MONETARY AND ECONOMIC STUDIES/OCTOBER 2003 The Choice of Invoice Currency in International Trade: Implications for the Internationalization of the Yen Hiroyuki Oi, Akira Otani, and Toyoichiro Shirota In this paper, we present an overview of theoretical research on the choice of an invoice currency for exports from the perspective of expected profit maximization. We then use this theory as a basis to offer a current assess- ment and future outlook regarding the use of the yen in trade transactions, which is one aspect of the internationalization of the yen. Our analysis demonstrates that the current use of the yen to price exports is largely consistent with levels that can be explained by theory. This suggests that the current measures for improving Japanese financial markets are, by themselves, likely to have only a limited impact on expanding the use of the yen as a denomination for trade transactions, given the current international competitiveness and market share of Japan’s manufacturing industry and the current exchange rate regimes. Moreover, the currency- basket regime that has been proposed for East Asia from the perspective of the internationalization of the yen is not necessarily theoretically desirable for the region, nor is expanded use of the yen in trade transactions necessarily a free lunch for Japan, in that it may very well bring with it new problems for implementing economic policies. Keywords: Invoice currency; Local currency pricing (LCP); Producer’s currency pricing (PCP); Internationalization of the yen; New open-economy macroeconomics; Currency-basket regime JEL Classification: F41, F42, L11 Hiroyuki Oi: Research Division I, Institute for Monetary and Economic Studies, Bank of Japan (E-mail: [email protected]) Akira Otani: Deputy Director and Senior Economist, Research Division I, Institute for Monetary and Economic Studies, Bank of Japan (E-mail: [email protected]) Toyoichiro Shirota: Research Division I, Institute for Monetary and Economic Studies (currently Human Resources Management Department), Bank of Japan (E-mail: shirota.3@ osu.edu) We would like to thank Professor Shin’ichi Fukuda, Faculty of Economics, University of Tokyo, and staff at the International Department and the Institute for Monetary and Economic Studies (IMES) of the Bank of Japan for their valuable comments. Furthermore, we would like to express our appreciation to Ryoji Koike in Research Division I of IMES for his help with data on trade between Japan and East Asia. The opinions and inevitable errors contained in this paper are purely those of the authors, and do not represent the official views of either the Bank of Japan or IMES. MONETARY AND ECONOMIC STUDIES/MARCH 2004 27 DO NOT REPRINT OR REPRODUCEWITHOUT PERMISSION. I. Introduction In response to recent developments in international macroeconomics, there has been strong interest among academics and central bankers regarding the firm’s choice of a currency to price its exports. Since Obstfeld and Rogoff (1995) published their work on new open-economy macroeconomics, a dynamic general equilibrium open- economy model with micro foundations, many researchers have incorporated the firm’s invoicing decision into this model. This line of research shows that the transmission of monetary policy, optimal monetary policy rules, and the optimal exchange rate regime all depend on the firm’s choice of an invoice currency for exporting its goods, that is, whether it chooses producer’s currency pricing (PCP) or local currency pricing (LCP).1 One problem with this area of research, however, is that the exporting firm’s invoicing decision is given exogenously (Fujiki and Otani [2002] and Gerlach [2002]). Consequently, in recent years focus has begun to shift toward theoretical research using models in which the currency choice is endogenous. Until now, research on the choice of an invoice currency has largely focused on why the U.S. dollar has become the world’s vehicle currency for international transactions. This research on vehicle currency can be divided into several categories according to the essential function of money.2The first category is analysis focused on money as a medium of exchange, and the research is based on the transaction cost of currency conversion. Swoboda (1968) is a pioneer in this area. Regarding why only a small number of currencies, led by the U.S. dollar, were used as vehicle currencies in international trade, Swoboda pointed out that (1) a higher transaction cost in converting between the home and foreign currencies resulted in a larger amount of foreign currency held, and (2) the total amount of overall foreign currency holdings could be reduced by holding a single vehicle currency for all trade settlement rather than holding the currencies of each trading partner, leading to a reduction in overall transaction cost. Regarding which country’s currency became the vehicle currency, Swoboda found that the vehicle currency chosen was the currency of a country with (1) a large value of international trade and a large volume of transactions in its currency in the forex markets,3 and (2) well-developed financial markets.4 Krugman (1980) also focused on the transaction cost between the home and foreign currencies, and found that when the average transaction cost was decreasing in trading volume, the currency with the lowest translation cost, i.e., the currency with the largest transaction volume, would become the vehicle currency. He also found that a currency’s status as a vehicle currency was aided by inertia.5 1.See Lane (2001) regarding recent progress in theoretical research incorporating the firm’s price-setting behavior into new open-economy macroeconomics. 2.For more on this, see Magee and Rao (1980). 3.This is because the greater the trading volume, the lower the transaction costs of exchanging currencies. 4.Chrystal (1977) used the U.S. dollar, British sterling, French franc, and German mark to provide empirical support to the criteria for selecting a vehicle currency identified by Swoboda (1968). 5.To support this, Krugman (1980) provides the example of Great Britain, which although it declined in economic importance following World War I, was able to maintain the pound sterling’s status as the vehicle currency together with the U.S. dollar until World War II. 28 MONETARY AND ECONOMIC STUDIES/MARCH 2004 The Choice of Invoice Currency in International Trade: Implications for the Internationalization of the Yen Rey (2001) built a more rigorous model to analyze the research done by Swoboda and Krugman. Rey (2001) introduced transaction costs of currency exchange to a three-country general equilibrium model and theoretically showed how multiple equilibria as to the choice of a vehicle currency arose from the strength of trade ties and the size of transaction costs. She found that the currency of the country with the greatest degree of openness and the currency with the lowest transaction costs of exchange with other currencies become the vehicle currency.6 The second category of research on vehicle currency focuses on money as a unit of account. McKinnon (1979) stated that international transactions of highly homoge- nous primary goods were concentrated in specialized exchange markets in the United States and the United Kingdom, and concluded that a single vehicle currency would be used for trading in homogenous goods because expressing prices in the same currency made more efficient transactions possible when trading in such goods.7,8 Nevertheless, the fraction of primary goods invoiced in U.S. dollars continues to decline, whereas the fraction of machinery and other highly heterogeneous products traded in dollars in international trade increases. McKinnon (1979) argued that the home currency is selected for pricing highly heterogeneous goods.9 Consequently, the above-noted research on vehicle currency does not adequately explain the actual invoicing decision made, and this in turn makes it necessary to examine the choice of non-vehicle currency, i.e., the decision on which country’s currency is chosen as the invoice currency in bilateral trade. Regarding this point, Giovannini (1988) analyzed the currency choice made by a monopolistic exporting firm from the perspective of maximizing expected profits under uncertainty in exchange rate movements. He concluded that the choice of an invoice currency depended on the shape of the profit function.10 Since his research, there has been a large body of theoretical research on choosing the invoice currency from the perspective of maximizing expected profits. 6.As noted above, research focused on money as a medium of exchange was largely dependent on the transaction costs between currencies. There is one theoretical work, however, that ignores the transaction cost between currencies to discover the mechanism that creates a vehicle currency: Matsuyama, Kiyotaki, and Matsui (1993). Using a random matching model, Matsuyama, Kiyotaki, and Matsui (1993) analyzed the type of equilibrium that would arise as to the regional use of money, in a world where only two types of money, the home currency and the foreign currency, existed. They found that three types of equilibrium would arise: (1) the regional currency case, in which absolutely no international transactions took place, and the home currency was only used in the home country and the foreign currency only used in the foreign country; (2) the single vehicle currency case, whereby one currency became a regional currency, and the other currency was used not only in its country of issue but also in the foreign country; and (3) the dual vehicle currency case, whereby both currencies were used in both the home country and the foreign country. Furthermore, they showed that the currency of a country with a large economy is more likely to become the vehicle currency, and the higher the degree of economic integration, the greater the likelihood that two vehicle currencies would coexist. 7.The same argument can be made for financial transactions. That is, it is possible to lower the cost of collecting information and trade more efficiently by using a single vehicle currency for financial transactions and holding financial assets denominated in that vehicle currency, rather than by using multiple currencies and holding financial assets denominated in each of the currencies. For related literature, see Brunner and Meltzer (1971). 8.There is also research on vehicle currency that focuses on money as a store of value, arguing that when currency is used for settlement at a future date, the currency with a stable value is chosen as the invoice currency and becomes the vehicle currency. 9.Grassman (1973) studied the invoice currency used in the trade of Sweden and Denmark and found that both countries tended to use the producer’s currency as the invoice currency in their trade. This tendency for the producer’s currency to be used as the invoice currency in international trade is now known as Grassman’s Law, following Grassman (1973). 10.The advantage of this approach is that it enables simultaneously solving the problems of choosing an invoice currency and setting the export price, and that it is possible to describe the relationship between the choice of 29 Such theoretical research can be an extremely useful guideline for assessing the current state, and projecting the future, of the use of the yen as the invoice currency in trade transactions, one aspect of the internationalization of the yen.11 Given that a large proportion of Japan’s exports are differentiated, heterogeneous goods such as machinery, we believe that Giovannini (1988) and later research on choosing an invoice currency based on maximization of expected profits is extremely germane. Up until now, however, the analysis and policy proposals on the use of the yen as an invoice currency have been based on research focusing on money as a medium of exchange and as a unit of account. As far as we know, none of these studies or policy proposals have taken advantage of the partial or general equilibrium analysis based on expected profit maximization from Giovannini (1988) and later research.12 Recently, some economists, particularly in Japan, have been advocating the introduction of a currency-basket regime in East Asia.13Many of the countries in East Asia are now using a de factoU.S. dollar peg.14If high volatility in the yen-dollar rate, which implies high volatility in the exchange rates between the yen and East Asian currencies, is standing in the way of expanded use of the yen as an invoice currency, it is likely that the introduction of a currency-basket regime in East Asia would stabilize the exchange rate between the yen and East Asian currencies and thereby promote use of the yen. Thus, there is a need to examine whether a currency-basket regime is desirable in East Asia when considering the use of the yen as an invoice currency in the future. New open-economy macroeconomics is extremely beneficial in this regard, given that it enables examination of the optimal currency regime from an economic welfare perspective. In this paper, we will examine the optimality of a currency-basket regime in East Asia, taking advantage of recent developments in new open-economy macroeconomics. Our paper is organized as follows. In Section II, we provide an overview of endogenous currency choice theory. We first survey research using the partial equilib- rium models that have dominated the analysis to date, and then introduce recent research based on a general equilibrium model. In actual trade, a large percentage of trade transactions is invoiced in U.S. dollars, even in trade not involving the United invoice currency and the exchange rate pass-through. For example, Friberg (1998) showed that the condition for choosing the local currency as the invoice currency is the same as the condition requiring the exchange rate pass-through of the export prices to be less than one. On the other hand, there are also problems with this approach. That is, this literature assumes that the price is set beforehand and that the export volume can be flexibly determined. In actual trade transactions, however, not only the price but also the export volume is decided when making the export contract. Therefore, the model’s assumptions are inconsistent with actual trade. Furthermore, even a single firm can choose from among the home currency, the foreign currency, and a vehicle currency for the invoice currency. Under the profit maximization approach, however, the firm can only choose between two options—PCP or LCP—and thus this model is also limited in its ability to explain actual invoice currency decisions. 11.The internationalization of the yen signifies the expanded use of the yen not only in conducting trade but also in capital transactions and as a denomination of foreign reserves. For example, the Ministry of Finance (1999) defined yen internationalization as “increasing the percentage of Japan’s cross-border transactions and transactions conducted overseas denominated in yen as well as raising the fraction of nonresidents’ asset portfolios denominated in yen, pointing specifically to raising the yen’s profile in the international currency regime and increasing the weight of business transactions, capital transactions, and foreign currency reserves held in yen.” 12.See Section III for further discussion regarding this point. 13.Literature on this topic includes Ogawa and Ito (2000). 14.See Kawai (2002) and McKinnon and Schnabl (2002). 30 MONETARY AND ECONOMIC STUDIES/MARCH 2004 The Choice of Invoice Currency in International Trade: Implications for the Internationalization of the Yen States (where the dollar is a third country’s currency). Then, we examine the possi- bility for the third country’s currency to be chosen as an invoice currency using the expected profit maximization framework that allows for use of a third country’s currency in addition to PCP or LCP, rather than traditional research on vehicle currency. In Section III, we start by looking at the use of the yen as an invoice currency. We then assess this current use and forecast future use by examining the extent to which the actual invoicing decision in Japan and other industrialized countries can be explained by the conditions found in the theoretical research discussed in Section II. In Section IV, we take advantage of new open-economy macroeconomics to examine the desirability of a currency-basket regime in East Asia from the perspective of the use of the yen as an invoice currency. In Section V, we consider the effect of an increase in the use of the yen as an invoice currency on economic policy, and then close by presenting our conclusions. In Appendices 1 and 2, we explain our methodology for deriving the equations for choosing between PCP and LCP examined in Section II, and also provide a more detailed explanation of the conditions governing the invoicing decision when a third-country currency is available. In Appendix 3, we explain the methodology for estimating the price elasticity for each product category of Japan’s exports to East Asia (excluding China) and the estimated result, which was used in the empirical analysis of Section III. In Appendix 4, we introduce prior research analyzing the impact on the international transmission of monetary policy in the hypothetical case of growth in the yen’s use as an invoice currency. Our paper introduces a theory on the choice of an invoice currency for exports and uses that theory to examine the use of the yen as an invoice currency for export transactions. The yen is used as an invoice currency considerably less for imports than for exports, and the use of the yen for pricing Japan’s imports is outside the scope of this paper. II. Theory on the Endogenous Choice of Invoice Currency Theoretically, a firm chooses an invoice currency based on which currency maximizes expected profits (or the expected utility of profits) in the presence of uncertainty. Theoretical research in this area can be broadly divided into two types. The first type, a partial equilibrium approach in which the only uncertainty is exchange rate fluc- tuations,15 has been the predominant analytical framework in research to date. The second type is a general equilibrium approach that has drawn increasing attention due to recent advances in new open-economy macroeconomics. In this approach, which takes into account that the exchange rate varies due to various shocks such as 15.Japan made a large amount of foreign direct investment, primarily in East Asia, in response to the rapid apprecia- tion of the yen following the Plaza Accord. As a result, some firms have globalized their production organizations. The globalization of these firms has led to the increased use of yen as an invoice currency (Otani, Shiratsuka, and Shirota [2003]). As indicated, a dramatic change in the exchange rate forces changes in firms’ production systems and influences their choice of an invoice currency. Nevertheless, our paper surveys the existing theoretical research from the perspective of uncertainty over the exchange rate fluctuations, rather than of huge changes in the exchange rate level. 31 monetary shocks and production shocks and that such shocks also affect other macroeconomic variables, the invoicing decision is made in light of all of the effects from these shocks. By surveying developments in the literature on endogenous currency choice theory, we aim to shed light on both the criteria used and the decision made regarding which currency to use as the invoice currency. A. Partial Equilibrium Approach The partial equilibrium approach assumes uncertainty regarding exchange rate fluctuations, but no uncertainty regarding demand or production costs, and examines the choice of an invoice currency by a monopolistic firm facing a downward-sloping demand curve. This partial equilibrium approach can be subdivided into two different models: the simplest monopoly model where only one monopolistic firm exists, and an oligopoly model in which multiple monopolistic firms compete in the export market.16 1. Monopoly model a. Choosing between the home currency and local currency Research to date has shown that the invoicing decision in a monopoly model is largely determined by the shapes of the demand function, the cost function, and the resulting profit function. Suppose that, with uncertainty in the variation of the home-currency denomi- nated nominal exchange rate e, the exporting firm sets the price prior to knowing the exchange rate for that period. Additionally, the firm has two choices: (1) setting the export price at the foreign currency equivalent of the domestic sales price (PCP); or (2) setting the export price in local currency terms (LCP). Let the demand curve for the goods produced by the firm be D(p) and the firm’s cost function be C(q) (where pis the price faced by the consumer of the exports, and q is the production volume). With pP representing the home currency-denominated price, the export price denominated in the foreign currency under PCP is pP/e. The export price under LCP is given by pL. Based on these assumptions, profit under PCP, (cid:2)P, and profit under LCP, (cid:2)L, are defined as follows: (cid:2)P=pPD(pP/e) −C(D(pP/e)), (1) (cid:2)L=epLD(pL) −C(D(pL)). (2) Given that the exchange rate eis uncertain, the firm’s decision on whether to choose PCP or LCP is made based on which price-setting behavior gives the highest expected 16.We introduce a static model for the choice of the invoice currency by a monopolistic or oligopolistic firm, based on a partial equilibrium approach. In the real world, however, firms are thought to make decisions from a long-run perspective, and thus a dynamic model for the invoicing decision would also seem beneficial. As far as we know, however, no research has been conducted on the choice of an invoice currency using a dynamic partial equilibrium model. In trade theory, however, there is a large body of research based on a dynamic partial equilibrium model that explores oligopolistic firms’ decision-making on export prices, and the volume of production, and exports. For example, Krugman (1987) analyzes the dynamic changes in exchange rate pass-through of exporting firms, taking account of the time required for the establishment of a sales network and for changes in prices to affect the level of consumer demand. 32 MONETARY AND ECONOMIC STUDIES/MARCH 2004 The Choice of Invoice Currency in International Trade: Implications for the Internationalization of the Yen utility of profits.17In other words, if the expected utility of profits under PCP is greater than under LCP (EU((cid:2)P) > EU((cid:2)L)), the home currency will be selected as the invoice currency, and if LCP provides the greater expected utility (EU((cid:2)L) >EU((cid:2)P)), the currency of its trading partner will be chosen as the invoice currency. Below, we examine the conditions under which the relative size of EU((cid:2)P) and EU((cid:2)L) are determined, following Bacchetta and van Wincoop (2002a). Bacchetta and van Wincoop (2002a), under the assumption that the firm chooses the optimal price in both the PCP and LCP cases,18 showed the relationship of the difference in expected utilities under PCP and under LCP (EU((cid:2)P) − EU((cid:2)L)) and the source of uncertainty, given by the exchange rate fluctuation (variance (cid:3)2 in the exchange rate), with the following equation:19 EU((cid:2)P) −EU((cid:2)L) =0.5U′—(cid:4)2(—(cid:2)—P −—(cid:2)—L) (cid:3)2. (3) (cid:4)e2 As is clear from equation (2), the second derivative of (cid:2)L with respect to the exchange rate is zero. Thus, equation (3) suggests that the home currency will be selected as the invoice currency when (cid:2)P is convex with respect to the exchange rate ((cid:4)2(cid:2)P/(cid:4)e2 > 0) and the local currency will be selected when (cid:2)P is concave ((cid:4)2(cid:2)P/(cid:4)e2 < 0). This result that the invoicing decision depends on the shape of the profit func- tion is the same as in Giovannini (1988), the pioneering theoretical work analyzing the invoice currency choice through the maximization of expected profits. The intu- ition behind this result is as follows. Suppose the exchange rate fluctuates around an expected level. Under the LCP case, since the profit function is linear with respect to the exchange rate, the expected profit is the same as the profit with the actual exchange rate being equal to its expected level. Under the PCP case, in contrast, when the profit function is concave, expected profit is lower than profit with the actual exchange rate being equal to its expected level. Thus, LCP is selected to stabilize the local currency price against exchange rate fluctuations (the opposite is true when the profit function is convex). Whether the profit function is convex or concave depends on the shapes of the demand function and the cost function. Bacchetta and van Wincoop (2002a) used the following demand and cost functions to show that the degree of differentiation in the firm’s products affects its choice of invoice currencies: D(p) =p−(cid:5), (4) C(q) =wq(cid:6), (5) 17.Although we follow Bacchetta and van Wincoop (2002a) and Friberg (1998) in using a framework whereby the choice of the invoice currency depends on the expected utility of profits, interpreting the utility functionUas a value function of profits does not change our results. If the firm is risk neutral, it is indifferent in its choice of invoice currencies, even if the exchange rate fluctuation is uncertain. For this reason, the firm is assumed to be risk averse. 18.Without uncertainty, when a firm sets the optimal price based on a given exchange rate, the price is the same whether under PCP or LCP, provided it is measured in the same currency. 19.For the derivation of equation (3), see Appendix 1. This condition does not apply under various exchange rate levels, but rather is a local condition that applies only in the neighborhood around the equilibrium exchange rate. 33 where (cid:5)is the price elasticity of demand20 and w is the wage rate.21 By substituting equations (4) and (5) into equation (3), equation (3) can be shown in the following form: EU((cid:2)P) −EU((cid:2)L) =0.5U′((cid:5)−1)p–1−(cid:5)[1 −(cid:5)((cid:6)−1)](cid:3)2. (6) p– is the firm’s optimal price under the assumption that E(e) =1, and p–P = p–L = p– holds. Therefore, when (cid:5)((cid:6)−1) < 1 (the profit function being convex under PCP), PCP is chosen, and when (cid:5)((cid:6)− 1) > 1 (the profit function being concave under PCP), LCP is selected (Figure 1). As noted earlier, (cid:5)is the price elasticity of demand, and the lower (cid:5)is, the more differentiated and the more competitive the product. Accordingly, given (cid:6), the firm chooses PCP when the degree of differentiation is high and chooses LCP when differentiation is low. b. Choosing an invoice currency when a third country’s currency is an option Friberg (1996, 1998) showed that the U.S. dollar had more than a 50 percent share of world trade in terms of the invoice currency used, despite the United States having only a 14 percent share of the worldwide trade in goods. Then, Friberg pointed out the need to consider the possibility of using a third country’s currency, rather than the Figure 1 Relationship between Profits and the Exchange Rate under PCP and LCP (cid:2) (cid:2)P if (cid:5) ( (cid:6) – 1) < 1 (cid:2)L (cid:2)P if (cid:5) ( (cid:6) – 1) > 1 e 1 Source: Bacchetta and van Wincoop (2002a). 20.(cid:5)>1 is assumed to ensure that the production of the monopoly firm is positive. 21.Assuming that Lis the labor input and the production function is given by q =L1/(cid:6), (cid:6)is the reciprocal of labor’s share. This can be easily verified by using the property that the marginal productivity oflabor is equal to the real wage. 34 MONETARY AND ECONOMIC STUDIES/MARCH 2004 The Choice of Invoice Currency in International Trade: Implications for the Internationalization of the Yen home currency or the trading partner’s currency, as the invoice currency and examined the criteria for such use from a theoretical perspective.22Friberg demonstrated that the choice of an invoice currency depended not only upon the shape of the profit function, but also on the degree of uncertainty (size of the variance) for two distinct exchange rates: the home currency with the trading partner’s currency and the third country’s currency with the trading partner’s currency. Below, we examine the criteria for choosing a third country’s currency by using the above-noted framework from Bacchetta and van Wincoop (2002a).23 Let the exchange rate for the trading partner’s currency per unit of third-country currency be given as eO, and the export price denominated in the third country’s currency as pO. When the firm uses the third country’s currency as its invoice currency, its profit (cid:2)Ois given by the following equation: (cid:2)O=—e pOD(—pO)−C(D(—pO)). (7) eO eO eO Assuming that e and eO are independent of each other,24 and using the same methodology shown in Appendix 1, the conditions for selecting between the third country’s currency and LCP, and between the third country’s currency and PCP are given as follows: (cid:4)(cid:2) EU((cid:2)O) −EU((cid:2)L) =0.5U′—2—O–((cid:3)O)2, (8) (cid:4)(eO)2 (cid:4)(cid:2) (cid:4)(cid:2) EU((cid:2)O) −EU((cid:2)P) =−0.5U′—2—–P(cid:3)2+0.5U′—2—O–((cid:3)O)2. (9) (cid:4)e2 (cid:4)(eO)2 Assume that the firm sets its optimal price at a given exchange rate and that E(e) =E(eO) =1. We can then derive, from equations (3), (8), and (9), the following conditions for the invoicing decision when a third country’s currency is an option. (1) When the profit functions (cid:2)Pand (cid:2)O are concave with respect to the exchange rates e and eO((cid:4)2(cid:2)P/(cid:4)e2 <0, (cid:4)2(cid:2)O/(cid:4)(eO)2 < 0), LCP offers the highest expected profits. If the fluctuation in the exchange rate between the third country’s currency and the trading partner’s currency is smaller than that in the rate between the home currency and the trading partner’s currency (((cid:3)O)2 < (cid:3)2), the next highest expected utility after LCP25 is obtained by choosing the third country’s currency as the invoice currency.26 22.Friberg (1998) incorporated forward currency transactions, a factor we do not consider explicitly, into his model for analyzing theoretically the choice between LCP, PCP, and a third country’s currency. The result is the same, however, whether or not forward currency transactions are modeled. Virtually no research has been done on the invoicing decision in the presence of a futures market, and this line of research would be promising. 23.For the derivation of the conditions when a third country’s currency is an option, see Appendix 2. 24.It has been widely pointed out that movements in both directions tend to be contagious between the yen-U.S. dollar rate and the Eurodollar rate, so this assumption may be fairly strong. 25.Given that Japanese exports to East Asia are almost never invoiced in the local currency, it would be beneficial to study a second-best solution in which the choice of LCP is ruled out and the choice is between PCP and a third country’s currency. One likely reason that LCP is rarely used for exports by Japanese firms to East Asia is the lack of a forex market offering direct exchange between the yen and local currencies in East Asia. 26.This result is identical to that of Friberg (1998). 35 (2) When the profit functions (cid:2)Pand (cid:2)O are convex with respect to the exchange rates e and eO((cid:4)2(cid:2)P/(cid:4)e2 >0, (cid:4)2(cid:2)O/(cid:4)(eO)2 > 0), whichever of the home currency and the third country’s currency has the greatest fluctuation in exchange rate is selected as the invoice currency. LCP offers the lowest expected profits. 2. Oligopoly model In the case of one monopolistic firm, the invoicing decision is made solely by that firm and is not influenced by other firms. In the case of multiple monopolistically com- petitive firms, however, a firm’s decision is affected by the decisions made by other firms, and likewise its behavior also affects the behavior of other firms. This points to the need to examine the invoicing decision under a game theoretical framework. Below, we extend the above-mentioned monopoly model to an oligopoly model. Bacchetta and van Wincoop (2002a) examined an extension of the above-noted monopoly model in which the home country has multiple firms producing homogenous final goods and those firms compete with each other in the foreign country. Let N be the number of firms producing the homogenous product in the home country and N* be the number of such firms in the foreign country, with the home country’s market share shown by n(n = N/(N +N*)). The demand function for the good produced by firm j is defined as follows:27,28 D(p,P*)=——1—–(—pj)−(cid:5)d*, (10) j j N +N* P* where p is the price of firm j’s product denominated in the foreign currency, P* j is the general price index in the foreign country, and d* is the real consumption expenditure in the foreign country. The general price index in the foreign country P*is given by the following equation: P*=[(1 −n)(p*)1−(cid:5)+nf (pP/e)1−(cid:5)+n(1 −f )(pL)1−(cid:5)]1/(1−(cid:5)), (11) where f represents the fraction of firms in the home country that set export prices based on PCP. Equation (11) illustrates that the general price index in the foreign country is affected by the invoicing decision of the home country’s firms. Thus, equation (10) demonstrates that the demand for a firm’s exports is affected not only by that firm’s export prices but also by the invoicing decision made by competing firms in the home country. To simplify the calculations, we assume that d*/(N +N*) =1, and using equations (10) and (11), we recalculate equation (3) to arrive at the following condition for selecting the invoice currency: 27.The demand function for firm j’s product is defined as in equation (10) because overall real demand in the foreign country is implicitly assumed to be a CES function. Furthermore, the general price index in the foreign country is given by equation (11), which is the dual of real demand determined by a CES function. 28.To ensure that demand does not fall to zero for any of the goods (that a corner solution is excluded), it is assumed that the price elasticity of demand (cid:5)for the goods is greater than one. Given the assumption that real overall demand is determined by a CES function, the price elasticity of demand (cid:5)shows the elasticity of substitution between competing goods. 36 MONETARY AND ECONOMIC STUDIES/MARCH 2004