Tradability, Productivity, and Understanding International Economic Integration

Transcription

1 FEDERAL RESERVE BANK OF SAN FRANCISCO WORKING PAPER SERIES Tradability, Productivity, ad Uderstadig Iteratioal Ecoomic Itegratio Paul R. Bergi Uiversity of Califoria at Davis, ad NBER ad Reuve Glick Federal Reserve Bak of Sa Fracisco September 2005 Workig Paper The views i this paper are solely the resposibility of the authors ad should ot be iterpreted as reflectig the views of the Federal Reserve Bak of Sa Fracisco or the Board of Goverors of the Federal Reserve System.

2 Tradability, Productivity, ad Uderstadig Iteratioal Ecoomic Itegratio Paul R. Bergi Departmet of Ecoomics, Uiversity of Califoria at Davis, ad NBER Reuve Glick Ecoomic Research Departmet, Federal Reserve Bak of Sa Fracisco This draft: September 6, 2005 Abstract: This paper develops a two-coutry macro model with edogeous tradability to study features of iteratioal ecoomic itegratio. Recet episodes of itegratio i Europe ad North America suggest some surprisig observatios: while quatities of trade have icreased sigificatly, especially alog the extesive margi of goods previously ot traded, price dispersio has ot decreased ad may eve have icreased. These observatios challege the usual uderstadig of itegratio i the literature. We propose a way of recocilig these price ad quatity observatios i a macroecoomic model where the decisio of heterogeeous firms to trade iteratioally is edogeous. Trade is shaped both by the ature of heterogeeity -- trade costs versus productivity -- ad by the ature of trade policies -- cuts i fixed costs versus cuts i per uit costs like tariffs. For example, i cotrast to tariff cuts, trade policies that work maily by lowerig various fixed costs of trade may have large effects o etry decisios at the extesive margi without havig direct effects o price-settig decisios. Whether this etry raises or lowers price dispersio depeds o the type of heterogeeity that distiguishes the ew etrats from icumbet traders. JEL classificatio: F4 We thak semiar participats at the Lodo School of Ecoomics, Uiversity Pompeu Fabra, Uiversity Autooma Barceloa, Europea Cetral Bak, Istitute for Advaced Studies i Viea, Birkbeck College, the Uiversity of Califoria at Berkeley, ad the Aual Meetigs of the America Ecoomic Associatio. The views expressed below do ot represet those of the Federal Reserve Bak of Sa Fracisco or the Board of Goverors of the Federal Reserve System. Part of this research was udertake while Bergi was a Jea-Moet Fellow at the Europea Uiversity Istitute. P. Bergi / Departmet of Ecoomics / Uiversity of Califoria at Davis/ Oe Shields Ave. / Davis, CA 9566 USA prbergi@ucdavis.edu, ph (530) , fax (530) R. Glick / Ecoomic Research Departmet / Federal Reserve Bak of Sa Fracisco / 0 Market Street, Sa Fracisco, CA 9405 USA reuve.glick@sf.frb.org, ph (45) , fax (45)

3 I. Itroductio Iteratioal macroecoomics is iterested i the issue of market segmetatio ad itegratio for several reasos. Firstly, the broad literature o pricig to market ad deviatios from purchasig power parity relies upo the assumptio that atioal markets are segmeted, so that firms have the ability to charge differet prices i differet coutries. Secodly, such failures i the law of oe price are fudametal to our theories of real exchage rate behavior. Thirdly, give recet policies aimed at promotig iteratioal market itegratio i Europe ad North America, there is heighteed iterest i uderstadig the implicatios of such itegratio policies. Recet experieces with policy reforms have provided some ew evidece regardig market segmetatio which is difficult for our stadard ope ecoomy macro models to explai. I particular, we refer to the Caada-U.S. Trade Agreemet (CUSTA) ad the North America Free Trade Agreemet (NAFTA) aimed at promotig ecoomic itegratio i North America i the early 990s, ad the Sigle Market Program (SMP) i the early 990s ad the Europea Moetary Uio (EMU) i 999 desiged to further cosummate ecoomic itegratio i Europe. Oe set of observatios ivolves quatities: trade volume seems to respod more sigificatly tha stadard models predict, ad much of the icreased trade volume occurs i the form of ew goods that were ot previously traded, rather tha icreased itesity i trade of previously traded goods (Kehoe ad Ruhl, 2002). This is ofte referred to as the extesive margi of trade. A secod set of observatios refers to prices. Recet research by Egel ad Rogers (2004) suggests that average deviatios from the law of oe price deviatios for may groups of traded goods i Europe stopped covergig i 999 ad may eve be divergig. A similar coclusio is suggested i other research for North America, where price covergece appears to have stopped i the early 990s, with divergece i may classes of traded goods. These price ad quatity observatios preset a challege to our stadard models of iteratioal itegratio, ad this paper proposes a way of recocilig them. It provides a illustratio of how macro models that edogeize firms decisios to trade ca be useful. The results also shed a ew light o the debate over how best to measure the degree of iteratioal itegratio: i terms of trade quatities or prices. I geeral, our ope ecoomy macro models are ill-suited for studyig the process of ecoomic itegratio, sice they ted to take market segmetatio as give, simply assumig firms ca set differet prices i differet atioal markets. Stadard trade theory also has difficulty here. Recet advaces have bee made i modelig the costs of trade, ad how they determie the decisio of firms to export (see Melitz, 2003; Ghiroi ad Melitz, 2004; Kehoe ad Ruhl, 2002; ad Ruhl 2003). Emphasis i this literature has bee placed o heterogeeity of firms i terms of productivities, where oly the more productive firms fid it profitable to eter the export market. But uiform trade costs i such models imply that there is a uiform price wedge for goods across coutries. However, evidece idicates that there is a great deal of

4 heterogeeity i price wedges (Crucii, Telmer, ad Zachariadis, 200), as well as i the trade costs that drive them (Hummels, 999, 200; Aderso ad va Wicoop, 2003). To address this fact, we emphasize the role of heterogeeity i the trade cost dimesio. To be more precise, this paper formulates a two-coutry macro model where each coutry has a cotiuum of moopolistically competitive producers which must choose whether to sell i the foreig market i additio to the domestic market. This decisio is affected by two types of real trade frictios: oe i the form of per-uit (iceberg) trade costs which ca vary by good, ad the other a fixed cost of iteratioal trade which does ot deped upo the quatity traded ad does ot vary by good. The first type of cost is motivated by tariffs ad trasportatio costs, as discussed above; the secod type reflects establishmet costs or the cost of learig to deal with a foreig laguage or legal system. While iceberg costs have bee favored i recet macroecoomic studies of segmetatio (Obstfeld ad Rogoff, 2000), fixed costs are essetial if some goods are to be otraded uder the assumptio of moopolistic competitio. A firm will participate i the iteratioal market oly if it ca geerate additioal positive profits by doig so. I equilibrium, the traded goods will be those with low trade costs or high productivity. The paper s fidigs arise from two importat distictios raised by our model. First, what type of trade cost is the liberalizatio policy reducig: per uit costs like tariff rates or the various fixed costs of trade? Secod, which of the two types of heterogeeity distiguishes ew etrats ito trade from icumbet traders: trasport costs or productivity? The first ad most geeral theoretical fidig of the paper is that it is icorrect to assume that policies promotig itegratio i terms of trade volume must also promote price covergece. If prices are set uder moopolistic competitio as a markup over per-uit costs, icludig per-uit trade costs for exports, the a policy that reduces per-uit tariffs ideed will have a direct impact i price-settig behavior i the foreig market ad will reduce pricedispersio betwee the coutries. But fixed costs do ot eter the price-settig decisio i a stadard model of moopolistic competitio, so policies workig maily through fixed costs of trade do ot affect foreig prices here. Cosequetly, such trade policies may ot reduce iteratioal price dispersio. The model also implies that these two types of policies have very differet implicatios for quatities: with fixed cost reductios workig much more strogly through the extesive margi of ew goods ot previously traded. A secod fidig is that if ew trade arises largely at the extesive margi, it may lead to the type of price dispersio observed recetly. For example, suppose that goods are heterogeeous i terms of their per-uit trade costs such as trasportatio costs. The the ew goods beig traded systematically will have higher per-uit costs tha previously traded goods. After all, this is precisely the reaso why these goods were previously otraded. These will be goods with higher price wedges betwee atioal markets, ad their etry ito trade will raise the average iteratioal price wedge, ad thereby a mea-squared error measure of price dispersio. Sectio II presets empirical observatios of recet trade liberalizatios ad other policies promotig greater ecoomic itegratio i Europe ad North America. Sectio III develops a 2

5 ope ecoomy macro model with edogeous trade. Sectio IV discusses aalytically how the model ca be used to recocile price ad quatity observatios, where Sectio V uses umerical simulatios to address theoretical ambiguities. Sectio VI cocludes by drawig implicatios for the recet experieces of Europe ad North America, ad by raisig questios for future research. II. Empirical Observatios A. Price Evidece Foremost amog the empirical observatios we wish to highlight is the fidig that trade liberalizatios eed ot lead to covergece of price levels across atioal markets. There is a extesive ad active literature measurig failures i the law of oe price across atioal markets. Oe fidig over much of this literature is that the law of oe price fails also for tradable goods (Egel, 999). Aother is that there is a good deal of heterogeeity i the degree of price deviatios at the disaggregated level, with about as may goods uderpriced as overpriced (Crucii et. al, 200). The Europea case is especially surprisig, give that a ostesible goal of moetary uio was to promote price trasparecy ad arbitrage. Of special iterest here is recet research by Egel ad Rogers (2004), who fid that while there was price covergece withi the Eurozoe i the early to mid 990s, there has bee o covergece sice the adoptio of the euro i 999. We replicate ad exted this result i Figure to iclude more recet data. The figure is costructed from price level data for idividual goods from , usig data from the Ecoomist Itelligece Uit for about 00 traded as well as 38 otraded items, coverig 8 cities withi the Eurozoe. 2 Data collectors at each locatio are give discretio to idetify represetative examples of particular classes of goods (such as wome s cardiga sweaters or 00-cout aspiri bottles) Sice each observatio is draw from a potetially wide ad evolvig rage of varieties available i the market, the prices ca be affected by ew etry. The EIU sales literature states that its price measures are affected by the opeig up of markets ad deregulatio: As govermets welcome foreig ivestmet ad ope up their markets to iteratioal compaies, so the variety ad availability of imported products improves. Followig Egel ad Rogers, the metric used i Figure is the mea squared error of (the relative logs of) product item prices across cities i the Euro zoe, averaged over groups of goods. The figure shows the chages i price dispersio for differet product categories ad This result is distict from micro-level studies that fid covergece to the law of oe price i particular idustries for arrowly defied goods, such as brads of autos ad televisios (see Imbs et al., 2004; Goldberg ad Verbove, 2005). It is also a distict issue from the evidet lack of covergece i Europea atioal iflatio rates: for example, diverget iflatio rates may still be associated with covergece i price levels if the higher rates of chage are i coutries that iitially had low price levels. 2 This data set is becomig widely used i the literature. I additio to Egel ad Rogers (2004), see also Crucii ad Shitai (2004) for a leadig applicatio. 3

6 subperiods. 3 Oe observatio is the heterogeeity i price deviatios amog differet categories of goods. But eve more strikig is that of the eight categories of traded goods, seve show greater price dispersio i the period sice 998. The fact that this fidig cotiues to hold i our exteded data set through 2004 idicates it is ot just a temporary byproduct of trasitio, as prices were coverted to ew currecy uits at the oset of the moetary uio. Other recet papers support this geeral coclusio for Europe. The Europea Commissio (2004) fids that price idices i the most expesive ad least expesive coutries were covergig i the early 990s, but stopped covergig i the middle of the decade. Baye et al. (2002) examie the effects of EMU o a small set of homogeous goods that shoppers buy olie, mostly electroic goods, ad fid that EMU had little effect o price dispersio. Lutz (2002) cosiders a small set of goods with oly post-999 price survey data ad also fids that EMU has ot reduced price dispersio sigificatly. I our empirical ivestigatio, we fid that further isight is obtaied by distiguishig betwee core ad peripheral coutries withi the Euro zoe, as reported i the top pael of Table, where we deote Filad, Irelad, Portugal, ad Spai as peripheral coutries, ad Austria, Belgium, Frace, Germay, Italy, Luxemburg, ad the Netherlads as the core coutries. This distictio makes sese based o both geography ad the extet to which lowered trade barriers have had time to foster stroger cross-coutry trade liks. The former coutries are located i the outer areas of Europe. Moreover, Irelad joied i 973, Portugal ad Spai i 986, ad Filad i 995, well after the core members formed the Europea Uio i Cosistet with the message of Figure, the top pael of Table shows that overall price dispersio for traded goods i Europe fell over the period , was flat for , ad the rose over after the formal adoptio of the euro. What is of mai iterest i Table is that the icrease i price dispersio durig the latter period was greatest amog the core coutries. I fact, for these coutries the icrease i price dispersio sice 998 has almost fully offset the declie i price dispersio experieced i the early 990s. I cotrast, the peripheral coutries experieced a much greater declie i price dispersio i the early 990s ad a much weaker icrease i dispersio with core coutries sice adoptio of the euro. We also fid similar coclusios for price itegratio whe we examie the effects of trade liberalizatio i North America, followig the CUSTA trade liberalizatios betwee Caada ad the U.S. i 989, Mexico s comprehesive trade liberalizatio ad ecoomic reforms begu i the late 980s, ad Mexico eterig ito NAFTA i The bottom pael 3 Egel ad Rogers (2004) fid that this result holds, eve after cotrollig for relative wages, relative icomes, VAT taxes, slow adjustmet of prices, etc 4 Austria did ot joi the Europea Uio util 995, but is treated as a core coutry because of its logstadig trade liks with Germay ad its cetral geographic positio withi Europe. 5 Although NAFTA etailed a immediate reductio i various tariffs ad otariff barriers whe it was eacted i 994, most of the trade reforms uder the agreemet ivolved gradual liberalizatio. Cosequetly, ecoomic itegratio i North America has bee a gradual process over a exteded period of time.. 4

7 of Table reports calculatios of chages i price dispersio i North America based o EIU data for idividual product items i 2 U.S. cities, 4 Caadia cities, ad Mexico City. Price dispersio declied cosiderably i the early 990s, but icreased sharply after 994 at the time of the adoptio of NAFTA. 6 While the Mexica crisis of most probably played a role i the upward movemets ivolvig Mexico, it does ot explai why price dispersio betwee U.S. ad Caada also rose. Other studies support this fidig of greater price dispersio i North America sice the adoptio of NAFTA. See Globerma ad Storer (2003) for a more detailed discussio ad aalysis of this literature. I particular, Egel ad Rogers (998) fid that ay price covergece durig the 990s was ot due to NAFTA. Further, sice 994 they foud that cross-border price variability icreased for some very tradable categories, such as clothig ad footwear, where oe would expect that trade liberalizatio should have bee most likely to ecourage price covergece. The coclusio arisig from these recet studies is that price covergece may be limited followig policies ecouragig itegratio, ad furthermore, there eve appears to be a tedecy for price divergece i may tradable groups of goods. Oe possible explaatio suggested by past theoretical literature is the presece of sticky goods prices ad fluctuatios i omial exchage rates. Earlier work by Egel ad Rogers (996) foud a role for such a explaatio, but that accouts for less tha half of the LOP deviatios. Clearly, we eed to fid other types of sources for price deviatios. Further, this explaatio caot explai icreased price divergece across Europea coutry borders after the EMU elimiated currecy fluctuatios i 999. A secod possible explaatio is that price covergece i Europe ad North America stopped because goods market itegratio had bee completed by that poit ad price covergece had reached its atural limit. However, the presece of price divergece rather tha just a lack of covergece argues agaist this explaatio. Further, evidece of sigificat additioal goods market itegratio i terms of trade flows suggests that itegratio had ot reached its limit previously. We tur to this quatity evidece ext ad draw additioal lessos. B. Quatity Evidece Despite the lack of evidece of market itegratio i terms of price covergece, there does seem to be evidece that trade liberalizatio promotes itegratio i terms of icreased trade volume. A importat aspect of this fidig is that much of the ew trade is i the form of ew goods ot previously traded. Evidece of this extesive margi of trade is documeted i Kehoe ad Ruhl (2002), who study six differet trade liberalizatios, icludig the EU Sigle Market ad NAFTA. They defie growth at the extesive margi as growth i the share of 6 Sice the EIU data are oly available from 990 o, we were uable to examie earlier price dispersio movemets withi North America. 5

8 exports by products accoutig for 0 percet or less of total trade prior to liberalizatio. 7 They fid that iitially these least traded product categories experieced the largest icreases i export shares followig trade liberalizatio. For example, as show i Table 2, Europea itegratio durig the 990s was associated with a icrease i this share from 0 percet to 7 percet i the case of Swede, 4 percet of Italy, ad 9 percet of Portugal. Adjustig these results for the icrease i total trade, oe ca compute that the exteral margi accouted for more tha 00 percet of the icreased trade of Swede ad Italy ad almost 90 percet of that of Portugal with their EU trade parters. Extesive margi effects are sigificat i the case of NAFTA itegratio durig the 990s as well. The extesive margi share rose from 0 percet to 5 percet i the case of U.S. exports to Mexico ad to 4 percet i the case of Caadia exports to Mexico. Adjustig for the icrease i total trade, the exteral margi accouted for roughly 25 percet of the icreased trade betwee Mexico ad the Uited States, 40 percet of icreased Mexica exports to Caada, ad almost 00 percet of icreased Caadia exports to Mexico. Hillberry ad McDaiel (2002), usig a alterative measure, fid evidece of smaller, but still sigificat, extesive margi growth for the Uited States followig the implemetatio of NAFTA. Usig the methodology of Hummels ad Kleow (2005), they defie a coutry s extesive margi as its share of world exports that occur i those product categories (measured S lies at the 0-digit level) i which a coutry exports. Other thigs equal, by this measure if a coutry cocetrates its exports i a few product categories, it will have a lower extesive margi. Hillberry ad McDaiel estimate that Mexica exports to the US grew by $86 billio betwee 993 ad 200, of which 2.5% is attributable to greater extesive margi trade. Correspodigly, Mexica imports from the US grew by $44 billio, of which 9.7 percet occurred at the extesive margi. Their lower magitude estimates i compariso to Kehoe ad Ruhl ca be attributed to their differet metric: Hillberry ad McDaiel defie a product category as traded eve if actual exports, though positive, are virtually isigificat. I additio, they focus o the effects of NAFTA per se ad ot of trade liberalizatio udertake by Mexico i earlier years. Evidece regardig quatities for EMU is more limited. But there are good theoretical reasos ad prior empirical evidece for expectig the adoptio of a sigle currecy to lead to icreased trade amog the members of a currecy uio (see Rose, 2000). While the data limitatios are evidet, there is already some evidece that EMU has boosted itra-euro area trade sice 999 (HM Treasury, 2003). EMU-specific calculatios based o a structural model icorporatig multilateral resistace suggest a icrease i trade as high as 40 to 60 per cet. Other studies, e.g. Bu ad Klasse (2002), yield smaller, though still, sigificat effects. 7 This approach towards determiig whether a particular set of goods are ot traded assumes that the cutoff depeds o the relative importace of these goods i a coutry s trade (e.g. 0 percet of total export value) rather tha o whether their yearly value of trade falls below a fixed dollar-value cutoff (e.g. $500, 000). 6

9 Is there ay coectio betwee the quatity evidece ad price evidece preseted above? Specifically, is there ay associatio betwee the observatios that the extesive margi has icreased ad price dispersio has rise withi Europe sice the adoptio of the euro? We preset suggestive evidece that there is, through a simple regressio of the chage i price dispersio o the chage i the extesive trade margi across idividual coutry pairs. The price dispersio figures are costructed as above; the extesive trade margi figures are calculated from OECD data o Iteratioal Trade by Commodity Statistics (ITCS), disaggregated at the 4 digit SITC product level. (We measure price dispersio chages ad the extesive margi over the period because of the absece of bilateral product-disaggregated trade data for most coutries beyod 2002.) The results are reported i Table 3. A bivariate regressio (i col. ) idicates a positive, though isigificat relatio. Cotrollig for differeces betwee core ad peripheral tradig relatioships yields more iterestig results (see col. 2). The coefficiet of the extesive margi variables, reflectig the effect for core-peripheral coutry pairs, is positive ad sigificat at better tha 5%. For core-core coutry pairs the coefficiet is eve more positive. For peripheral pairs the effect is weaker. This suggests that the etry of ew goods sice 998 is associated with a icrease i price dispersio. These results poit out the eed for a theoretical framework to uderstad trade liberalizatio that permits etry of ew goods ito the export market. We preset oe approach doig so i the followig sectio. Alteratives have bee proposed by Kehoe ad Ruhl (2002), Ghiroi ad Melitz (2004), as well as others. But i additio, we propose a model that tries to accout for the puzzlig price evidece. Give the clear role for the extesive margi i explaiig the quatity observatios, our model will also cosider how such a extesive margi ca coicide with ad eve facilitate price divergece. III. Model Specificatio I this sectio we formulate a ope ecoomy macro model that specifies real trade frictios i the form of both per uit (iceberg) trade costs as well as a fixed cost of iteratioal trade. The model cosists of two coutries, home ad foreig, i which each coutry s output cosists of a distict cotiuum of differetiated goods, deoted by labels H ad F, respectively. Each coutry s goods are idexed o the uit iterval ad are produced by moopolistically competitive firms usig labor as the sole iput i a liear (costat returs to scale) techology. I priciple, ay good ca be exported but there are variable costs τ ad fixed costs of exportig X f for ay good, which are bore by the exportig firm. Cosequetly, a edogeously determied fractio will be otraded i equilibrium. Notraded goods are labeled N ad traded goods T. Home ad foreig agets cosume CES aggregates of their ow domestic goods ad the other coutry s traded (export) goods. Quatities ad prevailig prices for the goods varieties cosumed i the foreig coutry are deoted by. (Below we geerally preset 7

10 cosumptio ad price expressios for the home coutry oly; the correspodig expressios for the foreig coutry are aalogous.) There are several key assumptios i our framework. First, each coutry specializes i a rage of goods that are uique to that coutry (albeit goods from differet coutries are substitutes) ad that the cotiua of goods produced are exogeously give. 8 Thus, i focusig o tradability, we abstract from possible ew etrats ito domestic productio. Secod, we aggregate cosumptio oly over the mass of goods that are actually available to cosumers; this mass may chage over time as the umber of imported tradable goods varies. I order to facilitate the costructio of CES aggregates this ecessitates assumig that elasticity betwee idividual varieties of domestic ad foreig goods are the same. This precludes the possibility of separate elasticities betwee home ad foreig goods, ad betwee traded ad otraded goods, which have ofte prove useful i ope macro models. Third, we follow the traditio of stadard ope ecoomy macro models by defiig cosumptio aggregates as (weighted) averages of the cosumptios of idividual varieties, implyig that cosumptio is ivariat to the etry of ew varieties. 9 This rules out the love of variety effect characteristic of Dixit-Stiglitz specificatios which are popular i models of iteratioal trade ad imply that utility rises with the umber of varieties cosumed. 0 The implicatios of havig love of variety or ot are abset from ope ecoomy macro models, where the mass of firms is assumed costat, the umber of available varieties ever chages, ad hece the baskets of goods cosumed are fixed. Fourth, we permit productivity ad iceberg trasport costs to vary heterogeeously across goods varieties. As will be see below, this gives our model flexibility ecessary to explai the price ad quatity puzzles of iteratioal ecoomic itegratio trade liberalizatio discussed i Sectio II. A. Cosumptio The cotiuum of goods produced i each coutry is idexed by i o the iterval [ 0, ]. Let deote the (edogeous) share of these goods i the home coutry that are otraded, where goods are ordered such that i [ 0, ] are otraded ad i [,] are traded. (Aalogously for the foreig coutry, where represets the share of foreig otradeds.) Residets cosume a basket of locally-produced goods ad tradable goods imported from the other coutry. 8 A differet approach is to allow a commo set of goods to be potetially produced i all coutries, ad the have oly the lowest-cost supplier actually export the good to each market. 9 The love of variety effect also implies that the aggregate price idex falls with ew varieties. This implies that the real exchage rate may move i the wrog directio (i.e. depreciate) if productivity gais geerate etry, cotrary to the predictio of the Balassa-Samuelso theory. The average price idex that correspods to our cosumptio idex does ot display this property. 0 Kehoe (2003) poits out that trade models with a love of variety specificatio ad large home bias weights couterfactually predict that, i respose to trade liberalizatio, the largest icreases i trade should occur i sectors i which there already is sigificat trade. Beassy (996) formulates a geeral specificatio with a parameter that ests o love of variety ad Dixit-Stiglitz love as special cases. 8

11 Cosequetly, the total mass of varieties of goods available for cosumptio i the home coutry is the sum of the mass of domestic varieties ad of the goods exported by the foreig coutry, i.e. ( ) 2 Accordigly, aggregate cosumptio ( C ) ca be defied as a CES aggregate of cosumptio of the home coutry s ow goods ( C H ) ad imports of the foreig coutry s traded (export) goods ( C ): + =. FT C = C + C ( θ[ ] ) ( ) H ( θ[ ] ) ( FT ) where > is the elasticity of substitutio betwee home ad foreig goods, ad θ [ ] is the ow-goods bias coefficiet that depeds edogeously o the umber of imported varieties (see the appedix for the derivatio): θ [ ], [ ], 0 [ ] 2 θ 2 θ Cosumptio of the home coutry s ow-good is i tur defied as a CES cosumptio idex of its otraded ( C HN ) ad traded ow goods ( C ): C C HN ( C ) H = ( c Hi) + ( c Hi) di = + ( ) (2) where ( ) 0 Hi 0 CHN c di, ( Hi ) () C c di (3, 4) ad lower cases are used to deote cosumptio of idividual varieties i of each differetiated good. Agai ote that the elasticity of substitutio amog idividual varieties of the home good ad the foreig good is also assumed equal to. 2 At home, the HN goods occupy[ 0, ] ad the goods [,]. (Correspodigly, abroad the FN goods occupy 0, ad the FT goods,.) Aalogously, the cosumptio idex of the foreig good imported by domestic agets C FT is defied as CFT ( cfi ) di (5) B. Prices ad Relative Demads Price idexes are defied as usual for each category of goods, i correspodece to the cosumptio idices above: 2 That is, chi / chj ( phi / phj ), cfi / cfj ( pfi / pfj ) = = for ay two goods i ad j. 9

12 ( ( ) ( )( ) ) [ ] [ ] θ H θ FT P= P + P (6) where PH = ( phi) di + ( phi) di = ( PHN ) + ( ) ( P ) (7) 0 Hi, 0 PHN p di Fi Hi P p di (8, 9) PFT p di (0) where P is the aggregate domestic coutry price level, P H is the price idex of all home goods, P HN is the price idex of otraded home goods, P is the price idex of traded home goods, ad P FT is the price (to domestic residets) of imported foreig goods. Note that the cosumptio ad price idices imply the followig relative demad fuctios for domestic residets: 3 = ( θ )( H ), FT / ( θ [ ])( FT / ) C / C [ ] P / P H C C = P P () = ( ), / ( )( / ) CHN / CH PHN / P H C CH = P P H (2) ad aalogously for foreig residets. C. Productio ad Productivity The productio sector i each coutry cosists of costat-returs-to-scale techologies for the output of each differetiated good: yhi = Al i Hi, (3) where y Hi represets the level of home output, l Hi deote workers employed i productio, ad A i is the home productivity coefficiet for each idividual good i. We employ the usual assumptio that labor is mobile across sectors withi each ecoomy, but immobile across coutries. Profit maximizatio uder moopolistic competitio implies pricig is determied by the stadard cost markup rule. For domestic sales of all home goods, either traded or otraded goods: W phi =, i [ 0,], (4) Ai where W deotes the home wage rate, ad /( ) is the markup factor. For export sales of traded goods, 3 Also ote that the CES specificatio implies for idividual goods variety i chi / CH = ( phi / PH ), chi / C = ( ) ( phi / P ), ad cfi / CFT ( ) ( pfi / PFT ) =. 0

13 W p = Hi, i [, ] Ai τ W, pfi =, i, i Ai τ (5, 6) i where τ i ( 0< τ i < ) is the fractio of each good i lost durig shipmet ad it is assumed that cosumers fully absorb these iceberg costs of shippig. 4 Thus for each traded good the foreig / τ > sales price exceeds the domestic price by the proportio ( ) Hi = phi i : p, pfi = pfi τ i τ i Note that, i the absece of trasport costs, sales prices are equalized across markets for each good i, i.e. phi = phi, pfi = pfi. Oe importat feature of the model is the distributio of productivities across each coutry. Firms i the domestic coutry have a distributio of productivity levels give by F[ A i ]. Amog these firms, = F[ A ] are otraders ad = F[ A ] are exporters. We defie special weighted productivity averages for home goods A, otraded home goods A N, ad traded home goods A T : 5 A Ai di, (7) 0 [ ] A N Ai di, (8) 0 ( ) ( ) ( ) A Ai di. (9) ( T[ ]) The foreig productivity averages are aalogous. If goods are ordered with icreasig productivity, the A T / > 0, A / 0 N <, i.e. average productivity rises (falls) i the traded sector (otraded) sector with icreasig. Ituitively, as the share of otraded goods i the ecoomy rises, goods at the low productivity ed of the traded goods sector become otraded, ad the average level of productivity of all remaiig traded goods rises. 6 Trasport costs may also vary heterogeeously across firms. We defie the effective productivity of home good exports as Ai( τ i), i.e. productivity adjusted by the trasport costs of goods exported abroad, sice higher τ effectively lowers the productivity of these goods relative to the same goods sold domestically. 4 For example, if τ = 0.5, the 50% of good i is lost i shipmet ad the firm doubles the price of the i good that reaches the foreig market. 5 As poited out by Melitz (2003), weightig by the elasticity parameter, makes the weights proportioal to the relative output shares of firms. A = A [ ] + ( ) A [ ]. 6 Note ( ) ( ) ( ) N T

14 We defie the average effective productivity of home exports ( )T as ( ( τ ) T [ ]) (( τ i) i ) A A di (20) where the T i the subscript idicates that these averages are computed over the rage of goods that are traded. It is straightforward to express the price idex for otraded ad traded home goods i terms of these productivity averages by usig (4) to substitute for p Hi i (8) ad (9): W W PHN =, P A = N[ ] A (2, 22) T [ ] with (7) implyig W PH = (23) A Correspodigly, the price of home goods exported to foreig residets is W P = A (24) ( τ ) T [ ] Equatios (2) ad (22) express the prices of otraded ad traded goods as fuctios of the wage rate W, the relevat productivity averages, ad the share of otraded goods. Observe that these prices are icreasig i the wage rate ad decreasig i average productivity. Sice A is idepedet of, the otraded vs. traded goods compositio of the ecoomy affects P oly H through its effect o the average wage level i the ecoomy. I the absece of ay trasport costs at all, all goods are traded ( = 0 ), implyig A = A ( )T = A T, ad prices of all goods are equalized: P = P = P. Keep i mid that (ad H be solved as part of the geeral equilibrium system τ A τ ) is itself a edogeous variable that will D. Margial Tradig Coditio The additioal profit to a home firm i of exportig to the foreig market may be writte: W π Hi = phi chi WfX (25a) Ai τ i where the operatig profits are defied as the export price mius margial cost, times the volume of sales to foreig residets. We follow Ghiroi ad Melitz (2004) i assumig that firms employ domestic workers to cover the fixed costs. With f X measured i uits of effective domestic labor ad W as the wage rate of this labor, labor costs are expressed as Wf X. 7 If this additioal profit is 7 I geeral, the effective labor employed to cover the fixed costs should deped o the productivity of the labor employed ad the wage rate should be scaled by this level of productivity, which we ca 2

15 positive, the firm will choose to export; if egative, the firm will ot. This provides the coditio that pis dow the idex of the margial tradig firm ad hece the share of otraded goods. For firm idex i = the profit from exportig is exactly zero, so W ph ch = WfX (25b) A τ E. Closig ad Solvig the Model Labor market equilibrium i each coutry requires that labor employed i productio of otraded ad traded home goods plus labor employed to cover the fixed costs of exportig equal the (exogeous) domestic labor supply L H. I the appedix we show that this coditio implies the followig relatio for the home coutry 8 : WLH ( ) fxw = PHCH + PC (26) i.e. the domestic wage bill et of wages paid for workers employed i coverig fixed costs, W( ) f X is proportioal to the value of home goods cosumed domestically or exported, with the proportioality costat equal to mius the profit rate /. We close the model with the balaced trade coditio that the value of exports equals the value of imports PC = PFT CFT (27) ad the ormalizatio coditio P =. (28) Equilibrium determies the 24 variables C, CH, CHN, C, C FT, P, PH, PHN, P, PFT, W, ad ad their foreig couterparts (deoted by ) by solvig the system of 24 equatios ()-(7), (2)-(22), (25b), ad (26) plus their foreig couterparts, together with (27) ad (28). I words, productio markups lik prices to wages. Stadard CES demad coditios lik prices to cosumptio quatities ad, thece, via techology, to derived labor demad. Market clearig (icludig balaced trade) ad the uméraire choice yield a solutio coditioal o give otraded shares ad. The margial tradig coditios reder the producers of the borderlie traded-otraded good idifferet betwee home ad foreig sales, ad, give the costs of shippig, this pis dow ad i equilibrium ad completes the solutio. deote A fx AfX may be assumed exogeously give or related to productivity elsewhere i the ecoomy, e.g. A, the average aggregate productivity level. We abstract from this issue by ormalizig A to. fx 8 Whe all home goods are otraded, i.e. =, the o labor is employed to cover fixed costs of exportig. 3

16 IV. Aalytical Results ad Discussio I this sectio we discuss some of the geeral isights of our framework for ecoomic itegratio. I particular, we focus o illustratig the differetial effects of chages i iceberg ad fixed costs o cross-coutry price differeces ad trade flows. Simulatios i the followig sectio will complete the aalysis ad uderstadig of the model. 9 A. Prelimiaries: Decompositio ito Homogeous ad Heterogeeous Compoets. Our model potetially permits heterogeeity i two differet dimesios: i terms of productivity ad i iceberg trasport costs. I the followig discussio it will prove useful to decompose productivity ad iceberg trasport costs for good i ito homogeous (α ) ad heterogeeous ( β ) compoets. We will address two (polar) cases: (i) heterogeeity i productivity oly, ad (ii) heterogeeity i iceberg costs oly (we report oly home coutry expressios; the foreig coutry couterparts are aalogous): I the case of heterogeeity i productivity oly, we may write the distributios as A =, [ 0,] τ =, [ 0,] i α [] AβA i i, 0 < α, β i α τ i, 0 α τ implyig effective productivity ca be expressed as Ai( τi) = ( α AβA[ i] ) α τ. Chages i α A, α τ represet balaced chages i productivity ad trasport costs affectig all goods equally. Note a rise i α τ implies a declie i iceberg costs. It follows that the productivity averages ca be expressed (with the foreig couterparts defied aalogously) as: A ( []) ( A A i di = α β αa β A ) (29a) 0 [ ] A ( []) ( T = αa βa i di αa β AT [ ] ) (30a) [ ] A ( ) ( ( τ) T = αα A τ βa[] i di αα A τ β AT [ ] ) (3a) A A 9 Bergi, Glick, ad Taylor (2004) formulate a similar model without iceberg costs i order to ivestigate the effects of productivity growth o the real exchage rate ad the rage of goods traded. Their framework provides a more geeralized approach to the Balassa-Samuelso hypothesis ad its relatioship to log-ru growth. 4

17 Assumig that goods are ordered with icreasig productivity i.e. β A / i > 0, the β AT / > 0, A T / > 0. That is, average productivity i the traded sector rises as icreases ad the traded goods share declies. I the alterative case of heterogeeity i trasport costs oly, we write the distributios Ai = α A, i [ 0,], 0 < α A τi α τ β τ [ i] i, 0 α τ, β τ implyig effective productivity ca be expressed as A( i τ ) = i α A( α τβ τ [ i] ). The correspodig averages are A = α A (29b) =, [ 0, ] A [ ] = α (30b) T A ( ) ( τ ) T A [ ] ( ) ( τ) T = αα A τ β τ[] i di αα A τ β [ ] (3b) Assumig that goods are ordered with decreasig iceberg costs, i.e. β τ / i > 0, the ( ) / > 0, A ( ) / > 0, i.e., average heterogeeity ad trasportability rise i the traded β τ T τ sector with icreasig. T B. Tradability Oe immediate coclusio is the equivalece, i terms of their effects o tradability, of the trade cost heterogeeity that we advocate ad the heterogeeity i productivity that has bee the focus of other recet papers. This may be see by cosiderig the tradig coditio for firm i (25a), substitutig out all firm-specific edogeous variables ad makig some additioal simplifyig substitutios. We use the price settig coditios (5) ad (24) to substitute for ad P ad the relative demad coditio ( ( τ ) T[ ]) chi / C = ( ) ( phi / P ) for c Hi to fid: A C ( Ai( τ i) ) = fx. ( )( ) I this equatio, the good-specific trade cost term ad that for techology appear oly as a A τ, so it is oly the et effect of the two terms that matters for the relative product, i ( i ) rakig of varieties i terms of their tradability. For example, eve if a good i is more costly to trade tha a good j, τ i > τ j, good i evertheless ca be more tradable if it has a sufficietly high level of productivity so that A( τ ) > A ( τ ). Coversely, there also may be some highly i i j j productive goods that evertheless will probably ever be traded, because they have particularly p Hi 5

18 high good-specific trasport costs. Goods ca i priciple be raked i terms of tradability usig this composite metric. We ext obtai some isight ito the extesive margi of trade by cosiderig the tradig coditio for the margial good (25b). Usig the price settig coditio (5) for that the relative demad coditio c / ( ) ( / Hi C phi P ) [,]: p H ad otig = holds for all goods i i the rage p H C f = X. (32) A( τ) P I this form, we ca ifer that the th firm s variable profits deped o two factors: () per uit export profits the term i the first set of curlicue brackets o the LHS, expressed as a proportio /( ) of margial costs, ad (ii) the quatity of exports sold the term i the secod set of curlicue brackets. The latter, i tur, ca be decomposed ito the relative price p / P, ad its share of the aggregate level of effect o demad for the th firm s exports, ( H ) exports sold abroad, C /( ). Whe variable exports profits exceed the fixed costs of exportig either because per uit profits or the volume of exports are high goods with effective productivity lower tha that of the iitial th good will become traded (sice eve though Ai( τ i) < A( τ ) for these goods, it has become profitable to export them). The resultig declie i ad rise i the share of tradable goods - raises the margial cost ad price of the margially traded good ad reduces its share of aggregate exports. These effects cause both per uit profits ad the export volume to fall. I equilibrium, profits are reduced to just coverig the fixed costs of the th good eterig ito the foreig export market. Equatio (32) is useful for uderstadig the effect of trade policies o the etry of ew goods ito trade, ad how this depeds o the type of trade policy. We cosider cuts i iceberg costs ad fixed costs i tur. Cosider first a balaced cut i per uit (iceberg) costs, i.e. a rise i α τ, α τ. Equatio (32) suggests a umber of offsettig effects that could make the effect o ew etry of exporters small. First, uder moopolistic competitio, firms pass o tariff chages ito the sales price charged to foreig cosumers (see expressio (5)); cosequetly the lower export price implies lower per uit export profits for the th firm. Secod, because the cut i tariffs affects all traded p / P is uaffected. 20 Lastly, it is goods equally, the relative price of the th firm s exports ( H ) 20 These effects ca be see more clearly by otig that (29)-(3) imply (32) may be expressed as β ( ) T [ ] C τ = αα A τβ τ[ ] β τ[ ] f X with productivity heterogeeity oly, ad 6

19 oly though a icrease i demad for aggregate exports C, i.e. a icrease i trade at the itesive margi, that the th firm may experiece a overall icrease i export profits. If aggregate exports icrease sufficietly to raise variable profits above fixed costs, the ew goods may become traded ad trade will icrease at the extesive margi (i.e. the equilibrium falls ad the share of traded goods - icreases). The icrease i aggregate exports reflects icreased trade at the itesive margi. The amout by which aggregate exports rise depeds o the elasticity of demad for exports. Cosiderig the foreig couterpart to equatio (0) ( θ[ ])( / ) = C P P C we see that a per uit cost cut iduces firms to lower the relative price of tradables (i.e. P / P falls), which boosts foreig demad for home goods exported to the foreig market. It is apparet that the magitude of icreased demad for exports falls as the elasticity of demad declies. Cosequetly, the effect o the profits of the margial trader ad the icetive for ew etrats is less as well. 2 I fact, because of the egative effects of a cut i tariffs o per uit profits, we caot rule out the possibility that this effect domiates ay icrease i export volume, implyig profits of the margial trader actually declie, leadig him to exit the tradables market. Numerical simulatios for a calibrated versio of the model will show later that the et effect teds to be a rise i profits, implyig some fall i, ad some icrease i trade at the extesive margi. Cosider ow the alterative policy, a declie i fixed costs ( f f ). Sice fixed trade costs oly eter ito the margial tradig coditio; they do ot eter ito the decisio rules about price settig or how much to produce ad sell. Hece, i the case of a fixed trade cost reductio, there is a direct effect raisig the export profits of the margial exporter, sice variable profits will exceed the ow lower fixed costs of exports. There is o effect o per uit profits ulike the case of a tariff cut or the relative price of the margial exporter. The positive export profits for the margial trader leads to a icrease i trade at the extesive margi (i.e. declie i ) as it becomes profitable for ew goods to eter the traded sector. To summarize, a cut i fixed costs will work largely through the etry of ew goods ito the traded sector, implyig greater trade at the extesive margi. I cotrast, a cut i per-uit trade costs will ted to raise exports mostly through icreasig the itesity of trade i X, X β AT [ ] C f X αaα τ βa[ ] = βa[ ] with trasport cost heterogeeity oly. 2 We cojecture that this is most likely to occur as oe approaches the limitig case of Cobb-Douglas prefereces betwee home ad foreig goods, where elasticity for imports is uity. I our curret specificatio with edogeous home bias weights, however, we are precluded from cosiderig this case because of the costrait that the elasticity betwee home ad foreig goods be the same as that amog idividual varieties of home (ad foreig ) goods, which must exceed uity with CES prefereces. With exogeous home bias weights, this costrait ca be dropped ad the differet elasticities ca be posited. 7

20 previously traded goods; i.e. firms already tradig, will export more. The extesive effect o trade is dampeed i this case because lower margial costs lead to proportioately lower prices, ad hece lower per uit profits from exportig. This limits the extet to which ew firms fid it profitable to egage i exportig. C. Law of Oe Price ad Price Divergece We ext examie the circumstaces uder which deviatios from the law of oe price may emerge i our model. At the level of idividual goods i, it is immediately apparet that moopolistic pricig see expressios (5) ad (6) implies the export price exceeds the domestic price of good i by a wedge associated with trasport costs: phi = = >, i [, ]. phi τi α τβ τ[ i] With homogeeous trade costs the degree of price divergece is costat across sectors. However, if β τ [] i ad τ i vary with i, the degree of price divergece varies with i as well. Thus variatios across sectors i the degree of LOP deviatios deped o the presece of heterogeeous trasport costs; with moopolistic pricig, heterogeeous productivity is ot sufficiet. We will summarize results for price dispersio i terms of cross-border deviatios i average tradable prices. Expressios (22) ad (24) together with (9) ad (20) imply P AT [ ] P = A [ ] > (33) τ ( ) T sice the presece of trasport costs implies A T > A ( τ ) T, i.e. the average effective productivity of tradable goods (i.e., icludig trasport costs) is less tha the average productivity of tradable goods. Cosequetly, the average price to foreig residets of exported home goods is higher tha the average domestic price of the same goods at home. This relative price ratio roughly correspods to the measure of price dispersio used i our empirical results reported i Table. 22 How does ecoomic itegratio affect price deviatios? The aswer depeds o the form of liberalizatio iceberg trasport costs or fixed trade costs ad o whether heterogeeity exits i the form of productivity or iceberg costs. We kow from the previous sectio that both forms of liberalizatio iduce some icrease i trade at the extesive margi, i.e. declie i, with this icrease beig greater i the case of a fixed trade cost reductio. As we shall see, the effect o trade liberalizatio depeds o how the edogeous chage i the degree of tradability iteracts with the ature of heterogeeity. We agai cosider the effects of cuts i iceberg costs ad i fixed costs i tur, ad this time we must also distiguish betwee alterative types of 22 Our empirical measure of dispersio is costructed from mea squared errors with equal weights across goods. Our theoretical measure does ot square price deviatios ad uses CES weights. But because all deviatios are positive here by costructio, squarig does ot matter ad the two measures of price dispersio are mootoically related. 8

21 heterogeeity. The reader will fid the results for the four cases discussed here summarized i Figure 2. First, cosider a declie i iceberg costs ( α τ, α τ rise) uder the assumptio of productivity heterogeeity. I this case, (30a) ad (3a) imply (33) reduces to P =, (34a) P α τ idicatig that deviatios from LOP at the aggregate level deped oly o the homogeous trasport cost parameter α τ, A icrease i α τ, i.e. balaced decrease i trasport costs, implies a fall i P / P ad reduces the average deviatio from LOP. Next, cosider how this policy chages uder trasport cost heterogeeity. Trasport cost heterogeeity implies that (33) reduces to P =, (34b) P α τ β ( τ ) T [ ] ad deviatios from LOP at the aggregate level deped o the relative heterogeeity of trasport costs ( β ( τ )T ) as well as o the homogeeous trasport cost compoet ( α τ ). The direct effect of a homogeous cut i costs (i.e. icrease i α τ ) is to reduce price divergece. But there is also a potetially offsettig effect to cosider through the edogeous chages i tradability o the heterogeeous compoet of trasport costs. Specifically, a decrease i, implyig a icrease i the umber of tradable varieties, implies that trade costs are averaged over goods with higher costs, i.e., lower. The resultig fall i β ( ) [ ](sice ( ) [ ]/ > 0) raises τ i τ T β τ T the degree of price divergece. Our simulatio exercises (i Sectio V) reveal that the latter effect is domiated by the direct effect of the cut i costs, ad price divergece falls o balace. Now cosider the type of policy that cuts fixed costs ( f f fall). Fixed costs do ot affect deviatios from LOP at the sector level, but they ca affect deviatios at aggregate level to the extet they affect. I the case of productivity heterogeeity, the relatio (34a) applies, ad the degree of price divergece is uaffected by ay chage i fixed costs. Ituitively, give that price settig is determied by per uit costs ad ot fixed costs, a cut i fixed costs has o effect o export prices. Thus i this case there is o reaso i this model to expect prices to coverge as the ecoomies become more itegrated. However, i the presece of trasport cost heterogeeity, (34b) holds ad deviatios from LOP deped o the heterogeeity of trasport costs ( β ( τ )T ) as well homogeeous trasport costs ( α τ ). I this case a declie i fixed costs that fosters decreased ad icreased tradability, reduces β ( ) [ ] ad raises price disparity. I words, if the source of heterogeeity is i terms τ T of iceberg costs, the the ewly tradable goods systematically will be those goods with higher per uit costs. Give the lower fixed costs, it ow becomes profitable to trade these goods, despite the higher per uit costs. Give that price settig respods to these costs, the ewly X, X 9