## 1.  Calculated Quota Shares Based on a Linear Formula

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### I. Introduction
- Executive Board discussion in July highlighted need to make significant further progress to report concrete and substantial progress to the Board of Governors at the Annual Meetings.
- Staff and management to consider views and guidance from Directors to identify scope for specific proposals.
- The present paper makes a relatively narrow range of proposals for the second round reform package; proposals are illustrative rather than definitive.

### II. Towards consensus—key issues
- Broad objectives and emerging agreements:
  - Enhance representation of dynamic economies, many of which are emerging market countries.
  - Increase voting shares of emerging market and developing countries as a whole.
  - Enhance voice and participation of low income countries remains a core goal.
- Governance and procedural constraints:
  - Board of Governors Resolution No 61-5 (Singapore) provides for at least a doubling of basic votes, and at a minimum protecting the voting power of low income countries as a group during the two rounds of ad hoc quota increases.
  - Staffing resources for offices of Executive Directors with largest number of members have been increased; staff paper on amendment to the Articles to be circulated.
- Quota formula considerations:
  - Formula should be simple, transparent, consistent with multiple roles of quotas, produce broadly acceptable results, and be feasible to implement statistically.
  - Variables limited to updated/modernized versions of GDP, openness, variability, and reserves.
  - GDP seen as most important variable; openness and variability also important; reserves likely have relatively small weight.
  - Considerable support that PPP GDP should play a role; two strands emerged:
    - Blend approach: include PPP GDP in a GDP blend (market rates + PPP). Simulations illustrated a 75 percent market rate / 25 percent PPP blend in examples.
    - Filter approach: formula based solely on market rate GDP plus a PPP-based supplementary filter to add under-represented countries.
- Compression:
  - Compression narrows dispersion of calculated quota shares without altering ranking.
  - Most Directors favored a compression factor to reduce influence of economic size.
  - Compression reduces share of a small group (seven members with largest calculated quota shares) and increases shares of all other members.
  - Judgment needed on compression level; excessive compression can reduce reflectiveness of relative economic positions.

### III. Elements of a possible approach (common across proposals)
- Variable weights and formula variants:
  - Proposed new formula weights include 50 percent on GDP and 5 percent on reserves.
  - Two alternative weightings for openness and variability: 30–25 percent for openness and 15–20 percent for variability.
  - Specific linear formula variants referenced:
    - 0.5*GDP + 0.3*Openness + 0.15*Variability + 0.05*Reserves (referred to as 50/30/15/05).
    - 0.5*GDP + 0.25*Openness + 0.2*Variability + 0.05*Reserves (referred to as 50/25/20/05).
- Size and allocation of second round:
  - All proposals based on overall increase (first and second round combined) of 10 percent, implying a second round increase of 8.1 percent.
  - Allocation to under-represented members by achieving a uniform proportionate reduction in the gap between calculated quota shares and pre-Singapore actual quota shares (consistent with first round approach).
  - Four members receiving first round increases in Singapore receive second round increases as required to deliver same overall proportionate reduction in out-of-lineness under the two rounds.
- Eligibility, foregoing, and basic votes:
  - In most scenarios all under-represented countries assumed eligible; some scenarios include a higher threshold to concentrate increases.
  - Assumes major advanced countries willing to forego part of increases; illustrative assumption: eligible major advanced countries forego increases beyond level that would restore their pre-Singapore voting shares (two countries expressed willingness to forego any increase beyond that level and paper adopts this assumption for all major advanced countries).
  - Assumes doubling of basic votes; simulations also illustrate impact of a tripling in basic votes.

### IV. Two strands for using PPP GDP in second round
- Blend approach (examples used in simulations):
  - GDP blend: 75 percent market rate GDP and 25 percent PPP GDP.
  - Combined formula scenarios include a compression factor of 0.95 in all presented examples.
- Filter approach (supplementary PPP filter):
  - Formula uses solely market rate GDP plus supplementary filter based on PPP GDP to add a small number of emerging market and developing countries to the list of under-represented countries eligible for second round increases.
  - Filter adds countries only (not to exclude).
  - Filter condition: member’s share of global PPP GDP is more than 50 percent larger than its actual quota share (PPP GDP/AQS ratio > 1.5).
  - Under filter approach, countries brought in by the filter receive a 5 percent increase over their pre-Singapore voting share. Under-represented emerging market and developing countries that also meet the filter test receive no less than a 5 percent increase over pre-Singapore voting share.

### V. Simulation approaches and parameters (explicit)
- Combined formula example used: Q = (0.5*GDP Blend + 0.25*Openness + 0.2*Variability + 0.05*Reserves)^0.95 and variant with 0.5*GDP + 0.3*Openness + 0.15*Variability + 0.05*Reserves raised to 0.95.
- GDP blend: 75 percent market exchange rates and 25 percent PPP exchange rates.
- Assumed aggregate increases: an 8.1 percent increase (total first and second round increase of 10.0 percent).
- Basic votes (BV) scenarios shown: BV = 500 and BV = 750 in voting-share illustrations.
- Filter eligibility parameter details:
  - Supplementary filter calculated as member's average share of global PPP GDP for the three year period ending in 2005 divided by member's pre-Singapore quota share (PPP data from quota database in Quotas—Updated Calculations and Data Adjustments (2007)).
  - To meet filter, member’s share of global PPP GDP must exceed its quota share by more than 50 percent (ratio greater than 1.5).
  - Under supplementary filter scenarios, member eligible for ad hoc increase if it meets the filter and its out-of-lineness (CQS/AQS) is greater than 0.667 under the specified formula (implying member is over-represented by less than 50 percent using calculated quota share as base).
- Compression parameter used: K = 0.95 in many quota formula simulations (also K = 0.90 explored).

### VI. Key findings from simulations (preserved exact reported outcomes)
- Aggregate effects:
  - Combined formula (GDP blend + compression) outcomes: Aggregate calculated quota share of emerging market and developing countries increases by 1.1 to 1.5 percentage points relative to outcome of existing quota formulas, with most sub-groups showing an increase.
  - Solely market rate GDP formulas (no compression) outcomes: Aggregate calculated quota share of emerging market and developing countries declines by 3.7 to 4 percentage points.
- Voting-share examples (post second round, selected):
  - Emerging Market and Developing Countries voting shares range in examples from 39.4 to 42.0 percent across scenarios and parameter choices.
  - Developing countries voting shares range in examples from 30.9 to 34.4 percent across scenarios.
  - Advanced economies voting shares range in examples from 60.6 to 58.0 percent across scenarios.
- Filter vs combined formula:
  - Filter approach results in a shorter list of countries eligible for second round increases and a slightly higher uniform reduction in out-of-lineness for these countries compared with combined formula approach.
  - Movement of shares shows a similar but slightly smaller increase in aggregate voting share of emerging market and developing countries compared with combined formula approach.
- Levers for larger change:
  - To generate significantly more movement toward emerging market and developing countries would require changes in key assumptions, such as greater foregoing by advanced countries, or a different allocation method that concentrates more increases on emerging market and developing countries.

### VII. Representative numeric outcomes from tables (selected exact figures)
- Aggregate voting-share examples (post second round, selected entries from Tables 2–4 preserved exactly):
  - Emerging Market and Developing Countries: examples include 39.4; 39.5; 39.1; 38.8; 39.5; 39.1; 39.4; 39.0; 39.7; 39.3 (Table 5 combined formula columns).
  - Advanced economies (Table 5 combined formula columns): 61.6; 60.5; 60.9; 61.2; 60.5; 60.9; 60.6; 61.0; 60.3; 60.7.
  - Memoranda examples (selected): No. of countries receiving ad hocs: 54; 53; 54; 54; 54; 53; 54; 54; Uniform reduction factor examples: 33.8; 30.4; 38.6; 33.7; 36.4; 32.6; 40.4; 36.3.
- Filter approach (Table 6 selected aggregates preserved exactly):
  - Emerging Market and Developing Countries examples: 38.4; 39.5; 39.0; 38.7; 39.5; 39.1; 39.0; 38.7; 39.4; 39.0.
  - No. of countries receiving ad hocs: 41; 40; 41; 41; 39; 38; 39; 39.
  - Uniform reduction factor examples: 38.5; 31.1; 44.9; 37.9; 38.8; 32.0; 45.1; 38.2.
- Filter approach with a threshold (Table 7 selected aggregates preserved exactly):
  - Emerging Market and Developing Countries examples: 38.4; 39.5; 39.4; 39.0; 39.8; 39.4; 39.4; 39.0; 39.7; 39.4.
  - No. of countries receiving ad hocs: 33; 33; 33; 33; 34; 34; 34; 34.
  - Uniform reduction factor examples: 45.7; 39.1; 51.6; 45.1; 44.1; 37.7; 49.8; 43.5.
- Selected member-level examples (Table excerpts preserved exactly):
  - Member Countries Meeting Filter Parameters (Linear Formula) — CQS/AQS under 50/30/15/05; CQS/AQS under 50/25/20/05; PPP GDP/AQS:
    - Korea: 2.855  2.862  2.162
    - Turkey: 1.957  2.050  2.055
    - China: 1.939  1.901  5.107
    - Equatorial Guinea: 1.809  1.886  1.950
    - Thailand: 1.384  1.403  1.784
    - Turkmenistan: 1.292  1.350  1.792
    - Bhutan: 1.061  1.088  1.639
    - Vietnam: 1.046  1.002  2.631
    - Brazil: 0.994  1.029  1.849
    - Philippines: 0.914  0.943  1.658
    - India: 0.755  0.749  3.017
    - Indonesia: 0.740  0.755  1.647
    - Colombia: 0.673  0.682  1.548
  - Country-level calculated quota share examples (Table 5a preserved exactly):
    - United States (Existing 17.023; Pre First Round 16.732): calculated examples include 16.284; 20.102; 18.107; 20.339; 18.302.
    - China (Existing 2.928; Pre First Round 3.652): calculated examples include 6.137; 5.602; 5.397; 5.497; 5.299.
    - India (Existing 1.916; Pre First Round 1.883): calculated examples include 1.287; 1.524; 1.573; 1.513; 1.561.
    - Korea (Existing 0.760; Pre First Round 1.329): calculated examples include 2.512; 2.221; 2.247; 2.226; 2.250.
    - Brazil (Existing 1.402; Pre First Round 1.378): calculated examples include 1.069; 1.469; 1.518; 1.517; 1.565.
    - Singapore (Existing 0.406; Pre First Round 0.399): calculated examples include 1.929; 1.023; 1.078; 1.058; 1.112.
    - Luxembourg (Existing 0.139; Pre First Round 0.137): calculated examples include 1.369; 0.631; 0.682; 0.693; 0.745.

### VIII. Simulation design variations and observed mechanics
- Eligibility and thresholds:
  - Eligibility rule variants: out-of-lineness > 1.0 or out-of-lineness > 1.1 for second round eligibility in different scenarios.
  - Supplementary filter for emerging market and developing countries: PPP GDP share > 1.5 times actual quota share and CQS/AQS > 0.667.
- Compression effects:
  - Compression implemented by raising linear formula to power K (examples use K = 0.95 and K = 0.90).
  - Compression materially changes distribution of calculated quota shares; lower K (stronger compression) alters shares at both aggregate and country levels.
- Basic-vote parameterization:
  - BV scenarios reported: BV = 500 and BV = 750. Voting shares reported separately for these BV choices across scenarios.
- Policy treatment rules applied consistently across simulations:
  - Protection of pre-Singapore voting shares of LICs (PRGF-eligible).
  - Foregoing by eligible G-7 members to specified levels in scenarios.
  - For underrepresented countries not eligible under the filter: uniform proportionate reduction in out-of-lineness.
  - For underrepresented countries also eligible under the filter: uniform proportionate reduction in out-of-lineness or a 5 percent increase above pre-Singapore voting shares, whichever is greater.
  - For over-represented members eligible under the filter: a 5 percent increase above pre-Singapore voting shares.

### IX. Data vintage, coverage, and adjustments (explicit)
- Data basis: 1993–2005 data.
- PPP and GDP data as of January 31, 2007 (WEO) converted to SDRs for 176 countries; for nine countries with no WEO data PPP GDP estimated based on share in global GDP at market rates.
- Adjustments included re-exports, international banking interest, and non-monetary gold.
- Includes Montenegro (member on January 18, 2007); for three countries not yet consenting/paid, 11th Review proposed quotas used.

### X. Issues for discussion (items for Directors)
- Appropriate objectives for the second round reform package.
- Relative merits of the two approaches proposed—formula incorporating a blended GDP variable and compression versus the filter approach.
- Desirable weights for variables in the formula, especially the relative weights for openness and variability.
- Appropriate aggregate size of the second round ad hoc quota increase (illustrated as 8.1 percent second round, 10.0 percent total), the mechanism for allocating the increase to eligible members, and the size of the increase in basic votes (examples include doubling and tripling basic votes; BV = 500 and BV = 750 illustrated).

*Prepared by the Quota and Voice Working Group; source: Finance Department (excerpts from IMF staff paper).*

### 1.  Calculated Quota Shares Based on a Linear Formula .................................................10

### 1.  Calculated Quota Shares Based on a Linear Formula

### I. Introduction
- Executive Board discussion in July highlighted need to make significant further progress to report concrete and substantial progress to the Board of Governors at the Annual Meetings.
- Staff and management to consider views and guidance from Directors to identify scope for specific proposals.
- The present paper makes a relatively narrow range of proposals for the second round reform package; proposals are illustrative rather than definitive.

### II. Towards consensus—key issues
- Broad objectives and emerging agreements:
  - Goal to enhance representation of dynamic economies, many of which are emerging market countries.
  - Growing recognition that outcome should increase voting shares of emerging market and developing countries as a whole.
  - Enhancing voice and participation of low income countries remains a core goal.
- Board of Governors Resolution No 61-5 (Singapore) provides for at least a doubling of basic votes, and at a minimum protecting the voting power of low income countries as a group during the two rounds of ad hoc quota increases.
- Staffing resources for offices of Executive Directors with largest number of members have already been increased; staff paper on amendment to the Articles (allowing elected Executive Directors representing large numbers of members to appoint more than one Alternate Executive Director) to be circulated.
- Quota formula considerations:
  - Agreement formula should be simple and transparent, consistent with multiple roles of quotas, produce broadly acceptable results, and be feasible to implement statistically.
  - Variables limited to updated/modernized versions of the four variables in existing formulas—GDP, openness, variability, and reserves.
  - Some areas (e.g., definitions of openness and variability) lack sufficient support for change and remain for further work.
- Weights and measurement:
  - General convergence that GDP should be most important; openness and variability also important; reserves likely have relatively small weight.
  - Considerable support that PPP GDP should play a role in determining second round quota increases, but the precise role is open and linked to measurement/data issues (ICP upgrades).
- Two broad strands for PPP GDP use emerged:
  1. Include PPP GDP in a GDP blend (market exchange rates + PPP) to capture non-financial roles of quotas; relative weights open. Simulations suggest some use of PPP GDP likely needed to raise calculated quota share of emerging market and developing countries as a whole, probably combined with compression.
  2. Maintain formula based solely on market rate GDP and add supplementary filter using PPP GDP to capture countries whose global role is underrepresented; concerns that a filter would have only a one-time effect—could extend durability via Board of Governors Resolution commitment to consider PPP GDP for some time into the future.
- Compression:
  - Compression narrows dispersion of calculated quota shares between large and smaller countries without altering ranking.
  - Most Directors in July favored use of a compression factor to reduce influence of economic size.
  - Compression reduces share of a small group (seven members with largest calculated quota shares, six of which are advanced) and increases shares of all other members.
  - Judgment needed on compression level; too large compression could reduce reflectiveness of relative economic positions.

### III. Elements of a possible approach
- Common elements across proposals:
  - Variable weights: new formula with 50 percent weight on GDP and 5 percent weight on reserves. Two alternatives for openness and variability: weights of 30–25 percent for openness and 15–20 percent for variability, respectively.
  - Size of the second round: All proposals based on overall increase (first and second round combined) of 10 percent, implying a second round increase of 8.1 percent.
  - Allocation of second round increases: allocated to under-represented members under new quota formula based on achieving a uniform proportionate reduction in the gap between calculated quota shares and pre-Singapore actual quota shares (consistent with first round approach). Four members receiving first round increases in Singapore receive second round increases as required to deliver same overall proportionate reduction in out-of-lineness under the two rounds.
  - Eligibility: In most scenarios all under-represented countries assumed eligible for second round; some scenarios include a higher threshold concentrating increases on relatively more out-of-line countries.
  - Foregoing: Assumes major advanced countries willing to forego part of increases to which they would otherwise be entitled. For illustrative purposes, assumes a common approach for all eligible major advanced countries and that two countries have expressed willingness to forego any increase beyond level that would restore their pre-Singapore voting shares (paper adopts this assumption for all major advanced countries). Proposals indicate sensitivity to larger foregoing (to post-Singapore rather than pre-Singapore voting shares).
  - Increase in basic votes: Assumes doubling of basic votes, sufficient in simulations to preserve pre-Singapore voting share of low income countries. Proposals also illustrate impact of a tripling in basic votes.
- Two strands for using PPP GDP in second round:
  1. Blend approach:
     - Blend variable assumed here: 75 percent market rate GDP and 25 percent PPP GDP.
     - For all scenarios presented under this approach, formula includes compression factor of 0.95.
  2. Filter approach:
     - Formula uses solely market rate GDP plus supplementary filter based on PPP GDP to add a small number of emerging market and developing countries to list of under-represented countries eligible for second round increases.
     - Filter used only to add countries, not to exclude.
     - Filter based on members’ shares in global PPP GDP and includes countries whose shares in global PPP GDP are more than 50 percent larger than their actual quota shares.
     - Under filter approach, assumed that countries brought in by the filter receive a 5 percent increase over their pre-Singapore voting share. Under-represented emerging market and developing countries that also meet the filter test would receive an increase of no less than 5 percent over their pre-Singapore voting share.
- Specific formula variants referenced:
  - 0.5*GDP + 0.3*Openness + 0.15*Variability + 0.05*Reserves (referred to as 50/30/15/05).
  - 0.5*GDP + 0.25*Openness + 0.2*Variability + 0.05*Reserves (referred to as 50/25/20/05).
- Eligibility filter parameter details:
  - Under supplementary filter scenarios, a member eligible for ad hoc quota increase if it meets the filter and its out-of-lineness (CQS/AQS) is greater than 0.667 under the specified formula (implying member is over-represented by less than 50 percent using calculated quota share as base).
  - The filter (per a participant proposal at a G-20 meeting in Durban) is calculated as member's average share of global PPP GDP for the three year period ending in 2005 divided by member's pre-Singapore quota share. PPP data for filter from quota database in Quotas—Updated Calculations and Data Adjustments (2007). To meet filter, member’s share of global PPP GDP must exceed its quota share by more than 50 percent (ratio greater than 1.5).
- Table excerpt: Member Countries Meeting Filter Parameters (Linear Formula)
  - Columns shown: CQS/AQS under 50/30/15/05; CQS/AQS under 50/25/20/05; PPP GDP/AQS.
  - Selected rows (values preserved exactly):
    - Korea: 2.855  2.862  2.162
    - Turkey: 1.957  2.050  2.055
    - China: 1.939  1.901  5.107
    - Equatorial Guinea: 1.809  1.886  1.950
    - Thailand: 1.384  1.403  1.784
    - Turkmenistan: 1.292  1.350  1.792
    - Bhutan: 1.061  1.088  1.639
    - Vietnam: 1.046  1.002  2.631
    - Brazil: 0.994  1.029  1.849
    - Philippines: 0.914  0.943  1.658
    - India: 0.755  0.749  3.017
    - Indonesia: 0.740  0.755  1.647
    - Colombia: 0.673  0.682  1.548
  - Note: China includes China, P.R., and Hong Kong SAR per source.

### IV. Results
- Combined formula (GDP blend + compression) outcomes:
  - Aggregate calculated quota share of emerging market and developing countries increases by 1.1 to 1.5 percentage points relative to outcome of existing quota formulas, with most sub-groups showing an increase.
  - Increases somewhat larger in formula with higher weight for variability.
- Solely market rate GDP formulas (no compression) outcomes:
  - Aggregate calculated quota share of emerging market and developing countries declines by 3.7 to 4 percentage points.
- Voting share outcomes (combined formula approach):
  - All simulations result in a further increase in aggregate voting share of emerging market and developing countries following the second round.
  - Largest increases come from simulations involving a tripling of basic votes and a greater degree of foregoing.
- Filter approach outcomes:
  - Results in a shorter list of countries eligible for second round increases and a slightly higher uniform reduction in out-of-lineness for these countries compared with combined formula approach.
  - Movement of shares shows a similar but slightly smaller increase in aggregate voting share of emerging market and developing countries compared with combined formula approach.

*Source: Finance Department (excerpts from IMF staff paper)._

### 19.      As noted, a higher threshold could potentially be used to concentrate the second

### 19.      As noted, a higher threshold could potentially be used to concentrate the second

### Simulation approaches and parameters
- Filter threshold: out-of-lineness ratio of 1.1 for eligibility in the second round (Table 4 scenarios).
- Supplementary filter condition for emerging market and developing countries: member's share of global PPP GDP is 50 percent greater than its actual quota share, and out-of-lineness (calculated quota share over actual quota share, or CQS/AQS) is greater than 0.667.
- Combined formula example (used in simulations): Q = (0.5*GDP Blend + 0.25*Openness + 0.2*Variability + 0.05*Reserves)^0.95 (and variant with 0.5*GDP + 0.3*Openness + 0.15*Variability + 0.05*Reserves)^0.95).
- GDP blend: 75 percent at market exchange rates and 25 percent at PPP exchange rates.
- Assumed aggregate increases: an 8.1 percent increase (total first and second round increase of 10.0 percent).
- Basic votes (BV) scenarios shown: BV = 500 and BV = 750 in voting-share illustrations.
- Protection and allocation assumptions used in scenarios:
  - Protection of the pre-Singapore voting shares of LICs (PRGF-eligible countries).
  - Foregoing by eligible G-7 members to specified levels in the scenarios.
  - For underrepresented countries not eligible under the filter: uniform proportionate reduction in out-of-lineness.
  - For underrepresented countries also eligible under the filter: uniform proportionate reduction in out-of-lineness or a 5 percent increase above pre-Singapore voting shares, whichever is greater.
  - For over-represented members eligible under the filter: a 5 percent increase above pre-Singapore voting shares.
- Compression parameter used in some quota formula simulations: K = 0.95 (quota formula raised to the power K).

### Key findings from simulations
- Different second-round approaches (combined formula with blended GDP and compression, filter approach, filter with higher threshold) can deliver broadly similar results in terms of actual quota and voting shares, despite substantial differences in calculated quota shares.
- Using a higher filter threshold (1.1) can concentrate second-round increases on under-represented countries that are relatively more out of line and can permit a somewhat larger uniform proportionate reduction factor, yielding a similar aggregate movement in voting share toward emerging market and developing countries as a combined formula with no filter.
- To generate significantly more movement in aggregate shares toward emerging market and developing countries would require changes in key assumptions, such as greater foregoing by advanced countries, or a different allocation method for the second round that concentrates more increases on emerging market and developing countries.

### Representative numeric outcomes from tables (selected)
- Aggregate voting-share examples (post second round, selected entries from Tables 2–4):
  - Emerging Market and Developing Countries voting shares range in examples from 39.4 to 42.0 percent across scenarios and parameter choices.
  - Developing countries voting shares range in examples from 30.9 to 34.4 percent across scenarios.
  - Advanced economies voting shares range in examples from 60.6 to 58.0 percent across scenarios.
- Uniform reduction factors (examples reported in tables):
  - Table 2 examples: 33.8, 30.4, 38.6, 33.7, 36.4, 32.6, 40.4, 36.3.
  - Table 3 examples: 38.5, 31.1, 44.9, 37.9, 38.8, 32.0, 45.1, 38.2.
  - Table 4 examples with threshold 1.1: 45.7, 39.1, 51.6, 45.1, 44.1, 37.7, 49.8, 43.5.
- Membership and data notes used in simulations:
  - PPP data retrieved from the WEO database as of January 31, 2007 (converted to SDRs) for 176 countries; for nine countries with no WEO data, PPP GDP was estimated based on the countries' share in global GDP at market rates.
  - Includes Montenegro, which became a member on January 18, 2007 (pre-Singapore shares adjusted accordingly).
  - Data basis: 1993–2005 data with adjustments to current receipts and payments for re-exports, international banking interest, and non-monetary gold.

### Issues for discussion (items for Directors)
- The appropriate objectives for the second round reform package.
- The relative merits of the two approaches proposed in the paper—a formula incorporating a blended GDP variable and compression, and the filter approach.
- The desirable weights for variables in the formula, especially the relative weights for openness and variability.
- The appropriate aggregate size of the second round ad hoc quota increase, the mechanism for allocating the increase to eligible members, and the size of the increase in basic votes.

*Prepared by the Quota and Voice Working Group; Approved by David Burton; September 14, 2007.*

### 7.  Second Round Simulation—Illustration of Actual Quota Shares Based on the Filter

### 7. Second Round Simulation—Illustration of Actual Quota Shares Based on the Filter Approach with a Threshold

### Simulation design, formulas, and key assumptions
- Formula variants:
  - Q = (0.5*GDP Blend + 0.3*Openness + 0.15*Variability + 0.05*Reserves)^0.95 (denoted K=0.95 in some tables).
  - Q = (0.5*GDP Blend + 0.25*Openness + 0.2*Variability + 0.05*Reserves)^0.95.
  - Linear formula variants: 0.50*GDP + 0.3*Openness + 0.15*Variability + 0.05*Reserves; and 0.50*GDP + 0.25*Openness + 0.2*Variability + 0.05*Reserves.
- GDP Blend specification:
  - GDP blended using GDP weighted 75 percent at market exchange rates and 25 percent at PPP exchange rates.
  - PPP data from the quota database reported in Quotas—Updated Calculations and Data Adjustments (2007) retrieved from the WEO database as of January 31, 2007 (converted to SDRs) for 176 countries; for nine countries with no WEO data, PPP GDP was estimated based on the countries' share in global GDP at market rates.
- Scenario assumptions common across simulations:
  - a) an 8.1 percent increase (total first and second round increase of 10.0 percent);
  - b) basic votes to the level specified above, and protection of the pre-Singapore voting shares of LICs;
  - c) foregoing by eligible G-7 members to the level specified above.
- Filter eligibility rules (in filter scenarios):
  - Members eligible for a quota increase if out-of-lineness (calculated quota share divided by actual quota share) exceeds 1.0 (or 1.1 under threshold scenarios).
  - Supplementary filter: emerging market and developing countries eligible if member's share of global PPP GDP is 50 percent greater than its actual quota share and CQS/AQS > 0.667.
- Basic votes scenarios:
  - BV = 500 and BV = 750 are both reported as alternative basic-vote parameterizations.

### Aggregated outcomes — Actual quota shares post second round (selected group-level results preserved exactly)
- From Table 5 (Combined formula approach) — Actual Quota Share Post Second Round (examples of scenario columns shown):
  - Advanced economies: 61.6; 60.5; 60.9; 61.2; 60.5; 60.9; 60.6; 61.0; 60.3; 60.7.
  - Major advanced economies: 46.0; 45.2; 45.3; 45.7; 44.8; 45.3; 45.0; 45.4; 44.5; 45.0.
    - Of which: US: 17.4; 17.1; 17.7; 17.9; 17.4; 17.7; 17.7; 18.0; 17.4; 17.7.
  - Emerging Market and Developing Countries: 38.4; 39.5; 39.1; 38.8; 39.5; 39.1; 39.4; 39.0; 39.7; 39.3.
  - Developing countries: 30.9; 32.1; 31.9; 31.7; 32.3; 31.9; 32.2; 31.9; 32.5; 32.2.
  - Transition economies: 7.6; 7.4; 7.2; 7.2; 7.2; 7.2; 7.2; 7.2; 7.2; 7.2.
  - Total: 100.0 (all scenario columns).
  - Memoranda:
    - No. of countries receiving ad hocs: 54; 53; 54; 54; 54; 53; 54; 54; (varies by column).
    - Uniform reduction factor: 33.8; 30.4; 38.6; 33.7; 36.4; 32.6; 40.4; 36.3; (varies by column).
    - EU 27: 32.9; 32.4; 32.5; 32.3; 32.5; 32.5; 32.2; 32.1; 32.3; 32.2.
    - LICs (PRGF-eligible countries): 7.5; 7.4; 7.1; 7.1; 7.1; 7.1; 7.1; 7.1; 7.1; 7.1.
- From Table 6 (Filter approach) — Actual Quota Shares Post Second Round (selected aggregates preserved exactly):
  - Advanced economies: 61.6; 60.5; 61.0; 61.3; 60.5; 60.9; 61.0; 61.3; 60.6; 61.0.
  - Major advanced economies: 46.0; 45.2; 45.4; 45.9; 44.8; 45.4; 45.4; 45.9; 44.8; 45.4.
    - Of which: US: 17.4; 17.1; 17.7; 18.0; 17.4; 17.7; 17.7; 18.0; 17.4; 17.7.
  - Emerging Market and Developing Countries: 38.4; 39.5; 39.0; 38.7; 39.5; 39.1; 39.0; 38.7; 39.4; 39.0.
  - Developing countries: 30.9; 32.1; 32.0; 31.6; 32.4; 32.0; 32.0; 31.6; 32.4; 32.0.
  - Transition economies: 7.6; 7.4; 7.1; 7.1; 7.1; 7.1; 7.1; 7.0; 7.1; 7.1.
  - Total: 100.0 (all scenario columns).
  - Memoranda:
    - No. of countries receiving ad hocs: 41; 40; 41; 41; 39; 38; 39; 39 (varies by column).
    - Uniform reduction factor: 38.5; 31.1; 44.9; 37.9; 38.8; 32.0; 45.1; 38.2 (varies by column).
    - EU 27: 32.9; 32.4; 32.5; 32.4; 32.5; 32.5; 32.4; 32.4; 32.5; 32.4.
    - LICs: 7.5; 7.4; 7.2; 7.2; 7.2; 7.2; 7.2; 7.2; 7.2; 7.2.
- From Table 7 (Filter approach with a threshold) — Actual Quota Share Post Second Round (selected aggregates preserved exactly):
  - Advanced economies: 61.6; 60.5; 60.6; 61.0; 60.2; 60.6; 60.6; 61.0; 60.3; 60.6.
  - Major advanced economies: 46.0; 45.2; 45.0; 45.6; 44.5; 45.0; 45.0; 45.6; 44.5; 45.0.
    - Of which: US: 17.4; 17.1; 17.7; 18.0; 17.4; 17.7; 17.7; 18.0; 17.4; 17.7.
  - Emerging Market and Developing Countries: 38.4; 39.5; 39.4; 39.0; 39.8; 39.4; 39.4; 39.0; 39.7; 39.4.
  - Developing countries: 30.9; 32.1; 32.3; 31.9; 32.7; 32.3; 32.3; 31.9; 32.7; 32.3.
  - Transition economies: 7.6; 7.4; 7.1; 7.1; 7.1; 7.1; 7.1; 7.1; 7.1; 7.1.
  - Total: 100.0 (all scenario columns).
  - Memoranda:
    - No. of countries receiving ad hocs: 33; 33; 33; 33; 34; 34; 34; 34 (varies by column).
    - Uniform reduction factor: 45.7; 39.1; 51.6; 45.1; 44.1; 37.7; 49.8; 43.5 (varies by column).
    - EU 27: 32.9; 32.4; 32.2; 32.2; 32.3; 32.2; 32.2; 32.2; 32.3; 32.2.
    - LICs: 7.5; 7.4; 7.2; 7.2; 7.2; 7.2; 7.2; 7.2; 7.2; 7.2.

### Notable results and mechanics (preserved exact numeric examples from tables)
- The United States pre- and post-first-round quota shares presented in Table 1a: 17.380; 17.076; calculated formula scenarios show values such as 16.284; 19.149; 19.387; 22.173; 22.457 across different formula columns.
- China (including China, P.R., and Hong Kong SAR per notes) example values in Table 1a: 2.980; 3.719; under some formulas calculated quota shares include 6.137; 6.731; 6.627; 5.777; 5.666.
- Illustrative compression parameter: The compression (K) raises the quota formula to the power of K; K=0.95 is applied in multiple scenarios (noted across tables).
- Basic-vote parameterization impact: Voting shares and actual quota shares are reported separately for BV = 500 and BV = 750 across scenarios — results vary by small decimal amounts depending on BV choice (tables provide full numeric outputs for each member and scenario).

### Implementation-related metrics preserved from the statistical appendix
- Data vintage and coverage:
  - Calculations based on 1993-2005 data.
  - PPP and GDP data as of January 31, 2007 (WEO).
- Adjustment factors and data treatments:
  - Reflects impact of adjustments to current receipts and payments for re-exports, international banking interest, and non-monetary gold.
- Membership and quota status caveats:
  - For the three countries that have not yet consented to, and paid for, their quota increases, 11th Review proposed quotas are used.
  - Includes Montenegro, which became a member on January 18, 2007 (pre-Singapore shares have been adjusted accordingly).

*Prepared by the Quota and Voice Working Group; source: Finance Department (statistical appendix tables reproduced in the document)._

### 0.667 under the specified formula, implying that the member is over-represented by less than 50 percent using its calcul

### _091407 - 0.667 under the specified formula, implying that the member is over-represented by less than 50 percent using its calcul

### Scenarios and assumed parameters
- "Under these scenarios, all members are eligible for a quota increase if their out-of-lineness (calculated quota share divided by actual quota share) is greater than 1.1."
- "Emerging market and developing countries are also eligible under a supplementary filter if the member's share of global PPP GDP is 50 percent greater than its actual quota share, and its level of out-of-lineness (calculated quota share over actual quota share, or CQS/AQS) is greater than 0.667 under the specified formula, implying that the member is over-represented by less than 50 percent using its calculated quota share as a base."
- "These scenarios also assume: a) an 8.1 percent increase (total first and second round increase of 10.0 percent); b) basic votes to the level specified above, and protection of the pre-Singapore voting shares of LICs; c) foregoing by eligible G-7 members to the level specified above; d) for underrepresented countries not also eligible under the filter, a uniform proportionate reduction in out-of-lineness; e) for underrepresented countries also eligible under the filter, a uniform proportionate reduction in out-of-lineness or a 5 percent increase above their pre-Singapore voting shares, whichever is greater; and f) for over-represented members eligible under the filter, a 5% increase above their pre-Singapore voting shares."

### Formulae and simulation specifications
- "0.50*GDP + 0.3*Openness + 0.15*Variability + 0.05*Reserves." (Linear Formula (50/30/15/5))
- "0.50*GDP + 0.25*Openness + 0.2*Variability + 0.05*Reserves." (Linear Formula (50/25/20/5))
- Basic vote (BV) scenarios shown for "BV = 500" and "BV = 750".
- Compression scenarios referenced in table of contents: "Compression (0.95)" and "Compression (0.90)" with and without a Threshold.

### Data scope, vintage, and adjustments
- "Based on 1993-2005 data."
- "Reflects the impact of adjustments to current receipts and payments for re-exports, international banking interest, and non-monetary gold."
- "For the three countries that have not yet consented to, and paid for, their quota increases, 11th Review proposed quotas are used."
- "Includes Montenegro, which became a member on January 18, 2007 (pre-Singapore shares have been adjusted accordingly)."
- "PPP data from the quota database reported in Quotas—Updated Calculations and Data Adjustments (2007) were retrieved from the WEO database as of January 31, 2007 (converted to SDRs) for 176 countries and, for nine countries with no WEO data, PPP GDP was estimated based on the countries' share in global GDP at market rates, as published in Quotas—Updated Calculations and Data Adjustments (2007)."

### Simulation outputs and organization (as presented)
- Table 4b title: "Second Round Simulation – Members Receiving Ad Hoc Quota Increases Based on the Filter Approach with a Threshold 1/ 2 / 3/"
- Members are "Listed according to degree of out-of-lineness."
- The tables present pre-Singapore and post-Singapore "Voting Shares" for multiple country cases under combinations of:
  - Linear formula variants (50/30/15/5) and (50/25/20/5)
  - Basic vote levels BV = 500 and BV = 750
  - Scenarios of "Foregoing to Pre-Singapore" and "Foregoing to Post-Singapore" (as indicated in table headings)
- The document includes a multi-part Table of Contents enumerating simulation tables and member-by-member breakdowns:
  - Tables 1, 1a, 1b: Filter Approach with Compression (0.95)
  - Tables 2, 2a, 2b: Filter Approach with Compression (0.95) and a Threshold
  - Tables 3, 3a, 3b: Filter Approach with Compression (0.90)
  - Tables 4, 4a, 4b: Filter Approach with Compression (0.90) and a Threshold

### Key procedural rules applied in the simulations
- Eligibility rule: "all members are eligible for a quota increase if their out-of-lineness ... is greater than 1.1."
- Supplementary filter for emerging market and developing countries: simultaneous conditions on global PPP GDP share and CQS/AQS > 0.667.
- Treatment rules for categories of members:
  - "foregoing by eligible G-7 members to the level specified above"
  - "protection of the pre-Singapore voting shares of LICs"
  - reductions or minimum increases applied to underrepresented and over-represented members as specified in the scenarios.

*Source: Finance Department.*

### 5. Calculated Quota Shares Based on a Linear Formula with Compression .............33

### 5. Calculated Quota Shares Based on a Linear Formula with Compression

### Methodology and scenario parameters
- Linear formulas evaluated:
  - (0.50*GDP + 0.3*Openness + 0.15*Variability + 0.05*Reserves)^K
  - (0.50*GDP + 0.25*Openness + 0.2*Variability + 0.05*Reserves)^K
- Compression parameter (K) considered: K = 0.95 and K = 0.90.
- Filter eligibility and thresholds used in scenarios:
  - Under some scenarios, all members are eligible for a quota increase if out-of-lineness (calculated quota share divided by actual quota share) > 1.0.
  - Under threshold scenarios, eligibility requires out-of-lineness > 1.1.
  - Supplementary filter for emerging market and developing countries: member's share of global PPP GDP is 50 percent greater than its actual quota share and CQS/AQS > 0.667.
- Other shared scenario assumptions (as stated in notes):
  - a) an 8.1 percent increase (total first and second round increase of 10.0 percent);
  - b) basic votes to the level specified above, and protection of the pre‑Singapore voting shares of LICs;
  - c) foregoing by eligible G-7 members to the level specified above;
  - d) for underrepresented countries not also eligible under the filter, a uniform proportionate reduction in out‑of‑lineness;
  - e) for underrepresented countries also eligible under the filter, a uniform proportionate reduction in out‑of‑lineness or a 5 percent increase above their pre‑Singapore voting shares, whichever is greater;
  - f) for over‑represented members eligible under the filter, a 5 percent increase above their pre‑Singapore voting shares.
- Data basis: Based on 1993–2005 data with adjustments (re-exports, international banking interest, non‑monetary gold). PPP data from WEO database as of January 31, 2007 for 176 countries; nine countries with no WEO data estimated per SM/07/251. Includes Montenegro (member as of January 18, 2007). For three countries not yet consenting/paid, 11th Review proposed quotas are used.

### Aggregate results (Table 5 — calculated quota shares by group)
- Actual Quotas (Existing) and calculated shares under two linear formulas and two compression exponents (K):
  - Advanced economies:
    - Existing: 61.6
    - Pre First Round: 60.5
    - Linear Formula K=0.95 (50/30/15/5): 65.6
    - Linear Formula K=0.90 (50/30/15/5): 67.5
    - Linear Formula K=0.95 (50/25/20/5): 65.2
    - Linear Formula K=0.90 (50/25/20/5): 67.1
    - Linear Formula K=0.95 (alternate listing): 64.8 (table shows multiple formula columns)
  - Emerging Market and Developing Countries:
    - Existing: 38.4
    - Pre First Round: 39.5
    - Linear Formula K=0.95 (50/30/15/5): 34.4
    - Linear Formula K=0.90 (50/30/15/5): 32.5
    - Linear Formula K=0.95 (50/25/20/5): 34.8
    - Linear Formula K=0.90 (50/25/20/5): 32.9
    - Linear Formula K=0.95 (alternate listing): 35.2
  - Developing countries:
    - Existing: 30.9
    - Pre First Round: 32.1
    - Linear Formula K=0.95 (50/30/15/5): 28.6
    - Linear Formula K=0.90 (50/30/15/5): 27.0
    - Linear Formula K=0.95 (50/25/20/5): 28.7
    - Linear Formula K=0.90 (50/25/20/5): 27.3
    - Linear Formula K=0.95 (alternate): 29.1
  - Asia (including Korea and Singapore per note 6/):
    - Existing: 10.3
    - Pre First Round: 11.5
    - Linear Formula K=0.95 (50/30/15/5): 16.2
    - Linear Formula K=0.90 (50/30/15/5): 14.1
    - Linear Formula K=0.95 (50/25/20/5): 14.4
    - Linear Formula K=0.90 (50/25/20/5): 14.0
    - Linear Formula K=0.95 (alternate): 14.3
  - Africa:
    - Existing: 5.5
    - Pre First Round: 5.4
    - Linear Formula K=0.95 (50/30/15/5): 2.4
    - Linear Formula K=0.90 (50/30/15/5): 2.5
    - Linear Formula K=0.95 (50/25/20/5): 3.0
    - Linear Formula K=0.90 (50/25/20/5): 2.6
    - Linear Formula K=0.95 (alternate): 3.0
- Memorandum items (Table 5):
  - EU 27:
    - Existing: 32.9
    - Pre First Round: 32.4
    - Linear Formula K=0.95 (50/30/15/5): 37.8
    - Linear Formula K=0.90 (50/30/15/5): 34.3
    - Linear Formula K=0.95 (50/25/20/5): 34.6
    - Linear Formula K=0.90 (50/25/20/5): 33.7
    - Linear Formula K=0.95 (alternate): 34.0
  - LICs (PRGF-eligible countries):
    - Existing: 7.5
    - Pre First Round: 7.4
    - Linear Formula K=0.95 (50/30/15/5): 3.6
    - Linear Formula K=0.90 (50/30/15/5): 4.0
    - Linear Formula K=0.95 (50/25/20/5): 4.5
    - Linear Formula K=0.90 (50/25/20/5): 4.0
    - Linear Formula K=0.95 (alternate): 4.6

### Selected country-level calculated quota shares (Table 5a — highlights)
- United States:
  - Existing: 17.023
  - Pre First Round: 16.732
  - Linear Formula (50/30/15/5)^K:
    - K=0.95: 16.284
    - K=0.90: 20.102
  - Linear Formula (50/25/20/5)^K:
    - K=0.95: 18.107
    - K=0.90: 20.339
    - alternate: 18.302
- China (includes China, P.R., and Hong Kong SAR per note 6/):
  - Existing: 2.928
  - Pre First Round: 3.652
  - Linear Formula (50/30/15/5)^K:
    - K=0.95: 6.137
    - K=0.90: 5.602
  - Linear Formula (50/25/20/5)^K:
    - K=0.95: 5.397
    - K=0.90: 5.497
    - alternate: 5.299
- Japan:
  - Existing: 6.108
  - Pre First Round: 6.003
  - Linear Formula (50/30/15/5)^K:
    - K=0.95: 7.011
    - K=0.90: 8.751
  - Linear Formula (50/25/20/5)^K:
    - K=0.95: 8.236
    - K=0.90: 8.819
    - alternate: 8.292
- Germany:
  - Existing: 5.968
  - Pre First Round: 5.866
  - Linear Formula (50/30/15/5)^K:
    - K=0.95: 6.850
    - K=0.90: 6.584
  - Linear Formula (50/25/20/5)^K:
    - K=0.95: 6.289
    - K=0.90: 6.461
    - alternate: 6.176
- India:
  - Existing: 1.916
  - Pre First Round: 1.883
  - Linear Formula (50/30/15/5)^K:
    - K=0.95: 1.287
    - K=0.90: 1.524
  - Linear Formula (50/25/20/5)^K:
    - K=0.95: 1.573
    - K=0.90: 1.513
    - alternate: 1.561
- Brazil:
  - Existing: 1.402
  - Pre First Round: 1.378
  - Linear Formula (50/30/15/5)^K:
    - K=0.95: 1.069
    - K=0.90: 1.469
  - Linear Formula (50/25/20/5)^K:
    - K=0.95: 1.518
    - K=0.90: 1.517
    - alternate: 1.565
- Korea:
  - Existing: 0.760
  - Pre First Round: 1.329
  - Linear Formula (50/30/15/5)^K:
    - K=0.95: 2.512
    - K=0.90: 2.221
  - Linear Formula (50/25/20/5)^K:
    - K=0.95: 2.247
    - K=0.90: 2.226
    - alternate: 2.250
- Singapore:
  - Existing: 0.406
  - Pre First Round: 0.399
  - Linear Formula (50/30/15/5)^K:
    - K=0.95: 1.929
    - K=0.90: 1.023
  - Linear Formula (50/25/20/5)^K:
    - K=0.95: 1.078
    - K=0.90: 1.058
    - alternate: 1.112
- Ireland:
  - Existing: 0.395
  - Pre First Round: 0.389
  - Linear Formula (50/30/15/5)^K:
    - K=0.95: 1.660
    - K=0.90: 1.209
  - Linear Formula (50/25/20/5)^K:
    - K=0.95: 1.262
    - K=0.90: 1.276
    - alternate: 1.329
- Luxembourg:
  - Existing: 0.139
  - Pre First Round: 0.137
  - Linear Formula (50/30/15/5)^K:
    - K=0.95: 1.369
    - K=0.90: 0.631
  - Linear Formula (50/25/20/5)^K:
    - K=0.95: 0.682
    - K=0.90: 0.693
    - alternate: 0.745
- Selected other country examples (values shown in Table 5a as K variations and formulas; examples below preserve listed numbers):
  - Mexico (Existing 1.196; Pre First Round 1.430): K=0.95 (50/30/15/5) = 1.841; K=0.90 (50/30/15/5) = 1.891; alternative formula K=0.95 = 1.929; alt K=0.90 = 1.896; alternate = 1.933.
  - Spain (Existing 1.408; Pre First Round 1.384): K=0.95 (50/30/15/5) = 2.237; K=0.90 = 2.377; alternative formula K=0.95 = 2.395; K=0.90 = 2.329; alternate = 2.349.
  - Turkey (Existing 0.453; Pre First Round 0.547): K=0.95 (50/30/15/5) = 0.751; K=0.90 = 0.940; alternative K=0.95 = 0.995; alternative K=0.90 = 0.982; alternate = 1.037.
  - Lebanon (Existing 0.104; Pre First Round 0.103): K=0.95 (50/30/15/5) = 0.182; K=0.90 = 0.148; alternative K=0.95 = 0.172; alternative K=0.90 = 0.155; alternate = 0.180.
  - Turkmenistan (Existing 0.046; Pre First Round 0.045): K=0.95 (50/30/15/5) = 0.046; K=0.90 = 0.056; alternative K=0.95 = 0.069; alternative K=0.90 = 0.059; alternate = 0.072.
- Many country-level results (Tables 1–4, 1a–4a, 1b–4b) provide detailed voting shares and ad hoc increase lists across combination of:
  - formula weights (50/30/15/5 vs 50/25/20/5),
  - compression exponent (K = 0.95, 0.90),
  - basic votes BV = 500 vs BV = 750,
  - eligibility threshold (out-of-lineness > 1.0 or > 1.1),
  - scenarios with foregoing by eligible G-7 members to specified levels,
  - protection of pre‑Singapore voting shares of LICs,
  - uniform proportional reduction factors applied to gaps between calculated and actual pre‑Singapore quota shares (uniform reduction factors reported in various tables).

### Voting-share group simulations (selected numbers from multiple tables)
- Table 1 (Filter with compression, scenarios with BV = 500 and BV = 750, various pre/post rounds):
  - Advanced economies voting shares examples: 60.6, 59.5, 59.3, 58.7, 58.9, 58.4 (multiple columns reflect scenario permutations).
  - Emerging Market and Developing Countries examples: 39.4, 40.5, 40.7, 41.3, 41.1, 41.6.
  - Memorandum: No. of countries receiving ad hocs reported as 54, 53, 54, 54, 55, 54, 55, 54 across scenarios.
  - Uniform reduction factors shown in Table 1: e.g., 33.9, 27.6, 39.7, 33.3, 33.4, 27.8, 39.1, 32.8 (various scenarios).
- Table 2 and Table 2a (Filter with compression and a threshold, out-of-lineness > 1.1):
  - Advanced economies examples: 60.6, 59.5, 58.4, 57.9, 58.1, 57.6 (scenario-dependent).
  - Emerging Market and Developing Countries examples: 39.4, 40.5, 41.6, 42.1, 41.9, 42.4.
  - No. of countries receiving ad hocs in Table 2: 42, 42, 42, 42, 47, 47, 47, 47 (different formula/parameter combinations).
  - Uniform reduction factors in Table 2: 47.2, 42.3, 51.4, 46.6, 44.9, 40.0, 49.0, 44.2.
- Table 3 and Table 3a (compression exponent 0.90 in (50/30/15/5)^0.90 and (50/25/20/5)^0.90 scenarios):
  - Advanced economies examples: 60.6, 59.5, 59.2, 58.4, 58.9, 58.4.
  - Emerging Market and Developing Countries examples: 39.4, 40.5, 40.8, 41.6, 41.1, 41.6.
  - No. of countries receiving ad hocs in Table 3: 70, 69, 71, 69, 70, 69, 71, 69.
  - Uniform reduction factors in Table 3: 29.7, 28.2, 34.3, 29.3, 29.2, 27.8, 33.8, 28.8.
- Table 4 and Table 4a (compression 0.90 with threshold out-of-lineness > 1.1):
  - Advanced economies examples: 60.6, 59.5, 57.4, 56.6, 57.3, 56.6.
  - Emerging Market and Developing Countries examples: 39.4, 40.5, 42.6, 43.4, 42.7, 43.4.
  - No. of countries receiving ad hocs in Table 4: 56, 55, 56, 55, 58, 57, 58, 57.
  - Uniform reduction factors in Table 4: 56.3, 54.9, 57.3, 55.9, 55.4, 53.9, 56.3, 54.9.

### Implementation-relevant outputs and interpretations
- Compression (raising formula to power K) materially changes the distribution of calculated quota shares across countries and regions; higher compression (lower K) tends to increase the share for larger contributors under some formulas and parameterizations (see advanced economies and major advanced economies entries across K=0.95 vs K=0.90).
- Choice of openness/variability weights (50/30/15/5 vs 50/25/20/5) also shifts calculated shares—differences shown both at aggregate region level and at single-country level (Table 5 and Table 5a provide side-by-side comparisons).
- Application of filters, thresholds (out‑of‑lineness > 1.0 vs > 1.1), and policy rules (protection of LIC pre‑Singapore shares; foregoing by G‑7 members; uniform proportional reductions) determine the set of members receiving ad hoc increases and the magnitude of uniform reduction factors required to fit increases within the simulated redistribution envelopes (see Tables 1–4 and accompanying ad hoc lists in Tables 1b–4b).

*Source: Finance Department (tables and notes as provided in the chapter "5. Calculated Quota Shares Based on a Linear Formula with Compression").*

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