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1、1Price levels and Exchange Rate in the Long RunWONG Ka Fu7th February 20012Basic 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)3Basic 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(
2、s) P(s+1) - P(s) /1= P(s+1) - P(s) / P(s)= percentage change in P at time s. 4Law of one pricezIn a competitive markets zfree of 1. transportation costs and 2. official barriers to trade (such as tariffs),zidentical goods sold in different countries must sell for the same price when their prices are
3、 expressed zin terms of the same currency.5Law of one price implies exchange ratez For any good i sold in both home and foreign countriesPHi = (EH/F) (PFi)zHence, the implied exchange rate is EH/F = PHi / PFi6Absolute Purchasing Power Parity (Absolute PPP)zFor a given reference commodity basket sold
4、 in both the home and the foreign countriesPH = (EH/F) (PF)zHence, the implied exchange rate is EH/F = PH / PFzThe implied exchange rate from the Economists Big Mac index7Relative PPPzPrices and exchange rates change such that the ratio of each currencys domestic and foreign purchasing powers are pr
5、eserved.z Hence, (EH/F,t - EH/F,t-1 )/ EH/F,t-1 = H,t - F,twhere t = (Pt - Pt-1 ) / Pt-1 8Relative PPPzIf 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 (
6、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 PF(t)/dt 9Relative PPPzHence, (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,t1
7、0Long-run exchange rate based on absolute PPPz EH/F = PH / PFz PH = MHs / L ( RH, YH )z PF = MFs / L ( RF, YF )zMonetary policy = money supply11Effect of an increase in home money supply on LR EH/FMHs PH EH/Fbecause PH = MHs / L ( RH, YH )because EH/F = PH / PF12Effect of an increase in foreign mone
8、y supply on LR EH/FMFs PF EH/Fbecause PF = MFs / L ( RF, YF )because EH/F = PH / PF13Effect 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 )14Interest rate can change due to reasons other than monetary policyFor exam
9、ple: 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 the L(R,Y) function15Effect of an increase in foreign interest rate on LR EH/FRF PF EH/Fbecause PF = MFs
10、/ L ( RF, YF )because EH/F = PH / PFLFbecause L ( RF, YF )16Effect 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 )17Effect of an increase in foreign output on LR EH/FYF PF EH/Fbecause PF = MFs / L ( RF, YF )because EH/F =
11、PH / PFLFbecause L ( RF, YF )18Long-run exchange rate based on absolute PPPz EH/F = PH / PFz PH = MHs / L ( RH, YH )z PF = MFs / L ( RF, YF )zEH/F = (MHs / MFs ) L ( RF, YF ) /L ( RH, YH )19How is long-run exchange rate determined?zAnything that raises (lowers) LH lowers (raises) EH/F zAnything that
12、 lowers (raises) LF lowers (raises) EH/F zAn increase (A decrease) in MHs raises (lowers) EH/F zAn increase (A decrease) in MFs lowers (raises) EH/F 20Growth rate of money supply: a mathematical derivationzMoney supply level : MHs (t)zGrowth rate : (MHs (t+1) - MHs (t) ) / MHs (t) zDefine y(t) = ln(
13、 MHs (t) )zdy(t)/d(t) = d ln( MHs (t) )/dt= dy(t)/d MHs (t) d MHs (t) /dt= 1/ MHs (t) d MHs (t) /dtz dt = t+1 - t = 121Fisher effectzUncovered interest parity:RH,t = EH/F,t+1e - EH/F,t / EH/F,t + RF,tzlet t+1 e = (Pt+1e - Pt ) / Pt and z t+1 = (Pt+1 - Pt ) / Pt zRelative PPP :(EH/F,t+1 - EH/F,t )/ E
14、H/F,t = H,t+1 - F,t+1z(EH/F,t+1e - EH/F,t )/ EH/F,t = H,t+1e - F,t+1ezRH,t - RF,t = H,t+1e - F,t+1e22If MHS is growing at a rate of zPH grows at a rate of because PH = MHs / L ( RH, YH )zI.e., expect H,t+1 = zor , H,t+1 e = zHence, RH,t - RF,t = H,t+1e - F,t+1e = if F,t+1e = 023If MHS is growing at
15、a rate of Slope = t0Log(MHS)24If MHS is growing at a rate of t0RHRH125If MHS is growing at a rate of t0Log (PH)Slope = 26If MHS is growing at a rate of t0Log(EH/F)Slope = 27If MHS is growing at a rate of ( + )zPH grows at a rate of ( + )because PH = MHs / L ( RH, YH )zI.e., expect H,t+1 = ( + ); zor
16、 , H,t+1 e = ( + )zHence, RH,t - RF,t = H,t+1e - F,t+1e = ( + )if F,t+1e = 028If the rate of MHS growth increases from to ( + )zSuppose RF,t fixed and F,t+1e = 0 because a stable monetary policy, for example.zRH,t increases by because H,t+1e is expected to increase by .zNote that, however, MHS does
17、not change at time t0 - only the future growth ratezHence, PH has to jump from PH1= MHs / L ( RH1, YH ) to PH2= MHs / L ( RH2, YH ) 29Effect of an increase in the growth rate of MHSSlope = Slope = + t0Log(MHS)30Effect of an increase in the growth rate of MHSt0RHRH1RH2 = RH1 + 31Effect of an increase
18、 in the growth rate of MHSt0Log (PH)Slope = Slope = + 32Effect of an increase in the growth rate of MHSt0Log(EH/F)Slope = Slope = + 33The lesson learnt is much more generalzThe story was: yA change in money supply growth leads to change in expected inflation. yA change in expected inflation leads to
19、 a jump in interest rate. (Through Fisher)yA jump in interest rate leads to a jump in exchange rate.zMore generally,yAny thing that cause a change in expected inflation will lead to a jump in interest rate. yA jump in interest rate leads to a jump in exchange rate.34The lesson learnt is much more ge
20、neralzWhat will cause a change in expected inflation?yThe release of economic indicators (say, unemployment, GDP, interest rate, confidence index, etc.) may change our expectation of inflation.zAny release of indicators that cause a change in expected inflation will lead to a jump in exchange rate.
21、35Empirical testPH = (EH/F) (PF) ln PH = ln EH/F + ln PFzRegression: 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.36Hypotheses: zAbsolute PPP implies z 0 = 0, 1 = 1, 2 = 1zRelative PPP implies z 0 = ?, 1 = 1, 2 = 13
22、7Empirical evidence on Absolute PPPzWay off the mark:The prices of identical commodity baskets, when converted to a single currency, differ substantially across countries.38Empirical evidence on Relative PPPzUsually performs poorly although it sometimes is a reasonable approximation to the data.zMor
23、e reliable in the 1960s as a guide to the relationship among inflation and national price levels but less so since 1970s.39Why PPP fails?zTransport costs and restriction on tradezMonopolistic or oligopolistic practices in goods marketszMeasure sof inflation differ across countries.40Exchange rate pa
24、ss-through (ERPT)zThe percentage change in local currency import prices resulting from a one percent change in the exchange rate between the exporting and importing countries. zFull or complete ERPT if the following two conditions are met:yconstant markups of price over cost (e.g., when industries a
25、re perfectly competitive, and markups are constant at zero) and yconstant marginal cost.41Exchange rate pass-through (ERPT)zEmpirical: 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 (importe
26、rs currency per unit of exporters currency)42The interpretation of cC = d ln P / d ln E = d ln P / dt / d ln E / dt = % change in P / % change in EzERPT is “full” or “complete” if c=1 and is “incomplete” if c1.43Exchange rate pass-through (ERPT)zEmpirical: ln( pt ) = a + b Xt +c ln( Et ) + d Zt + et
27、zEstimate of c is around 60%. This implies that 40% of the exchange rate change was offset by changes in the markup.44Pricing to MarketzConsider a monopolistic firm that sells its product in n countries (I.e., n segmented markets)zIts objective is to maximize profit(p1,pn) = pi qi(Eipi,vi) - C( qi(E
28、ipi,vi),w)45Pricing 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 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)
29、 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.46Pricing 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 prob
30、lem of a monopoly maximizing profits in n segmented markets. We should all know its solution from basic microeconomics.47Pricing to MarketzThe optimal export price is the product of the common marginal cost and a destination-specific markup:zpi= Cq - i /(- i +1)zwhere Cq is the marginal cost,z i is
31、the absolute value of the elasticity of demand in the foreign market with respect to changes in price, pi.48Pricing to MarketzThus, prices are different across markets and are related to a destination-specific markup which is a function of demand elasticity.zIf pricing to market behavior dominates,
32、PPP is unlikely to hold.Further readings:zGoldberg, Pinelopi Koujianou and Michael M. Knetter (1997): “Goods Prices and Exchange Rates: What Have we Learned?” Journal of Economic Literature, Vol. XXXV (September, 1997), pp. 1243-1272.49Empirical test of Fishers EquationzRH,t - RF,t = H,t+1e - F,t+1e
33、z H,t+1e - F,t+1e = RH,t - RF,tz( ( H,t+1 - F,t+1) e = RH,t - RF,tz( ( H,t+1 - F,t+1) = RH,t - RF,t + twhere ( ( H,t+1 - F,t+1) = ( ( H,t+1 - F,t+1) e + tzRun the regression z( ( H,t+1 - F,t+1) = + (RH,t - RF,t ) + tzshould get 0 and 1 50EvidencezCumby and Obstfeld (1984) and Mishkin (1984) both rej
34、ected the hypothesis. 51Real exchange ratezThe 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.zqH/F = (EH/F PF) / PH zPF : price of a basket of foreign goods in foreign currencyzPH : price of a di
35、fferent basket of home goods in home currency52Real Exchange Ratehome goodshome currencyforeign goodsforeign currencyPHPFEH/F53Real exchange ratezqH/F = (EH/F PF) / PHzThe units of home good basket per foreign good basket.zThe relative price of foreign good basket in terms of home good baskets.zReal
36、 depreciation: a rise in qH/F 54Factors affecting the long-run real exchange ratezA change in relative output demandyAn increase in world relative demand for home output causes a long-run real appreciation of the home currency against the foreign currency (I.e., a fall in qH/F )zA change in relative
37、 output supplyyA 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 )55Nominal and Real exchange rates in long-run equilibriumzqH/F = (EH/F PF) / PHzEH/F = qH/F (PH / PF) zNote that under Absolute PPP, qH/F = 1.
38、 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.56Effect of an increase in home money supply levelMHs PH EH/Fbecause PH = MHs / L ( RH, YH )because EH/F = qH/F (PH / PF) RH, YH, q
39、H/FWhy?57Effect 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+1e58Effect of an increase in world relative demand for home pdtsRe
40、lative demand for home pdtsEH/Fbecause EH/F = qH/F (PH / PF) qH/F59Effect 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 )60An insight in the failure of relative PPPzWhen all disturbances are monetary in
41、 nature, exchange rates obey relative PPP in the long run.zWhen 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).61Fisher effect with real exchange rate movementzqH/F = (EH/F PF) / PHz(qH/F,t+1 - qH/F,t
42、 )/ qH/F,t = (EH/F,t+1 - EH/F,t )/ EH/F,t + F,t+1 - H,t+1z(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+1ezRH,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,t62Real interest parityzDefine re = R - ezrH,te - rF,
43、te = (RH,t - H,t+1e) - ( RF,t - F,t+1e)zrH,te - rF,te = (qH/F,t+1e - qH/F,t )/ qH/F,t zIf relative PPP holdszrH,te - rF,te = 0zI.e. rH,te = rF,te 63Empirical test of Fishers EquationzRH,t - RF,t = H,t+1e - F,t+1ez H,t+1e - F,t+1e = RH,t - RF,tz( ( H,t+1 - F,t+1) e = RH,t - RF,tz( ( H,t+1 - F,t+1) =
44、RH,t - RF,t + twhere ( ( H,t+1 - F,t+1) = ( ( H,t+1 - F,t+1) e + tzRun the regression z( ( H,t+1 - F,t+1) = + (RH,t - RF,t ) + tzshould get 0 and 1 64EvidencezCumby and Obstfeld (1984) and Mishkin(1984) both rejected the hypothesis. zReason?zPPP and UIP do not holdzand real interest parity is derived from them.65Want to know more .zChapter 15 of Krugman and Obstfeldzespecially for various case studieszGibson, Heather D. (1996): INTERNATIONAL FINANCE, Longman Publishing, New York. Chapter 2 for discussion of empirical evidence.
