## Annex I. Adjusting for Two-Way Containerized Trade (Netting Effect)

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### Problem statement: netting effect in containership AIS data
- Containerships often load and unload cargo simultaneously during a port call, so AIS-based estimates observe only the net change in a vessel’s draft.
- This "netting effect" can lead AIS-derived shipment estimates to understate the true level of containerized trade for ports where two-way containerized activity is common.
- Vessels most impacted are those that simultaneously load and unload cargo during port calls; this behavior is most characteristic of containerships.
- Analytical implication: with two-way trade AIS provides two observable quantities (a, b) but three unknowns (x, y, z), producing an underdetermined system unless an additional equation is supplied.

### Adjustment approaches (overview)
- Two complementary approaches are outlined:
  - Simple approach using official container throughput data to complement AIS data and estimate the netting effect.
  - Bootstrapping technique usable when container throughput data are absent.

### Implementation and coverage (high level)
- The simple (throughput-based) approach is implemented for 83 of the largest container ports in the world.
- These 83 ports make up about two-thirds of global containerized trade.
- Based on this adjustment, container trade volume estimates for those ports move closer to official data.

### Validation example (Rotterdam)
- Adjusted container trade volume (inflow and outflow) for Rotterdam, 2019-24, is closer to the official series than the unadjusted AIS-based series.
- The source compares Unadjusted, Adjusted, and Official series in million metric tons for 2019-24.

### Role within PortWatch enhancements
- The netting adjustment is one enhancement among:
  - Ballast water adjustments (Annex II) to avoid overstating cargo volumes when ships carry ballast water.
  - Expanded port coverage (from 1378 to 1666 ports globally).
  - Refinements to historical averaging for incomplete draft data (probability-weighted averages and grouping by vessel type when vessel-specific history is unavailable).

### Approach #1 — Netting adjustment using official (container throughput) data
- Key idea: use container throughput c = x + y reported by port or national authorities to convert the 2×3 problem into a 3×3 system.
- System of equations:
  - a = x + z (A1.1)
  - b = y + z (A1.2)
  - c = x + y (A1.3)
- Closed-form solution:
  - x = (a – b + c) / 2 (A1.4)
  - y = (b – a + c) / 2 (A1.5)
  - z = (a + b – c) / 2 (A1.6)
- Numerical example:
  - If a = 10, b = 15, c = 8 (metric tons), then x = 1.5, y = 6.5, z = 8.5 (metric tons).
- Implementation details:
  - Applied to 83 largest container ports covering about two-thirds of global container trade.
  - Throughput data are expressed in metric tons or TEUs. Primary use: metric tons.
  - TEU-to-metric-ton conversion factor: 12 metric tons/TEU (global average).
  - Where container throughput data are lagging, a three-year historical average of the scaling factor for the respective month is used.
- Empirical outcome:
  - The adjusted AIS-derived series are much closer to official data in levels and trends (examples include Busan, Rotterdam, Santos).

### Approach #2 — Netting adjustment using a bootstrapping approach
- Key idea: model the observed distribution of payload changes at a port as the difference (convolution) of two distributions: one for loading (exports) and one for unloading (imports).
- Calibration example (Los Angeles-Long Beach):
  - Simulate 100,000 draws from two normal distributions calibrated for LA-LB:
    - Imports: mean = -26% and standard deviation = 11%.
    - Exports: mean = 4.5% and standard deviation = 0.1%.
  - The simulated joint distribution approximates the observed distribution and allows estimation of the netting effect.
- Port-level principles:
  - Principle I — Magnitude of payload changes: larger average payload changes imply larger average netting effects.
  - Principle II — Symmetry of payload changes: ports with both high import and export activity (more symmetric) experience larger netting effects.
- Symmetry factor:
  - s = Min(N_imports / N_exports , N_exports / N_imports) (A1.8)
- Bootstrapping adjustment formula for imports (exports analogous):
  - ∆L_Netting_adj = ∆L_orig + α · s · ( ∆L_avg(imports) − Abs(∆L_orig) / β ) (A1.9)
    - ∆L_orig = original payload change.
    - ∆L_avg = average payload change for imports/exports.
    - s = symmetry factor (A1.8).
    - α and β are calibrated scaling factors.
- Calibration details:
  - α = 1.58 (calibrated by minimizing average RMSE across five ports).
  - β = 3.12 (calibrated same way).
  - Special cases:
    - If observed payload change is zero, adjusted payload change = α · s · ∆L_avg(imports).
    - Formula phases out the netting adjustment as observed payload changes increase in absolute value.
  - Additional scaling: multiply adjustment by 0.8 to exclude container tare weight (a TEU container weighs about 2 metric tons, ~20 percent of average loaded container weight), so the 0.8 factor captures cargo weight only.
- Empirical outcome:
  - For 20 ports with container throughput data available in metric tons, port-level container trade estimates rise from an average of 26 percent to 68 percent of official data after the bootstrapping adjustment.
  - Example ports with results: Santos, Los Angeles-Long Beach, Rotterdam, Algeciras.

### Comparative notes and operational considerations
- Data requirements:
  - Approach #1 requires official container throughput data (metric tons preferred); where unavailable TEUs are converted using 12 metric tons/TEU.
  - Approach #2 is an alternative when throughput data are absent, relying on port-level calibration and α, β, s parameters.
- Both approaches produce adjusted series that align more closely with official statistics in levels and trends.
- Calibration caveats:
  - α and β were calibrated across five ports; optimal values for individual ports typically fall within ±15% of the collective optimal value.
  - Conversion factor 12 metric tons/TEU is a global average; port-level variation exists (example: Port of Santos average weight 10–12 metric tons/TEU over 20 years).

*Source: Annex I. Adjusting for Two-Way Containerized Trade (Netting Effect) — content supplied from wpiea2025093-print-pdf*

### Annex I. Adjusting for Two-Way Containerized Trade (Netting Effect) ....................................................

### Annex I. Adjusting for Two-Way Containerized Trade (Netting Effect)

### Problem statement: netting effect in containership AIS data
- Containerships often load and unload cargo simultaneously during a port call, so AIS-based estimates observe only the net change in a vessel’s draft.
- This "netting effect" can lead AIS-derived shipment estimates to understate the true level of containerized trade for ports where two-way containerized activity is common.
- Vessels most impacted are those that simultaneously load and unload cargo during port calls; this behavior is most characteristic of containerships.

### Adjustment approaches detailed in Annex I
- Two complementary approaches are outlined for addressing the netting effect:
  - A simple approach that uses official container throughput data to complement AIS data and estimate the netting effect.
  - A bootstrapping technique that can be used in the absence of container throughput data.

### Implementation and coverage
- The simple (throughput-based) approach is implemented for 83 of the largest container ports in the world.
- These 83 ports make up about two-thirds of global containerized trade.
- Based on this adjustment, container trade volume estimates for those ports move closer to official data.

### Validation example
- Figure 1 (described in the source) shows the effect of the netting adjustment for the port of Rotterdam, the largest container port in Europe:
  - Adjusted container trade volume (inflow and outflow) for Rotterdam, 2019-24, is closer to official series than the unadjusted AIS-based series.
  - The figure compares Unadjusted, Adjusted, and Official series in million metric tons for 2019-24.

### Role within PortWatch enhancements
- The netting adjustment is one of several enhancements to IMF PortWatch since its November 2023 beta launch, alongside:
  - Ballast water adjustments (Annex II) to avoid overstating cargo volumes when ships carry ballast water.
  - Expanded port coverage (from 1378 to 1666 ports globally).
  - Refinements to historical averaging for incomplete draft data (probability-weighted averages and grouping by vessel type when vessel-specific history is unavailable).

*Source: Annex I. Adjusting for Two-Way Containerized Trade (Netting Effect) — content supplied from wpiea2025093-print-pdf*

### 3. A Nowcasting Model for Global Maritime Trade

### 3. A Nowcasting Model for Global Maritime Trade

### (A) General Approach
- Purpose: provide a timely indicator of global merchandise trade (7 working days after the reference month) using satellite-based vessel data.
- Rationale:
  - More than 80 percent of global trade volume is transported by ships.
  - Maritime trade underpins global supply chains and often supports other modes of trade (air, land).
- Conceptual design:
  - Mimics key features of official trade statistics compilation.
  - Estimates trade value using data at the Harmonized System (HS) code level and estimates trade volume by deflating trade value with export/import price deflators.
  - Fits within nowcast models that replicate official compilation methods (e.g., Atlanta Fed’s GDPNow).

### (B) Methodology
- Scope and objectives:
  - Global in scope (not country-based) and implementable in near real-time.
  - Aimed at early warning of turning points in global trade and economic activity.
  - Parsimonious three-step approach: physical volume → trade value → trade volume (indices with 2019 base year).
- Step 1: Global vessel shipments in physical volume
  - Aggregate metric ton shipments by vessel type across all ports tracked by IMF PortWatch:
    - Tankers: Metric ton of goods shipped by tankers.
    - Dry bulk carriers: Metric ton of goods shipped by dry bulk carriers.
    - Containerships and other cargo vessels: Metric ton of goods shipped by containerships, general cargo and roro cargo vessels.
  - Note: Tankers include oil, gas, product, and chemical tankers. Dry bulk carriers transport unpackaged bulk cargo, such as coal, iron ore and grains. The third group includes general cargo and roll-on-roll-off (roro) cargo ships; containerships carry most (around 80 percent) of the volume of goods transported by this group.
- Step 2: Global trade value index
  - Compute average unit values (US$/metric ton) by vessel type and multiply by physical volumes to obtain value (Equations 1 and 2).
  - Notation highlights:
    - Vt_x and Vt_m: global exports and imports in value terms at period t.
    - Ut_x,j and Ut_m,j: global export and import shipments in physical volume by vessel type j at period t.
    - UVt_x,j and UVt_m,j: average unit values for exports and imports by vessel type j at period t.
    - Ft_x,j and Ft_m,j: percentage changes in average unit values between base period (t0) and t.
    - Vessel type codes: tn (tanker), bc (dry bulk carrier), cs (containership/other cargo).
  - Base year unit values:
    - CEPII BACI provides harmonized trade data at 6-digit HS codes in value (US$) and volume (metric tons) for base period (2019).
    - Mapping between vessel types and HS codes is used to compute unit values by vessel type.
  - Changes in unit values (Ft_i,j):
    - Tankers: percentage change in the fuel price index (excluding coal) from IMF’s Primary Commodity Prices database. Data lag: 5-7 working days.
    - Dry bulk carriers: percentage change in the non-fuel commodity price index (including coal but excluding precious metals) from IMF’s Primary Commodity Prices database. Data lag: 5-7 working days.
    - Containerships and other cargo vessels: percentage change in the manufactured goods price index compiled by the WTO. Typical data lag: 3 months. For missing months, bridging uses: (i) US CPI index (excluding food, energy, and services); and (ii) Cleveland Fed’s US CPI inflation nowcast for the latest month.
  - Empirical observation:
    - The average unit value of goods transported by containerships/other cargo vessels is 8-12 times higher than those transported by tankers and dry bulk carriers (2019–24 series shown in Figure 4).
- Step 3: Global trade volume index
  - Move from trade value to trade volume using export/import price deflators (Equation 3): Qt_i = Vt_i / Pt_i for i ∈ {x, m}.
  - Price deflator construction:
    - Laspeyres-type index is used to mimic national statistical agency practice (Equation 4).
    - Pt_i uses base period quantities Ut0_i,j and current-period unit values UVt_i,j; base period is t0 = 2019.

### (C) Results
- Benchmark data:
  - Use Netherlands Bureau for Economic Policy Analysis (CPB) monthly index of world trade (first estimate available with a lag of two months), covering 81 countries and nearly 96 percent of world trade.
- Goodness-of-fit measures (monthly year-over-year nowcast vs CPB):
  - Correlation coefficient:
    - 0.95 for global trade value.
    - 0.80 for global trade volume.
  - RMSE:
    - 0.05 for global trade value.
    - 0.04 for global trade volume.
    - Excluding COVID period (2020-21): RMSE is 0.03 for global trade value and 0.03 for global trade volume.
- Interpretation of results:
  - Model achieves a reasonably good fit with official data.
  - Captures major turning points:
    - Large decline in world trade in early 2020 (COVID-19) and subsequent rebound.
    - Slowdown in world trade in 2023 and gradual recovery thereafter.
  - Limitations:
    - Estimates cover maritime trade only and are based on timing of port entry; official data cover all modes and are based on timing of customs clearance.
- Summary statement:
  - Nowcasting model follows changes in global trade well during large shocks (COVID in 2020, supply chain disruptions in 2021, war in Ukraine in 2022).

### (D) Regional Breakdown of Trade
- Regional grouping: IMF WEO country groups (G7, euro area, other advanced economies; EMDEs split into Emerging and Developing Asia, Emerging and Developing Europe, Latin America and the Caribbean, Middle East and Central Asia, Sub-Saharan Africa).
- Maritime trade share (volume terms, 2019):
  - For all regions other than Europe (euro area and emerging and developing Europe), maritime trade represents more than 70 percent of trade in volume terms (Figure 6).
  - Implication: maritime trade is a good indicator of regional trade except for Europe, where intra-regional land and air trade are significant.
- Regional implementation:
  - Use IMF PortWatch data by region.
  - Regional unit values computed for base period 2019 (Table 5) and monthly changes estimated with same price indices as global model.
- Regional goodness-of-fit (monthly y/y nowcast vs CPB) — select figures:
  - Advanced economies:
    - Correlation coefficient (imports value) 0.94 and (imports volume) 0.71.
    - RMSE (imports value) 0.05 and (imports volume) 0.05. Excluding COVID: 0.05 and 0.05 respectively.
  - Emerging market and developing economies (EMDEs):
    - Correlation coefficient (imports value) 0.91 and (imports volume) 0.77.
    - RMSE (imports value) 0.07 and (imports volume) 0.06. Excluding COVID: 0.05 and 0.03 respectively.
- Tabulated model performance (excerpt):
  - Value of trade (correlation, RMSE overall, RMSE 2020-21, RMSE 2022-24):
    - World: correlation 0.95; RMSE 0.05; RMSE (2020-21) 0.07; RMSE (2022-24) 0.03.
    - Advanced economies (export): correlation 0.89; RMSE 0.07; RMSE (2020-21) 0.08; RMSE (2022-24) 0.06.
    - EMDEs (export): correlation 0.96; RMSE 0.06; RMSE (2020-21) 0.09; RMSE (2022-24) 0.03.
  - Volume of trade (correlation, RMSE overall, RMSE 2020-21, RMSE 2022-24):
    - World: correlation 0.80; RMSE 0.04; RMSE (2020-21) 0.06; RMSE (2022-24) 0.03.
    - Advanced economies (export): correlation 0.75; RMSE 0.06; RMSE (2020-21) 0.08; RMSE (2022-24) 0.04.
    - EMDEs (export): correlation 0.70; RMSE 0.05; RMSE (2020-21) 0.06; RMSE (2022-24) 0.03.
- Regional unit values (2019, US$/metric ton) — selected entries from Table 5:
  - World (Exports): Tanker 539; Dry bulk carrier 288; Containership/cargo vessel 4350.
  - Advanced economies (Exports): Tanker 639; Dry bulk carrier 344; Containership/cargo vessel 5117.
  - EMDEs (Exports): Tanker 480; Dry bulk carrier 237; Containership/cargo vessel 3635.
  - World (Imports): Tanker 539; Dry bulk carrier 288; Containership/cargo vessel 4350.
  - Advanced economies (Imports): Tanker 561; Dry bulk carrier 406; Containership/cargo vessel 5071.
  - EMDEs (Imports): Tanker 505; Dry bulk carrier 216; Containership/cargo vessel 3444.

### (E) Global Economic Activity
- Motivation: trade and growth are closely associated; evaluate nowcast as proxy for global economic activity.
- Benchmark: CPB global industrial production data (production-weighted), covering 85 countries and 96 percent of global industrial production; released with a 2-month lag.
- Performance:
  - Correlation coefficient between monthly nowcast and CPB global industrial production (y/y): 0.78.
  - RMSE: 0.03 (and 0.03 excluding the COVID period).
- Visual comparison: Figure 7 shows nowcast vs official series for global industrial production, 2020-24 (percent change; year-over-year).

### (F) Seasonal Adjustment
- Need: to analyze month-over-month or quarter-over-quarter fluctuations, seasonal adjustment is required.
- Recommendation:
  - Use CPB’s seasonal adjustment approach:
    - Apply X12-ARIMA procedure.
    - Apply additional adjustment to January and February for countries affected by Lunar New Year timing (e.g., China, Hong Kong SAR, Korea, Singapore, Taiwan Province of China).
- Illustration (3m/3m series, 2019–24):
  - Comparison to CPB seasonally adjusted 3m/3m series:
    - Correlation coefficient: 0.97 for global trade value; 0.83 for global trade volume.
    - RMSE: 0.04 for global trade value; 0.04 for global trade volume.
    - Excluding COVID period: RMSE 0.03 for trade value; RMSE 0.03 for trade volume.

*Source: IMF Working Paper — 3. A Nowcasting Model for Global Maritime Trade*

### 4. Monitoring Global Trade Trends in Real Time

### 4. Monitoring Global Trade Trends in Real Time

### Overview and methodology
- The methodology uses satellite-based port-level data and a nowcast model to monitor fragmentation (friend-shoring) and regionalization (near-shoring) in global maritime trade in a timelier manner than traditional macro-level trade data.
- The model:
  - Leverages data from IMF PortWatch (beta launched November 2023).
  - Mimics key features of how statisticians compile merchandise trade data.
  - Tackles issues related to two-way containerized trade and ships’ use of ballast water.
  - Expands port coverage and refines historical averaging for incomplete observations to better align PortWatch estimates with official data.
- Analyses are performed by vessel type to assess intra-bloc and intra-region trade at a broad product level.
- Limitations of conventional data motivating this approach:
  - Macro-level trade data for some countries suffer from significant delays.
  - Bilateral trade data can be sparse with missing values for various country pairs.
  - The AIS data may not detect transshipments and ships can deactivate AIS to avoid detection during ship-to-ship transfers.

### (A) Fragmentation (Friend-shoring)
- Identification of politically aligned blocs:
  - Countries categorized into three groups based on UN voting patterns: (i) a U.S.-leaning bloc; (ii) a China-leaning bloc; (iii) a set of nonaligned countries.
- Construction of bloc trade flows:
  - Trade flows constructed from port-level estimates by assuming goods are traded between two countries when their ports are visited back-to-back (example procedural rule provided).
  - Trade between countries aggregated into trade within and across blocs.
- Key findings (2019-24):
  - Trade between the U.S.-leaning and China-leaning blocs as a share of trade among all three blocs has declined since 2019.
  - General pattern among the three blocs: decrease in trade between the U.S.-leaning and China-leaning blocs, alongside an increase in trade with the nonaligned bloc.
  - China-leaning bloc export dynamics shifted: export share to the U.S.-leaning bloc diminished while shares to within the China-leaning bloc and to the nonaligned bloc grew—consistent with the connector country hypothesis.
- Vessel-type decomposition:
  - A substantial portion of changes in trade shares is due to changes in tankers (primarily transporting oil and gas).
  - These tanker developments are largely attributable to sanctions imposed on Russia by countries in the U.S.-leaning bloc.

### Box 1. The Shift in Oil Trade After the War in Ukraine
- Coverage and framing:
  - Box covers all products transported by tankers—including crude oil, refined petroleum products, chemicals, and liquefied natural gas—but refers to them collectively as “oil”.
- Sanctions context:
  - Following the war in Ukraine, the EU, the U.K., and the U.S. imposed sanctions on most imports of oil products from Russia, including bans and restrictions on dollar payments.
  - G7 instituted prohibitions on transportation and insurance services for tankers carrying Russian commodities exceeding specified price thresholds.
- AIS evidence (2019 to 2024):
  - Tanker traffic patterns and outgoing tanker capacity departing from Russia changed substantially after sanctions.
  - Countries with the largest increases in oil imports from Russia include China, India, and Brazil.
  - Countries with drastic reductions in oil imports from Russia include the Netherlands, Finland, France, Germany, and Poland.
  - The gap in Europe’s oil imports from Russia has been filled by increased imports from the U.S. and Norway; the U.S. has increased supplies to Europe (EU and UK) the most and now accounts for a sizeable share of Europe’s maritime oil imports in volume terms.
- Conclusions from the box:
  - First, sanctions on Russian oil led to a decoupling of Europe’s oil trade with Russia.
  - Second, China, India, and Brazil have emerged as key importers of Russian oil.
  - Third, Europe has deepened its oil trade with other geopolitically aligned countries.
- Notes:
  - For Japan, estimates exclude LNG imports from the Sakhalin-2 project, which remained exempt from sanctions through 2024.
  - In most jurisdictions, port authorities mandate AIS transponders during port visits; ships can deactivate AIS to avoid detection, particularly during ship-to-ship transfers in open seas.

### (B) Regionalization (Near-shoring)
- Objective:
  - Assess whether global maritime trade shows regionalization trends since 2019 in light of geopolitical tensions, COVID-19, supply chain resilience, and environmental concerns.
- Regional grouping:
  - Countries categorized into eight regions based on major regional trade agreements and geographical proximity: USMCA, Latin America, Africa, Europe (EU and potential enlargement countries), Eurasian Economic Union, Middle East, East Asia, and South Asian Free Trade Area.
  - Countries in each region are listed in Annex IV (annex content not reproduced here).
- Regionalization index (Equation 5):
  - 퐼_reg = (sum_{k=1}^8 (X_kk + M_kk)) / (sum_{k=1}^8 (sum_{j=1}^8 (X_kj + M_kj)))
  - Where 퐼_reg is the regionalization index, X_kj is exports of region k to region j, M_kj is imports of region k from region j, and j,k ∈ {1,2,...,8}.
  - The index measures intra-regional trade relative to global trade for each region.
- Key findings (2019-24):
  - No clear trend toward or away from regionalism since 2019.
  - The index declined from the middle of 2020 to early 2022, coinciding with a surge in Asian exports driven by strong demand from advanced economies during the COVID-19 pandemic.
  - There has been an upward trend since the war in Ukraine, returning the indicator to its pre-pandemic level.
  - Three quarters of the contribution to within-region maritime trade since 2019 comes from East Asia, and a fifth from Europe—indicating these two regions largely drive overall maritime trade regionalization.
- Regional within-region trade shares:
  - Analysis of within-region trade as the share of a region’s total trade shows some slight variations across regions but no clear, consistent pattern indicating a definitive shift toward or away from regional trade.
- Additional note:
  - Within-region trade is larger in Europe and USMCA than in East Asia when considering all forms of trade, not just maritime; although a significant portion of intra-regional trade in the EU is conducted by air or land, maritime trade remains substantial and makes the EU the region with the second largest intra-regional maritime trade.

### Conclusions and implications
- The nowcast model provides a timelier indicator of global maritime trade than traditional trade data, enabling more prompt monitoring of fragmentation and regionalization.
- Empirical conclusions from the analysis:
  - Evidence of trade fragmentation among geopolitically aligned countries in recent years.
  - No clear global trend toward regionalization; regionalization dynamics vary by region.
- Future research directions:
  - Explore use of the PortWatch global trade proxy in other nowcasting models.
  - Extend the approach to produce country-level estimates of maritime trade with adjustments.

*Source: Authors’ calculations.*

### Annex I. Adjusting for Two-Way Containerized Trade

### Annex I. Adjusting for Two-Way Containerized Trade (Netting Effect)

### Problem statement: the netting effect
- The netting effect arises because AIS data observe only the net change in a containership’s draft (and therefore payload) when cargo is both unloaded and loaded during a port call.
- Illustration: if a containership unloads three containers for imports and loads one container for exports, AIS would record a net import of two containers and no exports.
- Analytical implication: with two-way trade, AIS provides two observable quantities (a, b) but three unknowns (x, y, z), producing an underdetermined system unless an additional equation is supplied.

### Approach #1 — Netting adjustment using official (container throughput) data
- Key idea: use container throughput (c = x + y) reported by port or national authorities to convert the 2×3 problem into a 3×3 system.
- System of equations (as presented):
  - a = x + z (A1.1)
  - b = y + z (A1.2)
  - c = x + y (A1.3)
- Closed-form solution (Equations A1.4–A1.6):
  - x = (a – b + c) / 2 (A1.4)
  - y = (b – a + c) / 2 (A1.5)
  - z = (a + b – c) / 2 (A1.6)
- Numerical example:
  - If a = 10, b = 15, c = 8 (metric tons), then x = 1.5, y = 6.5, z = 8.5 (metric tons).
- Implementation details:
  - Applied to 83 of the largest container ports covering about two-thirds of global container trade.
  - Throughput data are expressed in metric tons or TEUs. Primary use: metric tons.
  - For TEU-to-metric-ton conversion, a factor of 12 metric tons/TEU is used (global average).
  - Where container throughput data are lagging, a three-year historical average of the scaling factor for the respective month is used.
- Empirical outcome:
  - The adjusted AIS-derived series are much closer to official data in levels and trends (examples shown for Busan, Rotterdam, Santos, and others in the source).

### Approach #2 — Netting adjustment using a bootstrapping approach
- Key idea: model the observed distribution of payload changes at a port as the difference (convolution) of two distributions: one for loading (exports) and one for unloading (imports).
- Calibration example (Los Angeles-Long Beach):
  - Simulate 100,000 draws from two normal distributions calibrated for LA-LB:
    - Imports: mean = -26% and standard deviation = 11%.
    - Exports: mean = 4.5% and standard deviation = 0.1%.
  - The simulated joint distribution approximates the observed distribution and allows estimation of the netting effect.
- Port-level principles underpinning the bootstrapping formula:
  - Principle I — Magnitude of payload changes: larger average payload changes imply larger average netting effects.
  - Principle II — Symmetry of payload changes: ports with both high import and export activity (more symmetric) experience larger netting effects.
- Symmetry factor (Equation A1.8):
  - s = Min(N_imports / N_exports , N_exports / N_imports) (A1.8)
- Bootstrapping adjustment formula for imports (Equation A1.9; exports analogous):
  - ∆L_Netting_adj = ∆L_orig + α · s · ( ∆L_avg(imports) − Abs(∆L_orig) / β ) (A1.9)
    - where ∆L_orig is the original payload change, ∆L_avg is the average payload change for imports/exports, α and β are calibrated scaling factors, and s is the symmetry factor.
  - Calibration:
    - α = 1.58 (calibrated by minimizing average RMSE across five ports).
    - β = 3.12 (calibrated same way).
  - Special cases:
    - If observed payload change is zero, adjusted payload change = α · s · ∆L_avg(imports).
    - The formula phases out the netting adjustment as observed payload changes increase in absolute value.
  - Additional scaling:
    - Adjust formula by 0.8 to exclude container tare weight (a TEU container weighs about 2 metric tons, ~20 percent of average loaded container weight), so the 0.8 factor captures cargo weight only.
- Empirical outcome:
  - For 20 ports with container throughput data available in metric tons, port-level container trade estimates rise from an average of 26 percent to 68 percent of official data after the bootstrapping adjustment.
  - Example results and figures provided for Santos, Los Angeles-Long Beach, Rotterdam, and Algeciras in the source.

### Comparative notes and operational considerations
- Approach #1 requires official container throughput data (metric tons preferred); where unavailable, TEUs converted using 12 metric tons/TEU.
- Approach #2 provides an alternative when container throughput data are absent, relying on port-level statistical calibration and the α, β, s parameters.
- Both approaches produce adjusted series that align more closely with official statistics in levels and trends.
- Calibration caveats:
  - α and β were calibrated across five ports; optimal values for individual ports typically fall within ±15% of the collective optimal value.
  - Conversion factor 12 metric tons/TEU is a global average; port-level variation exists (example: Port of Santos average weight 10–12 metric tons/TEU over 20 years).

*Source: Annex I. Adjusting for Two-Way Containerized Trade, wpiea2025093-print-pdf.*

### Annex III. Why Are Unit Values Important for

### Annex III. Why Are Unit Values Important for Measuring Trade Volume Accurately?

### Example: cars and rice imports
- Initial situation:
  - Imports: 10 cars (each car is 2 tons and costs $20,000 per ton) and 20 tons of rice (at $500 per ton).
- Tabulated values (as presented):
  - Current Year
    - Cars: 20 tons at $20,000 per ton
    - Rice: 20 tons at $500 per ton
    - Import Value: $410,000
    - Physical Volume of Imports: 40 tons
  - Next Year
    - Cars: 40 tons at $20,000 per ton
    - Rice: 20 tons at $500 per ton
    - Import Value: $810,000
    - Physical Volume of Imports: 60 tons

### Quantitative findings
- Import value change:
  - Increased from $0.41 million to $0.81 million.
  - Change described as approximately by 100 percent.
- Physical volume change:
  - Increased from 40 to 60 tons.
  - Change is 50 percent.
- Price deflator:
  - Import price deflator is unchanged between the two years.
- Correct measure of import volume (official statistics method):
  - Because import value increased by 100 percent and import price deflator is unchanged, import volume is up by 100 percent (not 50 percent).

### Interpretation and conceptual point
- Trade volume is a hypothetical concept measuring how much trade value would have increased if prices were unchanged.
- Simply aggregating the physical volume of traded goods (tons) is not an accurate measure of trade volume when unit values differ across goods.
- The example illustrates that changes in the composition of imports (more high-unit-value goods like cars) can raise trade value and hence trade volume even if aggregated physical tons rise by a smaller proportion.

### Implications for vessel-type and product-group aggregation
- The same logic applies at the product-group or transport-mode level:
  - The average unit value of goods transported by containerships (manufactured goods) is an order of magnitude larger than those transported by tankers/bulk carriers (commodities).
- Therefore:
  - Aggregating physical volume of goods shipped by different types of vessels without considering unit values leads to incorrect measures of trade volume.
  - This issue is especially important for countries with relatively non-homogenous imports or exports (mixtures of manufactured and commodity products).

*Source: Nowcasting Global Trade from Space, Working Paper No. WP/2025/093 — Annex III.*

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_Source: https://www.imf.org/-/media/files/publications/wp/2025/english/wpiea2025093-print-pdf.pdf_