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Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,65,Price levels and Exchange Rate in the Long Run,WONG Ka Fu,7th February 2001,Basic math review,X=A/B,ln X = ln A - ln B,Y=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(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 of one price implies exchange rate,For any,good i,sold in both home and foreign countries,P,H,i,= (E,H/F,),(P,F,i,),Hence, the implied exchange rate is,E,H/F,= P,H,i,/ P,F,i,Absolute Purchasing Power Parity (Absolute PPP),For,a given reference commodity basket,sold in both the home and the foreign countries,P,H,= (E,H/F,),(P,F,),Hence, the implied exchange rate is,E,H/F,= P,H,/ P,F,The 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,(E,H/F,t,- E,H/F,t-1,)/ E,H/F,t-1,=,H,t,-,F,t,where,t,= (P,t,- P,t-1,) / P,t-1,Relative PPP,If absolute PPP does not hold because of frictions and other factors and we have E,H/F,=,P,H,/ P,F,where, is a constant that measures the difference from absolute PPP.,E,H/F,(t) =,P,H,(t) / P,F,(t),ln E,H/F,(t)= ln, + ln,P,H,(t) - ln P,F,(t),Taking derivative with respect to t:,dln E,H/F,(t)/dt = dln, /dt + dln,P,H,(t)/dt - dln P,F,(t)/dt,Relative PPP,Hence,(E,H/F,t,- E,H/F,t-1,)/ E,H/F,t-1,=,H,t,-,F,t,where,t,= (P,t,- P,t-1,) / P,t-1,percentage change in E,H/F,t,= percentage change in P,H,t,- percentage change in P,F,t,Long-run exchange rate based on absolute PPP,E,H/F,= P,H,/ P,F,P,H,= M,H,s,/ L ( R,H, Y,H,),P,F,= M,F,s,/ L ( R,F, Y,F,),Monetary policy = money supply,Effect of an increase in home money supply on LR E,H/F,M,H,s,P,H,E,H/F,because P,H,= M,H,s,/ L ( R,H, Y,H,),because E,H/F,= P,H,/ P,F,Effect of an increase in foreign money supply on LR E,H/F,M,F,s,P,F,E,H/F,because P,F,= M,F,s,/ L ( R,F, Y,F,),because E,H/F,= P,H,/ P,F,Effect of an increase in home interest rate on LR E,H/F,R,H,P,H,E,H/F,because P,H,= M,H,s,/ L ( R,H, Y,H,),because E,H/F,= P,H,/ P,F,L,H,because L ( R,H, Y,H,),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 the L(R,Y) function,Effect of an increase in foreign interest rate on LR E,H/F,R,F,P,F,E,H/F,because P,F,= M,F,s,/ L ( R,F, Y,F,),because E,H/F,= P,H,/ P,F,L,F,because L ( R,F, Y,F,),Effect of an increase in home output on LR E,H/F,Y,H,P,H,E,H/F,because P,H,= M,H,s,/ L ( R,H, Y,H,),because E,H/F,= P,H,/ P,F,L,H,because L ( R,H, Y,H,),Effect of an increase in foreign output on LR E,H/F,Y,F,P,F,E,H/F,because P,F,= M,F,s,/ L ( R,F, Y,F,),because E,H/F,= P,H,/ P,F,L,F,because L ( R,F, Y,F,),Long-run exchange rate based on absolute PPP,E,H/F,= P,H,/ P,F,P,H,= M,H,s,/ L ( R,H, Y,H,),P,F,= M,F,s,/ L ( R,F, Y,F,),E,H/F,= (M,H,s,/ M,F,s,),L ( R,F, Y,F,) /L ( R,H, Y,H,),How is long-run exchange rate determined?,Anything that raises (,lowers,) L,H,lowers (,raises,) E,H/F,Anything that lowers (,raises,) L,F,lowers (,raises,) E,H/F,An increase (,A decrease,) in M,H,s,raises (,lowers,) E,H/F,An increase (,A decrease,) in M,F,s,lowers (,raises,) E,H/F,Growth rate of money supply: a mathematical derivation,Money supply level : M,H,s,(t),Growth rate : (M,H,s,(t+1) - M,H,s,(t) ) / M,H,s,(t),Define y(t) = ln( M,H,s,(t) ),dy(t)/d(t),= d ln( M,H,s,(t) )/dt,= dy(t)/d M,H,s,(t),d M,H,s,(t) /dt,= 1/ M,H,s,(t),d M,H,s,(t) /dt,dt = t+1 - t = 1,Fisher effect,Uncovered interest parity:,R,H,t,= E,H/F,t+1,e,- E,H/F,t, / E,H/F,t,+ R,F,t,let,t+1,e,= (P,t+1,e,- P,t,) / P,t,and,t+1,= (P,t+1,- P,t,) / P,t,Relative PPP :,(E,H/F,t+1,- E,H/F,t,)/ E,H/F,t,=,H,t+1,-,F,t+1,(E,H/F,t+1,e,- E,H/F,t,)/ E,H/F,t,=,H,t+1,e,-,F,t+1,e,R,H,t,- R,F,t,=,H,t+1,e,-,F,t+1,e,If M,H,S,is growing at a rate of,P,H,grows at a rate of,because P,H,= M,H,s,/ L ( R,H, Y,H,),I.e., expect,H,t+1,=,or ,H,t+1,e,=,Hence,R,H,t,- R,F,t,=,H,t+1,e,-,F,t+1,e,=,if,F,t+1,e,= 0,If M,H,S,is growing at a rate of,Slope =,t,0,Log(M,H,S,),If M,H,S,is growing at a rate of,t,0,R,H,R,H,1,If M,H,S,is growing at a rate of,t,0,Log (P,H,),Slope =,If M,H,S,is growing at a rate of,t,0,Log(E,H/F,),Slope =,If M,H,S,is growing at a rate of,(,+,),P,H,grows at a rate of,(,+,),because P,H,= M,H,s,/ L ( R,H, Y,H,),I.e., expect,H,t+1,= (,+,);,or ,H,t+1,e,= (,+,),Hence,R,H,t,- R,F,t,=,H,t+1,e,-,F,t+1,e,= (,+,),if,F,t+1,e,= 0,If the rate of M,H,S,growth increases from,to (,+,),Suppose,R,F,t,fixed and,F,t+1,e,= 0 because a stable monetary policy, for example.,R,H,t,increases by,because,H,t+1,e,is expected to increase by,.,Note that, however, M,H,S,does not change at time t,0,- only the future growth rate,Hence, P,H,has to jump from,P,H,1,= M,H,s,/ L ( R,H,1, Y,H,) to P,H,2,= M,H,s,/ L ( R,H,2, Y,H,),Effect of an increase in the growth rate of M,H,S,Slope =,Slope =,+,t,0,Log(M,H,S,),Effect of an increase in the growth rate of M,H,S,t,0,R,H,R,H,1,R,H,2 =,R,H,1,+,Effect of an increase in the growth rate of M,H,S,t,0,Log (P,H,),Slope =,Slope =,+,Effect of an increase in the growth rate of M,H,S,t,0,Log(E,H/F,),Slope =,Slope =,+,The lesson learnt is much more general,The 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 generally,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 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 change in expected inflation will lead to a jump in exchange rate.,Empirical test,P,H,= (E,H/F,),(P,F,),ln P,H,= ln E,H/F,+ ln P,F,Regression:,ln P,H,t,=,0,+ ,1,ln E,H/F,t,+,2,ln P,F,t,+,t,or,ln P,H,t,=,0,+ ,1,ln E,H/F,t,+,2,ln P,F,t,+,3,X,t,+,t,where X,t,serves as a control variable.,Hypotheses:,Absolute PPP implies,0,= 0, ,1,= 1, ,2,= 1,Relative PPP implies,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 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 trade,Monopolistic or oligopolistic practices in goods markets,Measure 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 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 are perfectly competitive, and markups are constant at zero) and,constant marginal cost.,Exchange rate pass-through (ERPT),Empirical:,ln( p,t,) = a + b X,t,+c ln( E,t,) + d Z,t,+ e,t,p,t,: local currency import price,X,t,: a measure of exporters cost,Z,t,: import demand shifters,E,t,: the exchange rate (importers currency per unit of exporters 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 E,ERPT is “full” or,“complete” if c=1,and is,“incomplete” if c1.,Exchange rate pass-through (ERPT),Empirical:,ln( p,t,) = a + b X,t,+c ln( E,t,) + d Z,t,+ e,t,Estimate of,c,is around 60%. This implies that 40% of the exchange rate 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,(p,1,p,n,) = p,i,q,i,(E,i,p,i,v,i,) - C(q,i,(E,i,p,i,v,i,),w),Pricing to Market,(p,1,p,n,) = p,i,q,i,(E,i,p,i,v,i,) - C(q,i,(E,i,p,i,v,i,),w),p,i,is the price charged in i-th market, in the firms domestic currency,q,i,(E,i,p,i,v,i,) is the demand in i-th market, a function of E,i,p,i, price in i-th foreign currency and v,i, some demand shifters (say, income).,Thus, p,i,q,i,(E,i,p,i,v,i,) is the total revenue in domestic currency.,C(q,i,(E,i,p,i,v,i,),w) is the total cost of producing q,i,(E,i,p,i,v,i,) and w is the factors that may shift production cost.,Pricing to Market,(p,1,p,n,) = p,i,q,i,(E,i,p,i,v,i,) - C(q,i,(E,i,p,i,v,i,),w),Note that without exchange rate, E,i, 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 Market,The optimal export price is the product of the common marginal cost and a destination-specific markup:,p,i,= C,q,-,i,/(-,i,+1),where,C,q,is the marginal cost,i,is the absolute value of the,elasticity of demand,in the foreign market with respect to changes in price, p,i,.,Pricing to Market,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 Rates: What Have we Learned?” Journal of Economic Literature, Vol. XXXV (September, 1997), pp. 1243-1272.,Empirical test of Fishers Equation,R,H,t,- R,F,t,=,H,t+1,e,-,F,t+1,e,H,t+1,e,-,F,t+1,e,= R,H,t,- R,F,t,(,H,t+1,-,F,t+1,),e,= R,H,t,- R,F,t,(,H,t+1,-,F,t+1,) = R,H,t,- R,F,t,+,t,where,(,H,t+1,-,F,t+1,) =,(,H,t+1,-,F,t+1,),e,+,t,Run the regression,(,H,t+1,-,F,t+1,) =, + ,(R,H,t,- R,F,t,) +,t,should 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.,q,H/F,= (E,H/F,P,F,) / P,H,P,F,: price of a basket of foreign goods in foreign currency,P,H,: price of a,different,basket of home goods in home currency,Real Exchange Rate,home goods,home currency,foreign goods,foreign currency,P,H,P,F,E,H/F,Real exchange rate,q,H/F,= (E,H/F,P,F,) / P,H,The units of home good basket per foreign good basket.,The relative price of foreign good basket in terms of home good baskets.,Real depreciation: a rise in q,H/F,Factors affecting the long-run real exchange rate,A change in relative output demand,An 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 q,H/F,),A change in relative output supply,A relative expansion of home output causes a long-run real depreciation of the home currency against the foreign currency (I.e., rise in q,H/F,),Nominal and Real exchange rates in long-run equilibrium,q,H/F,= (E,H/F,P,F,) / P,H,E,H/F,= q,H/F,(P,H,/ P,F,),Note that under Absolute PPP, q,H/F,= 1. Thus the fact that q,H/F,may not equal 1 allows the possible deviations from Absolute PPP. This deviation q,H/F,is an additional determinant of the nominal exchange rate.,Effect of an increase in home money supply level,M,H,s,P,H,E,H/F,because P,H,= M,H,s,/ L ( R,H, Y,H,),because E,H/F,= q,H/F,(P,H,/ P,F,),R,H, Y,H, q,H/F,Why?,Effect of an increase in home money supply growth rate,Growth of M,H,s,Y,H, q,H/F,E,H/F,because a nominal change has no real effect,because E,H/F,= q,H/F,(P,H,/ P,F,),R,H,P,H,= M,H,s,/ L ( R,H, Y,H,),H,Because Fisher :,R,H,t,- R,F,t,=,H,t+1,e,-,F,t+1,e,Effect of an increase in world relative demand for home pdts,Relative demand for home pdts,E,H/F,because E,H/F,= q,H/F,(P,H,/ P,F,),q,H/F,Effect of an increase in relative home supply,Relative home supply,E,H/F,?,because E,H/F,= q,H/F,(P,H,/ P,F,),q,H/F,L,H,P,H,= M,H,s,/ L ( R,H, Y,H,),P,H,E,H/F,E,H/F,L ( R,H, Y,H,),An insight in the failure of relative PPP,When all disturbances are monetary in nature, 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 q,H/F,may change over time).,Fisher effect with real exchange rate movement,q,H/F,= (E,H/F,P,F,) / P,H,(q,H/F,t+1,- q,H/F,t,)/ q,H/F,t,= (E,H/F,t+1,- E,H/F,t,)/ E,H/F,t,+,F,t+1,-,H,t+1,(q,H/F,t+1,e,- q,H/F,t,)/ q,H/F,t,= (E,H/F,t+1,e,- E,H/F,t,)/ E,H/F,t,+,F,t+1,e,-,H,t+1,e,R,H,t,- R,F,t,= (q,H/F,t+1,e,- q,H/F,t,)/ q,H/F,t,+,H,t+1,e,-,F,t+1,e,because R,H,t,= E,H/F,t+1,e,- E,H/F,t, / E,H/F,t,+ R,F,t,Real interest parity,Define,r,e,= R -,e,r,H,t,e,- r,F,t,e,= (R,H,t,-,H,t+1,e,),-,(,R,F,t,-,F,t+1,e,),r,H,t,e,- r,F,t,e,= (q,H/F,t+1,e,- q,H/F,t,)/ q,H/F,t,If relative PPP holds,r,H,t,e,- r,F,t,e,= 0,I.e. r,H,t,e,= r,F,t,e,Empirical test of Fishers Equation,R,H,t,- R,F,t,=,H,t+1,e,-,F,t+1,e,H,t+1,e,-,F,t+1,e,= R,H,t,- R,F,t,(,H,t+1,-,F,t+1,),e,= R,H,t,- R,F,t,(,H,t+1,-,F,t+1,) = R,H,t,- R,F,t,+,t,where,(,H,t+1,-,F,t+1,) =,(,H,t+1,-,F,t+1,),e,+,t,Run the regression,(,H,t+1,-,F,t+1,) =, + ,(R,H,t,- R,F,t,) +,t,should get, 0 and , 1,Evidence,Cumby and Obstfeld (1984) and Mishkin(1984) both,rejected,the hypothesis.,Reason?,PPP and UIP do not hold,and real interest parity is derived from them.,Want to know more .,Chapter 15 of Krugman and Obstfeld,especially for various case studies,Gibson, Heather D. (1996): INTERNATIONAL FINANCE, Longman Publishing, New York. Chapter 2 for discussion of empirical evidence.,
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