## _110812a

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---

### Introduction
- Executive Board aimed to complete the quota formula review by January 2013; Directors reaffirmed this timetable at most recent meetings.
- Paper focuses on a narrower range of reform options given limited time and need for broad consensus.
- Staff team led by M.S. Kumar and S. Bassett.

### Towards consensus—key issues
- Guiding principles:
  - Formula should be simple and transparent, consistent with multiple roles of quotas, result in calculated quota shares broadly acceptable to the membership, and be feasible to implement using timely, high quality, and widely available data.
- Areas of considerable common ground:
  - Dropping variability:
    - Staff technical work highlights shortcomings of the current variability measure as an indicator of potential need for Fund resources and difficulties of developing a superior measure.
    - Many Directors indicated they could support dropping variability; others prefer retaining it (possibly with reduced weight) or await agreement on weight reallocation.
  - Maintaining GDP as the most important variable:
    - GDP should continue to have the largest weight.
    - Outstanding issues: whether to increase GDP weight, and composition of the GDP blend (current blend is 60/40 percent shares of market/PPP GDP; alternatives include 50/50, 65/35, 55/45).
  - Retaining reserves:
    - Most Directors could support retaining reserves with its current small weight; views differ on raising or eliminating it.
  - Protecting the poorest members:
    - Agreement that voice and representation of poorest members should be protected, generally considered to be addressed outside the quota formula as part of the 15th General Review.
- Divergent views:
  - Openness:
    - Most Directors favor retaining openness; some call for higher weight; others argue the current openness measure is seriously flawed and favor its elimination.
    - Possible bridging approach: an "openness cap" limiting members’ share of openness relative to GDP; views divided.
  - New variables:
    - Financial contributions: many Directors favor or are open to adding it; many oppose as inconsistent with a quota-based institution.
    - Financial openness: some favor increasing weight; many oppose.
    - Population: a few Directors called for population to protect poorest members.
  - Compression:
    - Broad support for retaining compression; some favor higher compression (benefits smaller economies and EMDCs), others contend it disproportionately benefits small advanced economies and should be eliminated.
- Data and methodology notes:
  - PPP GDP data improvements noted with the 2005 ICP; 2011 ICP results expected at end-2013.
  - Value-added trade measures not currently feasible for formula due to partial and untimely data; gross trade may overstate external flows for some members.

### Possible ways forward (staff approach and considerations)
- Focus on elements with most common ground to build broader consensus, while not excluding more far-reaching reforms.
- Simulations aim to clarify impacts of alternative reform packages and whether combinations could broaden consensus or indicate need for more far-reaching reform.
- Openness cap rationale and trade-offs:
  - A cap may reduce excessive boost to small highly open economies until value-added data are available.
  - Cap is somewhat arbitrary and adds complexity.
  - Illustration: cap of 1.5 on the ratio of openness to GDP shares (compared with cap of 2 in the September paper).
  - Between 54 and 67 countries lose calculated quota share as a result of capping openness shares at 1.5 though for roughly half of those members, the changes would be small in absolute terms.

### Possible reform of the quota formula—illustrative simulations (common features)
- All simulations drop variability from the formula and maintain reserves with its current 5 percent weight.
- GDP continues to have the largest weight and openness is retained with at least its current weight.
- Simulations do not present higher weight on financial openness given limited support.
- All simulations include a compression factor.

### Reallocation of weight freed by dropping variability (illustrative options)
- Option (i): all freed weight allocated to GDP.
- Option (ii): freed weight allocated between GDP and openness with two-thirds of available weight going to GDP (broadly maintaining current proportions).

### GDP blend options illustrated
- Retain current 60/40 split (market/PPP).
- Higher share for PPP GDP at 50/50.
- Modestly higher share for market GDP at 65/35.
- Modestly higher share for PPP GDP at 55/45.

### Openness cap and compression simulations
- Openness cap:
  - Cap on the ratio of openness to GDP shares set at 1.5 in these simulations.
  - Between 54 and 67 countries lose calculated quota share as a result of capping openness shares at 1.5.
- Compression:
  - Higher compression illustrated by reducing compression factor from 0.95 to 0.925.
  - Higher compression tends to benefit smaller economies and EMDCs; reduction from 0.95 to 0.925 compresses distribution further.

### Financial contributions simulations
- Illustrate impact of adding a measure of financial contributions (which tends to heavily favor advanced economies).
- Show it is possible to combine inclusion of financial contributions with other elements that offset its impact on overall group shares.

### Purpose of simulations
- Clarify likely effects of alternative combinations of reforms.
- Assess whether combinations of elements with varying support could build a broader consensus or whether support for more far-reaching reform exists.

### Summary of simulations and scope
- Simulations report indicative results based on the current database; results could change with updated data expected in mid-2013.
- Detailed results for the largest 35 members are shown in Tables 1–4; individual country results are in Statistical Appendix Tables A1–A4.
- Simulated reform elements explored:
  - Dropping variability (set Variability to 0.00) and reallocating its weight (all to GDP or split between GDP and openness).
  - Different GDP blends: 65/35, 60/40, 55/45, 50/50 (GDP/PPP GDP).
  - Openness cap at 1.5.
  - Higher compression (k = 0.925).
  - Inclusion of a measure of financial contributions (a portion of variability weight: 0.05 allocated to financial contributions and 0.10 allocated as indicated).

### Key findings from the simulations
- Aggregate EMDC share:
  - Most simulations result in an overall increase in the aggregate share of EMDCs relative to the current formula.
  - Aggregate changes for EMDCs range from -0.3 to +0.8 based on the current GDP blend and +0.6 to +1.7 with a higher weight on PPP GDP (50/50).
  - Larger increases for EMDCs would require more far-reaching reforms previously considered (e.g., dropping openness or reducing its weight, significantly higher compression) which have not obtained broad support.
- Effects of removing/reallocating variability:
  - Reducing the share of PPP GDP in the blend variable tends to lower the aggregate share of EMDCs unless offset by other changes (e.g., more compression).
- Openness cap and individual country effects:
  - An openness cap (capped at 1.5) produces large declines in share for some highly open economies.
  - While aggregate changes are moderate, changes for individual members can be sizeable.
- Higher compression:
  - Increased compression raises the CQS of a large number of countries, including smaller EMDCs.
  - The number of countries gaining relative to CQS under the current formula increases with higher compression.
- Inclusion of financial contributions:
  - Introducing financial contributions into the formula tends by itself to reduce the share of EMDCs.
  - It may be outweighed by other elements in a package (e.g., higher weight for PPP GDP, openness cap, higher compression — as in set 4).

### Quantified outcomes and scenarios (selected illustrative points)
- Number of gainers under alternative configurations:
  - Dropping variability (unchanged GDP blend): some 53-61 countries gain; 45-50 of these are EMDCs.
  - With openness cap used in set 2: 80-88 gainers; 71-77 EMDCs.
  - With higher compression used in set 3 and set 4: about 110-120 gainers; over 100 are EMDCs.
- Set definitions referenced:
  - Set 1: Simplification—Dropping Variability.
  - Set 2: Same as Set 1 with Openness Shares Capped at 1.5.
  - Set 3: Same as Set 1 with Higher Compression (k = 0.925).
  - Set 4: Combination—Dropping Variability, Openness Capped at 1.5, Financial Contributions and Higher Compression (k = 0.925).
- Specific coefficient and parameter values appearing in tables:
  - Compression Factor examples: 0.95 and 0.925.
  - Variability weight in current formula: 0.15; scenarios set Variability to 0.00.
  - Reserves coefficient: 0.05 in all scenarios shown.
  - Financial contributions (FCS III) coefficient in set 4: 0.05 (a portion of the variability weight).
  - GDP coefficients across scenarios include values such as 0.30, 0.42, 0.39, 0.36, 0.33, 0.31, 0.28 depending on blend and set.
  - PPP GDP coefficients across scenarios include values such as 0.20, 0.23, 0.21, 0.26, 0.24, 0.29, 0.27, 0.30, 0.28.
  - Openness coefficients in various scenarios include 0.30, 0.35, 0.00 (when capped or removed), and capped-at-1.5 allocations by blend as shown in tables.
- Representative aggregate changes in CQS by EMDC grouping:
  - Aggregate changes moderate: ranging from -0.3 to +0.8 (current GDP blend) and +0.6 to +1.7 (50/50 blend).
- Memorandum items and group shares shown in tables (selected examples preserved exactly as in source tables):
  - Total always reported as 100.0 under all calculated scenarios.
  - EU27 memorandum items in example table: values such as 30.2, 30.9, 29.8, 30.5, 29.6, 30.3, 29.4, 30.1, 29.2, 29.9 depending on scenario.
  - LICs memorandum items in example table: values such as 4.0, 2.7, 2.6, 2.6, 2.6, 2.6, 2.7, 2.7, 2.7, 2.7 (varies by table).
- Examples of country-level CQS changes in summary table header:
  - Set 1 (65/35 GDP blend, all to GDP) example line: "1.6-1.1-0.5-0.1 48 40".
  - Set 2 (65/35 blend, all to GDP with openness capped at 1.5) example line: "2.8-2.8-0.1 75 66".
  - Set 3 (65/35 blend, all to GDP with higher compression k = 0.925) example line: "0.4-0.8 0.3 0.1 118 106".
  - Set 4 (65/35 blend, all to GDP with openness cap, financial contributions and k = 0.925) example line: "2.3-1.9-0.4 0.1 104 93".
- Footnote on financial contributions:
  - A portion of the variability weight (0.05) is allocated to financial contributions; the remaining 0.10 is allocated as indicated.
  - Financial contributions are illustrated as the weighted average of a member’s share in NAB contributions including new pledges (0.3), FTP participation based on resources (0.3), PRGT loans and subsidies (0.2) and TA activities (0.2).

### Issues for discussion and director-level questions
- Could Directors support dropping variability from the formula, recognizing conditional support for some?
- Given that GDP should remain the most important variable, how should the weight of variability be reallocated?
- Would Directors consider a higher weight of PPP GDP to build broader consensus?
- Do Directors support further consideration of an openness cap, given diverging views on openness and the current absence of reliable balance of payments data on value added in trade?
- Views on adding new variables (e.g., measure of financial contributions, higher weight for financial openness, population) and whether recognizing particularly generous financial contributions should be considered as part of the 15th General Review.
- Is there scope for a higher compression factor as part of a reform package, for example one that includes a higher weight on GDP?
- Next steps to meet the goal of concluding the review by January 2013.

### Annex I — GDP Per Capita as a Measure of Vulnerability (summary)
- Empirical correlation:
  - Correlation between approval of a Fund arrangement and per capita GDP is estimated at -0.16 for the period 1990-2010 and is statistically significant at the 1% level.
  - For LICs only, the correlation coefficient is -0.07 and remains significant.
- Distributional facts:
  - In 92 percent of the cases, the country seeking financial assistance from the IMF had per capita GDP below the average.
  - In 81 percent of the cases, the country seeking assistance had per capita GDP less than 50 percent of the average.
- Limitations:
  - No single variable, including per capita income, is a strong proxy for use of Fund financing; correlation with per capita income remains low (-0.16 for all members).
  - Sign and scaling challenges: a negative coefficient could produce negative calculated quota shares for some members under the current formula structure because variables are expressed as shares in global totals.
- Staff conclusion:
  - Analysis highlights conceptual and practical issues and does not suggest a strong basis for including per capita income as a stand-alone measure in the quota formula.

### Annex II — PPP GDP (summary)
- Definition and interpretation:
  - PPP GDP obtained by deflating GDP measured in national currency by the associated PPP relative to the United States; PPP measures relative volume of goods and services.
- Differences vs market exchange rates:
  - Market rates more applicable to internationally traded goods and services; market rates tend to underestimate purchasing power in developing countries.
  - PPPs are more stable than currency exchange rates.
- Uses:
  - PPP data used by World Bank, IMF WEO, European Commission, UNDP, WHO, UNESCO.
- Data sources and compilation:
  - Quota PPP GDP data from WEO; WEO PPP indices based on ICP.
  - ICP history: first global coverage in 1993; 2005 ICP round covered 146 economies; 2011 round results expected end-2013 with coverage to at least 154 countries.
- Data quality and measurement challenges:
  - Improvements in 2005 ICP: global linkage via "ring comparison", expanded coverage, improved frameworks.
  - Remaining challenges: nonmarket production valuation, imputed rents for housing, value of work in progress and fixed capital formation in structures.

### Annex III — Openness and Economic Size (summary)
- Core empirical relationship:
  - Inverse relationship between country size (GDP blend share) and nominal openness-to-GDP ratio; negative correlation is -0.14 and statistically significant.
- Definitions:
  - Openness defined as annual average of sum of current payments and current receipts (goods, services, income, and transfers) for 2006-2010.
  - Market GDP and GDP blend averaged over 2008-2010.
- Group statistics on openness-to-GDP ratios (Table A3.1):
  - Large Countries: 10 / 0.61
  - Medium Countries: 80 / 0.80
  - Small Countries: 127 / 1.13
  - Very Small Countries: 43 / 1.52
  - Total: 188 / 1.17
- Impact of openness in quota formula (Table A3.2):
  - Thresholds by GDP blend share: Large > 2.5%; Medium 2.5% > share > 1%; Small 1% > share > 0.01%; Very small < 0.01%.
  - Summary of gains from openness:
    - Large Countries: Number 10; Openness Share > CQS*: 4; Percentage gaining: 40%
    - Medium Countries: Number 81; Openness Share > CQS*: 44; Percentage gaining: 54%
    - Small Countries: Number 127; Openness Share > CQS*: 70; Percentage gaining: 55%
    - Very Small Countries: Number 43; Openness Share > CQS*: 32; Percentage gaining: 74%
    - Total: Number 188; Openness Share > CQS*: 110; Percentage gaining: 59%
- Key finding:
  - Smaller countries tend to gain more from including openness in the quota formula: about 74 percent of the smallest members gain, compared to about 40 percent of the largest ones.

### Annex IV — Adding a Compressed Population Variable (summary)
- Background:
  - Population discussed in past quota reviews; no sufficiently broad support historically.
  - Concerns: relevance to monetary institution, overloading formula objectives, high correlation with PPP GDP.
- Distributional facts:
  - EMDCs account for 86.5 percent of world population; AEs account for 13.5 percent.
  - Using compressed population (unless very large) would not change AE vs EMDC shares much, but would redistribute within EMDCs and shift shares from Asia to other groups.
  - LICs population shares are much larger than for other variables; compressed population would tend to further increase LICs shares.
- Correlations:
  - Correlation coefficients between population and PPP GDP: 0.64 (whole membership); 0.99 (AEs); 0.91 (EMDCs).
- Illustrative simulations:
  - Weight for population in simulations: 5 percent.
  - Simulation redistributions: (i) Drop variability and redistribute 5 percent to population and 10 percent to GDP. (ii) Drop variability, give 5 percent to population and split remaining 10 percent between GDP (2/3) and openness (1/3).
  - Compression factors illustrated: 0.95 and 0.90 (also mention of 0.85 in table headings).
  - Example outcome: approach (i) with compression factor 0.95 leads to increase in CQS of EMDCs by 2.1 percentage points.
  - Inclusion of population would also increase the CQS of LICs by about 1 percentage point.

*Source: _110812a - 1. Simplification of the Current Formula—Dropping Variability; _110812a - 17. Summary of simulations and scope; Annex I–IV as provided in the content unit.*

### 1. Simplification of the Current Formula—Dropping Variability ...........................................12

### 1. Simplification of the Current Formula—Dropping Variability ...........................................12

### Introduction
- Executive Board aimed to complete the quota formula review by January 2013; Directors reaffirmed this timetable at most recent meetings.
- Paper focuses on a narrower range of reform options given the limited time remaining and the need for broad consensus.
- Staff team led by M.S. Kumar and S. Bassett; team members listed in the source.

### Towards consensus—key issues
- Guiding principles for the review: formula should be simple and transparent, consistent with the multiple roles of quotas, result in calculated quota shares broadly acceptable to the membership, and be feasible to implement using timely, high quality, and widely available data.
- Areas of considerable common ground:
  - Dropping variability:
    - Staff technical work highlights shortcomings of the current variability measure as an indicator of potential need for Fund resources and difficulties of developing a superior measure.
    - Many Directors indicated they could support dropping variability; others prefer retaining it (possibly with reduced weight) or await agreement on weight reallocation.
  - Maintaining GDP as the most important variable:
    - GDP should continue to have the largest weight.
    - Outstanding issues: whether to increase GDP weight, and composition of the GDP blend.
    - Current blend is 60/40 percent shares of market/PPP GDP; alternatives discussed include higher PPP share and higher market share.
  - Retaining reserves:
    - Most Directors could support retaining reserves with its current small weight; views differ on raising or eliminating it.
  - Protecting the poorest members:
    - Agreement that voice and representation of poorest members should be protected, generally considered to be addressed outside the quota formula as part of the 15th General Review.
- Divergent views:
  - Openness:
    - Most Directors favor retaining openness, some call for higher weight; others argue the current openness measure is seriously flawed and favor its elimination.
    - Possible bridging approach: limit members’ share of openness relative to GDP (an "openness cap")—views divided on rationale and potential added complexity.
  - New variables:
    - Financial contributions: many Directors favor or open to adding it; many oppose as inconsistent with quota-based institution.
    - Financial openness: some favor increasing weight; many oppose.
    - Population variable: a few Directors called for population to protect poorest members.
  - Compression:
    - Broad support for retaining compression; some favor higher compression (benefits smaller economies and EMDCs), others contend it disproportionately benefits small advanced economies and should be eliminated.
- Notes on data and methodology:
  - PPP GDP data improvements noted with the 2005 ICP; 2011 ICP results expected at end-2013.
  - Value-added trade measures are not currently feasible for formula due to partial and untimely data, but external work suggests gross trade may overstate external flows for some members.

### Possible ways forward (staff approach and considerations)
- Focus on elements with most common ground to build broader consensus, while not excluding more far-reaching reforms.
- Simulations aim to clarify impacts of alternative reform packages and whether combinations could broaden consensus or indicate need for more far-reaching reform.
- Openness cap rationale:
  - A cap may reduce excessive boost to small highly open economies until value-added data are available.
  - Trade-off: cap is somewhat arbitrary and adds complexity.
  - The September paper explored caps and other approaches; a cap of 1.5 on the ratio of openness to GDP shares is illustrated here (compared with cap of 2 in the September paper).
  - Between 54 and 67 countries lose calculated quota share as a result of capping openness shares at 1.5 though for roughly half of those members, the changes would be small in absolute terms.

### Possible reform of the quota formula—illustrative simulations
- Common features across simulations:
  - All simulations drop variability from the formula and maintain reserves with its current 5 percent weight.
  - GDP continues to have the largest weight and openness is retained with at least its current weight.
  - Simulations do not present higher weight on financial openness given limited support.
  - All simulations include a compression factor.
- Reallocation of weight freed by dropping variability:
  - Option (i): all freed weight allocated to GDP.
  - Option (ii): freed weight allocated between GDP and openness with two-thirds of available weight going to GDP (broadly maintaining current proportions).
- GDP blend options illustrated:
  - (i) Retain current 60/40 split (market/PPP).
  - (ii) Higher share for PPP GDP at 50/50.
  - (iii) Modestly higher share for market GDP at 65/35.
  - (iv) Modestly higher share for PPP GDP at 55/45.
- Openness cap simulations:
  - Cap on the ratio of openness to GDP shares set at 1.5 in these simulations.
  - This follows the approach of setting an upper limit on the extent a member’s share in openness can exceed its share in the GDP blend.
- Compression simulations:
  - Illustrate impact of higher compression by reducing compression factor from 0.95 to 0.925.
  - Higher compression tends to benefit smaller economies and EMDCs; reduction from 0.95 to 0.925 compresses distribution further.
- Financial contributions simulations:
  - Illustrate impact of adding a measure of financial contributions (which tends to heavily favor advanced economies).
  - Show it is possible to combine inclusion of financial contributions with other elements that offset its impact on overall group shares.
- Purpose of simulations:
  - Clarify likely effects of alternative combinations of reforms.
  - Assess whether combinations of elements with varying support could build a broader consensus or whether support for more far-reaching reform exists.

*Source: _110812a - 1. Simplification of the Current Formula—Dropping Variability ...........................................12; https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/np/pp/eng/2012/_110812a.pdf*

### 17.      The results of the above simulations are summarized on page 11. More detailed

### _110812a - 17.      The results of the above simulations are summarized on page 11. More detailed

### Summary of simulations and scope
- Simulations report indicative results based on the current database; results could change with updated data expected in mid-2013.
- Detailed results for the largest 35 members are shown in Tables 1–4; individual country results are in Statistical Appendix Tables A1–A4.
- Simulated reform elements explored:
  - Dropping variability from the formula and reallocating its weight (all to GDP or split between GDP and openness).
  - Different GDP blends: 65/35, 60/40, 55/45, 50/50 (GDP/PPP GDP).
  - Openness cap at 1.5.
  - Higher compression (k = 0.925).
  - Inclusion of a measure of financial contributions (a portion of variability weight: 0.05 allocated to financial contributions and 0.10 allocated as indicated).

### Key findings from the simulations
- Aggregate EMDC share:
  - Most simulations result in an overall increase in the aggregate share of EMDCs relative to the current formula.
  - Aggregate changes for EMDCs range from -0.3 to +0.8 based on the current GDP blend and +0.6 to +1.7 with a higher weight on PPP GDP (50/50).
  - Larger increases for EMDCs would require more far-reaching reforms previously considered (e.g., dropping openness or reducing its weight, significantly higher compression) which have not obtained broad support.
- Effects of removing/reallocating variability:
  - Reducing the share of PPP GDP in the blend variable tends to lower the aggregate share of EMDCs unless offset by other changes (e.g., more compression).
  - Dropping variability and allocating freed-up weight to GDP only or to GDP and openness were central scenarios.
- Openness cap and individual country effects:
  - An openness cap (capped at 1.5) produces large declines in share for some highly open economies.
  - While aggregate changes are moderate, changes for individual members can be sizeable.
- Higher compression:
  - Increased compression raises the CQS of a large number of countries, including smaller EMDCs.
  - The number of countries gaining relative to CQS under the current formula increases with higher compression.
- Inclusion of financial contributions:
  - Introducing financial contributions into the formula tends by itself to reduce the share of EMDCs.
  - It may be outweighed by other elements in a package (e.g., higher weight for PPP GDP, openness cap, higher compression — as in set 4).

### Quantified outcomes and scenarios (selected illustrative points)
- Number of gainers under alternative configurations:
  - Dropping variability (unchanged GDP blend): some 53-61 countries gain; 45-50 of these are EMDCs.
  - With openness cap used in set 2: 80-88 gainers; 71-77 EMDCs.
  - With higher compression used in set 3 and set 4: about 110-120 gainers; over 100 are EMDCs.
- Set characteristics referenced in tables:
  - Set 1: Simplification—Dropping Variability.
  - Set 2: Same as Set 1 with Openness Shares Capped at 1.5.
  - Set 3: Same as Set 1 with Higher Compression (k = 0.925).
  - Set 4: Combination—Dropping Variability, Openness Capped at 1.5, Financial Contributions and Higher Compression (k = 0.925).
- Specific coefficient and parameter values appearing in tables:
  - Compression Factor examples: 0.95 and 0.925.
  - Variability weight in current formula: 0.15; scenarios set Variability to 0.00.
  - Reserves coefficient: 0.05 in all scenarios shown.
  - Financial contributions (FCS III) coefficient in set 4: 0.05 (a portion of the variability weight).
  - GDP coefficients across scenarios include values such as 0.30, 0.42, 0.39, 0.36, 0.33, 0.31, 0.28 depending on blend and set.
  - PPP GDP coefficients across scenarios include values such as 0.20, 0.23, 0.21, 0.26, 0.24, 0.29, 0.27, 0.30, 0.28.
  - Openness coefficients in various scenarios include 0.30, 0.35, 0.00 (when capped or removed), and capped-at-1.5 allocations by blend as shown in tables.
- Representative aggregate changes in CQS by EMDC grouping (from narrative):
  - Aggregate changes moderate: ranging from -0.3 to +0.8 (current GDP blend) and +0.6 to +1.7 (50/50 blend).
- Memorandum items and group shares shown in tables (selected examples preserved exactly as in source tables):
  - Total always reported as 100.0 under all calculated scenarios.
  - EU27 memorandum items in example table: values such as 30.2, 30.9, 29.8, 30.5, 29.6, 30.3, 29.4, 30.1, 29.2, 29.9 depending on scenario.
  - LICs memorandum items in example table: values such as 4.0, 2.7, 2.6, 2.6, 2.6, 2.6, 2.7, 2.7, 2.7, 2.7 (varies by table).
- Examples of country-level CQS changes in summary table header (Change in CQS / Number of Gainers):
  - Sample entries for sets: e.g., for Set 1 (65/35 GDP blend, all to GDP) the line shows "1.6-1.1-0.5-0.1 48 40" (reflecting percentage point change in CQS by group and number of gainers).
  - For Set 2 (65/35 blend, all to GDP with openness capped at 1.5) the line shows "2.8-2.8-0.1 75 66".
  - For Set 3 (65/35 blend, all to GDP with higher compression k = 0.925) the line shows "0.4-0.8 0.3 0.1 118 106".
  - For Set 4 (65/35 blend, all to GDP with openness cap, financial contributions and k = 0.925) the line shows "2.3-1.9-0.4 0.1 104 93".
  - (Tables contain many additional specific numeric entries for each blend, split option, set, and country group.)
- Footnotes and illustrative allocations:
  - A portion of the variability weight (0.05) is allocated to financial contributions; the remaining 0.10 is allocated as indicated.
  - Financial contributions are illustrated as the weighted average of a member’s share in NAB contributions including new pledges (0.3), FTP participation based on resources (0.3), PRGT loans and subsidies (0.2) and TA activities (0.2).

### Issues for discussion and director-level questions
- Could Directors support dropping variability from the formula, recognizing conditional support for some?
- Given that GDP should remain the most important variable, how should the weight of variability be reallocated?
- Would Directors consider a higher weight of PPP GDP to build broader consensus?
- Do Directors support further consideration of an openness cap, given diverging views on openness and the current absence of reliable balance of payments data on value added in trade?
- Views on adding new variables (e.g., measure of financial contributions, higher weight for financial openness, population) and whether recognizing particularly generous financial contributions should be considered as part of the 15th General Review.
- Is there scope for a higher compression factor as part of a reform package, for example one that includes a higher weight on GDP?
- Next steps to meet the goal of concluding the review by January 2013.

*Source: Finance Department (text and tables as provided in the content unit).*

### Annex I. GDP Per Capita as a Measure of Vulnerability

### Annex I. GDP Per Capita as a Measure of Vulnerability

### Use of GDP per capita to capture vulnerability
- Historical evidence: GDP per capita exhibits the highest correlation among frequently-tested macroeconomic determinants with the approval of an IMF arrangement.
  - Correlation between approval of a Fund arrangement and per capita GDP is estimated at -0.16 for the period 1990-2010 and is statistically significant at the 1% level.
  - For LICs only, the correlation coefficient is -0.07 and remains significant.
- Distributional facts:
  - In 92 percent of the cases, the country seeking financial assistance from the IMF had per capita GDP below the average.
  - In 81 percent of the cases, the country seeking assistance had per capita GDP less than 50 percent of the average.
- Conceptual rationale:
  - Low-income countries are likely to be more vulnerable because they generally have less diverse economic structures and lower capacity to cope with shocks.

### Limitations and practical issues with inclusion in the quota formula
- No single variable, including per capita income, is a strong proxy for use of Fund financing; correlation with per capita income remains low (-0.16 for all members).
- Sign and scaling challenges:
  - Lower per capita income should imply higher vulnerability (an inverse relationship in the formula).
  - A negative coefficient could produce negative calculated quota shares for some members under the current formula structure.
    - Reason: all variables in the formula are expressed as shares in global totals; calculated quota shares could become negative for some small members if their share in GDP per capita is substantially higher than their shares in the other variables.
- Political and historical context:
  - Past proposals to include per capita income (or a “poverty index”) in the quota formula have not received sufficient support, reflecting both conceptual and practical problems.

### Staff conclusion on per capita income
- The analysis highlights important conceptual and practical issues and does not suggest a strong basis for including per capita income as a stand-alone measure in the quota formula.

*Source: Annex I. GDP Per Capita as a Measure of Vulnerability*

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### Annex II. PPP GDP

### PPP GDP: definition and interpretation
- Purchasing Power Parity (PPP) refers to the purchasing power to buy a given amount of goods and services in a given country (compared with the numéraire country).
  - The numéraire country for the PPP estimates is the United States.
- PPP GDP is obtained by deflating GDP measured in national currency by the associated PPP relative to the United States.
  - PPP GDP measures the relative volume of goods and services between two countries.
- PPP-adjusted final consumption data measure the relative volume of final consumption and are used to assess and compare relative living standards.

### Differences between PPP and market exchange rate conversions
- Market exchange rates measure current currency exchange and are more applicable to internationally traded goods and services.
- Market exchange rates tend to underestimate purchasing power in developing countries relative to advanced economies.
- PPPs are more stable than currency exchange rates, which are affected by monetary policy stance, speculation, temporary current and capital account changes, and official interventions.
- PPPs provide more stable underlying valuations and are used to assess countries’ relative importance in world production for final uses.

### Uses of PPP data
- PPP data are widely used by international organizations and researchers, including for:
  - poverty headcounts (World Bank)
  - WEO (IMF)
  - allocation of structural and cohesion funds (European Commission)
  - Human Development Index (UNDP)
  - health inequality assessment (WHO)
  - assessing per capita expenditures in education (UNESCO)

### Data sources and compilation
- Quota PPP GDP data are obtained from the World Economic Outlook (WEO) database; WEO PPP price indices are based on the International Comparison Program (ICP) survey.
- ICP history and coverage:
  - ICP began in 1968; first round in 1970 included 10 countries.
  - Regionalization began after 1975; Eurostat-OECD PPP Program joined in early 1980s.
  - First global coverage across all regions was in 1993.
  - Since 1993, the World Bank has been global coordinator for the ICP.
  - The 2005 ICP round covered 146 economies; work on a 2011 round was near completion, with results expected at end-2013 and coverage to broaden to at least 154 countries.
- IMF contributions: Statistics Department builds capacity (e.g., Asia-Pacific GDP estimates used for ICP weights), provides technical assistance on real sector statistics, and staff serve on the ICP Technical Advisory Committee.

### Data quality and measurement challenges
- PPP data quality depends on national GDP and price statistics and is broadly comparable to other data used in the quota formula.
- Improvements in the 2005 ICP round:
  - First-time global linkage via “ring comparison” to directly compare economies across regions.
  - Expanded coverage and improved survey frameworks, homogenous product sets, and better rural coverage.
- Remaining measurement challenges for PPP and GDP by expenditure:
  - Nonmarket production (general government services: education, health, public administration):
    - Final expenditures measured as sum of production costs; need to account for productivity differences and capital intensity when separating price and volume components.
  - Value of housing services from rented and owner-occupied dwellings:
    - Housing characteristics vary; imputed rentals affect imputed level and price of owner-occupied housing and rental housing.
  - Value of work in progress, construction, and fixed capital formation in structures:
    - Comparability across countries requires data and methods that are not always readily available.
- Conceptual approaches to these issues are reasonably well understood, but implementation data are sometimes lacking.

*Source: Annex II. PPP GDP*

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### Annex III. Openness and Economic Size

### Core empirical relationship
- There is an inverse relationship between country size (measured by GDP blend share) and the nominal openness-to-GDP ratio.
  - The negative correlation between GDP share and openness-to-GDP ratio is -0.14 and is statistically significant.

### Definition and averaging conventions
- Openness is defined as the annual average of the sum of current payments and current receipts (goods, services, income, and transfers) over the period 2006-2010.
- Market GDP and GDP blend are averaged over 2008-2010.

### Group statistics on openness-to-GDP ratios (Table A3.1)
- Number of Countries / Average Nominal Openness/GDP Ratio:
  - Large Countries: 10 / 0.61
  - Medium Countries: 80 / 0.80
  - Small Countries: 127 / 1.13
  - Very Small Countries: 43 / 1.52
  - Total: 188 / 1.17
- Observations:
  - For the 10 largest countries, openness-to-GDP ratios are all below 1.0 except Germany (slightly above 1.0), with an average of 0.61.
  - The smallest economies have the highest average openness-to-GDP ratio at 1.52.

### Impact of openness in the quota formula by size group (Table A3.2)
- Method: A country “gains” from openness if its openness share minus its “uncompressed” CQS (CQS*) is positive (openness share > CQS*).
- Country group thresholds by GDP blend share:
  - Large countries: GDP blend share > 2.5%
  - Medium countries: 2.5% > GDP blend share > 1%
  - Small countries: 1% > GDP blend share > 0.01%
  - Very small countries: GDP blend share < 0.01%
- Summary of gains from openness:
  - Large Countries: Number of Countries 10; GDP Blend Share 65.0%; Openness Share > CQS*: 4; Openness Share < CQS*: 6; Percentage of Countries Gaining from Openness: 40%
  - Medium Countries: Number of Countries 81; GDP Blend Share 13.1%; Openness Share > CQS*: 44; Openness Share < CQS*: 37; Percentage of Countries Gaining from Openness: 54%
  - Small Countries: Number of Countries 127; GDP Blend Share 21.8%; Openness Share > CQS*: 70; Openness Share < CQS*: 57; Percentage of Countries Gaining from Openness: 55%
  - Very Small Countries: Number of Countries 43; GDP Blend Share 0.1%; Openness Share > CQS*: 32; Openness Share < CQS*: 11; Percentage of Countries Gaining from Openness: 74%
  - Total: Number of Countries 188; GDP Blend Share 100%; Openness Share > CQS*: 110; Openness Share < CQS*: 78; Percentage of Countries Gaining from Openness: 59%
- Key finding:
  - Smaller countries tend to gain more from including openness in the quota formula: about 74 percent of the smallest members gain, compared to about 40 percent of the largest ones.

*Source: Annex III. Openness and Economic Size*

### Annex IV. Adding a Compressed Population Variable to the Formula?

### Annex IV. Adding a Compressed Population Variable to the Formula?

### Background and past discussions
- Inclusion of population in the quota formula has been discussed in past quota reviews (10th, 11th, Twelfth, and 2008 reform work).
- The Quota Formula Review Group (QFRG) listed population as one variable that could be considered.
- Past discussions: no sufficiently broad support for including population. Key reasons:
  - The Fund is considered essentially a monetary institution and population does not bear directly on international monetary issues.
  - Concern that the quota formula should not be overloaded with too many objectives.
  - Population is argued to be similar to PPP GDP in effect and relatively highly correlated with PPP GDP.

### Distributional findings on population and correlation with PPP GDP
- EMDCs account for 86.5 percent of the world’s population; advanced economies (AEs) account for 13.5 percent.
- Using compression on population, unless very large, would not change much the population shares of AEs and EMDCs but would change the distribution within EMDCs and shift shares from Asia to other groups.
- The population shares of LICs are much larger than for other variables; using compression for the population variable would tend to further increase the population shares of LICs (at the expense of other EMDCs).
- Correlation coefficients between population and PPP GDP:
  - Whole membership: 0.64
  - AEs (separately): 0.99
  - EMDCs (separately): 0.91
- Figure A4.1 (described): plots PPP GDP shares against population shares for AEs and EMDCs; slope of trend line for AEs is much higher than for EMDCs — implying inclusion of population would have a larger effect on calculated quota shares of EMDCs.

### Illustrative simulations and scenarios examined
- Simulations examined including a compressed population variable with a small weight of 5 percent (weight chosen as the smallest weight of variables in the existing formula—i.e., the weight of reserves).
- Simulation variants described:
  - (i) Drop variability and redistribute 5 percent to population and 10 percent to GDP.
  - (ii) Drop variability, give 5 percent to population and split the remaining 10 percent between GDP (2/3) and openness (1/3).
- Compression factors on population shares illustrated: 0.95 and 0.90 (also a mention of 0.85 in Table A4.1 headings).
- Illustrative outcome summaries:
  - Inclusion of population results in redistribution of calculated quota shares (CQS) from advanced economies to EMDCs, particularly to countries with large populations.
  - Example: applying approach (i) with a compression factor of 0.95 on population shares leads to an increase in CQS of EMDCs by 2.1 percentage points.
  - Inclusion of population would also increase the CQS of LICs by about 1 percentage point.

### Key numeric parameters and values cited
- Population share: EMDCs 86.5 percent; AEs 13.5 percent.
- Correlation coefficients: 0.64 (whole membership); 0.99 (AEs); 0.91 (EMDCs).
- Weight used in simulations for population: 5 percent.
- Simulation redistributions considered: 5 percent to population and 10 percent to GDP (or 10 percent split between GDP(2/3) and openness(1/3)).
- Compression factors illustrated: 0.95 and 0.90.
- Effect example: EMDCs CQS increase by 2.1 percentage points (approach (i) with compression 0.95); LICs CQS increase by about 1 percentage point.

*Source: IMF Finance Department, Annex IV. Adding a Compressed Population Variable to the Formula?*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/np/pp/eng/2012/_110812a.pdf_