Real Exchange Rate, Competitiveness and Policy Implications: a formal analysis of alternative macro models. Massimiliano La Marca *

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1 Real Exchange Rae, Compeiiveness and Policy Implicaions: a formal analysis of alernaive macro models Massimiliano La Marca * (5/24/04) he paper provides a broad overview on he definiion, deerminaion and adjusmen mechanism of he real exchange rae and he macro inernal and exernal equilibrium condiions, in a wide range of macromodels. By adoping he mehod of he alernaive closures we sar from basic relaions, add complemenary hypoheses (real wage resisance, capial mobiliy, exernal balance, or full employmen) and show how he differen frameworks (Keynesian, Kaleckian, eoclassical) depar and reach alernaive policy implicaions. he muual consisency and impac of hose differen assumpions are highlighed; in paricular we show he role of price compeiiveness and erms of rade in he inernaional adjusmen mechanism, he hidden linkages and real conribuion of dynamic models relaive o saic ones and of general equilibrium relaive o Keynesian models and he nexus beween he shor-run income effec of ne expors and long-run general-equilibrium balanced rade and price equalizaion ha allow for consisency beween sandard macro and rade policies. he evoluion of he concep of equilibrium real exchange rae is also explored, while IMF medium- and long-run applicaions are also criically framed in he exising lieraure. * ew School Universiy, ew York and Research Fellow a he Universiy of Pisa, Ialy. he paper is he resul of he research underaken as an inern a he Division and Globalizaion and Developmen Sraegies. I am indebed o Dr. Heiner Flassbeck and o all he Macroeconomic and Developmen Policies Branch professionals who kindly ook par o my presenaion las summer and graeful o Prof. Lance aylor for useful commens and advising a he ew School Universiy, ew York. he usual disclaimer applies.

2 I. Inroducion 1 II. Exchange Rae Definiions and PPP 4 II.1 Alernaive Definiions of RER II.2 he PPP as an Equilibrium Real Exchange Rae heory III.2 "Consensus" Esimaes of PPP and LOP Dynamics III.3 Long-Run Deviaions from PPP III. Aggregae-Demand Models of Equilibrium Real Exchange Rae 11 III.1 Sandard Keynesian model in he shor and long run III.2 A srucuralis model III.3 Inernal and Exernal Balance in Parial equilibrium IV. General Equilibrium Saic Macro Models 22 IV.1 A raded/nonraded-good model IV.2 Models wih hree goods V. Dynamic Models of Equilibrium Exchange Rae and Curren Accoun 29 V.1 he ineremporal approach o he curren accoun V.2 Muli-commodiy Ineremporal Opimizing Models VI. Evoluion of Sandard Views and Empirical Models 35 VI.1 IMF Empirical Models: FEER, DEER, CGER, BEER, and PEER VI.2 win defici, saving-invesmen gaps and dynamics of he economic hough VII. Conclusions: equilibrium, real exchange rae, rade, and policy implicaions 39 VII.1 he definiion and role of he exchange rae, expendiure and rade VII.2 Inernal and exernal balance condiions and he ineremporal exension VII.3 he macro- micro gap and he adjusmen problem Appendix I. Revenue Funcion, Expendiure, Price Indices and Consumpion Bundles 46 Appendix II. eoclassical general equilibrium saic models: unified reamen 47 A.2.1 wo secors closed economy models A.2.2 he Heckscher-Ohlin model A.2.3 raded/onraded good model wihou inernaional facor mobiliy A.2.4 raded/onraded good model wih inernaional capial mobiliy A.2.5 raded/nonraded good and wih secorally fixed capial. Appendix III: he ineremporal approach 53 References 55 i

3 I. Inroducion he relaion beween exchange rae, inernal and exernal equilibrium, compeiiveness and rade is one of he mos conroversial subjecs boh in heory and in policy. here is no universal agreemen on he definiion of he exernal balance and on he way compeiiveness beween similar goods can shape he rade paern, nor a unique concep of exchange rae or a shared view on is role in he adjusmen process. Moreover, he analysis of rade flows and exchange raes has radiionally belonged o wo separae domains which have long coexised in sandard economics: sandard rade heory, which analyzes he allocaion of scarce resources among secors of producion and he inernaional exchange of goods and services, and he macroeconomic sabilizaion heory, which concerns he flucuaion of aggregae variables, he resuling underuilizaion of resources and provides guidance for policies pursuing he aainmen of an overall desirable equilibrium. 1 Macro heories of exchange rae deerminaion define he naure of he overall equilibrium and he fundamenal driving forces of he equilibrium real exchange rae, ERER, in a variey of ways. Wih he excepion of he purchasing power pariy heory, PPP (or he Balassa-Samuelson-augmened PPP), which relies on an arbirage argumen in he good markes, heories are based on macrorelaions and linkages beween aggregaes and require he exchange rae o clear some macro balances and o be consisen wih he equilibrium in some oher markes. 2 Edwards, for insance, defines he ERER as he relaive price of radable o nonradables ha, for a given susainable (equilibrium) values of oher relevan variables such as axes, inernaional prices, and echnology resuls in he simulaneous aainmen of inernal and exernal equilibrium (Edwards, 1989, p. 16). Hence, he ERER would reac o real disurbances and policy induced shocks such as erms of rade, ax, and echnological changes while he acual RER would respond o boh real and moneary variables. If a deparure of he RER from is equilibrium does no merely sem from shor-erm adjusmen coss and fricions, hen he exchange rae is misaligned, ha is, here is a susained deparure of he acual real exchange rae from is equilibrium value. Williamson (1983), on he oher hand, calls Fundamenal Equilibrium Exchange Rae (FEER) he 1 he borderline beween he wo domains is less and less clear-cu, wih microeconomic general equilibrium models of resource allocaion aking over he macro field. However, he logical inegraion of he wo broad frameworks is generally problemaic. rade balance is ofen deermined ogeher wih he exchange rae, bu is naure changes wih he role of rade iself. 2 According o mos heories, he ERER would be based on real fundamenals, ha is, real macro deerminans of he acual real exchange rae: equilibrium levels of he real exchange rae are achieved consisenly wih he equilibrium level of oher fundamenal aggregaes. However, if some form of nominal sickiness is assumed in he shor run, he acual RER is influenced by nominal shocks and oher "no fundamenal" variables. 2

4 real exchange rae ha is expeced o generae a curren accoun surplus or defici equal o he underlying capial flow over he cycle, given ha he counry is pursuing inernal balance as bes as i can and i is no resricing rade for balance of paymens reasons. Models can be classified according o heir level of disaggregaion (one good, wih raded and nonraded, wih exporables, imporables and nonraded goods) and ime horizon (saic and dynamic models). he mos criical difference is however he assumpions on he degree of coordinaion and he capaciy of he economy o achieve, hrough a complee price and quaniy adjusmen, an efficien and desired equilibrium in he producion and exchange relaions, i.e., a general/walrasian equilibrium. he efficien allocaion in consumpion and producion in he classical general equilibrium rade heory requires boh full employmen of resources and absence of unexploied arbirage opporuniies so ha homogeneous goods should sell a he same price, while he marke clearing condiion a he inernaional level requires relaive prices o balance rade. Counries can engage in rade for hree reasons: (i) o exploi heir difference in endowmens and/or in echnology and expor he caegory of goods which hey produce beer and exploi heir comparaive advanages in he inerindusry rade; (ii) o exploi he inernal economies of scale on imperfecly compeiive markes wihin a caegory of good, specializing on he producion of a se of varieies of he same good and allowing for inraidusry rade; (iii) o allow income and expendiure differences and allocae consumpion and invesmen ineremporally. Wihin his framework, he idea ha a counry could compee wih ohers hrough price variaions, as businesses do, is misleading (Krugman, 1996): rade is a non-sum-zero game and is beneficial for boh parners. I is undeniable ha conrary o any firm, a counry can avoid bankrupcy even if i fails o increase is produciviy and undercu coss and prices of some goods a he same speed of is acual and poenial compeiors. On he conrary, i can be able o sell he goods which i is relaively beer a producing as he celebraed law of comparaive advanages predics. his opimal oucome, however, requires a full nominal commodiy- and facor-price adjusmen so ha he comparaive advanages can manifes in he form of lower acual relaive price in he relaively more producive secors. In oher words, he comparaive advanages would lead counries ha differ in heir facor endowmens or echnology o he mos muually beneficial rade exchange paern, bu se in only once all he necessary nominal adjusmens are carried ou. his means ha real exchange variaions due o nominal exchange rae flucuaions or price inflaion differenials can plainly have 3

5 real effecs on he rade paern in he shor run. 3 As long as he real exchange rae has no seled o is comparaive advanage level, rade paerns can diverge from wha he classical rade heories would predic and absolue price compeiiveness plays a role. Hence, even acceping he classical rade equilibria as a long-run posiion, price compeiiveness is conceivable as a disequilibrium phenomenon bu, since he heory explains he rade paerns on saes of equilibrium, no clear insighs can be provided by he comparaive advanage models. Similar consideraions apply o imperfec compeiion models ha explain inraindusry rade where specializaion on he producion side on a se of varieies allows he saisfacion of a world demand for a larger number of varieies. racabiliy of hese models ofen requires symmeric equilibria where he similar goods and prices are indeed idenical and rade is balanced. Ironically, models of imperfec compeiive inraindusry rade, embedded ino sandard comparaive advanage-based inerindusry rade models, need o assume uniform prices in equilibrium so ha he rade paern is no affeced by heir relaive price changes. he ineremporal approach o he curren accoun exends he general equilibrium o he ime dimension. General equilibrium requires ha he income generaed wih he use of scarce resources has o be profiably used eiher as curren expendiure or len for fuure expendiure o foreign borrowers. his implies ha, while he curren accoun has o be balanced in saic rade models, curren accoun imbalances (income-expendiure differences) are allowed in ineremporal models and are he inenional device for allocaing and smoohing consumpion over ime. Imbalanced rade is he means of allowing income and spending desired misalignmens. Open economy macroeconomics, on he oher hand, has been long dominaed by he Mundell- Fleming-ype of models in which moneary componens (such as money base and ineres rae changes) and direc expendiure policies (such as fiscal defici) affec resource uilizaion boh by changing he level of expendiure and by swiching he composiion of i hrough exchange rae changes and subsiuion beween domesic and foreign goods. Why do compeiiveness and moneary variables disappear in he rade heory and how can hese wo bodies of heories be consisen? he radiional raionale is he long run neuraliy of money: when nominal sickiness disappears in he longer run, nominal variables adjus consisenly wih he underlying real (perhaps, general-equilibrium rade) model. his implies ha exchanges in raded goods and prices have o be balanced and resources full employed economy-wide in he long run. Moreover, since rade analysis provides he real equilibrium allocaion, which is efficien in he absence of inervenions, a possibly acive macro managemen has o be separaed from a necessarily laissez-faire rade policy. 3 A counry can herefore be reasonably concerned of he coss of swiching from a rade paern o anoher and if he ransiion implying reallocaion of labor and capial (and he implemenaion of a supposedly known echnology) can acually lead o higher per capia income. 4

6 he exising views on he role of he exchange rae in he adjusmen process and he exisence of an expendiure swiching effec canno however be classified as shor- and long-run approaches, respecively. A real medium-run and full-employmen Mundell-Fleming model is he benchmark of mos IMF empirical models of ERER esimaion; a he same ime widespread ineremporal models assume fricionless marke clearance a any single poin of he ime horizon ha allows a sequence of insananeous general equilibria. 4 he relaion beween RER, compeiiveness, and rade changes dramaically in he alernaive approaches. In he following we concenrae on some popular macro frameworks and show heir differences in linking compeiiveness, ERER and macrobalances. he ouline of he paper is as follows. Secion II inroduces some alernaive real exchange rae definiions obained by decomposing he index price raio ino a compeiive and a noncompeiive componen and reviews he curren sae on he everlasing search for a long run endency of he RER o rever o a consan value, he purchasing power pariy and he law of one price, he wo fundamenal empirical proposiions ha rule ou unexploied arbirage opporuniies and compeiive differenials in he good marke. Wha is he relevance of he whole idea of equilibrium real exchange raes, is relaion wih he compeiiveness in he differen seings and heir policy implicaions? Secions III o V presen a brief review of saic and ineremporal models of equilibrium real exchange rae. We find ou how he mos differing implicaions depend on he assumpion on price equalizaion in boh he shor and medium run and no on he ime horizon of he model. he aim is no o provide a complee hisorical overview, bu o deconsruc and pu ogeher he models in a consisen and comparable framework allowing for differen closures and emphasizing he shorcomings and he insighs provided by he differen classes of models. 5 In secion VI, we discuss some empirical applicaions implemened in he inernaional finance insiuions such as he IMF and hen move from he analyics o he hisory, offering a view on he logical evoluion from radiional Keynesian sabilizaion models o he microfounded general equilibrium models which allow consisency wih rade heory even in he shor run. Secion VII draws some conclusions on he sae-of-he-ar heoreical frameworks and he policy recommendaions ha can be drawn from hem. 4 More precisely once we exend he ime horizon here one general equilibrium which is ineremporal. he idea ha he ineremporal equilibrium is a chain of emporary equilibria ied by sae variables dynamics and solvency consrains gives an immediae undersanding of he conribuion of he ineremporal exension. 5 A closure boils down o saing which variables are endogenous and exogenous in an equaion sysem largely based upon macroeconomics accouning ideniies, and figuring ou how hey influence one anoher (aylor, 1999, p. 41). his mehodology is paricularly useful for comparing how alernaive behavioral equaions (i.e. demand and supply funcions, and pricing mechanisms) affec models sharing he same accouning ideniies. More modesly we will jus allow some exra variables o be se exogenously o deermine a sysem of economic variables of ineres in a consisen way. 5

7 II. Exchange Rae Definiions and PPP In he presen secion we decompose he aggregae price index, compare some alernaive definiions of real exchange raes, summarize he evidence on he dynamics of is componens and lay he ground o he analysis of he equilibrium exchange models. he PPP is an equilibrium condiion ha ies he nominal exchange rae o he domesic and foreign price indices. In is sronges version i requires cross-counry equalizaion of raded goods price levels expressed in he same currency so ha he real value of a currency or he value of a baske of goods is equalized across counries. In is relaive version, i simply requires he nominal exchange rae o offse price inflaion differenials across counries. Since PPP is merely an equilibrium condiion, he following quesions arise: 1) Which is he causal relaion among he variables involved? Does PPP provide a heory of he real or of he nominal exchange rae? Are prices deermined by he nominal exchange rae or he oher way round? 2) Which prices are poenially affeced by he pariy condiion and which price indexes have o be considered for a meaningful es of he heory? 3) Which is he relevan adjusmen horizon? 4) Which are he acual mechanisms o obain he equilibrium? Arbirage in he goods marke or in he asses marke? 5) How sricly does he pariy condiion have o be inended: in absolue levels or raes of change? Mos of hese quesions are relaed o each oher and depend on he heory chosen o ground he pariy. PPP is relevan for our analysis for i provides a concepually simple RER equilibrium level opposed o hose obained by macromodels balance adjusmens, bu also because evidence in favor of PPP a he macro level and he price equalizaion of homogeneous goods a he micro level provide suppor o a se of models ha rule ou price compeiion as a cause of rade in he long, medium and even shor run. II.1 Alernaive Definiions of RER Real exchange rae has been defined in he lieraure boh as he relaive price of wo counries oupus and as one counry raded-nonraded good price raio: * EP p (1) P P P p (2) where E is he nominal bilaeral exchange rae, is he radable and is he nonradable goods price indices, and he aserisk denoe foreign variables. he law of one price (ofen named LOP or LOOP) * saes ha for any single commodiy i, P i = EP i, where P is he price of a single raded good and * P i P is foreign counerpar. Disorion due o ariff wedges beween expor and impor prices can i P 6

8 preven full equalizaion of prices so ha forces work well. * EP i / P i can be differen from one, bu consan if arbirage Suppose for simpliciy ha he domesic and foreign price indices are Cobb-Douglas geomeric α 1 α * averages and P *) β 1 β P = P ) ( P ) P = ( P *). 6 * hen define p EP / P, p P / P, ( * * p P, and p EP / P. * * / P Lop ( Subsiuing hese definiions in he indices we obain a decomposiion for he RER: α * β ( plop )( p p ( p ) ). (3) Log differeniaing he RER we obain he relaion of he growh raes, denoed as ^ variables: pˆ α pˆ + pˆ β. (3 ) Lop * pˆ Equaion (3) relaes he wo differen definiions of exchange raes, p and, wih he foreign raded-nonraded price raio, p, and he raio beween domesic and foreign radable prices, p. he wo definiions of RER, (1) and (2), can have differen dynamics no only if he raio of foreign raded and nonraded good price changes over ime, bu also if he law of one price fails o hold p Lop wih changing over ime. * If he price of raded goods is pinned down by he world marke and expor demand is perfecly elasic ( p is consan), he endogenous nonraded good price adjusmen relaive o he raded price, p, Lop drives boh he inersecoral demand and supply allocaion and gives he direcion of he overall change of domesic vis-à-vis foreign prices. An appreciaion, a fall in (2) due o eiher a nominal appreciaion or a rise in P, would swich demand from nonradables o radables and producion in he opposie direcion, generaing an excess demand for radables and deerioraion of he curren accoun, while he rise of relaive price of nonradables raises he overall price level vis-à-vis he res of he world. Hence, he definiions (1) and (2) of he exchange rae are inerchangeable only if is consan (hough no necessarily equal o one) and * p p is exogenously deermined. Lop p Lop he radiional argumen for assuming an exogenously deermined p Lop is ha perfec compeiion leads o he LOP among homogeneous goods: a small open economy producing nondiffereniaed commodiies faces a perfecly elasic expor demand and ses he price o he foreign level correced by any possible ransporaion cos and ax disorion. An exogenous p Lop can be moivaed paradoxically wih an opposie argumen: some pricing o marke mechanism, some form of mark-up and monopoly power in he raded good, can jusify he 6 he Cobb-Douglas form is employed here for analyical convenience, bu can be raionalized as opimal consumpion-based price index as shown in appendix 1. 7

9 insensiiviy of P macrobalance adjusmens. o demand and supply variaions and oher domesic relaive prices and hese consideraions are somehow relaed o he Keynes vs. Ohlin conroversy on he erms of rade effec of an income ransfer: while Keynes mainained ha expendiure changing policies (fiscal and inernaional ransfers) would induce an expendiure swich hrough erms of rade change, Ohlin argued ha he laer was no a necessary oucome of he former. Our poin, however, goes beyond he problem of he role of he erms of rade: 1. he sandard rade (Heckscher-Ohlin-Ricardian) heory focuses on differen raded goods: he erms of rade (expored over impored good price) drive he rade paern, while he real exchange rae, p = p Lop, converges o he pariy. rade can be imbalanced bu inernaionally idenical preferences neuralize any effec of he resource ransfer on he relaive prices: i does no maer where income is allocaed inernaionally as long as i is spen in he same way. 2. Inroducing nonradables in a sandard general equilibrium rade model allows for boh endogenous erms of rade and raded/nonraded price raios. A resource ransfers due o imbalanced rade reduce nonradables demand and increase exporables supply in surplus counries (and vice versa in defici counries), erms of rade deerioraes for he surplus counry which experience a devaluaion. If similar goods are homogeneous o he pariy and he relevan adjusing price is p, wih pˆ α pˆ. p Lop converges 3. he economy can be so small in is expor and impor markes ha he erms of rade are exogenous. In he dependen economy models wih raded and nonraded goods or wih imporables, exporables and nonraded goods a erms of rade adjusmen is excluded by assumpion; he homogeneiy of raded goods leads he convergence of he p, and becomes once again he adjusing exchange rae. 4. If each counry produces a single raded good and preferences (or more simply he absorpion for domesic and foreign goods) differ beween counries, he relevan exchange rae is he inverse of he erms of rade, Lop p p = plop = z. erms of rade/real exchange rae adjusmen is necessary o allow any expendiure change. his simplificaion of he sandard rade model ogeher wih case 2.) would show how radiional Keynesian models are based on presumpions over more general equilibrium seings. 5. his is no necessarily he case. If he economy produces radables and nonradables, and home radable goods are similar and compee imperfecly wih he foreign counerpars, 8

10 p Lop p Lop plays an expendiure-swiching role beween domesic and foreign good bundles. he raded/nonraded price raio would affec he value of he oupu and possibly is composiion, bu no he conribuion of he ne expors o he aggregae demand: he is he measure of domesic compeiiveness vis-à-vis he res of he world. Obviously, he raio of raded o nonraded goods driving resources allocaion and inersecoral domesic compeiiveness, is incapable o explain inernaional compeiiveness among similar goods which is assumed o vanish in he equilibrium. he use of one or he oher has o rely on he basic producion and rade feaures of he economy and on he relevance of he LOP for he raded goods. II.2 he PPP as an Equilibrium Real Exchange Rae heory his decomposiion of he price level raio becomes exremely helpful for relaing he empirical sudies on he Purchasing Power Pariy (PPP) and LOP o he models relying on adjusmen of plop or p. he PPP condiions (p =EP * /P =1 in he absolue and p ˆ = 0 in he relaive version) do no provide iself any casual relaion beween nominal values. While Gusav Cassel, who rediscovered he pariy in he early 1920s, viewed he PPP as a cener of graviaion of a broad measure of domesic and foreign relaive prices such as CPI or GDP deflaors, he modern prevailing heoreical underpinning of he PPP condiion relies on an arbirage argumen in he good secor: he obvious index o look a 7 would be he raio of domesic and foreign raded goods, p Lop. In he long run boh prices and nominal exchange raes may conribue o he adjusmen of he RER o is pariy level, since he former cease o be sicky and he laer may adjus or be adjused o regain los compeiiveness. As a consequence of he commodiy arbirage inerpreaion, he PPP equilibrium relies on he long-run validiy of he LOP for a sufficien number of radable goods of he price bundle. Moreover, if single commodiy prices have differen mean and adjusmen speed, an unbiased dynamics is obained only by idenical aggregaed commodiy baske, and. P * P p Lop and RER he presence of nonraded goods in he aggregae price indices generaes a long-erm deviaion of he real exchange rae, p ( p ) ( p )( p ) α * β Lop, from he good marke arbirage-based relaion = 1. p Lop 7 A higher RER (an undervaluaion) would generae arbirage opporuniy o buy goods domesically and sell hem abroad while a lower RER (overvaluaion) would induce o buy goods abroad and sell hem in he domesic marke, ec.. 9

11 Recall equaion (3 ) and suppose ha α pˆ = βp, ha is, he growh raes in he raded and nonraded goods relaive prices in he wo counries are eiher boh zero or offse each oher; deviaions of he p Lop from is mean becomes he only source of deviaion of he PPP from is equilibrium. However, if we narrowly focus on disaggregaed raded good relaion, we easily noice ha boh levels and speed of reversion owards he LOP hold differenly from good o good because of (i) ransporaion coss, (ii) radable and nonradable conen (of services and oher nonradable inpus), (iii) ariffs and nonariff barriers, and (iv) pricing o marke. * ˆ II.3 Consensus esimaes of PPP and LOP dynamics Froo and Rogoff (1995), Rogoff (1996), and Sarno and aylor (2002) provide a complee and exensive survey on he available lieraure and offer an official inerpreaion and consensus empirical evidence on he exisence and relevance of he differen forms of price equalizaion across counries. We summarize he conclusions obained by he auhors. 1) he only heoreical ground for cross-counry price equalizaion is poenial arbirage and price compeiion on he goods marke, his requires he "law of one price" o hold a leas for a sufficien number of goods as precondiion for he aainmen, a leas on he very long run, of a pariy in he price indices. herefore, in he measuremen of he PPP, he price index has o include only radable and homogeneous commodiies ha can be subjec of price arbirage. 2) However, microeconomic analyses on single raded goods have offered dauning resuls showing a very high volailiy and persisen deviaions from he LOP pariy; such deviaions are highly correlaed wih nominal exchange rae flucuaions. Price differenials are persisen boh in sophisicaed goods and "commodiy manufacures". he "border effec" has been considered as he major obsacles o poenial arbirage and price equalizaion: price equalizaion fails more for similar goods a shor disance across he US and Canada border han for differen wihin a counry. In he laer case, he resuling price wedge canno be explained in erms of ransporaion coss, ariffs and nonraded-good conens of raded goods. Among he possible non-ariffs barriers inspecion requiremens, differing sandards as well as "price o marke" price discriminaion have o be included. 3) On he macro fron, he "consensus" empirical lieraure is no more encouraging: he RER ends o he PPP in he very long run, wih large and volaile deviaions of he same order of magniude of he nominal exchange rae, dumping a 15% rae per year, and wih an half life of 3-5 years. hese resuls would be, however, sufficien o dispel "he embarrassing resiliency of he random walk model" (Rogoff, 1996, p. 655), ha is, he difficuly o rejec he esing hypohesis of no mean reversion in he RER. In his perspecive PPP can be preserved as a cener of graviaion or equilibrium RER. 10

12 he embarrassmen has been hen reduced o explaining he persisence of he deviaion ha moneary shocks and price sickiness canno accoun for and o explaining he shor-erm volailiy of RER ha canno be ascribed o real shocks. herefore, he evidence for PPP and LOP is weak and conroversial even in he long run: dismissed as shor- and medium-run condiions, he failure of PPP and LOP is he puzzling evidence of a general difficuly of assuming he price and rade convergence required by general equilibrium models. II.4 Long-Run Deviaions from PPP he purchasing pariy condiion is based on an arbirage argumen in he goods marke and, in is relaive version, allows for bu does no explain changes in he absolue level of he RER. Changes in he level of ariffs, for insance, would affec he arbirage free level of real exchange rae bu would no affec he long run endency of nominal exchange rae changes o follow relaive price inflaion in raded goods, pˆ Lop = 0. Balassa (1964) and Samuelson (1964) provided one of he firs explanaions for low frequency (long run) changes in he equilibrium RER, ha is, he exisence of a consan or sochasic rend in he RER. heir argumen is based on an empirical regulariy beween real income and CPI price level expressed in dollars in differen counries: he richer he counry he higher is dollar price level. his is because rich counries are relaively more producive in he raded goods secor which is less service inensive and where he scope for produciviy increases is larger. If he raded goods price is given by he LOP, he higher overall wage rae generaed by he raded secor produciviy increase drives up nonraded goods prices and he overall domesic relaive o he foreign price index. In erms of equaion (3 ) he relaive price of raded o nonraded goods of he richer counry falls faser han he relaive price of he poor counry, * pˆ αpˆ βpˆ < 0, hus, leading o a real appreciaion. he main implicaion of relaive PPP is a consan or increasing level of ERER in indusrial counries he long run. he exended PPP is nohing bu a PPP real exchange rae esimaion correced wih he Samuelson-Balassa effec. An arbirage-based argumen canno, however, accoun for he effec of oher facors, which supposedly can influence he ERER such as: (i) ariffs and quoas, (ii) erms of rade (noe he income effec and subsiuion effec), (iii) demand shifs (due o consumer preferences and governmen consumpion), (iv)inernaional ransfers, and (v) relaxaion of exchange conrols. In order o explain he incidence of hese facors, equilibrium-exchange-rae macromodels are required. 8 8 Rogoff (1996) shows ha even if here is a posiive relaionship beween income and price for a large number of counries, his relaion is less clear if analyzed wihin he mos rich and mos poor counries separaely. Moreover, he heory can be quesioned on he srong underlying assumpion ha fas growing counries have higher produciviies in he raded goods indusries. 11

13 able 1 anicipaes he presenaion of he mos relevan model of RER in he lieraure according o heir reamen of he p or p, in he following we will deal for convenience wih he orh-wes Lop and Souh-Eas par of he able. Endogenous exchange rae p Lop Keynesian, Effecive Demand One-Secor Imperfec-Compeiion (Mundell-Fleming and Srucuralis Models) Class of Models General-Equilibrium, Full-Employmen Mulisecor General Equilibrium Imperfec-Compeiion (ew Open Economy Macroeconomics Models) p raded-onraded Fix-Price/Flex-Price (Srucuralis Models) Flexible-Price raded/onraded Models (Dependen Economy Model and hree Goods Models) Ineremporal Approach (Ineremporal one, wo and hree goods models) able 1. Boh Keynesian effecive demand models and neoclassical general equilibrium models have deal wih differen levels of aggregaion and hypohesis on he raded good price adjusmen mechanism. III. Aggregae-Demand Models of Equilibrium Real Exchange Rae From he exchange rae decomposiion and he sylized facs of is componens, we now urn o exploring how hose differen definiions have been adoped o deermine he equilibrium real exchange rae and is relaion wih he curren accoun. In he presen and following secions we briefly presen some exising classes of macro models of equilibrium real exchange rae deerminaion: we condense a few influenial alernaive approaches ino classes of saic and dynamic models and se hem in a consisen and comparable framework, allowing for alernaive possible closures o underline he relevance of he assumpion and heir analyical implicaions. We sar wih he mos popular framework of exchange rae deerminaion in he class of shorand medium-run models and we assume he producion of a one (or composie) commodiy, which is imperfec subsiue wih foreign ones. 12

14 III.1 Sandard Keynesian Model in he Shor and Long Run In he radiional Keynesian one-commodiy effecive-demand model, he real exchange rae is defined as he relaive price of he impored in erms of he expored good, p=ep * /P. he economy produces a single or composie good so ha he real exchange rae is he inverse of he erms of rade. he wo goods are boh raded and imperfec subsiues; heir relaive price drives heir demand and, hrough he real wage changes, deermines he domesic supply: 9 X = A( X ; Θ) + CA, (4.1) CA = CA( X, X *, p), (4.2) X = X (L) (4.3) L d (ω) = L, (4.4) where A is domesic absorpion (or oal expendiure), CA is he curren accoun, L and supply and demand, respecively, and d L are labor ω he real wage expressed in erms of he only domesic produced good X, while X * is he exogenously given foreign income and Θ is a parameer represening he effecs redisribuion and fiscal policy on he effecive demand. he exernal balance may be defined as a desired level of curren accoun, say CA 0 in (4.2), while he inernal equilibrium enails an equilibrium condiion in he good marke (4.1) and a supply side represened by he shor run producion funcion (4.3) and he equilibrium in he labor marke (4.4). Sysem (4) has four equaions and five variables: X, L,ω, p, and CA, where he derivaives have he following signs: CA < 0, CA * > 0, A > 0, X > 0, and L ω <. In he one-secor Keynesian models a counry X X can have an excess capaciy and a monopoly degree on is expor goods so ha prices and quaniies can boh adjus below he full employmen level. X d L 0 A sandard IS curve is obained by combining he income equaion (4.1) and he curren accoun (4.2); if we furher assume he Marshall-Lerner condiion, he IS is posiively sloped in he (p, X) space as he aggregae demand increases wih a real depreciaion and expor real expansion offse he impor value increase of a depreciaion, CA p > 0 (figure 1). here is one degree of freedom in sysem (4) which is no found in sandard presenaions of he radiional Keynesian one-commodiy effecive-demand model. In he simples version of he * Mundell-Fleming model prices are fixed in he shor run, he ineres rae equals he foreign level,i, since spreads are arbiraged away under perfec capial mobiliy and saic expecaions, he exchange rae or he money supply is fixed as a nominal anchor: a LM curve such as 9 radiionally, inernaional facor paymens have been negleced in his macro parial equilibrium se up, so ha we will no disinguish beween GDP and GP and beween curren accoun and rade balance. 13

15 M = * LM ( X, i ) (4.5) P closes he sysem. Since prices are sicky in he shor run, he level of income for a given money supply under flexible exchange rae is deermined by he LM, while he IS would deermine he exchange rae. Alernaively, a given exchange rae deermines he level of oupu on he IS, while he LM he endogenous money supply (figure 2, orh-eas quadran). Labor demand and real wages are deermined in boh cases by (4.3) and (4.4). Anoher usual hypohesis is o assume some oher nominal rigidiy in he shor run such as he nominal exchange and wage rae. Forω / p = w / EP * *, his oher fifh equaion EP p = ω (4.5 ) w would close he sysem (figure 1, orh-wes quadran). 10 An aggregae demand relaion as he IS in no necessarily a shor run concep. Suppose a longer adjusmen horizon where nominal rigidiies are removed: sysem (4) can represen a fully real model in which commodiy price and exchange rae adjusmens are indisinguishable. 11 Moreover, his real (medium run) framework allows us o compare effecive demand models wih general equilibrium full-employmen models of he nex secions. he one degree of freedom of sysem (4) allows for alernaive closures by simply seing exogenously one key variable a ime. a) Full Employmen. he equilibrium exchange rae can be deermined on he IS curve eiher by seing income o is full employmen level X (or any level desired level of economic aciviy). Curren accoun, employmen level and wage rae follow sui (figure 2). Fully flexible prices drive he equilibrium a is full capaciy uilizaion level, ha is, labor demand aains is full employmen level, L, and deermineω, while (4.1), (4.2) and (4.3) solve for he income level, X, he curren accoun, C A, and he real exchange rae, p. b) Exernal Equilibrium. By choosing an equilibrium level for he curren accoun, CA 0, and solving for boh p and X; full employmen is no guaraneed in he shor run, L L 0. c) Real Wage Resisance. If he real wages ω' are exogenously given and held consan by some form of indexaion above he marke clearing level ω, he sysem can be solved for p, X ', CA, and 10 Equaion (4.5 ) can be combined wih (4.3) and (4.4) o obain a downward sloping curve in he orh-eas quadran represening a supply consrain due o wage resisance. 11 By absracing from any nominal rigidiy, we can concenrae on he good and facor marke componen of he model neglecing he money and he bonds marke, ha is, he LM componen of he radiional Mundell- Fleming model. aylor (2004), for insance, showed ha IS, LM and balance of paymens componens of he model are indeed sock-flow inconsisen. 14

16 he level of employmen L' L. oe ha equaion (4.5 ) can represen a wage resisance in erms of impor price level and can lead o unemploymen from he supply side. his is because producers' profi maximizaion in a conex of shor-erm decreasing marginal produciviy of labor generaes a wage-employmen rade-off: he labor demand funcion (4.4) is downward sloping and he inernal equilibrium is obained by cuing real wages. 15

17 LM E P * w IS CA 0 p 0 ω 0 X 0 X L 0 L X(L) Figure 1. ominal rigidiies (orh-wes quadran) or he LM curve (orh-eas) close he classical-keynesian model. oe ha aggregae demand can fall shor of full employmen even if nominal wages are flexible. IS CA p CA 0 CA p 0 ω' ω 0 ω p X ' X 0 X X L' L 0 L X(L) Figure 2. Good marke equilibrium and curren accoun, producion funcion and labor demand schedule in he classical-keynesian model. 16

18 III.2 A Srucuralis Model Differen resuls are obained by assuming a Kaleckian-Keynesian seing where imperfecly compeiive markes and he exisence of spare capaciy allow for mark-up pricing while differeniaed saving propensiies among income recipiens ie he income disribuion o he effecive demand and oupu levels. Srucuralis models, moreover, assume ha here is an impor componen of inpus rigidly required for domesic good producion: his does no exclude he exisence of compeing impors, bu brings abou a relevan disribuional effec of impor price changes. Equaion (4.4) ha gives he disribuion beween facors a varying oupu levels can be subsiued by a mark-up pricing rule such as: PX = (1 +τ )[ wl + EP γ X ] * or, equivalenly, ( 1 π ) = [ ω β + pγ ], (4.4 ) where β is he labor inpu coefficien in he producion echnology L = β X, (4.3 ) β can be variable or consan indifferenly, for i does no affec disribuion, π is he profi share,τ is he mark-up rae and π = τ / 1+ τ, γ is he coefficien of impored inpu componen in he domesic producion, X is oal supply and [ 1 p γ ] X = [ π + ω β ] X is aggregae income. According o (4.4') here is an inverse relaionship beween he disribuional componens π, ω, and p: we can se eiherπ assuming ha price seers manage o preserve heir margins in face of variaions of he oher wo variables, or fixω, assuming an effecive wage indexaion. If price of he impored inpus rises, firms are able o preserve a fixed mark-up and heir profi share only by reducing real wages. his gives an inverse relaion beween p and ω (orh-wes quadran of figure 3 and 4) as in he neoclassical downward sloping labor demand plus IS curve, which however is no he oucome of labor-consrained supply expansion bu only of income redisribuion whose consequen oupu effec depend on he resuling aggregae demand change. he noncompeiive naure of some impors leads o a relevan implicaion of he model: a depreciaion can have an adverse effec on absorpion, and herefore on income, even wih a posiive response of he compeiive ne expors, defined as he expors minus he compeiive impor componen of he rade balance, E( p, X ), where E > 0 and E < 0. his is nohing bu a qualificaion of he Marshall-Learner condiions which can hold for he compeiive par of he rade balance, bu need no o apply on he overall balance if impored inpus canno be readily subsiued wih domesically produced alernaive inermediaes and heir share is large. he absorpion funcion can be specified as A ( X, p) c( p) X, where c( p) c [ π + ω β ] = c [1 pγ ] : a devaluaion reduces absorpion by increasing inermediae good prices and redisribuing revenues from consumpion-generaing naional income o he res of he p X 17

19 world in he form of higher impors value. he curren accoun is he sum of compeiive and noncompeiive ne expors CA = E( p, X ) pγ X, which differeniaed gives dx dp CA E p γ = γ p X E X. he IS becomes [ 1 pγ ] X = c [1 pγ ] X + E( p, X ) pγ X, so ha dx dp IS where E p cγx = 1 c + cpγ E X X : 1 c + cpγ E has been radiionally labeled in he Keynesian lieraure as s + m, he leakages of saving and impor propensiies. A devaluaion becomes conracionary (and he IS and curren accoun curve downward sloping) if he expor demand elasiciy E p run and he fall in absorpion due o he non-compeiive impors cγ X relaively srong. If for insance c( p) c π π + cωω β = cππ + cω [ 1 π pγ ], wih cπ c cω, he slope of he IS pγ ) γx > 0 is small in he shor he srucuralis radiion has however emphasized he more relevan case of differeniaed propensiies o save ou of profi and wage income: if he elasiciy E p > 0, is small, he conracionary effec of a devaluaion is magnified hrough he regressive disribuion from higher consumpion-generaing wages o he res of he world. becomes dx dp IS E p cγx cω (1 pγ ) γx =. 1 c + cpγ E X he exra erm c ω ( 1 12 shows he addiional leakage from wage consumpion o foreign savings (figure 3 and 4, orh-eas quadran). If condiion c + cω ( 1 pγ ) > E p / γx > 1 is saisfied, a devaluaion ha improves he curren accoun (Marshall-Learner condiions hold for overall ne expors) can worsen income (figure 3 and 4). 12 See aylor (1991, Chp. 7) and Krugman and aylor (1978) for examples of possible conracionary devaluaions. 18

20 CA 0 p 0 IS ω 0 X 0 X L 0 X(L) L Figure 3. ominal rigidiies and mark-up pricing deermine he real wage and exchange raes, while aggregae demand deermines capaciy uilizaion and he curren accoun. CA 0 p 0 IS ω 0 X 0 X L 0 X(L) L Figure 4. Goods marke equilibrium and curren accoun, producion funcion and labor demand schedule in a srucuralis model. 19

21 he sysems above are again undeermined. Srucuralis models are ypically se in nominal erms since in he shor run nominal rigidiies can affec he equilibrium. If nominal wages and exchange rae are given, ω / p = w / EP * EP p = ω, w *, he model is once again closed by which, combined wih he mark-up pricing rule, deermines he facors disribuion and real exchange rae (figure 3, orh-wes quadran). Oupu, curren accoun and employmen follow sui. If, once again, we absrac from moneary rigidiies, we can close he model as he classical- Keynesian case by assuming ha a) capaciy is consrained by producive capaciy or full employmen; or ha b) he availabiliy of foreign exchange necessary o by inermediae impors binds so ha he curren accoun has o be se o a desired level; or c) here is an effecive real wage indexaion ogeher wih given profi margins ha generae he required inflaion and devaluaion o obain he equilibrium. III.3 Inernal and Exernal Balance in Parial Equilibrium Figures 2 and 4 show ha if he sysem is solved by seing he curren accoun o a desired level CA 0 ha allows for exernal equilibrium, boh L, and ω have o adjus endogenously and full employmen, he inernal equilibrium, is no guaraneed in he shor run for a given IS. his raises wo issues: wha are exernal and inernal equilibrium and how are hey aained simulaneously in he shor run and/or in he long run? A rade imbalance can be eiher he manifesaion of a emporary invesmen growh paern financed hrough exernal borrowing, or simply he oucome of bad expor performances leading o an oupu level lower han aggregae expendiure. Saic Keynesian models need o find a concep of susainabiliy (susainable capial flows or susainable saving/invesmen gap) o se he level of curren accoun. From a general equilibrium perspecive his choice would be ad hoc and no opimal in a fully and correcly specified model. While saic models need o se he curren accoun or even he rade balance o zero and canno deermine he endogenous ime paern for he desired level of he curren accoun economic, ineremporal models (secion V) deermine he sequence of curren accouns as he resul of he opimal inernaional lending and borrowing ime paern beween counries. On he oher fron, full employmen or naural unemploymen is he benchmark of inernal equilibrium in mos policy analyses. Models ha require boh inernal and exernal equilibrium add wo consrain L = L and CA = CA 0 o sysem (4) which becomes overdeermined: he IS curve needs o become endogenous and adjus o he equilibrium (shif o he righ in figure 1) hrough some form of absorpion adjusmen and change in Θ. his simply means ha he expendiure parameer, Θ ha can 20

22 represen real ineres rae effecs or oher fiscal policies, needs o be consisen wih a susainable saving invesmen gap or capial flow. he IMF models of desired equilibrium exchange rae, DEER, Fundamenal Equilibrium Exchange Rae, FEER, or IMF s Coordinaing Group of Exchange Rae issues model, CGER, require boh inernal and exernal balance a leas in he medium run. his kind of models is presened in secion VI. able 2 summarizes how he srucuralis and sandard-keynesian models are deermined under alernaive assumpion of inernal, exernal balance and perfec wage indexaion. Srucuralis Classical Keynesian Closure Endogenous Closure Endogenous Capaciyconsrained adjusmen: X = X, or L = L CA and p deermined by IS ω = ω by mark-up pricing Full Employmen: X = X, or L = L. CA and p deermined by IS ω = ω by labor-marke/ marginal produciviy Medium-Run IMF models, he IS adjuss CA = CA 0 and p = p. Real wage resisance ω = ω' p by mark-up pricing, X ', CA by IS L' L by producion Real wage rigidiy ω' ω = X ' and L' L by labor-marke/ marginal produciviy p, CA by IS Desired Exernal Balance CA = CA 0 p,, 0 X 0 by IS L0 L by producion Desired Exernal Balance CA = CA 0 p, 0 X 0 by IS L0 L by producion able 2: he wo models can be closed in alernaive ways. For full employmen is no necessarily aained for a desired exernal balance, IMF models assume IS adjusmen in he medium run o achieve boh full employmen and desired curren accoun. 21

23 IV. General Equilibrium Saic Macro Models General equilibrium models assume full employmen hrough Say s law, price equalizaion of homogeneous radable goods, and uiliy- and profi-maximizaion-driven consumpion and invesmen demand. Given he accouning ideniy X ( C + I + G) = X, (5) where ( C + I + G) is he previously defined absorpion, A, in a one-good saic world agens could borrow an unlimied amoun of good a a given price and obain unlimied consumpion and/or invesmen level and here would no be any realisic opimal choice for he acors. General equilibrium models need o add eiher some nonradables whose producion and consumpion is limied by resources availabiliy, or an ineremporal solvency consrain: he firs case leads o he saic dependen economy model (his secion), he second o he baseline ineremporal approach o he curren accoun, a blend of he wo o a nonradable augmened ineremporal approach (secion V). One sriking feaure of he general equilibrium seing wih or wihou nonradables is he line of causaion beween expendiure and rade: he demand for (ne) expors is perfecly elasic and heir price given inernaionally, he relevan variable for he deerminaion of he rade balance is he gap beween he (resource deermined) oupu level and (endogenously deermined) expendiure level. In oher words raded goods are smoohly pushed by surplus counries and pulled by defici ones across he border wihou any relaive raded good price change. rade is somehow passively driven by desired income-expendiure differenials. Recalling he Keynes-Ohlin conroversy, Ohlin proposiion indeed holds if preferences are homogeneous across counries and similar goods are homogeneous. General equilibrium modeling has oped for his second soluion, supporing wha has been labeled by Williamson he immaculae ransfer. If here are nonradables, expendiure changes can affec he raded/nonraded price and possibly change he erms of rade, bu do no aler p Lop. In a class of models named dependen economy or Ausralian models, originaed by Swan (1960) and Saler (1959), he general equilibrium is obained by allocaing resources beween raded/nonraded goods following he price signals of he real exchange rae,. he small dependen economy canno affec is erms of rade and faces a perfecly elasic demand for (ne) expors a a given price for radables. Full employmen of labor and capial is assumed, so ha he only economic problem for consumpion maximizing agens is he allocaion of heir resources among secors and, possibly, allowing desired income-expendiure differenials horough rade in commodiies and real asses. p 22

24 Capial can be secor specific or inersecorally mobile. 13 he producion and consumpion srucure is analog o he 2x2 Heckscher-Ohlin or specific-facor model; in he dependen economy, however, he commodiy relaive price canno be deermined by commodiy rade solely, and he facor price equalizaion does no necessarily apply. Finally, he hree-good model simply exends he radednonraded goods model and allows o ake ino accoun he effec of exogenous erms of rade (expor/impors prices) shocks over he real exchange rae p. IV.1 A raded/onraded Good Model Boh kinds of goods are produced and consumed domesically while he inernal equilibrium is achieved when he nonradables and labor markes clear. he producion, consumpion levels, facor prices and inensiies are deermined for any relaive raded/non-raded price (here, for breviy p, appendix provides a formal presenaion). he model is described by he following equaions: p E = pc ( p, E) + C ( p, E) (6.1) X ( p) C ( p, E) X (6.2) = X ( p) = C ( p, E) (6.3) L ( ω ( p)) + L ( ω( p)) = L (6.4) where E is he aggregae expendiure in erms of he nonraded good (replacing absorpion A in he neoclassical erminology), X are ne expors. he domesic demand for raded, C, and nonraded goods, C, are inverse and direc funcions of he relaive price p, respecively, and boh increase wih he aggregae expendiure E; raded X and nonraded X good producion falls and rises wih relaive price increases, respecively. Equaion (6.1) expresses expendiure in erms of nonradables, (6.2) and (6.3) are he equilibrium in he nonraded and raded good markes, respecively, while (6.4) is he aggregae labor demand funcion. Since only wo of he hree equaions (6.1)-(6.3) are independen (as shown in he appendix 2), he model has again a degree of freedom ha can be closed eiher (i) on he demand side by fixing a level of expendiure E or uiliy u or real consumpion C, or on he (ii) supply side inroducing a real rigidiy on facor prices, real wage rae ω or real ineres rae r, or (iii) by assuming a desired level of rade balance X, for insance. More specifically: (i.a) he radiional dependen economy model analyzes he effec of differen levels of policy deermined expendiure on expors and exchange rae. If expendiure is exogenously 13 A formal and complee se up of he model is provided in appendix 2, where we show ha his assumpion is irrelevan o he model s basic oucomes. 23