Quaderni di Storia Economica

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1 Quadern d Stora Economca (Economc Hstory Workng Papers) Real Exchange Rates, rade, and Growth: Italy by Vrgna D Nno, Barry Echengreen and Massmo Sbraca October 20 number 0

2 Quadern d Stora Economca (Economc Hstory Workng Papers) Real Exchange Rates, rade, and Growth: Italy by Vrgna D Nno, Barry Echengreen and Massmo Sbraca Paper presented at the Conference Italy and the World Economy, Rome, Banca d Itala 2-5 October 20 Number 0 October 20

3 he purpose of the Economc Hstory Workng Papers (Quadern d Stora economca) s to promote the crculaton of prelmnary versons of workng papers on growth, fnance, money, nsttutons prepared wthn the Bank of Italy or presented at Bank semnars by external speakers wth the am of stmulatng comments and suggestons. he present seres substtutes the Hstorcal Research papers - Quadern dell'uffco Rcerche Storche. he vews expressed n the artcles are those of the authors and do not nvolve the responsblty of the Bank. Edtoral Board: MARCO MAGNANI, FILIPPO CESARANO, ALFREDO GIGLIOBIANCO, SERGIO CARDARELLI, ALBERO BAFFIGI, FEDERICO BARBIELLINI AMIDEI, GIANNI ONIOLO. Edtoral Assstant: ANONELLA MARIA PULIMANI. prnt

4 Real exchange rates, trade, and growth: Italy Vrgna D Nno (Banca d Itala) Barry Echengreen (Unversty of Calforna, Berkeley) Massmo Sbraca (Banca d Itala) Abstract What s the relatonshp between real exchange rate msalgnments and economc growth? And what e ect, f any, dd undervaluatons or overvaluatons of the lra/euro have on Italy s growth? We address these questons by presentng, rst, three man facts: () there s a postve relatonshp between undervaluaton and growth; () ths relatonshp s strong for developng countres and weak for advanced countres; () these results tend to hold for both the pre- and the post-world War II perod. Buldng a smple analytcal model, we explore channels through whch undervaluaton may exert a postve e ect on real GDP. We assume that productvty s hgher n the tradeable-goods than n the non-tradeable-goods sector, and examne the roles of market structure, scale economes and wage exblty n channellng resources from the latter to the former sector, ncreasng exports and real GDP. We then turn to Italy and verfy emprcally that, as the theory suggests, undervaluaton has postvely a ected ts exports. Undervaluaton has been helpful, n partcular, to ncrease the exports of hgh-productvty sectors, such as most manufacturng ndustres. Fnally, we descrbe the msalgnments of the lra/euro snce 86, analyze ther determnants and draw the mplcatons for Italy s economc growth. JEL class caton: F30, F0, O0, N00 Keywords: Currency msalgnments, Compettveness, Italy, Export, Growth Quadern d Stora Economca n. 0 Banca d Itala October 20

5 Contents Introducton I Exchange rates, trade and economc growth 6 2 Exchange rates and growth: cross-country evdence 6 3 Exchange rates and growth: a vew from trade theory 3 3. Perfect competton and constant returns to scale Closed economy Open economy Changes n trade barrers wth exble and stcky wages Bertrand competton and ncreasng returns to scale Autarky and free trade equlbra Non-neglgble trade barrers Changes n trade barrers II Italy Undervaluaton of the lra/euro and Italy s exports Export growth Value of exports Extensve margn he lra/euro and Italy s economc growth Real exchange rate and msalgnments of the lra/euro Some caveats Msalgnments of the lra/euro An overvew of the msalgnments Man determnants of the msalgnments Implcatons for Italy s growth III Appendx 50 A Data 50 B Proofs for the model wth constant returns to scale 50 B. Closed economy B.2 Open economy C rade equlbrum wth ncreasng returns to scale 53

6 Introducton Italy s nteractons wth Europe and the world and the role of the external sector n ts growth and development are, lke those of any other country, complex and multfaceted. In ths paper we focus on one spec c facet: the real exchange rate, or the prce of goods and servces n Italy relatve to other countres. We utlze the real exchange rate as a wndow onto the polces and crcumstances shapng the mpact of external condtons on domestc economc development. Why focus on the real exchange rate, one of many d erent prces a ectng the allocaton of resources and the growth of the economy? For one thng, a substantal lterature connects the real exchange rate to economc development and growth. Balassa (964) s an early and n uental statement of the mportance of a compettvely valued real exchange rate n supportng exports and, n turn, of ther role for economc growth. More recently, smlar arguments have been made by, nter ala, Acemoglu, Johnson, Robnson and hacharoen (2003), Easterly (2005), Galndo, Izquerdo and Montero (2006), Bhalla (2007), Johnson, Ostry and Subrmanan (2007), Echengreen (2008a) and Rodrk (2008). hese recent studes also o er emprcal evdence, generally from cross-country regressons on post-980 data, suggestng a connecton runnng from the real exchange rate to economc growth evdence that tends to be most robust for developng countres. What are the determnants of the real exchange rate? Snce Balassa (964) and Samuelson (964), t has been wdely observed that the real exchange rate vares wth economc development. Whle there s a tendency for the prce of tradeable goods to be equalzed across countres, the relatve prce of non-tradeable goods wll tend to be lower n developng countres. In more advanced countres, where labor productvty and wages are hgher, the relatve prce of non-tradeable goods wll smlarly tend to be hgher. he Internatonal Comparson Program, producer of the Penn World able, of whch we make use n ths paper, s predcated on these nsghts (see Kravs, 986). At the same tme, the mappng from per capta ncome to the real exchange rate s not mechancal. In open economes lke Italy, when the domestc demand for tradeable and nontradeable goods rses, the prce of tradeable goods wll stll be ted down by the law of one prce, at least to a rst approxmaton. But the prce of non-tradeable goods wll be drven up by the addtonal demand and the real exchange rate wll apprecate. Relatve to the benchmark where domestc aggregate demand equals supply (trade s balanced), t wll become "overvalued." Smlarly, wage stckness and other frctons, that prevent relatve prces from adjustng followng a change n the nomnal exchange rate, produce temporary undervaluaton or overvaluaton of the real exchange rate. As the textbooks tell us (vz Dornbusch 980), a varety of polces a ectng the balance of aggregate supply and demand wll tend to n uence the real exchange rate. An expansonary 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 Mary Amt, Jonathan Eaton, Phlppe Martn, Fabrzo Onda, Paolo Pesent, Gann onolo and semnar partcpants at the Brxen Workshop 20, SADBa (Peruga Conference) and the New York Fed for many useful comments. We are also grateful to Alberto Ba g, Clauda Borghese, Clare Gordano, Denns Qunn, Sandra Natol, Angelo Pace and Alan aylor for ther help n the constructon of the data set. E-mal: vrgna.dnno@bancadtala.t, echengr@econ.berkeley.edu, massmo.sbraca@bancadtala.t

7 scal polcy that stmulates domestc spendng wll produce real apprecaton and be assocated wth problems of overvaluaton. Captal controls wll lmt the contrbuton of captal n ows to demand, avodng those problems of overvaluaton. Interventon n the foregn exchange market wll prevent a sharp shft n the nomnal exchange rate, whatever ts source, from producng a sudden and uncomfortable change n the real exchange rate. As we wrte ths, a surge of captal n ows creatng pressure for real apprecaton and rasng concerns about overvaluaton s causng emergng-market economes to respond wth all three polces ntervenng n the foregn exchange market, mposng controls, and tghtenng scal polcy conscous as they are of the advantages of a compettvely valued exchange rate. hs s a dstnctly modern perspectve, however. How should we thnk about real exchange rate determnaton n the XIX century, before the advent of dscretonary scal polcy, captal controls, and sterlzed nterventon? Decsons of what monetary regme to adopt and at what level to set the domestc prce of gold or slver can stll a ect the real exchange rate f competton n goods or labor markets s mperfect and relatve prces are slow to adjust. Captal n ows and out ows, whch rase and lower demand, wll stll a ect the real exchange rate (as the lterature remnds us: see Fenoaltea, 988). Labor market dstortons that slow the reallocaton of labor from the low-productvty sheltered sector to the hgh-productvty export sector, of the sort descrbed by Lews (954), wll tend to depress the relatve prce of home goods, resultng n a persstently undervalued exchange rate. And by a ectng the real exchange rate, these factors a ect the development of the export sector and the growth of the economy. As we wll show, there s evdence of the operaton n Italy of all these mechansms n the era snce un caton. Some of them, we wll suggest, are pvotal for understandng the contours of the country s economc development n the post-un caton perod. We start by revstng and broadenng the evdence provded by Rodrk (2008) on the relatonshp between economc growth and undervaluaton, where the latter s measured by the real exchange rate, corrected for the Balassa-Samuelson e ect. We extend Rodrk s analyss n three drectons. Frst, we use a more recent release of the Penn World able, whch ncludes sharp revsons for those countres, lke Chna, that experenced very hgh rates of growth and very hgh degrees of undervaluaton. Second, we consder a varety of d erent measures of undervaluaton. hrd, and most mportant, we expand the tme span (Rodrk covers only the post-world War II years), gong back to as far as 86. hs analyss ponts to three man conclusons. he rst two support Rodrk s man ndngs: there s a postve relatonshp between undervaluaton and economc growth; and whle ths relatonshp s strong, and both statstcally and economcally sgn cant for developng countres, t s weak for advanced countres. In addton, we nd that these results hold regardless of the tme perod: n partcular, they tend to hold for the pre- and the post-world War II perod. We then examne, by developng a smple analytcal model, channels through whch undervaluaton may exert a postve e ect on growth. Our key assumpton s that productvty s hgher n the tradeable-goods sector than the non-tradeable-goods sector consstent wth Lews tenet about the productvty d erental between the modern and tradtonal sectors. We nvestgate the roles of market structure, scale economes and wage exblty n channelng resources to the hgh-productvty tradeable-goods sector and rasng GDP. In the models of trade that we consder, we replcate the e ects of a nomnal deprecaton of the currency wth an ncrease n the barrers to mports and a symmetrc declne n the barrers 2

8 to exports. hs captures the essence of what a real deprecaton does: t makes exports cheaper and mports more expensve. 2 We are comforted about the soundness of ths assumpton by the results from the baselne model. By extendng the Eaton-Kortum model of trade (Eaton and Kortum, 2002) to encompass the non-tradeable-goods sector, we show that wth perfect competton, constant returns to scale, and perfectly exble wages, a deprecaton does not have any e ect on equlbrum quanttes and relatve 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 rse, of the same extent as the deprecaton, n nomnal wages. hs model, n fact, assumes that wages and product prces are perfectly exble, so that, rght after the deprecaton, the economy jumps to a new equlbrum wth hgher wages and product prces. In other words, a nomnal deprecaton does not produce a real deprecaton. he real exchange rate cannot be undervalued nor overvalued: followng the nomnal deprecaton, the rse n wages and product prces mmedately restores pre-deprecaton equlbrum quanttes and relatve prces. he 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. Wth stcky wages and standard assumptons about the elastcty of substtuton between tradeable and non-tradeable goods, an undervalued currency channels resources to the tradeable 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 (such as, persstence of "unlmted supply of labor" to the tradeable sector, extent of unemployment, frequency of foregn exchange rate nterventons, presence of captal controls, etc.). As the adjustment takes place, however, gans n margnal costs are reversed and the deprecaton has no real e ects n the long run. A nomnal deprecaton may exert persstent real e ects, also f we replace the assumptons of perfect competton and constant returns to scale wth Bertrand competton and ncreasng returns. 3 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. hese 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. 4 A deprecaton by %, n fact, cuts rms 2 For nstance, n dscussng the current relatonshp between the U.S. and Chna, Krugman (200a) asserts 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 subsdzng exports" (Krugman 200b, emphass added). 3 We are not the rst to unvel persstent real e ects of changes n the nomnal exchange rate n the presence of ncreasng returns to scale. Baldwn (988) and Baldwn and Krugman (989), for nstance, prove that these e ects arse n the presence of sunk costs. Smlarly, Krugman (987) shows these e ects n the presence of dynamc external economes of scale. (More recently, Meltz (2005) shows that tar s and quotas yeld welfare enhancng e ects n the presence of dynamc external economes of scale.) Our results, however, are more general than those n the prevous lterature, because they draw on the presence of ncreasng returns to scale only, and do not requre that costs are sunk nor that external economes of scale are dynamc. 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, analyzed by Ether (982), yelds several "pathologes," such as multple equlbra, that hamper the possblty of makng comparatve statcs. Second, the model wth Bertrand competton and constant returns to scale, developed by Bernard, Eaton, Jensen 3

9 average costs by more than %, thanks to the addtonal cost gans comng from the economes of scale. Hence, a rse n relatve wages by % 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 hghproductvty tradeable-goods sector and, then, nto a rse n real GDP. hese gans obtan wth the real exchange rate set at ts equlbrum level and are even larger durng the transton to the new equlbrum, when the currency s undervalued (owng to the same mechansms descrbed above). Our analyss also explans why a growth strategy based on currency undervaluaton or seral nomnal deprecatons n the presence of ncreasng returns to scale cannot be pursed ad n ntum. Wth perfect competton and constant returns to scale, wages and prces eventually adjust, o settng the deprecaton. Wth Bertrand competton and ncreasng returns to scale, the compettve gans declne wth ndustry output and, then, become ncreasngly smaller as the economy develops. Fnally, the mantaned assumpton of a postve productvty d erental between the tradeable-goods and non-tradeable goods sectors whch s reasonable f these sectors broadly correspond to what Lews (954) dubbed as modern and tradtonal sectors, as t happens n many low-ncome countres may not be approprate n advanced economes where non-tradeable products nclude, for nstance, hgh-productvty nancal servces. We then turn to Italy and verfy whether, as the theory suggests, undervaluaton supported growth by ncreasng exports. We consder d erent features of Italy s exports: ther growth rate, ther nomnal and real value, and ther extensve margn (number of dstnct goods sold abroad). he results show that undervaluaton has postvely a ected all these features. Yet, these postve e ects do not take place homogeneously across ndustres. Plausbly, undervaluaton does not rase exports of prmary products. It s, nstead, especally helpful to ncrease the exports of hghproductvty sectors such as machnery and transport equpment, as well as other manufactures. Fnally, we focus on the undervaluaton of the lra/euro and, n lght of the prevous results, we assess ts connecton wth Italy s growth and trade. Fgure shows two measures of undervaluaton for Italy n the perod 86-20: one s blateral, calculated wth respect to the US dollar (for whch we also provde a 5% con dence band); the other s computed aganst a trade-weghted basket of currences (see Secton 5 for detals). Evdently, Italy bene ted from a strongly undervalued currency durng the key catchng-up phase of Durng ths crucal perod, Italy recorded a very strong economc growth. Its real GDP per capta trpled, almost closng the ncome gap wth respect to the major European countres. he currency was 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 exchange rate also n the presence of exble wages, whle Bertrand competton s needed to show these e ects wth a tractable model. 5 Although relatve wages could rse by more than %, there s no rse n relatve wages that can restore the pre-deprecaton equlbrum. 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. Even f ncreasng returns to scale were the same across ndustres, however, 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. 4

10 Fgure : Measures of undervaluaton of Italy s currency: () blateral undervaluaton (vs. the US) 5% confdence nterval trade weghted ndex.4 Source: authors calculatons. () Data n logs. A postve (negatve) value corresponds to undervaluaton (overvaluaton). he two shaded areas correspond to the perods and broadly at equlbrum n and agan undervalued n the 970s and 980s (based on the trade-weghted ndex). In both these perods, Italy s growth was sustaned, and somewhat better than that of the man European countres. From the early 990s, a perod of very slow growth, the currency was overvalued and the exchange rate provded a negatve, albet small, contrbuton to growth. On the other hand, Italy s currency was undervalued n and durng the nterwar perod, when growth rates were, n contrast to the predctons of the theory, very low. Economc, nancal and poltcal nstablty n the rst 30 years of the new regn and the Great Depresson n the nterwar perod prevented the country from takng advantage of ts undervalued currency. In general, these results seem to con rm the hypothess that an undervalued currency s a facltatng condton, but not an engne, of economc growth (Echengreen, 2008a). he rest of the paper s organzed as follows. Secton 2 provdes the man stylzed facts about undervaluaton and growth. Secton 3 presents a theoretcal model whch llustrates how undervaluaton may a ect growth by boostng exports and reallocatng labor toward the tradeable sector. We then turn to Italy and, n Secton 4 we examne the e ect of undervaluaton on Italy s exports. In Secton 5, we compute and descrbe a measure of undervaluaton of the lra/euro n the perod 86-20, analyze ts determnants, and then draw the mplcatons for Italy s economc growth. 5

11 Part I Exchange rates, trade and economc growth 2 Exchange rates and growth: cross-country evdence We start by revstng the evdence provded by Rodrk (2008), for the perod followng World War II, that undervaluaton s postvely related to the growth of real GDP per capta. We then ask whether the same relatonshp also holds n earler years. he key varable needed to compute the real exchange rate and, n turn, undervaluaton s the purchasng power party (PPP) rate, that s the value of the exchange rate that would yeld the same prce level as n the reference country, n general the Unted States, when expressed n a common currency (usually US dollars). he real exchange rate s de ned as the rato between the market and the PPP exchange rate, usually measured n term of unts of domestc currency per one US dollar, so that an ncrease means deprecaton. A real exchange rate above one means that goods and servces are cheaper n a country than n the Unted States. hs measure, by tself, does not capture a msalgnment of the exchange rate. As t has been well known snce Balassa (964) and Samuelson (964), non-tradeable goods are cheaper n developng than n advanced countres, re ectng the hgher productvty and, then, the hgher nput costs n the latter. herefore, measures of msalgnment are bult by correctng for ths Balassa-Samuelson e ect. he correcton nvolves regressng the real exchange rate on a varable related to the degree of development of each country (typcally, real GDP per capta); undervaluaton s then de ned as the d erence between the observed and the predcted real exchange rate. In ths way, undervaluaton captures the prce d erental between the Unted States and the country n excess of what can be predcted by consderng the country s level of development. 6 Followng Rodrk (2008), undervaluaton can be obtaned by runnng the regresson: rer P W n;t = a + by pc n;t + c t + " n;t, () where rern;t P W, the log of real exchange rate from the Penn World able (PW) of country n at tme t, s computed as rer P W n;t = ln xrat n;t P P P n;t, wth xrat n;t and P P P n;t denotng, respectvely, the nomnal and the PPP exchange rate vs-àvs the US dollar; y pc n;t s the log of real GDP per capta; c t s a set of tme dummes; " n;t the 6 here are other possble methodologes to measure the equlbrum level of the real exchange rate. For nstance, followng Nurske (945), the equlbrum real exchange rate can be de ned as the relatve prce of tradable to domestc non-tradable goods that acheves nternal (full employment) and external equlbrum (trade balance). Msalgnment s then computed as the resdual from a regresson of the real exchange rate on a set of varables that a ect prces over the long run. hese varables usually nclude not only real GDP per capta, but also, among the others, trade openness, government consumpton, and terms of trade (see, n partcular, Lee, Mles-Ferrett, Ostry, Prat and Rcc, 2008, for a recent survey of the methodologes utlzed by Internatonal Monetary Fund). Berg and Mao (200) show that ths d erent methodology to measure undervaluaton yelds very smlar results (see for nstance, Fgure 2 n Berg and Mao, 200). Not surprsngly, Berg and Mao (200) and MacDonald and Vera (200) con rm that estmates of the relatonshp between undervaluaton and growth are robust to the method chosen to measure the former. 6

12 resdual; and a; b 2 R. Undervaluaton s then de ned as: u P W n;t = ^" n;t = rer P W n;t crer P W n;t. In the second step, one can examne whether undervaluaton a ects growth by estmatng: g n;t = n + y pc n;t + up W n;t + d t + n;t, (2) where g n;t s the growth rate of real GDP per capta, y pc n;t controls for the ntal condtons and d t for tme spec c unobserved e ects, n are xed e ects, n;t s the resdual, and ; 2 R. Because t takes tme for msalgnments to exert ther e ect on growth, Rodrk uses ve-year averages of all the varables. herefore, each tme t denotes non-overlappng ve-year perods. In ths paper we follow the same methodology as Rodrk (2008), extendng the analyss n three man drectons. Frst, we use a more recent release of the PW: the verson 6.3, from Heston, Summers and Aten (2009), that covers the perod , whch we extend to 2009 usng the May release of PW verson 7.0; 7 we also use some alternatve data sources for prces, exchange rates and real GDP per capta. hs s more than a just techncal pont, because the PW undergoes frequent and often extensve revsons of PPP-adjusted rates (see Johnson, Larson, Papageorgou and Subramanan, 2009, for a crtque). Many authors, for nstance, recommended usng other versons of the PW as a robustness test (see the secton General Dscusson of Rodrk s paper). he two most recent releases, n partcular, ental strong revsons for those very countres, lke Chna, experencng the hghest rates of growth and degrees of undervaluaton (partly leadng the result that undervaluaton s postvely related to growth). For example, n the perod (the one common to Rodrk s as well as our data set), the new data suggests that Chna s average rate of growth of real GDP per capta s 4:6%, as opposed to 5:5% n the prevous release (verson 6.2). he ntal 950 level of the same varable s 70% larger n the newer than n the older release. 8 Second, we consder both corrected and "weakly" corrected measures of undervaluaton. In partcular, two alternatve de ntons of the real exchange rate are: rer W P I n;t = ln xrat n;t W P I us;t W P I n;t rer CP I n;t = ln xrat n;t CP I us;t CP I n;t where W P I n;t s the wholesale prce ndex (or producer prce ndex) of country n at tme t, CP I n;t s the consumer prce ndex of country n at tme t, and the subscrpt us denotes the Unted States. Followng Woodford (2008), we can plug (alternatvely) rern;t W P I and rern;t CP I nto 7 he verson 7.0 of the Penn World able has undergone very frequent revsons: a rst verson was released n March 20, another one n Aprl and a thrd one n May, when we were revsng our estmates. hs verson, however, stll had several problems, so we kept usng the verson 6.3 and exploted the verson 7.0 only to extend the data set to 2009 (usng changes of the man varables). A fourth verson of the data set has been released n June 20, too late to be consdered for ths paper. 8 he revson for Chna s so strong that the two latest releases of the Penn World able make avalable two d erent country seres: one (Chna Verson ) s smlar to the seres contaned n the verson 6.2 of the table; the other (Chna Verson 2), whch s recommended by the Penn World able producers and the one used n our emprcal analyss, ncorporates stronger revsons. 7

13 the emprcal model (2) n the place of u P n;t W. Even though rern;t W P I and rern;t CP I measure only the real exchange rate, and not the degree of msalgnment, accordng to Woodford (2008) both these measure do ental a form of correcton (although "weak"), once they are plugged nto the growth regresson (2). he reason s that ths model ncludes country xed e ects that, n turn, can account for the d erent growth rates due to factors such as the Balassa-Samuelson e ect. hs form of correcton s "weak," because t neglects changes n the country s level of development durng the sample perod. hus, t s more precse for shorter tme perods (n whch changes n a country level of development are small) or for countres n whch real GDP per capta s more stable. Note, also, that both these rates can be corrected to obtan and u CP n;t I, as resduals of the estmates of (), where rern;t P W s replaced wth, respectvely, rern;t W P I and rern;t CP I. o sum up, n our emprcal analyss we use ve d erent measures of undervaluaton: the corrected measures u P n;t W, u W n;t P I measures of undervaluaton, denoted wth u W P I n;t and u CP I n;t, and the "weakly corrected" measures rer W P I n;t and rer CP I n;t. 9 Our thrd and most mportant extenson concerns the tme span of the sample, whch we brng back to as far as 86, the tme of Italy s un caton. We gather data on exchange rates vs-à-vs the US dollar, wholesale prce ndces and consumer prce ndces (from several sources), as well as real GDP per capta (from Maddson, 200), for 34 countres from 86 to 939 (detals are n Appendx A). We then merge these data wth the PW to obtan a data set spannng almost 50 years. Equaton () s estmated, as n Rodrk, usng OLS when the dependent varable s rern;t P W. he estmated coe cent for y n;t s equal to 0:26 and t s strongly sgn cant (Rodrk nds a smlar coe cent of 0:24). 0 he negatve sgn means that, as expected, hgher ncome per capta reduces the degree of undervaluaton for a gven real exchange rate. When the dependent varable s rern;t W P I or, alternatvely, rern;t CP I, we estmate a panel model wth random e ects (see footnote 8) and the correspondng coe cents are 0:6 and 0:29, respectvely, wth only the latter strongly sgn cant. Equaton (2) s estmated usng a varety of methods (lnear panel wth xed e ects and GMM), for d erent samples of countres and tme perods. able reports the results of the estmates for the whole tme span (.e. from 86 to 2009), d erent sets of countres, and 9 Unlke rern;t P W, both rern;t W P I and rern;t CP I are only ndex numbers and can descrbe the behavor over tme of the real exchange rate, but do not provde any nformaton about ts level. Yet, these varables can stll be ncluded nto a growth regresson lke equaton (2), as long as the estmated spec caton contans country unobserved e ects. Smlarly, they can be used as dependent varables nto a spec caton lke () n order to derve corrected measures of undervaluaton, as long as we account for level-d erences n the base year by ncludng xed or random e ects. In partcular, we chose a random e ect model,whch s not rejected by a Hausman test, when we estmate equaton () wth rer W P I n;t and rer CP I n;t as dependent varables. 0 Notce that a queston concerns the estmaton method, because real exchange rates and real GDP per capta are lkely to be non-statonary and co-ntegrated. hen, spec catons lke () are usually estmated wth panel contegrated technques, rather that wth OLS wth tme dummes as n Rodrk and n ths paper. However, as long as the relevant co-ntegrated varable s ncluded nto the spec caton (), the OLS method yelds super-consstent estmates, even though standard errors may not be well-behaved n small samples. Whle panel bootstrap methods could return precse small-sample estmates of standard errors, gven the very large sample sze of our sample (and the fact that provng that ncome per capta a ects the real exchange rate s not the purpose of ths study, but a result of a fty-year-old lterature), we can safely use OLS. 8

14 able : Economc growth and undervaluaton ( ) () All Countres Developng Countres u CPI u WPI rer CPI rer WPI u CPI u WPI rer CPI rer WPI y t [7.77]*** [3.79]*** [7.27]*** [3.56]*** [5.85]*** [.83]* [5.50]*** [.6] undervaluaton [2.69]*** [.80]* [2.43]** [.08] [2.8]*** [3.24]*** [3.]*** [2.24]** Constant [9.50]*** [3.84]*** [8.40]*** [2.86]*** [4.30]*** [.95]* [3.38]*** [.32] Country fxed effects Yes Yes Yes Yes Yes Yes Yes Yes Perod dummes Yes Yes Yes Yes Yes Yes Yes Yes Observatons Number of countres R squared () Estmates of equaton (2) usng OLS. Robust t statstcs n brackets; * sgn cant at 0%, ** at 5%, *** at %. d erent measures of undervaluaton. he coe cent on undervaluaton s always postve. Corrected measures of undervaluaton always return very sgn cant coe cents, whle weakly corrected measures do not return a sgn cant coe cent n one case (rern;t W P I on all countres). When estmates are restrcted to the sample of developng countres only de ned as the countres n whch real GDP per capta s below 6,000 US dollars (2005 nternatonal dollars) the estmated coe cents for undervaluaton tend to be larger and more sgn cant than for the full sample. he estmated coe cents for undervaluaton, when measured by u W n;t P I and u CP n;t I, are n the -3% range. hus, a 30% undervaluaton, as n Italy n the early 950s, would rase real GDP by.5% to 4.5% over ve years (.e. the annual rate growth would rse by 0.3% to 0.9%). In other words, results from the estmates are not only statstcally sgn cant, but also economcally sgn cant. Notce, also, the coe cent for the ntal condtons s always sgn cant wth the predcted negatve sgn. When we restrct the sample to the post-world War II perod, we can consder also estmates n whch undervaluaton s measured wth u P n;t W, whch s the most precse ndex (able 2). All the coe cents are postve, rrespectvely of the sample of countres. However, only the coe cents for the full sample and the sample of developng countres are strongly sgn - cant (2-3%), whle the coe cent for advanced countres s consderably smaller (0.3%) and not sgn cant. It s mportant to note that we do not have a contnuous seres for consumer and wholesale prce ndces (whch would have mpled usng data that span through the World War years, see Secton 5.. for a dscusson). Our tme seres are avalable n three d erent wndows: 86-93, , and , each of them wth a d erent base year (900, 929 and 2000, respectvely). Hence, when estmates are performed for the whole sample perod, we have ncluded three sets of country xed e ects, one for each of the three tme wndows. he reason s that f equaton (2) s the true data generatng process, then we should expect the same slopes across tme wndows but d erent ntercepts (due to the rebasement) for each country. In other words, the three d erent e ects are meant to capture the d erent degree of undervaluaton n the three base years and, as a consequence, the d erent growth rates on those years. hus, the three d erent sets of xed e ects catch those d erent ntercepts, whle stll provdng a sngle estmate for the slope. 9

15 able 2: Economc growth and undervaluaton after World War II ( ): undervaluaton based on Penn World able () All countres Developng countres Advanced countres y t [6.24]*** [4.47]*** [8.6]*** undervaluaton [3.4]*** [3.99]*** [0.48] Constant [8.33]*** [5.08]*** [.40]*** Country fxed effects Yes Yes Yes Perod dummes Yes Yes Yes Observatons Number of countres R squared () Estmates of equaton (2) usng OLS; undervaluaton measured by u P W n;t. Robust t statstcs n brackets; * sgn cant at 0%, ** at 5%, *** at %. he pcture s essentally the same when we consder the other ndces of undervaluaton (able 3). All the coe cents for the full sample as well as the sample of developng countres are strongly sgn cant across all measures (except rern;t W P I ), and magntudes are agan the same (- 3% for the corrected measures). Smlarly the hgher dmenson of the coe cent for developng countres s also con rmed. able 4 reports the results for the perod before World War II. he coe cents are stll postve, even though somewhat smaller (up to 2%). he estmates are less precse due to the dramatc declne n the number of observatons. In ths subsample, all the countres have an ncome per capta below the threshold of 6,000 US dollars. If we choose a d erent, lower threshold, to separate the more advanced from developng countres (2,000 US dollars, whch s close to the medan ncome for ths subsample), we nd that another fact tends to be con rmed: the e ect of undervaluaton on economc growth tends to be stronger for less developed countres. 2 Whle these results hghlght the postve correlaton between undervaluaton and growth, they do not allow to assess the drecton of causalty. For ths, one would need to nd a varable correlated wth the real exchange rate but exogenous to economc growth (an nstrument). In order to obtan at least some prelmnary ndcatons about ths queston, we estmate a dynamc panel model wth the d erence GMM method of Arellano and Bond (99), wth addtonal 2 For the ndcator based on consumer prces, we also estmate a verson of equaton (2) on a country-by-country bass. It emerges that the poorer countres n the sample (Brazl, Japan, Portugal, Italy, Span and Norway, that are the countres wth ncomes per capta below 2,000 U.S. dollars at the turn of the century) all feature postve (albet nsgn cant) coe cents. On the other hand, the rcher countres n the sample (the Unted Kngdom and Australa, wth an ncome per capta close to or above 4,000 U.S. dollars) dsplay negatve coe cents. he negatve correlaton across countres between the estmated coe cent and real GDP per capta s con rmed across the full sample. 0

16 able 3: Economc growth and undervaluaton after World War II ( ): alternatve ndces of undervaluaton () All countres Developng countres u CPI u WPI rer CPI rer WPI u CPI u WPI rer CPI rer WPI y t [7.80]*** [3.74]*** [7.28]*** [3.5]*** [5.67]*** [.47] [5.32]*** [.25] undervaluaton [2.72]*** [.73]* [2.55]** [.05] [2.85]*** [2.77]*** [3.7]*** [2.03]* Constant [.30]*** [5.35]*** [9.95]*** [4.66]*** [6.56]*** [2.6]** [5.70]*** [.45] Country fxed effects Yes Yes Yes Yes Yes Yes Yes Yes Perod dummes Yes Yes Yes Yes Yes Yes Yes Yes Observatons Number of countres R squared () Estmates of equaton (2) usng OLS. Robust t statstcs n brackets; * sgn cant at 0%, ** at 5%, *** at %. able 4: Economc growth and undervaluaton before World War II (86-939) () All Countres Less Developed Countres (2) u CPI u WPI u CPI u WPI y t [4.69]*** [5.34]*** [3.86]*** [3.43]*** undervaluaton [0.2] [.45] [0.83] [0.92] Constant [4.75]*** [5.34]*** [3.85]*** [3.43]*** Country fxed effects Yes Yes Yes Yes Perod dummes Yes Yes Yes Yes Observatons Number of countres R squared () Estmates of equaton (2) usng OLS. Robust t statstcs n brackets; * sgn cant at 0%, ** at 5%, *** at %. (2) Real ncome per capta up to 2,000 US dollars (2005 nternatonal dollars).

17 able 5: Economc growth and undervaluaton (dynamc panel) () Whole sample All Countres Whole sample Developng countres (2) Whole sample Less developed countres (3) Pre WW II perod All Countres u CPI u WPI u CPI u WPI u CPI u WPI u CPI u WPI y t [8.80]*** [6.63]*** [5.05]*** [2.5]** [4.5]*** [0.59] [5.37]*** [2.94]*** ln(gdp t ) [5.05]*** [0.70]*** [8.30]*** [5.2]*** [3.55]*** [.26] [.03] [0.85] undervaluaton [3.40]*** [3.53]*** [3.26]*** [2.82]*** [.90]* [4.57]*** [0.38] [0.22] Country fxed effects Yes Yes Yes Yes Yes Yes Yes Yes Perod dummes Yes Yes Yes Yes Yes Yes Yes Yes Observatons Number of countres Sargan test P value AR (2) P value () Estmates of equaton (2) usng OLS. Absolute value of z statstcs n brackets; * sgn cant at 0%, ** at 5%, *** at %. (2) Real ncome per capta up to 6,000 US dollars (2005 nternatonal dollars). (3) Real ncome per capta up to 2,000 US dollars (2005 nternatonal dollars). lags of GDP growth and undervaluaton as nstruments for the lagged dependent varable and the ndependent varable. 3 Usng lagged values as nstruments shows that the coe cents for undervaluaton are postve and hghly sgn cant for the whole sample perod. Coe cents tend to be hgher for less developed countres (ncome below 6,000 or 2,000 US dollars) and smaller and nsgn cant for the sole pre-world War II perod (for whch the Sargan test warns that we do not have vald nstruments). he elastcty of growth wth respect to currency msalgnments goes from to 4% on the whole sample perod, and from 0.4% for the perod precedng World War II. Overall, three man facts emerge from ths emprcal analyss, wth the rst two of whch con rmng Rodrk s man ndngs: () there s a postve relatonshp between undervaluaton and economc growth; () ths relatonshp s strong, and both statstcally and economcally sgn cant for developng countres, whle t s weak for advanced countres; () these results tend to hold for both the post- and the pre-world War II perod. Elastctes of economc growth wth respect to undervaluaton are generally comprsed between -4% (both for the full sample and for developng countres); they are as low as 0.3% for advanced countres. Results also provde at least suggestve evdence that causalty runs from undervaluaton to growth. But what s the mechansm? In the next secton, we analyze ths queston and develop the followng hypothess. Un- 3 In our sample, the Sargan test tended to accept the null that the error term s uncorrelated wth the nstruments when we estmated the model usng D erence GMM and to reject t when we used System GMM. For an extensve set of estmates usng post 980 data wth System GMM, however, see MacDonald and Vera (200). All ther estmates con rm the man result that the relatonshp between undervaluaton and growth s postve and the drecton of causalty s lkely to run from the former to the latter. 2

18 dervaluaton acts by enhancng the prce compettveness of tradeable goods and by shftng resources from the non-tradeable-goods to the tradeable-goods sector. o the extent that productvty n the latter sector s hgher, undervaluaton would successfully rase GDP growth. 3 Exchange rates and growth: a vew from trade theory We assume that the tradeable-goods sector has a hgher productvty than the non-tradeablegoods sector and we nvestgate the condtons under whch a currency deprecaton s successful n shftng labor from the latter to the former, thereby rasng output. Our workng assumpton s that, n the real models of trade consdered n ths secton, we can replcate the e ects of a nomnal deprecaton wth a declne n the barrers to the country s exports, coupled wth a symmetrc rse n the barrers to the country s mports. We consder rst a framework wth perfect competton and constant returns to scale, whch s a mod ed verson of the model of Eaton and Kortum (2002). hen, we turn to a model wth Bertrand competton and constant returns to scale, à la Grossman and Ross-Hansberg (200) Perfect competton and constant returns to scale We consder an economy wth the followng features: a tradeable-goods and a non-tradeablegoods 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. 5 We analyze rst the closed economy and then the open economy. In the latter, we ntroduce asymmetrc trade barrers, modeled as Samuelson s 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 nontradeable-goods sectors has a key role n our analyss. 4 Both constant and ncreasng returns to scale are consdered to be emprcally relevant n many contexts. Antweler and re er (2002), usng data from 7 countres, provde the somewhat Solomonc result that at least one thrd of all good-producng ndustres are characterzed by ncreasng returns to scale (nduced by plant-level or ndustry-level externaltes), whle at least one thrd of all goods-producng ndustres dsplay constant returns to scale. Focusng on the manufacturng sector (often used as a proxy for the tradeable-goods 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. 5 Whle we could also consder only one sngle non-tradeable good, by assumng a contnuum of non-tradeable ndustres we preserve some symmetry wth the tradeable sector, whch allows to smplfy the results. Analogously, we could obtan smlar results from a model wth only two tradeable goods but, followng the lesson of Dornbusch, Fscher and Samuelson (977), we consder a model wth a contnuum of tradeable goods n order to represent ndustry productvtes wth a functon and use the tools of calculus, smplfyng the analyss neatly 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 obtan even smpler theoretcal results. 3

19 3.. Closed economy Consumer s problem s 8 < max c N : c (j);cn (j) + c Z wth: c m = X ; subj. to: [c m (j)] m=n; Z dj, 8m = N; 9 = p m (j) c m (j) dj w L ; (3) where the superscrpts N and dstngush non-tradeable from tradeable goods and denotes the country; c N (c ) s the consumpton bundle of non-tradeable (tradeable) goods; cn (j) (c (j)) s consumpton of the non-tradeable (tradeable) good j, where goods j are ndexed n the nterval [0; +); p N (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 (3) 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. 6 hs frameworks allows for both elastc (; ) and nelastc demand (; < ). However, n the followng, we mplctly assume >, whle for we explctly consder both and <, the latter beng the emprcallyrelevant case (see Stockman and esar, 995). Goods are produced wth constant returns to scale: q m (j) = z m (j) L m (j), m = N;, where q m (j) s the quantty of good j of sector m produced by country, z 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 =z m (j), for any, m, and j. Industry productvtes n the non-tradeable-goods and the tradeable-goods sector are respectvely descrbed by Z N F rechet (N ; ) and Z F rechet ( ; ), wth N ; > 0 and >. he parameters N and are related to the rst moments of, respectvely, Z N and Z : an ncrease n 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 N and Z.7 6 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. 7 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 Rcardan 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). 4

20 he key equatons of the autarky equlbrum (see Appendx B. for detals) are: 8 L N L p p N c N c = = N N = N = (4) ( )= (5) = (6) A N A = N Q = A N L N + A L = q N = w h = p w N ( )= + = (7) ( )= + = L (8) =( ) (9) where q and w are constants. 9 hese equatons show: the prce of the bundle of the tradeable goods relatve to that of the non-tradeable goods (equaton (4)); the sze of the non-tradeablegoods sector relatve to the tradeable-goods sector (equaton (5)); the demand for the bundle of non-tradeable goods relatve to that of the tradeable goods (equaton (6)); aggregate productvty of the non-tradeable-goods sector relatve to that of the tradeable-goods sector (equaton (7)); 20 real GDP,.e. aggregate producton of non-tradeable and tradeable goods (equaton (8)); 2 the real wage (equaton (9)), that, gven L, measures welfare (utlty s w L =p n the equlbrum) Open economy Representatve consumers are dentcal n all countres and solve the same problem (3) descrbed above (analytc detals are n Appendx B.2). Prces. As n the standard Rcardan model, producton and trade are governed by comparatve advantages and each good s bought from the producer who sells t at the lowest prce. Hence, the prce of a tradeable good j n country s: () p (j) = w =z (j), f j s domestcally produced; () p (j) = w nd n =zn (j), f j s mported from country n, where d n 8 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 B.. o economze on the notaton, we report ratos not only for prces, but also for some quanttes, deferrng to Appendx B. for detals. 9 In partcular, q = +. B +, ; where B denotes Euler s Beta functon, whle w = 20 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 sze 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). 2 Real GDP s de ned as Q = Q N + Q, where Q m = R q m (j) dj for m = N;. hs de nton resembles the P one used by statstcal agences, whch proxy real GDP wth the "quantty ndex": p (j) q 0 (j) = P p (j) q (j), where p and q are good prces and quanttes at tme 0, whle q0 are good quanttes at tme. 5