Does International Trade Stabilize Exchange Rate Volatility?

Transcription

1 Does Inernaional Trade Sabilize Exchange Rae Volailiy? Hui-Kuan Tseng, Kun-Ming Chen, and Chia-Ching Lin * Absrac Since he early 980s, major indusrial counries have been suffering severe muli-laeral rade imbalance, accompanying wih remendously volaile exchange raes. This paper examines he relaionship beween rade balance and exchange rae volailiy. A sochasic macroeconomic model wih sicky price is developed. Our comparaive saics and numerical simulaion resuls indicae ha increased rade balance (relaive o domesic aggregae demand) ends o reduce exchange rae volailiy when he domesic absorpion shock perurbs he economy. In he presence of all oher domesic and foreign shocks, however, increased rade balance ends o augmen exchange-rae volailiy, excep for he case of disurbance of domesic real income in which he effec of increased rade balance is indeerminae. Our resuls sugges ha wheher rade imbalance has aggravaed exchange rae volailiy in many indusrial counries is an open quesion, which needs o be solved hrough empirical invesigaion. Keywords: Trade Imbalance, Exchange Rae Volailiy, Sochasic Macroeconomic Model JEL Classificaion: F7, F3, F47 * Corresponding auhor, Hui-Kuan Tseng, is a Visiing Associae Professor, Deparmen of Inernaional Trade, Naional Chengchi Universiy, Taiwan and Associae Professor, Deparmen of Economics, Universiy of Norh Carolina a Charloe. Tel: (704) , Fax: (704) , hseng@ .uncc.edu.: Kun-Ming Chen, is an Associae Professors, and Chia-Ching Lin is a graduae suden, Deparmen of Inernaional Trade, Naional Chengchi Universiy, Taipei, Taiwan

2 I. Inroducion Since he early 980s, major indusrial counries have been suffering severe muli-laeral rade disequilibrium he U.S. has exhibied huge rade deficis agains Japan, Canada, Wes Germany, he Asian newly indusrializing counries, and more recenly, China. Moreover, foreign exchange raes in many counries have been remendously volaile since he breakdown of he Breon Woods sysem in 973. Are hese wo phenomena relaed? To he bes of our knowledge, his issue is sill no well invesigaed. A popular view is ha exchange rae volailiy ends o reduce he volume of inernaional rade, evidence is no unanimous. For insance, Abrahms [980] and Thursby and Thursby [987] found a large negaive effec of exchange rae volailiy on rade, whereas Hooper and Kohlgagen [978] found no significan effecs on rade volumes bu a large effec on commodiy prices. Laer sudies, including Frankel and Wei [993], Eichengreen and Irwin [996] and De Grauwe and Skudelny [000] all repored small or insignifican negaive effecs. Tenreyro [003] argued ha he esimaion echniques used in previous sudies of he impacs of exchange rae volailiy on rade have muliple sources of problems ha appear o bias heir empirical findings. Mos of exising sudies, boh heoreical and empirical, focus on he effec of exchange rae volailiy on rade. Few papers had aemped o examine he reverse causaliy of wheher inernaional rade can dampen exchange rae volailiy. In his opimal currency area hypohesis, Mundell [96] firsly looked ino his reverse direcion of causaliy. He found ha rade flows reduce real exchange rae volailiy. This paper reexamines he same reverse direcion of causaliy using numerical simulaions. Coe [994] provides an exensive survey of he lieraure boh heoreical and empirical on exchange rae volailiy and rade. Anoher srand of research also emerged o explore wheher cenral banks can somehow inervene in foreign exchange markes so as o reduce exchange rae volailiy. For example, Kawai [984], Eaon and Turnovsky [983], Tseng

3 In his paper we develop a sochasic macroeconomic model o answer he cenral quesion: Does rade imbalance play a role in aggravaing exchange rae flucuaions due o random disurbances originaing in he home counry and abroad? This sudy can supplemen he lieraure by focusing on he causaliy relaionship from inernaional rade o exchange rae volailiy raher han he way around. In addiion, i can provide more evidence of wheher inernaional rade may help sabilize exchange rae movemens, as seen in Mundell [96]. The remainder of his paper proceeds as follows. Secion II oulines he srucure of our heoreical model. Secion III firs solves he model for he equilibrium exchange rae and is volailiy under he raional expecaions hypohesis, and hen he impac of rade imbalance on he volailiy of exchange rae is examined. Secion IV conducs numerical simulaions of he effec of rade imbalance on volailiy of nominal exchange rae and real exchange rae wih baseline parameer values. Sensiiviy analysis on he resuls is also implemened. Brief concluding remarks are given in he final secion. II. The Model The model of a small open economy is summarized by he following equaions: d = ba + bt b > 0, b > 0 () ( [ ]) a = αy α r E p+ p + u > α > 0, α > 0 () ( ) T = β e + p p + β y β y, β > 0, i =,, 3 (3) 3 ( ) i p = p + d y, > 0 (4) = +, 0, 0 (5) m p y r u > > [99] and Dominguez [998].

4 [ ] r = r + E e e (6) + y = y+ u (7) 3 y = y + u 4 (8) p = p (9) r = r + u (0) 5 where all variables excep capial leers, r and r * are measured in logarihm, subscrip denoes period, and E [.] is an expecaion operaor based on all informaion available in period. The definiion of each variable is given in Table. Equaion () is a log-linearized aggregae demand funcion specifying ha domesic aggregae demand is composed of real domesic absorpion, a, and real rade surplus, T, (or real rade defici as T is negaive) in period. 3 The parameers b and b reflec he weighs of domesic absorpion and real rade balance in he economy s aggregae demand, respecively. Equaion () saes ha real domesic absorpion a depends posiively on real domesic oupu, y, and negaively on domesic real ineres rae, r E [p + - p ]. The curren domesic absorpion is also affeced by a sochasic disurbance, u, which conains random changes in eiher domesic fiscal policy or privae consumpion (invesmen). Equaion (3) indicaes ha real rade balance, T, is deermined by curren erms of rade ( e p p + ), foreign income y *, and domesic income y. Equaion (4) sipulaes he same price adjusmen rule specified in Dornbusch s [976] seminal sicky price model, where he goods price is predeermined a any poin in ime. The posiive parameer,, represens he speed of price adjusmen in response o excess demand (d - - y - ) for domesic goods in period -. The greaer 3 In fac, his specificaion of domesic aggregae demand is in line wih Bhandari [983]. 3

5 he value of parameer, he more flexible is he goods price. As goes o infiniy, he goods marke is coninuously cleared along he ime horizon. However, since is assumed o be finie, equilibrium in he domesic goods marke is unlikely o be achieved in he shor run. Table Variable Definiions Variable Definiion d Domesic real aggregae demand Domesic real absorpion, which is he sum of privae and governmen a consumpion and gross invesmen T Real aggregae rade balance y Domesic oupu level; y = long-run saionary level of y. p Domesic goods price r Domesic nominal rae of ineres m Domesic nominal money supply y * Foreign oupu level; y = long-run saionary level of y *. p * Foreign price level; p = long-run saionary level of p * r * Foreign nominal rae of ineres; r = long-run saionary level of r * The nominal exchange rae (measured in erms of unis of domesic currency per e uni of foreign currency) q The real exchange rae E [X + ] Expecaions of X in period + condiional on informaion available in period u Random disurbance in domesic absorpion u Random disurbance in excess supply of domesic nominal money u 3 Random disurbance in domesic real income u 4 Random disurbance in foreign real income Random disurbance in nominal foreign rae of ineres u 5 Equilibrium in he domesic money marke is characerized by equaion (5). The nominal sock supply of domesic money m is assumed o be fixed. The domesic real money demand is of he usual form in ha i is posiively associaed wih domesic real income and negaively associaed wih domesic nominal ineres rae r. I is assumed ha foreigners do no hold domesic money and he only opporuniy cos of holding domesic money is domesic nominal ineres rae. Like he goods marke, he domesic money marke is subjec o a random disurbance, u, 4

6 represening random changes in domesic moneary policy or privae money demand. Equaion (6) is an uncovered ineres pariy condiion, linking domesic nominal ineres rae r o foreign nominal ineres rae r plus an uncovered risk premium E [e + ] - e. This condiion implies agens are risk-neural and poliical risk is non-exisen. 4 Equaions (7), (8) and (0) sae ha domesic income y, foreign income y and foreign nominal ineres rae r flucuae around heir own seady sae equilibrium, respecively, subjec o random disurbances u 3, u 4 and u 5. Equaion (9) implies ha foreign price level p is exogenous and fixed a he long-run saionary level. In fac, all foreign variables menioned above are exogenous, reflecing he fac ha he home counry is a small open economy. There are five random disurbances in he model one domesic demand shock u, one domesic moneary shock u, one domesic income shock u 3, one foreign income shock u 4 and one foreign moneary shock u 5. These disurbances are whie noises and are assumed o be independen of each oher wih mean E [u j+i ] = 0 and have a bounded variance, V[ u j + ] < for j =,, 3, 4 and 5 and i. III. Derivaion of Raional Expecaions Equilibria and Comparaive Saics. Derivaion of raional expecaions equilibria We can reduce he model o a sysem of wo equaions wih wo endogenous variables, e and p. In wha follows we proceed o solve he reduced-form sysem under he raional expecaions hypohesis. The raional-expecaions soluion for each endogenous variable will hen be expressed in erms of all random disurbances and srucural parameers. The firs sep is o obain a se of 4 Eaon and Turnovsky [983] showed ha covered ineres pariy would collapse in he presence of poliical risk. 5

7 reduced form equaions. For simpliciy, we se he values of hose exogenous variables such as y, y, p and r equal o zero. Thus, from equaion (5), he domesic nominal ineres rae r is given by: r = p + u + u. (5 ) 3 Using equaions (), (), (3), (5 ), (7), (8) and (9), he domesic price adjusmen equaion (4) becomes, p = γ p + γ e + γ u γ u + γ u + γ u (a) where bα bα bβ γ = bα γ b 3 =, bα ( b b b ) α α β3 γ 5 = bα,, γ γ γ b β =, bα bα 4 =, bα b β 6 =. bα Subsiuing equaion (5 ) for r in equaion (6), we rewrie he uncovered ineres pariy condiion as [ ] E e + = e + p + u + u u. (b) 3 5 Equaions (a) and (b) represen he reduced-form sysem menioned above. To solve his sysem, we use a wo-sep procedure under he assumed Muhian raional expecaions. 5 Firs, we find he soluion for [ ] E e +, a condiioned expecaion of he exchange rae, by aking expecaions for (a) and (b) in period i (i > 0) condiional on period 0 (Noe X E [ X ] = ). i,0 0 In so doing, all he disurbance erms are washed ou for heir condiioned means equal zero and herefore we can obain. i 6

8 p = γ p + γ e (a) i,0 i,0 i,0 e = p + e (b) i,0 i,0 i,0 Equaions (a) and (b) can be rewrien in he marix form as pi,0 γ γ pi,0 e = i,0 e i,0 or X = AX. i,0 i,0 The characerisic equaion of he sysem of (a) and (b) can be derived by seing he deerminan of ( λ I A) equal o zero, where λ denoes he characerisic vecor and I a x ideniy marix. Assuming he characerisic roos are disinc, we solve he characerisic equaion p e : for i,0 and i,0 p = Bλ + B λ, (3a) i i i,0 e = BZ λ + B Z λ, (3b) i i i,0 where B and B are wo arbirary coefficiens deermined by wo iniial condiions, and Z and Z are he elemens of a normalized characerisic marix of which he firs row is an uni vecor. The characerisic roos, λ and λ, are ( + γ ) ± ( + γ ) 4( γ γ ) λ, λ =. (4) As is well known, λ and λ mus saisfy he following: λ λ = γ γ, (5a) λ + λ = + γ. (5b) 5 See Muh [96]. 7

9 To ensure he sysem o be sable, i mus be parameerized such ha he inequaliy condiion holds: ( )( b β bα) + + > 0. 6 We hen employ he general soluions for expecaions variables in equaions (3a) and (3b) o obain + + [ ] λ λ E e BZ B Z + = + (6) Second, we subsiue equaion (6) back ino (b) and divide he laer equaion by. This procedure yields ( λ λ ) p = e u u + u + BZ + B Z. (7) Now, subsiuing (7) ino (a), he whole sysem furher reduces o one firs-order difference equaion: ( γ γ ) L e = W, (8) where L is a lag operaor such ha LX n =X n-,and ( ) ( ) W = u +u u + γ u γ + γ u + γ γ u + γ u + γ u ( BZλ BZ λ ) γ ( BZλ BZ λ ) We can easily solve equaion (8) for e : k ( γ γ ) ( γ γ ) (9a) e = W + D k k = 0 where D is an arbirary coefficien deermined by iniial condiions. Moreover, we obain he soluion of real exchange rae q, or e + p p, as k = ( +) ( γ γ ) k k = 0 q W u u u ( ) D( γ γ ) + +. (9b) 6 ( )( b β bα) 0 λ λ > implies > > since λ λ [ ( )( b β bα ) ]( bα ) = + +. I also implies γ > 0. Therefore, we have > λ λ > 0 and λ + λ >. In oher words, λ > > λ > 0 or > λ > λ > 0. 8

10 . Comparaive saics We are now ready o derive he variance of he exchange rae, which measures he degree of exchange rae variabiliy. For he purpose of exposiion, we assume ha he variance of each random disurbance equals uniy. We also assume ha all disurbances do no joinly impinge on he economy. Under hese assumpions, he use of equaion (9a) allows us o derive he variance of he nominal exchange rae e ha flucuaes due o disurbance i as follows: where σ ( ) ξ = γ γ, M e, 3 = γ, = { M ei}, i =,, 3, 4, 5 (0a) ξ ei,, ( ) ( ) M e, = + γ + γ4 γ + γ 4 ξ, ( ) ( ) M e,3 = + γ5 γ + γ5 γ ξ, M = γ, e,4 6 M e,5 = + γ γξ. Similarly, from equaion (9b) we can derive he variance of he real exchange rae q ha flucuaes due o disurbance i as follows: where σ = ( + ) { M qi } qi,, ξ, i =,, 3, 4, 5 (0b) 9

11 M = M, q, e, ( ) ( ) M q, = 4 3ξ + γ+ γ 4 γ+ γ 4 ξ, ( 4 3 ) ( ) ( ) M q,3 = ξ + γ5 γ + γ5 γ ξ, M = M, q,4 e,4 ( ) M q,5 = 4 3ξ + γ γξ. Equaions (0a) and (0b) are of grea ineres o he purpose of he paper for i measures exchange rae volailiy. Based on hese equaions, we will proceed o examine how increased rade balance affecs exchange rae volailiy. Differeniaing equaions (0a) and (0b) wih respec o b, we have he following proposiion ( proof is provided in Appendix): Proposiion:. When he domesic absorpion shock (u ) perurbs he economy, increased rade balance (relaive o domesic aggregae demand) reduces nominal (and real) exchange rae volailiy; ha is, e, < 0, q, < 0.. In he presence of foreign real income disurbance (u 4 ) and foreign nominal rae of ineres disurbance (u 5 )], increased rade balance augmens nominal (and real) exchange rae volailiy; ha is, e,4 > 0, e,5 > 0, q,4 > 0, and q,5 > If >, and when domesic nominal money disurbance (u ) disurbs he economy, increased rade balance augmens nominal (and real) exchange rae volailiy; ha is, 0

12 e, > 0,and q, > 0. The above proposiion indicaes ha increased rade balance migh aggravae or alleviae nominal (and real) exchange rae, depending on he source of he disurbances. As for he effec of increased rade balance on exchange rae volailiy when domesic real income disurbance (u 3 ) disurbs he economy, he comparaive saics resul is oo complicaed o deermine is sign, which we resors o numerical simulaions in he following secion. IV. Numerical Simulaions. Parameer values For he purpose of numerical simulaions, he second column of Table presens a se of baseline parameer values and he hird column says he range for a parameer o change. The explanaions of baseline parameer values are in order. Firs, he share of domesic absorpion in aggregae demand b is se equal o 0.90, and he parameer b reflecing he imporance of inernaional rade balance in aggregae demand is calibraed under he assumpion ha d is equal o zero and rade balance relaive o aggregae demand ranges from 0.0 o I urns ou ha he value of b is beween 0.9 and.07 (see Table 3 for deails.) Second, he value of α measuring he elasiciy of domesic income o aggregae demand is se equal o 0.3 and is allowed o range from 0. o 0.8, while he value of α measuring he real ineres rae semi-elasiciy of domesic absorpion is se a Third, he semi-elasiciy of rade balance wih respec o curren erms of rade β is se equal o 0., while he semi-elasiciy of rade balance wih respec o foreign income β and ha wih respec o domesic income β 3 are equally se a 0.3 and boh are allowed o range from 0. o 0.8.

13 Fourh, he income elasiciy of real money demand is se a 0.3 and is allowed o change from 0. o 0.8. Mos empirical esimaes indicae ha he ineres-rae elasiciy of real money demand is around 0.0. I hus urns ou ha he ineres-rae semi elasiciy / is , or approximaes.5. Finally, he baseline parameer value of he degree of price flexibiliy is se equal o 0.5, bu i is allowed o change in a wide range from 0.00 o ; ha is, from being inelasic o uniary elasic. Noe ha he parameer values chosen in Table ensure ha he sysem exiss a leas one sable characerisic roo (see Foonoe 6). Parameer Se Table Parameer Values Baseline Values Varians b 0.9 b α α 0.3 β 0. β β ( )( β α ) + b + b λλ = γ γ Table 3 Trade Balance and he Value of b Scenario D Y = A T d a b b

14 Simulaion resuls wih baseline parameer values Given he baseline parameer values, he firs par of numerical simulaions is conduced by allowing b o ake on values ranging from 0.90 o.07. The variance of he nominal exchange rae (equaion 0a) and he variance of he real exchange rae (equaion 0b) are hen compued for each chosen value of b. The numerical resuls of he effecs of rade balance on nominal exchange rae volailiy and real exchange rae volailiy are repored in Table 4 and Table 5, respecively, and heir qualiaive oucomes are summarized in Table 6. A sriking finding is ha an increase in he weigh of rade balance in aggregae demand (b ) ends o decrease boh nominal and real exchange rae volailiy when domesic absorpion disurbance (u ) disurbs he economy. However, in he presence of all oher disurbances (domesic nominal money disurbance (u ), domesic real income disurbance (u 3 ), foreign real income disurbance (u 4 ), or foreign nominal rae of ineres disurbance (u 5 )), increased rade balance weigh ends o be desabilizing raher han sabilizing boh nominal and real exchange rae volailiy. Some oher findings from Table 4 and Table 5 also deserve aenion. Firs, he variance of real exchange rae volailiy is much larger han he variance of nominal exchange rae is in all cases. Second, in he presence of foreign real income disurbance (u 4 ), he variance of he exchange rae urns ou o be far below uniy. Bu he exchange rae variance exceeds uniy in he presence of all oher disurbances in mos scenarios. Third, he domesic moneary shock is seen o have he mos powerful desabilizing effec on exchange rae movemens, for he nominal (real) exchange -rae variance is more han wo (weny-six) imes as much as he variance of u in all cases, which 3

15 accord wih he overshooing phenomenon firsly formulaed in Dornbusch [976]. Table 4 Variance of Nominal Exchange Rae: Baseline Parameer Values b u u u 3 u 4 u Table 5 Variance of Real Exchange Rae: Baseline Parameer Values b u u u 3 u 4 u Table 6 Summary of Qualiaive Resuls wih Baseline Parameer Values Source of Disurbance Effec on Exchange Rae Volailiy domesic absorpion, u - domesic nominal money, u + domesic real income, u 3 + foreign real income, u 4 + nominal foreign rae of ineres, u Sensiiviy analysis The second par of numerical simulaions is sensiiviy analysis, which is o see wheher he above numerical resuls are robus o changes in he values of some parameers including α, β, β 3, and. Since he qualiaive resuls for all disurbance excep for domesic real income disurbance (u 3 ) are known from our comparaive saics resuls, our sensiiviy analysis hus focuses on he case of domesic real income disurbance. Tables 7-8 repor he resuls of sensiiviy 4

16 analysis. I is found ha he exchange rae variance is sensiive o he parameer values of α, β 3 and in he presence of u 3. When he values of α, or β 3, or, are small, increased rade balance b ends o decrease exchange rae volailiy if price adjusmen is inelasic, bu i urns ou o be desabilizing if price adjusmen is uni elasic. However, when he values ofα, β 3 and are se a 0.4 or higher, increased rade balance ends o increase exchange rae volailiy wheher price adjusmen is inelasic or uni elasic. Table 7 Sensiiviy Analysis of Nominal Rae Variance agains Domesic Real Income Disurbance α, β3, b Noes: Robus o changes in he values of β. Table 8 Sensiiviy Analysis of Real Rae Variance agains Domesic Real Income Disurbance α, β3, b Noes: Robus o changes in he values of β. 5

17 V. Conclusion This paper examines he relaionship beween rade balance and exchange rae volailiy, using a sochasic small open economy model wih sicky price. Several random disurbances ha perurb he economy and cause exchange rae flucuaions are considered. These disurbances include shocks o domesic absorpion, domesic money sock, domesic income, foreign income, and foreign nominal ineres rae. Boh Comparaive saics and numerical simulaions wih sensiiviy analysis are conduced. This paper has found ha increased rade balance (relaive o domesic aggregae demand) ends o reduce exchange rae volailiy when he domesic absorpion shock perurbs he economy. In he presence of all oher domesic and foreign shocks, however, increased rade balance ends o augmen exchange-rae volailiy, excep for he case of disurbance of domesic real income in which he effec of increased rade balance is indeerminae. Our resuls sugges ha wheher rade imbalance has aggravaed exchange rae volailiy in many indusrial counries is an open quesion. Furher research o solve his quesion hrough empirical invesigaion seems warraned. The paper herefore calls ino quesion he role of inernaional rade in dampening exchange rae flucuaions in an inernaional environmen affeced simulaneously by muliple sources of random disurbances, be i domesic or foreign. 6

18 References Abrahms, R., 980, "Acual and Poenial Trade Flows wih Flexible Exchange Raes, Federal Reserve Bank of Kansas Ciy Working Paper No Bhandari, Jagdeep, 983, Aggregae Dynamics in an Open Economy, The Mancheser School, June, 9-5. Coe, A., 994, "Exchange Rae Volailiy and Trade: A Survey, Bank of Canada Working Paper De Grauwe, P. and F. Skudelny, 000, The Impac of EMU on Trade Flows, Welwirschafliches Archiv, 36, Dominguez, K. M., 998, Cenral Bank Inervenion and Exchange Rae Volailiy, Journal of Inernaional Money and Finance, 7,, Dornbusch, R., 976, Expecaions and Exchange Rae Dynamics, Journal of Poliical Economy, 84, 6-76 Eaon, J. and Turnovsky, Sephen J., 983, Exchange Risk, Poliical Risk, and Macroeconomic Equilibrium, American Economic Review, March, Eichengreen, B. And D. Irwing, 996, "The Role of Hisory in Bi8laeral Trade Flows, NBER Working Paper No Frankel, J. and S. Wei, 993, "Trade Blocs and Currency Blocs, NBER Working Paper No Hooper, P. and S. Kohlhagen, 978, The Effec of Exchange Rae Uncerainy on The Prices and Volume of Inernaional Trade, Journal of Inernaional Economics, 8, Kawai, M., 984, The Effec of Forward Exchange on Spo-Rae Volailiy under Risk and Raional Expecaions, Journal of Inernaional Economics, 6, Mundell, Rober A., 96, A Theory of Opimal Currency Areas, American Economic Review, 5, 4, Muh, John F., 96, Raional Expecaions and The Theory of Price Movemens, Economerica, 9, Thursby, J. and M. Thursby, 987, Bilaeral Trade Flows, he Linder Hypohesis, and Exchange Risk, The Review of Economics and Saisics, 69, Tseng, Hui-Kuan, 99, Forward Marke Inervenion and Exchange Rae Variabiliy: A Simulaion Approach, Alanic Economic Journal, XIV,, -. Tenreyro, S., 003, On he Trade Impac of Nominal Exchange Rae Volailiy, Federal Reserve Bank of Boson Working Paper No

19 Appendix: Comparaive Saics A. The volailiy of he nominal exchange rae Differeniaing equaion (0a) wih respec o b, we have where ( ) ( ) ( b, b, β, α,, ) e, bβ + Ψ b, b, β, α,, =, (Aa) Γ ( ) ( ) ( b, b, β, α,, ) 4 e, β bα + bβ Ψ b, b, β, α,, =, (Ab) Γ ( ) ( b, b, β, α,, ) e,4 bβ Ψ 3 b, b, β, α,, =, (Ac) Γ ( ) ( b, b, β, α,, ) e,5 bβψ 3 b, b, β, α,, =, (Ad) Γ ( b, b, β, α,, ) bα b β ( ) b β( ) bα ( ) Γ = ( b, b, β, α,, ) ( )( bα b β ) Ψ = + + +, ( b, b, β, α,, ) b α bα ( ) b β ( ) Ψ = + + +, ( b, b, β, α,, ) b β ( ) bα ( ) bα bα ( ) Ψ3 = The sabiliy condiion, ( + )( bα + b β ) > 0,implies ( b b β α ) Ψ,,,,, < 0.Thus, e, < 0. (Aa) Moreover, since b β = > ( + ) bα ( + )( bα + b β ) bα ( + )( bα + b β ) 0 8

20 and ( ) ( )( ) bα + bβ( +) ( )( )( ) = > 0, + bα + bα + b β bα + + bα + b β hese imply ( b b β α ) Ψ,,,,, > 0, or 3 e,4 > 0, (Ab) and e,5 > 0. (Ac) Finally, if >, we have e, > 0. (Ad) A. The volailiy of he real exchange rae Differeniaing equaion (0b) wih respec o b and applying similar reasoning as we use in proving he change in he volailiy of nominal exchange rae in A., we have 3 ( ) ( ) ( b, b, β, α,, ) q, bβ + Ψ b, b, β, α,, = < 0, (A3a) Γ ( ) ( ) ( ) ( b, b, β, α,, ) q, β + bα + bβ Ψ b, b, β, α,, = > 0 Γ, if > (A3b) ( ) ( ) ( b, b, β, α,, ) σ q,4 bβ + Ψ3 b, b, β, α,, = > 0, (A3c) Γ ( ) ( ) ( b, b, β, α,, ) σ q,5 bβ + Ψ3 b, b, β, α,, = > 0. (A3d) Γ 9