IMES DISCUSSION PAPER SERIES

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1 IMES DISCUSSIN PAPER SERIES Th Choic of Invoic Currncy in Intrnational Trad: Implications for th Intrnationalization of th Yn Hiroyuki I, Akira TANI, and Toyoichirou SHIRTA Discussion Papr No. 003-E-13 INSTITUTE FR MNETARY AND ECNMIC STUDIES BANK F JAPAN C.P. BX 03 TKY JAPAN You can download this and othr paprs at th IMES Wb sit: Do not rprint or rproduc without prmission.

2 NTE: IMES Discussion Papr Sris is circulatd in ordr to stimulat discussion and commnts. Viws xprssd in Discussion Papr Sris ar thos of authors and do not ncssarily rflct thos of th Bank of Japan or th Institut for Montary and Economic Studis.

3 IMES Discussion Papr Sris 003-E-13 ctobr 003 Th Choic of Invoic Currncy in Intrnational Trad: Implications for th Intrnationalization of th Yn Hiroyuki I*, Akira TANI**, Toyoichirou SHIRTA*** Abstract In this papr w prsnt an ovrviw of thortical rsarch on th choic of an invoic currncy for xports from th prspctiv of xpctd profits maximization. W thn us this thory as a basis to offr a currnt assssmnt and futur outlook rgarding th us of th yn in trad transactions, which is on aspct of th intrnationalization of th yn. ur analysis dmonstrats that th currnt us of th yn to pric xports is largly consistnt with lvls that can b xplaind by thory. This suggsts that th currnt masurs for improving Japans financial markts ar, by thmslvs, likly to hav only a limitd impact on xpanding th us of th yn as a dnomination of trad transactions, givn th currnt intrnational comptitivnss and markt shar of Japan s manufacturing industry and th currnt xchang rat rgims. Morovr, th currncy-baskt rgim that has bn proposd for East Asia from th prspctiv of th intrnationalization of th yn is not ncssarily thortically dsirabl for th rgion, nor is xpandd us of yn in trad transactions ncssarily a fr lunch for Japan, in that it may vry wll bring with it nw problms for implmnting conomic policis. Ky words: Invoic currncy, CP (local currncy pricing), PCP (producr s currncy pricing), intrnationalization of th yn, nw opn-conomy macroconomics, currncy-baskt rgim JE classification: F41, F4, 11 * Rsarch Division I, Institut for Montary and Economic Studis, Bank of Japan ( ** Dputy Dirctor and Snior Economist, Rsarch Division I, Institut for Montary and Economic Studis, Bank of Japan ( *** Human Rsourcs Managmnt Dpartmnt, Bank of Japan, formrly assignd to Rsarch Division I, Institut for Montary and Economic Studis W would lik to thank Profssor Shin ichi Fukuda, Faculty of Economics, Univrsity of Tokyo, and staff at th Intrnational Dpartmnt and th Institut for Montary and Economic Studis of th Bank of Japan for thir valuabl commnts. Furthrmor, w would lik to xprss our apprciation to Mr. Ryouji Koik in Rsarch Division I of th Institut for Montary and Economic Studis for his hlp with data on trad btwn Japan and East Asia. Th opinions and invitabl rrors containd in this papr ar purly thos of th authors, and do not rprsnt th official viws of ithr th Bank of Japan or th Institut of Montary and Economic Studis.

4 Tabl of Contnts I. Introduction... 1 II. Thory on th Endognous Choic of Invoic Currncy... 5 A. Partial quilibrium approach... 6 B. Gnral quilibrium approach C. Summary of conditions for th invoicing dcision III. Assssing th Us of th Yn as an Invoic Currncy A. Currnt us of th yn as an invoic currncy and prior rsarch B. Th us of th yn viwd from ndognous invoicing dcision thory... 0 C. Assssing th currnt us, and forcasting futur us, of th yn as an invoic currncy... 3 IV. Incras in th Us of th Yn as an Invoic Currncy and th Currncy-Baskt Rgim... 4 A. Th impact of a currncy-baskt rgim on th us of th yn as an invoic currncy... 5 B. Th dsirability of a currncy-baskt rgim if th us of th yn as an invoic currncy has xpandd -- An application of nw opn-conomy macroconomics... 5 V. Conclusion... 7 Appndix A. Drivation of th Conditions for Choosing PCP and CP... 9 Appndix B. Conditions for Choosing an Invoic Currncy Whn a Third Country s Currncy is Availabl Appndix C. Th Pric Elasticity of Japan s Exports to East Asia by Product Catgory Appndix D. Th Intrnational Transmission of Montary Policy undr Asymmtric Pric Stting... 34

5 I. Introduction In rspons to rcnt dvlopmnts in intrnational macroconomics thory, thr has bn strong intrst among acadmics and cntral bankrs rgarding th firm s choic of a currncy to pric its xports. Sinc bstfld and Rogoff (1995) publishd thir work on nw opn-conomy macroconomics, a dynamic gnral quilibrium opn-conomy modl with micro foundations, many rsarchrs hav incorporatd th firm s invoicing dcision into this modl. This lin of rsarch shows that th transmission of montary policy, optimal montary policy ruls and th optimal xchang rat rgim all dpnd on th firm s choic of an invoic currncy for xporting its goods, that is, whthr it chooss PCP (producr s currncy pricing) or CP (local currncy pricing). 1 n problm with this ara of rsarch, howvr, is that th xporting firm s invoicing dcision is givn xognously (Fujiki and tani [00] and Grlach [00]). Consquntly, in rcnt yars focus has bgun to shift toward thortical rsarch using modls in which th currncy choic is ndognous. Until now, rsarch on th choic of an invoic currncy has largly focusd on why th US dollar has bcom th world s vhicl currncy for intrnational transactions. This rsarch on vhicl currncy can b dividd into svral catgoris according to th ssntial function of mony. Th first catgory is analysis focusd on mony as a mdium of xchang, and th rsarch is basd on th transaction cost of currncy convrsion. Swoboda (1968) is a pionr in this ara. Rgarding why only a small numbr of currncis, ld by th US dollar, wr usd as vhicl currncis in intrnational trad, Swoboda pointd out that (1) a highr transaction cost in convrting btwn th hom and forign currncis rsultd in a largr amount of forign currncy hld, and () th total amount of ovrall forign currncy holdings could b rducd by holding a singl vhicl currncy for all trad sttlmnt rathr than holding th currncis of ach trading partnr, lading to a rduction in ovrall transaction cost. Rgarding which country s currncy bcam th vhicl currncy, Swoboda found that th vhicl currncy chosn was th currncy of a country with (1) a larg valu of intrnational trad and a larg volum of transactions in its currncy on th forx 1 S an (003) rgarding rcnt progrss in thortical rsarch incorporating th firm s pric stting bhavior into nw opn-conomy macroconomics. For mor on this, s Mag and Rao (1980). 1

6 markts, 3 and () wll-dvlopd financial markts. 4 Krugman (1980) also focusd on th transaction cost btwn th hom and forign currncis, and found that whn th avrag transaction cost was dcrasing in trading volum, th currncy with th lowst translation cost, i.., th currncy with th largst transaction volum, would bcom th vhicl currncy. H also found that a currncy s status as a vhicl currncy was aidd by inrtia. 5 Ry (001) built a mor rigorous modl to analyz th rsarch don by Swoboda and Krugman. Ry (001) introducd transaction costs of currncy xchang to a thr-country gnral quilibrium modl and thortically showd how multipl quilibria as to th choic of a vhicl currncy aros from th strngth of trad tis and th siz of transaction costs. H found that th currncy of th country with th gratst dgr of opnnss and th currncy with th lowst transaction costs of xchang with othr currncis bcom th vhicl currncy. 6 Th scond catgory of rsarch on vhicl currncy focuss on mony as a unit of account. McKinnon (1979) statd that intrnational transactions of highly homognous primary goods wr concntratd in spcializd xchang markts in th US and th UK, and concludd that a singl vhicl currncy would b usd for trading in homognous goods bcaus xprssing prics in th sam currncy mad mor 3 This is bcaus th gratr th trading volum, th lowr th transaction costs of xchanging currncis. 4 Chrystal (1977) usd th US dollar, British strling, Frnch franc and Grman mark to provid mpirical support to th critria for slcting a vhicl currncy idntifid by Swoboda (1968). 5 To support this, Krugman (1980) provids th xampl of Grat Britain, which although it dclind in conomic importanc du to World War I, was abl to maintain th pound strling s status as th vhicl currncy togthr with th US dollar until World War II. 6 As notd abov, rsarch focusd on mony as a mdium of xchang was largly dpndnt on th transaction costs btwn currncis. Thr is on thortical work, howvr, that ignors th transaction cost btwn currncis to discovr th mchanism that crats a vhicl currncy Matsuyama, Kiyotaki and Matsui (1993). Using a random matching modl, Matsuyama, Kiyotaki and Matsui (1993) analyzd th typ of quilibrium that would aris as to th rgional us of mony, in a world whr only two typs of mony, th hom currncy and th forign currncy, xistd. Thy found that thr typs of quilibrium would aris: (1) th rgional currncy cas, in which absolutly no intrnational transactions took plac, and th hom currncy was only usd in th hom country and th forign currncy only usd in th forign country; () th singl vhicl currncy cas, whrby on currncy bcoms a rgional currncy, and th othr currncy is usd not only in its country of issu but also in th forign country; and (3) th dual vhicl currncy cas, whrby both currncis ar usd in both th hom country and th forign country. Furthrmor, thy showd that th currncy of a country with a larg conomy is mor likly to bcom th vhicl currncy, and th highr th dgr of conomic intgration, th gratr th liklihood that two vhicl currncis would co-xist.

7 fficint transactions possibl whn trading in such goods. 7 8 Nvrthlss, th fraction of primary goods invoicd in US dollars continus to dclin, whras th fraction of machinry and othr highly htrognous products tradd in US dollars is going up in th intrnational trad. McKinnon (1979) argud that th hom currncy is slctd for pricing highly htrognous goods. 9 Consquntly, th abov-notd rsarch on vhicl currncy dos not adquatly xplain th actual invoicing dcision mad, and this in turn maks it ncssary to xamin th choic of non-vhicl currncy, i.., th dcision on which country s currncy is chosn as th invoicing currncy in bilatral trad. Rgarding this point, Giovannini (1988) analyzd th currncy choic mad by a monopolistic xporting firm from th prspctiv of maximizing xpctd profits undr uncrtainty in xchang rat movmnts. H concludd that th choic of an invoic currncy dpndd on th shap of th profit function. 10 Sinc his rsarch, thr has bn a larg body of thortical rsarch on choosing th invoic currncy from th prspctiv of maximizing xpctd profits. Such thortical rsarch can b an xtrmly usful guidlin for assssing th currnt stat, and projcting th futur, of th us of th yn as th invoic currncy in 7 Th sam argumnt can b mad for financial transactions. That is, it is possibl to lowr th cost of collcting information and trad mor fficintly by using a singl vhicl currncy for financial transactions and holding financial assts dnominatd in that vhicl currncy, rathr than by using multipl currncis and holding financial assts dnominatd in ach of th currncis. For rlatd litratur, s Brunnr and Mltzr (1971). 8 Thr is also rsarch on vhicl currncy that focuss on mony as a stor of valu, arguing that whn currncy is usd for sttlmnt at a futur dat, th currncy with a stabl valu is chosn as th invoic currncy and bcoms th vhicl currncy. 9 Grassman (1973) studid th invoic currncy usd in th trad of Swdn and Dnmark and found that both countris tndd to us th producr s currncy as th invoic currncy in thir trad. This tndncy for th producr s currncy to b usd as th invoic currncy in intrnational trad is now known as Grassman s aw, following Grassman (1973). 10 Th advantag of this approach is that it nabls simultanously solving th problms of choosing an invoic currncy and stting th xport pric, and that it is possibl to dscrib th rlationship btwn th choic of invoicing currncy and th xchang rat pass-through. For xampl, Fribrg (1998) showd that th condition for choosing th local currncy as th invoic currncy is th sam as th condition rquiring th xchang rat pass-through of th xport prics to b lss than on. n th othr hand, thr ar also problms with this approach. That is, this litratur assums that th pric is st bforhand and that th xport volum can b flxibly dtrmind. In actual trad transactions, howvr, not only th pric but also th xport volum is dcidd whn making th xport contract. Thrfor, th modl s assumptions ar inconsistnt with actual trad. Furthrmor, vn a singl firm can choos from among th hom currncy, th forign currncy and a vhicl currncy for th invoic currncy. Undr th profit maximization approach, howvr, th firm can only choos btwn two options PCP or CP and thus this modl is also limitd in its ability to xplain actual invoic currncy dcisions. 3

8 trad transactions, on aspct of th intrnationalization of th yn. 11 Givn that a larg proportion of Japan s xports ar diffrntiatd, htrognous goods such as machinry, w bliv Giovannini (1988) and latr rsarch on choosing an invoic currncy basd on maximization of xpctd profits is xtrmly grman. Up until now, howvr, th analysis and policy proposals on th us of th yn as an invoic currncy hav bn basd on rsarch focusing on mony as a mdium of xchang and as a unit of account. As far as w know, non of ths studis or policy proposals hav takn advantag of th partial or gnral quilibrium analysis basd on xpctd profit maximization from Giovannini (1988) and latr rsarch. 1 Rcntly, som conomists, particularly in Japan, hav bn advocating th introduction of a currncy-baskt rgim in East Asia. 13 Many of th countris in East Asia ar now using a d facto dollar pg. 14 If high volatility in th yn-dollar rat, which implis high volatility in th xchang rats btwn th yn and East Asian currncis, is standing in th way of xpandd us of th yn as an invoic currncy, it is likly that th introduction of a currncy-baskt rgim in East Asian would stabiliz th xchang rat btwn th yn and East Asian currncis and thrby promot us of th yn. Thus thr is a nd to xamin whthr a currncy-baskt rgim is dsirabl in East Asia whn considring th us of th yn as an invoic currncy in th futur. Nw opn-conomy macroconomics is xtrmly bnficial in this rgard, givn that it nabls xamination of th optimal currncy rgim from an conomic wlfar prspctiv. In this papr, w will xamin th optimality of a currncy-baskt rgim in East Asia, taking advantag of rcnt dvlopmnts in nw opn-conomy macroconomics. ur papr is organizd as follows. In Sction II, w provid an ovrviw of ndognous currncy choic thory. W first survy rsarch using th partial quilibrium modls that hav dominatd th analysis to dat, and thn introduc rcnt rsarch basd on a gnral quilibrium modl. In actual trad, a larg prcntag of 11 Th intrnationalization of th yn signifis th xpandd us of th yn not only in conducting trad but also in capital transactions and as a dnomination of forign rsrvs. For xampl, th Ministry of Financ (1999) dfind yn intrnationalization as incrasing th prcntag of Japan s cross-bordr transactions and transactions conductd ovrsas dnominatd in yn as wll as raising th fraction of nonrsidnts asst portfolios dnominatd in yn, pointing spcifically to raising th yn s profil in th intrnational currncy rgim and incrasing th wight of businss transactions, capital transactions and forign currncy rsrvs hld in yn. 1 S Sction III for furthr discussion rgarding this point. 13 itratur on this topic includs gawa and Ito (000). 14 S Kawai (00) and McKinnon and Schnabl (00). 4

9 trad transactions ar invoicd in US dollars, vn in trad not involving th US (whr th dollar is a third country s currncy). Thn, w xamin th possibility for th third country s currncy to b chosn as an invoic currncy using th xpctd profits maximization framwork that allows for us of a third country s currncy in addition to PCP or CP, rathr than traditional rsarch on vhicl currncy. In Sction III, w start by looking at th us of th yn as an invoic currncy. W thn assss this currnt us and forcast futur us by xamining th xtnt to which th actual invoicing dcision in Japan and othr industrializd countris can b xplaind by th conditions found in th thortical rsarch discussd in Sction II. In Sction IV, w tak advantag of nw opn-conomy macroconomics to xamin th dsirability of a currncy-baskt rgim in East Asian from th prspctiv of th us of th yn as an invoic currncy. In Sction V, w considr th ffct of an incras in th us of th yn as an invoic currncy on conomic policy, and thn clos by prsnting our conclusions. In Appndics A and B, w xplain our mthodology for driving th quations for choosing btwn PCP and CP xamind in Sction II, and also provid a mor dtaild xplanation of th conditions govrning th invoicing dcision whn a thirdcountry currncy is availabl. In Appndix C, w xplain th mthodology for stimating th pric lasticity for ach product catgory of Japan s xports to East Asia (xcluding China) and th stimatd rsult, which was usd in th mpirical analysis of Sction III. In Appndix D, w introduc prior rsarch analyzing th impact on th intrnational transmission of montary policy in th hypothtical cas of growth in th yn s us as an invoic currncy. ur papr introducs thory on th choic of an invoic currncy for xports and uss that thory to xamin th us of th yn as an invoic currncy for xport transactions. Th yn is usd as an invoic currncy considrably lss for imports than for xports, and th us of th yn for pricing Japan s imports is outsid th scop of this papr. II. Thory on th Endognous Choic of Invoic Currncy Thortically, a firm chooss an invoic currncy basd on which currncy maximizs xpctd profits (or th xpctd utility of profits) in th prsnc of uncrtainty. Thortical rsarch in this ara can b broadly dividd into two typs. Th first typ, a partial quilibrium approach in which th only uncrtainty is xchang rat 5

10 fluctuations, 15 has bn th prdominant analytical framwork in rsarch to dat. Th scond typ is a gnral quilibrium approach that has drawn incrasing attntion du to rcnt advancs in nw opn-conomy macroconomics. In this approach, which taks into account that th xchang rat varis du to various shocks such as montary shocks and production shocks and that such shocks also affct othr macroconomic variabls, th invoicing dcision is mad in light of all of th ffcts from ths shocks. By survying dvlopmnts in th litratur on ndognous currncy choic thory, w aim to shd light on both th critria usd and th dcision mad rgarding which currncy to us as th invoic currncy. A. Partial quilibrium approach Th partial quilibrium approach assums uncrtainty rgarding xchang rat fluctuations, but no uncrtainty rgarding dmand or production costs, and xamins th choic of an invoic currncy by a monopolistic firm facing a downward sloping dmand curv. This partial quilibrium approach can b subdividd into two diffrnt modls: th simplst monopoly modl whr only on monopolistic firm xists, and an oligopoly modl in which multipl monopolistic firms compt in th xport markt Monopoly modl a. Choosing btwn th hom currncy and local currncy Rsarchs to dat hav shown that th invoicing dcision in a monopoly modl is largly dtrmind by th shaps of th dmand function, th cost function, and th 15 Japan mad a larg amount of forign dirct invstmnt, primarily in East Asia, in rspons to th rapid apprciation of th yn following th Plaza Accord. As a rsult, som firms hav globalizd thir production organizations. Th globalization of ths firms has ld to th incrasd us of yn as an invoic currncy (tani, Shiratsuka and Shirota [003]). As is indicatd, a dramatic chang in th xchang rat forcs changs in firms production systms and influncs thir choic of an invoic currncy. Nvrthlss, our papr survys th xisting thortical rsarch from th prspctiv of uncrtainty ovr th xchang rat fluctuations, rathr than of hug changs in th xchang rat lvl. 16 W introduc a static modl for th choic of th invoic currncy by a monopolistic or oligopolistic firm, basd on a partial quilibrium approach. In th ral world, howvr, firms ar thought to mak dcisions from a long-run prspctiv, and thus a dynamic modl for th invoicing dcision would also sm bnficial. As far as w know, howvr, no rsarch has bn conductd on th choic of an invoic currncy using a dynamic partial quilibrium modl. In trad thory, howvr, thr is a larg body of rsarch basd on a dynamic partial quilibrium modl that xplors oligopolistic firms dcision making on xport prics, and th volum of production, and xports. For xampl, Krugman (1987) analyzs th dynamic changs in xchang rat pass-through of xporting firms, taking account of th tim rquird for th stablishmnt of a sals ntwork and for changs in prics to affct th lvl of consumr dmand. 6

11 rsulting profit function. Suppos that, with uncrtainty in th variation of th hom-currncy dnominatd nominal xchang rat, th xporting firm sts th pric prior to knowing th xchang rat for that priod. Additionally, th firm has two choics: (1) stting th xport pric at th forign-currncy quivalnt of thir domstic sals pric (PCP); or () stting th xport pric in local currncy trms (CP). t th dmand curv for th goods producd by th firm b D(p) and th firm s cost function b C(q) (whr p is th pric facd by th consumr of th xports, and q is th production volum). With p P rprsnting th hom currncy-dnominatd pric, th xport pric dnominatd in th forign currncy undr PCP is p P /. Th xport pric undr CP is givn by p P. Basd on ths assumptions, profit undr PCP, Π, and profit undr CP, Π, ar dfind as follows. P P P P Π = p D( p ) C( D( p )), (1) Π = p D( p ) C( D( p )). () Givn that th xchang rat is uncrtain, th firm s dcision on whthr to choos PCP or CP is mad basd on which pric stting bhavior givs th highst xpctd utility of profits. 17 In othr words, if th xpctd utility of profits undr PCP P is gratr than undr CP (EU( Π )>EU( Π )), th hom currncy will b slctd as th invoic currncy, and if CP provids th gratr xpctd utility (EU( Π ) > P EU( Π )), th currncy of its trading partnr will b chosn as th invoic currncy. P Blow, w xamin th conditions undr which th rlativ siz of EU( Π ) and EU( Π ) ar dtrmind, following Bacchtta and van Wincoop (00a). Bacchtta and van Wincoop, undr th assumption that th firm chooss th optimal pric in both th PCP and CP cass, 18 showd th rlationship of th P diffrnc in xpctd utilitis undr PCP and undr CP ( EU ( Π ) EU ( Π ) ) and th sourc of uncrtainty, givn by th xchang rat fluctuation (varianc σ in th xchang rat), with th following quation Although w follow Bacchtta and van Wincoop (00a) and Fribrg (1998) in using a framwork whrby th choic of th invoic currncy dpnds on th xpctd utility of profits, intrprting th utility function U as a valu function of profits dos not chang our rsults. If th firm is risk nutral, it is indiffrnt in its choic of invoic currncis, vn if th xchang rat fluctuation is uncrtain. For this rason, th firm is assumd to b risk-avrs. 18 Without uncrtainty, whn a firm sts th optimal pric basd on a givn xchang rat, th pric is th sam whthr undr PCP or CP, providd it is masurd in th sam currncy. 19 For th drivation of quation (3), s Appndix A. This condition dos not apply undr various xchang rat lvls, but rathr is a local condition that applis only in th nighborhood around th quilibrium xchang rat. 7

12 P P ( Π Π ) EU ( Π ) EU ( Π ) = 0.5U ' σ. (3) As is clar from quation (), th scond drivativ of Π with rspct to th xchang rat is zro. Thus, quation (3) suggsts that th hom currncy will b P slctd as th invoic currncy whn Π is convx with rspct to th xchang rat ( Π P >0) and th local currncy will b slctd whn Π P is concav ( Π P <0). This rsult that th invoicing dcision dpnds on th shap of th profit function is th sam as Giovannini (1988), th pionring thortical work analyzing th invoic currncy choic through th maximization of xpctd profits. Th intuition bhind this rsult is as follows. Suppos th xchang rat fluctuats around an xpctd lvl. Undr th CP cas, sinc th profit function is linar with rspct to th xchang rat, th xpctd profit is th sam as th profit with th actual xchang rat bing qual to its xpctd lvl. Undr th PCP cas, in contrast, whn th profit function is concav, xpctd profit is lowr than profit with th actual xchang rat bing qual to its xpctd lvl. Thus CP is slctd to stabiliz th local currncy pric against xchang rat fluctuations (th opposit is tru whn th profit function is convx). Whthr th profit function is convx or concav dpnds on th shaps of th dmand function and th cost function. Bacchtta and van Wincoop usd th following dmand and cost functions to show that th dgr of diffrntiation in th firm s products affcts its choic of invoic currncis. µ D ( p) = p, (4) η C ( q) = wq, (5) whr µ is th pric lasticity of dmand 0 and w is th wag rat. 1 By substituting quations (4) and (5) into quation (3), quation (3) can b shown in th following form, EU P 1 µ ( Π ) EU ( Π ) = 0.5U '( µ 1) p [1 µ ( η 1)] σ. (6) p is th firm s optimal pric undr th assumption that E() = 1, and P p = p = p holds. Thrfor, whn µ ( η 1) < 1 (th profit function bing convx undr PCP), PCP is chosn, and whn µ ( η 1) > 1 (th profit function bing concav undr PCP), CP is slctd (Figur 1). As notd arlir, µ is th pric lasticity of 0 µ > 1 is assumd to nsur that th production of th monopoly firm is positiv. 1 1 η Assuming that is th labor input and th production function is givn by q =, η is th rciprocal of labor s shar. This can b asily vrifid by using that th marginal productivity of labor is qual to th ral wag. 8

13 dmand, and th lowr is µ, th mor diffrntiatd and th mor comptitiv th product is. Accordingly, givn η, th firm chooss PCP whn th dgr of diffrntiation is high and chooss CP whn diffrntiation is low. b. Choosing an invoic currncy whn a third country s currncy is an option Fribrg (1996, 1998) showd that th US dollar had ovr a 50% shar of world trad in trms of th invoic currncy usd, dspit th US having only a 14% shar of th worldwid trad in goods. Thn, Fribrg pointd out th nd to considr th possibility of using a third country s currncy, rathr than th hom currncy or th trading partnr s currncy, as th invoic currncy and xamind th critria for such us from a thortical prspctiv. Fribrg dmonstratd that th choic of an invoic currncy dpndd not only upon th shap of th profit function, but also on th dgr of uncrtainty (siz of th varianc) for two distinct xchang rats -- th hom currncy with th trading partnr s currncy and th third country s currncy with th trading partnr s currncy. Blow, w xamin th critria for choosing a third country s currncy by using th abov-notd framwork from Bacchtta and van Wincoop (00a). 3 t th xchang rat for th trading partnr s currncy pr unit of third country currncy b givn as, and th xport pric dnominatd in th third country s currncy as p. Whn th firm uss th third country s currncy as its invoic currncy, its profit Π is givn by th following quation, ( p p Π = p D ) C( D( )). (7) Assuming that and ar indpndnt of ach othr, 4 and using th sam mthodology shown in Appndix A, th conditions for slcting btwn th third country s currncy and CP, and btwn th third country s currncy and PCP ar givn as follows. Fribrg (1998) incorporatd forward currncy transactions, a factor w do not considr xplicitly, into his modl for analyzing thortically th choic btwn CP, PCP and a third country s currncy. Th rsult is th sam, howvr, whthr or not forward currncy transactions ar modld. Virtually no rsarch has bn don on th invoicing dcision in th prsnc of a futurs markt, and this lin of rsarch would b promising. 3 For th drivation of th conditions whn a third country s currncy is an option, s Appndix B. 4 It has bn widly pointd out that movmnts in both dirctions tnd to b contagious btwn th yn-dollar rat and th uro-dollar rat, so this assumption may b fairly strong. 9

14 EU ( Π ( ) Π ) EU ( Π ) = 0.5U ' ( σ ), (8) P P Π Π EU ( Π ) EU ( Π ) = 0.5U ' σ + 0.5U ' ( σ ). (9) ( ) Assum that th firm sts its optimal pric at a givn xchang rat and that E() = E( ) = 1. W can thn driv, from quations (3), (8), and (9), th following conditions for th invoicing dcision whn a third country s currncy is an option. P (1) Whn th profit functions Π and Π ar concav with rspct to th xchang rats and ( Π P < 0, Π ( ) < 0), CP offrs th highst xpctd profits. If th fluctuation in th xchang rat btwn th third country s currncy and th trading partnr s currncy is smallr than that in th rat btwn th hom currncy and th trading partnr s currncy ( ( σ ) < σ ), th nxt highst xpctd utility aftr CP 5 is obtaind by choosing th third country s currncy as th invoic currncy. 6 P () Whn th profit functions Π and Π ar convx with rspct to th xchang rats and ( Π P > 0, Π ( ) > 0), whichvr of th hom currncy and th third country s currncy has th gratst fluctuation in xchang rat is slctd as th invoic currncy. CP offrs th lowst xpctd profits.. ligopoly modl In cas of on monopolistic firm, th invoicing dcision is mad solly by that firm and is not influncd by othr firms. In th cas of multipl monopolistically comptitiv firms, howvr, a firm s dcision is affctd by th dcisions mad by othr firms, and likwis its bhavior also affcts th bhavior of othr firms. This points to th nd to xamin th invoicing dcision undr a gam thortical framwork. Blow, w xtnd th abov-mntiond monopoly modl to an oligopoly modl. Bacchtta and van Wincoop (00a) xamind an xtnsion of th abov-notd monopoly modl in which th hom country has multipl firms producing homognous final goods and thos firms compt with ach othr in th forign country. 5 Givn that Japans xports to East Asia ar almost nvr invoicd in th local currncy, it would b bnficial to study a scond-bst solution in which th choic of CP is ruld out and th choic is btwn PCP and a third country s currncy. n likly rason that CP is rarly usd for xports by Japans firms to East Asia is th lack of a forx markt offring dirct xchang btwn th yn and local currncis in East Asia 6 This rsult is idntical to that of Fribrg (1989). 10

15 t N b th numbr of firms producing th homognous product in th hom country and N* b th numbr of such firms in th forign country, with th hom country s markt shar shown by n (n = N/(N + N*)). Th dmand function for th 7 8 good producd by firm j is dfind as follows, µ * 1 p j * ) =, (10) * * D j ( p j, P d N + N P whr p j is th pric of firm j s product dnominatd in th forign currncy, P * is th gnral pric indx in th forign country, and d * is th ral consumption xpnditur in th forign country. Th gnral pric indx in th forign country P* is givn by th following quation, * * 1 µ P 1 µ 1 µ 1/(1 µ ) P = [(1 n)( p ) + nf ( p / ) + n(1 f )( p ) ], (11) whr f rprsnts th fraction of firms in th hom country that st xport prics basd on PCP. Equation (11) illustrats that th gnral pric indx in th forign country is affctd by th invoicing dcision of th hom country s firms. Thus quation (10) dmonstrats that th dmand for a firm s xports is affctd not only by that firm s xport prics but also by th invoicing dcision mad by compting firms in th hom country. * * To simplify th calculations, w assum d /( N + N ) = 1, and using quations (10) and (11), w rcalculat quation (3) to arriv at th following condition for slcting th invoicing currncy, P EU ( Π ) EU ( Π ) = 0.5U '( µ 1) p[1 µ ( η 1)(1 fn)] σ, (1) P whr p is th firm s optimal pric assuming E() = 1, and p = p = p. A comparison of quation (1), th oligopoly cas, with quation (6), th monopoly cas, rvals that th siz of th hom country s shar n affcts th firm s invoicing dcision. This rflcts th fact that dmand for that firm s product is affctd by th currncy choic mad by compting firms in th hom country through th gnral pric indx in th forign country. 7 Th dmand function for firm j s product is dfind as in quation (10) bcaus ovrall ral dmand in th forign country is implicitly assumd to b a CES function. Furthrmor, th gnral pric indx in th forign country is givn by quation (11), which is th dual of ral dmand dtrmind by a CES function. 8 To nsur that dmand dos not fall to zro for any of th goods (that a cornr solution is xcludd), it is assumd that th pric lasticity of dmand µ for th goods is gratr than 1. Givn th assumption that ral ovrall dmand is dtrmind by a CES function, th pric lasticity of dmand µ shows th lasticity of substitution btwn compting goods. 11

16 Equation (1) shows that whn µ ( η 1) < 1 (whn th profit function is convx undr PCP), th firm chooss PCP, just as in th monopoly modl. 9 Whn µ ( η 1) > 1 (th profit function is concav undr PCP), howvr, th rsult diffrs from th monopoly modl, and th firm dos not ncssarily slct CP. That is, as long as th hom country s shar of th trading partnr s markt n is blow a crtain valu n (= / µ ( η 1) ), CP is chosn. If this shar xcds n, in contrast, thr ar thr possibl quilibria: (1) all firms choos CP; () all firms choos PCP; and (3) a fraction chooss CP, whil th rst slcts PCP. 30 Not that whn n xcds n and compting firms coordinat, thy prfr to choos PCP. 31 In ordr to undrstand it, considr th cas whr n = 1. In this cas, th gnral pric indx in th forign country is dtrmind by th pric stting of th hom country firms. Whn firms othr than th firm in qustion choos PCP, th firm facs th risk that dmand for its product changs with fluctuations in th xchang rat. Whn this firm chooss PCP, howvr, th changs in both P and p j brought by xchang rat fluctuations ar th sam, and thus th ratio P/p j is constant, which liminats th dmand uncrtainty of this firm s product stmming from xchang rat fluctuations. Accordingly, whn hom country firms hav a high shar, xpctd utility can b maximizd by all th firms coordinating and choosing PCP. 3 9 This can b vrifid as follows. Assum that µ ( η 1) < 1. Givn that both f and n ar btwn 0 and 1, 1 1 fn 1 and thus µ ( η 1)(1 fn) < 1 hold. This mans that 1 µ ( η 1)(1 fn) > P 0 and thrfor EU( Π ) > EU( Π ). In othr words, th firm chooss PCP. It follows that whn µ ( η 1) < 1, PCP is chosn. 30 t µ ( η 1 ) > 1. If f = 0 (all firms choos CP) in this cas, 1 µ ( η 1)(1 fn) = 1 µ ( η 1) P > 0 and thus th inquality EU( Π ) < EU( Π ) holds. Rgardlss of th valu of n, no firm has any incntiv to choos PCP. Nxt, w assum that n = / µ ( η 1), µ ( η 1) > 1 and n > n. Undr ths assumptions, if f = 1 (all firms choos PCP), thn 1 µ ( η 1)(1 fn) > 1 µ ( η 1)(1 n) = 0, and P thus EU( Π ) > EU( Π ). No firm would choos CP in this situation. Finally, in th cas whr f = n n (0 < f < 1; i.., a fraction chooss CP, whil th rst P chooss PCP), thn 1 µ ( η 1)(1 fn) =0 and thus EU( Π ) = EU( Π ). In this cas, firms ar indiffrnt to th choic of an invoic currncy. Thr ar thus thr possibl quilibria whn µ ( η 1) > 1: (1) all firms choos CP; () all firms choos PCP; and (3) a fraction chooss CP, whil th rst chooss PCP. 31 This can b vrifid by comparing th xpctd utility whn all firms choos PCP with th xpctd utility of othr cass. 3 Bacchtta and van Wincoop (00b) built a modl in which thr wr multipl firms in th forign country producing intrmdiat goods, and multipl firms in th hom country producing final goods assmbld from th intrmdiat goods producd in th forign country, to analyz th choic of invoic currncis by ths firms. Thy showd that, whn th firms producing th final goods choos PCP, th xportrs of th intrmdiat goods would choos th hom currncy as th 1

17 B. Gnral quilibrium approach Th partial quilibrium approach taks xchang rat fluctuations as th only xognous uncrtainty. Rathr than just trating th xchang rat as a dirct, xognous shock, howvr, a mor rigorous approach would b to first gnrat xtrnal shocks via changs in th mony supply and productivity, and hav th ovrall conomy adjust to ths shocks through ndognous changs in th xchang rat. Such shocks would b xpctd to chang not only th xchang rat, but also ral consumption and othr macroconomic variabls at th sam tim. Thr has rcntly bn rsarch from this prspctiv, analyzing th invoicing dcision from a gnral rathr than partial quilibrium approach. Blow w introduc two modls using this gnral quilibrium approach, Bacchtta and van Wincoop (00a) and Dvrux and Engl (001) Bacchtta and van Wincoop (00a) To analyz th conditions for choosing an invoic currncy, Bacchtta and van Wincoop (00a) assumd th changs in th mony supply in th hom and forign countris as th sourc of uncrtainty, thn xtndd th abov-notd partial quilibrium modl to a two-country, gnral quilibrium modl by adding th following assumptions: (1) variancs of th mony supply in both countris ar idntical, () mony is hld undr a CIA (cash-in-advanc) constraint 34 and ral consumption in both countris also changs with th mony supply; and (3) dmand for ach product is affctd both by changs in th xchang rat and changs in ral consumption, whil th labor supply changs in rspons to changs in th dmand for ach good. In this modl, th quilibrium xchang rat is dtrmind by th ratio of th hom country s mony supply to th forign country s mony supply. Using th abov framwork, Bacchtta and van Wincoop compard th xpctd utility from profits undr th PCP and CP cass, undr both nominal wag rigidity and ral wag rigidity, to study th choic btwn th hom country s currncy and th invoic currncy if comptitiv prssurs on ths firms wr low (th pric lasticity of dmand for its product wr low), as in th monopoly modl. In this cas, th xchang rat pass-through to import prics is 100% and th pass-through to th consumr pric indx is 0%. 33 This gnral quilibrium analysis assums a floating xchang rat rgim. 34 Th CIA constraint implis that goods consumd in a givn priod ar purchasd with cash hld during that priod. 13

18 trading partnr s currncy. Examining first th cas of nominal wag rigidity, th rsults ar narly th sam as th conditions found in quation (1) abov. 35 Spcifically, whn ( µ 1)( η 1) < 1, th firm chooss PCP. Whn ( µ 1)( η 1) > 1, howvr, all firms choos CP if th hom country s shar of xports to that trading partnr is small, whras thr ar two possibl quilibria if th hom country s shar is sufficintly larg: (1) all firms choos PCP or () all firms choos CP. Evn in cas of two quilibria, if th firms coordinat, PCP will b chosn. Thus, rgardlss of th valu of ( µ 1)( η 1), th largr is th hom country s shar, th mor likly that th hom country s currncy will b chosn. Nxt, in th cas of ral wag rigidity, whr th nominal wag movs in proportion to th pric indx, it is concludd that th country s siz has a hug impact on th choic of invoic currncy. That is, th invoicing dcision mad by firms in a larg country is th sam as in th cas of nominal wag rigidity xplaind abov, whras it bcoms mor likly that a small country s firm slcts CP whn a larg country s firm slcts PCP. Th rason for this rsult is that, sinc th hom country firm prics its domstic sals in th hom currncy, as long as th hom country is larg, th hom country s pric indx is almost compltly unaffctd by th forign country xport pric; as a consqunc, fluctuations in th xchang rat hav vry littl ffct on th hom country s pric indx. Thrfor, assuming th pric of th good is sticky, th larg 35 As a rsult of th xtnsion to a gnral quilibrium modl by Bacchtta and van Wincoop (00a), th conditions for choosing PCP ar modifid from µ ( η 1) < 1 in quation (1) to ( µ 1)( η 1) < 1, thrby xpanding th rang for paramtrs µ and η undr which all firms choos PCP. That is, supposing th hom currncy dprciats, whn th hom country firm has chosn PCP, its product will bcom mor comptitiv and dmand will incras. n th othr hand, givn that a chang in th mony supply, such as a dcras in th forign country mony supply, causs th dprciation of th hom currncy, undr th CIA constraint, aggrgat dmand in th forign country will dcras. Consquntly, th ngativ ffct on dmand for this firm s product will b lssnd bcaus ths two ffcts ar offstting. Whn th firm has slctd CP, howvr, th comptitivnss of its product dos not chang vn with dprciation of th hom currncy, and thus thr is nothing to offst th impact from dclining dmand in th forign country. Consquntly, it is likly that th ngativ impact from xchang rat fluctuations will b lowr undr PCP than undr CP, thus xpanding th paramtr rgion undr which PCP is prfrabl. In contrast, considr th cas whr th hom country currncy dprciats du to growth in th hom country mony supply. Undr CP thr is no chang in th product s comptitivnss in th forign country whil sals in th hom country incras, whras undr PCP sals incras in both th hom and forign countris, bcaus th product bcoms mor comptitiv and dmand in th hom country grows. Thus PCP is prfrabl to CP. 14

19 country s pric indx will also b sticky, as will nominal wags. As a rsult, for a larg country, th conditions for choosing an invoic currncy ar narly th sam undr ral wag rigidity as undr nominal wag rigidity. For a small country, on th othr hand, whn th larg country slcts PCP, dprciation of th small country s currncy causs an incras in th small country s pric indx, and nominal wags incras accordingly. Thus nominal production costs in th small country incras. If th small country has slctd PCP in this cas, dmand for th small country s product in th larg country will incras in rspons to dprciation of its currncy. Nvrthlss, sinc it will not chang th nominal rcipts pr unit of xport masurd in its currncy, th ris in nominal costs will pull down profits. Whn th small country firm slcts CP, howvr, th nominal rcipt pr unit of xport gos up, and thus profits ar not squzd as much as undr PCP. Thrfor, as long as th larg country slcts PCP, th small country will slct CP.. Dvrux and Engl (001) In contrast with Bacchtta and van Wincoop (00a) which analyzs th cas whr both th hom country and forign country mony supplis hav th sam varianc, Dvrux and Engl (001) built a dynamic gnral quilibrium modl that incorporatd diffrnt uncrtaintis btwn th hom and th forign mony supply, to analyz diffrncs in firms pric stting bhavior btwn dvlopd and dvloping countris. 36 Th analysis by Dvrux and Engl dos not dirctly compar th xpctd profits undr PCP and CP as prviously shown. Thir analysis is focusd on th conditions for a firm to mak th sam choic as a compting firm, in th cas whr all of th othr firms mak th sam choic, b it PCP or CP. Thy thn show th conditions for choosing an invoic currncy that achivs th quilibrium whrin all firms slct th sam invoic currncy. Thy found that both domstic and forign firms would choos th currncy of th 36 Th main diffrnc btwn th gnral quilibrium modls of Bacchtta and van Wincoop (00a) and Dvrux and Engl (001) is th way in which mony is introducd into th modl. Th formr uss th CIA constraint, whil th lattr uss th mony in th utility function (MIU). Consquntly, in th formr th xchang rat is xprssd as th ratio of th hom country mony supply to th forign country mony supply, whil in th lattr, th xchang rat is affctd not only by th mony supply in th hom and forign countris, but also by th dgr of rlativ risk avrsion and by th pric lvl in th hom and forign countris. Accordingly, th mony supply s impact on th conomy is mor complx in th lattr rlativ to th formr. 15

20 country with th smallst mony-supply varianc. In othr words, whn th varianc of th mony supply in th hom country is small, th hom country firm chooss PCP and th forign country firm chooss CP, whras whn th varianc of th hom country s mony supply is larg, th hom country firm chooss CP and th forign country firm chooss PCP. 37 C. Summary of conditions for th invoicing dcision W bgan this sction with an introduction to th partial quilibrium approach to th choic of an invoic currncy, and followd that with an ovrviw of rcnt thortical rsarch using a gnral quilibrium approach. Th partial quilibrium approach abstracts from th mchanism by which th basic shocks montary shock and productivity shock ar transmittd to th xchang rat and othr macroconomic variabls. As a consqunc, th assumption is that an xognous shock dirctly causs xchang rat fluctuations, and that th othr variabls ar unaffctd othr than via th xchang rat. Although stting up th modl in this way maks it asir to handl, it also maks it lss rigorous. With th gnral quilibrium approach, on th othr hand, although th dirction of thortical xtnsion is corrct, th only shock allowd for is a mony supply shock, and thus, as notd in Gourinchas (00), at this stag, it is too arly to judg how robust th conclusions ar. To provid critria by which to valuat th currnt us of th yn as an invoic currncy in th nxt sction, w summariz blow th conditions for an ndognous invoicing dcision as obtaind from thortical rsarch on both sids: partial quilibrium and gnral quilibrium. (1) If thr is an option to us a third country s currncy for invoicing and CP is not slctd, 38 whichvr of th hom currncy and th third country s currncy that has th smallr xchang rat varianc with th trading partnr s currncy will b 37 Dvrux and Engl pointd out that thir rsult has important implications for th implmntation of montary policy. That is, th currncy of a country with a highly crdibl montary policy is going to b slctd as th invoic currncy by xporting firms in a forign country, and thus th xchang rat pass-through to that country s imports is low and prics in th hom country bcom mor stabl. n th othr hand, for countris with littl crdibility in montary policy, xporting firms in th forign country will choos PCP, crating a high xchang rat pass-through to imports of th hom country and thus thratning th stability of prics. For mor on this, s tani, Shiratsuka, and Shirota (003). 38 As xplaind in footnot 5, Japans firms almost nvr opt for CP on thir xports to East Asia. 16

21 slctd as th invoic currncy. 39 () Th gratr th dgr of product diffrntiation, th mor likly th firm is to slct PCP. (3) Th highr th hom country s shar in th trading partnr s markt, th mor likly th firm is to slct PCP. (4) Th largr th siz of th conomy, th mor likly that PCP will b chosn. (5) Whn varianc in th hom country mony supply is smallr (largr) than in th forign country, th hom country firm chooss PCP (CP). Conditions (1) through (5) ar summarizd in Figur. Condition (5) is for analyzing th diffrnc in firms pric stting bhavior btwn dvlopd and dvloping countris, and thus rquirs carful attntion for application to a gnralizd invoicing dcision. Additionally, this condition has vry littl mpirical support compard with othr conditions, considring that montary modls prform poorly in dtrmining xchang rats, and that, vn though varianc of th mony supply (M+CDs) in Japan has bcom smallr rlativ to othr countris in rcnt yars, th us of th yn as an invoic currncy has not incrasd in rcnt yars, as xplaind latr. Accordingly, in th nxt sction w will us conditions (1) through (4) to assss th currnt us of th yn as an invoic currncy. III. Assssing th Us of th Yn as an Invoic Currncy In sction II, w gav an ovrviw of th dvlopmnt to dat in thortical rsarch on th ndognous choic of an invoic currncy. In this sction, w us th rsults of ths thortical works to assss th currnt us and forcast futur us of th yn as an invoic currncy for Japan s xports. 40 W bgin this sction by considring th currnt us of th yn for pricing xports using data and thn introduc prior rsarch in this rgard. Nxt, w xamin th xtnt to which th conditions govrning th choic of an invoic currncy notd in th 39 Th assumption hr is that th profit function is concav with rspct to th xchang rat. In this cas, th condition is th sam as condition (1) found in Sction IIA.1.(), which xamins th possibility of slcting a third country s currncy. 40 Th analysis in this sction is xtrmly simpl in that it is limitd to comparisons by country and by product catgory, and dos not compris a dtaild mpirical analysis of data across catgoris as don by Fukuda and Ji (1994), a papr w will introduc blow. Nvrthlss, this provids th advantag of bing abl to gt a bird s y viw of th rlationship btwn invoicing dcision thory via xpctd profit maximizing and th actual invoicing dcisions mad. 17

22 prvious sction ar abl to xplain th actual invoicing dcision mad in industrializd countris including Japan, as wll as th actual shar by product catgory of Japan s xports to Asia dnominatd in yn. Thn, w assss th currnt us, and forcast th futur us, of th yn as an invoic currncy. A. Currnt us of th yn as an invoic currncy and prior rsarch 1. Trnds in th yn s us as an invoic currncy Th prcntag of Japan s xports dnominatd in yn was in a rising trnd from th 1970s until th arly 1980s, but has bn roughly flat around th 35% lvl sinc thn (Figur 3). Th prcntag of xports dnominatd in th hom currncy is much lowr for Japan than it is for th US (ovr 90%), Grmany (ovr 70%) and vn th UK and Franc (both ovr 50%) (Figur 4). ooking nxt at th prcntag of Japan s yn-dnominatd xports by rgion, in 1998, lss than 0% of xports to th US wr dnominatd in yn, whras approximatly 50% of xports to East Asia, whr conomic intgration with Japan is high, wr pricd in yn. Braking down Japan s xports to East Asia by product catgory, thos products with a high prcntag of xports dnominatd in yn includ food products and machinry products, including gnral machinry, transportation quipmnt and prcision quipmnt (Figur 5).. Prior rsarch As notd abov, Japan has a vry low prcntag of its trad transactions dnominatd in its own currncy compard with othr dvlopd countris. Kawai (199), Frankl and Wi (1993), Taguchi (1993) and th Ministry of Financ (001) analyzd th rason bhind this, and idntifid th following factors: (1) inrtia in us of th US dollar, () th lack of a markt for dirct transactions btwn th yn and Asian currncis, (3) rlativly small financial markts in Japan (compard with th US), (4) th d facto dollar pg adoptd in East Asia, (5) th high dgr of trad dpndnc with th US, 41 and (6) th prsnc in Japan of gnral trading companis. 4 Many of ths factors 41 Bcaus th prcntag of US imports dnominatd in dollars is xtrmly high, a high prcntag of trad with th US ffctivly mans a low us of hom country s currncy. 4 Th gnral trading companis hold a larg quantity of crdit claims and obligations dnominatd in forign currncy and ar abl to hdg against xchang rat fluctuations in-hous. Thus, thy hav littl incntiv to dnominat transactions in th hom country currncy as a way to avoid xchang rat risk. 18

23 ar basd on th classic analyss rlatd to vhicl currncy introducd in Sction I. As far as w know, th only prior rsarch from th prspctiv of maximization of xpctd profits ar Fukuda and Ji (1994) and Sato (1999). Fukuda and Ji (1994) usd th partial quilibrium modl introducd in Sction II, whrin PCP is chosn whn th firm s profit function is convx, CP whn it is concav. In othr words, whn th profit function is concav, th firm stabilizs its xport pric dnominatd in th local currncy irrspctiv of xchang rat fluctuations. Thus, th corrlation btwn xport prics dnominatd in th hom currncy and th xchang rat is high, and shocks to th firm s production costs do not impact xport prics dnominatd in th hom currncy. In contrast, whn th profit function is convx, xport prics dnominatd in th hom currncy hav a low corrlation with xchang rat fluctuations but ar affctd by shocks to production costs. Fukuda and Ji (1994) xamind th validity of this thory by focusing on th products for which dollars ar usd as th invoic currncy whn thy ar xportd to th US and for which th yn is usd whn thy ar xportd to Asia, such as TVs, vido casstt rcordrs and automobils. If this thory is consistnt with rality, th profit function for ths goods whn xportd to th US is concav, and xports to th US pricd in yn ar highly corrlatd with th xchang rat whil bing unaffctd by shocks to production costs. In contrast, if th profit function for xports to Asia is convx, xports to Asia pricd in yn would b unaffctd by th xchang rat but would b affctd by shocks to production costs. 43 Fukuda and Ji (1994) analyzd mpirically th rlationship btwn yndnominatd xport prics of ths products to th US and Asia on on sid and changs in th xchang rat and production costs on th othr. Thy found th rlationship consistnt with th thortical modl and thrby validatd th invoicing dcision modl basd on profit maximization. Additionally, Sato (1999) usd th analytical mthods of Fukuda and Ji (1994) to analyz smiconductor componnts xportd to Asia and to th US. His mpirical rsults wr consistnt with th hypothsis that th dollar would b usd as th invoic currncy in ordr to stabiliz th dollar-dnominatd xport pric, basd on th PTM pricing bhavior in that industry. Sato attributd th dclin in 43 Th rason why th shap of th profit function for th sam product diffrs by xport rgion could b that th shap of th dmand function is diffrnt. For xampl, if th numbr of compting firms in th US is larg and thus th product s pric lasticity is high, CP will b chosn for xports to th US. For th xports to East Asia, if th Japans firms hav strong monopolistic powr and thus pric lasticity is low, PCP will b slctd. 19

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