## wp1816

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---

### I. Introduction — DOTS upgrade and objectives
- DOTS publishes exports and imports of goods by partner economy at monthly, quarterly, and annual frequencies.
- Improvements from the March 2017 DOTS upgrade:
  - Coverage of world trade using official sources increased to about 97.9 percent for the year 2015 (from 92.0 percent prior to the upgrade).
  - Number of countries in DOTS rose to 210 (from 182, an increase of 28 countries). Full list of partner countries comprises 229 countries.
  - DOTS is now available 85 days after the end of the reference month (before the upgrade, timeliness was four months). Updates are made around the 25th of each month.
  - New methodology for monthly-level bilateral trade estimation (starting January 2000) substantially improves accuracy and consistency.
- Core methodological change: adoption of the Cholette-Dagum (2006) regression-based benchmarking model.
- Fundamental assumption change: monthly estimates are derived by linking (splicing) month-to-month changes shown by partner-reported flows rather than using levels adjusted for shipping and insurance costs.

### II. Overview — coverage, concepts, and major source data
- Concepts and valuation:
  - DOTS follow UN International Merchandise Trade Statistics 2010 (IMTS 2010).
  - Exports recorded on free-on-board (FOB) basis; imports recorded on cost, insurance, and freight (CIF) basis.
- Reported vs estimated data (2015):
  - Monthly estimated data account for only 2.1 percent of world trade, computed for over 13 thousand bilateral trade series (16 percent of total partner combinations).
  - About 90 percent of world trade is covered by monthly official trade statistics reported to the IMF.
  - 8.3 percent by annual data.
  - About 6 percent of annual data are received from UN COMTRADE.
- Major source data and integration:
  - Monthly reports supplied by countries to the IMF Statistics Department: monthly update relies on 100 countries covering more than 90 percent of world trade.
  - UN COMTRADE: about 170 countries report yearly, covering more than 98 percent of world trade. For 2015, COMTRADE data used in DOTS account for about 6 percent of world imports and 2.3 percent of world exports.
  - COMEXT (Eurostat): monthly trade statistics for all 28 EU countries; COMEXT is released within 55 days of the end of the reference month and EU countries account for around 30 percent of world trade.
  - Use of COMTRADE and COMEXT improves consistency between international trade databases; COMEXT and DOTS are aligned at all times.

### III. New methodology — structure, rationale, and three-step procedure
- Rationale:
  - Replaced a 1990s-era methodology that produced time-series breaks and excessive reliance on projections.
- Main components:
  - Expanded set of official sources of bilateral trade statistics.
  - New estimation procedure to impute missing monthly bilateral observations.
  - Streamlined list of partner countries and refined CIF/FOB assumptions.
- Three-step estimation procedure:
  1. Fill gaps in monthly bilateral trade using indicators (mirror trade, total trade, or counterpart-sum) via a splicing approach that preserves short-term movements of the chosen indicator.
  2. Reconcile monthly estimated data with official monthly, quarterly, and annual data via Cholette-Dagum benchmarking (least-squares optimal combination ensuring aggregation consistency).
  3. Use bilateral series from step 2 to estimate bilateral trade for non-reporting countries.

### IV. Step 1 — identification of missing monthly bilateral observations and indicators
- Definition of a missing monthly bilateral observation for country i with counterpart j in month t:
  1. Country i has reported trade with country j for at least one period prior to month t, and
  2. Country i has not reported trade with other partner countries for month t.
- Implication: when country i reports trade with other partners but not with partner j, bilateral trade between i and j (from country i’s perspective) is assumed to be nil.
- Indicators used to estimate a missing value (order of priority):
  1. Mirror trade: use counterpart j’s corresponding reported flow; splicing applied so the missing trade co-moves with counterpart changes.
  2. Total trade reported by country i (IFS): about 150 countries submit monthly total trade to the IFS; the month-to-month change of total trade is spliced to estimate bilateral trade, assuming the geographical breakdown of month t maintains the same structure as the latest partner-level observation.
  3. Sum of trade reported by all other partner countries with country i (counterpart-sum proxy): constructed from partners that report continuously; month-to-month percent change of this indicator is spliced to the missing bilateral series; current reporters account for about 90 percent of global trade.

- Splicing formula (notation in source):
  - The estimated value ˆt y is obtained as ˆt y = (t x / t-1 x) · t-1 y  (presentation in source text).
- Contrast with previous methodology:
  - Previous method used a CIF/FOB factor of 10 percent for reporting countries; splicing avoids use of CIF/FOB factor for reporting countries. CIF/FOB assumptions remain for non-reporting countries (Step 3).

### V. Step 2 — benchmarking monthly estimates to quarterly and annual reported data (Cholette-Dagum)
- Objective: Adjust monthly estimates from Step 1 to be consistent with official quarterly and annual data reported by country i.
- Benchmarking model: Cholette and Dagum (2006) regression-based generalized least-squares model.
  - Property: minimizes impact of adjustments on short-term movements in preliminary monthly series.
  - Produces backcasts and forecasts for months not covered by benchmarks using historical relationships.
- Application rules:
  - Applied only to bilateral trade flows with monthly estimates produced at Step 1.
  - Official monthly data are never benchmarked to overlapping official quarterly or annual data.
  - Official data reported by country authorities are never adjusted.
- Cholette-Dagum model specifics (as provided):
  - The standardized error e'_t = e_t / s_t and AR(1) specification e'_t = φ e'_{t-1} + v_t with φ < 1.
  - For DOTS estimation, the value of φ is set to 0.9.
  - When φ is very close to 1 (example: 0.999) function (7) converges to the proportional Denton method; lower φ adjusts for temporary bias.

### VI. Step 3 — estimation of non-reporting countries
- Objective: Estimate bilateral trade of non-reporting countries from partner-reported values.
- Rule: Exports and imports of non-reporting countries are estimated assuming symmetry with counterpart declarations (imports ↔ exports).
- CIF/FOB adjustment used: 6 percent.
  - Value of exports = value of imports from a partner divided by 1.06.
  - Value of imports = value of exports multiplied by 1.06.
- Publication note: Monthly estimates for non-reporting countries are newly published in DOTS; previously estimates were produced only for reporting countries.
- Aggregate impact: Monthly estimates for non-reporting countries (Step 3) are produced for 2.1 percent of world trade (year 2015).

### VII. Other methodological changes, definitions, and parameters
- Partner-country list: New list comprises 229 countries (includes 189 IMF member countries; others include non-member countries, non-sovereign entities, areas not specified, special categories, and former countries).
  - Start and end validity dates are defined for each partner for estimation purposes; official reported data are not constrained by validity dates.
- CIF/FOB factor changed from 10 percent to 6 percent.
  - Basis: OECD ITIC database and gravity-type model estimates (Miao and Fortanier, 2017).
  - OECD calculations show trade-weighted average of transportation and insurance costs for 1995-2014 is 6 percent of the CIF value (OECD, 2016).
  - Implicit world CIF/FOB ratio at world level (around 1.5 percent in 2015) differs from 6 percent and is not an accurate measurement of shipping/insurance costs due to valuation/recording differences.
- Missing vs zero trade:
  - Procedure distinguishes missing (unreported) from zero (reported) trade.
  - Historical cleanup removed zeroes in the reported dataset; an absent bilateral trade flow for a given period should be considered nil.

### VIII. Impact of the new estimates — key statistics and distributional effects
- Global trade level effects (annual 2000–2015 assessment):
  - World imports CIF revised down by an average of 0.31 percent per year during 2000-2015.
  - World exports FOB level remained broadly unchanged; increases for 2000-2003 largely due to realignment with COMEXT for EU countries.
  - Average 2000-2015 percent difference between imports and exports is 2.31 percent (new) vs. 2.69 percent (old).
- Advanced vs emerging and developing economies:
  - Emerging market and developing economies trade balance with advanced economies during 2000-2015 has increased by USD 64 billion (or 15 percent of the previous level).
  - Starting 2005, more than 85 percent of the increase in the emerging market and developing economies trade balance is explained by better external trade positions of “Middle East, North Africa, and Pakistan” and “Western Hemisphere” vis-à-vis advanced economies.
- Coverage and country additions:
  - The 28 new countries added to DOTS account for 0.12 percent of world exports and 0.30 percent of world imports during 2011-2015.
  - For 16 of these countries, shares are based on official annual data in COMTRADE; remaining 12 estimated based on counterpart trade data.
- Summary statistics excerpt (as presented in source):
  - 1. Counterpart trade 4.0 6.0 5.0
    - 12.6 15.5 14.1
  - 2. Total trade 1.6 2.0 1.8
    - 12.8 16.7 14.8
  - 3. Other partners trade 1.0 1.8 1.4
    - 10.3 14.6 12.4
  - Monthly estimates for non-reporting countries (Step 3) 3.5 0.6 2.1
    - 21.0 11.1 16.0

### IX. Conclusions, operational recommendations, and planned improvements
- Data availability and timeliness:
  - Automated links with COMTRADE and COMEXT provide real-time and continuous updates; DOTS full dataset released within 85 days of the end of the current month.
- Monitoring and validation:
  - Estimation procedure is monitored and validated at every DOTS update; adjustments implemented as needed.
- Planned improvements:
  - Backcasting for January 1981–December 1999 using the new methodology.
  - Use of country-specific, time-varying CIF-FOB margins from the OECD database instead of the flat 6 percent assumption for non-reporting countries.
  - Increase use of machine-to-machine technology and automated web services to source official statistics and reduce the current timeliness of 85 days.
  - Produce indicators of real trade growth in seasonally adjusted form (DOTS figures are currently nominal and unadjusted for seasonal effects). Seasonal adjustment could be applied to world and country group aggregates only using standard software (e.g., X13-ARIMA-SEATS, TRAMO-SEATS); examples used X-13-ARIMA-SEATS in JDemetra+ (version 2.1).
- Expanded uses within the IMF:
  - Monitor recent trends of global and regional trade with partner-country detail and wide coverage.
  - Cross-check quality of trade statistics using counterpart information; IMF country teams may consider adjusting official trade statistics in baseline scenarios when differences with counterpart data are substantial and difficult to justify.

*Source: wp1816 (wp1816.pdf).*

### References .............................................................................................................

### References

### I. Introduction — DOTS upgrade and objectives
- DOTS publishes exports and imports of goods by partner economy at monthly, quarterly, and annual frequencies.
- DOTS comprise official data reported by country authorities to the IMF, or collected by the IMF from official sources, complemented with estimated data for late or non-reporting countries.
- Key improvements from the March 2017 DOTS upgrade:
  - Increased use of official sources: coverage of world trade using official sources increased to about 97.9 percent for the year 2015 (from 92.0 percent prior to the upgrade).
  - Expanded geographical scope: number of countries in DOTS rose to 210 (from 182, an increase of 28 countries). They include all 189 IMF member countries, 2 UN member states not part of the IMF (Cuba, Democratic People's Republic of Korea), and 20 other states and non-sovereign entities. Full list of partner countries comprises 229 countries (see Annex I). Only 20 countries out of 210 are estimated fully using counterpart information.
  - Increased timeliness: DOTS is now available 85 days after the end of the reference month (before the upgrade, timeliness was four months). Updates are made around the 25th of each month.
  - Improved quality of estimates: new methodology for monthly-level bilateral trade estimation (starting January 2000) substantially improves accuracy and consistency.
- Core methodological change: adoption of the Cholette-Dagum (2006) regression-based benchmarking model to combine official sources at different frequencies.
- Fundamental assumption change: monthly estimates are derived by linking (splicing) month-to-month changes shown by partner-reported flows rather than using levels adjusted for shipping and insurance costs; this aligns monthly estimates with historical official series and avoids breaks caused by bilateral asymmetries.

### II. Overview of DOTS — coverage, concepts, and data sources
- Concepts and valuation:
  - DOTS follow UN International Merchandise Trade Statistics 2010 (IMTS 2010).
  - Exports recorded on free-on-board (FOB) basis; imports recorded on cost, insurance, and freight (CIF) basis.
  - By construction, imports CIF reported by partner countries are expected to be larger than exports FOB.
  - Asymmetries arise from differences in classification, time of recording, exchange rates, shipment and re-export through intermediate points, coverage, and processing errors; these asymmetries are not reconciled in DOTS.
- Shares of reported vs estimated data (2015):
  - Monthly estimated data account for only 2.1 percent of world trade, computed for over 13 thousand bilateral trade series (16 percent of total partner combinations).
  - About 90 percent of world trade is covered by monthly official trade statistics reported to the IMF.
  - 8.3 percent by annual data.
  - About 6 percent of annual data are received from UN COMTRADE.
- Major source data:
  - Monthly reports supplied by countries to the IMF Statistics Department: at the time of writing, the monthly update of DOTS relies on 100 countries covering more than 90 percent of world trade.
  - UN COMTRADE: annual bilateral trade totals used for countries not reporting to IMF; about 170 countries report to UNSD yearly, covering more than 98 percent of world trade. For 2015, COMTRADE data used in DOTS account for about 6 percent of world imports and 2.3 percent of world exports.
  - COMEXT (Eurostat): monthly trade statistics for all 28 EU countries sourced from “DS-057380 EU Trade Since 1999 by HS2,4,6 and CN8”; COMEXT is released within 55 days of the end of the reference month and EU countries account for around 30 percent of world trade.
- Integration outcomes:
  - Use of COMTRADE and COMEXT improves consistency between international trade databases; COMEXT and DOTS are aligned at all times; monthly DOTS estimates are consistent with annual COMTRADE data not reported to the IMF.

### III. New methodology — structure and rationale
- Rationale for change:
  - Previous 1990s-era methodology relied on partner data, total trade, IMF WEO regional projections, and trend extrapolations; it produced time-series breaks and excessive use of projections with limited connection to actual trade developments.
- Main components of the new methodology:
  - Expanded set of official sources of bilateral trade statistics.
  - New estimation procedure to impute missing monthly bilateral observations.
  - Streamlined list of partner countries.
  - Refined assumption for converting imports CIF into exports FOB (and vice versa).
- Three-step estimation procedure:
  1. Fill gaps in monthly bilateral trade using indicators related to the missing information: mirror trade (counterpart reports), the reporting country’s total trade, or bilateral trade reported by other partners. Gaps are filled using a splicing approach that preserves short-term movements of the chosen indicator.
  2. Reconcile the monthly estimated data with official monthly, quarterly, and annual data via a time-series benchmarking procedure (Cholette-Dagum), which combines the monthly estimates with official benchmarks in a least-squares optimal way, ensuring the sum of monthly estimates is consistent with quarterly and annual official statistics.
  3. Use bilateral series from step 2 (reported and estimated) to estimate bilateral trade for non-reporting countries.

### IV. Step 1 detailed — rules for identifying and imputing missing monthly bilateral trade
- Conditions defining a missing monthly bilateral observation for country i with counterpart j in month t:
  1. Country i has reported trade with country j for at least one period prior to month t, and
  2. Country i has not reported trade with other partner countries for month t.
- Implication: when country i reports trade with other partners but not with partner j, bilateral trade between i and j (from country i’s perspective) is assumed to be nil. Missing data are identified only when a country does not report data by partner country for a month; historical bilateral observations are necessary to identify missing observations.
- Indicators used to estimate a missing value (order of priority):
  1. Mirror trade: use corresponding trade reported by counterpart country j with country i (imports reported by j to estimate i’s exports; exports reported by j to estimate i’s imports). The new methodology applies splicing to mirror trade, assuming the missing trade co-moves with the corresponding flow reported by the counterpart (e.g., if exports reported by country j increase by 5 percent, the estimate of imports for country i would also increase by 5 percent). This splicing avoids introducing breaks due to asymmetries.

*wp1816 - References*

### 2. Total trade reported by country i. If the mirror trade is unavailable for month t

### wp1816 - 2. Total trade reported by country i. If the mirror trade is unavailable for month t

### Description of indicator 2
- If the mirror trade is unavailable for month t (indicator 1), the second-best indicator is the total value of exports (or imports) for month t reported by country i in the International Financial Statistics (IFS) database (IMF, 2018b).
- The IMF Statistics Department collects monthly data on total trade and publishes them in the IFS.

### Coverage and timeliness
- Total trade statistics are received earlier than data by partner country.
- Country coverage is large: about 150 countries submit monthly total trade to the IFS on a regular basis.

### Estimation method (splicing approach)
- A splicing approach is used with this indicator:
  - The month-to-month change of total trade is used to estimate trade with counterpart country j (and with any other partner country) for month t.
- Assumption underlying indicator 2:
  - The geographical breakdown of month t maintains the same structure of the latest observation by partner country received from the country.

*Source: wp1816 - 2. Total trade reported by country i. If the mirror trade is unavailable for month t (wp1816.pdf)*

### 3. Sum of trade reported by all other partner countries with country i. If country i has

### wp1816 - 3. Sum of trade reported by all other partner countries with country i. If country i has

### Indicator 3: Counterpart-sum proxy for missing total trade
- Purpose: Create a proxy indicator of total trade for country i when country i has not reported total trade statistics to the IFS for month t (indicator 2).
- Definition: Indicator 3 is the sum of exports or imports for month t reported by all partner countries with country i (other than country j).
- Coverage rule: Only the subset of countries that have reported trade with country i on a continuous basis are included in this indicator.
- Use: The month-to-month percent change calculated from this indicator is spliced to the missing bilateral trade series.
- Practical note: This indicator can be built using information available from current reporters, which are always available and accounts for about 90 percent of global trade.

### Splicing approach to estimate missing trade (methodology)
- Estimation target: Let t y denote the missing value to be estimated, and t x the chosen indicator.
- Estimation rule as presented:
  - The estimated value ˆt y is obtained as

    1
    1
    ˆ
    t
    tt
    t
    x
    yy
    x
    
    
    
    
    
    
    (1)
- Contrast with previous methodology:
  - Previous method for reporting countries used a CIF/FOB factor of 10 percent to convert reported exports and imports into mirror trade.
  - The splicing approach avoids the use of a CIF/FOB factor for reporting countries.
  - A CIF/FOB assumption remains in use to estimate bilateral trade series of non-reporting countries (see Step 3).

### Step 2 — Benchmarking monthly estimates to quarterly and annual reported data
- Objective: Adjust monthly estimates from Step 1 to be consistent with official quarterly and annual data reported by country i.
- Rationale: Monthly estimates reconciled with quarterly and annual “benchmarks” are of superior quality because they are reconciled with official data.
- Benchmarking model: Regression-based Cholette and Dagum (2006) model (see Annex 2 in source).
  - Property: Minimizes impact of adjustments on short-term movements in the preliminary monthly series.
  - Capabilities: Produces backcasts and forecasts for months not covered by benchmarks, using historical relationship between monthly data and quarterly/annual benchmarks.
- Application rules:
  - Applied only to bilateral trade flows with monthly estimates produced at Step 1.
  - Official monthly data are never benchmarked to overlapping official quarterly or annual data.
  - Official data reported by country authorities are never adjusted.
  - If quarters or years are only partially covered by official monthly data, quarterly and annual official figures are used to complement missing information so sums match official benchmarks.

### Step 3 — Estimation of non-reporting countries
- Objective: Estimate bilateral trade of non-reporting countries based on data reported by (and estimated for) their partners.
- Status after Step 2: All missing bilateral trade for reporting countries are estimated and reconciled; no further steps for reporting countries.
- Estimation rule for non-reporting countries:
  - Exports and imports of non-reporting countries are estimated assuming symmetry with values declared by counterpart countries (imports ↔ exports).
  - CIF/FOB adjustment used: 6 percent.
    - Value of exports = value of imports from a partner divided by 1.06.
    - Value of imports = value of exports multiplied by 1.06.
- Implementation note: Publication of data for non-reporting countries in DOTS is new; previously estimates were produced only for reporting countries.
- Aggregate impact: Monthly estimates for non-reporting countries (Step 3) are produced for 2.1 percent of world trade (year 2015).

### Other methodological changes and definitions
- Partner-country list:
  - New partner country list comprises 229 countries (includes 189 IMF member countries; 13 non-member countries; 9 non-sovereign entities; 6 areas not specified; special categories; and 11 former countries).
  - Start dates and end dates (validity dates) are defined for each country and used only for estimation of missing data. The methodology produces monthly estimates only for countries that exist in each month.
  - Official data reported by country authorities are not constrained by these validity dates.
- CIF/FOB factor: Changed from 10 percent (previous DOTS practice) to 6 percent.
  - Basis: OECD International Transport and Insurance Costs (ITIC) database and gravity-type model estimates (Miao and Fortanier, 2017).
  - OECD calculations (ITIC database) show trade-weighted average of transportation and insurance costs for all countries over 1995-2014 is 6 percent of the CIF value (OECD, 2016).
  - Note: Implicit world CIF/FOB ratio at world level (around 1.5 percent in 2015) differs from the 6 percent OECD weight; implicit ratio is not an accurate measurement of world shipping/insurance costs due to valuation and recording differences.
- Missing vs zero trade:
  - New procedure distinguishes missing trade (unreported) from zero trade (reported).
  - Historical cleanup removed zeroes in the reported dataset; missing values are distinguished from zero values.
  - Zero values have been removed from the published dataset; an absent bilateral trade flow for a given period should be considered nil.

### Impact of the new estimates (summary of main changes)
- General:
  - New methodology produced revisions due to incorporation of official data (COMTRADE or other official sources) and improved estimation methods.
  - Comparisons classify “new” DOTS data as those based on new methodology published on March 1, 2017; “old” data are those published in February 2017 based on 1993 methodology.
  - Revisions are assessed for annual data from 2000 to 2015.
- Global trade:
  - World imports CIF revised down by an average of 0.31 percent per year during 2000-2015.
  - World exports FOB level remained broadly unchanged; increases for 2000-2003 largely due to realignment with COMEXT official sources for EU member countries.
  - Causes of imports reduction:
    - Replacement of previous estimates with official data in COMTRADE (larger impact on imports).
    - Lower CIF/FOB ratio (6 percent vs. previous 10 percent), shifting downward imports CIF for countries reporting imports on an FOB basis.
  - Consequence: World exports and world imports are closer than before.
    - Average 2000-2015 percent difference between imports and exports is 2.31 percent (new) vs. 2.69 percent (old).
- Advanced economies vs emerging and developing economies:
  - Improvement in the trade balance of emerging market and developing economies vis-à-vis advanced economies since 2000.
  - On average, emerging market and developing economies trade balance with advanced economies during 2000-2015 has increased by USD 64 billion (or 15 percent of the previous level).
  - Drivers: Upward adjustment of exports to advanced economies and downward adjustment of imports from advanced economies (partly due to lower CIF/FOB factor).
  - Largest group-level revisions from “Middle East, North Africa, and Pakistan” and “Western Hemisphere”; starting 2005, more than 85 percent of the increase in the emerging market and developing economies trade balance is explained by better external trade positions of these two groups vis-à-vis advanced economies (notably an increase in the trade balance of oil-exporting countries in the Middle East).
- Trade weights and country coverage:
  - The 28 new countries in DOTS account for 0.12 percent of world exports and 0.30 percent of world imports during 2011-2015.
  - For 16 of these countries, shares are based on official annual data in COMTRADE; remaining 12 estimated based on counterpart trade data.
  - Countries with large partner concentration: Bhutan (with India), Lesotho and Swaziland (with South Africa), San Marino and the Vatican (with Italy), West Bank and Gaza (with Israel).
  - Revisions in weights driven by: increased use of official COMTRADE data, splicing approach replacing CIF/FOB transformation for missing observations, and use of partner data to replace past-trend extrapolations.

### Conclusions and way forward (policy/operational recommendations and planned improvements)
- Data availability and timeliness:
  - Automated links with COMTRADE and COMEXT provide real-time and continuous updates to DOTS.
  - DOTS provides long, methodologically consistent series on trade for 210 economies, with full dataset released within 85 days of the end of the current month (one month earlier than before).
- Monitoring and validation:
  - Estimation procedure is monitored and validated at every DOTS update; adjustments implemented as needed.
- Planned improvements:
  - Backcasting for January 1981–December 1999 using the new methodology.
  - Use of country-specific, time-varying CIF-FOB margins from the OECD database instead of the flat 6 percent assumption for non-reporting countries.
- Expanded uses of DOTS within IMF:
  - Monitor recent trends of global and regional trade: For the latest month published, coverage of world trade using official sources is always well above 90 percent.
    - Remaining share is estimated using counterpart or total trade data.
    - DOTS world trade series is coherent with the Centraal Planbureau (CPB) world trade series in nominal terms.
    - DOTS partner-country detail and wide coverage help identify drivers of global and regional trade fluctuations.
  - Cross-check quality of trade statistics using counterpart information:
    - Derive total exports and imports for a country as declared by partner countries and contrast with official statistics to identify quality issues (confidentiality omissions, informal cross-border trade, re-exports/re-imports asymmetries).
    - IMF country teams may consider adjusting official trade statistics in baseline scenarios when differences with counterpart data are substantial and difficult to justify.
- Potential extensions and methodological enhancements:
  - Extension to trade in services is constrained by lack of partner-country detail comparable to customs declarations for goods; left for future investigation.
  - Increase use of machine-to-machine technology and automated web services to source official statistics and reduce the current timeliness of 85 days.
  - Produce indicators of real trade growth in seasonally adjusted form:
    - Currently DOTS figures are nominal and unadjusted for seasonal effects; seasonal adjustment could improve assessment of short-term movements.
    - Seasonal adjustment could be applied to world and country group aggregates only to limit computational burden.
    - Standard software (e.g., X13-ARIMA-SEATS, TRAMO-SEATS) can be used to calculate seasonally adjusted series; seasonal adjustment performed in examples using X-13-ARIMA-SEATS in JDemetra+ (version 2.1).

*Source: wp1816 - 3. Sum of trade reported by all other partner countries with country i. If country i has (pdf).*

### 1. Counterpart trade 4.0 6.0 5.0

### wp1816 - 1. Counterpart trade 4.0 6.0 5.0

### Summary statistics (top of content unit)
- 1. Counterpart trade 4.0 6.0 5.0
  - 12.6 15.5 14.1
- 2. Total trade 1.6 2.0 1.8
  - 12.8 16.7 14.8
- 3. Other partners trade 1.0 1.8 1.4
  - 10.3 14.6 12.4
- Monthly estimates for non-reporting countries (Step 3) 3.5 0.6 2.1
  - 21.0 11.1 16.0

### Table 2 — New Countries in DOTS: Export Shares (Percent of total exports. Period: 2011-2015 average.)
- Table shows Export Shares (percent of country’s total exports) by partner grouping: Advanced Economies, Euro Area, Emerging & Dev. Economies, Emerging & Dev. Asia, Europe, Mid East, N Africa, Pak, Sub-Saharan Africa, Western Hemisphere, Other.
- Selected rows (as presented):
  - American Samoa * 42.8 0.8 57.2 21.2 2.8 2.4 19.5 11.3 0.0
  - Anguilla 32.0 3.3 68.0 3.6 3.9 3.1 1.7 55.7 0.0
  - Antigua and Barbuda 11.7 3.2 88.2 0.4 65.5 1.1 15.9 5.2 0.0
  - Bhutan 6.0 2.2 94.0 93.8 0.1 0.0 0.1 0.1 0.0
  - Botswana 68.7 13.9 31.3 8.3 0.0 2.3 20.7 0.0 0.0
  - Curacao * 12.0 10.2 88.0 0.1 0.2 15.1 3.7 68.9 0.0
  - Eritrea 25.9 2.7 74.1 53.6 2.1 15.2 1.0 2.2 0.0
  - F.T. French Polynesia 74.6 13.5 25.4 4.9 18.3 0.0 0.1 2.0 0.0
  - Falkland Islands * 88.2 76.3 11.8 1.6 5.0 0.2 5.0 0.0 0.0
  - Gibraltar * 84.7 67.8 15.3 0.2 6.2 4.2 4.6 0.1 0.0
- Note: * For these countries, weights based on counterpart data only.

### Table 3 — New Countries in DOTS: Import Shares (Percent of total imports. Period: 2011-2015 average.)
- Table shows Import Shares (percent of country’s total imports) by same partner grouping as Table 2.
- Selected rows (as presented):
  - American Samoa * 74.0 1.8 26.0 24.9 0.2 0.1 0.7 0.1 0.0
  - Anguilla 78.8 10.1 21.2 0.7 0.2 0.1 0.4 19.7 0.0
  - Antigua and Barbuda 48.8 3.9 20.8 6.0 0.3 0.1 0.3 14.2 30.4
  - Bhutan 12.5 3.4 87.1 86.5 0.2 0.4 0.0 0.0 0.4
  - Botswana 20.7 4.4 78.0 4.8 0.2 0.3 72.7 0.0 1.2
  - Curacao * 37.8 32.6 62.2 46.5 1.4 0.3 3.8 10.2 0.0
  - Eritrea 25.3 16.9 74.6 22.3 3.6 41.4 6.6 0.7 0.1
  - F.T. French Polynesia 79.9 36.5 20.1 17.1 1.1 0.3 0.2 1.3 0.0
  - Falkland Islands * 96.2 28.8 3.8 0.3 2.6 0.0 0.9 0.0 0.0
  - Gibraltar * 86.1 53.3 13.9 4.1 8.9 0.4 0.4 0.1 0.0
- Note: * For these countries, weights based on counterpart data only.

### Table 4 — Countries with Largest Changes in Export Shares (Difference New-Old, percent of total exports. Period: 2011-2015 average.)
- Table reports Difference in Export Shares (New – Old, in percent of country’s total exports) by partner grouping.
- Selected rows (as presented):
  - St. Lucia 51.5 2.5 -51.4 2.8 0.0 0.2 0.0 -54.5 0.0
  - Samoa 44.8 -0.1 -44.8 -46.1 0.1 0.3 0.3 0.7 0.0
  - Grenada 32.6 7.6 -32.3 -1.9 0.7 3.1 -42.4 8.1 -0.3
  - Papua New Guinea 26.5 6.2 -26.6 5.7 -35.1 0.0 0.0 2.7 0.0
  - Central African Rep. 25.5 22.2 -25.5 -17.8 -2.2 -3.2 -2.2 -0.1 0.0
  - Bahamas, The 24.5 1.7 -24.2 -5.3 -14.6 -0.1 17.5 -21.7 -0.3
  - Gabon 23.8 4.0 -11.5 -8.2 -0.2 0.5 1.2 -4.8 -12.3
  - Fiji 21.9 0.2 0.0 -1.5 0.2 0.0 0.3 1.0 -21.9
  - Barbados 21.5 -0.5 -21.6 0.0 -4.2 0.1 -0.3 -17.2 0.0
  - Tonga 20.4 -2.0 -20.6 -19.6 -0.3 0.1 0.3 -1.0 0.2
  - (Table continues with additional countries and corresponding differences.)
- Also shows countries with negative New–Old differences (examples, as presented):
  - Yemen, Republic of -10.0 1.1 10.0 1.6 0.2 7.7 0.1 0.4 0.0
  - Sierra Leone -10.3 -5.1 10.6 -14.0 8.0 6.0 9.8 0.6 -0.3
  - Bosnia and Herzegovina -10.6 -8.9 10.6 -0.7 10.8 0.5 0.0 -0.1 0.0
  - Ethiopia -11.0 -1.1 11.0 -12.6 -0.9 25.2 0.2 -0.9 0.0
  - (Table continues through Dominica -33.5 ... 33.6 ...)

### Table 5 — Countries with Largest Changes in Import Shares (Difference New-Old, percent of total imports. Period: 2011-2015 average.)
- Table reports Difference in Import Shares (New – Old, in percent of country’s total imports) by partner grouping.
- Selected rows (as presented):
  - St. Lucia 45.3 6.5 -45.3 2.0 0.1 0.0 0.0 -47.3 0.0
  - Netherlands Antilles 35.3 8.2 -36.6 3.7 0.7 -0.4 0.2 -40.9 1.3
  - Tonga 31.9 -1.0 -32.0 -32.2 0.1 0.1 0.1 -0.1 0.1
  - Guinea 30.5 23.8 -30.4 2.4 0.8 4.6 0.5 -38.7 -0.1
  - Bahamas, The 29.7 -2.5 -28.8 -15.9 -3.8 -1.1 0.4 -8.3 -0.9
  - St. Kitts and Nevis 26.1 -7.0 -26.0 3.0 -3.8 -8.9 0.2 -16.5 -0.1
  - Vanuatu 22.1 1.3 -20.4 -12.1 -9.8 0.1 1.2 0.2 -1.7
  - Grenada 21.8 1.1 -21.8 9.9 0.2 -0.1 0.1 -31.9 0.0
  - Djibouti 21.6 21.7 -20.2 -37.6 -1.0 15.1 3.8 -0.6 -1.4
  - Samoa 20.4 -0.2 -19.6 -18.4 -0.3 -0.3 -0.1 -0.5 -0.8
  - (Table continues with additional countries and negative differences such as Belize -4.2 ... Mali -4.3 ... up to Afghanistan, I.R. of -19.8 ... 33.9)
- (Table continues with further country entries as presented in the source.)

### References (selected citations provided in the source)
- Centraal Planbureau (2017), CPB World Trade Monitor October 2017.
- Denton, F. (1971), “Adjustment of Monthly or Quarterly Series to Annual Totals: An Approach based on Quadratic Minimization,” Journal of the American Statistical Association, Vol. 66, pp. 99–102.
- Dagum, E.B., and P.A. Cholette (2006), Benchmarking, Temporal Disaggregation, and Reconciliation Methods for Time Series, Springer edition.
- Di Fonzo, T., and M. Marini (2012), “On the Extrapolation with the Denton Proportional Benchmarking Method,” IMF Working Paper Series, WP/12/169.
- IMF (1993), “A Guide to Direction of Trade Statistics.”
- IMF (2017), Quarterly National Accounts Manual - 2017 Edition.
- IMF (2018a), Direction of Trade Statistics.
- IMF (2018b), International Financial Statistics.
- OECD (2016), “New OECD database on International Transport and Insurance Costs,” Statistical Insights, November 2016.
- Miao, G and F. Fortanier (2017), “Estimating Transport and Insurance Costs of International Trade,” OECD Working Paper, No. 2017/04.
- United Nations (2011), International Merchandise Trade Statistics: Concepts and Definitions 2010.

### Annex 1 — New List of Partner Countries (selected entries, Start Year/Month and End Year/Month where provided)
- 1 Afghanistan, Islamic Republic of
- 2 Africa not specified
- 3 Albania
- 4 Algeria
- 5 American Samoa
- 6 Angola
- 7 Anguilla
- 8 Antigua and Barbuda
- 9 Argentina
- 10 Armenia, Republic of 1992 1
- 11 Aruba
- 12 Asia not specified
- 13 Australia
- 14 Austria
- 15 Azerbaijan, Republic of 1992 1
- 16 Bahamas, The
- 17 Bahrain, Kingdom of
- 18 Bangladesh
- 19 Barbados
- 20 Belarus 1992 1
- 21 Belgium 1997 1
- 22 Belgium-Luxembourg 1996 12
- 23 Belize
- 24 Benin
- 25 Bermuda
- 26 Bhutan
- 27 Bolivia
- 28 Bosnia and Herzegovina 1993 1
- 29 Botswana
- 30 Brazil
- 31 Brunei Darussalam
- 32 Bulgaria
- 33 Burkina Faso
- 34 Burundi
- 35 Cabo Verde
- 36 Cambodia
- 37 Cameroon
- 38 Canada
- 39 Central African Republic
- 40 Chad
- 41 Chile
- 42 China, P.R.: Mainland
- 43 China, P.R.: Hong Kong
- 44 China, P.R.: Macao
- 45 Colombia
- 46 Comoros
- 47 Congo, Democratic Republic of
- 48 Congo, Republic of
- (Annex continues listing countries through 229 Zimbabwe as presented in the source.)

*Source: wp1816 - 1. Counterpart trade 4.0 6.0 5.0 (excerpt provided).*

### Annex 2. The Cholette-Dagum Benchmarking Method

### Annex 2. The Cholette-Dagum Benchmarking Method

### Overview
- The Cholette-Dagum benchmarking method (Cholette and Dagum, 2006) is based on a generalized least-squares regression model.
- It is a flexible approach to adjust and make consistent data available at different frequencies (monthly, quarterly, and annual).
- The Cholette-Dagum method is one of the benchmarking methods recommended in the 2017 edition of the IMF’s Quarterly National Accounts Manual (IMF, 2017).

### Model setup and notation
- Let t_s indicate a preliminary monthly series, and m_a benchmark values for the series t_s.
- Indices:
  - t = ,1,2, , T (notation in source: ,1,2,, t st T)
  - m = ,1,2, , M (notation in source: ,1,2,, m am M)
- Benchmarks m_a can be available monthly, quarterly, or annually and can be observed on non-contiguous periods.
- Two simultaneous equations define the model and both include the unknown benchmarked series t_θ as dependent variable:
  - High-frequency indicator equation (equation (3)): H
    - ,1, ,1, , tth hht h s r e t Tβ θ      
    - Assumptions: E(e_t) = 0, E(e_t e_{t-h}) ≠ 0
  - Benchmark aggregation equation (equation (4)):
    - ,1, , , fm mtm tm a m M θ ε      
    - Assumptions: E(ε_m) = 0, E(ε_m^2) = σ_ε^2, E(e_t ε_m) = 0
    - For simplicity, the source assumes binding benchmarks so 2()0. m Eε 

### Discrepancies and aggregation constraints
- Discrepancies between the indicator t_s and the benchmarks m_a are measured as:
  - m d_t = Σ_{t ∈ m} (s_t - a_m)  (notation in source: mmt tm das    )
- Discrepancies can also be estimated in proportional terms:
  - p_m = Σ_{t ∈ m} (s_t / a_m)  (notation in source: p m m t tm a d s    )
- If monthly benchmarks are present, the indicator t_s is adjusted to be equal to those benchmarks.
- For quarterly and annual benchmarks, the indicator series is adjusted so that the aggregation of corresponding monthly observations equals those benchmarks.

### Error structure and properties required for benchmarking
- Equation (3) assumes the indicator series t_s deviates from the true unknown series t_θ, while equation (4) ensures t_θ adds up to the benchmarks m_a.
- Deterministic regressors (r_th, β_h) can be defined as a constant effect to capture scale differences between t_s and t_θ.
- The error e_t (the quarterly discrepancy) should have two characteristics:
  - be proportional to the value of the indicator t_s to distribute errors proportionally to the indicator level;
  - present smooth movements from one period to the next so movements of t_s and t_θ are close.
- To obtain a proportional adjustment, the error is standardized by the value of the indicator:
  - e'_t = e_t / s_t  (equation (5) from the source)
  - By doing so, the standard deviation of e_t is assumed to be equal to s_t.
- To obtain smooth distribution, the standardized error e'_t is assumed to follow a first-order (stationary) autoregressive model, AR(1):
  - e'_t = φ e'_{t-1} + v_t  (equation (6) from the source)
  - with φ < 1
  - Innovations v_t are i.i.d. with assumptions: E(v_t) = 0, E(v_t^2) = σ_v^2, E(v_t v_{t-h}) = 0 for any t and h

### Objective function and role of φ
- Under assumptions (6) and the innovations properties, the Cholette-Dagum model minimizes the objective function displayed in the source (equation (7)).
- The AR parameter φ plays a crucial role in preserving short-term dynamics of the indicator series.
  - When φ is very close to 1 (example given: 0.999) function (7) converges to the proportional Denton method.
  - A value of φ lower than one should be used to adjust for a temporary bias in the indicator.
  - For DOTS estimation, the value of φ is set to 0.9.

### Implementation notes
- The method balances proportional distribution of discrepancies and smoothness of the adjusted series via the AR(1) specification and choice of φ.
- Further details on properties of the Cholette-Dagum method are referenced to chapter 6 of the IMF’s Quarterly National Accounts Manual (IMF, 2017).

*Source: Annex 2. The Cholette-Dagum Benchmarking Method, wp1816 - Annex 2. The Cholette-Dagum Benchmarking Method*

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_Source: https://www.imf.org/-/media/files/publications/wp/2018/wp1816.pdf_