La Follette School of Public Affairs

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1 Rober M. La Follee School of Public Affairs a he Universiy of Wisconsin-Madison Working Paper Series La Follee School Working Paper No hp:// Macro Approaches o Foreign Exchange Deerminaion Menzie D. Chinn Professor, La Follee School of Public Affairs and Deparmen of Economics a he Universiy of Wisconsin-Madison, and Naional Bureau of Economic Research mchinn@lafollee.wisc.edu April Observaory Drive, Madison, Wisconsin / The La Follee School akes no sand on policy issues; opinions expressed in his paper reflec he views of individual researchers and auhors.

2 Macro Approaches o Foreign Exchange Deerminaion By Menzie D. Chinn* Universiy of Wisconsin and NBER April 2013 Absrac Macroeconomic approaches o exchange rae deerminaion are reviewed, wih an emphasis on empirical models. Moneary and porfolio balance models of nominal exchange raes are described and evaluaed. The lieraure on real models of real exchange raes is reviewed. The chaper ends wih a brief survey of recen developmens in exchange rae modeling. JEL Classificaion Nos.: F32, F41 Keywords: exchange rae, currency, ineres rae, money, bonds, produciviy, purchasing power pariy, risk premium, Taylor rule, oupu gap Acknowledgemens: Draf chaper prepared for The Handbook of Exchange Raes, edied by Jessica James, Ian W. Marsh and Lucio Sarno. I hank he ediors, Ron Alquis, Yin-Wong Cheung, Jaewoo Lee, and David Papell for commens. 0

3 1. Inroducion In his chaper I review a number of models of exchange rae developed during he pos-breon Woods era. The approaches are broken down ino caegories of nominal and real exchange rae models, wih paricular reference o he empirical evidence. I hen discuss recen approaches ha do no nealy fall ino eiher caegorizaion. The defining feaure of he bulk of he models ha have been empirically assessed is ha hey rely upon sock equilibrium condiions, and hence are ofen caegorized as being wihin he asse marke approach, o disinguish hem from he earlier flow marke approach. Alhough he underpinnings of hese models are quie unsaisfying from he perspecive of recen heoreical developmens, hey remain he workhorses of empirical exchange rae modeling. This is rue largely because he empirical implicaions of, for insance, he New Inernaional Macroeconomics (Obsfeld and Rogoff, 1996) have no been proven easy o es in he economeric framework. For his same reason, mos of he empirical evidence discussed in he chaper comes from reduced form or quasi-reduced form specificaions, raher from srucural (i.e., calibraed) models of economies. While srucural approaches, mos prominenly in he form of dynamic srucural general equilibrium (DSGE) models, have become increasing imporan in he new research, evaluaion of goodness-of-fi remains difficul, for a variey of reasons. 1 1 Mos papers rely upon an informal assessmen of how impulse response funcions from a calibraed or esimaed model conform o priors. In addiion, he empirical resuls are ofen couched in erms of deviaions from seady sae, which in pracice have o be esimaed. See 1

4 2. Models of he Nominal Exchange Rae The early empirical lieraure peraining o moneary and porfolio balance models has been surveyed exensively (Taylor, 1995; Frankel and Rose, 1995; Sarno and Taylor, 2002). In he wake of he collapse of he Breon Woods sysem, wo major srands of models dominaed he lieraure: he moneary and porfolio balance approach. Boh approaches focused on socks of ouside asses money in he former and boh money and bonds in he laer. While his perspecive is compleely naural from oday s vanage poin, i is easy o forge how much his approach differed from he older flow perspecive of he Mundell-Fleming model. This approach sressed curren accoun and capial accoun flows as he deerminans of exchange raes, and was largely superseded in he 1970 s. Consequenly, I will no discuss his approach in deail. Alhough he moneary and porfolio approaches share a focus upon socks, hey differ in heir views of he subsiuabiliy of capial. In pracice, he difference amouns o wheher uncovered ineres pariy holds, or wheher he forward rae differs from he expeced fuure spo rae by an exchange risk premium. Of he wo approaches, by far he mos common approach in he nominal exchange rae lieraure has been he moneary model. 2.1 The Moneary Model The moneary approach views he exchange rae as he relaive price of currencies, when ha relaive price depends upon he relaive demands and supplies of he socks of money. Wihin ha srand, wo varians can be discerned: he flexible price (Frenkel, 1976; Bilson, 1981) and Morley (2010) for discussion. 2

5 sicky price versions (Dornbusch, 1976; Frankel, 1979); in he former, purchasing power pariy (PPP) holds coninuously, while in he laer, i only holds in he long run. To fix he noaion and moivae he empirical modeling, hese wo models are derived. Assume purchasing power pariy (PPP) in log-levels, s p p * (1) Where log s is he nominal exchange rae, expressed in unis of home currency per foreign currency, and p is he log price level. Aserisks denoe foreign variables. Money demand funcions in he wo counries are expressed as d m p y i (2) where m is he log nominal money sock, y is log income, i is he shor erm ineres rae, and he d superscrips indicae "demand". I assume for simpliciy ha he money demand parameers are he same across he wo economies. Rearranging, assuming money supply equals money demand, and imposing PPP one obains: * * * s ( m m ) ( y y ) ( i i ) (3) The moneary model yields wo key implicaions. The firs is he inuiive resul ha higher relaive income induces a sronger currency. The second is ha a higher relaive ineres rae induces a weaker currency. Boh of hese predicions are opposie of hose obained by he saic version of he Mundell-Fleming model. The reasons for hese differences are obvious. In he Mundell-Fleming model, higher income induces higher impors, ceeris paribus, and hence a weaker currency. In he moneary model, a higher income induces a higher money demand relaive o supply, and hence a sronger currency. Also, in he Mundell-Fleming model, a higher ineres rae causes a capial inflow, by 3

6 he ad hoc financial accoun funcion. In he moneary approach, a higher ineres rae causes a lower money demand, relaive o money supply, and hence a weaker currency. In empirical work on he flexible price model, i will prove convenien o work wih equaion (3). However, addiional insigh ino he inuiion of he monearis approach can be obained by noing ha uncovered ineres rae pariy (UIP) implies ha a higher domesic ineres rae implies a weaker currency in he fuure. To see his, noe UIP is denoed by e Es s s i i 1 1 * (4) The objec in he middle of he equaion is "expeced depreciaion" based on he ime informaion se. Subsiuion of his expression in o he equaion (3), and re-arranging indicaes ha he curren exchange rae is a funcion of he fuure expeced exchange rae. 1 e s F s (5) Where F * ( m m ) ( y y * ) Repeaed subsiuion for he expeced fuure spo rae will lead o an expression ha relaes he curren spo rae o he curren and fuure discouned expeced fundamenals. Clearly, such expressions are no very racable for empirical work; however, hey do yield insighs ino how changes in expecaions abou fuure variables can affec he curren exchange rae, even when he curren values of macroeconomic variables remain unchanged. The flexible price moneary approach (someimes ermed he monearis model) yields some very srong predicions. One of he mos implausible is ha increasing ineres differenial will be associaed wih weakening currencies. In he conex of a model wih purchasing power 4

7 pariy holding in boh he long run and shor run, his resul makes sense; posiive ineres differenials arise from posiive inflaion differenials (via he Fisher relaion). The more rapid a currency loses value agains a baske of real goods, he more rapid a currency loses value agains anoher currency, given ha PPP links prices of home and foreign real goods. The posiive relaionship beween he ineres differenial and he exchange rae runs couner o casual empiricism, a leas as far as he developed economies are concerned (economies experiencing high-inflaion such as Argenina and Brazil during he 1980's are anoher maer). Hence consider a sicky price version of he moneary model ha allows he PPP condiion o hold only in he long run. Then he flexible price moneary model equaion for he exchange rae perains o he long run, (3) is re-wrien: * * * s ( m m ) ( y y ) ( ) (6) where he overbars denoe long run values, and he secular inflaion raes sand in for long run ineres raes, given he Fisher relaion holds in he long run. Overshooing means ha exchange raes end o rever back owards he long run value a some rae θ. Tha is, if he exchange rae is oo high (he domesic currency oo weak), relaive o some long run value, hey will hen end o fall oward he long run value. Assuming raional expecaions, his suggess he following mechanism: e e e* s 1 s ( s s) ( ) (7) The θ parameer is he rae of reversion o he long run nominal exchange rae, and is an inverse funcion of he degree of price sickiness. Since higher rend inflaion implies a weaker expeced fuure spo exchange rae, he secular inflaion differenial eners ino his expression. However, by uncovered ineres pariy, he lef-hand side of equaion (7) is also equal he 5

8 ineres differenial.solving for s, and subsiuing in he expression for he long run s, one obains: * * * e e* s ( m m ) ( y y ) 1 ( i i ) 1 ( ) (8) This expression can be rewrien as: s m m * y y * r r * e e* ( ) ( ) 1 ( ) ( ) (9) where r i e Since he real ineres rae shows up in his expression, his model is someimes called he "real ineres differenial" model. 2 The curren exchange rae depends posiively on curren money socks, and inflaion raes, and negaively on income levels and ineres raes. This resul regarding ineres raes differs from he flex-price moneary model, because in he shor run inflaion rae differenials can differ from ineres rae differenials. The previous models have imposed PPP in he long run. However, here are persuasive reasons for allowing long run deviaions from PPP (as discussed in Chapers 6 and 7 of his Handbook, on purchasing power pariy), in which case some real facors ener ino nominal exchange rae deerminaion. One raionale ascribes such deviaions o he presence of nonradable goods. Assuming ha PPP holds only for radable goods, one obains he expression in (10), 2 Cerain papers focus on he role of he real ineres differenial in deermining he real exchange rae. See Edison and Pauls (1993), Meese and Rogoff (1998), Baxer (1994), and MacDonald and Nagayasu (2000). 6

9 s ( m m ) ( y y ) (1/ )( i i ) ( 1/ )( ) * * * e e* (10) N T N* T* where [( p p ) ( p p )], and for simpliciy, aggregae and radable secor inflaion raes are assumed o be approximaely he same (oherwise, one has o include separae inflaion erms). Equaion (10) indicaes ha in addiion o he usual moneary facors, real facors can also affec he nominal exchange rae; in his case, anyhing ha shifs he inercounry differenial in he relaive price of radables o nonradables. This expression is a sicky price version of ha used in Clemens and Frenkel (1980) and is similar o ha used by Wolff (1987). Wha deermines his relaive price? In principle, his variable can be affeced by supply facors (changes in endowmens, produciviy growh) or demand side facors (governmen spending, changing preferences). This seems o be an imporan facor for some currencies, bu is no usually incorporaed in he work on developed counry currencies. Furhermore, he exac mechanisms underlying movemens in ω are no usually oulined in such work. Since he deerminans of hese movemens are usually hough of as real facors, we will reserve exensive discussion of his approach o Secion Porfolio Balance Models The porfolio balance model differs from he moneary model in ha i assumes ha asses denominaed in differen currencies are no perfecly subsiuable; his means ha reurns on bonds, when expressed in a common currency, migh differ due o a risk premium. 3 This is 3 Risk premia can arise in models wihou his paricular srucure. In more microfounded approaches, he risk premia arises from he correlaion of relaive reurns wih consumpion growh. The implicaions of his ype of approach are discussed in Secion 4. 7

10 shown in a model drawn from Frankel (1984). Assume perfec capial mobiliy (CIP) holds, while perfec capial subsiuabiliy does no. Tha is, invesors view domesic and foreign bonds as imperfec subsiues. Then invesor j will allocae her holdings in response o expeced reurns (expressed in a common currency). Aggregaing over homogeneous invesors yields: B SB * * ( i i E s 1 ) (11) where B and B* are ne supplies of domesic and foreign bonds, and i is assumed for simpliciy ha governmens issue deb denominaed only in heir own currencies. The erm in he parenheses on he righ hand side of (11) is he deviaion from uncovered ineres pariy, or equivalenly, he exchange risk premium on domesic currency. This expression indicaes ha holdings of domesic bonds, relaive o foreign currency denominaed bonds, are a posiive funcion γ of he exchange risk premium. Assuming he funcional form for relaive bond demand is linear-exponenial in γ, hen afer rearrangemen, equaion (11) becomes: s * * 0 1( i i E s 1) b b (12) The difficuly in implemening equaion (12) is ha he erm in he parenheses is unobservable. 4 To obain an empirically implemenable specificaion, one could assume expeced depreciaion is zero -- an assumpion ha is consisen wih he near random walk exchange raes. Then (12) 4 As in he case of equaion (5), one could recursively subsiue ou for he expeced fuure exchange rae. This would lead o an expression saing ha he curren exchange rae is deermined as a negaive funcion of curren and discouned fuure expeced ineres raes, and a posiive funcion of curren and discouned fuure expeced socks of domesic currency bonds, relaive o foreign denominaed bonds. This expression, likes is moneary counerpar, is no racable from an empirical sandpoin. 8

11 becomes: s * * 0 1( i i ) b b (13) Noice he equaion indicaes ha as b* increases, s falls (appreciaes): As he sock of foreign asses held by home rises, he exchange rae appreciaes. In he specificaion represened by equaion (13), i is assumed ha all invesors have he same porfolio preferences, presumably because hey consume he same baske of goods. If on he oher hand he home counry is a small counry, such ha only home residens wish o hold domesically denominaed asses, hen one can equae capial inflows wih increases in he supply of foreign asses in he home marke. If he home counry is large relaive o he foreign, hen one migh wan o make he converse assumpion. Clearly, neiher of hese versions fi he ypical large counry. Then wha one needs o specify is a separae asse-demand funcion for each of he wo counries. As long as he responsiveness of home residens o he expeced reurn on domesic bonds exceeds he responsiveness of foreign residens, hen he exchange rae will appreciae in response o cumulaed rade balances ha re-allocae world wealh. 5 In line wih his approach, Hooper and Moron (1982) use a real exchange rae-arge curren accoun model o moivae inclusion of cumulaed curren accoun balances. 6 5 So far, we have discussed maers as if he only way in which B and B* can change is hrough curren accoun imbalances. In fac, foreign exchange inervenion can affec he sock of bonds, and hence he exchange rae. See Dooley and Isard (1982) for one sudy where he socks of bonds ake ino accoun foreign exchange inervenion. 6 Frankel (1982) uses a porfolio demand for money so ha wealh (measured as he sum of curren accoun balances and domesic bonds and money) eners ino he regression equaion. 9

12 2.3 Empirical Evidence The models described appear o consiue a quie disparae se of approaches; however, in erms of he empirics, he appearance is misleading. The above models can be subsumed ino he following general expression: = f ( mˆ, yˆ, iˆ, ˆ,, b, b, cb) (14) s * where he ime subscrips have been suppressed, cb denoes he cumulaed rade balance, and he circumflexes denoe inercounry differences. Differen models imply he inclusion of differen regressors wihin his se. Mos of he earlier sudies cied include an empirical componen. In mos insances, some supporive evidence is found, paricularly for he moneary model. Frankel (1979) provides evidence ha he sicky price moneary model fi he dollar/deuschemark rae well, using a quasi-reduced form expression. Papell (1984, 1988) esimaed he moneary model in a sysem, and find ha he degree of overshooing and undershooing is dependen upon he moneary policy being conduced. However, i is fair o say ha he empirical resuls of he 1980 s are no very robus o he addiion of new daa. The idenified relaionships ofen break down wih he addiion of new daa, suggesing model overfiing. Frankel (1983) provides an early overview of he empirical inadequacies of he moneary (flexible and sicky price), porfolio-balance and hybrid models. Paricularly in he laer wo cases, he key porfolio-balance variables -- domesic and foreign bond socks -- failed o show up wih he correc coefficien signs. Porfolio-balance models of exchange raes are merely ransformaions of porfoliobalance models of he exchange risk premium. The failure of hese ypes of models reflecs he 10

13 failure of aemps o explain he exchange risk premium using measures of governmen bonds, in he conex of an inernaional capial asse pricing model. 7 The fragile naure of hese empirical resuls moivaes a reliance on ou-of sample simulaions o guard agains in-sample over-fiing. Among he firs sudies o adop his approach was Meese and Rogoff (1983a,b). These auhors esed he ou of sample forecasing properies of hese various exchange rae models, plus he forward rae, a univariae ARIMA, and a Vecor AuoRegression (VAR). The procedure involves esimaing he models over a cerain period, forecas ou k periods using he acually realized values of he exogenous variables, hen "roll" he regression sample up a period, o accoun for parameer variaion. This procedure is repeaed unil all of he remaining daa poins are exhaused. They hen compare he forecass saisics, Mean Error (ME), Mean Absolue Error (MAE) and Roo Mean Absolue Error (RMSE). 8 Meese and Rogoff (1983a) obain he surprising resul is ha none of he srucural models (nor ime series models) consisenly ouperforms he random walk using any of he merics, and over any of he forecas horizons. This finding was robus o relaxing coefficien resricions (like he income elasiciy being he same across counries), or replacing one proxy for inflaionary expecaions wih anoher. The analysis of exchange rae forecass changes dramaically wih he developmen of he 7 See early sudies by Frankel and Engel (1984), and more recen surveys by Hodrick (1987) and Engel (1996). 8 Noice ha because in hese exercises, acually realized values of he exogenous variables are used, he usual argumen ha asse prices should no be predicable ex ane becomes moo. In hese forecas comparisons, knowledge abou conemporaneous informaion is available. Tha is, by using he ex pos values of he exogenous values in he forecass, one "purges" he forecass of uncerainy abou he fuure pahs of he exogenous variables. Hence, failure can be isolaed o 11

14 lieraure relaing o inegraed variables. The sudy of variables ha co-rend, namely he coinegraion lieraure, suggess ha one could respecify equaions in erms of error correcion models. A key issue here is wha he naure of he coinegraing vecor, i.e., he error correcion erm, would be. In mos cases, he coinegraion resuls are based upon moneary fundamenals, eiher imposed or esimaed. 9 One of he implicaions of long run relaionships holding, and possible shor run nonlineariies, is ha long horizon predicion migh be more successful han shor horizon. In he earlies implemenaion of his approach, Nelson Mark (1995) used a calibraed flexible price moneary model o perform ou-of-sample predicions of he dollar-deuschemark rae, and finds subsanial improvemen for he moneary model s performance vis-a-vis he random walk. Chinn and Meese (1995) examine a broader number of models including he flexible price, he Hooper-Moron, and augmened moneary, and imposing he coinegraing vecor in an error correcion framework, find ha a random walk can be ouperformed, in a saisically significan sense, a longer horizons of wo o hree years. This se of resuls is inuiive. The amoun of news ha moves exchange raes monh o monh ha is no capured in ypical macroeconomic variables such as money socks, ineres and inflaion raes, is very large. Mos likely, his ype of news dominaes a high frequencies, bu is less likely o play a large role a longer horizons. Moreover, he random walk model is a very naive model as i yields a no change forecas, so as he horizon lenghens, he random he misspecificaion of he equaions. 9 ECTs may be empirically moivaed, or based on heory. For he former, see for insance MacDonald and Taylor (1994). For he laer, see Edison (1991) replicaes he Meese-Rogoff (1983a) sudy, bu imposes a PPP error correcion erm. She finds some improvemen, especially over longer horizons. 12

15 walk forecas is more and more likely o be proved wrong. Noneheless, hese resuls did no prove o be conclusive. Firs, Faus e al. (2003) have shown ha hese long horizon resuls are specific o he paricular ime period examined, paricularly in he case of Mark s sudy. 10 Second, examining a slighly differen se of models, and aking ino accoun he possibiliy of no-coinegraion, Cheung, Chinn and Garcia Pascual (2005) find only very limied evidence of improved forecasing abiliy a long horizons, relaive o shorer horizons. Specifically, hey examine a more recen se of models developed over he las wo decade -- ineres rae pariy, 11 produciviy based models, and "behavioral equilibrium exchange rae" models. 12 The performance of hese models is compared agains a benchmark model -- he Dornbusch-Frankel sicky price moneary model in equaion (8). The models are esimaed in error correcion and firs-difference specificaions. Raher han esimaing he coinegraing vecor over he enire sample and reaing i as par of he ex ane informaion se as is commonly done in he lieraure, hey recursively updae he coinegraing vecor, hereby generaing rue ex ane forecass. Model performance a various forecas horizons (1 quarer, 4 quarers, 20 quarers) is examined, using differing merics (mean squared error, direcion of change), as well as he consisency es of Cheung and Chinn 10 In addiion, Kilian (1999) has argued ha he apparen ouperformance of he random walk a long horizons is largely spurious. He uses boosrapping o demonsrae ha he performance relaive o a random walk is approximaely he same a shor and long horizons. Kilian argues ha only if he underlying vecor error correcion model is nonlinear migh a long horizon regression ouperform a random walk. Kilian and Taylor (2003) argue ha even if a specific form of nonlineariy is used, he ouperformance may be difficul o deec. 11 The use of ineres rae pariy is analogous wih he forward rae examined by Meese and Rogoff (1983a,b). One should expec beer performance a he long horizon because Chinn and Meredih (2004) and Alexius (2001) find ha UIP holds beer a long horizons han shor. 12 The produciviy based model and BEER models can be considered varians of he produciviy based model described in Secion 3.2. See Secion

16 (1998). They find ha no model consisenly ouperforms a random walk, by a mean squared error measure; however, along a direcion-of-change dimension, cerain srucural models do ouperform a random walk wih saisical significance. Moreover, hey find ha hese forecass are coinegraed wih he acual values of exchange raes, alhough in a large number of cases, he elasiciy of he forecass wih respec o he acual values is differen from uniy. Overall, model/specificaion/currency combinaions ha work well in one period will no necessarily work well in anoher period A naural approach o improving he empirical performance of models is o use informaion across currencies. 13 One example of his approach includes Mark and Sul (2001). They use a panel of 17 exchange raes for indusrialized counries o implemen a panel version of Mark s (1995) paper. Specifically, hey firs es o see wheher he exchange rae and he moneary fundamenals are coinegraed in he panel, using a panel version of dynamic OLS. Afer rejecing he null hypohesis of no coinegraion, hey use he esimaed coinegraing vecor o conduc long horizon regressions as in Mark (1995). Moneary fundamenals oupredic a random walk a shor and long horizons, over he 1983q2-1997q1 period, when he US dollar is he numeraire currency. The resuls are slighly differen if he numeraire currency is he yen; hen he ouperformance is no usually saisically significan, alhough he predicions from he moneary model ypically have smaller roo mean squared errors han hose generaed from a random walk forecas (and smaller, as well, han hose from a PPP fundamenals model). 13 Anoher approach is o exend he sample over ime. Rapach and Wohar (2002) underake an analysis of 14 indusrialized counry exchange raes over a period of 115 years. They asser ha hey find subsanial evidence in favor of he moneary approach, despie he fac ha he 14

17 Two oher examples of using panel coinegraion mehods include Hused and MacDonald (1999) and Groen (2005). Hused and MacDonald (1997) use panel coinegraion echniques derived from Pedroni (1997). They conclude ha here is subsanial evidence in favor of moneary models of he exchange rae, based on coinegraion evidence. Groen (2005) uses a much smaller panel of hree currencies, and finds boh evidence of coinegraion of he exchange rae wih he moneary fundamenals, and model ouperformance of a random walk a boh shor and long horizons. Mos recenly, Cerra and Saxonhouse (2010) have used a large panel of currencies o find ha he moneary model works well a longer horizons. 14 These resuls sugges ha he empirical versions of he moneary model may enjoy renewed life, as researchers exploi cross-currency variaion in order o pin down he coefficien esimaes ha have proven elusive in he pure ime series conex Real Models of he Real Exchange Rae Mos real models of he exchange rae focus on real as opposed o nominal deerminans of he price level adjused exchange rae. Purchasing power pariy is a paricularly simple version, where he real exchange rae is assumed o be consan. The second porion of he secion describes wo oher approaches o modeling he real exchange rae; he firs of hese wo approaches is associaed wih he Balassa Samuelson framework, bu more generally allows for he presence of nonradable goods. The second of hese approaches encompasses he general samples span radically differen exchange rae regimes. 14 See Chaper 9 on panel mehods. 15 For he sake of breviy, I omi he discussion of funcional nonlineariies (Diebold and Nason, 1990; Meese and Rose, 1991; Chinn, 1991), hreshold auoregression (Taylor and Peel, 2000; Taylor, Peel and Sarno, 2001), regime swiching (Engel and Hamilon, 1990; Engel, 1994). 15

18 equilibrium models of he exchange rae arose in response o he ad hoc naure of he exan models of he 1970's. In his sense, hey represen he open economy analogue o he rejecion of ad hoc macroeconomic models dominan in he domesic conex. 3.1 Purchasing Power Pariy Purchasing power pariy (PPP) is one of he mos imporan conceps in inernaional finance. Several excellen surveys exis on he subjec, including Breuer (1994), Rogoff (1996), and Taylor and Taylor (2004). While a horoughgoing discussion of purchasing power pariy is beyond he scope of his chaper, some discussion of PPP is necessary o se he sage for a discussion of real exchange rae deerminaion. 16 The simples saemen of PPP is ha he common currency price of an idenical bundle of goods is equalized: s + p Where p corresponds o he price of a bundle of goods. * = p (15) Noice ha here is, in his conex, a direc relaionship beween he deviaion from PPP, and he real exchange rae. Suppressing he consan and rearranging (15), one obains: q * s - p + p (16) where q is measured in domesic unis of he domesic baske of goods required o purchase a single baske of foreign goods. If absolue PPP holds, hen he (log) real exchange rae should be a zero (and a consan if relaive PPP holds). In pracice, he disincion is of limied relevance, 16 As I alluded o earlier, here are a myriad of definiions for PPP. I define PPP as peraining o relaionships beween relaively broad price indices such as he consumer price index (CPI), he producer price index (PPI), or GDP deflaor, on he one hand, and he exchange rae on he oher. In oher words, I will no consider PPP o be a relaionship beween he exchange rae versus price levels and oher variables. Some auhors have ermed such relaionships generalized 16

19 since we ypically have access o only price indexes, raher han prices of bundles of goods. One can decompose he general price index along several dimensions. One is he radable/nonradable disincion; furhermore, he radable caegory can be furher divided ino imporables and exporables. Consider he firs dimension; hen, wriing he general price index as: p = p ( 1 ) p N T (17) where a N superscrip denoes nonradables and T radables, one obains he resuling expression for he real exchange rae (assuming he weighs are idenical): T q = q + ( pˆ where q T N - pˆ ) T s - p + p T T* (18) The real exchange rae hus deviaes from zero if eiher radables prices differ, or he relaive price of nonradables versus radables differs across counries. This decomposiion underpins Engel s (1999) analysis of he sources of US real exchange rae movemens. The relaive price variable may be deermined by any number of facors. In he Balassa (1964) and Samuelson (1964) model, relaive prices are driven by relaive differenials in produciviy in he radable and nonradable secors. 17 Wih respec o he Eas Asian counries, here is a widespread belief ha such facors are of cenral imporance (Cheung and Lai, 1998; Chinn, 2000d). purchasing power pariy. 17 This view is adoped in DeGregorio and Wolf (1994), Canzoneri, Cumby and Diba (1996), Chinn (1997a,b) among ohers. The firs wo sudies examine annual oal facor produciviy daa for 14 OECD counries in a panel conex, while Chinn (1997a) underakes a higher frequency analysis. He uses quarerly ime series regressions where labor produciviy in manufacuring is used as a proxy for relaive secoral produciviy, for he US, Canada, Germany, Japan and he UK. 17

20 Relaive prices may also be affeced by demand side facors. In he long run, he rising preference for services, which are largely nonradable, may induce a rend rise in he relaive price of nonradables. Over shorer horizons, governmen spending on public services may also induce changes in relaive prices (DeGregorio and Wolf (1994) and Chinn (1999)). 18 Early work on PPP relied upon Classical regression echniques, and addressed he quesion of wheher PPP held on a period by period basis. The early lieraure concluded ha absolue PPP did no hold for broad price indices, on a period by period basis. One imporan excepion was ha idenified by Frenkel (1976) who found ha during he German hyperinflaion of he 1920s, PPP did hold. Hence, he conclusion ha PPP held only when nominal (moneary) shocks were large relaive o real shocks. The adven of he uni roo and coinegraion brough a resurgence in he PPP lieraure. A he same ime, i produced a large amoun of confusion beween he economically ineresing hypohesis of PPP in levels, and he saisical hypoheses. To see his, recall from equaion (16) ha PPP implies ha he real exchange rae is equal o a consan. Findings of coinegraion, bu wihou uniary coefficiens, was someimes inerpreed as weak PPP, when i was consisen wih a rending real exchange rae. Even when coinegraion wih uniary coefficiens was found, allowance for a deerminisic rend mean ha he real rae was no consan over ime. The issue of purchasing power pariy a he shor and long horizon is examined a furher lengh in Chaper 7 in his Handbook. 3.2 Balassa-Samuelson and Produciviy Based Models The basic moivaion for mos empirical exercises addressing he exchange rae produciviy 18 See also Chen and Rogoff (2003) for a commodiies price channel. 18

21 nexus rely upon he radable-nonradable disincion highlighed by Balassa (1964) and Samuelson (1964). Recall ha in he presence of nonradables, one can wrie he real exchange rae as: q = q T where q ( pˆ T N - pˆ ) T s - p + p T T* (18) Assuming perfec capial mobiliy, free inersecoral facor mobiliy, he inernal relaive price of raded and nonraded goods is given by N T T N p p a a (19) where for exposiory simpliciy he producion funcions are assumed o be idenical; a T and a N are he oal facor produciviy levels in he raded and nonraded secors, respecively. In words, (19) implies ha he relaive price of raded goods moves one-for-one wih he produciviy differenial. As radable secor produciviy rises relaive o nonradable, he price of radable goods relaive o nonradable falls. Combining (19) wih (18) yields a sandard expression for he real exchange rae: T q = q + ( aˆ where q T N - aˆ ) T s - p + p T T* (20) In his framework, he real exchange rae is a funcion of he inercounry relaive produciviy differenial. And if PPP holds for radable goods, hen q T is 0, and he real exchange rae depends solely upon he produciviy differenial. A number of papers have examined he relaionship expressed in equaion (20) for developed economies, including Hsieh (1982), Marson (1990), DeGregorio and Wolf (1994), 19

22 Srauss (1996), Chinn (1997a,b), and Chinn (1999). The firs hree papers, like many ohers, esimae he real exchange rae and produciviy differenial relaionship in growh raes. Usually, a link is deeced. However, he specificaion allows for permanen shocks o he relaionship in levels, which migh no be desirable. The relaionship in levels has been more elusive. While Chinn (1997a,b) finds evidence for individual currencies, and Srauss (1996) finds evidence of coinegraion using he convenional asympoic criical values in eigh ou of foureen cases, he also finds he parameer resricions implied by he model are generally rejeced. More evidence of a long run relaionship beween he level of he real exchange rae and he produciviy differenial is found in a panel conex. Canzoneri, Cumby and Diba (1999, hereafer CCD) es he proposiion in equaion (20) using labor produciviy differenials, and find ha i holds fairly well in a panel coinegraion conex for he OECD counries. They also es he hypohesis ha purchasing power pariy holds for raded goods (i.e., ha he second line of (20) equals zero), and while hey do find evidence of coinegraion, he esimaed coefficiens are no of he expeced sign. Hence, CCD do no direcly confirm he proposiion embodied in he op line of equaion (20). 19 I is of ineres o noe ha he expressions in equaion (18) and he op line of (19) wih q T =0 require fairly srong assumpions. In paricular, if he form of he producion funcions differs in he wo secors, hen he coefficiens on radable and nonradable produciviy need no be of equal and opposie sign. Moreover, in some dynamic models incorporaing a fixed facor assumpion (Rogoff, 1992), he coefficien on nonraded produciviy differs from ha of raded, 19 Srauss (1999) found slighly more evidence in favor of a role for produciviy and governmen 20

23 because consumpion smoohing can only ake place hrough raded goods producion. Finally, if exac PPP does no hold for raded goods, i may be he case ha raded secor produciviy affecs he real exchange rae hrough he relaive price of raded goods. Engel (1999) has argued ha his is an imporan facor for developed counry exchange rae behavior. If his urns ou o be he case, hen he symmery resricions on radable and nonradable produciviy in (20) may be invalidaed. Chinn and Johnson (1999) find some evidence ha produciviy does no ener in he expeced manner, paricularly when oal facor produciviy (which is implied by he heory), is subsiued for labor produciviy. The analysis is conduced on annual daa over period, using panel dynamic OLS (DOLS). 20 They find ha relaive produciviy does no have a significan impac on he real exchange rae, bu radable secor produciviy does, wih a coefficien of If one believed ha he coefficien relaing relaive prices o relaive produciviies should insead be one, hen he implied value is -0.5; he acual poin esimae is insignificanly differen from his value. Lee and Tang (2007) provide one of he mos recen es of he Balassa-Samuelson hypohesis. Using daa for en OECD counries over he period, hey show (using panel regression echniques) ha he findings regarding he link beween produciviy and he real exchange rae -- or he relaive price of radables (boom line of equaion 19) is highly sensiive o he produciviy measure ha is used. Increases in oal facor produciviy, which is spending for exchange raes. 20 Bilaeral exchange raes are are deflaed by general price while he radable and nonradable secor oal facor produciviy (TFP) daa were consruced from he ISDB daabase which conains TFP disaggregaed by secor. The radable and nonradable caegorizaion is he same as ha used by DeGregorio and Wolf (1994). Tradable secors include agriculure, mining, 21

24 suggesed by heory, ends o depreciae he q T, so ha he ne effec on he real exchange rae is mued. Ricci, Milessi-Ferrei and Lee (forhcoming) exends his analysis o a sample encompassing 48 indusrial and emerging marke economies. They find ha while produciviy measures have a saisically significan impac on real exchange raes, in he posied direcion, he size of he effec is fairly small. Oher effecs, including hose associaed wih governmen consumpion and ne foreign asse accumulaion, are also saisically significan. To sum up, he evidence in favor of he sandard Balassa-Samuelson hypohesis is weak, when focusing on he developed economies, and using oal facor, raher han labor, produciviy. The mos recen research suggess ha his is he case because PPP rarely holds for raded goods, perhaps because hese goods are highly differeniaed (see Cheung, Chinn and Fujii, 2001). In fac, produciviy growh in he radable secor migh have a bigger impac on he inercounry price of raded goods han on he relaive price of raded o nonraded goods. If his is he case a leas for developed economies hen he difficuly in idenifying he produciviy/real exchange rae link migh be more explicable. 3.3 Two-Good Models Now depar from he case where here are nonradable goods, and suppose all goods are radable, bu hese raded goods are no perfec subsiues. One can hen define he real exchange rae as he raio of he wo raded goods prices. The nominal exchange rae is hen he real exchange rae, adjused for he socks of monies. This can be seen mos clearly in he Lucas (1982) model. manufacuring, and ransporaion, while he nonradable secors include all oher services. 22

25 Assume here are infiniely lived agens in wo counries are subjec o a sochasic endowmen and moneary shocks. The model uses a Clower, or cash-in-advance, consrain o moivae he holding of money. Each agen maximizes discouned uiliy. In a complee markes framework, wih perfec pooling of risk, each rader consumes his/her share of boh endowmens. Hence he equilibrium spo price of Y* in erms of Y (call his P Y*, he real exchange rae ) is given by he raio of he marginal uiliies of consumpion of he wo goods. The nominal exchange rae is given by he raio of nominal monies, he amouns of endowmens of each good, and he relaive price of Y*. This resul is ineresing, since his implies ha as endowmens change and he raio of marginal uiliies change, hen he real and hence nominal exchange raes also change. Under he ypical convenion ha an increase in endowmen of he home good only decreases he relaive price slighly, hen he exchange rae appreciaes. 21 Oherwise, he currency will depreciae. In erms of observables, he Lucas model is observaionally equivalen o he flexible price moneary model. Consider he specificaion ha allows for endowmens o be proxied by oupu. Then he resuling esimaing equaion is: * * s =( m -m ) - ( y -y )+ p * (21) y where a complicaing facor is ha p y* depends upon he endowmens Y and Y*. This equaion is herefore funcionally similar o he flexible price moneary model, wih he excepion of he absence of ineres rae erms arises from he binding cash-in-advance consrain. One difference 21 Lucas (1982) noes he condiions under which he home currency appreciaes. Suppose U is homoheic, such ha he marginal rae of subsiuion is a posiive, negaively sloped funcion of he endowmen raio, r = η/ξ, call i g(r). Then if he derivaive of rg(r) wih respec o r is greaer han zero, hen he currency will appreciae. Else, i will depreciae as he erms of rade urn agains he home counry s goods. 23

26 is ha in he moneary approach, he response of he exchange rae o a rise in income is unambiguously negaive ha is an increase in home income raises money demand and hence he value of he home currency. Here, noice ha as y rises, p y* also rises as before, since more of he home good, holding consan foreign, should induce a price change. The more inelasic demand for he home good (he poorer a subsiue he home good is for he foreign) he bigger he price drop. Sockman erms his he "relaive price effec". On he oher hand, as y in equaion (25) rises he "money demand effec" on he exchange rae is negaive. Hence here are wo counervailing effecs. Wha is he ne effec? Given he binding Clower consrain, one knows ha he income elasiciy of money demand is uniy; however, ln(p y* )/ ln(y) is unknown. If his objec is greaer han uniy because of low subsiuabiliy beween y and y*, hen he overall effec of higher GDP is a weaker currency. When ln(p y* )/ ln(y) < 1 (y and y* are good subsiues) he sandard effec of higher income leading o a sronger currency, familiar from he flex-price moneary model, holds. However, only when ln(p y *)/ ln(y) = 0 (perfec subsiuabiliy) will he exac quaniaive resul from he flex-price moneary model hold. 22 Ape, Sercu and Uppal (2004) have provided a recen general equilibrium endowmen model of he exchange rae ha ness he Lucas model, PPP and he Balassa-Samuelson formulaion. Using he no-arbirage condiion, homoheic uiliy funcions characerized by 22 The key disincion in his model vis a vis a sicky-price moneary model is ha he key driving variable in deermining real exchange raes is he py variable. To see his, consider he Dornbusch model. In ha framework, a nominal exchange rae movemen ges ranslaed ino a deviaion from PPP because prices are sicky. In he Sockman model, prices are perfecly flexible, so ha movemens in real exchange raes ge ranslaed ino movemens ino he nominal exchange rae. Movemens in he nominal magniudes (such as M) have an impac on he nominal exchange rae, bu no he real. Hence, his model possesses he Classical dichoomy 24

27 consan relaive risk aversion, hey find ha he nominal exchange rae can be expressed as a funcion of price levels and nominal consumpion (really expendiure), where he elasiciies of nominal consumpion and he price level sum o uniy. * * * s = p - p - y + y (22) Insead of esimaing his equaion, hey rearrange (26) o yield he real exchange rae on he righ side. They proxy y using real consumpion daa, and find ha here is a long run coinegraing relaionship beween he real exchange rae and consumpion levels. The auhors ake his as evidence in favor of he sandard power uiliy model. Equaion (22) highlighs he fac ha micro-founded models ofen yields specificaions ha are difficul o differeniae empirically from ad hoc models New Direcions in Exchange Rae Modeling 4.1 Taking Reacion Funcions Seriously One srand of developmen in macroeconomic based models has involved he incorporaion of cenral bank reacion funcions ino exchange raes models. Recen research repors ha ou-ofsample exchange rae forecasing can be improved by incorporaing moneary policy reacion funcions (Taylor rules) ino sandard models. Essenially, oupu gaps and inflaion gaps are hen brough ino he deerminaion of exchange raes. Engel and Wes (2005) were he firs o incorporae Taylor rule fundamenals in a formal derivaion of a model of exchange raes. In analyzing he dollar exchange rae, hey posied a beween nominal and real variables. 23 Discussion of generalized PPP models and behavioral equilibrium exchange rae (BEER) models are discussed in Chaper 11 on fair value models. 25

28 sandard Taylor rule for he US, and an ineres rae argeing rule for he foreign counry ha incorporaed an exchange rae gap, where he foreign counry arges a PPP value of he nominal exchange rae. Combined wih ineres rae pariy (allowing for an exchange risk premium), hey solve ou for he presen value expression for he exchange rae. One of he implicaions of his presen value relaionship is, wih a discoun facor close o uniy, he exchange rae should be essenially unpredicable. In his conex, here is no exchange rae disconnec, i.e., here is no puzzle why he exchange rae does no seem o be predicable on he basis of currenly observed fundamenals. Anoher implicaion of he model wih highly persisen fundamenals is ha he exchange rae should Granger cause he fundamenals. Of course, in heir approach, only ineres raes and price levels are observable (since arge oupu and inflaion are no). For he G-7 bilaeral exchange raes, he null hypohesis of no Granger causaliy is rejeced in mos cases. By conras, he null hypohesis ha he fundamenals do no cause Granger cause he exchange rae is almos never rejeced. Engel and Wes also evaluae he model by assessing he correlaion beween he change in he exchange raes and he change in consruced fundamenals. They consruc he fundamenals using eiher univariae regressions or bivariae VARs (wih imposed discoun facors), and find ha he correlaions are posiive, hereby supporive of he model. Engel and Wes (2006) examine he dollar-deuschemark rae more closely, and bring ino he analysis esimaes of he oupu and inflaion gaps. Depending on he imposed parameers and derending echnique, he correlaion beween he acual and fied real exchange rae changes is as high as

29 Following he insighs of Engel and Wes (2005, 2006), Chinn (2008) akes a more direc roue, regressing exchange rae changes on oupu and inflaion gaps. He finds subsanial insample predicive power for Taylor rule fundamenals. The analysis proceeds in he following manner. assume ha policymakers follow Taylor rules, allowing for smoohing of ineres raes: i ~ y ~ q~ r 0, 0, 0, 0 y y q q i 1 (23) Where q ~ is he deviaion of he real exchange rae from a arge exchange rae, and he ilde s denoe gaps. The moneary auhoriies move he policy rae in response o he deviaions of oupu from poenial GDP, deviaions of inflaion from arge inflaion, afer accouning for a naural level of ineres raes (i.e., he sum of he naural real ineres rae and he inflaion rae), as well as a deviaion of he real exchange rae from he arge rae. A lagged ineres rae is included in order o accoun for he endency of cenral banks o smooh ineres raes. The inclusion of he real exchange rae is no unconroversial; i presupposes ha he moneary auhoriy aemps o sabilize he exchange rae. However, i is no an uncommon approach, and has been employed by Clarida, Gali and Gerler (1998), as well as Chinn and Dooley (1998). In order o inroduce he exchange rae, I drop he uncovered ineres pariy assumpion, and rely upon an ad hoc characerizaion of he exchange rae/ineres differenial relaionship. s k s 0 ( i i * ) (24) In words, a larger ineres differenial is associaed wih an appreciaion of he currency over a four quarer horizon. 27

30 Combining (23) and (24), and assuming he foreign counry is characerized by a similar Taylor rule, one obains he following expression: s s y ˆ~ ( 1) ˆ qˆ~ iˆ c (25) k y y q 1 Where he circumflexes indicae inercounry differenials. 24 This specificaion accords well wih praciioner inuiion for how ineres raes (and hence exchange raes) move in response o inflaion and oupu gaps. Consider wha happens if he inflaion gap rises in he US relaive o he foreign economy. Then he Fed will raise he policy rae, hereby appreciaing he currency. Wha abou inflaion? This framework implies ha when inflaion rises above he arge level, hen he currency will appreciae. Hence, he answer o Clarida and Waldmann s (2007) quesion Is bad news abou inflaion good news for he dollar? is yes. Finally, if he real exchange rae rises (currency depreciaes), hen he cenral bank will lean agains he wind and raise ineres raes, hereby inducing a srenghening of he currency over he nex four quarers. Chinn (2008) finds ha he resuling specificaion fis well, in sample. In paricular, he oupu and inflaion gaps ener in wih expeced sign, and ypically wih saisical significance, for he dollar/euro ( ). For a longer period using synheic dollar/euro exchange raes and variables, he evidence is a lile less supporive, paricularly wih respec o he oupu gap. 25 The coefficien on he exchange rae gap is no ofen saisically significan. This migh 24 Noe ha I am imposing he same coefficiens for inflaion and oupu gaps for boh economies. Hence, his specificaion is a homogenous, asymmeric specificaion wih smoohing, in Molodsova and Papell s (2008) lexicon. 25 There is a subsanial complicaion in erms of implemenaion, since he oupu gap is direcly observable. I can be measured by eiher use of derending mehods (HP or band-pass filers) or 28

31 be because he imporance of his variable depends upon he wo respecive cenral bank reacion funcions ascribing differen weighs on he exchange rae. If hey ascribe he same weigh, hen he exchange rae gap erm drops ou. Molodsova, Nikolsko-Rzhevskyy and Papell (2008, 2011) and Molodsova and Papell (2009) invesigae he ou of sample forecasing properies of Taylor-rule based fundamenals. They find ha incorporaing Taylor rule variables helps wih ou-of-sample forecasing a shor horizons, improving upon convenional ineres rae, purchasing power pariy, or moneary models. For he exchange raes for he legacy currencies of he euro, as well as oher key bilaeral raes (pound, yen, Swiss franc, Ausralian and New Zealand dollars), Molodsova and Papell (2009) find ha a specificaion ha allows he coefficiens on he gap erms o vary across counries, and he exchange rae gap o ener, ypically does well in ou of sample forecasing exercises, a he one quarer horizon. This ouperformance is saisically significan, using ess Molodsova, e al. (2011) examines he dollar/euro exchange rae. In his case, hey find ha he specificaion imposing common coefficiens, and omiing he exchange rae, and omiing ineres rae smoohing does bes in ou of sample forecasing. This is rue a he onemonh horizon, as well as longer horizons up o one year. 26 Molodsova and Papell (2010) show ha hese resuls largely survive he arrival of zero ineres rae policy o he US and he euro area. 27 Benigno (2004), Corsei, Dedola, Leduc (2010) and Engel, Wes and Zhu (2010) show ha moneary policy rules ha can, among oher hings, generae some of he observed producion funcion based approaches. See Chinn (2008) for discussion. 26 Less promising resuls are obained by Binici and Cheung (2011). 27 One concern is ha equaion (24) is ad hoc in naure, and represens an empirical relaionship. 29