## _061915

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---

### Data update: scope and headline results
- Quota database updated by one year through 2013.
- Using the current quota formula, the calculated quota share (CQS) of EMDCs as a group increases by 1.3 percentage points (pp) relative to the 2014 update to 48.7 percent.
- The increase of 1.3 pp is lower than last year’s data update (2.1 pp) but broadly in line with previous increases.
- Over a longer timeframe, the aggregate CQS of EMDCs has risen by about 12.5 pp since the 2008 reform (based on data through 2005) and by 6.9 pp since the 14th Review (based on data through 2008).
- The share of EMDCs in global reserves rose slightly to 76.1 percent from 75.7 percent, driven by an increase in China’s share of 0.8 pp.

### Current quota formula (specification and inputs)
- Formula specification (exact): CQS = (0.50*GDP + 0.30*Openness +0.15*Variability + 0.05*Reserves)^K.
- GDP blend: 60 percent market and 40 percent PPP exchange rates.
- Compression factor: K = 0.95.
- The formula variables are expressed in shares of global totals; variable weights sum to 1.0.
- The formula includes a compression factor that reduces dispersion in calculated quota shares.

### Updated quota database: detailed shifts and country-level movements
- Data sources and cutoff:
  - Primary source: IFS; WEO used to supplement; cutoff date January 31, 2015.
- Aggregate CQS:
  - CQS of EMDCs (current 2013): 48.7 percent.
- Historical/Categorical CQS values (In percent):
  - Advanced economies: Post Second Round 60.4; 14th Review 57.6; 2008 Reform (2005) 63.8; 14th General Review (2008) 58.2; Previous (2012) 52.6; Current (2013) 51.3.
  - Major advanced economies: Post Second Round 45.3; 14th Review 34.3; 2008 Reform (2005) 47.6; 14th General Review (2008) 42.9; Previous (2012) 37.9; Current (2013) 36.8.
  - United States: Post Second Round 17.7; 14th Review 17.4; 2008 Reform (2005) 19.0; 14th General Review (2008) 17.0; Previous (2012) 14.9; Current (2013) 14.5.
  - China (region grouping): Post Second Round 12.6; 14th Review 16.0; 2008 Reform (2005) 15.8; 14th General Review (2008) 17.7; Previous (2012) 21.7; Current (2013) 22.6.
  - China (individual): Post Second Round 4.0; 14th Review 6.4; 2008 Reform (2005) 6.4; 14th General Review (2008) 7.9; Previous (2012) 10.5; Current (2013) 11.3.
  - LICs (memorandum): Post Second Round 4.4; 14th Review 4.1; 2008 Reform (2005) 2.2; 14th General Review (2008) 2.5; Previous (2012) 3.0; Current (2013) 3.3.
  - Total: 100.0 (all vintages).
- Notable individual changes (current update):
  - China recorded the largest individual increase in CQS: 0.75 pp.
  - Nigeria recorded an increase of 0.16 pp.
  - Argentina: +0.08 pp.
  - Korea, Republic of: +0.07 pp.
  - Switzerland: +0.27 pp.
  - France: +0.07 pp.
  - Largest individual declines: United States -0.4 pp; Japan -0.3 pp; Germany -0.2 pp.
- Regional/group movements:
  - Largest gains in EMDC shares recorded by Asia, followed by Africa.
  - Other advanced economies as a group falls by 0.1 pp (previous update decline was 0.5 pp).
- Causes and drivers:
  - EMDC gain in GDP share reflects continued divergence in global growth rates; growth divergence narrowed somewhat but remains sizable.
  - EMDCs recorded gains in share of global openness and, to a lesser extent, variability, associated with rebound in external flows after the global financial crisis.
  - Changes in openness and variability reflect broader BPM6 implementation and expanded country coverage (81 BPM6 reporters vs 42 previously); under BPM6 full value of goods for processing is no longer counted as gross exports/imports.

### Out-of-lineness and representation gaps
- Comparing CQS with 14th Review quota shares, at the aggregate level Advanced Economies are over-represented and EMDCs under-represented by 6.3 pp, compared with 5.1 pp in the previous update.
- Number of underrepresented members declined slightly to 72 compared with 74 in the previous update.
- These underrepresented members are under-represented by 10 pp of total quota shares (over half of this shortfall is accounted for by China), compared with 8.7 pp in the previous update.

### Data sources and methodology highlights
- PPP GDP: calculated by dividing nominal GDP in local currency by PPP factor; 2011 ICP PPP factors extended to include 2012 and 2013 using WEO methodology.
- Openness and variability data reflect BPM6 methodology and expanded country coverage; processing trade treatment under BPM6 means only processing fees are recorded under services rather than full goods value.
- Primary data source: Fund’s International Financial Statistics (IFS); missing data supplemented by WEO; remaining missing data from staff reports and country desk data as needed.

### Concluding summary (selected exact figures)
- Based on the current formula, the calculated quota share of EMDCs as a group stands at 48.7 percent compared with 47.4 percent at the last update and 41.8 percent at the time of the 14th General Quota Review.
- This implies that, on the same basis, EMDCs in aggregate would be under-represented by 6.3 pp when compared with the 14th Review quota shares.

---

### Illustrative simulations: approach and scenarios
- Simulations update those in the July 2014 data update using 2013 data; simulations are purely illustrative and no staff proposals are made.
- All simulations exclude variability and explore alternative reallocations of that weight.
- Simulation dimensions covered:
  - Alternative splits of variability weight between GDP and openness (even split; GDP 2/3 & openness 1/3; all to GDP; all to GDP with openness weight reduced to 0.25).
  - Different GDP blends (50/50, 55/45, 65/35 GDP market/PPP mixes and variations).
  - Different openness measures and caps (nominal openness capped at 85th and 75th percentiles; openness share capped at 1.8 and 1.5).
  - Higher compression (compression factor 0.925 vs standard 0.9500).
- General simulation findings (exact and verbatim summaries from source):
  - Dropping variability and allocating part or all of the weight to GDP reduces the CQS of other advanced economies and increases that of major advanced economies and EMDCs as a group. The shifts are larger when the weight of openness is also reduced. The majority of large countries gain from dropping variability, while less than one third of small countries gain.
  - Increasing the weight of PPP GDP in the GDP blend leads to a higher CQS for EMDCs relative to the current CQS. More EMDCs and small countries gain with an increased weight for PPP GDP. Conversely, increasing the weight of market GDP in the GDP blend reduces the share of both EMDCs and LICs.
  - Capping openness tends to reduce the CQS of other advanced economies and increases the CQS for major advanced economies and EMDCs as a group. There are generally a larger number of gainers among both EMDCs and small countries compared with reallocating variability without caps.
  - Higher compression reduces the share of the largest economies and increases the share of all other members. It leads to the largest number of gainers among EMDCs and LICs, as well as among small countries.

### Representative numeric results (selected exact figures)
- Representative group CQS (from figures/tables):
  - Major Advanced Economies — CQS: 36.8 Percent.
  - Other Advanced Economies — CQS: 14.5 Percent.
  - EMDCs — CQS: 48.7 Percent.
- Example country-level top positive changes in CQS (difference between current and previous shares, in percent):
  - China: 0.747
  - Switzerland: 0.271
  - Nigeria: 0.163
  - Argentina: 0.085
  - Korea, Republic of: 0.074
- Example country-level top negative changes in CQS (difference between current and previous shares, in percent):
  - United States: -0.379
  - Japan: -0.338
  - Germany: -0.197
  - Italy: -0.147
  - Spain: -0.097
- Selected table snapshots (exact entries as presented):
  - Table 2a snapshot (selected aggregates, quota shares current vs previous):
    - Advanced economies: 57.65 (current), 51.45 (previous)
    - Major advanced economies: 43.44 (current), 41.84 (previous)
    - Emerging Market and Developing Countries: 42.44 (current), 48.64 (previous)
  - Table 2b (GDP / PPP / GDP Blend snapshot, selected aggregates):
    - Advanced economies GDPPPP GDP/GDP Blend/Quota Shares: 57.65/51.35/58.5 (current where columns align as presented)
    - Emerging Market and Developing Countries GDPPPP GDP/GDP Blend/Quota Shares: 42.44/48.74/41.53 (as shown)
- Selected coefficients and methodological variants (exact):
  - Example coefficients reported: GDP: 0.3000; PPP GDP: 0.2000; Openness: 0.3000; Variability: 0.1500; Reserves: 0.0500; Compression factor: 0.9500.
  - Variants analyzed include dropping variability (variability coefficient set to 0.0000), weight splits between GDP and openness (even; GDP 2/3 & openness 1/3; all to GDP; openness = 0.25), GDP blends adjustments, openness caps (85th/75th percentiles; shares caps at 1.8 and 1.5), and compression factor sensitivity (0.9500 and 0.925).

### Selected scenario numeric vectors (Set 1 examples, values in order as in source)
- Scenario 1 (Weight of variability split evenly between GDP and openness): 37.29, 13.82, 48.88, 3.20, 63, 6, 27, 30, 12, 51
- Scenario 2 (Weight of variability split between GDP (2/3) and openness (1/3)): 37.37, 13.59, 49.04, 3.21, 57, 6, 25, 26, 13, 44
- Scenario 3 (All weight of variability to GDP): 37.53, 13.12, 49.36, 3.24, 52, 5, 26, 21, 12, 40
- Scenario 4 (Weight of openness reduced to 0.25): 37.69, 12.64, 49.67, 3.27, 49, 5, 23, 21, 12, 37

### Higher compression illustrative results (Set 4, compression = 0.925)
- Dropping variability, weight split evenly between GDP and openness: 36.30, 14.15, 49.55, 3.46, 120, 9, 57, 54, 10, 110
- Dropping variability, weight split between GDP (2/3) and openness (1/3): 36.38, 13.92, 49.70, 3.48, 113, 6, 55, 52, 11, 102
- Dropping variability, all weight to GDP: 36.53, 13.45, 50.02, 3.51, 107, 6, 51, 50, 12, 95
- Dropping variability, weight of openness reduced to 0.25: 36.69, 12.98, 50.33, 3.54, 106, 5, 49, 52, 12, 94

---

### Annex I — PPP GDP and Openness key characteristics
- PPP GDP findings:
  - EMDCs and LICs benefit from increasing the share of PPP GDP.
  - Based on the latest data update, over 90 percent of EMDCs would stand to benefit from an increase in the share of PPP GDP in the blend variable, compared with no AEs.
  - Benefits from a higher weight of PPP GDP are inversely related to income; almost all countries in the bottom quartile benefit and record the largest relative gains.
  - Size does not appear strongly related to benefits of higher PPP GDP weight.
- Openness findings:
  - More than two-thirds of the membership (129 countries) gain from inclusion of openness relative to GDP.
  - Gains from openness are positively related to income: over 90 percent of top-quartile per capita income countries (43 out of 47) gain; less than half (21 countries) in bottom quartile gain.
  - Small advanced countries are main aggregate gainers from openness; smaller EMDCs gain modestly in aggregate; LICs as a whole do not gain from openness.
  - Openness and variability shares are closely linked: correlation between openness and variability (excluding largest economies) is 0.92.
- Skewness and distributional metrics (openness ratios):
  - Median ratio of openness to market GDP: 1.00.
  - Mean ratio of openness to market GDP: 1.13.
  - 9 countries have ratios greater than 2 (highest above 10).
  - 34 countries have ratios above 1.5.
  - Openness relative to GDP blend shares: Mean = 1.59; Median = 1.31; 129 countries have ratio >= 1; 72 countries >= 1.5; 34 countries >= 2; one member > 18.
- Caps and compression approaches:
  - Two cap approaches explored: absolute cap (openness relative to market GDP) and shares cap (ratio of openness to GDP blend shares).
  - Thresholds corresponding to absolute ratios of openness to market GDP: 1.97 (95th percentile), 1.55 (85th), 1.33 (75th).
  - Historical context: June 2013 paper applied 1.7 cap equivalent to 75th percentile; July 2014 used 1.8 to maintain top quartile correspondence; based on current data, 1.8 is still close to 75th percentile (1.7 equals 73rd percentile).
  - Table I.4 provides example impacts (selected shares in percent for Advanced economies, Emerging Market and Developing Countries, China, India, EU28, LICs) under various caps and compressions; Total remains 100.00 across columns.
- Correlations among quota variables (selected exact figures):
  - Advanced Economies: Openness vs. Blend GDP: 0.92; Variability vs. Blend GDP: 0.97; Variability vs. Openness: 0.98; Reserves vs. Blend GDP: 0.30.
  - EMDCs: Openness vs. Blend GDP: 0.95; Variability vs. Blend GDP: 0.91; Variability vs. Openness: 0.95; Reserves vs. Blend GDP: 0.95.
  - All Countries: Openness vs. Blend GDP: 0.93; Variability vs. Blend GDP: 0.94; Variability vs. Openness: 0.97.
  - All Members excluding Top 10: Openness vs. Blend GDP: 0.81; Variability vs. Blend GDP: 0.79; Variability vs. Openness: 0.92.

---

### Directors’ views and process points (summary of Board discussion outcomes)
- Agreed principles from 2008 reform remain valid: formula should be simple, transparent, consistent with multiple roles of quotas, produce broadly acceptable results, and be feasible with timely, high quality, widely available data.
- Specific outcomes and considerations:
  - Agreement that GDP should remain the most important variable, with largest weight and scope to further increase its weight.
  - Agreement that openness should continue to play an important role; concerns regarding this variable need thorough examination.
  - Considerable support for dropping variability from the formula, with some members conditioning support on other elements of the reform package, including how its weight is reallocated and protection for poorest members.
  - Considerable support for retaining reserves with its current weight.
  - Consideration to be given to (i) the weight of PPP GDP in the GDP blend and (ii) the current level of compression.
  - Consideration of whether and how to take account of very significant voluntary financial contributions through ad hoc adjustments as part of the 15th Review.
  - Agreement that measures should be taken to protect voice and representation of the poorest members, with considerable support for addressing this as part of the 15th Review.

*Source: QUOTA FORMULA—DATA UPDATE, International Monetary Fund; Finance Department (selected extracts and tables).*

### EXECUTIVE SUMMARY

### _061915 - EXECUTIVE SUMMARY

### Data update: scope and headline results
- The quota database has been updated by one year through 2013.
- Using the current quota formula, the calculated quota share (CQS) of EMDCs as a group increases by 1.3 percentage points (pp) relative to the 2014 update to 48.7 percent.
- The increase of 1.3 pp is lower than last year’s data update (2.1 pp) but broadly in line with previous increases.
- Over a longer timeframe, the aggregate CQS of EMDCs has risen by about 12.5 pp since the 2008 reform (based on data through 2005) and by 6.9 pp since the 14th Review (based on data through 2008).
- The share of EMDCs in global reserves rose slightly to 76.1 percent from 75.7 percent, driven by an increase in China’s share of 0.8 pp.

### Current quota formula (as used for results)
- Formula specification (exact): CQS = (0.50*GDP + 0.30*Openness +0.15*Variability + 0.05*Reserves)^K.
- GDP blend: 60 percent market and 40 percent PPP exchange rates.
- Compression factor: K = 0.95.
- The formula variables are expressed in shares of global totals; variable weights sum to 1.0.
- The formula includes a compression factor that reduces dispersion in calculated quota shares.

### Illustrative simulations: approach and scope
- The paper updates the illustrative simulations of possible reforms to the quota formula presented in the July 2014 data update, using the new database.
- Simulations take as a starting point the outcome of the comprehensive review of the quota formula (QFR) and informal discussions in June 2013 and July 2014.
- All simulations exclude variability and explore alternative methods to re-distribute the weight of this variable.
- Simulations consider different options for the weight of PPP GDP in the GDP blend, alternative openness measures, and the impact of an increase in compression.
- The overall simulation results are broadly similar to those illustrated in the July 2014 paper, though starting from a different base given the data update.
- The simulations are explicitly described as purely illustrative; no staff proposals are made.

### Updated quota database: detailed shifts and country-level movements
- The update advances by one year the data presented last July, using the same sources as in past updates (primary source IFS; WEO used to supplement; cutoff date January 31, 2015).
- The CQS of EMDCs as a group: current (2013) = 48.7 percent.
- Historical/Categorical CQS values from Table 1 (In percent): 
  - Advanced economies: Post Second Round 60.4; 14th Review 57.6; 2008 Reform (2005) 63.8; 14th General Review (2008) 58.2; Previous (2012) 52.6; Current (2013) 51.3.
  - Major advanced economies: Post Second Round 45.3; 14th Review 34.3; 2008 Reform (2005) 47.6; 14th General Review (2008) 42.9; Previous (2012) 37.9; Current (2013) 36.8.
  - United States: Post Second Round 17.7; 14th Review 17.4; 2008 Reform (2005) 19.0; 14th General Review (2008) 17.0; Previous (2012) 14.9; Current (2013) 14.5.
  - China (region grouping): Asia aggregate Post Second Round 12.6; 14th Review 16.0; 2008 Reform (2005) 15.8; 14th General Review (2008) 17.7; Previous (2012) 21.7; Current (2013) 22.6.
  - China (individual): Post Second Round 4.0; 14th Review 6.4; 2008 Reform (2005) 6.4; 14th General Review (2008) 7.9; Previous (2012) 10.5; Current (2013) 11.3.
  - LICs (memorandum): Post Second Round 4.4; 14th Review 4.1; 2008 Reform (2005) 2.2; 14th General Review (2008) 2.5; Previous (2012) 3.0; Current (2013) 3.3.
  - Total: 100.0 (all vintages).
- Individual notable changes in current update:
  - China recorded the largest individual increase in CQS: 0.75 pp.
  - Nigeria recorded an increase of 0.16 pp (equivalent to one third of its previous CQS), reflecting mainly the revision of its National Income Accounts.
  - Argentina and Korea recorded increases of 0.08 pp and 0.07 pp, respectively.
  - Switzerland’s and France’s CQS increased by 0.27 pp and 0.07 pp, respectively.
  - The largest individual declines: United States -0.4 pp; Japan -0.3 pp; Germany -0.2 pp.
- Regional/Group movements:
  - Largest gains in EMDC shares continue to be recorded by Asia, followed by Africa.
  - Other advanced economies as a group falls by 0.1 pp, compared to a decline of 0.5 pp in the previous update.
- Causes and drivers:
  - EMDC gain in GDP share reflects continued divergence in global growth rates; the growth divergence narrowed somewhat but remains sizable (Figure 2).
  - EMDCs recorded gains in share of global openness and, to a lesser extent, variability, associated with rebound in external flows after the global financial crisis (Table 2a and Figure 3).
  - Changes in openness and variability data reflect broader BPM6 implementation and expanded country coverage (81 BPM6 reporters vs 42 previously); under BPM6 full value of goods for processing is no longer counted as gross exports/imports.

### Out-of-lineness and representation gaps
- Comparing CQS with 14th Review quota shares, at the aggregate level Advanced Economies are over-represented and EMDCs under-represented by 6.3 pp, compared with 5.1 pp in the previous update.
- Number of underrepresented members declined slightly to 72 compared with 74 in the previous update.
- These underrepresented members are under-represented by 10 pp of total quota shares (over half of this shortfall is accounted for by China), compared with 8.7 pp in the previous update.

### Data sources and methodology highlights
- Primary data source: Fund’s International Financial Statistics (IFS); missing data supplemented by WEO; remaining missing data from staff reports and country desk data as needed.
- Cutoff date for quota database: January 31, 2015; WEO Fall 2014 publication used for consistency.
- PPP GDP: calculated by dividing nominal GDP in local currency by PPP factor; 2011 ICP PPP factors extended to include 2012 and 2013 using WEO methodology.
- Openness and variability data reflect BPM6 methodology and expanded country coverage; processing trade treatment under BPM6 means only processing fees are recorded under services rather than full goods value.

*Source: QUOTA FORMULA—DATA UPDATE, International Monetary Fund, Approved By Andrew Tweedie; Prepared by the Finance Department (in collaboration with the Statistics Department), June 19, 2015.*

### 9.      From a longer-term perspective, the CQS gains recorded by EMDCs in recent data

### _061915 - 9.      From a longer-term perspective, the CQS gains recorded by EMDCs in recent data

### Longer-term perspective on CQS gains
- Recent data updates show rising shares across all quota variables for EMDCs.
- For EMDCs as a group, "the contributions of market GDP, PPP GDP and openness are broadly similar in scale based on the latest data update."
- "Over the five years combined, the increased contribution of PPP GDP to EMDCs’ CQS is similar to that of market GDP."
- For advanced countries, the group "has steadily lost share across 3 variables (market GDP, PPP GDP, and openness)."
- For major advanced economies, "Market GDP makes the most important contribution"; for other advanced economies, "openness is most important." PPP GDP "makes a significantly smaller contribution in both cases."
- Definition note: "The contribution of each quota variable is defined as each major group’s aggregate share multiplied by its coefficient in the quota formula (i.e., 0.3 for market GDP and 0.2 for PPP GDP). The contributions will not equal the corresponding CQS due to compression."

### Key data definitions and formula
- Quota formula used in calculations (as stated): CQS = (0.50*GDP + 0.30*Openness +0.15*Variability + 0.05*Reserves)^K.
- GDP blended using "60 percent market and 40 percent PPP exchange rates."
- K is a compression factor of 0.95.
- Data vintage comparison: current calculations based on IFS data through 2013; previous based on IFS data through 2012 (where specified).

### Representative numerical highlights from tables and figures
- Major Advanced Economies — CQS: 36.8 Percent (Figure 4).
- Other Advanced Economies — CQS: 14.5 Percent (Figure 4).
- EMDCs — CQS: 48.7 Percent (Figure 4).
- Example country-level top positive changes in Calculated Quota Share (difference between current and previous shares, in percent):
  - China: 0.747
  - Switzerland: 0.271
  - Nigeria: 0.163
  - Argentina: 0.085
  - Korea, Republic of: 0.074
- Example country-level top negative changes in Calculated Quota Share (difference between current and previous shares, in percent):
  - United States: -0.379
  - Japan: -0.338
  - Germany: -0.197
  - Italy: -0.147
  - Spain: -0.097
- Table 2a snapshot (selected aggregates, quota shares current vs previous):
  - Advanced economies: 57.65 (current), 51.45 (previous)
  - Major advanced economies: 43.44 (current), 41.84 (previous)
  - Emerging Market and Developing Countries: 42.44 (current), 48.64 (previous)
- Table 2b (GDP / PPP / GDP Blend snapshot, selected aggregates):
  - Advanced economies GDPPPP GDP/GDP Blend/Quota Shares: 57.65/51.35/58.5 (current where columns align as presented)
  - Emerging Market and Developing Countries GDPPPP GDP/GDP Blend/Quota Shares: 42.44/48.74/41.53 (as shown in table layout)
- Memorandum items (selected):
  - EU 28: 30.4 (14th General Review quota share, Table 2a)
  - LICs: 4.1 (14th General Review quota share, Table 2a)

### Illustrative calculations and reform simulation sets (staff simulations; purely illustrative)
- General assumptions:
  - Simulations take the outcome of the Quota Formula Review (QFR) as starting point.
  - Given considerable support for dropping variability, all simulations exclude variability.
  - Reserves are maintained with their current weight in line with the QFR.
- Set 1 — Simplification of the Current Formula (dropping variability; keep current GDP and openness measures):
  - Variants illustrated: (i) split variability evenly between GDP and openness (thereby increasing relative weight of openness), (ii) split variability between GDP (2/3) and openness (1/3) leaving relative weights broadly unchanged, (iii) all to GDP (increasing relative weight of GDP), (iv) all to GDP and a lower weight for openness (0.25), which "would effectively increase the weight of GDP to 0.7 in the formula."
  - Summary impact: "Dropping variability and allocating part or all of the weight to GDP reduces (compared to the current formula) the CQS of other advanced economies and increases that of major advanced economies and EMDCs as a group. The shifts are larger when the weight of openness is also reduced. The majority of large countries gain from dropping variability, while less than one third of small countries gain."
- Set 2 — Same as Set 1, but with different GDP blend weights:
  - Options include increasing PPP GDP weight to 45 and 50 percent, and reducing to 35 percent.
  - Summary impact: "Increasing the weight of PPP GDP in the GDP blend leads to a higher CQS for EMDCs relative to the current CQS. More EMDCs and small countries gain with an increased weight for PPP GDP relative to Set 1. Conversely, increasing the weight of market GDP in the GDP blend reduces the share of both EMDCs and LICs."
- Set 3 — Same as Set 1, but with capped openness measures:
  - Two cap types illustrated: an absolute cap (capping the absolute level of openness in relation to market GDP) and a share cap (capping the ratio of openness to GDP blend shares).
  - Summary impact: "Capping openness tends to reduce the CQS of other advanced economies and increases the CQS for major advanced economies and EMDCs as a group. Also, there are generally a larger number of gainers among both EMDCs and small countries compared with Set 1, including when the weight of openness is reduced, as capping openness redistributes the very large boost received by some countries under the current measure across the rest of the membership."
- Set 4 — Same as Set 1, but with higher compression:
  - Compression factor applied in Set 4: 0.925.
  - Summary impact: "Higher compression reduces the share of the largest economies and increases the share of all other members. As a result, it leads to the largest number of gainers among EMDCs and LICs, as well as among small countries."

### Directors’ views and process points (from Board discussions)
- Board agreed principles from the 2008 reform remain valid: formula should be simple, transparent, consistent with multiple roles of quotas, produce broadly acceptable results, and be feasible to implement with timely, high quality, widely available data.
- Specific outcomes of the QFR and follow-up deliberations:
  - "Agreement that GDP should remain the most important variable, with the largest weight in the formula and scope to further increase its weight."
  - "Agreement that openness should continue to play an important role in the formula, and concerns regarding this variable need to be thoroughly examined and addressed."
  - "Considerable support for dropping variability from the formula, with some conditioning their support on other elements of the reform package, including how its weight is reallocated and the adequacy of measures to protect the poorest members."
  - "Considerable support for retaining reserves with its current weight."
  - Consideration will be given to (i) the weight of PPP GDP in the GDP blend and (ii) the current level of compression.
  - Consideration will be given to whether and how to take account of very significant voluntary financial contributions through ad hoc adjustments as part of the 15th Review.
  - "Agreement that measures should be taken to protect the voice and representation of the poorest members, with considerable support for addressing this issue as part of the 15th Review."
- Subsequent informal exchanges in 2013 and 2014 maintained broadly similar views; differences remained on the weight of GDP, mix of market and PPP GDP, weight of openness, and whether to limit openness boosts.

*Source: Finance Department — Quota Formula—Data Update (selected extracts and tables).*

### 1. Weight of variability split evenly between GDP and openness

### 1. Weight of variability split evenly between GDP and openness

### Summary of illustrative calculations (Set 1)
- Scenario 1 (Weight of variability split evenly between GDP and openness)
  - Values (in order as in source): 37.29, 13.82, 48.88, 3.20, 63, 6, 27, 30, 12, 51
- Scenario 2 (Weight of variability split between GDP (2/3) and openness (1/3))
  - Values (in order as in source): 37.37, 13.59, 49.04, 3.21, 57, 6, 25, 26, 13, 44
- Scenario 3 (All weight of variability to GDP)
  - Values (in order as in source): 37.53, 13.12, 49.36, 3.24, 52, 5, 26, 21, 12, 40
- Scenario 4 (Weight of openness reduced to 0.25)
  - Values (in order as in source): 37.69, 12.64, 49.67, 3.27, 49, 5, 23, 21, 12, 37

### Contextual reference figures (from table)
- 14th Review Quota Share: 43.36, 14.28, 42.36, 4.13
- Current CQS: 36.80, 14.52, 48.68, 3.27

*Source: Finance Department*

---

### Set 2 — Same as Set 1, but with different GDP blends

### 1. Weight of variability split evenly between GDP and openness
- a. 50/50 GDP blend: 36.56, 13.59, 49.85, 3.31, 72, 3, 35, 34, 10, 62
- b. 55/45 GDP blend: 36.93, 13.71, 49.37, 3.26, 69, 5, 31, 33, 12, 57
- c. 65/35 GDP blend: 37.66, 13.94, 48.40, 3.14, 55, 9, 24, 22, 14, 41

### 2. Weight of variability split between GDP (2/3) and openness (1/3)
- a. 50/50 GDP blend: 36.61, 13.34, 50.05, 3.33, 63, 3, 31, 29, 10, 53
- b. 55/45 GDP blend: 36.99, 13.46, 49.55, 3.27, 62, 5, 30, 27, 12, 50
- c. 65/35 GDP blend: 37.75, 13.71, 48.53, 3.15, 53, 8, 22, 23, 14, 39

### 3. All weight of variability to GDP
- a. 50/50 GDP blend: 36.70, 12.85, 50.46, 3.37, 56, 1, 29, 26, 9, 47
- b. 55/45 GDP blend: 37.11, 12.98, 49.91, 3.31, 56, 5, 26, 25, 12, 44
- c. 65/35 GDP blend: 37.94, 13.25, 48.81, 3.18, 45, 6, 20, 19, 13, 32

### 4. Weight of openness reduced to 0.25
- a. 50/50 GDP blend: 36.79, 12.35, 50.86, 3.41, 56, 2, 28, 26, 10, 46
- b. 55/45 GDP blend: 37.24, 12.50, 50.27, 3.34, 55, 4, 27, 24, 11, 44
- c. 65/35 GDP blend: 38.13, 12.79, 49.08, 3.20, 44, 5, 22, 17, 12, 32

*Source: Finance Department*

---

### Set 3 — Same as Set 1, but with different openness measures

### 1. Weight of variability split evenly between GDP and openness
- a. Nominal openness capped at 85th percentile: 37.86, 13.22, 48.91, 3.23, 76, 10, 33, 33, 17, 59
- b. Nominal openness capped at 75th percentile: 38.16, 12.95, 48.89, 3.23, 78, 13, 32, 33, 17, 61
- c. Openness share capped at 1.8: 38.58, 12.11, 49.31, 3.29, 85, 12, 38, 35, 17, 68
- d. Openness share capped at 1.5: 38.78, 11.68, 49.54, 3.31, 83, 11, 39, 33, 16, 67

### 2. Weight of variability split between GDP (2/3) and openness (1/3)
- a. Nominal openness capped at 85th percentile: 37.91, 13.02, 49.07, 3.25, 72, 9, 32, 31, 16, 56
- b. Nominal openness capped at 75th percentile: 38.18, 12.77, 49.05, 3.25, 72, 10, 30, 32, 17, 55
- c. Openness share capped at 1.8: 38.57, 11.99, 49.44, 3.30, 79, 11, 35, 33, 17, 62
- d. Openness share capped at 1.5: 38.76, 11.59, 49.65, 3.32, 82, 11, 38, 33, 16, 66

### 3. All weight of variability to GDP
- a. Nominal openness capped at 85th percentile: 37.99, 12.63, 49.38, 3.27, 60, 7, 26, 27, 14, 46
- b. Nominal openness capped at 75th percentile: 38.23, 12.41, 49.37, 3.27, 61, 7, 27, 27, 14, 47
- c. Openness share capped at 1.8: 38.56, 11.74, 49.70, 3.32, 75, 9, 35, 31, 16, 59
- d. Openness share capped at 1.5: 38.72, 11.39, 49.89, 3.34, 74, 9, 34, 31, 15, 59

*Source: Finance Department*

---

### Set 4 — Same as Set 1, but with higher compression (0.925)

### Dropping variability, weight split evenly between GDP and openness
- 36.30, 14.15, 49.55, 3.46, 120, 9, 57, 54, 10, 110

### Dropping variability, weight split between GDP (2/3) and openness (1/3)
- 36.38, 13.92, 49.70, 3.48, 113, 6, 55, 52, 11, 102

### Dropping variability, all weight to GDP
- 36.53, 13.45, 50.02, 3.51, 107, 6, 51, 50, 12, 95

### Dropping variability, weight of openness reduced to 0.25
- 36.69, 12.98, 50.33, 3.54, 106, 5, 49, 52, 12, 94

*Source: Finance Department*

---

### Concluding remarks (excerpts)
- Based on the current formula, the calculated quota share of EMDCs as a group stands at 48.7 percent compared with 47.4 percent at the last update and 41.8 percent at the time of the 14th General Quota Review.
- This implies that, on the same basis, EMDCs in aggregate would be under-represented by 6.3 pp when compared with the 14th Review quota shares.
- The paper updates illustrative simulations of possible reforms of the quota formula presented in the July 2014 paper using the new data; the simulations are intended to be purely illustrative and other variants and combinations could also be considered.

*Source: Finance Department*

### 22.      Directors may wish to comments on the following issues:

### _061915 - 22.      Directors may wish to comments on the following issues:

### Purpose and context
- Illustrative calculations of IMF quota shares using the latest data update under alternative quota-formula parameterizations.
- Scenarios presented: dropping variability (variability coefficient set to 0.0000), alternative weight splits between GDP and openness, different GDP blends (PPP vs. market), different openness measures and caps, and higher compression (0.925) versus standard compression (0.9500).
- Source provided by Finance Department; tables present quota shares (in percent) for country groups and selected economies across formula variants.

### Questions for Directors (verbatim)
- How do Directors assess the relative merits of alternative possible reforms of the formula in light of the latest data update? Have these views changed in light of the latest data update?
- Are there any areas where additional work would be useful?

### Key illustrative results (selected exact figures from the tables)
- Table 6 — Formula w/o variability; different weight splits and GDP blends (In percent):
  - Advanced economies: 57.65; 51.35; 51.15; 51.05; 50.65; 50.3
  - Major advanced economies: 43.43; 36.8; 37.3; 37.3; 37.5; 37.7
  - United States: 17.4; 14.5; 14.9; 15.1; 15.4; 15.7
  - China: 6.4; 11.3; 11.9; 12.0; 12.2; 12.3
  - Emerging Market and Developing Countries 1/: 42.44; 48.7; 48.9; 49.0; 49.4; 49.7
  - Total: 100.0; 100.0; 100.0; 100.0; 100.0; 100.0

- Table 7 — Even split between GDP and openness; different GDP blends (In percent):
  - Advanced economies: 57.65; 51.3; 50.1; 50.6; 51.6
  - United States: 17.4; 14.5; 14.6; 14.8; 15.0
  - China: 6.4; 11.3; 12.1; 12.0; 11.8
  - Emerging Market and Developing Countries 1/: 42.44; 48.7; 49.9; 49.4; 48.4
  - Total: 100.0; 100.0; 100.0; 100.0; 100.0

- Table 8 — GDP (2/3), openness (1/3); different GDP blends (In percent):
  - Advanced economies: 57.65; 51.3; 49.9; 50.5; 51.5
  - United States: 17.4; 14.5; 14.8; 14.9; 15.2
  - China: 6.4; 11.3; 12.2; 12.1; 11.9
  - Emerging Market and Developing Countries 1/: 42.44; 48.7; 50.1; 49.5; 48.5
  - Total: 100.0; 100.0; 100.0; 100.0; 100.0

- Table 9 — All weight to GDP; different GDP blends (In percent):
  - Advanced economies: 57.65; 51.3; 49.5; 50.1; 51.2
  - United States: 17.4; 14.5; 15.1; 15.2; 15.5
  - China: 6.4; 11.3; 12.4; 12.3; 12.1
  - Emerging Market and Developing Countries 1/: 42.44; 48.7; 50.5; 49.9; 48.8
  - Total: 100.0; 100.0; 100.0; 100.0; 100.0

- Table 10 — Weight of openness reduced to 0.25; different GDP blends (In percent):
  - Advanced economies: 57.65; 51.3; 49.1; 49.7; 50.9
  - United States: 17.4; 14.5; 15.4; 15.5; 15.9
  - China: 6.4; 11.3; 12.6; 12.5; 12.2
  - Emerging Market and Developing Countries 1/: 42.44; 48.7; 50.9; 50.3; 49.1
  - Total: 100.0; 100.0; 100.0; 100.0; 100.0

- Tables 11–13 — Different openness measures (caps and shares) and different splits:
  - Example (Table 11, weight split evenly; GDP blend current):
    - Advanced economies: 57.65; 51.35; 51.15; 51.15; 50.75; 50.5 (columns: 14th General Review Quotas; Current Formula; Nominal openness capped at the 85th percentile; Nominal openness capped at the 75th percentile; Openness shares capped at 1.8; Openness shares capped at 1.5)
    - Emerging Market and Developing Countries 1/: 42.44; 48.7; 48.9; 48.9; 49.34; 49.5
  - Example (Table 13, all weight to GDP; different openness measures):
    - Advanced economies: 57.65; 51.35; 50.65; 50.65; 50.35; 50.1
    - United States: 17.4; 14.5; 15.5; 15.6; 15.7; 16.0
    - China: 6.4; 11.3; 12.3; 12.3; 12.4; 12.6
    - Emerging Market and Developing Countries 1/: 42.44; 48.7; 49.4; 49.4; 49.74; 49.9

- Table 14 — Current GDP and openness measures, dropping variability, and higher compression (0.925) (In percent):
  - Advanced economies across columns: 57.65; 51.35; 50.55; 50.35; 50.04; 49.7
  - Major advanced economies: 43.43; 36.8; 36.3; 36.6; 36.4; 36.7
  - United States: 17.4; 14.5; 14.2; 14.3; 14.7; 15.0
  - China: 6.4; 11.3; 11.4; 11.5; 11.7; 11.8
  - Emerging Market and Developing Countries 1/: 42.44; 48.7; 49.5; 49.5; 50.0; 50.3
  - Coefficients shown with higher compression scenario: Compression factor 0.9500; 0.9250; 0.9250; 0.9250; 0.9250

### Coefficients and methodological variants (exact values as presented)
- Commonly reported coefficients for quota variables across scenarios (examples drawn from tables):
  - GDP: 0.3000; 0.3450; 0.3600; 0.3900; 0.420
  - PPP GDP: 0.2000; 0.2300; 0.2400; 0.2600; 0.280
  - Openness: 0.3000; 0.3750; 0.3500; 0.3000; 0.250
  - Variability: 0.1500; 0.0000; 0.0000; 0.0000; 0.000
  - Reserves: 0.0500; 0.0500; 0.0500; 0.0500; 0.050
  - Compression factor: 0.9500; 0.9500; 0.9500; 0.9500; 0.950 (and alternative set 0.9500; 0.9250; 0.9250; 0.9250; 0.925)
- Variants explicitly analyzed:
  - Dropping variability (variability coefficient set to 0.0000).
  - Weight splits: even split between GDP and openness; GDP (2/3) and openness (1/3); all weight to GDP; openness weight reduced to 0.25.
  - GDP blends: combinations of GDP and PPP GDP coefficients adjusted across scenarios (see coefficients above).
  - Openness measures: nominal openness capped at the 85th percentile; nominal openness capped at the 75th percentile; openness shares capped at 1.8; openness shares capped at 1.5.
  - Compression factor sensitivity: standard compression factor 0.9500 and higher compression 0.925.

### Observations for Directors to consider (based on illustrative results)
- Dropping variability tends to shift quota shares modestly toward Emerging Market and Developing Countries 1/ (examples: Emerging totals moving from 48.7 to as high as 50.9 in some scenarios).
- Allocation weight placed entirely on GDP increases shares for larger economies (United States, China) relative to formulas that include openness.
- Reducing the weight of openness to 0.25 or applying stricter openness caps moderates the influence of high-openness outliers and affects shares across advanced and emerging economies in measurable increments (see exact column values above).
- Increasing compression (from 0.9500 to 0.925) slightly lowers shares for the largest groups and raises shares for smaller groups in the aggregate (compare Table 14 results with earlier tables).

*International Monetary Fund — Finance Department (illustrative calculations and coefficients as presented in the source tables).*

### Annex I. PPP GDP and Openness—Key Characteristics

### Annex I. PPP GDP and Openness—Key Characteristics

### PPP GDP — key findings
- EMDCs and low income countries (LICs) benefit from increasing the share of PPP GDP.
- Based on the latest data update, over 90 percent of EMDCs would stand to benefit from an increase in the share of PPP GDP in the blend variable, compared with no AEs.
- The benefits from a higher weight of PPP GDP in the blend are inversely related to income:
  - Almost all countries in the bottom quartile of the income distribution benefit from a higher weight on PPP GDP relative to market GDP, and they also record the largest relative gains.
  - This reflects that PPP GDP shares of countries with low per capita income tend to be significantly higher than their market-based GDP shares, reflecting in part low wage costs in services that are not tradable.
- Size does not appear to be strongly related to the benefits of a higher share of PPP GDP.
- These findings are consistent with previous data updates.

### Openness — key characteristics and distributional effects
- Openness benefits many smaller economies:
  - More than two-thirds of the membership (129 countries based on the latest data update) gain from the inclusion of openness in the formula relative to GDP.
  - The number of countries that benefit from openness is inversely related to size.
- Gains from openness are positively related to income:
  - Over 90 percent of countries (43 out of 47) in the top quartile in terms of per capita income gain from openness, compared with less than half (21 countries) in the bottom quartile.
  - Among the gainers, high income countries also gain more on average than low income countries.
- Group-level patterns:
  - Small advanced countries are the main aggregate gainers from openness; their openness share on average is roughly double their share in the GDP blend.
  - Smaller EMDCs in aggregate gain modestly from openness (though some individual countries have large gains).
  - Other groups, including LICs as a whole, do not gain from openness.
- Openness and variability shares are closely linked:
  - Once the largest economies are excluded, the correlation between openness and variability is 0.92.
  - The distribution of gainers from variability is broadly similar to that for openness across size, income levels, and major country groupings.
  - Small advanced countries gain the most from variability, benefiting almost as much as from openness; smaller EMDCs and LICs gain modestly from variability.
  - Many countries that gain the most from openness also have relatively high shares in variability.
- Skewness of openness shares:
  - Median ratio of openness to market GDP for the membership as a whole is 1 (Median = 1.00).
  - Mean = 1.13 for openness to market GDP.
  - 9 countries have ratios greater than 2 (with the highest being above 10).
  - 34 countries have ratios above 1.5.
  - In terms of openness relative to GDP blend shares:
    - Mean = 1.59
    - Median = 1.31
    - 129 countries have a ratio of 1 or more.
    - 72 countries have a ratio of 1.5 or more.
    - 34 countries have a ratio of 2 or more.
    - One member has a ratio of openness to GDP blend share above 18.
- Combined effect in current formula:
  - Openness and variability together have a 45 percent weight in the formula.
  - The combined high shares in openness and variability produce very large CQS outcomes for a narrower group of countries; these CQS appear large relative to other measures of relative economic position.

### Correlations among quota variables (selected figures)
- Advanced Economies:
  - Openness vs. Blend GDP: 0.92
  - Variability vs. Blend GDP: 0.97
  - Variability vs. Openness: 0.98
  - Reserves correlations lower (e.g., Reserves vs. Blend GDP: 0.30)
- EMDCs:
  - Openness vs. Blend GDP: 0.95
  - Variability vs. Blend GDP: 0.91
  - Variability vs. Openness: 0.95
  - Reserves correlations very high in EMDCs (e.g., Reserves vs. Blend GDP: 0.95)
- All Countries (full sample):
  - Openness vs. Blend GDP: 0.93
  - Variability vs. Blend GDP: 0.94
  - Variability vs. Openness: 0.97
  - Reserves correlations with other variables: 0.60–0.56–0.50 range
- All Members excluding Top 10:
  - Openness vs. Blend GDP: 0.81
  - Variability vs. Blend GDP: 0.79
  - Variability vs. Openness: 0.92

### Caps and compression of openness — approaches and implications
- Staff explored two cap approaches to address high openness outcomes:
  - Absolute cap: capping the absolute level of openness in relation to market GDP.
  - Shares cap: capping the ratio of openness to GDP blend shares.
- Both approaches require judgment in setting thresholds and add complexity to calculations.
- Staff also explored compressing the openness ratio.
- Table I.4 illustrates impacts of capping and compressing openness using thresholds the same as in the July 2014 paper; the thresholds correspond to absolute ratios of openness to market GDP of 1.97, 1.55, and 1.33 for the 95th, 85th and 75th percentile caps, respectively.
- Historical threshold context:
  - In the June 2013 paper, the 1.7 cap on the ratio of the openness share to GDP blend share was equivalent to the 75th percentile of the distribution of this ratio.
  - In the July 2014 paper, the 1.8 cap was applied to maintain the cap broadly corresponding to the top quartile; based on current data, 1.8 is still very close to the 75th percentile (1.7 is equal to the 73rd percentile).
- Examples from capped/compressed openness shares (selected entries from Table I.4; shares in percent):
  - Total: 100.00 (across columns, Total = 100.00)
  - Advanced economies openness shares: 57.74, 56.98, 56.72, 56.09, 57.85, 57.73, 57.79, 57.76, 57.89, 51.36
  - Emerging Market and Developing Countries (excluding specified economies): 42.26, 43.02, 43.28, 43.91, 42.15, 42.27, 42.21, 42.24, 42.11, 48.64
  - China: 9.40, 10.15, 10.36, 11.13, 9.63, 9.78, 9.98, 9.58, 10.43, 13.44
  - India: 2.07, 2.23, 2.28, 2.45, 2.12, 2.15, 2.20, 2.11, 2.29, 4.21
  - EU28 memorandum item: 36.74, 34.65, 33.91, 31.59, 36.28, 35.67, 35.35, 36.06, 32.69, 21.48
  - LICs memorandum item: 2.45, 2.62, 2.66, 2.70, 2.51, 2.53, 2.53, 2.45, 2.40, 2.97
- Table I.4 shading indicates countries with capped/compressed openness shares lower than their original openness shares.
- Further work would be needed to refine thresholds if interest exists in pursuing caps or compression.

*Source: Finance Department (Annex I. PPP GDP and Openness—Key Characteristics).*

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