RateintheLongRun(国际金融-香港大学,WONGKaF

1PricelevelsandExchangeRateintheLongRunWONGKaFu7thFebruary20012BasicmathreviewX=A/BlnX=lnA-lnBY=Y(x)dlnY/dx=dlnY/dYdY/dx=(1/Y)(dY/dx)3BasicmathreviewP=P(t)dlnP/dt=dlnP/dPdP/dt=(1/P)(dP/dt)Takethechangeoft(dt)fromstos+1.dlnP/dt=[1/P(s)][P(s+1)-P(s)/1]=[P(s+1)-P(s)]/P(s)=percentagechangeinPattimes.4LawofonepriceInacompetitivemarketsfreeof1.transportationcostsand2.officialbarrierstotrade(suchastariffs),identicalgoodssoldindifferentcountriesmustsellforthesamepricewhentheirpricesareexpressedintermsofthesamecurrency.5LawofonepriceimpliesexchangerateForanygoodisoldinbothhomeandforeigncountriesPHi=(EH/F)(PFi)Hence,theimpliedexchangerateisEH/F=PHi/PFi6AbsolutePurchasingPowerParity(AbsolutePPP)ForagivenreferencecommoditybasketsoldinboththehomeandtheforeigncountriesPH=(EH/F)(PF)Hence,theimpliedexchangerateisEH/F=PH/PFTheimpliedexchangeratefromtheEconomist’sBigMacindex7RelativePPPPricesandexchangerateschangesuchthattheratioofeachcurrency’sdomesticandforeignpurchasingpowersarepreserved.Hence,(EH/F,t-EH/F,t-1)/EH/F,t-1=H,t-F,twheret=(Pt-Pt-1)/Pt-18RelativePPPIfabsolutePPPdoesnotholdbecauseoffrictionsandotherfactorsandwehaveEH/F=PH/PFwhereisaconstantthatmeasuresthedifferencefromabsolutePPP.EH/F(t)=PH(t)/PF(t)lnEH/F(t)=ln+lnPH(t)-lnPF(t)Takingderivativewithrespecttot:dlnEH/F(t)/dt=dln/dt+dlnPH(t)/dt-dlnPF(t)/dt9RelativePPPHence,(EH/F,t-EH/F,t-1)/EH/F,t-1=H,t-F,twheret=(Pt-Pt-1)/Pt-1percentagechangeinEH/F,t=percentagechangeinPH,t-percentagechangeinPF,t10Long-runexchangeratebasedonabsolutePPPEH/F=PH/PFPH=MHs/L(RH,YH)PF=MFs/L(RF,YF)Monetarypolicy=moneysupply11EffectofanincreaseinhomemoneysupplyonLREH/FMHsPHEH/FbecausePH=MHs/L(RH,YH)becauseEH/F=PH/PF12EffectofanincreaseinforeignmoneysupplyonLREH/FMFsPFEH/FbecausePF=MFs/L(RF,YF)becauseEH/F=PH/PF13EffectofanincreaseinhomeinterestrateonLREH/FRHPHEH/FbecausePH=MHs/L(RH,YH)becauseEH/F=PH/PFLHbecauseL(RH,YH)14InterestratecanchangeduetoreasonsotherthanmonetarypolicyForexample:technologyadvancementmayimprovetheprofitabilityofinvestmentandhencetheinterestratewillingtopaytoborrowmoneytoinvest.FactorsthatarenotalreadyexplicitbutimplicitintheL(R,Y)function15EffectofanincreaseinforeigninterestrateonLREH/FRFPFEH/FbecausePF=MFs/L(RF,YF)becauseEH/F=PH/PFLFbecauseL(RF,YF)16EffectofanincreaseinhomeoutputonLREH/FYHPHEH/FbecausePH=MHs/L(RH,YH)becauseEH/F=PH/PFLHbecauseL(RH,YH)17EffectofanincreaseinforeignoutputonLREH/FYFPFEH/FbecausePF=MFs/L(RF,YF)becauseEH/F=PH/PFLFbecauseL(RF,YF)18Long-runexchangeratebasedonabsolutePPPEH/F=PH/PFPH=MHs/L(RH,YH)PF=MFs/L(RF,YF)EH/F=(MHs/MFs)[L(RF,YF)/L(RH,YH)]19Howislong-runexchangeratedetermined?Anythingthatraises(lowers)LHlowers(raises)EH/FAnythingthatlowers(raises)LFlowers(raises)EH/FAnincrease(Adecrease)inMHsraises(lowers)EH/FAnincrease(Adecrease)inMFslowers(raises)EH/F20Growthrateofmoneysupply:amathematicalderivationMoneysupplylevel:MHs(t)Growthrate:(MHs(t+1)-MHs(t))/MHs(t)Definey(t)=ln(MHs(t))dy(t)/d(t)=dln(MHs(t))/dt=dy(t)/dMHs(t)dMHs(t)/dt=1/MHs(t)dMHs(t)/dtdt=t+1-t=121FishereffectUncoveredinterestparity:RH,t=[EH/F,t+1e-EH/F,t]/EH/F,t+RF,tlett+1e=(Pt+1e-Pt)/Ptandt+1=(Pt+1-Pt)/PtRelativePPP:(EH/F,t+1-EH/F,t)/EH/F,t=H,t+1-F,t+1(EH/F,t+1e-EH/F,t)/EH/F,t=H,t+1e-F,t+1eRH,t-RF,t=H,t+1e-F,t+1e22IfMHSisgrowingatarateofPHgrowsatarateofbecausePH=MHs/L(RH,YH)I.e.,expectH,t+1=or,H,t+1e=Hence,RH,t-RF,t=H,t+1e-F,t+1e=ifF,t+1e=023IfMHSisgrowingatarateofSlope=t0Log(MHS)24IfMHSisgrowingatarateoft0RHRH125IfMHSisgrowingatarateoft0Log(PH)Slope=26IfMHSisgrowingatarateoft0Log(EH/F)Slope=27IfMHSisgrowingatarateof(+)PHgrowsatarateof(+)becausePH=MHs/L(RH,YH)I.e.,expectH,t+1=(+);or,H,t+1e=(+)Hence,RH,t-RF,t=H,t+1e-F,t+1e=(+)ifF,t+1e=028IftherateofMHSgrowthincreasesfromto(+)SupposeRF,tfixedandF,t+1e=0becauseastablemonetarypolicy,forexample.RH,tincreasesbybecauseH,t+1eisexpectedtoincreaseby.Notethat,however,MHSdoesnotchangeattimet0--onlythefuturegrowthrateHence,PHhastojumpfromPH1=MHs/L(RH1,YH)toPH2=MHs/L(RH2,YH)29EffectofanincreaseinthegrowthrateofMHSSlope=Slope=+t0Log(MHS)30EffectofanincreaseinthegrowthrateofMHSt0RHRH1RH2=RH1+31EffectofanincreaseinthegrowthrateofMHSt0Log(PH)Slope=Slope=+32EffectofanincreaseinthegrowthrateofMHSt0Log(EH/F)Slope=Slope=+33ThelessonlearntismuchmoregeneralThestorywas:Achangeinmoneysupplygrowthleadstochangeinexpectedinflation.Achangeinexpectedinflationleadstoajumpininterestrate.(ThroughFisher)Ajumpininterestrateleadstoajumpinexchangerate.Moregenerally,Anythingthatcauseachangeinexpectedinflationwillleadtoajumpininterestrate.Ajumpininterestrateleadstoajumpinexchangerate.34ThelessonlearntismuchmoregeneralWhatwillcauseachangeinexpectedinflation?Thereleaseofeconomicindicators(say,unemployment,GDP,interestrate,confidenceindex,etc.)maychangeourexpectationofinflation.Anyreleaseofindicatorsthatcauseachangeinexpectedinflationwillleadtoajumpinexchangerate.35EmpiricaltestPH=(EH/F)(PF)lnPH=lnEH/F+lnPFRegression:lnPH,t=