Quota Formula Review - Data Update and Further Considerations
Author: International Monetary Fund
Publication Date:
28 Jun 2012
eISBN:
9781498340335
ISBN:
9781498340335
Language:
English
Keywords:
PP; quota share; Transition economy; advanced economy; GDP ratio; PPP GDP; IIP share; variability share; quota formula review; standard deviation; openness share
Download PDF (681.3 KB)

In March 2012, the Executive Board held its first formal discussion on the comprehensive review of the quota formula. This review, to be completed by January 2013, is an important part of the quota and governance reforms agreed in 2010. Directors stressed the importance of agreeing on a quota formula that better reflects members’ relative positions in the global economy for future discussions on the 15th General Review of Quotas. This view was reiterated in April by the IMFC, which looked forward to an agreement by January 2013: "…on a simple and transparent quota formula that better reflects members’ relative positions in the world economy." The IMFC also reaffirmed its commitment to complete the 15th quota review by January 2014. It noted that any realignment is expected to result in increases in the quota shares of dynamic economies in line with their relative positions in the world economy, and hence likely in the share of EMDCs as a whole; and that steps shall be taken to protect the voice and representation of the poorest members. The Board held an informal follow-up meeting on June 13, 2012.

Abstract

In March 2012, the Executive Board held its first formal discussion on the comprehensive review of the quota formula. This review, to be completed by January 2013, is an important part of the quota and governance reforms agreed in 2010. Directors stressed the importance of agreeing on a quota formula that better reflects members’ relative positions in the global economy for future discussions on the 15th General Review of Quotas. This view was reiterated in April by the IMFC, which looked forward to an agreement by January 2013: "…on a simple and transparent quota formula that better reflects members’ relative positions in the world economy." The IMFC also reaffirmed its commitment to complete the 15th quota review by January 2014. It noted that any realignment is expected to result in increases in the quota shares of dynamic economies in line with their relative positions in the world economy, and hence likely in the share of EMDCs as a whole; and that steps shall be taken to protect the voice and representation of the poorest members. The Board held an informal follow-up meeting on June 13, 2012.

I. Introduction1

1. In March 2012, the Executive Board held its first formal discussion on the comprehensive review of the quota formula.2 This review, to be completed by January 2013, is an important part of the quota and governance reforms agreed in 2010. Directors stressed the importance of agreeing on a quota formula that better reflects members’ relative positions in the global economy for future discussions on the 15th General Review of Quotas. This view was reiterated in April by the IMFC, which looked forward to an agreement by January 2013: “…on a simple and transparent quota formula that better reflects members’ relative positions in the world economy.” The IMFC also reaffirmed its commitment to complete the 15th quota review by January 2014. It noted that any realignment is expected to result in increases in the quota shares of dynamic economies in line with their relative positions in the world economy, and hence likely in the share of EMDCs as a whole; and that steps shall be taken to protect the voice and representation of the poorest members. The Board held an informal follow-up meeting on June 13, 2012.

2. The importance of the quota formula review was also highlighted at the recent summit of G-20 Leaders in Los Cabos. Leaders reiterated their commitment to “completing the comprehensive review of the quota formula, to address deficiencies and weaknesses in the current quota formula, by January 2013.” G-20 Leaders agreed that “the formula should be simple and transparent, consistent with the multiple roles of quotas, result in calculated shares that are broadly acceptable to the membership, and be feasible to implement based on timely, high quality and widely available data.” They also reaffirmed “…that the distribution of quotas based on the formula should better reflect the relative weights of IMF members in the world economy, which have changed substantially in view of strong GDP growth in dynamic emerging markets and developing countries” and “the importance of protecting the voice and representation of the poorest members.”3

3. A wide range of views were expressed at the March discussion. Directors generally concurred that GDP is the most comprehensive measure of economic size and should continue to have the largest weight in the quota formula. Beyond that, however, views differed significantly both on measurement of GDP (the relative importance of market versus PPP GDP in the GDP blend variable) and on the role of other variables in the formula.

4. This paper provides background for the next Board discussion. It covers three broad areas. First, it presents results of updating the quota data base through end-2010 (Section II). Second, the paper reports on further staff work on three issues—financial openness, variability, and financial contributions—responding to requests made at the March meeting (Section III). Third, the paper presents several simulations aimed at illustrating the potential impact on calculated quota shares of increasing the weight of financial openness, of changing the weights of GDP measured at market exchange rates and at PPP in the GDP blend variable, and of capturing financial contributions, as well as possible options for simplifying the formula (Section IV). No proposals are made at this stage. Section V concludes, while the Annexes and Statistical Appendix (circulated separately) provide additional technical material and individual country details for the simulations.

II. Updated Quota Calculations

5. Staff has updated the quota database through 2010. This advances by one year the data presented last August,4 using the same sources and methodology as in past updates (see Box 1 and the Statistical Appendix). The results of these updates are shown in Tables 1 and A1.5 One further data update is expected in mid-2013 before the deadline for completing the 15th General Review of Quotas.

Table 1.

Distribution of Quotas and Calculated Quotas (In percent)

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Source: Finance Department.

Based on the following formula: CQS = (0.50*GDP + 0.30*Openness +0.15*Variability + 0.05*Reserves)^K. GDP blended using 60 percent market and 40 percent PPP exchange rates. K is a compression factor of 0.95.

The “post second round” reflects the ad hoc quota increases for 54 members under the 2008 reform, which became effective in March 2011. Includes South Sudan which became a member on April 18, 2012. For the two countries that have not yet consented to and paid for their quota increases, 11th Review proposed quotas are used.

Includes South Sudan which became a member on April 18, 2012; reflects the proposed doubling of its quota after the 14th Review becomes effective.

Based on IFS data through 2010.

Based on IFS data through 2009.

Based on IFS data through 2008.

Based on IFS data through 2005. Reflects the impact of adjustments to current receipts and payments for re-exports, international banking interest, and non-monetary gold.

Including Czech Republic, Estonia, Korea, Malta, Singapore, Slovak Republic, and Slovenia.

Including China, P.R., Hong Kong SAR, and Macao SAR.

PRGT-eligible countries.

6. The data update continued the broad trends observed in previous updates. The calculated quota share (CQS) of emerging market and developing countries (EMDCs) as a whole increased by 1.4 pp to 43.9 percent—compared to an increase of 0.7 pp in the previous update (Table 1). Compared with the data used for the 2008 Reform (which went through 2005), the aggregate CQS of EMDCs has now risen by 7.7 pp. Within this group, the largest gain was recorded by countries in Asia, with smaller gains for Western Hemisphere and Africa, while the Middle East and the Transition Economies recorded small losses (Figure 1). Among the advanced economies, two thirds of the decline was recorded by the major advanced economies—all except Canada recorded a decline. The share of other advanced economies as a group fell by 0.5 pp.

Figure 1.
Figure 1.

Evolution of CQS 2005-20101/

(In percent)

Citation: Policy Papers 2012, 050; 10.5089/9781498340335.007.A001

1/ For data ending in 2005, 2007, 2008, 2009, and 2010.Source: Finance Department

Data Sources and Methodology

The data sources and methodology remain in line with past practice (see the Statistical Appendix for further details):

The primary data source is the Fund’s International Financial Statistics (IFS). Missing data were supplemented in the first instance by the World Economic Outlook (WEO) database. Remaining missing data were computed based on staff reports and, in very few instances, country desk data. As is customary, a cutoff date of January 31, 2012 for incorporating new data in the quota database was employed for IFS; consistent with this cutoff, the Fall 2011 publication was used for WEO data.

PPP GDP data were taken from the WEO database and were calculated by dividing a country’s nominal GDP in its own currency by the PPP price level index.

7. The changes in CQS reflect a combination of factors. First, real economic growth rates have continued to diverge, with EMDCs as a group recording strong growth while most advanced economies have stagnated (Figure 2). This is reflected in a 2.0 pp. increase in the aggregate share of EMDCs in the GDP blend variable (Table 2). EMDCs also generally gained share of the openness variable, reflecting a stronger rebound in external flows for EMDCs than for advanced economies. For variability, the impact of the data update differs more across countries, with some significant gainers and losers, underscoring the measurement issues highlighted in the previous paper (see Section III). Overall, the share of EMDCs in variability increased—in part reversing the significant increase in the variability share of advanced economies in the previous data update. For reserves, the changes in shares reflect strong reserve accumulation by a number of individual countries.

Figure 2.
Figure 2.

Average GDP Growth Rates

Citation: Policy Papers 2012, 050; 10.5089/9781498340335.007.A001

Source: Finance Department
Table 2.

Distribution of Quotas and Updated Quota Variables

(In percent)

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Source: Finance Department.

Includes South Sudan which became a member on April 18, 2012; reflects the proposed doubling of its quota after the 14th Review becomes effective.

GDP blended using 60 percent market and 40 percent PPP exchange rates.

Based on IFS data through 2010.

Based on IFS data through 2009.

Variability of current receipts plus net capital flows.

Including Czech Republic, Estonia, Korea, Malta, Singapore, Slovak Republic, and Slovenia.

Including China, P.R., Hong Kong SAR, and Macao SAR.

PRGT-eligible countries.

8. There were significant changes for some individual countries. By far the largest gain in CQS was recorded by China, with sizable increases also recorded by several other EMDCs, including India and Brazil (Table 3). China recorded gains in share of all four quota variables. All but two of the top-10 gainers were EMDCs. The exceptions were Switzerland, which benefitted from an increase in its share of reserves, and Norway, which gained from variability. All but one of the 10 largest declines in CQS were recorded by advanced economies. The largest losses in absolute shares were recorded by the United Kingdom and the United States. These declines were mainly driven by losses on GDP and openness, while the picture for variability and reserves was more mixed.

Table 3.

Top 10 Positive and Negative Changes in Calculated Quota Shares

(In percentage points)

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Source: Finance Department.

Current calculations are based on data through 2010 using the existing formula.

Previous calculations are based on data through 2009 using the existing formula.

The difference between the current dataset through 2010 and the previous dataset through 2009, multiplied by the variable weight in the quota formula. The change in CQS also reflects the effect of compression.

GDP blended using 60 percent market and 40 percent PPP exchange rates.

Including China, P.R., Hong Kong SAR, and Macao SAR.

9. Out-of-lineness based on the current formula has increased compared to the last update. At the aggregate level, advanced economies are over-represented and EMDCs are under-represented by 1.6 pp (Table 4). This contrasts with the situation at the previous update, where the calculated quota shares for aggregate groups were broadly in line with 14th Review quota shares. Total over-and under-representation of countries measured in terms of quota share has increased marginally since the last update, though fewer countries are underrepresented—66 members compared with 69 in the previous update.

Table 4.

Under- and Overrepresented Countries by Major Country Groups 1/

(In percentage points)

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Source: Finance Department.

Under- and over-represented countries for the two datasets, respectively.

Includes South Sudan which became a member on April 18, 2012; reflects the proposed doubling of its quota after the 14th Review becomes effective.

Difference between calculated quota shares and 14th General Review quota shares.

Based on IFS data through 2010.

Based on IFS data through 2009.

The “post second round” reflects the ad hoc quota increases for 54 members under the 2008 reform, which became effective in March 2011. Includes South Sudan which became a member on April 18, 2012. For the two countries that have not yet consented to and paid for their quota increases, 11th Review proposed quotas are used.

Difference between calculated quota shares based on IFS data through 2009 and post second round quota shares.

PRGT-eligible countries.

III. Quota Formula Variables

10. At the March discussion, requests were made for additional technical work on three topics. These were: how to better capture financial openness; the scope for improving on the current measure of variability to better reflect members’ underlying vulnerability and potential demand for Fund resources; and the scope for including a measure of members’ financial contributions to the Fund in the quota formula. These issues are discussed in turn below.

Financial Openness

11. Views on openness have diverged in the discussions to date. Many Directors consider that openness is a measure of members’ integration into the world economy and should remain an important variable in the quota formula; and many of these Directors have favored further exploring options for better capturing financial openness. In contrast, other Directors have preferred either to reduce the weight on openness or drop it from the formula altogether, arguing that the existing openness variable overstates members’ integration into the global economy, is highly correlated with the GDP variable, and is affected by data availability constraints and measurement difficulties. These Directors have been unconvinced of the benefits of continuing work on financial openness.

12. In previous work, the International Investment Position (IIP) has been identified as the most promising option if a financial openness variable were to be introduced in the quota formula.6 The IIP provides a quantitative measure of a member’s foreign financial asset and liability position, and thus in principle captures the extent of investment in a country by non-residents and of investment abroad by residents of the same country. There have been significant improvements in measurement of IIP in recent years, which have led to the inclusion of a broader range of assets and liabilities (recent changes in the composition of IIP were discussed in Quota Formula Review—Initial Considerations. Nonetheless, a number of issues remain with the use of IIP in the quota formula. Beyond the conceptual differences of view over the relevance of this measure noted above, country coverage of available IIP has been an issue, and there is also the question of how to address international financial centers, which have relative large shares of the global data on IIP.

13. Country coverage of IIP continues to improve, but remains partial. As of the cut-off date for the latest data update, IIP data were available for 109 members (compared with 102 countries at the time of the cut-off for the 2009 database). Given this, staff sees two main options for including a measure of financial openness in the formula in the near term:7

  • One option illustrated previously (see Quota Formula Review—Initial Considerations is to use data on cross border investment income flows as a proxy for financial openness. Investment income is already included in the current openness variable and therefore is not constrained by data availability.8 However, as discussed in previous papers, investment income flows are an imperfect substitute for underlying IIP stocks, given that rates of return on similar investments can vary substantially across countries for a variety of reasons (e.g., exchange controls, domestic legislation), under-recording of investment income receipts,9 and also the recording of credit and debit components on a net rather than on a gross basis.10

  • The second option is to use the investment income series to gap-fill the IIP series.11 This approach requires some additional steps, but continues to rely on published data and is relatively transparent and easy to replicate.12 Also, those countries that report IIP data account for about 98.5 percent of the global IIP total derived in this manner, suggesting that the distortions resulting from gap-filling may not be very large at the aggregate level. Over time, as more countries report their IIP, the number of countries for which gap-filling is needed would be expected to decline so this approach may have an advantage over the first option in terms of continuity if a decision was taken to include a measure of financial openness in the formula. Table 5 compares the two approaches. The overall distribution is broadly similar in both cases, though there are significant differences for a few individual countries.

Table 5.

Measures of Financial Openness

(As percent of total)

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Source: Finance Department.n.a. --not available

Includes 109 countries.

IIP has been gap-filled using investment income (which is available for 185 countries).

Including Czech Republic, Estonia, Korea, Malta, Singapore, Slovak Republic, and Slovenia.

Including China, P.R., Hong Kong SAR, and Macao SAR.

PRGT-eligible countries.

14. Both approaches leave unresolved the issue of how to treat international financial centers. To the extent that the shares in financial openness of countries with international financial centers largely reflect the activities of non-residents, where the member is acting as a conduit, it is unclear that they should be included in the data used for quota calculations. In the past, staff attempted to correct for such “entrepot-like” activities by making adjustments to the underlying data used in the openness measure but this practice was discontinued in 2008 because it was seen as arbitrary and lacking a strong conceptual basis.13

15. Staff has explored two means of dampening the impact of large financial centers. Both take as a starting point the observation that international financial centers tend to have very high ratios of IIP to GDP, reflecting their role as a conduit for financial flows among non-residents. For instance, the ratio of IIP to GDP for Luxembourg, Ireland, and Barbados is 243, 33, and 22, respectively, compared with a ratio of less than 3 for the majority of countries (149 members). Thus, the distribution of the ratio of IIP to GDP is much more skewed than for other quota variables, including the current measure of openness (Figure 3). The two options considered to dampen the impact of high ratios for a few countries are somewhat arbitrary, but they would avoid a need to revert to the previous practice of making adjustments to the underlying data.

Figure 3.
Figure 3.

Openness

Citation: Policy Papers 2012, 050; 10.5089/9781498340335.007.A001

Source: Finance Department

16. One possibility is to apply a method akin to compression to the ratio of IIP to GDP. Such an approach would maintain the original ranking of the series and would not require additional data since the relevant data are already included in the quota database.14 The main difficulty is in choosing an appropriate compression factor. Staff explored two different factors. Using the same factor currently used for the quota formula as a whole (0.95) had only a modest impact on the dispersion of the series.15 A second compression factor of 0.70 was also applied, which reduces the mean of the modified IIP to GDP ratio from the original 3.4 to 2.2, roughly equal to the average of the original series excluding the ten members with the largest IIP to GDP ratio.16 With the 0.70 compression factor, there is a more pronounced effect for the top ranking members, though they still have significantly higher ratios than for the membership as a whole (Table 6).

Table 6.

Ratio of IIP to GDP 1/

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Source: Finance Department.Group and Total figures refer to weighted averages.

IIP has been gap-filled using investment income.

Including Czech Republic, Estonia, Korea, Malta, Singapore, Slovak Republic, and Slovenia.

Including China, P.R., Hong Kong SAR, and Macao SAR.

PRGT-eligible countries.

17. A second possibility is to cap the IIP to GDP ratio at some predetermined level. This approach would affect the countries with the highest ratios without modifying the ratios of the rest of the membership. The rationale would be that countries with large financial centers should not benefit beyond some point, linked to the statistical distribution of ratios of IIP to GDP for the membership as a whole, from their unusually high ratios. However, a judgment would be required on the appropriate level of the cap. For illustrative purposes, staff has explored caps at the 95th and 90th percentiles: the first affects 10 members, while the second affects 19 members. Depending on where the cap is set, this approach generally has a larger impact on those members that are most affected by the cap than the compression approach, and some countries with very high ratios actually have a lower share than under the current openness variable, which already captures financial openness to a limited extent (Table 7).

Table 7.

Measures of Financial Openness—International Investment Position (As percent of total) 1/

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Source: Finance Department.Shading denotes capped values.

The IIP shares are calculated as a percent of global IIP. As described in the main text, the capping or the compression are done on the original IIP/GDP ratios. The modified IIP shares are then expressed as percent of their corresponding global totals.

Includes South Sudan which became a member on April 18, 2012; reflects the proposed doubling of its quota after the 14th Review becomes effective.

IIP has been gap-filled using investment income.

Including Czech Republic, Estonia, Korea, Malta, Singapore, Slovak Republic, and Slovenia.

Including China, P.R., Hong Kong SAR, and Macao SAR.

PRGT-eligible countries.

18. Both these approaches require somewhat arbitrary assumptions and neither is totally satisfactory. In terms of their impact, the compression approach still tends to leave members with international financial centers with relatively high shares of the financial openness measures, albeit significantly less than their unadjusted shares. In contrast, the cap approach brings these members’ shares of financial openness closer to those applying to other members with relatively high but not extreme ratios, and could potentially reduce their overall share in trade and financial openness combined. Staff could pursue these options further in light of Directors’ views.

Variability

19. Variability is intended to reflect members’ potential need for Fund resources. In Quota Formula Review—Initial Considerations, staff examined how well the current measure of variability captures external vulnerabilities and the likelihood of an IMF supported program. Staff analysis suggested that there is virtually no correlation between the existing variability measure, adjusted for economic size (calculated as the difference between a country’s share in variability and its share in GDP), and potential use of Fund resources. Similar results were obtained for some alternative variability indicators considered in the past (such as five-year trend variability, downside variability, extreme variability, variability of current receipts plus variability of net capital flows, and volatility of GDP growth). Staff also noted that variability adds significant instability to the calculated quota shares for a wide range of members (see Figure 4).

Figure 4.
Figure 4.

Changes in Variability Shares (In percent)

Citation: Policy Papers 2012, 050; 10.5089/9781498340335.007.A001

Source: Finance Department

20. In light of this work, many Directors saw a case for dropping variability. A few were of the view that its weight should be significantly reduced in favor of openness, while others continued to see an important role for variability in the formula, and asked staff to further explore measures that might better capture members’ underlying vulnerability.

21. In response, staff has extended its previous work in two respects. The first addresses the issue of instability in the existing indicator by assessing different measures of dispersion, preserving current receipts and net capital flows as the relevant variables reflecting members’ external vulnerabilities. The goal was to assess whether the current measure can be improved to better capture the structural, and hence presumably less unstable, aspects of vulnerabilities arising from external flows. Second, staff examined whether it is possible to identify a variable that may have a stronger link to potential use of Fund resources by analyzing a measure based on a set of macroeconomic indicators, given that potential need can emanate from different sources of vulnerability.17

22. To address the instability of the current measure, staff examined a range of different measures of dispersion. The current measure of variability is a root mean squared deviation from a three-year moving average, calculated over a recent 13-year period. To reduce the impact of extreme observations on variability shares, one alternative is to use the average absolute deviation from a three-year moving average (13Y AAD) instead of the root squared deviation. Another approach is to use the five-year standard deviation (5Y SD), calculated relative to the sample mean rather than a trend, to reduce the influence of longer term trends.18 An instability index (10Y II) calculated over a recent ten-year period is also considered. This index is based on deviations from a trend estimated by ordinary least squares, which differs from the current practice of using moving averages for trend estimation (see Annex II for more detail).

23. None of the alternative measures consistently outperform the current measure. Figure 5 (panel (i) A) shows the cross-sectional standard deviation of year-on-year changes in variability shares based on the last two quota data updates: the shifts in shares based on the current variability measure in the 2009 data update were very large, and all of the alternative measures showed a smaller variation, though only the 5-year standard deviation measure showed a variation that was close to that for GDP or openness. (For comparison, panel (i) B shows the volatility of shares for the other quota variables; GDP and openness shares are relatively stable, while reserves shares are more volatile). In contrast, for the latest data update (changes from 2009 to 2010), the 13-year average absolute deviation and the instability index yielded the smallest variation in shares and the 5-year standard deviation showed the largest variation in shares.19 Looking at a longer time span, the 13-year absolute deviation produces the smallest variation in shares on average (Figure 5, panel (ii)), but there are still periods (e.g., 2004–07) where the existing variability measure yields more stable results than the alternatives.20 Overall, the results are highly dependent on the period chosen and do not provide a strong basis for choosing an alternative variability measure based on stability considerations alone.

Figure 5.
Figure 5.

Cross-Sectional Standard Deviation of Changes in Variables Shares 1/

Citation: Policy Papers 2012, 050; 10.5089/9781498340335.007.A001

1/ Standard deviation of the difference si,t-si,t-1, where si,t denotes the share of country i in year t, calculated over i for t=2009, 2010.2/ Based on quota data ending 2008, 2009, and 2010.Source: Finance Department

24. Staff also examined whether the modified variability indicators improve on the current measure in terms of indicating members’ potential need for Fund resources. Based on the data since 1990, the correlation between the modified variability measures (adjusted for economic size) and a binary variable indicating the approval of a Fund program is close to zero and statistically insignificant (Figure 6). Thus, none of these measures displays improved predictive power.

Figure 6.
Figure 6.

Correlations between Variability Indicators and Potential Need

Citation: Policy Papers 2012, 050; 10.5089/9781498340335.007.A001

Source: Finance Department

25. As an alternative approach, staff has explored whether it would be possible to develop a new variable based on a set of macroeconomic indicators that would better capture members’ vulnerabilities. In Appendix II of Quota Formula Review—Initial Considerations, the probability of approval of a Fund arrangement was modeled as a function of selected macroeconomic variables. Staff has extended this analysis by examining more closely how countries with IMF programs differ in terms of economic fundamentals from countries without such programs. Annex II provides an account of these differences using a set of variables that have been frequently identified as determinants of use of Fund resources. These variables include the current account to GDP ratio, reserve cover ratio, per capita GDP, fiscal deficit and external debt and debt service ratios. In nearly all cases, the analysis suggests that the data for the two groups of countries come from different distributions, e.g., countries with arrangements have higher current account deficits, higher fiscal deficits and debt ratios than countries without programs. These findings were used to construct a composite variability measure by combining variables that exhibit different patterns for program and non-program cases.

26. The main potential advantage of a composite indicator is that it can capture different kinds of vulnerabilities. Therefore, a measure of variability which combines several relevant variables is likely to have higher explanatory power for the potential use of Fund resources than a measure based on a single variable. This is broadly confirmed by the data—the correlation of a composite indicator derived as a combination of the current account to GDP ratio, reserve cover ratio, per capita GDP and real GDP growth with a variable reflecting the likelihood of a Fund program is 0.19 and is statistically significant (see Annex II). It is higher than the correlation with any of the individual components but still does not represent a very strong association with potential need. Adding more components could further increase the correlation but would also add to data requirements and complexity. In addition, these indicators may not capture well the characteristics of different types of economies, notably reserve currency issuers with low levels of reserves.

27. Incorporating such a composite vulnerability indicator into the quota formula poses considerable challenges. Unlike the other quota formula variables, the composite index lacks the economic size dimension. In addition, it can take both positive and negative values, which makes it difficult to incorporate directly into the formula. While it is possible to transform the measure to avoid negative values and to introduce the notion of size, such adjustments are largely arbitrary and, depending on the method, can result in very different outcomes, both for individual members and at a group level. In addition, such (non-linear) transformations could reduce considerably the correlation between the resulting variability measure and the potential use of Fund resources compared to the unadjusted indicator. For example, transforming the above composite vulnerability index into a size-related variable that could be used in the formula would reduce the correlation coefficient from 0.19 to 0.09, although it would still be statistically significant.21 The improvement in explanatory power over the existing measure is reflected to some extent in Figure 7 which plots the transformed composite variability shares against GDP shares for members with and without GRA arrangements since September 2008. For 28 of 32 countries with programs since 2008 (81 percent), the composite variability share is greater than their GDP share, compared with 70 out of 143 non-program countries (49 percent).22 This suggests that the measure provides some additional information.23 The composite measure also results in more stable shares throughout most of the sample, although in certain periods some of the alternative statistical definitions based on current receipts and net capital flows perform better.

Figure 7.
Figure 7.

Composite Variability and GDP Shares: Comparison of Countries with and without Recent GRA Programs 1/

Citation: Policy Papers 2012, 050; 10.5089/9781498340335.007.A001

Source: Finance Department1/ The chart compares the shares in blend GDP and composite variability (shown on a logarithmic scale) of two groups of members – members who have had a GRA program since September 2008 and those who have not.

28. Overall, based on the work in this paper, it does not appear that such an approach provides sufficiently robust results to support its inclusion as an alternative indicator of potential need in the quota formula. A composite variability indicator along the lines discussed above appears difficult to reconcile with the principle of simplicity and transparency, as a measure that performs reasonably well in predicting potential need would most likely be complex and require a substantial amount of data and assumptions. In many cases, the outcomes will depend critically on the choices of underlying variables and data transformations and there is no theory to guide these choices. They may also not be applicable to all countries, particularly reserve currency issuers, which can distort the overall results. On balance, staff continues to see a case for dropping variability from the formula, as the above analysis suggests that it is difficult to design a measure which fits all members, performs well under a wide range of circumstances and is simple and transparent.

Financial Contributions

29. In March, many Directors indicated that they could support further work on the scope for capturing members’ financial contributions to the Fund in the quota formula. In this regard, a few noted that the current resource mobilization efforts again highlighted the importance of members’ financial contributions. Other Directors viewed the inclusion of voluntary financial contributions in the quota formula as inconsistent with the Fund’s role as a quota-based institution, with a few considering that such contributions should be taken into account, if at all, outside of the quota formula, as has been done on several occasions in the past (Boxes 2 and 3 provide additional background, including on the approach followed for the most recent World Bank capital increase).

30. As discussed in Quota Formula Review—Initial Considerations, members’ financial contributions to the Fund come in a variety of forms, reflecting the cooperative nature of Fund membership. These include (i) voluntary contributions including bilateral and multilateral support for Fund liquidity in the GRA, loan and subsidy contributions to the PRGT, voluntary SDR trading arrangements, and technical assistance and training (TA); and (ii) contributions mandated by Fund policies such as the Financial Transactions Plan (FTP) which captures the key role of the strongest members who are included for transfers in the FTP, the charges and fees associated with borrowing from the Fund, and also burden-shared contributions.24 Not all of these contributions lend themselves to ready comparisons across members (for example, members’ voluntary SDR trading arrangements are not published and may be amended at any time). Table 8 summarizes several key channels of financial contributions that were identified in the March paper— NAB and bilateral lending, including the bilateral pledges made under the current fundraising exercise, PRGT loans, PRGT subsidies, and contributions to training and technical assistance activities. Members’ FTP participation, measured both in terms of duration and size, for the past 20 years