## wpiea2026183-source-pdf

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---

### Data and Measurement
- Data sources and mapping:
  - Bilateral trade: Base pour l’Analyse du Commerce International (BACI) at the HS6 exporter-importer-year level for 1995–2024 and 230 countries.
  - HS6 products mapped into OECD ICIO sectors and aggregated to bilateral country-sector-year exports X_ijut, where i = exporter, j = importer, u = upstream sector, t = year.
  - HS6-to-ICIO concordance:
    - Retains 89.7 percent of trade value.
    - Covers 17 manufacturing upstream sectors.
    - Unmapped products are dropped rather than imputed.
  - Network baseline window: 1995–1999. Baseline shares enter three objects:
    - Supplier destination shares for supplier demand shocks.
    - Downstream import shares for scalable-supplier exposure.
    - Downstream destination shares for foreign demand shocks.
  - Estimation sample begins in 2000 so that network weights are predetermined relative to downstream response.
- Preprocessing and construction notes:
  - Supplier-scalability first-stage elasticities are winsorized at the 1st and 99th percentiles before constructing downstream exposure.
  - Leave-out market-size terms exclude the exporter’s own exports when constructing demand shocks.

### Measuring supplier scalability
- Supplier demand shifter and first stage:
  - Shock_iut = sum_k s_iuk,95−99 * Δ log M_ROW,−i_kut, where s_iuk,95−99 is supplier i’s 1995–1999 export share to destination k in sector u and M_ROW,−i_kut is destination k’s total imports in sector u from all suppliers other than i.
  - First-stage estimation (from 2000 onward):
    - Δ log X_iut = a_iu + S_iu Shock_iut + e_iut.
    - S_iu is the estimate of scalability for supplier country i in upstream sector u.
- Empirical Bayes adjustments:
  - S_EB0_iu = ρ_iu S_iu; S_EBμ_iu = S̄_u + ρ_iu (S_iu − S̄_u).
  - ρ_iu = bσ^2_u / (bσ^2_u + bse(S_iu)^2), where bσ^2_u is the within-upstream-sector variance of raw scalability and S̄_u is the upstream-sector mean.
  - S_EB0 shrinks noisier estimates toward zero; S_EBμ shrinks noisy estimates toward the upstream-sector mean.

### From supplier scalability to downstream exposure
- Downstream scalable-supplier exposure:
  - SIE_jd,95−99 = sum_u θ_du sum_i s_jiu,95−99 S_iu, where s_jiu,95−99 is downstream country j’s 1995–1999 import share from supplier i in upstream sector u and θ_du is the ICIO input weight of upstream sector u in downstream sector d.
- Downstream demand shock:
  - DemandShock_jdt = sum_k s_jdk,95−99 * Δ log M_ROW,−j_kdt, where M_ROW,−j_kdt excludes downstream exporter j’s own exports to destination k in sector d.
- Main response sample uses positive demand shocks from 2000 onward.

---

### Fact 1: Supplier Scalability Is Country-Sector Specific
- Key empirical finding:
  - Supplier scalability varies at the country-sector level; it is not solely a country or sector characteristic.
- Variance decomposition (shares of variation explained):
  - Unadjusted:
    - Country FE R^2 = 0.231
    - Sector FE R^2 = 0.043
    - Country + sector FE R^2 = 0.278
    - Residual share = 0.722
  - Mean-centered Empirical Bayes:
    - Country FE R^2 = 0.164
    - Sector FE R^2 = 0.110
    - Country + sector FE R^2 = 0.277
    - Residual share = 0.723
  - Zero-centered Empirical Bayes:
    - Country FE R^2 = 0.315
    - Sector FE R^2 = 0.069
    - Country + sector FE R^2 = 0.400
    - Residual share = 0.600
- Interpretation:
  - Even after absorbing supplier-country and upstream-sector fixed effects, 60–72 percent of variation remains at the supplier-country-sector level.
  - The empirical object is the scalability of specific country-sectors within upstream industries.
- Correlates of supplier scalability (N = 1813; each coefficient from separate regressions including supplier-country and sector fixed effects):
  - Supplier-sector size:
    - Unadjusted: 0.076*** (0.012)
    - Mean-centered Empirical Bayes: 0.047*** (0.007)
    - Zero-centered Empirical Bayes: 0.098*** (0.007)
  - Log destinations served:
    - Unadjusted: 0.126 (0.079)
    - Mean-centered Empirical Bayes: 0.109** (0.043)
    - Zero-centered Empirical Bayes: 0.245*** (0.046)
  - Destination diversification:
    - Unadjusted: 0.135 (0.107)
    - Mean-centered Empirical Bayes: 0.098* (0.059)
    - Zero-centered Empirical Bayes: 0.152** (0.063)
  - Baseline export growth:
    - Unadjusted: 0.533*** (0.151)
    - Mean-centered Empirical Bayes: 0.178** (0.083)
    - Zero-centered Empirical Bayes: 0.248*** (0.089)
  - Baseline growth volatility:
    - Unadjusted: -0.212*** (0.045)
    - Mean-centered Empirical Bayes: -0.080*** (0.025)
    - Zero-centered Empirical Bayes: -0.215*** (0.026)
- Interpretation of correlates:
  - Scalable supplier country-sectors tend to be larger, serve more destinations, have more diversified destination portfolios, exhibit higher baseline export growth, and lower baseline growth volatility.

---

### Fact 2: Scalable Suppliers Tend to Have Scalable Suppliers
- Empirical finding:
  - Supplier country-sectors connected to more scalable input suppliers tend to be more scalable themselves — scalability is a network property.
- Evidence:
  - Figure 1 documents a strongly positive relationship between a supplier country-sector’s own scalability and the scalability of its input network (variables residualized by upstream-sector fixed effects; binned means plotted).
- Correlates (Table A2 summary):
  - Supplier-side scalability is positively associated with destination diversification, consistent with scalable suppliers having broad sales and scalable sourcing networks.

---

### Fact 3: Export Responses Rise with Scalable-Supplier Exposure
- Main estimating equation (positive demand shocks from 2000 onward):
  - Δ log X_jd,t+1 = α DemandShock_jdt + δ SIE_jd,95−99 + β (DemandShock_jdt × SIE_jd,95−99) + Γ_jdt + ε_jdt.
  - Outcome: cumulative one-year export growth for downstream country j and sector d (winsorized at the overall 5th and 95th percentiles).
  - Standard errors clustered by country-sector.
- Key result (interaction β compares how response to a demand shock differs with predetermined exposure to scalable suppliers; sample uses positive demand shocks from 2000 onward):
  - Table 3 interaction coefficients (standard errors in parentheses); N by sample:
    - All: N = 58,440
    - High input relationship stickiness: N = 31,699
  - Unadjusted SIE:
    - All: 0.022 (0.046), 0.019 (0.043)
    - High stickiness: 0.291** (0.138), 0.348*** (0.134)
  - Mean-centered Empirical Bayes SIE:
    - All: 0.032 (0.045), 0.023 (0.042)
    - High stickiness: 0.377** (0.148), 0.401*** (0.141)
  - Zero-centered Empirical Bayes SIE:
    - All: 0.033 (0.045), 0.029 (0.042)
    - High stickiness: 0.353*** (0.132), 0.432*** (0.128)
- Interpretation:
  - In the full sample, the interaction between demand shocks and scalable-supplier exposure is small and insignificant.
  - Among downstream sectors that rely more heavily on relationship-sticky inputs (defined following Martin et al. (2026)), the interaction is large and statistically significant across unadjusted and Empirical Bayes measures.
  - Scalable suppliers matter most where buyer-supplier links are harder to replace quickly.
- Dynamics and robustness:
  - Figure 2 (high stickiness subsample): binned country-sector demand elasticities plotted against scalable-supplier exposure show a positive fitted line — larger export responses for higher exposure.
  - Figure 3 (dynamic response, high stickiness): interaction coefficients from t−3 to t+4:
    - Pre-shock coefficients are close to zero and statistically insignificant (no differential pretrends).
    - Response turns positive on impact, peaks around the one-year horizon, remains positive over subsequent years, and gradually fades by t + 4.
    - Suggests exposure to scalable suppliers shapes the export adjustment path after a demand shock, strongest around the first year.
  - Robustness: Appendix Table A3 reconstructs scalable-supplier exposure leaving out demand variation associated with the downstream country-sector under study — estimates similar to baseline.

---

### Model (overview)
- Central mechanism:
  - A foreign demand expansion raises downstream production, increasing demand for intermediate inputs.
  - If downstream producers source from suppliers with steep supply curves, upstream input prices rise, downstream marginal costs increase, and export response is attenuated.
  - If the inherited supplier network is more scalable, the same foreign demand shock generates a larger downstream export expansion.
- Model ingredients:
  1. Sectors linked through input-output production.
  2. Downstream producers source intermediate inputs across foreign and domestic suppliers through constant elasticity of substitution (CES) sourcing nests.
  3. Supplier country-sectors face upward-sloping supply curves with supply elasticities that differ across suppliers within the same upstream sector.
  4. Upstream sectors differ in relationship stickiness: in sticky input markets, existing buyer-supplier links are harder to replace quickly.
- Environment and production (key equations and definitions preserved):
  - Gross output in downstream country-sector jd:
    - Y_jd = A_jd V_jd^(1−α_d) M_jd^(α_d), where α_d ∈ [0, 1].
  - Intermediate bundle:
    - M_jd = Π_u M_jdu^(θ_du), with sum_u θ_du = 1.
  - CES composite across supplier countries for upstream input u:
    - M_jdu = [sum_i ω_jiu^(1/σ) q_jiu^((σ−1)/σ)]^(σ/(σ−1)).
  - CES price index:
    - P_ju = [sum_i ω_jiu p_jiu^(1−σ)]^(1/(1−σ)).
  - Downstream intermediate input price index:
    - P_M_jd = Π_u P_ju^(θ_du).
  - Unit cost of producing downstream good:
    - c_jd = 1/A_jd [w_j^(1−α_d)]^(1−α_d) P_M_jd^(α_d).
  - In proportional changes:
    - b c_jd = b w_j^(1−α_d) + sum_u b P_ju^(α_d θ_du) + b A_−1_jd.

---

### Supplier Supply Curves
- Supplier supply specification:
  - Upward-sloping supply curve:
    - p_iu = κ_iu C_iu Q_iu^{1/η_iu}, where η_iu > 0 is the supplier supply elasticity.
  - Delivered prices:
    - p_jiu = τ_jiu p_iu, with τ_jiu ≥ 1.
  - In hat notation:
    - b p_jiu = b τ_jiu b C_iu b Q_iu^{1/η_iu} b κ_iu.
  - Supplier iu’s producer cost follows same input-output cost equation:
    - b C_iu = b w_i^{1−α_u} b P_v^{α_u} θ_{uv} b A_{iu}^{−1}.
- Operating cost and supplier rents:
  - V C_iu = ∫_0^{Q_iu} κ_iu C_iu q^{1/η_iu} dq = η_iu/(1 + η_iu) p_iu Q_iu.
  - Π_iu = p_iu Q_iu − V C_iu = 1/(1 + η_iu) p_iu Q_iu.
  - Low-η_iu suppliers generate larger scarcity rents when their output is demanded.
  - Supplier rents are owned domestically and rebated lump-sum to the representative household in supplier country i.
- Mechanism linking scalability to downstream responses:
  - Demand expansion raises upstream input demand; if suppliers have low η_iu, Q_iu rises and p_iu rises, increasing downstream marginal cost c_jd and attenuating export response.
  - Relationship stickiness ρ_u ∈ [0, 1] governs speed of sourcing adjustment:
    - High ρ_u: sourcing adjusts slowly; inherited suppliers matter more.
    - Low ρ_u: sourcing adjusts quickly; buyers reallocate away from constrained suppliers.
  - Net mechanism: Demand shock × input intensity and IO weights × supplier supply scalability × relationship stickiness.
- Calibration and empirical linkage:
  - Baseline objects: baseline sourcing shares s_jiu0 from trade data; θ_du and α_d from ICIO.
  - Relationship stickiness calibrated using RS_u with D_0 = 2 (years); implied D_u = D_0 exp(RS_u − RS) and ρ_u = exp(−1/D_u).
  - Other parameters:
    - Destination demand elasticity ε_d = 5.
    - σ chosen so that (1 − ρ_u) σ = 5 (mean one-year persistence-adjusted substitution margin).
    - Labor-supply elasticity φ = 3.
  - Supplier elasticity parameterization:
    - η_iu = ̄η_u exp(λ_u z_iu), where z_iu is the standardized empirical-Bayes scalability estimate.
    - (̄η_u, λ_u) chosen by simulated method of moments to reproduce first-stage empirical supplier-scalability moment.

### Quantitative results: impact of a 10 percent global demand shock
- Main messages:
  - Supplier bottlenecks attenuate aggregate gains from the shock relative to high- or perfect-scalability benchmarks.
  - Relationship stickiness determines where bottlenecks bind: high scalable-supplier-exposure sectors expand more in the short run but advantage fades as sourcing relationships adjust.
- Table 4 level outcomes (percentage-point log changes) and attenuations:
  - Baseline:
    - Export response (p.p.) = 4.32
    - Real income gain (p.p.) = 3.16
    - Marginal cost (p.p.) = 1.30
    - Input price (p.p.) = 1.55
  - Sector-p90:
    - Export response (p.p.) = 5.11
    - Real income gain (p.p.) = 4.09
    - Marginal cost (p.p.) = 1.11
    - Input price (p.p.) = 0.89
  - Infinite η:
    - Export response (p.p.) = 5.17
    - Real income gain (p.p.) = 4.17
    - Marginal cost (p.p.) = 1.09
    - Input price (p.p.) = 0.83
  - Attenuation:
    - Export attenuation (%) = –15.46 (baseline vs. sector-p90), 16.51 (baseline vs. infinite η)
    - Welfare attenuation (%) = –22.65 (baseline vs. sector-p90), 24.24 (baseline vs. infinite η)
- Interpretation:
  - Baseline export response is 4.32 percent and real income gain is 3.16 percent after a 10 percent global demand shock.
  - Compared to sector-p90 and infinite-elasticity benchmarks, supplier bottlenecks materially reduce export and welfare gains.

### Role of relationship stickiness in transition dynamics
- Aggregate transition (Table 5; level outcomes are percentage-point log changes; gains are percentages relative to T = 0):
  - Export response (p.p.):
    - T = 0: 4.32
    - T = 1: 4.46
    - T = 2: 4.51
    - Long run: 4.56
  - Export gain vs. T = 0 (%):
    - T = 1: –3.30
    - T = 2: 4.43
    - Long run: 5.69
  - Real income gain (p.p.):
    - T = 0: 3.16
    - T = 1: 3.180
    - T = 2: 3.184
    - Long run: 3.189
  - Welfare gain vs. T = 0 (%):
    - T = 1: –0.44
    - T = 2: 0.57
    - Long run: 0.72
- Interpretation:
  - Relaxing sourcing relationships has a modest aggregate effect: export response rises from 4.32 percent on impact to 4.56 percent in the long run (a 5.69 percent increase relative to initial response).
  - Relationship stickiness mainly affects distribution across sectors rather than aggregate amplification.
- Sectoral exposure premium (Table 6 summary; comparing within-downstream-sector 90th and 10th percentiles of SIE_model):
  - p90/p10 export response (%): 18.19, 9.56, 6.82, 3.93 (impact, T = 1, T = 2, long run)
  - p90/p10 marginal cost (%): -12.54, -7.60, -5.69, -3.46
  - p90/p10 input price (%): -23.97, -18.68, -16.71, -14.38
  - p10 export response (p.p.): 3.89, 4.22, 4.33, 4.46
  - p90 export response (p.p.): 4.60, 4.62, 4.63, 4.64
- Interpretation:
  - High-exposure group increases exports by 18.19 percent more on impact; premium falls over time to 3.93 percent in the long run.
  - Cost gaps are larger on impact for low-exposure sectors and shrink over time as sourcing adjusts.

---

### Global Policy: Fixed-budget supplier-upgrading
- Exercise setup:
  - Policy budget equal to 10 percent of supplier country-sectors.
  - For each targeted supplier country-sector, raise its supply elasticity up to the within-upstream-sector 90th percentile if it is below it.
  - Shock considered: 10 percent global demand shock.
- Scalable-supplier exposure gradient over adjustment horizon (Table 6):
  - p90/p10 export response (%): 18.19, 9.56, 6.82, 3.93
  - p90/p10 marginal cost (%): -12.54, -7.60, -5.69, -3.46
  - p90/p10 input price (%): -23.97, -18.68, -16.71, -14.38
  - p10 export response (p.p.): 3.89, 4.22, 4.33, 4.46
  - p90 export response (p.p.): 4.60, 4.62, 4.63, 4.64
  - Notes: p90 and p10 compare country-sectors at the within-downstream-sector 90th and 10th percentiles of model-implied scalable-supplier exposure (SIE_model). Ratio rows are percentages. Export response rows are percentage-point log changes.
- Targeting rules compared (targets = 10 percent of supplier country-sectors below within-upstream-sector p90):
  - Random targeting: placebo-style benchmark.
  - Lowest-η targeting: upgrades the most inelastic supplier country-sectors.
  - Largest-sector targeting: prioritizes supplier country-sectors with the largest baseline export value.
  - Central-supplier targeting: prioritizes supplier nodes with the largest baseline intermediate-input demand in the model network.
  - Sticky-bottleneck targeting: ranks supplier country-sectors by the product of inverse supply elasticity, baseline intermediate-input demand, and an upstream-sector stickiness weight.
- Quantitative outcomes by targeting rule (Table 7; level outcomes are percentage-point log changes; gains are percentages vs. baseline):
  - Baseline:
    - Export response (p.p.): 4.3194
    - Real-income gain (p.p.): 3.1663
    - Input-price change (p.p.): 1.5451
  - Random:
    - Export response (p.p.): 4.4744
    - Real-income gain (p.p.): 3.3703
    - Input-price change (p.p.): 1.4071
    - Export gain vs. baseline (%): 3.59
    - Real-income gain vs. baseline (%): -0.20
    - Input-price change vs. baseline (%): -8.95
  - Lowest-η:
    - Export response (p.p.): 4.5104
    - Real-income gain (p.p.): 3.4033
    - Input-price change (p.p.): 1.3791
    - Export gain vs. baseline (%): 4.43
    - Real-income gain vs. baseline (%): 0.23
    - Input-price change vs. baseline (%): -10.75
  - Largest-sector:
    - Export response (p.p.): 4.5894
    - Real-income gain (p.p.): 3.6503
    - Input-price change (p.p.): 1.3041
    - Export gain vs. baseline (%): 6.27
    - Real-income gain vs. baseline (%): 0.47
    - Input-price change vs. baseline (%): -15.61
  - Central:
    - Export response (p.p.): 4.5934
    - Real-income gain (p.p.): 3.6533
    - Input-price change (p.p.): 1.3051
    - Export gain vs. baseline (%): 6.36
    - Real-income gain vs. baseline (%): 0.47
    - Input-price change vs. baseline (%): -15.57
  - Sticky:
    - Export response (p.p.): 4.738
    - Real-income gain (p.p.): 3.794
    - Input-price change (p.p.): 1.186
    - Export gain vs. baseline (%): 9.72
    - Real-income gain vs. baseline (%): 0.61
    - Input-price change vs. baseline (%): -23.26
- Key findings from fixed-budget exercise:
  - Random targeting raises aggregate export response by 3.59 percent relative to baseline; lowest-η targeting raises it by 4.43 percent.
  - Largest-sector and central-supplier targeting raise export response by 6.27 percent and 6.36 percent, respectively.
  - Sticky-bottleneck targeting performs best:
    - Raises export response by 9.72 percent relative to baseline.
    - Improvement over random targeting: 5.92 percentage points.
    - Improvement over lowest-η targeting: 5.06 percentage points.
    - Raises real income by 0.61 percent relative to baseline.
    - Lowers input-price pressure by 23.26 percent relative to baseline.
- Policy implication:
  - Supplier upgrading is most valuable when directed toward bottlenecks that are economically central in production networks and difficult for downstream firms to bypass quickly. Prioritizing sticky, central bottlenecks yields substantially larger aggregate export and welfare gains and reduces input-price pressures more than non-targeted or purely size-based approaches.

*Source: wpiea2026183-source-pdf*

### 2.1    Data and Measurement

### 2.1    Data and Measurement

### Data sources and mapping
- Bilateral trade: Base pour l’Analyse du Commerce International (BACI) at the HS6 exporter-importer-year level for 1995–2024 and 230 countries.
- HS6 products mapped into OECD ICIO sectors and aggregated to bilateral country-sector-year exports X_ijut, where i = exporter, j = importer, u = upstream sector, t = year.
- HS6-to-ICIO concordance:
  - Retains 89.7 percent of trade value.
  - Covers 17 manufacturing upstream sectors.
  - Unmapped products are dropped rather than imputed.
- Network baseline window: 1995–1999. Baseline shares enter three objects:
  - Supplier destination shares for supplier demand shocks.
  - Downstream import shares for scalable-supplier exposure.
  - Downstream destination shares for foreign demand shocks.
- Estimation sample begins in 2000 so that network weights are predetermined relative to downstream response.

### Preprocessing and construction notes
- Supplier-scalability first-stage elasticities are winsorized at the 1st and 99th percentiles before constructing downstream exposure.
- Leave-out market-size terms exclude the exporter’s own exports when constructing demand shocks.

---

### 2.1.1 Measuring supplier scalability
- Supplier demand shifter for supplier country i, upstream sector u, year t:
  - Shock_iut = sum_k s_iuk,95−99 * Δ log M_ROW,−i_kut,
    - where s_iuk,95−99 is supplier i’s 1995–1999 export share to destination k in sector u.
    - M_ROW,−i_kut is destination k’s total imports in sector u from all suppliers other than i.
- First-stage estimation (from 2000 onward):
  - Δ log X_iut = a_iu + S_iu Shock_iut + e_iut.
  - S_iu is the estimate of scalability for supplier country i in upstream sector u.
- Empirical Bayes adjustments considered to reduce sensitivity to noisy first-stage elasticities:
  - S_EB0_iu = ρ_iu S_iu,   S_EBμ_iu = S̄_u + ρ_iu (S_iu − S̄_u),
  - ρ_iu = bσ^2_u / (bσ^2_u + bse(S_iu)^2),
  - where bσ^2_u is the within-upstream-sector variance of raw scalability, and S̄_u is the upstream-sector mean.
  - S_EB0 shrinks noisier estimates toward zero; S_EBμ shrinks noisy estimates toward the upstream-sector mean.

---

### 2.1.2 From supplier scalability to downstream exposure
- Downstream scalable-supplier exposure:
  - SIE_jd,95−99 = sum_u θ_du sum_i s_jiu,95−99 S_iu,
    - where s_jiu,95−99 is downstream country j’s 1995–1999 import share from supplier i in upstream sector u.
    - θ_du is the ICIO input weight of upstream sector u in downstream sector d.
- Downstream demand shock:
  - DemandShock_jdt = sum_k s_jdk,95−99 * Δ log M_ROW,−j_kdt,
    - where M_ROW,−j_kdt excludes downstream exporter j’s own exports to destination k in sector d.
- Main response sample uses positive demand shocks from 2000 onward.

---

### 2.2    Fact 1: Supplier Scalability Is Country-Sector Specific

- Key empirical finding: supplier scalability varies at the country-sector level; it is not solely a country or sector characteristic.
- Variance decomposition (Table 1): shares of variation explained
  - Unadjusted:
    - Country FE R^2 = 0.231
    - Sector FE R^2 = 0.043
    - Country + sector FE R^2 = 0.278
    - Residual share = 0.722
  - Mean-centered Empirical Bayes:
    - Country FE R^2 = 0.164
    - Sector FE R^2 = 0.110
    - Country + sector FE R^2 = 0.277
    - Residual share = 0.723
  - Zero-centered Empirical Bayes:
    - Country FE R^2 = 0.315
    - Sector FE R^2 = 0.069
    - Country + sector FE R^2 = 0.400
    - Residual share = 0.600
- Interpretation:
  - Even after absorbing supplier-country and upstream-sector fixed effects, 60–72 percent of variation remains at the supplier-country-sector level.
  - The empirical object is the scalability of specific country-sectors within upstream industries.

### Correlates of supplier scalability (Table 2)
- Each reported coefficient is from a separate regression of the indicated supplier-scalability measure on the row variable; all regressions include supplier-country and sector fixed effects. N = 1813.
- Coefficients (with standard errors in parentheses):
  - Supplier-sector size:
    - Unadjusted: 0.076*** (0.012)
    - Mean-centered Empirical Bayes: 0.047*** (0.007)
    - Zero-centered Empirical Bayes: 0.098*** (0.007)
  - Log destinations served:
    - Unadjusted: 0.126 (0.079)
    - Mean-centered Empirical Bayes: 0.109** (0.043)
    - Zero-centered Empirical Bayes: 0.245*** (0.046)
  - Destination diversification:
    - Unadjusted: 0.135 (0.107)
    - Mean-centered Empirical Bayes: 0.098* (0.059)
    - Zero-centered Empirical Bayes: 0.152** (0.063)
  - Baseline export growth:
    - Unadjusted: 0.533*** (0.151)
    - Mean-centered Empirical Bayes: 0.178** (0.083)
    - Zero-centered Empirical Bayes: 0.248*** (0.089)
  - Baseline growth volatility:
    - Unadjusted: -0.212*** (0.045)
    - Mean-centered Empirical Bayes: -0.080*** (0.025)
    - Zero-centered Empirical Bayes: -0.215*** (0.026)
- Interpretation:
  - Scalable supplier country-sectors tend to be larger, serve more destinations, have more diversified destination portfolios, exhibit higher baseline export growth, and lower baseline growth volatility.

---

### 2.3    Fact 2: Scalable Suppliers Tend to Have Scalable Suppliers

- Empirical finding: supplier country-sectors connected to more scalable input suppliers tend to be more scalable themselves — scalability is a network property.
- Evidence:
  - Figure 1 shows a strongly positive relationship between a supplier country-sector’s own scalability and the scalability of its input network (variables residualized by upstream-sector fixed effects; binned means plotted).
- Correlates (Table A2, summarized):
  - Supplier-side scalability is positively associated with destination diversification, consistent with scalable suppliers having broad sales and scalable sourcing networks.

---

### 2.4    Fact 3: Export Responses Rise with Scalable-Supplier Exposure

### Main estimating equation
- Δ log X_jd,t+1 = α DemandShock_jdt + δ SIE_jd,95−99 + β (DemandShock_jdt × SIE_jd,95−99) + Γ_jdt + ε_jdt,
  - Estimated on country-sector-year observations with positive demand shocks from 2000 onward.
  - Outcome: cumulative one-year export growth for downstream country j and sector d (winsorized at the overall 5th and 95th percentiles).
  - DemandShock_jdt: leave-out foreign demand shock constructed from predetermined destination shares.
  - SIE_jd,95−99: scalable-supplier exposure from the 1995–1999 input-sourcing network.
  - Γ_jdt: fixed effects. Standard errors clustered by country-sector.

### Key result
- Interaction β compares how the response to a demand shock differs with predetermined exposure to scalable suppliers.
- Table 3: interaction coefficients (standard errors in parentheses), sample uses positive demand shocks from 2000 onward, N reported per column:
  - All (columns 1–2) and High input relationship stickiness (columns 3–4)
  - Unadjusted SIE:
    - All: 0.022 (0.046), 0.019 (0.043)
    - High stickiness: 0.291** (0.138), 0.348*** (0.134)
  - Mean-centered Empirical Bayes SIE:
    - All: 0.032 (0.045), 0.023 (0.042)
    - High stickiness: 0.377** (0.148), 0.401*** (0.141)
  - Zero-centered Empirical Bayes SIE:
    - All: 0.033 (0.045), 0.029 (0.042)
    - High stickiness: 0.353*** (0.132), 0.432*** (0.128)
  - N:
    - All: 58,440
    - High input relationship stickiness: 31,699
- Interpretation:
  - In the full sample, the interaction between demand shocks and scalable-supplier exposure is small and insignificant.
  - Among downstream sectors that rely more heavily on relationship-sticky inputs (defined following Martin et al. (2026)), the interaction is large and statistically significant across unadjusted and Empirical Bayes measures.
  - Scalable suppliers matter most where buyer-supplier links are harder to replace quickly.

### Figures and dynamics
- Figure 2 (high stickiness subsample): binned country-sector demand elasticities plotted against scalable-supplier exposure show a positive fitted line — larger export responses for higher exposure.
- Figure 3 (dynamic response, high stickiness): interaction coefficients from t−3 to t+4 (each point is coefficient on DemandShock × SIE with cumulative export growth outcome):
  - Pre-shock coefficients are close to zero and statistically insignificant (no differential pretrends).
  - Response turns positive on impact, peaks around the one-year horizon, remains positive over subsequent years, and gradually fades by t + 4.
  - Suggests exposure to scalable suppliers shapes the export adjustment path after a demand shock, strongest around the first year.

### Robustness check
- Appendix Table A3: reconstruct scalable-supplier exposure using supplier-scalability estimates that leave out demand variation associated with the downstream country-sector under study — estimates similar to baseline, indicating results are not driven by mechanical overlap.

---

### 3    Model (overview)

### Central mechanism
- A foreign demand expansion raises downstream production, increasing demand for intermediate inputs.
- If downstream producers source from suppliers with steep supply curves, upstream input prices rise, downstream marginal costs increase, and export response is attenuated.
- If the inherited supplier network is more scalable, the same foreign demand shock generates a larger downstream export expansion.

### Model ingredients
- Four ingredients:
  1. Sectors linked through input-output production.
  2. Downstream producers source intermediate inputs across foreign and domestic suppliers through constant elasticity of substitution (CES) sourcing nests.
  3. Supplier country-sectors face upward-sloping supply curves with supply elasticities that differ across suppliers within the same upstream sector.
  4. Upstream sectors differ in relationship stickiness: in sticky input markets, existing buyer-supplier links are harder to replace quickly.

### 3.1 Environment
- Indices:
  - Countries: i, j, n.
  - Sectors: d (downstream), u (upstream).
- Country-sector jd produces using value added and intermediate inputs. Value added supplied by labor in country j. Household consumes a Cobb-Douglas bundle of sectoral goods with expenditure shares β_jd. Labor is mobile across sectors within a country.

### 3.2 Production (key equations and definitions)
- Gross output in downstream country-sector jd:
  - Y_jd = A_jd V_jd^(1−α_d) M_jd^(α_d), where α_d ∈ [0, 1] is the intermediate input share.
- Intermediate bundle is Cobb-Douglas across upstream sectors:
  - M_jd = Π_u M_jdu^(θ_du), with sum_u θ_du = 1; θ_du are input-output weights.
- For upstream sector u, the input aggregate is a CES composite across supplier countries:
  - M_jdu = [sum_i ω_jiu^(1/σ) q_jiu^((σ−1)/σ)]^(σ/(σ−1)),
    - q_jiu is quantity of input u purchased by country j from supplier i.
    - ω_jiu are sourcing weights.
    - σ > 1 is elasticity of substitution across suppliers.
- CES price index for input u used by country j:
  - P_ju = [sum_i ω_jiu p_jiu^(1−σ)]^(1/(1−σ)), where p_jiu is delivered price.
- Downstream intermediate input price index:
  - P_M_jd = Π_u P_ju^(θ_du).
- Unit cost of producing downstream good:
  - c_jd = 1/A_jd * [w_j^(1−α_d)]^(1−α_d) * P_M_jd^(α_d)  (as presented: c_jd = 1/A_jd [w_j^(1−α_d)]^(1−α_d) P_M_jd^(α_d)) .
- In proportional changes, marginal cost hat:
  - b c_jd = b w_j^(1−α_d) + sum_u b P_ju^(α_d θ_du) + b A_−1_jd.

*Source: wpiea2026183-source-pdf - 2.1    Data and Measurement*

### 3.3    Supplier Supply Curves

### 3.3    Supplier Supply Curves

### Supplier supply specification
- Each supplier country-sector iu produces upstream good u with an upward-sloping supply curve:
  - p_iu = κ_iu C_iu Q_iu^{1/η_iu}, where Q_iu is total quantity supplied, C_iu is the producer cost component, κ_iu is a supply shifter, and η_iu > 0 is the supplier supply elasticity.
  - A high η_iu means the supplier can expand output with little price pressure. A low η_iu means output expansion is costly and creates bottlenecks.
- Delivered prices satisfy:
  - p_jiu = τ_jiu p_iu, where τ_jiu ≥ 1 is a bilateral sourcing cost.
  - In hat notation: b p_jiu = b τ_jiu b C_iu b Q_iu^{1/η_iu} b κ_iu.
- If supplier iu is itself a country-sector in the production network, its producer cost satisfies the same input-output cost equation:
  - b C_iu = b w_i^{1−α_u} b P_v^{α_u} θ_{uv} b A_{iu}^{−1}.
  - Thus supplier bottlenecks interact with input-output linkages: a supplier’s price can rise because its own output expands, its wage rises, or its upstream inputs become more expensive.

### Operating cost and supplier rents
- Inverse supply curve interpreted as marginal-cost schedule. Conditional on C_iu, total operating cost and supply-curve rents:
  - V C_iu = ∫_0^{Q_iu} κ_iu C_iu q^{1/η_iu} dq = η_iu/(1 + η_iu) p_iu Q_iu.
  - Π_iu = p_iu Q_iu − V C_iu = 1/(1 + η_iu) p_iu Q_iu.
- Low-η_iu suppliers therefore generate larger scarcity rents when their output is demanded.
- Supplier rents are owned domestically and rebated lump-sum to the representative household in supplier country i.

### Mechanism (how supplier scalability alters downstream responses)
- Positive foreign demand shock for downstream country-sector jd increases desired sales X_jd; to produce more, jd increases expenditure on each upstream input u in proportion to α_d θ_du, allocated across inherited suppliers according to CES sourcing shares π_jiu.
- If relevant suppliers have low η_iu (steep supply curves):
  - Demand expansion raises Q_iu → raises p_iu → raises delivered input prices p_jiu → raises P_ju → raises P_M_jd → raises downstream marginal cost c_jd.
  - Higher marginal cost offsets part of the original demand expansion, attenuating the downstream export response.
- Relationship stickiness amplifies this effect:
  - ρ_u ∈ [0, 1] governs how quickly buyers move from inherited sourcing weights ω_jiu toward frictionless desired weights ω*_jiu.
  - High ρ_u: sourcing adjusts slowly, buyer remains tied to inherited input suppliers after a shock, so supplier scalability matters more.
  - Low ρ_u: sourcing adjusts quickly, buyer can reallocate away from constrained suppliers, mitigating bottlenecks.
- Net mechanism operates through interaction of four objects:
  - Demand shock × input intensity and IO weights × supplier supply scalability × relationship stickiness.

### Calibration and empirical linkage
- Baseline network and directly observed objects:
  - Baseline sourcing shares s_jiu0 from trade data; input-output weights θ_du from ICIO tables; sectoral intermediate input shares α_d from ICIO.
- Relationship stickiness and sourcing persistence:
  - ρ_u calibrated using relationship-stickiness index RS_u (from Martin et al. (2026) measure of firm-to-firm relationship durations).
  - Implied relationship duration D_u = D_0 exp(RS_u − RS) with D_0 = 2 (years). Annual sourcing persistence ρ_u = exp(−1/D_u).
- Other elasticities and normalizations:
  - Destination demand elasticity ε_d = 5.
  - Choose σ so that mean one-year persistence-adjusted substitution margin satisfies (1 − ρ_u) σ = 5.
  - Labor-supply elasticity φ = 3.
  - Productivities, bilateral sourcing costs, and non-shocked demand shifters normalized to one in baseline.
- Supplier scalability and supply elasticities:
  - η_iu parameterized as η_iu = ̄η_u exp(λ_u z_iu), where z_iu is the standardized empirical-Bayes scalability estimate.
  - (̄η_u, λ_u) chosen by simulated method of moments to reproduce first-stage empirical supplier-scalability moment:
    - ∆ log X^{model}_{iu,t} = α_{iu} + b S^{model}_{iu} Shock^{model}_{iu,t} + ε^{model}_{iu,t}.
  - Calibration compares b S^{model}_{iu} with empirical supplier-scalability estimates minimizing export-weighted squared deviations.

### Quantitative results: impact of a 10 percent global demand shock
- Two main messages:
  - Supplier bottlenecks attenuate aggregate gains from the shock relative to high- or perfect-scalability benchmarks.
  - Relationship stickiness determines where bottlenecks bind: high scalable-supplier-exposure sectors expand more in the short run but advantage fades as sourcing relationships adjust.
- Benchmarks:
  - Sector-p90 benchmark: assign each supplier country-sector the within-sector 90th percentile supply elasticity (high-scalability benchmark).
  - Infinite-elasticity benchmark: removes supplier bottlenecks entirely (perfectly elastic suppliers).
- Table 4 (level outcomes are percentage-point log changes; attenuations are percentages by which baseline response is below benchmark response):
  - Baseline:
    - Export response (p.p.) = 4.32
    - Real income gain (p.p.) = 3.16
    - Marginal cost (p.p.) = 1.30
    - Input price (p.p.) = 1.55
  - Sector-p90:
    - Export response (p.p.) = 5.11
    - Real income gain (p.p.) = 4.09
    - Marginal cost (p.p.) = 1.11
    - Input price (p.p.) = 0.89
  - Infinite η:
    - Export response (p.p.) = 5.17
    - Real income gain (p.p.) = 4.17
    - Marginal cost (p.p.) = 1.09
    - Input price (p.p.) = 0.83
  - Attenuation:
    - Export attenuation (%) = –15.46 (baseline vs. sector-p90), 16.51 (baseline vs. infinite η)
    - Welfare attenuation (%) = –22.65 (baseline vs. sector-p90), 24.24 (baseline vs. infinite η)
- Interpretation from Table 4:
  - Baseline export response is 4.32 percent and real income gain is 3.16 percent after a 10 percent global demand shock.
  - Compared to sector-p90 and infinite-elasticity benchmarks, supplier bottlenecks materially reduce export and welfare gains because upstream inputs raise supplier prices that feed into downstream marginal costs.

### Role of relationship stickiness in transition dynamics
- Aggregate transition as sourcing relationships adjust (Table 5; level outcomes are percentage-point log changes; gains are percentages relative to T = 0):
  - Export response (p.p.):
    - T = 0: 4.32
    - T = 1: 4.46
    - T = 2: 4.51
    - Long run: 4.56
  - Export gain vs. T = 0 (%):
    - T = 1: –3.30
    - T = 2: 4.43
    - Long run: 5.69
  - Real income gain (p.p.):
    - T = 0: 3.16
    - T = 1: 3.180
    - T = 2: 3.184
    - Long run: 3.189
  - Welfare gain vs. T = 0 (%):
    - T = 1: –0.44
    - T = 2: 0.57
    - Long run: 0.72
- Interpretation:
  - Relaxing sourcing relationships has only a modest aggregate effect: export response rises from 4.32 percent on impact to 4.56 percent in the long run (a 5.69 percent increase relative to initial response).
  - Relationship stickiness mainly affects the distribution of adjustment across sectors rather than aggregate amplification.
- Sectoral exposure premium and its fade (Table 6 summary):
  - Comparing downstream country-sectors at the 90th and 10th percentiles of scalable-supplier exposure within downstream sectors:
    - High-exposure group increases exports by 18.19 percent more on impact.
    - Premium falls to 9.56 percent after one year, 6.82 percent after two years, and 3.93 percent in the long run.
  - Cost gaps (marginal costs and input prices) are larger on impact for low-exposure sectors and shrink over time together with the export-response gap.
- Overall implication:
  - Supplier scalability matters quantitatively at the aggregate level by attenuating gains from demand shocks via upstream price-pressure.
  - Relationship stickiness determines where and when these bottlenecks bind: it creates short-run exposure premia that fade as firms reconfigure sourcing toward more scalable suppliers.

*Source: wpiea2026183-source-pdf - 3.3    Supplier Supply Curves*

### 4.3    Global Policy:  Fixed-budget supplier-upgrading

### 4.3    Global Policy:  Fixed-budget supplier-upgrading

### Exercise setup
- Policy budget: fixes a policy budget equal to 10 percent of supplier country-sectors.
- Mechanism: For each targeted supplier country-sector, the model raises its supply elasticity up to the within-upstream-sector 90th percentile if it is below it.
- Shock considered: the same 10 percent global demand shock.

### Scalable-supplier exposure gradient over the adjustment horizon (Table 6)
- p90/p10 export response (%): 18.19, 9.56, 6.82, 3.93
- p90/p10 marginal cost (%): -12.54, -7.60, -5.69, -3.46
- p90/p10 input price (%): -23.97, -18.68, -16.71, -14.38
- p10 export response (p.p.): 3.89, 4.22, 4.33, 4.46
- p90 export response (p.p.): 4.60, 4.62, 4.63, 4.64
- Notes: p90 and p10 compare country-sectors at the within-downstream-sector 90th and 10th percentiles of model-implied scalable-supplier exposure (SIE_model). Ratio rows are percentages. Export response rows are percentage-point log changes.

### Targeting rules compared (Table 7)
- Targeting rules (descriptions):
  - Random targeting: placebo-style benchmark.
  - Lowest-η targeting: upgrades the most inelastic supplier country-sectors.
  - Largest-sector targeting: prioritizes supplier country-sectors with the largest baseline export value.
  - Central-supplier targeting: prioritizes supplier nodes with the largest baseline intermediate-input demand in the model network.
  - Sticky-bottleneck targeting: ranks supplier country-sectors by the product of inverse supply elasticity, baseline intermediate-input demand, and an upstream-sector stickiness weight.
- Implementation detail: The exercise upgrades 10 percent of supplier country-sectors under each rule, restricting targets to supplier cells below their within-upstream-sector p90 supply elasticity. Targeted cells are moved to the maximum of their baseline elasticity and the within-sector p90. Outcomes compare a 10 percent global demand shock.

### Quantitative outcomes by targeting rule (Table 7)
- Baseline outcomes:
  - Export response (p.p.): 4.3194
  - Real-income gain (p.p.): 3.1663
  - Input-price change (p.p.): 1.5451
- Random:
  - Export response (p.p.): 4.4744
  - Real-income gain (p.p.): 3.3703
  - Input-price change (p.p.): 1.4071
  - Export gain vs. baseline (%): 3.59
  - Real-income gain vs. baseline (%): -0.20
  - Input-price change vs. baseline (%): -8.95
- Lowest-η:
  - Export response (p.p.): 4.5104
  - Real-income gain (p.p.): 3.4033
  - Input-price change (p.p.): 1.3791
  - Export gain vs. baseline (%): 4.43
  - Real-income gain vs. baseline (%): 0.23
  - Input-price change vs. baseline (%): -10.75
- Largest-sector:
  - Export response (p.p.): 4.5894
  - Real-income gain (p.p.): 3.6503
  - Input-price change (p.p.): 1.3041
  - Export gain vs. baseline (%): 6.27
  - Real-income gain vs. baseline (%): 0.47
  - Input-price change vs. baseline (%): -15.61
- Central:
  - Export response (p.p.): 4.5934
  - Real-income gain (p.p.): 3.6533
  - Input-price change (p.p.): 1.3051
  - Export gain vs. baseline (%): 6.36
  - Real-income gain vs. baseline (%): 0.47
  - Input-price change vs. baseline (%): -15.57
- Sticky:
  - Export response (p.p.): 4.738
  - Real-income gain (p.p.): 3.794
  - Input-price change (p.p.): 1.186
  - Export gain vs. baseline (%): 9.72
  - Real-income gain vs. baseline (%): 0.61
  - Input-price change vs. baseline (%): -23.26

### Key findings from the fixed-budget exercise
- Random targeting raises the aggregate export response by 3.59 percent relative to the no-upgrade baseline; lowest-η targeting raises it by 4.43 percent.
- Targeting by economic mass performs better: largest-sector and central-supplier targeting raise the export response by 6.27 percent and 6.36 percent, respectively.
- Sticky-bottleneck targeting performs best:
  - Raises the export response by 9.72 percent relative to the baseline.
  - Improvement over random targeting: 5.92 percentage points.
  - Improvement over lowest-η targeting: 5.06 percentage points.
  - Raises real income by 0.61 percent relative to the baseline.
  - Lowers input-price pressure by 23.26 percent relative to the baseline.
- Interpretation: Supplier upgrading is most valuable when it targets bottlenecks that are both economically central and hard for downstream producers to avoid in the short run.

### Policy implication
- Lesson: Supplier upgrading is most valuable when directed toward bottlenecks that are economically central in production networks and difficult for downstream firms to bypass quickly. Prioritizing sticky, central bottlenecks yields substantially larger aggregate export and welfare gains and reduces input-price pressures more than non-targeted or purely size-based approaches.

*Source: wpiea2026183-source-pdf - 4.3    Global Policy:  Fixed-budget supplier-upgrading*

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_Source: https://www.imf.org/-/media/files/publications/wp/2026/english/wpiea2026183-source-pdf.pdf_