andExchangeRateintheLongRun國際金融香港

1、Price levels and Exchange Rate in the Long RunWONG Ka Fu7th February 2001Basic math reviewX=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 reviewP=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)

2、P(s+1) - P(s) /1= P(s+1) - P(s) / P(s)= percentage change in P at time s. Law of one priceIn 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 expres

3、sed in terms of the same currency.Law 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 / PFiAbsolute Purchasing Power Parity (Absolute PPP)For a given reference commodity basket sold in both the

4、home and the foreign countriesPH = (EH/F) (PF)Hence, the implied exchange rate is EH/F = PH / PFThe implied exchange rate from the Economists Big Mac indexRelative PPPPrices and exchange rates change such that the ratio of each currencys domestic and foreign purchasing powers are preserved. Hence, (

5、EH/F,t - EH/F,t-1 )/ EH/F,t-1 = H,t - F,twhere t = (Pt - Pt-1 ) / Pt-1 Relative PPPIf 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) -

6、 ln PF(t) Taking derivative with respect to t:dln EH/F (t)/dt = dln /dt + dln PH (t)/dt - dln PF(t)/dt Relative PPPHence, (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,tLong-run exchange rate

7、based on absolute PPP EH/F = PH / PF PH = MHs / L ( RH, YH ) PF = MFs / L ( RF, YF )Monetary policy = money supplyEffect of an increase in home money supply on LR EH/FMHs PH EH/Fbecause PH = MHs / L ( RH, YH )because EH/F = PH / PFEffect of an increase in foreign money supply on LR EH/FMFs PF EH/Fbe

8、cause PF = MFs / L ( RF, YF )because EH/F = PH / PFEffect of an increase in home interest rate on LR EH/FRH PH EH/Fbecause PH = MHs / L ( RH, YH )because EH/F = PH / PFLHbecause L ( RH, YH )Interest rate can change due to reasons other than monetary policyFor example: technology advancement may impr

9、ove 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 the L(R,Y) functionEffect of an increase in foreign interest rate on LR EH/FRF PF EH/Fbecause PF = MFs / L ( RF, YF )because EH/F = PH / PFLF

10、because L ( RF, YF )Effect of an increase in home output on LR EH/FYH PH EH/Fbecause PH = MHs / L ( RH, YH )because EH/F = PH / PFLHbecause L ( RH, YH )Effect of an increase in foreign output on LR EH/FYF PF EH/Fbecause PF = MFs / L ( RF, YF )because EH/F = PH / PFLFbecause L ( RF, YF )Long-run exch

11、ange 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 (raises) EH/F Anything that lowers (raises) LF lowers (raises) EH/F An increase

12、 (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 derivationMoney supply level : MHs (t)Growth rate : (MHs (t+1) - MHs (t) ) / MHs (t) Define y(t) = ln( MHs (t) )dy(t)/d(t) = d ln( MHs (t) )/dt= dy(t)/d MHs (t)

13、d MHs (t) /dt= 1/ MHs (t) d MHs (t) /dt dt = t+1 - t = 1Fisher effectUncovered 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+1e

14、RH,t - RF,t = H,t+1e - F,t+1eIf 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 = 0If MHS is growing at a rate of Slope = t0Log(MHS)If MHS is growing at a rate of t0RHRH1If MHS is gr

15、owing at a rate of t0Log (PH)Slope = If MHS is growing at a rate of t0Log(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 = 0If the rate of

16、 MHS growth increases from to ( + )Suppose RF,t fixed and F,t+1e = 0 because a stable 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 ( RH

17、1, YH ) to PH2= MHs / L ( RH2, YH ) Effect of an increase in the growth rate of MHSSlope = Slope = + t0Log(MHS)Effect of an increase in the growth rate of MHSt0RHRH1RH2 = RH1 + Effect of an increase in the growth rate of MHSt0Log (PH)Slope = Slope = + Effect of an increase in the growth rate of MHSt

18、0Log(EH/F)Slope = Slope = + The lesson learnt is much more generalThe story was: A change in money supply growth 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 gener

19、ally,Any thing that cause a change in expected inflation will lead to a jump in interest rate. A jump in interest rate leads to a jump in exchange rate.The lesson learnt is much more generalWhat will cause a change in expected inflation?The release of economic indicators (say, unemployment, GDP, int

20、erest rate, confidence index, etc.) may change our expectation of inflation.Any release of indicators that cause a change in expected inflation will lead to a jump in exchange rate. Empirical testPH = (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

21、= 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 implies 0 = ?, 1 = 1, 2 = 1Empirical evidence on Absolute PPPWay off the mark:The prices of identical commodity baskets, when converted to a single currency,

22、 differ substantially across countries.Empirical evidence on Relative PPPUsually performs poorly although it sometimes is a reasonable approximation to the 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?T

23、ransport costs and restriction on tradeMonopolistic or oligopolistic practices in goods marketsMeasure sof inflation differ across countries.Exchange rate pass-through (ERPT)The percentage change in local currency import prices resulting from a one percent change in the exchange rate between the exp

24、orting and importing countries. Full or complete ERPT if the following two conditions are met:constant markups of price over cost (e.g., when industries are perfectly competitive, and markups are constant at zero) and constant marginal cost.Exchange rate pass-through (ERPT)Empirical: ln( pt ) = a +

25、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 exporters currency)The interpretation of cC = d ln P / d ln E = d ln P / dt / d ln E / dt = % change in P / % change in EERPT

26、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 change was offset by changes in the markup.Pricing to MarketConsider a monopolistic

27、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 price charged in i-th market, in the firms domestic currencyqi(Eipi,vi) is the dem

28、and 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,vi) and w is the factors that may shift production cost.Pricing to

29、 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 microeconomics.Pricing to MarketThe optimal export price is the p

30、roduct 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 MarketThus, prices are different across markets and are relat

31、ed 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 Rates: What Have we Learned?” Journal of Economic Lite

32、rature, Vol. XXXV (September, 1997), pp. 1243-1272.Empirical test of Fishers EquationRH,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 - R

33、F,t ) + tshould get 0 and 1 EvidenceCumby and Obstfeld (1984) and Mishkin (1984) both rejected the hypothesis. Real exchange rateThe 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)

34、 / PH PF : price of a basket of foreign goods in foreign currencyPH : price of a different basket of home goods in home currencyReal Exchange Ratehome goodshome currencyforeign goodsforeign currencyPHPFEH/FReal exchange rateqH/F = (EH/F PF) / PHThe units of home good basket per foreign good basket.T

35、he relative 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 rateA change in relative output demandAn increase in world relative demand for home output causes a long-run real appreciation of the home currency ag

36、ainst 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 equilibriumqH/F = (EH/F PF) /

37、 PHEH/F = qH/F (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 levelMHs PH EH/Fbecause

38、PH = MHs / L ( RH, YH )because EH/F = qH/F (PH / PF) RH, YH, qH/FWhy?Effect of an increase in home money supply growth rateGrowth of MHs YH, qH/F EH/Fbecause a nominal change has no real effectbecause EH/F = qH/F (PH / PF) RHPH = MHs / L ( RH, YH )HBecause Fisher : RH,t - RF,t = H,t+1e - F,t+1eEffec

39、t of an increase in world relative demand for home pdtsRelative demand for home pdtsEH/Fbecause EH/F = qH/F (PH / PF) qH/FEffect of an increase in relative home supplyRelative home supplyEH/F ?because EH/F = qH/F (PH / PF) qH/FLHPH = MHs / L ( RH, YH )PHEH/FEH/FL ( RH, YH )An insight in the failure of relative PPPWhen all disturbances are monetary in nature, exchange rates obey relative PPP in the long run.When distu