Exchange rates in the long run (Purchasing Power Parity: PPP)

Transcription

1 Exchang rats in th long run (Purchasing Powr Parity: PPP) Jan J. Michalk JJ Michalk Th law of on pric: i for a product i; P i = E N/ * P i Or quivalntly: E N/ = P i / P i Ida: Th sam product should hav th sam pric at comptitiv markts (no trad barrirs and low transport costs) but thr ar many rsrvations 1

2 Empirical vrification of law of on pric: buttr Empirical analysis of law of on pric: pric in grams of silvr pr hctolitr f charcoal 2

3 JJ Michalk PPP thory: absolut vrsion Thory of PPP: Purchasing powr parity (PPP): th xchang rat is qual to rlations of purchasing powr among analyzd countris If P : Prics in Poland P : Prics in rmany Thn PPP forss that: E N/ = P / P or mor gnral: E=P/P* According to PPP: ris in domstic pric lvl lads to th proportional dprciation of domstic currncy. Anothr notation: P = E N/ *P JJ Michalk PPP thory: rlativ vrsion Exchang rats quals to rlativ prics Rlativ PPP thory: prcntag chang in th xchang rat = diffrnc in th prcntag changs in rlativ prics: * E E E t t1 / t1 t t whr t is th rat of inflation in tim t.: t = (P t -P t-1 )/P t-1 3

4 Purchasing Powr Parity: onc again in two vrsions Purchasing powr parity coms in 2 forms: Absolut PPP: purchasing powr parity that has alrady bn discussd. Exchang rats qual pric lvls across countris. E N/ = P /P EU Rlativ PPP: changs in xchang rats qual changs in prics (inflation) btwn two priods: (E N/,t - E N/, t 1 )/E N/, t 1 =, t - EU, t whr t = inflation rat from priod t-1 to t Modl basd on PPP: montary approach JJ Michalk P = M s /L(R N,Y ); and th sam abroad; Whr L(R N,Y ) is th ral aggrgat dmand for mony. Fundamntal quation of th montary approach: M L R, Y E N P / P / s M L RN, Y long run changs in th x-rat is fully dtrmind by th rlativ supplis of thos monis an th rlativ ral dmand for thm Or in th abbrviatd form:: M E N / RN R, Y Y M whr: (.) is th rlativ aggrgat dmand for monis in rmany in rlation to Poland. 4

5 Montary Approach to Exchang Rats To th dgr that PPP holds and to th dgr that prics adjust to quat ral mony supply with ral mony dmand, w hav th following prdiction: Th xchang rat is dtrmind in th long run by prics, which ar dtrmind by th rlativ supply of mony across countris and th rlativ ral dmand of mony across countris. Montary Approach to Exchang Rats (cont.) Prdictions about changs in: 1. Mony supply: a prmannt ris in th domstic mony supply causs a proportional incras in th domstic pric lvl, causing a proportional dprciation in th domstic currncy (through PPP). sam prdiction as long run modl without PPP 2. Intrst rats: a ris in th domstic intrst rat lowrs domstic mony dmand, incrasing th domstic pric lvl, causing a proportional dprciation of th domstic currncy (through PPP). 5

6 PPP and intrst rat: xchang rat and th Fishr ffct JJ Michalk Ral intrst rat: intrst rat rflcting ral productivity of conomy = nominal intrst rat corrctd by xpctd rat of inflation: (but w do know th actual); = (P P)/P P : xpctd pric lvl (on yar prspctiv); P: currnt pric lvl; : xpctd rat of inflation r = R lub R = r + Fishr ffct: Undr ctris paribus assumption: a ris in th domstic xpctd inflation rat will vntually caus ris in th intrst rat that dposits of its currncy offr. A Long-Run Exchang Rat Modl Basd on PPP Figur 15-2: Inflation and Intrst Rats in witzrland, th Unitd tats, and Italy,

7 A Long-Run Exchang Rat Modl Basd on PPP Figur 15-2: Continud A Long-Run Exchang Rat Modl Basd on PPP Figur 15-2: Continud 7

8 Problms with mpirical vrification of PPP JJ Michalk trad barrirs and transportation costs xist in ral conomy; Thr ar diffrnt baskt of consumptions in diffrnt countris; imprfct (monopolistic) comptition xist: oligopolistic pric practics undrmin th law of on pric. JJ Michalk Th ral xchang rat Ral x-rat (N to ): brad summary masur of th pric in Polish prics goods and srvics to th othr. Ral x-rat = (E N/ * P ) / P P EN P qn P E P P / ral x-rat : masurs th baskt of xpnditur in Pl to rman on * A ral apprciation: of th PN against indicats dcras in th rlativ pric of products purchasd in rmany, or a ris in th zloty s rman purchasing powr compard with th Polish on In accordanc with absolut vrsion of PPP, th ral x-rat must b qual 1: E P E P / P 1 / N qn / N / P Whil in accordanc with rlativ vrsion of PPP ral x-rat must b constant (but not ncssary qual to 1) 8

9 1973 DEC 1975 MAR 1976 JUN 1977 EP 1978 DEC 1980 MAR 1981 JUN 1982 EP 1983 DEC 1985 MAR 1986 JUN 1987 EP 1988 DEC 1990 MAR 1991 JUN 1992 EP 1993 DEC 1995 MAR 1996 JUN 1997 EP JJ Michalk Exchang rat fluctuations Figur 3(c): Bilatral xchang rats and xport comptitivnss: 12 month prcntag changs, rmany-u.. 60% 50% 40% 30% 20% 10% 0% gr/us.r gr/us.xppr -10% -20% -30% -40% JJ Michalk Changs in ral xchang rats Yar Consum r pric indx (CPI) in UA Consum r pric indx (CPI) in U.K. Nominal xchang rat Ral xchang rat Changs of ral xchang rat P P* E q=(ep*)/p [q(t)-q(t-1)]/q(t-1) Inflation rat in UA Inflation rat in UK ,3 19,3 2,80 1, ,7 20,1 2,81 1,539 3,38 1,1 4, ,2 20,5 2,80 1,543 0,26 1,4 2, ,6 21,2 2,79 1,573 1,95 1,1 3, ,3 22,2 2,80 1,623 3,17 1,9 4, ,4 23,0 2,79 1,629 0,35 2,9 3, ,5 23,6 2,75 1,602-1,61 2,8 2, ,0 100,0 2,33 2, ,4 111,9 2,03 2,058-11,69 10,4 11, ,2 121,5 1,75 1,814-11,83 6,2 8, ,9 127,1 1,52 1,598-11,92 3,2 4, ,1 133,5 1,34 1,419-11,22 4,3 5, ,6 141,6 1,30 1,409-0,64 3,6 6, ,1 146,4 1,47 1,617 14,71 1,9 3,4 9

10 Empirical Evidnc on PPP and th Law of On Pric Figur 15-3: Th Dollar/DM Exchang Rat and Rlativ U../rman Pric Lvls, hortcomings of PPP (cont.) 10

11 Byond Purchasing Powr Parity: A nral Modl of Long-Run Exchang Rats Figur 15-5: Th Ral Dollar/Yn Exchang Rat, Explaining th Problms with PPP Figur 15-4: Pric Lvls and Ral Incoms,

12 Byond Purchasing Powr Parity: A nral Modl of Long-Run Exchang Rats Figur 15-6: ctoral Productivity rowth Diffrncs and th Chang in th Rlativ Pric of Nontradd oods, JJ Michalk Intrnational Fischr ffct If popl xpct rlativ PPP to hold, th diffrnc btwn th intrst rats offrd by N and uro dposits will qual th diffrnc btwn th inflation rats xpctd in Poland and rmany: EN / EN / / EN / And combining th xpctd vrsion of rlativ PPP with intrst parity condition: R R E E E N / N / / N / w rciv th intrnational Fishr ffct: R N R i..: th currncy dprciation is xpctd to offst th intrnational inflation diffrnc 12

13 Th montary modl of xchang rat changs JJ Michalk W can gt th nominal xchang rat (as a function of ral x-rat): 15.5 Org E P N/ qn/ P and comparing this with fundamntal quation of montary approach w gt: E N / DM P / P M L s M R, Y L R N i.. xchang rats fluctuations rflct changs in rlativ supply and dmand for mony or in th abbrviatd form:, Y M E N / RN R, Y M Y whr: (.) is th aggrgat rlativ dmand for mony in in rlation to : nral modl of xchang rat changs If w assum that th PPP dos not hold (and changs in ral x-rat ar possibl) thn w gt gnral quation for long trm changs: Th gnral modl (quation) of xchang rat changs: M E N / qn / RN R, Y M If th PPP dos not hold th xpctd chang in th ral x-rat is qual to: Or ( q q )/ q E E E And comparing this with normal intrst parity: R R E E E N W gt th following quation: N / N / N / N / N / / N / N / N / / N / 15.11Or R R ( q q ) q N N / N / / N / and this mans: that th diffrnc in intrst rats dpnd on: 1. xpctd changs in ral xchang rats 2. xpctd diffrncs in xpctd rts of inflation Y JJ Michalk 13

14 Th gnral modl of xchang rat changs: continud JJ Michalk I f w dnot th xpctd rat of ral dprciation of N to as: ( qn / qn / )/ qn / Thn th long run xchang rat lvl can b writtn as:.12 Or E q M / M, Y / Y 15 / N / N Nominal xchang chang rat in th long run: Montary approach 1. PPP: 2. Equilibrium at domstic montary markts E / N/ DM P P P M / LR, Y P M, Y / L R JJ Michalk E N / M 3. Equation of th xchang rat P M P 4. Intrst parity combind with th PPP R M M Y R, Y LR, Y / LR, Y R N R N 5. Equation of th long run quilibrium: montary approach ( ) ( ) s s M / M Y Y E, N / DM ( ) 14

15 Pric Lvls and Incoms 15

16 Rlativ unit labour costs (invrs of ral xchang rats) in Eurozon 16