## 5.1 Methodology, machine learning models, and choice of variables

## Source details

**Canonical URL:** [5.1 Methodology, machine learning models, and choice of variables](https://www.imf.org/-/media/files/publications/wp/2026/english/wpiea2026002-source-pdf.pdf)

## Other formats

- [Markdown version](/-/media/files/publications/wp/2026/english/wpiea2026002-source-pdf.pdf.md)
- [Structured JSON version](/-/media/files/publications/wp/2026/english/wpiea2026002-source-pdf.pdf.json)

---

### 5.1.a. Machine learning models — approach and interpretability
- Purpose:
  - Apply a machine learning (ML) approach to identify drivers of GVC participation and integration for both global and intra-EU linkages.
  - Report associations (not causal relationships); causal ML methods are not applied.
- Rationale for ML:
  - Capture intricate, nonlinear interactions and relax strong parametric restrictions of traditional econometrics.
  - Handle multicollinearity and overfitting in high-dimensional datasets.
- Algorithms applied (six):
  - Linear regression
  - Elastic Net Regression
  - Support Vector Regression (SVR)
  - Random Forest Regression
  - Extreme Gradient Boosting (XGBoost)
  - K-Nearest Neighbors (KNN)
- Interpretability:
  - SHAP values computed to estimate each feature’s contribution to predictions.
  - SHAP decomposition: Prediction = Baseline (average prediction) + ∑ SHAP values of all predictors.
  - SHAP values normalized by expressing each as a percentage of the absolute value of the sum of all SHAP values for that model.
  - Additional interpretability tools discussed: Permutation feature importance, Partial Dependence Plots (PDP), LIME.
  - SHAP implementation uses Kernel SHapley Additive exPlanations approximating Shapley values with perturbed samples and linear-proxy regressions.
  - Desired SHAP properties listed: Efficiency, Symmetry, Dummy, Additivity.
- Caveats:
  - Analysis reports associations rather than causal effects.

### 5.1.b. Variables included
- Primary trade and value-added measures:
  - OECD Trade in Value Added (TiVA) decomposition of gross trade flows into domestic and foreign value-added components, with sectoral breakdowns.
  - Forward linkages: the share of a country’s value added in other countries’ exports (role as upstream supplier).
  - Backward linkages: the share of foreign value added in the country’s own exports (reliance on imported intermediates).
  - Economic complexity (Hausmann et al., 2013).
  - Share of exports by technology intensity using Eurostat product-level gross exports (high-technology exports per Eurostat definition include pharmaceuticals, computers, electronic and optical products, and the manufacture of air and spacecraft).
- Complementary explanatory variables / drivers (sources):
  - Eurostat variables, World Bank World Development Indicators, Worldwide Governance Indicators, OECD indicators, Economic complexity data from Hausmann et al. (2013).
- Grouping of determinants:
  - Technical factors: infrastructure (length of railway and road infrastructure per square meter of country territory), OECD Index of Digital Trade Integration and Openness (INDIGO).
  - Structural drivers: unit labor cost (wages-to-labor productivity ratio or compensation of employees divided by real GDP), labor productivity (real GDP divided by total hour worked), share of employed individuals with educational attainment below upper secondary level, share of manufacturing in GDP.
  - Policy determinants: Economic freedom index (Fraser Institute) and its subcomponents.

### 5.1.c. Panel, data coverage, and preprocessing
- Main dataset:
  - OECD TiVA constructed from Inter-Country Input–Output (ICIO) tables covering 76 countries and 45 industries over the period 1995–2022.
  - Caveat: TiVA data has a lag and does not provide information beyond 2022.
- Supplementary sources: Eurostat, World Bank WDI, Worldwide Governance Indicators, OECD.
- Analytical scope:
  - Panel country-industry-time analysis across 1995–2022 covering manufacturing and services; enables decomposition into domestic and foreign value-added and measurement of forward/backward linkages for ML outcomes.
- Data preparation and model setup:
  - Panel dataset for all EU countries with country fixed effects.
  - Outcome variables (four): Global value chains (GVC, sum of backward and forward linkages), Value-added chains within EU, Global GVC for goods, Global GVC for services.
  - Explanatory variables expressed as a percentage of their EU average to highlight country-specific dynamics.
  - Data centered and standardized prior to ML.
  - Unit labor costs and labor productivity taken with a lag of one year to mitigate simultaneity.
  - Fixed effects included for each EU country and a dummy for the global financial and COVID-19 crises.
- Annex references:
  - Annex I: ML model application details.
  - Annex II: ML models forecasting performance.

### Key aggregate finding from ML analysis
- Labor productivity and costs and human capital are the strongest and most consistent drivers of both global and intra-EU integration in GVCs.
- Infrastructure, manufacturing depth, governance quality, and digital readiness also play important supportive roles.

---

### 5.2 Results from ML analysis

### 5.2.a. Global GVC vs. EU (intra-EU) GVC integration — primary correlates
- Global GVC participation key correlates:
  - Economic structure, unit labor cost, and quality of human capital.
  - Infrastructure quality (land transport) and labor productivity have high positive associations.
  - Institutional quality and cost competitiveness contribute moderately but positively.
  - INDIGO index and Fraser Institute Economic Freedom Index have positive SHAP values.
  - Global financial crisis and COVID-19 crisis contributed marginally negatively.
- Within the EU:
  - Labor productivity is the dominant associated variable, surpassing manufacturing share.
  - Manufacturing share remains important, followed by institutional quality, infrastructure, and cost competitiveness.
  - Low educational attainment and high unit labor cost constrain EU-scale participation.

### 5.2.b. Goods GVCs vs. Services GVCs — distinct correlates
- Commonality:
  - Both goods and services value chains depend on high institutional capacity.
- Goods GVCs:
  - Strongly benefit from manufacturing share (robust industrial base).
  - Productivity is the second largest positive correlate.
  - High labor costs become less relevant; estimated positive effect of unit labor cost on goods GVCs could reflect automation or technological upgrading.
- Services GVCs:
  - Labor productivity is the strongest positive correlate.
  - High labor costs have a significant negative impact on services GVC integration.
- Economic structure:
  - Highly correlated with both types—positively for goods and negatively for services.

### 5.2.c. Forward linkages vs. Backward linkages
- Forward linkages:
  - Favor economies with high productivity, strong manufacturing, and good institutions.
  - INDIGO and Fraser Institute Freedom indices exert moderate positive influence.
  - High labor costs and skill shortages undermine competitiveness in supplying intermediates.
  - Land transport has a less relevant but negative effect (forward linkages may rely more on air and maritime transport).
- Backward linkages:
  - Highly correlated with land transport and institutional quality.
  - Economies with strong domestic production and high productivity tend to have lower dependence on foreign inputs (negative signs for labor productivity and manufacturing share may indicate domestic supply capacity reduces backward dependence).
  - Institutional and digital capacity exert a moderate but positive effect.
  - Low skill level and high labor costs constrain backward linkages.

---

### Annex I — ML setup and validation (summary)
- Data split: Training subsample: 75 percent; Testing subsample: 25 percent.
- Hyperparameter optimization: cross-validated grid search with k-fold cross validation.
- Performance metrics on test set: Coefficient of determination (R²), Mean squared error (MSE), Diebold-Mariano test (modified by Harvey, Leybourne and Newbold 1997).
- ML methods: Linear model, Elastic Net, Support Vector Regression, Random Forest Regression, Extreme Gradient Boosting (XGBoost), K-Nearest Neighbors (kNN).
- Interpretability: Permutation feature importance, PDP, LIME, SHAP (Kernel SHAP).

---

### Annex II — Forecasting performance (selected test-set MSE and R2)
- General conclusion: All models perform similarly; k-Nearest Neighbors, Support Vector Machine, and Random Forest do slightly better than the rest.
- Selected entries (MSE and R2 on test subsample):

  - Global value chains:
    - Linear regression: MSE 0.07  R2 0.92
    - Elastic net: MSE 0.07  R2 0.92
    - k-Nearest Neighbors: MSE 0.05  R2 0.95
    - Support vector machine: MSE 0.05  R2 0.95
    - Random forest: MSE 0.03  R2 0.96
    - Extreme gradient boosting: MSE 0.05  R2 0.95

  - European value chains:
    - Linear regression: MSE 0.04  R2 0.96
    - Elastic net: MSE 0.04  R2 0.96
    - k-Nearest Neighbors: MSE 0.02  R2 0.98
    - Support vector machine: MSE 0.02  R2 0.98
    - Random forest: MSE 0.02  R2 0.97
    - Extreme gradient boosting: MSE 0.04  R2 0.95

  - Global value chains in goods:
    - Linear regression: MSE 0.07  R2 0.94
    - k-Nearest Neighbors: MSE 0.03  R2 0.97
    - Support vector machine: MSE 0.03  R2 0.97
    - Random forest: MSE 0.03  R2 0.97
    - Extreme gradient boosting: MSE 0.04  R2 0.97

  - Global value chains in services:
    - Linear regression: MSE 0.07  R2 0.92
    - k-Nearest Neighbors: MSE 0.05  R2 0.95
    - Support vector machine: MSE 0.05  R2 0.94
    - Random forest: MSE 0.05  R2 0.95
    - Extreme gradient boosting: MSE 0.07  R2 0.93

  - Forward linkages:
    - Linear regression: MSE 0.07  R2 0.94
    - k-Nearest Neighbors: MSE 0.04  R2 0.96
    - Support vector machine: MSE 0.04  R2 0.96
    - Random forest: MSE 0.04  R2 0.96
    - Extreme gradient boosting: MSE 0.05  R2 0.95

  - Backward linkages:
    - Linear regression: MSE 0.07  R2 0.93
    - k-Nearest Neighbors: MSE 0.04  R2 0.96
    - Support vector machine: MSE 0.04  R2 0.96
    - Random forest: MSE 0.03  R2 0.97
    - Extreme gradient boosting: MSE 0.06  R2 0.94

- Modified Diebold-Mariano test summary:
  - k-Nearest Neighbors and Support Vector Machine have statistically significant better forecasting performance than several other models.
  - Random forest performs better than extreme gradient boosting in multiple comparisons.
  - Linear regression and elastic net generally exhibit slightly worse statistics than the remaining models, but excluding them from SHAP recalculation did not yield conceptually different results.
  - Significance notation: *p<0.1; **p<0.05; ***p<0.01

---

### 6.1 Portugal — exports, GVC integration, and drivers

### 6.1.a Exports — structure and destinations
- Structural shifts:
  - Gradual transformation: business services growing, manufacturing declining in relative importance.
  - Exports concentrated in manufacturing and business services; other sectors (mining and agriculture) make up less than 10 percent.
- Manufacturing composition:
  - Pharmaceuticals share has grown; textiles declined sharply.
- Business services composition:
  - Trade and food services (tourism) largest components but shares have fallen.
  - Information, professional and scientific services have gained prominence from a small base.
- Destination shares (2022):
  - EU: about half of Portugal’s gross exports.
  - United Kingdom: about 7 percent.
  - United States: about 10 percent.
  - Exports to China: small but growing.
- Technology intensity and complexity:
  - Large share from low- and medium-low-technology products.
  - High-technology contribution modest; high-technology exports have persistently lagged the EU average with limited convergence.
  - Portugal’s economic complexity remains among the lowest in Europe alongside Greece and Cyprus.
- Services:
  - Share of tourism higher than EU average.
  - Share of knowledge-intensive services lower than EU average; declined since 2009 and has since stagnated.

### 6.1.b Integration in GVCs — opportunities and risks
- Integration pattern:
  - Portugal lags in global value chain integration, especially in forward linkages.
  - Forward linkages converged toward EU average until 2007 then stagnated.
  - Backward linkages broadly in line with or slightly above EU average.
  - Portugal more integrated as a downstream importer of intermediates than as an upstream supplier.
- Decomposition of forward linkages gap:
  - Sectoral composition effect accounts for 90 percent of Portugal’s forward linkages gap relative to other EU countries.
  - Interpretation: weaker forward integration largely reflects export mix (smaller shares in high-forward-linkage sectors like IT services; larger shares in low-forward-linkage sectors like tourism).
- Exposure and vulnerabilities:
  - Foreign value-added accounts for roughly 30 percent of Portugal’s gross exports.
  - Limited forward linkages reduce exposure to external demand shocks (smaller value-added contribution to other countries’ exports).
  - Example: limited direct and indirect reliance on U.S. demand implies U.S.–EU trade frictions would likely have a more muted impact on Portugal than on peers.
- Policy implication:
  - Measures to enhance upstream integration and strengthen domestic value creation would help Portugal reap more of GVC benefits.

### 6.1.c Drivers of GVC integrations for Portugal
- Institutional and factor positioning:
  - Relatively good institutional framework and higher-than-average economic freedom index.
  - Lags in labor productivity and human capital education level:
    - Much lower labor productivity relative to peers.
    - Higher share of employment with lower than upper secondary education.
- Implications:
  - Lower labor productivity and lower quality of labor force could constrain movement into knowledge-intensive segments and risk lock-in to lower-value stages of production.

---

### 6.2 Belgium — exports, GVC integration, pharmaceutical sector, risks, drivers

### 6.2.a Exports — structure and destinations
- Structural shifts:
  - Transformation toward high value-added manufacturing and knowledge-intensive services.
  - Manufacturing and business services together account for more than 90 percent of total exports.
  - Agriculture, mining, construction, utilities marginal.
- Manufacturing composition:
  - Pharmaceuticals increased markedly and are a top export item.
  - Motor vehicles declined as a share.
  - Chemicals, petroleum products and metals remain strong contributors.
- Business services:
  - Professional and scientific services largest and rising component.
  - Finance and insurance and information services have grown.
  - Trade and food services declined in relative importance.
- Destinations:
  - Strong dependence on the European Union; share of EU27 destinations has gradually declined.
  - Modest increase in exports to the U.S. and other non-European partners (slow diversification).
  - U.S. exports concentrated in manufacturing (pharmaceuticals) and knowledge-intensive business services.

### 6.2.b Forward and backward linkages
- Belgium more integrated than EU average in both forward and backward linkages.
- Forward linkages rose steadily but declined during COVID, driven mainly by business services.
- Backward linkages picked up in 2021 and 2022, largely from manufacturing (pharmaceuticals, chemicals, petroleum).
- Value-added sources:
  - Exports rely mostly on domestic value added and inputs from the rest of the EU.
  - Shares of U.S., UK, China and other parts of the world steady.
  - In pharmaceuticals, foreign value added—particularly from the EU and the US—has grown alongside rising exports, with some recent reversal.

### 6.2.c The Pharmaceutical Industry — role and dynamics
- Rapid growth in exports and GVC integration over past decades.
- Source activities of value added in pharmaceuticals:
  - Manufacturing dominant contributor.
  - Business services grown steadily (R&D, marketing, knowledge-intensive activities).
  - Notable share of mining suggests some input ingredients are sourced abroad.
- U.S. linkages:
  - Manufacturing provides the backbone of U.S.-origin value added.
  - U.S. business services (research, licensing, IP) have gained significance.
- Belgium’s global position:
  - Rising share of value added in other countries’ exports has outpaced its share in total exports, indicating growing specialization and competitiveness in pharma.

### 6.2.d Risks for Belgium
- COVID-era dynamics reveal vulnerabilities from deep GVC integration:
  - Decline in forward linkages driven mainly by business services; pickup in backward linkages driven by manufacturing.
- Key vulnerabilities:
  - Dependence on foreign intermediates exposes production to supply-chain disruptions, logistics bottlenecks, or trade restrictions on inputs such as active pharmaceutical ingredients.
  - Strong forward linkages tie performance to external demand, making exports sensitive to partner slowdowns.
  - Sectoral concentration (pharmaceuticals and chemicals) could amplify macroeconomic impact of sector-specific shocks.
  - Growing reliance on the U.S. market, especially for pharmaceuticals, introduces risks from U.S. regulatory and pricing policies, patent cycles, and industrial strategy shifts.
  - Integration into global R&D and licensing networks exposes the sector to intellectual property and data-governance risks.
  - Geopolitical tensions and geoeconomic fragmentation heighten risks associated with reliance on globally connected industries.
- Operational dynamics:
  - Disruptions can quickly reduce demand for Belgian value added abroad while boosting imports of intermediate inputs, producing sharp swings in activity.

### 6.2.e Drivers of GVC integrations for Belgium
- Strengths:
  - High labor productivity and educated labor force.
  - Exceptional connectivity: densest land transport infrastructure in the EU and strategic geographic location.
  - Comparative advantage in knowledge-intensive stages of GVCs (pharmaceuticals, financial services).
- Constraints:
  - High unit labor cost limiting competitiveness in traditional manufacturing.
  - Low share of manufacturing in GDP could limit capitalization on GVC integration benefits.

### Conclusions and policy implications (Belgium in EU context)
- Core drivers of GVC integration: labor productivity, labor cost, economic structure, human capital quality; infrastructure, governance, and digital readiness also important.
- Belgium leverages logistics strength and specialization in high-value industries but faces risks from sectoral concentration and external demand shocks.
- Implied policy directions:
  - Preserve openness while managing vulnerabilities via diversification of products and destinations, strengthening innovation and human capital, and deepening EU single market and saving and investment union to promote resilience and efficient resource allocation.

---

*Source: IMF Working Paper — "The Integration of Global Value Chain in the EU: Stylized Facts and Drivers—With a Zoom on Belgium and Portugal" (sections 5.1–6.2; Annexes I–III summaries).*

### 5.1 Methodology, machine learning models, and choice of variables ____________________ 10

### 5.1 Methodology, machine learning models, and choice of variables

### 5.1.a. Machine learning models
- The paper applies a machine learning (ML) approach to identify the drivers of GVC participation and integration.
- ML models used in the analysis are applied to explain both global and intra-EU integration in GVCs.
- Key aggregate finding from the ML analysis reported in the paper:
  - Labor productivity and costs and human capital are the strongest and most consistent drivers of both global and intra-EU integration in GVCs.
  - Infrastructure, manufacturing depth, governance quality, and digital readiness also play important supportive roles.
- Annex I documents the application of machine learning models to the analysis of the drivers of GVC integration.
- Annex II reports machine learning models forecasting performance.

### 5.1.b. Variables included
- Primary trade and value-added measures:
  - OECD Trade in Value Added (TiVA) decomposition of gross trade flows into domestic and foreign value-added components, with sectoral breakdowns.
  - Forward linkages: the share of a country’s value added in other countries’ exports (role as upstream supplier).
  - Backward linkages: the share of foreign value added in the country’s own exports (reliance on imported intermediates).
  - Economic complexity (Hausmann et al., 2013) to measure diversity and uniqueness of export baskets.
  - Share of exports by technology intensity using Eurostat product-level gross exports (high-technology exports per Eurostat definition include pharmaceuticals, computers, electronic and optical products, and the manufacture of air and spacecraft).
- Complementary explanatory variables and drivers sourced from multiple databases:
  - Eurostat variables capturing drivers of GVC integration and export statistics.
  - World Bank World Development Indicators for macro and development indicators.
  - Worldwide Governance Indicators for institutional quality measures.
  - OECD indicators (including manufacturing depth and related measures).
  - Economic complexity data from Hausmann et al. (2013).
- The variables capture both manufacturing and services sectors, permitting analysis of goods and services value-chain integrations, forward vs. backward linkages, and intra-EU versus global linkages.

### 5.1.c. Panel and data coverage
- Main dataset:
  - OECD Trade in Value Added (TiVA).
  - TiVA is constructed from Inter-Country Input–Output (ICIO) tables covering 76 countries and 45 industries over the period 1995–2022.
  - Caveat: TiVA data has a lag and does not provide information beyond 2022.
- Supplementary data sources:
  - Eurostat for product-level gross exports, shares of exports by technology intensity, and additional variables capturing GVC drivers.
  - World Bank World Development Indicators for macroeconomic and development series.
  - Worldwide Governance Indicators for governance measures.
  - OECD for additional sectoral and structural indicators.
- Analytical scope:
  - The panel structure supports country-industry-time analysis across 1995–2022 covering manufacturing and services.
  - The dataset enables decomposition of exports into domestic and foreign value-added and the measurement of forward and backward linkages as outcomes for the ML models.

*Source: IMF Working Paper — "The Integration of Global Value Chain in the EU: Stylized Facts and Drivers—With a Zoom on Belgium and Portugal" (section 5.1; dataset and annex references).*

### 5.1 Methodology, machine learning models, and choice of variables

### 5.1 Methodology, machine learning models, and choice of variables

### 5.1.a. Machine learning models
- Rationale:
  - ML methods capture intricate data patterns and relax some assumptions of traditional econometrics, avoiding strong parametric restrictions on functional form and errors.
  - ML models can capture complex, nonlinear interactions between the dependent (outcome) variable and predictors (features), and some methods better handle multicollinearity and overfitting in high-dimensional datasets.
  - The analysis reports associations (not causal relationships) because causal ML methods are not applied.
- Interpretability approach:
  - SHAP values (based on Shapley values from coalition game theory) are computed to estimate the contribution of each feature to the prediction of the outcome variable.
  - Illustration for each observation:
    - Prediction of the outcome variable = Baseline (average prediction) + ∑ SHAP values of all predictors
  - SHAP values are normalized by expressing each as a percentage of the absolute value of the sum of all SHAP values for that model because SHAP ranges differ across models and depend on the scale of the output variable.
- Algorithms applied (six ML algorithms):
  - Linear regression: assumes linear relationships between variables.
  - Elastic Net Regression: incorporates regularization to address multicollinearity and enhances model sparsity.
  - Support Vector Regression (SVR): utilizes kernel methods to capture complex, non-linear relationships.
  - Random Forest Regression: aggregates multiple decision trees to improve predictive accuracy and reduce overfitting.
  - Extreme Gradient Boosting (XGBoost): sequentially builds trees to correct errors, optimizing both speed and performance.
  - K-Nearest Neighbors (KNN): predicts outcomes based on the proximity of similar observations.

### 5.1.b. Variables included
- Grouping of determinants: technical factors, structural drivers, and policy determinants.
- Technical factors (infrastructure, logistics, digital):
  - Infrastructure: length of railway and road infrastructure per square meter of country territory.
  - Digital infrastructure and uptake: OECD Index of Digital Trade Integration and Openness (INDIGO).
- Structural drivers (economic and labor market characteristics):
  - Unit labor cost: wages-to-labor productivity ratio, or alternatively, calculated as the compensation of employees divided by real GDP.
  - Labor productivity: calculated as real GDP divided by total hour worked.
  - Quality of labor force: share of employed individuals with educational attainment below upper secondary level (proxy for lower human capital quality).
  - Economic structure: share of manufacturing in GDP.
- Policy determinants:
  - Economic freedom index (Fraser Institute): includes four subcomponents—size of government, legal system and property rights, sound money, freedom to trade internationally, and regulation of labor, business and finance.

### 5.1.c. Panel (data preparation and model setup)
- Data scope: panel dataset for all EU countries with country fixed effects.
- Outcome variables (four):
  - Global value chains (GVC), measured as the sum of backward and forward linkages.
  - Value-added chains within EU.
  - Global GVC for goods.
  - Global GVC for services.
- Data transformations and preprocessing:
  - Each explanatory variable is expressed as a percentage of its EU average to highlight country-specific dynamics.
  - Data are centered and standardized prior to applying machine learning methods to mitigate scaling sensitivity and ensure comparability across variables.
  - Unit labor costs and labor productivity variables are taken with a lag of one year to remove simultaneity and thus mitigate possible endogeneity.
  - Fixed effects are included for each EU country and a dummy variable for the global financial and COVID-19 crises.

### 5.2 Results

#### 5.2.a. Global value-chain vs. EU value-chain integrations
- Key correlates for global GVC participation:
  - Economic structure, unit labor cost, and quality of human capital emerge as key correlates, implying importance of industrial capacity, cost competitiveness and skill adequacy.
  - Infrastructure quality (proxied by land transport) and labor productivity exhibit high positive associations.
  - Institutional quality and cost competitiveness contribute moderately but positively.
  - INDIGO index and Fraser Institute Economic Freedom Index have positive SHAP values, indicating that digital solutions and strong governance reduce uncertainty and foster investment.
  - The global financial crisis and the COVID-19 crisis contributed marginally negatively to GVC integrations.
- Within the EU:
  - Labor productivity emerges as the dominant factor, surpassing manufacturing share as the primary associated variable of GVC participation.
  - Manufacturing share remains important, followed by institutional quality, infrastructure, and cost competitiveness.
  - Low educational attainment and high unit labor cost constrain participation at EU scale.

#### 5.2.b. Goods value chain vs. service value chain integrations
- Commonality:
  - Both services and goods value chains depend on high institutional capacity.
- Goods GVCs:
  - Benefit strongly from a robust industrial base (manufacturing share).
  - Productivity is the second largest positive correlate for goods.
  - High labor costs become less relevant for goods GVC integration; estimated positive effect of unit labor cost on goods GVCs could reflect automation or technological upgrading in some sectors or EU economies.
- Services GVCs:
  - Reward productivity: labor productivity is the strongest positive correlate for services.
  - High labor costs maintain a significant negative impact on service GVC integration.
- Economic structure:
  - Highly correlated with both types of trade integration—positively for goods and negatively for services.

#### 5.2.c. Forward vs. backward linkages
- Forward linkages:
  - Favor economies with high productivity, strong manufacturing, and good institutions.
  - INDIGO and Fraser Institute Freedom indices exert moderate positive influence, suggesting governance and openness facilitate integration into upstream segments.
  - High labor costs and skill shortages undermine competitiveness in supplying intermediate goods.
  - Land transport has a less relevant but negative effect, possibly because forward linkages rely more on air and maritime transport than on roads and railways.
- Backward linkages:
  - Exhibit high correlation with land transport and institutional quality.
  - Economies with strong domestic production and high productivity tend to have lower dependence on foreign inputs (negative signs for labor productivity and manufacturing share may indicate domestic supply capacity reduces backward dependence).
  - Institutional and digital capacity exert a moderate but positive effect.
  - Low skill level and high labor costs constrain backward linkages.

*IMF Working Paper — 5.1 Methodology, machine learning models, and choice of variables (section content).*

### 6.1 Portugal

### 6.1 Portugal

### 6.1.a Exports
- Export structure has undergone a gradual transformation, similar to the overall EU trend, with business services growing in importance to the detriment of manufacturing.
- Exports are concentrated in manufacturing and business services, which together account for the majority of exports; other sectors, such as mining and agriculture, make up less than 10 percent.
- Within manufacturing:
  - The share of pharmaceutical goods has grown over time.
  - The share of textiles has declined sharply.
- Within business services:
  - Trade and food services remain the largest components, reflecting the importance of tourism, although their shares have fallen.
  - Information, and professional and scientific services have gained prominence, albeit from a small base.
- Destination shares:
  - The EU accounted for about half of Portugal’s gross exports in 2022.
  - The United Kingdom accounts for about 7 percent.
  - The United States accounts for about 10 percent.
  - Exports to China remain small but have grown in recent years.
- Technology intensity:
  - A large share of Portugal’s exports continues to come from low- and medium-low-technology products.
  - Contribution from high-technology sectors is modest.
  - The share of high-technology exports, such as pharmaceuticals, computers, and aerospace/spacecraft, has persistently lagged the EU average and shown limited convergence over time.
  - Portugal’s economic complexity remains among the lowest in Europe alongside Greece and Cyprus.
- Services composition:
  - The share of tourism in Portugal’s exports has been higher than the EU average.
  - The share of knowledge-intensive services has been lower than the EU average.
  - The share of knowledge-intensive services has declined since 2009 and has since stagnated.

### 6.1.b Integration in GVC, opportunities and risks
- Overall integration pattern:
  - Portugal’s integration in global value chain has been lagging, especially in forward linkages.
  - Forward linkages showed some convergence with the EU average (weighted by countries’ gross exports) until 2007 but have stagnated since.
  - Backward linkages have been broadly in line with, or slightly above, the EU average.
  - Portugal remains more integrated as a downstream importer of intermediates than as an upstream supplier within cross-border production networks.
- Policy implication:
  - Measures to enhancing upstream integration and strengthening domestic value creation would help Portugal reap more of GVC benefits.
- Decomposition of forward linkages gap:
  - Formula presented in source:
    푓푤푑
    퐸푈
    −푓푤푑
    푃푇
    =∑{훼
    푠
    퐸푈
    (
    푓푤푑
    푠
    퐸푈 
    −푓푤푑
    푠
    푃푇
    )
    +
    (
    훼
    푠
    퐸푈
    −훼
    푠
    푃푇
    )
    푓푤푑
    푠
    푃푇
    }
    푠
    .
  - Here, 훼s denotes gross export share of sector s, and 푓푤푑s represents value added exports in sector s that is reexported by other countries, divided by gross exports in sector s.
  - The first term represents the within-sector contribution, while the second term denotes contribution from sectoral composition.
  - For Portugal, the sectoral composition effect accounts for 90 percent of forward linkages gap relative to other EU countries.
  - Interpretation: much of Portugal’s weaker forward GVC integration reflects its export mix—smaller export shares in high-forward-linkage sectors (e.g., IT services) and larger shares in low-forward-linkage sectors (e.g., tourism-related services) compared to other EU countries.
- Benefits and vulnerabilities:
  - Foreign value-added accounts for roughly 30 percent of Portugal’s gross exports, implying disruptions in imported intermediate inputs could weigh on export performance.
  - Portugal’s limited forward linkages temper its exposure to external demand shocks: its value-added contribution to other countries’ exports is smaller than in most European economies.
  - Example: Portugal’s direct and indirect reliance on U.S. demand is limited, implying that trade frictions between the U.S. and the EU would likely have a more muted impact on Portugal than on its peers.

### 6.1.c Drivers of GVC integrations for Portugal
- Institutional and factor positioning:
  - Portugal benefits from a relatively good institutional framework.
  - Portugal has higher-than-average economic freedom index.
  - Portugal lags in labor productivity and human capital education level:
    - Much lower labor productivity relative to peers.
    - Higher share of employment with lower than upper secondary education.
- Implications:
  - Lower labor productivity and the quality of the labor force could potentially constrain the country’s ability to move into knowledge-intensive segments.
  - These constraints create risks for remaining locked into lower-value stages of production, where competitive pressures are high and margins are thin.

*IMF WORKING PAPERS The Integration of Global Value Chain in the EU: Stylized Facts and Drivers—With a Zoom on Belgium and Portugal — INTERNATIONAL MONETARY FUND*

### 6.2 Belgium

### 6.2 Belgium

### 6.2.a Exports
- Export structure has transformed toward high value-added manufacturing and knowledge-intensive services, similar to EU exports.
- Manufacturing and business services together account for more than 90 percent of total exports.
- Agriculture, mining, construction, and utilities remain marginal.
- Within manufacturing:
  - Pharmaceuticals have increased markedly and are one of Belgium’s largest export items.
  - Motor vehicles have declined as a share of total exports.
  - Chemicals remain a strong and stable contributor, alongside petroleum products and metals.
- Within business services:
  - Professional and scientific services are the largest and rising component.
  - Finance and insurance and information services have grown in importance.
  - Trade and food services have seen gradual declines in relative importance.
- Export destinations and composition:
  - Strong dependence on the European Union; the share of EU27 destinations has gradually declined.
  - Modest increase in exports directed to the U.S. and other non-European partners, indicating slow diversification away from intra-EU trade.
  - Exports to the U.S. are tilted toward manufacturing (notably pharmaceuticals) and knowledge-intensive business services (professional and scientific services).
  - The U.S. market is a growing but still secondary destination, with a sectoral profile more concentrated in pharmaceutical products and professional services.

### 6.2.b Forward and backward linkages
- Belgium exhibits consistently stronger global value chain (GVC) integration than the EU average, both through forward and backward linkages.
- Forward linkages:
  - Have risen steadily over time, underscoring Belgium’s role as a supplier of intermediates in international production networks.
  - Experienced a recent decline during the COVID period, driven mainly by business services (professional and scientific activities, and information sector).
- Backward linkages:
  - Reflect reliance on imported inputs for export industries, with a significant pickup in 2021 and 2022.
  - The pickup stems largely from manufacturing, especially pharmaceuticals, chemicals, and petroleum.
- Value-added sources:
  - Exports rely mostly on domestic value added and inputs from the rest of the EU.
  - Shares of the U.S., UK, China and other parts of the world have remained steady.
  - In pharmaceuticals, foreign value added—particularly from the EU and the US—has grown alongside rising exports, with some recent reversal.
  - Petroleum products draw on a diversified set of foreign inputs.
  - Motor vehicles receive a small but increasing contribution from China and the rest of the world.

### 6.2.c The Pharmaceutical Industry
- Rapid growth in exports and GVC integration over past decades.
- Source activities of value added in pharmaceuticals:
  - Manufacturing has long been the dominant contributor.
  - Business services have grown steadily, highlighting rising importance of R&D, marketing, and other knowledge-intensive activities sourced from abroad.
  - Notable share of mining suggests some input ingredients are sourced abroad.
- U.S. linkages:
  - Manufacturing provides the backbone of U.S.-origin value added.
  - Business services from the U.S. (research, licensing, intellectual property) have gained significance.
- Belgium’s global position:
  - Rising share of value added in other countries’ exports has outpaced its share in total exports, indicating growing specialization and competitiveness of the Belgian pharma sector relative to other industries.

### 6.2.d Risks for Belgium
- COVID-era evolution of forward and backward linkages highlights vulnerabilities from deep GVC integration:
  - Decline in forward linkages driven mainly by business services, possibly reflecting lower downstream demand from foreign industries, tax system effects on special purpose entities, or other factors.
  - Pickup in backward linkages driven by manufacturing (pharmaceuticals, chemicals, petroleum), reflecting greater reliance on foreign intermediates.
- Key vulnerabilities:
  - Dependence on foreign intermediates leaves production exposed to supply-chain disruptions, logistics bottlenecks, or trade restrictions on key inputs such as active pharmaceutical ingredients.
  - Strong forward linkages tie performance closely to external demand, making exports sensitive to slowdowns in partner countries.
  - Sectoral concentration (pharmaceuticals and chemicals) could amplify macroeconomic impact of sector-specific shocks or policy changes.
  - Growing reliance on the U.S. market, especially for pharmaceuticals, introduces risks from shifting U.S. regulatory and pricing policies, patent cycles, and industrial strategy shifts.
  - Integration into global R&D and licensing networks exposes the sector to intellectual property and data-governance risks; strict compliance requirements can trigger sudden production disruptions.
  - Rising geopolitical tensions and geoeconomic fragmentation (including U.S.–EU trade frictions, competition for strategic technologies, and security concerns in medical supply chains) heighten risks associated with reliance on globally connected industries.
- Operational dynamics:
  - Disruptions (e.g., pandemic) can quickly reduce demand for Belgian value added abroad while boosting imports of related intermediate inputs, leading to sudden and sharp swings in economic activities.

### 6.2.e Drivers of GVC integrations for Belgium
- Primary strengths:
  - High labor productivity and educated labor.
  - Exceptional connectivity: densest land transport infrastructure in the EU and strategic geographical location.
  - Comparative advantage in knowledge-intensive stages of GVCs (pharmaceuticals, financial services).
- Constraints and limits:
  - High unit labor cost limits competitiveness in traditional manufacturing segments.
  - Low share of manufacturing in GDP could prevent full capitalization on GVC integration benefits.

### Conclusions (Belgium in the EU context)
- GVC integration is driven by labor productivity, labor cost, economic structure, and human capital quality; infrastructure, governance, and digital readiness also matter.
- Belgium is highly integrated both upstream and downstream, leveraging logistics strength and specialization in high-value industries, but faces risks from sectoral concentration and external demand shocks.
- Policy implications (implied by analysis):
  - Preserve gains from openness while managing vulnerabilities through diversification of products and destinations, strengthening innovation and human capital, and deepening EU single market and saving and investment union to promote resilience and efficient resource allocation.

*Source: IMF Working Paper chapter 6.2 — Belgium*

### References

### References and Annexes (wpiea2026002-source-pdf - References)

### Key bibliographic sources
- Selected works cited (authors and topics include): Amador & Cabral (Global Value Chains drivers and measures); Antràs (De-Globalization?); Baldwin (Information Technology and New Globalization); Bonadio et al. (Global Supply Chains in the Pandemic); Constantinescu, Mattoo & Ruta (Global Trade Slowdown); Criscuolo & Timmis (GVCs and Productivity); Hummels et al. (Wage Effects of Offshoring); Ignatenko, Raei, & Mircheva (GVC participation benefits); Taglioni & Winkler (Making GVCs Work for Development); Timmer et al. (Slicing Up Global Value Chains); World Bank (World Development Report 2020: Trading for Development in the Age of Global Value Chains); International Monetary Fund (2023) (Geoeconomic Fragmentation and the Future of Multilateralism).
- Methodology and machine-learning interpretability references include: Diebold & Mariano (1995); Harvey, Leybourne & Newbold (1997); Lundberg & Lee (2017); Ward (1963).

### Annex I — Machine learning model setup and validation
- Data split:
  - Training subsample: 75 percent
  - Testing subsample: 25 percent
- Hyperparameter optimization: cross-validated grid search with k-fold cross validation.
- Performance metrics used on test set:
  - Coefficient of determination (R²)
  - Mean squared error (MSE)
  - Diebold-Mariano test (modified by Harvey, Leybourne and Newbold 1997)
- Machine learning methods applied:
  - Linear model
  - Elastic Net
  - Support Vector Regression
  - Random Forest Regression
  - Extreme Gradient Boosting (XGBoost)
  - K-Nearest Neighbors (kNN)
- Interpretability methods discussed:
  - Permutation feature importance
  - Partial Dependence Plots (PDP)
  - Local Interpretable Model-agnostic Explanations (LIME)
  - SHapley Additive exPlanations (SHAP)
- SHAP implementation details:
  - Uses Shapley-value concept: estimates expected marginal contribution of each feature and averages contributions across all possible feature combinations.
  - Kernel SHapley Additive exPlanations used to approximate Shapley values by generating perturbed samples, replacing omitted features with expected values, and training a linear regression whose coefficients are proxies for Shapley values.
- Desired SHAP properties explicitly listed:
  - Efficiency
  - Symmetry
  - Dummy
  - Additivity

### Annex II — Forecasting performance (summary of results)
- General conclusion: All models perform similarly in forecasting accuracy; k-Nearest Neighbors, Support Vector Machine, and Random Forest do slightly better than the rest.
- Table 1 (Machine learning models’ forecasting statistics) — selected entries (MSE and R2 on test subsample):
  - Global value chains:
    - Linear regression: MSE 0.07  R2 0.92
    - Elastic net: MSE 0.07  R2 0.92
    - k-Nearest Neighbors: MSE 0.05  R2 0.95
    - Support vector machine: MSE 0.05  R2 0.95
    - Random forest: MSE 0.03  R2 0.96
    - Extreme gradient boosting: MSE 0.05  R2 0.95
  - European value chains:
    - Linear regression: MSE 0.04  R2 0.96
    - Elastic net: MSE 0.04  R2 0.96
    - k-Nearest Neighbors: MSE 0.02  R2 0.98
    - Support vector machine: MSE 0.02  R2 0.98
    - Random forest: MSE 0.02  R2 0.97
    - Extreme gradient boosting: MSE 0.04  R2 0.95
  - Global value chains in goods:
    - Linear regression: MSE 0.07  R2 0.94
    - k-Nearest Neighbors: MSE 0.03  R2 0.97
    - Support vector machine: MSE 0.03  R2 0.97
    - Random forest: MSE 0.03  R2 0.97
    - Extreme gradient boosting: MSE 0.04  R2 0.97
  - Global value chains in services:
    - Linear regression: MSE 0.07  R2 0.92
    - k-Nearest Neighbors: MSE 0.05  R2 0.95
    - Support vector machine: MSE 0.05  R2 0.94
    - Random forest: MSE 0.05  R2 0.95
    - Extreme gradient boosting: MSE 0.07  R2 0.93
  - Forward linkages:
    - Linear regression: MSE 0.07  R2 0.94
    - k-Nearest Neighbors: MSE 0.04  R2 0.96
    - Support vector machine: MSE 0.04  R2 0.96
    - Random forest: MSE 0.04  R2 0.96
    - Extreme gradient boosting: MSE 0.05  R2 0.95
  - Backward linkages:
    - Linear regression: MSE 0.07  R2 0.93
    - k-Nearest Neighbors: MSE 0.04  R2 0.96
    - Support vector machine: MSE 0.04  R2 0.96
    - Random forest: MSE 0.03  R2 0.97
    - Extreme gradient boosting: MSE 0.06  R2 0.94

- Modified Diebold-Mariano test (Table 2) — summary of inferences:
  - The modified Diebold-Mariano test confirms that k-Nearest Neighbors and Support Vector Machine have statistically significant better forecasting performance than several other models.
  - Random forest performs better than extreme gradient boosting in multiple comparisons.
  - Linear regression and elastic net generally exhibit slightly worse statistics than the remaining models, but excluding them from SHAP recalculation did not yield conceptually different results.

- Significance notation used in Table 2:
  - *p<0.1; **p<0.05; ***p<0.01
  - Note: A positive sign of the statistics indicates that the model in the column performs better than the model in the row.

### Annex III — Cluster analysis of EU member states on GVC drivers
- Data preparation:
  - Data centralized and standardized; average values computed for the 2010-2022 period.
- Clustering method:
  - Ward’s method for hierarchical clustering (Ward 1963) using Euclidean distance.
- Resulting clusters (three clusters identified):
  - Advanced economies, Estonia and Latvia
  - Southeastern European Economies: Bulgaria, Romania, Croatia and Cyprus
  - Central European Economies: Lithuania, Italy and Greece
- Characterization of clusters:
  - Cluster 1 (Advanced economies, Estonia and Latvia): integration into GVCs primarily through efficiency and institutional quality rather than manufacturing intensity; high labor productivity, good infrastructure, strong governance; constraints in cost competitiveness and educational attainment; less manufacturing-oriented.
  - Cluster 2 (Southeastern European Economies): transitional economies with balanced but modest drivers and limited specialization; lower wages offset by low productivity; reliance on incremental improvements in productivity and governance to deepen GVC participation.
  - Cluster 3 (Central European Economies): leverage manufacturing intensity, educational and infrastructural strength and favorable labor costs; weaknesses in governance and labor productivity constrain movement into higher-value GVC segments.

### Visuals and rankings (as presented)
- A series of ranked charts provided (variables listed and ordering preserved):
  - Unit labor cost: rank from Estonia through Ireland (visualized scale 0.2–0.7)
  - Labor productivity: rank from Ireland through Bulgaria (scale 0–100)
  - Employed with lower than upper secondary education: rank from Netherlands through Slovakia (scale 0–50)
  - Manufacturing (% GDP): rank from Ireland through Luxembourg (scale 0–40)
  - Economic Freedom Index: scale shown 6.6–8.0 with country ordering from Ireland through Croatia
  - Land transport: country ordering from Malta through Bulgaria (scale 0–1)
  - INDIGO index: country ordering from France through Cyprus (scale 0.05–0.25)

*The Integration of Global Value Chain in the EU: Stylized Facts and Drivers—With a Zoom on Belgium and Portugal. Working Paper No. WP/2026/002*

---


_Source: https://www.imf.org/-/media/files/publications/wp/2026/english/wpiea2026002-source-pdf.pdf_