Trade, Inequality, and the Endogenous Sorting of Heterogeneous Workers

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1 Trade, Inequalty, and the Endogenous Sortng of Heterogeneous Workers Eunhee Lee Unversty of Maryland October 11, 2016 Latest verson avalable here. Abstract Ths paper presents a new framework to quanttatvely nvestgate the effect of nternatonal trade on between- and wthn-educatonal-type nequalty for a large number of countres. I embed workers occupatonal choce problem nto a mult-country, mult-ndustry, and mult-factor trade model. Internatonal trade and worker s comparatve advantage affect workers labor supply decson together, and, as a consequence, gans from trade dffer across workers. I quantfy the model for 33 countres, 5 educatonal types, 4 ndustres, and 5 occupatons to examne the dstrbutonal effect of trade lberalzaton between 2000 and 2007, usng the mcrodata from household surveys of each country. I fnd that (1) between-educatonal-type nequalty ncreases n hgh-ncome countres and low-ncome countres wth a manufacturng comparatve advantage such as Chna, but decreases n Latn Amercan countres due to trade; (2) trade ncreases wthn-educatonal-type nequalty everywhere; (3) occupaton-level labor reallocaton s an mportant channel by whch trade affects domestc nequalty; and (4) trade sgnfcantly contrbutes to ndustry- and occupatonlevel employment shfts. Keywords: trade, worker heterogenety, nequalty, occupatonal choce JEL Codes: F16, F66, J24, C68, D33 I am very grateful to my advsors Costas Arkolaks, Lorenzo Calendo, Penny Goldberg, and Samuel Kortum for ther gudance and support. I also thank Joe Altonj, Joaqun Blaum, Jonathan Eaton, Federco Esposto, Sharat Ganapat, Matthew Grant, James Harrgan, Sebastan Hese, Nuno Lmao, Guseppe Moscarn, Sungho Noh, Tommaso Porzo, Peter Schott, John Shea, Meredth Startz, Danel Trefler, Yujung Whang, and Chong Xang. All errors are my own. Department of Economcs, Unversty of Maryland. Emal: lee@econ.umd.edu

2 1 Introducton Ths paper presents a new framework to quanttatvely nvestgate the effect of nternatonal trade on between- and wthn-educatonal-type nequalty for a large number of countres. Although tradtonal trade theory predcts that trade ncreases nequalty n hgh-ncome countres and decreases nequalty n low-ncome countres (.e., the Stolper-Samuelson theorem (1941)), ths predcton s at odds wth emprcal evdence whch pants much more complcated pctures see Goldberg and Pavcnk (2003; 2004; 2007). To better reconcle ths fact, I present a multcountry, mult-ndustry, and mult-factor general equlbrum trade model, focusng on worker-level comparatve advantage and labor reallocaton as the man channels by whch trade affects between- and wthn-educatonal-type nequalty. In ths model, two dstnct comparatve advantage structures characterze the nternatonal trade envronment and domestc labor markets, respectvely. Frst, trade s drven by comparatve advantage across countres based on productvty dfferences and relatve factor endowments. Second, the effect of trade s dssemnated dfferentally across workers wthn a country based on comparatve advantage across workers. Workers draw ndustry- and occupaton-specfc productvtes condtonal on ther exogenously endowed educatonal type. Then they endogenously sort nto ndustry and occupaton n order to maxmze ther ncomes, as n the Roy (1951) model. Internatonal trade mpacts ths sortng mechansm and, as a consequence, gans from trade are dfferent across workers based on ths trade-nduced labor reallocaton. Ths labor supply channel by whch trade mpacts nequalty has not been studed much n the lterature as standard models smply assume that workers are homogeneous gven ther educatonal type. I also add another mportant ngredent to the model: workers not only choose an ndustry but also an occupaton. Workers engage n dfferent occupatonal tasks wthn the same ndustry based on ther comparatve advantage. As a result, they are affected by ndustry-level trade shocks dfferently dependng on what they actually do wthn an ndustry. Occupaton s another mportant margn through whch trade mpacts domestc nequalty, because workers wth dfferent skll levels show sgnfcantly dfferent patterns of occupaton-level labor allocaton as shown n Fgure A1. Thus, gnorng ths dmenson wll sgnfcantly underestmate the dfferental effect of trade on workers wth dfferent characterstcs. 1

3 A unfed framework wth these new features explores how trade affects varous measures of nequalty. I frst focus on how trade changes between-educatonaltype nequalty measured by relatve welfare gans from trade as well as the skll premum. 1 Second, the model also shows how trade changes wthn-educatonaltype nequalty based on changes n varance of equlbrum real wage wthn types. Ths part s mportant, especally because wthn-educatonal-type nequalty has ncreased sgnfcantly n recent years. The effect of trade on betweeneducatonal-type nequalty s thus only a partal explanaton for the dstrbutonal effect of trade. 2 Lastly, I derve trade-nduced changes n ndustry and occupaton wage prema and employment shfts across ndustres and occupatons n order to demonstrate to what extent trade tself explans aggregate outcomes. I use ths model to quantfy the dstrbutonal effects of changes n the trade envronment between 2000 and 2007 across 5 worker types defned by educatonal attanment, 4 ndustres, and 5 occupaton categores n 33 countres. Ths tme perod s partcularly nterestng, because nternatonal trade became an ncreasngly sgnfcant factor after Chna joned the World Trade Organzaton (WTO) n I use nternatonal mcrodata gleaned from household surveys for each country to quantfy workers dfferental responses to trade shocks n dfferent countres. To take the model to the data, I estmate the key parameter, the labor supply elastcty, for four dfferent countres and fve educatonal types. Ths parameter s drectly related to the degree of worker heterogenety. I allow t to be country- and educatonal-type-specfc rather than pre-commt to a specfc assumpton on the degree of worker heterogenety. 3 The model n ths paper also nests exstng trade models n a tractable way usng dfferent values of ths key parameter. Armed wth the parameter estmates, I separately ntroduce two types of trade shocks to perform counterfactuals. I frst measure trade shocks by changes n blateral trade costs, whch are calbrated to match changes n blateral trade flows n 1 I defne the skll premum by the wage premum of college graduates over non-college graduates. In lne wth the nternatonal trade lterature, welfare gans from trade are measured by changes n real ncome caused by changes n the trade envronment assumng consumers have a homothetc preference. 2 Helpman et al. (2010; 2012) and Grossman et al. (2014) dscuss the effect of trade on changes n the wthn-type nequalty based on the search and matchng framework. Grossman (2013) also ponts out the lmtaton of nvestgatng the effect of trade only on the skll premum. 3 Workers are homogeneous n most trade models, ncludng the Rcardan and the Heckscher- Ohln trade models. The specfc factors model s the other extreme case, where workers are extremely heterogeneous and thus constraned to a certan ndustry. 2

4 the data. The calbraton result shows that trade costs have decreased prmarly n the manufacturng ndustry between 2000 and Next, the second trade shock of nterest s the change n Chna s manufacturng labor productvty, snce Chna has been on the rse n the global market durng the tme of nterest. 4 The result from counterfactual experments show that changes n the trade envronment between 2000 and 2007 have rased between-educatonal-type nequalty n most hgh-ncome countres and n low-ncome countres wth a comparatve advantage n the manufacturng ndustry such as Chna. For example, combnng two trade shocks, U.S. workers wth advanced degrees have had a 0.45% ncrease n welfare, whereas hgh school dropouts n the U.S. have actually lost welfare by 0.008%. For Chna, ths dscrepancy s predcted to be even larger: e.g., 1.17% ncrease and 0.46% decrease, respectvely. In contrast, n most Latn Amercan countres, between-educatonal-type nequalty has decreased due to trade. On the other hand, trade ncreases wthn-educatonal-type nequalty n all countres n the sample: 1.48% ncrease of wthn-type wage varance on average across worker types and countres. Ths paper also quanttatvely shows that trade changes nequalty measures mostly through labor reallocaton across ndustres and occupatons, wth a sgnfcant emphass on the occupaton level. 5 Moreover, the result has an aggregate mplcaton about trade-nduced employment shfts. Trade nduces a sgnfcant contracton of manufacturng employment as well as a job polarzaton n hgh-ncome countres. 6 In contrast, t generates a contracton of agrcultural employment n low-ncome countres such as Chna and an expanson of agrcultural employment n Latn Amercan countres. The motvaton for ths paper stems from many prevous emprcal studes that document the relatonshp between trade and nequalty: e.g., Autor et al. (2013; 2015) and Ebensten et al. (2014) for developed countres, Goldberg and Pavcnk (2003; 2005) and Topalova (2007) for developng countres. I provde a structural 4 Many emprcal papers, such as Autor et al. (2013), connect the mport competton from Chna n hgh-ncome countres to the ncrease of productvty n Chna, whch eventually mproves Chna s export supply capablty manly through ther cost advantage. 5 Ths s consstent wth Kambourov and Manovsk (2008) and Groes et al. (2015). 6 The polarzaton across skll levels of occupaton s both theoretcally and emprcally wellstuded n the labor economcs lterature see Baumol (1967), Acemoglu (1999) and Autor et al. (2003) on models of the skll-based techncal change, as well as Autor et al. (2008) and Goos and Mannng (2007) for emprcal evdence. A recent paper by Harrgan et al. (2015) studes the effect of trade on polarzaton. 3

5 model that complements emprcal fndngs n those papers. Ths paper s not the frst to use a general equlbrum framework to examne trade-nduced nequalty n a large number of countres. Bursten and Vogel (2015) focus on the reallocaton of factors across heterogeneous frms wthn a sector, and Parro (2013) focuses on captal-skll complementarty. Unlke these papers, I focus on workers heterogeneous productvtes and endogenous sortng as the key channel through whch trade mpacts nequalty. In addton, ths paper uncovers the effect of trade not only on between-educatonal-type nequalty but also on wthn-educatonal-type nequalty whch has been drawng much attenton recently. Most mportantly, ths paper contrbutes to the fast-growng lterature on the Roy-lke assgnment model wth worker heterogenety, by Lagakos and Waugh (2013), Hseh et al. (2013), and Bursten et al. (2015). I embed worker-level comparatve advantage nto the gravty structure of standard trade models based on country-level comparatve advantage. 7 Ths paper s dstnct from prevous works n three mportant ways. Frst, workers have heterogeneous productvtes across both ndustres and occupatons. I show quanttatvely that consderng both dmensons s mportant to quantfy the dstrbutonal effect of trade. Second, I quantfy trade-nduced changes of varous nequalty measures wthn a unfed framework. Lastly, ths paper quantfes a hgh-dmensonal model of trade, nequalty, and worker heterogenety wth rch mcrodata from household surveys across a large number of countres nstead of focusng on the outcome of a sngle country. Ths paper also contrbutes to the lterature by provdng a quanttatve strategy to experment wth a wde range of trade lberalzaton epsodes regardng changes n trade costs or partner countres productvty nstead of restrcted trade epsodes such as movng to autarky. Moreover, I estmate the key parameter the labor supply elastcty, whch s drectly related to the degree of worker heterogenety n a more general setup accountng for heterogeneous wage dstrbutons between worker types and countres. Generalzng the quanttatve Rcardan model of Eaton and Kortum (2002) wth heterogeneous workers, I provde a quanttatve framework for theoretcal foundatons of workers comparatve advantage and trade studed by Ohnsorge and Trefler (2007) and Costnot and Vogel (2010). I ntroduce a new trade model wth worker heterogenety, whch also dffers from the search and matchng model 7 Galle et al. (2015) follow a smlar approach wth heterogenety defned across ndustres. 4

6 n an open economy (Grossman et al. (2014)) or from the model wth transtonal dynamcs of ndustry-level reallocaton (Artuç et al. (2010), Dx-Carnero (2014), and Calendo et al. (2015).) Wth the gravty structure that s n lne wth the welfare analyss of Arkolaks et al. (2012), the model remans quanttatvely tractable by applyng the technque of hat algebra used by Dekle et al. (2008). The algorthm to solve the model s based on Alvarez and Lucas (2007) and Calendo and Parro (2015), but wth multple producton factors occupatons. The structure of ths paper s as follows. In Secton 2, I develop a general equlbrum trade model wth endogenous sortng of heterogeneous workers, and derve welfare and dstrbutonal effects of trade. Secton 3 dscusses the quanttatve strategy, ncludng the estmaton of parameters and the calbraton of trade shocks. In Secton 4, I present counterfactual results to dscuss the dstrbutonal effect of trade. Secton 5 presents senstvty analyses, and Secton 6 concludes. 2 Model In ths secton, I construct a general equlbrum trade model that connects workers occupatonal choce problem wthn a country to the trade envronment. Two comparatve advantage structures characterze the model: one, across countres and the other, across workers wthn each country. Workers choose an ndustry and an occupaton to work n based on ther heterogeneous productvtes as n Roy (1951). The parametrzaton of worker heterogenety s closely related to Hseh et al. (2013) and Bursten et al. (2015). Ths model uncovers the mechansm by whch trade affects workers sortng and, as a consequence, nequalty. 2.1 Envronment Consder an economy wth N countres ndexed by {1,..., N}. Each country has J ndustres ndexed by j {1,..., J} and a contnuum of products e j [0, 1] wthn each ndustry j. The trade envronment of each ndustry follows Eaton and Kortum (2002) (EK, hereafter). 8 8 A Rcardo-Roy model combnes the assgnment-based Roy model and the Rcardan trade envronment. Costnot and Vogel (2010) provde a theoretcal foundaton based on the noton of log-supermodularty. Costnot and Vogel (2015) provde an authortatve overvew of both theory and emprcs n ths lterature. 5

7 Preferences Indvduals have common nested CES preferences over J ndustres and wthn-ndustry product varetes: U = ( j (C j ) η 1 1 η 1 ) η 1 η and C j = ( C (e j ) η 2 1 η 2 de j ) η 2 η 2 1, 0 where C j s a CES aggregate consumpton bundle, and η 1, η 2 > 0 are elastctes of substtuton across ndustres and across product varetes, respectvely. Workers Workers nelastcally supply one unt of tme and earn labor ncome. Workers are exogenously classfed by ther types τ {1,..., T} ex ante, whch are mutually exclusve and exhaustve groups emprcally defned by observable worker characterstcs, ncludng educatonal attanment, age, or gender. The total number of type τ workers n country s exogenously gven by L,τ. Each worker solves an occupatonal choce problem by smultaneously choosng the ndustry and occupatonal afflaton generatng the hghest labor ncome, as n the Roy (1951) model. There are O occupatons ndexed by o {1,..., O}. The labor market s perfectly compettve, so that workers earn ther margnal revenue product. The workers occupatonal choce problem depends on workers productvty and the market value of labor n dfferent ndustres and occupatons. I assume that an ndvdual worker ω of type τ has an dosyncratc productvty ɛω j,o for each par of ndustry j and occupaton o, where ɛω j,o s randomly drawn from a Fréchet dstrbuton: F j,o,τ (ɛ) = exp( Tj,o,τ ɛ θ,τ). Ths dosyncratc productvty s nterpreted as effcency unts of labor that worker ω s able to provde to ndustry j wth occupaton o. For smplcty, t s assumed that there s no correlaton between ndustry- and occupaton-specfc draws, but ths assumpton can be easly generalzed to allow correlatons. 9 Ths parametrza- 9 If a correlaton s allowed, the jont dstrbuton functon wll be where ρ s a correlaton parameter. F,τ (ɛ) = exp[ { (T j,o,τ ɛ θ,τ ) 1/(1 ρ) } 1 ρ ] j,o 6

8 ton s analogous to the quanttatve Rcardan trade model poneered by Eaton and Kortum (2002). The Fréchet dstrbuton s a type II extreme value dstrbuton, and thus the maxmum of ndependently drawn Fréchet random varables agan follows another Fréchet dstrbuton. Ths feature lends great tractablty to derve smple analytc solutons for equlbrum outcomes. Frst, the shape parameter of ths dstrbuton θ,τ governs the wthn-type dsperson of productvty, whch can potentally dffer across countres. As shown n Secton 2.5, ths parameter s related to the elastcty of labor supply at the ndustry and occupaton level. Hence, I wll call t the labor supply elastcty parameter. Worker types wth hgher θ,τ have a more elastc labor supply at the ndustry and the occupaton level. Ths s due to the fact that types wth hgher θ,τ have fewer outlers n productvty, makng them more lkely to adjust to changes n per-unt wages by ndustry and occupaton. Second, the scale parameter T j,o,τ represents the level of workers productvtes, whch governs the absolute advantage of type τ workers n country for (j, o). The worker-level comparatve advantage s determned by ratos of ths parameter: for example, type τ workers have a comparatve advantage n (j, o) compared to type τ workers n (j, o ) f Tj,o,τ T j,o,τ Producton > Tj,o,τ T j,o,τ. 10 Workers engage n the producton of fnal goods by choosng an ndustry and an occupaton, where Occupatons are factors of producton. Producton of a product varety e j follows a CES technology: Y (e j ) = z (e j ) ( o µ j,o (y j,o (e j γ 1 γ )) ) γ γ 1, (1) where z (e j ) s a country s factor-neutral productvty of producng e j. The occupatonal labor nput from all workers wth occupaton o s denoted by y j,o (e j ). The occupaton-ntensty parameter s gven by µ j,o, and sums to one for each ndustry. The elastcty of substtuton γ between occupatons captures the complementarty between occupatons. In the quanttatve analyss, I consder occupatons as complementary producton nputs, as evdenced by Goos et al. (2014) Ths s a stochastc verson of log-supermodularty as Costnot and Vogel (2015) pont out. 11 If γ, the producton functon becomes lnear n occupatons, analogous to Costnot and Vogel (2010). In ths lmt case, country-level comparatve advantage s exactly transferred to worker-level comparatve advantage wthn countres, and as a consequence, the model predcton becomes closer to the predctons of tradtonal trade theory: e.g., the Stolper-Samuelson theorem. 7

9 2.2 Internatonal Trade There are N countres partcpatng n nternatonal trade, and only fnal goods are traded. I assume that the fnal goods market s perfectly compettve, n whch each country purchases each product from the lowest-cost suppler. The prce of product e j depends on the unt cost of the occupatonal nput bundle c j as well as on the productvty z (e j ). The Heckscher-Ohln channel of ths model s based on the relatve type-leve labor supply and endogenous occupatonal choces. The Rcardan force of trade, on the other hand, s actve through productvty z (e j ). Wthn-ndustry product varetes are traded as n the EK framework. The productvty z (e j ) s drawn from a Fréchet dstrbuton ndependently for each e j : H j (z) = exp( Aj z νj ), (2) where the scale parameter A j s connected to the absolute advantage of country for ndustry j, and ν j governs the dsperson of productvty across countres. The degree of dsperson s dfferent across ndustres, as ν j depends on the ndustry. Ths framework s bult on mult-ndustry extensons of the EK model by Chor (2010), Costnot et al. (2011), Donaldson (2012), and Calendo and Parro (2015). 12 Trade s subject to standard ceberg-type costs: d j n 1 for any product n ndustry j produced n and shpped to n. It s assumed that d j n > 1 for = n, d j = 1 for every, and dj n = dj n. Trade costs are dfferent across ndustres Partal Equlbrum Partal equlbrum results are derved separately for workers occupatonal choces, producton, and trade flows between countres. Each result s determned gven the per-unt prce p j,o of occupatonal nput for each country, ndustry, and occupaton. 14 These prces are, n turn, determned n general equlbrum. 12 The parametrzaton n ths paper s most closely related to Calendo and Parro (2015) wth ndustry-specfc ν j. I generalze the labor supply sde by consderng workers endogenous occupatonal choces but smplfy the nput-output lnkage. 13 Ths model can easly be extended to consder tarff and non-tarff parts of trade costs separately wthout much change to the man mplcaton of the model. 14 The per-unt prce for occupatonal nput vares both by ndustry and by occupaton, because the labor supply s upward-slopng due to heterogeneous productvtes. Ths varable s dfferent from the actual wage observable n the data whch ncludes unobservable effcency unts of labor. 8

10 Occupatonal choce problem A potental wage of worker ω n country wth an dosyncratc productvty ɛω j,o for (j, o) s w j,o,ω = pj,o ɛω j,o. The workers occupatonal choce problem s to choose an ndustry and occupaton that maxmzes w j,o,ω. Usng the Fréchet dstrbuton of workers productvty, the equlbrum probablty that a worker ω of type τ works n ndustry j n occupaton o s π j,o,τ = T j,o,τ (pj,o ) θ,τ,o,o j,o Tj,τ (pj, (3) ) θ,τ whch determnes the ndustry and occupaton-level labor supply. Worker-level comparatve advantage affects ths labor supply functon: workers are more lkely to supply ther labor to the ndustry and the occupaton where they have a comparatve advantage. The same change n p j,o may nduce dfferental labor reallocaton patterns across dfferent worker types because of worker-level comparatve advantage. A detaled dervaton of (3) can be found n the Appendx. Gven workers equlbrum choce of (j, o), the probablty dstrbuton of the equlbrum wage of type τ workers s derved by G,τ (w) = exp{ [ T j,o,o,τ (pj ) θ,τ]w θ,τ}. (4) j,o Ths s another Fréchet dstrbuton wth a scale parameter j,o Tj,o,o,τ (pj ) θ,τ and a shape parameter θ,τ. It s mportant to have both a type-specfc and countryspecfc parameter θ,τ, because the data show that the degree of wage dsperson wthn worker types vares sgnfcantly by worker type and country. 15 Ths wage dstrbuton gves the equlbrum average wage: w,τ = [ T j,o,o,τ (pj ) θ θ,τ] 1,τ Γ(1 1 ), (5) j,o θ,τ where Γ( ) s a Gamma functon. I assume θ,τ > 1 for all and τ so that the average wage s well-defned. From (5), f type τ workers have a comparatve advantage n the hgh-payng (j, o), they have relatvely hgher wages on average. In addton, 15 For example, the data clearly show that better-educated workers are more dspersed n earned wages wthn ther type than less-educated workers are. 9

11 varance of wage wthn each type s: var,τ (w) = [ T j,o,o,τ (pj ) θ θ,τ] 2,τ 2 (Γ(1 ) (Γ(1 1 )) 2 ). (6) j,o θ,τ θ,τ Industry- and occupaton-level average wages are derved from the type-level average wage (5), employment allocaton (3), and type-level labor supply L,τ, where the frst two depend on the endogenous varable p j,o. 16 Producton and Trade Each frm solves a cost mnmzaton problem by choosng y j,o (e j ). The CES technology results n the followng equlbrum unt cost functon: c j = ( o (µ j,o ) γ (p j,o ) 1 γ ) 1/(1 γ). (7) The effectve unt cost to produce a varety e j n country s c j /z (e j ). The prce of a product e j n country n, f t were produced n country s P n (e j ) = ( cj z (e j ) )dj n. Due to perfect competton, the actual prce of ej n country n s gven by P n (e j ) = mn P n (e j ). Equlbrum prce and trade flow are analogous to the results of the EK model. Detals are provded n the Appendx. Next, a gravty equaton shows patterns of wthn-ndustry specalzaton. The probablty that a country n buys a good n ndustry j from a country s λ j n = Aj (cj dj n ) νj Φ j n = Xj n Xn j, (8) where Φ j n N =1 Aj (cj dj n ) νj. From ths gravty equaton, ν j s the elastcty of mports wth respect to trade costs, whch s called the trade elastcty. An ndustry wth less dsperson of productvty across countres has a hgher trade elastcty, because trade flows respond more to changes n trade costs when countres are smlar n productvty. The exact prce ndex P j for ndustry j and country s P j = (Γ( νj + 1 η 2 ν j )) 1 1 η 2 (Φ j ) 1 ν j, (9) 16 The average wage of ndustry j s w j = τ,o w,τ L,τ π j,o,τ / τ,o L,τ π j,o,τ and that of occupaton o s w o = τ,j τ,o w,τ L,τ π j,o,τ / τ,j L,τ π j,o,τ. 10

12 where Γ( ) s a gamma functon. I assume ν j + 1 > η 2 so that the prce ndex s well-defned. A country-level exact prce ndex, P = [ j (P j 1 1 η 1 and the )1 η 1] aggregate expendture share λ j are derved from the nested CES preference: λ j = (Pj )1 η 1 j (P j ) 1 η 1. (10) 2.4 General Equlbrum In general equlbrum, goods markets and occupaton markets clear n all countres, and the trade balance condton holds. Fnal goods markets are cleared when E j = N n=1 λ j n Xj n (11) holds for each and j, where E j s gross output n ndustry j n country. The total expendture s X j = λ j I, where I s the total spendng whch s equal to the total ncome, I = τ,j,o w,τ L,τ π j,o,τ + D, wth D beng an aggregate trade defct. Snce workers have heterogeneous productvtes across ndustres and occupatons, the occupaton market clearng condtons are defned for each ndustry and occupaton, makng the total number of equatons (J O) for each country, (µ j,o ) γ ( pj,o c j ) 1 γ E j = w,τ L,τ π j,o,τ. (12) τ Two market clearng condtons mply the trade balance condton for each country, j N =1 λ j n Xj n D n = j N =1 λ j n Xj. (13) The equlbrum s solved for the per-unt occupatonal prce p j,o o that satsfes the equlbrum condtons (3), (5)-(13). for each, j, and Equlbrum n proportonal changes For more convenent comparatve statcs, another way to characterze the equlbrum s to solve the model for proportonal changes of equlbrum varables. A proportonal change of any varable x s de- 11

13 noted by ˆx = x /x, where x s a varable x at the counterfactual equlbrum. The so-called exact hat algebra (Costnot and Rodríguez-Clare (2014)) followng Dekle et al. (2008) reduces the number of parameters that need to be determned and thus reduces data requrement for quantfcaton. I ntroduce two exogenous shocks n the counterfactual analyss: changes n blateral trade costs ( d ˆj n ) and changes n labor productvty. For the second shock, I frst decompose the parameter T j,o,τ by defnng Tj,o,τ Tj,o τ T j To, where Tj,o τ descrbes the ft of type τ workers to ndustry j and occupaton o, and s not necessarly country-specfc. The remanng components are related to the fundamentals of each country. Snce trade costs are defned at the ndustry level, I only allow T j to be tme-varyng, holdng other components of T j,o,τ fxed over tme.17 Specfcally, I consder ˆT M f g CHN as one of two trade shocks n the counterfactual analyss, gven that changes n Chna s productvty are closely related to ther exportng capablty, especally n the manufacturng ndustry. A counterfactual equlbrum n changes can be easly extended to ncorporate the effect of changes on the other parameters, whch s dscussed n the onlne appendx. All equlbrum condtons (3), (5)-(13) can be re-wrtten n terms of proportonal changes. The counterfactual equlbrum determnes ˆp j,o for each,j, and o that satsfy the followng equlbrum condtons. - Labor supply: - Type-level average wage: ˆπ j,o,τ = ( ˆp j,o ) θ,τ ˆT j j,o (,o ˆpj ) θ,τ ˆT j π j,o,τ (14) ŵ,τ = [ j,o ( ˆp j,o - Unt cost of producton: Assumng ˆµ j,o = 1, ĉ j = [ o ) θ,τ ˆT j πj,o,τ ] θ 1,τ (15) ξ j,o ( ˆp j,o ) 1 γ ] 1/(1 γ) (16) 17 In order to account for changes n productvty, I consder changes n T j nstead of A j. Whle  j has frst-order effects only on the labor demand, ˆT j has frst-order effects for both labor supply and demand n ths model. 12

14 where ξ j,o (µj,o ) γ (p j,o ) 1 γ o (µ j,o ) γ (p j,o ) 1 γ s a cost share of occupaton o n ndustry j. - Occupaton market clearng condton: Assumng ˆL,τ = 1, ( ˆpj,o ĉ j ) 1 γ Ê j = τ w,τ L,τ π j,o,τ ( τ w,τ L,τ π j,o )ŵ,τ ˆπ j,o,τ (17),τ The world total output s kept constant as a normalzaton:,j E j =,j E j = E. I consder the aggregate trade defct D as an exogenous varable whch s fxed as a share of the world GDP, as n Dekle et al. (2008) and n Calendo and Parro (2015). 18 Detaled dervatons for Ê j and other varables are descrbed n the Appendx. 2.5 Model Mechansm The model frst captures the labor demand channel, whch s the tradtonal channel by whch trade shocks affect factor prces. A dfferental response s generated frst across ndustres wth ndustry-specfc trade elastctes ν j. Together wth the dfferental pattern of the ntal labor allocaton, ths ndustry-specfc trade elastcty s the key parameter that captures dfferental mpact of trade across workers. 19 The elastcty of substtuton γ between occupatons n producton also carres weght n the labor demand channel, snce demands for dfferent occupatons are nterrelated. Despte the same ndustry-level trade shock, demands for dfferent occupatons may respond dfferentally. Ths channel engenders dfferent gans from trade dependng on workers ntal occupaton afflaton. The second channel s the labor supply channel through whch trade mpacts the labor supply decsons of heterogeneous workers. Ths channel has not been wdely studed n the lterature. If workers of the same type are all homogeneous, p j,o entrely decdes the labor allocaton whch should be same for all workers wth 18 Smlarly to the equlbrum condtons n levels, two market clearng condtons mply the trade balance condton at the counterfactual equlbrum. j N =1 λ j n X j n D n = j N =1 λ j n X j. 19 Ossa (2015) ponts out that ndustry-specfc trade elastctes magnfy the aggregate welfare effect of trade. I focus on the relatonshp between ndustry-specfc trade elastctes and the dstrbutonal effect of trade. 13

15 the same type. In contrast, ths model s based on workers comparatve advantage whch generates a dfferental pattern of labor reallocaton. The elastcty of ndustry- and occupaton-level labor supply wth respect to p j,o s θ,τ (1 π j,o,τ ). The parameter θ,τ governs the responsveness of type τ workers to changes n p j,o. The self-selecton of workers and compostonal shft wthn worker types thus affect the dstrbuton of gans from trade. Ths model nests exstng models by consderng dfferent values of θ,τ. In the extreme case when θ,τ and T j,o,τ = 1 for all (, τ, j, o), workers are homogeneous n ther productvtes wthn a type. If there s only one occupaton, then ths case collapses to the mult-ndustry EK model. If t s assumed that θ,τ ; T j,o,τ = 1 for all (, τ, j, o); µj,o = µ j,o for all ; and z (e j ) = z for all and e j, then ths model s equvalent to the mult-ndustry Heckscher-Ohln model wth CES producton. In both mult-ndustry EK and mult-ndustry Heckscher-Ohln cases, the labor demand sde s a domnatng factor determnng ndustry-level labor reallocaton. Another extreme case s where θ,τ s equal to 1, and workers are extremely heterogeneous n ther productvtes. Ths case corresponds to the ntuton of the specfc factors model. Instead of assgnng a specfc value for the parameter θ,τ ex ante, I estmate ths parameter n the next secton n order to take the model most closely to the data. 2.6 Aggregate and Type-level Welfare Effect The model delvers both aggregate gans and type-level gans from trade. Gven the same homothetc preference for workers, the proportonal change n country s welfare s Ŵ = Î /[ j 1 λ j (ĉj ( ˆλ j ) 1 ν j ) 1 η 1 1 η ] 1, (18) where ˆλ j s the change n domestc absorpton, and Î s the change n total spendng, as derved n the Appendx. Once the model s solved for the counterfactual equlbrum ˆp j,o, welfare changes are calculated accordngly. Ths formula for welfare changes nests prevous works wth several smplfyng restrctons to my model. If trade s balanced n all countres (D = D = 0 for all ), and there s only one ndustry (J = 1), a sngle type of labor (T = 1) wth a perfectly nelastc supply, and one occupaton, then equaton (18) exactly matches the wel- 14

16 fare formula derved by Arkolaks et al. (2012) (ACR, hereafter): Ŵ = ˆλ 1 ν for the EK model wth a trade elastcty ν. If we consder a mult-ndustry EK model wth ACR restrctons as well as the Cobb-Douglas structure across ndustres, but wthout the endogenous labor allocaton, equaton (18) collapses to Ŵ = j ( ˆλ j λj ) ν j, where λ j s a Cobb-Douglas share of ndustry j. As the man focus of my paper, I now derve the welfare effect for each worker type to dscuss the dstrbuton of trade-nduced welfare changes across worker types. Assumng that each worker type shares the aggregate trade defct based on the rato of ther total labor ncome, the change n type-level welfare s Ŵ,τ = Î,τ /[ j 1 λ j (ĉj ( ˆλ j ) 1 ν j ) 1 η 1 1 η ] 1, (19) where Î,τ s the counterfactual change of type-level spendng I,τ = w,τ L,τ + D,τ, and D,τ s type τ s share of the aggregate trade defct. 20 The change n aggregate welfare (18) s then a smple weghted average of the change n typelevel welfare (19), where the weght s type-level ncome share n the base year. Changes n between-type-nequalty are dscussed by comparng ths type-level welfare change across worker types n counterfactual analyses. 2.7 Changes n Real Wages and Employment Shfts I frst defne the skll premum by the wage premum of college graduates over non-college graduates, where ts proportonal change depends on equaton (15). Ths measure, as well as changes n type-level welfare (19), captures the modelpredcted changes n between-type nequalty. The model also derves wthn-type varance of wage as n equaton (6). If the shape parameter θ,τ of workers productvty does not change over tme, the proportonal change n the wthn-type varance of wage s gven by var ˆ,τ (w) = (ŵ,τ ) 2. Proportonal changes n wthn-type varance wll be quantfed for each worker type and country n the counterfactual exercse to show the effects of trade on both between- and wthn-type nequalty. Ths paper also shows the endogenous pattern of workers sortng nto ndustry 20 Galle et al. (2015) derve a smlar formula for changes n type-level welfare. If I assume that there s only one occupaton and that the preference follows a Cobb-Douglas, equaton (19) matches ther formula. 15

17 and occupaton. Based on the model-predcted ˆπ j,o,τ and the data on πj,o,τ, I calculate π j,o,τ π j,o,τ πj,o,τ to capture the employment shfts wthn a type, snce πj,o,τ s defned as a share whch s summed to 1 for each type. The employment shfts can be further aggregated up to the ndustry or the occupaton level wth the data on L,τ n order to quantfy the patterns of labor reallocaton nduced by trade across ndustres and occupatons, respectvely. In addton, ths model also predcts changes n ndustry- and occupaton-level average real wages after takng compostonal shfts nto account. Those changes are defned by ŵ j / ˆP and ŵ o / ˆP, respectvely, where ŵ j = [ τ,o ŵ o = [ τ,j w,τ L,τ π j,o,τ ( τ,o w,τ L )ŵ,τ ˆπ j,o,τ ]/[ L,τ π j,o,τ ( ) ˆπ j,o,τ πj,o,τ τ,o τ,o L,τ ] (20),τ πj,o,τ w,τ L,τ π j,o,τ ( τ,j w,τ L )ŵ,o,τ ˆπ j,o,τ ]/[ L,τ π j,o,τ ( ) ˆπ j,o,τ πj,τ τ,j τ,j L,o,τ ]. (21),τ πj,τ These results are structural counterparts to the trade-nduced change n the ndustry and the occupaton wage prema studed n many reduced-form analyses. 3 Quanttatve Analyss In ths secton, I dscuss the data, the estmaton of parameters, the calbraton of changes n blateral trade costs, and the algorthm to solve the model. I quantfy the dstrbutonal effects of changes n the trade envronment between 2000 and 2007, wth 2000 as the base year. From an nternatonal trade perspectve, ths tme perod s nterestng, especally because Chna joned the WTO n Data I consder N = 33 countres whch consst of 32 countres and a constructed rest of the world. These 32 countres account for 76.19% of the world total trade volumes n I also consder T = 5 worker types, J = 4 ndustres, and O = 5 occupatons. Worker types are defned by educatonal attanment: hgh school dropouts (HD), hgh school graduates (HG), workers wth some college educaton (SC), col- 16

18 lege graduates (CG), and workers wth advanced degrees (AD). 21 I assume that there are 4 ndustres: agrculture (AGR), mnng (MIN), manufacturng (MFG), and servce (SVC). Table 1 gves the occupaton categores defned by aggregatng the occupaton classfcaton by Dorn (2009) and the Internatonal Standard Classfcaton of Occupatons (ISCO) classfcaton. The fve categores are based both on the level of requred sklls and on the routneness of the occupatonal task, as used n Autor and Dorn (2013). 22 More detals are descrbed n the Appendx. Table 1: Lst of Occupaton Categores 1. Low skll Occupatons (LSO) 2. Assemblers and Machne Operators (AMO) 3. Precson Producton and Crafts Occupatons (PPC) 4. Admnstratve, Clercal, and Sales Occupatons (ACS) 5. Managers, Professonals, and Techncans (MPT) The Integrated Publc Use Mcrodata Seres (IPUMS) Internatonal database provdes labor market nformaton from household survey for the 22 countres n the sample for As descrbed n Fgure A1, the household-level survey data show that patterns of labor allocaton vary sgnfcantly by worker type and country. Whle much exstng work n the lterature focuses only on ndustry-level labor reallocaton due to trade, the data show that t s also mportant to consder occupatons to explan the full scope of the dstrbutonal effect of trade. In fact the ndustry-level pattern of labor allocaton does not vary much by worker type. By contrast, dfferent worker types show very dfferent patterns of occupaton-level labor allocaton, whch suggests that workers sklls have hgher complementarty wth occupaton-specfc tasks than wth ndustry-specfc tasks. I obtan blateral trade flows for agrculture, mnng, and manufacturng n- 21 The defnton of educatonal attanment vares by household survey n dfferent countres. As summarzed n the Appendx, I make the defnton consstent wthn each country. 22 In hs most aggregate categorzaton, Dorn (2009) dstngushes between transportaton, constructon, and agrcultural occupatons and low-skll servce occupatons for the U.S. However, the ISCO codes nclude agrcultural laborers n low-skll (elementary) occupatons. I thus aggregate all agrcultural occupatons and low-skll servce occupatons nto low-skll occupatons. 23 For the remanng countres, I proxy ther labor market allocaton wth the lagged data or the data from other countres wth a smlar ncome level and adjust them wth the data from ILOSTAT and LABORSTA. I also use the Barro and Lee (2013) dataset to supplement the nformaton on the labor supply wth workers educatonal type. Detaled strategy s summarzed n the Appendx. 17

19 dustres from the UN Commodty Trade (COMTRADE) database. In addton, the Trade n Servces Database of the World Bank provdes blateral trade flows n the servce ndustry. Aggregate varables are obtaned from varous sources: UN Statstcal Dvson (UNSD) natonal accounts, OECD STructural ANalyss (STAN), World Input-Output Database (WIOD), KLEMS, ILOSTAT and LABORSTA from the Internatonal Labor Organzaton (ILO), and the Occupatonal Wage around the World (OWW.) 24 Detaled descrptons can be found n the Appendx. 3.2 Parameters The model parameters are ether estmated, calbrated to the base year, or based on prevous work. The key parameter, the labor supply elastcty θ,τ, s estmated usng data from base year The occupaton ntensty parameter µ j,o s calbrated to match the share of occupaton wthn each ndustry n the base year. Estmaton of labor supply elastcty θ,τ For notatonal smplcty, I denote T j,o,τ Tj,o,τ (pj,o ) θ,τ for the estmaton of parameters. The Fréchet scale parameter j,o T j,o,τ and the shape parameter θ,τ of the dstrbuton of the equlbrum wage n (4) are jontly estmated usng the maxmum lkelhood (ML) method. 25 Denotng ndvdual worker ω s equlbrum wage by w ω condtonal on the choce of (j, o), then the log-lkelhood functon for worker type τ n country s: ln L(θ,τ, T j,o,τ w 1,... w L ) = L(ln θ,τ + ln( T j,o,τ )) (θ,τ + 1) j,o j,o L ω=1 where L s the number of workers n the sample out of the total L,τ workers wth type τ n country. The baselne estmaton s done for countres wth avalable ndvdual wage profles for the base year: Brazl, Inda, Mexco, and the U.S. Table A1 summarzes the estmaton result. The ML estmates of θ,τ vary from 1.48 to 1.97 for the U.S., and better-educated workers have smaller estmates. 26 The 24 The basc methodology used to obtan the nput-output table n the WIOD s summarzed by Tmmer (2012). The OWW database are made publcly avalable by Oostendorp (2012). 25 Ths method assumes that there s no correlaton between dosyncratc productvty draws. Wth correlaton allowed, a further normalzaton s requred to dentfy the scale parameter. 26 Usng GMM, I get larger estmates of θ,τ wth an average of approxmately 2.5 for the U.S. Compared to recent works by Lagakos and Waugh (2013), Hseh et al. (2013), and Bursten et al. (2015), I get smlar or slghtly lower estmates. Ths s related to the defnton of worker types and 18 L ln w ω ( T j,o,τ ) w θ,τ ω, j,o ω=1

20 result mples that better-educated workers are more dspersed n ther productvtes and wages wthn the type, whch s consstent wth the evdence n wage data. The result also shows that less sklled workers have a larger labor supply elastcty generatng dfferental mpacts of trade across worker types. In addton, the estmated θ,τ s larger n the U.S. on average. Ths result supports the exstng research pontng out a lack of labor reallocaton n developng countres after trade lberalzaton: e.g., Goldberg and Pavcnk (2003; 2005) and Topalova (2007). The baselne counterfactual result n the next secton s derved wth the actual estmates of θ,τ for the U.S., Brazl, Inda, and Mexco. For the other OECD (non-oecd) countres, the average of the estmates for the U.S. and Mexco (Brazl and Inda) s used, respectvely. 27 As shown n Fgure A2, the predcted wage dstrbuton fts the dstrbuton of the actual wage data very well. Assgned parameters Type-level labor supply L,τ and occupaton ntensty µ j,o are obtaned from the 2000 data. The trade elastcty ν j s taken from the estmates n Calendo and Parro (2015) for the agrculture, mnng, and manufacturng ndustres (9.59, 14.83, and 5.5, respectvely.) 28 I use Eaton and Kortum (2002) s man estmate, 8.28, for the servce ndustry. The elastcty of substtuton across occupatons n producton γ s set to 0.90 from Goos et al. (2014), whch allows complementarty between occupatons. The elastcty of substtuton η 1 across ndustres n preference s set to 0.75 followng Comn et al. (2015). 29 Results wth dfferent values of ν j, γ and η 1 are dscussed n the robustness secton. 3.3 Measurng Trade Shocks I examne the effect of two exogenous shocks: changes n blateral trade costs ( ˆ d j n ) and changes n the manufacturng labor productvty n Chna ( ˆT M f g CHN ) between 2000 and Frst, I calbrate changes n blateral trade costs to match changes the ndependence assumpton across productvty draws. 27 For the other countres where the wage data are avalable n dfferent years from the base year, I estmate ths parameter for avalable years, and the man counterfactual result s very robust. 28 Calendo and Parro (2015) estmate the sector-level trade elastctes for 20 sectors ncludng agrculture, mnng, and 18 2-dgt Internatonal Standard Industral Classfcaton (ISIC) manufacturng sectors. I take an average of ther estmates across 18 manufacturng ndustres. 29 Ths value s the estmate when consderng three ndustres (agrculture, manufacturng, and servces) and trade controls n Comn et al. (2015). Buera et al. (2015) and Cravno and Sotelo (2016) consder a much lower elastcty of 0.2 between the two aggregate sectors of goods and servces. 19

21 n blateral trade flows n the data. Two standard assumptons are requred for dentfcaton: 1) symmetry,.e., d j n = dj n for all and n, and 2) no domestc trade cost,.e., d j = 1 for all and j. Wth these two dentfyng assumptons, I follow the Head and Res (2001) approach to back out changes n trade costs from blateral trade flow data see also Parro (2013). The gravty equaton from the model results n the followng relatonshp between trade flows and trade costs: ˆλ j n ˆλ j ˆλ j n ˆλ j nn = ( ˆ d j n ) 2νj. (22) The change n trade costs d ˆj n s calbrated to exactly match equaton (22) gven νj from Calendo and Parro (2015) and Eaton and Kortum (2002). Table A2 and Fgure A3 llustrate the results, showng blateral trade costs decreasng mostly n the manufacturng ndustry between 2000 and 2007 (by 3.86% on average). 30 Changes n trade costs depend on a partner country. For nstance, trade costs wth Chna have decreased by 22% on average, whch s a substantally larger declne than a declne of 1.81% for all country pars. In addton, trade costs have fallen more wth low-ncome trade partners. For example, manufacturng trade costs wth OECD partners have declned by 2.75% on average, whle they have fallen by 7.20% wth non-oecd or Latn Amercan partners. Ths based trade lberalzaton pattern between 2000 and 2007 s expected to have nduced a major structural change n all countres engaged n nternatonal trade. I then use the result n Hseh and Ossa (2016) for changes n the manufacturng labor productvty n Chna. The baselne shock I use for counterfactual smulaton s an 11.2% ncrease of T M f g CHN durng the tme perod of nterest, whch s the medan result of Hseh and Ossa (2016). Other components of T j,o,τ are tme-nvarant. 3.4 Solvng for the World Equlbrum Wth the model n proportonal changes, I only need to obtan the data on E j, λj, λ j n, Dj j,o, and ξ for the base year To take the model to the data, E j s frst 30 The result shows that trade costs for servces have ncreased on average. Snce trade n servces n fact has recently ncreased, ths result seems aganst the data. Servces have a dfferent nature whch depends more on source-country specfc components, compared to goods whose physcal blateral trade costs are easy to measure. Thus, the symmetry assumpton that I mpose for dentfcaton may mask the actual changes n trade envronment n the servce ndustry. 20

22 measured by gross output by ndustry and country. Blateral trade flows X j n are then used to calculate the domestc absorpton X j = Ej n = X j n, blateral trade shares λ j n, and trade defcts Dj. After that, I compute the total expendture Xj = n = X j n + Xj to construct the expendture share λj j,o. Lastly, ξ s measured by the share of hourly wage pad to a certan occupaton relatve to the hourly wage pad to all occupatons n ndustry j. The computaton strategy to solve the model for the equlbrum ˆp j,o s based on Calendo and Parro (2015) and the step-wse method of Alvarez and Lucas (2007). I frst guess the ntal ˆp j,o and then solve for the change n the ndustry-level prce ˆP j. After that, I calculate correspondng equlbrum quanttes derved n the model. The counterfactual equlbrum s ˆp j,o whch elmnates excess demands of occupatons for both base and counterfactual years. I repeat these steps wth the updated ntal guess of ˆp j,o detals of the soluton strategy are descrbed n the Appendx. untl the system of equatons (17) s satsfed. The techncal 4 Counterfactuals The man advantage of ths model s to be able to quantfy the nterplay of trade lberalzaton, nequalty, and labor reallocaton for a large number of countres. Another advantage of ths model s the ablty to easly test any specfc counterfactual trade shocks. In ths paper, I consder d ˆj n and ˆT M f g CHN as trade shocks. Parameters outsde these two are assumed to be tme-nvarant. The baselne counterfactual results are derved wth the prevously estmated θ,τ. Then, the mportance of havng a correct specfcaton for the degree of worker heterogenety s argued by comparng results wth dfferent values of θ,τ. Gven ˆp j,o solved at the counterfactual equlbrum, correspondng equlbrum quanttes of nterest are derved: changes n aggregate welfare, type-level welfare, skll premum, wthn-type varance of real wages, ndustry- and occupaton-level real wages, as well as employment shares across ndustres and occupatons. 4.1 Effect of Changes n Blateral Trade Costs Calbrated changes of blateral trade costs between 2000 and 2007 are frst ntroduced holdng other parameters fxed. The calbraton shows the declne of trade 21

23 costs occurrng mostly n agrculture, mnng, and manufacturng ndustres, wth the largest declne n manufacturng. Thus, ths exercse nvestgates the effect of an actual but based trade lberalzaton especally toward manufacturng. Fgure 1 descrbes the counterfactual changes n aggregate welfare of each country aganst ts trade shares n Trade share s defned by the rato of total mports and exports to gross output. Aggregate welfare ncreases n most countres, and countres wth a larger trade share n 2007 gan more on average. Fgure 1: Counterfactual Changes n Aggregate Welfare from Changes n Trade Costs (%) Changes n aggregate welfare (%) USA BRA INDARG ESP GRC JPN FRA TUR ITA GBR AUS NZL ISL MEX IDN PRT POL KOR ISR CAN CHN CHL SWE DEU FIN DNK Trade shares n 2007 (%) ROW AUT CHE NLD HUN IRL Changes n between-type nequalty The model predcts an unequal dstrbuton of welfare gans across worker types, whch s the man focus of ths paper. Between-type nequalty measured by relatve changes n the type-level welfare ncreases n most hgh-ncome countres due to changes n trade costs. Gven that trade costs have declned on average durng the tme perod of nterest, ths result s consstent wth the Stolper-Samuelson predcton. Fgure 2 shows counterfactual changes n the type-level welfare for some hgh- and low-ncome countres n the sample. In some hgh-ncome countres, less-educated workers even lose n absolute terms. In other hgh-ncome countres where all worker types gan from trade lberalzaton n absolute terms, better-educated workers gan sgnfcantly more. On the other hand, the model predcts mxed results for low-ncome countres. In most Latn Amercan countres, between-type nequalty decreases, whch s 22

24 n lne wth the emprcal facts that many Latn Amercan countres have experenced a decrease of nequalty n recent years. However, Table A3 also shows that among workers wth a at least hgh school educaton n those countres, better-educated workers gan more from trade. Ths result can be explaned by occupaton-level specalzaton, whch wll be dscussed n more detal later. Between-type nequalty sgnfcantly ncreases n Chna and Indonesa due to trade lberalzaton, whch s also consstent wth the emprcal evdence. Ths result s manly because of trade-nduced structural change and reallocaton of workers based on ther comparatve advantage, whch wll be further dscussed. Although tradtonal trade theory, such as the Stolper-Samuelson theorem, predcts that trade decreases nequalty n low-ncome countres wth larger endowments of unsklled workers, ths model shows more complcated predctons, whch s n fact n lne wth a lot of the emprcal evdence. Detaled results are summarzed n Table A3. Fgure 2: Changes n Type-level Welfare Resultng from Changes n Trade Costs (%) (a) Hgh-ncome countres (b) Low-ncome countres Changes n welfare (%) Changes n welfare (%) AUS DEU DNK FRA GBR JPN USA ARG BRA CHL CHN IDN IND MEX Hgh school dropouts Some college edu Advanced degrees Hgh school graduates College graduates Hgh school dropouts Some college edu Advanced degrees Hgh school graduates College graduates A trade-nduced change n between-type nequalty s also captured by counterfactual changes n the skll premum. Fgure 3 shows that the skll premum also ncreases n most hgh-ncome countres as well as manufacturng-orented lowncome countres, but decreases n other low-ncome and Latn Amercan countres due to changes n trade costs between 2000 and These results depend crucally on two factors: before-shock labor allocaton 23