Measured Aggregate Gains from International Trade. Ariel Burstein (UCLA and NBER) and Javier Cravino (UCLA) 1. January 2012 Abstract

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1 Measured Aggregate Gas from Iteratoal Trade Arel Burste (UCLA ad NBER) ad Javer Cravo (UCLA) 1 Jauary 2012 Abstract Do theoretcal welfare gas from trade traslate to aggregate measures of ecoomc actvty? We calculate the chages real GDP ad real cosumpto that result from chages trade costs a rage of workhorse trade models, followg the procedures outled by statstcal ageces the Uted States. Our ma fdgs are as follows: Frst, real GDP ad measured aggregate productvty rse respose to reductos varable trade costs f GDP deflators capture the decle trade costs. Secod, wth balaced trade each coutry, chages world real cosumpto ad chages world real GDP (.e.: weghtg the chage each coutry by ts omal GDP) respose to chages varable trade costs cocde, up to a frst-order approxmato, wth chages world theoretcal (welfare-based) cosumpto. The equvalece betwee measured cosumpto ad theoretcal cosumpto holds coutry-by-coutry uder stroger codtos. Thrd, for gve trade shares ad chages varable trade costs, chages real GDP ad chages world real cosumpto are approxmately equal magtude across the models we cosder. 1 Itroducto What are the aggregate gas from reductos the costs of teratoal trade? There are two major approaches to address ths questo. A frst approach uses structural models to fer uobservable welfare gas from chages trade costs or trade patters (see e.g. Eato ad Kortum 2001, Alvarez ad Lucas 2007, Arkolaks, Costot ad Rodrguez-Clare 2011, Doaldso 2010, ad Waugh 2010). A secod approach documets the emprcal lk betwee the level or the chage teratoal trade ad aggregate dcators of ecoomc actvty (see e.g. Frakel ad Romer 1999, Rodrguez ad Rodrk 2001, ad Feyrer 2009a, 2009b). Ths paper coects these two approaches by studyg, wth a rage of workhorse models of teratoal trade, the relatoshp betwee theoretcal welfare gas from trade ad aggregate measures of ecoomc actvty, amely real GDP ad real cosumpto as costructed by atoal statstcal ageces. I dog so, we shed lght o the followg questos. Should we expect measured aggregate productvty ad real GDP to rse wth trade? Are aggregate measures of ecoomc actvty formatve of theoretcal gas from 1 A prevous verso of ths paper crculated uder the ttle "Trade Lberalzatos ad Measured Real GDP Models of Iteratoal Trade". We thak Costas Arkolaks, Adrew Atkeso, Araud Costot, Robert Feestra, Joatha Vogel, ad Ivá Werg for very useful commets.

2 trade? Do dfferet models have commo suff cet statstcs for the mpact of trade o aggregate measures of ecoomc actvty? The models that we base our aalyss o clude Armgto models wth perfect competto ad exogeous specalzato producto (e.g. Aderso 1979), Rcarda models wth edogeous specalzato producto (e.g. Dorbusch, Fsher ad Samuelso 1977 ad Eato ad Kortum 2001), ad moopolstcally compettve frm models wth heterogeous frms ad costat markups (e.g. Krugma 1980 ad Meltz 2003). We cosder extesos of the model wth multple factors of producto (but commo factor testes across producers) ad wth edogeous qualty choce. We clude teratoal trade costs of the form of ceberg varable trade costs, fxed export costs ( the model wth moopolstc competto), ad mport tarffs. I all of these models, reductos teratoal trade costs typcally result a rse welfare for the represetatve cosumer. We calculate these models mplcatos of reductos trade costs for real GDP ad real cosumpto calculated followg the procedures outled by the Bureau of Labor Aalyss to costruct the Natoal Icome ad Product Accouts (NIPA) the Uted States. For may dustres ad compoets of GDP, comprehesve measures of physcal quattes are dff cult to obta practce. I such cases, real quattes are typcally calculated by deflatg curret dollar measures of output or cosumpto wth prce dces e.g. most cases the producer prce dex (PPI) for output ad the cosumer prce dex (CPI) for cosumpto. We frst calculate the chage measured aggregate productvty ad real GDP followg a chage teratoal trade costs. We show that, respose to a decle varable trade costs, aggregate productvty ad real GDP ay coutry rse oly f trade costs are recorded GDP ad GDP deflators reflect the fall trade costs. That s, measured productvty ad real GDP rse whe varable trade costs fall f the servces ad actvtes requred to sell goods abroad (whch clude shppg servces provded by the trasportato dustry ad, more broadly, ay other producto, marketg, regulatory, ad formato costs that apply dfferetally to exported products) 2 are performed ad recorded the home coutry, as opposed to beg performed abroad or ot measured at all. Ths s because, uder certa codtos, measured aggregate productvty ay gve coutry oly respods to shfts ts producto possblty froter as s, prcple, desrable for a measure of productvty. 3 2 Aderso ad Va Wcoop (2004) argue that these addtoal costs are at least as mportat as arrowly-defed trasportato costs. 3 As show Kohl (2004) ad Kehoe ad Ruhl (2008), the value of producto at costat prces does ot respod, to a frst-order approxmato, to chages teratoal prces that leave the domestc producto 2

3 The respose of real GDP also depeds o the form of trade lberalzato. I partcular, chages fxed trade costs (f these are expesed ad hece ot recorded GDP) have o drect mpact o GDP deflators ad hece leave real GDP uchaged. Reductos mport tarffs crease real GDP from the expedture sde f tarff reveues at costat prces rse (whch requres a crease the physcal quatty of mports). Next, we compare chages real GDP ad real cosumpto ( our basele model, chages cosumpto expedtures are equal to chages total absorpto). Real GDP ad real cosumpto ca dffer eve whe trade s balaced due to movemets the prce of exports relatve to the prce of mports (the terms of trade). We show, however, that f trade s balaced each coutry, chages world real GDP are equal, up to a frst-order approxmato, to chages world real cosumpto (where each coutry s weghted by ts curret-dollar GDP). The equalty holds at the world aggregate level because terms of trade mprovemets oe coutry are assocated to terms of trade worseg aother coutry. Whle chages real GDP coutry-by-coutry deped crtcally o the patters of specalzato the producto of trade servces, the equalty betwee chages world real GDP ad world cosumpto does ot. Perhaps more mportatly, we compare chages measured real cosumpto wth chages theoretcal (or welfare-based) cosumpto. Dffereces betwee theoretcal ad measured cosumpto arse from dffereces betwee cosumpto deflators ad the theoretcal prce dex. Cosumpto deflators our model dffer from the welfare-based prce dex three respects. Frst, cosumpto deflators do ot fully take to accout substtuto cosumpto from chages relatve prces. Secod, they do ot take to accout chages the mass of cosumed goods whch, the presece of love for varety, matter for theoretcal cosumpto. Thrd, they do ot take to accout mprovemets product qualty f qualty chages are measured accurately cosumpto deflators. The report by the Bosk Commsso (1996) exames detal how these ad other bases the CPI lead to a uderstatemet of real cosumpto growth the U.S. We show how, uder certa codtos, these multple bases cosumpto deflators may ot result a msmeasuremet of theoretcal cosumpto. If the set of cosumed goods ad product qualty are fxed (so that the secod ad thrd sources of the bas are abset), the respose to ay type of trade cost movemet, chages theoretcal cosumpto are bouded betwee measured real cosumpto calculated usg tal base-year prces ad real cosumpto usg ed base-year prces. Ths mples, as s well-kow (see e.g. possblty froter uchaged. 3

4 Hausma 2003), that the substtuto bas s of secod order: each coutry, chages real cosumpto equal chages theoretcal cosumpto, up to a frst-order approxmato. Whe the set of cosumed goods ad product qualty are ot fxed, we establsh the followg result. I respose to chages varable trade costs, wth trade balace each coutry, chages world real cosumpto equal chages world theoretcal cosumpto (defed aalogously to world real cosumpto ad world real GDP), up to a frst-order approxmato. That s, whle chages theoretcal cosumpto ad real cosumpto may dffer coutry-by-coutry, these dffereces cacel-out whe addg them across coutres the world. Uder stroger assumptos (.e. Pareto dstrbuto of eterg frms productvty ad fxed export costs pad the destato market, as Eato, Kortum, ad Kramarz 2010), the equalty betwee measured cosumpto ad theoretcal cosumpto holds coutry-by-coutry, up to a frst-order approxmato, as the model wth a fxed set of cosumed goods. We also show that, respose to large reductos varable trade costs (for whch we must solve the model umercally), the elastctes of theoretcal cosumpto ad real cosumpto ca be qute close, coutry-by-coutry (ad hece also at the world level), depedetly of whether fxed export costs are curred domestcally or abroad. Fally, we ask whether the dfferet models that we cosder gve rse to dfferet suffcet statstcs for measured gas from trade. We cosder ths questo separately for our measures of real GDP ad real cosumpto. Across our rage of models, we obta a commo expresso for the chage real GDP as a average of chages varable trade costs weghted by export shares of cotug exportg producers. Codtoal o ths drect mpact of chages trade costs, reallocato of producto from less productve to more productve producers, etry ad ext to producto ad exportg, ad chages the mass of producers, have o addtoal effects o chages measured aggregate productvty ad real GDP. We also show that across our rage of models, chages world real cosumpto ad world real GDP are equal magtude, up to a frst-order approxmato, for gve trade shares ad for gve chages varable trade costs. Ths frst-order equvalece measured gas from trade cosumpto across seemgly dfferet models does ot reflect a adequacy of the aggregate measures of real cosumpto. Istead, ths equvalece measured gas from trade s cosstet wth the uderlyg equvalece the welfare mplcatos of these models uder some restrctos, as demostrated by Arkolaks, Costot ad Rodrguez-Clare (2011) ad Atkeso ad Burste (2010). Note, however, that chages fxed trade costs or foreg coutry sze that crease trade shares (ad also welfare, u- 4

5 der the assumptos of Arkolaks, Costot ad Rodrguez-Clare 2011) may ot result measured gas from trade. Our paper s related to a recet paper by Bajoa, Gbso, Kehoe, ad Ruhl (2010), who ask whether the crease welfare followg a trade lberalzato traslates to a crease real GDP as measured NIPA. They coclude, as summarzed Kehoe ad Ruhl (2010), that...stadard trade models do ot mply that opeg to trade creases productvty or real GDP, but that t creases welfare. The two ma dffereces of our paper relatve to Bajoa et. al. (2010) are as follows. Frst, whle Bajoa et. al. (2010) focus o the mplcatos of trade lberalzato o real GDP, we also study the effects o real cosumpto ad provde codtos uder whch the respose of real cosumpto to chages trade costs equals that of theoretcal cosumpto. Secod, Bajoa et. al. (2010) focus o cases whch prce dces do ot drectly reflect chages teratoal trade costs, ether because trade costs are fully curred abroad or because coutres are autarky before the trade lberalzato ( whch case prce dces of exported goods, as measured by the BLS, are ot well defed sce there are o cotug exported goods). I the class of models cosdered both papers, ths mples that measured real GDP s uchaged wth trade lberalzato (abstractg from chages real tarff reveues). We show, however, that startg wth postve trade levels, ay reducto trade costs that s reflected prce dces does result a crease real GDP. Our work s also related to Feestra (1994) ad Broda ad Weste (2006), who quatfy the msmeasured growth real cosumpto the U.S due to the rse the umber of mported varetes that s ot accouted for the CPI, wthout takg a stad o the source of the growth the umber of mported varetes. 4 We show our models that, respose to a reducto varable trade costs that results a rse the umber of mported varetes, to a frst-order approxmato there s o bas cosumpto deflators at the world aggregate level or, uder stroger codtos, coutry-by-coutry, whe smultaeously takg to accout geeral equlbrum other bases the prce dces. Hece, ay uderestmate of real cosumpto growth stemmg from a crease the mass of mported varetes that s ot captured the mport prce dex s offset by the other bases the CPI. Fally, our paper s related to the work of Pavck (2002) ad others, that costruct measures of aggregate productvty as weghted averages of productvty estmates across producers. Whle those measures of aggregate productvty may reflect the reallocato of 4 Relatedly, Feestra, Resdorf, ad Slaughter (2008) ad Nema ad Gopath (2011) argue that f export ad mport prce dces are msmeasured (amog other reasos, due to chages mport varety), chages tarffs or the terms of trade ca result chages measured aggregate productvty. 5

6 producto towards more productve producers duced by trade lberalzato, we argue, usg a rage of models of trade ad frm heterogeety as a laboratory, that measures of aggregate productvty costructed from NIPA do ot capture ths reallocato. The paper s orgazed as follows. Secto 2 presets a overvew of the measuremet procedures that we use our models. Secto 3 presets our basele Armgto model wth exogeous specalzato the set of goods that are produced ad traded each coutry. Secto 4 derves our basc results o measured real GDP, real cosumpto, ad theoretcal cosumpto the Armgto model. Secto 5 shows that these basc results apply a Rcarda model wth edogeous specalzato ad perfect competto. Secto 6 exteds the basc results to the verso of the model wth edogeous specalzato ad moopolstc competto. Secto 7 cosders two addtoal extesos: edogeous qualty choce ad multple factors of producto. Secto 8 cocludes. Varous proofs ad detals are relegated to the Appedx. 2 Aggregate Measuremet: Overvew I ths secto we provde a bref overvew of the procedures that we use to calculate chages aggregate quattes. We follow as closely as possble the procedures outled by the Bureau of Ecoomc Aalyss the Uted States to costruct the Natoal Icome ad Product Accouts (NIPA). 5 To calculate aggregate measures of output such as real GDP, or aggregate measures of expedtures such as real cosumpto, we use a Fsher dex, whch s a geometrc average of a Laspeyres ad a Paasche quatty dex. For example, real GDP perod t relatve to perod t 1 s gve by ( ) 0.5 ( ) 0.5 RGDP t pt 1 q t pt q t, (1) RGDP t 1 pt 1 q t 1 pt q t 1 where p t ad q t deote prces ad quattes perod t of the detaled compoets of GDP, ad where the sum s calculated across all of these compoets. The terms p t 1 q t ad p t q t 1 represet "real" quattes of ay gve GDP compoet evaluated at costat prces. The frst term expresso (1) s a Laspeyres quatty dex (based o t 1 prces), whle the secod term s a Paasche quatty dex (based o t prces). 6 Real GDP perod T relatve 5 See, e.g. Cocepts ad Methods of the U.S. Natoal Icome ad Product Accouts (2009). The procedures that we cosder are broadly cosstet wth the recommedatos by the Uted Natos ther System of Natoal Accouts. 6 The mplct GDP deflator s calculated as the rato of curret-dollar GDP to real GDP, 6

7 to perod 0 s gve by RGDP T RGDP 0 T t1 RGDP t RGDP t 1. (2) The detaled compoets of GDP expresso (1) ca be dustres, sectors, or groups of arrowly defed goods that jotly coform aggregate GDP or other aggregate measures of output ad expedtures. Whle estmates of the curret-dollar value of producto, p t q t, are typcally avalable for each of these dvdual compoets, data o physcal quattes, q t, are ofte ot. For those compoets of GDP for whch data o physcal output are avalable, real quattes are computed usg ether the drect valuato method (sum of quattes evaluated at costat prces) or the quatty extrapolato method (usg a quatty dcator that approxmates the movemets of the compoet seres). For those compoets of GDP for whch estmates of physcal quattes are ot avalable, real quattes are estmated usg the deflato method, dvdg curret-dollar values by approprate prce dces. 7 I partcular, for ay compoet of GDP, p t 1 q t (p t q t ) / (P t /P t 1 ) ad p t q t 1 (p t 1 q t 1 ) (P t /P t 1 ), where P t /P t 1 deotes the chage the prce dex betwee perods t 1 ad t. I our basele calculatos, we compute aggregate quattes usg the deflato method. To calculate real GDP from the producto sde usg the deflato method, we deflate the curret-dollar value added of producto (cludg the value added of the actvtes performed at home to sell goods teratoally) usg the producer prce dex (PPI) as a deflator. 8 The chage the PPI betwee perods t 1 ad t s a weghted average of prce chages betwee these two perods across goods ad servces that are produced domestcally to sell at home or to export abroad. 9 ( p t q t / p t 1 q t 1 ) / (RGDP t /RGDP t 1 ), whch s equal to a geometrc average of a Laspeyres ad a Paasche prce dex. 7 The drect valuato method s used, for example, to calculate real output of autos ad lght trucks, whle quatty extrapolato s used to calculate real output of housg ad utltes servces. The majorty of the other subcompoets of GDP are calculated usg the deflato method sce physcal output s ot recorded across producers (see "Summary of NIPA Methodologes", p.12 for a descrpto of the method used to estmate each subcompoet of GDP). 8 Ths s the procedure used the GDP by dustry accouts publshed by the BEA. Whe termedate puts are used producto, real value added s calculated usg the double deflato method. Ths cossts of frst deflatg gross output ad puts separately (usg ther respectve PPIs), ad the computg real value added as the dfferece betwee real gross output ad real termedate puts. 9 To costruct the PPI, the Bureau of Labor Statstcs (BLS) collects prces for a sample of tems that ca be prced cosstetly through tme. Prce dces are the costructed by averagg prce chages of dvdual tems weghted by the the value of producto some base year. The set of sampled tems ad the weghts are updated every few years (betwee 5 ad 7 years for the typcal good the PPI). Prce chages from product replacemets ted to be dropped from the dex, whch s equvalet to attrbutg to dscotued goods the rate of chage the overall prce dex. For more detals o the costructo of 7

8 We cosder two alteratve deflato procedures. The frst procedure deflates the total value of producto usg a sgle aggregate prce dex. The secod procedure deflates the value of output boud for each destato usg a destato-specfc prce dex. We show that, usg dsaggregated deflators by destato coutry, real GDP s equal to that obtaed usg the drect valuato method based o data o physcal quattes of each commodty. Export prces the PPI ad the export prce dex (EPI) are typcally measured at fob (.e. free-o-board) values, ad hece exclude shppg servces curred abroad. A crtcal assumpto determg the mpact of chages teratoal trade costs o measured real GDP s whether chages measured prces the PPI reflect, at least partly, these chages trade costs. I addto to shppg costs (that are cluded the trasportato dustry), teratoal trade costs clude producto ad marketg costs that apply dfferetally to exported goods, formato costs, costs assocated wth the use of dfferet curreces, cotract eforcemet costs, legal regulatory costs, ad other tme costs assocated to teratoal trade (see e.g. Aderso ad Va Wcoop 2004). To uderstad the mplcatos of the ature of trade costs o aggregate measuremet, we cosder two alteratve specfcatos. I our basele specfcato, we assume that the actvtes requred to sell goods abroad are performed the home coutry, ad hece chages the varable compoet of these trade costs are reflected the home PPI. I a alteratve specfcato, we assume that all export costs are curred foreg coutres, whch case chages trade costs are ot reflected the PPI. We also calculate GDP from the expedture sde, defed as curret-dollar absorpto (whch our basele model s equal to cosumpto), plus exports less mports. cosumpto s calculated aalogously to real GDP (usg expressos 1 ad 2), but deflatg each compoet of omal cosumpto (whe physcal quattes are ot avalable) by ts cosumer prce dex (CPI) stead of the PPI. The chage the CPI s a weghted average of cosumer prce chages of domestc ad mported goods cosumed both tme perods. 10 Real I the presece of mport tarffs, curret-dollar GDP from the expedture sde (defed as the sum of fal expedtures cludg tarffs) s ot equal to curret-dollar GDP from producer prce dces ad teratoal prce dces the US, see Chapters 14 ad 15 of the BLS Hadbook of Methods. 10 See "Updated Summary of NIPA Methodologes", for detals o the deflator used each expedture compoet of GDP. See McCully, Moyer, ad Stewart (2007) for a detaled comparso of the CPI ad the mplct deflator for persoal cosumpto (where the latter s costructed as the rato of omal ad real cosumpto). See Feestra, Hesto, Tmmer, ad Deg (2009) for a detaled dscusso of the relato betwee real GDP from the producto sde ad real GDP from the expedture sde as measured the Pe World Tables. 8

9 the producto sde (defed as the sum of frm value added excludg tarffs). I order to recocle estmates of GDP from the producto ad expedture sdes, the BEA adds mport taxes to factor paymets whe computg value added by dustry. 11 To be cosstet wth ths procedure, the model wth tarffs we calculate real GDP from the expedture sde. I deflatg cosumpto expedtures, the CPI s costructed usg prces clusve of tarffs. I deflatg mports, the mport prce dex (IPI) s costructed usg prces exclusve of mport tarffs. 3 Model wth Exogeous Specalzato ad Perfect Competto I ths secto we preset a Armgto verso of our model wth exogeous specalzato ad perfect competto. setup. The extesos of the model that follow buld upo ths basc The world ecoomy s composed of I coutres. The utlty of the represetatve cosumer coutry s U β t u (C t ), β 1, t0 where C t deotes theoretcal cosumpto of the fal good at tme t, gve by [ C t q t (ω) ρ 1 ρ Ω t ] ρ dω ρ 1. (3) Here, q t (ω) deotes the cosumpto of good ω ad Ω t deotes the set of avalable dfferetated goods coutry. The parameter ρ deotes the elastcty of substtuto across varetes. I the model wth moopolstc competto below we assume ρ > 1. Demad for each good s q t (ω) [p t (ω) /P t ] ρ C t, where p t (ω) deotes the cosumer prce of [ 1 good ω coutry, ad P t p Ωt t (ω) dω] 1 ρ 1 ρ s the welfare-based prce dex coutry. We assume that cosumpto of the fal good C t ad the welfare-based prce dex P t caot be drectly observable (or smlarly, that the fal good s ot a physcally traded commodty). If C t ad P t were drectly observable, the measurg the gas from trade would be straghtforward. Each producer specalzes the producto of a sgle dfferetated good. Producto 11 I partcular, the "Gross Domestc Product by Idustry Accouts" computed by the BEA, value added s defed as the sum of: "Compesato of employees", "Taxes o producto ad mports less subsdes" ad "Gross operatg surplus". For a detaled descrpto of the trasactos that are cluded value added, see "Cocepts ad Methods of the U.C. Iput-Output Accouts", Chapter 6, uder "Value-added trasactos". 9

10 uses labor accordg to the producto fucto y zl, where y ad l deote output ad labor of a producer wth productvty z (multple puts are troduced Secto 7). We deote by M t (z) the dstrbuto of producers, dcatg the mass of producers wth productvty z coutry at tme t. Gve the symmetry of goods the producto fucto of the fal good (3), we terchageably dex goods by ω, or by ther productvty z ad source coutry. For example, q t (z) ad p t (z) deote the cosumpto quatty ad prce, respectvely, coutry of good produced by z producers coutry. We assume that all prces are already expressed a commo currecy (whch we refer to as dollars). Goods ca be teratoally traded subject to a techology descrbed below. We deote by Ω t the set of producers (dexed by ther productvty) from coutry that sell a postve quatty to coutry at tme t. I the absece of teratoal trade betwee coutres ad at tme t, the set Ω t s empty. I the model wth exogeous specalzato, we assume that the dstrbuto of producers, M t (z), s exogeously gve ad costat over tme. We also assume that the set of goods that are teratoally traded, Ω t, s exogeously gve ad that, as log as there s ay trade betwee coutres ad, t s costat over tme. We do ot make assumptos o how the set of goods Ω t vares across destatos, hece ot all goods sold domestcally eed to be exported, ad vce-versa. For example, oly goods wth hgh productvty z mght be traded. The case of Ω t Ω t correspods to the Armgto model whch all goods are teratoally traded (uless coutres are autarky). Goods ca be shpped across coutres subject to ceberg varable teratoal trade costs. I our basele specfcato, we assume that teratoal trade costs are curred each source coutry, as s typcally assumed the lterature. 12 I partcular, each ut of a good produced coutry wth productvty z shpped to coutry at tme t requres (τ t 1) /z uts of labor from coutry, where τ t 1 ad τ t 1. Iteratoal trade servces could be provded by the same producer of the good, or by some thrd-party termedary. 13 Summg-up producto ad shppg costs, the total amout of coutry labor requred to delver a ut of coutry s good coutry s τ t /z. Equvaletly, ths techology 12 Whle ths formulato we assume that trade costs use factors of producto the exportg coutry, we ca stead assume that they use factors from the mportg coutry (or from both). Ths would complcate the otato wthout chagg substatally the results. 13 The assumpto of ceberg varable teratoal trade costs mples that producers that are more eff cet at producto are also more eff cet at sellg goods abroad. Cosder a alteratve formulato of the model whch goods vary by qualty (as dscussed Secto 7) stead of productvty. If producto of hgher qualty goods etal hgher margal costs, the assumpto of ceberg trade costs mples that hgher qualty goods are more expesve to sell abroad. 10

11 trasforms 1 ut of a good produced coutry to 1/τ t ut of the good for cosumpto coutry. Coutry s resource costrat s Ω t τ t q t /zdm t L, where L deotes the labor supply coutry, tegrals are evaluated wth respect to z, ad the depedece of q t o the argumet z s omtted. I the model wth perfect competto, producer prces for goods maufactured coutry ad sold coutry equal p t W t /z, where W t deotes the wage coutry. Prces for the servces to sell goods from coutry to coutry equal p s t (τ t 1) W t /z. Cosumer prces coutry equal p t p t + p s t τ t W t /z. Cosumpto expedtures at fal prces coutry are gve by E t P t C t Ω t p t q t dm t. GDP curret dollars from the producto sde (the sum of value added across all producers), s equal to GDP from the come sde (total wage paymets plus profts), ad to GDP from the expedture sde (cosumpto expedtures plus exports less mports). Ths three-way equvalece ca be expressed as: GDP t p t q t dm t W t L + Π t (4) Ω t E t + p t q t dm t p t q t dm t, Ω t Ω t The varable Π t deotes aggregate profts, whch equal zero uder perfect competto ad costat returs to scale. We deote by λ t the share of coutry s GDP accouted for by producto sold to coutry, λ t GDP t GDP t, (5) where GDP t Ω t p t q t dm t. Note that 1 λ t dcates the share of total exports coutry s GDP. 4 Results: Exogeous Specalzato ad Perfect Competto I ths secto, we preset our results the basc model wth exogeous specalzato ad perfect competto. We frst calculate chages real GDP respose to chages varable trade costs. We the show how chages real GDP vary f we assume that the producto 11

12 of teratoal trade servces s specalzed oe coutry. We the compare chages real cosumpto ad theoretcal cosumpto, ad ext compare chages world real GDP ad world real cosumpto. Fally, we calculate the respose of real GDP ad cosumpto to chages tarffs. We coclude ths secto by summarzg the results. Real GDP We frst costruct real GDP from the producto sde. I order to apply expressos (1) ad (2), we must specfy how goods are grouped to compoets of GDP. We cosder two cases. Frst, we aggregate producto by all producers to all destatos to a sgle compoet, ad costruct real quattes by deflatg curret-dollar GDP usg a sgle, aggregate deflator. Secod, we decompose total producto by destato coutry, ad calculate real quattes by deflatg destato-specfc producto values usg destato-specfc prce dces. 14 We show that real GDP uder the secod case s equal to real GDP costructed usg the drect valuato method whch data o physcal quattes ad prces of dvdual producers (.e. q t, p t ) s used. Real GDP usg aggregate deflators: We costruct real quattes by deflatg the total curret-dollar value of producto wth the aggregate PPI. The PPI s a weghted average of chages producer prces of cotug goods, based o producto weghts perod t 0. We do ot make assumptos o what the base-year t 0 s or how frequetly t s updated wth the ext of exstg products or the etry of ew products. The PPI coutry perod t relatve to perod t 1 s gve by 15 P P I t P P I t 1 Ω c t Ω c t p t0 q t0 ( p t p t 1 ) dm t0 p t0 q t0 dm t0 τ t λ t τ t 1 W t W t 1, (6) where Ω c t Ω t0 Ω t 1 Ω t s the set of goods sold from coutry to coutry wth postve sales at tme t 0, t 1 ad t, ad λ t s the share of coutry s reveues to coutry 14 I both cases, defg these detaled compoets of GDP, we are mplctly assumg that the model there s a represetatve sector or dustry composed of dfferetated goods whch aggregate accordg to (3). Extedg the model to allow for heterogeeous dustres or sectors, aggregated to the fal good wth a outer CES techology, s straghforward at the expese of extra otato, ad does ot substatally alter our results. 15 Here we are assumg that producer prces the PPI are the sum of maufacturg ad shppg prces, p t ad p s t respectvely. Alteratvely, we could assume that producer prces ad shppg prces are etered separately stead of summed to the PPI (because these actvtes are performed by dstct producers or dustres). The PPIs uder both assumptos are equvalet up to a frst-order approxmato. 12

13 at tme t 0 of these cotug goods, λ t Ω c t Ω c t p t0 q t0 dm t0. (7) p t0 q t0 dm t0 I dervg (6), we have used the fact that, wth ceberg varable trade costs, the percetage chage prces s depedet of productvty z. Note that, f coutres, do ot trade at tme t 0, t 1 or t, the Ω c t ad the P P I excludes prce chages from ths par of coutres. Hece, f a coutry s autarky at tme t 0, t 1 or t the the PPI oly takes to accout chages domestc prces. Real GDP perod t relatve to perod t 1, usg expresso (1) wth a sgle aggregate compoet, s gve by RGDP t RGDP t 1 ( ) 0.5 ( ) 0.5 GDPt / (P P I t /P P I t 1 ) GDP t (8) GDP t 1 GDP t 1 (P P I t /P P I t 1 ) 1 τ t. λt τ t 1 Note from (8) that, usg a sgle aggregate deflator, the Laspeyres ad the Paasche quatty dces betwee perods t 1 ad t are equal. From expresso (8), we ca see that f the share of exports GDP s postve at tmes t 0, t 1 ad t (.e. λ t > 0) ad varable trade costs coutry fall betwee tme t 1 ad tme t (.e. τ t τ t 1 for wth at least oe strct equalty), the real GDP rses. If trade costs are uchaged betwee ay two cosecutve perods, τ t τ t 1, the real GDP remas uchaged. Therefore, f trade costs chage permaetly betwee t 0 ad t 1, the chaed real GDP ay perod T 1 relatve to perod t 0 (usg expresso 2) s gve by RGDP T RGDP 0 RGDP 1 RGDP 0. (9) Itutvely, a reducto varable trade costs etals a mprovemet of domestc techologes, whch lowers producer prces relatve to the wage, ad creases real GDP. Ths rse real GDP shows up as a rse aggregate productvty. If the PPI does ot take to accout chages trade costs (or f a coutry s tally autarky), the P P I t W t /W t0, ad RGDP t /RGDP t 1 1. Note that ay reallocato producto towards more productve producers (due to, for example, a hgher productvty of exporters relatve to o-exporters) does ot result 13

14 larger chages measured aggregate productvty. To uderstad ths mplcato of the model, we ca rewrte the rato of real GDP perod t to relatve to perod t 1, usg (4) ad (8), as RGDP t RGDP t 1 Ω t l t L t l t 1 Ω t 1 L t 1 p tq t l t dm t L t 1, (10) l t 1 dm t 1 L t 1 P P I t /P P I t 1 p t 1q t 1 where l t (z) deotes producto labor used by coutry producers wth productvty z to sell coutry, ad L t deotes the aggregate quatty of labor used for producto coutry (equal to L ths model). Note that value added per worker by dvdual producers, p t (z) q t (z) /l t (z), s equal to the wage, W t, for all producers depedet of ther productvty z. Usg l t Ω t L t dm t 1 ad (6) we obta expresso (8). Therefore, ay reallocato of labor towards more productve producers does ot result ay further crease of aggregate productvty beyod the drect effect from a reducto varable trade costs. 16 Real GDP usg dsaggregated deflators: We ow compute real quattes by deflatg destato-specfc producto values usg destato-specfc PPIs. The PPI perod t relatve to perod t 1 for goods produced coutry ad shpped to coutry s P P I t P P I t 1 Ω c t ( ) p p t0 q t t0 p t 1 dm t0 Ω c t p t0 q t0 dm t0 τ t τ t 1 W t W t 1. (11) Here we used the fact that percetage chages producer prces are equal for all goods boud to a gve destato. The dsaggregated deflator P P I t /P P I t 1 s well defed oly whe the set of cotug goods s o-empty. Real GDP perod t relatve to perod t 1, usg equato (1) wth destato-specfc GDP compoets, s gve by RGDP t RGDP t 1 ( ( GDP t P P I t /P P I t 1 GDP t 1 λ t τ t 1 τ t λ t 1 τ t τ t 1 ) 0.5. ) 0.5 ( GDP ) 0.5 t GDP (12) t 1 P P I t /P P I t 1 Note that, cotrast to the measures of real GDP based o aggregate deflators, the 16 Note that f the PPI were calculated as a chage average prces (stead of a average chage prces), the reallocato of producto towards more productve producers would result a larger decle the PPI ad a hgher crease real GDP. 14

15 Laspeyres ad the Paasche quatty dces of real GDP are ot equal whe we use dsaggregated deflators. From expresso (12), f trade costs fall betwee tme t 1 ad t, the real GDP rses. If trade costs chage permaetly betwee t 0 ad t 1, the chaed real GDP ay perod T 1 relatve to perod t 0, s equal to RGDP 1 /RGDP 0, as expresso (9). The expressos for chages real GDP based o aggregated ad dsaggregated deflators, gve by (8) ad (12), dffer terms of the base-year whch trade shares are calculated. However, up to a frst-order approxmato (.e. aroud τ t /τ t 1 1), the two measures of chages real GDP are equal ad gve by d log RGDP t d log W t λ t d log P P I t λ t d log τ t. (13) Note that we ca re-wrte the chage real GDP based o dsaggregated deflators the frst le of expresso (12) as RGDP t RGDP t 1 ( Ω t p t 1 q t dm t Ω t 1 p t 1 q t 1 dm t 1 ) 0.5 ( Ω t p t q t dm t Ω t 1 p t q t 1 dm t 1 ) 0.5. Here we used the fact that the term GDP t / (P P I t /P P I t 1 ) (12) s equal to Ω t p t 1 q t dm t, ad the term GDP t 1 P P I t /P P I t 1 s equal to Ω t 1 p t q t 1 dm t 1. Ths expresso correspods to the chage real GDP calculated accordg to the drect valuato method (a geometrc average of Laspeyres ad Paasche quatty dces), evaluatg usg producto values at costat prces. Whle ths procedure requres data o physcal quattes ad prces of dvdual commodtes (whch s typcally ot avalable may dustres ad subset of goods), what we showed s that the mpled chage real GDP s equal to that usg the deflato method wth coutry specfc prce deflators. Real GDP uder teratoal specalzato of shppg servces We ow cosder a alteratve specfcato o the ature of trade costs whch a subset of coutres specalzes producg shppg servces for all other coutres. For cocreteess (but wthout loss of geeralty for our results), we assume that the world-wde producto of shppg servces s cocetrated coutry s. That s, shppg oe ut of a good produced coutry wth productvty z to coutry at tme t, for all coutres ad, requres (τ t 1) /z uts of coutry s s labor. Prces receved by producers of these 15

16 servces coutry s for the servces to sell goods from coutry to coutry equal p s t (τ t 1) W st/z, ad cosumer prces coutry equal p t (W t + (τ t 1) W st) /z. The resource costrat coutry s Ω t q t /z dm t L for s, whle coutry s t s τ stq st/z dm st + Ω st s Ω t (τ t 1) q t /z dm t L s. GDP curret dollars from the producto sde coutry s s GDP t whle coutry s t s Ω t p t q t dm t, GDP st ( pst + p s st) qstdm st + p s tq t dm t. Ω st s Ω t I coutres s that do ot specalze shppg servces, the PPI s smply P P I t /P P I t 1 W t /W t 1, ad the rato of real GDP perods t ad t 1 s RGDP t /RGDP t 1 1. I cotrast to the prevous specfcato, chages trade costs ow leave domestc techologes uchaged for those coutres that do ot specalze shppg servces. Hece, these coutres chages the PPI are equal to chages the wage, so real GDP remas uchaged. Ths result holds more geerally, f chages foreg trade costs also chage relatve prces faced by dfferet domestc producers (as the Hecksher-Ohl model, for example) but ot ther techologes. To see ths, recall that whe calculatg real quattes by deflatg the value of producto wth destato specfc PPIs, real GDP s equal to the value of producto evaluated at costat-year prces. From revealed producto choces, the value of producto falls (rses) betwee t 1 ad t whe evaluated at t 1 (t) prces. To a frst-order approxmato, real GDP remas costat. Ths le-of-argumet caot be used whe chages trade costs chage domestc techologes, as our basele specfcato. I Appedx B we derve the chage real GDP coutry s that specalzes the producto of shppg servces. Reductos trade costs (across ay par of coutres) do mprove domestc techologes coutry s. Hece, respose to ay reducto trade costs, the PPI falls relatve to the wage, ad real GDP rses. 16

17 Measured real cosumpto ad theoretcal cosumpto each coutry We ow calculate chages real cosumpto, ad compare them to chages theoretcal (or welfare-based) cosumpto of dvdual coutres. As we dd for real GDP, we use the deflato method, frst usg a aggregate deflator ad the usg coutry-specfc deflators. Real cosumpto usg aggregate deflators: We calculate real cosumpto usg the deflato method, deflatg cosumpto expedtures wth a cosumer prce dex (CPI). We costruct the CPI as a weghted average of ratos of fal prces betwee two perods (of goods that are cosumed both perods) usg t 0 weghts. The CPI coutry at tme t relatve to tme t 1 s gve by CP I t CP I t 1 Ω c t ( pt0 q t0 Ω c t ) ( ) p t dm p t0 t 1. (14) p t0 q t0 dm t0 Real cosumpto coutry at tme t relatve to t 1, usg expresso (1) wth a sgle aggregate compoet, s gve by ( ) 0.5 ( ) 0.5 RC t Et / (CP I t /CP I t 1 ) E t (15) RC t 1 E t 1 E t 1 (CP I t /CP I t 1 ) E t/ (CP I t /CP I t 1 ). E t 1 The rato of theoretcal cosumpto perods t ad t 1 s equal to C t /C t 1 (E t /E t 1 )/(P t /P t 1 ), where P t s the welfare-based prce dex defed above. Hece, dffereces betwee chages real cosumpto ad theoretcal cosumpto stem oly from dffereces betwee the CPI ad the theoretcal CES prce dex. It s straghtforward to show that, to a frst-order approxmato, the log chage the CES prce dex wth a fxed set of goods s equal to a expedture-weghted average of log prce chages of dvdual goods, as t s for the CPI defed expresso (14). Hece, for margal chages prces, chages real cosumpto cocde wth chages theoretcal cosumpto, coutry-bycoutry. Large chages prces gve rse to the well-kow substtuto bas. However, f the CPI s evaluated usg t 0 t 1 or t 0 t weghts, we ca boud ths substtuto bas. I partcular, Appedx A we show that, f the set of goods cosumed each perod s uchaged, the the CPI wth tal (fal) perod weghts, t 0 t 1 (t 0 t) overstates 17

18 (uderstates) chages the welfare-based prce dex betwee perods t 1 ad t. That s, CP I t CP I t 1 t0 t P t P t 1 CP I t CP I t 1 t0 t 1. (16) Hece, chages theoretcal cosumpto are bouded above (below) by real-cosumpto calculated wth the CPI based o fal (tal) perod weghts. 17 both specfcatos of teratoal trade costs. These results hold uder Real cosumpto usg dsaggregated deflators: We ow calculate chages real cosumpto by deflatg source coutry specfc cosumpto expedtures usg ther respectve CPIs. Coutry specfc expedtures ad CPIs are defed, respectvely, as E t Ω t p t q t dm t ad CP I t CP I t 1 Ω c t ( ) pt p t0 q t0 dm p t0 t 1. p t0 q t0 dm t0 Ω c t Real cosumpto perod t relatve to perod t 1, usg equato (1) wth coutryspecfc expedture compoets, s gve by RC t RC t 1 ( E t CP I t /CP I t 1 E t 1 ) 0.5 ( E t ) 0.5 (17) E t 1 CP I t /CP I t 1 ( ) 0.5 ( ) 0.5 Ω t p t 1 q t dm t Ω t p t q t dm t, Ω t 1 p t 1 q t 1 dm t 1 Ω t 1 p t q t 1 dm t 1 where we used the fact that percetage chages all prces for goods comg from a commo source coutry are equal. Ths expresso cocdes wth a geometrc average of Laspeyres ad Paasche quatty dces usg the drect-valuato method. Up to a frst-order approxmato, chages real cosumpto based o aggregate deflators ad dsaggregated deflators (as well as theoretcal cosumpto) are equal ad gve by d log RC t d log E t E t E t d log CP I t. (18) 17 Iequalty (16) does ot hold the case whch there s o trade betwee coutres ad at tme t 1 or t, so that Ω c t. I ths case, equalty (16) would hold f the CPI to corporated prce chages for all goods, cludg those that are ot cosumed, ad assumed that uavalable goods have a fte prce. However, ths s ot the approach take by the atoal statstcs whe calculatg the CPI. 18

19 World real GDP, cosumpto, ad theoretcal cosumpto As ca be observed by comparg expressos (13) ad (18), dffereces betwee chages real GDP ad real cosumpto, coutry-by-coutry, arse from (1) dffereces betwee the curret-dollar value of cosumpto ad GDP ( the presece of trade mbalaces) ad (2) dffereces betwee chages the PPI ad the CPI due to movemets relatve wages ad relatve trade costs that chage the prce of exports relatve to mports (.e. the terms of trade) each coutry. We ow show that, f trade s balaced each coutry, a weghted-average (based o each coutry s curret-dollar GDP) of chages real cosumpto across coutres s equal to the same weghted average of chages real GDP across coutres, up to a frst-order approxmato. Here we cosder the basele specfcato of trade costs whch these are curred usg labor each exportg coutry. I the Appedx we show that the equvalece betwee chages world real GDP ad world real cosumpto also holds the model whch a subset of coutres specalzes the producto of shppg servces. Defe s t to be coutry s share total curret-dollar GDP across all coutres perod t: s t GDP t / GDP t. From expresso (13), the world chage real GDP s, to a frst-order approxmato, s t d log RGDP t [ 1 GDP GDP t d log W t t ] GDP t d log P P I t. From expresso (18), assumg balaced trade each coutry (so that, as ca be see 4, GDP ad expedtures curret-dollars are equal, GDP t E t ), the world chage real cosumpto s, to a frst-order approxmato, s t d log RC t [ 1 GDP GDP t d log GDP t t (19) ] E t d log CP I t. (20) The frst term expresso (19) s equal to the frst term expresso (20) because d log W t d log GDP t. The secod term expresso (19) s equal to the secod term expresso (20) because GDP t d log P P I t E t d log CP I t. Itutvely, for ay par of tradg coutres, a mprovemet the blateral terms of trade for oe coutry mples a worseg the terms of trade for the other coutry. Hece, chages the world CPI are equal to chages the world PPI, ad so are world real cosumpto ad world real GDP The equvalece betwee world chages real GDP ad real cosumpto also holds for large chages 19

20 Note that, from our results o the equalty of chages real cosumpto ad theoretcal cosumpto coutry-by-coutry, t follows mmedately that chages world real GDP ad chages world real cosumpto are both equal, to a frst-order approxmato, to a weghted average of the chage theoretcal cosumpto across coutres: s t d log RGDP t s t d log RC t s t d log C t. (21) We ca solve explctly for the chage world real GDP ad world real cosumpto respose to chages varable trade costs. I partcular, from (13) ad (21), t follows that, to a frst-order approxmato, s t d log RGDP t 1 s t d log RC t GDP t Exports t d log τ, (22) where Exports t Ω t ( p t + p s t) q t dm t. Chages world real GDP ad real cosumpto respose to chages varable trade costs are, to a frst-order approxmato, equal to a weghted average of chages blateral varable trade costs, where the weghts are smply the shares of blateral exports world GDP. Tarffs ad real GDP from the expedture sde We ow troduce ad-valorem mport tarffs. We deote by d t 1 the gross tarff set by coutry at tme t for mports from coutry (wth d t 1). Cosumer prces coutry are p t d t ( p t + p s t). Tarffs reveues are rebated back to cosumers. To smplfy the otato, we calculate our aggregate statstcs oly for the case whch trade costs are curred each exportg coutry, but t s straghtforward to exted the results to the case whch coutry s specalzes the producto of shppg servces. The local equvalece, coutry-by-coutry, betwee chages real cosumpto ad theoretcal cosumpto s mmedate because, to a frst-order approxmato, the CPI s equal to the welfare-based prce dex (both of whch are calculated usg fal prces clusve of mport tarffs). For large prce chages, we stll obta the boud stated equalty (16). The relato betwee curret-dollar GDP from the producto sde ad curret-dollar GDP from the expedture sde, provded (4), must be modfed by the presece of tarffs. trade costs f real GDP ad real cosumpto are calculated usg ether Laspeyres or Paasche quatty dces (stead of usg a geometrc average of both, as stated expresso 1) based o dsaggregated deflators. 20

21 For example, coutry s, we have GDP t ( p t + p s t) q t dm t + Υ t W t L + Π t + Υ t (23) Ω t E t + ( p t + p s t) q t dm t ( p t + p s t) q t dm t, Ω t Ω t where Υ t deotes tarffreveues collected coutry : Υ t (d t 1) Ω t ( p t + p s t) q t dm t. Real GDP calculated from the producto sde excludg mport tarffs from both curretdollar GDP ad from prce deflators s uchaged to chages tarffs for the same reasos that real GDP the model wth oly trade costs s uchaged to chages trade costs f these are excluded from prce dces. We ow calculate real GDP from the expedture sde by separately deflatg each coutry-specfc expedture compoet of GDP. The export prce dex (EPI) for goods sold by coutry to coutry s gve by EP I t EP I t 1 Ω c t ( pt0 + p s t 0 ) qt0 ( Ω c t pt + p s t p t 1 + p s t 1 ) dm t0 ( pt0 + p s t 0 ) qt0 dm t0. (24) The mports prce dex (IPI) coutry for goods mported from coutry (clusve of trade costs curred abroad but exclusve of tarffs) s gve by IP I t /IP I t 1 EP I t /EP I t 1. The Laspeyres real GDP dex coutry s gve by RGDP t RGDP t 1 E t CP I t /CP I t 1 + [ ] Exports t EP I t /EP I t 1 Exports t EP I t /EP I t 1 GDP t 1 (25) ( pt 1 Ω + p t 1) s qt dm t + Ω t (d t 1 1) ( p t 1 + p t 1) s qt dm t ( pt 1 Ω t 1 + p t 1) s qt 1 dm t 1 + Ω t 1 (d t 1 1) ( p ). t 1 + p s t 1 qt 1 dm t 1 The frst term expresso (25) dcates the chage the costat-prce value of producto, ad the secod term represets the chage the costat prce value of tarffs. The Paasche real GDP dex s calculated aalogously to the Laspeyres real GDP dex, but usg costat perod t prces ad tarffs stead of perod t 1 prces ad tarffs. The chage real GDP betwee perod t 1 ad t s a geometrc average of the Laspeyres ad Paasche dces, as defed expresso (1). 21

22 Note that, the absece of tarffs, real GDP from the expedture sde cocdes wth real GDP from the producto sde usg dsaggregated deflators. 19 I the presece of tarffs, there s a addtoal source of chages real GDP. Specfcally, real GDP rses f the value of tarff reveues evaluated at base-prces ad base-tarffs, Ω t (d t0 1) ( p ) t0 + p s t qt 0 dm t (wth t 0 t 1 or t 0 t), creases. That s, real GDP rses f mported physcal quattes weakly crease. Fally, cosder the equvalece betwee world real cosumpto ad world real GDP. Suppose that each coutry s uder balaced trade (exclusve of tarffs),.e. Ω t ( p t + p s t) q t dm t Ω t ( p t + p s t) q t dm t. I ths case, from (23), curret-dollar GDP (clusve of mport-tarffs) s equal to curret-dollar expedtures. Defe coutry-specfc weghts based o curret-dollar GDP (clusve of mport-tarffs), s t GDP t / GDP t. It s straghtforward to show, followg the steps above the model wthout tarffs, that the chage world real GDP s equal, to a frst-order approxmato, to the world chage real cosumpto, as dcated expresso (21). Summary of Results Our cetral results o the mplcatos of chages trade costs o measures of real GDP ad real cosumpto our model wth exogeous specalzato ad perfect competto ca be summarzed as follows: Result 1: I respose to reductos varable teratoal trade costs curred coutry that are captured GDP ad ts deflators, real GDP coutry rses. If chages varable teratoal trade costs are ot captured coutry s GDP or ts deflators (ether because producer prces prce dces exclude trade costs, or because coutry starts autarky, or because teratoal trade servces are produced other coutres), real GDP coutry s uchaged; Result 2: I respose to chages physcal trade costs or tarffs, the chage theoretcal (welfare-based) cosumpto each coutry les betwee the chages real cosumpto calculated usg cosumpto deflators wth pre- ad post-trade lberalzato base-year weghts. To a frst-order approxmato, chages real cosumpto ad theoretcal cosumpto cocde coutry-by-coutry; Result 3: I respose to chages mport tarffs that rase the value of coutry s tarff reveues at costat prces, real GDP from the expedture sde coutry rses; 19 If we use sgle aggregate deflators, real GDP from the producto ad from the expedture sde are equal up to a frst-order approxmato. 22

23 Result 4: Wth balaced trade each coutry, the chage world real cosumpto s equal, up to a frst-order approxmato, to the chage world real GDP (defed as cross-coutry weghted averages of chages real cosumpto ad GDP, respectvely, usg curret-dollar GDP weghts). Combg Results 2 ad 4, we obta the corollary that f each coutry s uder balaced trade, chages world real GDP equal, to a frst-order approxmato, chages world theoretcal cosumpto, depedetly of where are trade servces produced. 5 Edogeous Specalzato ad Perfect Competto I the model studed the prevous secto, we assumed that the sets Ω t, dcatg the rage of goods that are produced ad sold each coutry, were exogeously gve. I ths secto, we brefly dscuss how our prevous results hold a model that edogeezes the set of traded goods, whle keepg the assumpto of perfect competto. Specfcally, we cosder a Rcarda verso of our model, as e.g. Dorbusch, Fsher ad Samuelso (1977) ad Eato ad Kortum (2001). Istead of assumg that each coutry produces ts ow dfferetated goods, we assume that every good ω ca be produced by all coutres. To corporate ths assumpto our geeral framework, the otato must be slghtly modfed as follows (see e.g. Alvarez ad Lucas 2007). Each good s dexed by the vector z of productvtes for ths good all coutres, ad M (z) deotes the exogeous dstrbuto of goods the world. We do ot make ay parametrc assumptos o M (z). Every perod, coutres purchase each good from the source coutry wth lowest margal cost of delverg the good. These sourcg choces determe the sets Ω t. Wth perfect competto, the fal prce of good z coutry s p t (z) m { p t (z) + p s t (z)}, where p t (z) ad p s t (z) are equal to the margal cost to produce ad delver, respectvely, good z from coutry to. We focus o the specfcato whch trade costs are curred each exportg coutry, but the results exted to the specfcato whch the producto of shppg servces s cocetrated a subset of coutres. Real GDP I costructg the PPI ad EPI, goods for whch the detty of the producer chages over tme are dscotued ad hece are ot cluded the respectve prce dex, as ca be see expressos (6) ad (24) wth M t substtuted for M. All cotug producers cluded the prce dex (.e. those the set Ω c t) chage prces by the same percetage. Followg 23