The IMF's Statistical Systems in Context of Revision of the United Nations' A System of National Accounts
Chapter

5 Currency Conversion in a Multiple Exchange Rate System

Author(s):
Vicente Galbis
Published Date:
September 1991
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Author(s)
Marianne Schulze-Ghattas

Because data on economic transactions are frequently expressed in a variety of national currencies and, occasionally, in other units of account such as the SDR, they can only be compared and aggregated if they are converted into a single unit of account. In a unitary exchange rate system, currency conversion is essentially a matter of determining the time period to which the conversion rate should relate. In contrast, in a multiple exchange rate system, currency conversion is complicated by the fact that at any time, the national currency is exchanged against any other currency at different rates, depending on the type of transaction or transactor (or both) involved.1 In these circumstances compilers of national accounts and balance of payments statistics have to determine not only the time period to which the conversion rate, or rates, should relate but also the exchange rate at which a given transaction should be converted.

In a multiple exchange rate system there are, in principle, two possible methods for converting transactions denominated in foreign currencies into the national currency: conversion of each individual transaction at the exchange rate at which it was effected or conversion of all transactions at a unitary conversion rate. This paper examines these conversion methods in view of existing guidelines for the compilation of national accounts and balance of payments statistics. More specifically, it examines which of these methods agrees with the general principles of valuation and conversion underlying these guidelines and which method ensures that, for statistical purposes, the taxes and subsidies implicit in a multiple exchange rate system are treated like corresponding explicit taxes and subsidies in a unitary rate system. The main conclusion of the paper is that, given these criteria, conversion of all transactions at a unitary exchange rate is the appropriate conversion method in a multiple exchange rate system.

Multiple exchange rate systems can take various forms, ranging from relatively simple dual exchange rate systems, in which an official fixed rate for selected transactions coexists with another rate, fixed or floating, for the remaining transactions, to more complex systems with a large number of rates differentiated according to the type of transaction or transactor (or both). For the conversion problems arising in a multiple exchange rate system, these are differences of degree, not of substance. Moreover, it is also immaterial whether all exchange rates in a multiple exchange rate system are officially recognized.2 Consequently, the arguments developed in this paper apply to multiple exchange rate systems in general, regardless of the form a particular system takes.

The paper is organized as follows. Section I briefly examines whether the conversion problems arising in a multiple exchange rate system can be avoided if national statistics are expressed in a unit of account other than the national currency. It argues that, under the circumstances most likely to prevail, compilers of national statistics will confront conversion problems no matter which unit of account they choose. Section II discusses the alternative conversion methods outlined above in view of the general principles of valuation and conversion underlying existing guidelines for the compilation of national accounts and balance of payments statistics. Section III focuses on the implications of each conversion method for the treat ment of the taxes and subsidies implicit in a multiple exchange rate system. Section IV discusses problems relating to the determination of a unitary conversion rate. Finally, the conclusions summarize main findings of the paper.

I. Can a Judicious Choice of Unit of Account Avoid Conversion Problems?

Because of the difficulties associated with determining the appropriate exchange rate for converting a given transaction from foreign into national currency in an economy that maintains a multiple exchange rate system, compilers of national accounts and balance of payments statistics may find it preferable to try to avoid conversion problems by expressing national statistics in a unit of account other than the national currency. This is possible when a country's economic transactions are exclusively denominated in one or more foreign currencies. When a country's transactions are not exclusively but predominantly denominated in foreign currencies, using a foreign currency as the unit of account does not avoid conversion problems, but it does reduce the errors that result if an inappropriate conversion method is applied.

Some countries maintaining multiple exchange rates have chosen to express the balance of payments in a unit of account other than the national currency. This option is also suggested in the fourth edition of the IMF's Balance of Payments Manual (BPM). The majority of transactions between residents of a country, however, are likely to be denominated in domestic currency. Thus, using a unit of account other than the national currency may avoid conversion problems in the case of balance of payments statistics, but it will do so by compounding these problems for the national accounts statistics—if these are expressed in the same unit of account—or by losing comparability between balance of payments and national accounts statistics, if the latter are expressed in national currency. Hence, compilers of national accounts and balance of payments statistics who wish to ensure the comparability of both systems will generally not be able to avoid or even substantially reduce the conversion problems arising from a multiple exchange rate system by expressing statistics in a unit of account other than the national currency.

II. Choice of Conversion Method: General Principles of Valuation and Conversion

Because current methodologies for national accounts3 and balance of payments statistics (for example, the BPM) establish general principles for the valuation and conversion of transactions, it appears appropriate to consider the application of these principles to the special conversion problems that arise in a system of multiple exchange rates. More specifically, the choice between the alternative conversion methods—between conversion of each individual transaction denominated in foreign currency into national currency at the rate at which it was effected, or conversion of all transactions at a unitary rate—should be based on these general principles.

To determine the value of a given transaction, generally an exchange of real or financial assets, compilers of economic statistics have to determine at least one, and frequently two, prices: the price of the good, service, or financial asset exchanged in terms of the currency in which the transaction was originally expressed, and, if this currency differs from the chosen unit of account, the price of that currency in terms of the unit of account. However, neither the price of a real or financial asset nor the price of a currency or unit of account in terms of another is a unique concept. Guidelines for the compilation of economic statistics, therefore, define the price that is to be used to determine the value of a given transaction in terms of the currency or unit of account in which it was originally expressed, as well as the exchange rate that is to be used to convert a transaction from one national currency or unit of account into another.

In the SNA and in the BPM, the recommendations about the valuation of transactions are based on the market price principle. The BPM (paragraph 76), following the United Nations' Provisional Guidelines (paragraph 6.5), defines a market price as “the amount of money that a willing buyer pays to acquire something from a willing seller, when such an exchange is one between independent parties into which nothing but commercial considerations enter.” This definition neither implies that a market price is the price applicable to a set of supposedly identical transactions nor presupposes a certain market structure. Instead, it views a specific market price as relating to one specific transaction only, which may take place in any type of market-purely competitive, monopolistic, or monopsonistic.

However, the definition of a market price outlined here draws a clear distinction between transactions carried out by independent parties and transactions that do not fulfill this criterion. The Brussels Definition of Value,4 from which the criterion of independence is derived, stipulates that buyer and seller shall be considered independent of each other only if the price is the sole consideration relevant to a transaction and if

the price is not influenced by any commercial, financial or other relationship, whether by contract or otherwise, between the seller or any person associated in business with him and the buyer or any person associated in business with him, other than the relationship created by the sale itself … [and] no part of the proceeds of any subsequent resale, other disposal or use of the goods will accrue, either directly or indirectly, to the seller or any person associated in business with him.

For transactions between parties that do not fulfill the criterion of independence—for example, affiliated enterprises—the BPM (paragraph 82) suggests that any transfer prices associated with such transactions be adjusted to reflect market value equivalents.

In agreement with the principle of market price valuation, the BPM suggests that transactions should be converted from one unit of account into another at exchange rates that qualify as market prices in the above sense. More specifically, for the system of par values, the BPM (paragraph 127) recommended conversion at parity. For the currently prevailing system of floating exchange rates, the BPM (paragraph 128) suggested conversion at the exchange rate for spot delivery at the time of contract.5

In a system of multiple exchange rates, the question arises whether conversion at the rates prescribed for individual transactions agrees with the principles of valuation and conversion outlined above. Consider, for example, the following system. For a certain group of export goods, exporters have to surrender their foreign exchange proceeds at the exchange rate e1, defined as the price of a foreign currency in terms of the domestic currency. For a certain group of import goods, importers purchase foreign exchange at the same rate. All remaining current and capital account transactions are settled at the rate e2, which is floating freely. At e2 the domestic currency is more depreciated than at e1; that is, e1 < e2. The question then is whether the exchange rate e1 qualifies as a market price in the sense of the BPM.

As emphasized earlier, the definition of market prices adopted in the BPM does not presuppose the existence of a unique price for a group of supposedly identical transactions. Therefore, the fact that, in a system of multiple exchange rates, foreign exchange transactions take place at different rates does not violate the principle of market rate conversion. However, the BPM concept of market prices presupposes independence of buyer and seller. In a system in which the seller of foreign exchange (in the above case, the exporter of those goods for which e1 is prescribed) is prevented by law from selling his foreign exchange proceeds at the most favorable available rate (that is, e2), the buyer (the government through the monetary authority or some other government institution) uses its legal authority over the seller to determine the purchase price for foreign exchange. In these circumstances, the criterion of independence of buyer and seller is not fulfilled, and the legally prescribed exchange rate e1 cannot be considered a market price.

The legally prescribed exchange rate e1 in the above example differs fundamentally from a legally prescribed unitary rate in a par value system. In a par value system it is the monetary authority that is required, by law, to buy and sell foreign exchange in order to keep the exchange rate within a given margin around par value. Private agents buy and sell foreign exchange at the existing rate because it is the current market price, not because they are prevented by law from concluding transactions at different rates. Hence, in contrast to the legally prescribed exchange rates in a multiple exchange rate system, exchange rates in a par value system qualify as market prices according to the definition outlined above.6

If in the above example of a multiple exchange rate system the legal restrictions forcing certain sellers to sell at the rate e1 were removed, these sellers would clearly prefer to sell their foreign exchange proceeds at the higher price e2. At the same time, buyers of foreign exchange, who previously could purchase at the preferential rate e1, would be forced to pay a higher price. The system of multiple rates would be replaced by a unique equilibrium rate e0. This rate qualifies as a market price, irrespective of whether it is floating freely (that is, is determined entirely by private demand for and supply of foreign exchange) or is kept within a more or less narrow band around a fixed value, because the monetary authority assumes responsibility for closing the gap between demand for and supply of foreign exchange at that rate. Hence, in a multiple exchange rate system only conversion at the equivalent of the rate e0 would be consistent with the principles of market price valuation and the conversion adopted in existing guidelines for national accounts and balance of payments statistics.

III. Choice of Conversion Method: Treatment of Taxes and Subsidies Implicit in a Multiple Exchange Rate System

In a system of multiple exchange rates, exchange regulations drive a wedge between the rates at which transactions are settled and the equilibrium exchange rate that would prevail if all transactions were carried out at a single rate.7 This creates a system of implicit taxes and subsidies.8 The following example illustrates this point.

Let q be the foreign currency price of a certain good (that is, the amount of foreign currency an exporter or importer receives or pays for that good); let p be the amount of domestic currency that an exporter or importer receives or pays for one unit of the same good; and let t denote the tax or subsidy rate. For a certain group of export and import goods, exporters or importers have to sell or buy foreign exchange at the rate e1, defined as the price of one unit of foreign currency is more appreciated than at the equilibrium rate e0 that would prevail if all current and capital account transactions were settled at the same rate, e1 < e0. An exporter who is forced to sell his foreign exchange proceeds at the rate e1 < e0, and hence receives p = e1q = e0q[1 − (e0e1)/e0] in domestic currency for one unit of his export goods, is effectively taxed at the rate t = (e0e1)/e0 > 0. Similarly, an importer who is able to purchase foreign exchange at the rate e1 is effectively subsidized at the same rate.9 In contrast, if the rate e2 were more depreciated than e0 (if e1 > e0), then exporters entitled to sell foreign exchange at the exchange rate e1 would be effectively subsidized at the rate t = (e0e1)/e0 < 0. Similarly, importers forced to purchase foreign exchange at the exchange rate e1 would be effectively taxed at the same rate.

Depending on the exchange rate that is used to convert foreign currency values into domestic currency, the domestic currency value of exports or imports will reflect the price the exporter or importer would receive or pay before paying or receiving the tax or subsidy implied by the exchange rate system, or it will reflect the price the exporter or importer receives or pays after paying or receiving this tax or subsidy. If, in the above example, the foreign currency value of exports is converted at the rate e1, the domestic currency value will reflect the proceeds the exporter receives after paying or receiving the implicit tax or subsidy. If, however, the foreign currency value of exports is converted at the rate e0, then the domestic currency value will reflect the proceeds that the exporter would receive before paying or receiving the implicit tax or subsidy. Similarly, if imports are converted at the rate e1, the domestic currency value will reflect the price the importer pays after receiving or paying the implicit subsidy or tax. If the same imports are converted at the rate e0, however, the domestic currency value will reflect the price the importer would pay before receiving or paying the implicit subsidy or tax.

Because the taxes and subsidies implicit in a multiple exchange rate system are equivalent to comparable explicit taxes and subsidies on international transactions in a unitary rate system, it appears appropriate to choose a conversion method that implies equal treatment of implicit and explicit taxes and subsidies. The BPM recommendations regarding the treatment of explicit taxes and subsidies on international transactions focus on the question of whether the payment or receipt of a tax or subsidy represents a resident-resident or a resident-nonresident transaction. If explicit taxes or subsidies are paid or nonresident transaction. If explicit taxes or subsidies are paid or received by residents of the reporting economy, they represent resident-resident transactions, and the value of the transaction on which a given tax or subsidy is levied or granted should reflect the price that the resident of the reporting economy receives or pays before paying or receiving the tax or subsidy.

In the case of the exports in the example outlined above, the foreign importer pays q units of foreign currency for one unit of goods purchased from the domestic exporter. If the multiple exchange rate system were changed into a unitary rate system with the equilibrium rate e0, and if the implicit taxes or subsidies were replaced by explicit taxes or subsidies, the exporter would receive e0q units of domestic currency for one unit of export goods, on which he would pay or receive a tax or subsidy to or from his government equivalent to t = e0q (e0 +e1)/e0. This tax or subsidy is a resident-resident transaction, since it is the exporter who actually pays or receives it. Consequently, the domestic currency value of the resident-nonresident transaction involved is e0q; that is, the proceeds the exporter would receive before paying or receiving the tax or subsidy. Similarly, in a unitary rate system with explicit taxes or subsidies, the importer in the example outlined above would pay e0q units of domestic currency for one unit of import goods but would receive or pay a subsidy or tax equivalent to e0q (e0e1)/e0, which would reduce or increase his cost to the equivalent of e1q. This subsidy or tax is a resident-resident transaction. Hence, the domestic currency value of the resident-nonresident transaction involved is e0q; that is, the price the importer would pay before receiving or paying the subsidy or tax.

The argument outlined here can be summarized as follows. Since taxes or subsidies on exports and imports generally represent resident-resident transactions, the domestic currency value of a given export or import should reflect the domestic currency price the exporter or importer receives or pays before paying or receiving a tax or subsidy.10 Consequently, if the taxes or subsidies implicit in a system of multiple exchange rates are to be treated like comparable explicit taxes or subsidies in a unitary rate system, the conversion method chosen must ensure that the value of exports or imports in terms of domestic currency reflects this price. As shown above, however, conversion at the exchange rates at which transactions are actually settled in a multiple exchange rate system implies that the derived value of exports or imports reflects the domestic currency price exporters or importers receive or pay after paying or receiving the taxes or subsidies implicit in the exchange rate system. Hence, conversion at the equivalent of the equilibrium exchange rate is required.

IV. Determining a Unitary Conversion Rate

The discussion in the preceding sections suggests that, from an analytical point of view, in a system of multiple exchange rates transactions denominated in currencies other than the chosen unit of account should be converted at a single conversion rate.11 According to a recent survey, several countries maintaining multiple exchange rates have adopted unitary conversion rates at least in the area of foreign trade statistics.12 However, there is no detailed information about how this rate is defined.

In theory, the unitary rate at which transactions should be converted is the rate that would prevail if all foreign exchange transactions were carried out at the same rate. According to the BPM (paragraph 129), this “notional rate could be considered as the equivalent of either an equilibrium rate that the authorities would be able to defend under a system of fixed par values or a market rate prevailing under a regime of free floating.” In practice, however, such a notional equilibrium rate cannot easily be determined. In general, the exchange rate that would prevail if all foreign exchange transactions were carried out at the same rate depends not only on the price elasticities of the different components that constitute total demand for and supply of foreign exchange but also on a whole range of potential policy measures, including compensatory financing transactions and direct central bank interventions in the foreign exchange market, designed to influence the exchange rate according to given policy objectives.

Recognizing that a notional equilibrium rate cannot be determined without detailed knowledge about the structure of the economy in question and about the policy assumptions that should reasonably be made, the BPM does not provide specific recommendations for defining the appropriate single conversion rate. This lack of detailed guidelines leaves room for defining unitary conversion rates that suit the specific conditions in individual countries, but it also leaves ample scope for defining conversion rates that are not necessarily ''realistic.” A more standardized approach taken by the Fund staff is to construct a weighted average of the different exchange rates observed in a multiple exchange rate system, the weights being the estimated shares of the transactions effected at a particular rate. Admittedly, this is but one possible approach to approximating the notional equilibrium rate.

V. Conclusions

The major findings of this paper can be summarized as follows.

  • Compilers of national accounts and balance of payments statistics who wish to ensure the comparability of these statistical systems will in general not be able to avoid conversions involving the national currency, irrespective of what unit of account they choose.

  • Given the necessity to convert transactions denominated in foreign currency into domestic currency, or vice versa, compilers operating in a multiple exchange rate system have to choose between two possible conversion methods: conversion of each transaction at the exchange rate at which it was effected, or conversion of all transactions at a unitary conversion rate.

  • From the point of view of existing guidelines for the valuation and conversion of transactions, which are based on the market price principle, conversion at a unitary exchange rate is preferable because the different rates at which transactions are effected in a multiple exchange rate system do not qualify as market prices according to the definition adopted in these guidelines.

  • From the point of view of the taxes or subsidies implicit in a multiple exchange rate system, conversion at a unitary exchange rate is preferable because it ensures that, for statistical purposes, these implicit taxes or subsidies are treated like corresponding explicit taxes or subsidies in a unitary rate system. More specifically, conversion at a unitary exchange rate ensures that the domestic currency value of a given transaction reflects the amount the transactor would receive or pay before paying or receiving an explicit tax or subsidy.

  • The unitary conversion rate at which all transactions in a multiple exchange rate system should be converted is the equilibrium exchange rate that would prevail if all transactions were effected at the same rate. This notional equilibrium rate cannot be easily determined because it depends on the price elasticities of the different components that constitute total demand for and supply of foreign exchange, as well as potential policy measures designed to influence the exchange rate according to given policy objectives. One possible approach to approximating such a rate is to construct a weighted average of the different exchange rates observed in a multiple exchange rate system, the weights being the shares of the transactions effected at a particular rate.

Although in a unitary exchange rate system buying and selling rates for foreign currencies differ by certain margins, these margins usually reflect normal costs and risks of exchange transactions and do not constitute separate exchange rates. Based on a standard of reasonableness for such margins, the IMF’s Executive Board has adopted the view that a multiple currency practice exists if, as a result of official action, spreads between buying and selling rates for spot foreign exchange exceed 2 percent, unless such spreads reflect additional costs and risks, or midpoint spot exchange rates for other members’ currencies deviate by more than 1 percent and for more than one week from the corresponding rates derived from the spot exchange rates for these currencies in their principal markets. See Executive Board Decision No. 6790–(81/43), March 20, 1981, reprinted in Joseph Gold, SDRs, Currencies, and Gold: Sixth Survey of New Legal Developments, Pamphlet Series, No. 40 (Washington: International Monetary Fund, 1983), pp. 107–08.

In contrast, from the Fund’s perspective, this distinction is crucial because the Fund’s jurisdiction does not apply to multiple exchange rates arising from illegal markets for foreign exchange, unless these are officially recognized.

The United Nations’ A System of National Accounts (SNA) and Provisional International Guidelines on the National and Sectoral Balance-Sheet and Reconciliation Accounts of the System of National Accounts, Statistical Papers, Series M, No. 60 (New York, 1977).

Customs Cooperation Council, General Secretariat, The Brussels Definition of Value for Customs Purposes: Its Origins, Characteristic Features, and Applications (Brussels, July 1972), Article II, p. 35.

However, the BPM (paragraphs 131–33) recognizes that balance of payments compilers may find it difficult to determine the contract date of a transaction, and that, in practice, average spot rates for the period in which the transaction is recorded may have to be used for conversion.

The recommendation of the BPM (paragraph 127) regarding conversion in a par value system rests on the assumption that par values are, in fact, observed, and that the movements of the exchange rates within the margins, especially when averaged over a certain period, are sufficiently small to be neglected in conversion.

Note that this equilibrium exchange rate is not necessarily the free market rate that would prevail if all restrictions on foreign exchange transactions, and on international transactions such as import quotas, licenses, and so on were removed.

The equivalence of explicit taxes or subsidies and the taxes or subsidies implicit in a multiple exchange rate system is embodied in the Fund’s concept of multiple currency practices. This concept relates to “effective exchange rates”; that is, the price of foreign exchange received or paid after allowing for taxes or subsidies that are closely related to foreign exchange transactions. However, whereas the Fund’s concept of multiple currency practices considers only taxes or subsidies applying to the payments aspect of a transaction, as opposed to taxes or subsidies relating to the trade aspect, the discussion in this section applies to taxes or subsidies on international transactions in general.

Note that t > 0 implies a tax on exports and a subsidy on imports, whereas t < 0 implies a subsidy on exports and a tax on imports.

This recommendation agrees with the guidelines for valuation in international trade statistics suggested in the United Nations’ International Trade Statistics: Concepts and Definitions, Department of Economic and Social Affairs, Statistical Office, Statistical Papers, Series M, No. 52 (New York, 1970), p. 43.

For an alternative view, see International Monetary Fund, International Financial Statistics, Supplement on Exchange Rates, Supplement Series, No. 9 (Washington, 1985), p. vii.

Dev Kar, “Currency Invoicing and Exchange Conversion in International Trade,” Papers in International Finance Statistics, PIFS/86/1 (Washington: International Monetary Fund, February 14, 1986).

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