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---

### Contributions to literature
- Extends theoretical literature on trade disruptions by quantifying impacts in a multi-country and multi-sector model that incorporates diversification policies and resilience.
- Links to prior findings and models:
  - Relates to Bhagwati and Srinivasan (1976); Bergström, Loury, and Persson (1985); Cheng (1989) on trade disruptions and inventories or embargo threats.
  - Most closely related to Grossman, Helpman, and Lhuillier (2023) on diversification achieving a constrained social optimum in a two-country model with a critical input.
  - Incorporates relationship stickiness in trade, connecting to Monarch (2022); Grossman, Helpman, and Redding (2024); Ornelas and Turner (2008); Antràs and Staiger (2012); Alfaro et al. (2024); Martin, Mejean, and Parenti (2023); Boehm, Levchenko, and Pandalai-Nayar (2023).
  - Builds on dynamic multi-country and multi-sector quantitative trade models in the Eaton and Kortum (2002) tradition and related work (e.g., Alvarez (2017); Mutreja, Ravikumar, and Sposi (2018); Anderson, Larch, and Yotov (2020); Ravikumar et al. (2022); Brooks and Pujolas (2018)).
- Novel model elements:
  - Trade network rigidities from sticky importer-exporter contracts.
  - Frictions in labor and local factor mobility, with labor mobility becoming more elastic over time.
  - Focus on transition dynamics relevant for diversification and resilience.

### Stylized facts and data
- Objective: Document empirical relationships linking geographic concentration of imports, exporter-specific supply shocks, and resilience to trade cost shocks.
- Key stylized facts:
  - Fact 1: Products with geographically concentrated import sources are more exposed to supply shocks from individual exporters.
  - Fact 2: Products with more diversified import sources exhibit greater resilience to trade cost shocks.
  - Fact 3: US imports of geographically more diversified products were more resilient to the 2018–2019 tariffs on China.
- Data sources and construction:
  - US import quarterly country-product dataset at HS10 level, 2013–2024; duties collected, value of general imports subject to duties, and CIF import values used to construct effectively applied tariff rates and CIF values.
  - Bilateral tariff data at HS6 from UNCTAD TRAINS (WITS) and MAcMap-HS6 (CEPII); global bilateral HS6-level trade flows from BACI (CEPII).
  - Empirical method to recover exporter-level supply shock: PPML specification V_ijst = exp[β ln τ_ijst + FE_ijs + FE_ist + FE_jst] ε_ijst and supply shock measure recovered by exponentiating FE_ist.
- Concentration and risk measures:
  - Herfindahl-Hirschman Index: HHI_st = Σ_{i=1}^{N_st} (S_ist)^2.
  - Product-level risk: σ^2_s = W C W′ (W = exporter-level time-averaged market shares; C = covariance matrix of exporter-product-level supply shocks FE_ist).
- Empirical findings:
  - Strong positive correlation between HHI and exporter supply shock risk.
  - Negative correlation between HHI and estimated product-level substitutability γ_s: higher concentration → larger reductions in overall imports in response to positive trade cost shocks.
  - 2018–2019 US-China tariffs: targeted goods from China declined significantly relative to the rest of the world after a quarter; products with higher HHI experienced larger import declines.

### Model structure and rigidities
- General framework:
  - Multi-country (N) and multi-sector (J) general equilibrium trade model in discrete time t = 0,1,2,...
  - Representative firm produces an intermediate variety under perfect competition and constant returns to scale, using labor, a composite local factor (structures), and materials from all sectors.
  - Continuum of importers aggregates intermediate varieties into final goods.
  - Fixed supplies of total labor and local factors per country.
- Three sources of trade network rigidities:
  1. Staggered (sticky) importer-exporter contracts: importers receive Poisson-distributed opportunities to switch suppliers; only a proportion can switch each period.
  2. Labor market frictions: workers have heterogeneous sector-specific Fréchet productivity ε^L (F^L_nj(ε^L) = exp(−T^L,nj_t ε^{−θ^L,n})); labor mobility inelastic short-run, re-skilling over time (δ^L governs speed).
  3. Immobile local factors: heterogeneous sector-specific productivities, repurposed over time.
- Labor module highlights (Section 3.1):
  - MeasureL n workers; each supplies one unit of time; earnings w_nj_t ε^L_nj.
  - Sectoral labor income share: π^L,nj_t = T^L,nj_t (w_nj_t)^{θ^L,n} / Σ_k T^L,nk_t (w_nk_t)^{θ^L,n}.
  - Wage index: W_n_t = Γ[θ^L,n −1 / θ^L,n] (Σ_j T^L,nj_t (w_nj_t)^{θ^L,n})^{1/θ^L,n}.
  - Retraining dynamics: (T^L,nj_t / T^L,nj_{t−h}) = (w_nj_t / w_nj_{t−h})^{δ^L (h−1)} for h > 0.
  - In the long run (t → ∞), wages equalize across sectors; short-run frictions remain.

### Calibration: trade elasticities, stickiness, and labor mobility
- Trade elasticity and stickiness estimation (Section 4.3.1):
  - Joint estimation of θ^I,j (production efficiency dispersion) and α_j (importer-exporter stickiness) using cross-product ratios and data 2010–2019.
  - Identification: ˆα_j = 1 − ˆβ_j2/ˆβ_j1; ˆθ^I,j = ˆβ_j1/ˆα_j.
- Estimated ranges and examples:
  - θ^I,j range: 1.7 to 13.2.
  - α_j range: 0.69 to 0.99 (larger α_j ⇒ less stickiness).
  - Selected entries (θ^I,j ; α_j):
    - Agriculture, hunting, forestry: 3.19; 0.80
    - Fishing and aquaculture: 5.79; 0.91
    - Mining and quarrying, energy producing products: 9.83; 0.83
    - Mining and quarrying, non-energy producing products: 13.20; 0.99
    - Food products, beverages and tobacco: 1.66; 0.96
    - Textiles, textile products, leather and footwear: 2.24; 0.86
    - Computer, electronic and optical equipment: 9.46; 0.78
    - Coke and refined petroleum products: 10.11; 0.98
    - Pharmaceuticals, medicinal chemical and botanical products: 7.07; 0.89
    - Motor vehicles, trailers and semi-trailers: 5.04; 0.93
    - Fabricated metal products: 3.56; 0.74
    - Machinery and equipment, nec: 9.74; 0.69
    - Electrical equipment: 3.86; 0.86
  - α_j negatively correlated with product specificity and complexity measures (coefficients reported, e.g., Relationship Stickiness: −0.018 ∗∗∗ (0.002), Observations 3,464, R^2 0.018).
  - Long-run trade elasticities stabilize after up to around 5 years.
- Labor mobility and re-skilling (Section 4.3.2):
  - Empirical relation: ∆^h log π^L,nj_t = (θ^L,n + h δ^L) ∆^h log w_nj_t − ∆^h log(Σ_k T^L,nk_t (w_nk_t)^{θ^L,n}).
  - Two-stage least squares with instrument (changes in effective sectoral tax rates).
  - Aggregate estimates (representative):
    - ˆβ0 (θ^L) ≈ 2.5 (reported column estimates: 2.468*** (0.124), 2.500*** (0.123), 2.580*** (0.125), 2.636*** (0.128), 2.572*** (0.137)).
    - ˆβ1 reported: 2.679*** (0.184), 2.632*** (0.170), 2.722*** (0.190), 2.732*** (0.181), 2.773*** (0.187).
    - Derived δ^L = 0.21 (= 2.679 − 2.468).
  - Country-specific θ^L,n negatively correlated with OECD Employment Protection Legislation (EPL) index.
  - Interaction estimates show higher employment protection reduces labor mobility elasticity (e.g., coefficient −0.518*** (0.149)).
- Other calibration inputs and simplifications (Section 4.3.3):
  - θ^H,n = 7; δ^H = 0.1.
  - Country capital and value-added shares ξ_nj, γ_nj from UNIDO INDSTAT4.
  - Input-output coefficients γ_njk from OECD ICIO; main simulations zero out off-diagonal I-O elements for computational tractability (γ_njj = 1 − γ_nj), with robustness checks reported in appendix.
  - Consumption shares β_nj from country final absorption minus intermediates.

### Fragmentation and diversification scenarios (Section 4.4 and results)
- Fragmentation scenario setup:
  - Geopolitical decoupling into blocs centered on China and the United States; EU+ and other advanced economies aligned with US; India, Indonesia, Latin America & Caribbean nonaligned; rest aligned with China.
  - Rising trade barriers modeled as a 50% bilateral non-tariff barrier on imports from opposing-bloc members.
- Baseline impacts on United States (no pre-fragmentation diversification):
  - Share of imports from China bloc falls from 25 to 9 percent in first year after shock; reaches new steady state of 5 percent after 4 years.
  - Welfare impact (United States) relative to no-shock scenario:
    - Year 1: −0.34%
    - Year 2: −0.17%
    - Long-run steady state decline: −0.15%
  - Distributional pattern: welfare impact larger for China bloc than US; nonaligned countries benefit.
- Diversification policy simulation (targeted pre-fragmentation diversification by US):
  - For goods with more than one-third sourced from China bloc, simulate a 10% increase in trade costs between US and China bloc to reallocate import shares:
    - China (direct) decline: 3.5 p.p.
    - Rest of China bloc decline: 1.1 p.p.
    - Increase in others in US bloc: 2.8 p.p.
    - Increase in rest of world: 1.9 p.p.
  - Effect on fragility and welfare:
    - Share of imports from China bloc is lower in all years following shock compared to baseline.
    - Year 1 welfare decline with diversification: −0.24% (vs −0.34% baseline) — transition losses reduced.
- Global tariff scenario (40% tariff with retaliation):
  - Context: imports ≈ 10 percent of US expenditures; certain goods have high import shares.
  - Diversification assumptions: 10% increase in trade costs between US and all other countries, restricted to goods with high rigidities (α_j below median), re-shoring 15 percent of high-rigidity imports.
  - Baseline domestic production cost: small negative baseline welfare impact of −0.04%.
  - Welfare impacts post-global tariff:
    - First-year welfare losses: −1.66 percent (no diversification) vs −1.46 percent (with diversification) — first-year losses 12 percent smaller with diversification.
    - Second-year welfare losses: 4 percent smaller with diversification.
    - Cumulative five-year welfare losses: 5 percent smaller with diversification.
  - Minimum probabilities P for diversification to be optimal under global tariff scenario:
    - About 2% with low risk aversion.
    - About 6% with high risk aversion.

### Social planner problem and optimal diversification thresholds
- Planner's utility: W_n = Σ_{t=0}^{∞} β^t (U_{n,t})^{1−σ} / (1−σ).
- Diversification is optimal when:
  - P · Σ_{t=1}^{∞} β^t ( (Ū_{n,df,t})^{1−σ} − (Ū_{n,nf,t})^{1−σ} ) ≥ (Ū_{n,nn,0})^{1−σ} − (Ū_{n,dn,0})^{1−σ}.
- Estimated minimum probabilities P for US case:
  - About 7% with low risk aversion.
  - About 9% with high risk aversion.
- Targeting reductions in costs and thresholds:
  - Diversification of all products (simulated 10% increase in trade costs for all goods):
    - Costs are 2.5 times larger.
    - Cumulative benefits are only 40 percent larger.
  - Diversification restricted to products with α_j below median among products with over one-third import share (same 10% increase):
    - Costs are 88 percent smaller.
    - Cumulative benefits are only 8 percent smaller.
    - Optimal when P > about 1 percent (vs 7–9 percent without rigidity restriction).
  - Targeting upstream products (above median by Antràs et al. measure):
    - Costs are 57 percent smaller.
    - Cumulative benefits are 34 percent smaller.

### Decomposition of gains and role of frictions
- Diversification reduces welfare losses from fragmentation by 12 percent in the baseline.
- If labor and local factors are perfectly mobile: diversification would reduce losses by 8 percent.
- Labor market frictions account for most of the remaining 4 percent reduction.
- Sticky import-exporter contracting accounts for most of the gains from diversification.

### Key quantitative figures (preserved)
- Trade elasticity θ^I,j range: 1.7 to 13.2.
- Importer-exporter stickiness α_j range: 0.69 to 0.99.
- Representative θ^L ≈ 2.5; δ^L = 0.21.
- Fragmentation scenario bilateral non-tariff barrier: 50%.
- US import share from China bloc: 25% → 9% in year 1 → 5% steady state after 4 years.
- US welfare impacts (baseline fragmentation, relative to no-shock):
  - Year 1: −0.34%
  - Year 2: −0.17%
  - Long-run steady state: −0.15%
- Diversification simulation (targeted goods with > 1/3 China share) reallocation:
  - China (direct) decline: 3.5 p.p.; Rest of China bloc decline: 1.1 p.p.; Increase in others in US bloc: 2.8 p.p.; Increase in rest of world: 1.9 p.p.
- Diversification reduces fragmentation welfare losses by 12 percent (baseline).
- Global tariff scenario:
  - Tariff size: 40%.
  - Imports ≈ 10 percent of US expenditures.
  - Re-shoring share: 15 percent of high-rigidity imports.
  - Baseline domestic-production welfare hit: −0.04 percent.
  - First-year welfare losses: −1.66 percent (no diversification) vs −1.46 percent (with diversification).
  - Cumulative five-year mitigation: 5 percent smaller losses.
  - Minimum P for diversification optimal: 2% (low σ), 6% (high σ).

### Policy implications and recommendations
- Diversification can improve resilience by reducing transition losses due to trade network rigidities but entails efficiency costs because imports are diverted from lower-cost sources.
- Targeted diversification is more cost-effective than broad diversification:
  - Prioritize products with greater exposure to exporter-specific shocks, higher importer-exporter contracting stickiness (α_j low), and more upstream positioning.
  - Under estimated parameters, targeted diversification of high-rigidity products with large import shares can be optimal at much lower probabilities of a large trade shock (P ≈ 1%) compared to undifferentiated diversification (P ≈ 7–9%).
- Consider labor market reforms or policies that reduce labor re-skilling frictions (increase δ^L or θ^L) to amplify the gains from diversification and reduce transition losses.
- Recognize trade-off between resilience and efficiency; policy design should weigh the probability of large trade shocks, risk aversion, and fiscal/implementation costs of diversification measures.

_Italic: Source document wpiea2025102-print-pdf - 0.26 percent of welfare) over five years._

### 0.26 percent of welfare) over five years.

### wpiea2025102-print-pdf - 0.26 percent of welfare) over five years.

### Contributions to literature
- Extends theoretical literature on trade disruptions by quantifying the impact of trade disruptions in a multi-country and multi-sector model that considers diversification policies and resilience.
- Links to prior findings:
  - Relates to Bhagwati and Srinivasan (1976), Bergström, Loury, and Persson (1985), Cheng (1989) on trade disruptions and inventories or embargo threats.
  - Most closely related to Grossman, Helpman, and Lhuillier (2023) on diversification achieving a constrained social optimum in a two-country model with a critical input.
  - Incorporates relationship stickiness in trade, connecting to Monarch (2022), Grossman, Helpman, and Redding (2024), Ornelas and Turner (2008), Antràs and Staiger (2012), Alfaro et al. (2024), Martin, Mejean, and Parenti (2023), and Boehm, Levchenko, and Pandalai-Nayar (2023).
  - Builds on dynamic multi-country and multi-sector quantitative trade models in the Eaton and Kortum (2002) tradition and related work (e.g., Alvarez (2017); Mutreja, Ravikumar, and Sposi (2018); Anderson, Larch, and Yotov (2020); Ravikumar et al. (2022); Brooks and Pujolas (2018)).
- Novel modeling elements:
  - Introduces trade network rigidities from sticky importer-exporter contracts.
  - Introduces frictions in labor and local factor mobility, allowing labor mobility to become more elastic over time.
  - Focuses on transition dynamics relevant for diversification and resilience.

### Limitations of the model
- Does not incorporate capital accumulation; investment decisions do not have persistent effects over time.
- Assumes perfectly competitive markets and constant returns to scale; does not allow for monopolistic competition with free entry of heterogeneous firms.
- Deterministic framework; does not model stochasticity or policy uncertainty (noted as potentially significant in International Monetary Fund (2025)).
- Aggregates final production at the country-product level, potentially overlooking firm-level within-sector distortions.
- Notes: Garcia-Macia and Goyal (2020) finds that monopolistic rents and preventing technology outflows can motivate onshoring.

### Organization of the paper
- Section 2: Stylized facts about diversification and supply chain resilience using US import and trade cost data.
- Section 3: Quantitative trade model.
- Section 4: Simulation exercises and results.
- Section 5: Conclusion.

### Stylized Facts — Overview
- Objective: Motivate supply chain diversification by documenting empirical relationships linking geographic concentration of imports, exporter-specific supply shocks, and resilience to trade cost shocks.
- Empirical facts summarized:
  - Fact 1: Products with geographically concentrated import sources are more exposed to supply shocks from individual exporters.
  - Fact 2: Products with more diversified import sources exhibit greater resilience to trade cost shocks.
  - Fact 3: US imports of geographically more diversified products were more resilient to the 2018-2019 tariffs on China.

### Data
- US import dataset:
  - Quarterly dataset at the country-product level constructed from US Census Bureau monthly data at the HS10 level.
  - Sample spans 2013 to 2024 and includes the full universe of HS-10 codes and trading partners.
  - Data provide duties collected, value of general imports subject to duties, and CIF import values; enables construction of effectively applied tariff rates and CIF values.
- Global tariff and trade data:
  - Bilateral tariff data at HS6 level from UNCTAD TRAINS (WITS) and MAcMap-HS6 (CEPII).
  - WITS provides MFN rates, applied preferential rates, prohibitive non-MFN rates, and AVE conversions for non–ad valorem tariffs.
  - Global bilateral HS6-level trade flows from BACI (CEPII) provide FOB trade flow data.
- Empirical method to recover exporter-level supply shock:
  - Estimate specification using PPML:
    - V_ijst = exp[β ln τ_ijst + FE_ijs + FE_ist + FE_jst] ε_ijst
    - Recover supply shock measure by exponentiating exporter-product-year fixed effects term (FE_ist).

### Geographic concentration and exporter supply shocks (Fact 1)
- Concentration measure:
  - Herfindahl-Hirschman Index (HHI) at product level: HHI_st = Σ_{i=1}^{N_st} (S_ist)^2 where S_ist is share of imports from country i.
- Risk measure:
  - Weighted covariance of supply shocks at product level: σ^2_s = W C W′ where W is exporter-level (time-averaged) market shares and C is covariance matrix of exporter-product-level supply shocks from FE_ist.
- Empirical finding:
  - Strong positive correlation between geographic concentration (HHI) and exporter supply shock risk, consistent with a portfolio-theory interpretation: diversification across less correlated suppliers reduces risk.

### Geographic concentration and resilience to trade cost shocks (Fact 2)
- Product-level elasticity/ substitutability estimation:
  - Use product-level regression (PPML variant):
    - V_st = exp[γ ln τ_st + FE_s + FE_t] ε_st
  - τ_st is product-level weighted sum of trade costs (tariffs and CIF) with weights weight_ist = V_{ist−1} / Σ_i V_{ist−1}.
  - ln τ_st = Σ_i (weight_ist × ln τ_ist).
- Empirical finding:
  - Negative correlation between product-level concentration (HHI) and estimated substitutability γ_s: products concentrated among a few exporters exhibit larger reductions in overall imports in response to positive trade cost shocks; more diversified products show greater substitution across suppliers and greater resilience.

### Case study: 2018–2019 US-China tariff hikes (Fact 3)
- Approach:
  - Aggregate non-China exporters into a single group and estimate HS10-level specification:
    - ln V_ist = Σ_k β_k · I(k=t) + Σ_k γ_k · I(k=t) × CHN_i + FE_is + FE_st + ε_ist, for targeted products.
    - I(k=t) is quarterly indicator; CHN_i = 1 if exporter is China.
  - Coefficient γ_t captures time-varying average level of imports from China relative to others for products targeted by 2018–2019 tariffs.
- Empirical observations:
  - Following tariff imposition, imports of targeted goods from China declined significantly relative to the rest of the world after a quarter—reflecting substitution to other suppliers and absolute decreases when substitution was insufficient.
- Product-level resilience heterogeneity:
  - Estimate product-quarter-level regression:
    - ln V_st = Σ_k β_t · I(k=t) + Σ_k γ_t · I(k=t) × HHI_s + FE_s + ε_st, for targeted products.
    - HHI_s = 1 if product s HHI is above median, 0 otherwise.
  - Finding: Products with higher import source concentration experienced a particularly pronounced decline in imports following the China tariff hikes, indicating lower resilience.

### Model — structure and key rigidities
- Model framework:
  - Multi-country (N) and multi-sector (J) general equilibrium trade model in discrete time t = 0,1,2,...
  - Representative firm for each country-good produces an intermediate variety under perfect competition and constant returns to scale, demanding labor, a composite local factor (structures), and materials (final goods) from all sectors.
  - Continuum of importers aggregates intermediate varieties (including home) into final goods.
  - Each country has fixed supplies of total labor and local factors.
- Three sources of trade network rigidities:
  1. Staggered (sticky) importer-exporter contracts:
     - Importers receive Poisson-distributed opportunities to switch suppliers; a proportion of firms can switch each period while the rest remain fixed.
  2. Labor market frictions:
     - Workers have heterogeneous sector-specific productivities (Roy (1951) framework).
     - Labor mobility across sectors is inelastic in the short-run; workers re-skill over time (labor mobility becomes more elastic over time).
  3. Immobile local factors:
     - Local factors (structures) have heterogeneous sector-specific productivities and are repurposed over time.
- Modeling lineage:
  - Builds on Eaton and Kortum (2002), Caliendo and Parro (2015), and Caliendo, Dvorkin, and Parro (2019).

*Italic: Source document wpiea2025102-print-pdf - 0.26 percent of welfare) over five years.*

### 3.1    Workers

### 3.1    Workers

### Representative population and labor supply
- There are measureL n workers in each countryn.  
- Each worker inelastically supplies one unit of time and earns labor incomew nj t ε nj L wherew nj t is the wage per efficiency unit of labor in countryn and sectorj.  
- The labor market is perfectly competitive: workers earn their marginal revenue product.

### Idiosyncratic productivity: Fréchet specification
- Each worker has an idiosyncratic productivity (efficiency units of labor) ε nj L for each sectorj, randomly drawn from a Fréchet distribution:
  - F nj L (ε L ) = exp(−T L,nj t ε −θ L,n L )(5)
- Interpretation of parameters:
  - Scale parameters T L,nj t control the overall level of worker productivity in each sector.
  - Shape parameter θ L,n determines dispersion of worker productivities and thus labor mobility across sectors.  
    - When θ L,n is low, workers exhibit significant productivity differences across sectors, reducing responsiveness to wage changes and increasing labor market frictions.
    - θ L,n can vary across countries n, so some countries can reallocate labor to adjust to demand more easily than others.

### Occupational choice and sectoral labor income shares
- Workers choose the sector generating the highest labor income (Roy (1951) framework).  
- Sectorj’s share of labor income is:
  - π L,nj t = T L,nj t (w nj t ) θ L,n / Σ k T L,nk t (w nk t ) θ L,n (6)
- The wage index in countryn is:
  - W n t = Γ [ θ L,n −1 / θ L,n ] ( Σ j T L,nj t (w nj t ) θ L,n ) 1/θ L,n (7)
  - Γ(.) is the Gamma function.

### Retraining, skill adjustment, and mobility dynamics
- Workers retrain and adjust skills based on wages/demand according to:
  - ( T L,nj t / T L,nj t−h ) = ( w nj t / w nj t−h ) δ L (h−1) (8) for h > 0, where δ L governs the speed of re-skilling.
- Dynamics and limits:
  - Following a shock in period t−h, as t → ∞, wages w nj t are equalized across sectors.  
  - Implication: short-run labor market frictions exist; long-run labor is perfectly mobile.

### Preferences, consumption, and price index
- Workers have Cobb-Douglas preferences over final goods. Utility in period t for a worker in countryn and working in sectorj is:
  - U(C nj t ) = Π_{k=1}^J ( c nj,k t )^{β nk } (9)
  - c nj,k t is consumption of goodk in period t; β nk is the final consumption share of goodk in countryn with Σ_{k=1}^K β nk = 1.
- The price index in countryn is:
  - P n t = Π_{k=1}^J ( P nk t / β nk )^{β nk }.
- Worker income components:
  - Income is derived from wages w nj t, rents from ownership of local factors r nj t, and lump-sum transfers (tariff revenues).

### Role in general equilibrium and interactions with other modules
- Labor income shares π L,nj t enter goods market clearing and interact with:
  - Local factors (whose own Fréchet specification and dynamics are described in Section 3.4).
  - Production unit costs and final good prices (Sections 3.2 and 3.3).
- Labor dynamics feed into the exact-hat simulation system (Section 4.1) through the change expressions:
  - ˆπ L,nj t = ˆT L,nj t (ˆw nj t )^{θ L,n} / Σ_k ˆT L,nk t (ˆw nk t )^{θ L,n} π L,nj t−h (28)
  - ˆW n t = ( Σ_j ˆT L,nj t (ˆw nj t )^{θ L,n} π L,nj t−h )^{1/θ L,n} (29)
  - ˆT L,nj t = (ˆw nj t )^{δ L (h−1)} (30)

*Source: 3.1 Workers, wpiea2025102-print-pdf*

### 4.3    Calibration

### 4.3 Calibration

### 4.3.1 Trade Elasticities θI,j and Stickiness in Import-Exporter Contracting αj — Method
- Jointly estimate dispersion parameter θI,j for production efficiency and importer-exporter stickiness parameter αj for each good j, building on Caliendo and Parro (2015).
- Identification strategy:
  - Use cross-product ratios of bilateral trade shares for three countries and the same good across directions to eliminate price and parameter terms (see Equation 43 and log-linearized Equation 44).
  - Model non-tariff trade costs as log(1 + d_nij_t) = ν_nij + φ_nj_t + ψ_ij_t + ε_nij_t, where ν_nij captures symmetric bilateral costs, φ_nj_t and ψ_ij_t are importer-good and exporter-good fixed effects, and ε_nij_t is an orthogonal disturbance.
  - Estimate, for each product j and using data 2010–2019, an equation of the form (Equation 45) with contemporaneous and lagged log product of (1+κ) terms up to two lags, plus time fixed effects Ψ_t.
  - Identification of αj and θI,j from estimated coefficients ˆβj1 and ˆβj2 using:
    - ˆαj = 1 − ˆβj2/ˆβj1  (Equation 46)
    - ˆθI,j = ˆβj1/ˆαj     (Equation 47)
- Assumptions and orthogonality:
  - ̃ε_nj_t assumed orthogonal to tariffs; tariffs before t−2 orthogonal to tariffs in t and t−1 conditional on tariffs in t−2, which supports unbiasedness of ˆβj1 and ˆβj2 as K→∞ (since (1−αj)^K → 0).

### 4.3.1 Trade Elasticities θI,j and Stickiness αj — Key Estimates and Findings
- Trade elasticity estimates:
  - Elasticities range from 1.7 to 13.2.
  - Heterogeneity across goods is statistically significant (null of common estimates rejected).
  - Estimates are in the range of broader literature (examples cited: Eaton and Kortum (2002) range 3.60 to 12.86, preferred 8.28; other studies ranges cited).
  - Correlation shown with Caliendo and Parro (2015) estimates (Figure 4a).
- Importer-exporter stickiness αj:
  - αj ranges from 0.69 to 0.99. A larger αj implies less stickiness (importers can more quickly switch suppliers).
  - Estimates correlate with Martin, Mejean, and Parenti (2023) measures of relationship stickiness (Figure 4b).
  - αj negatively correlated with product specificity and complexity measures (Table 2):
    - Relationship Stickiness (Martin et al.): coefficient −0.018 ∗∗∗ (standard error 0.002), Observations 3,464, R^2 0.018.
    - Product complexity (Hausmann & Hidalgo): coefficient −0.006 ∗∗∗ (0.001), Observations 3,182, R^2 0.011.
    - Differentiated (Rauch): coefficient −0.033 ∗∗∗ (0.002), Observations 3,282, R^2 0.067.
    - Share of not homogen. products (Nunn): coefficient −0.165 ∗∗∗ (0.007), Observations 2,994, R^2 0.161.
  - Interpretation: differentiated and more complex goods are more “sticky” (lower αj).
  - Implication: long-run trade elasticities stabilize after up to around 5 years, consistent with Boehm, Levchenko, and Pandalai-Nayar (2023).
- Selected entries from Table 1 (trade elasticities θI,j and stickiness αj by good):
  - Agriculture, hunting, forestry: θI,j = 3.19; αj = 0.80
  - Fishing and aquaculture: θI,j = 5.79; αj = 0.91
  - Mining and quarrying, energy producing products: θI,j = 9.83; αj = 0.83
  - Mining and quarrying, non-energy producing products: θI,j = 13.20; αj = 0.99
  - Food products, beverages and tobacco: θI,j = 1.66; αj = 0.96
  - Textiles, textile products, leather and footwear: θI,j = 2.24; αj = 0.86
  - Computer, electronic and optical equipment: θI,j = 9.46; αj = 0.78
  - Other notable entries:
    - Coke and refined petroleum products: θI,j = 10.11; αj = 0.98
    - Pharmaceuticals, medicinal chemical and botanical products: θI,j = 7.07; αj = 0.89
    - Motor vehicles, trailers and semi-trailers: θI,j = 5.04; αj = 0.93
    - Fabricated metal products: θI,j = 3.56; αj = 0.74
    - Machinery and equipment, nec: θI,j = 9.74; αj = 0.69
    - Electrical equipment: θI,j = 3.86; αj = 0.86

### 4.3.2 Labor Mobility θL,j and Speed of Re-skilling δL — Method
- Relate equilibrium changes in sectoral labor supply to changes in sectoral wages over horizon h:
  - ∆^h log π^L,nj_t = (θL,n + h δL) ∆^h log w_nj_t − ∆^h log(Σ_k T^L,nk_t (w_nk_t)^{θL,n})  (Equation 48)
- Empirical specification (two-stage least squares):
  - ∆^h log π^L,nj_t = β^h ∆^h log w_nj_t + X_njt + φ_nt + ψ_jt + φ_nj + ε_njt  (Equation 49)
  - Fixed effects: country-year (φ_nt), sector-year (ψ_jt), country-sector (φ_nj).
  - Controls X_njt include lagged sectoral wage changes ∆ log w_nj_t−k.
  - Instrument: changes in effective sectoral tax rates (Taxes less subsidies on products / Output at basic prices) to account for simultaneity of wages and labor supply.
- Parameter interpretation:
  - ˆβ0 is estimate of θL (aggregate labor elasticity).
  - ˆβ1 − ˆβ0 is estimate of δL (speed of re-skilling).

### 4.3.2 Labor Mobility θL,j and δL — Key Estimates and Findings
- Aggregate estimates (Table 3):
  - ˆβ0 (θL) reported across specifications; representative estimate: 2.5 (noted in text as 2.5).
  - Reported column-level estimates for ˆβ0: 2.468*** (0.124), 2.500*** (0.123), 2.580*** (0.125), 2.636*** (0.128), 2.572*** (0.137).
  - ˆβ1 reported: 2.679*** (0.184), 2.632*** (0.170), 2.722*** (0.190), 2.732*** (0.181), 2.773*** (0.187).
  - Derived estimate of δL = 0.21 (= 2.679 − 2.468).
  - Verification: implied θL + h δL lie within confidence intervals of ˆβh for h ∈ [2,5].
- Country-specific estimates:
  - ˆβ1 from country-level regressions gives θL,n.
  - Country-specific θL,n estimates are negatively correlated with OECD Employment Protection Legislation (EPL) index (Figure 5 and Table 4).
- Interaction results (Table 4):
  - Baseline coefficient on ∆ log w_nj_t: estimates 2.033*** (0.132), 2.005*** (0.126), 2.272*** (0.157), 2.261*** (0.153) across specifications.
  - Interaction ∆ log w_nj_t * log(Employment Protection Index): coefficients −0.518*** (0.149), −0.474*** (0.144), −0.514*** (0.169), −0.461*** (0.167).
  - Interpretation: higher employment protection rigidity reduces labor mobility elasticity.

### 4.3.3 Other Parameters and Calibration Inputs
- Assumptions and external calibrations:
  - Dispersion parameter for local factors efficiency θH,n = 7 (as in Tintelnot (2017)).
  - Depreciation rate δH = 0.1 (based on BEA’s depreciation estimates).
  - Country capital and value-added shares ξ_nj, γ_nj taken from UN Industrial Development Organization data.
  - Input-output coefficients γ_njk taken from Inter-country Input-Output Tables (OECD).
- Computational simplification for main simulations:
  - To reduce dimensionality, assume materials are used in production (γ_nj < 1) but zero out off-diagonal elements of I-O matrix so firms only use materials sourced from the same sector they operate in (γ_njj = 1 − γ_nj). I-O tables used to calibrate γ_njj.
  - Appendix reports alternative simulations relaxing these simplifications and confirms consistency of results where labor and capital are perfectly mobile and off-diagonal I-O elements non-zero.
- Consumption shares β_nj computed from country total expenditure on good j net of intermediate expenditure and divided by total final absorption (Equation 50).

### 4.4 Fragmentation Scenario — Baseline and Diversification (brief, calibration-relevant highlights)
- Fragmentation scenario setup (Section 4.4 summary):
  - Geopolitical decoupling between blocs centered on China and the United States; EU+ and other advanced economies aligned with US; India, Indonesia, Latin America & Caribbean nonaligned; rest aligned with China (Table 5).
  - Rising trade barriers between blocs modeled as a 50% bilateral non-tariff barrier imposed on imports from opposing-bloc members.
- Baseline (no pre-fragmentation diversification) impacts on United States:
  - Share of imports from China bloc falls from 25 to 9 percent in first year after shock; reaches new steady state of 5 percent after 4 years (Figure 7a).
  - Welfare impact on United States relative to no-shock scenario:
    - Year 1: −0.34%
    - Year 2: −0.17%
    - Long-run steady state decline: −0.15%
  - Distributional note: welfare impact larger for China bloc than US; nonaligned countries benefit (consistent with IMF WEO Chapter 4 findings).
- Diversification policy simulated:
  - US diversifies imports of goods with more than one-third sourced from China bloc by simulating a 10% increase in trade costs between US and China bloc for those goods, resulting in assumed initial reallocation of import shares:
    - China (direct) decline: 3.5 p.p.
    - Rest of China bloc decline: 1.1 p.p.
    - Increase in others in US bloc: 2.8 p.p.
    - Increase in rest of world: 1.9 p.p.
  - Effect on fragility and welfare:
    - Diversification lowers initial reliance on China bloc and brings pre-fragmentation configuration closer to post-fragmentation optimum.
    - Share of imports from China bloc is lower in all years following shock compared to baseline (Figure 9a).
    - Welfare decline with diversification is smaller in year 1: −0.24% (compared to −0.34% baseline) — transition losses from supply chain rigidity are reduced under diversification (Figure 9b).

*Italic: Source — Excerpt from “4.3 Calibration” (Content unit: wpiea2025102-print-pdf - 4.3    Calibration).*

### 0.34 percent in the baseline.  Cumulatively, the welfare losses over five years are 12 percent

### wpiea2025102-print-pdf - 0.34 percent in the baseline.  Cumulatively, the welfare losses over five years are 12 percent

### Social planner problem
- Social planner has constant relative risk aversion utility:
  - W_n = Σ_{t=0}^{∞} β^t (U_{n,t})^{1−σ} / (1−σ).
- Decision reduces to a one-period choice to diversify in period t.
- Diversification is optimal when:
  - P · Σ_{t=1}^{∞} β^t ( (Ū_{n,df,t})^{1−σ} − (Ū_{n,nf,t})^{1−σ} ) ≥ (Ū_{n,nn,0})^{1−σ} − (Ū_{n,dn,0})^{1−σ}.
- Key comparative-statics:
  - If P·Σ_{t=1}^{∞} β^t( (Ū_{n,df,t})^{1−σ} − (Ū_{n,nf,t})^{1−σ} ) > 0, higher P makes diversification more likely to be optimal.
  - Larger potential gains from diversification relative to its costs, and higher risk aversion σ, make diversification more likely to be optimal.
- Estimated minimum probabilities P for diversification to be optimal (US case):
  - About 7% with low risk aversion.
  - About 9% with high risk aversion.
- Note: The costs of diversification could be higher if measures enacted to achieve diversification introduce fiscal costs or other economic distortions not captured in the model.
- Specific steady-state impacts cited:
  - Impact on welfare in the pre-fragmentation shock steady state: 0.02 percent decline.

### Decomposition of gains from diversification
- Diversification reduces welfare losses from fragmentation by 12 percent in the baseline.
- If labor and local factors are perfectly mobile:
  - Diversification would reduce losses by 8 percent.
- Frictions in labor market mobility account for most of the remaining 4 percent reduction (labor supply elasticities are generally more inelastic than those of local factors).
- Sticky import-exporter contracting accounts for most of the gains from diversification.

### Targeting diversification
- Diversification targeted to products with higher exposure to shocks, more rigidities, and more upstream positioning improves efficiency relative to broad diversification.
- Scenario: Diversification of all products (simulated 10% increase in trade costs between US and China bloc for all goods):
  - Costs are 2.5 times larger.
  - Cumulative benefits are only 40 percent larger.
- Scenario: Diversification restricted to products with greater import-exporter contracting stickiness (α_j below the median) among products with over a third import share (simulated 10% increase in trade costs limited to these products):
  - Costs are 88 percent smaller.
  - Cumulative benefits are only 8 percent smaller.
  - Given estimated parameters and the social planner problem, such targeted diversification is optimal when P is greater than about 1 percent (compared to 7-9 percent without the rigidity restriction).
- Targeting more upstream products (above the median by the Antràs, Chor, et al. (2012) measure):
  - Costs are 57 percent smaller.
  - Cumulative benefits are only 34 percent smaller.

### Global tariff scenario
- Shock modeled: 40% tariff imposed on all US trade with retaliation (Costinot and Rodríguez-Clare (2014) scenario).
- Context:
  - Imports make up about 10 percent of US expenditures.
  - Certain goods (fishing and aquaculture, textiles, textile products, leather and footwear) have particularly high import shares.
- Diversification assumptions for this scenario:
  - Diversified (or re-shored) trade shares result from a simulated 10% increase in trade costs between the United States and all other countries, restricted to goods with high rigidities (α_j below the median).
  - Diversification re-shores 15 percent of imports with high rigidities.
  - Producing domestically is more costly than importing, causing a small negative baseline impact on welfare of -0.04 percent.
- Welfare impacts following the global tariff shock:
  - First-year welfare losses are 12 percent smaller with diversification:
    - −1.66 percent without diversification.
    - −1.46 percent with diversification.
  - Second-year welfare losses are 4 percent smaller with diversification.
  - Cumulative welfare losses over five years are 5 percent smaller with diversification.
- Minimum probabilities P for diversification to be optimal under the global tariff scenario:
  - About 2% with low risk aversion.
  - About 6% with high risk aversion.

### Key quantitative findings and thresholds
- Baseline impact metric mentioned: 0.34 percent (in the baseline).
- Welfare change in pre-fragmentation steady state: 0.02 percent decline.
- Diversification reduces fragmentation welfare losses by 12 percent (baseline).
- Mobility counterfactuals:
  - Perfect labor and local factor mobility: 8 percent reduction in losses.
  - Labor frictions account for ~4 percent of remaining gains.
- Targeting vs broad diversification:
  - Diversify all products: costs 2.5 times larger; cumulative benefits 40 percent larger.
  - Target high-rigidity products (α_j below median, import share > 1/3): costs 88 percent smaller; cumulative benefits 8 percent smaller; optimal for P > 1 percent.
  - Target upstream products (Antràs et al. measure): costs 57 percent smaller; cumulative benefits 34 percent smaller.
- Global tariff shock specifics:
  - Tariff size: 40%.
  - Imports ≈ 10 percent of US expenditures.
  - Re-shoring share: 15 percent of high-rigidity imports.
  - Baseline domestic-production welfare hit: -0.04 percent.
  - First-year welfare losses: −1.66 percent (no diversification) vs −1.46 percent (with diversification).
  - Cumulative five-year mitigation: 5 percent smaller losses.
  - Minimum P for optimal diversification: 2% (low σ), 6% (high σ).

### Conclusion: resilience-efficiency trade-off
- Three stylized facts established for US imports:
  - Concentrated supply chains are more exposed to exporter-specific supply shocks.
  - Imports are less sensitive to trade costs when the supply chain is diversified.
  - Sectors with diversified supply chains exhibited greater resilience to the 2018-2019 tariffs on Chinese imports (event study evidence).
- Model highlights:
  - Multi-country, multi-sector general equilibrium model with frictions in goods, labor, and local factor markets.
  - Diversification can enhance resilience by reducing transition losses due to trade network rigidities, but entails efficiency costs because imports diverted from lower-cost sources increase production costs.
- Policy design implication:
  - Diversifying targeted imports—those more exposed to shocks, more upstream, and subject to greater rigidities—can improve expected welfare when the probability of a large trade shock is sufficiently high.
- Future work stated:
  - Leverage the model to study the design and implications of optimal diversification policy.

*Source: https://www.imf.org/-/media/files/publications/wp/2025/english/wpiea2025102-print-pdf.pdf*

### Appendix A. Tables and Figures

### Appendix A. Tables and Figures

### Figures: Fragmentation and Diversification Analyses
- Figure A1: Fragmentation Shock – Baseline: Impact on Welfare (All Blocs)
  - Presents the impact of the fragmentation scenario on welfare by country bloc.

- Figure A2: Social Planner Problem: Minimum Probability of Fragmentation for Diversification to be Optimal
  - Panel (a) Diversification of all goods.
  - Panel (b) Diversification of rigid goods with 1/3 import share.
  - Notes: Presents the minimum probability of the fragmentation scenario required for diversification to be optimal based on Equation 52 for all goods in (a) and for only on products with over one-third import share and greater rigidities defined as α_j above the median in (b).

- Figure A3: Targeting Upstream Products - Model with Perfectly Mobile Labor and Capital and Input-output Linkages (Fragmentation Scenario)
  - Panel (a) Impact on US Welfare.
  - Panel (b) Percentage Difference in Costs and Cumulative Benefits.
  - Notes: Panel (a) presents the impact of fragmentation on welfare for the United States under baseline policies, diversification on all goods with over 1/3 import share, and diversification restricted to upstream good with over 1/3 import share. Panel (b) presents the percentage difference in cost of diversification in year 0 and the cumulative benefits of diversification from year 1 to 5 between diversification which targets upstream products versus diversification that does not.

- Figure A4: Aggregate Weighted Average Bilateral Effective Tariff Rates
  - Presents a binned scatter plot illustrating the relationship between weighted average bilateral effective tariff rates from two distinct sources at the aggregate level for the year 2017.
  - X-axis values: calculated by combining the WITS and MAcMap databases as described in the text.
  - Y-axis values: taken from the Global Tariff Database in Teti (2024).

### Appendix B. Data Description

### B.1. Sector-level Gross Output and Bilateral Trade
- Primary data source: OECD’s Inter-country Input-Output Tables (ICIO) database.
- Data content: flows of production, consumption, investment within countries, and cross-country flows of goods.
- Original coverage: 45 sectors for 76 countries and the rest of the world (ROW) over the period 1995-2020.
- Sample restrictions for compatibility: restricted to 69 countries plus ROW and shortened the time span to 2000–2020.

### B.2. Sector-level Labor and Capital Income Shares
- Primary data source: UNIDO INDSTAT4 from the UNIDO Industrial Statistics (INDSTAT) Revision 4 Database.
- Sector classification: ISIC Rev.4, mapped to the 45 sectors in the OECD ICIO through two-digit ISIC Rev.4 codes.
- Labor compensation data: available for 69 of the original 76 countries in the OECD ICIO database, starting from the year 2000.
- Capital income share calculation: sector-level capital income share is calculated as the residual of sectoral value added after subtracting labor compensation.

### B.3. Sector-level Bilateral Tariff
- Primary data sources:
  - UNCTAD TRAINS available from WITS (bilateral tariff data at the 6-digit Harmonized System (HS6) level).
  - MAcMap-HS6 dataset available at CEPII (used to complement WITS).
  - Adjustments to account for additional retaliatory tariffs following Fajgelbaum et al. (2024).
- Key data processing steps:
  - Apply average tariff rates to bilateral country pairs at the HS6 level.
  - Apply zero tariff rates to intra-EU trade and fill in missing rates among EU importers using common EU-wide rates.
  - For missing tariff observations, apply the latest available bilateral tariff rates; for remaining missing values, replace with the closest available future tariff rates.
  - Merge with the MAcMap-HS6-CEPII database (interpolated for missing years) and retain the lower of the two values to better reflect effectively applied rates.
  - Use concordance between HS6 and ISIC Rev.4 classifications to construct bilateral tariff rate data at the 45-sector level of the OECD ICIO.
- Consistency check: The resulting tariff data are consistent at the aggregate level with the Global Tariff Database from Teti (2024), which revamps the WITS data through a close examination.

*Source: Appendix A and Appendix B, "Appendix A. Tables and Figures" and "Appendix B. Data Description" from Supply Chain Diversification and Resilience Working Paper No. WP/2025/102.*

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_Source: https://www.imf.org/-/media/files/publications/wp/2025/english/wpiea2025102-print-pdf.pdf_