## 2.1 Structural Gravity and Bilateral Trade Imbalances

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---

### Framework and approach
- Start from sector-level structural gravity (Anderson and van Wincoop (2003)); aggregate across sectors to identify three exact sources of variation in bilateral trade balances across country pairs.
- Use a first-order approximation to obtain a linear decomposition of proportional bilateral imbalances (bilateral trade balances relative to the geometric average of bilateral trade flows).
- Back out unobserved (asymmetries in) bilateral trade frictions as “residuals” from a theory-consistent gravity estimation (PPML following Fally (2015)), and embed results in a dynamic many-country, many-sector quantitative trade model for counterfactuals.
- Calibration matches deep parameters to corresponding objects in the data (WIOD, PWT) and is consistent with the variance decomposition assumptions.

### Exact sources of bilateral imbalance variation (structural-gravity implication)
- Differences in unilateral macro trade balances (NX_n):
  - Macro-deficit economies will have deficits with their average partner; macro-surplus economies will have surpluses.
- Triangular trade (differences in sectoral expenditure and production patterns; d_sn and e_sn):
  - Sectoral spending and production linkages can generate bilateral imbalances even with zero macro imbalances.
- Pairwise asymmetries in trade frictions (bilateral trade wedges τ_sn′_n ≠ τ_snn′):
  - Asymmetric obstacles to trade between two economies that penalize trade in one direction more than the other.

### Proportional bilateral imbalance decomposition (first-order approximation)
- Definition:
  - Proportional bilateral imbalance ≡ (M_n′n − M_nn′) / (M_n′n^1/2 M_nn′^1/2)
- Approximate decomposition terms (from equation (6)):
  - ln((1 − NX_n / D_n)/(1 − NX_n′ / D_n′)) — differences in macro trade balances.
  - ln((d_sn′ e_sn)/(d_sn e_sn′)) — triangular trade (production and spending patterns).
  - −θ_s ln(τ_sn′_n / τ_snn′) — bilateral asymmetries in trade frictions.
  - −θ_s ln(O_sn P_sn′ / (O_sn′ P_sn)) — MRT interaction term (zero if first three terms are zero).
- Dollar bilateral imbalance relation:
  - M_n′n − M_nn′ = M_n′n^1/2 M_nn′^1/2 × (proportional bilateral imbalance).
  - Thus dollar imbalances = geometric-average bilateral flows × proportional bilateral imbalance.

### Estimation identification and computation
- Estimate sector-level gravity via PPML: M_sn′_n = exp{Ω_sn′ + Π_sn} ε_sn′_n, with exporter and importer sector fixed effects, imposing Π_sN = 0 for benchmark economy N.
- Recover:
  - P_sn^−θ_s = E_sn / E_sN × exp{−Π̂_sn}
  - O_sn′^−θ_s = E_sN D_sn′ / D_s × exp{−Ω̂_sn′}
  - Implied τ^−θ_s_sn′_n = ε̂_sn′_n
- Estimation requires a full matrix of bilateral expenditures including domestic flows M_snn.

---

### Empirical findings (WIOD 2010-2014 averages; sample: 40 economies + RoW → 41 economies)
- Data and sample:
  - Sector aggregation: 56 → 31 sectors (16 manufacturing, 15 services).
  - Observations: 820 distinct bilateral trade balances (41×40/2 = 820).
  - Less than 2% of the 52,111 sector-country-pair flows are zero-valued.
  - Median proportional imbalance = .46; smallest ≈ 0; largest = 5.01.
- U.S. example:
  - U.S. overall trade deficit between 2010 and 2014: 3% of GDP on average.
  - Average of the bilateral trade balance displayed in Figure 1: Average = -0.07.
- Variance decomposition of proportional bilateral imbalances (regression slopes sum to 1):
  - Differences in macro trade balances (Macro NX): slope = 0.022 → accounts for 2% of variation.
  - Triangular trade (Prod./spend.): slope = 0.123 → accounts for 12% of variation.
  - Asymmetric bilateral trade frictions (Trade wedges): slope = 0.854 → accounts for 85% of variation.
  - MRTs: slope = 0.000 → negligible.
- Summary statistics for decomposition components (absolute values, 820 observations):
  - Macro NX: mean = .027; st. dev. = .072; 10th pctl. = .004; med. = .021; 90th pctl. = .058
  - Prod./spend.: mean = .095; st. dev. = .082; 10th pctl. = .012; med. = .073; 90th pctl. = .208
  - Trade frictions: mean = .396; st. dev. = .343; 10th pctl. = .062; med. = .302; 90th pctl. = .879
  - MRTs: mean = .000; st. dev. = .000; 10th pctl. = .000; med. = .000; 90th pctl. = .000
- Correlations (pairwise, 820 positive-valued bilateral balances):
  - Macro NX vs Prod./spend. = .326
  - Macro NX vs Trade frictions = -.014
  - Macro NX vs MRTs = -.076
  - Prod./spend. vs Trade frictions = .093
  - Prod./spend. vs MRTs = -.250
  - Trade frictions vs MRTs = -.041
- Robustness:
  - 1995-1999 decomposition yields similar shares: Macro trade balances = 3%; Prod./spend. = 9% (Figure A2 reports slopes = 0.030 and 0.094); Asymmetric trade wedges = 88%; MRTs = 0.000.
  - Restricting to top 50% of pairs by geometric-average bilateral trade flows yields nearly identical shares (Macro = 3%; Prod./spend. = 12%; Asymmetric wedges = 85%).

---

### Counterfactuals and quantitative model results (dynamic many-country, many-sector model)
- Model features and calibration highlights:
  - Agents face constant probability of death ξ = .13.
  - δ = .06; γ = 1.044; R = 1.030.
  - {ρ_n} set to match NX ratios via equation (23); {α_n}, {η_n}, {σ_sn}, {μ_sn}, {θ_s} calibrated to PWT and WIOD; {τ_{sn′n}} and relative {z_sn / z_sN} set to match PPML estimates.
  - Calibrated correlation between discount rates and aggregate trade balances = -.75.
- Counterfactual: fully bilaterally symmetric trade wedges
  - Construction: set higher wedge equal to lower wedge (or geometric average alternative); see equation (31).
  - Would eliminate 75% of the variation in proportional bilateral imbalances (slope of best-fit line between counterfactual and original proportional bilateral imbalances = .24).
  - Would raise the median country’s real GDP and consumption level by almost 11%.
  - Would reduce most economies’ exposure to China somewhat (Appendix A.5.1).
  - Macro trade balances: almost unchanged (world interest rate nearly unchanged).
- Counterfactual: elimination of macro trade imbalances via financial autarky
  - Financial autarky: prohibit international asset trade → all macro trade balances zero in new steady state.
  - Would reduce the variation in bilateral imbalances by 15% (reported in summary).
- Counterfactual: extend E.U. Single Market bilateral trade-wedge-levelling effect to all economies (partial symmetry)
  - Implementation: for goods-producing sectors in pairs where at least one partner is non-E.U., change the higher wedge by exp{ˆψs} if τsn′n > τsnn′ (equation (37)); intra-E.U. and service-sector wedges left unchanged in the specific exercise described in Section 4.2.3.
  - Impact on proportional bilateral imbalances: slope of best-fit line = 0.728 (variation declines noticeably—roughly one third of full symmetry effect).
  - Median economy per-worker real GDP increases by more than 5%.
  - Largest long-run income gains: Mexico: 38%; South Korea: 20%; Turkey: 19%.
- Counterfactual: U.S.-China trade war simulation (tariffs January 2018–June 2019 held permanently)
  - Tariff changes: U.S. average tariffs on Chinese imports under Section 301 increased by 14.4 percentage points; China increased average tariffs on U.S. imports by 13.5 percentage points.
  - Result: U.S.-China bilateral deficit halved in the new steady state.
  - Primary mechanism: weakening and costly reduction of trade ties between the two economies (geometric-average bilateral flows decline); proportional imbalance declines modestly.
  - World interest rate: very limited effect; macro trade balances virtually unchanged.
  - Welfare: Both U.S. and China lose about a fifth of a percent in steady-state real GDP per capita and consumption per capita.
  - Third-country effects small; Mexico gains an additional .15% of GDP from diverted U.S. imports.
  - Global distribution: correlation across all pairs between empirical bilateral imbalances and post-trade-war counterparts = .98.

---

### Global trade-wedge symmetry: macro channels and magnitudes
- Under global wedge symmetry:
  - Slope of best-fit line for proportional bilateral imbalances = .24 (major compression).
  - Median per-worker real GDP ↑ almost 11% (Table 4, column 1: median ˆy_n ≈ 1.11).
  - Changes in real GDP driven by:
    - Lower import wedges → higher purchasing power of domestic income (Arkolakis et al. (2012) mechanism via equation (28)).
    - International capital mobility amplifies gains via higher marginal product of capital and larger steady-state k_n (equation (22)).
  - Correlation between decline in import trade wedges and changes in own-spending terms = .91.
  - Macro trade balances: almost unchanged (column 5 of Table 4).
- Representative entries from Table 4 (selected economies; columns correspond to ˆy_n, ˆv_nn, ˆk_n, ˆτ_n, ˜nx_n−nx_n, ˆc_n):
  - AUS: 2.4 -1.2 2.7 -.1 .0 2.1
  - AUT: 12.6 -6.6 12.9 -1.6 .0 12.3
  - BEL: 10.2 -5.8 10.5 -1.3 .0 9.8
  - CHN: 6.0 -3.1 6.3 -.2 .0 5.7
  - CZE: 30.1 -12.6 30.4 -2.5 .0 29.4
  - KOR: 21.2 -9.2 21.6 -.7 .0 20.6
  - MEX: 16.1 -5.5 16.4 -1.2 -.1 15.6
  - USA: 2.4 -1.3 2.7 -.2 -.1 2.3
  - SVK: 44.3 -18.0 44.7 -2.5 .0 43.8
  - TWN: 12.8 -5.5 13.2 -.9 .0 12.0

---

### Properties of aggregate and sectoral asymmetries (measurement and stylised facts)
- Aggregate asymmetry measure:
  - ln(τn′n/τnn′) using θ = 4 and calibrated on WIOD/PWT averages 2010-14.
  - Summary statistics for 820 distinct absolute values |ln(τn′n/τnn′)|:
    - # obs.: 820; mean: .099; st. dev.: .086; 10th pctl.: .015; median: .076; 90th pctl.: .220
  - Interpretation: median pair has an average import wedge .08 log points (roughly 8%) higher in one direction than the other; for 10% of pairs gap > .20 log points (roughly 22%).
  - U.S.–China example: U.S. import wedge from China is .18 log points (roughly 16%) smaller than Chinese import wedge from U.S.
  - Persistence: distribution for 1995-99 very similar to 2010-14.
- Sectoral contributions to aggregate asymmetries (31 sectors; top 5 account for 70% of variation):
  - 12 Electrical and optical equipment — Contribution: .307; Median weight: .073; Median |ln(ˆεsn′n/ˆεsnn′)|: .778
  - 8 Chemicals and chemical products — Contribution: .112; Median weight: .070; Median |ln(ˆεsn′n/ˆεsnn′)|: .683
  - 11 Basic metals and fabricated metal — Contribution: .110; Median weight: .059; Median |ln(ˆεsn′n/ˆεsnn′)|: .654
  - 14 Transport equipment — Contribution: .084; Median weight: .040; Median |ln(ˆεsn′n/ˆεsnn′)|: .903
  - 15 Machinery, nec. — Contribution: .082; Median weight: .040; Median |ln(ˆεsn′n/ˆεsnn′)|: .790
- Mechanism: these sectors matter because they constitute large shares of bilateral trade flows, not because their sectoral asymmetries are exceptionally large.
- Alternative triple-ratio Caliendo–Parro measure:
  - Sectoral medians of the triple-ratio highly correlated with sectoral wedge asymmetry medians (correlation = .86).
  - Table 7 reports sectoral distributions for 10,660 cross-border triplets; sample medians vary by sector (examples preserved in source).

---

### Trade policy evidence: Single Market (E.U.) effects on trade-wedge symmetry
- Sample and tariffs context:
  - Sample heavily biased toward low-tariff economies: 24 of 40 individual economies were E.U. members in 2010-14.
  - E.U. weighted average external tariff rate = 1.7% in 2010-14; median non-E.U. economy weighted average tariff = 2.6% (WDI 2021 edition).
  - Pairwise tariff asymmetries can at best explain a small fraction of measured trade-wedge asymmetries.
- Cross-sectional triplet evidence (Caliendo–Parro triple-ratio):
  - Triplets with exactly two E.U. members exhibit distributions shifted toward zero relative to triplets with at most one E.U. member; shift larger for triplets with exactly three E.U. members.
  - Pattern consistent across sectors: intra-E.U. trade characterised by greater pairwise symmetry in trade wedges.
- E.U. accession (panel evidence, 1995-99 → 2010-14):
  - Regression of changes in ln(τsn′n/τsnn′) on a dummy 4EUn′n equal to 1 if n′ and n are both E.U. members in 2010-14 but at least one was not in 1995-99 (equation (35)).
  - Estimated ˆψs are statistically significantly negative across all goods sectors (selected estimates):
    - Sector 3 Food, beverages and tobacco — ˆψs: -.351*** (.040)
    - Sector 9 Rubber and plastics — ˆψs: -.642*** (.055)
    - Sector 12 Electrical and optical equipment — ˆψs: -.505*** (.042)
    - Sector 14 Transport equipment — ˆψs: -3.749*** (.307)
  - Interpretation: accession associated with declines in new members’ trade-wedge asymmetries vis-à-vis other members; in some sectors Single Market effect accounts for more than 10% of over-time change in asymmetries.
- Counterfactual extension (Section 4.2.3):
  - Apply estimated Single Market symmetry effects to extra-E.U. goods wedges (leave intra-E.U. and services unchanged).
  - Result: slope of best-fit line = 0.728 (proportional bilateral imbalance variation shrinks by roughly one third of full symmetry effect).
  - Median economy real GDP ↑ > 5%; large winners include Mexico: 38%; South Korea: 20%; Turkey: 19%.

---

### Interpretation, limitations, and policy relevance
- Main empirical implication: pairwise asymmetries in trade frictions explain the bulk of cross-pair variation in proportional bilateral imbalances (≈ 84–88% depending on period/sample).
- Caveats and limitations:
  - Variance decomposition is based on a linear first-order approximation and abstracts from some general-equilibrium effects (feedback of trade-barrier changes on expenditure patterns or macro trade balances).
  - Bilateral trade-wedge “residuals” may capture structural asymmetries (preferences, technologies, geography), model misspecification, measurement error, and policy-induced asymmetric barriers.
  - The static decomposition does not establish macroeconomic and welfare consequences; the dynamic quantitative model addresses some of these concerns.
- Policy-relevant evidence and implications:
  - Measured asymmetries appear smaller among European Single Market members; E.U. accession is associated with declining trade-wedge asymmetries vis-à-vis other members.
  - Eliminating bilateral trade-wedge asymmetries would:
    - Substantially reduce variation in proportional bilateral imbalances (up to 75% under full symmetry).
    - Leave macro trade balances almost unchanged in many counterfactuals (world interest rate nearly unchanged).
    - Raise median real GDP and consumption materially (almost 11% under full symmetry; >5% under Single Market–like extension).
  - Unilateral tariff increases targeted at a specific partner can reduce a bilateral deficit by shifting trade away from that partner, but macro trade balances are largely unaffected and such policies are economically costly and ultimately futile as a means to reduce aggregate imbalances.
- Research motivation:
  - Findings motivate further investigation into origins of trade-wedge asymmetries and their macroeconomic and welfare consequences, including the role of trade policy and non-policy sources (geography, technologies, preferences).

*Italic: Extracted and summarized from "2.1 Structural Gravity and Bilateral Trade Imbalances" and related sections of wpiea2022090-print-pdf.*

### 2.1  Structural Gravity and Bilateral Trade Imbalances . . . . . . .9

### 2.1  Structural Gravity and Bilateral Trade Imbalances

### Framework and approach
- Start from sector-level structural gravity equations as in Anderson and van Wincoop (2003); aggregate across sectors to identify three exact sources of variation in bilateral trade balances across country pairs.
- Use a first-order approximation to obtain a linear decomposition of proportional bilateral imbalances (bilateral trade balances relative to the geometric average of bilateral trade flows).
- Back out unobserved (asymmetries in) bilateral trade frictions as “residuals” from a theory-consistent gravity estimation, and embed results in a dynamic many-country, many-sector quantitative trade model for counterfactuals.
- Calibration matches deep parameters to corresponding objects in the data and is consistent with the variance decomposition assumptions.

### Three sources of bilateral imbalance variation (exact, aggregated implication of structural gravity)
- Differences in (unilateral) macro trade balances:
  - Economies with a macro deficit (e.g., the U.S.) will have a deficit with their average trade partner; macro-surplus economies (e.g., China) will have a surplus.
- Differences in sectoral expenditure and production patterns (“triangular trade”):
  - Sectoral spending and production linkages can generate bilateral imbalances even if macro trade balances are balanced.
- Pairwise asymmetries in trade frictions (bilateral trade wedges):
  - Asymmetric obstacles to trade between two economies that penalize trade in one direction more than the other.

### Empirical findings (WIOD, 40 economies + RoW; average 2010-2014)
- U.S. overall trade deficit between 2010 and 2014: 3% of GDP on average.
- The average bilateral trade balance displayed in Figure 1: Average = -0.07.
- Variance decomposition of proportional bilateral imbalances:
  - Differences in macro trade balances account for roughly 2% of the variation.
  - Triangular trade (differences in sectoral expenditure and production patterns) accounts for roughly 12% of the variation.
  - Asymmetries in bilateral trade frictions account for roughly 84% of the variation.
- Measured bilateral trade-wedge asymmetries are sizeable and capture all determinants of sector-level bilateral trade patterns that elude the gravity framework (including asymmetric preferences, technologies, geography, and policy barriers).

### Counterfactuals and quantitative model results
- Counterfactual: fully bilaterally symmetric trade wedges
  - Would eliminate 75% of the variation in proportional bilateral imbalances.
  - Would raise the median country’s real GDP and consumption level by almost 11%.
  - Would cause a small rebalancing of international trade away from China, reducing most economies’ exposure to China somewhat.
- Counterfactual: elimination of macro trade imbalances via financial autarky
  - Would reduce the variation in bilateral imbalances by 15%.
- Counterfactual: extending the bilateral trade-wedge-levelling effect of E.U. membership to all economies in the sample
  - Would significantly reduce bilateral imbalances and lead to long-run income increases for selected countries:
    - Mexico: 38%
    - South Korea: 20%
    - Turkey: 19%
- Counterfactual: U.S.-China trade war simulation
  - May reduce the U.S.-China trade imbalance primarily via a weakening (and costly reduction) of trade ties between the two economies.

### Interpretation, limitations, and policy relevance
- Main empirical implication: pairwise asymmetries in trade frictions explain the bulk of cross-pair variation in bilateral imbalances.
- Caveats:
  - The variance decomposition relies on a linear approximation and abstracts from some general equilibrium effects (e.g., feedback of trade-barrier changes on expenditure patterns or macro trade balances).
  - Bilateral trade-wedge “residuals” may reflect both structural asymmetries (preferences, technologies, geography) and policy-induced asymmetric barriers.
- Policy-relevant evidence:
  - Measured asymmetries appear smaller among member countries of the European Single Market; E.U. accession is associated with declining trade-wedge asymmetries vis-à-vis other members.
  - Findings motivate further investigation into the origins of trade-wedge asymmetries and their macroeconomic and welfare consequences, including the role of trade policy.

*IMF Working Paper — 2.1 Structural Gravity and Bilateral Trade Imbalances (excerpt).*

### 2.1  Structural Gravity and Bilateral Trade Imbalances

### 2.1  Structural Gravity and Bilateral Trade Imbalances

### 2.1.1  Bilateral Imbalances Through the Lens of Structural Gravity
- Model setup:
  - Consider a set of N economies, denoted by n = 1,...,N. These countries trade in S sectors, denoted by s = 1,...,S.
  - Sector-level structural gravity equation:
    - M_sn′_n = (τ_sn′_n O_sn′ P_sn)^−θ_s D_sn′ E_sn / D_s
      - M_sn′_n: dollar value of expenditure by country n on country-n′ output in sector s
      - τ_sn′_n: ad-valorem-equivalent trade frictions for this flow
      - θ_s: trade elasticity
      - D_sn′: dollar value of country-n′ output in sector s
      - E_sn: dollar value of country-n expenditure on sector-s output
      - D_s: arbitrary, potentially sector-specific normaliser
      - P_sn and O_sn′: inward and outward multilateral resistance terms (MRTs), defined as:
        - P_sn ≡ [∑_{n′=1}^N (τ_sn′_n O_sn′)^−θ_s D_sn′ / D_s]^−1/θ_s
        - O_sn′ ≡ [∑_{n=1}^N (τ_sn′_n P_sn)^−θ_s E_sn / D_s]^−1/θ_s
  - MRTs capture importer’s access to all import sources (P_sn) and exporter’s access to all export destinations (O_sn′).
  - τ_sn′_n can be interpreted as an ad-valorem equivalent trade wedge reflecting physical/policy barriers and spending biases (e.g., home bias).

- Structural conditions yielding the gravity form:
  1. Spending share v_sn′_n ≡ M_sn′_n / E_sn is multiplicatively separable:
     - v_sn′_n = F_sn′ D_s (τ_sn′_n P_sn)^−θ_s, with P^−θ_s_sn D_s ≡ ∑_{n′=1}^N F_sn′ τ_sn′_n^−θ_s.
  2. Market clearing for each origin:
     - D_sn′ = ∑_{n=1}^N M_sn′_n = F_sn′ ∑_{n=1}^N (τ_sn′_n P_sn)^−θ_s E_sn D_s ≡ F_sn′ O_sn′^−θ_s.

- Determinants of the sector-s bilateral imbalance M_snn′ − M_sn′_n and aggregate bilateral imbalance:
  - Aggregate bilateral imbalance (summed across sectors):
    - M_nn′ − M_n′n = D_n (D_n′ − NX_n′) ∑_{s=1}^S (τ_snn′ O_sn P_sn′)^−θ_s d_sn e_sn′ / D_s
      + − D_n′ (D_n − NX_n) ∑_{s=1}^S (τ_sn′_n O_sn′ P_sn)^−θ_s d_sn′ e_sn / D_s
    - Definitions:
      - M_n′n ≡ ∑_s M_sn′_n
      - NX_n: macro (unilateral) trade balance of country n
      - d_sn ≡ D_sn / D_n
      - e_sn ≡ E_sn / E_n
      - D_n ≡ ∑_s D_sn, E_n ≡ ∑_s E_sn
    - National-accounting identity: D_n = E_n + NX_n
    - Paper normalises D_s to equal world gross output in sectors.

- Intuition: Everything else constant, bilateral trade surplus of country n with n′ is larger when:
  1. Country n′ has smaller aggregate net exports (NX_n′ smaller) and country n has larger aggregate net exports (NX_n larger).
  2. Country n′ spends in sectors that account for much of country n’s output (d_sn large where e_sn′ large), while country n spends less in sectors that account for much of n′’s output.
  3. Country n′ faces smaller importing frictions from country n (τ smaller) and country n faces larger importing frictions from country n′ (τ larger).
- Key implication: Under standard structural-gravity assumptions, bilateral trade imbalances are determined only by:
  - macroeconomic imbalances (NX_n),
  - triangular trade (differences in production and spending patterns, d_sn and e_sn),
  - and asymmetries in trade frictions (τ_sn′_n ≠ τ_snn′).
  - If NX_n = 0 for all n, d_sn = e_sn = d_s = e_s for all s and n, and τ symmetric, then bilateral trade is balanced bilaterally (P_sn = O_sn).

### 2.1.2  Proportional Bilateral Imbalances
- Definition:
  - Proportional bilateral imbalance ≡ (M_n′n − M_nn′) / (M_n′n^1/2 M_nn′^1/2)
- Approximate decomposition (Appendix A.1):
  - (M_n′n − M_nn′) / (M_n′n^1/2 M_nn′^1/2)
    ≈ ∑_{s=1}^S (M_sn′n M_snn′ M_n′n M_nn′)^1/2 [
      ln( (1 − NX_n / D_n) / (1 − NX_n′ / D_n′) )
      + ln( (d_sn′ e_sn) / (d_sn e_sn′) )
      − θ_s ln( τ_sn′_n / τ_snn′ )
      − θ_s ln( O_sn P_sn′ / (O_sn′ P_sn) )
    ]
  - Interpretation of terms:
    1. ln((1 − NX_n / D_n)/(1 − NX_n′ / D_n′)) — differences in macro trade balances.
    2. ln((d_sn′ e_sn)/(d_sn e_sn′)) — triangular trade (differences in production and spending patterns).
    3. −θ_s ln(τ_sn′_n / τ_snn′) — bilateral asymmetries in trade frictions.
    4. −θ_s ln(O_sn P_sn′ / (O_sn′ P_sn)) — differences in ratios of outward/inward MRTs; arises as an interaction effect and would be zero if first three terms were zero for n and n′ vis-à-vis all partners.
- Relationship to dollar-value imbalance:
  - M_n′n − M_nn′ = M_n′n^1/2 M_nn′^1/2 × (proportional bilateral imbalance)
  - Thus dollar bilateral imbalances decompose into:
    1. Geometric average of bilateral trade flows (M_n′n^1/2 M_nn′^1/2) — driven by gravity factors (average bilateral frictions, market sizes).
    2. Proportional bilateral imbalance — driven by the determinants in the approximate decomposition above.
- Empirical insight (U.S. example):
  - Large dollar deficits can arise from:
    - Large proportional imbalance with large average bilateral flows (e.g., China).
    - Small proportional imbalance with large average bilateral flows (e.g., Canada).
    - Large proportional imbalances on small average bilateral flows (many small partners).
  - Proportional imbalances are largely uncorrelated with partner economic mass or average bilateral flows; much of the observed dollar imbalance patterns reflect the size of bilateral flows rather than proportional imbalances.

### 2.1.3  Estimating Trade Wedges and Multilateral Resistance Terms
- Observability:
  - Observable: trade weights, macro trade balances, outputs, output and spending shares.
  - Unobserved: sectoral bilateral trade frictions {τ_sn′_n}_s,n′,n and MRTs {P_sn, O_sn}_s,n.
- Identification strategy — sufficient restriction:
  - E[M_sn′_n | n′, n] = D_sn′ E_sn / D_s (O_sn′ P_sn)^−θ_s
    - Interprets bilateral trade frictions as residual variation not explained by country-sector exporter/importer effects and MRTs.
    - Minimises variance in unobserved bilateral frictions, working against overstating role of asymmetric frictions.
- Estimation via PPML (following Fally 2015):
  - Estimate M_sn′_n = exp{Ω_sn′ + Π_sn} ε_sn′_n by PPML, where:
    - Ω_sn′: exporter fixed effect (economy-n′-sector-s)
    - Π_sn: importer fixed effect (economy-n-sector-s)
    - ε_sn′_n: error term
    - Impose Π_sN = 0 for benchmark economy N since fixed effects are not full rank.
  - Fally (2015) results yield:
    - P_sn^−θ_s = E_sn / E_sN × exp{−Π̂_sn}
    - O_sn′^−θ_s = E_sN D_sn′ / D_s × exp{−Ω̂_sn′}
    - Implied τ^−θ_s_sn′_n = ε̂_sn′_n
  - Requirements:
    - Estimation must be performed on a full matrix of bilateral expenditures, including economies’ expenditures on their own outputs in sectors {M_snn}_s,n.
- Outcome:
  - Equations provide the necessary elements to compute bilateral trade frictions and MRTs from available data under the identifying restriction, enabling decomposition of observed proportional bilateral imbalances into contributions from macro imbalances, triangular trade, asymmetric frictions, and MRT interactions.

*Source: 2.1  Structural Gravity and Bilateral Trade Imbalances (wpiea2022090-print-pdf).*

### 2.2  Bilateral Balance Accounting

### 2.2  Bilateral Balance Accounting

### Data and sample
- Data source: World Input Output Database (WIOD 2016 release; Timmer et al., 2015).
- Time coverage used: five-year average for 2010-14.
- Geographic coverage and aggregation:
  - Original WIOD: annual global input-output tables covering 43 economies and the “Rest of the World”.
  - Merged/aggregated sample used in analysis: 40 economies and the “rest of the world” (referred to as 41 economies for simplicity).
  - Sector aggregation: from 56 sectors at 2-digit ISIC (Rev. 4) to 16 broad manufacturing sectors and 15 service sectors → final table covers 31 sectors.
- Constructed observations:
  - For each sector, economy-n spending on economy-n′ output is M_sn′n.
  - Summing sector-level bilateral flows yields 820 distinct bilateral trade balances (41×40/2 = 820).
- Treatment of flows: less than 2% of the (31×41×41 =) 52,111 sector-country-pair flows are zero-valued.
- Key summary metrics (from the data and aggregation):
  - Median proportional imbalance = .46.
  - Smallest proportional imbalance ≈ 0.
  - Largest proportional imbalance = 5.01.
- Definitions:
  - Economy-n spending on sector s: E_sn = ∑_n′ M_sn′n.
  - Economy-n output in sector s: D_sn = ∑_n′ M_snn′.
  - Macro trade balance: NX_n = ∑_s ∑_n′≠n (M_snn′ − M_sn′n).
  - Sector-level bilateral trade frictions and MRTs derived as in Section 2.1.3.

### Linear approximation and decomposition approach
- Linear approximation used: first-order linear approximation of (M_n′n − M_nn′)/(M_n′n M_nn′)^{1/2}, described in expression (6).
- Validation of approximation:
  - Correlation of approximated vs actual proportional bilateral imbalances: R^2 = 0.899 (Figure 3).
  - Only a handful of significant outliers; approximation is informative for the large majority of pairs.
- Decomposition terms (the four right-hand-side terms in equation (6)):
  - “Macro NX” — macro trade balances.
  - “Prod./spend.” — differences in production and spending patterns.
  - “Trade frictions” — asymmetric bilateral trade wedges (economy-pair residual).
  - “MRTs” — ratio of inward to outward marginal rates of transformation.

### Summary statistics and correlations (proportional bilateral imbalance components)
- Panel A: Summary statistics (based on 820 unique absolute values)
  - Macro NX: mean = .027; st. dev. = .072; 10th pctl. = .004; med. = .021; 90th pctl. = .058
  - Prod./spend.: mean = .095; st. dev. = .082; 10th pctl. = .012; med. = .073; 90th pctl. = .208
  - Trade frictions: mean = .396; st. dev. = .343; 10th pctl. = .062; med. = .302; 90th pctl. = .879
  - MRTs: mean = .000; st. dev. = .000; 10th pctl. = .000; med. = .000; 90th pctl. = .000
- Panel B: Pairwise correlations (computed for the 820 positive-valued bilateral trade balances)
  - Macro NX vs Prod./spend. = .326
  - Macro NX vs Trade frictions = -.014
  - Macro NX vs MRTs = -.076
  - Prod./spend. vs Trade frictions = .093
  - Prod./spend. vs MRTs = -.250
  - Trade frictions vs MRTs = -.041

### Variance decomposition results and interpretation
- Regression slopes (share of variation attributed by each term; slopes sum to 1 by construction):
  - Macro trade balances: slope = 0.022 → accounts for 2% of variation.
  - Prod./spend. shares: slope = 0.123 → accounts for 12% of variation.
  - Trade wedges (asymmetric bilateral trade frictions): slope = 0.854 → accounts for 85% of variation.
  - MRTs: slope = 0.000 → negligible share of variation.
- Three main takeaways:
  - Macro trade balances explain only a vanishingly small portion of the variation in proportional bilateral imbalances (2%).
  - Differences in production and spending patterns (“triangular trade”) explain a materially larger share (12%).
  - The vast majority of the cross-pair variation (85%) is accounted for by asymmetric, economy-pair residual trade wedges (bilateral trade frictions).
- Robustness checks cited in the text:
  - Repeating the decomposition for 1995-1999 yields virtually the same quantitative results.
  - Restricting to the top 50% of country pairs by geometric-average bilateral trade flows yields almost identical shares: Macro trade balances = 3%; Prod./spend. = 12%; Asymmetric trade wedges = 85%.

### Limitations and motivation for a dynamic quantitative model
- Limitations of the static linear decomposition:
  - The linear approximation may poorly capture some larger proportional imbalances.
  - Changes that alter determinants of bilateral imbalances can have significant general-equilibrium effects (prices, distribution of per-effective-worker capital stocks, world interest rate, steady-state macro trade balances), potentially amplifying or damping impacts on bilateral imbalances.
  - The decomposition establishes that asymmetries in residual trade wedges are required to explain cross-pair variation, but does not establish whether these asymmetries have meaningful macroeconomic and welfare consequences.
- Next step signposted in the source:
  - To address these shortcomings, the paper embeds the assumptions in a fully-fledged dynamic quantitative trade model in Section 3.

*Source: 2.2 Bilateral Balance Accounting, based on WIOD (2016 release), averaged for the years 2010-14.*

### 3.1  Model Assumptions

### 3.1  Model Assumptions

### Overview
- Dynamic many-country, many-sector model of international trade with forward-looking agents who make consumption and savings decisions.
- International asset trade is permitted; differences in technology and rate of time preference across economies generate aggregate trade surpluses and deficits.
- Final consumption and investment require tradable inputs from many sectors; sectoral inputs are differentiated by country of origin, creating motives for international trade within and across sectors.
- Two crucial modelling assumptions:
  - Agents face a constant probability of death each period (Blanchard (1985) style), which breaks the Ramsey link between aggregate consumption growth and individual Euler equations and yields a non-degenerate cross-country distribution of assets in steady state.
  - Trade within sectors follows a standard structural gravity equation (Armington (1969) microfoundation used; Eaton and Kortum (2002) microfoundation would deliver equivalent results).

### Key assumptions on demographics, preferences, and endowments
- Time lasts forever; no aggregate uncertainty; each economy n = 1,...,N contains a unit mass of agents.
- Constant probability of death per period: ξ (specified in calibration as ξ = .13).
- Net population growth is zero: each period an exogenous mass ξ of agents is born in n.
- Agents in n discount the future at rate ρ_n.
- Agents are endowed with H_nt units of human capital supplied inelastically; H_nt grows exogenously at gross rate γ so that H_nt+1 = γ H_nt.
- Agents are born without wealth; actuarially fair life insurance is available yielding 1/(1−ξ) times wealth if they live; no bequest motive; negative bequests prohibited.
- Period utility is logarithmic in final consumption. Aggregate final consumption in n is:
  - C_nt = sum_{t′=-∞}^t ξ(1−ξ)^{t−t′} C_nt(t′) (equation (15)).

### Technologies and production structure
- Non-traded aggregate "all-purpose" good X_nt assembled from sectoral inputs:
  - X_nt = ∏_{s=1}^S (X_snt^{σ_sn})^{σ_sn} with σ_sn ∈ (0,1) and ∑_s σ_sn = 1 (equation (16)).
- Sector-s input X_snt assembled from tradable, place-specific varieties:
  - X_snt = (∑_{n′=1}^N ω_{sn′n}^{1/(1+θ_s)} x_{sn′nt}^{θ_s/(1+θ_s)})^{(1+θ_s)/θ_s} with θ_s ≥ 0 (equation (17)).
- Economy-n variety in sector s produced with Cobb-Douglas technology:
  - Q_snt = z_sn (K_snt^{α_n} H_snt^{1−α_n−μ_sn} J_snt^{μ_sn})^{1−μ_sn} (J_snt^{μ_sn})^{μ_sn} (equation (18)) — parameters α_n, μ_sn ∈ (0,1); z_sn is sector-economy-specific efficiency.
- Non-traded aggregate X_nt used for final consumption, intermediate inputs, or investment:
  - X_nt = C_nt + η_n I_nt + ∑_s J_snt, where η_n captures inverse investment efficiency and I_nt adds to capital via K_nt+1 = I_nt + (1−δ)K_nt (δ ∈ (0,1)) (equation (19)).

### Market structure and international trade
- Perfect competition in goods and factor markets.
- Iceberg transport costs: κ_{sn′n} ≥ 1 units shipped for one unit to arrive.
- Factors mobile within economies but immobile across borders.
- Agents can trade a one-period international riskless bond (zero net supply) with nominal return R_t common across economies.
- Wealth notation: A_nt(t′) is beginning-of-period wealth for cohort t′; cohort surviving wealth after uncertainty equals A_nt(t′)/(1−ξ).

### Steady state characterization
- Analysis focuses on model steady states where aggregate variables C_nt, I_nt, K_nt, B_nt, Y_nt grow at constant rate γ; prices are constant. Define ratios per human capital:
  - c_n ≡ C_nt/H_nt, i_n ≡ I_nt/H_nt, k_n ≡ K_nt/H_nt, b_n ≡ B_nt/H_nt, y_n ≡ Y_nt/H_nt.
- Steady-state prices:
  - P^C_n = P^J_n = P^I_n η_n = P_n = ∏_{s=1}^S [∑_{n′=1}^N (τ_{sn′n} p_{sn′})^{−θ_s}]^{−σ_sn θ_s} (equation (20)).
  - p_sn = 1/z_sn f_n^{1−μ_sn} P_n^{μ_sn}, f_n ≡ (r_n α_n)^{α_n} (w_n^{1−α_n})^{1−α_n} (equation (21)).
  - Trade wedge τ_{sn′n} ≡ ω_{sn′n}^{−1/θ_s} κ_{sn′n} (interpreted as ad-valorem equivalent of trade costs and home biases).
- Return equalization (steady-state return R):
  - R = α_n η_n f_n P_n k_n^{α_n−1} + 1 − δ (equation (22)).
- Steady-state ratio of aggregate net exports to GDP of n:
  - NX_nt / (f_n k_n^{α_n} H_nt) = 1 − α_n (1 − (1−δ)/γ) R/γ − ξ(ρ_n + ξ) R/γ (1−α_n) [1 + ρ_n − R/γ (1−ξ)]^{-1} [R/γ − (1−ξ)]^{-1} (equation (23)).
  - This ratio depends negatively on α_n; if γ > R it depends negatively on ρ_n (patient economies run surpluses; impatient economies run deficits under γ > R).
- Sectoral imports by n from n′:
  - M_{sn′nt} = (τ_{sn′n} p_{sn′})^{−θ_s} / (∑_{n′′=1}^N (τ_{sn′′n} p_{sn′′})^{−θ_s}) × σ_sn (∑_s p_sn Q_snt − NX_nt) (equation (24)).
- Market-clearing conditions and gravity-form expression for spending shares presented in equations (25)–(28).
- Steady-state real GDP per effective worker:
  - y_nt ≡ Y_nt / H_nt = f_n P_n k_n^{α_n} = Z_n k_n^{α_n} × ∏_{s=1}^S (M_s n n t / ∑_{n′=1}^N M_s n′ n t)^{−(1/θ_s) σ_sn (1−∑_s σ_sn μ_sn)} with Z_n ≡ ∏_{s=1}^S (z_sn / τ_{s n n})^{σ_sn/(1−∑_s σ_sn μ_sn)} (equation (28)).

### Calibration highlights (links to subsequent section)
- Baseline calibrated to sectoral trade patterns, trade imbalances, real incomes and capital stocks averaged over 2010-14 using WIOD and Penn World Tables (PWT, edition 9.0).
- Key parameter values and targets (full calibration described in Section 3.2):
  - ξ = .13 (life expectancy: 60 years)
  - δ = .06
  - γ = 1.044 (PWT: 1985-2014)
  - R = 1.030 (King and Low, 2014: 1985-2014)
  - {ρ_n} set to match {NX_nt / (f_n k_n^{α_n} H_nt)} from WIOD via equation (23).
  - {α_n} set to match 1 − economy-n labour share (PWT).
  - {η_n} set to match {k_n} from PWT using equation (22) (note calibration implies γ > R).
  - {σ_sn}, {μ_sn} set to match sectoral spending and input shares from WIOD.
  - {θ_s} set from trade elasticities in Caliendo and Parro (2015) and Costinot and Rodríguez-Clare (2014).
  - {τ_{sn′n}} and relative {z_sn / z_sN} set to match PPML estimates (Section 2.1.3) via relationships (29) and (30).
  - {Z_n} set to match {y_n} from PWT.
- Calibration implications:
  - γ > R in baseline calibration.
  - Calibrated correlation between discount rates and aggregate trade balances is -.75 (more impatient economies tend to have trade deficits).
  - Interpretation of η_n: η_n ≈ 1 for Germany and Switzerland, making calibrated R approximately equal to real marginal product of capital in low-risk-premia countries.

### Counterfactual parameter changes and exact-hat algebra
- Three types of counterfactuals explored via exact-hat algebra:
  1. Changes in inter-economy trade wedges {τ_{sn′n}} (interpreted as changes in iceberg trade costs {κ_{sn′n}}).
  2. Proportional, across-sectors productivity changes {z_sn} uniform within economies (economy-specific productivity shocks).
  3. Changes in barriers to international asset trade: from negligible to prohibitive for all economies ("financial autarky") — in this case all macro trade balances are zero in the new steady state.
- Exact-hat algebra extends standard static gravity counterfactual algebra by adding three equations capturing impacts via international asset markets and capital accumulation on the steady-state world interest rate and macro trade balances (Appendix A.4).
- This framework allows counterfactuals where macro trade balances respond endogenously to structural parameter changes, unlike approaches that treat trade balances as exogenous.

*Source: wpiea2022090-print-pdf — 3.1 Model Assumptions.*

### 3.3  Global Trade-Wedge Symmetry

### 3.3  Global Trade-Wedge Symmetry

### Assumptions
- Start from the calibration described in Section 3.2.1.
- Impose proportional changes in inter-economy trade wedges, {ˆτsn′n}s,n′≠n, such that ˆτsn′n = min { 1, τsnn′ / τsn′n } for all s, n′ ≠ n. (Equation (31))
- This sets the higher of the two bilateral trade wedges to equal the lower wedge (complete global bilateral trade-wedge symmetry).
- Alternative symmetry considered (geometric average): ˆτsn′n = (τsnn′ τsn′n)1/2 for all s, n′ ≠ n; main results hold under this alternative.

### Impact on Trade Patterns
- Figure-based findings:
  - The slope of the line of best fit between counterfactual and original proportional bilateral imbalances is .24 in the global trade-wedge symmetry counterfactual.
  - Interpretation: a lot less variation in bilateral imbalances under full bilateral symmetry; asymmetric trade wedges account for by far the greatest share of variation in proportional bilateral imbalances.
  - Non-linearities and general-equilibrium effects cause the remaining variation in proportional imbalances under symmetry to be somewhat larger than implied by the simple variance decomposition in Section 2.2.2.
- U.S. bilateral net exports under trade-wedge symmetry (Figure 6):
  - The large majority of bilateral net export positions shrink in absolute value; distribution becomes more “compressed”.
- Decomposition of changes in U.S. bilateral net exports (Figure 7):
  - Panel A: Counterfactual reduction in trade barriers increases average bilateral trade flows with all U.S. trade partners (geometric average of bilateral flows), expressed as percentage of U.S. GDP.
  - Panel B: Most U.S. proportional bilateral imbalances decrease in the symmetry counterfactual.
  - Net effect: Decline in proportional imbalances outweighs increased average trade flows, leading to less variation in conventionally reported bilateral imbalances.

### Impact on Macro Outcomes and the Global Economy
- Macro trade balances:
  - Move towards trade-wedge symmetry has almost no impact on macro trade balances (column 5 of Table 4).
  - Reason: New trade barriers leave the world interest rate almost unchanged; without significant changes in the world interest rate there are no changes in macro trade balances via equation (23).
- Real income and channels:
  - For the median economy (column 1 of Table 4) per-worker real GDP increases by almost 11%.
  - Two channels driving gains:
    - Lower trade barriers raise the purchasing power of domestic income (smaller shares of spending on domestically produced output; Arkolakis et al. (2012) and Ossa (2014) mechanism, referenced via equation (28)).
    - International capital mobility amplifies effects: lower trade barriers raise an economy’s marginal product of capital and, for a given world interest rate, result in a higher steady-state per-worker capital stock (equation (22)).
  - Columns 2 and 3 of Table 4 report changes in the two components of real GDP from equation (28); these components are highly correlated.
- Import wedges and gains:
  - Column 4 of Table 4: weighted average decline in import trade wedges for each economy.
  - Correlation between decline in import trade wedges (column 4) and changes in economies’ own-spending terms (column 2) is .91.
  - First-order interpretation: magnitude of economies’ gains derives from the decline in import trade wedges they experience.
- Consumption and welfare:
  - Changes in real GDP are accompanied by almost one-for-one changes in real aggregate consumption in the model; real aggregate consumption is a more meaningful measure of aggregate welfare here.
- Exposure to China:
  - Appendix A.5.1 documents that global trade-wedge symmetry would reduce economies’ exposure to China.
  - Most economies’ trade wedges in importing from China are lower than China’s wedges in importing from them; counterfactual implies trade liberalisation vis-à-vis partners other than China, rebalancing exposure towards the rest of the world.
- Overall implication:
  - Trade-wedge asymmetries could explain most variation in bilateral imbalances and have substantive implications for macro outcomes and global interconnectedness; motivates further study of origins of bilateral trade-wedge asymmetries.

### Key quantitative findings and statistics
- Slope of best-fit line (proportional bilateral imbalances) under global trade-wedge symmetry: .24.
- Median economy per-worker real GDP increases by almost 11% (column 1, Table 4).
- Correlation between decline in import trade wedges and changes in own-spending terms: .91.
- Macro trade balances: almost unchanged under trade-wedge symmetry (column 5, Table 4).
- Table 4 (selected illustrative rows, columns correspond to ˆy_n, ˆv_nn, ˆk_n, ˆτ_n, ˜nx_n−nx_n, ˆc_n — presented in the source in concatenated form):
  - AUS: 2.4 -1.2 2.7 -.1 .0 2.1
  - AUT: 12.6 -6.6 12.9 -1.6 .0 12.3
  - BEL: 10.2 -5.8 10.5 -1.3 .0 9.8
  - BGR: 11.1 -5.1 11.5 -.9 -.1 11.1
  - BRA: 2.4 -1.2 2.7 -.2 -.1 2.3
  - CAN: 4.0 -2.2 4.3 -.4 .0 3.8
  - CHE: 7.0 -4.2 7.3 -.7 .1 6.5
  - CHN: 6.0 -3.1 6.3 -.2 .0 5.7
  - CZE: 30.1 -12.6 30.4 -2.5 .0 29.4
  - DEU: 12.6 -7.0 13.0 -1.3 .1 12.2
  - DNK: 6.9 -4.1 7.2 -.8 .1 6.5
  - ESP: 6.7 -3.7 7.1 -.9 -.1 6.6
  - EST: 15.6 -8.1 16.0 -1.7 0.0 15.4
  - FIN: 6.8 -3.8 7.1 -.6 .0 6.6
  - FRA: 6.0 -3.5 6.3 -.6 -.1 5.9
  - GBR: 6.5 -3.7 6.8 -.7 -.1 6.4
  - GRC: 3.5 -1.6 3.8 -.2 -.2 3.6
  - HRV: 8.4 -5.1 8.7 -.9 -.1 8.3
  - HUN: 19.6 -10.1 20.0 -2.3 .0 19.2
  - IDN: 4.1 -1.6 4.4 -.3 -.1 3.7
  - IND: 4.7 -2.1 5.0 -.3 -.1 4.5
  - IRL: 19.0 -8.0 19.4 -1.9 .0 17.8
  - ITA: 6.3 -3.1 6.7 -.6 .0 6.1
  - JPN: 7.8 -4.3 8.1 -.5 -.1 7.6
  - KOR: 21.2 -9.2 21.6 -.7 .0 20.6
  - LTU: 14.8 -6.2 15.2 -.9 .0 14.4
  - LVA: 9.2 -4.8 9.5 -.9 -.1 9.1
  - MEX: 16.1 -5.5 16.4 -1.2 -.1 15.6
  - NLD: 9.7 -5.2 10.0 -1.2 .1 9.1
  - NOR: 5.2 -2.5 5.5 -.4 .1 4.5
  - POL: 11.7 -6.0 12.1 -1.5 .0 11.5
  - PRT: 8.1 -4.4 8.4 -.7 -.1 8.1
  - ROU: 14.9 -6.1 15.2 -1.1 -.1 14.7
  - RUS: 2.3 -1.5 2.6 -.3 -.2 4.6
  - RoW: 4.5 -2.2 4.8 -.3 -.2 4.6
  - SVK: 44.3 -18.0 44.7 -2.5 .0 43.8
  - SVN: 19.6 -11.2 19.9 -2.1 .0 19.4
  - SWE: 10.9 -5.5 11.2 -1.0 .0 10.4
  - TUR: 11.8 -4.6 12.1 -.8 -.1 11.4
  - TWN: 12.8 -5.5 13.2 -.9 .0 12.0
  - USA: 2.4 -1.3 2.7 -.2 -.1 2.3
  - (Table 4 notes: for each steady-state outcome x, ̃x denotes the new outcome after the counterfactual parameter change, and x̂ ≡ ̃x/x. Definitions for y_n, k_n, nx_n, c_n, v_nn, τ̂_n provided in source.)
- Figures and data calibration:
  - “Net exports (% GDP)” figures and decompositions calibrated on data from PWT (edition 9.0) and WIOD (2016 release), average for the years 2010-14.
  - Proportional bilateral imbalance definition: (M_n′nt − M_n n′t) / (M_n′nt M_nn′t)1/2 (WIOD 2016 release, average 2010-14).

### Broader interpretation and next steps
- The counterfactual demonstrates:
  - i) most proportional bilateral imbalances vanish under full bilateral symmetry;
  - ii) macro trade balances remain almost unchanged;
  - iii) per-worker real income and consumption changes primarily reflect the changes in import wedges that economies experience.
- The existence of bilateral trade-wedge asymmetries likely matters substantively for macro outcomes and global interconnectedness.
- Section 4 (and Appendix material) explores:
  - Stylised facts about bilateral trade-wedge asymmetries at aggregate and sectoral levels.
  - Evidence that the E.U. Single Market reduces trade-wedge asymmetries between member countries.
  - Counterfactual extensions of Single Market effects to all economies meaningfully reduce global variation in proportional bilateral imbalances.
  - Model implications for the U.S.-China trade war: it may reduce the U.S.-China deficit long run primarily via a weakening of trade ties (costly).

*Source: wpiea2022090-print-pdf — Section 3.3 Global Trade-Wedge Symmetry (calibration and figures based on PWT edition 9.0 and WIOD 2016 release, averages 2010-14).*

### 4.1  Properties of Aggregate and Sectoral Asymmetries

### 4.1  Properties of Aggregate and Sectoral Asymmetries

### Aggregate Trade-Wedge Asymmetries
- Definition and calibration
  - Aggregate log difference measure: ln(τn′n/τnn′) defined as in equation (32), using θ = 4.
  - Calibrations are based on data from PWT (edition 9.0) and WIOD (2016 release), averaged for the years 2010-14. The data covers 40 individual economies and the Rest of the World.
- Key summary statistics (Table 5) for the 820 distinct absolute values of |ln(τn′n/τnn′)| (2010-14)
  - # obs.: 820
  - mean: .099
  - st. dev.: .086
  - 10th percentile: .015
  - median: .076
  - 90th percentile: .220
- Interpretations and examples
  - For the median pair of economies, the average import wedge in one direction is .08 log points (roughly 8%) higher than in the other direction.
  - For 10% of pairs, this gap is larger than .20 log points (roughly 22%).
  - U.S.–China example: the U.S. import wedge from China is .18 log points (roughly 16%) smaller than the Chinese import wedge from the U.S.
  - The U.S. has lower aggregate import than export wedges for roughly two thirds of its trade partners; China has a lower aggregate import than export wedge for only one fifth of its trade partners.
- Persistence
  - The distribution of aggregate trade-wedge asymmetries for 1995-99 is characterised by summary statistics very similar to those for 2010-14.
  - The persistence of these measured asymmetries mirrors almost exactly the persistence of proportional bilateral imbalances documented in Appendix A.2.

### Sectoral Trade-Wedge Asymmetries
- Decomposition of aggregate asymmetries
  - Contribution of each of 31 sectors (baseline 2010-14) to cross-pair variation in aggregate asymmetries is reported in Table 6.
  - Five sectors on their own account for 70% of the aggregate variation.
- Top five sectoral contributions (from Table 6)
  - 12 Electrical and optical equipment — Contribution: .307; Median weight: .073; Median |ln(ˆεsn′n/ˆεsnn′)|: .778
  - 8 Chemicals and chemical products — Contribution: .112; Median weight: .070; Median |ln(ˆεsn′n/ˆεsnn′)|: .683
  - 11 Basic metals and fabricated metal — Contribution: .110; Median weight: .059; Median |ln(ˆεsn′n/ˆεsnn′)|: .654
  - 14 Transport equipment — Contribution: .084; Median weight: .040; Median |ln(ˆεsn′n/ˆεsnn′)|: .903
  - 15 Machinery, nec. — Contribution: .082; Median weight: .040; Median |ln(ˆεsn′n/ˆεsnn′)|: .790
- Mechanism
  - These sectors contribute most to aggregate trade-wedge asymmetries primarily because they make up a relatively large share of bilateral trade flows, not because they are characterised by especially large sectoral trade-wedge asymmetries.
- Alternative measure: Caliendo and Parro (2015) triple-ratio measure (equation (34))
  - Table 7 reports summary statistics for the absolute value of ln of the triple ratio for 10,660 unique cross-border trade-flow triplets (2010-14), focusing on the 15 goods-producing sectors that make 90% of the variation in aggregate asymmetries.
  - Example entries from Table 7 (Obs., p(10), p(50), p(90))
    - 1 Agriculture, hunting, forestry and fishing — 10,660; .275; 1.491; 4.130
    - 2 Mining and quarrying — 10,583; .383; 2.017; 5.365
    - 3 Food, beverages and tobacco — 10,660; .188; 1.018; 2.869
    - 8 Chemicals and chemical products — 10,660; .174; .973; 2.696
    - 12 Electrical and optical equipment — 10,660; .143; .813; 2.283
    - 14 Transport equipment — 10,660; .208; 1.155; 3.137
  - The sectoral median of the Caliendo–Parro measure is highly correlated with the median sectoral trade-wedge asymmetry reported for the 15 goods sectors in Table 6, with a correlation coefficient of .86.
  - Both measures capture largely the same “residual” pairwise asymmetries in sectoral trade flows.

### 4.2  Trade-Cost Asymmetries in a Single Market

### Trade Policy and Trade-Cost Asymmetries
- Role of tariffs and sample properties
  - Sample is heavily biased toward economies with low or zero tariff barriers: out of 40 individual sample economies, 24 were E.U. members in 2010-14.
  - About a third of the 820 trade-partner pairs in the data are not subject to tariffs at all.
  - Based on WDI data (2021 edition): the E.U.’s weighted average external tariff rate was 1.7% in 2010-14; the weighted average tariff rate for the median non-E.U. economy in the sample was 2.6%.
  - Conclusion: pairwise asymmetries in tariffs can at best account for a small fraction of the magnitude of trade-wedge asymmetries implied by the calculations.
- Focus on single-market membership
  - Examine whether membership in a single market that eliminates both tariff and non-tariff barriers reduces trade-cost asymmetries, exploiting overrepresentation of E.U. members and 11 countries that joined the Single Market between 1995-99 and 2010-14.

### Cross-Sectional Evidence on the Single Market Effect
- Use of the triple-ratio Caliendo–Parro measure by triplet composition
  - Triplets are grouped into: at most one E.U. member; exactly two E.U. members; exactly three E.U. members.
  - For each sector, Table 8 reports p(10), p(50), p(90) of the triple-ratio measure by group.
- Main empirical pattern
  - Relative to triplets with at most one E.U. country, the distribution of the asymmetry measure is shifted towards zero for triplets with exactly two E.U. countries.
  - The distribution is shifted further towards zero for triplets with exactly three E.U. countries.
  - This shift toward zero is consistent across all sectors, offering evidence that intra-E.U. trade is characterised by greater pairwise symmetry in trade wedges.
  - By construction of the Caliendo–Parro measure, differences in economies’ attributes or symmetric geographic elements are effectively controlled for in this comparison.

### Evidence on the Single-Market Effect from E.U. Accessions
- Identification approach
  - Use 11 countries present in both 1995-99 and 2010-14 datasets that joined the E.U. between the two periods.
  - Regression specification (equation (35)) estimates ˆψs from
    - 4(ln τsn′n − ln τsnn′) = Ψs + ψs 4EUn′n + υn′n,
    - where 4(ln τsn′n − ln τsnn′) is the change in measured trade-wedge asymmetries between 1995-99 and 2010-14 as defined in (36), and 4EUn′n is a dummy equal to 1 if n′ and n are both E.U. members in 2010-14 but at least one was not in 1995-99.
  - Sample: after excluding the “Rest of the World”, 38 individual economies are in both periods, yielding 666 unique pairs for the regression.
- Estimated impacts (Table 9): ˆψs, R2, Obs.
  - 1 Agriculture, hunting, forestry and fishing — ˆψs: -.108*** (.012); R2: .06; Obs.: 664
  - 2 Mining and quarrying — ˆψs: -.100*** (.012); R2: .08; Obs.: 604
  - 3 Food, beverages and tobacco — ˆψs: -.351*** (.040); R2: .08; Obs.: 663
  - 4 Textiles and textile products;... — ˆψs: -.097*** (.017); R2: .04; Obs.: 664
  - 5 Wood and products of wood and cork — ˆψs: -.039*** (.009); R2: .02; Obs.: 661
  - 6 Pulp, paper; paper, printing and publishing — ˆψs: -.091*** (.011); R2: .06; Obs.: 664
  - 7 Coke, refined petroleum and nuclear fuel — ˆψs: -.025*** (.003); R2: .05; Obs.: 619
  - 8 Chemicals and chemical products — ˆψs: -.154*** (.018); R2: .08; Obs.: 666
  - 9 Rubber and plastics — ˆψs: -.642*** (.055); R2: .13; Obs.: 664
  - 10 Other non-metallic, mineral products — ˆψs: -.320*** (.038); R2: .10; Obs.: 665
  - 11 Basic metals and fabricated metal — ˆψs: -.096*** (.009); R2: .07; Obs.: 666
  - 12 Electrical and optical equipment — ˆψs: -.505*** (.042); R2: .09; Obs.: 664
  - 13 Machinery, nec — ˆψs: -.113*** (.008); R2: .19; Obs.: 628
  - 14 Transport equipment — ˆψs: -3.749*** (.307); R2: .11; Obs.: 664
  - 15 Manufacturing, nec; recycling — ˆψs: -.175*** (.020); R2: .08; Obs.: 664
- Interpretation
  - Estimates of ˆψs are statistically significantly negative across all goods sectors.
  - In a handful of sectors, the Single Market effect on its own accounts for more than 10% of the over-time change in trade-wedge asymmetries.
  - Conclusion: intra-E.U. trade is characterised by smaller bilateral trade-wedge asymmetries, and accession to the E.U. is associated with declines in new members’ trade-wedge asymmetries vis-à-vis other members. This trade-wedge-levelling effect is separate from reductions in average bilateral trade barriers documented elsewhere.

### Extending the Single Market Effect to Non-E.U. Countries (setup)
- Counterfactual implementation (equation (37))
  - For goods-producing sectors and any pair in which at least one of n′ and n is not an E.U. member, impose proportional changes in inter-economy trade wedges for 2010-14:
    - ˆτsn′n = exp{ˆψs} if τsn′n > τsnn′
    - ˆτsn′n = 1 otherwise
  - Interpretation: for all non-E.U. economies, keep the lower of each bilateral goods trade wedge unchanged, and change the higher wedge in line with the estimated Single Market symmetry effect ˆψs.

*Italic source attribution: Extracted and summarized from "4.1 Properties of Aggregate and Sectoral Asymmetries" and subsequent sections of the supplied IMF content unit (wpiea2022090-print-pdf).*

### Section 4.2.3. All intra-E.U. and all service-sector trade wedges remain as they

### Section 4.2.3. All intra-E.U. and all service-sector trade wedges remain as they are.

### Counterfactual setup
- Counterfactual captures only the trade-wedge-levelling effect of E.U. membership (not the reduction in average bilateral trade barriers).
- Scope: Only extra-E.U. goods trade wedges are affected; these move towards symmetry in line with estimated E.U. accession effects (Table 9), instead of becoming fully symmetric.
- Calibration and data: WIOD (2016 release), PWT (edition 9.0), average for the years 2010-14. Data covers 40 economies and the Rest of the World.

### Impact on proportional bilateral imbalances (Figure 11)
- Slope of best-fit line: 0.728.
- Result: Variation in proportional bilateral imbalances declines noticeably—equivalent to roughly one third of the effect of full global trade-wedge symmetry.
- Interpretation: A Single Market–like trade policy environment could have substantive effects on bilateral imbalances, even when applied only to the bilateral trade flows of the 17 non-E.U. economies in the data.

### Macroeconomic impacts across economies (Figure 12)
- Median economy experiences a real GDP increase of more than 5%.
- Largest winners in this counterfactual:
  - Mexico: 38%
  - South Korea: 20%
  - Turkey: 19%
- Mechanism: Gains concentrated in middle-to-high-income countries that currently enjoy close trade relationships with major markets in their regions short of a Single Market environment.
- Distributional effect: Top end of the international income distribution in the data narrows, though the overall extent of international income differences remains broadly unchanged.

### U.S.-China Trade War — Assumptions (Section 4.3.1)
- Counterfactual: U.S.-China trade wedges rise to simulate tariffs imposed by the U.S. on China (January 2018 to June 2019) and retaliatory Chinese tariffs during this period; new tariffs are assumed to remain permanently in place; everything else constant.
- Tariff changes:
  - U.S. increased average tariffs on Chinese imports under Section 301 by 14.4 percentage points.
  - China increased average tariffs on U.S. imports by 13.5 percentage points.
- Calibration: Sectoral-level tariff changes computed consistent with sectoral aggregation; effects on U.S.-China trade wedges reported in Table A4. Calibration on PWT (edition 9.0) and WIOD (2016 release), average for the years 2010-14.

### U.S.-China Trade War — Impact on trade patterns and macro outcomes (Figures 13–15)
- World interest rate: Very limited effect; macro trade balances remain virtually unchanged.
- U.S.-China bilateral deficit: Halved in the new steady state.
- Decomposition of U.S. bilateral net export changes (Figure 14):
  - Panel A: Primary impact is to reduce the geometric average value of bilateral flows between the U.S. and China.
  - Evidence of some trade diversion: U.S. trade flows with Mexico, Germany and Ireland rise slightly (much smaller magnitude).
  - Panel B: Proportional bilateral imbalance between the U.S. and China declines, but only modestly.
- Interpretation: The trade war reduces the U.S.-China deficit primarily by weakening trade ties between the two countries rather than by substantially changing proportional imbalances.
- Distributional and welfare effects:
  - Both the U.S. and China lose equally from the trade war, with steady-state reductions in real GDP per capita and consumption per capita of around a fifth of a percent.
  - Third-country effects generally small; notable exception: as U.S. imports are diverted to Mexico, Mexico gains an additional .15% of GDP in the long run.
- Global distribution: Changes in U.S. imbalances have little effect on the global distribution of proportional bilateral imbalances; correlation across all pairs between empirical bilateral imbalances and post-trade-war counterfactual counterparts is .98.

### Broader conclusions drawn in this section
- Under the structural gravity assumption, observed variation in bilateral trade balances requires large bilateral trade-wedge asymmetries.
- Eliminating trade-wedge asymmetries would have sizeable effects on welfare and the global economy.
- Measured trade-wedge asymmetries may reflect data errors, model shortcomings, or underlying factors (geography, technologies, preferences).
- Evidence suggests the trade policy environment matters: European Single Market membership is associated with more bilaterally symmetric (and lower) trade barriers, implying deep cross-border integration can facilitate reductions in bilateral imbalances.
- Policy implication on unilateral tariff increases: Higher trade barriers vis-à-vis a specific partner can reduce an individual bilateral deficit, but with macro trade balances mostly unaffected, the deficit is merely shifted to other partners; such policies are economically costly and ultimately futile as a means to reduce aggregate imbalances.

*Source: wpiea2022090-print-pdf - Section 4.2.3. All intra-E.U. and all service-sector trade wedges remain as they are.*

### References

### wpiea2022090-print-pdf - References

### References overview
- Bibliographic list of cited works in the chapter, including journal articles, working papers, staff papers, books, and policy pieces. Notable entries (as listed): Alessandria & Choi (2020); Allen & Arkolakis (2016); Anderson (1979); Anderson & van Wincoop (2003); Antràs et al. (2017); Arkolakis et al. (2012); Armington (1969); Baldwin & Freeman (2021); Bernard & Moxnes (2018); Blanchard (1985); Bown (2019); Caliendo & Parro (2015); Dekle, Eaton & Kortum (2007, 2008); Eaton & Kortum (2002); Feenstra et al. (2015); Melitz (2003); Obstfeld & Rogoff (2000); Tinbergen (1962); Waugh (2010); and others as listed in the source.

### Appendix A.1 — Approximating bilateral trade imbalances
- Presents algebraic derivation approximating the proportional bilateral imbalance (equation (38) and expansions through (41)).
- Key expressions:
  - Proportional bilateral imbalance definition via M variables and first-order Taylor expansion (see equations (38)–(41)).
  - Linearization yields terms involving ln(1−NXn/Dn), ln(d/e ratios), −θs ln(τ ratios), and −θs ln(O/P ratios).

### Appendix A.2 — Variance decomposition for 1995-1999
- Data:
  - Uses WIOD (2013 release) covering years starting 1995; 37 individual economies plus Rest of the World → 703 distinct bilateral trade imbalances.
  - Figure A1: correlation of 1995-99 with 2010-14 bilateral imbalances = .36.
  - More than two thirds of bilateral balances that were in surplus in 1995-1999 remained in surplus in 2010-14.
- Variance decomposition (Figure A2; 1995-99):
  - Variation in economies’ aggregate trade balances accounts for 3 percent of the variation in bilateral imbalances.
  - Differences in production and spending patterns (“triangular trade”) account for 9 percent of the variation.
  - Asymmetric trade wedges account for the remaining 88 percent of the variation.
  - Reported panel slopes in Figure A2: Macro trade balances slope = 0.030; Prod./spend. shares slope = 0.094; Trade wedges slope = 0.876; MRTs slope = 0.000.

### Appendix A.3 — Dynamic model (agents, steady state)
- Agents’ optimality:
  - Lifetime utility maximization (equation (42)) subject to budget and capital accumulation constraints ((43)–(45)).
  - Euler equation: Cnt+1(t′)/Cnt(t′) = PCnt/PCnt+1 · (Rt+1)/(1+ρn) (equation (46)).
  - Optimal portfolio condition: rnt+1 + PINt+1(1−δ)/PInt = Rt+1 (equation (47)).
- Steady-state optimal savings:
  - Closed-form expressions for steady-state consumption and asset holdings of an agent (equations (48)–(52)).
  - Stationary distribution of assets exists under condition (1−ξ)/(1+ρn) · R/γ < 1.
  - Steady-state PnCt and Ant expressions (equations (51) and (52)) as functions of parameters and factor endowments.
- Steady-state net exports:
  - Capital stock expression: Knt = αn ηn Pn (R−1 +δ)^{-1} f_n K^{α_n}_{nt} H^{1−α_n}_{nt} (equation (53)).
  - Investment price relation: ηn Pn Int = αn (γ−1 +δ)/(R−1 +δ) f_n K^{α_n}_{nt} H^{1−α_n}_{nt} (equation (54)).
  - GDP identity: f_n K^{α_n}_{nt} H^{1−α_n}_{nt} = PnCt + ηn Pn It + NXnt (equation (55)).

### Appendix A.4 — Exact-hat algebra
- Own-spending shares and steady-state relations:
  - Rewritten conditions in terms of “own spending” shares v_{sn′}^{n} and price aggregates (equations (56)–(59)).
- Changes in trade costs and productivity:
  - Exact-hat expressions for changes in trade shares, factor allocations, and macro aggregates (equations (60)–(67)).
  - Definitions: nx_n = NX_nt / (f_n K^{α_n}_{nt} H^{1−α_n}_{nt}); h_n = f_n K^{α_n}_{nt} H^{1−α_n}_{nt} / ∑_n (...); q_n = ∑_s p_{sn} Q_{snt} / (f_n K^{α_n}_{nt} H^{1−α_n}_{nt}).
- Financial autarky:
  - Under complete financial autarky B_nt = 0 for all n,t; economies have own steady-state interest rates R_n.
  - Steady-state A_nt and capital relations under autarky (equations (68)–(69)).
  - Closed-form expression for R_n/γ (equation (70)) — unique positive root given parameter restrictions.
  - Under financial autarky NX_nt = 0 for all n,t.
  - Exact-hat system for autarky steady state summarized in equations (71)–(76), where R_n given by (70) and ̃nx_n = 0.

### Appendix A.5 — Additional details on counterfactuals
- Bilateral exposure and global trade-wedge symmetry (Section A.5.1):
  - Exposure definition: percent change in economy-n steady-state real GDP in response to a permanent 1 percent increase in aggregate productivity of economy n′.
  - Computed via exact-hat algebra (equations (60)–(66)) calibrated to PWT 9.0 and WIOD (2016), averaged 2010-14.
  - Key quantitative findings:
    - Many bilateral exposures are small in absolute value.
    - Productivity changes in large economies (U.S., China, Germany) have economically significant effects on other economies.
    - China: median country gains .12 percent of real income from a 1 percent increase in Chinese aggregate productivity.
    - Global trade-wedge symmetry (making trade wedges symmetric) leads to a median decline in exposure to China of .01 percentage point and increases exposures to the Rest of the World.
  - Interpretation: China’s prominence in cross-border production networks reflects size, comparative advantage, and asymmetric trade wedges.
- Financial autarky (Section A.5.2):
  - Macro impacts illustrated in Figure A5:
    - Real-GDP and real-consumption changes primarily reflect relocation of capital.
    - Economies that were net debtors under full integration see capital stocks and real income shrink in autarky; net creditors see capital stocks and real income grow.
    - Both groups experience declines in real consumption.
  - Transfer effect from disappearance of macro trade surpluses/deficits alters terms of trade but is quantitatively small relative to capital relocation effects.
- U.S.-China trade-war tariffs (Section A.5.3):
  - Tariff-change data sources:
    - U.S. tariff changes and import values at 10-digit HS from Bown (2019).
    - China tariff changes and import values at 8-digit HS from Bown, Jung & Zhang (2019).
  - Concorded to ISIC Rev. 4 and aggregated to the sector set used in the paper; resulting changes in trade wedges shown in Table A4.

### Appendix A.6 — Eaton and Kortum (2002) variant
- Presents a version of Eaton-Kortum (2002) that yields same steady-state relationships as benchmark Armington model.
- Key model elements:
  - CES assembly of tradable varieties (equation (77)).
  - Variety production technology with Fréchet-distributed productivity shifters (equations (78)–(79)).
  - Competitive goods markets with iceberg trade costs κ_{sn′n} ≥ 1.
- Mapping: define κ_{sn′n} ≡ τ_{sn′n}, β_s ≡ θ_s, and Z_n as product of z_{sn} terms to recover same key steady-state relationships and permit same calibration/counterfactuals (see equations (80)–(82)).

### Appendix A.7 — Dollar-value versus proportional bilateral imbalances
- Contrast between analyses of unnormalised dollar-value bilateral trade imbalances and proportional bilateral imbalances:
  - A gravity regression (PPML) of the form M_{n′n} = exp{Ω_{n′} + Π_n + δ_{n′n}} ε_{n′n} (equation (83)) estimated on WIOD (2013) 1995-99 averages (37 economies + RoW → 1406 pairs).
  - Constructed fitted values ˆM_{n′n} = exp{ˆΩ_{n′} + ˆΠ_n + ˆδ_{n′n}} (equation (84)) — captures variation absent trade-wedge asymmetries.
- Empirical comparisons:
  - Figure A6 (unnormalised differences): regression of fitted on actual unnormalised differences yields slope = 0.649 — suggesting structural gravity explains much of dollar-value imbalance variation.
  - Figure A7 (proportional imbalances): when scaled by geometric mean (proportional bilateral imbalances), slope falls to 0.145 — indicating most variation in proportional bilateral imbalances remains unexplained without allowing asymmetric trade wedges.
- Conclusion: analyses based on dollar-value imbalances conflate ability to explain average bilateral flows with ability to explain proportional bilateral imbalances; structural gravity does well on the former but not on the latter without asymmetric wedges.

### Appendix A.8 — Appendix tables (samples, sectors, elasticities, trade-cost changes)
- Table A1: Sample of economies — mapping WIOD (2016) entries to the paper’s final data grouping (examples include Australia AUS, Austria AUT, Belgium BEL, Brazil BRA, China CHN, U.S. USA, Rest of the World RoW).
- Table A2: Sector sample — WIOD (2016) sector names and codes mapped to final data sector groups and new 2-digit codes (31 final sectors listed).
- Table A3: Sector sample and trade elasticities — trade elasticity by sector (examples preserve exact numeric elasticities):
  - Sector 1 Agriculture, hunting, forestry and fishing: 8.11
  - Sector 2 Mining and quarrying: 15.72
  - Sector 3 Food, beverages and tobacco: 2.55
  - Sector 7 Coke, refined petroleum and nuclear fuel: 51.08
  - Sector 12 Electrical and optical equipment: 10.60
  - Sector 14 Transport equipment: 0.37
  - Many sectors assigned elasticity = 5 where specific estimates not used.
- Table A4: Trade-cost changes as a result of the USA-CHN trade war (ˆκ_{s,CHN,USA} and ˆκ_{s,USA,CHN} for listed sectors; table entries exactly as reported):
  - New code 1 Agriculture, hunting, forestry and fishing: ˆκ_{s,CHN,USA} = 1.16, ˆκ_{s,USA,CHN} = 1.25
  - New code 2 Mining and quarrying: ˆκ_{s,CHN,USA} = 1.06, ˆκ_{s,USA,CHN} = 1.10
  - New code 3 Food, beverages and tobacco: ˆκ_{s,CHN,USA} = 1.19, ˆκ_{s,USA,CHN} = 1.19
  - New code 4 Textiles and textile products; leather, leather apparel and footwear: ˆκ_{s,CHN,USA} = 1.05, ˆκ_{s,USA,CHN} = 1.14
  - New code 5 Wood and products of wood and cork: ˆκ_{s,CHN,USA} = 1.20, ˆκ_{s,USA,CHN} = 1.19
  - New code 6 Pulp, paper; paper, printing and publishing: ˆκ_{s,CHN,USA} = 1.20, ˆκ_{s,USA,CHN} = 1.16
  - New code 7 Coke, refined petroleum and nuclear fuel: ˆκ_{s,CHN,USA} = 1.18, ˆκ_{s,USA,CHN} = 1.25
  - New code 8 Chemicals and chemical products: ˆκ_{s,CHN,USA} = 1.14, ˆκ_{s,USA,CHN} = 1.11
  - New code 9 Rubber and plastics: ˆκ_{s,CHN,USA} = 1.13, ˆκ_{s,USA,CHN} = 1.08
  - New code 10 Other non-metallic, mineral products: ˆκ_{s,CHN,USA} = 1.17, ˆκ_{s,USA,CHN} = 1.12
  - New code 11 Basic metals and fabricated metal: ˆκ_{s,CHN,USA} = 1.18, ˆκ_{s,USA,CHN} = 1.19
  - New code 12 Electrical and optical equipment: ˆκ_{s,CHN,USA} = 1.18, ˆκ_{s,USA,CHN} = 1.10
  - New code 13 Machinery, nec: ˆκ_{s,CHN,USA} = 1.11, ˆκ_{s,USA,CHN} = 1.08
  - New code 14 Transport equipment: ˆκ_{s,CHN,USA} = 1.23, ˆκ_{s,USA,CHN} = 1.00
  - New code 15 Manufacturing, nec; recycling: ˆκ_{s,CHN,USA} = 1.10, ˆκ_{s,USA,CHN} = 1.06
  - New code 16 Electricity, gas and water supply: ˆκ_{s,CHN,USA} = 1.23, ˆκ_{s,USA,CHN} = 1.06
- Notes:
  - ˆκ_{sn′n} = 1 for all s,n′,n not shown in Table A4.
  - Iceberg-cost changes based on Bown (2019) and Bown et al. (2019); concorded from HS to ISIC Rev. 4 and aggregated to the sector set used in the paper.

*Italic: References and Appendix content as provided in the source PDF wpiea2022090-print-pdf - References.*

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