Real E ects of Exchange Rates: A View From Trade Theory*

Transcription

1 eal E ects of Exchange ates: A Vew From rade heory* Vrgna D no #, Barry Echengreen x, Massmo Sbraca # I POGESS VEY PELIMIAY AD ICOMPLEE DO O CICULAE hs verson: August 202 Abstract Can changes n nomnal exchange rates rase welfare, employment and real GDP? We address ths queston by buldng a smple analytcal model and explorng the channels through whch a change n the nomnal value of the currency may a ect the real economy. Under the assumpton that productvty s hgher n the tradeable-goods than n the nontradeable-goods sector, we examne the roles of market structure, scale economes and wage exblty n channellng resources from the latter to the former sector, rasng output. Our results unvel persstent real e ects of changes n nomnal exchange rates not only when wages are stcky, but also when wages are exble and returns to scale are ncreasng. In the rst case, we show that f stcky relatve wages are "uncompettve", a deprecaton of the nomnal exchange rate can restore equlbrum condtons, ncreasng output and welfare. In the second case, the presence of real e ects does not requre that costs are sunk nor that economes of scale are dynamc, as n the prevous lterature, but t draws on the assumpton of (statc) ncreasng returns to scale only. JEL class caton: F30, F0, O0, 00 Keywords: Eaton-Kortum model, ncreasng returns to scale * he vews expressed n ths paper are those of the authors and do not necessarly re ect those of the Bank of Italy. We thank Jonathan Eaton and Mark Melt for ther suggestons n the early stages of ths research. E-mal: vrgna.dnno@bancadtala.t, echengr@econ.berkeley.edu, massmo.sbraca@bancadtala.t. # Banca d Itala x Unversty of Calforna, Berkeley

2 Introducton A large body of emprcal studes shows that movements n real exchange rates tend to have persstent real e ects, a ectng output and employment. Balassa (964) and Samuelson (964) provde early and n uental statements of the mportance of a compettvely valued real exchange rate n supportng exports and, n turn, of ther role for economc development. Smlar arguments have been made, more recently, by Johnson, Ostry and Subrmanan (2007), Echengreen (2008) and odrk (2008). hese studes tend to conclude that there s a postve relatonshp between an "undervalued" currency and economc growth and that ths relatonshp s stronger for developng countres. omnal exchange rates, n turn, are the man drvers of changes n real exchange rates n the short term, as t has been known at least snce Mussa (986). Yet, ther e ects have generally been overlooked n theoretcal models of economc growth and nternatonal trade. hese models, n fact, are real frameworks n whch changes n nomnal varables do not play any role. In partcular, n a frctonless open economy wth perfect competton and perfectly exble prces, changes n nomnal exchange rates cannot a ect equlbrum quanttes and relatve prces. But what are the e ects of nomnal exchange rates when wages and prces are less than perfectly exble? And what f returns to scale are not constant? Are there condtons under whch changes n exchange rates a ect output and employment as the emprcal lterature suggests? In ths paper we examne these questons from a theoretcal pont of vew. We extend the model of Eaton and Kortum (2002), wth perfect competton and constant returns to scale, to encompass both tradable and non-tradable goods. We then replace the assumpton of constant returns to scale and perfect competton wth ncreasng returns to scale and Bertrand competton endng up wth a varant of the model developed by Grossman and oss-hansberg (200). 2 Wthn these frameworks, we nvestgate whether changes n exchange rates are successful n shftng resources between tradeable and non-tradeable goods, a ectng welfare, employment and real GDP. he analyss rests on the key assumpton that productvty s hgher n the tradeable-goods than the non-tradeable-goods sector an hypothess consstent wth the tenet of Lews (954) about the productvty d erental between the modern and the tradtonal sector. Most mportantly, we mmc the e ects of a nomnal deprecaton of the currency wth an ncrease n the barrers to mports and a smultaneous symmetrc declne n the barrers to exports. As already conjectured by Keynes (93), ths perturbaton captures the essence hese results have been scrutned and con rmed by a number of studes that followed odrk (2008), ncludng Berg and Mao (200), MacDonald and Vera (200), and D no, Echengreen and Sbraca (202). 2 Both constant and ncreasng returns to scale are emprcally relevant n the tradeable-goods sector. Antweler and re er (2002), usng data from 7 countres, provde the "Solomonc" result that one thrd of all good-producng ndustres are charactered by ncreasng returns to scale (nduced by plant-level or ndustry-level externaltes), one thrd of all goods-producng ndustres dsplay constant returns to scale, whle for the remanng thrd the evdence s nconclusve. Focusng on the manufacturng sector, Morrson and Segel (999) nd that scale economes are prevalent n the U.S. and that, at least n part, they may be due to factors that are external to rms.

3 of what a real deprecaton does, as t makes exports cheaper and mports more expensve. 3 We are comforted about the soundness of ths conjecture by the results of the baselne model: under perfect competton, constant returns to scale, and perfectly exble wages, a deprecaton does not have any e ect on equlbrum quanttes and relatve good prces as s to be expected n ths type of model. he declne n margnal costs due to the deprecaton, n fact, s completely o set by a proportonal rse n nomnal wages. In other words, followng the deprecaton, the economy jumps to a new equlbrum wth hgher wages and product prces, so that a nomnal deprecaton does not carry over a real deprecaton. However, the model also shows that f wages and product prces adjust slowly, then, durng the transton to a new equlbrum, the currency remans undervalued and some gans n margnal costs obtan. In partcular, under the standard assumpton of low elastcty of substtuton between tradeable and non-tradeable goods, an undervalued currency channels resources to the tradeable-goods sector. hus, even wth perfect competton and constant returns to scale, undervaluaton has real e ects n the short-medum run. Clearly, ther duraton depends on the strength of the frctons that prevent wages and prces from rsng. In addton, t depends on the "compettve poston" of the economy: f the deprecaton takes place at a tme n whch domestc wages are too hgh (.e. relatve wages are hgher than ther equlbrum level), then the deprecaton facltates the return of the economy to ts equlbrum, wth welfare enhancng e ects. hus, a deprecaton can substtute for the adjustment of relatve wages, as descrbed by Fredman (953) wth the famous daylght savng tme metaphor. A nomnal deprecaton exerts persstent real e ects f we replace the assumptons of perfect competton and constant returns to scale wth, respectvely, Bertrand competton and ncreasng returns. 4 he story goes as follows. Wth ncreasng returns to scale, rms may have an ncentve to sell ther goods abroad even f they make negatve pro ts on foregn markets: these rms may decde to export n order to produce at larger scale, cut ther average costs, and make large enough pro ts n the domestc market a possblty precluded n models wth constant returns to scale, because there s no cost advantage from producng at a hgher scale. In ths economy, a gven deprecaton cuts rms average costs more than 3 Durng the gold standard, when countres could not devalue ther currences, Keynes (93) conjectured that an ncrease n the barrers to mports and a declne n the barrers to exports could replcate the e ects of an exchange rate devaluaton. Hence, he proposed, as an e ectve polcy, to cut real wages and ncrease employment, leavng the sterlng nternatonal oblgatons unchanged n terms of gold. More recently, n dscussng the current relatonshp between the U.S. and Chna, Krugman (200a) asserted that: "Chna s followng a polcy that s, n e ect, one of mposng hgh tar s and provdng large export subsdes because that s what an undervalued currency does" (emphass added); and, smlarly: "Chna s delberately keepng ts currency art cally weak. he consequences of ths polcy are also stark and smple: n e ect, Chna s taxng mports whle subsdng exports" (Krugman 200b, emphass added). 4 We remove the assumptons of perfect competton and constant returns to scale smultaneously for two man reasons. Frst, the model wth perfect competton and ncreasng returns to scale, analyed by Ether (982), yelds several "pathologes," such as multple equlbra, that hamper the possblty of makng comparatve statcs. Second, models wth Bertrand competton and constant returns to scale, such as the one developed by Bernard, Eaton, Jensen and Kortum (2003), would yeld essentally the same results as the model wth perfect competton. hus, assumng ncreasng returns to scale s key n order to have real e ects of changes n the nomnal exchange rate also n the presence of exble wages, whle Bertrand competton s needed to show these e ects wth a tractable model. 2

4 proportonally, thanks to the addtonal cost gans comng from the economes of scale. Hence, a rse n relatve wages equal to the deprecaton s not su cent to o set the gan n average costs. 5 Whle the economy converges to a new equlbrum wth hgher (relatve) wages followng the deprecaton, some domestc rms gan a compettve advantage. hus, some domestc rms nd access to the foregn market, whle some goods are no longer mported and are domestcally produced. Gven standard elastctes, ths translates nto a shft of resources to the hgh-productvty tradeable-goods sector and, then, nto a rse n output. hese gans obtan wth the real exchange rate set at ts equlbrum level and are even larger durng the transton to the new equlbrum, whle the currency s undervalued (owng to the same mechansms descrbed above). he analyss also explans why a growth strategy based on currency undervaluaton or seral nomnal deprecatons cannot be pursed ad n ntum and can only bene t economes n the early stages of development but not advanced countres. Wth perfect competton and constant returns to scale, wages and prces eventually adjust, o settng the deprecaton, gans can only be transtory for every country. Wth Bertrand competton and ncreasng returns to scale, the compettve gans declne wth ndustry output and, then, become ncreasngly smaller as the economy develops. Moreover, the mantaned assumpton of a postve productvty d erental between the tradeable-goods and non-tradeable goods sectors whch s reasonable n many low-ncome countres where these sectors broadly correspond to what Lews (954) dubbed as modern and tradtonal sectors may not be approprate n advanced economes where non-tradeable products nclude, for nstance, many hgh-productvty servces. he rst part of ths paper, whch assumes perfect competton and constant returns to scale, generales prevous studes to a context wth any number of countres, and many tradeable and non-tradeable goods. In partcular, Chpman (2006) demonstrated the equvalence between a devaluaton and an mport tar -cum-export subsdy polcy n a small-open economy wth exble prces n the presence of two tradeable goods and one non tradeable good. Stager and Sykes (2009) further analyed t n a model wth two countres and two tradeable goods, and n the cases of both stcky and exble wages. 6 We are able to provde neat results n a context wth many countres and goods, by explotng the generalty of the cardan framework lad out by Eaton and Kortum (2002), whch we further extend. hs extenson s an mportant by-product of ths paper, as the modelng choces that we have 5 Although relatve wages could also rse more than proportonally to the deprecaton, there s no rse n relatve wages that can restore the pre-deprecaton equlbrum. In fact, because the degree of ncreasng returns to scale s heterogeneous across ndustres, the declne n average costs connected to the rse n output s also d erent across ndustres. However, even f ncreasng returns to scale were the same across ndustres, the latter are heterogeneous n productvtes and, then, startng from heterogeneous output levels, the declne n average costs would be d erent across ndustres. hus, pre-deprecaton equlbrum quanttes and relatve prces cannot be restored across all ndustres. 6 Stager and Sykes (2009) also explaned the apparent paradox for why a combnaton of two polcy nterventons (tar s and subsdes) that, separately, dstort trade and have real e ects even wth exble prces, do not create any dstorton and have no real e ect when packaged together. he spec c combnaton of trade polcy nterventons, whch s equvalent to a devaluaton, does not alter relatve prces, as a consequence of Lerner s symmetry theorem (Lerner, 936). hs well-known proposton smply re ects the long-run neutralty of money n a settng n whch all prces are fully exble. 3

5 ntroduced (such as the representaton of productvtes of non-tradeable-goods ndustres wth an approprate probablty dstrbuton) allow us to obtan useful and analytcally very smple solutons. Under ncreasng returns to scale, Baldwn (988) and Baldwn and Krugman (989) had proved the persstence of real e ects of changes n nomnal exchange rates n a context wth sunk costs. Smlarly, Krugman (987) showed these e ects n the presence of dynamc external economes of scale. 7 Our results, however, are more general than those n the prevous lterature, because they draw on the presence of (statc) ncreasng returns to scale only, and do not requre that costs are sunk nor that external economes of scale are dynamc. hs paper s also related to the recent debate on scal devaluatons, whch are generally envsaged as an ncrease n VA and a reducton n payroll taxes or as an ncrease n mport tar s and export subsdes. In partcular, the paper s very close to the sprt of Farh, Gopnath and Itskhk (20), who study the e ects of an ncrease n mport tar and export subsdy (as well as that of a value-added tax ncrease and a payroll tax reducton). her analyss uses a standard dynamc ew Keynesan open economy model to explore alternatve prcng assumptons (producer and local currency prcng), alternatve asset market structures, and dstngushes between antcpated and unantcpated "devaluatons," whereas we use a standard statc nternatonal trade model to nvestgate d erent assumptons on wage stckness, market structures, and economes of scale. 8 Here s a roadmap of the paper. Secton 2 ntroduces the model wth perfect competton and constant returns to scale. Secton 3 mod es t to replace perfect wth Bertrand competton and constant wth ncreasng returns to scale. Secton 4 draws the man conclusons. 2 Perfect competton and constant returns to scale We consder an economy charactered by the followng features: a tradeable-goods and a non-tradeable-goods sector, each of them producng a contnuum of goods; ndustres wth heterogeneous e cences, descrbed by Fréchet dstrbutons; labor, the only producton factor, s perfectly moble across sectors wthn each country and mmoble across countres; the market structure s perfect competton. 9 We analye rst the closed economy and then the open economy. In the latter, we ntroduce asymmetrc trade barrers, modeled as Samuelson s 7 In a smlar fashon, Melt (2005) showed that tar s and quotas may yeld welfare enhancng e ects n the presence of dynamc external economes of scale. hus, n that model, the nomnal exchange rate could a ect welfare, gven that ts e ects can be replcated through changes n tar s. 8 Feenstra (985) provded an exploraton of the polcy equvalence between a devaluaton and a tar cum-subsdy polcy n a 2-good ntertemporal small-open-economy model, where agents face cash-n-advance constrants. 9 Whle we could also consder only one sngle non-tradeable good, by assumng a contnuum of non-tradeable ndustres we preserve a symmetry wth the tradeable sector that allows to smplfy the results. Analogously, we could obtan smlar results from a model wth a dscrete number tradeable goods but, followng the lesson of Dornbusch, Fscher and Samuelson (977), we consder a contnuum of tradeable goods n order to represent ndustry productvtes wth a functon and use the tools of calculus, makng the model more tractable wth respect to the dscrete many-commodty case. Fnally, by explotng the nsght of Eaton and Kortum (2002) of usng spec c dstrbuton functons and the language of probablty to descrbe ndustry productvtes, we 4

6 ceberg costs. he resultng framework s a varant of the Eaton-Kortum model of trade (Eaton and Kortum, 2002; EK hereafter) n whch the non-tradeable-goods sector s explctly modeled. he reason for ths mod caton s that the nterplay between the tradeable-goods and the non-tradeable-goods sector plays a key role n our analyss. 2. Closed economy Consumer s problem s 8 < max c : c (j);c (j) + c Z wth: c m X ; subj. to: [c m (j)] m; Z dj, 8m ; 9 p m (j) c m (j) dj w L ; () where the superscrpts and dstngush non-tradeable from tradeable goods and denotes the country; c (c ) s the consumpton bundle of non-tradeable (tradeable) goods; c (j) (c (j)) s consumpton of the non-tradeable (tradeable) good j, where goods j are ndexed n the nterval [0; +); p (j) (p (j)) s the prce of the non-tradeable (tradeable) good j; w s the nomnal wage; L s labor supply; and ; > 0 are elastctes. he parameter n the nested CES functon () s the elastcty of substtuton between two tradeable goods and between two non-tradeable goods; governs the elastcty of substtuton between tradeable and non-tradeable goods. 0 hs frameworks allows for both elastc (; ) and nelastc demand (; < ). However, n the followng, we mplctly assume >, whle for we explctly consder both and <. Goods are produced wth constant returns to scale: q m (j) m (j) L m (j), m ;, where q m (j) s the quantty of good j of sector m produced by country, m (j) s the e cency (productvty) of that ndustry j, and L m (j) s the number of workers employed n that ndustry. Perfect competton mples p m (j) w m (j), for any, m, and j. Industry productvtes n the non-tradeable-goods and the tradeable-goods sector are respectvely descrbed by Z F rechet ( ; ) and Z F rechet ( ; ), wth ; > 0 and >. he parameters and are related to the rst moments of, respectvely, Z and Z : an ncrease n ( ) mples an ncrease n the share of non-tradeable (tradeable) goods that country produces more e cently. he parameter s nversely related to the dsperson of Z and Z. obtan even smpler theoretcal results. 0 he assumpton that the elastctes of substtuton for non-tradeable and tradeable goods are the same (equal to ) can be relaxed, at the cost of a slghtly more cumbersome algebra. If X F rechet (; ), then the moment of order k of X (whch exsts > k) s k [( k) ], where denotes Euler s Gamma functon. In an open economy, and are the the theoretcal counterparts, n a context wth many countres and a contnuum of goods, of the cardan concepts of absolute advantage (due to the close lnk of wth the mean of Z ) and comparatve advantage ( s closely connected wth the dsperson of Z and the gans from trade). For some background, see Eaton and Kortum (2002). 5

7 he key equatons of the autarky equlbrum (see Appendx A. for detals) are: 2 L L p p c c (2) ( ) (3) (4) A A Q A L + A L q w h p w ( ) + (5) ( ) + L (6) ( ) (7) where q and w are constants. 3 hese equatons show: the prce of the bundle of the tradeable goods relatve to that of the non-tradeable goods (equaton (2)); the se of the non-tradeable-goods sector relatve to the tradeable-goods sector (equaton (3)); the demand for the bundle of non-tradeable goods relatve to that of the tradeable goods (equaton (4)); aggregate productvty of the non-tradeable-goods sector relatve to that of the tradeablegoods sector (equaton (5)); 4 real GDP,.e. aggregate producton of non-tradeable and tradeable goods (equaton (6)); the real wage, whch measures welfare (equaton (7)). 2.2 Open economy epresentatve consumers are dentcal n all countres and solve the problem () descrbed above (analytc detals are n Appendx A.2). Internatonal trade s constraned by barrers modeled as Samuelson s ceberg costs: delverng one unt of a good from country n to country requres producng d n > unts of t for 6 n; whle d. 5 Iceberg costs nclude transportaton costs as well as all tar and non-tar barrers to trade. Prces. As n the standard cardan model, producton and trade are governed by comparatve advantages and each good s bought from the producer who sells t at the lowest 2 Here we are mostly nterested n the man macroeconomc aggregates, rather than n the sngle tradeable and non-tradeable goods, whose equlbrum quanttes and relatve prces are nevertheless determned n Appendx A.. o econome on the notaton, we report ratos not only for prces, but also for some quanttes, deferrng to Appendx A. for detals. 3 In partcular, q, B + ; where B denotes Euler s Beta functon, whle w + s equal to the constant n Eaton and Kortum (2002). 4 In the closed economy, t s easy to show that by aggregatng producton across ndustres n equlbrum, we obtan a functon Q m A m L m, where A m s the aggregate productvty (or labor productvty) of sector m and L m s the se of ths sector. In partcular, A m s gven by the rato between the moment of order and the moment of order of the productvty dstrbuton of sector m (see Fncell, Pagano and Sbraca, 20, for detals). 5 otce that by arbtrage d n < d nk d k 8 n, and k, so that trade barrers obey the trangle nequalty. 6

8 prce. Hence, the prce of a tradeable good j n country s p (j) mn w n d n n n (j) :hat s () p (j) w (j) f j s domestcally produced; () p (j) w nd n n (j), f j s mported from country n. he prce of a non-tradeable good j s smply p (j) w (j). Usng the Fréchet assumpton, t s easy to obtan the followng prce ndces: p w w p w w X n6 n w w nd n 3 5 (8) (9) where w, as before, represents a constant whch s only functon of the parameters and. herefore, the rato p p s 2 3 p p X w n n6 w nd n 7 5 (0) ot surprsngly, n the open economy the rato p p s lower than n autarky. Of course, p p s ncreasng n and d n, and decreasng n, n, and w w n. Average productvty. We can also compute the productvty dstrbuton of the survvng ndustres. Whle n autarky ths s descrbed by Z F rechet ( ; ), because all tradeable goods are produced at home, n the open economy ths s descrbed by a new random varable, call t Z;o, such that Z ;o F rechet ( ; ), 6 where + X n6 n w w n d n () (see Fncell, Pagano and Sbraca, 20, for detals). hus, the average productvty of the tradeable-goods sector of the open economy, E Z;o, s larger than that of the closed economy. 7 he "productvty gan" from trade s measured by 0 E Z;o E + X n w A w n d n n6. (2) hese gans n productvty comes entrely from a selecton mechansm as some goods that under autarky were produced less e cently and sold domestcally are now mported 6 In the case of two countres, t s easy to compute also the productvty dstrbuton of the exporters. hs s descrbed by a new random varable, that we can denote by Z ;e, such that Z ;e F rechet ( ;e; ), where ;e + n (w d nw n). Clearly, ;e >, whch mples that exporters are more productve than the rest of the survvng tradeable ndustres, a result consstent wth the "exceptonal export performance" documented by Bernard and Jensen (999). 7 In the open economy, the lnk between average productvty and real GDP s somewhat less straghtforward. 7

9 at lower prces. For ths reason the gans n productvty of (2) correspond exactly to the nverse rato between the prce of tradeable goods n the open economy (tradeable goods become cheaper n the open economy) and the prce of the same goods under autarky. Of course, the productvty dstrbuton n the non-tradeable-goods sector stays the same, because the producton of all non-tradeable goods remans domestc (n other words, Z ;o Z ). Snce the average productvty for non-tradeable goods does not change, the relatve prce ndex s unmod ed too. Sector ses. Expendtures on non-tradeable and tradeable goods are smply p c w L and p c w L, where L and L are the ses of the non-tradeable-goods and tradeable-goods sectors, and L p p + p L (3) whle L L L. Hence, the relatve se of the non-tradeable-goods sector s 2 3 L L p p X w n n6 w nd n 7 5 ( ) (4) ecall that n the open economy p s lower than n the closed economy. hen, equaton (4) suggests that the relatve se of the tradeable-goods sector after openng to trade depends on the exact value of the elastcty. If >, then the share of workers n the tradeable-goods sector rses after openng to trade, even though some domestc ndustres shut down. On the contrary, f <, then the share of workers n the tradeable-goods sector declnes, as some domestc tradeable ndustres are forced out of the market. otce that the case when < s the one emprcally relevant. In partcular, usng cross-sectonal data from the Internatonal Comparson Program, Stockman and esar (995) have estmated an elastcty of substtuton between tradeable and non-tradeable goods equal to 0:44. Followng ther study, dynamc stochastc general equlbrum models usually calbrate at around 0:5. Demand. From the soluton to the consumer s problem, we obtaned: c (p ) w L and c (p ) w L where p h p p p + p ( ). he man d erence wth respect to the autarky case s that, as dscussed above, the prce ndex p now ncludes the prces of both domestcally-produced and mported goods. elatve consumpton then s: 2 3 c c X w n n6 w nd n 7 5 ; (5) 8

10 clearly, thanks to the declne n p p, country consumes a larger share of tradeable goods after openng to trade. Expendture on non-tradeable and tradeable goods s smply: p c w L and p c w L. Before turnng to trade ows, t s worth to sum up the e ects of openng to trade on the tradeable-goods sector. Frst, the producton of some tradeable goods ceases (and these goods are mported). In partcular, country keeps producng the tradeable goods j such that (j) w max n n (j) (w n d n ) holds (and mports the others). Second, the goods (non-tradeables and tradeables) whose producton contnues to take place at home and that are sold only domestcally face a tougher competton (from foregn producers). hrd, the goods whose producton contnues and that are sold both domestcally and abroad meet a larger demand (less demand at home, but some addtonal demand from abroad). Fourth, the relatve se of the tradeable-goods sector depends on the elastcty : ths se ncreases (decreases) f > ( < ). rade. It s easy to compute the value of exports from country to country n, usng the fact that the tradeable good j made n country s exported n n f and only f w d n (j) < w n n (j). We only have to calculate the share of these goods: n X n (w d n ) X (6) X n k (w k d nk ) k and where X n s the value of exports from country to country n, and X n c n p n s the total expendture of country n on tradeable goods. For what concerns the e ect of trade barrers, note that the export share of country nto country n only depends on the barrer from country to country n, d n ; the barrer from country n to country, d n, whch contrbutes to determne prces (equaton (0)) only has an ndrect e ect through relatve wages. Wages, welfare, and real output. he model s closed by determnng relatve wages. Income n country, whch s w L, must be equal to the expendture for non-tradeable goods and the value of ts exports of tradeable goods around the world, ncludng at home (trade balance); that s: w L w L + P n X n. Hence, w L P n nx n from whch we obtan: 8 w L X n w n L n. (7) n6 Usng equatons (8)-(9), we can also compute the real wage as a measure of welfare: >< 9 ( ) ( ) > w p p ( ) >: X n6 n w w n d n whch s always hgher than n autarky, rrespectvely of the exact value of relatve wages or of the elastcty. 8 In the case of ero-gravty (d n d ), equaton (7) smpl es further to w w n L 2. n n L 9 5 >; (8)

11 In the specal case of ero-gravty (d n d n ), t s also easy to compute real GDP, whch s: 2 0 Q A L + A L q For the general case, see Appendx A X w 7 n 5 L n6 Equlbrum. o sum up, the full general equlbrum s gven by the soluton of equatons (8) (9), (3), (7), and (7), whch form a system of M 2 + 4M non-lnear equatons n M 2 + 4M unknowns (where M s the number of countres), whch are: p, p, L, w and n. he parameters of the model whch are,,,,, L, d n and d n can all be estmated or calbrated. Because of non-lneartes, there s no closed-form soluton. 9 evertheless, t s possble to smulate the model and analye some counterfactuals. For parameter changes such as those concernng trade barrers, however, the model s smple enough n that t allows to nd analytc results, as we show below. w n 2.3 Changes n trade barrers wth exble and stcky wages For smplcty, let us focus on the model wth two countres only (denoted wth and n). 20 o smulate the e ects of a deprecaton of country n a model that has no money, we consder an ncrease n the barrers to ts mports from country n (whch makes country s mports more expensve) and a symmetrc decrease n the barrers to ts exports to country n (whch makes country s exports cheaper). Proposton Under costant returns to scale and exble wages, a rse of d n to d 0 n d n and a smultaneous declne of d n to d 0 n d n, wth > ; does not produce any e ect on the equlbrum quanttes and the relatve prces. Such trade polces can be nterpreted as a deprecaton n the nomnal exchange rate from e to e > (where the exchange rate s expressed n terms of unts of country s currency for one unt of foregn currency). For gven wages w and w n, these changes n trade barrers reproduce exactly what happens rght after a deprecaton: f good j s mported, ts prce ncreases from w n d n n (j) to w n d n n (j); f good j s exported, ts prce decreases from w d n (j) to w d n (j); f good j s domestcally produced and sold only at home, ts prce does not change (and remans equal to w (j)). Let us dstngush two cases: stcky vs. exble wages. On mpact (that s before wages change), the ncrease n d n makes mports from country n more expensve, favorng mport substtuton and boostng the demand for both domestc tradeable and non-tradeable goods. By the same token, the declne n d n makes country s 9 esults by Alvare and Lucas (2007), however, grant that a soluton of the model exsts and s unque. 20 ecall that the model assumes trade balance and gnores tar revenues that trade barrers mght generate. It s, however, possble to extend the model both to ncorporate mbalances (see Dekle, Eaton, and Kortum, 2007) and to take revenue e ects nto account (see Eaton and Kortum, 2002). 0

12 exports cheaper, rasng foregn demand for domestc tradeable goods. Hence, after the deprecaton all ndustres n the economy (tradeable and non-tradeable) requre more workers, thanks to the rse n both domestc and foregn demand. Of course, wth exble wages and full employment, the rse n demand puts pressure on domestc wages. For the sake of smplcty, let us normale wages n country n, settng w n. Under full employment, w ncreases to exactly w 0 w. ote that ths rse n w restores all equlbrum quanttes and relatve prces to ther pre-deprecaton levels (see (4)). In other words, the result of the deprecaton s just a change n all the nomnal varables (wages and prces), so that all real varables (quanttes and relatve prces) return to the prevous equlbrum levels (for a formal argument, see Appendx A.4). Clearly, whether and when the pre-deprecaton equlbrum quanttes and relatve prces are reestablshed depends on the degree of exblty of wages and prces. Proposton 2 Under constant returns to scale and perfect competton, a rse of d n to d 0 n d n and a smultaneous declne of d n to d 0 n d n, wth > ; a ect the equlbrum quanttes and the relatve prces f wage are stcky over the short-medum run. he e ects wll vansh over the medum-long run as the wagee rgdty fades away. If, for nstance, unlmted labor supply n a low-ncome country prevents wages from rsng, then compettve gans reman. o make ths argument more formal, suppose that wages are stcky n country and, n partcular, suppose that they are set to a level w whch s too hgh to delver full employment. In other words, L s lower than the full employment level. 2 Hence, as before, the rse n d n makes mports from country n more expensve, favorshes mport substtuton, and ncreases the demand for domestc tradeable goods. By the same token, the rse n d n makes country s exports cheaper, augmentng foregn demand for domestc tradeable goods. hus, L ncreases (equaton (7)), because both n and ncrease. On the other hand, the ncrease n d n rases the prce of the bundle of tradeable goods p (because the goods that are stll mported and the new domestcally-produced tradeable goods are more expensve) and, therefore, demand for non-tradeable goods ncreases (equaton (5)). hus, employment rses n both sectors, boostng real GDP (for a formal argument see the appendx A.4). ote that the ntuton accordng to whch a deprecaton makes the tradeable-goods sector more compettve and rases the se of ths sector depends on the exact value of the elastcty of substtuton between tradeable and non-tradeable goods. If >, then the absolute se of the tradeable-goods sector rses due to the ncrease n employment (equaton (7)), but the relatve se of ths sector (wth respect to the non-tradeable-goods sector) declnes (equaton (4)). If <, then both the absolute and the relatve se of the tradeable-goods sector rse. 2 Broadly speakng, whle so far we have consdered L gven (set at ts full employment level) and w endogenous, now we consder the polar case n whch w s gven and L s endogenous.

13 3 Bertrand competton and ncreasng returns to scale We now remove the assumptons of perfect competton and constant returns to scale and replace them wth Bertrand competton and ncreasng returns to scale, followng the model of Grossman and oss-hansberg (200; GH hereafter). We consder two countres, that we keep on labelng wth and n. As n the prevous secton, there s a contnuum of tradeable goods, denoted wth j 2 [0; +). For the sake of smplcty, we now focus on tradeable goods only: n fact, we already know from the prevous secton that the drecton n whch workers ow n and out the tradeable-goods and non-tradeable-goods sectors depends solely on the change n the relatve prce of tradeables as well as on the exact value of the elastcty ; that s: L L p. p Hereafter, we follow GH closely, makng only one man departure. GH consder trade barrers that are ndustry spec c and symmetrc between countres. Here, nstead, we consder trade barrers that, as n the prevous secton, are dentcal across ndustres but not necessarly symmetrc across countres. 22 An extenson to trade barrers that are not symmetrc between countres nor dentcal across sectors, however, would be straghtforward usng GH and ths paper. 3. Autarky and free trade equlbra We retan the same notaton as n the prevous sectons and replace constant returns to scale wth ncreasng returns to scale by assumng q (j) (j) A j q (j) L (j), where A j s a functon wth A 0 j > 0, A00 j < 0, and elastcty smaller than. For example, the functon A j q (j) q (j) ( ), where >, used n Ether (982), ful lls these propertes. In models wth perfect competton and external economes of scale, such as Ether (982), ndustres are composed of small rms that act as prce takers and treat ndustryscale productvtes as gven. Frms correctly recogne ther own productvty when they make decsons about prce and quanttes, but do not perceve the possblty of a ectng ndustry output and prces. By assumng Bertrand competton, nstead, n ths model rms are no longer prce takers and perceve that, by rasng output and producng at a larger scale, they can abate average costs and shave prces. In each country, t s assumed that there are at least two dentcal potental producers of good j. hs assumpton, coupled wth Bertrand competton, s pvotal n returnng a unque equlbrum n a framework wth ncreasng returns to scale. he presence of many rms wth the same productvty mples ero pro ts and, under autarky, that rms charge a prce equal to ther average cost. In addton, f there are multple ntersectons between the demand and the cost curve (as t may happen wth ncreasng returns to scale) and, then, 22 In other words, GH consder trade barrers from country to country n for good j, d n (j), wth followng propertes: d n (j) d n (j) 8 (; n) and 8j, and d n (j) Q d n (j 0 ) 8 (; n) and 8j 6 j 0. Here, we consder trade barrers d n (j) such that d n (j) d n (j 0 ) d n 8 (; n) and 8j 6 j 0, and d n Q d n 8 (; n). 2

14 Fgure : Multple ntersectons of demand and cost curves potentally multple equlbra wth d erent prces and quanttes, the fact that each rm recognes that t rases ts market share by shavng the prce s su cent to select a unque equlbrum. he equlbrum s at the ntersecton between the demand and the cost curve charactered by the lowest prce and the hghest producton. hs result s llustrated by GH by means of a smple example. Suppose that the demand (DD) and cost (CC) curves have multple ntersectons, as n Fgure (whch corresponds to Fgure II n GH). ether E 0 nor E 00 represents an equlbrum, because f rms charge a prce assocated wth these ponts, then a devant rm can announce a lower prce for good j, get the whole market, and make postve pro ts. Hence, the equlbrum n each ndustry j s at the lowest ntersecton of the demand and cost curve, so long as the former cuts the latter from above. In ths equlbrum, an arbtrary number of rms make sales and earn ero pro ts. ote that further shavng the prce from the pont E n Fgure s not feasble, because the devant rm would not be able to cover ts costs. On the other hand, f the demand curve cuts the cost curve from below, then the prce of good j would tend to ero and ts producton to n nty. Imposng that the demand curve cuts the cost curve from above, then, grant exstence and unqueness of an ndustry equlbrum wth nte producton. Wth CES preferences, the demand of the tradeable good j s p c (j) w L p (j) p, (9) where p (j), p, w, and L are de ned n the prevous secton. he cost curve for the rm producng a quantty q (j) of good j s p (j) w L (j) q (j), where L (j) s de ned above. A su cent condton for the exstence of an ndustry equlbrum wth nte producton s A q (j) < for any q (j), where A q (j) 3

15 A 0 j q (j) q (j) A j q (j). 23 hs condton s always ful lled, for nstance, f > (as we assume n ths paper) and A j A j (as n Ether, 982). he autarky and the free trade equlbra can be easly determned. In the former, equlbrum quanttes are c (j) q (j), wth c (j) from equaton (9), whle relatve prces are: p w (j) (j) A j q (j), (20) where wages w could be normaled to one. Equatons (9) and (20) jontly determne equlbrum quanttes and relatve prces. 24 In general, ths compettve equlbrum s not Pareto e cent, due to the presence of producton externaltes. Pareto e cency s establshed, however, n the specal case n whch all ndustres bear a constant and common degree of scale economes (such as f A j A j 8j; see GH for detals). Wth free trade (d n d n ), demand s stll gven by equaton (9), whle the equlbrum prce of good j n countres and n (recall that the law of one prce holds, absent trade barrers) s p (j) p n (j) mn w (j) A j [~q (j)] ; w n n (j) A j [~q (j)], (2) where ~q (j) c (j) + c n (j), whle c (j) and c n (j) are the same as n equaton (9). A remarkable result of GH, then, s that, wth free trade, the patter of specalaton conforms to the pattern of comparatve advantages: good j s produced n the country that makes t at the lowest cost, once that costs are evaluated at the common scale ~q (j). In addton, there are no multple equlbra: the possblty of multple locatons for a gven ndustry dsappears when rms recogne that ther own average cost declnes as the scale of producton rses. 3.2 on-neglgble trade barrers We now turn to the emprcally relevant case of non-neglgble trade barrers. Solvng for the equlbrum becomes substantally harder wth respect to both the model wth ncreasng returns to scale and no trade barrers and the model wth constant returns to scale and trade barrers. elatve to the former, we have to account for the fact that domestc rms enjoy a cost advantage relatve to foregn rms as they can serve the domestc market wthout ncurrng trade barrers. Wth respect to the latter, here a rm servcng only the domestc market faces a dsadvantage relatve to rms that sell goods n both markets, because produces at a smaller scale. Lke GH, we focus on the somewhat smpler case of segmented markets, that s the case n whch rms can announce d erent prces n d erent geographc locatons. 25 Let us focus on country. In the equlbrum, some domestc ndustres export ther goods, others serve only the domestc market, whle other goods are mported. Let us analye these three cases, startng from exports. 23 Formally, ths s the same as the condton of "Marshallan stablty" (that s of stablty wth respect to perturbatons of equlbrum quanttes) nvoked by Ether (982). 24 Although one can always set one prce, usually nomnal wages, as the numerare (w ), we prefer to keep w (as both EK and GH), because t mproves the clarty of the arguments. 25 In the polar case of ntegrated markets, prce d erences across d erent geographc locatons cannot exceed the value of trade barrers. esults for ths case are qualtatvely smlar to those for segmented markets. 4

16 Suppose for a moment that rms gnore the possblty of targetng a sngle market, and only contemplate sellng n both markets. o devant rm n n can capture both markets f: w (j) A j [~q (j)] w d n + (j) A j [~q (j)] w n d n n (j) A j [~q c (j) (j)] w n n (j) A j [~q (j)] c n (j) 0. (22) he rst (second) addendum n (22) s the revenue that a rm of country n obtans by shavng slghtly the prce of good j n country (country n). 26 hs nequalty grants that a rm located n n does not pro t from sellng n both countres and n. Smple as t s, nequalty (22) marks a very sharp d erence wth respect to the model wth constant returns to scale. In partcular, rms n country n may have an ncentve to export good j n country even f they make negatve pro ts n that country ( rst addendum s negatve), provded that they make large enough postve pro ts at home. In ths case, country n sells good j n country n order to produce at larger scale, cut ts average cost, and make large enough pro ts at home. hs possblty s precluded n models wth constant returns to scale, because there s no cost advantage from producng at a hgher scale. 27 Inequalty (22) also suggests that country can protect ts domestc ndustres and encourage exports by lftng d n and lowerng d n whch s precsely what happens wth a currency deprecaton. 28 Even f (22) s sats ed, good j s not necessarly exported by country. A devant rm located n country n could stll undermne country s exports by targetng ts own market only. hs devaton s unpro table f and only f: w d n (j) A j [~q (j)] w n n (j) A j [c c n (j) 0. (23) n (j)] hus, good j s produced by country and sold both at home and abroad f and only f nequaltes (22) and (23) are sats ed. ote that, of these two condtons, we do not know whch one s more restrctve. If trade barrers vansh (d n ; d n! ), then condton (23) s the more restrctve one (and t collapses to condton (2)). For non-neglgble trade barrers, nstead, t may be condton (22) that determnes whether country exports good j. hs s gong to have a crucal mportance when we analye the e ects of a currency deprecaton. 26 ecall that country s average costs of makng good j are w (j) A j ~q (j) at home, and w d n (j) A j ~q (j) n country n; country n s average costs are, respectvely, w nd nn (j) A j ~q (j) n country, and w nn (j) A j ~q (j) at home. 27 ecall that Bertrand competton n the presence of many dentcal rms mples ero pro ts, as n the model wth perfect competton and constant returns to scale. oughly speakng, however, wth economes of scale there are two ways of makng ero pro ts. As wth constant returns to scale, one way s to set prces equal to average costs n all markets. Another way s to set prces lower than average costs n some markets, and hgher than average costs n some other markets. 28 hs possblty s more than just a theoretcal speculaton. In the early post-world War II perod, one of Italy s most mportant manufacturng companes, FIA, sold cars at a loss n foregn markets. he aggressve export strategy adopted by Vttoro Valletta, FIA general manager at that tme, was feasble because pro ts could be made n the domestc market, also thanks to the hgh tar barrers mposed to foregn producers (see Echengreen, 2007, pp. 2-6, and Faur, 996). 5

17 Let us now turn to non-exported goods. Good j s produced by and sold only at home f and only f the followng three condtons are sats ed: () nequalty (22) holds (.e. country n does not have an ncentve to sell n both and n); () nequalty (23) does not hold (.e. country n has an ncentve to serve ts own market); and (): " # w (j) A j c (j) w (j) A j [~q c (j) (j)] w n w d n + n (j) A j [c n (j)] (j) A j [~q c n (j) 0 ; (24) (j)] when nequalty (24) s sats ed, rms n country do not have an ncentve to devate and capture both markets. Inequalty (24) can be volated even whle the rst two condtons are sats ed. In ths case, there s no equlbrum n pure prcng strateges, but there s at least one symmetrc equlbrum n mxed strateges. 29 In ths equlbrum, a rm n country n sells good j at the unt cost w n n (j) A j c n (j) n the domestc market, whle rms n country randome among two prcng strateges: one yelds only local sales, the other yelds sales n both markets (for a characteraton of these mxed strateges, see GH). 30 here are stll two possbltes left. One s that country produces and sells domestcally good j, whle rms n country n adopt a mxed prcng strategy (that s the recprocal of the prevous case). he other s that good j s mported by country (that s the recprocal of the rst case). In partcular, country mports good j f and only f: () nequalty (22) does not hold (.e. rms n country n have ncentves to sell n both and n ); and () " # w n d n w n (j) A j [~c (j)] (j) A j c (j) c (j) 0, (25).e. no rm n country has ncentve to devate usng a prcng strategy that targets the domestc market. Clearly, mports wll be lower, the hgher the mport barrer d n (because rms n n have less ncentves to sell n and rms n have more ncentves to target at least ther domestc market). 3 Fgure 2 shows the possble allocaton of the producton of one good j for d erent values of (j) n (j) n both the cases on non-neglgble trade barrers and free trade. Wth trade barrers, country exports good j wth a pure prcng strategy, provded that ts relatve productvty s su cently hgh; produces and sells at home and abroad good j usng a mxed prcng strategy for somewhat lower levels of relatve productvtes; produces and sells good j only domestcally for stll lower levels of relatve productvtes, whle country n produces 29 he presence of mxed prcng strateges s not surprsng gven the fact that rms are no longer prce takers. For an early exploraton of mxed prcng strateges n nternatonal trade wth Bertrand competton (and ntegrated markets), see Venables (994). 30 Symmetrc equlbra can be more than one. hese multple equlbra, however, share the same qualtatve features, even though they d er n ther mxng probabltes. In partcular, n all these equlbra good j s ether produced and exported by country, or t s not traded. 3 Appendx A.3 rearranges the condtons under whch the producton of good j occurs n country, n country n, or n both countres (wth ether pure or mxed prcng strateges). 6

18 Fgure 2: Allocaton of producton for one ndustry, relatve productvtes, and trade barrers the same good and ether sells t both at home and abroad wth a mxed strategy, or sells t only at home; mports good j for the lowest levels of (j) n (j) (Fgure 2, upper panel). ot all these possbltes necessarly coexst. he smultaneous presence of the ve ones n the upper panel of Fgure 2, n fact, depends on ndustry spec c factors (such as the degree of ncreasng returns to scale) as well as trade barrers. For some goods, for nstance, mxed strateges and strateges targetng only the domestc market may not be feasble. In partcular, when trade barrers declne, the three central ones n the upper panel of Fgure 2 shrnk, up to the pont n whch, under free trade, only complete specalaton s feasble: each good j s ether mported, or t s domestcally produced and sold both at home and abroad (Fgure 2, lower panel) Changes n trade barrers: a nomnal deprecaton What are the e ect of the same trade polces analyed under constant returns to scale n the presence of postve economes of scale at ndustry level? What happens when productves and economes of scale are heterogeneous across ndustres? Proposton 3 Wth ncreasng returns to scale at ndustry level, a rse of d n to d 0 n d n and a declne of d n to d 0 n d n, wth >, a ect permanently the equlbrum quanttes and the relatve prces. Some producers wll bene t more than others dependng on the extent of the economes of scale n ther ndustry. 7

19 On mpact (that s, before wages start rsng), more goods are exported and less goods are mported nto country. In fact, for what concerns exports, both nequaltes (22) and (23) are ful lled also for smaller values of (j) n (j) (.e. for relatvely less productve rms of country ). Smlarly, for what concerns mports, the recprocal of (22) and nequalty (3) are not ful lled only for smaller values of (j) n (j) (.e. now only less-e cently produced goods are mported). In general, n ndustres n whch all the ve ones n the upper panel of Fgure 2 coexst, all the four one-borders move leftwards. How do wages respond to the change n trade barrers? Smlarly to what happens n the model wth constant returns to scale, wages tend to rse. Wth ncreasng returns to scale, however, there are some major d erences. he most mportant s that an ncrease n relatve wages to w 0w0 n w w n does not restore the prevous equlbrum (the one before the change n trade barrers). It s easy to check that nequalty (22) keeps holdng for smaller values of (j) n (j) also after such a change n relatve wages. 32 In other words, more goods wll be exported also after a rse n relatve wages by %. By the same token, the same nequalty wll contnue to be volated only for smaller values of (j) n (j), so that less goods wll be mported. he ntuton for ths result s the followng. Wth ncreasng returns to scale, a deprecaton by ( ) % cuts rms average costs by more than ( ) %, thanks to the addtonal cost gans that come from the economes of scale. hs s mportant, n partcular, for the rms (at home and abroad) that target both the domestc and the foregn market, whose success n ths strategy depends on whether nequalty (22) s sats ed. In partcular, less foregn rms nd t convenent to target both markets, favorng mport substtuton (f foregn rms keep servng at least ther own market) and exports (f they shut down). On the other hand, more domestc rms of country have an ncentve to start servng both the home and the foregn market, further boostng exports. elatve wages, however, would rse above w w n. Moreover, t s easy to show that there s no rse n relatve wages that can restore the prevous equlbrum. Agan, the ntuton s straghtforward. Because the degree of ncreasng returns to scale are d erent across ndustres (A j Q A j 0 f j 6 j 0 ), the declne n average costs after the deprecaton connected to rse n output s also d erent across ndustres. However, even though ncreasng returns to scale were the same across ndustres, ndustres are nevertheless heterogeneous n productvtes. Startng from d erent productvty levels, the declne n average costs would then be d erent across ndustres. Hence, the pre-deprecaton equlbrum quanttes and relatve prces cannot be restored across all ndustres (for a formal argument, see Appendx A.4). After the deprecaton, the economy converges to a new equlbrum wth hgher (relatve) wages, but wth some rms that can now access the foregn markets, and some goods that are no longer mported and are domestcally produced. How does the se of the tradeable sector change? ecall that, under the standard assumpton that <, workers ow to the sector n whch the rse n prces s larger. Of course, productvtes do not change n the non-tradeable sector and the prces of the tradeable goods that were already domestcally produced also do not change. On the other hand, the 32 Indeed the rst addendum, representng the revenue that a rm n country nobtans by shavng the prce of good j n country, results multpled by but the second addendum, representng the revenues obtaned by a rn n country n shavng the prce of good j n ts own country, stay unchanged. 8