Final Exam Answers Exchange Rate Economics

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1 Kiel Insiu für Welwirhschaf Advanced Sudies in Inernaional Economic Policy Research Spring 2005 Menzie D. Chinn Final Exam Answers Exchange Rae Economics This exam is 1 ½ hours long. Answer all quesions. Use equaions and figures if helpful. [Because of he omission in Quesion 1.2, he exam is graded ou of 80 poins] 1. Porfolio Balance model. [20 minues] Suppose he risk premium (rp) on euro denominaed asses is given by: rp = 1 1 β α + β x where x is he share of euro denominaed asses in he world (assume here are only wo currencies, he US$ and he euro). 1.1 (10 minues) In he conex of his model, wha do you hink will happen if one s assessmen of he size of fuure Unied Saes Governmen budge deficis rises (and hose of he euro zone governmens remain he same)? Define he risk premium as he addiional reurn necessary o induce he holding of a paricular asse. This means one drops explicily he uncovered ineres rae pariy condiion. Hence: rp i Eu i US e s + 1 (1) where depreciaion expeced beween ime and +1, based on ime informaion, is expressed as: e s ε ( s ) s (2) One hen obains he following diagram: rp rp(x) rp 0 rp 1 1/β α x 1 x 0 x -α/β Here x is he share of he oal porfolio ha is euro denominaed. If x=α, hen he risk premium is zero. However, if x=x 0, hen in some sense, he ineres raes on euro asses mus be higher in order o

2 compensae individuals for he fac ha hey are holding greaer amouns of euro asses han hey would like (consisen wih no risk premium). Wha does α equal? In a mean-variance framework (familiar o hose of you who know he capial asse pricing model, or CAPM, for sock reurns), α is a funcion of he degree of risk aversion, and he exen o which real reurns on euro asses are correlaed wih he dollar reurns on US dollar denominaed asses. The quesion asks abou wha happens if he budge defici and hence he deb denominaed in dollars rises above wha is currenly expeced. Then in he fuure, he x should fall o x 1 (remember, his is all from he Euro area residen s perspecive), so he risk premium on euro denominaed asses should fall. Bu since he value of a bond depends upon he value i is expeced o have in he fuure, he value oday of US bonds should fall, while hose of euro area bonds should rise. 1.2 (10 minues) If he variance of relaive reurns on he wo asses rises, in US$ erms, wha do you hink is he quaniaive magniude of he effec you indicae in your answer o quesion 1.1? [Since I accidenally omied rises in he quesion, I made he oal number of poins allocaed o problem 1 equal 10, giving exra credi if anybody answered he quesion assuming eiher rises or falls.] In he mean-variance framework β -1 = ρω. Ω is he variance of reurns in euro erms; bu i is also he variance of reurns in USD erms, so when his rises, he slope is fla, hen β -1 rises and asses become less subsiuable. Graphically, his means he rp(x) curve roaes couner-clockwise. rp 0 rp rp(x) Ω large rp(x) Ω small rp 1 1/β α x 1 x 0 x -α/β Noice ha now, any change in x now causes a larger change in he risk premium. 2. Purchasing power pariy. [20 minues] Define he real exchange rae for he US dollar agains he Thai bah as: * Q ( S P ) / P (1) where S is measured in US$/bah, P and P* are price indices (namely, CPI in he US and Thailand, wih a base year of 1995=100). One obains he following picure: 2

3 XTH*CPITH/CPIUS Figure 1: Real US$/Thai bah exchange rae (CPI deflaed). Source: IMF, Inernaional Financial Saisics, auhors calculaions. 2.1 (10 minues) Can one conclude from his picure ha he Thai bah was overvalued, in absolue purchasing power pariy erms, in a he end of 1996? Explain why or why no. No, one canno conclude ha, according o absolue PPP, he Thai bah was overvalued in Tha is because he price variable is no a price of a bundle of goods, bu raher a price index, which equals 100 in a paricular base year. One could conclude ha Q was high relaive o he average value of Q over he sample period; bu ha using ha crierion is consisen wih he concep of relaive PPP. 2.2 (10 minues) Now consider his diagram which plos he real exchange rae as he number of bundles of goods evaluaed a US prices, required o purchase a single bundle of goods evaluaed a Thai prices. In oher words, P and P* are now measured for idenical bundles of goods (i.e., food accouns for he same proporion in each bundle, ec.). 1.0 Unied Saes Thailand THPPP 1 Figure 2: Price levels for bundles of goods in US and Thailand (US=1.0). Source: World Bank, World Developmen Indicaors. 3

4 Can one conclude ha he Thai bah was overvalued by absolue purchasing power pariy in 1996? Why or why no? Here, he prices are for (heoreically) idenical bundles of goods, expressed in a common currency, hence one can make assessmens of absolue purchasing power pariy. However, now wih his daa, one can conclude ha by his crierion, he Thai bah was undervalued (he dollar was overvalued) in This couner-inuiive resul suggess ha absolue PPP may no be very useful for deermining exchange rae misalignmen for many quesions. 3. Compeing models of he exchange rae. [20 minues oal] Consider he graph of he (rade-weighed) value of he euro, agains a broad baske of currencies Nominal value of he euro Real (CPI-deflaed) value of he euro 80 99:01 99:07 00:01 00:07 01:01 01:07 02:01 02:07 TWCEEU_ECB_BR TWCQEU_ECB_BR Figure 3: (Broad) Trade weighed effecive exchange raes for he euro, nominal and real. Source: European Cenral Bank. Wha model (or models) of he exchange rae does his figure suppor? Use equaions o suppor your argumen. This figure suppors boh models of he exchange rae. In oher words, he high correlaion beween nominal and real exchange raes is consisen wih eiher a real business cycle model of he exchange rae, as in Sockman s approach, or he sicky price moneary models of Dornbusch and Frankel. The high covariaion beween he nominal and real exchange rae can arise for (a leas) wo reasons: (i) moneary shocks in he presence of sicky nominal prices or (ii) real shocks in he conex of perfec price flexibiliy. Consider firs he following ideniy: * * s= p p q = s p+ p If p and p* are fixed in he very shor run, bu he common currency relaive price, q, is no, hen definiionally s and q will covary. This sicky price assumpion is common in he Dornbusch (1976) and Frankel (1979) models. On he oher hand, consider he Lucas model: px(, s M) py() s esm (,, N) = = p (, s N) y M N η p ξ y () s 4

5 In his case, he exchange rae e can move because of money shocks or real shocks (he laer include he goods-endowmens ζ and η, as well as he p y (s) which may or may no move depending on hese goodsendowmens and he uiliy funcion). If real shocks are large relaive o he nominal shocks (here shocks o M and N), hen e will end o covary wih p y. Bu p y is he real exchange rae, alhough i is assumed ha he home counry and he foreign produce differen goods. 4. Presen value models. [30 minues] 4.1 (15 minues) Solve for he presen value relaion of he nominal exchange rae in he flexible price moneary model, assuming no bubbles, and ha he fundamenals follow a random walk (wihou drif) process. Show your work. 5

6 4.2 (5 minues) Show ha in his case ha he change in he exchange rae equals he change in he fundamenals. Clearly, from equaion (19) above, aking he oal differenial yields: ds = dm ~ In oher words, since he level of he spo exchange rae depends upon he curren level of fundamenals, hen he change in he spo rae depends upon he change in curren fundamenals. Since all fuure fundamenals move up (or down) by exacly he same amoun ha he curren fundamenals changed by. 4.3 (10 minues) Obain a general expression for he change in he exchange rae oday as a funcion of he change in he fundamenals oday, and he discouned value of fundamenals in he fuure. Can you explain why he expression you obain in 4.2 is so simple? Consider he presen value no bubbles formulaion of he spo exchange rae: s 1 λ ~ = E M λ 1+ λ 1 λ ~ s = E M λ 1+ λ (1) (2) Subracing (1) from (2) yields: 1 λ ~ ~ s 1 s = E M E M + ( λ 1+ λ ) (3) 1 λ s+ 1 s = ( M ~ + M ~ ~ ~ 1 ) + E+ M+ + E M+ + ( ) (4) 1 λ + 1 λ Noice ha he change in he spo exchange rae is equal o he presen discouned value of differences in expeced fundamenals, as well as he curren change in he fundamenals. When he fundamenals follow a random walk, hen all he erms afer he summaion operaor in (4) sum o zero. Kielasp_final