## 1. The three components of product fragility

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---

### A. Presence of central players
- Definition and importance:
  - A product’s network may be dominated by a small number of central players whose output or trade position concentrates market power and creates single points of failure.
  - The presence of central players increases the potential for localized supply shocks to propagate globally through trade links.
- Analytical approach:
  - Network analysis is used to detect central players in the product-level trade network.
  - Measurement uses the standard deviation of weighted outdegree centrality for each product network.
  - Weighted outdegree centrality: ܥ_{i}^{k,out} = ∑_{j} (d_{ij} / ⟨d_{j}⟩).
  - Product risk from exporter concentration measured as std_{k} = sqrt( (1/n) ∑_{i} (ܥ_{i}^{k,out} - ܥ̄^{k,out})^2 ).
- Implication:
  - A higher standard deviation implies a greater tendency toward a star shape and higher potential risk.
- Notes and caveats:
  - Data are at 6-digit HS level; lack of more disaggregated information may underestimate the centrality component but detected 6-digit star-shaped networks effectively include star-shaped 10-digit networks.
  - Unweighted conceptual illustration: star-shape standard deviation = 0.45; fully connected standard deviation = 0.

### B. Tendency to cluster
- Definition and importance:
  - A product’s trade network may exhibit clustering where groups of countries are densely interconnected for that product.
  - Clustering creates regionalized or modular concentrations of production and trade; shocks within a cluster can cascade within the cluster and then transmit outward via inter-cluster links.
- Analytical approach and measurement:
  - Two characteristics combined: the weighted average local clustering coefficient and the network diameter.
  - Weighted local clustering coefficient (Barrat et al. (2004) extension) measures triangle-weight contributions; ranges 0 to 1.
  - Diameter = length of the shortest path between the most distant nodes (directed measure, not weighted).
  - Clustering metric = weighted average local clustering coefficient × network diameter.
  - Example: clustering coefficient = 1 and diameter = 12 yields tendency-to-cluster = 1x12 = 12 (scale capped by maximum parameter value).
- Implication:
  - High clustering raises the risk that localized shocks become concentrated and amplified before they reach other parts of the network.
- Notes:
  - Standard cluster-detection algorithms are not directly applicable to trade data; the chosen approach adapts cluster analysis characteristics suitable for trade networks.

### C. International substitutability
- Definition and importance:
  - International substitutability captures how easily buyers can switch among foreign suppliers of the same product.
  - Low international substitutability increases vulnerability because importers have limited alternative sources if a supplier is hit by a shock.
  - Conceptual basis: Armington (1969)—products differentiated by country of origin.
- Measurement and role:
  - Direct Armington elasticity data unavailable; proxy uses an indicator inspired by Revealed Factor Intensity (RFI).
  - Focus on the level and distribution of human capital of exporter countries for each product.
  - IS_{k} = sqrt( (1/n) ∑_{i} (H_{i}^{k} - Ḣ^{k})^2 ).
  - A wider distribution of exporter human capital implies more heterogeneous production methods, complicating international substitutability and increasing vulnerability.
- Implication:
  - Products with low international substitutability are more likely to cause supply disruptions to importers when exporters experience shocks.
- Supporting evidence:
  - Tanaka (2012) documents low substitutability for some Japanese auto parts after the 2011 earthquake; literature includes Aspalter (2016), Feenstra (2014), Saito (2004), Feenstra, Luck, Obstfeld, and Russ (2014).

### Empirical methodology and dataset
- Data sources and scope:
  - Detailed BACI bilateral trade data based on HS2002 classification at the 6-digit level for 2003-2014.
  - Initial universe: 5224 products and 223 countries and self-governed territories.
- Sample construction and exclusions:
  - Final goods and consumption goods (UN BEC) excluded to focus on products used by other industries.
  - HS2002 and HS2007 merged using correspondence tables; products with many-to-many or one-to-many matches excluded.
  - Two products referring to crude oil and refined oil dropped.
  - Products not reported in all years dropped.
  - Final sample after cleaning: 3578 products.
- Analytical focus:
  - Evaluate product-specific vulnerability using three components: (i) presence of central players; (ii) tendency to cluster; (iii) international substitutability.
  - Network analysis tools applied to each of the 3578 product-level networks to identify risky products, track top exporters and importers, and benchmark import-basket vulnerabilities across countries, country groups, and regions.
- Modeling assumption:
  - Analysis of localized supply shocks conducted assuming constant demand.

### Research contribution and applications
- Novelty:
  - First approach to identify risky products in global trade by examining network properties of individual goods at 6-digit HS level.
  - Extends literature on trade-network propagation of supply shocks by operating at detailed product level rather than only country-sector levels.
- Outputs and potential uses:
  - Identification of the most vulnerable products in global trade.
  - Tracking of top exporters and importers of risky products.
  - Benchmarking framework for countries’ import-basket vulnerabilities.
  - A new dataset for cross-country analysis of fragility and supply-shock spillover potential.

### Classification of overall product fragility
- Procedure:
  - Normalize the three components by calculating z-scores for each component, year, and product: z(Φ_{k,t}) = (Φ_{k,t} - Φ̄_{t}) / σ(Φ_{k,t}).
  - Apply k-median cluster analysis to standardized component scores to partition products into mutually exclusive groups.
  - A product is classified as risky if it scores high in each of the three components; one cluster (Group 4) emerges with high values for each component and is defined as risky.
- Usage:
  - Track importers’ and exporters’ exposure via the risky-product share of total imports or exports in a country’s trade basket.

---

### Key empirical results and findings

- Descriptive statistics (sample and classification):
  - Bilateral trade database, years 2003–2014, 223 countries and territories.
  - Products grouped into four risk levels; Group 4 is riskiest.
  - Over 2003-2014, an average of 655 products are classified in Group 4.
  - 421 products are consistently classified in Group 4 in each of the fourteen years of the sample.

- Composition of risky products (industry/HS comparisons, 2014):
  - Risky products mainly: Machinery and mechanical appliances (HS 84 and 85); Transport equipment (HS 87 and 88).
  - Other overrepresented sections in Group 4: pharmaceutical products (30), rubber articles (40), precision instruments (90).
  - By BEC:
    - Parts and accessories (P&A) of transport equipment: 3% of full sample, but 6% of risky products.
    - Processed industry category: ~60% of full sample but 37% of risky group.
  - By HS2002 2-digit:
    - Mechanical appliances and electrical equipment: ~17% of full sample, but >38% of risky group.
    - Precision and medical equipment: 4% of full sample, but 11% of risky products.

- Top risky import products (consistently classified as risky over 2003-2014; ranking by value of imports; Share Value of Imports preserved exactly):
  - 1847170 Storage units (of auto. data processing machines) — 0.964%
  - 2880330 Parts of aeroplanes/helicopters, other than propellers, rotors, under-carri ... — 0.761%
  - 3870829 Parts & accessories of bodies (incl. cabs) of the motor vehicles of 87.01-8 ... — 0.717%
  - 4300210 Antisera & oth. blood fractions & modified immunological prods., whether or ... — 0.671%
  - 5870421 Motor vehicles for the tpt. of gds. (excl. of 8704.10), with C-I int. comb. ... — 0.573%
  - 6848180 Taps, cocks, valves & sim. appls. for pipes/boiler shells/tanks/vats or the ... — 0.537%
  - 7850440 Static converters — 0.523%
  - 8841191 Parts of the turbo-jets/turbo-propellers of 8411.11-8411.22 — 0.470%
  - 9401110 New pneumatic tyres, of rubber, of a kind used on motor cars (incl. station ... — 0.463%
  - 10901890 Instruments & appls. used in medical/surgical/veterinary sciences, incl. ot ... — 0.455%

- Countries’ fragility and origins of risk (aggregate exposure and examples, 2014):
  - The group of products identified as risky comprises on average 25% of total imports (over the sample) with large variation by country.
  - High exposure importers (share of risky products in imports, 2014):
    - Chad — 43.4%
    - Republic of Congo — 39.4%
    - Gabon — 38.9%
    - Equatorial Guinea — 37.8%
    - Turkmenistan — 37.6%
  - Supply-chain participants with high shares (2014):
    - Mexico — 37%
    - Hungary — 36.2%
    - Romania — 34.2%
    - Slovakia — 34%
    - Czech Republic — 33.9%
    - Canada — 31.5%
    - Germany — 30.8%
    - Austria — 30.7%
  - Lowest exposure importers (2014):
    - Bahamas — 7.9%
    - Liberia — 9.8%
    - Somalia — 12.7%
    - Cyprus — 13%
  - Major economies with low shares (2014):
    - India — 13.2%
    - Japan — 16.6%
    - Korea — 17.6%
    - China — 21.2%
  - The U.S. (24.9%), France (27.4%), and U.K. (23.9%) import baskets are near the mean (2014).

- Concentration of exporters of risky products (2014):
  - G8 countries export 59.7% of the total world exports of risky products.
  - Shares of world exports of fragile products:
    - U.S.: 13.1%
    - Germany: 13%
    - Japan: 8.6%
    - China: 7.9%
  - Other notable exporters (2014):
    - Mexico: approximately 3%
    - Korea: 2.4%
    - Austria: 1.6%
    - Switzerland: 1.6%
    - Malaysia: 1.5%
    - Thailand: 1.2%
  - African exporters of risky products (combined): South Africa, Egypt, Tunisia, and Morocco export less than one percent of the world’s risky products.

---

### Validation: case studies and cross-country regression evidence

- Validation approaches:
  1. Case studies testing the index’s predictive power one year before disaster:
     - 2011 Japanese earthquake and nuclear disaster (March 11, 2011).
     - 2011 Thailand floods (2011 monsoon season).
  2. Cross-country regression analysis estimating impact on exports of importing risky products from a country suffering a disaster.

- Case study A — 2011 Japanese earthquake:
  - Event details and impacts:
    - Date: March 11, 2011; magnitude 9.0; human toll: more than 21,000 killed and injured in total; physical damage: 125,000 buildings totally collapsed and over one million damaged; manufacturing facilities damaged in three prefectures; 2011 GDP growth figures 2 percentage points below March 2011 forecast.
  - Selected affected products and observations:
    - Diesel engines: exports decreased by nearly 20% in 2011; example of importer (USA) importing 46% of diesel engines from Japan and imported 2.8 billion US of diesel engines (2010).
    - Capacitors and resistors: prices increased after the earthquake; production of electronics and automotive parts slowed.
    - LCD screens: affected but not categorized as high-risk by the methodology.
  - Table 2 selected entries (standardized component z-scores preserved in source):
    - HS2002 8408904 — Combustion Engines # Other engines — Risk category in 2010: 1; z-score Comp. 1: 1.39; z-score Comp. 2: 0.95; z-score Comp. 3: 1.68.
    - HS2002 8532294 — Electrical Capacitors # Other — Risk category in 2010: 0.89; z-score Comp. 1: 0.74; z-score Comp. 2: 0.32.
    - HS2002 9013803 — LCDs # Other devices, appliances and instruments — Risk category in 2010: 1.09; z-score Comp. 1: 1.10; z-score Comp. 2: -0.79.

- Case study B — 2011 Thailand floods:
  - Event details and impacts:
    - Flooded 65 of 77 provinces; human toll: more than 815 deaths; property damage: 45 billion USD.
    - Hard disk drives, semiconductors, and pick-up trucks were affected; hard disk drives exports fell, prices almost doubled and remained elevated for two years.
    - Semiconductors and integrated circuits: production suspension slowed other countries’ production that use semiconductors as intermediate inputs.
    - Selected products exported by Thailand in 2010 were categorized in the highest risk group one year before the event.

- Cross-country regression hypothesis:
  - Hypothesis: the more a country imports risky goods from a partner suffering a disaster, the more substantial the impact on the importing country’s exports.
- Regression specification and data:
  - Within-group (fixed effects) estimation at country-year level, 2003-2014.
  - Dependent variable: growth of exports’ volumes of country i in period t.
  - Key regressors: ln(REER) (i,t-1); Total exports (i,t-1); Risky Imports (RM) (i,t-1); Imports from an Impacted Country (MIC) (i,t-1); Risky Imports from Impacted Country (RMIC) (i,t-1).
  - Large disasters: EM-DAT; disasters defined as large if damage in the 90th percentile by damage as a share of GDP; 112 such events during 2004-2014.
  - Outlier handling: drop symmetrically 1% of distribution.
- Key regression results (Table 4 summary; coefficients preserved exactly):
  - Risky imports (RM) (i,t-1):
    - Column (1): -0.216 (s.e. 0.185)
    - Column (2): -0.208 (s.e. 0.189)
  - Imports from an impacted country (MIC) (i,t-1):
    - Column (1): 0.175 (s.e. 0.139)
    - Column (2): 0.198 (s.e. 0.146)
  - Risky Imports from impacted country (RMIC) (i,t-1):
    - Column (1): -0.655 (s.e. 0.438)
    - Column (2): -0.751* (s.e. 0.453)  [asterisk preserved]
  - Controls:
    - ln(REER) (i,t-1): Column (1): -0.128 (s.e. 0.114); Column (2): -0.133 (s.e. 0.119).
    - Total exports (i,t-1): Column (1): -0.000** (s.e. 0.000); Column (2): -0.000* (s.e. 0.000).
  - Model fit and sample:
    - Observations: Column (1): 1,725; Column (2): 1,625.
    - R-squared: Column (1): 0.325; Column (2): 0.317.
    - Number of countries: 169. Year fixed effects: Y.
    - Column (2) excludes observations when disaster in (t-1).
  - Magnitude interpretation reported in text:
    - "A 1% increase in imports of risky products from a country suffering a natural disaster is associated with a 0.7% decrease in exports the year of the event."
    - Note: this 0.7% figure corresponds to the combined effect of coefficients associated with RMIC, RM, and MIC from Table 4, column (1).
- Robustness and additional tests (Annex III / Table A3):
  - RMIC coefficients across alternative specifications (selected exact values preserved):
    - -0.914*, -1.019**, -0.883*, -0.990**, -0.643, -0.731, -0.649, -0.741, -0.644, -0.743 (standard errors reported in source).
  - Interpretation notes (verbatim preserved):
    - "Note that the coefficient associated with risky imports from impacted countries in column (6) to (12) are statistically significant at 15%."
    - "From column (1) to (10), the coefficient associated to the share of total imports that are risky and importing from a country suffering a disaster is consistently negative and always statistically significant with a 15% confidence interval."
    - "It is also remarkable that the share of total imports that are risky is never statistically significant, while the total imports from an impacted country is in general not statistically significant, and when it is (from column 1 to 4) the coefficient is inferior clearly inferior to the share of risky imports from impacted country."
    - "Also, all the regressions control for the REER. The coefficient associated is consistently negative."
    - "Columns (9) and (10) control for REER and the ratio of exports to GDP. The higher the relative importance of exports in the economy, the worse the impact on exports."

- Interpretation and limitations:
  - Estimated effects likely a lower bound because:
    - Effects measured on total exports, not total production.
    - Some negative supply shock effects may be absorbed via domestic input-output adjustments and demand adjustments (demand assumed constant).
    - Use of annual trade-flow data may dilute shocks concentrated in one or two quarters.

---

### Policy implications and suggested applications
- Suggested applications:
  - (i) as a vigilance tool,
  - (ii) to evaluate spillovers,
  - (iii) to assess policies.
- Additional uses and extensions:
  - Supplement country-level share with information on main exporters of risky products and domestic economic structure.
  - Assess potential global or country-specific impacts of natural disasters or political shocks; visualize via maps and network graphs.
  - Expand sample to all goods to evaluate impacts on consumer goods and raw materials prices—important for low income countries and island countries.
  - Extensions: cross-country business-cycle analysis with localized supply shocks; interaction with global value chains; analysis of permanent supply shocks (technological progress); apply methodology to trade in services, FDI, financial instruments; micro-level firm or industry interconnections (input-output tables).
- Mitigation approaches:
  - Macroeconomic policies that change properties of export-import matrices (in- and out-degrees, exposure to central players, clustering).
  - Diversification of suppliers for risky products where imports are highly concentrated.
  - Insurance mechanisms or policy instruments to mitigate domestic risk from trade in risky goods.
  - Building strategic physical reserves of certain risky products (at country or firm level).
  - Trade regulations (for example, tax incentives) and trade promotion agencies to mitigate market volatility while ensuring sufficient supply.

*Source: IMF working paper section “1. The three components of product fragility” (pdf wp1730).*

### 1. The three components of product fragility ......................................................................... 8

### 1. The three components of product fragility

### A. Presence of central players
- Definition and importance:
  - A product’s network may be dominated by a small number of central players whose output or trade position concentrates market power and creates single points of failure.
  - The presence of central players increases the potential for localized supply shocks to propagate globally through trade links.
- Analytical approach:
  - Network analysis is used to detect central players in the product-level trade network (see Fig. 1 for detection methodology).
- Implication:
  - Products with central players are identified as more vulnerable because shocks to those central nodes can generate large spillovers.

### B. Tendency to cluster
- Definition and importance:
  - A product’s trade network may exhibit clustering where groups of countries are densely interconnected for that product.
  - Clustering creates regionalized or modular concentrations of production and trade; shocks within a cluster can cascade within the cluster and then transmit outward via inter-cluster links.
- Analytical approach:
  - Network metrics such as the clustering coefficient are applied to product networks to detect and quantify tendency to cluster (see Fig. 2 for detection methodology).
- Implication:
  - High clustering raises the risk that localized shocks become concentrated and amplified before they reach other parts of the network.

### C. International substitutability
- Definition and importance:
  - International substitutability captures how easily buyers can switch among foreign suppliers of the same product.
  - Low international substitutability increases vulnerability because importers have limited alternative sources if a supplier is hit by a shock.
- Measurement and role:
  - The methodology incorporates measures of substitutability at the product level to assess how constrained importers are in finding alternative suppliers.
- Implication:
  - Products with low international substitutability are more likely to cause supply disruptions to importers when exporters experience shocks.

### Empirical methodology and dataset
- Data sources and scope:
  - Detailed BACI bilateral trade data based on the harmonized system 2002 (HS2002) classification at the 6-digit level for the period 2003-2014.
  - Initial universe: 5224 products and 223 countries and self-governed territories in the database.
- Sample construction and exclusions:
  - Final goods and consumption goods, defined using the UN BEC classification, are excluded to focus on products used by other industries and with potential for negative spillovers.
  - HS2002 and HS2007 classifications are merged using correspondence tables; products with many-to-many or one-to-many matches are excluded.
  - Two products referring to crude oil and refined oil are dropped.
  - Products not reported in all years of the sample are dropped.
  - Final sample after cleaning: 3578 products.
- Analytical focus:
  - The methodology evaluates product-specific vulnerability to potential supply shocks using three components: (i) presence of central players; (ii) tendency to cluster; and (iii) international substitutability.
  - Network analysis tools are applied to each of the 3578 product-level networks to identify risky products, track top exporters and importers of these products, and benchmark import-basket vulnerabilities across countries, country groups, and regions.
- Modeling assumption:
  - Analysis of localized supply shocks is conducted assuming constant demand (see footnote noting this assumption and that simultaneous demand and supply adjustments can complicate propagation analysis).

### Research contribution and applications
- Novelty:
  - First approach to identify risky products in global trade by examining network properties of individual goods (presence of central players, clustering tendency, and low international substitutability).
  - Extends the literature on trade-network propagation of supply shocks by operating at the detailed product (6-digit HS) level rather than only at country-sector levels.
- Outputs and potential uses:
  - Identification of the most vulnerable products in global trade.
  - Tracking of top exporters and importers of risky products.
  - Benchmarking framework for countries’ import-basket vulnerabilities.
  - A new dataset for cross-country analysis of fragility and supply-shock spillover potential.

*Source: IMF working paper section “1. The three components of product fragility” (pdf wp1730).*

### 1. The Three Components of Product Fragility

### 1. The Three Components of Product Fragility

### A. Presence of Central Players
- Definition and rationale:
  - The presence of central players in the network of traded goods increases the extent to which microeconomic shocks explain aggregate fluctuations (reference to Gabaix (2011)).
  - Star-shaped trade networks (few central exporters) are riskier for importers than fully connected networks.
- Measurement:
  - Use the standard deviation of weighted outdegree centrality for each product network.
  - Weighted outdegree centrality measures the intensity of a country’s exports as a share of the total value of its partners’ imports of the product (see Annex IA).
  - A higher standard deviation implies a greater tendency toward a star shape and higher potential risk.
- Notes and caveats:
  - Data are at 6-digit HS level; lack of more disaggregated information (for example, HS 10-digit or firm level) may underestimate the centrality component but detected 6-digit star-shaped networks effectively include star-shaped 10-digit networks.
  - An unweighted conceptual illustration: Panel A (star-shape) standard deviation = 0.45; Panel B (fully connected) standard deviation = 0.

### B. Tendency to Cluster
- Definition and rationale:
  - Risk increases when groups of countries cluster—trade more among themselves than with the rest of the world—because a destabilized cluster has fewer nearby alternative suppliers.
- Measurement:
  - Two characteristics combined: the weighted average local clustering coefficient and the network diameter (see Annex IB).
  - The clustering metric = weighted average local clustering coefficient × network diameter.
  - The weighted average local clustering coefficient ranges from 0 to 1; the diameter is the maximum number of steps separating the two most distant countries.
  - Example: A network with clustering coefficient = 1 and diameter = 12 yields a tendency-to-cluster measure = 1x12=12 (scale capped by the maximum parameter value).
- Notes:
  - Standard cluster-detection algorithms are not directly applicable to trade data; the chosen approach adapts cluster analysis characteristics suitable for trade networks.

### C. International Substitutability
- Definition and rationale:
  - Based on Armington (1969): products are differentiated by country of origin; spillovers depend on availability of substitutes.
  - Low substitutability means a temporary supply shock to major suppliers affects all users.
- Measurement (proxy):
  - Direct Armington elasticity data are unavailable; proxy uses an indicator inspired by Revealed Factor Intensity (RFI) from Shirotori, Tumurchudur, and Cadot (2010).
  - Focus on the level and distribution of human capital of exporter countries for each product.
  - A wider distribution of exporter human capital implies more heterogeneous production methods, complicating international substitutability and increasing vulnerability.
- Supporting references and examples:
  - Tanaka (2012) documents low substitutability for some Japanese auto parts leading to global supply-chain disruptions after the 2011 earthquake in Japan.
  - Literature on Armington elasticity estimates includes Aspalter (2016), Feenstra (2014), Saito (2004), and Feenstra, Luck, Obstfeld, and Russ (2014).

### 2. Classifying Overall Product Fragility
- Classification approach:
  - A product is classified as risky if it scores high in each of the three components (Presence of Central Players; Tendency to Cluster; International Substitutability).
  - Cluster analysis (the k-median procedure) is applied to standardized component scores to group products into risk categories.
  - From the partition exercise, one cluster emerges with high values for each component; this cluster is defined as risky.
- Usage:
  - After categorization, importers’ and exporters’ exposure can be tracked via the risky-product share of total imports or exports in a country’s trade basket.

### IV. RESULTS AND ANALYSIS

### 1. Descriptive Statistics
- Sample and procedure:
  - Bilateral trade database, years 2003–2014, for 223 countries and territories.
  - Products grouped into four levels of risk (see Annex II Table A.1.; group 4 is the riskiest).
- Aggregate findings:
  - Over 2003-2014, an average of 655 products are classified in Group 4.
  - 421 products are consistently classified in Group 4 in each of the fourteen years of the sample.
- Product composition of risky group:
  - Risky products mainly belong to:
    - Machinery and mechanical appliances (HS codes starting with 84 and 85).
    - Transport equipment (HS codes starting with 87 and 88).
  - Other overrepresented sections in Group 4: pharmaceutical products (30), rubber articles (40), and precision instruments (90).
- Table 1 — Top 10 Risky Import Products by their Value in Trade (consistently classified as risky over 2003-2014; ranking by value of imports; Share Value of Imports preserved exactly):
  - HS2002_6d Product Description — Share Value of Imports
  - 1847170 Storage units (of auto. data processing machines) — 0.964%
  - 2880330 Parts of aeroplanes/helicopters, other than propellers, rotors, under-carri ... — 0.761%
  - 3870829 Parts & accessories of bodies (incl. cabs) of the motor vehicles of 87.01-8 ... — 0.717%
  - 4300210 Antisera & oth. blood fractions & modified immunological prods., whether or ... — 0.671%
  - 5870421 Motor vehicles for the tpt. of gds. (excl. of 8704.10), with C-I int. comb. ... — 0.573%
  - 6848180 Taps, cocks, valves & sim. appls. for pipes/boiler shells/tanks/vats or the ... — 0.537%
  - 7850440 Static converters — 0.523%
  - 8841191 Parts of the turbo-jets/turbo-propellers of 8411.11-8411.22 — 0.470%
  - 9401110 New pneumatic tyres, of rubber, of a kind used on motor cars (incl. station ... — 0.463%
  - 10901890 Instruments & appls. used in medical/surgical/veterinary sciences, incl. ot ... — 0.455%
- Industry and HS-section comparisons (2014):
  - By Broad Economic Categories (BEC):
    - Processed industrial supply and capital goods are most represented in global trade overall.
    - Parts and accessories (P&A) of transport equipment: 3% of products in the full sample, but 6% of the risky products.
    - Processed industry category: ~60% of the full sample but only 37% of the risky group.
  - By HS 2002 2-digit section:
    - Mechanical appliances and electrical equipment: ~17% of the full sample, but more than 38% of the risky group.
    - Precision and medical equipment: 4% of the full sample, but 11% of the risky products group.

### 2. Countries’ Fragility and Origins of Risk
- Aggregate exposure:
  - The group of products identified as risky comprises on average 25% of total imports (over the sample) with large variation by country.
- High exposure importers (2014 shares of risky products in imports):
  - Chad — 43.4%
  - Republic of Congo — 39.4%
  - Gabon — 38.9%
  - Equatorial Guinea — 37.8%
  - Turkmenistan — 37.6%
  - Interpretation: Many high-share countries have limited domestic economic diversification and are dependent on foreign supply of goods.
- Supply-chain participants with high shares (2014):
  - Mexico — 37%
  - Hungary — 36.2%
  - Romania — 34.2%
  - Slovakia — 34%
  - Czech Republic — 33.9%
  - Canada — 31.5%
  - Germany — 30.8%
  - Austria — 30.7%
  - Interpretation: These countries import raw materials and intermediates, add domestic value, and export assembled/final products—vulnerable to spillovers affecting labor supply or transmitting disruptions through the trade network.
- Lowest exposure importers (2014):
  - Bahamas — 7.9%
  - Liberia — 9.8%
  - Somalia — 12.7%
  - Cyprus — 13%
  - Major economies with low shares:
    - India — 13.2%
    - Japan — 16.6%
    - Korea — 17.6%
    - China — 21.2%

*Source: wp1730 - 1. The Three Components of Product Fragility (IMF PDF chapter).*

### 2014. The U.S. (24.9%), France (27.4%), and U.K. (23.9%) import baskets are near the mean.

### wp1730 - 2014. The U.S. (24.9%), France (27.4%), and U.K. (23.9%) import baskets are near the mean.

### Concentration of exporters of risky (fragile) products
- Exporters of fragile products are highly concentrated.
- G8 countries export 59.7% of the total world exports of risky products.
- Shares of world exports of fragile products (2014):
  - U.S.: 13.1%
  - Germany: 13%
  - Japan: 8.6%
  - China: 7.9%
- Other notable exporters (2014):
  - Mexico: approximately 3% of the world’s risky goods
  - Korea: 2.4%
  - Austria: 1.6%
  - Switzerland: 1.6%
  - Malaysia: 1.5%
  - Thailand: 1.2%
- African continent representation among risky product exporters is limited to South Africa, Egypt, Tunisia, and Morocco, which combined export less than one percent of the world’s risky products.
- Many countries involved in international supply chains and highly specialized production are exporters of products exhibiting the identified risky characteristics.

### Risk transmission mechanism: producers as origins of supply shocks
- Producers of fragile products can serve as origins of risk when domestic production of exports is severely constrained.
- A temporary domestic shock (political events or natural disasters) can be transmitted to other countries through trade of risky products.
- Importer concentration examples (2014):
  - U.S. import share of fragile products: 24.9%
  - France import share of fragile products: 27.4%
  - U.K. import share of fragile products: 23.9%

### Validation of methodology: case studies and regression approach
- Two complementary validation approaches:
  1. Case studies of two events to test predictive power of the index one year before a disaster:
     - 2011 Japanese earthquake and nuclear disaster
     - 2011 Thailand floods
  2. Cross-country regression analysis estimating impact on exports (as proxy for production impact) of importing risky products from a country suffering a disaster.

- Case study A — 2011 Japanese Earthquake and Nuclear Disaster:
  - Event details:
    - Date: March 11, 2011
    - Magnitude: 9.0 earthquake, 70 km off eastern coast of Japan
    - Human toll: more than 21,000 people killed and injured in total
    - Physical damage: 125,000 buildings totally collapsed and over one million damaged
    - Manufacturing facilities damaged or destroyed in three prefectures
    - Economic toll: 2011 GDP growth figures 2 percentage points below their March 2011 forecast
  - Affected products identified in literature and matched to data:
    - Diesel engines, power supply and aluminum capacitors, LCD screens used in TV sets, notebook computers, smartphones, and tablets.
  - Table 2 summary (selected risky products exported by Japan in 2010):
    - HS2002 8408904 — Combustion Engines # Other engines (includes diesel engines)
      - Risk category in 2010: 1
      - z-score Comp. 1: 1.39
      - z-score Comp. 2: 0.95
      - z-score Comp. 3: 1.68
    - HS2002 8532294 — Electrical Capacitors # Other (includes power supply capacitors and aluminium capacitors)
      - Risk category in 2010: 0.89
      - z-score Comp. 1: 0.74
      - z-score Comp. 2: 0.32
    - HS2002 9013803 — LCDs # Other devices, appliances and instruments (includes LCD screens in TV sets, notebook computers, smartphones, and tablets)
      - Risk category in 2010: 1.09
      - z-score Comp. 1: 1.10
      - z-score Comp. 2: -0.79
  - Observed impacts:
    - Exports of diesel engines by Japan decreased by nearly 20 percent in 2011.
    - Example: a major French automobile manufacturer delayed the launch of two car models and had to source from another supplier.
    - Diesel engines categorized as risky: produced by “central players”, clustered in trade network, highly systemically relevant, not easily substitutable.
    - Network dynamics for diesel engines (product 840890): Japanese cluster disappears in 2011 and reappears in 2012 with a more connected network; 2010 example: USA imports 46% of diesel engines from Japan and imported 2.8 billion US of diesel engines.
    - Capacitors and resistors: critical inputs; prices increased after the earthquake and production of electronics and automotive parts slowed in importer countries.
    - LCD screens affected but not categorized as high-risk by the methodology.

- Case study B — 2011 Thailand Floods:
  - Event details:
    - 2011 monsoon season flooded 65 of Thailand’s 77 provinces
    - Human toll: more than 815 deaths
    - Property damage: 45 billion USD
    - Triggered by a tropical storm at the end of July; floodwaters reached Bangkok
  - Affected sectors and products:
    - Industrial estates and manufacturing facilities flooded, affecting production and exports.
    - Products with outsized consequences: hard disk drives, semiconductors, and pick-up trucks — all listed as risky by the methodology; two display all three risky characteristics.
  - Observed impacts:
    - Hard disk drives: Thailand is the world’s second largest producer; factory flooding led to decreased exports, prices almost doubled and remained elevated for two years, and slowed production of devices that use hard disk drives.
    - Semiconductors and integrated circuits: suspension of production slowed other countries’ production that use semiconductors as intermediate inputs. Thailand is a fairly central player for these exports and they register above average in three areas of trade risk.
  - Table 3 summary: Selected risky products exported by Thailand in 2010 are categorized in the highest risk group one year before the event; columns detail standardized values of each component.

*Source: authors calculation based on BACI database and Maplecroft data.*

### 2. Cross-Country Past Event Validity of the Index

### 2. Cross-Country Past Event Validity of the Index

### Hypothesis and Japan 2011 case study
- Hypothesis: the more a country imports risky goods from a partner suffering a disaster, the more substantial the impact on the importing country’s economy, particularly on export flows.
- Japan 2011 earthquake evidence:
  - Figure 8 Panel A: plots real export growth in 2011 (y-axis) against share of imports from Japan in 2010 (x-axis). Relation: slightly negative and non-statistically significant.
  - Figure 8 Panel B: plots real export growth in 2011 (y-axis) against share of imports of risky goods from Japan (x-axis). Relation: more negative and statistically significant.
  - Fitted-line equations reported:
    - Panel A: ݕൌെ50.4ߚെ22.2∗∗∗
    - Panel B: ݕൌെ129.5
      ∗∗
    ߚെ23.5
      ∗∗∗
  - Only countries for which Japan represents at least 2% of total imports are displayed.

### Regression specification and identification
- Estimation: within-group (fixed effects) estimation at country-year level for period 2003-2014.
- Dependent variable: growth of exports’ volumes of country i in period t (ܺ
෠
௜,௧).
- Key regressors and controls:
  - ln(REER) (i,t-1) — natural logarithm of the real effective exchange rate (controls for exchange-rate changes).
  - Total exports (i,t-1).
  - Risky Imports (RM) (i,t-1): share of total imports in t-1 of goods classified as risky.
  - Imports from an Impacted Country (MIC) (i,t-1): share of total imports in t-1 from countries suffering a disaster in t.
  - Risky Imports from Impacted Country (RMIC) (i,t-1): share of total imports in t-1 that are risky goods sourced from countries that suffer a large natural disaster in t.
  - Year fixed effects and country fixed effects; robust standard errors clustered at country level.
- Interpretation logic: importing goods classified as fragile has adverse effects only if supply is disrupted; therefore RMIC is the focal interaction.

### Data sources and definitions
- Total exports, total imports, GDP: IMF Balance of Payments Statistics (BOPS) database; adjusted to constant prices using data from U.S. Federal Reserve Bank of St. Louis FRED database.
- REER: World Bank, indexed to 2010.
- Product-level trade: BACI database used to construct country-level shares.
- Large natural disasters: EM-DAT database; disasters defined as large if damage is in the 90th percentile by damage as a share of GDP. There are 112 such events during 2004-2014.
- Outlier handling: drop symmetrically one percent of distribution to avoid unexpected events and/or data mistakes.

### Key regression results (Table 4 summary)
- Coefficients of interest (columns (1) and (2)):
  - Risky imports (RM) (i,t-1) as a share of total imports:
    - Column (1): -0.216 (standard error 0.185)
    - Column (2): -0.208 (standard error 0.189)
  - Imports from an impacted country (MIC) (i,t-1) as a share of total imports:
    - Column (1): 0.175 (standard error 0.139)
    - Column (2): 0.198 (standard error 0.146)
  - Risky Imports from impacted country (RMIC) (i,t-1) as a share of total imports:
    - Column (1): -0.655 (standard error 0.438)
    - Column (2): -0.751* (standard error 0.453)  [asterisk preserved as in source]
- Controls:
  - ln(REER) (i,t-1):
    - Column (1): -0.128 (standard error 0.114)
    - Column (2): -0.133 (standard error 0.119)
  - Total exports (i,t-1):
    - Column (1): -0.000** (standard error 0.000)
    - Column (2): -0.000* (standard error 0.000)
- Model fit and sample:
  - Observations:
    - Column (1): 1,725
    - Column (2): 1,625
  - R-squared:
    - Column (1): 0.325
    - Column (2): 0.317
  - Number of countries: 169
  - Year fixed effects: Y
  - Column (2) excludes observations when disaster in (t-1).
- Magnitude interpretation reported in text:
  - "A 1% increase in imports of risky products from a country suffering a natural disaster is associated with a 0.7% decrease in exports the year of the event."
  - Note: this 0.7% figure corresponds to the combined effect of coefficients associated with risky imports from impacted country, risky imports, and imports from impacted country from Table 4, column (1).

### Robustness and additional tests
- The coefficient on imports of fragile products from countries that do not suffer a natural disaster has no statistical significance.
- The share of total imports in t-1 from a country that suffers a disaster in t is not statistically significant.
- Annex III (Table A3) confirms results under alternative sets of controls.

### Interpretation and limitations
- Estimated effect likely a lower bound of total economic impact because:
  - Effects measured on total exports, not total production.
  - Some negative supply shock effects may be absorbed via domestic input-output adjustments and demand adjustments (demand assumed constant in model).
  - Use of annual trade-flow data may dilute shocks that are concentrated to one or two quarters.
- Evidence supports that supply disruptions of risky products transmit to measurable export declines.

### Conclusion and potential applications
- Network analysis of trade at high product disaggregation identifies "risky" products whose fragile supply networks imply higher vulnerability to shocks.
- Country-level measure (share of risky products in import basket) can assess potential spillovers from importing specific goods from specific countries.
- Suggested applications:
  - (i) as a vigilance tool,
  - (ii) as a tool to evaluate spillovers,
  - (iii) to assess policies.
- Additional uses:
  - Supplement country-level share with information on main exporters of risky products and domestic economic structure.
  - Assess potential global or country-specific impacts of natural disasters or political shocks; visualize via maps and network graphs.
  - Expand sample to all goods to evaluate impacts on consumer goods and raw materials prices—important for low income countries and island countries.
  - Extensions: cross-country business-cycle analysis with localized supply shocks; interaction with global value chains; analysis of permanent supply shocks (technological progress); apply methodology to trade in services, FDI, financial instruments; micro-level firm or industry interconnections (input-output tables).

### Policy implications
- Better monitoring and more-detailed data improve understanding of global trade system risks.
- Mitigation approaches include:
  - Macroeconomic policies that change properties of export-import matrices (in- and out-degrees, exposure to central players, clustering).
  - Diversification of suppliers for risky products where imports are highly concentrated.
  - Insurance mechanisms or policy instruments to mitigate domestic risk from trade in risky goods.
  - Building strategic physical reserves of certain risky products (at country or firm level).
  - Trade regulations (for example, tax incentives) and trade promotion agencies to mitigate market volatility while ensuring sufficient supply.

*Italic source: IMF Working Paper — "2. Cross-Country Past Event Validity of the Index" (wp1730 - section content).*

### Annex I. Technical Details on the Definition of Components and the Overall Product

### Annex I. Technical Details on the Definition of Components and the Overall Product

### Fragility Measure — Overview
- Methodology explores the trade network of individual goods using exporter–importer pairs and annual export values.  
- Countries = nodes; exports = directed ties.  
- Three network-analysis components defined and used to assess product fragility: A. Outdegree Centrality, B. Tendency to Cluster, C. International Substitutability.  
- Products are classified by riskiness by normalizing the three components (z-scores) and applying k-median cluster analysis to partition products into mutually exclusive groups.

### A. Outdegree Centrality
- Purpose: identify influential exporters and concentration risk from a few very central exporters.  
- Weighted outdegree centrality for country i in product network k:
  - ܥ_{i}^{k,out} = ∑_{j} (d_{ij} / ⟨d_{j}⟩)  (as defined following Barrat et al. (2004) in the source)
  - where n = total number of nodes, d_{ij} = value of exports of country i to country j, and ⟨d_{j}⟩ = average value of j’s imports for that product.
- ⟨d_{j}⟩ defined as: ⟨d_{j}⟩ = ∑_{i} d_{ij} / k_{j}, where k_{j} is the number of nodes j imports from.
- Product risk from exporter concentration measured as the standard deviation of outdegree centrality:
  - std_{k} = sqrt( (1/n) ∑_{i} (ܥ_{i}^{k,out} - ܥ̄^{k,out})^2 )
  - where ܥ̄^{k,out} is the average centrality of countries for product k.

### B. Tendency to Cluster
- Uses two complementary measures to capture clustering properties of product trade networks.

B.1. Weighted average of local clustering coefficient
- Based on the local clustering coefficient (Watts and Strogatz (1998)) with weighted extension per Barrat et al. (2004).
- Weighted local clustering coefficient for node i:
  - C_{i}^{w} = (1 / (k_{i} (k_{i}-1))) ∑_{j,ℓ} (1/⟨d_{i}⟩) d_{ij} d_{iℓ}  / (w_{ij} w_{iℓ} w_{jℓ})  (formula as given in source)
  - where k_{i} is the number of nodes connected to i, d_{ij} is value of tie between i and j, and ⟨d_{i}⟩ = ∑_{j} w_{ij} / k_{i}.
- Direction of ties is taken into account in this measure.
- Interpretation: weighted local clustering calculates the contribution of each triangle, weighted by the arithmetic average of the two adjacent ties, to the average weight of all connections of node i.

B.2. Diameter
- Diameter = length of the shortest path between the most distant nodes (the longest geodesic path).
- Measures number of steps necessary for a node to reach the furthest node.
- Directed measure (direction of ties matters) but not weighted.

B.3. Value of the component
- The tendency-to-cluster component value for product k equals:
  - Component_{k}^{cluster} = weighted average of local cluster coefficient and diameter (as assembled in the source).

### C. International Substitutability
- Measures dispersion of human capital levels among exporters of a good.
- Formulation (standard deviation of human capital across exporters for product k):
  - IS_{k} = sqrt( (1/n) ∑_{i} (H_{i}^{k} - Ḣ^{k})^2 )
  - where H_{i}^{k} is level of human capital of country i exporting product k.
- Interpretation: wider distribution of exporter human capital makes it more difficult for an importer to find a substitute supplier matching its standard.

### D. Classifying Overall Product Fragility
- Normalize the three components by calculating z-scores for each component, year, and product:
  - z(Φ_{k,t}) = (Φ_{k,t} - Φ̄_{t}) / σ(Φ_{k,t})
  - where Φ_{k,t} is raw score for component Φ, product k, year t; Φ̄_{t} is average across products in year t; σ(Φ_{k,t}) is standard deviation of raw scores.
- Cluster analysis: k-median procedure partitions products into mutually exclusive groups using standardized scores for the three components, iterating to minimize:
  - ∑_{c} ∑_{k in c} |X_{k} - median_{c}|
  - where X_{k} is the vector of component z-scores for product k and median_{c} is the cluster median.
- After categorization, track importers and exporters of risky products by computing the risky-product share of total imports or exports in a country’s trade basket.

---

### Annex II. Descriptive Statistics

### A. Frequency of Products
- Table A1 reports number of products in each risk group over time (Group 4 = riskiest).  
- Note from source: "On average across years, 655 products are categorized in the riskier group (Group 4)."  
- Products unassigned by the algorithm are shown as "non-classified" in the original table.

### B. List of Risky Products (100 Most Traded Risky Products During 2003-2014)
- Notes: Products are considered risky if they constantly are classified in Group 4 during 2003-2014. Products are sorted by their relative importance in world trade between 2003-2014.
- Extracted examples with HS2002_6d, Product Description, and Share Value of Imports:
  - 1847170 — Storage units (of auto. data processing machines) — 0.964%
  - 2880330 — Parts of aeroplanes/helicopters, other than propellers, rotors, under-carri ... — 0.761%
  - 3870829 — Parts & accessories of bodies (incl. cabs) of the motor vehicles of 87.01-8 ... — 0.717%
  - 4300210 — Antisera & oth. blood fractions & modified immunological prods., whether or ... — 0.671%
  - 5870421 — Motor vehicles for the tpt. of gds. (excl. of 8704.10), with C-I int. comb. ... — 0.573%
  - 6848180 — Taps, cocks, valves & sim. appls. for pipes/boiler shells/tanks/vats or the ... — 0.537%
  - 7850440 — Static converters — 0.523%
  - 8841191 — Parts of the turbo-jets/turbo-propellers of 8411.11-8411.22 — 0.470%
  - 9401110 — New pneumatic tyres, of rubber, of a kind used on motor cars (incl. station ... — 0.463%
  - 10901890 — Instruments & appls. used in medical/surgical/veterinary sciences, incl. ot ... — 0.455%
  - 11853400 — Printed circuits — 0.445%
  - 12854140 — Photosensitive semiconductor devices, incl. photovoltaic cells whether or n ... — 0.443%
  - 13732690 — Articles of iron/steel, n.e.s. — 0.423%
  - 14853710 — Boards, panels, consoles, desks, cabinets & oth. bases, equipped with 2/mor ... — 0.413%
  - 15840734 — Spark ignition recip. piston engines of a kind used for the propulsion of v ... — 0.399%
  - 16853690 — Electrical app. for switching/protecting electrical circuits,/for making co ... — 0.399%
  - 17840820 — Compression-ignition int. comb. piston engines (diesel/semi-diesel engines) ... — 0.392%
  - (List continues through 100 entries; selected entries shown above with exact shares preserved as in the source.)

---

### Annex III. Fragility Maps Over Time
- 1. Share of Total Imports of Fragile Products (maps for 2003, 2009, 2013)
  - Note in source: "Over time, the share of imports of risky products have increased in Latin America, Russia and Australia, and decreased in Europe and East Asia."
- 2. Share of World Exports of Fragile Products (maps for 2003, 2009, 2013)
  - Note in source: "Regions exporting risky goods are stable over time, and have become more concentrated in recent years."

---

### Annex IV. Robustness Check

### Table A3 — Complementary Regressions to Table 4 (Summary of key results)
- Dependent variable: country’s annual export growth in t. Estimations use within-estimators regression. Robust standard errors in parentheses. Significance levels: *** p<0.01, ** p<0.05, * p<0.1.
- Key variables and representative coefficients (exact values preserved from source columns (1)–(10)):
  - Risky imports (RM) (i,t-1) as a share of total imports:
    - coefficients: -0.205, -0.195, -0.183, -0.176, -0.224, -0.217, -0.204, -0.199, -0.287, -0.282
    - standard errors: (0.185), (0.189), (0.188), (0.192), (0.184), (0.188), (0.185), (0.189), (0.175), (0.178)
  - Imports from an impacted country (MIC) (i,t-1) as a share of total imports:
    - coefficients: 0.265*, 0.295*, 0.244*, 0.273*, 0.183, 0.206, 0.174, 0.196, 0.164, 0.187
    - standard errors: (0.149), (0.158), (0.146), (0.154), (0.141), (0.147), (0.139), (0.146), (0.138), (0.145)
  - Risky Imports from impacted country (RMIC) (i,t-1) as a share of total imports:
    - coefficients: -0.914*, -1.019**, -0.883*, -0.990**, -0.643, -0.731, -0.649, -0.741, -0.644, -0.743
    - standard errors: (0.476), (0.495), (0.462), (0.481), (0.444), (0.459), (0.438), (0.453), (0.439), (0.454)
  - ln(REER) (i,t-1):
    - coefficients: -0.123, -0.131, -0.140, -0.146, -0.114, -0.121, -0.130, -0.136, -0.120, -0.124
    - standard errors: (0.122), (0.128), (0.117), (0.122), (0.119), (0.125), (0.114), (0.119), (0.113), (0.118)
  - Volume of exports growth (i,t-1):
    - coefficients in relevant columns: -0.017, -0.016, -0.013, -0.012
    - standard errors: (0.012), (0.011), (0.012), (0.011)
  - Imports as a share of GDP (i,t-1):
    - coefficients in relevant columns: 0.151, 0.143, 0.131, 0.122
    - standard errors: (0.133), (0.141), (0.127), (0.134)
  - Exports as a share of GDP (i,t-1):
    - coefficients: -0.000**, -0.000**
    - standard errors: (0.000), (0.000)
- Additional regression details preserved from source:
  - Observations by column: 1,688; 1,588; 1,701; 1,601; 1,712; 1,612; 1,725; 1,625; 1,718; 1,619.
  - R-squared by column: 0.335; 0.326; 0.333; 0.324; 0.325; 0.316; 0.323; 0.315; 0.326; 0.317.
  - Number of countries: 169 (for all columns).
  - Year fixed effects: included (as indicated in source).
  - Odd columns include full sample; even columns exclude observations of countries suffering a shock.
  - Regression type: within-estimators. Clustered standard errors at country-level.
- Interpretative notes from source (verbatim content preserved):
  - "Note that the coefficient associated with risky imports from impacted countries in column (6) to (12) are statistically significant at 15%."
  - "From column (1) to (10), the coefficient associated to the share of total imports that are risky and importing from a country suffering a disaster is consistently negative and always statistically significant with a 15% confidence interval."
  - "It is also remarkable that the share of total imports that are risky is never statistically significant, while the total imports from an impacted country is in general not statistically significant, and when it is (from column 1 to 4) the coefficient is inferior clearly inferior to the share of risky imports from impacted country."
  - "Also, all the regressions control for the REER. The coefficient associated is consistently negative."
  - "Columns (9) and (10) control for REER and the ratio of exports to GDP. The higher the relative importance of exports in the economy, the worse the impact on exports."

*Source: wp1730 - Annex I. Technical Details on the Definition of Components and the Overall Product*

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_Source: https://www.imf.org/-/media/files/publications/wp/wp1730.pdf_