Global Value Chains and Inequality with Endogenous Labor Supply

Transcription

1 Global Value Chans and Inequalty wth Endogenous Labor Supply Eunhee Lee Ke-Mu Y November 20, 2017 Abstract We assess the role of global value chans transmttng global ntegraton shocks to aggregate trade as well as dstrbutonal outcomes. We develop a mult-country general equlbrum trade model that features mult-stage producton, wth dfferent stages havng dfferent productvtes and usng factors (occupatons) wth dfferent ntenstes. The model also features a Roy mechansm, n whch heterogeneous workers endogenously choose ther sector and occupaton. Country- and worker-level comparatve advantages nteract. A reducton n trade costs leads to countres specalzng n ther comparatve advantage sectors and producton stages. Ths specalzaton changes labor demand and also leads to more workers shftng to ther comparatve advantage sectors and occupatons. Wth a specal case of our model, we show that the ntensty of the global value chan (GVC) magnfes the aggregate effects of trade lberalzaton, but t has a non-monotonc effect on the skll prema. We calbrate our model to the U.S., Chna, and the rest of the world n 2000 and we smulate a declne n Chna s costs of trade, desgned to mmc Chna s entry nto the WTO. Our smulaton results mply an ncrease n the skll premum n both the U.S. and Chna, and the GVC,.e., stage-level specalzaton, s crtcal to ths outcome. The vews expressed here are those of the authors and are not necessarly reflectve of vews of the Federal Reserve Banks of Dallas, Mnneapols or the Federal Reserve System. We thank Pol Antras, Gordon Hanson, Elhanan Helpman, Chnhu Juhn, Steve Reddng and especally Alonso de Gortar for very helpful dscussons. We also thank partcpants at the Asan Meetngs of the Econometrc Socety, at the Unversty of Vrgna, and at the NBER Trade and Labor Markets Conference for ther comments. Heesuk Jung provded excellent research assstance. All errors are our own. Unversty of Maryland Unversty of Houston, NBER, Federal Reserve Bank of Dallas, and Federal Reserve Bank of Mnneapols 1

2 1 Introducton One of the most sgnfcant economc developments over the past half-century s the ncreased fragmentaton of producton across borders. Goods are produced n sequental stages that traverse multple countres a global value chan. Countres specalze n partcular stages of a good s producton process. Ths ncrease n vertcal specalzaton has occurred under a backdrop of a broad ncrease n nternatonal trade, one of the defnng features of globalzaton across the world durng ths perod. Partly because of ths backdrop, most of the research examnng the effects of global ntegraton on wages, employment, and other varables has focused on total trade. Autor et al. (2013) s a recent example. Ths has also been exemplfed n the factor content studes that trade and labor economsts have conducted snce the 1990s. The purpose of our paper s to assess the role of global value chans as a propagaton mechansm transmttng global ntegraton shocks, such as Chna jonng the WTO, to aggregate trade outcomes, as well as dstrbutonal outcomes, such as the skll prema. Our approach s to buld a model of global value chans and nternatonal trade and then to calbrate t and use t to study global ntegraton shocks. We ntroduce global value chans followng the work of Antràs and de Gortar (2017) and de Gortar (2017). They develop a tractable framework for ncorporatng mult-stage producton n an nternatonal trade model that generalzes and extends prevous research on ths subject. In addton, a key feature of our model s to nclude for multple sectors, multple factors, and a labor supply channel. In partcular, followng Lee (2017), we nclude Roy selecton effects, n whch heterogeneous workers choose occupatons and sectors based on ther ndvdual productvtes n these occupatons and sectors, as well as on prevalng prces. Lee (2017) and others have shown that these channels enhance our understandng of how trade affects nequalty and are quanttatvely mportant n explanng the ncrease n nequalty. The core elements of our model revolve around the producton of a fnal good and the worker s choce of sector and occupaton. A fnal good s made n a sequence of stages. Each stage nvolves labor, a composte ntermedate, and output from the prevous stage. There are several labor nputs, whch we call occupatons. Dfferent stages use these occupatons wth dfferent ntenstes. The presence of the composte ntermedate and the prevous stage s output helps generate both roundabout and snake features n producton. The fnal goods have two uses, consumpton and nput nto the composte ntermedate. On the worker s sde, each worker s of an exogenous type. Wthn each type, a worker draws occupaton and sector specfc productvtes. Based on these productvtes, as well as on prevalng prces, workers choose ther optmal sector and occupaton. Our ndvdual goods and workers are embedded 2

3 n a mult-country general equlbrum framework. Ths framework features both countryand worker-level comparatve advantages. For our analyss, we frst ntroduce a general verson of the model and then study a smplfed verson of the model n order to develop ntuton. We study a 2 5 verson of the model n terms of countres, worker types, sectors, stages, and occupatons. We examne the response of GVCs, skll prema, and other varables to lower trade costs. The lower trade costs are medated through several demand and supply forces before ultmately affectng GVCs and skll prema. The lower trade costs facltate specalzaton at the sector-level and at the producton stage-level. In addton, ths changng specalzaton pattern shfts the relatve demand for occupatons based on stage-specfc occupaton ntenstes. Ths affects the equlbrum wage, whch then affects workers choces of occupatons and sectors. Ultmately, the skll prema are affected. The 2-stage verson of our model llustrates the role of GVC ntensty on the skll premum. A hgher GVC ntensty mples a greater relance on the stage-one output used n stage-two producton. Numercal exercses show that, n response to a declne n trade costs, aggregate outcomes are magnfed f the GVC ntensty s hgher, but the skll premum responds non-monotoncally to hgher GVC ntensty. The largest effect occurs wth ntermedate GVC ntenstes. Extreme GVC ntenstes shut down stage-level specalzaton, whch s an mportant margn through whch trade shocks change the skll premum. In addton, condtonal on the stage-level comparatve advantage channel, dfferences n the GVC ntensty across sectors put dfferent weghts on the shft of labor demand across sectors and occupatons. We then calbrate the general verson of our model for three countres, Chna, U.S.A, and constructed rest of the world; fve worker types; four sectors; two stages; and fve occupatons. Some of our parameters draw drectly from the data, others are assgned, and the others ncludng the worker productvty parameters, and the producton functon parameters (productvtes of sector and stage, occupatonal ntensty coeffcents, value-added share, and GVC ntensty parameters) are calbrated to match moments n the data. Our calbrated parameters reveal several patterns. Frst, based on relatve endowments and productvtes, Chna has a comparatve advantage n the manufacturng sector and the downstream producton stage, and the U.S. has a comparatve advantage n servces and the upstream producton stage. Second, producton stages have dfferent occupaton ntenstes across countres. For example, the downstream producton stage s relatvely hgh-sklled-occupaton-ntensve n Chna, but low-sklled-occupaton-ntensve n the U.S.. Thrd, sectors sgnfcantly dffer n GVC ntensty. Upstream producton stages have relatvely larger value-added n the agrculture and manufacturng sectors than n the servce sector. Lastly, workers wth dfferent 3

4 levels of skll have a clear comparatve advantage both across sectors and occupatons. We use our calbrated model to perform counterfactual exercses quantfyng aggregate and dstrbutonal mpacts of the Chna shock. We study a 50 percent declne n Chna s trade costs wth ts tradng partners. When trade costs wth Chna go down, all countres specalze further n ther comparatve advantage stages and sectors. The degree of stagelevel specalzaton s larger n sectors wth a hgher GVC ntensty, e.g., manufacturng. The greater the GVC ntensty, the larger the magnfcaton of aggregate effects such as trade. Ths s consstent wth prevous research. In addton, we fnd that the skll premum rses n all three countres. In the U.S. and Chna, the lower trade costs nduce specalzaton to shft towards sectors and stages that use hgh-sklled-occupatons more ntensvely. As ndcated above, for Chna that nvolves manufacturng and the downstream stage, and for the U.S., that nvolves the servce sector and the upstream stage. In addton, the worker-level productvty estmates mply that better educated workers are better off n the hgh-sklled occupatons. Hence, our rch framework s able to reproduce the stylzed fact that trade lberalzatons are often assocated wth skll prema ncreases n both skll-abundant and non-skll-abundant countres. We show that n the absence of GVCs, ths result would not occur. On the other hand, our counterfactual shows that the ncrease n skll prema s lmted n magntude, around 1% or less. Ths s because, accordng to our calbrated parameters, each country specalzes n sectors and stages that do not have a large share of value-added n the entre producton chan. Hence, whle there are large changes n specalzaton owng to the lower trade costs, these large changes do not translate nto large skll prema effects. 1.1 Related Lterature Our research s connected to several strands of research. One strand s the trade and wages research that sought to examne the effects of ncreased U.S. mports from developng countres on the skll prema. Ths research was especally actve n the md-1990s, and ncludes Katz and Murphy (1992), Lawrence and Slaughter (1993), Krugman (1995), and Feenstra and Hanson (1999) among others. All of these papers essentally employed a Heckscher-Ohln type (HO) framework wth ts Stolper-Samuelson and factor content of trade mplcatons. The man fndngs tended to be that the effect of trade was not large. However, the survey artcle by Goldberg and Pavcnk (2007) showed that the predctons of a smple Heckscher- Ohln (HO) framework do not hold up n the data. In partcular, skll prema tended to rse n both developed and developng countres followng trade lberalzatons. Krugman (2008) revsts the trade and wage ssues from the md-1990s wth the beneft of 15 years 4

5 of addtonal data. In addton, Krugman argues that ncreased vertcal specalzaton can generate nequalty va Stolper-Samuelson effects. To our knowledge, Krugman s paper s the only paper that makes a case for examnng the consequences of vertcal specalzaton for nequalty. In recent years, there has been a new wave of nterest on the employment and wage effects of ncreased trade. Ths s not surprsng, because the emergence of Chna as a sgnfcant global economc force has only come about n the past years. Autor et al. (2013), Perce and Schott (2016), and many other papers n the lterature document sgnfcant effects of Chna on labor markets of major partner countres such as the U.S. Wth the new nterest has come an expanded set of methodologes. One new approach nvolves applyng models wth numbers,.e., quanttatve theory. Bursten and Vogel (2016) combne an HO framework n a model that features heterogeneous frms and skll-based productvty. Our framework s n ths ven. Our paper s also related to a lterature about offshorng and skll upgradng. Feenstra and Hanson (1995), Costnot and Vogel (2010), and Zhu and Trefler (2005) dscuss how offshorng may ncrease the skll premum n both North and South by makng both countres specalze n hgh-skll-ntensve sectors. These papers do not explctly model a vertcal producton structure. Our model looks at ths argument through the lens of GVCs, because offshorng nvolves vertcal specalzaton across producton stages by nature. A second strand of research s on documentng the extent of global value chans, vertcal specalzaton, value-added exports, and related concepts, as well as on buldng models of these concepts. Contrbutons on the documentaton sde nclude Hummels et al. (2001), Johnson and Noguera (2012); Antràs and Chor (2013), and Koopman et al. (2014). Contrbutons on the modelng sde nclude Y (2003, 2010), Johnson and Moxnes (2016), and most recently, Antràs and de Gortar (2017) and de Gortar (2017). The latter two papers develop a general framework for GVCs and show how to map specal cases of ths framework nto the Eaton and Kortum (2002) framework. Our modelng of GVCs draws from Antràs and de Gortar (2017); t combnes that paper wth Lee (2017). To nvestgate the lnk between trade and labor market outcomes, such as wage nequalty and labor reallocaton, ncreasngly, papers focus on heterogeneous workers. Whle tradtonal trade models such as the HO model and the specfc factors model assume that workers are all homogeneous n ther productvtes condtonal on observable characterstcs, ths assumpton msses the fact that workers dffer n ther productvtes n realty. Ths worker-level heterogenety s mportant especally when we study the effect of trade on labor market outcomes, because workers wth same observable characterstcs may respond to trade shocks dfferently dependng on ther dosyncratc productvtes. In recent years, 5

6 trade models brng the dea of the Roy (1951) model to ntroduce worker heterogenety under the settng of assgnment models: e.g., Teulngs (2005), Ohnsorge and Trefler (2007), and Costnot and Vogel (2010, 2015). Worker heterogenety s ntroduced to trade models also based on a search and matchng framework: e.g., Grossman et al. (2015), Helpman and Itskhok (2010), and Helpman et al. (2016). Our paper s also closely related to a recent strand of lterature on quanttatve models wth the Roy-based assgnment structure. One of the key assumptons n ths lterature s that workers dosyncratc productvty s randomly drawn from a type-ii extreme value dstrbuton, a Fréchet dstrbuton. Hseh et al. (2013), Bursten et al. (2015), Lagakos and Waugh (2013), Galle et al. (2017), and Lee (2017) use ths assumpton to nvestgate the role of worker heterogenety n dsentanglng labor market outcomes n one country from labor demand shocks such as technologcal change or trade lberalzaton. Our paper also reles on ths dstrbutonal assumpton when we characterze workers heterogeneous productvtes. We ntroduce ths Roy-based assgnment framework nto a mult-stage GVC model, where each stage of producton s formulated based on the EK model. We can thus nvestgate the general equlbrum relaton between workers endogenous labor supply and trade through GVC n our model. To numercally solve our mult-country GVC model for a general equlbrum, we base our work on the teratve algorthm provded by Alvarez and Lucas (2007). More papers n the lterature recently focus on the occupatonal dmenson as an mportant channel through whch trade shocks are dssemnated across workers--e.g., Autor et al. (2015), Ebensten et al. (2014), Traberman (2016), Harrgan et al. (2016). Our framework also allows workers to endogenously choose occupatons n response to trade shocks under the GVC settng. We show that worker heterogenety plays also a sgnfcant role for occupaton-level labor reallocaton. The occupatonal dmenson s mportant n the GVC context, because dfferent producton stages have dfferent occupaton ntenstes. The core mechansm of our model can be further connected to the lterature on trade, nequalty, and a declnng labor share around the world. A recent paper by Dao et al. (2017) provdes suggestve evdence about the effect of ncreased partcpaton n GVCs on declnng labor shares n both developed and developng countres. Countres specalze n ther captalntensve and hgh-sklled-task-ntensve stages as they partcpate n GVCs more. Although we do not explctly consder captal n our model, the stage-wse specalzaton pattern and stage-specfc occupaton ntenstes that we quantfy n ths paper can be lnked to explan declnng labor shares wth captal-skll complementarty as n Grossman et al. (2017). The next secton lays out our baselne model. Ths s followed by a descrpton of a smpler verson of our model wth just two stages of producton, two countres, two occupatons, and 6

7 two labor types. We solve the smpler verson of the model and conduct several numercal exercses to llustrate how the model works. Secton 4 descrbes our calbraton, and secton 5 dscusses our counterfactual exercses wth the model. 2 Model In ths secton, we descrbe our model. Because the model has many features, we provde an overvew frst. Our model draws from the general global value chan (GVC, hereafter) model developed by Antràs and de Gortar (2017). We extend ther framework by addng three features: multple factors of producton, multple sectors, and heterogeneous workers. All three features are essental to nvestgate the role of GVCs n the effect of ncreased trade on nequalty. In our model, each sector s comprsed of a contnuum of fnal goods. Each fnal good s produced through a specfc global value chan encompassng multple stages of producton that can potentally cross multple countres. Each stage of producton s produced wth value-added and wth ntermedate nputs. Value-added conssts of multple factors of producton, called occupatons. There are two categores of ntermedate nputs. One category s a composte aggregate good. The second category of ntermedates s good and stage-specfc: the prevous stage s output. The ncluson of the prevous stage s output s the key GVC component. Countres have comparatve advantages both across sectors and stages. To dstngush these two types of comparatve advantages, we assume that the prmary source of each comparatve advantage s dfferent. Sector-wse comparatve advantage s prmarly from the Rcardan channel based on dfference n Rcardan productvtes as n Eaton and Kortum (2002). On the other hand, stage-wse comparatve advantage arses manly from the standard Heckscher-Ohln (HO) channel, as we assume that dfferent stages of producton have dfferent factor ntenstes and that countres have dfferent factor endowments. In addton, workers are heterogeneous n ther sector and occupaton-specfc productvtes. Workers endogenously choose ther occupaton and sector based on ther productvtes: the Roy channel. Introducng the Roy framework nto a general equlbrum trade model s based on Lee (2017). Our model wll delver nteracton between the Rcardan and HO channels, the Roy channel, and GVCs. 7

8 2.1 Preferences, Technologes, and Workers Our model features N countres, S sectors, value chans of fxed length J, O occupatons, and T worker types. Each country s dstngushed by ts producton technologes and endowment of worker types. Wthn each sector s, s = 1,..., S, there s a contnuum of fnal goods over a set Ω s of mass 1. Each fnal good ω [0, 1] s produced followng a specfc value chan of length J. The optmal value chan for a fnal good ω consumed n country n s a J-dmensonal vector of countres where each stage j of producton takes place. In other words, ntermedate stages of a product can cross multple borders along the value chan. For each stage, the producton factors are occupatons (managers, clercal staff, etc.) o, o = 1,..., O. Occupaton ntenstes vary across stages of producton and countres. As mentoned above, the producton technology also conssts of two categores of ntermedates, an aggregate composte ntermedate, and a good and stage-specfc ntermedate. Each country, = 1,..., N, s exogenously endowed wth L,t workers of type t, t = 1,..., T. In our quanttatve analyss, these types wll be assocated wth observable worker characterstcs, such as educaton. Each worker of each type draws" a sector and occupaton specfc productvty, and on the bass of that productvty and prevalng occupaton-sectorspecfc wages, chooses to work n the occupaton and sector that delvers the hghest return. Preferences Consumers have common nested CES preference over fnal goods U = S (C s ) bs, s=1 where C s ( (C s,f (ω)) (σ 1)/σ dω) σ/(σ 1). Ω s C s,f (ω) s consumpton of a fnal good ω of sector s n country. The expendture share of each sector s gven by b s wth s bs = 1. σ > 0 s the elastcty of substtuton between goods wthn the sector. Producton Technology As outlned above, each fnal good ω s produced from a specfc value chan of length J durng producton, and ths value chan s potentally spread over multple countres. l(ω) = (l 1 (ω),..., l J (ω)). We denote the sequence of producng countres for a product ω by At each stage j of the value chan for a product ω, frms use domestc labor, the stage j 1 good for ω, and a composte ntermedate. The use of the mmedately precedng stage captures the snake" structure of producton (as n Y (2003)) and s the key feature of the value chan. Countres possess technologes for any ntermedate stage of producton from j = 1 to 8

9 j = J 1, and also for fnal assembly of stage J, for all goods n all sectors. The producton functon n country for stage j of good ω n sector s s Cobb-Douglas: f s,j (x s,j = z s,j, L s,j,1 (ω),..., L s,j,o (ω)((x s,j ) 1 αs o (L s,j,o (ω), m s,j 1 (ω)) (ω)) βj,o α s ) γ s,j (m s,j 1 (ω)) 1 γs,j. Focusng frst on the ntermedate nputs nto producton, x s,j s the composte ntermedate good used by stage j producers of sector s n country. It s a nested CES aggregate of the fnal goods, and has the same structure as the utlty functon. Ths captures the roundabout structure of producton, as n Calendo and Parro (2015) and Eaton and Kortum (2002). Our roundabout structure s smpler than that of Calendo and Parro (2015) and also de Gortar (2017) n that the nput-output share between sectors s completely determned by the expendture share and the sector-specfc value-added share. The other papers consder a more general nput-output structure between sectors focusng on aggregate outcomes of the model. Value-added nputs nto producton are occupatonal tasks L s,j,o (ω) from each of O occupatons. Fnally, the snake structure of our model s descrbed by m s,j 1 (ω), the stage j 1 good for ω of sector s. We assume a constant elastcty of substtuton for all nputs to focus on the role of GVCs n generatng dfferental gans from trade between worker types. An alternatve approach would be to model the complementarty between ntermedate nputs and dfferent skll levels of occupatons. Krusell et al. (2000) and Parro (2013) have shown that ths captal-skll complementarty s mportant n explanng macroeconomc and nternatonal trade behavor. The three key parameters governng the mportance of each of these nputs are β j,o γ s,j, and α s. All three parameters range from 0 to 1. β j,o captures the mportance of each occupatonal nput o. Ths parameter vares across occupatons, stages, and countres. For each stage j and country, o βj,o = 1. 1 γ s,j captures the mportance of the j 1 stage nput n stage j. Ths parameter vares across stages and sectors. A lower value of γ s,j corresponds to a greater mportance of the snake structure, and a lower mportance of the composte ntermedate and value-added taken together. 1 More formally, as γ j 0, the snake or value chan term domnates the roundabout and value-added terms, and vce versa for γ j 1. α s captures the relatve mportance of value-added and the composte ntermedate wth hgher values of α s correspondng to greater mportance of value-added. Ths parameter vares across sectors and countres. We wll call ths parameter as value- 1 Note that these two terms consttute the typcal" Eaton and Kortum (EK) strucure of producton; hence, γ s,j can also be thought of as capturng the mportance of the EK structure., 9

10 added share. Fnally, we assume that the ntal stage 1 s produced usng only occupatons and composte ntermedates; n other words, we assume γ s,1 1 for every s = 1,..., S. To summarze, for each stage of producton, the mportance of the prevous stage,.e., of the value chan, s captured by 1 γ s,j, the mportance of the composte ntermedate,.e., the roundabout term, s captured by (1 α s )γ s,j, and the mportance of the occupatons, taken together,.e., value-added, s captured by α s γ s,j. Factor-neutral productvty for stage j of sector-s product ω n country s denoted by z s,j (ω). We assume the productvty follows a Fréchet dstrbuton from Eaton and Kortum (hereafter, EK, 2002). Productvty z s,j (ω) s randomly drawn from F s,j (z) = exp( A s z ν γs,j ), where γ s,j N j =j+1 (1 γs,j ) [0, 1]. We further assume that productvty draws are ndependent across sectors and stages. A s governs the scale of productvty for sector s n country. We assume that ths scale parameter does not vary by stage. ν γ s,j captures the dsperson of stage j productvtes. ν s the standard Fréchet shape parameter, and governs the common varance of stage j productvty. The effectve varance of stage j s stage-specfc and s based on γ s,j. The stage-specfc shape parameter ν γ s,j has two advantages. Frst, as argued n Antràs and de Gortar (2017), ths probablty dstrbuton makes a sequental sourcng decson equvalent to the case where a lead frm chooses the entre sourcng path from the begnnng. Ths feature provdes great analytc tractablty, whch we wll dscuss n more detal n the next subsecton. Second, we can convenently characterze the magnfcaton effect of GVC as dscussed n Y (2003). At the equlbrum, the effectve trade elastcty ν γ s,j larger n downstream producton stages, as γ s,j s monotoncally ncreasng n j for every s. The magnfcaton effect of GVC s thus actve through γ s,j and potentally dfferent across sectors. (In addton, j γs,j γ s,j = 1 for every s by the defnton of γ s,j, and we assume γ s,j 1 for every s.) Our rch structure provdes Rcardan and HO motves for trade. The Rcardan channel s captured by z s,j (ω), and s present across stages and sectors. The HO channel operates through β j,o. Dfferent stages use occupatons wth dfferent ntenstes. For example, a desgn stage would use more desgners or engneers, whle an assembly stage would employ relatvely more producton workers. Note that the value-added by a partcular occupaton depends on the stage, not on the sector. However, the effectve occupaton ntensty β j,o α s γ s,j depends also on sectors. s Workers Workers are heterogeneous n ther productvtes for each sector and occupaton 10

11 par (s, o). A characterzaton of worker heterogenety s based on Lee (2017). Each worker supples one unt of tme. Workers vary n ther effcency unts of that tme. The number of effcency unts ɛ s,o that each ndvdual worker of type t can supply for a specfc (s, o) s randomly drawn from the followng Fréchet dstrbuton: G s,o t (ɛ) = exp( T s,o t ɛ θt ). We assume that these dstrbutons do not vary by country. Worker heterogenety characterzed by G s,o t (ɛ) n ths model s related to fundamental complementarty between workers sklls and sector- and occupaton-specfc tasks, whch s not necessarly dfferent across countres. Two types of stochastc comparatve advantage arse from ths probablstc assumpton. Frst, between-worker-type comparatve advantage s governed by the relatve magntude of parameters T s,o t. For example, f T s,o t T s,o t > T s,o t T s,o t holds, then t s more lkely that a type t worker has comparatve advantage for sector s and occupaton o compared to another worker of type t and for another par (s, o ). Second, wthn-worker-type comparatve advantage depends on the shape parameter θ t. If workers productvtes are more dspersed wthn a type.e., lower θ t, then effects from the wthn-worker-type comparatve advantage wll be stronger than n the case of a larger θ t. We further assume that draws of dosyncratc productvty for each (s, o) are ndependent, whch gves us the followng jont dstrbuton for a vector of worker productvty ɛ = (ɛ 1,1,..., ɛ s,o,..., ɛ S,O ): G t (ɛ) = exp( s,o T s,o t ɛ θt ). Ths framework for the labor supply sde s an mportant channel whch has not been wdely studed n the lterature. Whle changes n trade costs operate as one of the labor demand shocks along the GVC, workers potentally respond to these shocks dfferently based on ther own comparatve advantage. Ths Roy channel allows for a more general sortng pattern of workers. Instead of assumng an exact one-to-one relatonshp between workers sklls and occupatons, we allow for endogenous matchng between sklls, sectors, and occupatons. 2 2 The standard trade model wth fxed, homogeneous, factors can be recovered va the followng assumptons, whch elmnate the Roy channel: 1. θ t for all worker types. In ths case, workers have the same productvty condtonal on ther type and ther choce of sector and occupaton. 2. Each occupaton has a correspondng worker type. 3. T s,o t 0 for every o t and T s,t t = 1 for all s and t. 11

12 2.2 Equlbrum Sourcng Decson In the above model, a fnal producer for ω chooses the entre path of l(ω) = (l 1 (ω),..., l J (ω)) by mnmzng the total cost of producton across all J stages. However, ths approach makes solvng the model challengng, because we can no longer take advantage of the convenent characterstcs of the Fréchet dstrbuton. To deal wth ths ssue, Antràs and de Gortar (hereafter, AG, 2017) ntroduce two alternatve approaches. The frst s a sequental approach n whch each stage j producer chooses an optmal source for the j 1 stage by mnmzng only ts stage-specfc producton cost. The key assumpton that they ntroduce s that stage j producers know the exact productvty draw of the stage j 1 producers, but do not know that of stage 1,..., j 2 producers. Instead, stage j producers know only the productvty dstrbuton of upstream producers up to stage j 2; thus, they take the expectaton of productvty up to stage j 2 as gven when they mnmze the producton cost for stage j. Thus, ths s a lmted nformaton approach. The second approach s a lead-frm approach n whch the assumpton of a country-stage-specfc Fréchet productvty parameter s replaced by a sngle Fréchet productvty parameter for an entre GVC. So, n a world wth N countres and J stages, there are N J possble GVCs, each wth ts own Fréchet productvty parameter. AG show that these two approaches are equvalent at the equlbrum under the probablstc assumpton of z s,j (ω) as prevously descrbed. Our model draws from ther result and, hereafter, we apply the sequental approach. Another key assumpton for the sourcng problem of ths model s that each stage s sourcng decson s ndependent. Combnng ths assumpton and the assumpton of lmted nformaton on upstream productvtes, we can derve an analytcal soluton for the equlbrum GVC probablty. We assume perfect competton for fnal goods and ntermedate nputs, so each country sources from the lowest-cost suppler around the world. Gven perunt wages w s,o for each country, sector, and occupaton, and a CES prce ndex for fnal goods P, the unt cost for the nput bundle excludng materals from the prevous stage s gven by c s,j ϕ s,j (P ) 1 αs Cobb-Douglas constant. o (ws,o ) αs βj,o, where ϕ s,j (1 α s ) (1 αs ) o (αs β j,o ) αs βj,o Whenever stage j materals n country are shpped to another country n to be used n stage j + 1 producton, there s an ceberg trade cost τ s n 1. Trade costs vary by sector. We adopt standard assumptons for ceberg trade costs: τ s = 1 and τn s τk s τ kn s for every s,,n, and k. Gven these assumptons, stage 2 producers of sector s n country choose the optmal source l s,1 (ω) for stage 1 materals of product ω by solvng the followng problem: l s,1 (ω) = arg mn [(p s,1 l l (ω)τl) s 1 γs,2 ] = arg mn[( l z s,1 l c s,1 l (ω) τ s l) 1 γs,2 ], s a 12

13 where c s,1 = ϕ s,1 (P ) 1 αs o (ws,o ) αs β1,o. Before we derve the sourcng decson for stage j + 1 producers, we defne the followng expectaton varable as ntroduced by AG usng the law of terated expectatons: Θ s,j (x) E j [(p s,j = E j [( (ω) (ω)τ s l s,j (ω) )x ] l s,j (c s,j )γs,j l s,j (ω) z s,j l s,j (ω) )x Θ s,j 1 (x(1 l s,j (ω) γs,j )) (τ s (ω) l s,j (ω) )x ]. We denote the optmal source for stage j materals of sector-s product ω for stage j + 1 producers of sector s n country by l s,j (ω). Then, ths expectaton varable Θ s,j (x) descrbes the expected prce of stage j materals of sector-s product ω to the power of some constant x, f they are shpped from the optmal source country l s,j (ω) to country. The sourcng decson for stage j + 1 producers n country can be wrtten usng ths expectaton varable. l s,j (ω) = arg mn l {( (cs,j l ) γs,j )1 γs,j+1 z s,j l (ω) Θ s,j 1 l ((1 γ s,j+1 )(1 γ s,j )) (τl) s 1 γs,j+1 } Smlarly, fnal good consumers n country buy ω from l s,j (ω) whch solves l s,j (ω) = arg mn l { (cs,j l ) γs,j z s,j l (ω) Θs,J 1 l (1 γ s,j ) τ s l} Probablty of GVC source stage j materals from another country n s Pr(l s,j (ω) = n) = Pr[( (cs,j The probablty that stage j + 1 producers of sector s n country n ) γs,j )1 γs,j+1 zn s,j (ω) mn n ( (cs,j n ) γs,j For notatonal smplcty, we defne B s,j n z s,j n (ω) )1 γs,j+1 Θ s,j 1 n ((1 γ s,j+1 )(1 γ s,j )) (τn) s 1 γs,j+1 Θ s,j 1 n ((1 γ s,j+1 )(1 γ s,j )) (τ s n ) 1 γs,j+1 ]. (c s,j n ) γs,j (1 γ s,j+1) Θ s,j 1 n ((1 γ s,j+1 )(1 γ s,j )) (1 γ s,j ) τn. s Usng (τn) s 1 γs,j+1 for each s and j = 1,..., J 1, and B s,j n (c s,j n ) γs,j Θ s,j 1 n the Fréchet dstrbuton of product-specfc productvty for each stage and each country, the equlbrum probablty of the sourcng decson by stage j+1 producers of sector s n country 13

14 can be wrtten as Pr(l s,j (ω) = n) = A s n(b s,j n ) ν γs,j /(1 γ s,j+1 ) n A s n (B s,j n ) ν γs,j /(1 γ s,j+1 ) for j = 1,..., J 1. Smlar to the EK model, ths probablty s equal to the share of stage j goods of sector s that are produced n country n and used for stage j + 1 producton n country. Ths GVC probablty clearly shows the magnfcaton effect of herarchcal producton as we go downstream. Because γ s,j s ncreasng n j for a gven sector s, the effectve elastcty of blateral trade flows ν γ s,j s ncreasng n j. Therefore, the effect of changes n trade costs between two countres s magnfed n downstream producton compared to upstream producton. As dfferent producton stages use occupatons wth dfferent ntenstes, the demand for occupatons wll depend on ths magnfcaton effect. To the extent γ s,j vares across sectors, the sze of the magnfcaton effect wll also vary by sector. Usng the GVC probablty result and the ndependence assumpton for sourcng decsons, we derve the equlbrum probablty of an entre GVC path. The probablty that a fnal good ω of sector s consumed n country has followed a specfc GVC path l = (l 1,..., l J ) s λ s l, = Pr(l s,j = (ω) = l J l s,j 1 l J... Pr(l s,1 l (ω) = l 1 ) 2 J j=1 As l [(c s,j j l j (ω) = l J 1 ) Pr(l s,j 1 ) γs,j (τ s l j l j+1 )] ν γs,j l N J J j=1 As l j [(c s,j l j ) γs,j (τ s l j l j+1 )] ν γs,j, l J (ω) = l J 1 l s,j 2 l J 1 (ω) = l J 2 )... where N J s the set of all possble sequences of N countres along J stages, and l J+1 = and l J+1 = for all l l N J. The dervaton of ths probablty agan uses the law of terated expectaton and characterstcs of the Fréchet dstrbuton. The expresson for blateral trade flows of fnal goods of sector s from the locaton of fnal assembly n to country s derved smlarly: Pr(l s,j (ω) = n) = A s n(b s,j n ) ν n A s n (B s,j n ) ν. The exact prce ndex of fnal goods s also derved n a smlar way to EK: P = S ( P s s=1 b s )bs, 14

15 where P s = [Γ( ν + 1 σ )] 1/(1 σ) ( ν l N J J j=1 A s l j[(cs,j l j ) γs,j (τ s l j l j+1)] ν γs,j ) 1/ν. (1) Agan, n ths prce ndex, l J+1 = and also l J+1 = for all l l N J. We assume σ < ν + 1 so that the gamma functon n the prce ndex s well-defned. 2.3 Equlbrum Labor Supply Workers labor supply response à la Roy model s based on Lee (2017). We assume that every worker nelastcally supples all of ther tme for workng. Hence, the worker s labor supply decson s only about allocatng that tme to a sector, occupaton par. Each worker chooses a par of sector s and occupaton o to maxmze her potental labor ncome condtonal on her (S O)-dmensonal productvty matrx ɛ. In other words, worker s problem can be wrtten as max s,o ws,o ɛ s,o, where w s,o s per-unt wage for workers n sector s of country wth occupaton o. Workers take the per-unt wages as gven. Snce ɛ s randomly drawn from a jont Fréchet dstrbuton G t (ɛ), the equlbrum labor supply decson for workers of type t for sector s and occupaton o s π s,o,t = T s,o t (w s,o ) θt s,o T s,o t (w s,o ) θt. The shape parameter θ t for type t workers productvty dstrbuton s thus the labor supply elastcty of type t workers at the sector and occupaton level. Dfferent worker types are allowed to potentally have dfferent labor supply elastcty n ths model. Condtonal on the optmal labor supply decson, the equlbrum average wage of type t workers can be derved as w,t = [ s,o T s,o t (w s,o ) θt ] 1/θt Γ(1 1 θ t ). If we defne worker types based on educatonal attanment, the relatve w,t of hgh-sklled workers over low-sklled workers wll be a model counterpart of the skll premum, whch s one of our core objects of nterest n the quanttatve exercses. 2.4 General Equlbrum The equlbrum per-unt wages w s,o and the prces P s are solved n general equlbrum from market clearng condtons for each occupaton. We have occupaton market clearng 15

16 condtons for each country, sector, and occupaton: t w,t π s,o,t L,t = α s where we defne j γ s,j γ s,j β j,o b s N λ s l,n( n=1 l Λ j t Λ j {l = (l1,..., l J ) N J l j = } w n,t Ln,t + s (1 α s n ) α s n o t w n,t π s,o n,t L n,t ), (2) as the set of GVCs that produce the j-th stage n country. The left-hand sde of the above occupaton market clearng condton s the total labor ncome earned by workers n sector s of country wth occupaton o. Ths term should be equal to the rght-hand sde, whch s the total payment for those specfc workers. The goods market clearng condton s embedded n the share of sector s n total ncome on the rght-hand sde. Let us now dscuss the components of the rght-hand sde n more detal. A key part of the rght-hand sde s total spendng from the countres purchasng" the goods and servces produced by the partcular country-sector-occupaton. The spendng has two sub-parts, spendng for fnal use (consumpton), and spendng for ntermedate use. Ths spendng s then multpled by a factor related to the roundabout nature of producton, whch s n turn multpled by the probablty λ s l,n that country s producng stage j of a GVC that wnds up n the purchasng country. Ths term s then multpled by the sectoral consumpton share, so we now have total spendng on the partcular stage and sector, controllng for roundabout effects. Ths s then multpled by the value-added component of ths spendng, whch s the product of the relevant α, γ, and β terms. Fnally, the rght-hand sde s summed over all stages of producton. To solve the model, we frst normalze the wages to satsfy,s,o ws,o = 1. Wth ths normalzaton, and wth the occupaton market clearng condtons and the exact prce ndex as derved above, we can solve the model for the equlbrum w s,o and Lucas (2007) algorthm. We frst guess ntal w s,o (1). Wth the ntal guess of w s,o and P s and solve for P s usng the Alvarez followng equaton and the solved P s, we calculate all equlbrum varables of the model to construct the occupaton market clearng condtons (2). We then update w s,o accordng to the excess demand or supply of labor calculated from (2). Iteratons contnue untl the excess occupatonal demand or supply s suffcently close to zero. 2.5 Dscusson The core mechansm of our model s the nteracton between country-level comparatve advantage (the Rcardan and HO channels) and worker-level comparatve advantage (the Roy 16

17 channel) along the GVC. If trade costs change n ths economy, the relatve demands for country s ntermedate materals and fnal goods change n all sectors, whch, n turn wll affect each country s specalzaton pattern across sectors and stages. These changes n specalzaton patterns, n conjuncton wth the relatve occupaton ntensty of each producton stage and the sector-specfc GVC ntenstes, nduce changes n the relatve labor demand for sectors and occupatons. Ths labor demand change, n turn, affects sector- and occupatonspecfc per-unt wages. Workers then re-optmze ther choce of sector and occupaton. Even though workers observe the same change n wages for each sector and each occupaton, the ndvdual worker s response wll dffer dependng on hs/her dosyncratc productvty. We now dscuss how partcular parameters of the model map nto comparatve advantage. For countres, there s comparatve advantage at the sector-level and at the stage-level. Sector-level comparatve advantage of countres s based prmarly on the relatve magntude of A s. Relatve factor endowments also shape sector-level comparatve advantage of countres through L,t and T s,o,t, because sectors also use dfferent occupatons wth dfferent ntenstes based on β j,o α s γ s,j. Note that f both α s and γ s,j are the same across sectors, then sector-level comparatve advantage of countres s determned only by the Rcardan channel. A country s stage-level comparatve advantage s drven prmarly from the HO channel through the relatve endowment governed by L,t and T s,o,t, and the occupaton ntenstes β j,o. The Rcardan channel also shapes the stage-level comparatve advantage through the nteracton between A s and γ s,j. If γ s,j does not vary by sector, then the stage-level comparatve advantage s determned entrely by the HO force. Therefore, n the most general case wthout any restrcton on the model parameters, we can have both sector-level and stage-level comparatve advantages, each of whch s affected by both the Rcardan and the HO forces as explaned above. Workers have heterogeneous productvtes, T s,o t, at the sector and occupaton level; thus, they have comparatve advantage along these two dmensons, as well as between types t. The combnaton of L,t and T s,o t determne the effectve labor endowment, whch lnks to country-level comparatve advantage and specalzaton across sectors and stages. Note that there s overlap between the Roy and Rcardan channels (prmarly at the sector level), and between the Roy and HO channels (prmarly at the stage level). When trade costs declne, the effectve labor endowment affects specalzaton patterns, whch n turn affects the fundamental wages w s,o. Sector-level specalzaton has frst-order effects on relatve wages across sectors, whle stage-level specalzaton has frst-order effects on relatve wages across occupatons. These changes n sector- and occupaton-level wages, n combnaton wth workers comparatve advantage, represented by the relatve magntudes of T s,o t, lead to changes n the skll premum. 17

18 We note that stage-level specalzaton, whch occurs only because of the GVC structure of our model, provdes a potentally mportant margn of changes n the skll premum through labor demand shfts at the occupaton level owng to the stage-specfc occupaton ntenstes. Also, Lee (2017) shows that workers comparatve advantage s much more clearly pronounced across occupatons than across sectors. Therefore, the GVC channel of our model captures an mportant facet of the Roy mechansm by accountng for countres specalzaton across producton stages. In order to further study the effect of GVCs, we need to focus on the role of γ s,j. γ s,j captures the relatve mportance of the roundabout structure over the snake structure. Because (1 γ s,j ) denotes the share of stage j 1 used for producton of stage j n sector s, the sequental structure of producton through GVC becomes less mportant as γ s,j 1. In the extreme case where γ s,j = 1 for all j = 1,..., J, only stage J producton remans actve usng only domestc labor nputs and composte ntermedates of fnshed goods through the roundabout structure. Our baselne model would then be equvalent to the mult-sector EK model wth ntermedate nputs (but wth just one producton stage). As dscussed n many papers n the lterature ncludng Y (2003, 2010) and Johnson and Noguera (2012), ntroducng GVCs nto standard trade models can yeld magnfed effects of changes n trade costs on aggregate outcomes such as blateral and aggregate trade flows and prces. Our result s n lne wth the mplcaton for the magnfcaton effect from the lterature. As γ s,j 0, producton stages become more nter-dependent, and the effectve trade elastcty ν γ s,j becomes larger. Thus, aggregate effects from trade lberalzaton are ncreasngly magnfed wth GVC ntensty. By contrast, the dstrbutonal effect of a reducton n trade costs s not necessarly monotonc n GVC ntensty. As γ s,j 0 n all sectors and stages, the full snake structure occurs. But, note that the model effectvely reduces to just one value-added stage. By defnton, occupatonal ntensty varaton across stages dsappears. Hence, stage-level comparatve advantage also dsappears. As γ s,j 1 n all sectors and stages, the dfference n occupaton ntensty across producton stages also becomes rrelevant, because prevous-stage materals have essentally zero demand and thus are essentally unused n downstream stages. Because the stage-level comparatve advantage plays an mportant role n endogenous changes n the skll premum n conjuncton wth the Roy channel, as dscussed above, a reducton n trade costs can have small effects on between-worker-type nequalty e.g., the skll premum, f a trade model features ether the full roundabout structure (γ s,j 1) or the full snake structure (γ s,j 0) n all sectors. Furthermore, varaton n GVC ntensty γ s,j across sectors puts dfferent weghts on labor demand shfts across sectors and stages. How much of specalzaton effect across sectors and 18

19 stages translates nto wage responses s governed by the contrbuton of each stage n each sector. γ s,j accounts for the sze of the contrbuton. We wll further dscuss nteracton of dstrbutonal effects of trade wth the GVC ntensty usng a smple 2-stage verson of our model n the next secton. 3 A Smple Two" Model In ths secton, we smplfy our baselne model to two countres, sectors, producton stages, occupatons, and worker types. We frst descrbe the set up of the smplfed model and derve the labor market equlbrum condtons. We then conduct numercal exercses wth ths smplfed model to convey ntuton on the role of GVCs n aggregate and dstrbutonal outcomes. 3.1 Model Setup and Equlbrum We begn by brefly revewng the bg pcture of worker choce, producton, and aggregaton, and then we set up the smplfed model. Each country has an exogenous supply of two types of workers. Each worker draws a productvty for each sector-occupaton par. Based on the productvty draw, and the market wages for the sector-occupaton pars, the worker chooses the sector-occupaton that maxmzes hs/her ncome. Ths corresponds to the left part of Fgure 1 below. Indvdual goods (n a gven sector and country) are produced n two stages. Frst, a composte ntermedate and the occupatonal factor nputs are combned to make the stage 1 good. Then, the stage 1 good s combned wth a composte ntermedate and occupatonal factors to make the stage 2 good. The use of the stage 1 good n stage 2 producton captures the GVC part of our model. The producton process s llustrated n the boxes n the mddle of Fgure 1 below. Fnally, the ndvdual goods are aggregated (across sectors) nto a composte good, whch s used for fnal consumpton at home and abroad, and also as a composte ntermedate n stage 1 and stage 2 producton. The flows of the composte ntermedate capture the roundabout producton part of the model. Ths s llustrated n the rght part of Fgure 1 below. We now descrbe the worker choce and producton of an ndvdual good more formally. We denote countres by = 1, 2, sectors by s = 1, 2, producton stages by j = 1, 2, worker types by t = H, L, and occupatons by o = 1, 2. 19

20 Type H workers (# : L,H ) Type L workers (# : L,L ) Fgure 1: A 2-stage GVC Model wth Endogenous Labor Supply Sector 1 occupaton H Stage 1 labor composte ntermedates occupaton L Stage 2 labor stage 1 materals composte ntermedates sector 1 fnal goods Sector 2 mports occupaton H Stage 1 labor composte ntermedates occupaton L Stage 2 labor stage 1 materals composte ntermedates sector 2 fnal goods mports domestc consumers foregn consumers foregn composte producers 20

21 The producton functon vares by country, sector, and stage: f s,j (.). Hence, we denote the Fréchet productvty of goods as z s,j, the composte ntermedate as x s,j, the stage 1 good used n stage 2 producton as m s,1, and the use of occupatonal factors 1 and 2 as L s,j,1 and L s,j,2, respectvely. The frst and second stage producton functons n country, sector s for a good ω are gven by: f s,2 (x s,2 f s,1 (x s,1, L s,1,1 (ω), L s,1,2 (ω)) = z s,1 (ω)(x s,1, L s,2,1 (ω), L s,2,2 (ω), m s,1 (ω)) = z s,2 ) 1 αs ((L s,1,1 (ω)[(x s,2 ) 1 αs ((L s,2,1 (m s,1 (ω)) 1 γs. (ω)) β1,1 (L s,1,2 (ω)) β1,2 ) αs (ω)) β2,h (L s,2,2 (ω)) β2,2 ) αs ] γ s The relatve mportance of the composte ntermedate, value-added, and the stage 1 good n producton depends on two parameters, α s, and γ s. 1 α s governs the mportance of the composte ntermedate,.e., the roundabout structure. 1 γ s governs the mportance of the stage 1 good n stage 2 producton. We assocate greater GVC ntensty wth a larger 1 γ s. Note that, as wth any producton functon wth a roundabout structure, the composte good x s,j can be netted out, and the effectve" value-added of stage 2 s γ s. Note that the coeffcent on the occupatonal factor only vares by stage and occupaton: β j,o. The Fréchet productvty dstrbuton for each country and sector s s gven by: z s,1 (ω) F s,1 (z) = exp( A s z ν(1 γs) ) z s,2 (ω) F s,2 (z) = exp( A s z ν ). We contnue to mantan the sequental ndependence and the lmted nformaton assumptons of Antràs and de Gortar (2017) that fnal good consumers n ths two-stage setup do not know the exact productvty draw of stage 1 producers. For each good ω, stage 2 producers source the lowest cost suppler of stage 1 goods, and, smlarly, fnal good consumers source the lowest cost supplers of the stage 2 goods. Owng to our assumpton that productvtes are drawn from country- and sector- and stagespecfc Fréchet dstrbutons, these sourcng problems mply the followng blateral GVC probabltes: Pr(l s,1 (ω) = n) = Pr(l s,2 (ω) = n) = A s n(c s,1 n τ s n) ν(1 γs ) n A s n (c s,1 n τ s n ) ν(1 γs ) A s n((c s,2 n ) γs Θ s nτn) s ν n A s n ((c s,2 n ) γs Θ s n τ. s n ) ν Usng the above sourcng probabltes, and the Antràs and de Gortar (2017) assumptons 21