## wpiea2020210-print-pdf

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---

### 1. Introduction — context, motivation, and conceptual decomposition
- International trade grew spectacularly in the last three decades, accompanied by rising aggregate and bilateral trade imbalances.
- Examples:
  - The US aggregate annual trade deficit increased by about $600 billion between 1991 and 2019.
  - China’s trade surplus increased by about $400 billion between 1991 and 2019.
  - The US–China bilateral trade balance alone grew by about $300 billion over the same period.
- Two motivating puzzles:
  - Policy debate: economists’ “common wisdom” asserts aggregate trade balances are driven by macroeconomic factors (saving–investment balances) and that how aggregate balances are split bilaterally is of little macro policy interest; other observers argue that bilateral-targeted policies (e.g., bilateral tariffs) can influence aggregate trade balances.
  - Empirical gap: determinants of bilateral trade balances are poorly understood.
- Conceptual decomposition of drivers:
  - Macroeconomic factors that affect aggregate trade balances (level of aggregate demand and supply, saving–investment balances, multilateral resistance terms).
  - Pairwise trade costs (bilateral tariffs and other bilateral trade costs) that determine how aggregate balances are split across partners.
- Paper’s main goal: quantitatively estimate the relative role of these two groups.

### Data, empirical setup, and MRT proxying
- Main data sources and construction:
  - 2016 and 2018 Trade in Value Added (TiVA) databases from the OECD.
    - 2016 TiVA: bilateral exports and gross production at ISIC 3 level for 34 sectors and 63 countries from 1995–2011.
    - 2018 TiVA: at ISIC 4 level for 34 sectors and 63 countries from 2005–2015.
  - Databases combined by splicing the 2016 TiVA forward from 2006 onward using changes in shares from the 2018 TiVA.
  - Two sectors in each database are combined to yield a final total of 33 sectors.
  - Intra-national trade constructed as the difference between gross production and exports; a small number of negative constructed intra-national values at the sectoral level are set to zero.
- Tariff and trade-cost variables:
  - Tariff data from World Bank WITS, aggregated to sector level using trade-weighted averages; tariffs set to zero for all service sectors.
  - Distance, colonial history, contiguity, common language, and free trade agreement dummies from CEPII.
  - Non-tariff measures (NTMs) from UNCTAD TRAINS used in robustness checks; many missing sector-level NTMs are assumed zero.
- MRT proxy construction and estimation approach (Section 3.2):
  - MRTs are not proxied with time-varying exporter/importer fixed effects to avoid absorbing country-specific macroeconomic characteristics of interest.
  - Two-step procedure:
    - First-stage MRTs proxied by “remoteness” measures: bilateral GDP-weighted distances as in Wei (1996), Baldwin and Harrigan (2011) and Martin et al. (2008).
    - Trade elasticity 휀 is set to 3.
    - First-stage outward and inward MRTs are equal because the distance variable is symmetric.
    - Equation (1) is estimated using these proxies and predicted bilateral trade costs 푇
෠
௜௝௧ obtained from an exponential form including ln(Distance), Lan, Col, Bord, FTA, interaction with SM, and ln(1+τ) raised to power 1/(1−휀).
    - Second-stage MRTs constructed as GDP-weighted averages of predicted bilateral trade costs (equations (5) and (6)); sectoral regressions use gross sectoral outputs as weights.
  - Limitation: MRTs based on remoteness proxies are only partially consistent with theory (Head and Mayer 2014); analysis focuses on changes over time to mitigate misspecification concerns.
  - Allowance for an unobservable multiplicative scaling factor in MRTs: 푀푅푇
෫
௜௦௧ = 푢
௜௦
푀푅푇
௜௦௧, with 푢
௜௦ constant over time; main conclusions are unaffected by 푢
௜௦.
- Estimation details:
  - Baseline model estimated with pseudo Poisson maximum likelihood (PPML) as in Silva and Tenreyro (2006).
  - Time period: five-year averages over the sample 1995-2015 (five non-overlapping cross sections).

### Baseline regression results, fit for flows and levels
- Baseline sectoral specification:
  - Coefficients on output and expenditure constrained to unity (훽
ଵ = 훽
ଶ = 1).
  - Coefficients on multilateral resistance terms constrained equal (훽
ଵଶ = 훽
ଵଷ).
  - Trade cost coefficients allowed to differ between tradable and non-tradable sectors.
- Main empirical findings (sectoral and country-level):
  - Estimates of elasticities of exports to bilateral tariffs, distance and MRTs are in line with the literature.
  - Trade costs are notably larger for trade in services than trade in goods.
  - The estimated elasticity of exports to tariffs is approximately consistent with the assumption that 휀 = 3 used in MRT construction.
- Robustness:
  - Unconstrained and partially constrained specifications yield broadly consistent qualitative results; inclusion of NTMs reported in a robustness column.
  - Country-level model including country-pair fixed effects absorbs time-invariant bilateral proxies and addresses omitted variables/endogeneity concerns (Baier and Bergstrand 2007).
- Sample sizes and fit (selected):
  - Sector-level observations: 475,567 (Col 1) and 474,933 (Cols 2–5).
  - Sector-level R-squared values: 0.947, 0.962, 0.962, 0.984, 0.963 respectively for columns (1)–(5).
  - Country-level observations: 15,560 (most columns); country-level R-squared values: 0.969, 0.986, 0.999, 0.996, 1.000 respectively across columns.
- Fit of levels versus flows:
  - Gravity models fit observed bilateral export flows very well but fit bilateral trade-balance levels less well.
  - Regression of actual bilateral balances 푇퐵
௜௝௧ against baseline predicted values 푇퐵
෢
௜௝௧:
    - R-squared falls from 99 percent (column (2) of Table 2 for exports) to 31 percent (column (2) of Table 3 for trade balances).
    - High fit for bilateral trade balances achieved when gravity estimation includes country-pair fixed effects: R-squared increases to around 95 percent.
  - Interpretation: gravity variables do not capture all bilateral factors that are constant over time and shape trade costs; motivates focusing on decompositions of changes rather than levels.
- Selected Table 3 results (country level, 5-year averages):
  - Regression coefficients for predicted trade balance (columns (1)–(5)): 0.80***, 0.97***, 1.00***, 2.29***, 0.99***.
  - Constant = 0 in all five regressions.
  - Observations: 15,282 in each regression.
  - R-squared values: 0.260, 0.314, 0.931, 0.286, 0.921.
  - R-squared subsample of largest bilateral balances: 0.429, 0.449, 0.953, 0.454, 0.939.

### Analytical decomposition of changes and empirical fit
- Predicted sectoral bilateral trade balance: 푇퐵
෢
௜௝௦௧ = 푋
෠
௜௝௦௧ − 푋
෠
௝௜௦௧.
- Log-linear approximation for changes (equation (7)):
  - Δ푇퐵
෢
௜௝௦௧ ≈ Δln(푋
෠
௜௝௦௧)⋅푋
௜௝௦௧іଵ − Δln(푋
෠
௝௜௦௧)⋅푋
௝௜௦௧іଵ.
- Aggregate predicted changes sum across sectors (equation (8)): Δ푇퐵
෢
௜௝௧ = ∑ Δ푇퐵
෢
௜௝௦௧௦.
- Log-linearization approximation:
  - Authors note approximation error is small for relatively small changes (less than 10 percent).
  - About 90 percent of observed changes are within this threshold.
- Decomposition of sectoral predicted change into drivers (equation (9)):
  - Δ푇퐵
෢
௜௝௦௧ ≈ ∆푁푆
෢
௜௦௧ + ∆푁퐷
෢
௝௦௧ + ∆푊
෡
௦௧ + ∆푆퐶
෢
௜௦௧ − ∆푆퐶
෢
௝௦௧ + ∆푀퐶
෢
௜௦욕 − ∆푀퐶
෢
௝௦௧ + ∆퐵퐶
෢
௜௝௦௧.
- Component definitions (selected):
  - ∆푁푆
෢
 and ∆푁퐷
෢
: changes in net supply and net demand driven by Δln(Y) and Δln(E) weighted by initial trade shares and estimated coefficients 훽
መ.
  - ∆푊
෡
: world output channel.
  - ∆푆퐶
෢
: sectoral composition changes using sector shares 훼.
  - ∆푀퐶
෢
: multilateral-cost channel via Δln(MRT) terms; construction unaffected by a constant multiplicative scaling 푢
௜௦ of MRTs.
  - ∆퐵퐶
෢
: bilateral-cost channel including Δln(1+τ) and ΔFTA.
- Empirical fit of changes:
  - Regression of actual changes in bilateral balances on predicted changes yields:
    - R-squared = 82 percent.
    - Regression slope point estimate = 0.82 with standard deviation 0.003.
  - Decomposition uses estimated 훽
መ
 from the baseline sectoral specification (column (2) of Table 1).

### Main empirical findings from decompositions
- Over 1995–2015, changes in bilateral trade costs played a negligible role; changes in bilateral balances were predominantly driven by macro factors not specific to any bilateral relation.
- Macro factors are by far the most important drivers of changes in bilateral trade balances since 1995:
  - Within macro factors, changes in countries’ net demand and net supply played the lion’s share.
  - These are influenced by structural characteristics (productivity, demography) and macroeconomic policies.
  - Example: US–China — changes in US net supply contributed negatively to the US trade balance with China; changes in China’s net demand also contributed negatively.
- Changes in bilateral trade costs, including tariffs, played only a very minor role overall:
  - Partly because tariffs were already low in the mid-1990s in many countries and tariff reductions were often reciprocal with offsetting effects.
- Sectoral composition changes are generally moderate but can be significant in specific cases:
  - Positive contribution arises when the output share of sectors where a country had large initial exports rises more than the corresponding spending share, or when spending share in sectors with high initial imports falls more than output share.
- Contributions of changes in multilateral resistance factors are non-negligible but generally not very large; in the US–China case the two countries’ contributions largely cancel in net.
- Residual in decompositions includes model statistical error plus log-linearization approximation error; figures report average 2010-15 minus average 1995-99.

### Robustness, appendices, and model diagnostics
- Sector-level trade balance fit (Appendix 3, Table A3.1, 5-year average panel) selected results:
  - Predicted trade balance, constrained model with distance-MRT: coefficient 0.94*** (0.24).
  - Predicted trade balance, constrained model with cost-MRT: coefficient 1.05*** (0.21).
  - Predicted trade balance, partially constrained model: coefficient 1.07*** (0.22).
  - Predicted trade balance, unconstrained model: coefficient -0.09 (0.24).
  - Predicted trade balance, constrained model with NTMs: coefficient 1.06*** (0.22).
  - Observations: 15,876 for each specification.
  - R-squared values: 0.235, 0.288, 0.269, 0.001, 0.295 respectively.
  - R-squared, subsample of largest bilateral balances: 0.330, 0.357, 0.424, 0.003, 0.376 respectively.
- Cross-section gravity model (Appendix 2, Table A2.1) summary statistics:
  - R-Squared values reported: 0.964, 0.964, 0.967, 0.959, 0.969.
  - Observations reported: 87,436; 58,414; 68,353; 81,076; 62,373.

### Conclusions and policy implication
- Main conclusion: bilateral trade balances are by and large driven by the same macro factors that determine aggregate trade balances, providing new evidence of the practical irrelevance of bilateral trade balances in the conduct of macroeconomic policy.
- Empirical strategy and findings:
  - Gravity model difficulties in fitting bilateral trade balances attributed to omission of unobservable, time invariant components of bilateral trade costs.
  - After accounting for these components, gravity estimates fit the change over time in bilateral balances successfully.
  - Log-linear approximation decomposes changes into underlying macro factors and bilateral trade-cost changes.
- Core empirical result: macroeconomic factors—especially the evolution of countries’ aggregate demand and supply—are by far the main determinants of changes in bilateral trade balances; changes in bilateral trade costs play a very minor role.
- Policy implication: policymakers should primarily focus on aggregate macro determinants when assessing external balance dynamics because bilateral trade balances add little new information for macroeconomic policy beyond what aggregate balances convey.

*Source: IMF working paper — 1. INTRODUCTION; 3.2 PROXYING MULTILATERAL RESISTANCE TERMS (MRTS); 3.4 LEVELS OF BILATERAL TRADE BALANCES: EVALUATING THE FIT; 4 CHANGES IN BILATERAL TRADE BALANCES: FIT AND DECOMPOSITION; 5. CONCLUSIONS (wpiea2020210-print-pdf).*

### 1. INTRODUCTION

### 1. INTRODUCTION

### Context and motivation
- International trade grew spectacularly in the last three decades, accompanied by rising aggregate and bilateral trade imbalances.
- Examples:
  - The US aggregate annual trade deficit increased by about $600 billion between 1991 and 2019.
  - China’s trade surplus increased by about $400 billion between 1991 and 2019.
  - The US–China bilateral trade balance alone grew by about $300 billion over the same period.
- Two motivating puzzles:
  - Policy debate: economists’ “common wisdom” asserts aggregate trade balances are driven by macroeconomic factors (saving–investment balances) and that how aggregate balances are split bilaterally is of little macro policy interest; other observers argue that bilateral-targeted policies (e.g., bilateral tariffs) can influence aggregate trade balances.
  - Empirical gap: determinants of bilateral trade balances are poorly understood.

### Conceptual decomposition of drivers
- Bilateral trade balances are influenced by two broad groups of drivers:
  - Macroeconomic factors that affect aggregate trade balances (level of aggregate demand and supply, saving–investment balances, multilateral resistance terms).
  - Pairwise trade costs (bilateral tariffs and other bilateral trade costs) that determine how aggregate balances are split across partners.
- Paper’s main goal: quantitatively estimate the relative role of these two groups.

### Empirical challenges and approach
- Empirical trade models have difficulty explaining the level of bilateral trade balances even with detailed sectoral data.
  - The paper traces this difficulty to time-invariant unobservable variables specific to bilateral relations (possibly unobserved components of bilateral trade costs).
- This motivates focusing on:
  - The statistical fit of the gravity model in explaining changes over time in bilateral trade balances.
  - Decomposing changes in bilateral trade balances into distinct drivers using a sectoral gravity regression and a log-linear approximation.

### Key empirical results (summary)
- The gravity model performs poorly in explaining cross-sectional levels of bilateral trade balances due to time-invariant unobservables, but:
  - The gravity model is successful in explaining changes over time in bilateral trade balances.
- Main quantitative decomposition (changes in world bilateral balances between 1995 and 2015 are decomposed into five types of drivers):
  - Countries’ aggregate demand/supply.
  - World demand/supply.
  - Countries’ sectoral composition of spending and output.
  - Multilateral trade costs (“multilateral resistance terms”).
  - Bilateral trade costs.
- Principal finding: over 1995–2015, changes in bilateral trade costs played a negligible role; changes in bilateral balances were predominantly driven by the first four groups (macro factors not specific to any bilateral relation).
- Implication: empirical support for the economists’ common wisdom that bilateral trade balances are largely an outcome of macro factors; bilateral-targeted policies affect composition but not the level of aggregate balances.

### Illustrative evidence: US–China case
- The paper presents an example (Figure 1) showing:
  - The actual US–China trade balance scaled by the product of US GDP and China’s share of world GDP.
  - A predicted (double-scaled) bilateral balance constructed from the difference between the two countries’ aggregate trade-balance-to-GDP ratios multiplied by a calibrated constant (“trade bias”).
- Conclusion from the illustration: the evolution of the two countries’ aggregate trade balances determines almost entirely the pattern of their scaled bilateral balance once appropriate double-scaling is applied. Double-scaling (including partner’s share of world output) is crucial to avoid misinterpretation (e.g., apparent steady deterioration of the US deficit vis-à-vis China when scaling only by US GDP).

### Literature connections
- Feenstra et al. (1998): for US–China, evolution mainly driven by macro forces affecting saving–investment balances; this paper generalizes that conclusion across many country pairs and sectors.
- Davis and Weinstein (2002): find bilateral balances harder to predict than bilateral exports and identify the “mystery of excess imbalances” (actual bilateral balances larger than predicted); this paper:
  - Confirms the “mystery” for cross-sectional levels and attributes it to time-invariant bilateral unobservables.
  - Shows the “mystery of excess imbalances” does not hold for changes over time.
- Cunat and Zymek (2019): calibrate a sectoral general equilibrium model that yields similar need for unobservable asymmetric bilateral wedges to explain cross-sectional levels.

### Roadmap of the paper
- Section 2: introduces the gravity framework and a special case for constructing bilateral trade balances.
- Section 3: discusses gravity regression empirical results and fit for levels of bilateral trade balances.
- Section 4: shows how the gravity equation is used to approximate changes in bilateral trade balances and to decompose determinants.
- Section 5: concludes.

---

### Data and empirical setup (preview from Section 3)
- Main data sources:
  - 2016 and 2018 Trade in Value Added (TiVA) databases from the OECD.
    - 2016 TiVA: bilateral exports and gross production at ISIC 3 level for 34 sectors and 63 countries from 1995–2011.
    - 2018 TiVA: at ISIC 4 level for 34 sectors and 63 countries from 2005–2015.
  - Databases are combined by splicing the 2016 TiVA forward from 2006 onward using changes in shares from the 2018 TiVA.
  - Two sectors in each database are combined to yield a final total of 33 sectors.
  - Intra-national trade is constructed as the difference between gross production and exports; a small number of negative constructed intra-national values at the sectoral level are set to zero.
- Tariff and trade-cost variables:
  - Tariff data from World Bank WITS, aggregated to sector level using trade-weighted averages; tariffs set to zero for all service sectors.
  - Distance, colonial history, contiguity, common language, and free trade agreement dummies from CEPII (Head, Mayer, Riess 2010; Head and Mayer 2014).
  - Non-tariff measures (NTMs) from UNCTAD TRAINS used in robustness checks; many missing sector-level NTMs are assumed zero.
- Multilateral Resistance Terms (MRTs) and their construction are discussed in Section 3.2; MRTs are sector-specific in the sectoral model and capture average trade-cost exposures outward and inward for each country-sector.

*Source: IMF working paper — 1. INTRODUCTION (wpiea2020210-print-pdf)*

### 3.2 PROXYING MULTILATERAL RESISTANCE TERMS (MRTS)

### 3.2 PROXYING MULTILATERAL RESISTANCE TERMS (MRTS)

### Proxy construction and estimation approach
- Multilateral resistance terms (MRTs) are not proxied with time-varying exporter/importer fixed effects because those would absorb country-specific macroeconomic characteristics of interest.
- Two-step procedure:
  - First-stage MRTs proxied by “remoteness” measures: bilateral GDP-weighted distances as in Wei (1996), Baldwin and Harrigan (2011) and Martin et al. (2008).
  - Trade elasticity 휀 is set to 3.
  - First-stage outward and inward MRTs are equal because the distance variable is symmetric.
  - Equation (1) is estimated using these proxies and predicted bilateral trade costs 푇
෠
௜௝௧ are obtained from an exponential form that includes terms for ln(Distance), Lan, Col, Bord, FTA, interaction with SM, and ln(1+τ) raised to power 1/(1−휀).
  - Second-stage MRTs are constructed as GDP-weighted averages of predicted bilateral trade costs (equations (5) and (6)).
- Sectoral regressions use gross sectoral outputs in place of aggregate output as weights.
- Limitation: MRTs based on remoteness proxies are only partially consistent with theory (Head and Mayer 2014). The analysis focuses on changes over time to mitigate misspecification concerns.
- Allowance for an unobservable multiplicative scaling factor in MRTs: 푀푅푇
෫
௜௦௧ = 푢
௜௦
푀푅푇
௜௦௧, with 푢
௜௦ constant over time; Section 4.1 notes main conclusions are unaffected by 푢
௜௦.

*Estimation details and data frequency*
- Baseline model estimated with pseudo Poisson maximum likelihood (PPML) as in Silva and Tenreyro (2006).
- Time period: five-year averages over the sample 1995-2015 (five non-overlapping cross sections).

---

### Baseline results (sectoral and country-level)
- Baseline sectoral specification:
  - Coefficients on output and expenditure constrained to unity (훽
ଵ = 훽
ଶ = 1).
  - Coefficients on multilateral resistance terms constrained equal (훽
ଵଶ = 훽
ଵଷ).
  - Trade cost coefficients allowed to differ between tradable and non-tradable sectors.
- Main empirical findings:
  - Estimates of elasticities of exports to bilateral tariffs, distance and MRTs are in line with the literature.
  - Trade costs are notably larger for trade in services than trade in goods.
  - The estimated elasticity of exports to tariffs is approximately consistent with the assumption that 휀 = 3 used in MRT construction.
- Robustness exercises:
  - Column (3) of Table 1: unconstrained coefficients on MRTs — outward MRT coefficient ~1.5 times magnitude of inward, but other coefficients largely unchanged.
  - Column (4): fully unconstrained model — magnitudes of some bilateral trade-cost coefficients differ, but results qualitatively consistent.
  - Column (5): baseline model including non-tariff measures (NTM) — reported.
- Country-level model (Table 2):
  - Results generally consistent with sector-level estimates.
  - Inclusion of country-pair fixed effects absorbs time-invariant bilateral proxies and addresses omitted variables/endogeneity concerns (Baier and Bergstrand 2007).
  - Coefficients remain broadly stable across specifications.
- Sample sizes and fit (selected):
  - Sector-level (Table 1) observations: 475,567 (Col 1) and 474,933 (Cols 2–5).
  - Sector-level R-squared values: 0.947, 0.962, 0.962, 0.984, 0.963 respectively for columns (1)–(5).
  - Country-level (Table 2) observations: 15,560 (most columns) and 15,552/15,554 in some.
  - Country-level R-squared values: 0.969, 0.986, 0.999, 0.996, 1.000 respectively across columns in Table 2.

---

### 3.4 LEVELS OF BILATERAL TRADE BALANCES: EVALUATING THE FIT

### Fit of levels versus flows
- The baseline gravity models fit observed bilateral export flows very well, but they fit bilateral trade-balance levels less well.
- Regression of actual bilateral balances 푇퐵
௜௝௧ against baseline predicted values 푇퐵
෢
௜௝௧ shows:
  - R-squared falls from 99 percent (column (2) of Table 2 for exports) to 31 percent (column (2) of Table 3 for trade balances).
  - High fit for bilateral trade balances is achieved when gravity estimation includes country-pair fixed effects: R-squared increases to around 95 percent.
- Interpretation:
  - Gravity variables do not capture all bilateral factors that are constant over time and shape trade costs.
  - This motivates focusing on decompositions of changes in bilateral trade balances rather than levels.

Selected results from Table 3 (trade balance fit, country level, 5-year averages)
- Regression coefficients for predicted trade balance (columns (1)–(5)): 0.80***, 0.97***, 1.00***, 2.29***, 0.99*** (standard errors reported in table).
- Constant = 0 in all five regressions (with standard errors reported).
- Observations: 15,282 in each regression.
- R-squared values: 0.260, 0.314, 0.931, 0.286, 0.921.
- R-squared subsample of largest bilateral balances: 0.429, 0.449, 0.953, 0.454, 0.939.

---

### 4 CHANGES IN BILATERAL TRADE BALANCES: FIT AND DECOMPOSITION

### Analytical decomposition framework
- Focus on changes over time and allow for asymmetric bilateral trade costs and MRTs; concentrate on sectoral model (2).
- Predicted sectoral bilateral trade balance: 푇퐵
෢
௜௝௦௧ = 푋
෠
௜௝௦௧ − 푋
෠
௝௜௦௧.
- Log-linear approximation for changes (equation (7)):
  - Δ푇퐵
෢
௜௝௦௧ ≈ Δln(푋
෠
௜௝௦௧)⋅푋
௜௝௦௧іଵ − Δln(푋
෠
௝௜௦௧)⋅푋
௝௜௦௧іଵ.
- Aggregate predicted changes sum across sectors (equation (8)): Δ푇퐵
෢
௜௝௧ = ∑ Δ푇퐵
෢
௜௝௦௧௦.
- The log-linearization introduces approximation error; authors note approx. equal to growth rates for relatively small changes (less than 10 percent), and about 90 percent of observed changes are within this threshold.
- Decomposition of sectoral predicted change into drivers (equation (9)):
  - Δ푇퐵
෢
௜௝௦௧ ≈ ∆푁푆
෢
௜௦௧ + ∆푁퐷
෢
௝௦௧ + ∆푊
෡
௦௧ + ∆푆퐶
෢
௜௦௧ − ∆푆퐶
෢
௝௦௧ + ∆푀퐶
෢
௜௦௧ − ∆푀퐶
෢
௝௦௧ + ∆퐵퐶
෢
௜௝௦௧.
- Definitions (selected components):
  - ∆푁푆
෢
 and ∆푁퐷
෢
: changes in net supply and net demand driven by Δln(Y) and Δln(E) weighted by initial trade shares and estimated coefficients 훽
መ.
  - ∆푊
෡
: world output channel.
  - ∆푆퐶
෢
: sectoral composition changes using sector shares 훼.
  - ∆푀퐶
෢
: multilateral-cost channel via Δln(MRT) terms.
  - ∆퐵퐶
෢
: bilateral-cost channel including Δln(1+τ) and ΔFTA.
- Note: construction of ∆푀퐶
෢
 is unaffected by a constant multiplicative scaling 푢
௜௦ of MRTs (Section 3.2).

### Empirical implementation and fit of changes
- Regression of actual changes in bilateral balances on predicted changes yields:
  - R-squared = 82 percent.
  - Regression slope point estimate = 0.82 with standard deviation 0.003.
- The decomposition uses estimated 훽
መ
 from the baseline sectoral specification (column (2) of Table 1).

### Main empirical findings from decompositions (Figures 2 and 3)
- Macro factors are by far the most important drivers of changes in bilateral trade balances since 1995.
  - Within macro factors, changes in countries’ net demand and net supply played the lion’s share.
  - These are influenced by structural characteristics (productivity, demography) and macroeconomic policies.
  - Example: US–China — changes in US net supply contributed negatively to the US trade balance with China; changes in China’s net demand also contributed negatively.
- Changes in bilateral trade costs, including tariffs, played only a very minor role overall.
  - Partly because tariffs were already low in the mid-1990s in many countries and tariff reductions were often reciprocal with offsetting effects.
- Sectoral composition changes are generally moderate but can be significant in specific cases.
  - Positive contribution arises when the output share of sectors where a country had large initial exports rises more than the corresponding spending share, or when spending share in sectors with high initial imports falls more than output share.
- Contributions of changes in multilateral resistance factors are non-negligible but generally not very large; in the US–China case the two countries’ contributions largely cancel in net.
- Residual in decompositions includes model statistical error plus log-linearization approximation error; figures report average 2010-15 minus average 1995-99.

---

*Source: wpiea2020210-print-pdf — 3.2 PROXYING MULTILATERAL RESISTANCE TERMS (MRTS) through section 4.2 as provided in the source content.*

### 5. CONCLUSIONS

### 5. CONCLUSIONS

### Re-evaluation of the irrelevance of bilateral trade balances
- The paper re-examines the argument that bilateral trade balances are irrelevant for the conduct of macroeconomic policy, contrasting the "common wisdom" that aggregate trade balances are the variable of interest while bilateral balances are a by-product determined by bilateral trading costs.
- Main conclusion: bilateral trade balances are by and large driven by the same macro factors that determine aggregate trade balances, providing new evidence of the practical irrelevance of bilateral trade balances in the conduct of macroeconomic policy.

### Empirical strategy and gravity model findings
- Approach: study of the determinants of bilateral trade balances based on the gravity model of international trade.
- Identification of a key estimation issue: the gravity model's difficulty in fitting bilateral trade balances is likely due to omission of unobservable, time invariant components of bilateral trade costs.
- After accounting for these components, gravity estimates fit the change over time in bilateral balances successfully.
- Constructed a log-linear approximation to decompose changes in bilateral trade balances into:
  - underlying changes in macro factors (variables not specific to a given trade relation), and
  - changes in bilateral trade costs.

### Core empirical results
- Macroeconomic factors—especially the evolution of countries’ aggregate demand and supply—are by far the main determinants of changes in bilateral trade balances.
- Changes in bilateral trade costs play a very minor role in driving changes in bilateral trade balances.
- This evidence supports the view that bilateral trade balances add little new information for macroeconomic policy beyond what aggregate balances convey.

### Theoretical derivation (appendix summary)
- A typical theoretical gravity model with empirical specification is presented:
  - X_ij = Y_i E_j / Y_w * (τ_ij^-σ) * (Π_i^-1) * (P_j^-1)  (notation as in the source)
  - τ_ij represents bilateral trade costs; Π_i and P_j are the theoretical MRTs (multilateral resistance terms).
- Definitions and properties:
  - Outward MRT (Π_i) is an average of tariffs faced by the exporting country in the global market.
  - Inward MRT (P_j) captures the overall tariff that the importing country imposes on the rest of the world.
  - θ_i = y_i / y_w denotes the share of country i's nominal output in world output.
- Under approximations that output shares ≈ spending shares and countries’ aggregate trade balances are close to zero, and assuming symmetric trade costs (τ_ij = τ_ji) so Π_i = P_i, the gravity equation can be rewritten to express bilateral exports relative to world output and to define a trade bias σ_ij that is symmetric (σ_ij = σ_ji).
- Computing the analogous quantity for X_ji and taking differences yields equation (3) in the paper.

### Robustness and model fit (appendices)
- Cross-section gravity model (Appendix 2, Table A2.1) summary statistics:
  - R-Squared values reported: 0.964, 0.964, 0.967, 0.959, 0.969
  - Observations reported: 87,436; 58,414; 68,353; 81,076; 62,373
  - Note: coefficients reported for many regressors (distance, border, language, colony, FTA, SM_ij, LN(MRT_ist), LN(MRT_jst), etc.) with significance indicators (*** p<0.01, ** p<0.05, * p<0.1).
- Sector-level trade balance fit (Appendix 3, Table A3.1, 5-year average panel):
  - Predicted trade balance, constrained model with distance-MRT: coefficient 0.94*** (standard error (0.24))
  - Predicted trade balance, constrained model with cost-MRT: coefficient 1.05*** (0.21)
  - Predicted trade balance, partially constrained model: coefficient 1.07*** (0.22)
  - Predicted trade balance, unconstrained model: coefficient -0.09 (0.24)
  - Predicted trade balance, constrained model with NTMs: coefficient 1.06*** (0.22)
  - Observations: 15,876 for each specification
  - R-squared values: 0.235, 0.288, 0.269, 0.001, 0.295 respectively
  - R-squared, subsample of largest bilateral balances: 0.330, 0.357, 0.424, 0.003, 0.376 respectively
  - Robust standard errors in parentheses; significance indicators maintained (*** p<0.01, ** p<0.05, * p<0.1).

### Policy implication
- Given that macro factors (aggregate demand and supply) overwhelmingly drive changes in bilateral trade balances while bilateral trade-cost changes play only a minor role, bilateral trade balances are practically irrelevant for the conduct of macroeconomic policy; policymakers should primarily focus on aggregate macro determinants when assessing external balance dynamics.

*Source: 5. CONCLUSIONS (wpiea2020210-print-pdf).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020210-print-pdf.pdf_