The Financial Implications of Reserve Supply Arrangements
Author: John Williamson

It is widely agreed that the primary objective of any reform of the international arrangements on the supply of reserves should be to establish control over the global volume of liquidity, with a view to ensuring that such control will be conducive to stable growth of the world economy. However, the long-standing academic discussion of “seigniorage,” the practical concern of national officials to safeguard the interest earnings on their reserves, and the campaign by the developing countries to establish a link, all attest to the importance of the financial implications arising from the selection of a set of reserve supply arrangements. This is the subject explored in the present paper.


It is widely agreed that the primary objective of any reform of the international arrangements on the supply of reserves should be to establish control over the global volume of liquidity, with a view to ensuring that such control will be conducive to stable growth of the world economy. However, the long-standing academic discussion of “seigniorage,” the practical concern of national officials to safeguard the interest earnings on their reserves, and the campaign by the developing countries to establish a link, all attest to the importance of the financial implications arising from the selection of a set of reserve supply arrangements. This is the subject explored in the present paper.

It is widely agreed that the primary objective of any reform of the international arrangements on the supply of reserves should be to establish control over the global volume of liquidity, with a view to ensuring that such control will be conducive to stable growth of the world economy. However, the long-standing academic discussion of “seigniorage,” the practical concern of national officials to safeguard the interest earnings on their reserves, and the campaign by the developing countries to establish a link, all attest to the importance of the financial implications arising from the selection of a set of reserve supply arrangements. This is the subject explored in the present paper.

The financial effects of reserve supply arrangements are demonstrated by a simple model which relates the income accruing to a country from the processes of reserve holding and reserve creation to the policies adopted by the country and to the arrangements adopted by the international community. The various arrangements analyzed are those discussed during the negotiations on world monetary reform: 1 (1) “on demand” convertibility, (2) holding limits for primary assets, (3) the yield on the SDR, (4) restriction on the freedom of reserve composition, (5) the distribution of SDR allocations, (6) substitution, and (7) mandatory asset settlement.

The model used to investigate each of these arrangements is constructed in Section I, and the optimal reserve composition policies of an individual country are derived from it in Section II. The financial effects of these reserve supply arrangements on countries in different situations, as well as the extension of the analysis to a world with additional reserve assets, are treated in Section III. The final section sums up the conclusions of the analysis.

I. The Model

The formal model contains only two reserve assets: a single reserve currency, which is denoted by D; and a fiduciary reserve asset, called the SDR and denoted S. There are two types of countries: the reserve center, which issues reserve currency liabilities; and n relatively small nonreserve centers. The reserve center is denoted by the subscript u, and nonreserve centers by the subscript i (i=1 … n). The reserve currency is assumed to have a yield d, determined exogenously by the reserve center, and the SDR to have a yield s, determined as a policy variable by the international community. Both yields are measured in terms of some common standard (goods, SDRs, or the reserve currency), and they include both the own interest rate on the asset and the change in the value of the asset in terms of the standard.

A basic assumption of the model is that the volume of reserves (R) is unaffected by differences in the arrangements considered in this paper.2 This is an unexceptionable assumption so long as the yield on the SDR is at a level high enough to preserve a positive demand for SDRs and so long as the quantity of SDR creation is determined by some concept of the need for reserves that actually satisfies the collective long-run desire to hold reserves. The total supply of reserves is thus assumed to equate demand and supply, with the corollary that the composition of reserves between reserve currency and SDRs would be determined by demand. If, for example, the nonreserve centers collectively desired to hold more D and less S, this would be accomplished either by countries’ converting S into D at the reserve center or, if convertibility arrangements precluded such a conversion, by the rest of the world’s seeking a payments surplus with the reserve center; in either case, the result would be an increase in world liquidity, which would then be nullified by SDR cancellation. It is clear that such a mechanism can only operate in the very long run, and the analysis is indeed intended to apply only to the long-run situation. Thus, for example, Ri should be interpreted as the target reserve level of the ith country in the sense of the literature on optimal reserves 3 (or, under a reserve indicator mechanism, as the ith country’s reserve norm); and d and s should be interpreted as expected long-run average yields. Until discussing substitution in Section III below, it will be assumed that any action that curtailed the reserve currency role would compel the reserve center to run a surplus so as to replenish its reserves, and the situations compared will be those in which this adjustment had already been completed.

The income resulting from reserve supply arrangements (that is, “reserve-related income”) is denoted by Y. It is defined from an arbitrary base, which may be thought of as the income of a nongoldproducing country under a pure gold standard in which the price of gold is fixed in terms of whatever standard (numeraire) is being used to measure d and s. Y is thus defined as the excess of the country’s income over what it would obtain if its reserves yielded no income and if it received no reserve credit. The fact that the base position is essentially arbitrary is immaterial, since all that is analyzed in this paper is the difference in income between one position and another.

The first element in Y is the income earned on reserves. This is equal to the sum of the yield on each form of reserves multiplied by the size of the reserves held in each form (dDi + sSi).

Reserve supply arrangements have a second set of financial consequences, which concern the benefits that a country receives from the process of reserve creation (often referred to as “seigniorage” benefits). When a country receives the credit that is the counterpart to the creation of fiduciary reserves—for example, by being allocated SDRs, or by having its currency held as a reserve currency by other countries—it is thereby enabled to build up more reserves, to sustain greater net imports of goods, to expand its foreign investments, or to curtail its foreign borrowing, as compared to what would otherwise have been possible. In general, it would be expected that the country would modify its policies so as to induce some change in all (or at least several) of these directions. In building a model to show the financial consequences of reserve creation, however, it is convenient to assume that countries always adjust their policies by either expanding foreign investment or curtailing foreign borrowing; this permits the benefit of receiving reserve credit to be measured as the difference between the opportunity costs of foreign lending or borrowing, which are assumed equal to each other and denoted by c, and the servicing cost for the reserve credit, which is dimensionally the same.4 (Other forms of adjustment would, at the margin, yield equivalent benefits to variations in foreign borrowing or lending, if the country were initially pursuing an optimum set of policies; therefore, any errors from the assumption would be of only the second order.)

Nonreserve centers receive reserve credit only in the form of SDR allocations. If the ith country receives a constant share (βi) in SDR allocations, then its cumulative past allocation is βiS. It is then obliged to pay a yield of s on this sum, but it saves an interest cost of ci on the net reduction in foreign borrowing permitted by the receipt of SDR allocations. Hence, the seigniorage benefit is (cis)βiS. In total:

Yi = dDi + sSi + (ci − s)βiS.(1)

The reserve center benefits from the reserve credit resulting from foreign official holdings of its currency D(≡ΣiDi), as well as from SDR allocations. However, it is erroneous to represent the effect of the reserve currency role as simply that of enabling the reserve center to save the sum cu (at the cost, of course, of a payment of d) on D. There are two reasons for this:5 (1) In the presence of on demand convertibility, the reserve center needs to hold a certain volume of primary reserve assets in order to maintain confidence in its ability to sustain its convertibility obligations. (The minimum SDR holdings needed for this purpose are denoted by Sumin.) (2) In addition to the seigniorage benefit from past deficits, the reserve currency role provides a benefit in the form of the ability to finance future deficits without the prior need to stockpile reserve assets. (This benefit can be represented by including in the reserve center’s “reserves” a term (DmaxD), where Dmax is defined as the maximum quantity of the reserve currency that the rest of the world would be prepared to hold when the reserve center is in deficit.) Thus, the reserve center’s effective free reserves are:

Ru = Su − Sumin + (Dmax − D).

It is natural to suppose that Dmax will be related to the average stock of dollars that the rest of the world wishes to hold (D). Assuming a proportionate relationship, one postulates Dmax = α1D, with α1>1. It also seems natural to presume that the minimum level of SDR holdings needed to sustain confidence will be related to the maximum indebtedness of the reserve center; again assuming proportionality, one postulates Sumin = α2Dmax, with α2<1. Therefore

Ru = Su + [α1(1 − α2) − 1]D.(2)

There is no inherent reason for expecting that [α1(l – α2) – 1] must have a particular sign.

The reserve-related income of the reserve center consists of the interest receipts on its SDR holdings, minus the interest payments on its cumulative past SDR allocations and on its dollar liabilities, plus the net increase in interest receipts on the increased volume of net foreign lending which is permitted by its reserve credit. It receives reserve credit of βuS from SDR allocations and of (Dmax − Sumin)) from its position as a reserve center. Therefore

Yu = sSu − sβuS − dD + cu(βuS + Dmax − Sumin)(3a)
 = sSu + (cu − s)βuS + [cuα1(1 − α2) − d]D.(3b)

World reserves are given by summing the reserves of the nonreserve centers (i) and those of the reserve center, which are given by equation (2):

R = ΣiRi + Ru = D + ΣiSi + Su + [α1(1 − α2) − 1]D(4) = S + α1(1 − α2)D.

Equation (4) demonstrates that the reserve currency system increases liquidity only so far as the maximum reserve currency liabilities that the rest of the world is willing to hold exceed the SDRs that the reserve center needs to hold as “backing.” In general, there is little reason to suppose that the customary procedure of summing S and D gives a good approximation to the relevant concept of global liquidity.

It is also interesting to derive the expression for world reserve-related income (Y) by summing the n countries in equation (1) and the reserve center from equation (3b). Thus

Y = ΣiYi + Yu = ΣiuciβiS + cuα1(1 − α2)D.(5)

In the special case where the opportunity cost of foreign investment is the same for all countries (ci = cu = c), this simplifies to

Y = cS + cα1(1 − α2)D = cR.(6)

Equation (6) represents the economic fact that the replacement of commodity reserves by credit reserves provides a social saving equal to the product of the marginal product of capital and the volume of reserves. It is also interesting to note that it is only in the special case represented by equation (6) that Y is independent of the distribution of reserve credit. In the general case of equation (5), Y will be greater the larger is the proportion of reserve credit that is directed to countries where the opportunity cost of foreign investment (ci) is high. If differences in ci reflect real differences in the social rate of return on capital which private markets fail to equalize because of private risks that are not social risks from a global standpoint, the result again represents a real economic fact.

II. Reserve Composition Policy of an Individual Country

Since the average level of reserves of the ith country (Ri) is assumed to be given, the optimizing problem facing the ith country is that of distributing its reserves between Di and Si so as to maximize the expected utility of its reserve-related income (Yi) as given by equation (1). In principle the decision made by the ith country will affect the total demand for SDRs vis-à-vis reserve currency; given that the total level of reserves (R = ΣiRi) is to be held constant by manipulating the volume of SDRs created, this will influence the size of S. But, since only a small fraction of any increase in SDRs would accrue to the ith country itself, a country can rationally ignore the feedback from its choice of reserve composition to the size of S. In selecting its reserve composition, therefore, a country will treat the final term of equation (1) as a constant and will simply seek to maximize the expected utility of (dDi+sSi). In a world of perfect certainty, this aim would be achieved by choosing a portfolio consisting entirely of either the reserve currency or SDRs, depending upon which had the higher yield. In a world of uncertainty, it will in general be optimal to hold a diversified portfolio containing both the reserve currency and SDRs, with the proportion held in each asset being a positive function of its own yield and a negative function of the yield of the other asset:

Di = Di(d,s),Di/d>0,Di/s<0;(7a)
Si = Si(d,s),Si/d<0,Si/s>0.(7b)

In principle these demand functions should depend on the variances and co-variance of d and s as well as their expected values, but it will be assumed in this analysis that these do not vary with the arrangements considered and can therefore be neglected.

Similarly, the reserve center is interested in maximizing the expected utility of Yu as given by equation (3b). However, unless the reserve center chooses to manipulate d with a view to influencing foreign holdings of reserve currency rather than with a view to domestic stabilization, all the terms in equation (3b) are parameters. Unlike other countries, the reserve center has no decision to make regarding reserve composition, because there is no choice between different reserve assets available to it. The reserve center’s demand function for SDRs is therefore given directly by equation (2) above, as

Su = Ru + [1 − α1(1 − α2)]D.

Equations (2) and (7) can be summed to give aggregate demand functions:

D = D(d,s),D1>0,D2<0;(8)
S = Z(d,s) + Ru + [1 − α1(1 − α2)]D,(9)

where Z(d,s)ΣiuSi and Z1 < 0, Z2 > 0. By substituting for Z from equation (9), it is easy to confirm that total reserves R ≡ D + Z + Ru = S + α1(l – α2)D as given by equation (4) above.

III. Financial Effects of Different Reserve Arrangements


In the reserve currency system as it traditionally operated, the reserve currency was convertible into a primary reserve asset at the option of the holder. One of the proposals discussed during the negotiations on world monetary reform is that such a system of “on demand” convertibility should be restored, in the form of an obligation on the part of the issuer of a reserve currency to convert its liabilities into SDRs at the request of the holder. There are systemic reasons, briefly explained under asset settlement below, which have led others to argue that the restoration of on demand convertibility would be undesirable. However, the purpose here is to compare the financial position of different countries under a regime of on demand convertibility with that under a regime of the type currently prevailing, where conversion is possible only under limited circumstances and, essentially, with the consent of the reserve center.

The effect of introducing a convertibility obligation would be to require the reserve center to maintain the minimum reserve level (Sumin) to “back” its liabilities. The sign of its financial effect on the ith country may therefore be found by differentiating equation (1) with respect to α2, after substituting from equation (4):

Yi = dDi + sSi + (ci − s)βi[R − α1(1 − α2)D].(10)

Therefore ∂Yi/∂α2 = (cisiα1 D > 0 provided, as would normally be assumed, that ci>s: that is, that the yield on the SDR is less than the opportunity cost of foreign investment.

Similarly, the impact on the reserve center may be found by substituting from equations (2) and (4) into equation (3b) and differentiating with respect to α2 :

Yv = s[Ru + (1 − α1(1 − α2))D]+(cu − s)βu[R − α1(1 − α2)D]+[cuα1(1 − α2) − d]D.Yu/α2 = α1(s − cu)(1 − βu)D<0so long ass<cu.(11)

Thus, quite apart from any considerations of the distribution of adjustment incentives or lack of control over the volume of international liquidity that may arise through the absence of convertibility obligations, nonreserve centers have a financial interest in the existence of convertibility. Conversely, the reserve center has a financial interest in avoiding a convertibility obligation. The mechanism producing this result is simple. In the presence of convertibility, a prudent reserve center would need to hold more SDRs than would otherwise be necessary. These additional SDRs would initially be allocated to all members of the International Monetary Fund but would eventually be held exclusively by the reserve center, which would be obliged to pass on to other countries a part of the benefits that it would otherwise obtain as a result of its position as a supplier of reserve currency liabilities.

primary asset holding limits

Another suggestion for reform is that a return to on demand convertibility should be accompanied by a restriction in its scope, in the form of a limit on the total quantity of primary reserve assets which any country is entitled to hold. A country continuing to run a payments surplus after reaching such a limit—the “primary asset holding limit”—would be denied the right to request conversion of further accruals of reserve currency.

A set of primary asset holding limits would have the effect of obliging surplus countries to continue adding to their reserve currency holdings beyond the point when they would choose to do otherwise, and of preventing creditor countries from converting the reserve currency into SDRs when they might otherwise have lost confidence in the ability of the reserve center to sustain its convertibility obligation. It would therefore tend to increase α1 and reduce α2. The effect of the latter has already been investigated above. By differentiating equations (10) and (11) with respect to α1 it is easy to confirm that the two effects would reinforce each other in reducing the financial benefits of convertibility to non-reserve centers and the financial costs to the reserve center:

Yi/α1 = − (ci − s)βi(1 − α2)D<0,Yu/α1 = (cu − s)(1 − βu)(1 − α2)D>0,

provided, as before, that s <ci,cu.

yield on the SDR

In order to determine the financial effect on the ith country of a change in the yield on the SDR, equation (10) is differentiated with respect to 5, recognizing that ∂Di/∂s = – ∂Si/∂s and substituting from equation (4):

Yi/s = Si − βiS + (s − d)(Si/s) − (ci − s)βiα1(1 − α2)D2.(12)

The first term in equation (12) represents the effect of an increased SDR yield in raising the earnings of the country’s reserves, and the second term expresses the effect of increasing the payments made on cumulative SDR allocations. The two effects will exactly cancel out for a country that has holdings equal to allocations, while the net effect will be positive for a country that has excess holdings and will be negative for a country with net use. However, it does not follow that a country can rationally appraise its national interest in the choice of an SDR yield by confining attention to the direct effect on its receipts and payments, because there are two additional effects. It is legitimate to discount the first of these, which represents the change in earnings on reserves resulting from the shift in the country’s own asset composition, on the ground that any differential between s and d that a country accepts voluntarily is essentially a risk premium and that therefore a voluntary shift involves no income or cost. But the final term, which is necessarily positive, reflects the important economic fact that a rise in the SDR yield will lead countries in general to shift reserves from the reserve currency to SDRs and that this will increase the SDRs that can be allocated to each country, with consequential financial benefits. It was argued in Section II that a country could rationally ignore the feedback from its own reserve composition policy to the volume of SDR creation, but in forming its attitude to the choice of an international policy variable that will influence the policy on reserve composition of countries in general, a country could not rationally ignore the feedback on the volume of SDR creation. There is an obvious analogy with the theory of public goods.

The counterpart to the final term in equation (12) is to be found in a cost to the reserve center. This is shown by differentiating equation (11) with respect to s (substituting from equations (2) and (4) as necessary):

Yu/s = Su − βuS + (s − d)D2+(cu − s)α1(1 − α2)(1 − βu)D2.(13)

The first two terms again show the direct effect of an increased SDR yield on the reserve center’s income from its net creditor or debtor position in the Special Drawing Account. The third term need not in principle be a second order term, since the reserve center does not itself choose the extent of its reserve currency liabilities. The final term is necessarily negative provided cu>s, and it shows the loss sustained by the reserve center as a result of the redirection of reserve credit from it to the rest of the world. Hence, even in the absence of substitution arrangements, a reserve center tends to have a financial interest in a low yield on the SDR.

restrictions on the freedom of reserve composition

As long as individual countries are free to choose their own reserve composition, a generalization of the benefits of reserve creation from the reserve center toward the rest of the world has to be accomplished by increasing the attractiveness of holding SDRs relative to the reserve currency. This imposes a cost on countries that are net debtors in SDRs. An alternative way of generalizing the distribution of the benefits of receiving reserve credit would be for countries to agree to limit their holdings of reserve currencies to levels less than those that would be individually optimal. For example, this might be accomplished if each country restricted its reserve currency holdings to the level needed as working balances.

Any collective restrictions on the freedom to hold reserve currencies will tend to lead to a rise in the SDRs held by the ith country (ΔSi≧0) and to an equal decline in its currency reserves (ΔDi= –ΔSi). The change in the total stock of SDRs will be the sum of the increase in the SDR holdings of each nonreserve center (ΔZ = ΣiΔSi) and of the change in the SDR holdings of the reserve center (ΔSu). The latter may be expected to change because the reserve center will aim to hold its effective reserves constant in the face of a fall in average reserve currency holdings (D) and a still greater fall in the maximum level of such holdings (Dmax). This effect, which is sometimes described as reducing the “elasticity” of the reserve currency system, is represented in the model by a fall in α1. From equation (2), the reserve center’s reserves will remain constant when

ΔSu = (1 − α2)DΔα1 + [1 − α1(1 − α2)]ΔD.(14)

The first term is positive, while the second is ambiguous in sign. There is a presumption, but no certainty, that ΔSu>0. There is nevertheless no ambiguity about the sign of ΔS, since total differentiation of equation (9) and substitution of ΔD = – ΔZ yields

ΔS = α1(1 − α2)ΔZ − (1 − α2)DΔα1>0.

The financial effect on the ith country of restrictions on reserve currency holdings may be found by taking the total differential of equation (1) and substituting from the preceding paragraph:

ΔYi =(s − d)ΔSi +(ci − s)βiΔS.

The utility of the first term is necessarily negative, since otherwise the country would have switched its reserves into SDRs even in the absence of restrictions that obliged it to do so. The second term is positive; it will tend to be relatively large in comparison to the first in those countries that receive a large share in SDR allocations relative to the switch in reserves that they are obliged to make, and vice versa. There would, however, seem to be a presumption that Δ Yi will typically be positive. Let us define γiSiS, so that

ΔYi/ΔS =(s − d)γi +(ci − s)βi.

This expression would necessarily be positive for the “typical” country, defined as that where γi = βi, so long as ci>d. While the latter condition is not axiomatic, since foreign official holders are customarily exempt from taxation by the reserve center while foreign private holders are sometimes taxed on interest earnings (though often at concessional rates on account of tax treaties), there is a strong presumption that it is normal, because reserve centers acquire that role as a result of good credit standing, broad financial markets, and so on. Moreover, once a reserve center has acquired the role, that will in itself tend to keep the yield on its foreign liabilities below that which other countries need to pay in order to borrow, since the reserve role provides a captive source of funds.

The effect on the income of the reserve center is found from equation (3b), by substituting from equation (14):

ΔYu=(cu − s)(1 − α2)DΔα1 + (cu − s)α1(1 − α2)ΔD+(s − d)ΔD + (cu − s)βuΔS.

The first two terms are negative, representing the loss of seigniorage on potential and actual reserve credit, respectively. The third term would presumably be positive, since restrictions on reserve currency holdings would not be necessary unless the yield on the SDR were below that on the reserve currency; it represents the saving made by the reserve center on the reduced need to hold low-yielding SDRs to back high-yielding currency liabilities. The final term, representing the reserve center’s share in increased SDR allocations, is also positive. The net effect is presumably, but not certainly, negative.

As well as comparing a situation where SDRs are a relatively small part of the reserve stock with one in which their role is increased as a result of restrictions on reserve composition, it is of interest to compare two situations where the proportion of reserves held in SDRs is the same but in which the instrument used to raise the proportion is portfolio restrictions rather than the yield on the SDR. This comparison can be made by considering the effect of a change in s that is not accompanied by a change in S or D (or, for the typical country, of Di or Si): that is, by taking only the first two terms of equations (12) and (13). These will be positive for countries with net creditor positions in the Special Drawing Account of the Fund and negative for net users of SDRs, whether or not the country is a reserve center. Hence, one reaches the unsurprising conclusion that, given that the role of the SDR is to be increased to a prespecified level, it is to the advantage of SDR creditors that this be done by raising interest rates and to the advantage of SDR debtors that it be done by restricting the freedom of reserve choice.

the distribution of SDR allocations

The effect of a change in the share of SDRs allocated to a country on that country’s income is found by differentiating equation (1) with respect to βi :

Yi/βi =(ci − s)S>0,providedci>s.

This no doubt explains why developing countries favor a link, and perhaps also why some developed countries oppose it. (In addition to its effect in redistributing income to the developing countries, the link would also increase the efficiency of resource allocation to the extent that developing countries typically have a high ci which does not attract a capital inflow because of the existence of private risks that are not social risks.)

If a link were to be implemented, it would have the effect of making most developing countries net debtors in the Special Drawing Account. It follows from the above discussion that these countries would tend to acquire an interest in the imposition of restrictions on the freedom of reserve composition, since this would enable the SDR yield to be kept down and so would increase the value of the SDR/aid link allocations.


It has been shown that nonreserve centers would generally benefit financially from a curtailment of the reserve currency system and that net debtors in the Fund’s Special Drawing Account—which would include most developing countries, if a link were introduced—have a financial interest in any such curtailment being brought about by restrictions on reserve composition rather than by an increase in the SDR yield. It is, however, important to recognize that these conclusions are based on a comparison between alternative long-run equilibrium positions in which the change in reserve credit available to the reserve center has been fully reflected in the reserve center’s balance of payments. The outcome would be quite different if the composition of reserves were altered in favor of SDRs, not by the reserve center earning a payments surplus but by a substitution operation in which reserve holders surrender the reserve currency to the Fund tin exchange for SDRs and the Fund acquires a claim on the reserve center.

Let us define the sum of SDRs created by substitution, and not amortized, as S8. If the yield on the assets held by the substitution facility is denoted by r, the profit or loss of the facility is equal to (r-s)S8. This profit (or loss) would be distributed to Fund members in proportions πi (which presumably might be equal to the proportions βi). Since SDRs received as allocations are only (S – S8), equation (1) is modified to

Yi = dDi + sSi + (ci − s)βi(S − S8) + πi(r − s)S8.(15)

It would not be legitimate to substitute for S from equation (4) in equation (15), as was done in some of the previous equations, since it is not legitimate to assume that substitution either would leave the parameters α1 and α2 unchanged or would change them in one specific direction; there are several possibilities that merit recognition. It is more illuminating to substitute S=Z+Su:

Yi = dDi + sSi + (ci − s)βi(Z + Su − S8) + πi(r − s)S8.

Since ΔDi = – ΔSi and ΔZ = ΔS8 (= –ΔD), the total differential is:

ΔYi = (s − d)ΔSi + (ci − s)βiΔSu + πi(r − s)ΔS8.(16)

The first term is the change in interest income as a result of the change in the country’s own reserve composition. The utility of this change would depend on the circumstances causing substitution to be undertaken. If portfolio composition was initially in equilibrium, and countries collectively agreed to restrictions on reserve composition which were implemented by a program of mandatory substitution, the utility of the change in interest income would be negative. On the other hand, if countries were initially unable to satisfy their portfolio preferences because the reserve currency was inconvertible, substitution would be voluntary and the utility of the change represented by the first term would be positive. The second term represents the seigniorage accruing to the ith country as a result of the change in the SDR holdings of the reserve center brought about by modifying the reserve currency system. The sign is ambiguous, since ΔSu = ΔSumin − ΔDmax − ΔS8. There are two factors that would tend to make it positive: if substitution were the condition for a restoration of convertibility, which resulted in ΔSumin>0, or if it were associated with arrangements to prevent a subsequent growth in reserve currency balances, implying ΔDmax<0. On the other hand, if convertibility arrangements remained unaltered and there were no provisions to circumscribe the future growth of reserve currency holdings, the result would be ΔSu=–ΔS8<0. The third term would be zero if the reserve center serviced its liabilities at the SDR yield, and it would be positive only if it paid a higher rate on its liabilities than this (perhaps as a reflection of their long-term character).

The scope for nonreserve centers to benefit financially from substitution in the short run is therefore distinctly limited. The financial benefit could be substantial only if (1) the SDR were regarded as a significantly more attractive asset than the reserve currency, (2) substitution were the condition for a return to convertibility or a curbing of the future growth of reserve currency holdings, (3) the reserve center paid a substantially higher charge on its long-term liabilities to the substitution facility than the SDR yield. In the long run, however, substitution might have two additional effects, both of which would be financially favorable to nonreserve centers: (1) As amortization occurred, the final term in equation (16) would be replaced by (ci-s)βi instead of (rs)πi, since the reduction in liquidity caused by amortization would be offset by increased SDR allocations—generalizing the benefits of the reserve credit to the world as a whole; (2) If substitution was accompanied by a curb on the size of reserve currency liabilities, this would not merely ensure that the reserve center would need to build up its SDR holdings to compensate for its loss of “elasticity” but would also prevent secular growth in the role of the reserve currency pre-empting the need for future SDR allocations to meet the growth in the demand for liquidity. (The second objective could also be achieved, of course, by a restriction on the freedom of reserve composition which would merely freeze the maximum permitted holdings of reserve currency at their current level.)

To derive the expression for the reserve-related income of the reserve center, it is necessary to go back to equation (3a), replacing S by (SS8), to recognize that substituted SDRs do not generate SDR allocations; adding a term (cu – r)S8, to recognize that the reserve center still receives the reserve credit on the substituted reserve currency, even though this is granted through the intermediary of the substitution facility, at a cost of r; and adding the reserve center’s share in the profit or loss of the facility, πu (r – s)S8. Thus

Yu =sSu + (cu − s)βu(S − S8) − dD + cu(Dmax − Sumin)+(cu − r)S8 + πu(r − s)S8.

Recognizing that ΔSu = ΔSumin − ΔDmax − ΔS8, this gives

ΔYu = [(d − r) + πu(r − s)]ΔS8 − (cu − s)(1 − βu)ΔSu.(17)

The first term represents the change in the cost of servicing the reserve center’s obligations as a result of their transformation from currency liabilities to debts owed to the substitution facility, as modified by its share in the profits or losses of the facility; its sign would largely depend upon whether the yield on liabilities to the facility was higher or lower than that on the reserve currency. The second term would be positive if the reserve center were enabled to effect economies in SDR holdings (for example, because consolidation of its debts into a nonliquid form permitted it to reduce Sumin. while Dmax fell by no more than Ss rose); and it would be negative if its necessary SDR holdings rose (for example, because substitution was associated with a return to convertibility or a reduction in the “elasticity” of the reserve currency system). Similarly, the other potential long-run costs to the reserve center stem from the measures that may accompany substitution (amortization and the curbing of the secular growth of the reserve currency role) rather than directly from substitution itself.

asset settlement

The analysis up to this point has assumed a system in which “convertibility” is of the traditional “on demand” type, under which countries holding reserve currencies have the right—but not the obligation—to request conversion. Such a system, however, contains an inherent element of instability. This results from the fact that individual pursuit of national self-interest, on the lines established as rational in Section II, dictates a strategy of shifting into a reserve currency when it is strong (and d is therefore expected to be high) and shifting out when it is weak (so that the expected value of d is low), which results in an accentuation of the effects of payments imbalances on the reserve position of the reserve center. In principle a prudent reserve center would allow for this effect in estimating Dmax and Sumin, and would therefore be prompted into adjustment actions before the elasticity in the reserve currency system turned perverse, and led to either a contraction of liquidity (if the reserve center maintained convertibility) or a loss of control over the growth of liquidity (if the reserve center abandoned convertibility but continued to run a deficit). However, since experience has shown that the necessary prudence cannot be taken for granted, it has sometimes been concluded that systemic needs demand that the reserve center be obligated to settle its imbalances in reserve assets, rather than simply stand ready to convert them if the reserve holder requests it to do so.

The financial implications of asset settlement depend on the technique used to effect it. It was formerly envisaged that asset settlement would be realized, or at least approximated, by all countries’ reducing their holdings of reserve currencies to working balances and thenceforth maintaining them at that level. This would involve either a surplus by the reserve center over a relatively short period, in order to reduce outstanding reserve currency balances, or a substitution operation. In either case, the reduction in reserve currency balances would have to be matched by an equal increase in the volume of outstanding SDRs if liquidity was to be maintained unchanged. In the first case, the additional SDRs would be created through allocations; in the second case, they would initially be created through substitution, although the substituted SDRs would in turn be gradually replaced by allocated SDRs when amortization occurred. To the extent that the reserve currency balances were replaced by allocated SDRs, the financial effects would be those described above under yield on the SDR or under restrictions on the freedom of reserve composition, depending upon whether or not it was necessary to raise the yield on the SDR in order to persuade countries to replace reserve currencies by SDRs in their portfolios. To the extent that reserve currencies were replaced by substituted SDRs, the effects would be along the lines analyzed under substitution above. Since the arrangement would have the effect of eliminating the elasticity of the reserve currency system—that is, reducing Dmax to D, as well as curbing the secular growth of the reserve currency system—the second term of equation (16) would be positive and the second term of equation (17) would be negative, so that this method of securing asset settlement would be financially attractive to nonreserve centers and costly to the reserve center.

Because of a widespread reluctance on the part of countries to curtail the freedom of reserve composition as much as would be required to establish asset settlement by limiting currency holdings to working balances, it has been suggested that an alternative technique might be used.6 This alternative would involve the establishment of a substitution facility and its use, not only to undertake a once-for-all substitution operation but also to permit continuing substitution by non- reserve centers and to engage in transactions with reserve centers which would ensure that they were subject to asset settlement even if other countries in total substituted SDRs for reserve currency or, conversely, wished to build up their reserve currency holdings. Asset settlement would be achieved by the substitution facility’s buying SDRs from (selling SDRs to) the reserve center in an amount equal to any increase (decrease) in outstanding official reserve currency balances.

Such a system would enable nonreserve centers to convert reserve currencies into SDRs at any time without the need for the reserve center to hold SDRs to meet this contingent demand, so that the reserve center could prudently Sumin = 0. The extent of substitution would also presumably be less, since countries would substitute only to the extent that it was individually advantageous to them to do so; this would reduce the scope for the rest of the world to benefit from any excess of r over s and also from the ultimate redirection of reserve credit as the substitution facility’s holdings were amortized. Establishment of asset settlement would still probably be costly to the reserve center (and beneficial to the rest of the world), because it would still eliminate the elasticity of the reserve currency system and oblige the reserve center to rely on the use of SDRs for the elasticity needed to accommodate temporary imbalances, as well as circumscribing the secular growth of reserve currency holdings. But asset settlement secured through a continuing substitution facility would appear financially more attractive to the reserve center than asset settlement achieved by the reduction of reserve currency holdings to working balances (unless, at least, r was less than s; that is, unless the reserve center was subsidized on its liabilities to the substitution facility).

other reserve assets

In reality the world contains other reserve assets besides SDRs and a single reserve currency. These consist of gold, reserve positions in the Fund, and secondary reserve currencies. In addition, Euro-currency holdings have significantly different financial implications from regular reserve currency holdings.

The characteristics of gold as a reserve asset are: (1) its yield is highly speculative (consisting entirely of changes in capital value); (2) no country is responsible for servicing that yield because gold is an asset with no counterpart liability; and (3) an increase in the volume of gold reserves involves a sacrifice of real resources rather than an extension of reserve credit. The fact that no country is responsible for servicing the yield which gold provides when there is an increase in the price at which monetary authorities can dispose of it does not mean that no country suffers from such an increase. If the volume of liquidity is to remain constant, an increase in the gold price necessitates a curtailment of fiduciary reserve creation, with a consequential reduction in the reserve credit accruing either to reserve centers or to SDR allocatees (or both). The beneficiaries are the countries that hold or produce gold.

Reserve positions in the Fund are similar to SDRs in the characteristics of their yield. They differ in that the reserve credit resulting from their creation is either nonexistent (insofar as they are created by the deposit of gold with the Fund) or is directed to countries drawing on the Fund because of payments difficulties rather than to Fund members in general.

Secondary reserve currencies are virtually certain to be less profitable to their reserve centers than is operation of the primary reserve currency. Inconvertibility is not a serious option to a secondary reserve center, which implies that considerable reserves need to be held as “backing” and/or that the yield on its liabilities has to be high. “New” reserve centers generally acquire this role because the yield on their currencies appears particularly attractive: it may indeed be so attractive that the reserve center sustains a loss from its reserve role. Clearly, the rest of the world can benefit, at the cost of the secondary reserve center, if the latter is willing to perform such unprofitable financial intermediation.

Reserve currencies held in the Euro-markets differ from regular reserve currency holdings in that the reserve credit corresponding to them is received by the countries that borrow in the Euro-markets, rather than by the country in whose currency the balances are denominated. The role of the reserve center is essentially that of providing an implicit guarantee to the lender against the possibility of default by the borrower—a role that might indeed justify the once-traditional habit of describing the reserve currency role as a burden. Insofar as a reserve currency system is to be perpetuated, therefore, the nonreserve centers have a financial interest in its being centered in the Euro-markets. (This interest may, of course, run counter to their interest in ensuring stability in the supply of reserves.) In a choice between an SDR-based system and a reserve currency system, it would be necessary to compare the proportion of reserve credit that a particular country could hope to obtain under the two systems, and it would also be necessary to recognize that reserve credit is likely to be cheaper under an SDR system (which would be beneficial to those who receive more reserve credit than the amount of their reserves).

IV. Conclusions

If a particular country is concerned with maximizing its financial benefits from the reserve supply process, it should address itself to two questions.

(1) How can it maximize its access to reserve credit? A primary reserve center achieves this objective by perpetuating a traditional reserve currency system. Nonreserve centers would achieve it either by securing an SDR-based system or by transferring reserve currency holdings to the Euro-markets; the former strategy is especially likely to be beneficial to developing countries if a link is established. (There is, however, one category of country which may not find it advantageous to maximize its access to reserve credit—the secondary reserve center.)

(2) Is the reserve credit it receives likely to exceed the reserves it holds? If the answer is yes, its interest lies in the imposition of restrictions on the freedom of reserve composition, in the form of inconvertibility (for the primary reserve center), or in the form of prohibitions on foreign official holdings of their currency (for secondary reserve centers), or in the form of restrictions on the holding of all reserve currencies (for countries which generally expect to be net users of SDRs). If the answer is no, its financial interest lies in high yields rather than restricted reserve composition as the instrument to achieve balance between the supply and demand of different assets.

Nothing in this paper should be construed as implying that the author believes that countries either do determine or should determine their attitudes toward international monetary reform exclusively in view of a concern for their national financial self-interest. If they did, international monetary cooperation would be an almost impossible goal, for in this context—as in most other instances where the issue is one of income distribution—the interests of different parties are characteristically in conflict rather than in harmony. In fact, countries have very important common interests in the construction of a well-functioning international monetary system. But it is futile to pretend that monetary reform can secure these common interests for all countries without decisions that will also influence the international distribution of income, and it is futile to expect countries to be indifferent to these distributional implications. To secure agreements which further the common interest it is necessary either to endorse some generally acceptable distributional principle (such as the principle of neutrality aimed for in the formula governing SDR allocations) or to resort to bargaining—in which case some countries may choose to bargain away some financial advantages that their power would otherwise enable them to obtain, in return for nonfinancial goals to which they give greater weight than other countries (for example, more reliable control of international liquidity).


Mr. Williamson, Advisor in the Research Department, is a graduate of the London School of Economics and Political Science and of Princeton University. He has been a lecturer at the University of York, England, and a consultant to Her Majesty’s Treasury and was on leave from his post as a professor at the University of Warwick, England, when this paper was written. He has contributed a number of articles to economic journals.

In addition to colleagues in the Fund, the author is indebted to participants in seminars at Columbia University and the Johns Hopkins University (particularly to Miss N. Goyal and Mr. S. Leite) for helpful comments on a previous draft of this paper. Views expressed are those of the author.


Discussions of the Committee of Twenty (formally the Committee on Reform of the International Monetary System and Related Issues), a committee of the International Monetary Fund’s Board of Governors, in 1973–74.


Since the changes considered in the paper include variations in the yield on the SDR, this implies that the demand for reserves is assumed to be insensitive to the rate of interest. The empirical evidence seems to support this assumption. See John Williamson, “Surveys in Applied Economics: International Liquidity,” Economic Journal, Vol. 83 (September 1973), p. 696.


For a survey of this literature, see ibid., pp. 688–97.


Seigniorage benefits can be measured either from a flow standpoint as the present value of reserve credit received during the current period, or—as in the present paper—from a stock standpoint as the income on cumulative past receipts of reserve credit. See Harry G. Johnson, “Appendix: A Note on Seigniorage and the Social Saving from Substituting Credit for Commodity Money,” in Monetary Problems of the International Economy, ed. by Robert A. Mundell and Alexander K. Swoboda (University of Chicago Press, 1969), p. 324.


The analysis of the reserve currency system essentially follows that in John Williamson, “Liquidity and the Multiple Key-Currency Proposal,” American Economic Review, Vol. 53 (June 1963), pp. 427–33.


The first suggestion along these lines was made by Maxwell Stamp, “The Reform of the International Monetary System,” Moorgate and Wall Street, Summer 1965, p. 12. It was first included in official proposals as the “third approach” to asset settlement in Reform of the International Monetary System: A Report by the Executive Directors to the Board of Governors, International Monetary Fund (Washington, 1972), Chap. 3, par. 4.