4. International Parity Conditions

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1 4. Inernaional ariy ondiions 4.1 urchasing ower ariy he urchasing ower ariy ( heory is one of he early heories of exchange rae deerminaion. his heory is based on he concep ha he demand for a counry's currency is derived from he demand for he goods ha his counry produces. hus, he exchange rae for a cerain counry's currency depends on he demand for he goods produced in ha counry. If prices of goods are low relaive o hose in oher counries, hen his exchange rae will be high. he relaionship is imporan because i ells us wheher changes in he nominal exchange rae have an impac on real variables such as he value of a firm or he reurn on a porfolio of asses. ommodiy rice ariy (: Arbirage in perfec goods marke implies ha a paricular good mus have he same price across differen counries, afer ranslaion ino a common currency. ha is, if he price of he same commodiy were no he same across counries, hen one could make profis by buying he commodiy in he counry where i is cheap and selling i where i is more expensive. can be expressed as follows: S( D / AD k k his relaion saes ha he price of commodiy "k" mus be he same in boh anada and he Unied Saes.

2 In he real world, may no hold for he following reasons: Imperfecions: ransacion oss: ariffs, ransporaion coss, insurance fees, and oher such coss mean ha i may no be possible o make arbirage profis even in he presence of price differences across counries. Nonraded Goods: Several goods, such as services (haircus are nonradable. Quoas: Quoas and oher such barriers o rade resric he abiliy o make arbirage profis. Imperfec ompeiion: Imperfec compeiion in commodiy markes may preven prices from being equalized across counries. For example, price discriminaion, enry coss, and menu coss would preven. Absolue urchasing ower ariy: In an economy wih many goods, purchasing power is defined in erms of a represenaive bundle of goods. I describes he number of baskes of goods you can buy. One condiion, called Absolue, relaes he absolue price levels in wo counries o he level of he exchange rae beween hem. he Absolue condiion saes ha: S( D / AD According o he Absolue view of exchange rae deerminaion, exchange raes mus be such ha here is equaliy beween he domesic and foreign price levels. he price level indicaes he price of a paricular baske of goods. he mos common price index is he onsumer rice Index (I. may no hold because: Imperfecions: Violaions of : Differences in Baskes: Absolue is unlikely o hold if is violaed. ha is, if he individual goods in he represenaive consumpion baske do no saisfy, hen is likely o be violaed. Absolue will no hold if he composiion of he baskes differs across counries. For example, he presence of nonraded goods would make baskes differen across counries.

3 Relaive urchasing ower ariy: he Relaive hypohesis saes ha he percenage change in he exchange rae reflecs he difference beween inflaion a home and abroad. he Relaive condiion is (<: S ( D / AD S ( D / AD he linear version of his relaion is: S, π, π, ha is, he inflaion differences beween counries should be refleced in percenage changes in he exchange rae. For example, if he inflaion rae is 5 % in he and 2 % in anada, hen he anadian dollar should appreciae by 3 %. ha is, if prices in he are rising faser han prices in anada, hen anada's expors are becoming relaively cheaper. his should arac imporers, hereby increasing anadian ne expors and reducing ne expors. his should generae a relaively higher demand for AD and promoe an appreciaion of he AD agains he D. he Real Exchange Rae: he empirical evidence suggess ha and do no hold in he shor run, and ha hey may hold in he long run. he informaion summarized by, however, may sill be useful o deermine he compeiive posiion of a paricular counry. his empirical evidence also suggess ha domesic and foreign baskes of goods on which price levels are compued are differen across counries. he Real Exchange Rae summarizes his informaion. he Real Exchange Rae is: Q( / S( D / AD he real exchange rae is he relaive price of a foreign baske of goods in erms of a domesic baske of goods. For example, assume ha he price level is AD 150 per baske of anadian goods in anada and D 100 per baske of goods in he. Also assume ha he exchange rae is D 0.65/AD. he real exchange rae is hen: D0.65/ AD AD150 / B D100 / B Q ( / B / B

4 I coss baske of goods o purchase 1 baske of anadian goods. ha is, he anadian baske is cheaper han he American baske, which suggess ha he American economy is somewha less compeiive han he anadian economy. Anoher inerpreaion is ha he coss of living are lower in anada. Flucuaions in he real exchange rae hus give informaion abou he relaive compeiiveness of differen counries. For example, if he real exchange rae is increasing, hen he domesic economy's compeiive posiion is improving. If he real exchange rae is decreasing, hen he domesic economy's compeiive posiion is slipping. he real exchange rae is he relaive price of a foreign baske of goods. In he long run, his relaive price is deermined by he supply and demand for baskes of goods. hese marke forces can be summarized by: An increase in world relaive demand for anadian goods causes an increase in he price of he anadian baske of goods and an increase in he real exchange rae. An increase in world relaive supply of anadian goods causes a reducion in he price of he anadian baske of goods and a reducion in he real exchange rae. 4.2 overed Ineres ariy he arbirage condiion called he Ineres Rae ariy (IR condiion or overed Ineres ariy (I condiion saes ha he prices from risk-free asses wih idenical mauriy should be equaed across counries, afer ranslaion in a common currency. his condiion can be simply derived from he following invesmen example. Suppose ha a invesor has o decide beween invesing a home or in anada. If she invess a home, her oupu will be: DX DX h ( 1 + r, If she invess abroad, her oupu will depend no only on he invesmen, bu also on boh a spo and a forward ransacion. he oupu of he spo ransacion will be: DX S ( D / AD ADY he oupu of he invesmen ransacion will be: ADY ADY ( 1 + r,

5 Finally, he oupu of he forward ransacion will be: f ADY F, ( AD / D DX F, f DX ( D / AD he oupu of his overall invesmen is hen: F ( D / AD f, DX (1 + r, S ( D / AD DX Our arbirage argumen requires ha: h DX DX DX DX f he I condiion is hen: (1 + r, (1 + r hese ransacions can be shown on a diagram., F, ( D / AD S ( D / AD 4.3 Uncovered Ineres ariy Anoher widely discussed ineres pariy condiion is called he Uncovered Ineres ariy (UI condiion. o undersand UI, we mus firs discuss he forward rae as an unbiased predicor of fuure spo rae. he Forward Rae as an Unbiased redicor of Fuure Spo Raes: UI is based on he noion ha, under efficien and perfec markes, he forward exchange rae mus be an unbiased predicor of he fuure spo exchange rae. ha is, if he forward rae is an unbiased predicor of he fuure spo rae, he expeced value of he fuure spo rae given all he informaion available oday mus equal he presen forward rae: F E { S, }

6 An unbiased predicor, however, does no mean ha he fuure spo rae will acually be equal o he forward rae. Unbiased predicion only means ha he fuure spo rae will, on average, equal he forward rae. he raionale for his relaionship is based on he hypohesis ha he foreign exchange marke is efficien. Marke efficiency assumes ha all relevan informaion is quickly refleced in boh he spo and forward exchange markes, ha ransacion coss are low or nonexisen, and ha insrumens denominaed in differen currencies are perfec subsiues for one anoher. Empirical sudies on marke efficiency have yielded conflicing resuls. ha is, here appear o be a risk premium on he forward marke: F, E{ S } + R, he Uncovered Ineres ariy ondiion: he UI condiion is simply: ( 1 + r, (1 + r, E{ S } S he linear version of his condiion is widely used in exchange rae deerminaion models. he linear version is (a * denoes foreign counry variables: * E{ S } S r, r, + S his condiion has a diagrammaic exposiion. his diagram is useful o undersand he impac of news on exchange raes. he lef side of he equaion represens domesic reurn and he lef side of he equaion is he foreign reurn. Oher hings being equal, any news you obain abou he fuure spo exchange rae will be refleced in he curren spo rae. 4.4 Real Ineres ariy his las condiion is based on boh UI and. I is called real in ha i relaes he real reurns from asses across counries.

7 he Fisher Effec: he Fisher effec saes ha he nominal ineres rae is equal o he real ineres rae plus compensaion for expeced inflaion. he Fisher relaion is: Where ρ is he real ineres rae and π is he expeced inflaion rae. he nominal ineres rae describes he rae of reurn from an asse, in erms of unis of currency. he real ineres rae, however, is he rae of reurn from his asse, in erms of unis of a baske of goods ha can be purchased. Inflaion erodes he real value of a currency, because i is a general and susained increase in he price level of he baske of goods. hus, o obain he real ineres rae, we mus subrac inflaion from he nominal reurn. he linear version of his relaion is: ( 1 + ρ (1 + π, (1 + r,, r r, ρ, + π, he Inernaional Fisher Effec: he inernaional Fisher effec, or Fisher-open, saes ha he spo exchange rae should change in an equal amoun bu in he opposie direcion o he difference in ineres raes beween wo counries. his relaion is based on UI, Relaive, and he Fisher effec. For example, UI is: (1 + r, (1 + r *, E{ S } S he bes forecas of Relaive is: (1 + π + *, (1 π, E { S } S Finally, he Fisher effec is: (1 + ρ he inernaional fisher relaion is:, (1 + r (1 + π (1 + ρ (1 + ρ *,,,,

8 he Real Exchange Rae: he previous derivaion was underaken wih he idea ha holds. If his is no he case, here is a real version of UI ha can be esablished. his new condiion saes ha he real reurn from risk-free asses wih idenical mauriy should be equaed across counries, afer ranslaion in a baske of goods. his pariy condiion relaes he real reurn o invesmen a home and abroad, and changes in he real exchange rae. his pariy is: (1 + ρ + *, (1 ρ, E ( Q Q 4.5 Summary saes ha a paricular commodiy mus have he same price across differen counries, afer ranslaion ino a common currency. Several reasons migh explain violaions of : ransacion coss, nonraded goods, quoas, and imperfec compeiion. Absolue saes ha a paricular commodiy baske mus have he same price across differen counries, afer ranslaion ino a common currency. will likely be violaed if is iself violaed and if baskes are differen across counries. he Relaive hypohesis saes ha he percenage change in he exchange rae reflecs he difference beween inflaion a home and abroad. he real exchange rae is he relaive price of a foreign baske of goods. I provides informaion abou he compeiiveness and he coss of living of counries. In he long run, his real exchange rae is deermined by he supply and demand for baskes of goods.

9 he arbirage condiion called he overed Ineres ariy (I condiion saes ha he prices from risk-free asses wih idenical mauriy should be equaed across counries, afer ranslaion in a common currency. Uncovered Ineres ariy (UI is based on he noion ha, under efficien and perfec markes, he forward exchange rae mus be an unbiased predicor of he fuure spo exchange rae. he Fisher effec saes ha he nominal ineres rae is equal o he real ineres rae plus compensaion for expeced inflaion.

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