ratio.
- Table C11 — Summary statistics for model implied vs Head-Ries trade cost (between 2002 and 2007)
  - Log Change in Model implied Trade Cost: Average -0.105; Median -0.097; p25 -0.308; p75 0.106
  - Log Change in Head-Ries Trade Cost: Average -0.096; Median -0.085; p25 -0.303; p75 0.104
  - Difference: Average -0.009; Median -0.0004; p25 -0.162; p75 0.158
- Figure C3: Scatterplot compares model implied Δln휏_푚푛 + Δln휏_푛푚 to Head-Ries counterpart using ICIO dataset.

#### C.6 UN agreement regressions, all countries
- Figure C4 — Event study of bilateral trade flows, all countries:
  - Plots estimates of 훽_푈푁_푡 from regression 3.11 across years 2010, 2012, 2014, 2016, 2018, 2020, 2022.
  - Dot colors correspond to different controls:
    - Blue: fixed effects only.
    - Red: fixed effects + time-varying coefficients on distance.
    - Green: fixed effects + time-varying coefficients on 2000 bilateral trade flows.
  - Sample covers all countries in DOTS dataset.

*Playing with blocs: Quantifying Decoupling — Working Paper No. WP/2025/263*

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_Source: https://www.imf.org/-/media/files/publications/wp/2025/english/wpiea2025263-source-pdf.pdf_