Secion 4 he Exchange Rae in he Long Run 1
Conen Objecives Purchasing Power Pariy A Long-Run PPP Model he Real Exchange Rae Summary 2
Objecives o undersand he law of one price and purchasing power pariy (PPP). o undersand PPP as a heory of long-run exchange rae deerminaion. o undersand he real exchange rae. 3
Purchasing Power Pariy he Law of One Price: Idenical goods mus be priced idenically. Commodiy Price Pariy: Goods in differen counries mus sell for he same price, when heir prices are expressed in he same currency. 4
Purchasing Power Pariy Commodiy Price Pariy: US k P = S( USD / CAD) P Where P us k is he USD price of commodiy k in he U.S., P kc is he CAD price of commodiy k in Canada, S(USD/CAD) is he price of CAD in USD. C k 5
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Purchasing Power Pariy In he real world, CPP may no hold for he following reasons: ransacion Coss: 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. 7
Purchasing Power Pariy Quoas: Quoas and oher such barriers o rade resric he abiliy o make arbirage profis. Imperfec Compeiion: Imperfec compeiion in commodiy markes may preven prices from being equalized across counries. For example, price discriminaion, enry coss, and menu coss would preven CPP 8
Purchasing Power Pariy 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. he price level is he price of a paricular baske of goods. he mos common price index is he Consumer Price Index (CPI). 9
Purchasing Power Pariy Absolue Purchasing Power Pariy: Idenical baskes of goods in differen counries mus sell for he same price, when heir prices are expressed in he same currency. 10
Purchasing Power Pariy Absolue Purchasing Power Pariy: US P = S( USD / CAD) P Where P us is he USD price of a baske of goods in he U.S., P c is he CAD price of a baske of goods in Canada, S(USD/CAD) is he price of CAD in USD C 11
Purchasing Power Pariy In he real world, Absolue PPP may no hold for he following reasons: Violaions of CPP: Absolue PPP is unlikely o hold if CPP is violaed. ha is, if he individual goods in he represenaive consumpion baske do no saisfy CPP, hen PPP is likely o be violaed. 12
Purchasing Power Pariy Differences in Baskes: Absolue PPP will no hold if he composiion of he baskes differs across counries. For example, he presence of non-raded goods would make baskes differen across counries 13
Purchasing Power Pariy he Relaive PPP hypohesis saes ha he percenage change in he exchange rae reflecs he difference beween inflaion a home and abroad. Relaive Purchasing Power Pariy: P P US US = S S ( USD / CAD) ( USD / CAD) P P C C 14
Purchasing Power Pariy Relaive PPP can also be expressed as: US 1 + π, = [1 + ( S S ) / S ] (1 + π, C ) he linear version of relaive PPP is: π US C, = π, + ( S S ) / S 15
Purchasing Power Pariy Where π is he inflaion rae: π, = ( P P ) / P 16
Purchasing Power Pariy Relaive PPP saes ha inflaion differences beween counries should be refleced in percenage changes in he exchange rae. For example, if he inflaion rae is 5 % in he US and 2 % in Canada, hen he Canadian dollar should appreciae by 3 %. 17
Purchasing Power Pariy If prices in he US are rising faser han in Canada, Canada's expors are becoming relaively cheaper. his should arac imporers, hereby increasing Canadian ne expors and reducing US ne expors. his should generae a relaively higher demand for CAD and promoe an appreciaion of he CAD agains he USD. 18
A Long-Run PPP Model he Moneary approach o he exchange rae he Fundamenal Equaion: Price levels and he Demand for Money: P h = M h / L( i h, Y h ) f P = M f / L( i f, Y f ) 19
A Long-Run PPP Model Specific predicions from he moneary approach o longrun exchange rae deerminaion: Money supplies An increase in he USD money supply causes a proporional long-run depreciaion of he USD agains foreign currencies. Ineres raes A rise in he ineres rae on USD asses causes a depreciaion of he USD agains foreign currencies. Oupu levels A rise in U.S. oupu causes an appreciaion of he USD agains foreign currencies. 20
A Long-Run PPP Model he inernaional ineres rae difference is he difference beween expeced naional inflaion raes. Recall UIP: h f, Recall Relaive PPP: e i = i + ( S S ) /, S π h f e, = π, + ( S S ) / S 21
A Long-Run PPP Model So, π eh ef e, = π, + ( S S ) / S And he ineres differenial is: i h i f = π eh π ef,,,, 22
A Long-Run PPP Model he Real Ineres Rae: ( 1+ r ) = (1 + i ) /(1 + π,,, ) r = i π e,,, he Fisher Relaion (Real Ineres Pariy): r h = r f,, 23
A Long-Run PPP Model A simple numerical example. Assume ha: P = USD 100/Baske, P = USD 101/Baske and i, =0.03 oday, period If I have USD x = USD 100, I can buy 1 baske: B y = USD x / P = (USD 100)/(USD 100/Baske) = B 1 24
A Long-Run PPP Model If inves, I ge USD x = USD 103: USD x = (1+ i, ) USD x = (1+0.03)USD 100 = USD 103 If I have USD x = USD 103, I can buy 1.02 baske: B y = USD x / P = USD 103/USD 101/Baske = B 1.02 Inflaion is 1+π, =1.01 (1+π, )=P /P =(USD 101/B)/(USD 100/B) = 1.01 25
A Long-Run PPP Model USD rae of reurn is 3 percen: 1+ i, =USD x /USD x = 1.03 Real rae of reurn is 2 percen: (1+r, ) = B y / B y = b1.02/b1 = 1.02 hus, (1+r, ) = (1+ i, ) P /P = (1+ i, )/ (1+π, ) Or r, = i, -π, = 0.03 0.01 = 0.02 26
A Long-Run PPP Model he Fisher Effec A rise in a counry s expeced inflaion rae generaes an equal rise in he ineres rae: i, =r, + π e, In he long run, inflaion is a moneary phenomenon: 1+π, = M /M 27
A Long-Run PPP Model he Fisher Effec M i i 2 = i 1 + π growh = π + π growh = π i 1 P 0 ime S 0 ime Slope = π + π Slope = π + π Slope = π Slope = π 0 ime 0 ime 28
A Long-Run PPP Model Jump in prices: 1+π, = P / P = M M / L( i / L( i,,, Y, Y ) ) Jump in ineres rae for consan also force prices o jump. USD consanly depreciaes and jumps because of absolue PPP. 29
he Real Exchange Rae Recen empirical evidence suggess ha PPP does no hold in he shor run. I is a good approximaion for he currencies of counries experiencing hyperinflaion. Prices of idenical goods differ subsanially across counries (he Economis and he Big Mac Index). PPP (or somehing like i) appears o hold in he longrun. ha is, he real exchange rae is rend revering. 30
he Real Exchange Rae his empirical evidence also suggess ha domesic and foreign baskes of goods on which price levels are compued are differen across counries. 31
he Real Exchange Rae he informaion summarized by PPP may sill be useful o deermine he compeiive posiion of a paricular counry. he Real Exchange Rae summarizes his informaion. he Real Exchange Rae is: Q( US / C) = S( USD / CAD) P US P C 32
he Real Exchange Rae 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 CAD 150 per baske of Canadian goods in Canada and USD 100 per baske of US goods in he US. Also assume ha he exchange rae is USD 0.65/CAD. 33
he Real Exchange Rae he real exchange rae is hen: USD0.65 / CAD CAD150 / Q( US / C) = US USD100 / B US C Q( US / C) = B 0.975 / B B C ha is, he Canadian baske is cheaper han he American baske, which suggess ha he American economy is somewha less compeiive han he Canadian economy. Anoher inerpreaion is ha he coss of living are lower in Canada. 34
he Real Exchange Rae Real depreciaion of he USD A rise in he real home price of a foreign baske of goods. A rise in he real USD/CAD exchange rae A fall in he purchasing power of a USD in Canada relaive o he purchasing power of he USD in he U.S. 35
he Real Exchange Rae 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. 36
he Real Exchange Rae hese marke forces can be summarized by: An increase in world relaive demand for Canadian goods causes an increase in he price of he Canadian baske of goods and an increase in he real exchange rae. An increase in world relaive supply of Canadian goods causes a reducion in he price of he Canadian baske of goods and a reducion in he real exchange rae. 37
he Real Exchange Rae Nominal and Real Exchange Raes he real exchange rae is mean revering. he half life of changes in he real exchange rae is several years long. So, relaive PPP holds in he long-run. he real and nominal exchange raes are highly correlaed. C S( USD / CAD) P Q( US / C) = US P his suggess ha prices are sicky. 38
39 he Real Exchange Rae he real exchange rae and real ineres pariy. he relaive version of he real exchange rae is: or US C US C P P P P S S Q Q / / = US C S S S Q Q Q,, ) ( +π π =
40 he Real Exchange Rae Uncovered Ineres Pariy Real Exchange Rae: Real Ineres Rae: e C US S S S i i + =,, eus ec e e S S S Q Q Q,, ) ( +π π = e i r,,, π =
41 he Real Exchange Rae Real Ineres Pariy (Par II) Uncovered Ineres Pariy e C US Q Q Q r r + =,, e C US S S S i i + =,,
he Real Exchange Rae he real ineres pariy condiion saes ha differences in expeced real ineres raes depend on expeced movemens in he real exchange rae. 42
he Real Exchange Rae An inerpreaion of real ineres pariy r, = r *, + Q he real ineres rae is a measure or he real reurn o capial. he higher ha reurn, he higher he growh rae of he economy. So, if r>r*, he home economy is growing faser and mus see is compeiiveness improves. ha is, he real exchange rae (he price of a foreign baske of goods) mus rise. e Q Q 43
Summary Absolue PPP saes ha he purchasing power of any currency is he same in any counry: Relaive PPP predics ha percenage changes in exchange raes equal differences in naional inflaion π P = S *, = π, + ( he real ineres rae is: P e r, = i, π, * S S ) / S 44
Summary he real exchange rae is he price of a foreign * baske of goods: SP Q Real ineres pariy is: P If boh UIP and PPP hold: = r = r *,, If only UIP holds: r US, C = r, + Q e Q Q 45
Summary here are sizeable movemens in he real exchange rae. hese movemens are long-lasing, bu no permanen. hus, relaive PPP holds in he long run. he real and nominal exchange raes are highly correlaed. 46