When Are Variety Gains from Trade Important? Comparative Advantage and the Cost of Protectionism *

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1 When Are Variety Gain from Trade Important? Comparative Advantage and the Cot of Protectionim * Abtract: Adina Ardelean ** Santa Clara Univerity, Beacon Economic Volodymyr Lugovkyy *** Georgia Intitute of Technology December 2007 We argue that dometic differentiated good are ubtitute to the foreign good. A a reult, indutrie with comparative advantage experience lower welfare loe from trade barrier becaue thee indutrie are more efficient in ubtituting for the diappearing foreign varietie. Empirically we confirm our conjecture by howing that the demand for imported varietie i more elatic for indutrie with comparative advantage. For an average good facing a median barrier, doubling the importer' comparative advantage decreae the number of imported varietie by 17%. Our finding ugget that the damaging effect of high trade barrier i diproportionately placed on countrie with inefficient indutrie. JEL Claification: F1, F12 Key Word: variety gain, trade, comparative advantage, product differentiation, monopolitic competition * We are epecially grateful to David Hummel for excellent comment and encouragement throughout the entire project. We thank to Jaon Abrevaya, Sirha Chatterjee, Thoma Hertel, Ru Hillberry, Ricardo Lopez, Julian Emami Namini, Georg Schaur, Alexandre Skiba, Chong Xiang, participant of 2007 Spring Midwet Trade Meeting, and eminar at Purdue U, U Memphi, and USIC for helpful comment. Will Martin graciouly provided u acce to COMTRADE data. Lugovkyy thank Fogelman College and Wang CIBER for financial upport. ** Department of Economic, Santa Clara Univerity, 500 El Camino Real, Santa Clara, CA , atardelean@cu.edu *** Correponding Author: Georgia Intitute of Technology, School of Economic, Atlanta, GA ; volodymyr.lugovkyy@econ.gatech.edu.

2 I. Introduction Even though the importance of gain from new imported varietie ha been recognized ince Krugman (1979), the empirical literature on evaluating the variety gain from trade ha been emerging only recently. Largely, data availability and model tractability have been the major challenge that hinder the reearcher ability to etimate the variety gain. While trade data at a highly diaggregated commodity level have become available for many countrie, diaggregated data on dometic production are till carce. Thu, reearcher have to make implifying aumption regarding the interaction between foreign and dometic varietie. A a reult the importance of the dometic ector i often downplayed. Thi paper highlight the importance of the dometic varietie in evaluating the variety gain from trade. We demontrate theoretically and confirm empirically that the efficiency in producing dometic varietie ha a ignificant impact on the demand for foreign varietie. Subject to the ame data contraint we hed light on the importance of dometic varietie in calculating welfare gain from trade. And until better data become available, policymaker hould take caution in relying on current etimate in the literature. The magnitude of the variety gain etimate varie depending on the underlying aumption and data ued. In a calibrated model, Romer (1994) how that the GDP loe aociated with the exit of foreign varietie can reach up to 20% a a reult of only a 10% tariff. Klenow and Rodriguez-Clare (1997) confirm Romer qualitative prediction on the Cota Rican data, but find the ize of the effect to be an order of magnitude lower. More recently, Broda and Weintein (2006) etimate that the US imported varietie have quadrupled between 1972 and 2001, which ha increaed the US welfare by 3% of GDP. 1

3 Thee paper, however, aume away the competition between foreign and dometic varietie. In Romer (1994) model the importer i a mall open economy incapable of producing it own varietie. Klenow and Rodriguez-Clare (1997) relax thi aumption by allowing only one dometic variety in each ector. While allowing for multiple dometic varietie, Broda and Weintein (2006) aume away the ubtitutability between foreign and dometic varietie by uing a Cobb-Dougla upper-level utility function. We claim that the dometic productivity i a key factor in evaluating the variety gain from trade when foreign and dometic varietie are ubtitute. In our model we how that countrie with tronger dometic indutrie import fewer varietie and uffer maller welfare loe from trade barrier. To illutrate, we provide a numerical example where a 10% increae in a trade barrier will caue a 7.5% welfare lo if the importer i unable to produce it own varietie, a 3.75% welfare lo if the importer can produce it varietie at the ame cot a the exporter, and only a 0.83% welfare lo if the importer i twice a productive a the exporter. However, independent of the importer relative productivity, a 10% increae in a trade barrier generate a 3.75% welfare lo when dometic and foreign varietie are not ubtitute. Empirically we provide indirect evidence on the effect of comparative advantage on variety gain from trade ince data availability retrict our ability to tructurally etimate the direct effect. In particular we explore the impact of comparative advantage on the demand for imported varietie. Conitent with the previou literature, trade barrier have a negative effect on the number of imported varietie. However, in our model thi effect i magnified by the importer-exporter productivity: the higher i the relative productivity, the more foreign varietie exit the importer market becaue of a trade barrier. To tet thi hypothei we 2

4 etimate the demand for imported varietie and how that the elaticity of the number of imported varietie with repect to trade barrier co-varie poitively with the importer relative productivity in that ector. Under the alternative, if dometic and foreign good are not ubtitute, the elaticity i independent of the comparative advantage. Our dataet conit of a panel of bilateral trade data diaggregated at 6 digit Harmonized Sytem commodity level from UN COMTRADE that cover many country pair panning over We meaure the number of imported varietie a the extenive margin, which repreent the cro-ection equivalent of the variety growth meaure derived by Feentra (1994), and the bilateral productivity ratio by the correponding ratio of Relative Export Performance (henceforth, REP). Since tranport cot and tariff data are pare for a large number of countrie, we proxy trade cot with bilateral ditance. The reult are conitent with the prediction of our model. A expected, the ditance decreae the demand for foreign varietie. More importantly, the magnitude of thi effect increae in the importer comparative advantage proxied by the bilateral (importer-exporter) REP. In the pooled regreion, doubling the bilateral REP yield a 17 percent decreae in the number of imported varietie for a median trade barrier. The data reveal ubtantial variation in the effect acro ector: 41% for electronic, 34% for machinery and tranportation, and 0% for petroleum and platic, mining and baic metal, and wood and paper. A direct welfare implication i that laggard indutrie tand to loe more from higher trade barrier, even though they loe fewer varietie. The reult are robut to employing variou model pecification, dataet, and meaure of trade barrier. Thi paper relate, and contribute, to everal line of reearch. Firt, we contribute to a rapidly growing literature evaluating the variety gain from trade by focuing on the interaction 3

5 between dometic and imported differentiated product. We how that ignoring the ubtitutability between foreign and dometic varietie might overtate the welfare gain from trade for the more productive importer and undertate them for the le productive importer. Second, we identify an additional factor comparative advantage determining the demand for foreign varietie. Previouly the number of imported varietie wa hown to covary poitively with the market ize and GDP per capita (Hummel and Klenow 2002, 2005) and negatively with trade barrier (Klenow and Rodriguez-Clare -1997, Feentra and Kee 2004, 2007). We how theoretically and confirm empirically that in ector with higher degree of comparative advantage the number of imported varietie i maller, and, more importantly, the demand for imported varietie i more reponive to variation in trade barrier. The later i conitent with the empirical evidence provided by Kehoe and Ruhl (2002) who how that the untraded or leat traded good experience the highet trade growth after trade liberalization. The ret of the paper i tructured a follow: ection II preent the model and olve for the equilibrium; ection III take the prediction of the model to the data; ection IV check the robutne of our etimate; and ection V conclude. II. Theoretical Framework We want to explore how relative productivity affect the variety gain form trade when dometic and imported varietie are ubtitute. For thi purpoe we develop a two country general equilibrium model of trade. The world conit of F+1 countrie: a country named Importer (indexed by i) and f = 1,2,..., F other countrie. Conumer preference in each country are defined over many differentiated varietie produced by =1,2,,S differentiated ector and a homogeneou good (indexed by 0). Within each ector, dometic and imported 4

6 varietie are ubtitute, and varietie produced in the ame country are cloer ubtitute. We implement thi idea by combining the Armington and Dixit-Stiglitz preference: each differentiated ector i modeled a an index of country-pecific differentiated good, where each good i a CES compoite of many varietie. 1 On the production ide, the mix of imported and dometic varietie i defined by the fixed cot of entering the market, relative productivity, and trade barrier. By allowing the productivity to vary acro ector, we are able to pinpoint the effect of the comparative advantage on the welfare and the number of imported varietie. A. Preference The preference are ymmetric in all countrie. For brevity, we will et up the model only from Importer perpective. Iporter repreentative conumer ha a Cobb-Dougla utility function acro ector: S µ µ i i 0 i = 1 0 (1) U = q C S µ = 1, =0 where qi 0 -- i Importer individual conumption of the numeraire; µ > 0 -- i a contant repreenting the expenditure hare of ector ; in ector. Ci -- i a compoite index of Importer individual conumption of differentiated good The quantity index C i i a two-level CES ubutility function. The upper-cae 1 Alternatively, ubtitutability between foreign and dometic varietie can be achieved by employing the Melitz-type heterogeneity in differentiated ector, a, e.g., in Bernard et al. (2007) or Balitreri et al. (2007). Recall, however, that the main goal of our paper i to dicriminate between the cae of ubtitutability and no ubtitutability between foreign and dometic varietie. Our choice wa thu dictated by a preference to have a no ubtitutability cenario a a pecial cae of our model (ee dicuion in II.A), where the Melitztype approach aume the ame elaticity of ubtitution between any two varietie. 5

7 ubutility aggregate over good from different countrie with ε being the contant elaticity of ubtitution between thee good, while each good i a compoite of many ymmetric varietie with σ being the elaticity of ubtitution between any two of them: (2) where ε ε 1 ε 1 ε 1 σ σ ε ε Nii σ 1 σ 1 F N if σ 1 σ 1 σ σ i = iiu + if ν u= 1 f = 1 ν = 1 σ ε 1 C q q > >, Nif -- i the et of varietie imported by Importer from country f in ector ; Nii -- i the et of varietie produced and conumed by Importer in ector ; qiiu -- i Importer individual conumption of a dometic varietyu in ector ; qifv -- i Importer individual conumption of variety ν imported from f in ector ; The upper level preference tructure aume that varietie from different countrie are ubtitute. At one extreme, when ( ε ) 1 / ε 1, the conumer regard compoite of varietie from different countrie a perfect ubtitute. At the other extreme, when ( ε ) 1 / ε 0, the conumer pend a contant hare of her income on each compoite of varietie a in the Cobb- Dougla utility function. Ifσ = ε, all varietie enter the utility function ymmetrically and the conumer perceive them a equally ubtitutable. We impoe an aumption ofσ > ε, in which cae any two varietie from the ame country are better ubtitute than any two varietie from different countrie. At the ame time, given thatε > 1, the conumer ha a decreaing marginal valuation for ame country varietie. 2 2 Ardelean (2007) etimate conumer love of variety and provide evidence that indeed conumer perceive within-country varietie a better ubtitute than varietie originating from different countrie. 6

8 B. Production Labor i the only factor of production. Importer endowment of labor i L i where labor i aumed to move freely acro ector. Conequently, the wage w, defined in term of the numeraire, i the ame in all ector. The numeraire ector i characterized by perfect competition and contant return to cale. In Importer, one unit of labor can produce β i unit of the numeraire. The numeraire i traded at zero cot. We aume that the numeraire ector i large enough for both countrie to have trictly poitive output of the numeraire. The introduction of the numeraire in the model implifie the balance of trade calculation and tie the wage to productivity in the numeraire ector. In the differentiated ector, monopolitically competitive firm produce the varietie of the differentiated good and are free to enter and exit. In Krugman (1980) framework the fixed cot of production limit the number of varietie the country produce. At the ame time, all varietie produced are exported ince there i no fixed trade cot. Alternatively Romer (1994) introduce a fixed cot of entering the market for each foreign variety, which generate more realitic prediction 3 : the number of imported varietie increae in market ize and decreae in trade cot. In our model we introduce a market-pecific fixed cot for each variety. A a reult, we are able to endogenize both the number of dometic and imported varietie. The technologie are country and ector pecific: Importer marginal cot in ector i i 1 Ai β and market-pecific fixed cot i α h Ai βi unit of labor, where i A i Importer technological parameter in ector higher Ai correpond to a higher productivity. In 3 See Hummel and Klenow (2002, 2005) for empirical evidence. 7

9 country f the technological parameter in ector i defined a Af = Ai / ϕif, where ϕ i the technological gap between Importer and country f in ector the higher theϕ if, the more productive i Importer relative to country f in. The marginal and fixed cot of country f in 1 ector are then ( Ai ϕif ) β and α f ( ) A i if f ϕ β, repectively. To ummarize, there are everal level at which we allow for difference in productivity. Firt, countrie differ in productivity in the numeraire ector ( β and β ); econd, productivity varie acro ector ( productivity gap ( ϕ if ). A h ); and, third, there i a country pair-ector-pecific The trade cot are ad-valorem in nature: if we look at export from f to i in ector, the exporter will be receiving 1/ τif dollar for each dollar of the delivered price, whereτ if > 1. i f C. Equilibrium Number of Traded Varietie We tart the derivation of equilibrium by finding the link between the nominal wage and productivity in the numeraire ector. Recall that the numeraire good i produced in both countrie and i tradable at zero cot. A a reult, the wage in each country i equal to the labor productivity in the numeraire ector: (3) wi = βi and w f = β f ince otherwie there i an opportunity for arbitrage. Note that β, h { i,1,2,..., F} h, erve a a productivity multiplier in all ector: a 5% increae in β yield a 5% increae in productivity acro all ector of country h. That i, we can interpret the variation in β a aggregate hock h h 8

10 to labor productivity in country h. Thi will be important in our dicuion of the model prediction. Next we turn our attention to an Importer differentiated ector. Preference acro varietie within a good are CES with σ being the elaticity of ubtitution between any two varietie originating from the ame country. Building on the Dixit-Stiglitz (1977) reult, the equilibrium price are equal to the monopolitic markup multiplied by the marginal cot: (4) p ii σ 1 σ τ if = pif = σ 1 A σ 1 A ϕ i i if. Due to the free entry condition, monopolitically competitive firm earn zero profit, which allow u to olve for the quantity per variety: (5) Q Q α ( σ 1) ii = =. if Now let u derive the number of dometic and imported varietie conumed by Home in ector. In equilibrium, the marginal rate of ubtitution between any imported and dometic varietie i equal to the ratio of their price: σ ε 1 ε ( σ 1) ε ii ii ii N q p = N q p if if if. By ubtituting for the equilibrium price and quantitie with (4) and (5), we derive the relative number of varietie: N if (6) ( ϕifτ if ) N ii ε ( σ 1) σ ε =. To derive the number of dometic varietie, N ii, we ue the fact that that the uppercae utility function i Cobb-Dougla, and thu conumer allocate a contant expenditure hare to ector : 9

11 ε ε ε ε σ σ 1 ( ε 1 ) 1 ( ε 1 ) ε ε ε 1 F F σ 1 σ 1 σ 1 σ = µ N Q N Q N p N p L w ii ii, f = 1 if if ii ii f = 1 if if i i where the firt multiplier in quare bracket i the quantity index and the econd multiplier i the price index of ector. Next we replace w i with (3), p ii and p if with (4), Q ii and Q if with (5), and N N if ii with (6), to get σ ( ε 1) σ ε 1 F ασ Nii ( ϕ ) 1 f 1 ifτ if + = µ Li β = i, Ai from which the number of varietie produced and old dometically i: i i F (7) Nii Ai ( ϕifτ if ) σ ( ε 1) σ ε 1 µ L β = + 1 f = 1. σα By combining the reult in (7) with the relative number of varietie (6), we find the number of varietie imported from country i in ector : i i (8) N ( ) ε ( σ ) σ ε σ ( ε ) σ ε µ L β = ϕ τ ϕ τ + 1. σα 1 1 F if if if A i ( ) f = 1 if if 1 D. Variety Gain from Trade Now we are ready to how that the larger i the relative importer-exporter productivity in ector the le vulnerable i an importer welfare to trade barrier. By plugging the equilibrium number of dometic and imported varietie given by (7) and (8) and quantity per variety (5) into utility function (1), we obtain the indirect utility: 10

12 * Uh = qi 0 A 1/ i f = 1 if if + = 1 σα σ σ ε σ ( ε 1) ( ε 1)( σ 1 L ) µ µ β 0 σ ε S σ 1 F i i ( σ 1) ( ϕ τ ) 1 σ. For implicity let u conider a two country cae (F=1). It i eay to how that the indirect utility i decreaing in trade barrier: * σ (9) ( ) ( ε 1 lnu ) i σ ρ µ ϕ τ σ ε * Ui, τif 1 = = if if + 1 < 0. lnτ σ 1 if Note that the magnitude of the effect i weaker the higher i the relative productivity in : µ (10) 1 ln ρ * σ ( ε 1) U i, τ if σ ( ε 1) = ( ϕifτ if ) σ ε + 1 < 0. lnϕif σ ε Let u provide a numerical example. Aume that the varietie of conumed by Importer conit of both dometically produced varietie and imported varietie. Furthermore let u aume the parameter of the model are µ =0.5, σ =3, ε = 2, andτ if = 1. If, a in Romer (1994), the dometic ector were infinitely le competitive than the foreign ector (which i a pecial cae of our model whenϕif 0 ), the value of the elaticity evaluated at lnui thi point i lnτ * if = That i, a 10% increae in a trade barrier ( τ if = 1.1) would decreae the welfare by 7.5%. If Home productivity were a high a the Foreign ( ϕ if = 1 ), a 10% increae in a trade barrier would increae the welfare by only a half of the previou magnitude (3.75%). Finally, if Home were twice a productive a Foreign in ector ( ϕ if = 2 ), a 10% increae in a trade barrier would decreae Home welfare by only 0.83%. Note that, independent of the importer relative productivity, a 10% increae in a trade barrier generate a 3.75% welfare lo if we aume away the ubtitutability between dometic and 11

13 foreign varietie ( ε 1). That i, ignoring ubtitutability when it i, in fact, preent, would yield a 3.75/0.83=4.5 time larger welfare loe for a more productive importer, and a 7.5/3.75=2 time maller welfare loe for a le productive importer. E. Comparative Static Since the data on the number of dometic varietie are unavailable, we will retrict our attention to formulating tetable hypothee with repect to the number of imported varietie. In our model the productivity in the numeraire ector i equal to wage, β i = wi, and thu change in β i have no effect on cot in the differentiated ector ince they are completely aborbed by change in wage, w. A a reult, i βi ha no effect on the equilibrium quantitie and price of the differentiated varietie. At the ame time an increae in β i increae (proportionally) the aggregate income wi L i and, conequently, the number of imported varietie in all ector: (11) ln N ij ln β i > 0. An increae in Home productivity in ector, A i, while keeping the relative productivity ϕ ij contant, i equivalent to a imultaneou increae in ector productivity both in Importer and in country j. Therefore, the number of imported varietie i increaing in A i : (12) ln N ln A ij i > 0. Finally, an increae in the relative productivity in ector, ϕ hi, and an increae in the trade barrier τ hi will decreae the number of imported varietie in the ame fahion: 12

14 (13) η ij ( 1) σ ( ε 1) σ ε σ ε 1+ ( ϕifτ if ) + 1 f j ln Nij ln N σ ε ij = = = < 0. 1 lnτ ln σ ( ε 1) ij τ ij F σ ε ( ϕ ) 1 f 1 ifτ = if + Note that the magnitude of the elaticity η ij i increae in the relative productivity in ector : (14) ( ) 2 1 σ ( ε 1 ln N ) ij σ ε 1 F ( ϕ ) f 1 ifτ σ ε = if lnτ ij σ ε 1 lnϕ σ ε ij ε σ 1 σ ε ( ϕifτ if ) 1 ϕ σ ε f j ijτ + + ij ln 1+ = > 0. ( 1) σ ( ε 1 ) ( ) ( ) σ ε That i, the higher the importer-exporter relative productivity, the tronger the number of imported varietie react to change in trade barrier. Alternatively, if dometic and foreign varietie are not ubtitute ( ε = 1), ηij i contant and independent of the relative productivity. We take thi prediction to the data by teting whether an importer with a higher relative productivity ha a more enitive demand for foreign varietie. III. Empiric In thi ection we relate the number of imported varietie to trade barrier, relative productivity, and other control to tet the qualitative prediction of our model. Our main focu i to confirm empirically that the elaticity of the number of imported varietie with repect to trade cot co-varie poitively with importer relative productivity. Alternatively, if dometic and imported varietie are not ubtitute, the elaticity i contant and independent of importer relative productivity. 13

15 A. Data and Variable Contruction We ue a panel of bilateral trade data diaggregated at 6 digit Harmonized Sytem level (more than 5,000 product categorie) from the UN COMTRADE, obtained through UNCTAD/World Bank WITS data ytem. Our ample cover 108 importer and 219 exporter panning the year between 1995 and In the trade data, we meaure the bilateral number of imported varietie and contruct a proxy for importer relative productivity (dicued below). We alo ue data on GDP per capita and population ize for all the importer in our ample from World Development Indicator ( ) and bilateral great circle ditance data between capital citie of trading partner from Head and Mayer (2002). Extenive margin a meaure of imported varietie Empirical tudie define a product variety either a a commodity category or a marketcommodity category at different level of commodity diaggregation impoed by data availability. We meaure imported varietie a a weighted count of the number of categorie or market-categorie, known a extenive margin, where the weight are the world trade (or ret of the world) in each category or market-category. The extenive margin i the cro-ection equivalent of the product varietie meaure derived by Feentra (1994). The weighted count meaure i more appropriate than the imple count becaue it allow varietie to be traded in unequal price and quantitie. To formalize, following Feentra and Kee (2004), the bilateral extenive margin in ector can be defined a: 4 In our effort to contruct a balanced panel, we retrict our data ample to 9 year in which the number of reporting importer i roughly contant. 14

16 (15) EM ij = ν I ij M M wj wjν, where M wj i the world import from j in ector, and the nominator i the world import from j only in thoe categorie in which j export to i (within ector ). The extenive margin repreent the weighted number of varietie ν imported by country i from exporter j relative to the weighted number of varietie j ell worldwide. Note, that the bilateral extenive margin weigh each category uing the j world export (including importer i), M ν. 5. wj EM ij meaure the hare of the weighted number of varietie imported by i from j in the total number of varietie exported by j. Note that, if the world import from j are equal acro all varietie, then EM ij repreent the hare of the imple count of varietie that i import from j in the total number of varietie the world import from j. Empirically, we follow Hummel and Klenow (2005) and define a variety ν a a 6 digit HS category and a product/ector a a 2 digit HS category 6. We contruct the bilateral extenive margin EM ij for each year and for each 2 digit HS. Table 1 how that the number of varietie an importer buy within a ector varie coniderably acro exporter. Relative Export Performance - Productivity Proxy Ideally, in order to etimate ectoral productivity, we would need diaggregated production data for many countrie. Unfortunately the data are not readily available. We refrain from uing GDP per capita a a proxy for ector-pecific productivitie, ince it i ector 5 We could alo weigh each variety uing the j export to the ret of the world (the world export excluding i). However both meaure are highly correlated and our reult remain robut to thi alternative meaure of the number of imported varietie. 6 For example, Microwave oven (HS ), Electric toater (HS ), Telephone anwering machine (HS ), and Video monitor, color (HS ) are varietie of Electronic (HS 85). 15

17 invariant. 7. Intead we ue the GDP per capita a proxy for productivity in the numeraire ector, and export performance a a proxy for the ector-pecific productivity. The underlying aumption i that export performance i highly correlated with dometic productivity: a country with a productive indutry participate in the world market, and the more productive the indutry, the more it export worldwide (Melitz ). At the micro level, the aumption i upported by the empirical literature on firm level heterogeneity (Bernard et al. 2003). We meaure the export performance of country i uing the REP (Relative Export Performance) index, alo known a export-baed Revealed Comparative Advantage (Richardon and Zhang ) or Balaa Index (Balaa ): (16) REP i M wi M wi =, M ww M ww where M wi -- i the world import of product from country i; M wi -- i the world import of all product from country i; M ww -- i the world total import of product ; M ww -- i the world total trade. The REP index repreent country i hare of worldwide export of product relative to the world counterpart. The index alo meaure country i export performance. By uing the hare of product export in country i total export, the REP index control for country i having a higher REP becaue it export more of all product. Furthermore, contructing it relative to the world hare of product, we meaure the importance of country i export of 7 The correlation between relative export performance and GDP per capita acro all ector and for our ample of countrie in 1999 i very mall and equal to Moreover, ector-pecific correlation are oftentime negative. 16

18 product relative to the world counterpart. Conequently, in a cro-country comparion, the REP index give an appropriate ranking of countrie ectoral export performance. Conitent with the contruction of the extenive margin, we define a ector a a 2 digit HS category and we contruct the relative export performance for each ector, country and year uing UN COMTRADE data. Next we contruct the bilateral REP index, which meaure the export performance of country i relative to j: (17) REP M wi M wi REPi ij = = M wj REPj M wj A it. In the data we oberve a large diperion of the bilateral REP index for a given importer, year, and ector (ee Table 1). Thi give u ubtantial variation to ae whether the elaticity of extenive margin with repect to trade cot i increaing in importer relative productivity. Ditance a a proxy for trade barrier Detailed data on trade cot uch a tranport cot and tariff are pare for a large number of countrie. While detailed data on tranport cot are available only for a handful of countrie, MFN tariff data have better coverage. Still, the variation of tariff that importer levy on their trading partner in a 2 digit HS category i very mall (the coefficient of variation i ), which limit the uefulne of thee data for our purpoe. Thu we employ data on the bilateral great circle ditance which many paper in the literature ue a a crude proxy for trade cot. Following Hanon and Xiang (2004), we model trade cot a a function of 8 For each importer-year and HS 2 category, we calculate the coefficient of variation and then we report the median of the coefficient over all importer-year-hs 2. The data ource i UNCTAD TRAINS obtained through World Bank WITS data ytem. TRAINS data provide information on MFN tariff. 17

19 k ditance, lnτ = δ ln d, where d ij i the bilateral great circle ditance between the capital of ij k ij trading partner. A a robutne check, we employ the U.S. Import of Merchandie data which provide detailed information on dutie paid at the border (dicued in ection IV). B. Specification and Reult Baed on the qualitative prediction of the model (11)-(14), we etimate the demand for imported varietie: (18) log EM log 1 log 2 log 3 log 4 log *log ijt α δ X it γ dij γ REPit γ REPijt γ dij REPijt εijt = , where EM ijt i the extenive margin of importer i from exporter j, for product, at time t; X it are the control for importer i market ize, at time t uch a population and GDP per capita; REPit i the export performance of importer i for product, at time t; REPijt i the correponding export performance of importer i relative to exporter j; and d ij i the ditance between i and j. The importer population and GDP per capita capture the impact of the market ize and average productivity. REPit erve a a proxy for the importer ector-pecific productivity; REP a a proxy for the importer-exporter relative productivity in ector ϕ ; ijt and ditance d ij a a proxy for trade barrier τ ijt Recall that the extenive margin repreent the hare of the weighted number of varietie imported by i from j in the total number of varietie exported by j. Thu, by contruction, we difference out exporter-year fixed effect, uch a exporter market ize, average productivity, and production tructure. ijt 18

20 Our main hypothei i that an increae in bilateral ditance decreae the extenive margin and the magnitude of the effect co-varie poitively with the importer exporter Relative Export Performance. That i, to tet whether dometic and foreign varietie are ubtitute, we eek to confirm that the interaction coefficient between ditance and importerexporter REP i negative ( γ 4 < 0 ). Under the alternative hypotheiγ 4 = 0, which mean that dometic and foreign product varietie are not ubtitute. Additional prediction from our model are: i) the total effect of ditance on the extenive margin i negative ( γ 1 + γ 4 log < 0 ); REP ijt ii) the total effect of the relative importer-exporter REP on the extenive margin i negative ( γ 3 + γ 4 logτ ij < 0 ); iii) the impact of importer REP on the extenive margin i poitive ( γ 2 > 0 ). Initially, we pool acro all 2-digit HS categorie. Thi i equivalent to auming that the effect of trade cot on the bilateral extenive margin i identical acro all product 9 : (19) log EM = α log Pop logcgdp 0.29 log d + ijt it it ij (0.01) (0.01) (0.01) log REP 0.02 log REP 0.02 log d * log REP + ε (0.01) it (0.03) ijt (0.00) ij ijt ijt 2 R =0.13, N. ob.=3,022,129 The bilateral extenive margin i decreaing in ditance and the magnitude of the effect i increaing in bilateral REP. In particular, doubling ector-pecific productivity gap decreae the number of imported varietie by 17% for a median trade barrier, or, alternatively, if we rank importer according to their REP, ditance ha a 62% tronger (negative) effect on the number of varietie for the 90 th percentile importer compared with the 10 th percentile importer. 9 Our reult are baed on the panel etimation, but they remain robut if we run the etimation in croection or if we include importer-exporter-hs 2 fixed effect. 19

21 That i, we can clearly reject the alternative hypothei that dometic and foreign varietie are not ubtitute ( γ 4 = 0 ). All other ign alo match our theory. The extenive margin i increaing in importer market ize, average and ectoral productivitie, and decreaing in relative importer-exporter REP. Following Feentra and Kee (2004) we then claify the HS 2 categorie into even indutrie: agriculture, textile and garment, wood and paper, petroleum and platic, mining and baic metal, machinery and tranportation, and electronic. 10 We firt pool acro all 2 digit HS categorie within the manufacturing indutrie (i.e., machinery and tranportation and electronic ): (20) log EM = α log Pop log CGDP 0.27 log d + ijt it it ij (0.01) (0.01) (0.02) log REP log REP 0.06 log d * log REP + ε (0.02) it (0.06) ijt (0.01) ij ijt ijt 2 R =0.18, N. ob.=434,542 For thee indutrie we can clearly ee that the effect of ditance on the extenive margin a well a the variation of thi effect acro importer are higher. If we rank importer according to their REP a we did for the previou pecification, ditance ha a roughly eightfold tronger (negative) effect on the number of varietie for the 90 th percentile importer compared with the 10 th percentile importer. Furthermore doubling ector-pecific bilateral relative export performance decreae the number of imported varietie by 53% for a median ditance. The fact that the magnitude of the oberved effect are larger for the manufacture i conitent with our model. Indeed, the model i built on the aumption of product differentiation and 10 We pool acro HS 2 categorie within an indutry intead of etimating the effect for each HS 2 category becaue we have ufficiently few obervation within a HS 2 that our etimate loe preciion. 20

22 thu hould work better for differentiated indutrie, uch a electronic and machinery and tranportation. Next we run the regreion for each indutry and report the etimate in Table 2 and 3. The etimate for agriculture, textile and garment, electronic, and machinery and tranportation provide tatitically ignificant upport for the importance of dometic varietie and their ubtitutability to foreign varietie. The effect differ acro indutrie with indutrie uch a electronic and machinery and tranportation featuring the tronget effect. At the ame time the etimate of γ 4 i tatitically inignificant in petroleum and platic, wood and paper and mining and baic metal. That i, for thee indutrie, which are le likely to have differentiated product varietie, the ubtitutability between foreign and dometic varietie i negligible and the welfare calculation a applied by Broda and Weintein (2006) are jutified. IV. Robutne Check In thi ection, we explore the robutne of our etimate through three check. The firt exercie concern the potential imultaneity in our pecification; the econd et of exercie check whether our etimate are robut to the ample of good, year, and countrie; and the third et of check employ an alternative meaure of trade barrier dutie paid uing the U.S. Import of Merchandie dataet. A. Addreing the Potential Simultaneity Bia The dometic productivity may not be exogenou a we aume in our model. The number of imported varietie may increae an importer productivity, thu affecting export performance through two channel that are outide of our model. Firt, if we conider 21

23 imported varietie a input in production, more input varietie increae an importer productivity under the aumption of gain from pecialization (Romer , Feentra and Kee -2004). Second, tougher competition from foreign varietie lead to intra-ector reallocation toward the mot efficient firm and higher average productivity (Melitz ). Note, that if one or both ource of endogeneity are preent, the bia in our etimate work againt u and controlling for it will only trengthen the impact of the relative export performance on the number of imported varietie. To addre the potential endogeneity we intrument for the REP with the factor endowment in two manufacturing ector 11 : electronic and machinery and tranportation. The data on employment and capital endowment i available only for two year, 1995 and 2000, and for a ub-ample of countrie. 12 Thu we have to retrict our ample to thee two year and 63 importer. (21) log EM = α log Pop log CGDP 0.46log d + ijt it it ij (0.04) (0.08) (0.06) log REP 0.24 log REP 0.06 log d * log REP + ε (0.19) it (0.24) ijt (0.03) ij ijt ijt 2 R =0.09, N. ob.=33,109 Depite the fact that we have a maller ample of countrie and year, the IV etimate 13 provide further upport for our main hypothei: the negative effect of trade cot on the extenive margin i magnified by the relative REP. When compared to the OLS etimate on the ame ample of year, ector, and countrie 14, the IV etimate are ignificantly different in a tatitical ene but the economic ignificance of the magnitude for the impact of ditance on the imported number of varietie i quite imilar. A expected, the 11 We focu on the manufacturing ector ince the key factor employed in the other ector are more likely to be a country endowment of land for agriculture, mineral, climate, geography, etc., and, thu, employment and capital are likely to be very weak intrument. 12 We ued the dataet contructed by Choi (2006). 13 The firt tage regreion for the IV etimate how that the intrument are trongly partially correlated with relative export performance. 14 See lat column of Table 4 22

24 effect of the importer relative export performance on the extenive margin ha increaed relative to the OLS etimate but the potential imultaneity doe not eem to affect the magnitude of the interaction term etimate. B. Robutne with repect to Sample Selection To tet whether the prediction of the model work for intermediate good, we retrict the ample to 6 digit HS categorie claified a intermediate good and contruct the extenive margin and relative export performance on the retricted ample. (22) log EM = α log Pop logCGDP 0.11log d + ijt it it ij (0.01) (0.01) (0.01) log REP log REP 0.01log d * log REP + ε (0.01) it (0.05) ijt (0.00) ij ijt ijt 2 R =0.08, N. ob.=50,928 Even though the magnitude of the coefficient have decreaed compared to the full ample of good, the qualitative prediction of our model are confirmed. Depite the ample being everely retricted, the effect of ditance on the extenive margin varie coniderably: the (negative) effect for the 90 th percentile importer i twice a large a for the 10 th percentile importer. Table 4 how additional et of etimate when we etimate (18) in cro-ection (only for 2000) or a pooled cro-ection (including ector year fixed effect). The reult are imilar in tatitical and economic ignificance to the etimate in (19). C. Tariff a a Trade Barrier Finally, to addre the limitation of uing ditance a a proxy for trade barrier, we run the regreion uing the U.S. Import data with detailed information on dutie paid at the border. 23

25 There are a few change in the contruction of variable and the regreion pecification. Firt, for a given year and 2 digit HS category, the extenive margin i a weighted count of the varietie imported by the U.S. from exporter j relative to the weighted count of varietie imported by the U.S. from all exporter. The weight are the total dollar value of varietie imported by the US. Since the U.S. report trade flow for more than 13,300 highly detailed 10 digit-hs categorie, we are able to define a variety at a more diaggregated level. Thi give u an opportunity to tet whether the retrictive definition of variety a a 6 digit HS category for the large panel of countrie affect our reult. If anything, the extenive margin contructed by defining a variety at 10 digit HS level hould trengthen our etimate. Second, we employ the relative export performance for the U.S. a for any exporter j contructed uing COMTRADE data a in ection III. Since U.S. data ha detailed information on dutie paid, we ue ad-valorem tariff (one plu the ratio of dutie paid and total dollar import value) a a proxy for trade cot. We aggregate tariff to the 2 digit HS level in two way: by taking the imple mean of the dutie paid on the 10 digit HS categorie within an HS 2 and alo by calculating the weighted mean where weight are the value of trade for each HS 10 category. We run regreion for both tariff meaure. There are three difference between the U.S. pecification and (19). Firt, ince the U.S. i the only importer, we replace all i indice with US. Second, the tariff varie acro ector and year for a given U.S. trade partner. Third, by contruction of the extenive margin, we difference out any importer-year pecific effect faced by all exporter that determine the ize of extenive margin. For example, thee determinant might be the U.S. market ize and average productivity. 24

26 A in the pecification with ditance, all the ign match our theory and all etimate are tatitically ignificant (ee Table 5). For both imple mean and weighted mean tariff pecification, doubling the ector-pecific U.S.-exporter REP decreae the number of imported varietie by 36% for the median tariff. If we rank exporter to the U.S. according to their REP, the imple tariff ha a 334% tronger (negative) effect on the number of varietie for the 90 th percentile compared with the 10 th percentile U.S.-exporter relative export performance. The effect i halved when etimated uing the weighted tariff. The U.S. etimate provide further upport for the importance of the dometic varietie and, a expected, uing ditance a a crude proxy for trade cot introduce a downward bia in our etimate ince the elaticity of tranport cot with repect to ditance i le than one (Hummel ). V. Concluion Romer (1994) how that including the fixed cot of importing in a trade model with differentiated good magnifie the importance of trade cot in the calculation of the welfare loe. A higher trade cot not only decreae the volume of imported good a in traditional model, but alo hrink the et of imported differentiated good. The reduction in the number of imported varietie reult in firt-order welfare loe. However, while evaluating the variety gain from trade, Romer and ubequent literature aume that imported varietie cannot be ubtituted with the importer own varietie, which can potentially bia the impact of protectionim on welfare if the data reveal that dometic and foreign varietie are indeed ubtitute. Thi paper how that the production of dometic varietie adjut to change in the number of imported varietie. And the ubtitutability between dometic and foreign varietie ha important implication for evaluating the product variety gain from international trade. A 25

27 country with higher differentiated ector productivity depend le on foreign varietie and it welfare loe becaue of trade barrier are maller compared to a country whoe production of dometic varietie i le efficient. For intance, a country with comparative diadvantage in electronic reap higher benefit from trade liberalization than a country that i a world leader in electronic. The evidence provided in thi paper trengthen the argument for trade liberalization of a country inefficient ector irrepective of it aggregate level of development. 26

28 Reference: Ardelean, Adina (2007). How Strong i the Love of Variety? mimeo. Balaa, Bela "Trade Liberalization and Revealed Comparative Advantage." Mancheter School: 33: Balitreri, Edward J., Ruell H. Hillberry, and Thoma F. Rutherford (2007). "Structural Etimation and Solution of International Trade Model with Heterogeneou Firm", mimeo Bernard, Andrew, Jonathan Eaton, J. Bradford Jenen, and Samuel Kortum (2003), Plant and Productivity in International Trade, American Economic Review 93 (September), Bernard, Andrew, Stephen Redding, and Peter Schott (2007) "Comparative Advantage and Heterogeneou Firm," Review of Economic Studie 2007 vol 74 (1) Broda, Chritian and Weintein, David E. (2006), Globalization and the Gain from Variety, Quarterly Journal of Economic, 121(2) Choi, Yo Chul (2006) Eay on Product Quality Differentiation and International Trade, Purdue Univerity, Ph.D. Diertation. Feentra, Robert C. (1994), New Product Varietie and the Meaurement of International Price, American Economic Review, Vol. 84, No. 1 Feentra, Robert and Kee, Hiau Looi (2004), Export Variety and Country Productivity, NBER Working Paper #10830 Feentra, Robert and Kee, Hiau Looi (2007) Trade Liberaliation and Export Variety: A Comparion of Mexico and China The World Economy Volume 30 Iue 1 Page 5-21, January 2007 Head, Keith & Thierry Mayer, "Illuory Border Effect: Ditance Mimeaurement Inflate Etimate of Home Bia in Trade," Working Paper , CEPII reearch center Hanon H. G. and C. Xiang (2004) "The Home Market Effect and Bilateral Trade Pattern," American Economic Review, September 2004, 94(4), pp Hummel, David (2001) Toward a Geography of Trade Cot, Mimeo Hummel, David and Klenow, Peter J. (2002), The Variety and Quality of a Nation Trade, NBER Working Paper #8712 Hummel, David and Klenow, Peter J. (2005), The Variety and Quality of a Nation Export, American Economic Review 95, p

29 Kehoe, Timothy J. and Kim J. Ruhl (2002) "How Important i the New Good Margin in International Trade?", Mimeo. Klenow P. and A. Rodriguez (1997), Quantifying Variety Gain from Trade Liberalization, Mimeo. Krugman, P. (1980), Scale Economie, Product Differentiation, and the Pattern of Trade, American Economic Review, 70(5), Melitz, M. (2003), The Impact of Trade on Intra-Indutry Reallocation and Aggregate Indutry Productivity, Econometrica 71 (6). Richardon, David J., and Chi Zhang (1999) "Revealing Comparative Advantage: Chaotic or Coherent Pattern acro Time and Sector and U.S. Trading Partner," NBER Working Paper Romer, P. (1994), New Good, Old Theory, and the Welfare Cot of Trade Retriction, Journal of Development Economic, 43,

30 Table 1: Variation in Extenive Margin, Relative Export Performance and Ditance Coefficient of Variation EMijt REPijt Ditanceij All indutrie Agriculture Petroleum & Platic Wood & Paper Textile & Garment Mining & Baic Metal Electronic Machinery & Tranportation Note: For each importer(i) year(t) HS 2(), calculate coefficient of variation CoV ( x ijt ) = tdev( xijt ) mean( xijt ). The table report the median value of the coefficient of variation over all it for each indutry. Data Source: United Nation Comtrade dataet ( ) 29

31 Table 2: Dependent variable - Extenive margin Indutry Ditanceij REPit REPijt Ditanceij * REPijt Popit CGDPit Number of ob. Agriculture , (0.01) (0.01) (0.03) (0.00) (0.01) (0.01) R2 Petroleum & Platic , (0.02) (0.01) (0.05) (0.01) (0.01) (0.01) Wood & Paper , (0.01) (0.01) (0.04) (0.01) (0.01) (0.01) Textile & Garment , (0.02) (0.01) (0.04) (0.00) (0.01) (0.01) Mining & Baic Metal , (0.01) (0.01) (0.04) (0.00) (0.01) (0.02) Electronic , (0.02) (0.03) (0.09) (0.01) (0.02) (0.02) Machinery & Tranportation , (0.02) (0.02) (0.05) (0.01) (0.01) (0.01) Note: 1. i- importer, j-exporter, t-year, -HS2 category 2. All regreion include HS 2 fixed effect 3. All variable are in log and robut tandard error are in parenthee 4. Obervation are clutered by importer. 30

32 Table 3: The total effect of ditance and bilateral REP on the extenive margin Indutry Ditance 1 Doubling relative REP 2 Agriculture 42% -10% Petroleum & Platic 0% -19% Wood & Paper 0% -19% Textile & Garment 72% -20% Mining & Baic Metal 0% -9% Electronic 170% -41% Machinery & Tranportation 817% -34% Note: 1. The total effect of ditance i calculated for the 90th percentile importer relative to the 10th percentile importer. 2. The total effect of bilateral REP i evaluated for the median ditance. 31

33 Table 4: Variou OLS Specification Dependent variable: Extenive Margin Panel I Panel II Pooled croection Croection Manufacture, all year, all countrie Manufacture, retricted ample Ditanceij REPit REPijt Ditanceij * REPijt Popit CGDPit (0.01) (0.01) (0.01) (0.01) (0.02) (0.04) (0.01) (0.01) (0.01) (0.01) (0.02) (0.02) (0.03) (0.03) (0.03) (0.03) (0.06) (0.09) (0.00) (0.00) (0.00) (0.00) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.02) (0.01) (0.01) (0.01) (0.01) (0.01) (0.02) No. ob. 3,022, , ,542 33,109 R Year & 2000 Indutrie All All All All Only 6 & 7 No. of Importer Fixed HS 2 * HS 2 * HS 2 HS 2 HS 2 effect Imp*Exp Year Note: 1. i - importer, j-exporter, t-year, - HS 2 category. 2. All variable are in log and robut tandard error are in parenthee. 3. Obervation are clutered by importer in all pecification. 4. The retricted ample i baed on the availability of factor endowment data acro year and countrie. 32

34 Table 5: Robutne Check (U.S. Tariff) Dependent variable: Extenive Margin Simple Mean of Tariff Weighted Mean of Tariff Tariff USjt REP USt REP USjt Tariff USjt * REP USjt Pop jt CGDP jt (0.33) (0.25) (0.37) (0.28) (0.06) (0.05) (0.00) (0.00) (0.04) (0.05) (0.00) (0.01) (0.00) (0.01) (0.00) (0.00) (0.00) (0.00) No. of ob. 58,983 58,983 58,983 58,983 R Note: 1. j-exporter, t-year, - HS 2 category. 2. All variable are in log and robut tandard error are in parenthee. 3. Obervation are clutered by year in all pecification. 4. All regreion include HS 2 Data Source: U.S. Bureau of Cenu ( ), U.S. Import of Merchandie CD-ROM 33