Determinants of the currency composition of foreign exchange reserves The Currency Composition of Foreign Exchange Reservesare examined for both industrial and developing countries. Empirical results indicate that the currency composition of reserves during the period 1976–85 has been influenced by each country’s exchange rate arrangements, trade flows with reserve-currency countries, and the currency in which its debt service payments are denominated. The evidence suggests that managing the currency composition of a country’s net foreign asset position is done more cheaply by altering the currency of denomination of assets and liabilities that are not held as reserve assets. [JEL 431. 4321]

Abstract

Determinants of the currency composition of foreign exchange reserves The Currency Composition of Foreign Exchange Reservesare examined for both industrial and developing countries. Empirical results indicate that the currency composition of reserves during the period 1976–85 has been influenced by each country’s exchange rate arrangements, trade flows with reserve-currency countries, and the currency in which its debt service payments are denominated. The evidence suggests that managing the currency composition of a country’s net foreign asset position is done more cheaply by altering the currency of denomination of assets and liabilities that are not held as reserve assets. [JEL 431. 4321]

Determinants of the currency composition of foreign exchange reserves The Currency Composition of Foreign Exchange Reservesare examined for both industrial and developing countries. Empirical results indicate that the currency composition of reserves during the period 1976–85 has been influenced by each country’s exchange rate arrangements, trade flows with reserve-currency countries, and the currency in which its debt service payments are denominated. The evidence suggests that managing the currency composition of a country’s net foreign asset position is done more cheaply by altering the currency of denomination of assets and liabilities that are not held as reserve assets. [JEL 431. 4321]

Although concerns about official foreign exchange management practices were a key element in the discussions of the Fund’s Substitution Account during the 1970s, the emergence of the view that foreign exchange market intervention had little effect on exchange rates subsequently limited the attention focused on this topic. The sharp swings in exchange rates among currencies of the major industrial countries in the 1980s, however, have led to proposals for achieving greater exchange rate stability through the use of coordinated intervention, target zones, or a return to fixed parities. Reserve management practices could play an important role in determining the stability of any such arrangements.

This study examines one key aspect of reserve management practices—the factors influencing the currency composition of foreign exchange reserves in both industrial and developing countries for the period 1976–85. In contrast to most earlier analyses that relied on currency composition data for country groups (for example, the industrial countries), our empirical analysis uses individual country data in combined cross-country, time-series regressions. Use of such data avoids the difficulties involved in distinguishing between the changes in the currency composition of a group’s foreign exchange reserves because of shifts in the portfolio preferences of the authorities in individual countries from those associated with changes in the distribution of reserves across countries within the group. The results suggest that, although risk and return considerations play some role in determining countries’ net foreign asset (liability) positions in different currencies, countries’ gross holdings of reserve assets were more strongly influenced by transaction costs.

I. Trends in the Currency Composition of Foreign Exchange Reserves

Between the end of 1976 and the end of 1986, there was an ongoing diversification of the currency composition of foreign exchange reserves (Table 1).1

Table 1.

Share of National Currencies in Total Identified Official Holdings of Foreign Exchange, 1976–86

(In percent)

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Sources: International Monetary Fund, various publications, the Annual Report, and staff estimates.Note: Starting with 1979, the SDR value of European currency units (ECUs) issued against U.S. dollars is added to the SDR value of U.S. dollars, but the SDR value of ECUs issued against gold is excluded from the total distributed here.

This residual is equal to the difference between total identified reserves and the sum of the reserves held in the five currencies listed in the table.

Aggregate Data

For all countries combined, the proportion of reserve assets denominated in U.S. dollars has declined from nearly 80 percent at the end of 1976 to 66 percent at the end of 1986, and this shift has been matched by a rise in the proportions held as deutsche mark (from 8 percent to 15 percent) and yen (from 3 percent to nearly 8 percent).2 However, these changes in the aggregate currency composition of foreign exchange reserves have encompassed somewhat contrasting behavior on the part of industrial and developing countries. For the industrial countries, the erratic but significant decline in the share of reserves denominated in U.S. dollars—from 87 percent at the end of 1976 to 69 percent at the end of 1986—was accompanied by sharp increases in the shares of the deutsche mark (from 4 percent to 18 percent) and the yen (from 2 percent to 8 percent). For the developing countries, the pattern of currency diversification has been much more uneven. After an initial sharp decline in the dollar’s share between the end of 1976 and the end of 1980 (by 12 percentage points), this share was relatively stable between the end of 1981 and the end of 1986. In contrast, although the share of reserves denominated in yen more than doubled over the period between 1976 and 1986, the share of developing country reserves denominated in deutsche mark reached a peak of nearly 16 percent at the end of 1980 before declining to about 11 percent at the end of 1986.

Previous Studies

Previous analyses of the behavior of the currency composition of foreign exchange reserves have argued that the proportion of foreign exchange reserves denominated in a particular currency should be related either to the currency composition of the authorities’ exchange market activities (transaction approach) or to the risks and returns associated with holding reserve assets denominated in different currencies (the mean-variance approach). The transaction approach postulates that the desired currency composition of reserve assets is independent of the optimal distribution of net wealth across currencies. Instead, the holdings of reserve assets denominated in a particular currency would be related to transaction costs associated with the government’s purchases and sales of foreign exchange. The alternative mean-variance approach suggests that a rational government would not put all of its wealth in the one currency that has the highest expected yield, because of the possibility of highly variable outcome for its wealth depending on future exchange rates changes. Moreover, countries producing or consuming different goods and services would optimally hold different portfolios of financial assets.3

Heller and Knight (1978) provided evidence in support of the view that transaction needs played a major role in determining the currency composition of reserves. This study explained variations in the proportions of a country’s foreign exchange reserves held as assets denominated in the U.S. dollar, pound sterling, deutsche mark, French franc, and other reserve currencies as a function of the country’s exchange rate arrangements, which influenced both the foreign currencies bought and sold to defend such arrangements and the share of its trade with a particular reserve-currency country.4 Their results indicated that countries increased the proportion of their foreign exchange reserves held as a given reserve currency if they pegged their exchange rate to that currency or if the reserve center was an important trading partner.

In the late 1970s and early 1980s, several studies applied optimal portfolio theory to the selection of official reserve portfolios. For example, Ben-Bassat (1980, 1984) argued that a country’s optimal reserve- portfolio composition depends on three factors: (1) a country’s motivations for holding reserves, (2) the risk and return on the various reserve currencies, and (3) a country’s interest in maintaining international currency stability. Establishing the optimal reserve portfolio would first involve identifying the combinations of reserve positions that are on the efficiency frontier (that is, those positions which yield the highest rate of return for a given level of risk as measured by the variance of yields) and then allowing the authorities to select their preferred risk-return combination. Using data from the 1970s, Ben-Bassat (1984) compared actual and optimal reserve portfolios for both developing and industrial countries in 1976 and 1980. For the developing countries, actual and optimal portfolios in 1976 were regarded as similar. Moreover, this group reduced the U.S. dollar share in its actual portfolio between 1976 and 1980, which further reduced the gap between the actual and optimal reserve portfolios. The gap between the actual and optimal reserve portfolios for the industrial countries, however, increased between 1976 and 1980. In addition, the proportion of reserves denominated in the U.S. dollar held by industrial countries that were not part of the Snake arrangements (members of the European System of Narrower Exchange Rate Margins) increased, although the calculated optimal portfolio implied that this proportion should decline.5

In evaluating the use of the mean-variance and transaction approaches to explain the currency composition of reserves of developing countries, Dooley (1986) stressed that there were a number of difficulties associated with applying the mean-variance optimal portfolio approach.6 First, the mean-variance approach typically deals with allocation of wealth to net holdings of particular assets, whereas foreign exchange data refer to gross holdings of particular assets. Second, for the optimal portfolio approach to be useful it must encompass decisions regarding all of the financial positions, whereas reserve holdings constitute only a small subset of potential assets or liabilities. This means that both the yields on a variety of assets and liabilities other than reserve assets and the covariances of these yields with the returns on reserve assets would typically have to he included as determinants of optimal reserve positions. In addition, since reserve decisions are made by central banks that use their reserve instruments for transactions, it may be more efficient for the typical government to alter its net foreign currency position by changing the currency composition of its assets and liabilities that are held as reserves. As a result, the currency composition and level of foreign exchange reserves would most likely reflect the authorities’ transaction needs in the foreign exchange market. Finally, mean-variance portfolio considerations would be relevant for a single country, whereas data on the currency composition of foreign exchange reserves considered in most studies have referred to country groups rather than to individual countries. Dooley’s empirical analysis supported the view that reserve assets are held for transaction reasons, and the currency composition of such assets was determined by the consideration that they could be easily liquidated and used to make payments.

Recently, Horii (1986) examined reserve-currency diversification during the 1970s and 1980s. Although he noted that the currency composition of reserves should be studied on an individual country basis, Horii focused on country group data because individual country data were unavailable. After allowing for factors that altered the distribution of reserves across countries, he argued that, for all countries during the 1970s and 1980s, there was no large-scale diversification out of reserve assets denominated in the U.S. dollar. There was, however, some evidence of a movement out of reserves denominated in pounds sterling in 1972–76, a small shift from dollar- to deutsche-mark-denominated instruments in 1976–79 (mainly because of passive exchange rate changes), and a slight diversification out of dollar-denominated instruments in 1980–84. These results led Horii to conclude that the currency composition of reserve holdings could not be explained in terms of a transaction demand determined by trade flows alone, since capital flows have become increasingly important. Moreover, the stability of the currency composition of reserves during a period of significant changes in exchange rate arrangements did not support the view that such arrangements were important determinants of the currency composition, as suggested by Heller and Knight (1978). Finally, Horii calculated the reserve portfolios that should have existed under efficient portfolio theory for 1979 (using data from 1974 to 1979) and 1984 (using data from 1979 to 1984). In general, optimal holdings for reserves denominated in U.S. dollars were well below actual holdings in both years. In contrast, actual holdings of reserves denominated in deutsche mark, French francs, and pounds sterling were well below their calculated optimal levels.

II. Analysis of Currency Composition of Foreign Exchange Reserves on the Basis of Country Data

Our analysis focuses on developing and testing an empirical model that integrates the mean-variance and transaction approaches to specifying the determinants of the currency composition of foreign exchange reserves. It is argued that, although a country’s net foreign currency position in influenced in important ways by risk and return considerations, its gross holdings of foreign exchange reserves will be motivated principally by transaction concerns. In measuring these transactions needs, however, it is important to consider the scale of both trade and capital flows that the authorities are likely to encounter in the foreign exchange market. The model is a direct complement to those models of the demand for reserves that relate holdings of reserves to the scale of a country’s imports, its degree of openness, and the variability of the country’s balance of payments.7 Whereas such models seek to explain the overall holdings of reserves and take the currency composition of these reserves as exogenous, this study attempts to identify the determinants of the currency composition while taking overall holdings of foreign exchange reserves as exogenous.

The empirical analysis is based on a cross-country, time-series analysis of the International Monetary Fund’s data on the currency composition of foreign exchange reserves for individual industrial and developing countries during the period 1976–85. As already noted, these data allow us to avoid one of the principal shortcomings of most previous studies of the currency composition of foreign exchange reserves, which have used data on the portfolio holdings of country groups rather than those for individual countries. In particular, the use of data for country groups makes it impossible to distinguish between changes in the currency preferences of individual countries and shifts in the distribution of reserves across countries that are members of the group.8

The empirical results suggest that both developed and developing countries take into account the currency composition of their foreign exchange market transactions, as well as the nature of their exchange rate arrangements, when selecting the currency denomination of their foreign exchange reserves. Moreover, for developing countries, the currency composition of debt service flows has been as important as trade flows in determining the proportions of foreign exchange reserves held in each of the major reserve currencies.

Basic Model

In this section we consider a simple model that incorporates the role of the transaction costs into the traditional mean-variance approach to the determination of a country’s optimal portfolio of external assets and liabilities. It is argued that, although the mean-variance approach provides a description of the authorities’ net foreign asset (or liability) positions in each potential currency of denomination, the structure of transaction costs as well as the scale of a country’s anticipated foreign exchange market transactions are the principal determinants of each country’s gross asset positions, including its holdings of foreign exchange reserves.

In the standard optimal international portfolio model (see Roll (1977), Macedo (1980), and Horii (1986)), the optimal proportion of currency i in a country’s net foreign asset portfolio is determined by the expected real returns on holding positions in different currencies as well as by the covariances between the yields. If xi represents the proportion of currency i in the authorities’ portfolio and X is the vector of the xi, then the mean (m) and variance (σ2) of the return on the net foreign asset position will be given by

m=XR(1)
σ2=XVX,(2)

where R is the vector of expected real returns on maintaining a position in the various currencies and V is the covariance matrix of expected real yields.9

Under the assumption that the authorities’ utility is positively related to the expected return on their portfolio and negatively related to portfolio risk (for example, if U=m(b/2)σ2), the optimal vector of portfolio positions (X*) will be given by (see Horii (1986)):

X*=V1e/eV1e+(1/b)V1[R(RV1e/eV1e)e],(3)

where e is the unit vector and b is the degree of relative risk aversion.

To illustrate the relationship between net and gross asset positions implied by the solution to equation (3), it is convenient to focus on the situation in which there are only two currencies: U.S. dollars (currency 1) and deutsche mark (currency 2). Let Ai represent the holdings of assets in currency i, Li be the issuance of liabilities in currency i, and Ni equal the net asset position in currency i(=AiLi). Moreover, let the country be a net debtor, where W(<0) represents the overall size of its net debt position (taken as exogenous).10 Assume that the solution to equation (3) indicates that the optimal net portfolio implies that half of the country’s debtor position should be denominated in dollars and half in deutsche mark (N1=N2). A country with A* in gross assets can still maintain its desired net debt position in each currency (N1=N2) by altering the currency denomination of its liabilities (L*). Suppose, for example, that to minimize transaction costs the authorities chose to hold most of their gross assets in dollars, so that A1*>A2* (Figure 1). To maintain their desired net positions in each currency, the country would have to issue dollar and deutsche mark gross liabilities such that L1*A1*=L2*A2*. This implies that the theory of optimal net foreign exchange positions places no obvious theoretical restrictions on the currency denomination of a country’s gross reserve position.11

Figure 1.
Figure 1.

Gross and Net Foreign Asset and Liability Positions

Citation: IMF Staff Papers 1989, 002; 10.5089/9781451947045.024.A004

In this two-currency model, the roles of transaction costs and risk-return considerations in determining a country’s net and gross asset positions can be described more formally as follows. As noted earlier, let Ai be gross holdings of reserve assets denominated in currency i, and let Li be the gross external liabilities issued in that currency. The country can hold reserve assets in currency i that yield a random real world interest rate that has a mean of ri and a variance of σr12. Alternatively, the country can borrow in currency i and must pay ri+di, where di is a positive constant that reflects the spread between the lending and borrowing rates. The net interest earned on a given net asset position is ri(AiLi)diLi.

The expected return on the country’s foreign asset and liability positions will he given by

m=r1A1+r2A2(r1+d1)L1(r2+d2)L2=(r1+d1)N1+(r2+d2)N2d1A1d2A2,(4)

where Ni=AiLi. The variance of this return will therefore equal

σ2=N12σr12+N22σr22+2N1N2σr1r2,(5)

where

σri2 = the variance of yield ri

σrirj = the covariance of yields ri and ri.

In addition to earning net interest income, the authorities also incur transaction costs associated with their exchange market transactions.12 To simplify, assume that the amount of transactions the country undertakes in each currency in each time period can be described by three possible states of nature (Figure 2):

Figure 2.
Figure 2.

Reserve Holdings and Transaction Structure

Citation: IMF Staff Papers 1989, 002; 10.5089/9781451947045.024.A004

(t1, t2) occurs with probability π1 (point B in Figure 2)

(t1, Tt1) occurs with probability π2 (point C in Figure 2)

(Tt2, t2) occurs with probability π3 (point D in Figure 2),

with T>t1+t2andπ1+π2+π3=1.

Given this transaction structure, the country faces transaction costs that are influenced by two factors. First, there is the cost of converting one currency into another. If the authorities hold sufficient reserves denominated in a given currency (Ai) to meet the exchange market transactions in that currency, then it is assumed that the authorities do not incur any transaction cost. For example, assume that the authorities’ holdings of reserves are represented by point A in Figure 2, with A, of currency 1 and A2 of currency 2. If actual transactions t1 and t2 (point B in Figure 2), the country would not incur any transaction costs because its reserve holdings in each currency would be sufficient to meet all transactions in the respective currencies. When the transactions are such that the authorities exhaust their holdings of reserves denominated in one currency, however, the authorities must convert the holdings of reserves denominated in the other currencies into the first currency, and this results in transaction costs. In Figure 2, for example, if actual transactions were represented by either point C or D, the authorities would incur the costs of converting reserves from one currency to another currency because the amount of reserves in one of the currencies will be lower than the level of transactions in that currency.

The second type of cost is associated with the possibility that the authorities may exhaust their reserve holdings. As Figure 2 is drawn, points C and D represent situations in which the country’s total reserves are inadequate. Such an outcome could force the authorities to engage in emergency borrowing, which is assumed to be relatively costly.

The costs of converting currencies or of engaging in emergency borrowing to offset reserve shortages are taken as being represented by quadratic functions of the amounts involved. In terms of Figure 2, if the outcome of transactions is B, there is no transaction cost because the level of reserves held in each currency is higher than the level of transactions in the respective currency, A1 > t1 and A2 > t2. If the outcome is C, holdings of currency 1 are higher than transactions in that currency, A1 > t1, but holdings of currency 2 are lower than transactions in that currency, A2 > Tt1. In addition, total holdings of reserves A1 + A2 are lower than total transactions T. Therefore, there is a cost associated with the conversion of the excess of currency 1 into currency 2, A1t1, and a cost associated with the overall shortage of reserves, TA1A2. The same type of reasoning applies to outcome D. As a result, the expected conversion and reserve-shortage costs for holdings of reserves A1 and A2 are given by13

E(tc)=π2c(A1t1)2+π3c(A2A2)2+(π2+π3)p(TA1A2)2,(6)

where c and p are parameters associated with the conversion of reserves from one currency to another and with reserve shortages, respectively.

In determining their holdings of foreign assets and issuance of foreign liabilities, the authorities are assumed to maximize a utility function that is a positive function of the expected return (m) on their net foreign asset portfolio (net of expected transaction and emergency borrowing costs) and is negatively related to the variance (σ2) of the yield on that portfolio. In particular, the authorities select A1, A2, L1, and L2 subject to the constraint imposed by the size of their overall net foreign asset position, W=A1+A2L1L2=N1+N2(where W can be either positive or negative). Thus,

U=mbσ2E(tc),(7)

where

m=(r1+d1)N1+(r2+d2)(WN1)d1A1d2A2=(r2+d2)W+(r1+d1r2d2)N1d1A1d2A2
σ2=N12σr12+(WN1)2σr22+2N1(WN1)σr1r2,

and where E(tc) is as defined in equation (6).

As shown in Appendix II, the first-order conditions yield

N1=(r1+d1r2d2)2bD+W(σr22σr1r2)D(8)
N2=(r1+d1r2d2)2bD+W(σr12σr1r2)D,(9)

where D=σr12+σr222σr1r2, and A1 and A2 are given by

A1=π3A+π2t1π3t2(π2+π3)+d2d12c(π2+π3)(10)
A2=π2A+π3t2π2t1(π2+π3)+d1d22c(π2+π3)(11)
A=2p(π2+π3)2T+2cπ2π3(t1+t2)(π3d1+π2d2)2p(π2+π3)2+2π2π3c.(12)

Equations (8) and (9) imply that the country’s net foreign asset positions in each currency are determined by the expected yields (or borrowing costs), the variances and covariances of these yields, and the degree of relative risk aversion; these positions, however, are independent of the structure of transaction costs or the likely volume of exchange market transactions. In contrast, equations (10)—(13) imply that gross holdings of reserve assets will be influenced by transaction costs associated with currency conversion and reserve shortages, and by the minimum and maximum levels of potential exchange market transactions. As a result, the currency composition of foreign exchange reserves will also reflect these transaction considerations.

Empirical Model

The hypothesis that transaction needs are the principal determinants of the currency composition of foreign exchange reserves can be examined in terms of the behavior of the proportion of reserves denominated in each of the major reserve currencies. In particular, equations (10) and (11) imply that the currency composition of reserves (as represented by Ai/A) would he sensitive to the scale of transactions in a given currency relative to total transactions (as well as other variables). But the scale of exchange market transactions undertaken by the authorities would also be influenced by the nature of the exchange rate arrangements they select. For example, maintaining a fixed exchange rate might require a higher level of exchange market intervention in a particular currency than maintaining a floating exchange rate. This relationship between the currency composition of reserves, the relative scale of exchange market transactions in different currencies, and exchange rate arrangements can be represented empirically by

Ai,k,tA¯i,t=β0+Σv=1vi5β1,(vTRi,v,t/TTi,t)+Σv=1vi  5β2,(Di,v,tv/TTi,t)+Σs=15β3.sEi,s,t+μi,t,(13)

where

t = 1, …, T (number of periods)

i = 1, …, n (number of countries)

k = 1, …, 5 (number of reserve-currency countries)

s = 1, …, 5 (number of exchange rate arrangements)

Ai,k,t = reserves of country i held as assets denominated in the currency of reserve country k at time t (converted to U.S. dollars at the end of the period)

Di,v,t = debt service payments of country i denominated in the currency of reserve currency country v at time t

Ei,s,t = exchange rate arrangement of type s adopted by country i at time t

A¯i,t = total end-of-period foreign exchange reserves for country i at time t (measured in U.S. dollars)

TTi,t = sum of exports, imports, and (in the case of developing countries) debt-servicing payments

TRi,v,t = trade flows (exports plus imports between country i and reserve currency country v) at time t.

In this formulation, the proportion of a country’s reserves held in assets denominated in a particular currency is assumed to be influenced by the currency composition of both its trade flows and debt-servicing payments as well as by the nature of its exchange rate arrangements. Trade transactions denominated in a particular reserve currency are represented by the sum of imports and exports between country i and reserve-currency country v. The reserve-currency countries in this study are taken to be France, the Federal Republic of Germany, Japan, the United Kingdom, and the United States. Because the currency composition of a country’s import and export contracts need not correspond to the country pattern of its trade flows (for example, contracts for oil imports from a Middle East oil producer could be denominated in U.S. dollars), this measure can he taken as only an approximation to the true proportion of trade flows denominated in a particular currency. Despite these shortcomings, earlier studies (for example, by Heller and Knight (1978)) of the currency composition of foreign exchange reserves have found that this measure of the distribution of trade flows is a useful explanatory variable. However, the signs of the βi, v are subject to some ambiguity. Although an increase in trade flows to a given reserve currency v would he likely to lead to increased holding of reserves denominated in that reserve currency (βi,v>0), the signs of the other βi,v(iv) could be either negative or positive. For example, larger imports from reserve-currency country A could imply the need for larger holdings of reserve country B’s currency if some of these imports were priced in terms of B’s currency.

Because data on financial flows are not available for most countries, the scale of financial flows was proxied by the level of interest payments associated with the country’s external debt denominated in the different currencies. External debt was measured in terms of a country’s public and publicly guaranteed debt as reported in the World Bank’s World Debt Tables (various issues). Because these data are reported by currency of denomination, the interest payments in the different currencies were approximated by multiplying the stock of debt denominated in each currency by the six-month Eurocurrency deposit rate for that currency. Obviously, this measure captures only one component of financial flows; but, for many of the developing countries in the sample, interest payments on external debts account for a significant portion of total financial flows.

The effects of a country’s exchange rate arrangements on the currency composition of its foreign exchange reserves were represented by a series of dummy variables corresponding to the type of arrangements used by a country during each year under consideration. The arrangements were classified into categories similar to those used in the Fund’s Annual Report on Exchange Rate Arrangements and Trade Restrictions (various issues). The categories include pegging to the U.S. dollar, pegging to the French franc, pegging to a composite or other currency membership in a cooperative arrangement, and maintenance of a flexible exchange rate.14 Although the placement of countries within this spectrum of arrangements is to some degree arbitrary, these categories do reflect the employment of greater or lesser degrees of exchange rate flexibility. In the regressions, a country’s exchange rate arrangement is represented by a series of zero-one dummy variables, one for each type of arrangement. Because there is a general intercept term in each regression (the β0) and the set of exchange rate arrangements is exhaustive, one of the exchange rate dummies was excluded in each regression to avoid creating a linear dependency. The β0, in each regression therefore reflect the effects of both the excluded exchange rate arrangement and other factors not represented by trade and capital flows.

Because earlier analyses found that the behavior of the currency composition of reserves of the industrial and developing countries differed, the present study examines separate regressions for these groups. Moreover, although the World Bank reporting system for debt contains extensive information on the currency composition of the external debt of the developing countries, no such comparable reporting system exists for industrial countries. Some industrial countries do not appear to have any external debt denominated in foreign currencies (for example, the Federal Republic of Germany and Japan), but many others (for example, certain Scandinavian countries) have significant amounts of such debt. The absence of comprehensive information on the currency composition of external debt for the industrial countries means, however, that the interest payments variable has been excluded from the industrial country regressions.

This specification was estimated using data on the currency composition of foreign exchange reserves supplied to the International Monetary Fund on a regular basis by a large number of central monetary institutions. A series of five cross-section time-series regressions for each of the groups of industrial and developing countries were estimated. In these regressions, the dependent variables were the proportion of foreign exchange reserves held as instruments denominated in U.S. dollars, pounds sterling, deutsche mark, French francs, and yen. The explanatory variables were the exchange rate regime, the five variables representing trade with the reserve centers (as a proportion of total trade plus interest payments), and, in the case of developing countries, five variables reflecting the interest payments on external debt (as a proportion of total trade plus interest payments). Data from a total of 19 industrial countries and 39 developing countries were included.15 The data consist of annual observations for each country’s variables for the period 1976–85. Note that in this formulation the marginal effects of exchange rate arrangements, trade flows, and interest payments are assumed to be uniform across countries (that is, there are no country-specific parameters).16

Estimation Methods

Estimation of equation (13) using ordinary least-squares techniques would in general be inappropriate, since the dependent variable can only take values in the interval (0, 1). To illustrate the nature of the problems involved, let the standard regression model be represented by

yi=βxi+ui,(14)

where β is a k × 1 vector of unknown parameters; xi is a k × 1 vector of known independent variables, and the ui are residuals independently and normally distributed with a mean of zero and a common variance of σ2. Because the ui, are assumed to be distributed normally, this model implies that yi may take any positive or negative value, which is inconsistent with the particular dependent variable in the problem.

More appropriate for the purposes here is the censored-regression model, also known as the tobit model.17 In this particular case, the tobit model can be represented by

yi=βxi+ui(15)

if the right-hand side is greater than zero but less than unity,

yi=0(16)

if the right-hand side is less than or equal to zero, and

yi=1(17)

if the right-hand side is greater than or equal to unity, and where the β, and ui are defined as above. This model implies that the authorities decide on the share of a particular currency in their foreign exchange reserves according to the linear function in equation (15), but they hold a share of either zero or unity when that linear function indicates a negative share or a share higher than unity, respectively.

Estimation of a censored-regression model by ordinary least squares results in biased and inconsistent estimators. Maximum likelihood estimators, on the other hand, are consistent and asymptotically normal (see Amemiya (1973)). Among the various procedures available to obtain maximum likelihood estimates, we used an iteration method suggested by Fair (1977).18 Although the problem examined in this paper is strictly described by the two-limit censored-regression model in equations (15)–(17), we estimated a one-limit model because there were virtually no observations on the upper limit,19 and observations on both limits are needed to estimate a two-limit rnode1.20 Therefore, the estimated model was

yi=βxi+ui(18)

if the right-hand side is greater than zero, and

yi=0(19)

otherwise.

As indicated by Dhrymes (1986), it is convenient to have goodness of fit statistics for observations with yi > 0 that are separate from those for observations with yi = 0. For the set of observations with yi > 0, we have therefore used the square of the simple correlation coefficient between the predicted and actual values of the dependent variable (RT12).21 For the set of observations with yi = 0, we calculated the proportion of observations correctly predicted to be zero by the model (RT22) and the mean error (E¯T) for the observations for which the model incorrectly predicted yi > 0.22 To give an idea of the overall goodness of fit, we also calculated the square of the simple correlation coefficient between predicted and actual values of the dependent variable for the complete sample (RT32).23

One difficulty with the tobit maximum likelihood estimator is that it is sensitive to violations of the assumptions that its error terms have a normal distribution and are homoscedastic. The presence of either nonnormality (see Goldberger (1983)) or heteroscedasticity (see Hurd (1979)) can result in inconsistent tobit estimates. However, Powell (1986) has recently developed estimators that are robust for a wide set of nonnormal or heteroscedastic disturbance distributions. As noted by Newey (1987), Powell’s symmetrically censored least-squares (SCLS) estimator not only provides estimates of the regression parameters that are robust to failure in the normality assumption but also make feasible Hausman (1978) tests for the presence of heteroscedasticity or non-normality on the basis of differences between the tobit estimates and the SCLS estimators.

If the normality or homoscedasticity assumptions are violated, then the use of the SCLS estimator involves symmetrically censoring the dependent variable so that symmetry of its distribution about the regression (βxi) is restored, and least-squares techniques will yield consistent estimators. The nature of the SCLS procedures can he illustrated by Figure 3.24 As given in equations (18) and (19), yi=max{0,βxi+ui} (i=1,...,T). In a censored sample, for data points with ui<βxi, the value of yi is taken to be zero. In contrast to the sided (lower-bound) censoring of the tohit model, however, the SCLS procedures set yi equal to 2βxi when ui>βxi. Then the observations would have terms in the interval (0,2βxi). Because this approach assumes that the original errors were distributed symmetrically, the residuals of the “symmetrically censored” regressions will also be symmetrically distributed about zero, and the dependent variable will take on values between zero and 2βx and will be symmetrically distributed about βx (Figure 3). For such a symmetric sample, Powell (1986) derived a series of “normal” equations that allowed for the estimation of the SCLS parameter (βs) as well as their standard errors (see Appendix III for the normal equations).25

Figure 3.
Figure 3.

Symmetrically Censored Least Squares

Citation: IMF Staff Papers 1989, 002; 10.5089/9781451947045.024.A004

Source: Powell (1986, p. 1439)

In addition, Newey (1987) has shown that one can use the tobit and SCLS estimates (and their variance-covariance matrices) to derive a Hausman test statistic (h) which tests to see if the normality and homoscedasticity assumptions of the tobit analysis are violated. If β^t and β^s are the vectors of tobit and SCLS estimated parameters, then h=T(β^sβ^t)[V(β^sβ^t)]1(β^sβ^t), where T is the number of observations, V(β^sβ^t) are estimates of the asymptotic covariance matrix for T(β^sβ^t) and h will be distributed as x2 with k (number of exogenous variables) degrees of freedom. (See Appendix III for the estimate of V(β^sβ^t).) In the empirical analysis that follows the SCLS and tobit estimates are examined to see if the normality and homoscedasticity assumptions have been violated.

Empirical Results

The empirical results indicate that transaction variables and exchange rate arrangements have played important roles in determining the currency composition of foreign exchange reserves throughout the period 1976–85. The estimation results for both the developing and industrial countries for the period 1976–85 are reported in Tables 211, which appear together, for ease of comparison, following the appendices.

Developing Countries

The estimation results support the view that, for developing countries, the proportions of foreign exchange reserves held as U.S. dollars, French francs, and yen were most strongly influenced by exchange rate arrangements, especially when the country was pegged to a particular currency. For example, developing countries whose exchange rates were pegged to the U.S. dollar held significantly larger proportions of their foreign exchange reserves as dollars. In addition, countries pegged to the French franc tended to hold a much lower proportion of dollars and higher proportion of French francs. In contrast, countries pegged to other currencies or to composite indicators tended to hold significantly higher proportions of reserves denominated in the yen, which were offset by lower holdings of U.S. dollars and French francs.

These results also imply that an increase in the proportion of trade between a given developing country and a particular reserve-currency country (relative to the developing country’s total external payments) resulted in a significantly higher share of the country’s foreign exchange reserves being held in the currency of that reserve-currency country. In contrast, the cross effects of trade flows (for example, the influence of increased trade with France on the country’s holdings of U.S. dollars) showed a more mixed pattern, with some significant and positive coefficients (implying that the currencies were complements) and some negative and significant coefficients (implying that the currencies tended to be substitutes).

The proportions of interest payments on the external debt denominated in particular reserve currencies (relative to total external payments) were also a key variable in the developing country regressions. In all cases, the proportions of foreign exchange reserves denominated in a given reserve currency (except for the yen) were positively and significantly related to the proportion of interest payments denominated in that currency. Moreover, eight of the cross-effect parameters were significantly negative. These parameter estimates imply that a rise in the share of a country’s external debt denominated in a given currency (for example, the deutsche mark) resulted not only in a higher share of foreign exchange reserves held in that currency, but also in a reduction in the shares of reserves held in other reserve currencies included in the study (for example, the U.S. dollar).26

The correlation measures for both the ordinary least-squares and tobit estimators suggest that the explanatory power of these equations varies considerably for the different currencies.27 Although the regressions explained 99 percent of the observed variation in the share of foreign exchange reserves held as French francs, only 55 percent of the variation in the U.S. dollar share could be explained. The explanatory power de dined to about 50 percent, 40 percent, and 30 percent for the pound sterling, the deutsche mark, and the yen, respectively.

Industrial Countries

For the industrial countries, the absence of complete information about the currency composition of their external debt means that the regression analysis could consider only the role of trade flows and exchange rate arrangements. First, the explanatory power of the regressions for the industrial countries varied considerably. Although over 70 percent of the variability in the French franc share was accounted for by its regression (measured in terms of RT32), the proportions of variability explained for the pound sterling (51 percent), U.S. dollar (41 percent), deutsche mark (35 percent), and yen (35 percent) were lower.

In addition, these regressions suggest that, for the industrial countries, exchange rate arrangements most strongly affected the proportions of reserves held as U.S. dollars, French francs, and deutsche mark. For example, the adoption of a flexible exchange rate was accompanied by a significantly higher proportion of reserves held as U.S. dollar instruments, which was partially offset by a significantly lower share for the deutsche mark. This may reflect the option that countries with flexible exchange rates have of always intervening in U.S. dollars rather than in other currencies (as could occur under certain pegging arrangements). Similarly, participation in a cooperative agreement (for example, the European Monetary System or some of its earlier variants) resulted in a significantly higher proportion of foreign exchange reserves being held as U.S. dollars, which was offset by significantly lower proportions for the French franc and the deutsche mark. The results for the dummy variable for cooperative agreements are consistent with those obtained by Heller and Knight (1978). As they noted, these results reflect the fact that at times the countries that have been members of such arrangements as the European Monetary System (or European System of Narrower Exchange Rate Margins) have committed themselves to intervene in the U.S. dollar and to limit their holdings of other members’ currencies. As a result, a higher proportion of foreign exchange reserves was held as U.S. dollars.

In general, a higher level of trade between an industrial country and a particular reserve-currency country led the country to hold a significantly (except in the case of trade with the United States) higher proportion of its reserves in that reserve currency. The effects of an increase in trade with one reserve-currency country on holdings of other reserve currencies were more mixed, with eight negative and significant cross-effect coefficients and four positive and significant coefficients.

A Comparison of the Ordinary Least-Squares, Tobit, and Symmetrically Censored Least-Squares Estimates

Tables 211 also allow for a comparison of the estimation results for ordinary least squares based solely on the observations for which the proportions of reserves held in a given currency are nonzero, the tobit estimator, and the SCLS estimator. First, as noted earlier, the tobit estimates were derived under the assumptions that the error terms in the regression were normally distributed and homoscedastic. The test of the residuals from the tobit estimates indicates, however, that in general they were not normally distributed and homoscedastic. Thus, both the ordinary least-squares and tobit estimates were inconsistent. It is only in the case of the U.S. dollar that the hypothesis of normality and homoscedasticity could not be rejected. In part this reflects the fact that virtually all countries held some dollar-denominated reserve assets during each period. In this case, the ordinary least-squares regression on the U.S. dollar share were identical with the tobit estimates. Moreover, the point estimates of the SCLS estimator were also similar to those of the ordinary least-squares and tobit estimators, although the standard errors were smaller because of the censoring technique.

A second difference between the estimators is that the SCLS estimates often implied larger effects for trade flows and debt service payments. To the extent that the ordinary least-squares or tobit estimators are biased and inefficient, then the SCLS estimates suggest that earlier studies based on ordinary least-squares results have tended to understate the influence of trade and capital flows on the currency composition of foreign exchange reserves.

Finally, the SCLS estimates also often suggested larger effects of exchange rate arrangements on the currency composition of foreign exchange reserves.28 These exchange rate effects were most noticeable for the developing countries that pegged to a composite indicator or to some currency other than the U.S. dollar or French franc, and for industrial countries in the case where a flexible exchange rate was maintained.

III. Conclusions

This study has considered the determinants of the currency composition of foreign exchange reserves for both industrial and developing countries. On the basis of data on the currency composition of the foreign exchange reserves of individual countries, our empirical results indicate that for countries in these groups the currency composition has been influenced by each country’s exchange rate arrangements, its trade flows with reserve-currency countries, and the currency of denomination of its debt service payments. During the period 1976–85, a developing country tended to hold a greater proportion of its foreign exchange reserves in assets denominated in a particular reserve currency if its exchange rate was pegged to that currency, if a large share of its exports and imports was with the country issuing the reserve currency, and if a higher proportion of the interest payments on its external debt was denominated in this reserve currency. The currency composition of foreign exchange reserves for industrial countries was also influenced by exchange rate arrangements, although the effects were strongest for those countries that participated in cooperative agreements (for example, the European Monetary System), which tended to hold relatively higher shares of U.S. dollars. In addition, the shares of an industrial country’s exports and imports to the reserve-currency countries had significant influences on the proportion of reserves held in different currencies.

The evidence is consistent with the view that managing the currency composition of a country’s net foreign asset position is done more cheaply by altering the currency denomination of assets and liabilities that are not held as reserve assets. Although transaction costs in currency markets are low, it appears that they are high enough for central banks to find it optimal to avoid holding reserve assets in one reserve currency that must be converted into another reserve currency before it can be used to make payment. This, in turn, suggests that inferences about the stability of preferences for net currency positions on the part of governments cannot be drawn from an analysis of reserve holdings in isolation from the rest of the government’s financial portfolio.

APPENDIX I Data Sources

Data on foreign exchange reserves were obtained from the International Monetary Fund’s survey of the currency composition of members’ foreign exchange reserves. To maintain the confidentiality of the data file, all regressions were run “blind," without any country specific parameters.

Exchange rate arrangements were classified according to the system used in the Fund’s Annual Report on Exchange Arrangements and Exchange Restrictions (Washington, various issues). The classifications prevailing at the end of 1985 were extended back through the period beginning in 1976.

Data on exports and imports were taken from the Fund’s Direction of Trade Statistics data file.

For external debt, the currency denomination of public and publicly guaranteed debt was taken from the World Bank’s World Debt Tables (Washington, various issues).

Eurodollar six-month deposit rates were taken from the Fund’s International Financial Statistics (Washington, various issues).

APPENDIX II First-Order Conditions for Optimal Net and Gross Foreign Asset Portfolio

Selecting N1, N2, A1, and A2 so as to maximize equation (7) of the text yields

UN1 =r1+d1r2+d22bN1σr12+2b(WN1)σr222b(WN1)σr1r2+2bN1σr1r2=0(20)
N2=WN1(21)
UA1=d12π2c(A1t1)+2(π2+π3)p(TA1A2)=0(22)
UA2=d22π3c(A1A2)+2(π2+π3)p(TA2A2)=0.(23)

Equations (20) and (21) imply equations (8) and (9) in the text. Equations (22) and (23) imply that

A1t1=π3π2(A2t2)+d2+d12π2c,(24)

or, using A = A1 + A2, that

A1=π3A+π2t1π3t2(π2+π3)+d2d12c(π2+π3)(25)
A2=π2A+π3t2π2t1(π2+π3)+d1d22c(π2+π3).(26)

Thus, for a given total level of reserves, the holdings of a particular currency depend on the expected amount of transactions in that currency in comparison with the expected amount of transactions in other currencies, on the cost of converting from one currency to another, and on the differential net costs of borrowing reserves in the different currencies. Note that, from the assumed distribution of transactions,

E(T1)=(π1+π2)t1+π3(Tt2)(27)
E(T2)=(π1+π3)t2+π2(Tt1),(28)

so that E(T1) increases with t1 and declines with t2, whereas the opposite occurs with E(T2).

Replacing equations (25) and (26) in either equation (22) or equation (23), it is possible to solve for the total level of reserves A. Thus,

A=2p(π2+π3)2T+2cπ2π3(t1+t2)(π3d1+π2d2)2p(π2+π3)2+2π2π3c.(29)

APPENDIX III Calculation of Symmetrically Censored Least-Squares Estimates

As shown in Powell (1986), the SCLS estimates must satisfy

β^s=[Σt=1T1(β^sxt>0).xtxt]1Σt=1T1(β^sxt>0).min{yt,2βs^xt}x1,(30)

where xt, is the vector of independent variables at t:

1(A)=1

if A is true, and

1(A)=0

otherwise.

The procedures starts with the tobit estimates of the β and uses them to calculate the right-hand side of equation (30). This implies an initial vector of β^s0. The right-hand side of equation (30) was then recalculated using this value of β^s0. The iterations were continued until the largest difference between any element in the old and new values of β^s was less than 10-6. Between 12 and 60 iterations were required to calculate the β^s for the different currencies.

The variance-covariance matrix for the SCLS estimates was calculated as

V(β^s)=1TC^T1D^tC^T1,(31)

where T is the sample size:

C^T=1TΣt=1T1(0<yt<2β^sxt)xtxt
D^T=1TΣt=1T1(β^sxt>0)min(u^t2,(β^sxt)2)xtxt
u^t=ytβ^sxt.

The test statistic (h) for the test of normality and homoscedasticity of the error terms was calculated (see Newey (1987)) as

h=T(β^sβ^t)[V(β^sβ^t)]1(β^sβ^t),(32)

where βs are the SCLS estimates and βt are the tobit estimates. The V(βsβt) matrix was calculated following the procedures described in Newey (1987, pp. 129–30, equation (3.6)).

Table 2.

Determinants of Central Bank Holdings of Reserve Currencies: Developing Countries, 1976–85

(Portion of foreign exchange reserves denominated in U.S. dollars)

article image
article image
Note: Developing countries whose currencies are pegged to the French franc are excluded; figures in parentheses are t-ratios. Other symbols are defined in the text.

External payments is defined to equal the sum of exports and imports plus debt service payments.

One percent of the time, a X2 with 13 degrees of freedom will exceed the value of 27.7.

Table 3.

Determinants of Central Bank Holdings of Reserve Currencies: Developing Countries, 1976–85

(Portion of foreign exchange reserves denominated in French francs)

article image
article image
Note: Figures in parentheses are t-ratios. Other symbols are defined in the text.

External payments is defined to equal the sum of exports and imports plus debt service payments.

One percent of the time, a X2 with 14 degrees of freedom will exceed 29.1.

Table 4.

Determinants of Central Bank Holdings of Reserve Currencies: Developing Countries, 1976–85

(Portion of foreign exchange reserves denominated in pounds sterling)

article image
article image
Note: Developing countries whose currencies are pegged to the French franc are excluded; figures in parentheses are t-ratios. Other symbols are defined in the text.

External payments is defined to equal the sum of exports and imports plus debt service payments.

One percent of the time, a X2 with 13 degrees of freedom will exceed the value of 27.7.

Table 5.

Determinants of Central Bank Holdings of Reserve Currencies: Developing Countries, 1976–85

(Portion of foreign exchange reserves denominated in deutsche mark)

article image
article image
Note: Developing countries whose currencies are pegged to the French franc are excluded; figures in parentheses are t-ratios. Other symbols are defined in the text.

External payments are defined to equal the sum of exports and imports plus debt service payments.

One percent of the time, a X2 with 13 degrees of freedom will exceed the value of 27.7.

Table 6.

Determinants of Central Bank Holdings of Reserve Currencies: Developing Countries, 1976–85

(Portion of foreign exchange reserves denominated in yen)

article image
article image
Note: Developing countries whose currencies are pegged to the French franc are excluded; figures in parentheses are t-ratios. Other symbols are defined in the text.

External payments is defined to equal the sum of exports and imports plus debt service payments.

One percent of the time, a X2 with 13 degrees of freedom will exceed the value of 27.7.

Table 7.

Determinants of Central Bank Holdings of Reserve Currencies: Industrial Countries, 1976–85

(Portion of foreign exchange reserves denominated in U.S. dollars)

article image
article image
Note: Figures in parentheses are t-ratios. Other symbols are defined in the text.

Total trade is measured as the sum of exports and imports.

One percent of the time, a X2 with 8 degrees of freedom will exceed the value of 20.1.

Table 8.

Determinants of Central Bank Holdings of Reserve Currencies: Industrial Countries, 1976–85

(Portion of foreign exchange reserves denominated in French francs)

article image
article image
Note: Figures in parentheses are t-ratios. Other symbols are defined in the text.

Total trade is measured as the sum of exports and imports.

One percent of the time, a X2 with 8 degrees of freedom will exceed the value of 20.1.

Table 9.

Determinants of Central Bank Holdings of Reserve Currencies: Industrial Countries, 1976–85

(Portion of foreign exchange reserves denominated in pounds sterling)

article image
article image
Note: Figures in parentheses are t-ratios. Other symbols are defined in the text.

Total trade is measured as the sum of exports and imports.

Less than 0.01.

One percent of the time, a X2 with 8 degrees of freedom will exceed the value of 20.1.

Table 10.

Determinants of Central Bank Holdings of Reserve Currencies: Industrial Countries, 1976–85

(Portion of foreign exchange reserves denominated in deutsche mark)

article image
article image
Note: Figures in parentheses are t-ratios. Other symbols are defined in the text.

Total trade is measured as the sum of exports and imports.

One percent of the time, a X2 with 8 degrees of freedom will exceed the value of 20.1.

Table 11.

Determinants of Central Bank Holdings of Reserve Currencies: Industrial Countries, 1976–85

(Portion of foreign exchange reserves denominated in yen)

article image
article image
Note: Figures in parentheses are t-ratios. Other symbols are defined in the text.

Total trade is measured as the sum of exports and imports.

One percent of the time, a X2 with 8 degrees of freedom will exceed the value of 20.1.

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