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The Demand for International Reserves and Their Opportunity Cost

Author(s):
International Monetary Fund. Research Dept.
Published Date:
January 1989
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Monetary authorities hold international exchange reserves for reasons that arise out of their policy priorities and economic circumstances. These reasons include financing cyclical and seasonal external payments imbalances to smooth current consumption, intervening in exchange markets, and providing a buffer to cushion the economy against future exigencies.

Understanding the motivation for reserve holding is an important part of analyzing and predicting how far individual countries will be able to withstand payments shocks and, by extension, the interaction among the reserve holdings of individual countries and international financial conditions. Despite a considerable literature on the determinants of reserve holdings by different groups of countries, some aspects of reserve behavior are ill understood. After such structural shifts in conditions in reserve markets as the advent of floating exchange rates, for example, and the financial market disturbances of the early 1980s, it was widely expected that countries would make a large adjustment in the level of their reserves. But most studies show a relatively stable long-run demand for reserves since the 1960s.1

In an effort to increase understanding of how reserves function, this paper reports empirical work showing that the reserve holdings of countries that also borrow on international capital markets—particularly of countries that have debt-servicing difficulties—are significantly affected by the cost of holding these assets. When a country’s reserve holdings are assessed in terms of the interest rates it pays on international borrowing, two conclusions emerge: international reserves can be costly to hold, and they are vulnerable to changes in international financial markets. When international interest rates rise and spreads increase, according to the results of this analysis countries economize on reserves. When, in particular, the range of spreads expands so that the less creditworthy countries face higher borrowing costs, these countries, which are shown by the analysis to be more responsive to international borrowing costs than others, will adjust reserve holdings more quickly. The result is that those economies with the greatest need for reserves economize more than others on their holdings when international financial markets are tight.

Theory has traditionally argued that, unlike money demand by individuals, the motivation for a country’s reserve demand is based not on the need of domestic residents to meet payments for current transactions in foreign exchange, which is met by commercial banks and foreign exchange dealers, but on the need of the national monetary authorities to have a cushion to dampen the impact of future shocks on the domestic money supply (see Heller (1966)). A country’s demand for reserve holdings is conceptually equivalent to an individual’s precautionary money demand; it is a positive function of wealth and of the cost of covering an unplanned deficit and a negative function of returns on other assets.2 Traditional analysis, therefore, has included in reserve demand equations some scale factor (such as imports), some measure of potential payments fluctuations, and a proxy for the cost of adjustment (such as imports as a ratio of gross national product, GNP).3 The proposition was that the precautionary need for reserves arose out of the payments identity, which required some balancing item to cover deficits on the trade and capital accounts.

Although the opportunity cost of reserve holdings was recognized as important in theory, the measures chosen were found not to be empirically significant. Virtually every study that included a measure of forgone investment—such as the domestic discount rate or the international bond rate—to proxy the opportunity cost of reserve assets found that all determinants except the opportunity cost measure were significant.4

The present analysis begins with two propositions: first, that when the opportunity cost of reserve holdings as assets is appropriately defined, it should be a significant independent determinant of the demand for reserves; second, that the appropriate opportunity cost is the interest rate on the individual country’s international liabilities less the interest rate on the short-term liquid assets that countries typically hold as reserves.

The empirical results reported in this paper extend and update work by Edwards (1985a, b) that also included a net opportunity cost concept in a regression for reserve demand, defined as the gross forgone income from holding one unit of reserves less the return on investing that unit. In a regression based on data for 17 countries for 1976-80, this opportunity cost concept was found to be significant and of the correct sign. Edwards defined gross forgone income as a country’s international borrowing cost, on the principle that countries borrow abroad as long as the cost of borrowing is less than or equal to the social marginal product of the funds when invested.

The rest of this paper is organized as follows. Section I presents the theoretical basis for the empirical work, and Section II reports the results. A concluding section highlights some of the implications of the sensitivity of reserve holdings to international borrowing costs. Data definitions and the country composition of the sample are given in appendices.

I. Theoretical Foundations

Countries are assumed to minimize the total costs of reserves held as a precaution against future payments shocks by minimizing and equating in equilibrium two types of cost: the cost of holding reserves in terms of forgone domestic credit expansion and the cost of reserves held as an asset. The first cost can be defined as the cost of the adjustment that would occur if, with the money supply held constant, the country assigned the marginal unit of foreign exchange earnings to reserves instead of to increased domestic credit. The opportunity cost of reserves as assets is the cost of holding the marginal unit of foreign exchange earnings as reserves instead of repaying the marginal unit of debt. It is assumed, therefore, that countries minimize the following equation:

where TC is total costs; E is the expectations operator; r is the net opportunity cost of forgone debt repayment; R is the level of nongold foreign exchange reserves held by the monetary authorities; D is the gross payments deficit; MPM is the marginal propensity to import; [(D — R)/MPM] is the cost of a forgone reflation of the economy; and p(D) is a random function reflecting the probability of the deficit occurring.

To deal with each of these terms in turn, the net opportunity cost of holding reserves in terms of debt repayment is defined here as the gross average unit cost of a country’s borrowing on international markets (denominated in U.S. dollars) less the average unit return from reserves invested in short-term, secure, and liquid investments in money-center instruments.

Because reserves are an asset, theory would suggest that they should be costed at the marginal rate of the highest-yielding alternative asset in which they might be invested. In principle—with perfect capital markets, free entry, and otherwise perfectly competitive conditions—yields would be equalized, given exchange rate changes, across all assets, domestic and foreign. In practice, yields differ, reflecting differing perceptions of risk on the part of lenders, differing needs for liquidity by borrowers, differing expectations about relative exchange rates and inflation rates, and so on. The cost of a syndicated loan to a given country consists of the basic interbank rate (LIBOR—the London interbank offered rate—which can be a three-month, six-month, or an annual rate) plus a spread set for the maturity of the loan (which varies by borrower). It is the spread over LIBOR that varies according to market perceptions of the creditworthiness of the borrower. There are also loan-associated fees for the borrower—participation fees, the praecipium (paid to the lead bank of a syndicate), and front-end fees. But because all studies on these fees conclude that they form a stable share of the spread, the assumption will be made that they can be ignored, since they change all costs by a constant.5

Between 1978 and 1986 every country in the sample (except the debt countries after 1982, which were excluded from the analysis for that period) contracted sovereign loans over the period examined. Whether or not these countries borrowed abroad to finance reserves directly (which is difficult to ascertain), at any given time all countries held both reserves and some debt intermediated by the international banking system.

The rate on U.S. dollar-denominated borrowing was taken to be representative of the opportunity cost of reserves, since the information available on the currency denomination of reserve holdings shows that the majority are indeed denominated in dollars.6 In addition, a significant percentage of international transactions that gives rise to precautionary demand for reserves is also made in dollars. Most international borrowing was in dollars over this period and required servicing in dollars. Again, individual country data are difficult to obtain, but the Bank of International Settlements (BIS), in its quarterly reports, shows that the bulk of transactions filed by its reporting banks is in dollars.7 As for the current account, a large number of commodities traded have prices quoted in dollars. Because it makes sense for countries to hold dollar reserves against prospective dollar liabilities, it is assumed to be appropriate to use the interest rate on dollar assets as the opportunity cost of holding these reserves. Given the competitiveness of the international financial markets, it is also reasonable to assume that returns on assets denominated in different currencies are equated at the margin.

The assumption that international borrowing rates are the appropriate definition of the opportunity cost measure calls for some elaboration. When some reserves are borrowed and borrowing rates are higher than marginal returns on domestic investment, the marginal cost of borrowed funds will clearly raise the average cost of any reserves that are owned, and the definition of the opportunity cost measure arises directly from asset theory. But it is argued here that even when reserves are not borrowed, but the government issues or guarantees international liabilities, the value to the monetary authorities of paying off these liabilities on time will always be higher than investing domestically, even where the marginal returns on domestic capital are higher than those on foreign borrowing. There are benefits to the authorities of maintaining the country’s credit standing in international markets by repaying foreign liabilities on schedule, and there are costs to not doing so. The advantages of timely repayment for the authorities are continued access to financial and trade credit and to swaps with other monetary authorities; these benefits raise the effective cost of the nonrepayment of foreign liabilities. Thus, on the assumption that the authorities aim to equalize marginal returns on all assets, domestic and foreign, they will pay off external debt before investing domestically.8

The opportunity cost chosen is the prevailing quarterly average market interest rate on syndicated loans to a given country (weighted by the size of the loan) less returns on investing reserves. The issue arises whether marginal rates would be more appropriate.

An examination of the average spreads on loans to selected countries between 1978 and 1986 shows that there is evidence that countries believed to be more risky than others were charged higher spreads. Table 1 shows that Australia, Norway, and the Republic of Korea were, in the early years, generally able to borrow more cheaply than the Philippines (which was to have an official debt rescheduling in early 1985) and Mexico (which was to have an official rescheduling in mid-1983). However, this was not consistently so. During 1981, when Mexico’s debt problems were already in the news, it was borrowing at about the same rate as Korea. (There is a possibility of tags in reporting syndications, but it is unlikely that these would have been consistent, particularly given the interest in the loan markets in the financial journals at the time.) In the first quarter of 1982, when articles were being published about the possibility of Mexico’s inability to repay its debt, it was being charged only 0.04 percent more than Australia. Nor did spreads seem to rise systematically with the size of the loans being made. In the fourth quarter of 1981, for example, Colombia borrowed almost $200 million more than in the third quarter, but at a spread that was 4 basis points lower. In the first quarter of 1982, it borrowed $300 million less, at a spread that was 4 basis points higher.

Table 1.Spreads on Syndicated Borrowing, Selected Countries

(Quarterly averages of spreads over six-month LIBOR)a

Year and QuarterNorwayAustraliaIndiaRep. of KoreaColombiaMexicoPhilippines
1978:10.691.000.901.501.301.07
21.650.881.001.251.341.111,02
30.720.820.911.351.071.05
40.970.900.890.89
1979:10.580.640.731.000.770,97
20.570.610.570.970.800.95
30.920.721.140.630.96
40.610.750.690.740.770.82
1980:10.540,550.520.780.650,600.78
20.640.750.840.621.00
30.700,580.920,810.540.79
40.530.650.550.870.690,660.90
1981:10.600.480.460.900.730.841.04
20.640.410.620.630.510.88
30.630.440.700,650.740.75
40.380.500.350.660.610.710,77
1982:10.460.70-0.630.650.740.97
20.360.410.590.931.050.83
30.670.470.420.610.501.621.01
40.610.450.380.580.250.94
1983:11.000.580.490.680.99
20.760.760.791.001.04
30,890.500.731.63
40.560.700.470.76
1984:10.380.750.380.751.63
20.380.751.62
31.410.380,681.63
40.450.420.58
1985:10.150.681.75
20.810.260.65
30.250.240.52
40.260.060.58
1986:10.100.61
20.100.56
30.370.150.290.58
40.190.380.38
Source: Bank of England.Note: Mexico had a rescheduling agreement in August 1983, and the Philippines requested an extension for payments on principal in early October 1983.

London interbank offered rate.

Source: Bank of England.Note: Mexico had a rescheduling agreement in August 1983, and the Philippines requested an extension for payments on principal in early October 1983.

London interbank offered rate.

In addition to inconsistencies in the links between higher spreads, loan amounts, and risk, spreads on loans to all countries followed similar fluctuations over time, suggesting that more general forces were at work. Even the selected data show peaks around late 1978 and early 1979, with a trough a year later, and rates picking up again over the next six to nine months. It has in fact been argued (see Johnston 1982) that international banking activity is more sensitive to domestic banking conditions in the main industrial countries than to circumstances in the international markets.9

Following most work on international capital markets, therefore, it is assumed that these markets are competitive and that an individual monetary authority determining borrowing costs for reserve accumulation can take the average interest rate on syndicated loans as the gross cost, without being concerned about the marginal impact of the new loan on spreads.

Finally, the rate on short-term U.S. Treasury bills was taken to represent returns on the investment of reserves. The legislation underlying the management of the reserve holdings of many central banks specifies treasury bills as an example of the type of secure, liquid asset in which the holdings should be invested.10

The cost of reserve holdings in terms of deflation is measured by [(D - R)/MPM], where D - R is the net deficit (the deficit less use of reserves) and MPM is the marginal propensity to import.

The conceptual basis for using the net deficit as the cost of reserve holding (following Heller (1966)) derives from the primary purpose of reserves—to protect current consumption from payments shocks, defined here as a shock to the current account. When a deficit emerges, the authorities could either add the marginal unit of foreign exchange earnings to reserves or they could use it to finance the deficit. If they choose to do the former, the cost of doing so is the cost of the deflation that the country has to undertake to reduce the imbalance by one unit of foreign exchange. Given an initial equilibrium at full employment, if foreign demand for exports falls and an imbalance arises, expenditures either can be switched from tradable to nontradable goods or can be reduced.

Switching can occur by changing the exchange rate or altering domestic prices on specific tradable goods by means of tariffs or subsidies. Such price changes entail substitution and income effects on consumption, which may or may not be partially offsetting, as well as welfare costs. They also lead to factor reallocation and, often, create uncertainty that feeds back into capital flows. As a result, the net costs of switching expenditures are difficult to assess in a given country.

The costs of reducing an imbalance are more accessible to analysis. If one assumes initial payments equilibrium at full employment and abstracts from exchange rate actions, a fall in export demand can be measured in terms of forgone domestic consumption if the deficit is not financed by drawing down reserves or borrowing. This cost can be seen as similar to the cost imposed on an economy by money hoarding and can be derived directly from the money identity, in which the authorities are assumed to be holding the money supply constant, perhaps to prevent the payments position from further deteriorating.

The size of the deflation imposed by a current account deficit is expressed in terms of the country’s marginal propensity to import. For an open economy, the loss from lower export demand is far less than for a closed economy. This loss can be expressed as the reciprocal of the marginal propensity to import (see Heller (1966, p. 297)). One can, therefore, identify the opportunity cost to a country of reserves withheld from credit creation given a payments deficit as being the net imbalance, D —R (the deficit less reserve use), as a ratio of the marginal propensity to import, 1/MPM.

The concept of deflation cost must be qualified by the probability that a given country will incur an imbalance. Let the probability distribution of expected net deficits (D) be a continuous random variable and be defined over some positive range,

D and D,

or, more formally,

Let the function have a mean of zero and a dispersion defined by the standard deviation. Given the probability density function p(D), the probability distribution function can be defined as

with

Because costs are only positive where deficits are greater than reserve holdings, the total expected costs of reserve holdings are defined as

where

rR =the opportunity cost in terms of forgone debt repayment

r =the borrowing cost less the investment cost, which is given

(D — R)/MPM =the deflation cost of forgone credit expansion.

The lower bound of the integral, R, is where a country is assumed to be in payments balance, since it incurs no deflationary costs where reserve holdings are greater than or equal to the payments deficit. The upper bound is the size of the random payments deficit D, which could go to infinity.

Using Leibniz’s rule11 and differentiating with respect to R yields

from the first-order condition for minimum total costs. The second derivative is positive,

so the minimum is a true one.

From the minimization equation,

and the reserve demand equation can be derived as

To derive the signs of the determinants of reserve holdings, consider changing the riskiness of the probability distribution while preserving the mean of the original (see Rothschild and Stiglitz (1970, pp. 225-43)). Graphically, Figure 1 shows p(D) as the original probability function and p* (D) as the new, mean-preserving function. Then, for a given r and MPM, it can be seen that, if D was the original deficit (and, therefore, R the original optimum reserve holdings), the new distribution has caused [1 - P(R)] to increase. To maintain equality with the right-hand side of the equation, P(R) must also increase. Therefore, when the risk of a deficit rises, reserve holdings must also rise. Similarly, when either r or MPM rises, [1 — P{R)] must also rise, and P(R) and R thus must fail.

Figure 1.Original and More Risky Probability Distribution with Mean-Preserving Spread

More formally, let

be the new riskier distribution that preserves the original mean, where

with

Substitute in the equality condition

and totally differentiate

such that

The positive sign on the final equation comes from the fact that G(R) must be negative if the mean of the spread is to be preserved as the riskiness of the function increases. From Figure 1, with p*(D) flatter than p(D), the original hatched area under the curve above R must fall at the peak of the distribution if the area in the tails is to increase. This loss is captured by G(R). Thus, when risk rises, reserves also increase.

To derive the sign of r, totally differentiate the equality condition again:

so that

and

Reserves fall when the borrowing cost rises.

Similarly, to derive the sign of MPM, differentiate the equality condition totally:

so that

and

Reserves fall when the marginal propensity to import rises because this reduces the cost of deflation in terms of output of home goods.

This relationship makes sense; it is reasonable to assume that reserves increase when the average absolute magnitude of past imbalances rises, fall as the opportunity cost of reserves rises, and fall as a country’s marginal propensity to import rises, since, as explained earlier, the cost of a deficit in terms of home goods falls.

There is one further qualification, however, to make to equation (3). It is an empirical fact that reserve holdings increase with the scale of imports—whatever the marginal propensities, the absolute size of the demand for foreign exchange is an important factor.12 (This is the conceptual equivalent of wealth in precautionary money demand equations.) The final specification of the equation to be tested for the sample group of countries over the period 1978-86 is

where

and where Imp is the scale variable (here proxied by imports), VARB is the proxy for the entire distribution of the function that captures the probability of deficits occurring, r (or net rate) is the net borrowing cost on international markets, and MPM is the marginal propensity to import. (See Appendix I for details on the data used to estimate the regression.)

II. Estimation and Results

Two approaches have been used in the literature to estimate reserve demand: the first assumes that adjustment to determinate desired reserve levels occurs in the estimating period (Frenkel (1974) and (1983), and Frenkel and Hakkio (1980)), whereas the second assumes a slower adjustment process in which changes in actual reserves reflect the gap between desired and actual levels (Bilsen and Frenkel (1979), Edwards (1980, 1984)). (The determinants of reserve demand were very similar in each approach.) Both approaches have yielded significant results. This study, following the findings of recent literature on the speed of adjustment of reserves (see Edwards (1980)), uses the “equilibrium” approach and estimates reserve demand directly. The level of reserves rather than the rate of change was estimated, on the principle that reserve demand is demand for a stock rather than a flow.13

The equation was tested according to pooled cross-section methodology on the principle that determinants of reserve holdings have not shifted over the time period considered. The available evidence shows that the most important influence on reserve management is the maintenance of a currency mix appropriate to the pattern of foreign trade and external debt; since trade patterns and creditors do not change very rapidly, this supports the assumption that pooled analysis is appropriate (Group of Thirty (1982)). Ordinary least-squares (OLS) regressions were used with dummy variables to capture individual country characteristics. Although the constant-slope assumption of OLS regressions seems reasonable—the sensitivity of reserve demand to its independent determinants is not expected to change a great deal among countries or over time—it seems unreasonable to expect the intercept to remain constant among countries because these will have different demands for reserves as a result of different policy priorities and structural conditions (Pindyck and Rubinfeld (1981, pp. 254-55)).

Several authors have argued that reserve holdings are used by banks in determining the spreads to be charged to individual countries, and others have noted that countries manipulate published reserve figures to control borrowing costs.14 This points to possible simultaneity between reserve holding and borrowing costs and would suggest that OLS regressions would produce biased estimators. It was difficult, however, to select a cross-country sample of proxy variables that were highly correlated with borrowing costs and uncorrelated with the error term that would not lead to important information loss under the instrumental-variables technique. Moreover, the advantage of this technique was not relevant for this study: it yields consistent estimates as the sample size becomes large, and this test involved a maximum of 20 observations for 24 countries and a minimum of 20 observations for 6 countries (the industrial country group). For all these reasons, OLS was used.

Finally, these propositions were tested for the years 1978-86 for 24 countries falling into three main economic categories: a sample of non-reserve-center industrial countries, some developing countries that were not to develop debt-servicing problems after 1982, and some developing countries that were to develop such problems for the years 1978-82. After 1982, this last group was credit rationed, and the rate at which it borrowed was not a market rate and could not, therefore, be used as an independent determinant of reserve holdings. (See Appendix II for a list of sample countries.) The sample countries were chosen on the basis of available quarterly data; the core group of countries had no more than two sequential missing observations in the syndicated loan series. Reserve-currency countries were excluded because they have a demand for reserves that depends on that of other countries and cannot be compared with reserve demand in non-reserve-currency countries.15

The pooled cross-section analysis was initially applied to quarterly data on the entire sample of countries for 1978-82 (Table 2). Highly significant results are shown for all the variables chosen. Most of the signs are as predicted. MPM, the ratio of imports to gross domestic product (GDP) or to gross national product (GNP), the proxy for the marginal benefit to a country from holding reserves (measured in terms of the cost of the deflation that would otherwise occur), is, as predicted, consistently negative. Imports (Imp) are consistently and strongly positive; the higher the level of foreign exchange needed for imports, the higher the level of reserves demanded. And the opportunity cost of holding reserves (“net rate” in the table) has a consistently negative effect on reserve holdings.

The one surprising result is the sign of the variability of past reserves in the generalized least-squares (GLS) and first OLS regression (0LS1), in which reserves decline as reserve variability rises. This result seems counterintuitive. However, in the OLS regression the variable is insignificant, so that the sign is immaterial, whereas, as will be shown below, the GLS regression is the least satisfactory explanation of reserve demand of all those tested.

Three regressions were run on the entire sample. The GLS regression, the least constrained, had a low R2, even for cross-section analysis. It seemed that a more constrained regression might be more appropriate and give stronger support for the hypothesis. Constraining the constants of all countries to be the same through the OLS regression (OLS\ in Table 2) gave a respectable fit in terms of R2, and the F-statistic improved.

Plots of the reserve levels indicated some correlation from observation to observation; this could be due to qualitative determinants of reserve demand that were constant over time for each country, perhaps to do with institutional objectives for reserve holdings that were not captured by the other variables. A country relying for a large share of its foreign exchange earnings on remittances (for example, from low-skilled migrant labor, which fluctuates with labor demand in host countries) and with little access to international capital markets would justifiably consider that it needed higher reserves than a country with diversified exports and ready access to foreign capital markets. These “structural” needs for reserves are country specific, they tend not to vary over time, and, following the model developed by Balestra and Nerlove (1966), they can be captured by an “error-components” adjustment to the OLS equation that consists of using country dummy variables.

Table 2.Determinants of Reserve Demand: Pooled Cross-Section Results for Full Sample, 1978-82 and 1978-8
RegressionVARBMPMImpNet RateR2F
GLS-0.06297**-1.12898**1.25925**-1.13494**0.476.8
(5.5413)(-9.1994)(15.7135)(-4.71657)
OLS1-0.61258-0.8461**0.81241**-0.33**0.6161.6
(-1.4112)(-12.926)(21.5712)(-2.596)
OLS20.5629**-0.6375**0.74579**-0.22718**0.9135.9
(7.4539)(-3.3884)(7.6656)(-3.2147)
OLS30.2962**-0.6175**0.53759**-0.1213**0.9229.9
(5.3264)(-6.9204)(8.6696)(-3.0248)
>Note: GLS is a generalized least-squares regression. OLS I is a straightforward ordinary least-squares regression on the entire sample for 1978-82. OLS2 is the ordinary least-squares regression adjusted for country-specific dummies. OLS 3 is OLS2 run on all countries less the debt-problem group for 1978-86. All data are in natural logarithms and denominated in U.S. dollars. Observations are quarterly; (-statistics appear in parentheses; ** indicates significance at the 1 percent level; ff2 is the adjusted coefficient of determination; the F-statistic measures the ratio of the explained to the unexplained variance of the regression. See Appendix I for definitions of variables and Appendix II for sample countries.
>Note: GLS is a generalized least-squares regression. OLS I is a straightforward ordinary least-squares regression on the entire sample for 1978-82. OLS2 is the ordinary least-squares regression adjusted for country-specific dummies. OLS 3 is OLS2 run on all countries less the debt-problem group for 1978-86. All data are in natural logarithms and denominated in U.S. dollars. Observations are quarterly; (-statistics appear in parentheses; ** indicates significance at the 1 percent level; ff2 is the adjusted coefficient of determination; the F-statistic measures the ratio of the explained to the unexplained variance of the regression. See Appendix I for definitions of variables and Appendix II for sample countries.

The OLS regression was therefore adapted to include country-specific dummies, and the results are shown in Table 2 as OLS2. This regression gives the best results. Adding the dummies increases the fit in terms of R1 to 0.9, and the F-statistic shows a significant ratio of explained to unexplained errors.

This adjusted OLS equation was also used to see if the opportunity cost variable (“net rate”) was significant for the longer time period, 1978—86, shown as OLS3 in Table 2. The regression over the earlier period had assumed that no countries in the sample faced credit rationing, so the spread plus LIBOR could be taken to be the unconstrained market rate at which they could borrow. This assumption was supported by the Bank of England data on spreads on syndicated loans, which contained observations for all countries for almost every quarter. For no country were there more than two sequential quarters with no observations. For the regression over the longer period, the debt-problem countries had to be dropped. This group consisted of those that had debt reschedulings after 1982. Logically enough, many countries in this group received no—or very few—syndicated loans after that year, and the Bank of England reports no spread data for them. As the results for OLS3 in Table 2 show, for the 12 countries in the sample that had consistent access to credit markets between 1978 and 1986, all variables were highly significant and of the expected sign; the R was high, and the F-statistic was respectable.

Note that in this study, the sign on the coefficient of the average propensity to import (MPM) is consistently negative, as predicted, and the variable itself is consistently significant. This finding contrasts with the results in other studies, in which the average propensity to import frequently turned out to be positive and was interpreted as a measure of the openness of the economy (see Hippie (1974) and Iyoha (1976)). Actual results for this variable were, therefore, generally contradictory in the literature, with coefficients often approaching zero.

It is helpful to look at the relative importance of the four determinants for the level of current reserves. The beta coefficients in the regression run without the country-specific dummies show imports and the net rate variable to have the strongest impact on reserve holdings. These variables are also the most important ones when the regression is run for all countries up to 1982 with country dummies. The results by country grouping for this last regression show that reserves in the industrial countries were affected most by current account variability and imports, whereas reserve holdings of developing countries without debt problems were influenced more by current account variability and imports scaled by GDP or GNP. Reserves in countries that were to develop debt problems, however, were predictably more strongly affected by the net rate variable than by any other. When the regression was rerun for the sample group without the debt countries, the beta coefficient on the net rate variable was somewhat higher than that on the other variables.

In an effort to isolate the importance of different variables in the reserves demanded by different country groups, classified by income and debt vulnerability, the pooled cross-section analysis was run separately on these groups for the three first regressions on quarterly data for 1978-82 (Table 3). The country groups used were an industrial country group (group 1 in the table), a group of developing countries without debt problems (group 2), and a group of developing countries that were to develop debt problems after 1982 (group 3). Again, the test statistics are in general more satisfactory for the adjusted OLS regression (OLS2) for each group.

The significance of the variables, however, differs in interesting ways from those of the regressions on the entire sample (OLS1). In general, all significant variables are of the predicted sign except, as in the regression on the entire sample, for the variability measure (VARB) in the GLS equation. The disaggregated regression, however, shows that the counterintuitive negative sign on this variable comes from the nondebt developing countries, which seem to reduce their reserves as their past variability increases. Since the cost of deflation also induces reserves to fall, whereas the level of imports causes them to rise, these countries act as predicted otherwise. Because the nondebt developing countries generally had ready access to syndicated markets over the period, the unexpected sign on the variability measure in the GLS regression might be capturing the effect of a downward shift in their reserve demand schedules as their ability to borrow reserves rose. But, as noted earlier, the GLS equation is the weakest of those tested, so it would seem reasonable not to place too much weight on this result.

One striking difference between the results for the country groups and those for the entire sample is the significance of the net rate—the opportunity cost measure. Only for those countries that would encounter debt problems after 1982 is it significant, and for these countries it is highly and consistently significant across all regressions. For two out of the three regressions, both imports scaled by GNP (MPM) and imports (Imp) are also significant; for the third, OLS2, only imports are otherwise significant. Out of all the country groups, the opportunity cost measure is least significant for those countries that would not encounter debt problems later in the adjusted OLS regression.

Table 3.Determinants of Reserve Demand by Country Groups, 1978-8
RegressionVARBMPMImpNet RateR2F
GLS
10,0788**0.31280.36774-0.27590.423.2
(3.8185)(1.0732)(1.5181)(-0.8434)
2-0.0643**-0.8957**1.06379**-0.1450.651.4
(-5.7863)(-6.248)(7,9472)(-0.5066)
30.003-1.5122**1.241**-1.6383**0.545.0
(0.140)(-7.307)(8.407)(-3.841)
OLS1
10,4126**0.178970.7281**-0.28610.642.0
(4,69)(1,0183)(8.454)(-0.1456)
2-0.1956**-0.107**0.77447**0.106870.649.7
(-3,5238)(-13.1365)(9.2179)(0.6008)
30.2452-0.7956**0.7435**-0.72096**0.553.8
(0.289)(-6.104)(10.4644)(-3.073)
OLS2
10.937**-0.1109**0.98015**-0.64770.9193.5
(6.1777)(-3.8386)(6.4948)(-0.825)
20.8258**-0.10424**0.7576**0.339920.9106.8
(7.5723)(-3.4965)(4.8038)(0.3428)
30.23396-0.32430.71552**-0.4607**0.989.1
(1.9062)(-1.3111)(4.6391)(-3.4557)
Note: Regressions and data are as defined in Table 2; 1, 2, and 3 refer to industrial, nondebt, and debt developing countries, respectively.
Note: Regressions and data are as defined in Table 2; 1, 2, and 3 refer to industrial, nondebt, and debt developing countries, respectively.

This varying significance of reserve costs for the different groups supports the view discussed earlier—that monetary authorities manage their reserves both to provide a buffer against future crises and to maintain confidence in the country’s financial management. Even as early as 1978, observers were aware of the size of debt being accumulated by some countries. The first multilateral debt reschedulings were arranged in 1975; there were two in 1976, three in 1977, four in 1979 and 1980, and a large increase thereafter. Interest rates were also generally higher for the large debtor countries, although they varied. At the same time, their current account deficits were high, and owned reserves were likely to be low. It is reasonable to suppose that their reserve holdings were in part borrowed, so that net borrowing costs would be expected to be an important factor in the levels that were held. In addition, however, these countries would have been very concerned to maintain their reputation in international financial markets for as long as they could.

III. Conclusions

The significance of financial costs in the demand for foreign exchange reserves of a range of different types of economies adds to our understanding of how countries determine the level of reserves they hold and emphasizes the sensitivity of reserves to market conditions. The payments balances of a great number of countries have undergone a fundamental change over the past ten to fifteen years. On the one hand, unprecedented sums have been intermediated by the international banking system, giving rise to very large and variable payments surpluses and deficits. This, according to the findings of traditional reserve demand studies, should increase the need for reserves. In addition, some countries have been able to augment their reserves directly through borrowing from the syndicated loan markets. On the other hand, the financial resources shifted have been on terms that have been increasingly differentiated by borrower. These facts have two important effects: short of the appearance of debt-servicing problems, they have frayed the links that existed under the gold exchange standard between domestic economic conditions and the balance of payments (since countries could borrow to finance current consumption), and they have made reserve holdings vulnerable to international market conditions.

The first effect may be more apparent than real. As long as a country is creditworthy, it can go to the market as and when it needs reserves and may. therefore, hold fewer reserves than it would it could not borrow. Alternatively, it might borrow reserves to maintain expansionary domestic policies for longer periods before encountering in due course the reserve constraint. But market perceptions of creditworthiness impose their own discipline: a country seen to be holding too few reserves, or pursuing inflationary policies, might find its access to the market suddenly altered. (Sudden changes in market perceptions of creditworthiness have been a feature of the international banking system since 1982.)

The second effect—the vulnerability of reserve holdings to international financial market conditions—is more serious. The fine terms on borrowing on the international markets give opportunities for profit as well as for loss. Surplus countries may, because of a good credit rating, add to their reserves when investment conditions are good, whereas deficit countries whose real resources are being increasingly absorbed by debt repayments will be forced to borrow at a premium to maintain desired reserve levels. For both groups of countries, reserves should be sensitive to the opportunity cost of holding them. The present study has shown that the more vulnerable economies—with the greatest need for reserves—economize more than others on their reserves when international financial markets are tight.

APPENDIX I

The Data

This Appendix provides definitions of variables and sources of the data used. Countries in the sample are listed in Appendix II.

Sample Countries

Twenty-four countries were subdivided into a small industrial country group (major reserve-currency countries were excluded for reasons given in the text), a set of non-debt-problem countries, and a set of debt-problem countries. The difference between the last two groups was whether the country had entered into a rescheduling arrangement during the period. The debt-problem group was dropped for 1982-86 because it faced credit rationing.

Data

All aggregates were measured in U.S. dollars. In addition to the reasons quoted in the text for using dollar figures, the primary source of data was the Fund’s International Financial Statistics (IFS), which reports reserve and trade statistics in dollar terms. It is, therefore, sensible to use data converted into dollars by a consistent methodology at the same time, since this should minimize distortions from the effects of converting different exchange rates. Following Frenkel (1978), this study looked at nominal rather than real reserve demand.

Reserves

The IFS definition of total reserves of the monetary authorities minus gold (line 11.d in the monthly publication) was used. Gold was excluded for two reasons: first, there is some question whether central banks consider gold to be as liquid as, say, foreign currency holdings. Apart from the fact that large sales might depress the market price, central banks seem to regard gold as a reserve that is truly “of last resort,” to be sold only in extremis. The second reason for excluding gold holdings is that if they are valued at the official price, the value will be vastly underestimated; if valued at current market prices, the holdings will be overvalued. The price of gold has varied quite a bit over the period considered, and unless one considers that a country was ready to realize capital gains whenever the price rose, the price increase does not reflect a higher value of reserves.

Net Rate

This variable was defined as individual country spreads over the six-month LIBOR on syndicated loans to the sample countries, denominated in U.S. dollars, plus the six-month LIBOR rate and less the three-month U.S. Treasury bill rate. (Ideally the term structure of the interest rates should be matched. The three-month Treasury bill rate was chosen because the shorter-maturity assets were thought to correspond to authorities’ needs for liquid assets more closely than the longer-term maturities, whereas almost all syndicated loans are quoted over six-month LIBOR. As a practical matter, the three-month Treasury bill rates move closely with the six-month rates.) The syndicated loan rates chosen were average rates for loans to a given country in each quarter between 1978 and 1986, weighted according to the share in total loans to that country in that quarter. Syndicated borrowing spreads over six-monthly LIBOR were from the Bank of England, and the six-month LIBOR and the three-month Treasury bill rates were from Data Resources, Inc.

Probability of Deficits (VARB)

The literature has found that the variability of reserves (denoted VARB) over 14 past periods is a consistently significant determinant of reserve holdings for all economies. It was therefore assumed that reserve variability, measured over this time frame and detrended to exclude persistence, could be used to proxy p(D), the probability distribution of a future payments imbalance. Thus, the probability of deficits arising and of using reserves became

The definition for reserve variability was that used by most authors:

for country i and time t, where aT is the result of a regression to estimate the trend in R:

The Marginal Propensity to Import (MPM)

The marginal propensity to import was proxied here by the average propensity to import—that is, by imports as a ratio of GDP or GNP. Both these aggregates were taken from the Fund’s IFS.

Scale Variable (Imp)

The scale of imports was proxied here by the IFS dollar value of imports.

APPENDIX II Sample Countries

The country groups used in this study were as follows:

Industrial Countries
AustraliaNorway
DenmarkSpain
ItalySweden
Nondebt Developing Countries and Territories
GreecePortugal
IndiaTaiwan Province
Indonesiaof China
Korea, Rep. ofThailand
Debt Developing Countries
ArgentinaMorocco
BrazilPeru
ChilePhilippines
ColombiaVenezuela
EcuadorYugoslavia
Mexico
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Mrs. Landell-Mills is a Senior Economist in the Special Issues Unit of the Exchange and Trade Relations Department and was Assistant Division Chief of the Editorial Division, External Relations Department, at the time this paper was written. She holds graduate degrees from Cambridge University and George Washington University, This paper is based on the author’s Ph.D. dissertation.

The author is grateful for comments from Robert Dunn, Sebastian Edwards, Oli Havrylyshyn, Mike Loewy, and colleagues in the Fund.

Studies specifically asking whether reserve demand shifted after 1973 (Frenkel (1983), Frenkel and Hakkio (1980), and Frenkel (1978)) have consistently shown that there was no significant shift. Lizondo and Mathieson (1985), in a Fund study that updated earlier work, found some instability in equilibrium formulations of the equation but not in disequilibrium formulations.

See Williamson (1973), Hippie (1974), Edwards (1984), and Frenkel (1983) for reviews of the literature.

See Frenkel (1983) for a representative equation. See also Edwards (1984) and Harberger and Edwards (1982) for an integration of reserve demand equations with monetary analysis.

Several authors (Heller (1966) and Frenkel (1978 and 1983)) noted the need to include some proxy for forgone earnings in reserve demand equations; others attempted to proxy it but found it not significant—Ken en and Yudin (1965) and Kelly (1970) tried per capita income, whereas Hippie (1974) used the inverse of the gross marginal capital output ratio. Frenkel and Jovanovic (1981) took (with payments fluctuations) the government bond yield or discount rate and found it had the right sign and was significant. Other authors have dropped the opportunity cost variable.

On the basis of an analysis of front-end fees and LIBOR spreads for 183 Eurocurrency credits arranged in 1981-83, Mills and Terrell (1984, p. 2) found that: “A close statistical relationship exists between the level of fees and the level of spreads. This relationship indicates that fees are utilized to raise the level of total compensation to banks in a very consistent manner.” Johnston (1982, p. 169) also found that the available evidence suggests that the level of fees moves in line with spreads, so that the spread is a reasonable indicator of the price of the loan.

The Fund’s Annual Report shows that about 60 percent of total official placements was denominated in dollars over the sample period. This is confirmed by the survey by the Group of Thirty (1982) of reserve management by central banks holding more than half of global foreign exchange reserves, which shows that between 1978 and 1981 industrial countries held, on average, 82 percent of their reserves in dollars, whereas developing countries held an average of 60 percent.

Between 1978 and 1984, an annual average of 72 percent of the external assets of BIS reporting banks were denominated in dollars. Between 1984 and 1986, this share fell but was still, on average, 69 percent of the total.

This concept of opportunity cost assumes that the monetary authorities have priorities that are independent of those of the government. Whether these can be acted upon is another question.

In a test that estimated spreads during the 1970s as a function of domestic interest rates in the major currency countries, the banks’ source of funds, and two variables reflecting specific Euromarket conditions, Johnston (1982) found that the domestic interest rates had the strongest and most significant effect on spreads, whereas loan volume exerted a significant but negative impact.

Fund studies on reserves have also used the U.S. Treasury bill rate to proxy earnings on invested reserves. Edwards (1985a) used LIBOR to proxy these returns.

This approach draws on Sargent (1987, p. 117).

The impact of scale is emphasized in all the literature; a Fund study by Lizondo and Mathieson (1985) has a convenient presentation of the results of several equations over an extended time period. Frenkel (1978, pp. 130-34) shows that, using small-country assumptions, there is a positive link between openness defined as the average propensity to import and reserve holdings. The assumptions in question are that the price of imports is given (so that any exogenous change occurs in export prices) and that the income elasticity of money demand is greater than or equal to unity. Frenkel maintains that empirical work on money demand shows that this assumption is well founded.

Niehans (1970, p. 50) states that “basically reserves are useful because of what they are, not because of the way they grow.”

Williamson (1973, p. 17), quotes examples of underreporting (by the capital-surplus exporters) and overreporting (by Mexico, Brazil, and the Philippines).

A Fund study on reserves noted that, in any case, the net cost of reserve holding for reserve-center countries would not be large, since the opportunity cost would be the rate of interest on their public sector money market obligations net of returns from comparable domestic assets. The difference in the returns on these two instruments is not large.

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