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1、Price levels and Exchange Rate in the Long Run,WONG Ka Fu7th February 2001,Basic math review,X=A/B ln X=ln A-ln BY=Y(x)d ln Y/dx=d lnY/dY dY/dx=(1/Y)(dY/dx),Basic math review,P=P(t)d ln P/dt=d lnP/dP dP/dt=(1/P)(dP/dt)Take the change of t(dt)from s to s+1.d ln P/dt=1/P(s)P(s+1)-P(s)/1=P(s+1)-P(s)/P(
2、s)=percentage change in P at time s.,Law of one price,In a competitive markets free of 1.transportation costs and 2.official barriers to trade(such as tariffs),identical goods sold in different countries must sell for the same price when their prices are expressed in terms of the same currency.,Law
3、of one price implies exchange rate,For any good i sold in both home and foreign countriesPHi=(EH/F)(PFi)Hence,the implied exchange rate is EH/F=PHi/PFi,Absolute Purchasing Power Parity(Absolute PPP),For a given reference commodity basket sold in both the home and the foreign countriesPH=(EH/F)(PF)He
4、nce,the implied exchange rate is EH/F=PH/PFThe implied exchange rate from the Economists Big Mac index,Relative PPP,Prices and exchange rates change such that the ratio of each currencys domestic and foreign purchasing powers are preserved.Hence,(EH/F,t-EH/F,t-1)/EH/F,t-1=H,t-F,twhere t=(Pt-Pt-1)/Pt
5、-1,Relative PPP,If absolute PPP does not hold because of frictions and other factors and we have EH/F=PH/PF where is a constant that measures the difference from absolute PPP.EH/F(t)=PH(t)/PF(t)ln EH/F(t)=ln+ln PH(t)-ln PF(t)Taking derivative with respect to t:dln EH/F(t)/dt=dln/dt+dln PH(t)/dt-dln
6、PF(t)/dt,Relative PPP,Hence,(EH/F,t-EH/F,t-1)/EH/F,t-1=H,t-F,twhere t=(Pt-Pt-1)/Pt-1 percentage change in EH/F,t=percentage change in PH,t-percentage change in PF,t,Long-run exchange rate based on absolute PPP,EH/F=PH/PF PH=MHs/L(RH,YH)PF=MFs/L(RF,YF)Monetary policy=money supply,Effect of an increas
7、e in home money supply on LR EH/F,MHs,PH,EH/F,because PH=MHs/L(RH,YH),because EH/F=PH/PF,Effect of an increase in foreign money supply on LR EH/F,MFs,PF,EH/F,because PF=MFs/L(RF,YF),because EH/F=PH/PF,Effect of an increase in home interest rate on LR EH/F,RH,PH,EH/F,because PH=MHs/L(RH,YH),because E
8、H/F=PH/PF,LH,because L(RH,YH),Interest rate can change due to reasons other than monetary policy,For example:technology advancement may improve the profitability of investment and hence the interest rate willing to pay to borrow money to invest.,Factors that are not already explicit but implicit in
9、the L(R,Y)function,Effect of an increase in foreign interest rate on LR EH/F,RF,PF,EH/F,because PF=MFs/L(RF,YF),because EH/F=PH/PF,LF,because L(RF,YF),Effect of an increase in home output on LR EH/F,YH,PH,EH/F,because PH=MHs/L(RH,YH),because EH/F=PH/PF,LH,because L(RH,YH),Effect of an increase in fo
10、reign output on LR EH/F,YF,PF,EH/F,because PF=MFs/L(RF,YF),because EH/F=PH/PF,LF,because L(RF,YF),Long-run exchange rate based on absolute PPP,EH/F=PH/PF PH=MHs/L(RH,YH)PF=MFs/L(RF,YF)EH/F=(MHs/MFs)L(RF,YF)/L(RH,YH),How is long-run exchange rate determined?,Anything that raises(lowers)LH lowers(rais
11、es)EH/F Anything that lowers(raises)LF lowers(raises)EH/F An increase(A decrease)in MHs raises(lowers)EH/F An increase(A decrease)in MFs lowers(raises)EH/F,Growth rate of money supply:a mathematical derivation,Money supply level:MHs(t)Growth rate:(MHs(t+1)-MHs(t)/MHs(t)Define y(t)=ln(MHs(t)dy(t)/d(t
12、)=d ln(MHs(t)/dt=dy(t)/d MHs(t)d MHs(t)/dt=1/MHs(t)d MHs(t)/dt dt=t+1-t=1,Fisher effect,Uncovered interest parity:RH,t=EH/F,t+1e-EH/F,t/EH/F,t+RF,tlet t+1 e=(Pt+1e-Pt)/Pt and t+1=(Pt+1-Pt)/Pt Relative PPP:(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+1eRH,t-RF,t=H,t+1e-F,t
13、+1e,If MHS is growing at a rate of,PH grows at a rate of because PH=MHs/L(RH,YH)I.e.,expect H,t+1=or,H,t+1 e=Hence,RH,t-RF,t=H,t+1e-F,t+1e=if F,t+1e=0,If MHS is growing at a rate of,Slope=,t0,Log(MHS),If MHS is growing at a rate of,t0,RH,RH1,If MHS is growing at a rate of,t0,Log(PH),Slope=,If MHS is
14、 growing at a rate of,t0,Log(EH/F),Slope=,If MHS is growing at a rate of(+),PH grows at a rate of(+)because PH=MHs/L(RH,YH)I.e.,expect H,t+1=(+);or,H,t+1 e=(+)Hence,RH,t-RF,t=H,t+1e-F,t+1e=(+)if F,t+1e=0,If the rate of MHS growth increases from to(+),Suppose RF,t fixed and F,t+1e=0 because a stable
15、monetary policy,for example.RH,t increases by because H,t+1e is expected to increase by.Note that,however,MHS does not change at time t0-only the future growth rateHence,PH has to jump from PH1=MHs/L(RH1,YH)to PH2=MHs/L(RH2,YH),Effect of an increase in the growth rate of MHS,Slope=,Slope=+,t0,Log(MH
16、S),Effect of an increase in the growth rate of MHS,t0,RH,RH1,RH2=RH1+,Effect of an increase in the growth rate of MHS,t0,Log(PH),Slope=,Slope=+,Effect of an increase in the growth rate of MHS,t0,Log(EH/F),Slope=,Slope=+,The lesson learnt is much more general,The story was:A change in money supply gr
17、owth leads to change in expected inflation.A change in expected inflation leads to a jump in interest rate.(Through Fisher)A jump in interest rate leads to a jump in exchange rate.More generally,Any thing that cause a change in expected inflation will lead to a jump in interest rate.A jump in intere
18、st rate leads to a jump in exchange rate.,The lesson learnt is much more general,What will cause a change in expected inflation?The release of economic indicators(say,unemployment,GDP,interest rate,confidence index,etc.)may change our expectation of inflation.Any release of indicators that cause a c
19、hange in expected inflation will lead to a jump in exchange rate.,Empirical test,PH=(EH/F)(PF)ln PH=ln EH/F+ln PFRegression:ln PH,t=0+1 ln EH/F,t+2 ln PF,t+tor ln PH,t=0+1 ln EH/F,t+2 ln PF,t+3 Xt+twhere Xt serves as a control variable.,Hypotheses:,Absolute PPP implies 0=0,1=1,2=1Relative PPP implie
20、s 0=?,1=1,2=1,Empirical evidence on Absolute PPP,Way off the mark:The prices of identical commodity baskets,when converted to a single currency,differ substantially across countries.,Empirical evidence on Relative PPP,Usually performs poorly although it sometimes is a reasonable approximation to the
21、 data.More reliable in the 1960s as a guide to the relationship among inflation and national price levels but less so since 1970s.,Why PPP fails?,Transport costs and restriction on tradeMonopolistic or oligopolistic practices in goods marketsMeasure sof inflation differ across countries.,Exchange ra
22、te pass-through(ERPT),The percentage change in local currency import prices resulting from a one percent change in the exchange rate between the exporting and importing countries.Full or complete ERPT if the following two conditions are met:constant markups of price over cost(e.g.,when industries ar
23、e perfectly competitive,and markups are constant at zero)and constant marginal cost.,Exchange rate pass-through(ERPT),Empirical:ln(pt)=a+b Xt+c ln(Et)+d Zt+etpt:local currency import priceXt:a measure of exporters costZt:import demand shiftersEt:the exchange rate(importers currency per unit of expor
24、ters currency),The interpretation of c,C=d ln P/d ln E=d ln P/dt/d ln E/dt=%change in P/%change in EERPT is“full”or“complete”if c=1 and is“incomplete”if c1.,Exchange rate pass-through(ERPT),Empirical:ln(pt)=a+b Xt+c ln(Et)+d Zt+etEstimate of c is around 60%.This implies that 40%of the exchange rate
25、change was offset by changes in the markup.,Pricing to Market,Consider a monopolistic firm that sells its product in n countries(I.e.,n segmented markets)Its objective is to maximize profit(p1,pn)=pi qi(Eipi,vi)-C(qi(Eipi,vi),w),Pricing to Market,(p1,pn)=pi qi(Eipi,vi)-C(qi(Eipi,vi),w)pi is the pric
26、e charged in i-th market,in the firms domestic currencyqi(Eipi,vi)is the demand in i-th market,a function of Eipi,price in i-th foreign currency and vi,some demand shifters(say,income).Thus,pi qi(Eipi,vi)is the total revenue in domestic currency.C(qi(Eipi,vi),w)is the total cost of producing qi(Eipi
27、,vi)and w is the factors that may shift production cost.,Pricing to Market,(p1,pn)=pi qi(Eipi,vi)-C(qi(Eipi,vi),w)Note that without exchange rate,Ei,the problem is the same as the standard problem of a monopoly maximizing profits in n segmented markets.We should all know its solution from basic micr
28、oeconomics.,Pricing to Market,The optimal export price is the product of the common marginal cost and a destination-specific markup:pi=Cq-i/(-i+1)where Cq is the marginal cost,i is the absolute value of the elasticity of demand in the foreign market with respect to changes in price,pi.,Pricing to Ma
29、rket,Thus,prices are different across markets and are related to a destination-specific markup which is a function of demand elasticity.If pricing to market behavior dominates,PPP is unlikely to hold.Further readings:Goldberg,Pinelopi Koujianou and Michael M.Knetter(1997):“Goods Prices and Exchange
30、Rates:What Have we Learned?”Journal of Economic Literature,Vol.XXXV(September,1997),pp.1243-1272.,Empirical test of Fishers Equation,RH,t-RF,t=H,t+1e-F,t+1eH,t+1e-F,t+1e=RH,t-RF,t(H,t+1-F,t+1)e=RH,t-RF,t(H,t+1-F,t+1)=RH,t-RF,t+twhere(H,t+1-F,t+1)=(H,t+1-F,t+1)e+tRun the regression(H,t+1-F,t+1)=+(RH,
31、t-RF,t)+tshould get 0 and 1,Evidence,Cumby and Obstfeld(1984)and Mishkin(1984)both rejected the hypothesis.,Real exchange rate,The real exchange rate between two countries currencies is a broad summary measure of the prices of one countrys goods and services relative to the others.qH/F=(EH/F PF)/PH
32、PF:price of a basket of foreign goods in foreign currencyPH:price of a different basket of home goods in home currency,Real Exchange Rate,home goods,home currency,foreign goods,foreign currency,PH,PF,EH/F,Real exchange rate,qH/F=(EH/F PF)/PHThe units of home good basket per foreign good basket.The r
33、elative price of foreign good basket in terms of home good baskets.Real depreciation:a rise in qH/F,Factors affecting the long-run real exchange rate,A change in relative output demandAn increase in world relative demand for home output causes a long-run real appreciation of the home currency agains
34、t the foreign currency(I.e.,a fall in qH/F)A change in relative output supplyA relative expansion of home output causes a long-run real depreciation of the home currency against the foreign currency(I.e.,rise in qH/F),Nominal and Real exchange rates in long-run equilibrium,qH/F=(EH/F PF)/PHEH/F=qH/F
35、(PH/PF)Note that under Absolute PPP,qH/F=1.Thus the fact that qH/F may not equal 1 allows the possible deviations from Absolute PPP.This deviation qH/F is an additional determinant of the nominal exchange rate.,Effect of an increase in home money supply level,MHs,PH,EH/F,because PH=MHs/L(RH,YH),beca
36、use EH/F=qH/F(PH/PF),RH,YH,qH/F,Why?,Effect of an increase in home money supply growth rate,Growth of MHs,YH,qH/F,EH/F,because a nominal change has no real effect,because EH/F=qH/F(PH/PF),RH,PH=MHs/L(RH,YH),H,Because Fisher:RH,t-RF,t=H,t+1e-F,t+1e,Effect of an increase in world relative demand for h
37、ome pdts,Relative demand for home pdts,EH/F,because EH/F=qH/F(PH/PF),qH/F,Effect of an increase in relative home supply,Relative home supply,EH/F?,because EH/F=qH/F(PH/PF),qH/F,LH,PH=MHs/L(RH,YH),PH,EH/F,EH/F,L(RH,YH),An insight in the failure of relative PPP,When all disturbances are monetary in na
38、ture,exchange rates obey relative PPP in the long run.When disturbances occur in output markets,the exchange rate is unlikely to obey relative PPP,even in the long run(because qH/F may change over time).,Fisher effect with real exchange rate movement,qH/F=(EH/F PF)/PH(qH/F,t+1-qH/F,t)/qH/F,t=(EH/F,t
39、+1-EH/F,t)/EH/F,t+F,t+1-H,t+1(qH/F,t+1e-qH/F,t)/qH/F,t=(EH/F,t+1e-EH/F,t)/EH/F,t+F,t+1e-H,t+1eRH,t-RF,t=(qH/F,t+1e-qH/F,t)/qH/F,t+H,t+1e-F,t+1ebecause RH,t=EH/F,t+1e-EH/F,t/EH/F,t+RF,t,Real interest parity,Define re=R-erH,te-rF,te=(RH,t-H,t+1e)-(RF,t-F,t+1e)rH,te-rF,te=(qH/F,t+1e-qH/F,t)/qH/F,t If r
40、elative PPP holdsrH,te-rF,te=0I.e.rH,te=rF,te,Empirical test of Fishers Equation,RH,t-RF,t=H,t+1e-F,t+1eH,t+1e-F,t+1e=RH,t-RF,t(H,t+1-F,t+1)e=RH,t-RF,t(H,t+1-F,t+1)=RH,t-RF,t+twhere(H,t+1-F,t+1)=(H,t+1-F,t+1)e+tRun the regression(H,t+1-F,t+1)=+(RH,t-RF,t)+tshould get 0 and 1,Evidence,Cumby and Obstf
41、eld(1984)and Mishkin(1984)both rejected the hypothesis.Reason?PPP and UIP do not holdand real interest parity is derived from them.,Want to know more.,Chapter 15 of Krugman and Obstfeldespecially for various case studiesGibson,Heather D.(1996):INTERNATIONAL FINANCE,Longman Publishing,New York.Chapter 2 for discussion of empirical evidence.,
