## Possible Quota Formula Variables—Shares in Global Totals

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### Introduction and mandate
- Board of Governors Resolution adopted on September 18 requested the Executive Board reach agreement on a new quota formula, starting discussions soon after the Annual Meetings in Singapore.
- Timeline set by the Resolution:
  - work completed by the Annual Meetings in 2007, and no later than the IMFC Meeting in the Spring of 2008.
- Purpose of the paper:
  - explore key issues related to a new quota formula as background for an informal Board seminar;
  - review guiding considerations and principles, roles of quotas, selection of variables, and possible functional forms;
  - draw on prior quota formula discussions, including the Quota Formula Review Group (QFRG) work.
- The paper does not make specific proposals; it aims to narrow issues toward convergence on a proposal or narrow range of proposals for future quota adjustments.

### Role of quotas
- Quotas serve multiple inter-related purposes:
  - constitute the Fund’s financial base; a member’s quota determines its financial contribution which must be fully subscribed and paid in a combination of reserve assets and the member’s own currency; quotas of members with currencies considered usable effectively determine the Fund’s capacity to provide financing.
  - influence members’ access to Fund resources: current access policy allows annual access of 100 percent of quota with cumulative access limited to 300 percent of quota; access limits may be exceeded in exceptional circumstances.
  - determine voting power together with “basic votes”: each member receives 250 basic votes plus one additional vote for each part of its quota equivalent to SDR 100,000; the five members having the largest quotas are each required to appoint an Executive Director.
- Implications:
  - the quota formula must balance competing considerations across financial structure, financing operations, and governance.
  - fully delinking quotas from all access decisions would raise wider-ranging issues and require an amendment to the Articles.
  - the Resolution envisions the new formula providing the basis for a second round of ad hoc quota increases and playing a more prominent role in quota realignments, while the Board retains flexibility to recommend other factors.

### Principles and desirable mathematical properties
- Core principles the new formula should satisfy:
  - be simple and transparent;
  - be consistent with the roles of quotas, reflecting global economic and financial trends and members’ relative positions;
  - result in calculated quota shares that are broadly acceptable to the membership;
  - be feasible to implement statistically using timely, high quality, and widely available data.
- Noted problems with existing formulas:
  - system is neither transparent nor simple, involving five formulas and a complicated decision rule; impact of a change in a quota variable can be counterintuitive.
- Desirable mathematical properties:
  - homogeneity;
  - monotonicity;
  - non-convexity.
- Emphasis on intuitive appeal of results and modernization over time.

### Variable selection criteria and consensus on scope
- Consensus to limit variables to no more than the four utilized in existing formulas, updated and modernized — an evolutionary approach for continuity.
- Variables should capture:
  - capacity to contribute financial resources to the Fund;
  - potential need to use Fund resources;
  - economic position and role in the world economy.
- Variables must be supported by timely, high-quality, widely available data to minimize estimation.

### GDP (detailed points)
- GDP identified as a very important variable:
  - comprehensive measure of economic size;
  - single most relevant indicator of ability to contribute to the Fund’s finances, though not the only measure;
  - relevant to potential demand for Fund resources and relative positions in the global economy.
- Data availability:
  - widely reported and available on a timely basis for the vast majority of membership.
  - In the most recent quota database update, 119 members reported GDP data usable directly from IFS; staff supplemented with WEO data for most other members.
- Conversion debate:
  - market exchange rates (traditional) versus PPP-based conversion.
  - Market exchange rate GDP: viewed as more relevant to ability to contribute to the Fund’s finances and capacity to borrow.
  - PPP-based GDP: relevant for cross-country comparisons of volumes of goods and services produced; distribution across members differs substantially from market-exchange-rate-based GDP.
  - PPP-based GDP data of sufficient quality for quota calculations are only available for a small subset of members; ICP work expected to broaden coverage to about 130 countries, not expected to be completed until late 2007.
  - Introduction of a population variable could have similar effects to PPP-based GDP but population does not bear directly on international monetary issues; QFRG did not propose including population.
- Smoothing GDP:
  - consensus that GDP should be averaged over several years to avoid undue influence of temporary fluctuations.
  - a three-year average has been generally viewed as a reasonable trade-off, though slightly longer periods could be considered.

### Openness: concept, measurement issues, and extensions
- Conceptual relevance:
  - openness indicates involvement and stake in the global economy; more open countries may have greater interest in promoting global stability and be more vulnerable to external shocks.
- Role in existing formulas:
  - enters through current receipts and payments (both separately and combined) and through the ratio of current receipts to GDP as a multiplicative factor in three of the five existing formulas.
  - Ratio of current receipts to GDP can give very large effective weight to openness for highly open economies and can lead to anomalous results if GDP growth exceeds export growth.
- Practical approach:
  - considerable support for a single, simplified measure of openness (sum of current receipts and payments) averaged over a five-year period as used in recent staff work.
- Remaining issues:
  - unresolved technical and definitional issues remain, including whether to broaden openness to financial openness and how to treat intra-union trade and currency unions.

### Openness: gross flows versus value added; intra-union trade
- Current practice:
  - openness enters on a gross basis, which can double count cross-border flows and exaggerate measured economic size, especially for entrepôt trade, international financial centers, or heavy processing-for-re-export.
  - longstanding practice: adjustments to the quota database correct for such activities before determining actual quota increases; these adjustments are resource-intensive, judgment-dependent, and data-dependent.
- Treatment of trade within economic or currency unions:
  - increased integration raises question whether intra-union trade should be counted as foreign trade for quota calculations.
  - QFRG proposed excluding openness altogether from a new formula, but did not propose singling out intra-union trade for exclusion.
  - rationale: fund membership is per country and currency union membership does not preclude balance of payments difficulties requiring Fund assistance.
  - excluding intra-union transactions may be difficult given typical data availability.

### Financial openness and IIP data
- Conceptual appeal to include financial openness given expansion in cross-border capital flows.
- Data-related difficulties:
  - gross capital flows can be inflated by “churning” or short-term flows; net capital flows are not a useful indicator of integration.
- Indicator discussed:
  - stock measure such as the sum of accumulated foreign asset and liability positions reported in the international investment position (IIP).
  - Data availability improved: 106 economies now reporting full or partial IIP data, with 85 considered comprehensive reporters, compared with 83 in 2003.
  - Coverage still short of needed level; Appendix Table A1 summarizes latest available IIP data.
- Investment income flows suggested as proxy for missing IIP data but suffer significant statistical shortcomings.
- Legal/Article consideration:
  - Articles recognize the right to impose controls on capital transfers (Article VI, Section 3) and provide that a member may not "use the Fund's general resources to meet a large or sustained outflow of capital." (Article VI, Section 1).
  - Implication: use of capital-based measures would need to consider constraints on access to meet capital-account driven needs, reflected in Fund policies on exceptional access.

### Variability as a quota variable
- Concept:
  - variability is a measure of vulnerability to balance of payments shocks and potential need for Fund resources; also an indicator of stake in global financial stability.
- Historical inclusion: variability has been included in quota formulas from the beginning; it was one of the two variables proposed by the QFRG (along with GDP).
- Debates:
  - some argue need is already captured by openness, but relatively closed economies can face BoP crises with substantial financing needs.
  - concerns that including variability might reward unstable policies.
- Modernization:
  - consensus that variability should include a capital account aspect to reflect capital flow crises.
  - support for a variable measuring variability of current receipts and net capital flows.
  - agreed preference: deviation from a three-year average (rather than five years in existing formulas) to capture shorter-term trends while smoothing very temporary fluctuations.
  - data availability: required data broadly available from IFS and WEO databases.

### Reserves
- Role:
  - reserves as indicator of financial strength and ability to contribute to Fund finances.
- Divergent views:
  - support: reserves central since Fund inception; reserve adequacy relevant to external financial strength and ability to contribute to usable resources.
  - opposition: with growing importance of international capital markets, reserves may be a less relevant indicator of ability to contribute; particularly misleading for international reserve currencies.
  - concern: inclusion of reserves could reward excessive foreign exchange intervention and reserve accumulation.
- Policy responses suggested:
  - give reserves at most a relatively small weight;
  - consider capping their influence in some way.

### Correlation among variables
- High correlation among main quota variables reflects that they are measures of economic size:
  - correlation typically around 0.9 for GDP, openness, and variability.
  - correlation significantly lower — less than 0.5 — for reserves (partly due to reserve currencies).
- Consequences:
  - high correlation constrains range of results obtainable by varying weights on the first three variables but still allows differentiation.
  - creates multicollinearity problems complicating disentangling each variable’s relative influence.
  - alternative specifications considered historically to reduce correlation were not found to have desirable properties.

### Functional form choices and desiderata
- Desirable properties reiterated:
  - simplicity and transparency;
  - homogeneity;
  - monotonicity;
  - non-convexity.
- Three functional-form families considered:
  - Linear in shares:
    - quota shares are a linear combination of shares of individual country variables;
    - coefficients interpretable as weights (if positive and sum to one);
    - elasticities are member-specific, positive, and vary across membership.
  - Multiplicative in shares:
    - multiplicative combination; with positive exponents summing to one, interpretable as geometric average before rescaling;
    - elasticities are constant across membership and equal to exponents;
    - tends to lower calculated quota shares for members with significant dispersion across variable shares.
  - Compressed linear in shares:
    - introduces a compression factor λ (between 0 and 1) to adjust for high correlation favoring large economies;
    - lower λ implies greater compression and more impact on large economies;
    - member-specific elasticities; compression rescaling ensures calculated quota shares sum to 100 percent.
- Compression can also be applied to multiplicative formulas with broadly similar aggregate results.
- Choice of λ determines amount of compression; compression does not change rank order of countries by calculated quota shares relative to uncompressed distribution.

### Weights: guidance and historical perspective
- Board of Governors’ Resolution guidance: consider placing “significantly higher weight on members’ gross domestic product, together with ensuring that other variables, in particular the openness of members’ economies, also play an important role.”
- Executive Board report noted “some have stressed the importance of variability.”
- 2003 Executive Directors’ views: GDP considered most important variable, with lesser weights for openness, variability, and reserves.
- Estimated contributions in the current quota formulas (reported): GDP, 29 percent; reserves, 7 percent; variability, 14 percent; openness, 50 percent.
- Correlation among variables must be considered when selecting weights; most Directors acknowledged correlation is unavoidable and that attempts to reduce it entail significant drawbacks including reduced transparency.
- Final selection of variables, weights, and compression factors is a matter of judgment and political consensus among membership.

### Illustrative calculations: variables and data used (specifications preserved)
- Simulations are presented as purely illustrative; not staff views on the appropriate new quota formula.
- Variables used (denominated in SDRs):
  - GDP: annual data, converted at market exchange rates, averaged for 2002–2004.
  - Openness: annual average of the sum of current payments and current receipts for 2000–2004.
  - Variability: standard deviation from the centered three-year trend over 1992–2004 (a thirteen-year period) of current receipts and net capital flows.
  - Reserves: twelve-month average of gold, foreign exchange reserves, SDR holdings, and reserve positions in the IMF for 2004.
- Purpose: illustrate implications of different functional forms and weights for distribution of quota shares; only broad regional results described in text; detailed member implications reported in a supplement.

### Linear-formulation simulations: design and broad results
- Simulation design:
  - Six different sets of weights (Table 3).
  - The weight on GDP varies from 40 to 60 percent.
  - For each GDP weight, two different combinations of openness and variability weights are used.
  - Reserves are given a weight of 5 percent in all six scenarios.
- Broad results:
  - calculated quota shares of advanced countries as a group are higher in all six formulations than under the existing formulas, reflecting higher weight on GDP.
  - calculated quota shares of developing countries are lower in all six formulations than under the current formulas, reflecting relatively low share of developing countries in global GDP.
  - calculated quota share of advanced countries rises and that of developing countries falls as the weight on GDP increases.
  - higher weight on openness and lower weight on variability tends to increase the calculated quota share of advanced countries and lower that of developing countries; significant differences across regions.

### Non-linear and compressed specifications: design and main findings
- Simulation design:
  - single GDP weight: 50 percent.
  - high and low weights for openness and variability tested.
  - compressed formulas use compression factors of 0.9 and 0.95 (arbitrarily chosen).
  - multiplicative specification also considered.
- Main results:
  - multiplicative specification results are very similar to the linear form.
  - compressed linear form lowers calculated quota share of advanced countries as a group and raises calculated share of developing countries taken together.
  - compressed linear form lowers calculated quota share of the seven members with the highest calculated quota shares under equivalent linear forms and raises calculated quota share for all other countries.
  - smaller the compression factor, the greater the reduction of the calculated quota share of advanced countries and the larger the gain for developing countries.
  - number of countries whose quota share is reduced does not vary with moderate changes in the compression factor.
- Additional note on reserves:
  - higher weight on reserves tends to increase modestly the share of developing countries, particularly in Asia, and lower that of advanced countries.
- Compression threshold (preserved exactly):
  - Countries with a calculated quota share below 3.01 (3.22) percent before compression gain with compression at 0.90 (0.95); for the scenarios presented, most members (177) gain with compression and seven countries lose quota share.

### Key quantitative design parameters and example formulas (preserved exactly)
- Linear-form scenarios (Table 3): GDP weights tested: 40%, 50%, 60%; Reserves weight: 5% in all six scenarios; openness and variability weights varied across scenarios (examples in Table 3 headings: Openness 30% / Variability 25%; Openness 25% / Variability 30%; Openness 30% / Variability 15%; Openness 15% / Variability 30%; Openness 20% / Variability 15%; Openness 15% / Variability 20%).
- Single-weight nonlinear/compressed example formulas (Table 4 and Table 5 notes):
  - Q = 0.50*Average GDP + 0.30*Openness + 0.15*Variability + 0.05*Reserves.
  - Q = (Average GDP)^0.50 * (Openness)^0.30 * (Variability)^0.15 * (Reserves)^0.05.
  - Compressed forms: Q = (0.50*Average GDP + 0.30*Openness + 0.15*Variability + 0.05*Reserves)^0.9 and ^0.95 (requires rescaling of calculated shares).
  - Alternative weighting in Table 5: Q = 0.50*Average GDP + 0.15*Openness + 0.30*Variability + 0.05*Reserves; multiplicative analogue and compression exponents 0.9 and 0.95 noted.

### Sample aggregate outcome comparisons (preserved exactly)
- Advanced economies:
  - Actual Quotas 61.6; Existing Formulas (Pre Ad Hoc Increases) 60.5; example linear outcomes in panels: 67.1; 69.3; 68.8; 70.8; 69.5; 71.5; 71.1.
- Developing countries:
  - Actual Quotas 30.9; Existing Formulas 32.1; example linear/compressed outcomes include 27.6; 25.8; 26.1; 24.5; 25.6; 24.0; 24.4.
- Major advanced economies:
  - Actual 46.0; Existing 45.2; sample outcomes 47.3; 53.2; 52.9; 55.3; 54.4; 56.9; 56.6.
  - Of which: US: Actual 17.4; Existing 17.1; sample outcomes 16.8; 22.1; 22.3; 23.1; 23.8; 24.6; 24.8.
- Memorandum items:
  - EU 25: Actual 32.2; Existing 31.6; sample outcomes 37.6; 33.1; 32.5; 33.2; 31.2; 31.9; 31.2.
  - LICs: Actual 7.5; Existing 7.4; sample outcomes 3.6; 3.7; 3.8; 3.5; 3.8; 3.5; 3.6.

### Illustrative member-level results (selected entries preserved exactly)
- Table highlights (selected entries, shares in percent):
  - United States:
    - Actual Quotas: 17.382; Existing: 17.078; Pre Ad Hoc Increases: 16.795; Post Ad Hoc Five Formulas: 22.108; 22.336; 23.105; 23.792; 24.560; 24.789.
    - Other table entries: Post Ad Hoc Five Formulas (alternative columns): 23.105; 22.637; 18.846; 20.937.
    - Further columns: 23.792; 23.627; 19.293; 21.498.
  - Japan:
    - Actual Quotas: 6.229; Existing: 6.120; Pre Ad Hoc Increases: 6.120; Post Ad Hoc Five Formulas entries include: 6.120; 7.525; 9.360; 9.415; 9.870; 10.035; 10.490; 10.545.
    - Other table columns: 9.870; 9.813; 8.765; 9.332; and 10.035; 10.127; 8.872; 9.468.
  - Germany:
    - Actual Quotas: 6.087; Existing: 5.980; Pre Ad Hoc Increases: 5.980; Post Ad Hoc Five Formulas entries: 6.087; 6.953; 6.977; 6.879; 6.966; 6.672; 6.759; 6.660.
    - Other columns: 6.966; 7.270; 6.406; 6.702; and 6.672; 7.027; 6.144; 6.424.
  - China (Includes China, P.R., and Hong Kong, SAR):
    - Actual Quotas: 2.980; Existing: 3.719; Pre Ad Hoc Increases: 3.719; Post Ad Hoc Five Formulas entries include: 2.980; 5.197; 4.866; 4.764; 5.018; 4.713; 4.966; 4.865.
    - Other columns: 5.018; 5.102; 4.768; 4.907; and 4.713; 4.746; 4.494; 4.618.
  - Saudi Arabia:
    - Actual Quotas: 3.269; Existing: 3.211; Pre Ad Hoc Increases: 3.211; Post Ad Hoc Five Formulas entries: 3.269; 1.063; 0.752; 0.753; 0.724; 0.727; 0.698; 0.698.
    - Other columns: 0.724; 0.774; 0.835; 0.780; and 0.724; 0.774; 0.835; 0.780.

Notes on tables:
- Calculated as the sum of variable weights multiplied with a country's share in the global total of the respective variables.
- Based on 1992–2004 data. Reflects adjustments to current receipts and payments for re-exports, international banking interest, and non-monetary gold.
- Specification of GDP and variability differs from the existing five formulas as average GDP and variability of current receipts plus net capital flows are used.
- For the three countries that have not yet consented to, and paid for, their quota increases, Eleventh Review proposed quotas are used.
- Includes ad hoc increases for China, Korea, Mexico, and Turkey.
- Compressed and multiplicative variants (exponents 0.9 and 0.95) require rescaling of calculated shares.

### Historical background and QFRG summary
- During the Ninth Review, some interest in changes to formulas but not broad consensus; existing formulas endorsed in the Tenth Review.
- QFRG (appointed 1999) main findings:
  - (1) significant changes in the world economy since 1944 have made IMF member countries more exposed to external shocks;
  - (2) the quota formulas themselves have had only an indirect influence on actual quotas; and
  - (3) gaps between actual quota shares and calculated quota shares have persisted over time.
- QFRG proposal:
  - replace five formulas with a single linear formula with two variables: one for ability to contribute and one for external vulnerability.
  - suggested ability to contribute weight about twice that of external vulnerability.
  - measurement: GDP converted at market exchange rates and averaged over three years; vulnerability measured by variability of current receipts expanded to include variability of net long-term capital flows.
  - minority view: GDP should use PPP conversion.

### Data sources: PPP, IIP, population (preserved)
- PPP data:
  - WEO database PPP-based GDP for 175 countries from ICP: OECD/Eurostat, CIS, World Bank, and Fund-staff estimates.
  - OECD/Eurostat and CIS: combined coverage of 52 countries; price surveys reference year 2002 for OECD and 2000 for CIS.
  - World Bank: PPP-based GDP for 104 countries in WDI; mostly estimates with only 63 countries providing price survey-based information for reference year 1996.
  - Staff estimates for remaining 19 countries based on cross-section regression.
  - limitations: differences in survey reference periods, inconsistent methodologies, quality/coverage gaps; 2005 ICP round estimates expected in late 2007.
- International Investment Position (IIP):
  - IIP provides comprehensive measure of external balance sheet: foreign financial assets and liabilities at a point in time.
  - Full or partial IIP data available for 106 countries; 85 considered comprehensive reporters (members with 3 years or more of data during 2000–04).
  - valuation issues: book value versus market prices may differ across reporters.
- Population:
  - sourced from IFS based on Population Division of UN DESA;
  - represent mid-year estimates and revised every two years;
  - data available for almost all members.

### Selected country-level monetary and share statistics (preserved exactly)
- Selected Table 2 country-level figures (in millions of SDRs unless otherwise indicated):
  - United States:
    - Quotas: 37,149.3; PPP-GDP: 7,970,732.5; IIP Assets (2002–04 average): 5,641,528.1; IIP Liabilities (2002–04 average): 7,264,396.1; IIP Assets plus Liabilities (2002–04 average): 12,905,924.2; Population 2004 (in millions): 295.4.
  - Japan:
    - Quotas: 13,312.8; PPP-GDP: 2,614,553.7; IIP Assets: 2,384,546.6; IIP Liabilities: 1,328,260.0; IIP Assets plus Liabilities: 3,712,806.6; Population 2004: 127.9.
  - Germany:
    - Quotas: 13,008.2; PPP-GDP: 1,727,138.3; IIP Assets: 2,426,847.4; IIP Liabilities: 2,315,985.6; IIP Assets plus Liabilities: 4,742,833.0; Population 2004: 82.6.
  - China 4/:
    - Quotas: 8,090.1; PPP-GDP: 5,570,726.7; IIP Assets: n.a.; IIP Liabilities: n.a.; IIP Assets plus Liabilities: n.a.; Population 2004: 1,315.0.
  - India:
    - Quotas: 4,158.2; PPP-GDP: 2,202,342.0; IIP Assets: 75,620.3; IIP Liabilities: 118,786.4; IIP Assets plus Liabilities: 194,406.7; Population 2004: 1,087.1.
  - Russia:
    - Quotas: 5,945.4; PPP-GDP: 970,705.9; IIP Assets: 214,897.8; IIP Liabilities: 195,083.1; IIP Assets plus Liabilities: 409,980.9; Population 2004: 143.9.
  - Luxembourg:
    - Quotas: 279.1; PPP-GDP: 20,697.1; IIP Assets: 1,800,565.7; IIP Liabilities: 1,781,237.4; IIP Assets plus Liabilities: 3,581,803.1; Population 2004: 0.5.
- Selected Table 3 shares in global totals (in percent):
  - United States:
    - Quotas: 17.078; PPP-GDP: 20.706; IIP Assets (2002–04 average): 20.448; IIP Liabilities (2002–04 average): 24.578; IIP Assets plus Liabilities (2002–04 average): 22.584; Population share 2004: 4.661.
  - China 4/:
    - Quotas: 3.719; PPP-GDP: 14.472; IIP entries: n.a.; Population share 2004: 20.748.
  - Japan:
    - Quotas: 6.120; PPP-GDP: 6.792; IIP Assets: 8.643; IIP Liabilities: 4.494; IIP Assets plus Liabilities: 6.497; Population share 2004: 2.018.
  - India:
    - Quotas: 1.912; PPP-GDP: 5.721; IIP Assets: 0.274; IIP Liabilities: 0.402; IIP Assets plus Liabilities: 0.340; Population share 2004: 17.153.
  - Luxembourg:
    - Quotas: 0.128; PPP-GDP: 0.054; IIP Assets plus Liabilities share: 6.268; Population share 2004: 0.007.

### Issues for Directors (questions preserved)
- Should the quota formula be guided by the several roles of quotas described in Section II and balance competing considerations inherent in those roles?
- Should the quota formula include at most four variables—GDP, openness, variability, and reserves—or are there other variables that should be included? Related definitional questions:
  - Whether GDP should be measured at market or PPP exchange rates.
  - Whether openness should include a measure of financial openness and the treatment of intra-currency union trade.
  - Whether reserves should be capped in some way.
- Which functional forms are most appropriate, given guiding principles and desirable properties? Comment on relative merits of alternative functional forms presented.
- What structure of weights for the chosen variables is appropriate, and what other considerations should guide judgments on the structure of weights?

*Source: IMF staff paper excerpt — "Possible Quota Formula Variables—Shares in Global Totals" (selected sections); Statistical Appendix prepared by the Finance Department. Approved by Michael G. Kuhn. November 29, 2006.*

### 1.  Possible Quota Formula Variables—Shares in Global Totals.......................................19

### 1.  Possible Quota Formula Variables—Shares in Global Totals.......................................19

### Introduction
- Board of Governors Resolution adopted on September 18 requested the Executive Board reach agreement on a new quota formula, starting discussions soon after the Annual Meetings in Singapore.
- Timeline set by the Resolution:
  - work completed by the Annual Meetings in 2007, and no later than the IMFC Meeting in the Spring of 2008.
- Purpose of this paper:
  - explore key issues related to a new quota formula as background for an informal Board seminar;
  - review guiding considerations and principles, roles of quotas, selection of variables, and possible functional forms;
  - draw on prior quota formula discussions, including the Quota Formula Review Group (QFRG) work.
- The paper does not make specific proposals; it aims to narrow issues toward convergence on a proposal or narrow range of proposals for future quota adjustments.

### Role of Quotas and the Quota Formula
- Quotas serve several inter-related purposes:
  - Quotas constitute the Fund’s financial base; a member’s quota determines its financial contribution, which must be fully subscribed and paid in a combination of reserve assets and the member’s own currency. Quotas of members with currencies considered usable based on the strength of their external positions effectively determine the Fund’s capacity to provide financing.
  - Quotas influence members’ access to Fund resources: access limits for both GRA and PRGF-ESF borrowing are set in terms of quotas. Under normal circumstances, current access policy allows annual access of 100 percent of quota with cumulative access limited to 300 percent of quota. Access limits may be exceeded in exceptional circumstances.
  - Quotas, together with “basic votes,” determine the distribution of voting power: each member receives 250 basic votes plus one additional vote for each part of its quota equivalent to SDR 100,000. The five members having the largest quotas are each required to appoint an Executive Director.
- Implications:
  - Quotas affect financial structure, financing operations, and governance; thus the quota formula must balance competing considerations across these roles.
  - The possibility that quotas may be “overburdened” is acknowledged; fully delinking quotas from all access decisions would raise wider-ranging issues and require an amendment to the Articles.
  - The Resolution envisions the new formula providing the basis for a second round of ad hoc quota increases and playing a more prominent future role in quota realignments, while the Board retains flexibility to recommend other factors.

### Principles and Properties for a New Formula
- Core principles the new formula should satisfy:
  - be simple and transparent;
  - be consistent with the roles of quotas, reflecting global economic and financial trends and members’ relative positions;
  - result in calculated quota shares that are broadly acceptable to the membership;
  - be feasible to implement statistically using timely, high quality, and widely available data.
- Noted problems with existing formulas:
  - system is neither transparent nor simple, involving five formulas and a complicated decision rule; impact of a change in a quota variable can be counterintuitive.
- Desirable mathematical properties discussed (to be considered further in functional forms):
  - homogeneity;
  - monotonicity;
  - non-convexity.
- Emphasis on “intuitive appeal” of results and that the formula should be modernized over time to reflect global trends and improved data.

### Variables — Selection Criteria and Overview
- Consensus to limit variables to no more than the four utilized in existing formulas, but updated and modernized—an evolutionary approach for continuity.
- Variables should capture:
  - capacity to contribute financial resources to the Fund;
  - potential need to use Fund resources;
  - economic position and role in the world economy.
- Variables must be supported by timely, high-quality, widely available data to minimize estimation.

### GDP (detailed points)
- GDP identified as a very important variable:
  - provides a comprehensive measure of economic size;
  - viewed as the single most relevant indicator of a member’s ability to contribute to the Fund’s finances, though not the only measure;
  - relevant to potential demand for Fund resources and relative positions in the global economy.
- Data availability:
  - widely reported and available on a timely basis for the vast majority of membership.
  - In the most recent quota database update, 119 members reported GDP data usable directly from IFS; staff supplemented with WEO data for most other members.
- Conversion debate:
  - two approaches: convert GDP at market exchange rates (traditional) or use PPP-based conversion.
  - Market exchange rate GDP: viewed as more relevant to ability to contribute to the Fund’s finances and capacity to borrow.
  - PPP-based GDP: may be more relevant for cross-country comparisons of volumes of goods and services produced; distribution across members differs substantially from market-exchange-rate-based GDP.
  - PPP-based GDP data of sufficient quality for quota calculations are only available for a small subset of members; International Comparison Programme (ICP) work is expected to broaden coverage to about 130 countries, but not expected to be completed until late 2007.
  - Introduction of a population variable could have similar effects to PPP-based GDP and may have data advantages, but population does not bear directly on international monetary issues; the QFRG did not propose including population.
- Smoothing GDP:
  - consensus that GDP should be averaged over several years to avoid undue influence of temporary fluctuations.
  - a three-year average has been generally viewed as a reasonable trade-off, though slightly longer periods could be considered.

### Openness (detailed points)
- Conceptual relevance:
  - Openness indicates involvement and stake in the global economy; more open countries may have greater interest in promoting global stability and integration.
  - Openness may bear on ability to contribute to Fund finances and potential demand for Fund resources (more open countries may be more vulnerable to external shocks).
- Role in existing formulas:
  - enters through current receipts and payments (both separately and combined) and through the ratio of current receipts to GDP as a multiplicative factor in three of the five existing formulas.
  - The ratio of current receipts to GDP can give very large effective weight to openness for highly open economies and can lead to anomalous results if GDP growth exceeds export growth.
- Practical approach:
  - considerable support for a single, simplified measure of openness (sum of current receipts and payments) averaged over a five-year period as used in recent staff work.
- Remaining issues:
  - a number of unresolved technical and definitional issues regarding openness remain to be addressed.

*Source: IMF staff paper excerpt — "Possible Quota Formula Variables—Shares in Global Totals" (selected sections).*

### 19.       One concern is that openness enters the quota formulas on a gross rather than a

### _112206 - 19.       One concern is that openness enters the quota formulas on a gross rather than a

### Openness: gross flows versus value added
- Openness currently enters quota formulas on a gross basis rather than a value added basis, which can double count cross-border flows and exaggerate a member’s measured economic size and importance.
- Particular distortions arise for countries with large entrepôt trade activities, international financial centers, or heavy processing-for-re-export, where gross balance of payments flows may be very large relative to actual economic impact.
- Longstanding practice: adjustments are made to the quota database to correct for such activities before determining actual quota increases.
  - These adjustments are described as resource-intensive, judgment-dependent, and heavily data-dependent.
  - They are considered a second-best approach and the issue of data adjustments is proposed to be revisited in the work program on a new quota formula.

### Treatment of trade within economic or currency unions
- Increased integration in economic unions raises the question whether intra-union trade should be counted as foreign trade for quota calculations.
- Currency unions add the issue that intra-union transactions occur in a common domestic currency.
- Trend implications: increased integration may raise cross-border flows over time, affecting the openness variable relative to GDP growth.
- QFRG position:
  - Proposed to exclude openness altogether from a new formula, but did not propose singling out intra-union trade for exclusion.
  - Rationale: fund membership is per country and currency union membership does not preclude balance of payments difficulties requiring Fund assistance.
  - Data issues: excluding intra-union transactions may be difficult because data are typically available only for trade flows and not for services.

### Broadening openness to financial openness and IIP data
- Conceptual appeal to include financial openness because of expansion in cross-border capital flows since the last quota revision.
- Data-related difficulties noted:
  - Gross capital flows can be inflated by “churning” or short-term flows (hedging, portfolio activity) not tied to underlying economic trends.
  - Net capital flows are not a useful indicator of integration with international capital markets.
- Discussed indicator: a stock measure such as the sum of accumulated foreign asset and liability positions reported in the international investment position (IIP).
  - Data availability has improved: 106 economies now reporting full or partial IIP data, with 85 considered comprehensive reporters, compared with 83 in 2003.
  - Coverage still short of needed level; Appendix Table A1 summarizes latest available IIP data (referenced in source).
- Note: Investment income flows suggested as a proxy for missing IIP data but suffer significant statistical shortcomings.
- Legal/Article consideration: Articles recognize the right to impose controls on capital transfers (Article VI, Section 3) and provide that a member may not "use the Fund's general resources to meet a large or sustained outflow of capital.” (Article VI, Section 1).
  - Implication: use of capital-based measures would need to consider constraints on access to meet capital-account driven needs, reflected in Fund policies on exceptional access.

### Variability as a quota variable
- Variability is a measure of vulnerability to balance of payments shocks and potential need for Fund resources; also an indicator of stake in global financial stability.
- Historical inclusion: variability has been included in quota formulas from the beginning; it was one of the two variables proposed by the QFRG (along with GDP).
- Debates:
  - Some argue need is already captured by openness, but experience shows relatively closed economies can face BoP crises with substantial financing needs.
  - Concerns that including variability might reward unstable policies.
- Modernization: consensus that variability should include a capital account aspect to reflect capital flow crises of recent decades.
  - Support for a variable measuring variability of current receipts and net capital flows.
  - Agreed preference: deviation from a three-year average (rather than five years in existing formulas) to capture shorter-term trends while smoothing very temporary fluctuations.
  - Data availability: required data broadly available from IFS and WEO databases.

### Reserves
- Reserves as indicator of financial strength and ability to contribute to Fund finances.
- Divergent views on relevance for quota calculations:
  - Support: reserves central since Fund inception; reserve adequacy relevant to external financial strength and ability to contribute to usable resources.
  - Opposition: with growing importance of international capital markets, reserves may be a less relevant indicator of ability to contribute; particularly misleading for international reserve currencies.
  - Concern: inclusion of reserves could reward excessive foreign exchange intervention and reserve accumulation.
- Policy responses suggested:
  - Give reserves at most a relatively small weight.
  - Consider capping their influence in some way.

### Correlation of variables in quota formulas
- High correlation among main quota variables reflects that they are measures of economic size.
  - Correlation typically around 0.9 for GDP, openness, and variability.
  - Correlation significantly lower—less than 0.5—for reserves (partly due to reserve currencies).
- Consequences:
  - High correlation constrains range of results obtainable by varying weights on the first three variables but still allows differentiation.
  - Creates multicollinearity problems that complicate disentangling each variable’s relative influence on calculated quotas.
  - Alternative specifications considered historically to reduce correlation were not found to have desirable properties.

### Functional form choices and desiderata
- Desirable properties for quota formula:
  - Simplicity and transparency: parsimonious variables; transparent relationship between variables and calculated quotas.
  - Homogeneity: uniform multiplicative changes across all members and variables should leave quota shares unchanged.
  - Monotonicity: calculated quota should increase if one of its variables increases, ceteris paribus.
  - Non-convexity: quotas should increase equally or less than proportionally to underlying variables; marginal impact should remain constant or decline.
- Three functional-form families considered (properties summarized):
  - Linear in shares:
    - Quota shares are a linear combination of shares of individual country variables.
    - Coefficients can be interpreted as weights (if positive and sum to one).
    - Elasticities are member-specific and positive but vary across membership.
  - Multiplicative in shares:
    - Multiplicative combination of shares; with positive exponents summing to one, interpretable as geometric average before rescaling.
    - Elasticities are constant across membership and equal to exponents.
    - Tends to lower calculated quota shares for members with significant dispersion across variable shares.
  - Compressed linear in shares:
    - Introduces a compression factor λ (between 0 and 1) to adjust for high correlation favoring large economies.
    - Lower λ implies greater compression and more impact on large economies.
    - Member-specific elasticities; compression rescaling ensures calculated quota shares sum to 100 percent.
- Notes on interpretation:
  - Compression can also be applied to multiplicative formulas with broadly similar aggregate results.
  - Choice of λ determines amount of compression; compression does not change rank order of countries by calculated quota shares relative to uncompressed distribution.

### Weights: guidance and historical perspective
- Board of Governors’ Resolution guidance: consider placing “significantly higher weight on members’ gross domestic product, together with ensuring that other variables, in particular the openness of members’ economies, also play an important role.”
- Executive Board report noted “some have stressed the importance of variability.”
- 2003 Executive Directors’ views: GDP considered most important variable, with lesser weights for openness, variability, and reserves.
- Estimated contributions in the current quota formulas (reported): GDP, 29 percent; reserves, 7 percent; variability, 14 percent; openness, 50 percent.
- Correlation among variables must be considered when selecting weights; most Directors acknowledged correlation is unavoidable and that attempts to reduce it entail significant drawbacks including reduced transparency.
- Final selection of variables, weights, and compression factors is a matter of judgment and political consensus among membership.

### Illustrative calculations: variables and data used
- Simulations are presented as purely illustrative; not staff views on the appropriate new quota formula.
- Variables used (denominated in SDRs):
  - GDP: annual data, converted at market exchange rates, averaged for 2002–2004.
  - Openness: annual average of the sum of current payments and current receipts for 2000–2004.
  - Variability: standard deviation from the centered three-year trend over 1992–2004 (a thirteen-year period) of current receipts and net capital flows.
  - Reserves: twelve-month average of gold, foreign exchange reserves, SDR holdings, and reserve positions in the IMF for 2004.
- Purpose: illustrate implications of different functional forms and weights for distribution of quota shares; only broad regional results described in text; detailed member implications reported in a supplement.

*Source: IMF document content provided in the input.*

### 35.      The first group of simulations involves a simple linear formulation using six

### _112206 - 35.      The first group of simulations involves a simple linear formulation using six

### Linear-formulation simulations: design and broad results
- Simulation design:
  - Six different sets of weights (Table 3).
  - The weight on GDP varies from 40 to 60 percent.
  - For each GDP weight, two different combinations of openness and variability weights are used.
  - Reserves are given a weight of 5 percent in all six scenarios.
- Broad results:
  - The calculated quota shares of advanced countries as a group are higher in all six formulations than under the existing formulas. This reflects the higher weight in all six formulations on GDP, for which the advanced countries’ share is particularly large.
  - The calculated quota shares of developing countries are lower in all six formulations than under the current formulas. This reflects the relatively low share of developing countries in global GDP.
  - The calculated quota share of advanced countries as a group rises and that of developing countries as a group falls as the weight on GDP increases.
  - A higher weight on openness and lower weight on variability tends to increase the calculated quota share of advanced countries and lower the calculated quota share of developing countries; there are significant differences in impact across regions within these groups.

### Non-linear and compressed specifications: design and main findings
- Simulation design:
  - Single GDP weight: 50 percent.
  - High and low weights for openness and variability tested.
  - Compressed formulas use compression factors of 0.9 and 0.95 (arbitrarily chosen).
  - Also considered multiplicative specification.
- Main results:
  - The results for the multiplicative specification are very similar to those for the linear form.
  - Relative to the simple linear formulation, the compressed linear form lowers the calculated quota share of advanced countries as a group and raises the calculated share of developing countries taken together.
  - The compressed linear form lowers the calculated quota share of the seven members with the highest calculated quota shares under the equivalent linear forms and raises the calculated quota share for all other countries.
  - The smaller the compression factor, the greater the reduction of the calculated quota share of advanced countries as a group and the larger the gain in calculated share of developing countries as a group.
  - The number of countries whose quota share is reduced does not vary with moderate changes in the compression factor.
- Additional note on reserves:
  - A higher weight on reserves tends to increase modestly the share of developing countries, particularly in Asia, and lower that of advanced countries in calculated quotas.
- Compression threshold (Figure 1 note):
  - Countries with a calculated quota share below 3.01 (3.22) percent before compression gain with compression at 0.90 (0.95), while those above this threshold lose.
  - For the scenarios presented, most members (177) gain with compression and seven countries lose quota share.

### Existing formulas, historical contributions, and functional-form considerations
- Existing five formulas and calculation rule (Box A1 summary provided in source):
  - The current approach uses the Bretton Woods formula and four other linear and non-linear formulas; for each of the four non-BW formulas, quota calculations are multiplied by an adjustment factor so totals equal the BW total.
  - The calculated quota of a member is the higher of the BW calculation and the average of the lowest two of the remaining four calculations (after adjustment).
- Estimated contributions of variables using data through 2004:
  - GDP: 29 percent
  - Openness: 50 percent
  - Variability: 14 percent
  - Reserves: 7 percent
- Historical evolution (highlights):
  - Original BW formula (1944) contained five variables: national income, official reserves, imports, export variability, and the ratio of exports to national income.
  - Early 1960s changes increased weights on external trade and external variability and eliminated reserves in the new formulas; calculations were performed on two data sets.
  - Eighth General Review (1982/83) reforms: one data set eliminated; coefficient on variability reduced by 20 percent in all formulas except BW; reserves variable reintroduced.

### Issues for discussion (questions presented for Directors)
- Should the quota formula be guided by the several roles of quotas described in Section II and balance competing considerations inherent in those roles?
- Should the quota formula include at most four variables—GDP, openness, variability, and reserves—or are there other variables that should be included? Related definitional questions:
  - Whether GDP should be measured at market or PPP exchange rates.
  - Whether openness should include a measure of financial openness and the treatment of intra-currency union trade.
  - Whether reserves should be capped in some way.
- Which functional forms are most appropriate, given guiding principles and desirable properties? Comment on relative merits of alternative functional forms presented.
- What structure of weights for the chosen variables is appropriate, and what other considerations should guide judgments on the structure of weights?

### Key quantitative design parameters and results (preserved exactly as in source)
- Linear-form scenarios (Table 3): GDP weights tested: 40%, 50%, 60%; Reserves weight: 5% in all six scenarios; openness and variability weights varied across scenarios (examples in Table 3 headings: Openness 30% / Variability 25%; Openness 25% / Variability 30%; Openness 30% / Variability 15%; Openness 15% / Variability 30%; Openness 20% / Variability 15%; Openness 15% / Variability 20%).
- Single-weight nonlinear/compressed example formulas (Table 4 and Table 5 notes):
  - Q = 0.50*Average GDP + 0.30*Openness + 0.15*Variability + 0.05*Reserves.
  - Q = (Average GDP)^0.50 * (Openness)^0.30 * (Variability)^0.15 * (Reserves)^0.05.
  - Compressed forms: Q = (0.50*Average GDP + 0.30*Openness + 0.15*Variability + 0.05*Reserves)^0.9 and ^0.95 (requires rescaling of calculated shares).
  - Alternative weighting in Table 5: Q = 0.50*Average GDP + 0.15*Openness + 0.30*Variability + 0.05*Reserves; multiplicative analogue and compression exponents 0.9 and 0.95 noted.
- Sample aggregate outcome comparisons (from Tables 3–5, preserved in text):
  - Advanced economies: Actual Quotas 61.6; Existing Formulas (Pre Ad Hoc Increases) 60.5; Example linear outcomes in panels: 67.1; 69.3; 68.8; 70.8; 69.5; 71.5; 71.1 (various columns/tables).
  - Developing countries: Actual Quotas 30.9; Existing Formulas 32.1; example linear/compressed outcomes include 27.6; 25.8; 26.1; 24.5; 25.6; 24.0; 24.4 (various columns/tables).
  - Major advanced economies: Actual 46.0; Existing 45.2; sample outcomes 47.3; 53.2; 52.9; 55.3; 54.4; 56.9; 56.6.
  - Of which: US: Actual 17.4; Existing 17.1; sample outcomes 16.8; 22.1; 22.3; 23.1; 23.8; 24.6; 24.8.
  - Memorandum items: EU 25: Actual 32.2; Existing 31.6; sample outcomes 37.6; 33.1; 32.5; 33.2; 31.2; 31.9; 31.2. LICs: Actual 7.5; Existing 7.4; sample outcomes 3.6; 3.7; 3.8; 3.5; 3.8; 3.5; 3.6.
- Figure 1 compression threshold: Countries with a calculated quota share below 3.01 (3.22) percent before compression gain with compression at 0.90 (0.95); most members (177) gain with compression and seven countries lose quota share.

*Source: Finance Department (excerpted from the provided IMF content).*

### 6.      During the Ninth Review, some interest was expressed in effecting certain changes in

### 6.      During the Ninth Review, some interest was expressed in effecting certain changes in

### Background and procedural history
- During the Ninth Review, there was some interest in effecting changes in the formulas though “there was not a broad consensus for modification.”
- The existing formulas were endorsed in the Tenth Review as working as intended “to give a reasonably comprehensive measure of the relative economic size of member countries.”
- During the Eleventh General Review, Executive Directors expressed concern about shortcomings in the existing five formulas, and the Interim Committee in 1997 requested that “the Executive Board should also review the quota formulas promptly after the completion of the Eleventh Review of Quotas.”30

### Shortcomings of the current formulas
- Fundamental deficiencies identified: a lack of transparency and simplicity.
- Sources of these shortcomings:
  - (i) the formulas are a mix of linear and non-linear specifications;
  - (ii) the calculated quota for a member is based on a complicated decision rule (Box A1);
  - (iii) coefficients are fixed in each formula and the weights not directly observable;
  - (iv) the underlying data are expressed in levels that change over time, leading to instability in the weights of each variable;
  - (v) three of the five formulas contain a multiplicative element, the ratio of current receipts to GDP, that can lead to perverse results—e.g., ceteris paribus an increase in GDP can in some cases lead to a decline in calculated quota, as GDP is in the denominator of the multiplicative ratio.
- There is the possibility of formula switching in response to changes in underlying data and/or over time.
- Assessments of the relationship between changes in quota variables and calculated quotas are difficult and non-transparent.

### Quota Formula Review Group (QFRG): mandate and composition
- In 1999 the Managing Director appointed a group of external experts to provide the Executive Board with an independent report on the adequacy of the quota formulas, including proposals for changes. This group was known as the Quota Formula Review Group (QFRG).31
- The QFRG was asked to:
  - “review the quota formulas and their working, and to assess their adequacy to help determine members’ calculated quotas in the IMF in a manner that reasonably reflects members’ relative position in the world economy as well as their relative need for and contributions to the Fund’s financial resources, taking into account changes in the....world economy and the international financial system and in light of the increasing globalization of markets.”
  - “propose, as appropriate, changes in the variables and their specification to be used in the formulas” and to “examine other issues directly related to the quota formulas.”
- Membership of the QFRG included Richard Cooper (Harvard University), Chairman; Joseph Abbey (Center for Economic Analysis, Ghana); Montek Ahluwalia (Planning Commission, India); Muhammad Al-Jasser (Saudi Arabian Monetary Agency); Horst Siebert (Kiel Institute of World Economics, Germany); Gorgy Suranyi (National Bank of Hungary); Makoto Utsumi (Keio University, Japan); and Roberto Zahler (Central Bank of Chile).31

### QFRG main findings and analysis
- Main findings:
  - (1) significant changes in the world economy since 1944 have made IMF member countries more exposed to external shocks;
  - (2) the quota formulas themselves have had only an indirect influence on actual quotas; and
  - (3) gaps between actual quota shares and calculated quota shares have persisted over time.
- The report presented extensive background work on analysis of existing and possible new quota formulas.32

### QFRG criteria for assessing new formulas
- Three main criteria used by the QFRG:
  - (i) any new formula should have a sound economic basis and reflect the relevant changes in the world economy;
  - (ii) its form and content should be consistent with the multiple functions of quotas; and
  - (iii) it should be simple and transparent.

### QFRG proposal
- Recommended replacing the existing five formulas with a single linear formula containing two variables:
  - one representing a country’s ability to contribute to the IMF’s resources; and
  - the other representing its external vulnerability.
- Suggested weighting:
  - ability to contribute should have the larger weight, about twice that of external vulnerability.
- Measurement specifications:
  - GDP would be converted into a common currency at market exchange rates, and averaged over three years to avoid the effects of undue exchange rate and GDP variability.
  - Vulnerability should be measured by the variability of current receipts (in line with its measurement in the existing five formulas)—but expanded to cover also the variability of net long-term capital flows to reflect the large and growing impact of long-term capital flows.33
- A minority view in the report: GDP should be converted into a common currency using PPP exchange rates rather than market exchange rates.33

### IMF Board discussions and subsequent consensus elements
- The Board discussed the QFRG report and staff commentary in 2000 and had substantive discussions on quota formulas in 2001, 2002, and 2003 (see Appendix II).
- These discussions resulted in broad agreement on:
  - the principles of transparency and simplicity for a new quota formula limited to at most three to four variables;
  - endorsement, broadly, of four variables along the lines of those included in the current formulas, but updated and modernized—GDP, openness, variability, and reserves.

### Key statistics from Table A1: Distribution of International Investment Position of Reporting Members (in percent)
- Existing Quotas 1/2/ and International Investment Position 3/Assets plus Liabilities; Distribution by group:
  - Advanced economies: 60.56
  - Major advanced economies: 45.24
    - Of which: US: 17.11
  - Other advanced economies: 15.31
  - Developing countries: 32.12
  - Africa: 5.4
  - Asia 5/: 11.5
  - Middle East, Malta & Turkey: 7.6
  - Western Hemisphere: 7.6
  - Transition economies: 7.4
  - Total: 100.0
- International Investment Position 3/ (Average 2000-04) — Assets plus Liabilities, Assets, Liabilities, Number of Reporting Members 4/:
  - International Investment Position: 67.19 (Assets plus Liabilities), 93.5 (Assets), 90.4 (Liabilities), 91.9 (Members) — for Advanced economies row
  - Major advanced economies row: 67.36, 55.5, 63.0, 64.2
  - US row (Of which): 16.8, 20.4, 24.6, 22.6
  - Other advanced economies row: 19.8, 28.0, 27.4, 27.7
  - Developing countries row: 7.6, 5.1, 7.7, 6.5, 88 (Members)
  - Africa row: 2.4, 0.4, 0.6, 0.5, 35 (Members)
  - Asia row: 15.3, 2.7, 3.3, 3.0, 23 (Members)
  - Middle East, Malta & Turkey row: 4.7, 0.5, 0.7, 0.6, 12 (Members)
  - Western Hemisphere row: 5.2, 1.6, 3.2, 2.4, 18 (Members)
  - Transition economies row: 5.3, 1.4, 1.9, 1.6, 9 (Members)
  - Total row: 100.0, 100.0, 100.0, 99 (Members)
- Memorandum Item:
  - EU 25: 31.63, 7.65, 7.95, 5.5, 56.60
  - LICs 6/: 7.4, 3.6, 0.4, 0.8, 0.6, 58
- Notes associated with Table A1:
  - 1/ For the three countries that have not yet consented to, and paid for, their quota increases, 11th Review proposed quotas are used.
  - 2/ Includes ad hoc increases for China, Korea, Mexico, and Turkey.
  - 3/ Average 2000-04.
  - 4/ Members with fewer than 3 years of data during 2000-04. There are 7 members with 1 or 2 years of data.
  - 5/ Including Korea and Singapore.
  - 6/ PRGF-eligible countries.
- Source for Table A1: Finance and Statistics Departments.

*INTERNATIONAL MONETARY FUND — Quotas—Further Thoughts on a New Quota Formula—Statistical Appendix. Prepared by the Finance Department. Approved by Michael G. Kuhn. November 29, 2006.*

### 3.  Distribution of Quotas: Results of Alternative Specifications by Member .................14

### 3.  Distribution of Quotas: Results of Alternative Specifications by Member

### Table 1. Linear Formulas by Member (selected entries)
- United States:
  - Actual Quotas: 17.382
  - Existing: 17.078
  - Pre Ad Hoc Increases: 16.795
  - Post Ad Hoc Five Formulas: 22.108; 22.336; 23.105; 23.792; 24.560; 24.789
- Japan:
  - Actual Quotas: 6.229
  - Existing: 6.120
  - Pre Ad Hoc Increases: 6.120
  - Post Ad Hoc Five Formulas: 6.120; 7.525; 9.360; 9.415; 9.870; 10.035; 10.490; 10.545
- Germany:
  - Actual Quotas: 6.087
  - Existing: 5.980
  - Pre Ad Hoc Increases: 5.980
  - Post Ad Hoc Five Formulas: 6.087; 6.953; 6.977; 6.879; 6.966; 6.672; 6.759; 6.660
- France:
  - Actual Quotas: 5.025
  - Existing: 4.937
  - Pre Ad Hoc Increases: 4.937
  - Post Ad Hoc Five Formulas: 5.025; 4.334; 4.294; 4.197; 4.463; 4.170; 4.436; 4.338
- United Kingdom:
  - Actual Quotas: 5.025
  - Existing: 4.937
  - Pre Ad Hoc Increases: 4.937
  - Post Ad Hoc Five Formulas: 5.025; 5.176; 4.478; 4.268; 4.771; 4.142; 4.646; 4.436
- China (Includes China, P.R., and Hong Kong, SAR):
  - Actual Quotas: 2.980
  - Existing: 3.719
  - Pre Ad Hoc Increases: 3.719
  - Post Ad Hoc Five Formulas: 2.980; 5.197; 4.866; 4.764; 5.018; 4.713; 4.966; 4.865
- Italy:
  - Actual Quotas: 3.301
  - Existing: 3.243
  - Pre Ad Hoc Increases: 3.243
  - Post Ad Hoc Five Formulas: 3.301; 3.442; 3.323; 3.213; 3.529; 3.200; 3.516; 3.406
- Saudi Arabia:
  - Actual Quotas: 3.269
  - Existing: 3.211
  - Pre Ad Hoc Increases: 3.211
  - Post Ad Hoc Five Formulas: 3.269; 1.063; 0.752; 0.753; 0.724; 0.727; 0.698; 0.698
- Canada:
  - Actual Quotas: 2.980
  - Existing: 2.928
  - Pre Ad Hoc Increases: 2.928
  - Post Ad Hoc Five Formulas: 2.980; 3.098; 2.611; 2.549; 2.623; 2.436; 2.510; 2.447
- Russia:
  - Actual Quotas: 2.782
  - Existing: 2.733
  - Pre Ad Hoc Increases: 2.733
  - Post Ad Hoc Five Formulas: 2.782; 1.519; 1.616; 1.661; 1.511; 1.647; 1.497; 1.542

Notes (from source):
- Calculated as the sum of variable weights multiplied with a country's share in the global total of the respective variables.
- Based on 1992–2004 data. Reflects adjustments to current receipts and payments for re-exports, international banking interest, and non-monetary gold.
- Specification of GDP and variability differs from the existing five formulas as average GDP and variability of current receipts plus net capital flows are used.
- For the three countries that have not yet consented to, and paid for, their quota increases, Eleventh Review proposed quotas are used.
- Includes ad hoc increases for China, Korea, Mexico, and Turkey.

### Table 2. Distribution of Quotas: Results of Alternative Specifications by Member (selected entries)
- United States:
  - Actual Quotas: 17.382
  - Existing: 17.078
  - Linear Pre Ad Hoc Increases: 16.795
  - Linear Post Ad Hoc Five Formulas: 23.105; 22.637; 18.846; 20.937
- Japan:
  - Actual Quotas: 6.229
  - Existing: 6.120
  - Linear Pre Ad Hoc Increases: 7.525
  - Linear Post Ad Hoc Five Formulas: 9.870; 9.813; 8.765; 9.332
- Germany:
  - Actual Quotas: 6.087
  - Existing: 5.980
  - Linear Pre Ad Hoc Increases: 6.953
  - Linear Post Ad Hoc Five Formulas: 6.966; 7.270; 6.406; 6.702
- France:
  - Actual Quotas: 5.025
  - Existing: 4.937
  - Linear Pre Ad Hoc Increases: 4.334
  - Linear Post Ad Hoc Five Formulas: 4.463; 4.648; 4.291; 4.391
- United Kingdom:
  - Actual Quotas: 5.025
  - Existing: 4.937
  - Linear Pre Ad Hoc Increases: 5.176
  - Linear Post Ad Hoc Five Formulas: 4.771; 4.785; 4.557; 4.678
- China (Includes China, P.R., and Hong Kong, SAR):
  - Actual Quotas: 2.980
  - Existing: 3.719
  - Linear Pre Ad Hoc Increases: 5.197
  - Linear Post Ad Hoc Five Formulas: 5.018; 5.102; 4.768; 4.907
- Mexico:
  - Actual Quotas: 1.210
  - Existing: 1.449
  - Linear Pre Ad Hoc Increases: 1.928
  - Linear Post Ad Hoc Five Formulas: 1.937; 2.100; 2.025; 1.987
- Korea:
  - Actual Quotas: 0.764
  - Existing: 1.346
  - Linear Pre Ad Hoc Increases: 2.508
  - Linear Post Ad Hoc Five Formulas: 2.179; 2.262; 2.251; 2.222
- Brazil:
  - Actual Quotas: 1.421
  - Existing: 1.396
  - Linear Pre Ad Hoc Increases: 0.998
  - Linear Post Ad Hoc Five Formulas: 1.348; 1.419; 1.461; 1.408
- Saudi Arabia:
  - Actual Quotas: 3.269
  - Existing: 3.211
  - Linear Pre Ad Hoc Increases: 1.063
  - Linear Post Ad Hoc Five Formulas: 0.724; 0.774; 0.835; 0.780

Notes (from source):
- Table 2 columns include compressed formulas and multiplicative formulas (Q = 0.50*Average GDP + 0.30*Openness + 0.15*Variability + 0.05*Reserves and multiplicative variant Q = (Average GDP)^0.50 * (Openness)^0.30 * (Variability)^0.15 * (Reserves)^0.05), and power-compressed variants with exponents 0.9 and 0.95. These require rescaling of calculated shares.
- Based on 1992–2004 data with the same adjustments and specification notes as Table 1.
- Includes ad hoc increases for China, Korea, Mexico, and Turkey.

### Table 3. Distribution of Quotas: Results of Alternative Specifications by Member (selected entries)
- United States:
  - Actual Quotas: 17.382
  - Existing: 17.078
  - Linear Pre Ad Hoc Increases: 16.795
  - Linear Post Ad Hoc Five Formulas: 23.792; 23.627; 19.293; 21.498
- Japan:
  - Actual Quotas: 6.229
  - Existing: 6.120
  - Linear Pre Ad Hoc Increases: 7.525
  - Linear Post Ad Hoc Five Formulas: 10.035; 10.127; 8.872; 9.468
- Germany:
  - Actual Quotas: 6.087
  - Existing: 5.980
  - Linear Pre Ad Hoc Increases: 6.953
  - Linear Post Ad Hoc Five Formulas: 6.672; 7.027; 6.144; 6.424
- France:
  - Actual Quotas: 5.025
  - Existing: 4.937
  - Linear Pre Ad Hoc Increases: 4.334
  - Linear Post Ad Hoc Five Formulas: 4.170; 4.342; 4.024; 4.111
- United Kingdom:
  - Actual Quotas: 5.025
  - Existing: 4.937
  - Linear Pre Ad Hoc Increases: 5.176
  - Linear Post Ad Hoc Five Formulas: 4.142; 4.075; 4.001; 4.085
- China (Includes China, P.R., and Hong Kong, SAR):
  - Actual Quotas: 2.980
  - Existing: 3.719
  - Linear Pre Ad Hoc Increases: 5.197
  - Linear Post Ad Hoc Five Formulas: 4.713; 4.746; 4.494; 4.618
- Korea:
  - Actual Quotas: 0.764
  - Existing: 1.346
  - Linear Pre Ad Hoc Increases: 2.508
  - Linear Post Ad Hoc Five Formulas: 2.205; 2.296; 2.268; 2.244
- Brazil:
  - Actual Quotas: 1.421
  - Existing: 1.396
  - Linear Pre Ad Hoc Increases: 0.998
  - Linear Post Ad Hoc Five Formulas: 1.494; 1.591; 1.598; 1.551
- India:
  - Actual Quotas: 1.946
  - Existing: 1.912
  - Linear Pre Ad Hoc Increases: 1.200
  - Linear Post Ad Hoc Five Formulas: 1.362; 1.368; 1.470; 1.419
- Russia:
  - Actual Quotas: 2.782
  - Existing: 2.733
  - Linear Pre Ad Hoc Increases: 1.519
  - Linear Post Ad Hoc Five Formulas: 1.647; 1.714; 1.745; 1.701

Notes (from source):
- Table 3 presents alternative linear and multiplicative formula outcomes and compressed variants for a specification where Q = 0.50*Average GDP + 0.15*Openness + 0.30*Variability + 0.05*Reserves and corresponding multiplicative form Q = (Average GDP)^0.50 * (Openness)^0.15 * (Variability)^0.30 * (Reserves)^0.05, with exponents 0.9 and 0.95 for compressed variants.
- Based on 1992–2004 data; adjustments and specification differences as in Tables 1 and 2.
- Includes ad hoc increases for China, Korea, Mexico, and Turkey.

*Source: Finance Department. Tables and notes as provided in the Statistical Appendix to "Quotas—Further Thoughts on a New Quota Formula (2006)".*

### 1.  Origin of PPP Conversion Factors Used in the Latest World Economic Outlook ........5

### 1.  Origin of PPP Conversion Factors Used in the Latest World Economic Outlook ........5

### I. Introduction
- Purpose: Provide available individual member country data for the alternative variables reported in Table 1 of Quotas—Further Thoughts on a New Quota Formula (2006).

### II. Purchasing Power Parity (PPP) Data
- Role of PPP:
  - PPP-based GDP statistics measure the relative volume of production of goods and services for final uses among countries.
  - PPP-adjusted GDP data are used to assess countries’ relative importance in the world production of goods and services for final uses.
  - PPPs are also produced for the final consumption sub-aggregate of GDP; PPP-adjusted final consumption data measure the relative volume of final consumption and are used to assess relative living standards.
- Data sources and coverage:
  - The PPP-based GDP data currently available at the Fund are taken from the World Economic Outlook (WEO) database.
  - The WEO uses PPP data for 175 countries from the International Comparison Program (ICP) consisting of data from the OECD/Eurostat, Commonwealth of Independent States (CIS), and the World Bank, and Fund-staff estimates.
  - OECD/Eurostat and CIS: Provide a combined coverage of 52 countries. GDP estimates are based on a common methodology. The data rely on price surveys conducted during the reference year 2002 for the OECD countries and 2000 for the CIS countries.
  - World Bank: Publishes PPP-based GDP estimates for 104 countries in the World Development Indicators (WDI). World Bank data are based mostly on estimates, with only 63 countries providing price survey-based information for the reference year 1996.
  - Staff estimates: PPP data for the remaining 19 countries are based on a cross-section regression that relates PPP-based GDP to GDP at market exchange rates, trade openness, and regional dummies. The regression results derived from countries for which PPP data are available are then applied to countries for which price surveys are not available.
- Data limitations and comparability issues:
  - Significant differences across countries in the reference periods of the price survey sources for the ICP, with some surveys being more than a decade old.
  - Inconsistent survey methodology across countries; the goods and services included in the price surveys of individual countries are not necessarily fully comparable across countries.
  - Differences in product quality across countries may be mistaken for price differences rather than volume differences.
  - A large number of primarily small developing countries are not included in the price surveys, raising questions about the validity of the data for these countries.
  - To overcome lack of coverage, data for remaining countries are estimated with regression techniques, and missing years are filled in by extrapolation.
- Upcoming improvements:
  - The new estimates for the 2005 ICP round are expected to be available in late 2007. These estimates will be based on more countries’ data and a significantly improved and more consistent survey and estimation methodology compared with previous rounds.

### III. International Investment Position (IIP)
- Definition: The IIP provides a comprehensive measure of a country’s external balance sheet position, reflecting its holding of foreign financial assets and foreign financial liabilities at a given point in time.
- Coverage and reporting quality:
  - Full or partial IIP data currently available for 106 countries, of which 85 are considered comprehensive reporters.
  - Members with 3 years or more of data during 2000-04 are treated as comprehensive reporters.
  - Valuation issues: The valuation of assets and liabilities may not follow a harmonized methodology across countries; differences due to the use of book value or market prices can be significant.
  - Source of data: Balance of Payments database.

### IV. Population
- (Section header present; no detailed population data included in the supplied content.)

*Source: _112206 - 1.  Origin of PPP Conversion Factors Used in the Latest World Economic Outlook ........5*

### 8. Population data are sourced from IFS based on data provided by the Population

### _112206 - 8. Population data are sourced from IFS based on data provided by the Population

### Population data source and coverage
- Population data are sourced from IFS based on data provided by the Population Division of the Department of Economic and Social Affairs of the United Nations.
- The data represent mid-year estimates and are revised every two years.
- Data are available for almost all members.

### Origin of PPP conversion factors (Table 1) — methodology notes
- Sources referenced: OECD (data of OECD members and CIS countries provided by the OECD), WDI (World Development Indicators database), IMF (Fund staff estimates for countries not present in OECD or WDI data sets).
- Survey-year annotations appear next to country entries where available (e.g., Albania OECD 1996; Australia OECD 2002; China, P.R. WDI 1986).
- Blanks in the table indicate that PPP conversion factors are estimated rather than based on actual price surveys.

### Country-level PPP-GDP, International Investment Position (IIP), and population (Table 2) — selected key statistics (in millions of SDRs unless otherwise indicated)
- United States
  - Quotas: 37,149.3
  - PPP-GDP: 7,970,732.5
  - IIP Assets (2002–04 average): 5,641,528.1
  - IIP Liabilities (2002–04 average): 7,264,396.1
  - IIP Assets plus Liabilities (2002–04 average): 12,905,924.2
  - Population 2004 (in millions): 295.4
- Japan
  - Quotas: 13,312.8
  - PPP-GDP: 2,614,553.7
  - IIP Assets: 2,384,546.6
  - IIP Liabilities: 1,328,260.0
  - IIP Assets plus Liabilities: 3,712,806.6
  - Population 2004: 127.9
- Germany
  - Quotas: 13,008.2
  - PPP-GDP: 1,727,138.3
  - IIP Assets: 2,426,847.4
  - IIP Liabilities: 2,315,985.6
  - IIP Assets plus Liabilities: 4,742,833.0
  - Population 2004: 82.6
- China 4/
  - Quotas: 8,090.1
  - PPP-GDP: 5,570,726.7
  - IIP Assets: n.a.
  - IIP Liabilities: n.a.
  - IIP Assets plus Liabilities: n.a.
  - Population 2004: 1,315.0
- India
  - Quotas: 4,158.2
  - PPP-GDP: 2,202,342.0
  - IIP Assets: 75,620.3
  - IIP Liabilities: 118,786.4
  - IIP Assets plus Liabilities: 194,406.7
  - Population 2004: 1,087.1
- Russia
  - Quotas: 5,945.4
  - PPP-GDP: 970,705.9
  - IIP Assets: 214,897.8
  - IIP Liabilities: 195,083.1
  - IIP Assets plus Liabilities: 409,980.9
  - Population 2004: 143.9
- Top small-population/high-IIP example: Luxembourg
  - Quotas: 279.1
  - PPP-GDP: 20,697.1
  - IIP Assets: 1,800,565.7
  - IIP Liabilities: 1,781,237.4
  - IIP Assets plus Liabilities: 3,581,803.1
  - Population 2004: 0.5
- Notation: n.a. denotes data not available in the table for that entry.

### Shares in global totals (Table 3) — selected country shares (in percent)
- United States (shares of global totals)
  - Quotas: 17.078
  - PPP-GDP: 20.706
  - IIP Assets (2002–04 average): 20.448
  - IIP Liabilities (2002–04 average): 24.578
  - IIP Assets plus Liabilities (2002–04 average): 22.584
  - Population share 2004: 4.661
- China 4/
  - Quotas: 3.719
  - PPP-GDP: 14.472
  - IIP entries: n.a.
  - Population share 2004: 20.748
- Japan
  - Quotas: 6.120
  - PPP-GDP: 6.792
  - IIP Assets: 8.643
  - IIP Liabilities: 4.494
  - IIP Assets plus Liabilities: 6.497
  - Population share 2004: 2.018
- India
  - Quotas: 1.912
  - PPP-GDP: 5.721
  - IIP Assets: 0.274
  - IIP Liabilities: 0.402
  - IIP Assets plus Liabilities: 0.340
  - Population share 2004: 17.153
- European and other examples
  - Germany quotas share: 5.980; PPP-GDP share: 4.487; population share: 1.304
  - United Kingdom quotas share: 4.937; PPP-GDP share: 3.160; IIP Assets share: 14.392; population share: 0.939
  - Luxembourg quotas share: 0.128; PPP-GDP share: 0.054; IIP Assets plus Liabilities share: 6.268; population share: 0.007

### Table and data notes
- Table 1: country-level PPP conversion factor sources and survey years are listed; blanks indicate estimated conversion factors.
- Table 2: monetary figures are in millions of SDRs; population figures are in millions.
- Table 2 IIP columns labeled "2002–04 Assets", "Liabilities", "Assets plus Liabilities" represent averages for 2000–04 as noted.
- Table 3 reports shares in global totals (in percent) corresponding to the same metrics reported in Table 2.
- Footnotes in the source:
  - 1/ The PPP GDP data shown in Table 2 were downloaded from the WEO database on September 13, 2006.
  - 2/ OECD refers to data of OECD members and CIS countries provided by the OECD. WDI refers to data from the World Development Indicators database. IMF refers to data by Fund staff estimated for countries not present in the OECD or WDI data sets.
  - 3/ Blanks indicate that PPP conversion factors are estimated rather than based on actual price surveys.
  - 4/ Includes China, P.R., and Hong Kong, SAR.

*Source: Finance Department; World Economic Outlook data as presented in the supplied content.*

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