Comparative Advantage, End Use, and the Gains from Trade

Transcription

1 Comparatve Advantage, End Use, and the Gans from Trade Amanda Kurzendoerfer Unversty of Vrgna January 12, 2015 Abstract Ths paper studes the mportance of dstngushng between ntermedate and fnal use for the gans from trade. The domestc expendture share, whch s central to calculatng the gans from trade across a wde class of models, vares by end use. Falure to account for ths heterogenety n a one-sector, one-factor model systematcally understates the gans from trade and conceals dfferences n the returns to openness across end use. I construct a mult-sector, mult-factor model wth nput-output lnkages that ncorporates varaton n end use to nvestgate the full extent of these dscrepances, and to explore the relatonshp between relatve ncome and ntermedate relatve to fnal use estmates of Rcardan comparatve advantage, trade costs, and prces. I estmate the parameters of the model for 38 countres and 32 manufacturng and servce ndustres usng the World Input-Output Database. Lower ncome countres have a comparatve dsadvantage n producng and mportng ntermedate relatve to fnal goods, whch results n a hgher relatve prce of ntermedates for these countres. Includng end-use varaton rases the gans from trade by 4.1 percent on average. I am grateful for helpful comments from James Harrgan, John McLaren, Arell Reshef, and Peter Debaere. Ths research s supported by the Unversty of Vrgna s Bankard Fund for Poltcal Economy and the Albert Gallatn Graduate Research Fellowshp. 1

2 1 Introducton In the Rcardan model of nternatonal trade, countres beneft from trade by specalzng n the actvtes n whch they are relatvely more productve. A trade lberalzaton allows countres to produce and export more of ther comparatve advantage sectors and mport more of ther comparatve dsadvantage sectors. The larger the productvty dfferences, the larger the reallocatons, and the larger the gans from trade. Productvty dfferences are therefore central to determnng the gans from trade. Internatonal trade data suggests that productvty vares by ntermedate and fnal end use; that s, some countres are relatvely better at producng goods ntended for ntermedate use and others are relatvely better at producng goods ntended for fnal consumpton. Despte apparent productvty dfferences, comparatve advantage by end use has not been explored as an avenue for the gans from trade. In ths paper, I construct a general equlbrum Rcardan trade model that features productvty dfferences by ntermedate and fnal use to determne ther contrbuton to the gans from trade. Dstngushng productvty by end use hghlghts the dfferent roles of ntermedate and fnal goods n an economy, and ther dfferent contrbutons to the gans from trade. Intermedates are used n the producton of ntermedates, whch are used n the producton of other ntermedates and so on, so the gans from trade are magnfed when ntermedate productvty mproves or barrers to tradng ntermedates are reduced. In contrast, fnal goods are consumed once, so the beneft of a productvty mprovement or trade lberalzaton n fnal goods passes drectly to the consumer, but does not accumulate through the producton process. The exstng lterature does not allow productvty to vary by end use, effectvely treatng all goods as ntermedates or all goods as fnal goods. Falng to nclude ths source of heterogenety masks ths potentally asymmetrc response of the gans from trade to adjustments n the characterstcs of ntermedate and fnal use trade. The evdence that productvty vares by use comes from a sngle statstc, the domestc expendture share. In a Rcardan framework wth costly trade, a country s share of total expendture on domestcally produced goods, or ts domestc expendture share, contans nformaton about ts comparatve advantage and access to mports. A hgh share mples that a country s ether very productve at producng a partcular good or that t faces sgnfcant barrers to mportng the good from low cost locatons. Fgure 1 plots the domestc expendture share for ntermedates aganst the domestc expendture share for fnal goods for 40 countres. 1 If productvty and trade barrers dd not vary by end use, the shares would not vary by end use, 1 All calculatons are based on data from the World Input-Output Database ( ste/home.htm), whch I descrbe n Secton 6. 2

3 and the ponts n Fgure 1 would le on the 45 -lne. As the fgure shows, ntermedate and fnal domestc expendture shares are correlated countres that purchase a large share of ntermedates from home tend also to purchase a large share of fnal goods from home but the dfference s often large and vares by country. The dfference between shares shares ranges from as much as 32 percent (Luxembourg), to as lttle as mnus three percent (Russa, the only country for whch the ntermedate domestc share s hgher). Wthn-country dfferences n ntermedate and fnal domestc expendture shares ndcate that productvty, trade costs, or both vary by end use. Because the domestc expendture share captures nformaton about both a country s comparatve advantage and access to mports, t s central to determnng the country s gans from trade. Arkolaks, Costnot, and Rodríguez-Clare (2012) show that the domestc expendture share and the trade cost elastcty are the only varables needed to compute the gans from trade relatve to autarky across a wde class of models. I show that the expresson for the gans from trade n a one-sector, one-factor model wth end-use varaton s a functon of both the ntermedate and fnal domestc expendture shares. Ths s n contrast to the same model wthout end-use varaton (Eaton and Kortum, 2002), n whch the overall domestc expendture share determnes the gans from trade. I show that the model wthout end-use varaton wll always understate the gans from trade when trade s balanced. Further, I demonstrate the asymmetry of the elastcty of the gans from trade wth respect to ntermedate and fnal domestc expendture shares. Dfferences n ntermedate and fnal domestc expendture shares generate gans from trade, and the shares contrbute asymmetrcally to the gans from trade. Determnng the underlyng productvty dfferences that generate dfferences n the shares s therefore an nformatve exercse. The smple model provdes an expresson that relates ntermedate relatve to fnal domestc expendture shares to relatve technology and relatve prces. Relatve prces reflect a country s ablty to access ntermedates vs à vs fnal goods at low cost. In a frst look at comparatve advantage by use, I use data on the relatve prce of ntermedates whch s sharply decreasng n ncome to extract relatve productvtes from the domestc expendture shares. I fnd that low ncome countres have a comparatve dsadvantage n the producton of ntermedates. The smple model provdes an analytcal expresson for the gans from trade and the relatonshp between domestc expendture shares and comparatve advantage, but t does not ncorporate the full extent of productvty dfferences by end use. The data also show that domestc expendture shares vary by use wthn ndustres. Fgure 2 plots the ntermedate share aganst the fnal share for 32 goods and servce ndustres n the 40 countres. The pont Japan, Leather Goods, for example, demonstrates that Japan turns to domestc producers for 92 percent of ts ntermedate leather requrements, but s consderably 3

4 more open n ts purchases of leather fnal goods the domestc expendture share s just 20 percent. To capture ths varaton, and to ncorporate the fact that an ndustry s output s used n varyng ntenstes by other ndustres, I construct a mult-ndustry Eaton and Kortum (2002) model wth nput-output lnkages and end-use varaton wthn ndustres. The model features Rcardan motves for trade at the ndustry by end-use level, and also ncorporates multple factors (labor and captal). The full model does not provde an analytcal expresson for the gans from trade, so I estmate the parameters and solve the model numercally to determne the contrbuton of end-use varaton to the gans from trade; I fnd that the gans from trade are 4.1 percent hgher n a model wth end-use varaton than n a model wthout. I also use the parameter estmates from the full model to provde a closer look at comparatve advantage. The estmates support the aggregate result that lower ncome countres have a comparatve dsadvantage n producng ntermedates relatve to fnal goods. I fnd that ths result s drven by a comparatve dsadvantage n ntermedate agrculture and manufacturng ndustres n these countres. Further, low ncome countres pay relatvely more to mport ntermedates. A comparatve dsadvantage n ntermedate producton and a hgh cost to mport are consstent wth low ncome countres payng a hgher relatve prce for ntermedates, whch the aggregate data shows and my parameter estmates also support. The estmates mply a Balassa- Samuelson effect: countres that have a comparatve advantage n the producton of more tradable goods (ntermedates) pay a relatvely hgher prce for less-tradable goods (fnal goods). The lterature that studes the gans from trade and comparatve advantage has gravtated toward quantfyng the gans under the dfferent sources of heterogenety that Arkolaks et al. present n ther theoretcal paper. Costnot and Rodríguez-Clare (2013) fnd that multple sectors and tradable ntermedate goods have larger effects on the gans from trade than market structure and frm-level heterogenety. Levchenko and Zhang (2014) fnd that sectoral heterogenety ncreases the gans from trade by 30 percent relatve to a one-sector model, and show analytcally that the one-sector model wll always understate the gans from trade. Calendo and Parro (2012) estmate the welfare effects of NAFTA, and fnd that welfare s reduced by more than 40 percent when ntermedate goods and country-varyng nput-output lnkages are not consdered. Ths paper and those above use the mult-sector Eaton and Kortum framework that was ntroduced by Shkher (2011, 2012, and 2013) and Chor (2010). Sectoral heterogenety, ntermedates, and nput-output lnkages are therefore mportant channels for the gans from trade. I construct an extenson of the mult-sector Eaton and Kortum model that features each of these forms of heterogenety as well as end-use heterogenety. End-use heterogenety has not been ncorporated nto a theoretcal model to study the gans from trade, and hence ts effect has not been quantfed. Ths s an mportant omsson gven that 4

5 trade openness vares along ths dmenson and that the gans from openness n ntermedates accumulate through the producton process and the gans from openness n fnal goods do not. The lterature has less often used the parameter estmates to dscuss comparatve advantage, as I do by relatng the estmates to ncome levels. The excepton s Levchenko and Zhang (2013), who use a mult-sector Eaton and Kortum model to estmate technology parameters and fnd that comparatve advantage has weakened over tme. The lterature that dstngushes end use s outsde the context of the lterature on the gans from trade, and focuses on the mportance of low trade barrers and productvty n ntermedates vs à vs fnal goods. Amt and Konngs (2007) fnd that, n the context of an Indonesan trade lberalzaton, a declne n tarffs on ntermedate nputs leads to a productvty gan for frms that mport ther nputs that s at least twce as hgh as the gan from reducng tarffs on fnal goods. Jones (2011) shows that lnkages through ntermedate goods generate a productvty multpler that helps to explan large ncome dfferences across countres. A Unted Natons Conference on Trade and Development (2013) report dscusses the mportance of partcpaton n global value chans whch s determned by the proporton of a country s exports that are part of a mult-stage producton process, and s therefore an ndcaton of partcpaton n ntermedate goods trade for generatng employment and ncreasng GDP and ncome growth. These papers demonstrate that there are mportant benefts to mproved compettveness n ntermedates. I explore ths dea further frst by showng analytcally that the gans from trade are more responsve to changes n ntermedate trade, and second by showng that technology, trade costs, and prces vary by end use n a way that s related to ncome. The rest of ths paper s organzed as follows. In Secton 2 I set up a one-sector, one-factor model wth end-use varaton. I show that a model that fals to account for ths varaton wll always understate the gans from trade. I show the crcumstances under whch the gans from trade are more responsve to changes n the ntermedate domestc expendture than to changes n the fnal domestc expendture share, and use aggregate data to demonstrate the magntude of the dscrepancy n the gans from trade and to quantfy the elastctes. In Secton 3 I take a frst look at comparatve advantage, showng the mplcatons for relatve technology levels gven data on ntermedate and fnal prces and domestc expendture shares. In Secton 4 I set up the full general equlbrum model, ncorporatng varaton n end use at the ndustry level, nput-output lnkages, and captal. In Secton 5 I descrbe the estmaton procedure and the data. Secton 6 descrbes the data and mplementaton for estmaton. Secton 7 presents the results of the estmaton, shows that the relatve parameter estmates are related to ncome, and demonstrates evdence of the Balassa- Samuelson effect. In Secton 8, I use the estmated parameters to solve the full general equlbrum model to show the effect of ncorporatng end-use heterogenety on the gans from trade. Secton 9 concludes. 5

6 2 Smple Model and Some Magntude I frst descrbe an extenson of the Eaton and Kortum (2002) model that ncorporates varaton n end use. I demonstrate that the standard model always understates the gans from trade, and that the dscrepancy depends on two varables: the rato of the ntermedate domestc expendture share to the fnal domestc expendture share, and the labor share. I also show that the gans from trade are more responsve to changes n the ntermedate domestc expendture share when the ntermedate share n total output s greater than 50 percent, and more responsve than the standard model mples when the ntermedate domestc expendture share s less than the fnal domestc expendture share. I then turn to the data to demonstrate the potental magntude of the dscrepancy and the elastctes of the gans from trade wth respect to ntermedate and fnal domestc expendture shares. There are N countres. Producton s Cobb-Douglas over labor and ntermedates, wth unt costs n country gven by c = w β (pi, where w )1 β s the wage, p I β s the labor share n total output (0 < β < 1). 2 s the prce of a bundle of ntermedates, and Countres produce varetes of ntermedate and fnal goods, and varetes are produced wth productvty that vares by end use. End use s dstngushed by u = {I, F }, varetes are ndexed by l on [0, 1], and productvty s gven by z u (l). Productvty s drawn from a Fréchet dstrbuton wth locaton parameter T u and dsperson parameter θ. T u s the absolute productvty level for country, end use u, and the rato of ntermedate to fnal technology levels determnes comparatve advantage n producng goods suted for each end use. That s, T I/T F > T I /T F means that country has a comparatve advantage n the producton of ntermedate relatve to fnal goods compared to country. Trade costs take the ceberg form, so τn u unts of the good destned for end use u n country n must be shpped from for one unt to arrve (wthn-country trade costs are normalzed to one, τ u = 1). Perfect competton mples that a buyer n country n would pay p u n (l) = c τn u /zu (l), the productvtyadjusted unt cost tmes the ceberg trade cost, f the varety were bought from country. Buyers, who can be producers shoppng for ntermedates or consumers shoppng for fnal goods, purchase the varety from the lowest-cost source and combne varetes n CES fashon. The technology dstrbuton and CES prce ndex yeld a closed form expresson for prces pad for ntermedate and fnal goods n the destnaton country: p u n = γ [ N =1 T u (c τ u n ) θ ] 1/θ. The probablty that country s the lowest cost provder of varety l to country n, whch s also the fracton of expendture by country n on goods from country s π u n = Xu n X u n = T u ( γcτ u n p u n ) θ, where X u n s expendture by country n on goods of end-use u from country 2 In a mnor departure from Eaton and Kortum, I allow the labor share to vary by country. Ths has mplcatons for the full general equlbrum soluton, but, other than allowng the elastcty of the gans from trade wth respect to the overall domestc expendture share to vary by country, t does not change the standard gans from trade formula. 6

7 and X u n s expendture by country n on goods of end-use u from all countres. The fracton of expendture by country on goods from tself, the domestc expendture share, s then π u = T u ( ) γc θ. To solve for the gans from trade, I frst fnd real wages by substtutng the unt cost functon nto the fnal domestc expendture share equaton (u = F ) and rearrangng: p u w p F ( ) T F 1/βθ ( ) = γ 1/β p F 1/β 1 π F p I. (1) Welfare s measured by the purchasng power of wages n terms of the fnal good, the prce of whch may dffer from the prce of the ntermedate good. The prce of the ntermedate good affects real wages ndrectly through the use of ntermedates n producton of the fnal good (and through general equlbrum effects on the wage). I next use the domestc expendture share equaton for both fnal and ntermedate goods to wrte relatve prces as a functon of relatve domestc expendture shares and technology levels: p F p I [( ) ( π I = T F π F T I )] 1/θ, (2) and substtute (2) nto (1): w p F [ (T ) F β ( ) = γ 1/β T I 1 β ] 1/βθ π F π I. (3) The change n real wages, Ŵ ( ) w /p F ( ) / w /p F, assocated wth a move from autarky (π u = 1) to trade s then: [ (π ) F β ( ) Ŵ = π I 1 β ] 1/βθ. (4) Ths expresson has the counterpart π 1/βθ n the standard model. The expressons dffer n terms of the nteror component: the model wth end-use varaton reles on a geometrc weghted average of the ntermedate and fnal domestc expendture shares, whle the standard formulaton depends on the overall domestc expendture share (π ). Before formalzng the condtons under whch the two gans from trade expressons dverge, I dscuss the ntuton behnd the expresson that ncorporates end-use varaton. Rearrangng the exponents, we can rewrte (4) as Ŵ = ( π F ) 1/θ ( π I ) (1 β)/β θ. The elastcty of the gans from trade wth respect to the fnal domestc expendture share s 1/θ, as t s n the gans from trade expresson wth no ntermedates (see Arkolaks et al. equaton (1)), where θ s the trade cost elastcty. Fnal goods are not used n the producton of other goods, so openness n fnal goods s not subject to the amplfcaton n the gans from trade that arses when a good s part of an nput-output loop. In contrast, 7

8 ntermedates are used n the producton of other ntermedates, so the gans from trade are amplfed by the share of ntermedates n total expendture (precsely by the labor share, whch s one mnus the ntermedate share), hence the presence of β n the denomnator of the exponent on the ntermedate domestc expendture share (see Arkolaks et al. Secton IV.B). Because welfare s measured by the purchasng power of wages n terms of fnal goods, ths magnfcaton effect s only drectly relevant to the gans from trade through the extent to whch fnal goods rely on ntermedates, hence the presence of 1 β n the numerator of the exponent. Thus, we can thnk of the gans from trade as beng determned drectly by openness n fnal goods, and ndrectly by openness n ntermedates through two channels: the effect on other ntermedates, and on fnal goods. I now show that the gans from trade n a model wthout end-use varaton wll systematcally understate the true gans from trade, and that the sze of the dscrepancy depends on the rato of ntermedate to fnal domestc expendture shares and the labor share. Frst, rewrte the overall domestc trade share π as a lnear combnaton of the fnal domestc expendture share and the ntermedate domestc expendture share, where β and 1 β are the weghts when trade s balanced: π = β π F + (1 β )π I.3 Now we can easly compare the gans from trade formula wth end use varaton to the standard formulaton: n the former the nteror component s a geometrc weghted average of the fnal and ntermedate domestc trade shares, and n the latter t s a lnear weghted average of the fnal and ntermedate domestc trade shares. That s, [ (π ) F β ( ) Ŵ End-Use = π I 1 β ] 1/βθ, (5) Ŵ Standard = [ β π F + (1 β )π I ] 1/βθ. (6) Takng the logarthm of each nteror component we see that, by Jensen s Inequalty, the geometrc expresson wll always be less than or equal to the lnear expresson: β ln π F + (1 β ) ln π I ln(β π F + (1 β )π I ), (7) and strctly less when when π F πi. Because the gans from trade formulas are decreasng n the domestc expendture share expressons, the standard formulaton wll always understate the end-use formulaton when 3 To see that the labor and ntermedate shares n total output are the correct weghts when trade s balanced, frst recall notaton that X u s expendture by country on goods of end use u. In equlbrum, payments to labor (the only factor of producton) equal total expendture on fnal goods X F, and total output equals total expendture, X. Thus, β s also the share of expendture on fnal goods n total expendture, X F /X, and 1 β s the share of expendture on ntermedate goods n total expendture, X I/X. We can wrte the overall domestc expendture share as π = (X F + XI )/X, whch s the same as (X F /X )(X F /XF ) + (XI /X )(X I /XI ). It follows then that π = β π F + (1 β )π I. 8

9 the ntermedate and fnal domestc expendture shares are not the same. Ths s Proposton 1. Proposton 1 When trade s balanced, the gans from trade n the standard one-sector model weakly understate the gans from trade n the one-sector model wth end-use varaton. That s: Ŵ Standard = [ β π F + (1 β )π I ] 1/βθ [ (π F ) β ( π I ) 1 β ] 1/βθ = Ŵ End-Use. The nequalty s strct when π F πi. A corollary to the proposton s related to the sze of the dscrepancy, whch we can determne analytcally by takng the rato of the end-use (5) and standard (6) versons and rearrangng. Corollary 1 For a gven θ, the dscrepancy n the gans from trade between the end-use and standard models depends on the rato of domestc trade shares and the labor share: ( π F Ŵ End Use /ŴStandard = π I ) 1/θ [ ( ) ] π F 1/βθ β π I + (1 β ). (8) The further apart are the fnal and ntermedate domestc trade shares and the lower β, the larger the dscrepancy. The sze of the overall trade share π does not matter; t s only the extent to whch the domestc trade shares are dfferent that affects the dscrepancy n the gans from trade. Fgure 3 plots the dscrepancy n the gross gans from trade aganst a potental range of the rato of fnal to ntermedate domestc expendture shares and the range of possble labor shares for θ = 4. 4 As the fgure shows, the dscrepancy s largest when π F and πi are most dfferent and β s low. Turnng now to the elastcty of the gans from trade wth respect to each domestc expendture share, equaton (5) shows that the elastctes wth respect to the fnal and ntermedate domestc expendture shares are 1/θ and (1 β )/β θ, respectvely. Thus the elastcty wth respect to the ntermedate share wll be larger than the elastcty wth respect to the fnal share when β < 0.5, and t wll be larger by a factor of (1 β )/β. The lower the labor share, the more responsve are the gans from trade to the ntermedate domestc expendture share than to the fnal share. As dscussed prevously, ths s because ntermedates are used more ntensvely n the producton of other ntermedates and n the producton of fnal goods when the labor share s low. We can also compute the elastcty of the gans from trade wth respect to each domestc trade share for the standard formulaton. From equaton (6), we can show that the elastcty wth respect 4 I use θ = 4 here and throughout the paper followng Smonovska and Waugh (2014), who show that the Eaton and Kortum (2002) estmator s based and wll overestmate the elastcty of trade n fnte sample szes. Smonovska and Waugh develop a new estmator that reduces the bas and yelds an estmate of θ that s roughly equal to 4. 9

10 to the fnal domestc expendture share s ( 1/θ)(π F /π ), and wth respect to the ntermedate domestc expendture share s ( (1 β )/β θ)(π I /π ). Thus the gans from trade are ((1 β )/β )(π I /πf ) tmes more responsve to changes n the ntermedate domestc expendture share than to changes n the fnal domestc expendture share, and the standard model wll understate the mportance of changes n the ntermedate domestc expendture share when π I < πf. The analytcal expressons for the dscrepances between the end-use and standard models dscussed above rely on the assumpton of balanced trade that the overall domestc expendture share can be wrtten as a lnear combnaton of the ntermedate and fnal domestc expendture shares wth respectve weghts β and 1 β. Trade s not balanced n practce, however, and a researcher followng the standard procedure observes only the overall domestc expendture share. It s therefore mportant to quantfy n addton to the theoretcal dscrepancy the sze of the actual dscrepancy, or the dscrepancy that would result from usng the observed overall domestc expendture share (not the labor share weghted average) to compute the gans from trade. Table 1 reports the average overall, fnal, and ntermedate domestc expendture shares, the average rato of fnal to ntermedate shares, and the average labor share for hgh and low ncome countres. Hgh ncome countres are more open on average and the dfference s statstcally sgnfcant. Lookng at the ntermedate and fnal domestc expendture shares, we see that the overall dfference s largely due to ntermedates. Hgh ncome countres are more open n both ntermedates and fnal goods, but the dfference s more pronounced for ntermedates and t s statstcally sgnfcant. Thus the rato of fnal to ntermedate domestc expendture shares s hgher n hgher ncome countres, whch mples a larger dscrepancy n the gans from trade for a gven β. The dscrepancy s decreasng n β for a gven expendture share rato, however, and hgher ncome countres also have a hgher labor share. Therefore t s not obvous a pror whch group wll experence the larger dscrepancy n the the gans from trade calculatons. Table 2 reports the gans from trade, dscrepances n the gans from trade, and the relatve elastctes usng the data n Table 1. Panel A shows that the gans from trade usng the end-use model exceed the gans from trade usng the standard model under the assumpton of balanced trade. Ths result s guaranteed by Jensen s Inequalty, as shown n equaton (7). The gans from trade calculated usng the end-use model also exceed the gans from trade calculated usng the overall domestc expendture share. Ths result s not guaranteed, but arses because trade n ntermedates s more open than trade n fnal goods and s weghted more heavly n the end-use specfcaton. 5 Ths results n a lower nteror component and thus hgher gans 5 Intermedate shares n gross output (1 β ) are 0.66 and 0.70 n hgh and low ncome countres, respectvely, and expendture on ntermedates s about 58 percent of total expendture n both groups. 10

11 from trade usng the end-use model. Table 2, Panel B shows the magntude of the dscrepances. The dscrepances are small less than one percent for both hgh and low ncome countres. The magntude of ths dfference s the dfference that we can descrbe analytcally (equaton (8)) and from whch we can conclude that the standard model wll always understate the end-use model (equaton (7)). The dfference that derves from computng the standard gans from trade wth the observed domestc expendture share s somewhat larger. Comparng the end-use gans from trade fgures wth those computed usng the standard model and actual overall domestc expendture shares, we see that the standard formulaton understates the gans from trade by one percent for hgh ncome countres and 1.4 percent for lower ncome countres. Panel C of Table 2 reports the relatve elastctes of the gans from trade wth respect to ntermedate and fnal goods. As dscussed earler, the gans from trade wll be more responsve to changes n the ntermedate domestc expendture share when the labor share n gross output s less than 50 percent, and the standard model wll understate the mportance of changes n the ntermedate domestc expendture share when π I < πf. Usng the end-use model, we see that the gans from trade are 2.3 tmes more responsve to changes n the ntermedate domestc expendture share than to changes n the fnal domestc expendture share for lower ncome countres and two tmes more responsve for hgh ncome countres. Because π I < πf n both groups of countres, the standard model wth balanced trade also understates the relatve elastctes. As wth comparng the gans from trade across the two models, we are also nterested n the elastctes that a researcher usng the overall domestc expendture share wll compute. Because ntermedate and fnal domestc expendture shares are not observed, and not dstngushed n the model, the gans from trade are equally responsve to changes n ether share. Hence the relatve elastctes are equal to one, and the varaton n elastctes s altogether mssed. 3 Comparatve Advantage, a Frst Look Domestc expendture shares vary by end use and have dfferent effects on the gans from trade, so as a next step I look at the factors that contrbute to dfferences n relatve domestc expendture shares: prces and productvty. In ths secton I combne country-level data on prces of ntermedate and fnal goods wth the ntermedate and fnal domestc expendture shares to make an nference about the nature of comparatve advantage across countres and end use. I contnue to use the smple model n ths secton, showng n Secton 7 the mplcatons for comparatve advantage usng the full model. 11

12 A country that sources a relatvely larger share of ntermedates than fnal goods domestcally wll have a hgher relatve technology n producng ntermedates or a hgher relatve prce of ntermedates. We can see ths by rearrangng equaton (2): π I π F ( T I = T F ) ( ) p I θ. (9) p F If trade were completely costless and consequently the law of one prce held, the relatve prce would be the same across countres, and dfferences n the relatve domestc expendture share would be governed only by relatve technology levels. We would then conclude that low ncome countres, whch are relatvely less open n ntermedates than fnal goods ((π I /πf ) Low > (π I /πf ) Hgh, see Table 1), have a comparatve advantage n producng ntermedates. Trade s far from costless, however, so we cannot make a statement about the relatonshp between comparatve advantage and domestc expendture shares wthout some knowledge of relatve prces. Prces are n prncple observable, so together wth relatve domestc expendture shares and an estmate of θ we can extract relatve technology levels usng the expresson above. I obtan the prce of ntermedates from the GGDC Productvty Level Database for the benchmark year 1997 and the prce of fnal goods from the OECD, also for the year The ntermedate prces are constructed from sectoral ntermedate nput PPPs, whch reflect each sector s cost of acqurng ntermedate delveres. 6 The fnal prces are the PPPs for GDP, whch cover both fnal consumpton expendture (household and government) and gross captal formaton. 7 I take the rato of the ntermedate to the fnal prce and normalze t to one n the US. The prce data are avalable for 26 countres, and exclude the lowest ncome countres n my ntal data set. Despte excludng the lowest ncome countres, the prce of ntermedates relatve to fnal goods s sharply decreasng n ncome. Fgure 4, Panel (a) plots the relatonshp between relatve domestc expendture shares and ncome, and Panel (b) plots the relatonshp between relatve prces and ncome. 8 Gven that the rato of domestc expendture shares s flat to decreasng wth respect to ncome (the nverse relatonshp s weaker here where the lowest ncome countres are excluded), and the prce rato s sharply decreasng (and also rased to a power θ > 1), we can nfer from equaton (9) that the relatve technology to produce ntermedate goods wll be ncreasng n ncome. Panel (c) of Fgure 4 plots the precse relatonshp between relatve technology and ncome, calculated under the assumpton that θ = 4. Ths calculaton shows not only that lower 6 The prce of ntermedate nputs n a country s computed as the geometrc average of the PPP for sectoral ntermedate nputs (PPP II ), wth the share of sectoral ntermedate expendture (II ) n total ntermedate expendture as the weghts. The data are avalable at See Inklaar and Tmmer (2008) and Tmmer, Ypma, and van Ark (2007) for a detaled dscusson of the constructon of the PPPs. 7 The PPPs for GDP are avalable at 8 Income levels are gven by PPP-converted GDP per capta, rgdpl, from the Penn World Tables Verson 7.0, avalable at ste/pwt ndex.php. 12

13 ncome countres tend to have a comparatve dsadvantage n producng ntermedates, but also that there s consderable varaton n comparatve advantage across countres the relatve technology level for the country wth the largest comparatve advantage n producng ntermedates, Denmark, s 8 tmes that of the country wth the largest comparatve dsadvantage n producng ntermedates, the Czech Republc. The large amount of varaton suggests that productvty dfferences at the end-use level provde an mportant channel for the gans from trade. The calculaton s only suggestve, however, as t reles on the assumptons of a very basc model, uses hghly aggregate data, and prce data that may be measured wth error. In the next secton, I descrbe the full model, whch ncorporates many ndustres, labor and captal, and nputoutput lnkages. In addton to quantfyng the gans from trade under a more robust settng, I use the full model to further assess the relatonshp between comparatve advantage and ncome. 4 Full Model Domestc expendture shares vary by end use wthn sectors (Fgure 2), ndcatng the presence of comparatve advantage at ths level and a source for gans from trade. Prevous lterature has also hghlghted the mportance of sectoral heterogenety and nput-output lnkages n generatng gans from trade. In ths secton I construct the full model, whch extends a mult-sector Eaton and Kortum model wth nput-output lnkages to nclude end-use varaton. The extenson nvolves allowng the technology and trade cost parameters to vary by use, whch generates prces and trade shares that also vary by use. 4.1 Producton Countres are denoted n and, and ndustres are denoted k. End use s gven by u = [I, F ]. The cost of producton n country, ndustry k s a Cobb-Douglas functon of labor, captal, and ntermedate nputs: ( c k = w αk ) β k r ιk ( ) ρ k 1 β k, (10) where w s the wage, r s the rental rate, and ρ k s the prce of a bundle of ntermedates. Labor and captal are moble across ndustres wthn a country, and ther shares n value added are α k and ι k n. The share of value added n gross output s β k and the share of ntermedates n gross output s 1 β k. The prce of the bundle of ntermedates used to produce an ndustry k good n country s a Cobb-Douglas functon of the 13

14 prces of ntermedate nputs from each ndustry k : ρ k = k ( ) η k,k p I,k, (11) where η k,k s ndustry k s share of total expendture spent on ntermedates from ndustry k. The nput shares vary by country, and k ηk,k = 1. The lterature commonly assumes constant ndustry-level factor and nput shares across countres. I explot the World Input-Output Database to calculate country-specfc ndustry-level shares and fnd that the shares are not partcularly smlar across countres. 9 I allow nput costs to vary by ndustry and not use, mplyng that Heckscher-Ohln motves for trade exst only across ndustres. Ths decson s drven prmarly by data avalablty. Use-varyng costs would requre labor, captal, and nput shares that vary by use, and to my knowledge ths data does not exst. Rcardan comparatve advantage at the end-use level enters through the productvty parameter z uk (l). Each ndustry k n country n produces a contnuum of goods ndexed by l on [0, 1] for ntermedate use and for fnal use. In country, ndustry k s effcency n producng a good for end use u s gven by z uk (l). Iceberg trade costs are gven by τn uk. The unt cost of a good l produced by ndustry k n country, and delvered to ndustry u n country n s then p uk n (l) = ck τ uk n /zuk (l). Markets are perfectly compettve, so p uk n (l) s the prce that buyers n country n would pay f the good were bought from country. Instead, buyers shop around the world and purchase the good from the country wth the lowest prce. The prce actually pad s then p uk n (l) = mn { p uk n (l); = 1,..., N}. Facng these prces, buyers of end-use u goods n country n purchase amounts of ndustry k goods to maxmze a CES objectve functon. The prce ndex [ for the CES objectve functon s p uk 1 1/(1 σ), n = 0 puk n (l) dl] 1 σ where σ s the elastcty of substtuton between goods. 4.2 Technology The effcency parameter z uk (l) s the realzaton of a random varable drawn from a Fréchet dstrbuton F uk (z) = e uk T a hgher value of T uk z θ. The parameter T uk governs the average effcency wth whch goods are produced, and mples a hgher level of technology. Varaton n end use wthn country and ndustry mples that, though a country may have an advantage n producng an ndustry k good for ntermedate use, t may not be well suted to producng the ndustry k good for fnal consumpton. We can therefore thnk of 9 The coeffcent of varaton across countres wthn an ndustry (takng the average across all ndustres) s 0.37 for labor shares and 0.67 for captal shares. For nput shares lookng only at the dagonal entres to get a sense of varaton n the shares of the most mportant nput ths measure s

15 producton of the ndustry k good as beng talored to sut the needs of a partcular end use. The parameter θ governs the spread of the dstrbuton; lower values mply more varaton. More varaton n effcency draws (lower θ) ncreases the lkelhood that technologcal advantage wll overcome hgh producton or transport costs, mplyng that trade flows wll be more nfluenced by Rcardan comparatve advantage Consumpton Consumers have CES preferences over fnal goods produced by each ndustry k, wth elastcty of substtuton σ, and Cobb-Douglas preferences over ndustres. The share of fnal consumpton expendture on each ndustry s η F,k, wth k ηf,k = Prces The technology dstrbuton and the CES prce ndex (for consumers and buyers of ntermedates) yeld a closed form expresson for prces n each destnaton country n that vary by ndustry k and end use u: p uk n = γ [ N =1 ] 1/θ T uk (c k τn uk ) θ, (12) where γ = [ Γ ( )] σ 1/(1 σ) θ and Γ s the gamma functon. 11 Prces n country n are a functon of ts access (τn uk ) to the technology and costs of all countres. 4.5 Trade The probablty that ndustry k n country s the lowest-cost provder of good l for end-use u n country ) θ. n s πn uk = T uk 12 Because there s a contnuum of goods, πn uk s also the fracton of goods that ( γc k τ uk n p uk n ndustry u n country n buys from ndustry k n country. Further, the dstrbuton of mnmum prces s [ u 10 It s possble to embed correlaton across end use wthn ndustres, resultng n the jont dstrbuton F k (z) = exp { ( T uk z θ) 1/ρ ] ρ }, where z s the vector [z I,k, z F,k ] and ρ s a measure of correlaton that rses as correlaton decreases, wth 0 < ρ 1. The parameter ρ s not separately dentfable from θ, and ntroducng correlaton (low ρ) reduces the strength of comparatve advantage n the same way that hgher θ reduces the strength of comparatve advantage. 11 The effcency parameter z uk (l) s the realzaton of the random varable Z uk, so the delvered prce of a good p uk n (l) s a realzaton of the random varable Pn uk = c k τ n uk/zuk, and the lowest prce s a realzaton of Pn uk = mn { Pn uk; = 1,..., N}. Substtutng the expresson for Pn uk nto the technology dstrbuton yelds a dstrbuton of prces Guk n (p) = 1 F uk (c k τ n uk/p) = uk 1 e T (c k τ n uk ) θ p θ. Buyers purchase the good from the country wth the lowest prce, so the prce dstrbuton s the dstrbuton of mnmum prces: G uk n (p) = 1 N =1 [1 Guk n (p)] = 1 e Φuk n pθ, where Φ uk n = N =1 T uk (c k τ n uk) θ. Substtutng ths dstrbuton nto the CES prce ndex yelds the expresson for p uk n. 12 Ths probablty s Pr [ p uk n (l) mn { p uk n (l); }] = 0 [1 Guk n (p)] dg uk n (p). Substtutng the dstrbuton of prces G uk n yelds the expresson shown n the equaton. 15

16 nvarant to the source country, so the average prce per good s also nvarant to the source. Ths means that π uk n s the fracton of country n, ndustry u expendture on ndustry k goods that come from country : πn uk = Xuk n Xn uk = T uk ( γc k τn uk ) θ p uk, (13) n where X uk n s total spendng on ndustry k goods by ndustry u n country n, and X uk n s spendng on the goods that come from country. A destnaton country wll purchase a larger share of ts ndustry k, enduse u requrements from a country wth a hgher technology level, lower costs, or wth wth whch t has lower blateral trade costs. A hgh prce n the destnaton country ncreases the share that the country wll purchase from a gven orgn country relatve to a destnaton country wth a lower prce. 4.6 Market Clearng Total expendture by country n on ndustry k goods X k n can be dvded nto expendture on ntermedates X I,k n and expendture on fnal goods Xn F,k : Xn k = Xn I,k expendture to each orgn country usng the trade shares π uk n : + Xn F,k, and we can allocate ntermedate and fnal Xn k = π I,k n XI,k n + π F,k n XF,k n. (14) Goods markets clear, so the value of ndustry output Q k on ndustry k goods from country : Q k equaton, we have: Q k = equals the sum of expendture by all countres n = N n=1 Xk n. Substtutng (14) nto the goods market clearng N n=1 ( ) π I,k n XI,k n + π F,k n XF,k n. (15) Recallng the Cobb-Douglas producton structure, equlbrum ndustry expendtures on labor and captal are a constant share of ndustry output: w n L k n = α k nβ k nq k n and r n K k n = ι k nβ k nq k n, (16) where L k n and K k n are the ndustry demands for labor and captal. Factor markets clear, so k Lk n = L n and k Kk n = K n. Industry expendture on ntermedates s a fracton 1 β k n of ndustry output, so we can wrte expendture on ndustry k ntermedates as a functon of output n all ndustres k usng the nput 16

17 shares η k,k n : X I,k n = k η k,k n (1 β k n )Q k n. (17) I do not requre that trade s balanced. Denote S n as the exogenous trade surplus of country n, wth n S n = 0 and S n = k Sk n. The ndustry-level trade surplus S k n s output mnus expendture, S k n = Q k n X k n, so we can wrte equaton (17) as: X I,k n = k η k,k n (1 β k n )(X k n + S k n ). (18) Fnal consumpton expendture X F n equals natonal ncome Y n, the sum of payments to labor and captal across all ndustres, mnus the trade surplus S n : X F n = Y n S n = k (w n L k n + r n K k n) S n. (19) Fnal consumpton expendture s allocated to each ndustry k by consumpton shares ηn F,k, so Xn F,k = ηn F,k Xn F. Ths equaton, and equatons (16), (17), and (19) mply that we can wrte expendture on ndustry k ntermedates X I,k n of producton. That s, and expendture on ndustry k fnal goods X F,k n n = η k,k n (1 β k α k k n βn k X I,k n ) as functons of payments to the factors w n L k n (20) and X F,k n = η F,k n (w n L k n + r n Kn k Sn). k (21) k Substtutng equatons (20) and (21) nto (15), we can wrte: Q k = [ N n=1 π I,k n ( k ηk,k n (1 β k αn k βn k n ) w n L k n ) + π F,k n ηf,k n ] (w n L k n + r n Kn k Sn) k. (22) Ths equaton, along wth the cost and prce equatons (10)-(12), the trade share equaton (13), and the factor market clearng and trade balance condtons, characterzes the soluton. The parameters are α k n, ι k n, β k n, η k,k n, Tn uk, τn uk, L n, K n, S n, and θ. The model solves for costs c k n, wages w n, rental rates r n, prces p uk n, trade shares π uk n, ndustry demands for labor and captal, Lk n and K k n, and each ndustry-level trade surplus S k n. k 17

18 5 Estmaton In ths secton I descrbe the procedure that I use to estmate and recover the parameters of the model. I use the estmated parameters to solve the model and quantfy the contrbuton of end-use varaton to the gans from trade (Secton 8). I also use the parameter estmates to understand the extent to whch ntermedate relatve to fnal technology, trade costs, and prces are related to a country s ncome level (Secton 7). 5.1 Dervng the estmatng equaton The trade share equaton, (13), forms the bass of the estmaton procedure. I follow Levchenko and Zhang (2013), who use an adaptaton of the standard Eaton and Kortum procedure, to estmate the technology and trade cost parameters. I begn by normalzng the trade share equaton by ts domestc counterpart πnn. uk Dvdng by the domestc trade share elmnates prces p uk n and llustrates comparatve advantage: a country wll mport a larger share than t purchases domestcally f the exportng country has an overall cost advantage, nclusve of trade costs (whch are normalzed to one n the domestc country): Log-lnearzng, ths equaton becomes ln ( ) π uk ( n πnn uk = ln π uk n π uk nn T uk = T uk Tn uk ( ) c k θ ) ( ln ( c k τn uk ) θ c k. (23) n T uk n ( c k n ) θ ) θ ln τ uk n. 13 (24) The frst two terms on the rght hand sde of the equaton measure the orgn and destnaton country s technology and cost advantage for producng ndustry k goods for end use u. I estmate the sze of ths advantage usng fxed effects S uk and Sn uk. Next, I specfy a functonal form for the trade cost parameter τn uk usng trade cost proxes that are standard n the gravty lterature: dstance, presence of a shared border, and common language. Log trade costs are gven by ln τ uk n = ( d uk) m + buk + l uk + ex uk. (25) where ( d uk) m s the effect of lyng n dstance nterval m, buk s the effect of havng a shared border, and l uk s the effect of sharng a language. The dummy varable assocated wth each effect s suppressed to smplfy 13 Takng logs drops zeros from the estmaton. I dscuss dropped observatons n Secton 6. 18

19 notaton. The dstance ntervals n mles, followng Eaton and Kortum, are: [0,375), [375, 750), [750, 1500), [1500,3000), [3000,6000), and [6000, max]. I also nclude an exporter fxed effect ex uk ; Waugh (2010) shows that exporter fxed effects, as opposed to mporter fxed effects, produce estmates that are more consstent wth the observed pattern of prces and country ncomes. Substtutng the trade cost specfcaton (25) nto equaton (24), replacng the technology and cost advantage terms wth fxed effects, and ncorporatng an error term ε uk n, we arrve at the estmatng equaton: The fxed effects S uk ln ( ) π uk n πnn uk = S uk Sn uk θ ( d uk) m θbuk θl uk θex uk + ε uk n. (26) and S uk n them to be symmetrc. That s, S uk measure the same object the technology-adjusted unt cost so I restrct = S uk n for all = n. Further, the estmatng equaton reduces to an dentty for observatons n whch = n, so domestc flows are omtted. I estmate the equaton usng OLS and Posson and Gamma pseudo-maxmum lkelhood (PML) methods. I perform the Posson and Gamma PML estmaton methods to ncorporate zeros estmatng the equaton n logs drops zero trade flows and to address the problem posed by heteroskedastcty that arses n log-transformed regressons as dscussed n Santos-Slva and Tenreyro (2006) Recoverng the parameters In ths subsecton I descrbe the method that I use to recover the values T uk, τ uk n, and puk. These values are used to nvestgate the relatonshp between aspects of comparatve advantage and a country s ncome level, and the technology and trade cost parameters are used to solve the model. Each step requres an estmate of θ, whch I agan take to be four. Recall that the estmated fxed effect S uk S uk measures the technology-adjusted unt cost: ( = ln T uk ( c k ) θ ). 15 (27) To fnd prces I follow the method of Shkher (2012) by substtutng the exponentated fxed effect exp ( ) S uk 14 Santos-Slva and Tenreyro (2006) show that when the varance of the error term n a multplcatve model depends on the regressors, the expected value of the error term n the log-lnearzed model wll also depend on the regressors. 15 The fxed effects are estmated relatve to a reference country, whch I take to be the US, so all varables used n the recovery of the parameters are also transformed to be relatve to the US. 19

20 nto the domestc expendture share equaton and rearrangng: p uk = ( π uk exp ( S uk )) 1/θ. (28) To recover the technology parameter T uk, frst construct unt costs c k usng the Cobb-Douglas functonal ) β k form: c k (w = αk r ιk ( ) ρ k 1 β k. Wages, rental rates, and labor and captal shares are data from WIOD, and the prce of a bundle of ntermedates ρ k = ( ) η k,k k p I,k s constructed usng prces derved as descrbed above. Extract T uk cost parameters τ uk n from the fxed effect S uk usng ths value of c k are constructed by exponentatng equaton (25): ln τ uk n and equaton (27). The trade = ( d uk) m + buk + l uk + ex uk Data and Implementaton I estmate the parameters of the model usng the World Input-Output Database (WIOD), a global nputoutput table that reports trade flows between 35 ndustres (both manufacturng and servce classfcatons) and 40 countres (and a rest of world aggregate) for the years 1995 through The 40 countres comprse 85 percent of world trade and nclude 29 countres classfed as hgh ncome and 11 classfed as upper mddle or lower mddle ncome by the World Bank n The data set dstngushes the exportng country and ndustry and the mportng country and ndustry. 17 Because I am nterested n the dstncton between ntermedate and fnal use, I aggregate all ndustry-use categores to create the ntermedate classfcaton, and all fnal consumpton, nvestment, and nventory categores to create the fnal end-use classfcaton. 18 In order to mnmze the number of trade zeros whle keepng the data as dsaggregate as possble, I combne countres or ndustres that have zero ndustry output. Ths aggregaton scheme elmnates all country-by-ndustry output zeros, and reduces the number of countres from 40 to 38 and the number of ndustres from 35 to 32. See Tables 3 and 4 for WIOD countres and ndustres and the aggregaton scheme. 16 The US s also the reference country for the exporter fxed effect, so the trade cost estmates are, net of all blateral components, relatve to the cost to export from the US for each ndustry-end-use par. 17 WIOD dstngushes use by allocatng HS 6-dgt mport flows from the UN COMTRADE database to end-use categores (ntermedate, fnal consumpton, and nvestment) usng a correspondence based on the Broad Economc Categores (BEC) from the Unted Natons Statstcs Dvson. When a product can reasonably be classfed nto more than one end-use category, weghts are appled to dvde the trade flow nto the relevant categores. Servces trade s taken from varous sources (UN, Eurostat, and OECD), and s splt nto end-use categores usng average use shares from mport nput-output tables from Eurostat. Wthn the ntermedate, fnal consumpton, and nvestment categores trade flows are allocated by proportonalty assumpton. See Tmmer (2012) for a detaled dscusson of the constructon of the World Input-Output Database. 18 In some country-by-ndustry observatons, the change n nventores s negatve, reflectng a declne n nventores, and large enough that the total fnal use value s negatve. I handle negatve nventores usng the method of Costnot and Rodríguez-Clare (2013) (see the onlne appendx to ther paper), whch s to set negatve nventores to zero, and recalculate the total output vector and matrx of ntermedate flows usng the dentty X = (I A) 1 F, where X s the total output vector, A s the matrx of drect nput coeffcents, and F s the fnal demand vector, wth negatve nventores set to zero and postve nventores left unchanged. 20

21 I estmate the model for the year 2007 because t s the most recent year that fully predates the trade collapse, and because captal stocks are provded only for a lmted set of countres n 2008 and I exclude the rest of world aggregate because of the dffculty to create dstance, border, and shared language varables for ths regon. The dmensons of the fnal data set are 38 orgn by 38 destnaton countres by 32 ndustres by 2 types of end use. I use the Soco-Economc Accounts (SEA) that accompany the WIOD to construct wages, rental rates, and labor and captal shares. Wages are calculated as total labor compensaton n a country (LAB) dvded by the total number of hours worked by persons engaged (H EMP). The rental rate s constructed by dvdng total captal compensaton (CAP) by the value of the captal stock (K GFCF ), whch s converted from real to nomnal values usng the prce ndex for gross fxed captal formaton (P GFCF ). Labor and captal compensaton and the value of the captal stock are converted to US dollars usng exchange rates provded by WIOD. Labor and captal shares are computed by dvdng labor compensaton (LAB) and captal compensaton (CAP) by gross output (GO). Input shares are constructed drectly from WIOD by dvdng country-by-ndustry total expendture on ntermedates by country-by-ndustry expendture on ntermedates from a partcular ndustry. The estmaton strategy requres takng the log of relatve trade shares, so zeros are not ncluded. In total, 5.9 percent of the relatve trade share observatons are zeros. The prevalence of zeros vares by ndustry, and s hgher n servce ndustres 9.7 percent n servce ndustres and 1.8 percent n goods ndustres. Wthn ndustres, across end use, the proportons of zeros are very smlar. Ths means that, to the extent that mssng observatons ntroduce bas n the OLS estmates, concerns should be less pronounced for wthn-ndustry, across-end use comparsons, whch are the focus of ths paper. Even f zeros do not pose a sgnfcant problem, estmatng log-transformed regresson equatons wll produce nconsstent estmates when heteroskedastcty s present. To account for zeros and ths problem posed by heteroskedastcty, I estmate the model usng Posson and Gamma pseudo-maxmum lkelhood (PML) methods n addton to OLS. I follow the procedure outlned n Head and Mayer (2014) to determne whch of the three sets of estmates are most relable. 21

22 7 Results 7.1 Evaluatng the estmaton methods Determnng whether to use the OLS, Posson PML, or Gamma PML estmates requres assessng the smlarty of the estmates across models. Head and Mayer (2014) provde recommendatons for three scenaros: (1) the parameter estmates across the three methods are smlar, (2) Posson and Gamma PML estmates are smlar but dstnct from the OLS estmates, (3) the Gamma and OLS coeffcents are smlar and the Posson are smaller n absolute magntude. To assess the smlarty of the hgh number of estmates, I regress the set of estmates from one method on the set of estmates for the other methods and force the coeffcent on the regressor to equal one, ensurng that a good ft sgnfes that the estmates are not just correlated, but also smlar n magntude. 19 The R-squared from each regresson s reported n Table 5. I report the R-squared for the trade cost coeffcents (dstance, border, and language), the fxed effects (compettveness and exporter), and for all coeffcents. The trade cost estmates are smlar across models, and the OLS estmates are partcularly close to both the Posson and Gamma estmates, R-squared 0.84 and 0.81, respectvely. The fxed effects are less smlar and reduce the strength of the overall ft, but the R-squared remans close to or above 0.5 n each case; ths ponts toward scenaro (1) from Head and Mayer. Further, the Posson and Gamma estmates are less smlar to each other than the OLS estmates are to each of these methods (R-squared 0.48 versus 0.54 and 0.57), whch does not favor scenaro (2). Scatter plots that correspond to the R-squared calculatons, provded n Fgure 5, depct the relatonshp between coeffcents across models. Regardng scenaro (3), the Gamma and OLS estmates are smlar, but the Posson estmates are not smaller n absolute magntude. Table 6 shows the average absolute value of the estmate for each set of parameters, and the Posson estmates are not systematcally lower than the others. Ths ponts toward scenaro (1), n whch case the log-lnear model s well-specfed and consstency of the estmates s not a concern. I proceed here wth the OLS estmates, and all exercses performed usng the Posson and Gamma estmates are avalable upon request. 7.2 A closer look at comparatve advantage The exercse n Secton 3 gave a broad mpresson that low ncome countres have a comparatve dsadvantage n ntermedate relatve to fnal goods, and that these countres pay relatvely hgher prces for ntermedates. 19 The estmatng equaton produces 5,248 parameter estmates: there are ( 1) u k compettveness fxed effects S uk, ( 1) u k exporter fxed effects ex uk, m u k dstance coeffcents ( d uk) m, u k border coeffcents buk, and u k common language coeffcents l uk. 22

23 In ths secton I use the parameter estmates to nvestgate these relatonshps further. Before assessng the relatonshp between comparatve advantage at the end-use level and ncome, I frst evaluate the relatonshp between the ndvdual ntermedate and fnal estmates and ncome. I separately regress the ntermedate and fnal technology, trade cost, and prce estmates on log per capta GDP relatve to the US and ndustry fxed effects. The estmatng equaton for the technology and prce estmates s: ln Υ uk = β 0 + β 1 ln GDP + α k + ε uk, for u = {I, F }, (29) where Υ uk fxed effects, and ε uk represents technology (T uk ) 1/θ (the mean of each Fréchet dstrbuton) or prce p uk, α k are the s the error term. I expect that β 1 wll be postve n the technology and prce regressons because hgher ncome countres are on average more productve and pay hgher wages, whch mply hgher nput costs. For trade costs, whch vary by orgn and destnaton country, the estmatng equaton s: ln τ uk n = β 0 + β 1 ln GDP c + α k + ε uk n, for u = {I, F } and c = {n, }, (30) where the subscrpt c on the varable ln GDP c ndcates whether trade costs are regressed on exporter or mporter ncome. I expect β 1 to be negatve n the trade cost regressons, reflectng better transport nfrastructure and more open trade polces n hgher ncome countres. I run the regressons for all ndustres together and for four broad ndustry classfcatons: Agrculture, Mnng, Manufacturng, and Servces. The frst two sectons of Table 7 present the results. Hgh ncome countres have hgher average technology levels for both ntermedates and fnal goods than low ncome countres n all categores except Mnng. The coeffcent on ncome n the prce regressons s also postve n the majorty of the regressons. It s notably not statstcally dfferent from zero n the ntermedate Mnng and Manufacturng categores, lkely due to the very tradable nature of these goods. The export trade cost regressons show that the cost to export s decreasng n ncome for all categores except ntermedate Agrculture and Mnng, perhaps reflectng trade polces n lower ncome countres that promote commodty exports. The estmates from the mport trade cost regressons show that hgher ncome countres also pay less to mport than lower ncome countres. The relatonshp s less pronounced, but t exsts for all ndustry categores. To evaluate comparatve advantage at the end-use level, I next regress relatve values of the estmates on ncome. The specfcatons are the same as above, except the left hand sde s now the log of the rato of the 23

24 ntermedate estmate to the fnal estmate. The estmatng equaton for technology and prces s: and the estmatng equaton for trade costs s: ( ) Υ I,k ln Υ F,k = γ 0 + γ 1 ln GDP + α k + µ k, (31) ( ) τ I,k n ln τ F,k = γ 0 + γ 1 ln GDP c + α k + µ k n, for c = {n, }. (32) n The exercse n Secton 3 that related relatve domestc expendture shares to relatve technology and relatve prces showed that low ncome countres have a comparatve dsadvantage n the producton of ntermedates, and the data showed that the relatve prce of ntermedates s hgher n these countres. It s lkely that these fndngs do not hold for every ndustry category, but I do expect broadly smlar results that γ 1 s postve n the technology regressons and negatve n the prce regressons. Gven that relatve prces are decreasng n ncome, t s reasonable to expect that t s more dffcult for lower ncome countres to mport ntermedates relatve to fnal goods, mplyng that γ 1 s negatve n the mport trade cost regresson; the prce data do not have mplcatons for the export trade cost regressons, however. The results are shown n the thrd secton of Table 7. Hgh ncome countres have an overall comparatve advantage n ntermedates that s drven by comparatve advantage n the Agrculture and Manufacturng sectors. The export trade cost regresson coeffcents are sgnfcant and postve for Agrculture and Manufacturng, ndcatng that lower ncome countres are able to export ntermedate goods n these ndustres at a relatvely lower cost than fnal goods compared to hgh ncome countres. The coeffcents from the mport trade cost regressons are mostly negatve, ndcatng that low ncome countres have relatvely more dffculty mportng ntermedates than fnal goods relatve to hgh ncome countres. Relatve prces are negatvely related to ncome n all categores. Ths s consstent wth the aggregate data, and wth the fact that low ncome countres have a comparatve dsadvantage n ntermedates and that t costs these countres relatvely more to mport ntermedates. Recallng equaton (12), prces are a functon of the states of technology around the world and the mportng country s access to these technologes va trade costs. If low ncome countres are not productve n ntermedates and pay more to mport them, they wll pay a hgher overall prce. 7.3 Trade costs Table 8 takes a closer look at trade costs. Each column shows the average coeffcent across ndustres for ntermedates and fnal use for all ndustres, goods, and servces. The famlar gravty result that trade 24

25 decreases wth dstance and ncreases wth the presence of a shared border and common language holds up by end use, and for both goods and servces classfcatons. Across all ndustres, fnal goods and servces are less tradable than ntermedates, and the sze of the barrers are large. The average mpled effect on cost at a dstance of [1500,3000) mles s 293 percent for fnal goods and servces and 209 percent for ntermedates wth θ = Not surprsngly, servces are much less tradable than goods, and the result that fnal use goods or servces tend to be less tradable than ther ntermedate counterparts holds up wthn these classfcatons (wth the excepton of the two furthest dstance ntervals for goods). 7.4 Balassa-Samuelson effect The results n Tables 7, 8, and 9 provde evdence of a Balassa-Samuelson effect, whch says that countres wth a hgher productvty n the tradables sector wll have a hgher relatve prce of nontradables. I treat all goods as tradable, but fnal goods are comparatvely less tradable than ntermedates, as Table 8 shows. Greater tradablty n ntermedates means that the prces of ntermedates should be less varable across locatons than the prces of fnal goods and servces. Table 9 demonstrates ths by reportng the standard devaton by end-use classfcaton for ndustry-demeaned prces. Intermedate prces are less varable than fnal prces, and the same holds wthn goods and servces classfcatons. Hgher ncome countres have a hgher technology level n ntermedates, overall and for goods and servces, so t follows that these countres wll have a hgher relatve prce of the less tradable good or, equvalently, that lower ncome countres wll have a hgher relatve prce of the more tradable good, the ntermedate (Table 7). 8 Smulaton In ths secton I solve the full general equlbrum model to determne the effect that ncorporatng end-use varaton has on the gans from trade relatve to a model wthout end-use varaton. The labor, captal, and nput shares (αn, k βn, k and ηn k,k ), sze of the labor force (L n ) and captal stock (K n ) are constructed from WIOD as descrbed n Secton 6. The technology and trade cost parameters (T uk and τn uk ) are estmated accordng to the procedure descrbed n Secton 5, and θ s taken to be 4. The model solves for costs c k n, wages w n, rental rates r n, prces p uk n, trade shares π uk n, ndustry demand for labor and captal, Lk n and K k n, and each ndustry-level trade surplus S k n. I solve the model wth end-use varaton the technology and trade cost parameters are specfc to ntermedate or fnal use wthn country and ndustry and wthout 20 The mpled percentage effect on cost s 100(e ˆd/θ 1) for an estmated coeffcent ˆd. 25

26 and compare the gans from trade. In the verson wthout end-use varaton, I re-estmate the parameters usng trade data that s not dstngushed by end use that s, the left sde of the estmatng equaton (26) s ) ln. The dscrepancy n the gans from trade (relatve to autarky) between the two models s shown n ( π k n π k nn Table 10. The model wthout end-use varaton understates the gans from trade by 4.1 percent on average, and the dscrepancy s larger on average for low ncome countres 8.8 percent versus 1.9 percent for hgh ncome countres. 9 Concluson In ths paper I show that a proper calculaton of the gans from trade requres allowng for dfferences n the characterstcs of ntermedate and fnal goods trade. Domestc expendture shares and prces vary by ntermedate and fnal use, ndcatng the presence of productvty dfferences that generate gans from trade. Ths source of productvty dfferences has not prevously been dentfed nor has t been explored as an avenue for the gans from trade. Dstngushng ntermedate and fnal goods trade s of added mportance because ntermedate goods are used n the producton of other ntermedates and fnal goods are not meanng that the gans from trade n ntermedates, but not fnal goods, accumulate through the producton process. I construct a smple model that allows for productvty dfferences n the producton of ntermedate and fnal goods, and show analytcally that the gans from trade are always understated n a model that does not nclude ths varaton. Usng a novel data set, I show that the dfferences are one percent for hgh ncome countres and 1.4 percent for low ncome countres, and that the gans from trade are two tmes more responsve to changes n ntermedates trade than to fnal goods trade. To more fully assess the sze of the dscrepancy, I construct a model that features varaton n ntermedate and fnal use at the ndustry level, lnkages between ndustres, and multple factors of producton. Solvng the model numercally, I fnd that the gans from trade are 1.9 percent hgher for hgh ncome countres and 8.8 percent hgher for low ncome countres. Low ncome countres beneft more from trade across ntermedate and fnal use, and ths appears to be the related to the nature of comparatve advantage. The parameter estmates show that low ncome countres have a comparatve dsadvantage n the producton of ntermedates; thus, openng to trade allows these countres to mport ntermedates whch comprse two-thrds of the cost of producton and generate cumulatve gans from trade from the more productve hgh ncome countres. Gven ther comparatve dsadvantage, access to mported ntermedates s partcularly central to welfare n low ncome countres. Despte ths, the parameter estmates also reveal that trade costs pose a dsproportonate burden for trade 26

27 n ntermedates n low ncome countres: low ncome countres pay relatvely more to mport ntermedate goods than fnal goods compared to hgh ncome countres. The combnaton of a comparatve dsadvantage n ntermedates and a relatvely hgher cost to mport ntermedates results n a hgher relatve prce of ntermedates n low ncome countres. Hgher prces of ntermedates present an mportant polcy challenge, as they lmt the compettveness of countres seekng greater access to nternatonal producton networks. Ths study suggests that polces that target productvty mprovements n ntermedates and the lowerng of barrers to tradng ntermedates may generate mportant welfare gans n low ncome countres. 27

28 10 Tables Table 1: Domestc Expendture Shares Hgh Income Low Income Dfference Domestc expendture share, fnal goods and servces: π F (0.025) Domestc expendture share, ntermedate goods and servces: π I ** (0.035) Rato of fnal to ntermedate shares: π F /πi ** (0.036) Labor share n gross output: β * (0.021) Domestc expendture share, overall: π ** (0.030) Domestc expendture share, balanced trade: β π F + (1 β )π I Domestc expendture share, geometrc average: ( π F ) β ( π I ) 1 β Notes: Ths table reports the average country-level domestc expendture share and labor share for hgh and low ncome countres. The standard error of the dfference s gven n parentheses. The balanced trade and geometrc average domestc expendture shares are calculated at the average to facltate gans from trade calculatons whch are also computed at the average. Hgh ncome countres are those classfed as hgh ncome n 2007 by the World Bank (see Table 3). Low ncome countres are those classfed as upper mddle or lower mddle n Sgnfcance at the one percent level s represented by ***, at the fve percent level by **, and at the ten percent level by *. Table 2: Comparson of End-Use and Standard Model Hgh Income Low Income Panel A: Gans from Trade ( (π ) End-use model: F β ( ) ) π I 1 β 1/β θ Standard model, balanced trade: ( β π F + (1 β )π I ) 1/β θ Standard model, measured: π 1/β θ Panel B: Dscrepances n the Gans from Trade Compared to the End-Use Model Dscrepancy, balanced trade Dscrepancy, actual Panel C: Elastctes, Rato of Intermedate to Fnal End-use model Standard model, balanced trade Standard model, actual Notes: Gans from trade are computed at the average domestc expendture and labor shares reported n Table 1 wth θ = 4 and are net gans from trade,.e. subtract one from the formulas presented n the text. Hgh ncome countres are those classfed as hgh ncome n 2007 by the World Bank (see Table 3). Low ncome countres are those classfed as upper mddle or lower mddle n

29 Table 3: Lst of Countres Country Abbrevaton Income Classfcaton, 2007 Australa AUS Hgh Austra AUT Hgh Belgum BEL Hgh Bulgara BGR Upper Mddle Brazl BRA Upper Mddle Canada CAN Hgh Chna CHN Lower Mddle Cyprus, Luxembourg, and Malta CYP-LUX-MLT Hgh Czech Republc CZE Hgh Germany DEU Hgh Denmark DNK Hgh Span ESP Hgh Estona EST Hgh Fnland FIN Hgh France FRA Hgh Unted Kngdom GBR Hgh Greece GRC Hgh Hungary HUN Hgh Indonesa IDN Lower Mddle Inda IND Lower Mddle Ireland IRL Hgh Italy ITA Hgh Japan JPN Hgh Korea KOR Hgh Lthuana LTU Upper Mddle Latva LVA Upper Mddle Mexco MEX Upper Mddle Netherlands NLD Hgh Poland POL Upper Mddle Portugal PRT Hgh Romana ROM Upper Mddle Russa RUS Upper Mddle Slovak Republc SVK Hgh Slovena SVN Hgh Sweden SWE Hgh Turkey TUR Upper Mddle Tawan TWN Hgh Unted States USA Hgh Notes: Ths table shows the lst of countres, and ther abbrevatons and 2007 ncome classfcatons, ncluded n the World Input-Output Database. Income classfcatons are determned by GNI per capta thresholds set by the World Bank. The thresholds, n US dollars, for Lower Mddle, Upper Mddle, and Hgh ncome countres, respectvely, are: 936-3,705; 3,706-11,455, and > 11,

30 Table 4: Lst of Industres NACE Code Descrpton Classfcaton Aggregaton AtB Agrculture, Huntng, Forestry and Fshng AtB C Mnng and Quarryng C 15t16 Food, Beverages and Tobacco 15t16 17t18 Textles and Textle Products 17t18 19 Leather, Leather and Footwear Wood and Products of Wood and Cork 20 21t22 Pulp, Paper, Paper, Prntng and Publshng 21t22 23 Coke, Refned Petroleum and Nuclear Fuel 23 Goods 24 Chemcals and Chemcal Products Rubber and Plastcs Other Non-Metallc Mneral 26 27t28 Basc Metals and Fabrcated Metal 27t28 29 Machnery, Nec 29 30t33 Electrcal and Optcal Equpment 30t33 34t35 Transport Equpment 34t35 36t37 Manufacturng, Nec; Recyclng 36t37 E Electrcty, Gas and Water Supply E F Constructon F 50 Sale, Mantenance and Repar of Motor Vehcles and Motorcycles; Retal Sale of Fuel 51 Wholesale Trade and Commsson Trade, Except of Motor Vehcles and Motorcycles 50, Retal Trade, Except of Motor Vehcles and Motorcycles; Repar of Household Goods 52 H Hotels and Restaurants H 60 Inland Transport Water Transport Ar Transport Other Supportng and Auxlary Transport Actvtes; Actvtes of Travel Agences Servces Post and Telecommuncatons 64 J Fnancal Intermedaton J 70 Real Estate Actvtes 70 71t74 Rentng of M&Eq and Other Busness Actvtes 71t74 M Educaton M N Health and Socal Work N L Publc Admn and Defence; Compulsory Socal Securty O Other Communty, Socal and Personal Servces L, O, P P Prvate Households wth Employed Persons Notes: Ths table shows the NACE code, descrpton, Goods or Servces classfcaton, and aggregaton scheme of the ndustres ncluded n the World Input-Output Database. Table 5: OLS, PPML, and GPML R-squared PPML v. OLS GPML v. OLS PPML v. GPML Trade Cost Estmates Fxed Effects Entre Regresson Notes: Ths table shows the R-squared from a regresson of the coeffcents from one estmaton method aganst the coeffcents from another estmaton method wth the coeffcent on the ndependent varable constraned to be one. Table 6: Average Absolute Value of Estmate OLS PPML GPML Dstance [0,375) Dstance [375,750) Dstance [750,1500) Dstance [1500,3000) Dstance [3000,6000) Dstance [6000,max] Shared border Shared language Compettveness Fxed Effect Exporter Fxed Effect Notes: Ths table shows the average value of the absolute value of the estmated coeffcents across estmaton methods. 30

31 Table 7: Regresson of Log Parameters on Log GDP, OLS Estmates Intermedate Fnal Intermedate/Fnal Coef. Std. Err. R-sq. No. Obs. Coef. Std. Err. R-sq. No. Obs. Coef. Std. Err. R-sq. No. Obs. Technology All Industres 0.57*** (0.14) , *** (0.15) , ** (0.02) ,184 Agrculture 0.75** (0.29) * (0.28) *** (0.04) Mnng 0.09 (0.18) (0.21) (0.12) Manufacturng 0.39*** (0.10) *** (0.11) ** (0.03) Servces 0.75*** (0.18) *** (0.18) (0.02) Trade Costs (Exporter) All Industres -0.32*** (0.08) , *** (0.1) , (0.02) ,468 Agrculture (0.12) , *** (0.13) , *** (0.07) ,444 Mnng (0.15) , ** (0.13) , (0.13) ,333 Manufacturng -0.26*** (0.08) , *** (0.11) , ** (0.04) ,142 Servces -0.40*** (0.11) , *** (0.11) , * (0.02) ,549 Trade Costs (Importer) All Industres -0.09* (0.05) , * (0.04) , * (0.004) ,468 Agrculture -0.13* (0.07) , * (0.07) , (0.01) ,444 Mnng -0.14* (0.07) , * (0.04) , ** (0.04) ,333 Manufacturng -0.10* (0.05) , * (0.05) , * (0.01) ,142 Servces -0.07* (0.04) , * (0.04) , ** (0.001) ,549 Prces All Industres 0.08*** (0.03) , *** (0.03) , ** (0.02) ,184 Agrculture 0.14*** (0.04) *** (0.04) *** (0.04) Mnng 0.08 (0.06) *** (0.07) * (0.09) Manufacturng 0.05 (0.03) *** (0.02) * (0.02) Servces 0.10** (0.04) *** (0.05) ** (0.01) Notes: All regressons nclude ndustry fxed effects. The export trade cost estmates are obtaned by regressng blateral trade costs on exporter GDP and the mport trade cost estmates are obtaned by regressng blateral trade costs on mporter GDP. Standard errors are clustered at the country level. The dependent varable s a functon of estmates, so I have also followed the Lews and Lnzer (2005) FGLS method to account for samplng error n the estmaton of the dependent varable, usng bootstrapped standard errors of the technology, trade cost, and prce estmates to construct the weghts that are appled n the second-stage WLS regresson. The Stata routne for the procedure edvreg does not allow clustered standard errors, and the standard errors are more conservatve when they are clustered and the Lews and Lnzer approach s not used. For ths reason I present the clustered standard error estmates rather than the Lews and Lnzer estmates. Sgnfcance at the one percent level s represented by ***, at the fve percent level by **, and at the ten percent level by *. 31

32 Table 8: Trade Cost Components, OLS Estmates Coeffcents All Industres Goods Servces Varable Int. Fnal Int. Fnal Int. Fnal Dstance [0,375) Dstance [375,750) Dstance [750,1500) Dstance [1500,3000) Dstance [3000,6000) Dstance [6000,max] Shared border Shared language Exporter Effects All Industres Goods Servces Country Int. Fnal Int. Fnal Int. Fnal AUS AUT BEL BGR BRA CAN CHN CYP-LUX-MLT CZE DEU DNK ESP EST FIN FRA GBR GRC HUN IDN IND IRL ITA JPN KOR LTU LVA MEX NLD POL PRT ROM RUS SVK SVN SWE TUR TWN USA Notes: Coeffcents and exporter effects are averages across ndustres. 32

33 Table 9: Standard Devaton of Prces by End Use, OLS Estmates All Industres Goods Servces Intermedate Fnal Notes: Prces are demeaned by ndustry before computng the standard devaton. Table 10: Gans from Trade, End- Use vs. Standard Model Country GFT Dscrepancy AUS AUT BEL BGR BRA CAN CHN CYP-LUX-MLT CZE DEU DNK ESP EST FIN FRA GBR GRC HUN IDN IND IRL ITA JPN KOR LTU LVA MEX NLD POL PRT ROM RUS SVK SVN SWE TUR TWN USA Notes: GFT dscrepancy s the percentage ncrease n the gans from trade movng from the full model wth no end-use varaton to the full model wth end-use varaton. 33

34 11 Fgures Fgure 1: Country-Level Domestc Expendture Share, Intermedate vs. Fnal Domestc Expendture Share, Intermedate RUS USA BRA AUS CHN JPN GBR FRA ITA ESP IDN IND TUR CAN KOR DEU PRT POL ROMFINMEX LVA SWE GRC CZE RoW AUT DNK ESTCYPTWN NLD LTU BGR SVN BEL SVKIRL MLT HUN LUX Domestc Expendture Share, Fnal Notes: Ths fgure plots the ntermedate domestc expendture share π I aganst the fnal domestc expendture share π F for the 40 countres n the sample. The 45 -lne s ncluded for reference. Fgure 2: Country-by-Industry-Level Domestc Expendture Share, Intermedate vs. Fnal Domestc Expendture Share, Intermedate Japan, Leather Goods Domestc Expendture Share, Fnal Notes: Ths fgure plots the ntermedate domestc expendture share π I,k aganst the fnal domestc expendture share π F,k for the 38x32 country-ndustry pars n the sample. The 45 -lne s ncluded for reference. 34

35 Fgure 3: Gans from Trade Dscrepancy, End-Use vs. Standard Model Notes: Ths fgure plots the dscrepancy between the end-use GFT formula and the standard GFT formula gven by equaton (8). 35