NBER WORKING PAPER SERIES ESTIMATES OF THE TRADE AND WELFARE EFFECTS OF NAFTA. Lorenzo Caliendo Fernando Parro

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1 NBER WORKING PAPER SERIES ESTIMATES OF THE TRADE AND WELFARE EFFECTS OF NAFTA Lorezo Caliedo Ferado Parro Workig Paper NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Aveue Cambridge, MA November 2012 We are particularly grateful to Robert Lucas, Samuel Kortum, Nacy Stokey for their cotiuous ecouragemet, support ad advice. We also thak for helpful commets Ferado Alvarez, Costas Arkolakis, Kyle Bagwell, Fracesco Caselli, Thomas Chaey, Dave Doaldso, Joatha Eato, Rob Feestra, Cecilia Fieler, Gordo Haso, Timothy Kehoe, Kalia Maova, Bret Neima, Ralph Ossa, Stephe Reddig, Joh Romalis, Peter Schott, Robert Shimer, Bob Staiger, Daiel Sturm, Chag TaiHsieh ad Silvaa Tereyro, four aoymous referees ad may semiar participats for useful coversatiosad commets. We thak Zia Saijid for excellet research assistace. Correspodece: Parro, The views i this paper are solely theresposibility of the authors ad should ot be iterpreted as reflectig the views of the Board of Goverors.The views expressed herei are those of the authors ad ot ecessarily those of the Board of Goverorsof the Federal Reserve System, the Federal Reserve System, or the Natioal Bureau of Ecoomic Research. NBER workig papers are circulated for discussio ad commet purposes. They have ot bee peerreviewed or bee subject to the review by the NBER Board of Directors that accompaies official NBER publicatios by Lorezo Caliedo ad Ferado Parro. All rights reserved. Short sectios of text, ot to exceed two paragraphs, may be quoted without explicit permissio provided that full credit, icludig otice, is give to the source.

2 Estimates of the Trade ad Welfare Effects of NAFTA Lorezo Caliedo ad Ferado Parro NBER Workig Paper No November 2012, Revised December 2014 JEL No. F10,F11,F13,F14,F17 ABSTRACT We build ito a Ricardia model sectoral likages, trade i itermediate goods, ad sectoral heterogeeity i productio to quatify the trade ad welfare effects from tariff chages. We also propose a ew method to estimate sectoral trade elasticities cosistet with ay trade model that delivers a multiplicative gravity equatio. We apply our model ad use our estimated elasticities to idetify the impact of NAFTA's tariff reductios. We fid that Mexico's welfare icreases by 1.31%, U.S.'s welfare icreases by 0.08%, ad Caada's welfare declies by 0.06%. We fid that itra-bloc trade icreases by 118% for Mexico, 11% for Caada ad 41% for the U.S. We show that welfare effects from tariff reductios are reduced whe the structure of productio does ot take ito accout itermediate goods or iput-output likages. Our results highlight the importace of sectoral heterogeeity, itermediate goods ad sectoral likages for the quatificatio of the welfare gais from tariffs reductios. Lorezo Caliedo Yale Uiversity School of Maagemet 135 Prospect Street New Have, CT ad NBER lorezo.caliedo@yale.edu Ferado Parro Federal Reserve Board 20th street ad Costitutio Aveue NW Washigto D.C., ferado.j.parro@frb.gov

3 1. INTRODUCTION Sectors ad coutries are iterrelated. Whe the U.S. reduces tariffs applied to Mexico i a give sector, it ot oly affects prices i that idustry but also i sectors that purchase materials from that idustry. Moreover, a tariff reductio affects prices i o-tradable sectors that are usig iputs from tradable sectors. Of course, how importat are these direct ad idirect effects from tariff chages will deped o the extet to which sectors are iterrelated. For istace, the larger is the share of tradable goods used i the productio of o-tradable goods the larger are the gais for producers of o-tradable goods from a reductio i the price of tradables. Eve more, if o-tradable goods are also used as iputs i the productio of other goods, or as fial goods i cosumptio, the the beefits spread to the rest of the ecoomy. I fact, most of the fial goods cosumed are o-tradable goods. 1 However, recet developmets i iteratioal trade pay little attetio to uderstadig how the gais from tariff reductios spread across sectors. 2 I this paper, we build ito a multi-coutry, multi-sector Ricardia model the iteractio across tradable ad o-tradable sectors observed i the iput-output tables. We use the model to idetify the trade ad welfare effects of tariff reductios from the North America Free Trade Agreemet (NAFTA) betwee Mexico, Caada ad the U.S. NAFTA provides a uique example to quatify the trade ad welfare effects of tariff chages for three mai reasos. First, it is amog the largest free trade area i the world, both i terms of populatio ad GDP; secod, it ivolves coutries with very differet structures of productio, reflected by their GDP per capita ad differet sectoral specializatio of ecoomic activity; ad third, it is a archetypal agreemet that resulted i the creatio of a cross-border productio chai, as revealed by the large share of itermediate goods ad itra-idustry trade across members. 3 These features are the key characteristics from NAFTA that help us uderstad more broadly the quatitative importace of sectoral heterogeeity, trade i itermediate goods, ad sectoral likages. Addig more detail ito a model comes at the cost of losig track of the mechaisms that deliver the mai results. I fact, this complexity has lead to criticism of computatioal geeral equilibrium (CGE) models i the past. 4 To address this issue we build o the semial work of Eato ad Kortum (2002) to develop a tractable ad simple model for tariff policy evaluatio that escapes the black box deigratio of traditioal CGE models. As a result, we ca decompose ad quatify the differetial role that itermediate goods ad sectoral likages have as amplifiers of the gais from tariff reductios. We also show that regardless of the umber of sectors ad how complicated the iteractios across sectors are, the model ca be reduced to a system of oe equatio per coutry, ad the solutio depeds o estimates of oe set of parameters, the dispersio of productivity across sectors (trade elasticities). Our solutio method simplifies cosiderably the 1 No-tradable goods (services) accouted for more tha 80% of the total fial goods demaded i the year 1993 for the U.S. 2 A exceptio is the work of Arkolakis, Costiot, ad Rodriguez-Clare (2012) where they evaluate the welfare gais from trade opeess implied by a variety of iteratioal trade models icludig multi-sector models. 3 I Sectio 2 we documet that sectoral trade i itermediate goods is particularly importat for NAFTA members. 4 These models have bee criticized for their complexity, lack of trasparecy ad aalytical foudatios, ad the arbitrary choice of the value of key parameters (Baldwi ad Veables 1995 describe them as black boxes ). 2

4 data requiremets ad estimated parameters eeded for the evaluatio of tariff chages. I our theory, productio is at costat returs to scale ad markets are perfectly competitive. Coutries import itermediate goods subject to trade costs from the lowest cost supplier i the world. 5 Itermediate goods i a give sector are used for the productio of a sectoral good which is the used as fial good for cosumptio ad as material i the productio of tradable ad o-tradable itermediate goods from all sectors. Productivity differeces across idividual producers i a sector is itroduced i the same way as i Eato ad Kortum (2002). The larger is the dispersio of productivities across producers, the larger are the gais from trade itegratio. I our model, productivity, as well as the dispersio of productivity, varies across sectors. This heterogeeity i the dispersio of productivities together with the share of itermediate goods i productio ad sectoral iterrelatios are key i order to capture how a tariff reductio has differetial impact across sectors. We express the model i relative chages ad idetify the trade ad welfare effects of NAFTA s tariff reductios. 6 Our simulatios are performed with few data ad parameter requiremets. I particular, we oly use data o bilateral trade flows, productio, tariffs ad a estimate of sectoral trade elasticities. We develop a ew method to estimate sectoral trade elasticities. The estimatios are performed usig trade ad tariff data, without assumig bilaterally symmetric trade costs as is stadard i the literature. Moreover, the method is cosistet with ay trade model that delivers a gravity-type trade equatio. We estimate the parameters of the model at a sectoral level usig data from 1993, the year before NAFTA wet ito effect. We calibrate a 31 coutries 40 sector versio of our model. The, usig the estimated parameters ad icorporatig the chage i tariffs from 1993 to 2005, both betwee NAFTA members ad with the rest of the world, we use the model to evaluate the welfare effects ad quatify the chages i exports ad imports i aggregate ad at the sectoral level. We fid that NAFTA s tariffs reductios had a cosiderable impact o its member s ecoomies, i particular for Mexico. NAFTA augmeted aggregate itra-bloc trade by 118% for Mexico, 11% for Caada ad 41% for the U.S. We fid that NAFTA icreased the sectoral specializatio of export activity i Mexico. After NAFTA the most export orieted sector i Mexico (Electrical Machiery) represeted oe third of the total export shares, while before it was oly oe fifth. For the case of Caada ad U.S. the result is differet; sectoral cocetratio of export activity was reduced. We fid that ot all coutries gaied from NAFTA. Mexico ad the U.S. gaied 1.31% ad 0.08% respec- 5 The importace of trade i itermediate goods has bee documeted by several studies. For istace, Feestra ad Haso (1996) fid that the share of imported itermediates icreased from 5.3% of total U.S. itermediate purchases to 11.6% betwee 1972 ad Campa ad Goldberg (1997) fid similar evidece for Caada ad the Uited Kigdom. Hummels, Ishii, ad Yi (2001), ad Yeats (2001) show that iteratioal trade i itermediate iputs has icreased more tha that i fial goods. 6 We perform a model-based idetificatio of the trade effects due to NAFTA s tariff reductios by holdig techology ad other trade costs fixed. By doig this, we are ot sayig that techology or other trade costs might ot have chaged as a cosequece of the chage i tariffs. We are agostic about how they might have chaged ad focus istead o the direct effect of tariff chages over the allocatio of resources. A alterative exercise could have bee to quatify the implied chages i techology ad other trade costs i order for the model to deliver the observed chage i trade flows after NAFTA. But the problem there is how to idetify if these chages were due oly to NAFTA. Uless a model of TFP or trade costs is writte there is o hope for idetificatio. I our case, we take as exogeous the observable chage i tariff due to NAFTA to quatify the trade effects. 3

5 tively, while Caada suffered a welfare loss of 0.06%. Still, real wages icreased for all NAFTA members ad Mexico had the largest gais. We decompose the welfare effects ito terms of trade ad volume of trade effects ad fid that most of the gais from NAFTA are a result of a icrease i the volume of trade. We fid that the trade created, mostly betwee NAFTA members, was larger tha the trade diverted from other ecoomies. This was particularly so for Mexico ad Caada. The welfare gais from trade creatio with NAFTA members are 1.80% ad 0.08% while the welfare loss from trade diversio with the rest of the world are 0.08%, ad 0.04% for Mexico ad Caada respectively. Oly a hadful of sectors were resposible for the aggregate volume of trade effects. These were sectors highly protected before NAFTA, like Textiles i Mexico, with a large trade elasticity, like Petroleum, ad with a large share of material use ad sectoral iterdepedece, like Electrical Machiery ad Autos. The terms of trade effects were mixed. We fid that Mexico s ad Caada s terms of trade deteriorated by 0.41% ad 0.11%, respectively, mostly due to reductios i export prices, while for the U.S. terms of trade icreased by 0.04%; largely attributed to cheaper import prices from Mexico. We also decompose the terms of trade effects by sector ad fid that terms of trade effects were primarily cocetrated i a few sectors. We show that certai sectors had a larger aggregate effect compared to others depedig o the magitude of sectoral reductios i import tariffs, the share of materials used i productio, ad sectoral likages. We also evaluate the welfare effects from observed world tariff chages. We fid that all coutries i the world gaied. The welfare gais for NAFTA members were 1.36%, 0.10% ad 0.22% for Mexico, Caada ad the U.S. Nettig out the effect of NAFTA, these figures show that Caada was the largest wier from world tariff reductios, followed by U.S. ad the Mexico. Fially, we quatify the trade ad welfare effects from NAFTA s tariff reductios across differet class of models. We fid that welfare effects are o average 71% lower i a oe sector model, 62% lower i a model without materials, ad 50% lower i a model without sectoral likages. Trade effects are reduced o average 50%, 26%, ad 18%, respectively. These results cofirm that sectoral heterogeeity, itermediate iputs, ad sectoral likages are importat mechaisms to quatify the trade ad welfare effects from tariff chages. Quatifyig potetial welfare gais ad costs from trade policies has become icreasigly importat over the years. 7 Our paper relates to a large literature that evaluates trade policy ad is mostly related to studies that quatify the gais from trade from NAFTA. 8 I particular, Aderso ad va Wicoop (2002) who use a oe good gravity model to evaluate the gais from NAFTA. Relative to Aderso ad va Wicoop (2002) 7 The umber of regioal trade agreemets (RTAs) siged i the world has icreased dramatically i the last 20 years. I 1990 there were close to 25 RTAs siged, by 2010 more tha 180. By the year 2002 more tha oe third of world trade was covered by RTAs. 8 Jacob Vier s (1950) work was amog the first to study the welfare aalysis of trade policy. Bhagwati, Krisha, ad Paagariya (1999) put together may of the major theoretical cotributios sice Vier. More recets are Aderso ad va Wicoop (2004), Baier ad Bergstrad (2009), Deardorff (1998), Reddig ad Veables (2004), Rose (2004), ad Subramaia ad Wei (2007). Bagwell ad Staiger (2010) survey recet ecoomic research o trade agreemets, with special focus o the GATT/WTO. Several studies have focused o the case of NAFTA, for istace Krueger (1999) ad the refereces therei, Lederma, Maloey, ad Serve (2005), Romalis (2007), ad Trefler (2006). For results o CGE models i geeral see Brow, Deardorff, ad Ster (1994), Brow ad Ster (1989), Kehoe ad Kehoe (1994), ad for the case of NAFTA refer to Fox (1999), Kehoe (2003), Rolleigh (2008) ad Shikher (2010). 4

6 our model has multiple sectors, itermediate goods trade, a productio ecoomy, o-tradable sectors ad builds o Ricardia motives of trade istead of love from variety. 9 quatitatively importat. Our results show that these features are Our paper is closely related to a recet ad growig literature that exteds the Eato ad Kortum (2002) model to multiple-sectors. For istace Arkolakis, et al. (2012), Caliedo ad Parro (2010), Chor (2010), Costiot, Doaldso, ad Komujer (2012), Doaldso (2012), Dekle, Eato ad Kortum (2008), Eato, Kortum, Neima, ad Romalis (2011), Hsieh ad Ossa (2011), ad Shikher (2011). 10 Our paper differs from these studies i several dimesios. First, we explicitly cosider sectoral likages betwee tradable sectors ad betwee tradable ad o-tradable sectors ulike previous Ricardia trade models. I our model, producers of o-tradable goods differ i productivity levels, demad tradable ad o-tradable itermediate goods for productio ad supply goods ot oly for cosumptio but also for productio i all sectors. 11 This feedback i productio turs out to be importat i order to quatify the trade ad welfare effects of tariff reductios. Secod, we show how accoutig for itermediate goods i productio ad sectoral likages does amplify the trade ad welfare effects of trade costs ad tariff reductios. 12 Third, we exted the Ricardia model to perform a thoroughly quatitative evaluatio of the trade ad welfare effects from chages i trade policies. Fially, the way i which we take the model to the data is very differet compared to other studies. We solve the multi-coutry ad multi-sector model i chages, relative to a base year, allowig us to perform couterfactuals without relyig o estimates of uobserved structural parameters, like fudametal productivity. We show that this approach is simple ad useful i order to evaluate couterfactual chages i trade costs more broadly. Our paper is also related to studies that propose ew methods to estimate trade elasticities. 13 We propose a ew method that idetifies sectoral ad aggregate trade elasticities by exploitig the cross sectioal variatio i trade shares iduced by the cross sectioal variatio i tariffs. The method relies o the multiplicative properties of the gravity equatio cosistet with a large variety of trade models (Krugma 1981, Eato ad Kortum 2002, Aderso ad Wicoop 2003, Melitz 2003, ad Chaey 2008). The paper is structured as follows. I Sectio 2 we motivate the importace of modelig trade i itermediates, multiple sectors, ad sectoral likages for tariff policy evaluatio. I Sectio 3, we develop a methodology to evaluate the trade ad welfare effects of tariff chages, we preset the equilibrium coditios 9 This last distictio is importat sice it geerates chages at the extesive margi of trade while this is ot the case o a Armigto type model as commoly used i CGE aalysis. 10 The Eato ad Kortum (2002) model has bee exteded i may other directios also. Oe of the earliest studies was Yi (2003) who uses the model to uderstad if vertical specializatio ca explai the large growth i trade. More recet studies are Burstei, Cravio, ad Vogel (2013), Burstei ad Vogel (2012), Caselli, Kore, Lisicky, ad Tereyro (2012), Fieler (2011), Kerr (2009), Levcheko ad Zhag (2011), Parro (2013), Ossa (2012), Ramodo ad Rodriguez-Clare (2013), ad Waugh (2010). For a comprehesive survey of recet extesios of the Ricardia model of trade refer to Eato ad Kortum (2012). 11 No-tradable good sectors are ofte modeled as a outside sector that does ot use itermediate goods for productio. For example see Alvarez ad Lucas (2007). 12 I Sectio 5.3 we compare the effects of NAFTA across differet models ad show that sectoral heterogeeity, itermediate goods, ad sectoral likages are quatitatively importat. 13 For istace, Feestra (1994), Head ad Ries (2001), Aderso ad va Wicoop (2004) ad refereces therei, Romalis (2007), Simoovska ad Waugh (2013) ad Bergstrad, Egger, ad Larch (2013). 5

7 of the model, ad show how to solve ad calibrate the model. I Sectio 4, we propose a ew method ad estimate sectoral trade elasticities. I Sectio 5, we apply the model to evaluate the trade ad welfare effects of NAFTA. I Sectio 6 we coclude. 2. TARIFFS, INTERMEDIATE GOODS AND SECTORAL LINKAGES I this sectio we motivate the importace of modelig trade i itermediates, multiple sectors, ad sectoral likages for tariff policy evaluatio. The Appedix Data Sources ad Descriptio, at the ed of the documet, describes i detail the data sources that we use i this paper. Throughout the paper, wheever we make referece to a sector i the data, we refer to a 2-digit ISIC Rev. 3 idustry. Table A.1 i the Appedix Data Sources ad Descriptio provides a descriptio of the sectoral categories. Tariff rates vary substatially across sectors. I 1993, the year before NAFTA wet ito effect, sectoral tariff rates applied by Mexico, Caada ad the U.S. to NAFTA members were, o average, 12.5%, 4.2%, ad 2.7%, respectively, with a large heterogeeity across sectors (Figure A.1, i the appedix, presets the effective tariffs rates across NAFTA members for the year 1993). By 2005 they dropped almost to zero betwee NAFTA members, but tariffs that Mexico, Caada ad the U. S. applied to the rest of the world were, o average, 7.1%, 2.2%, ad 1.7%, respectively. 14 The fact to take away is that by 2005 average tariffs had decreased cosiderably, but they still remaied very dispersed across sectors. Trade ad welfare effects of average chages i tariffs ca be aalyzed usig a oe-sector trade model; however, the effects of chages i the dispersio of tariffs ca oly be aalyzed with a model that icludes multiple sectors, sectoral likages ad itermediate goods. Actually, most goods traded are itermediate goods. 15 I 1993, 68% of Mexico s imports from coutries ot belogig to NAFTA were itermediate goods. The share for Caada is 61.5% ad for the U.S. 64.6%. Itermediate goods trade is eve more importat for NAFTA members. I fact, 82,1% of Mexico s imports from NAFTA are itermediate goods, while for Caada ad the U.S. the values were 72.3% ad 72.8% respectively. Therefore, by 1993 most goods traded across NAFTA members were itermediate goods ad trade of these types of goods was more importat across NAFTA members tha with the rest of the world. Also, tradable ad o-tradable sectors are itercoected. Usig iput-output (I-O) tables we ca measure the proportio of spedig from sectors o fial ad itermediate goods from other sectors. Oe saliet characteristic of ay I-O matrix is that it presets a strog diagoal, amely that the share of ow idustry material iputs purchased are importat. However, this expediture share is far from 100%. For example, 14 The reaso why tariffs decreased is mostly that several free trade agreemets etered ito force durig the period For istace, Mexico siged free trade agreemets with Costa Rica i 1995, Nicaragua i 1998, Chile i 1999, the Europea Uio i 2000, El Salvador, Guatemala ad Hoduras i 2001, ad Japa i 2005; Caada siged agreemets with Chile i 1997 ad Costa Rica i 2002; ad the Uited States siged agreemets with Jorda i 2001, Chile, Costa Rica, the Domiica Republic, El Salvador, Guatemala, Hoduras, Nicaragua ad Sigapore i 2004, ad Australia i The descriptive statistics preseted i this paragraph use data from COMTRADE via WITS. The product categories are the HS Stadard Product Groups, UNCTAD. We refer to itermediate goods to categories UNCTAD-SoP2 ad UNCTAD-SoP4. The itermediate goods traded i the model that we preset below map to these two categories. 6

8 for the U.S., the mea diagoal share is 16% ad has a stadard deviatio of 15%, while for Mexico, the mea diagoal share is 13% ad has a stadard deviatio of 14%. 16 If we focus oly o tradable sectors, the mea share of the diagoal elemets is 20%, ad 19% while the mea share of the diagoal elemets for the o-tradable sectors are 11% ad 7%, respectively for the U.S. ad Mexico. This meas that idustries purchase mostly itermediate iputs from other idustries. 17 Moreover, I-O tables reflect that tradable ad o-tradable sectors are iterrelated. The average share of tradable sectors i the productio of otradable sectors is 23% for the U.S. ad 32% for Mexico, while the average share of o-tradable sectors i the productio of tradable sectors is 34% for the U.S. ad 26% for Mexico. This casual ispectio of the I-O tables shows that sectors are strogly iterrelated ad that o-tradable sectors are a relevat iput i the productio of tradables ad vice versa. We fiish this subsectio cocludig that a assessmet of the ecoomics effects of NAFTA eeds to take ito accout that most goods traded are itermediate goods, that coutries have differet structure of productio ad that there is substatial sectoral heterogeeity i tariffs. We ow proceed to describe a model that takes all of these mechaisms ito accout. 3. A QUANTITATIVE MODEL FOR TRADE POLICY EVALUATION We develop a quatitative geeral equilibrium model with trade i itermediate goods, sectoral heterogeeity ad iput-output likages, that takes ito cosideratio all the empirical facts described i the previous sectio. The model builds o the Ricardia trade model of Eato ad Kortum (2002). There are N coutries ad J sectors. We deote coutries by i ad ad sectors by j ad k. Sectors are of two types, either tradable or o-tradable ad there is oly oe factor of productio, labor. All markets are perfectly competitive ad labor is mobile across sectors ad ot mobile across coutries. 3.1 The Model Households. I each coutry there are a measure of L represetative households that maximize utility by cosumig fial goods C j. The prefereces of the households are give by u (C ) = J j=1 Cj α j, where J j=1 αj = 1. (1) We deote by I households icome. Icome is derived from two sources; households supply labor L at a wage w ad receive trasfers o a lump-sum basis (tariff reveues ad trasfers from the rest of the world, as we will see i a momet). 16 These figures are computed usig the I-O tables described i the Appedix Data Sources ad Descriptio. 17 Joes (2007) presets a detailed descriptio of the characteristics of I-O tables. He shows that, regardless of the level of sectoral disaggregatio, the largest share is always the share of ow idustry material iputs purchased. However, the higher the level of disaggregatio, the smaller the share is. For istace, the share of ow idustry material iputs purchased are, o average, 3.3% of total material purchases for the case of the U.S. usig a 6-digit I-O table. 7

9 3.1.2 Itermediate goods. A cotiuum of itermediate goods ω j [0, 1] is produced i each sector j. Two types of iputs, labor ad composite itermediate goods (also referred to as materials) from all sectors, are used for the productio of each ω j. Producers of itermediate goods across coutries differ i the effi ciecy of productio. We deote by z j ( ω j ) the effi ciecy of producig itermediate good ω j i coutry. The productio techology of a good ω j is q(ω j j ) = z j ( ω j ) [ l(ω j j ) ] γ j J k=1 [ m k,j (ω j ) ] γ k,j, where l(ω j j ) is labor ad m k,j (ω j ) are the composite itermediate goods from sector k used for the productio of itermediate good ω j. The parameter γ k,j 0 is the share of materials from sector k used i the productio of itermediate good ω j, with J k=1 γk,j = 1 γ j, ad the parameter γ j 0 is the share of value added. Both value added shares ad itermediate goods shares vary across coutries ad sectors. 18 Sice productio of itermediate goods is at costat returs to scale ad markets are perfectly competitive, firms price at uit cost, c j /z j ( ω j ), where c j deotes the cost of a iput budle. I particular c j = Υ j w γj J P k γ k,j k=1, (2) where P k is the price of a composite itermediate good from sector k, ad Υ j is a costat. 19 Equatio (2) captures a key differece compared to the oe-sector model or the multi-sector model without iterrelated sectors, as the cost of the iput budle depeds o wages ad o the price of all the composite itermediate goods i the ecoomy, tradable ad o-tradable. A chage i policy that affects the price i ay sigle sector will affect idirectly all the sectors i the ecoomy via the iput budle. We show later that this iterrelatio plays a importat role i evaluatig the trade ad welfare effects from trade opeess Composite itermediate goods. Producers of composite itermediate goods i sector j ad coutry, supply Q j at miimum cost by purchasig itermediate goods ω j from the lowest cost suppliers across coutries. 20 The productio techology 18 The mai reaso why we assume a uit elasticity of substitutio across materials is because, at the level of aggregatio at which we coduct our empirical aalysis, value added ad I-O shares are fairly costat over time. Usig I-O tables for the years 1995 ad 2005, at the two-digit ISIC rev 2, from 26 coutries sourced from WIOD ( we evaluated the stability of iput shares by calculatig the correlatio coeffi ciet across all iput shares over time. We fid that for all coutries, the correlatio was higher tha Still, Appedix CES Model presets a geeral versio of our model where we allow for ay degree of substitutability across iputs. 19 Specifically, Υ j J k=1 (γk,j ) γk,j (γ j ) γj. 20 Allowig for producers of composite itermediate goods to search for the lowest cost supplier is a key distictio from models with Armigto-type assumptios. I those models, because of the love for variety, regardless of the price, goods are always bought from all sources, sice they are differetiated by coutry of origi. I the Eato ad Kortum (2002) model, the source from which goods are purchased is edogeously determied ad ca chage as a cosequece of tariff reductios. This is crucial i order to uderstad why this model coceptually takes ito accout chages at the extesive ew goods margi ad ot oly chages at the itesive old goods margi, as is the case i Armigto-type models. However, both models deliver similar aggregate momets for trade flows. I fact, the gravity equatio implied from the Eato ad Kortum (2002) model, equatio (6) below, is idetical to the Armigto model after mappig the dispersio of productivity, θ, ad the techology parameter, λ, to the elasticity of substitutio ad the home bias parameter i the Armigto-type models. 8

10 of Q j is a Ethier (1982) or Dixit ad Stiglitz (1977) aggregator give by [ Q j = ] σ j /(σ j 1) r(ω j j ) 1 1/σj dω j, where σ j > 0 is the elasticity of substitutio across itermediate goods withi sector j, ad r j (ω j ) is the demad of itermediate goods ω j from the lowest cost supplier. The solutio to the problem of the composite itermediate good producer gives the followig demad for good ω j ( p r(ω j j j ) = (ω j ) where P j is uit price of the composite itermediate good [ P j = P j ) σ j Q j, p j (ω j ) 1 σj dω j ] 1 1 σ j, ad p j (ω j ) deotes the lowest price of itermediate good ω j across all locatios. Composite itermediate goods from sector j are used as materials for the productio of itermediate good ω k i the amout m j,k (ω k ) i all sectors k, ad as fial goods i cosumptio C j Iteratioal trade costs ad prices. We assume that trade i goods is costly. I particular, there are two types of trade costs: iceberg trade costs ad a ad-valorem flat-rate tariffs. Iceberg costs are defied i physical uits as i Samuelso (1954), where oe uit of a tradable itermediate good i sector j shipped from coutry i to coutry requires producig d j i 1 uits i i, with dj = 1. Goods imported by coutry from coutry i have to pay a ad-valorem flat-rate tariff τ j i applicable over uit prices. We combie both trade costs, represeted by κ j i = τ j i dj i, (3) where τ j i = (1 + τ j i ). We also assume that the triagular iequality holds; κj h κj hi κj i for all, h, i. After takig ito accout trade costs, a uit of a tradable itermediate good ω j produced i coutry i is available i coutry at uit prices c j ( ) i κj i /zj i ω j. Therefore, the price of itermediate good ω j i coutry is give by p j ( ω j ) = mi i { c j i κj i z j i (ωj ) We model o-tradable sectors i the same way as tradable sectors but impose that κ j i = ; thus, i some sectors goods are ot traded because it is always cheaper to buy goods from local suppliers. I o-tradable sectors, p j ( ω j ) = c j /z j ( ω j ) ad the demad of itermediate goods is give by r j (ω j ) = q j (ω j ). Ricardia motives to trade are itroduced followig Eato ad Kortum s (2002) probabilistic represetatio of techologies allowig productivities to differ by coutry ad also by sectors. I particular, we assume 21 The market clearig coditio for the composite itermediate good i sector j is Q j = Cj + J m j,k k=1 (ωk )dω k. }. 9

11 that the effi ciecy of producig a good ω j i coutry is the realizatio of a Fréchet distributio with a locatio parameter that varies by coutry ad sector, λ j 0 ad shape parameter that varies by sector, θ j. 22 I the cotext of this model, a higher λ j makes the average productivity i a sector higher, a otio of absolute advatage, while a smaller value of θ j implies a higher dispersio of productivity across goods ω j, a otio of comparative advatage. We assume that the distributios of productivities are idepedet across goods, sectors ad coutries, ad that 1 + θ j > σ j. With these assumptios o the distributio of effi ciecies we ca solve for the distributio of prices. 23 give by The price of the composite itermediate good is the [ N ] 1/θ j P j = A j i=1 λj i (cj i κj i, (4) ) θj for all sectors j ad coutries ; where A j is a costat. Note that (4) is also the price idex of the o-tradable goods sector. The differece is that i that case, sice κ j i =, the price idex is give by P j = A j λ j 1/θj c j. Cosumers purchase fial goods at prices P j. With Cobb-Douglas prefereces (1), the cosumptio price idex is give by Expediture shares. P = J j=1 (P j /α j ) αj. (5) Total expediture o sector j goods i coutry is give by X j = P j Q j. We deote by X j i to the expediture i coutry of sector j goods from coutry i. It follows that coutry s share of expediture o goods from i are give by π j i = Xj i /Xj. Usig the properties of the Fréchet distributio we ca derive expediture shares as a fuctio of techologies, prices ad trade costs π j i = As we ca see, bilateral trade shares π j i N λ j i [ h=1 λj h c j i κj i ] θ j [ ] θ c j j. (6) h κj h take the form of a multi-sector versio of a gravity equatio. Chages i tariffs have a direct effect i trade shares via κ j i, ad from (2) ote that chages i tariffs also have a idirect effect through the iput budle c j i sice it icorporates all the iformatio cotaied i the I-O tables Total expediture ad trade balace. Total expediture o goods j is the sum of the expediture o composite itermediate goods by firms ad 22 For a descriptio of the properties of the Fréchet distributio, refer to Eato ad Kortum (2002). Doaldso (2012) relates this assumptio to other stadard assumptios used i models of iteratioal trade with heterogeeous firms, like those i Melitz (2003), Chaey (2008), ad others. Costiot et al. (2012) cosider the case of more geeral distributios. 23 Appedix Distributio of Prices ad Expediture Shares presets a detailed derivatio of the distributio of prices ad how to solve for the price idex (4) as well as the expediture shares (6). The derivatio follows Eato ad Kortum (2002) applied to a multi-sector ecoomy. 10

12 the expediture by households. The, X j is give by X j = J N k=1 γj,k i=1 Xk i π k i 1 + τ k + α j I, (7) i where I = w L + R + D, (8) represets fial absorptio i coutry, as the sum of labor icome, trade deficit, ad tariff reveues. I particular, R = J N j=1 i=1 τ j i M j i where M j i = Xj π j i 1+τ j i are coutry s imports of sector j goods from coutry i. The summatio of trade deficits across coutries is zero, N =1 D = 0, ad atioal deficits are the summatio of sectoral deficits, D = J k=1 Dk. Sectoral deficits are defied by D j = N M j i=1 i N i=1 Ej i, where E j i = Xj π j i i are coutry s exports of sector j goods to coutry i. Aggregate trade deficits i 1+τ j i each coutry are exogeous i the model, however sectoral trade deficits are edogeously determied. Fially, usig the defiitio of expediture ad trade deficit we have that J j=1 N i=1 Xj π j i 1 + τ j i D = J j=1 N i=1 Xj i π j i 1 + τ j. (9) i This coditio reflects the fact that total expediture, excludig tariff paymets, i coutry mius trade deficits equals the sum of each coutry s total expediture, excludig tariff paymets, o tradable goods from coutry. We are addig over all sectors whether a sector is tradable or o-tradable. The o-tradable sectors will appear i both sides of the equatio ad cacel out. 24 We ow defie formally the equilibrium uder policies {τ j i } i this model. Defiitio 1 Give L, D, λ j ad d j i, a equilibrium uder tariff structure τ is a wage vector w RN ++ ad prices { } P j J,N that satisfy equilibrium coditios (2), (4), (6), (7), ad (9) for all j,. j=1,= Equilibrium i relative chages. Istead of solvig for a equilibrium uder policy τ we solve for chages i prices ad wages after chagig from policy τ to policy τ, what we defie as a equilibrium i relative chages. 25 There are several advatages of doig so. First, we ca match exactly the model to the data i a base year; secod, we ca idetify the effect o equilibrium outcomes from a pure chage i tariffs, which is what we are after i this paper; ad fially we ca solve for the geeral equilibrium of the model without eedig to estimate parameters which are diffi cult to idetify i the data, as productivities λ j ad iceberg trade costs d j i. We ow defie the equilibrium of the model uder policy τ relative to a policy uder tariff structure τ. 24 It is also possible to show that (9) implies labor market clearig. To see this, add (7) across sectors ad substitute ito (9) to obtai w L = J N π j j=1 γj i=1 Xj i i 1 + τ j. i 25 This idea of expressig the equilibrium i relative chages follows Dekle et al. (2008). They use it to uderstad the effects of a chage i trade deficits while we use it to compute the effects of a chage i the tariff structure. 11

13 Defiitio 2 Let (w, P ) be a equilibrium uder tariff structure τ ad let (w, P ) be a equilibrium uder ( tariff structure τ. Defie ŵ, ˆP ) as a equilibrium uder τ relative to τ, where a variable with a hat ˆx represets the relative chage of the variable, amely ˆx = x /x. equilibrium coditios i relative chages satisfy: Cost of the iput budles: Price idex: Bilateral trade shares: ˆP j = ĉ j = ŵ γj [ N Total expediture i each coutry ad sector j: Trade balace: where ˆκ j i J j=1 X j N i=1 = J J k=1 i=1 πj i [ˆκj iĉj i ] θj ˆπ j i = [ĉ j i ˆκj i ˆP j N k=1 γj,k i=1 = (1 + τ j i )/(1 + τ j i ) ad I = ŵ w L + J Usig (2), (4), (6), (7), ad (9) the ˆP k γk,j. (10) ] θ j ] 1/θ j. (11). (12) π k i X 1 + τ k i k + α j I. (13) i π j i 1 + τ j X j D = J N π j i j=1 i=1 i 1 + τ j X j i, (14) i N τ j j=1 i=1 i π j i 1+τ j i X j + D. From ispectig equilibrium coditios (10 through 13) we ca observe that the focus o relative chages allows us to perform policy experimets without relyig o estimates of total factor productivity or trasport costs. We oly eed two sets of tariff structures (τ ad τ ), data o bilateral trade shares (π j i ), the share of value added i productio (γ j ), value added (w L ), the share of itermediate cosumptio (γ k,j ), ad sectoral dispersio of productivity (θ j ). The share of each sector i fial demad (α j ) is obtaied from these data as we will show later o. The oly set of parameters to estimate is the sectoral dispersio of productivity θ j. We provide a ew method to estimate them i Sectio Relative chage i real wages. We coclude this subsectio by briefly discussig how importat it is to accout for multiple sectors ad sectoral likages i order to quatify the effects o real wages from couterfactual chages i trade costs. 26 Usig equatio (10) ad (12) we solve for the couterfactual chage i real wages ŵ / ˆP j i each sector j as a fuctio of the share of expediture o domestic goods ad sectoral prices. We the aggregate across sectors usig cosumptio expediture shares ad obtai the followig expressio for the logarithm chage 26 Chages i real wages are ot chages i welfare i a model where tariff reveue is lump sum trasferred. The chage i welfare is a weighted average measure of the chage i real wages ad real tariff reveue, amely Î/ ˆP = ηŵ / ˆP + (1 η) ˆR / ˆP, where η = w L /I. We focus o real wages i this subsectio oly as a mode to relate our fidigs to studies that evaluate welfare effects of trade opeess i models i which tariffs are abset (for istace Arkolakis, et al. 2012). 12

14 i real wages l ŵ α j J α j = J ˆP j=1 θ j l 1 γ j ˆπj j=1 }{{} θ j γ j l ˆπ j J j=1 γ j l J ( ˆP k / ˆP ) j γk,j, (15) k=1 }{{}}{{} Fial goods Itermediate goods Sectoral likages where ˆP is the chage i cosumptio prices (5). 27 This decompositio shows that all the geeral equilibrium effects o real wages ca be summarized by the chage i the share of domestic expediture i each sector, ˆπ j ad the chages i sectoral prices, ˆP j. Each term measures a additioal effect compared to a certai bechmark model. For istace, cosider the case where γ j = 1 for all j ad, the itermediate goods are produced oly with labor ad they are used oly to produce fial goods. I this case l ŵ / ˆP j = (1/θ j ) l ˆπ j ad sice α j is the share spet o fial goods from sector j, (α j /θ j ) l ˆπ j measures the cotributio of the chage i the real wage i sector j to the aggregate chage i real wages. α j Addig across all sectors, J j=1 (αj /θ j ) l ˆπ j measures the aggregate effect of trade i fial goods. This effect depeds o the share of each sector i fial demad ad the sectoral trade cost elasticity. Note that the more egatively correlated are α j /θ j with ˆπ j the larger are the welfare effects for small chages i ˆπ j. 28 From this expressio it is evidet that sectoral heterogeeity i trade elasticities matters for welfare. 29 Cosider the model where γ j 1 ad γ j,j = 1 γ j for all j ad. I this case there are o sectoral iterrelatios sice itermediate goods are produced with labor ad materials oly from the same sector. Reductios i trade cost reduce the price of tradable itermediate goods ad i tur reduce the price of the composite itermediate good. As a cosequece, producers of itermediate goods gai from this reductio i the cost of their iputs. This additioal effect o real wages compared to a model with o itermediates goods is captured by the term J α j 1 γ j j=1 θ j l ˆπ j γ. j Fially cosider the geeral model. The materials price idex J ( ˆP k ) γk,j captures the effect of a k=1 chage i the price of composite itermediates from sector k o real wages i sector j. The larger is γ k,j for sectors i which prices declie more, the larger is the reductio i the cost of material iputs used i productio. I other words, it captures the importace of the iput-output structure of the ecoomy. The cotributio to aggregate chage i real wages is give by J α j l J ( ˆP j=1 γ j k / ˆP ) j γk,j. Note that this k=1 term resembles a geometric weighted average of the chage i the price of materials. Oly i the case where substatial symmetry i parameters is assumed this term will be equal to zero To obtai the expressio for the chage i real wages use (12) ad (10) to solve for ŵ / ˆP, j ad the take the product for all sectors j weighted by α j. Fially, apply logarithms from both sides ad rearrage terms to obtai the expressio for the percetage chage i the real wage i coutry, as preseted i the text. 28 Arkolakis et al. (2012) show that withi a variety of trade models there are two suffi ciet statistics to evaluate welfare gais: the share of expediture o domestic goods ad trade elasticities. Doaldso (2012) makes the same observatio for the case of a multi-sector Eato ad Kortum (2002) model. 29 I a recet study, Ossa (2012) evaluates the importace of sectoral variatio i trade elasticities for welfare quatificatio. 30 I fact, to see this cosider the case of two sectors. Sectoral likages are give by (α 1 γ2,1 /γ 1 α2 γ 1,2 /γ 2 ) l( ˆP / 1 ˆP ). 2 Note that this term will oly be zero if prices chage i the same proportio, ad-or if the share of fial good i demad ad the share of itermediate goods i productio is the same across sectors together with a symmetric I-O table. 13

15 3.2 Welfare Effects From Tariff Chages I this subsectio we decompose the welfare effects from tariff chages ito terms of trade ad volume of trade effects. We use this decompositio i the quatitative sectio of the paper i order to evaluate the welfare effects of NAFTA s tariff chages. More geerally, this welfare decompositio allows us to uderstad the effects of tariffs chages across differet coutries ad sectors. We deote welfare of the represetative cosumer i coutry by W = I /P, where I is give by (8) ad P by (5). Totally differetiatig W ad after usig the equilibrium coditios of the model the chage i welfare is give by d l W = 1 J N I j=1 i=1 ( ) E j i d l cj M j i d l cj i + 1 J N }{{} I j=1 Terms of trade ( ) τ j i=1 i M j i d l M j i d l cj i, (16) }{{} Volume of trade where the first term measures the multilateral ad multisectoral terms of trade effect ad the secod term the multilateral ad multisectoral volume of trade effect from tariff chages. 31 The chage i welfare due to the terms of trade effects from tariff chages quatifies the gais from a icrease i exporter prices relative to the chage i importer prices, measured at world prices. 32 I our model, this measure of terms of trade is a multilateral weighted chage i export ad import prices at the sectoral level, where the weights are give by bilateral exports ad imports respectively. The cotributio of each sector to the aggregate chage i terms of trade depeds o sectoral trade deficits (the differece betwee E j i ad M j i ) ad sectoral chages i import ad exporter prices. I geeral it is ot possible to sig the particular cotributio of each sector to the aggregate effect. 33 quatitative assessmet, as we do below for the case of NAFTA. Doig so requires performig a The variatio across sectors o the terms of trade effects is a key distictio from a model with multiple sectors ad itermediate goods relative to a model with o itermediate goods. I fact, if there are o itermediate goods i productio the sectoral variatio i trade flows plays absolutely o role o ifluecig the aggregate terms of trade. To see this, cosider the case where γ j = 1 for all j ad, the itermediate goods are oly produced with labor. Iput costs do ot vary by sector, sice c j = w ad the d l c j = d l w, ad the aggregate terms of trade effects are give by J j=1 N i=1 M j i (d l w d l w i ) = N i=1 M i (d l w d l w i ), where M i are total imports by coutry from coutry i. Hece, coditioal 31 Appedix Welfare presets a detailed derivatio of equatio (16). Other studies have also preseted multilateral measures of terms of trade. For istace, Bagwell ad Staiger (1999) ad Ossa (2011). We borrow the term volume of trade effect from Dixit ad Norma (1980) which they defie i the cotext of a two-good two-coutry model. 32 Coditioal o exportig, the world price (et of tariffs) of the itermediate good that coutry exports to i is c j d j ( i /zj ω j ). Chages i tariffs impact oly the iput budle, c j ad affect all exporters of itermediate goods i sector j proportioally. Of course, chages i tariffs ca chage the set of goods sourced from each coutry, but sice prices chage proportioally to c j, the world price of the goods that coutry i is still sourcig from chage i the same way as the oes that it stops sourcig from. Therefore, chages i iput costs measure the chage i trade prices i this model. 33 A suffi ciet coditio for a sector to cotribute positively to aggregate welfare is that the sector et export to the rest of the world ad that exporter prices icrease relative to importer prices. To see this, ote that d l c j ca be aproximated by N i=1 (Ej iĉj M j iĉj i ) = J N j=1 i=1 ĉj M j i (Ej i /M j i ĉj i /ĉj ). Therefore, if sector j is a et exporter,, the the cotributio of that sector to the ĉ j 1, the J j=1 the E j i > M j i, ad if exporter prices improve relative to importer prices, ĉj > ĉ j i aggregate terms of trade is positive sice E j i /M j i ĉj i /ĉj > 0. 14

16 o a chage i wages ad aggregate trade flows, a multi-sector model delivers the same aggregate terms of trade effects as a oe sector model. Still, terms of trade are goig to vary bilaterally. 34 The secod term i (16) measures the welfare gais from chages i the volume of trade as a cosequece of the chage i tariffs. More trade is created the larger is the icrease i the volume of trade, measured as import values deflated by import prices, ad cotributes positively to welfare. Iitial tariffs ad import volumes weight how importat this effect is across sectors ad coutries. From (16) we ca defie bilateral ad sectoral measures of terms of trade ad volume of trade that ca be used to decompose the welfare effects across coutries ad sectors. The chage i bilateral terms of trade betwee coutries ad i is give by d l tot i = J j=1 while the chage i the bilateral volume of trade is give by d l vot i = J ( ) E j i d l cj M j i d l cj i, (17) j=1 τ j i M j i Similarly, we measure the chage i sectoral terms of trade by d l tot j = N i=1 while the chage i sectoral volume of trade is give by d l vot j = N ( ) d l M j i d l cj i. (18) ( ) E j i d l cj M j i d l cj i, (19) i=1 τ j i M j i ( ) d l M j i d l cj i. (20) Of course, give these defiitios, the chage i welfare i coutry ca also be computed as d l W = 1 N I i=1 (d l tot i + d l vot i ) = 1 J ( I j=1 d l tot j + d l vot) j. 3.3 Takig the Model to the Data A key advatage from solvig the model i relative chages is that it miimizes the data requiremets to calibrate the model. Cocretely, the data eeded are bilateral trade flows (M j i imports of from i), value added (V j ), gross productio (Y j ), ad I-O tables. With these data we ca calculate the data couterparts of π j i, γj, γ j,k, ad α j. To obtai the bilateral trade share π j i, we first calculate domestic sales i each coutry, M j as the differece betwee gross productio ad total exports; M j = Y j N i=1,i M j i. We the defie expediture by coutry of sector j goods imported from coutry i as X j i. We calculate Xj i by multiplyig trade flows by tariffs, that is, X j i = M j i (1 + τ j i ). We obtai πj i for each sector j ad pair of coutries, i as follows π j i = Xj i / N. The share of sector k s spedig o sector j s goods γj,k, is calculated from i=1 Xj i 34 Ossa (2011), usig a multi sector Armigto model, shows that the terms of trade effect ca be viewed as a relative wage effect sice world prices are proportioal to wages i a model with o itermediate goods. We show that whe there are itermediate goods, world prices are ot proportioal oly to wages. 15

17 the I-O matrix as the share of itermediate cosumptio of sector j i sector k over the total itermediate cosumptio of sector k times oe mius the share of value added i sector j, 1 γ j, where the share of value added i each sector ad coutry is give by γ j = V j /Y j. To calculate fial cosumptio share, α j we take the total expediture of sector j goods, substract the itermediate goods expediture ad divide by total fial absorptio, amely α j = (Y j + D j J k=1 γj,k Y k )/I, where trade deficits i each sector j ad coutry are give by D j = N i=1 M j i N i=1 M j i. Fially, the oly parameters missig are the sectoral dispersio of productivity, θ j. I the ext sectio we preset a ew method to estimate these parameters. 3.4 Solvig the Model for Tariff Chages Cosider a chage i policy from τ to the ew policy τ, captured by ˆκ j i. To solve for the equilibrium, we first guess a vector of wages ŵ = (ŵ 1,..., ŵ N ), for example, ŵ = 1. Give a vector of wages, the equilibrium coditios (10) ad (11) are JxN equatios i JxN ukow prices. Therefore, we ca solve for prices i each sector ad each coutry. Let ˆp j (ŵ) ad ĉ j (ŵ) be the solutio for the price ad cost of the iput budle i each sector j ad coutry cosistet with the vector of wages ŵ. The use π j i ad θj together with the calculated ˆp j (ŵ) ad ĉ j (ŵ) ad solve for π j i (ŵ) usig (12). Give πj i (ŵ), τ, γ j, γ j,k ad α j, solve for total expediture i each sector j ad coutry, X j (ŵ) cosistet with the vector of wages ŵ usig (14). Substitutig π j i (ŵ), Xj (ŵ), τ, ad D ito (13) we verify if the trade balace holds. If ot, we adjust our guess of ŵ util equilibrium coditio (13) is obtaied. The Appedix Solvig the Model describes i greater detail every step. 4. A NEW METHOD TO ESTIMATE TRADE ELASTICITIES The trade elasticities θ j are the key parameters for quatitative trade policy evaluatio. I our model, these are the oly parameters we eed to estimate i order to idetify the effects of tariff reductios. I the cotext of the Eato ad Kortum model, as well as ours, the trade elasticities are related to the dispersio of productivity parameter ad it determies how trade flows react to chages i tariffs. If productivity is less dispersed, as idicated by a larger value of θ j, the a chage i tariffs will ot chage the share of traded goods i a substatial way. The reaso is that goods are less substitutable. O the other had, if the productivities are very cocetrated -if there is high dispersio- small chages i tariffs ca traslate to large adjustmets i the share of goods traded. The reaso is that producers of the composite aggregate are more likely to chage their suppliers, sice goods are more substitutable. The chage i the measure of goods traded is the adjustmet at the extesive margi i this model. 35 To see these effects more formally, 35 I our model the elasticity of trade with respect to trade costs is the dispersio of productivity, ad is ot the elasticity of substitutio as i Armigto models. If we restrict producers of the itermediate good aggregate to purchase goods from the same source, regardless of the chage i trade costs, the the trade elasticity will be give by the elasticity of substitutio as i Armigto models. This is the sese i which the dispersio of productivity ca be related to the elasticity of substitutio i a Armigto model. Both models, the Ricardia ad the Armigto, deliver a similar gravity-type equatio. However, coceptually the models are very differet. Adjustmets from chages i tariffs occur for differet reasos i the two models. Refer to foototes 9 ad 20. Also, i a Ricardia trade model like, Eato ad Kortum (2002), there are productio-side gais 16