Global Value Chains and Inequality with Endogenous
Labor Supply∗
Eunhee Lee†

Kei-Mu Yi‡

November 20, 2017

Abstract
We assess the role of global value chains transmitting global integration shocks
to aggregate trade as well as distributional outcomes. We develop a multi-country
general equilibrium trade model that features multi-stage production, with different
stages having different productivities and using factors (occupations) with different intensities. The model also features a Roy mechanism, in which heterogeneous workers
endogenously choose their sector and occupation. Country- and worker-level comparative advantages interact. A reduction in trade costs leads to countries specializing intheir comparative advantage sectors and production stages. This specialization changes
labor demand and also leads to more workers shifting to their comparative advantage
sectors and occupations. With a special case of our model, we show that the intensityof the global value chain (GVC) magnifies the aggregate effects of trade liberalization,
but it has a non-monotonic effect on the skill premia. We calibrate our model to the
U.S., China, and the rest of the world in 2000 and we simulate a decline in China’s
costs of trade, designed to mimic China’s entry into the WTO. Our simulation results
imply an increase in the skill premium in both the U.S. and China, and the GVC, i.e.,
stage-level specialization, is critical to this outcome.

∗The views expressed here are those of the authors and are not necessarily reflective of views of theFederal Reserve Banks of Dallas, Minneapolis or the Federal Reserve System. We thank Pol Antras, Gordon
Hanson, Elhanan Helpman, Chinhui Juhn, Steve Redding and especially Alonso de Gortari for very helpful
discussions. We also thank participants at the Asian Meetings of the Econometric Society, at the Universityof Virginia, and at the NBER Trade and Labor Markets Conference for their comments. Heesuk Jungprovided excellent research assistance. All errors are our own.
†
University of Maryland‡
University of Houston, NBER, Federal Reserve Bank of Dallas, and Federal Reserve Bank of Minneapolis11Introduction

One of the most significant economic developments over the past half-century is the increased
fragmentation of production across borders. Goods are produced in sequential stages thattraverse multiple countries – a global value chain. Countries specialize in particular stagesof a good’s production process. This increase in vertical specialization has occurred under a backdrop of a broad increase in international trade, one of the defining features ofglobalization across the world during this period.
Partly because of this backdrop, most of the research examining the effects of global
integration on wages, employment, and other variables has focused on total trade. Autoret al. (2013) is a recent example. This has also been exemplified in the factor content studies
that trade and labor economists have conducted since the 1990s. The purpose of our paper
is to assess the role of global value chains as a propagation mechanism transmitting global
integration shocks, such as China joining the WTO, to aggregate trade outcomes, as well as
distributional outcomes, such as the skill premia.
Our approach is to build a model of global value chains and international trade and thento calibrate it and use it to study global integration shocks. We introduce global value chains
following the work of Antràs and de Gortari (2017) and de Gortari (2017). They develop
a tractable framework for incorporating multi-stage production in an international trademodel that generalizes and extends previous research on this subject. In addition, a key
feature of our model is to include for multiple sectors, multiple factors, and a labor supply
channel. In particular, following Lee (2017), we include Roy selection effects, in which heterogeneous workers choose occupations and sectors based on their individual productivities
in these occupations and sectors, as well as on prevailing prices. Lee (2017) and others haveshown that these channels enhance our understanding of how trade affects inequality andare quantitatively important in explaining the increase in inequality.
The core elements of our model revolve around the production of a final good and theworker’s choice of sector and occupation. A final good is made in a sequence of stages. Eachstage involves labor, a composite intermediate, and output from the previous stage. There areseveral labor inputs, which we call “occupations”. Different stages use these occupations withdifferent intensities. The presence of the composite intermediate and the previous stage’s
output helps generate both “roundabout” and “snake” features in production. The final goods
have two uses, consumption and input into the composite intermediate. On the worker’s side,
each worker is of an exogenous type. Within each type, a worker draws occupation and sector
specific productivities. Based on these productivities, as well as on prevailing prices, workers
choose their optimal sector and occupation. Our individual goods and workers are embedded2

in a multi-country general equilibrium framework. This framework features both countryand worker-level comparative advantages.
For our analysis, we first introduce a general version of the model and then study asimplified version of the model in order to develop intuition. We study a “25 ” version of themodel in terms of countries, worker types, sectors, stages, and occupations. We examine theresponse of GVCs, skill premia, and other variables to lower trade costs. The lower trade
costs are mediated through several demand and supply forces before ultimately affecting
GVCs and skill premia. The lower trade costs facilitate specialization at the sector-level
and at the production stage-level. In addition, this changing specialization pattern shifts
the relative demand for occupations based on stage-specific occupation intensities. Thisaffects the equilibrium wage, which then affects workers’ choices of occupations and sectors.
Ultimately, the skill premia are affected.
The 2-stage version of our model illustrates the role of GVC intensity on the skill premium. A higher GVC intensity implies a greater reliance on the stage-one output usedin stage-two production. Numerical exercises show that, in response to a decline in trade
costs, aggregate outcomes are magnified if the GVC intensity is higher, but the skill premium responds non-monotonically to higher GVC intensity. The largest effect occurs withintermediate GVC intensities. Extreme GVC intensities shut down stage-level specialization,
which is an important margin through which trade shocks change the skill premium. In addition, conditional on the stage-level comparative advantage channel, differences in the GVC
intensity across sectors put different weights on the shift of labor demand across sectors andoccupations.
We then calibrate the general version of our model for three countries, China, U.S.A, andconstructed rest of the world; five worker types; four sectors; two stages; and five occupations.
Some of our parameters draw directly from the data, others are assigned, and the others –including the worker productivity parameters, and the production function parameters (productivities of sector and stage, occupational intensity coefficients, value-added share, and
GVC intensity parameters) – are calibrated to match moments in the data. Our calibrated
parameters reveal several patterns. First, based on relative endowments and productivities,
China has a comparative advantage in the manufacturing sector and the downstream production stage, and the U.S. has a comparative advantage in services and the upstream production
stage. Second, production stages have different occupation intensities across countries. For
example, the downstream production stage is relatively high-skilled-occupation-intensive in
China, but low-skilled-occupation-intensive in the U.S.. Third, sectors significantly differ in
GVC intensity. Upstream production stages have relatively larger value-added in the agriculture and manufacturing sectors than in the service sector. Lastly, workers with different3levels of skill have a clear comparative advantage both across sectors and occupations.
We use our calibrated model to perform counterfactual exercises quantifying aggregate
and distributional impacts of the China shock. We study a 50 percent decline in China’s
trade costs with its trading partners. When trade costs with China go down, all countries
specialize further in their comparative advantage stages and sectors. The degree of stagelevel specialization is larger in sectors with a higher GVC intensity, e.g., manufacturing. The
greater the GVC intensity, the larger the magnification of aggregate effects such as trade.
This is consistent with previous research.
In addition, we find that the skill premium rises in all three countries. In the U.S. andChina, the lower trade costs induce specialization to shift towards sectors and stages thatuse high-skilled-occupations more intensively. As indicated above, for China that involves
manufacturing and the downstream stage, and for the U.S., that involves the service sector
and the upstream stage. In addition, the worker-level productivity estimates imply that
better educated workers are better off in the high-skilled occupations. Hence, our richframework is able to reproduce the stylized fact that trade liberalizations are often associatedwith skill premia increases in both skill-abundant and non-skill-abundant countries. We showthat in the absence of GVCs, this result would not occur.
On the other hand, our counterfactual shows that the increase in skill premia is limited
in magnitude, around 1% or less. This is because, according to our calibrated parameters,
each country specializes in sectors and stages that do not have a large share of value-addedin the entire production chain. Hence, while there are large changes in specialization owing
to the lower trade costs, these large changes do not translate into large skill premia effects.

1.1

Related Literature

Our research is connected to several strands of research. One strand is the trade and wages
research that sought to examine the effects of increased U.S. imports from developing countries on the skill premia. This research was especially active in the mid-1990s, and includes
Katz and Murphy (1992), Lawrence and Slaughter (1993), Krugman (1995), and Feenstra
and Hanson (1999) among others. All of these papers essentially employed a Heckscher-Ohlin
type (HO) framework with its Stolper-Samuelson and factor content of trade implications.
The main findings tended to be that the effect of trade was not large. However, the survey
article by Goldberg and Pavcnik (2007) showed that the predictions of a simple HeckscherOhlin (HO) framework do not hold up in the data. In particular, skill premia tended torise in both developed and developing countries following trade liberalizations. Krugman(2008) revisits the trade and wage issues from the mid-1990s with the benefit of 15 years4

of additional data. In addition, Krugman argues that increased vertical specialization can
generate inequality via Stolper-Samuelson effects. To our knowledge, Krugman’s paper isthe only paper that makes a case for examining the consequences of vertical specialization
for inequality.
In recent years, there has been a new wave of interest on the employment and wage effects
of increased trade. This is not surprising, because the emergence of China as a significant
global economic force has only come about in the past 10-15 years. Autor et al. (2013),
Pierce and Schott (2016), and many other papers in the literature document significant
effects of China on labor markets of major partner countries such as the U.S. With the newinterest has come an expanded set of methodologies. One new approach involves applying
models with numbers, i.e., quantitative theory. Burstein and Vogel (2016) combine an HO
framework in a model that features heterogeneous firms and skill-biased productivity. Our
framework is in this vein.
Our paper is also related to a literature about offshoring and skill upgrading. Feenstra andHanson (1995), Costinot and Vogel (2010), and Zhu and Trefler (2005) discuss how offshoring
may increase the skill premium in both North and South by making both countries specialize
in high-skill-intensive sectors. These papers do not explicitly model a vertical production
structure. Our model looks at this argument through the lens of GVCs, because offshoring
involves vertical specialization across production stages by nature.
A second strand of research is on documenting the extent of global value chains, verticalspecialization, value-added exports, and related concepts, as well as on building models ofthese concepts. Contributions on the documentation side include Hummels et al. (2001),
Johnson and Noguera (2012); Antràs and Chor (2013), and Koopman et al. (2014). Contributions on the modeling side include Yi (2003, 2010), Johnson and Moxnes (2016), andmost recently, Antràs and de Gortari (2017) and de Gortari (2017). The latter two papers
develop a general framework for GVCs and show how to map special cases of this framework
into the Eaton and Kortum (2002) framework. Our modeling of GVCs draws from Antràs
and de Gortari (2017); it combines that paper with Lee (2017).
To investigate the link between trade and labor market outcomes, such as wage inequality and labor reallocation, increasingly, papers focus on heterogeneous workers. While
traditional trade models such as the HO model and the specific factors model assume thatworkers are all homogeneous in their productivities conditional on observable characteristics, this assumption misses the fact that workers differ in their productivities in reality.
This worker-level heterogeneity is important especially when we study the effect of trade onlabor market outcomes, because workers with same observable characteristics may respondto trade shocks differently depending on their idiosyncratic productivities. In recent years,
5

trade models bring the idea of the Roy (1951) model to introduce worker heterogeneity under the setting of assignment models: e.g., Teulings (2005), Ohnsorge and Trefler (2007),and Costinot and Vogel (2010, 2015). Worker heterogeneity is introduced to trade models
also based on a search and matching framework: e.g., Grossman et al. (2015), Helpman andItskhoki (2010), and Helpman et al. (2016).
Our paper is also closely related to a recent strand of literature on quantitative models
with the Roy-based assignment structure. One of the key assumptions in this literature isthat workers’ idiosyncratic productivity is randomly drawn from a type-II extreme value
distribution, a Fréchet distribution. Hsieh et al. (2013), Burstein et al. (2015), Lagakos
and Waugh (2013), Galle et al. (2017), and Lee (2017) use this assumption to investigate
the role of worker heterogeneity in disentangling labor market outcomes in one country
from labor demand shocks such as technological change or trade liberalization. Our paper
also relies on this distributional assumption when we characterize workers’ heterogeneous
productivities. We introduce this Roy-based assignment framework into a multi-stage GVC
model, where each stage of production is formulated based on the EK model. We can thus
investigate the general equilibrium relation between workers’ endogenous labor supply andtrade through GVC in our model. To numerically solve our multi-country GVC model fora general equilibrium, we base our work on the iterative algorithm provided by Alvarez andLucas (2007).
More papers in the literature recently focus on the occupational dimension as an important channel through which trade shocks are disseminated across workers--e.g., Autoret al. (2015), Ebenstein et al. (2014), Traiberman (2016), Harrigan et al. (2016). Our framework also allows workers to endogenously choose occupations in response to trade shocks
under the GVC setting. We show that worker heterogeneity plays also a significant role foroccupation-level labor reallocation. The occupational dimension is important in the GVC
context, because different production stages have different occupation intensities.
The core mechanism of our model can be further connected to the literature on trade,
inequality, and a declining labor share around the world. A recent paper by Dao et al. (2017)provides suggestive evidence about the effect of increased participation in GVCs on declining
labor shares in both developed and developing countries. Countries specialize in their capitalintensive and high-skilled-task-intensive stages as they participate in GVCs more. Although
we do not explicitly consider capital in our model, the stage-wise specialization pattern andstage-specific occupation intensities that we quantify in this paper can be linked to explain
declining labor shares with capital-skill complementarity as in Grossman et al. (2017).
The next section lays out our baseline model. This is followed by a description of a simpler
version of our model with just two stages of production, two countries, two occupations, and6two labor types. We solve the simpler version of the model and conduct several numerical
exercises to illustrate how the model works. Section 4 describes our calibration, and section
5 discusses our counterfactual exercises with the model.

2

Model

In this section, we describe our model. Because the model has many features, we provide
an overview first. Our model draws from the general global value chain (GVC, hereafter)model developed by Antràs and de Gortari (2017). We extend their framework by adding
three features: multiple factors of production, multiple sectors, and heterogeneous workers.
All three features are essential to investigate the role of GVCs in the effect of increased tradeon inequality.
In our model, each sector is comprised of a continuum of final goods. Each final goodis produced through a specific global value chain encompassing multiple stages of production that can potentially cross multiple countries. Each stage of production is producedwith value-added and with intermediate inputs. Value-added consists of multiple factorsof production, called occupations. There are two categories of intermediate inputs. One
category is a composite aggregate good. The second category of intermediates is good andstage-specific: the previous stage’s output. The inclusion of the previous stage’s output isthe key GVC component.
Countries have comparative advantages both across sectors and stages. To distinguishthese two types of comparative advantages, we assume that the primary source of each comparative advantage is different. Sector-wise comparative advantage is primarily from the
Ricardian channel based on difference in Ricardian productivities as in Eaton and Kortum(2002). On the other hand, stage-wise comparative advantage arises mainly from the standard Heckscher-Ohlin (HO) channel, as we assume that different stages of production havedifferent factor intensities and that countries have different factor endowments.
In addition, workers are heterogeneous in their sector and occupation-specific productivities. Workers endogenously choose their occupation and sector based on their productivities:
the Roy channel. Introducing the Roy framework into a general equilibrium trade model isbased on Lee (2017). Our model will deliver interaction between the Ricardian and HO
channels, the Roy channel, and GVCs.

7

2.1

Preferences, Technologies, and Workers

Our model features N countries, S sectors, value chains of fixed length J, O occupations, andT worker types. Each country is distinguished by its production technologies and endowmentof worker types. Within each sector s, s = 1, . . . , S, there is a continuum of final goods
over a set Ωs of mass 1. Each final good ω ∈ [0, 1] is produced following a specific value
chain of length J. The optimal value chain for a final good ω consumed in country n is a
J-dimensional vector of countries where each stage j of production takes place. In otherwords, intermediate stages of a product can cross multiple borders along the value chain.
For each stage, the production factors are occupations (managers, clerical staff, etc.) o,o = 1, . . . , O. Occupation intensities vary across stages of production and countries. As
mentioned above, the production technology also consists of two categories of intermediates,
an aggregate composite intermediate, and a good and stage-specific intermediate.
Each country i, i = 1, . . . , N , is exogenously endowed with L̄i,t workers of type t, t =1, . . . , T . In our quantitative analysis, these types will be associated with observable worker
characteristics, such as education. Each worker of each type “draws" a sector and occupation
specific productivity, and on the basis of that productivity and prevailing occupation-sectorspecific wages, chooses to work in the occupation and sector that delivers the highest return.
Preferences

Consumers have common nested CES preference over final goods
S
Y
s
Ui =
(Cis )b ,s=1

Z

where Cis ≡ (Ωs(Cis,F (ω))(σ−1)/σ dω)σ/(σ−1) .

Cis,F (ω) is consumption of a final good ω of sector s in country i. The expenditure share ofPeach sector is given by bs with s bs = 1. σ > 0 is the elasticity of substitution between
goods within the sector.
Production Technology As outlined above, each final good ω is produced from a specificvalue chain of length J during production, and this value chain is potentially spread overmultiple countries. We denote the sequence of producing countries for a product ω byl(ω) = (l1 (ω), . . . , lJ (ω)). At each stage j of the value chain for a product ω, firms use
domestic labor, the stage j − 1 good for ω, and a composite intermediate. The use of theimmediately preceding stage captures the “snake" structure of production (as in Yi (2003))
and is the key feature of the value chain.
Countries possess technologies for any intermediate stage of production from j = 1 to8

j = J − 1, and also for final assembly of stage J, for all goods in all sectors. The production
function in country i for stage j of good ω in sector s is Cobb-Douglas:s,j,1
fis,j (xs,j(ω), . . . , Ls,j,O(ω), ms,j−1(ω))
i , Liii
s

1−αi= zis,j (ω)((xs,ji )Y s,j,o
j,o s
s,j
s,j
(Li (ω))βi αi )γ (ms,j−1(ω))1−γ .
ioFocusing first on the intermediate inputs into production, xs,jis the composite intermedii
ate good used by stage j producers of sector s in country i. It is a nested CES aggregateof the final goods, and has the same structure as the utility function. This captures the“roundabout” structure of production, as in Caliendo and Parro (2015) and Eaton and Kortum (2002). Our roundabout structure is simpler than that of Caliendo and Parro (2015)
and also de Gortari (2017) in that the input-output share between sectors is completely
determined by the expenditure share and the sector-specific value-added share. The otherpapers consider a more general input-output structure between sectors focusing on aggregate
outcomes of the model.
(ω) from each of O ocValue-added inputs into production are occupational tasks Ls,j,oi
cupations. Finally, the snake structure of our model is described by ms,j−1(ω), the stageij − 1 good for ω of sector s. We assume a constant elasticity of substitution for all inputs tofocus on the role of GVCs in generating differential gains from trade between worker types.
An alternative approach would be to model the complementarity between intermediate inputs and different skill levels of occupations. Krusell et al. (2000) and Parro (2013) haveshown that this captial-skill complementarity is important in explaining macroeconomic andinternational trade behavior.
The three key parameters governing the importance of each of these inputs are βij,o ,γ s,j , and αis . All three parameters range from 0 to 1. βij,o captures the importance of each
occupational input o. This parameter varies across occupations, stages, and countries. For
P j,oeach stage j and country i,= 1. 1 − γ s,j captures the importance of the j − 1
o βi
stage input in stage j. This parameter varies across stages and sectors. A lower value of
γ s,j corresponds to a greater importance of the snake structure, and a lower importance ofthe composite intermediate and value-added taken together.1 More formally, as γ j → 0,
the snake or value chain term dominates the roundabout and value-added terms, and viceversa for γ j → 1. αis captures the relative importance of value-added and the composite
intermediate with higher values of αis corresponding to greater importance of value-added.
This parameter varies across sectors and countries. We will call this parameter as value1
Note that these two terms constitute the “typical" Eaton and Kortum (EK) strucure of production;
hence, γ s,j can also be thought of as capturing the importance of the EK structure.

9

added share. Finally, we assume that the initial stage 1 is produced using only occupations
and composite intermediates; in other words, we assume γ s,1 ≡ 1 for every s = 1, . . . , S.
To summarize, for each stage of production, the importance of the previous stage, i.e., of
the value chain, is captured by 1 − γ s,j , the importance of the composite intermediate, i.e.,
the roundabout term, is captured by (1 − αis )γ s,j , and the importance of the occupations,taken together, i.e., value-added, is captured by αis γ s,j .
Factor-neutral productivity for stage j of sector-s product ω in country i is denoted bys,jzi (ω). We assume the productivity follows a Fréchet distribution from Eaton and Kortum(hereafter, EK, 2002). Productivity zis,j (ω) is randomly drawn froms,j

Fis,j (z) = exp(−Asi z −ν γ̃ ),Qs,j 0) ∈ [0, 1]. We further assume that productivity draws arewhere γ̃ s,j ≡ N
j 0 =j+1 (1 − γ
independent across sectors and stages. Asi governs the scale of productivity for sector s incountry i. We assume that this scale parameter does not vary by stage. νγ̃ s,j captures
the dispersion of stage j productivities. ν is the standard Fréchet shape parameter, andgoverns the common variance of stage j productivity. The effective variance of stage j isstage-specific and is based on γ̃ s,j .
The stage-specific shape parameter νγ̃ s,j has two advantages. First, as argued in Antràs
and de Gortari (2017), this probability distribution makes a sequential sourcing decisionequivalent to the case where a lead firm chooses the entire sourcing path from the beginning.
This feature provides great analytic tractability, which we will discuss in more detail in
the next subsection. Second, we can conveniently characterize the magnification effect of
GVC as discussed in Yi (2003). At the equilibrium, the effective trade elasticity νγ̃ s,j islarger in downstream production stages, as γ̃ s,j is monotonically increasing in j for every s.
The magnification effect of GVC is thus active through γ̃ s,j and potentially different acrossP
sectors. (In addition, j γ s,j γ̃ s,j = 1 for every s by the definition of γ̃ s,j , and we assumeγ̃ s,J ≡ 1 for every s.)
Our rich structure provides Ricardian and HO motives for trade. The Ricardian channel
is captured by zis,j (ω), and is present across stages and sectors. The HO channel operates
through βij,o . Different stages use occupations with different intensities. For example, adesign stage would use more designers or engineers, while an assembly stage would employ
relatively more production workers. Note that the value-added by a particular occupation
depends on the stage, not on the sector. However, the effective occupation intensity βij,o αis γ s,jdepends also on sectors.
Workers

Workers are heterogeneous in their productivities for each sector and occupation
10

pair (s, o). A characterization of worker heterogeneity is based on Lee (2017). Each worker
supplies one unit of time. Workers vary in their efficiency units of that time. The numberof efficiency units s,o that each individual worker of type t can supply for a specific (s, o) is
randomly drawn from the following Fréchet distribution:s,o −θt).
Gs,ot () = exp(−Tt 

We assume that these distributions do not vary by country. Worker heterogeneity characterized by Gs,ot () in this model is related to fundamental complementarity between workers’
skills and sector- and occupation-specific tasks, which is not necessarily different across countries.
Two types of stochastic comparative advantage arise from this probabilistic assumption.
First, between-worker-type comparative advantage is governed by the relative magnitude
T s,o
T s,o
of parameters Tts,o . For example, if st0 ,o0 > st00,o0 holds, then it is more likely that a type t
Tt

Tt0

worker has comparative advantage for sector s and occupation o compared to another worker
of type t0 and for another pair (s0 , o0 ). Second, within-worker-type comparative advantage
depends on the shape parameter θt . If workers’ productivities are more dispersed withina type–i.e., lower θt –, then effects from the within-worker-type comparative advantage will
be stronger than in the case of a larger θt . We further assume that draws of idiosyncratic
productivity for each (s, o) are independent, which gives us the following joint distribution
for a vector of worker productivity  = (1,1 , . . . , s,o , . . . , S,O ):Gt () = exp(−

X

0

0

Tts ,o −θt ).

s0 ,o0This framework for the labor supply side is an important channel which has not been widely
studied in the literature. While changes in trade costs operate as one of the labor demand
shocks along the GVC, workers potentially respond to these shocks differently based on theirown comparative advantage. This Roy channel allows for a more general sorting pattern ofworkers. Instead of assuming an exact one-to-one relationship between workers skills andoccupations, we allow for endogenous matching between skills, sectors, and occupations.2
2

The standard trade model with fixed, homogeneous, factors can be recovered via the following assumptions, which eliminate the Roy channel:
1. θt → ∞ for all worker types. In this case, workers have the same productivity conditional on their
type and their choice of sector and occupation.
2. Each occupation has a corresponding worker type.
3. Tts,o → 0 for every o 6= t and Tts,t = 1 for all s and t.

11

2.2

Equilibrium Sourcing Decision

In the above model, a final producer for ω chooses the entire path of l(ω) = (l1 (ω), . . . , lJ (ω))
by minimizing the total cost of production across all J stages. However, this approach makes
solving the model challenging, because we can no longer take advantage of the convenientcharacteristics of the Fréchet distribution. To deal with this issue, Antràs and de Gortari(hereafter, AG, 2017) introduce two alternative approaches. The first is a “sequential” approach in which each stage j producer chooses an optimal source for the j − 1 stage by
minimizing only its stage-specific production cost. The key assumption that they introduce
is that stage j producers know the exact productivity 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 productivity distribution of upstream producers up to stage j − 2; thus,
they take the expectation of productivity up to stage j − 2 as given when they minimize theproduction cost for stage j. Thus, this is a limited information approach. The second approach is a “lead-firm” approach in which the assumption of a country-stage-specific Fréchet
productivity parameter is replaced by a single Fréchet productivity parameter for an entire
GVC. So, in a world with N countries and J stages, there are N J possible GVCs, each with
its own Fréchet productivity parameter. AG show that these two approaches are equivalentat the equilibrium under the probabilistic assumption of zis,j (ω) as previously described. Ourmodel draws from their result and, hereafter, we apply the sequential approach.
Another key assumption for the sourcing problem of this model is that each stage’s
sourcing decision is independent. Combining this assumption and the assumption of limited
information on upstream productivities, we can derive an analytical solution for the equilibrium GVC probability. We assume perfect competition for final goods and intermediate
inputs, so each country sources from the lowest-cost supplier around the world. Given perunit wages wis,o for each country, sector, and occupation, and a CES price index for final
goods Pi , the unit cost for the input bundle excluding materials from the previous stage is
Q s,o αs β j,oQ s j,o −αs β j,o
s,j
s,j
1−αsi
s −(1−αsi )i i , where ϕi igiven by cs,jis ai ≡ ϕi (Pi )i ≡ (1 − αi )o (wi )o (αi βi )Cobb-Douglas constant.
Whenever stage j materials in country i are shipped to another country n to be used insstage j + 1 production, there is an iceberg trade cost τin≥ 1. Trade costs vary by sector.
ss
We adopt standard assumptions for iceberg trade costs: τiis = 1 and τin≥ τiks τkn
for every
s,i,n, and k. Given these assumptions, stage 2 producers of sector s in country i choose theoptimal source lis,1 (ω) for stage 1 materials of product ω by solving the following problem:cs,1s,2s 1−γ s,2lτlis )1−γ ],
)
]
=
arg
min
[(
lis,1 (ω) = arg min[(ps,1
(ω)τ
li
l
s,1
l
l
zl (ω)
12

Q s,o αs β 1,o
s,1
1−αsi
i i .
where cs,1
i = ϕi (Pi )o (wi )
Before we derive the sourcing decision for stage j + 1 producers, we define the following
expectation variable as introduced by AG using the law of iterated expectations:
s,j
x
s
Θs,j
i (x) ≡ Ej [(pls,j (ω) (ω)τls,j (ω)i ) ]
i

i

=

s,j
(cs,j
)γ
lis,j (ω))x × Θs,j−1(x(1 − γ s,j )) × (τlss,j (ω)i )x ].
Ej [( s,j
lis,j (ω)
izls,j (ω) (ω)
iWe denote the optimal source for stage j materials of sector-s product ω for stage j + 1
producers of sector s in country i by lis,j (ω). Then, this expectation variable Θs,j
i (x) describes
the expected price of stage j materials of sector-s product ω to the power of some constantx, if they are shipped from the optimal source country lis,j (ω) to country i. The sourcing
decision for stage j + 1 producers in country i can be written using this expectation variable.
γ s,j
(cs,j
s,j+1
s,j+1
s,j
l )
li (ω) = arg min{( s,j)1−γ× Θs,j−1((1 − γ s,j+1 )(1 − γ s,j )) × (τlis )1−γ}llzl (ω)

Similarly, final good consumers in country i buy ω from lis,J (ω) which solves
γ s,J
(cs,J
s,J
l )
× Θs,J−1(1 − γ s,J ) × τlis }li (ω) = arg min{ s,Jllzl (ω)

Probability of GVC The probability that stage j + 1 producers of sector s in country isource stage j materials from another country n iss,jPr(lis,j (ω) = n)

γ
(cs,j
s,j+1
n )
s 1−γ s,j+1)1−γ
× Θs,j−1((1 − γ s,j+1 )(1 − γ s,j )) × (τni)
= Pr[( s,jnzn (ω)
s,j

γ
(cs,j
s,j+1
s,j+1
n0 )
)1−γ
× Θs,j−1((1 − γ s,j+1 )(1 − γ s,j )) × (τns0 i )1−γ
].
≤ min
( s,j
n0
n0
zn0 (ω)
s,j

s,j+1

s,j
γ (1−γ)For notational simplicity, we define Bni≡ (cs,j× Θs,j−1((1 − γ s,j+1 )(1 − γ s,j )) ×
n )
n
s,J
s 1−γ s,j+1
γ s,J
s
(τni
)
for each s and j = 1, . . . , J −1, and Bni≡ (cs,J×Θs,J−1(1−γ s,J )×τni. Usingn )n
the Fréchet distribution of product-specific productivity for each stage and each country, theequilibrium probability of the sourcing decision by stage j +1 producers of sector s in country13

i can be written ass,jPr(lis,j (ω) = n)

s,j+1

)
As (B s,j )−ν γ̃ /(1−γ= P n s ni s,j−ν γ̃ s,j /(1−γ s,j+1 )n0 An0 (Bn0 i )for j = 1, . . . , J − 1. Similar to the EK model, this probability is equal to the share of stage
j goods of sector s that are produced in country n and used for stage j + 1 production incountry i.
This GVC probability clearly shows the magnification effect of hierarchical production as
we go downstream. Because γ̃ s,j is increasing in j for a given sector s, the effective elasticity
of bilateral trade flows νγ̃ s,j is increasing in j. Therefore, the effect of changes in trade
costs between two countries is magnified in downstream production compared to upstream
production. As different production stages use occupations with different intensities, thedemand for occupations will depend on this magnification effect. To the extent γ s,j varies
across sectors, the size of the magnification effect will also vary by sector.
Using the GVC probability result and the independence assumption for sourcing decisions, we derive the equilibrium probability of an entire GVC path. The probability that a
final good ω of sector s consumed in country i has followed a specific GVC path l = (l1 , . . . , lJ )isJ−2(ω) = lJ−1 ) × Pr(lls,J−1(ω) = lJ−1 |lls,J−2) × ...
λsl,i = Pr(lis,J (ω) = lJ |lls,J−1JJ
J−1 (ω) = l
1. . . × Pr(lls,12 (ω) = l )QJs,js,j γ s,js(τlsj lj+1 )]−ν γ̃
j=1 Alj [(clj ),= P
QJs,j γ s,jss−ν γ̃ s,j
A
[(c
)
(τ
)]
0
J
0j
0j
0j
0j+1
j=1 l
l ∈N
l
l l

where NJ is the set of all possible sequences of N countries along J stages, and lJ+1 = i and
l0J+1 = i for all l0 6= l ∈ NJ . The derivation of this probability again uses the law of iterated
expectation and characteristics of the Fréchet distribution.
The expression for bilateral trade flows of final goods of sector s from the location of final
assembly n to country i is derived similarly:
Pr(lis,J (ω) = n)s,J −ν
Asn (Bni)= P.
s,J −ν
sn0 An0 (Bn0 i )The exact price index of final goods is also derived in a similar way to EK:
S
Y
Ps s
Pi =
( si )b ,
b
s=1

14

ν + 1 − σ 1/(1−σ))](
where Pis = [Γ(
ν

J
X Y

s,j

s,j

Asl0j [(cs,j)γ (τls0j l0j+1 )]−ν γ̃ )−1/ν .
l0j

(1)

l0 ∈NJ j=1

Again, in this price index, lJ+1 = i and also l0J+1 = i for all l0 6= l ∈ NJ . We assume
σ < ν + 1 so that the gamma function in the price index is well-defined.

2.3

Equilibrium Labor Supply

Workers’ labor supply response à la Roy model is based on Lee (2017). We assume that every
worker inelastically supplies all of their time for working. Hence, the worker’s labor supply
decision is only about allocating that time to a sector, occupation pair. Each worker chooses
a pair of sector s and occupation o to maximize her potential labor income conditional onher (S × O)-dimensional productivity matrix . In other words, worker’s problem can be
written as
max wis,o s,o ,
s,owhere wis,o is per-unit wage for workers in sector s of country i with occupation o. Workers
take the per-unit wages as given. Since  is randomly drawn from a joint Fréchet distribution
Gt (), the equilibrium labor supply decision for workers of type t for sector s and occupationo is
T s,o (ws,o )θts,oπi,t= P t s0 ,o0i s0 ,o0 .
(wi )θts0 ,o0 Tt
The shape parameter θt for type t workers’ productivity distribution is thus the labor supply
elasticity of type t workers at the sector and occupation level. Different worker types areallowed to potentially have different labor supply elasticity in this model. Conditional on
the optimal labor supply decision, the equilibrium average wage of type t workers can bederived as
X s0 ,o0 s0 ,o01
Tt (wi )θt ]1/θt Γ(1 − ).
w̄i,t = [θts0 ,o0If we define worker types based on educational attainment, the relative w̄i,t of high-skilledworkers over low-skilled workers will be a model counterpart of the skill premium, which isone of our core objects of interest in the quantitative exercises.

2.4

General Equilibrium

The equilibrium per-unit wages wis,o and the prices Pis are solved in general equilibriumfrom market clearing conditions for each occupation. We have occupation market clearing

15

conditions for each country, sector, and occupation:
Xs,ow̄i,t πi,tL̄i,t = αis

X

t

j

γ s,j γ̃ s,j βij,o bs

N X
X

X
X (1 − αs0 ) X X
s0 ,o
n
w̄
π
L̄n,t ),
λsl,n (
w̄n,t L̄n,t +
n,t
0
n,t
s
α
n
0
j
o
t
t
s

n=1 l∈Λi(2)where we defineΛji ≡ {l = (l1 , . . . , lJ ) ∈ NJ |lj = i}as the set of GVCs that produce the j-th stage in country i. The left-hand side of theabove occupation market clearing condition is the total labor income earned by workers in
sector s of country i with occupation o. This term should be equal to the right-hand side,which is the total payment for those specific workers. The goods market clearing condition
is embedded in the share of sector s in total income on the right-hand side.
Let us now discuss the components of the right-hand side in more detail. A key part of
the right-hand side is total spending from the countries “purchasing" the goods and services
produced by the particular country-sector-occupation. The spending has two sub-parts,
spending for final use (consumption), and spending for intermediate use. This spending isthen multiplied by a factor related to the roundabout nature of production, which is in turnmultiplied by the probability λsl,n that country i is producing stage j of a GVC that winds up
in the purchasing country. This term is then multiplied by the sectoral consumption share,so we now have total spending on the particular stage and sector, controlling for roundabout
effects. This is then multiplied by the value-added component of this spending, which is the
product of the relevant α, γ, and β terms. Finally, the right-hand side is summed over all
stages of production.
P
To solve the model, we first normalize the wages to satisfy i,s,o wis,o = 1. With thisnormalization, and with the occupation market clearing conditions and the exact price index
as derived above, we can solve the model for the equilibrium wis,o and Pis using the Alvarezand Lucas (2007) algorithm. We first guess initial wis,o and solve for Pis following equation(1). With the initial guess of wis,o and the solved Pis , we calculate all equilibrium variables ofthe model to construct the occupation market clearing conditions (2). We then update wis,oaccording to the excess demand or supply of labor calculated from (2). Iterations continue
until the excess occupational demand or supply is sufficiently close to zero.

2.5

Discussion

The core mechanism of our model is the interaction between country-level comparative advantage (the Ricardian and HO channels) and worker-level comparative advantage (the Roy16channel ) along the GVC. If trade costs change in this economy, the relative demands forcountry i’s intermediate materials and final goods change in all sectors, which, in turn willaffect each country’s specialization pattern across sectors and stages. These changes in specialization patterns, in conjunction with the relative occupation intensity of each production
stage and the sector-specific GVC intensities, induce changes in the relative labor demand for
sectors and occupations. This labor demand change, in turn, affects sector- and occupationspecific per-unit wages. Workers then re-optimize their choice of sector and occupation.
Even though workers observe the same change in wages for each sector and each occupation,
the individual worker’s response will differ depending on his/her idiosyncratic productivity.
We now discuss how particular parameters of the model map into comparative advantage.
For countries, there is comparative advantage at the sector-level and at the stage-level.
Sector-level comparative advantage of countries is based primarily on the relative magnitudeof Asi . Relative factor endowments also shape sector-level comparative advantage of countriess,othrough L̄i,t and Ti,t, because sectors also use different occupations with different intensities
j,o s s,jbased on β αi γ . Note that if both αis and γ s,j are the same across sectors, then sector-levelcomparative advantage of countries is determined only by the Ricardian channel.
A country’s stage-level comparative advantage is driven primarily from the HO channels,othrough the relative endowment governed by L̄i,t and Ti,t, and the occupation intensitiesj,oβ . The Ricardian channel also shapes the stage-level comparative advantage throughthe interaction between Asi and γ s,j . If γ s,j does not vary by sector, then the stage-levelcomparative advantage is determined entirely by the HO force. Therefore, in the mostgeneral case without any restriction on the model parameters, we can have both sector-leveland stage-level comparative advantages, each of which is affected by both the Ricardian andthe HO forces as explained above.
Workers have heterogeneous productivities, Tts,o , at the sector and occupation level; thus,
they have comparative advantage along these two dimensions, as well as between types t.
The combination of L̄i,t and Tts,o determine the effective labor endowment, which links tocountry-level comparative advantage and specialization across sectors and stages. Note that
there is overlap between the Roy and Ricardian channels (primarily at the sector level),and between the Roy and HO channels (primarily at the stage level). When trade costs
decline, the effective labor endowment affects specialization patterns, which in turn affects
the fundamental wages wis,o .
Sector-level specialization has first-order effects on relative wages across sectors, while
stage-level specialization has first-order effects on relative wages across occupations. Thesechanges in sector- and occupation-level wages, in combination with workers’ comparative advantage, represented by the relative magnitudes of Tts,o , lead to changes in the skill premium.
17

We note that stage-level specialization, which occurs only because of the GVC structure of
our model, provides a potentially important margin of changes in the skill premium throughlabor demand shifts at the occupation level owing to the stage-specific occupation intensities.
Also, Lee (2017) shows that workers’ comparative advantage is much more clearly pronounced
across occupations than across sectors. Therefore, the GVC channel of our model captures
an important facet of the Roy mechanism by accounting for countries’ specialization acrossproduction stages.
In order to further study the effect of GVCs, we need to focus on the role of γ s,j . γ s,jcaptures the relative importance of the “roundabout” structure over the “snake” structure.
Because (1 − γ s,j ) denotes the share of stage j − 1 used for production of stage j in sector s,
the sequential structure of production through GVC becomes less important as γ s,j → 1. In
the extreme case where γ s,j = 1 for all j = 1, . . . , J, only stage J production remains active
using only domestic labor inputs and composite intermediates of finished goods through theroundabout structure. Our baseline model would then be equivalent to the multi-sector EK
model with intermediate inputs (but with just one production stage).
As discussed in many papers in the literature including Yi (2003, 2010) and Johnson andNoguera (2012), introducing GVCs into standard trade models can yield magnified effects
of changes in trade costs on aggregate outcomes such as bilateral and aggregate trade flows
and prices. Our result is in line with the implication for the magnification effect from theliterature. As γ s,j → 0, production stages become more inter-dependent, and the effective
trade elasticity νγ̃ s,j becomes larger. Thus, aggregate effects from trade liberalization are
increasingly magnified with GVC intensity.
By contrast, the distributional effect of a reduction in trade costs is not necessarily monotonic in GVC intensity. As γ s,j → 0 in all sectors and stages, the full snake structure occurs.
But, note that the model effectively reduces to just one value-added stage. By definition,
occupational intensity variation across stages disappears. Hence, stage-level comparativeadvantage also disappears. As γ s,j → 1 in all sectors and stages, the difference in occupation
intensity across production stages also becomes irrelevant, because previous-stage materials
have essentially zero demand and thus are essentially unused in downstream stages. Because
the stage-level comparative advantage plays an important role in endogenous changes in theskill premium in conjunction with the Roy channel, as discussed above, a reduction in trade
costs can have small effects on between-worker-type inequality–e.g., the skill premium–, ifa trade model features either the full roundabout structure (γ s,j → 1) or the full snake
structure (γ s,j → 0) in all sectors.
Furthermore, variation in GVC intensity γ s,j across sectors puts different weights on labordemand shifts across sectors and stages. How much of specialization effect across sectors and18

stages translates into wage responses is governed by the contribution of each stage in eachsector. γ s,j accounts for the size of the contribution. We will further discuss interaction of
distributional effects of trade with the GVC intensity using a simple 2-stage version of ourmodel in the next section.

3

A Simple “Two" ModelIn this section, we simplify our baseline model to two countries, sectors, production stages,
occupations, and worker types. We first describe the set up of the simplified model andderive the labor market equilibrium conditions. We then conduct numerical exercises withthis simplified model to convey intuition on the role of GVCs in aggregate and distributional
outcomes.

3.1

Model Setup and Equilibrium

We begin by briefly reviewing the big picture of worker choice, production, and aggregation,and then we set up the simplified model. Each country has an exogenous supply of two types
of workers. Each worker draws a productivity for each sector-occupation pair. Based on the
productivity draw, and the market wages for the sector-occupation pairs, the worker chooses
the sector-occupation that maximizes his/her income. This corresponds to the left part of
Figure 1 below.
Individual goods (in a given sector and country) are produced in two stages. First, a
composite intermediate and the occupational factor inputs are combined to make the stage
1 good. Then, the stage 1 good is combined with a composite intermediate and occupational
factors to make the stage 2 good. The use of the stage 1 good in stage 2 production captures
the GVC part of our model. The production process is illustrated in the boxes in the middleof Figure 1 below.
Finally, the individual goods are aggregated (across sectors) into a composite good, which
is used for final consumption at home and abroad, and also as a composite intermediatein stage 1 and stage 2 production. The flows of the composite intermediate capture theroundabout production part of the model. This is illustrated in the right part of Figure 1
below.
We now describe the worker choice and production of an individual good more formally.
We denote countries by i = 1, 2, sectors by s = 1, 2, production stages by j = 1, 2, worker
types by t = H, L, and occupations by o = 1, 2.

19

20

Type L
workers(# : L̄i,L )Type H
workers(# : L̄i,H )occupationL

occupation
H

Sector 2

occupationL

occupation
H

Sector 1

laborStage 2laborStage 1laborStage 2laborStage 1

imports

stage 1materials

imports

stage 1materials

composite
intermediates

composite
intermediates

composite
intermediates

composite
intermediates

sector 2
final
goods

sector 1
final
goods

Figure 1: A 2-stage GVC Model with Endogenous Labor Supply

foreigncomposite
producers

foreignconsumers

domestic
consumers

The production function varies by country, sector, and stage: fis,j (.). Hence, we denote
the Fréchet productivity of goods as zis,j , the composite intermediate as xs,j
i , the stage 1s,1good used in stage 2 production as mi , and the use of occupational factors 1 and 2 as Ls,j,1i
s,j,2and Li , respectively.
The first and second stage production functions in country i, sector s for a good ω aregiven by:
s

1,1

s

2,H

1,2

s

s,1,1
1−αi
fis,1 (xs,1(ω), Ls,1,2(ω)) = zis,1 (ω)(xs,1((Lis,1,1 (ω))β (Lis,1,2 (ω))β )αii , Li
i
i )
s,2,1
s,2
s,2 1−αifis,2 (xs,2(ω), Ls,2,2(ω), ms,1((Lis,2,1 (ω))β
i , Lii
i (ω)) = zi (ω)[(xi )2,2s(Lis,2,2 (ω))β )αi ]γ

s

s

1−γ
×(ms,1.
i (ω))The relative importance of the composite intermediate, value-added, and the stage 1 goodin production depends on two parameters, αis , and γ s . 1 − αis governs the importance of thecomposite intermediate, i.e., the roundabout structure. 1 − γ s governs the importance of thestage 1 good in stage 2 production. We associate greater GVC intensity with a larger 1 − γ s .
Note that, as with any production function with a roundabout structure, the compositesgood xs,ji can be netted out, and the “effective" value-added of stage 2 is γ . Note that thecoefficient on the occupational factor only varies by stage and occupation: β j,o .
The Fréchet productivity distribution for each country i and sector s is given by:szis,1 (ω) ∼ Fis,1 (z) = exp(−Asi z −ν(1−γ ) )zis,2 (ω) ∼ Fis,2 (z) = exp(−Asi z −ν ).
We continue to maintain the sequential independence and the limited information assumptions of Antràs and de Gortari (2017) that final good consumers in this two-stage setup do
not know the exact productivity draw of stage 1 producers.
For each good ω, stage 2 producers source the lowest cost supplier of stage 1 goods,
and, similarly, final good consumers source the lowest cost suppliers of the stage 2 goods.
Owing to our assumption that productivities are drawn from country- and sector- and stagespecific Fréchet distributions, these sourcing problems imply the following bilateral GVC
probabilities:s −ν(1−γ s )Asn (cs,1s,1n τni )
Pr(li (ω) = n) = P
s,1 s −ν(1−γ s )sn0 An0 (cn0 τn0 i )γ s s s −νAsn ((cs,2s,2n ) Θn τni )Pr(li (ω) = n) = P
s,2 γ s s s −ν .
sn0 An0 ((cn0 ) Θn0 τn0 i )Using the above sourcing probabilities, and the Antràs and de Gortari (2017) assumptions
21

of independence for the stage-specific productivity draws, and of limited information acrossstages, the equilibrium probability that a sector-s product consumed by country i consumers
follows a specific GVC l = (l1 , l2 ) is given by:ss

λsl,i = P

γ s −νs−ν(1−γ )× Asl2 [(cs,2Asl1 (cs,1l 2 ) τl 2 i ]l 1 τl 1 l 2 )

,
s,1 s
s
−ν(1−γ s ) × As [(cs,2 )γ s τ s ]−νl0 ∈N2 Al01 (cl01 τl01 l02 )
l02 i
l02
l02

where N2 = {(l1 , l2 ) : (1, 1), (1, 2), (2, 1), (2, 2)}. The above equation shows that, as in thebaseline model, the effective trade elasticity varies by production stage with (weakly) larger
effective trade elasticities for stage 2 goods than for stage 1 goods.
With two countries, two sectors, and two occupations, there are eight labor market
clearing conditions. For each country i, sector s, and occupation o, the labor market clearing
condition sets the value of wage income earned by the occupational factor – the left-handside – equal to the implicit demand for these occupational services across the two stages,
and across both final goods and intermediate goods – the right-hand side:Xs,ow̄i,t πi,t
L̄i,t

s

= (1 − γ )β1,oαis bs

t

N X
X

X

λsl,n (

n=1 l∈Λ1+γ β

αis bsN X
X
n=1 l∈Λ2iX

λsl,n (

tw̄n,t L̄n,t +

n

αns0

s0

t

i

s 2,o

w̄n,t L̄n,t +X (1 − αs0 ) X XoX (1 − αs0 ) X X
n

s0

αns0

o

0

s ,o
w̄n,t πn,tL̄n,t )t0s ,ow̄n,t πn,tL̄n,t ),twhere Λ1i , Λ2i ∈ N2 are defined as in the baseline model. The key term on the left-hand sides,oof the above equation is πi,t
, which, as a reminder, is the share of type t workers who choose
sector s and occupation o. On the right-hand side, the two terms are the implicit demand for
occupational service o to make stage 1 goods and stage 2 goods, respectively. For each stage,
P
there is the implied occupational demand from final use (the term that includes t w̄n,t L̄n,t ),as well as the implied occupational demand for intermediate use (the term that includes
P (1−αsn0 ) P P
s0 ,o
s0
o
t w̄n,t πn,t L̄n,t )). As in Caliendo and Parro (2015) and de Gortari (2017),
αsn0
this term depends on the exact expenditure from each sector s0 on intermediates, which
requires identification of the exact input-output coefficients between sectors. However, theRoy feature of our model makes that calculation straightforward. All downstream demandcan be characterized as proportional to the payments to the workers in a given sector, whichequals total expenditure in that sector in general equilibrium.
We now discuss the implications of this model for the skill premium and for the role of
the GVC intensity 1 − γ s in propagating declines in trade costs to the skill premium. The
decline in trade costs leads, of course, countries to specialize further in their comparative22

advantage sector and stage. There are at least three sources of comparative advantage:
Heckscher-Ohlin, Ricardian, and Roy.
Owing to our assumption that the occupation intensity coefficients β j,o do not vary by
sector, the textbook Heckscher-Ohlin (HO) channel is not present. However, there are twoother sources of HO forces. The first is that the occupation intensity coefficients vary bystage, so this variation across stages, in conjunction with differences in supplies of the two
types of labor, L̄it , will generate the HO channel. Clearly, without GVCs, in the form ofmulti-stage production, this channel would not exist. The second is that to the extent theroundabout parameter 1−αs , and/or GVC intensity 1−γ s vary across sectors, it will generate
differences in the “effective” factor intensity of the occupations across sectors. This, in turn,generates the classic HO sector-level specialization. Hence, Stolper-Samuelson effects occur,and the question becomes one of magnitude.3
Ricardian comparative advantage also occurs according to relative differences in zis,jacross countries. Under typical circumstances, this type of comparative advantage would
have no effect on the skill premium. However, in conjunction with the Roy feature – type
H workers draw from a different distribution of sector-by-occupation productivities than dotype L workers – Ricardian comparative advantage can impact the skill premium. The sector that a country will have a Ricardian comparative advantage in will draw relatively moreworkers from the type that has relatively higher productivity in that sector. Moreover, theseworkers will choose the occupation for which they have the relatively higher productivity.
Hence, this Ricardian-Roy channel can generate changes in skill premium independent of
the Stolper-Samuelson effect from the HO channel. Finally, the GVC intensity 1 − γ s plays
a role, because it determines how much the sector-level specialization feeds into the demandfor occupations.
The discussion above highlights several channels through which the GVC intensity canaffect the nature of specialization across sectors and stages, and, in turn, affect the skill
premium. Even in this simple model, it should be clear that it is not obvious that there
is a monotonic relationship between higher GVC intensity, i.e., higher 1 − γ s , and a higher
change in the skill premium in one or both countries induced by lower trade barriers. We
provide two examples to illustrate this before we turn to our numerical exercises.
In the first example, the GVC intensity 1 − γ s is the same across both sectors. This rulesout the HO channel at the sector level, but it still exists at the stage level. In addition,
there is still the Ricardo-Roy mechanism at the sector level. Now, let us consider an extreme
In our calibrated model, we allow for occupational intensities to vary by country, i.e., βij,o ; this variationby country, in conjunction with variation across sectors in the GVC intensity, 1−γ s can also generate changes
in skill premia that go in the same direction in both countries.
3

23

case in which γ = 0 or γ = 1, i.e., in which the GVC intensity is maximized or minimized,
respectively. In each case, there is no HO channel at the stage level, because there iseffectively only one stage of production. There is only the Ricardo-Roy channel to affect theskill premium. This suggests the possibility that the effects of declining trade costs on theskill premium may not be monotonic in the GVC intensity, because the less extreme valuesof γ s are associated with two channels for affecting the skill premium, while the extreme
values are associated with just one channel. We explore this case further in the numerical
exercises in the next sub-section, as well as in one of the alternative counterfactuals in themain results section.
In the second example, suppose that a country has a comparative advantage in sector
1 and stage 1. In other words, the distribution of goods productivities and worker productivities favor sector 1, and the production function coefficient β j,o , in conjunction withthe distribution of worker productivities, also favors stage 1. Then, if 1 − γ 1 is as high as
possible, it will maximize the impact on the skill premium, because it ensures that more of
the specialization effect translates into wage responses. We also explore this case further in
the numerical exercises in the next subsection.
The effects of lower trade costs on the skill premia are in sharp contrast with the effects
on aggregate trade, which are increasingly magnified as 1 − γ s increases. When γ s → 0 for
all s = 1, 2, our model has only the pure snake channel of trade in intermediates. Thus, theeffect of a reduction in trade costs on aggregate trade flows has the maximum magnification.
In summary, a simple 2-stage case of our model reiterates the importance of having an
accurate measure of sector-level GVC intensity when we investigate the effect of GVC on
inequality. Even though aggregate effects are monotonically magnified with a larger GVC
intensity, distributional effects of GVC will not necessarily be monotonic in GVC intensity.
In addition, sector-level variation in the GVC intensity is important for the magnitude of
the Ricardian, HO and Roy effects.

3.2

Numerical Exercises

In this section, we solve the “Two" model to provide further intuition. We focus on the HO
comparative advantage channels. In other words, we eliminate the Ricardian comparativeadvantage motive by setting the productivity distribution for goods production equal acrosssectors and countries.
The parameters and exogenous variables of our simple model are set so that country 1
is relatively abundant in type L workers, who have a comparative advantage in sector 1
and occupation 1. Moreover, stage 1 production uses occupation 1 more intensively; hence,24

country 1 has a comparative advantage in stage 1 production, as well. It should be clearthat the HO comparative advantage depends on the interaction of the endogenous labor
supply and worker heterogeneity in productivity (Roy channel) with occupational intensity
variation across stages.4
The particular parameters and exogenous variables are given by: 1) Ricardian comparative advantage parameter Asi = 1 for all i and s; 2) type-level labor supply (L̄1,H , L̄1,L , L̄2,H , L̄2,L ) =(0.3, 0.7, 0.7, 0.3); 3) occupation intensity for each productions stage (β 1,1 , β 1,2 , β 2,1 , β 2,2 ) =( 32 , 31 , 13 , 32 ); 4) the scale parameter of workers’ productivity distribution (TH1,1 , TH1,2 , TH2,1 , TH2,2 ) =(1, 3, 2, 4) and (TL1,1 , TL1,2 , TL2,1 , TL2,2 ) = (4, 2, 3, 1); and 5) γ 1 = 0.3 and γ 2 = 0.7. We set thetrade elasticity (i.e., the part common across the two stages), ν = 4; the elasticity of substitution across products in preferences, σ = 2; and the labor supply elasticity, θt = 2
for all t. Consumers are assumed to have the same expenditure share across sectors– i.e.,b1 = b2 = 0.5, and the roundabout parameter is the same across all sectors and countries–i.e.,
αis = 0.3 for all i and s.
In the exercises below, we compare a high trade cost case to a free trade cost case.
sSpecifically, we compare the case with τin= 2 for i 6= n and τiis = 1 (“high trade costscase”) to a “free trade case” with τin= 1 for all i, n, s. Given trade costs and parametervalues, we solve the occupation market clearing conditions and the exact price indices forthe equilibrium wis,o and Pis following the Alvarez and Lucas (2007) algorithm. In so doing,P
we normalize wages to satisfy i,s,o wis,o = 1. From the solutions for the wages and prices,
we can solve for all the other variables.
We will define the skill premium as the ratio of the average wage of the type H worker
to the average wage of the type L worker: SPi = w̄i,H /w̄i,L . Owing to the importance of
the GVC intensity parameter γ s for both aggregate and distributional effects of reduction intrade costs, we will experiment with different values of γ s and with a sector-level variationin γ s later in this section.
Results
We first discuss the effects of lower trade costs on aggregate prices and thes,opattern of GVCs λsl,i . We then turn to the worker allocation pattern πi,t
and the skill
premium.
A reduction in trade costs enables producers to source intermediates from the lowest cost
supplier and also enables consumers to purchase final goods from the lowest cost producer.
Consequently, not surprisingly, as trade costs fall to zero, the aggregate price index decreases
in each country – by 91% in country 1 and by 89% in country 2.
4

Both sector- and stage-level comparative advantages come from the HO force in this numerical exercise.
Because the model assumes that the occupation intensity does not vary by sector, sector-level HO comparativeadvantage is of second-order.

25

The first two columns of numbers in Table 1 give the prevalence of particular GVCs whens
trade costs τin= 2 for i 6= n. For example, 83.7 percent of the sector 1 GVCs whose finaldestination is country 1 involve both stage 1 and stage 2 made in country 1. Because trade
costs are high, both countries source stage 1 materials and final goods primarily domestically.
The next two columns show the prevalence of particular GVCs when trade costs are uniformly
reduced to zero, i.e., τin = 1 for all i and n. Now, there is more specialization according tocomparative advantage. For example, the particular GVC mentioned above represents only
26.4 percent of all the sector 1 GVCs whose final destination is country 1. By contrast, a“vertical specialization” GVC, such as one in which stage 1 is made in country 1 and stage
2 is made in country 2, rises in prevalence from 0.08 percent under high trade costs to 26.5
under free trade (for final consumers of sector 1 goods in country 1).

Table 1: Changes in λsl,i from the Benchmark Simulations=2(1) τins=1(2) τin(3) change (pp)l2 = 1 l2 = 2 l2 = 1 l2 = 2 l2 = 1
λ1l,1
λ2l,1
λ1l,2
λ2l,2

l2 = 2l1 = 1

0.837

0.008

0.264

0.265

-57

26

l1 = 2

0.108

0.048

0.235

0.236

13

19

l1 = 1

0.644

0.021

0.236

0.265

-41

24

l1 = 2

0.286

0.049

0.235

0.264

-5

22

l1 = 1

0.056

0.129

0.264

0.265

21

14

l1 = 2

0.007

0.808

0.235

0.236

23

-57

l1 = 1

0.034

0.284

0.236

0.265

20

-2

l1 = 2

0.015

0.666

0.235

0.264

22

-40

These results mirror those in Yi (2003, 2010). One additional point to highlight is thatwhen trade costs fall, domestic sourcing (l1 , l2 ) = (1, 1)) falls by more in sector 1 than insector 2. This is because γ 1 = 0.3 < γ 2 = 0.7; in other words, stage 1 goods are more
important in stage 2 production in sector 1, which implies the effective trade elasticity ishigher in sector 1.
Table 2 shows the within-type labor allocation pattern predicted by our simple model.
The table shows that regardless of trade costs, workers are more likely to work in theircomparative advantage sector and occupation. Also, even though each worker type has
a comparative advantage in a particular sector and occupation, owing to heterogeneity in26

productivity within each type, the within-type labor allocation does not involve complete
specialization. For example, about 8.1% of type H workers in country 1 work in sector 1
in occupation 1, even though type H workers have on average a comparative advantage insector 2 and occupation 2.

s,oTable 2: Changes in πi,tfrom the Benchmark Simulations=2(1) τins,oπi,tCountry 1, Type H

Country 1, Type L

Country 2, Type H

Country 2, Type Ls=1(2) τin(3) change (pp)o=1 o=2 o=1 o=2 o=1

o=2

s=1

0.081

0.255

0.084

0.261

0.3

0.6

s=2

0.138

0.526

0.138

0.516

0.02

-0.9

s=1

0.391

0.204

0.398

0.205

0.8

0.1

s=2

0.248

0.157

0.244

0.152

-0.4

-0.5

s=1

0.157

0.249

0.152

0.244

-0.5

-0.4

s=2

0.204

0.390

0.205

0.398

0.08

0.8

s=1

0.524

0.138

0.516

0.138

-0.8

-0.02

s=2

0.256

0.081

0.261

0.084

0.5

0.3

When trade costs fall, and specialization according to comparative advantage increases,
workers of both types move between sectors accordingly. For example, because country 1
has a comparative advantage in sector 1, both type H and L workers in country 1 shift tosector 1, and similarly in country 2. In addition, workers choose different occupations when
they move between sectors. This pattern depends on worker-level comparative advantage
for occupations. For example, while some of both type H and L workers in country 1 movefrom sector 2 to sector 1, type H workers in occupation 2 increase by 0.6 percentage points,
and type H workers in occupation 1 increase by 0.3 percentage points within sector 1. Bycontrast, type L workers of country 1 in occupation 1 increase by 0.8 percentage points, andthose type workers in occupation 2 increase by 0.1 percentage points, in sector 1.
To summarize, in response to the reduction in trade costs, the Roy channel of our model
reallocates workers across sectors and occupations within their type. Workers may stay inthe same sector, but move to a different occupation, an outcome not present in standard
trade models with homogeneous workers. This endogenous labor supply reallocation mirrors
what is in Lee (2017). However, what is different here is the importance of stage-level specialization. Owing to our choice of parameters – identical factor intensities and distribution27

of productivities across sectors – in the absence of two stages of production, and the different
GVC intensity (1 − γ s ) across sectors, there would be no Roy channel impacting the HO
mechanism. The GVCs provide additional propagation mechanisms for Roy and HO.
The reduction in trade costs changes the skill premium in the direction predicted by the
Stolper-Samuelson theorem. As a reminder, country 1 is abundant in type L workers, whohave a comparative advantage in occupation 1, which is used more intensively by stage 1
and sector 1. Therefore, as trade costs go down, the relative demand for type L workers
increases in country 1 and decreases in country 2. The opposite is true for type H workers.
Hence, our model implies that as trade costs decline, the skill premium increases by 1.1% incountry 2, and decreases by 1.1% in country 1. This numerical exercise is set up to highlightthe Stolper-Samuelson effect through the GVC. As we have mentioned above, our generalmodel allows for non-Stolper-Samuelson effects.
Two Exercises to Highlight The Role of GVC Intensity The key parameter of our
two-stage model that governs the relative importance of the GVC is 1 − γ s for each sectors = 1, 2. The effective GVC intensity, as well as the effective trade elasticity, decreases in γ s .
In the extreme case of γ s = 1, the effective trade elasticity for stage 1 is zero. This mightsuggest that the γ s = 0 generates the strongest GVC effect. It does for aggregate trade, but
not for the skill premium, as we will see below.
To illustrate the role of the 1 − γ s , we repeat the exercise of a reduction in trade costswith different values of γ s . We continue to assume that γ 1 < γ 2 , which means that in sector
1, stage 1 plays a more important role in stage 2 production. We conduct two exercises. In
the first exercise, we assume γ 2 ≡ γ and γ 1 = γ − 0.4 to have the same difference betweenγ 1 and γ 2 as in the baseline simulation. Then, we vary γ from 0.4 to one to assess how the
distributional effects of a decline in trade costs are affected by the GVC intensity. In thesecond exercise, we set γ 2 = 0.5, i.e., the average of the two γ’s in the baseline simulation,2and vary γ 1 within [ γ2 , γ 2 ] to investigate the effect of sectoral variation in γ s .
Figure 2 shows for each sector, the changes in the two GVCs involving domestic sourcing
for both stages of production. Notice first that the y-axis on all four graphs contains negative numbers signifying that when trade costs decline, the prevalence of domestic sourcing
declines. The key point of the figure is that as we move from right to left in each panel, theextent of the decline in domestic sourcing increases. In other words, as the GVC intensity,and the effective trade elasticity, increase, the substitution of GVCs involving trade and vertical specialization for the domestic sourcing GVCs increases. The multi-stage production
and intermediate trade through GVCs magnify the effect of the reduction in trade costs,
and the magnification effect is monotonically increasing in the GVC intensity. Changes ofall other aggregate variables from the model, such as the price index and other elements of28

λsl,i matrices are also monotonic in 1 − γ.

Figure 2: Changes in λs(1,1),1 and λs(2,2),2 with Different Values of γ (%)(a) λ1(1,1),1(b) λ2(1,1),1

-44

-20

-46
-25

for l=(1,1)

for l=(1,1)

-48
-50

l1

-30

-35

2

-54

Changes inChanges in

1

l1

-52

-56
-58

-40

-45

-60
-50
-62
-64
0.4

0.5

0.6

0.7

0.8

0.9

-55
0.4

1

0.5

0.6

2

0.7

0.8

0.9

1

0.9

1

2

(c) λ1(2,2),2(d) λ2(2,2),2

-44

-20

-46

for l=(2,2)

-50

-30

-35

2

-54

Changes in

1

Changes in

l2

-52

l2

for l=(2,2)

-25
-48

-56
-58

-40

-45

-60
-50
-62
-64
0.4

0.5

0.6

0.7

0.8

0.9

-55
0.4

1

2

0.5

0.6

0.7

0.8

2

The distributional effect of a reduction in trade costs, on the other hand, is not monotonic
in the GVC intensity. Figure 3 shows the change in the skill premium in each country when
trade costs are reduced under different values of γ with γ 2 ≡ γ and γ 1 = γ − 0.4. While theskill premium decreases in country 1 and increases in country 2 for all values of γ, the figure
clearly shows the magnitude of the change in the skill premium (resulting from the reduction
in trade costs) is not monotonic in the GVC intensity – rather, it is largest at intermediate
values of average γ s .
This result illustrates the importance of comparative advantage across stages in generating large skill premia effects from reductions in trade costs. When the GVC intensity takes
extreme values, i.e., at least one of the sectoral γ s approaches 0 or 1, then, at least one of
the sectors effectively has only one stage of production. By reducing the effective number ofstages, we will get smaller effects on the skill premium. Put differently, workers have fewer
opportunities to sort into the sectors and stages that provide the best fit, which reduces the29variation in wages across worker types.
We offer an additional interpretation. It is not the GVC intensity, 1 − γ s , per se, that is
crucial, but rather, the presence of multi-stage production, with its additional opportunities
for specialization, that can lead to larger skill premia effects from reduced trade costs. When
the GVC intensity is maximized, it ironically eliminates multi-stage production, which thenreduces skill premia.

Figure 3: Changes in the Skill Premium with Different Values of γ (%)(b) Country 2

-0.75

1.1

-0.8

1.05

Changes in the skill premium (%)

Changes in the skill premium (%)(a) Country 1

-0.85
-0.9
-0.95
-1
-1.05

0.95
0.9
0.85
0.8
0.75

-1.1
-1.15
0.4

1

0.5

0.6

0.7

0.8

0.9

0.7
0.4

1

2

0.5

0.6

0.7

0.8

0.9

1

2

Our results also suggest that GVCs transfer country-level comparative advantages toworker-level comparative advantages by putting different value-added weights on different
production stages in different sectors. This mechanism makes the distributional impactof trade shocks non-monotonic in GVC intensities. Therefore, we should expect sectoralvariation in the GVC intensity to play an important role. In our first exercise, the differencein γ s between sector 1 and sector 2 was fixed.
To further explore the importance of sectoral variation in γ s , in our second exercise,
we set γ 2 = 0.5 and explore different ratios γ 1 /γ 2 ∈ [0.5, 1]. Sector 1 depends relatively
more on stage 1 (for stage 2 production) as in the baseline simulation. As γ 1 gets smaller,
we put larger relative weights on each country’s comparative advantage sector and stage
combination, because our baseline parameter values assume that country 1 (country 2) has
a comparative advantage in sector 1 and stage 1 (sector 2 and stage 2.) Figure 4 showsthat the size of increase (decrease) of the skill premium in country 2 (country 1) is larger
when γ 1 and γ 2 are further apart (geometrically.) In our model, sectoral variation in the
GVC intensity governs how much country-level comparative advantage is transmitted into
worker-level comparative advantage by putting different weights on each sector and each30

stage. Equivalently, it affects how much trade shocks affect relative gains among different
types of workers. As long as the relative magnitude of the GVC intensity does not reverse
the HO comparative advantage, i.e., γ 1 < γ 2 , the effect of a decline in trade costs on skill
premia is larger the larger the weights on their comparative advantage stages.

Figure 4: Changes in the Skill Premium with Different Values of γ (%)(b) Country 2

-0.55

0.85

-0.6

0.8

Changes in the skill premium (%)

Changes in the skill premium (%)(a) Country 1

-0.65

-0.7

-0.75

-0.8

-0.85

-0.9
0.5

0.6

0.7

0.8
1

/

0.9

0.75

0.7

0.65

0.6

0.55

0.5
0.5

1

2

0.6

0.7

0.8
1

/

0.9

1

2

In summary, the results from our numerical exercises show how the GVC mechanism
and the Roy mechanism interact with standard HO comparative advantage. As trade costs
decline, countries specialize in their comparative advantage production stage, which shifts
relative labor demand for occupations in our model. Second, depending on different GVC
intensities across sectors, sector-level labor demand is also affected. Third, the Roy mechanism makes workers respond to trade shocks differently across sectors and occupations, eventhough workers are exposed to the same trade shock. Fourth, as predicted in existing papers in the literature, aggregate effects of reduction in trade costs on trade flows and prices
are monotonically increasing in the GVC intensity. Lastly, the distributional effects of the
reduction in trade costs are not monotonic in the GVC intensity. The effects on the skill
premium are larger, when both sector- and stage-level comparative advantages operate withintermediate GVC intensity values. In addition, the skill premium changes more when GVCs
put larger weights on each country’s comparative advantage sector and stage combination.

4

Calibration

Our numerical exercise above shows the basic mechanism of our model in a simple two-stage
case with only two countries, two worker types, two occupations, and two sectors. We now
31calibrate the general version of our model to data. Our goal is to assess the role of GVCs
as a propagation mechanism transmitting global integration shocks, such as China joining
the WTO, for aggregate trade outcomes, as well as distributional outcomes, such as the skill
premia. In particular, our focus is on the role of sectoral variation in the GVC intensity.

4.1

Countries, Worker Types, Occupations, and Production Stages

We calibrate the model to three countries–China, U.S.A, and a constructed rest of the world(ROW) for the year 2000, the year before China joined the WTO. Workers are classified by
T = 5 types, defined by educational attainment: 1) high school dropouts; 2) high school
graduates; 3) workers with some college education; 4) college graduates; and 5) workers
with advanced degrees. When we calculate the skill premium, we define skilled workers
as those who have at least some college education. We define five occupation categories(O = 5) following Dorn (2009): 1) low-skilled service occupations and agricultural workers;2) assemblers and machine operators; 3) precision production and crafts occupations; 4) administrative, clerical, and sales occupations; and 5) managers, professionals, and technicians.
This categorization is based on both skill levels required by occupation and the routinenessof occupation.
In addition, we use the World Input-Output Database (WIOD) for 2000. We reduce the
WIOD tables for that year into one with China, U.S.A, and the rest-of-the-world, and withfour sectors (S = 4): agriculture, mining, manufacturing, and services. AG and de Gortari(2017) show how to map the GVC concepts into input-output flows. We will do this fromour framework with two stages of production. In AG, the number of stages that fit theirdata the best is J = 2. Accordingly, we calibrate our model with two production stages,
J = 2.5

4.2

Assigned Parameters or Exogenous Variables

We assign ν = 4 from Simonovska and Waugh (2014) for the common stage-invariant partof trade elasticity. Conditional on the assigned value of ν, we calibrate bilateral trade
costs for each country pair and each sector using bilateral trade flows of final goods in the
WIOD 2000. Type-level labor supply (L̄i,t ) is obtained from Barro and Lee (2013), and thesector expenditure share bs is calibrated to exactly match the sector expenditure share in
the WIOD. We set σ = 2 for the elasticity of substitution between within-sector productvarieties. Finally, we jointly calibrate the sector-specific GVC intensity γ s , the value-added5

In a more general version of calibration, J can be also jointly calibrated with other parameters of themodel.

32

share αis , Ricardian productivities Asi , and country- and stage-specific occupation intensity
βij,o . We now turn to the details of calibrating the bilateral trade costs, the parameters related
to worker productivity (i.e., the Roy parameters), and the production function parameters.

4.3

Calibration of Bilateral Trade Costs

Our model delivers a mapping from the GVC probability λsl,n to bilateral trade flows ofgoods. Similarly to AG, trade flows of final goods from country i to country n are definedPby λ̃F,sλsl,n , where ΛJi is a set of all GVC paths which perform the final production
in =
l∈ΛJ
i
stage in country i. We obtain the data counterparts to these bilateral trade flows from the
WIOD. In order to use λ̃F,sin from the WIOD to calibrate bilateral trade costs, we impose two
identifying assumptions. First, there is no trade cost for domestic transactions–i.e., τiis = 1ssfor every i and s. Second, bilateral trade costs are symmetric–i.e., τin= τni
for every (i, n)and s.
Using the expression of λsl,n from the model, the common trade elasticity ν, and theses
two identifying assumptions, we can back out bilateral trade costs τinby following the Headand Ries (2001) method:1
λ̃F,s λ̃F,sni − 2νsτin= [ in]F,s F,sλ̃ii λ̃nn
Table 3 summarizes calibrated trade costs for each country-pair and sector. Not surprisingly,
bilateral trade costs are lowest in the manufacturing sector and highest in the service sector
on average. We will use these trade costs to calibrate other parameters of the model fromthe 2000 WIOD.

s
Table 3: Calibrated τinCountry pair

Agriculture

MiningManufacturing

Service

China - U.S.

5.9

5.3

2.6

7.8

China - ROW

2.7

1.9

2.1

1.8

U.S.- ROW

3.0

3.7

2.9

3.0

33

4.4

Estimation of the Roy Parameters

We estimate the Roy parameters, Tts,o and θt , using the U.S. American Community Survey(ACS) for 2000 following the estimation method in Lee (2017). Workers draw sector- andoccupation-specific idiosyncratic productivities from a Fréchet distribution Gs,ot () as definedin Section 2. Different worker types have different productivity distributions. The scaleparameter Tts,o governs the level of worker type t’s average productivity for sector s andoccupation o. The shape parameter θt is inversely related to within-type heterogeneityof productivity. Using the independence assumption between productivity draws and thecharacteristics of Fréchet distribution, we can derive the distribution of the equilibrium
observed wage w̃ for each worker type t6 :X s0 ,o0 s0 ,o0G∗t (w̃) = exp{−[
Tt (wi )θt ]w̃−θt }.
s0 ,o0We use hourly wage profiles and individual’s educational attainment in the U.S. ACS 2000
data to estimate the parameters of G∗t (w̃) for each worker type t. We jointly estimatePs0 ,o0s0 ,o0 θt) and θt using the maximum likelihood.
(wus
s0 ,o0 TtP
0 0s,os0 ,o0 θt
The estimated s0 ,o0 Tts ,o (wus) , the labor allocation πus,tfrom the U.S. ACS 2000,s,os,oand the expression for πus,t from our model pin down individual Tt ’s up to a normalization.
Similarly to Hsieh et al. (2013), we normalize the scale parameter of high school dropouts,
i.e., T1s,o = 1 for all (s, o). Then, we back out Tts,o for t 6= 1. This normalization does notaffect worker-level comparative advantage, because we compare ratios, not levels, of Tts,o toshape worker-level comparative advantage.

Table 4: ML Estimates of θtHigh School
Dropouts

High School
Graduates

Some College
Education

College
Graduates

Advanced
Degrees

θ̂t

1.972

1.862

1.735

1.603

1.480

S.E.

(0.0043)(0.0055)(0.0057)(0.0015)(0.0005)

Table 4 reports the estimates of θt and standard errors. The estimates show that bettereducated workers have more dispersed productivity distributions within their type. Because
The observed wage w̃ is different from per-unit wage wis,o . Wages we observe in data are not wis,o but w̃
which takes both per-unit wage and worker productivity into account.
634

θt is also the shape parameter of the distribution of equilibrium observed wages, this result
also suggests that the wage distribution of high-skilled workers is more dispersed than thatof low-skilled workers. This feature can be easily confirmed with individual wage profiles
data as documented by Lee (2017).

Table 5: Sector- and Occupation-level Averages of Estimated Tts,o(a) Sector-level Average
Agriculture

MiningManufacturing

ServiceHigh school graduates

0.91

1.67

1.83

1.85

Some College Education

0.91

1.11

1.99

2.57

College Graduates

0.87

1.30

3.67

4.85

Advanced Degrees

0.77

0.70

2.72

5.91

(b) Occupation-level Average
Low-skill
Service
Jobs

Assemblers
MachineOperators

Precision
Production
Crafters

Admin
ClerksSales

Managers
Prof TechniciansHigh school graduates

0.90

0.84

1.32

2.31

2.47

Some College Education

0.47

0.34

0.94

2.23

4.24

College Graduates

0.18

0.12

0.44

1.60

11.03

Advanced Degrees

0.08

0.05

0.14

0.48

11.88

Table 5 summarizes the estimates of Tts,o for each type except for high school dropouts
whose Tts,o ’s are normalized to one. Worker-level comparative advantage is clearly identified
across both sectors and occupations. While all worker types are more productive in absoluteterms when they are in the service sector than in the agriculture sector, better-educatedworkers have a comparative advantage in the service sector. On the other hand, low-skilledworkers have a comparative advantage in agriculture and mining sectors. Worker-level comparative advantage is much more clearly pronounced across occupations. While the average
estimates of Tts,o range from 0.898 to 2.466 across five occupations for high school graduates,
the average Tts,o of workers with advanced degrees for managerial and professional occupations is about 152 times larger than their average for low-skill service jobs. In other words,
better educated workers have a much larger advantage for having high-skilled occupations
35

than for being in the service sector. In addition, the relative magnitudes of Tts,o show that,for better educated workers, having high-skilled occupations is much more beneficial if they
are in the service sector than in other sectors.
The estimated θt and Tts,o shape worker-level comparative advantage within and acrosstypes, which is the Roy channel in our model. Because workers have different productivities
across sectors and occupations, the same trade shocks can generate different sector- andoccupation-level responses among workers, as we showed in the previous section. In addition,
the relative magnitude of Tts,o , along with the type-level labor supply L̄i,t , Tts,o , affects theeffective occupation-level labor endowment, which shapes the Heckscher-Ohlin comparativeadvantage across sectors and production stages.

4.5

Calibration of the Production Parameters

After we calibrate the trade costs, the common trade elasticity, the type-level labor supply,
the Roy parameters, and the demand parameters, we calibrate the remaining production
side parameters, γ s , αis , Asi , and βij,o for the year 2000. Calibration of the first three sets ofparameters follows the approach in AG by targeting similar sets of moments. Because ourmodel has multiple sectors, we target sector-specific moments. Each set of targeted moments
discussed below can be linked to each parameter. However, the relationship between targeted
moments and parameters is not one-to-one, of course. All of the calibrated parameters arejointly related to all of the targeted moments through the general equilibrium.
First, we calibrate the expressions for domestic absorption of final goods and intermediate
goods from the corresponding WIOD 2000 data. The model expression for bilateral tradeflows of final goods is λ̃F,sin as derived above. Intermediate trade flows can be a part of theroundabout structure or a part of the GVC structure. We denote bilateral trade flows of2,sintermediate goods from each structure by λ̃1,sik for the roundabout structure and λ̃ik for the
GVC structure. The model expressions of these two variables are:
F,s s
λ̃1,s
ik = λ̃ik b

X 1 − α s0 X X
k

s0

λ̃2,s
ik =

J−1
X
j=1

γ̃

s,j

XX
n

l∈Λjikλsl,n bs [

X

0
αks

o

w̄n,t L̄n,t +t

X 1 − α s0 X X
n

s0

s0

t

0

s ,o
w̄k,t πk,t
L̄k,t

αn

o

0

s ,o
w̄n,t πn,tL̄n,t ],twhere Λjik ≡ {l = (l1 , . . . , lJ ) ∈ NJ |lj = i and lj+1 = k} is a set of all GVC paths thatcross country i at stage j and country k at stage j + 1. Taking both roundabout andGVC production structures into account, bilateral trade flows of intermediate goods between36λ̃1,s +λ̃2,sik
ik
country i and country k in our model are given by λ̃I,sik = P [λ̃1,s +λ̃2,s ] . As in AG, the diagonal
i0

i0 k

i0 k

I,s
s
entries of λ̃F,sin and λ̃ik matrices help identify the GVC intensity γ . Unlike in AG, wealso exploit sector-level variation in domestic absorption to obtain the sector-specific GVC
intensity.
The WIOD also reports value-added and gross output in each industry and each country.
We aggregate the tables to three countries and four sectors. We then compute the ratioof value-added to gross output in each sector and each country. We use this moment tohelp calibrate the country- and sector-specific value-added shares αis . We also calibrate theRicardian productivity parameters Asi by targeting the share of GDP of each sector and eachcountry in total world GDP.
The occupation intensity βij,o at each production stage in each country is identified fromI,sa combination of the diagonal entries of the λ̃F,sin and λ̃ik matrices, the share of value-added
to gross output, and the share of wage payment to a particular occupation within eachsector in each country. This last moment is obtained from the ILOSTAT database from theInternational Labor Organization (ILO.)
Summarizing, we jointly calibrate γ s , αis , Asi , and βij,o to match as closely as possible
the model moments to their data counterparts. Table A1 and Table A2 in the Appendix
report the calibration results for γ s , αis , Asi , and βij,o for the year 2000. The model-generated
moments fit the targeted moments reasonably well. The correlation between these two sets ofmoments is 0.82. Our model fits the diagonal entries of final and intermediate goods matrices
and GDP shares the best; the correlation between these targeted moments and the modelgenerated moments is about 0.9. Our model also fits several non-targeted moments well.
For example, the correlation coefficients between the model-predicted off-diagonal entries ofI,sthe λ̃F,sin and λ̃ik matrices and their data counterparts range from 0.82 to 0.88.
We highlight several features of our calibrated parameters. First, there is variation in γ sacross sectors. The range is from 0.12 for agriculture to 0.5 for mining, with 0.4 and 0.48 formanufacturing and services, respectively. As a reminder, lower values of γ s imply a greater
share of stage-two production is coming from the stage-one good. For example, agriculture
stage-two production depends greatly on its stage-one input.
Second, the calibrated value-added shares αis vary a great deal across countries and sectors
with a mean of 0.50 with a standard deviation of 0.22. Third, the Ricardian productivity
parameters Asi suggest that China has a comparative advantage in the manufacturing sector,
and the U.S. has a comparative advantage in the services sector. This Ricardian comparativeadvantage will shape the sector-level specialization patterns, while the endowment-based
comparative advantage from the Roy channel will mainly determine stage-level specialization
pattern.

37

Fourth, the calibrated occupation intensities βij,o indicate that a production stage has
different interpretations across countries in terms of occupation intensity. In relative terms,
stage one uses high-skilled occupations more intensively in the U.S., but the same stage
uses less-skilled occupations more intensively in China. If the United States specializes instage 1 and China specializes in stage 2 following a trade liberalization, this pattern in βij,owill be consistent with the skill upgrading story of Feenstra and Hanson (1995), Zhu andTrefler (2005), and Costinot and Vogel (2010). This is one implication of our model that goesbeyond that of Lee (2017). In addition, in our model, with its explicit vertical production
structure, occupation intensities carry different weights based on the GVC intensity for eachsector. In previous research on offshoring without a vertical production structure, factor
intensities essentially carry the same weight in the entire value chain. From the lens of our
GVC structure, the calibrated γ s shows that the condition of the same weight across stages
is not satisfied. In other words, the role of occupation intensity is more or less important
across stages and sectors depending on the magnitude of γ s . We will further discuss thismechanism in the next section.

5

Counterfactuals

Based on the calibrated and estimated parameters from Section 4, we perform counterfactual
exercises in order to quantitatively assess the aggregate and distributional impacts of tradeliberalization. We solve the model with bilateral trade costs and other model parameters
calibrated to the year 2000. We then introduce exogenous changes in bilateral trade costs tothe model. The main counterfactual scenario we look at is a 50% decline in trade costs for
China-U.S.A. and China-ROW. The goal of this counterfactual is to quantitatively assess theaggregate and distributional effects of China’s integration into world economy in an explicit
GVC setting.
This shock is especially relevant for our paper, because since China joined the WTO in
2001, it has had an enormous impact on the global economy, and, as part of that impact,
it has heavily specialized in global value chains. Our model should capture the multiple
facets in which the China shock affects labor demand and labor supply in different countries
through sector- and stage-level specialization, interaction between country- and worker-levelcomparative advantages, and the relative GVC intensity across sectors.
Another form of the China shock studied in recent research is an increase in China’s
productivity–e.g., Autor et al. (2013). In our model, this would show up as an exogenous
increase in AsCHN . However, we focus only on the effect of a decline in trade costs with
China in this paper, because trade costs have a direct relationship with the effective trade38

elasticity, which relies on our main GVC mechanism. Lee (2017) introduces both types ofChina shocks separately and shows that the quantitative magnitude of distributional effects
is much larger from the trade-cost-related China shock.
We then study the role of our GVC channel in explaining distributional effects of the
China shock by running alternative counterfactuals where the GVC channel does not operate
or magnifies country-level comparative advantage. Our main counterfactual results are also
robust to alternative values of the elasticity of substitution (σ) or the common part of the
trade elasticity (ν).
We note that all of the results presented below are quantitative, not qualitative. They
depend on the general equilibrium interaction of all the mechanisms we have discussed in
our paper, with the specific magnitude of each mechanism dictated by the calibrated valuesof the parameters.

5.1

Baseline Counterfactual Results

In our baseline counterfactual exercise, we use our model calibrated to the year 2000 andthen reduce the trade costs involving China. We first show the impact on the goods specialization patterns, and then we turn to the distributional impacts. Our primary measure of
distributional impact will be the skill premium, which we defined earlier in the data as thewage premium of workers who have at least some college education over workers without any
college education. The model counterpart of the skill premium is w̄i,H /w̄i,L , where worker
types H and L are defined as they are in the data.
Figure 5 shows the implied changes in the prevalence of domestic sourcing λs(i,i),i . The
figure shows that all three countries, and especially China and the ROW, are less likely tosource both production stages from domestic producers. Of the four sectors, the manufacturing sector has the largest decline in the prevalence of domestic sourcing in all countries;
the declines range from -37 percentage points (pp) to -56 pp. This result is related to thefact that China has a comparative advantage in the manufacturing sector and also to therelatively high GVC intensity–lower γ s –in the manufacturing sector. The magnification of
aggregate outcomes, including the aggregate effective trade elasticity, is larger in the sector
with a higher GVC intensity.

The counterfactual also implies that the likelihood of domestic sourcing in the service
sector increases slightly– 0.52 pp –in the United States. Based on the calibrated Ricardian
productivity Asi , the United States has a comparative advantage in the services sector. When
China’s trade costs are lowered, there are two offsetting effects on the U.S. services sector.
39

Changes in likelihood of domestic sourcing (pp)Figure 5: Counterfactual Changes in the Prevalence of Domestic Sourcing λs(i,i),i
10
0
-10
-20
-30
-40
-50
-60
China
Agriculture

USA
MiningROW
Manufacturing

ServiceFirst, the lower trade barriers will mean that China can start producing and exporting thedownstream part of services to the U.S., which reduces the prevalence of sourcing both stages
domestically. Second, China’s specialization in manufacturing facilitates the U.S. specializing
more in both stages of services.
To illustrate the importance of stage-level specialization in response to the decline in trade
costs, Table 6 shows for each country-sector pair the percentage change in stage 1 output asa share of total output across both stages. The table shows that China specializes in stage
2 in all sectors and the United States specializes in stage 1 in all sectors, but agriculture.
The small increase in the stage 1 output share in the U.S. service sector (compared to othersectors) is related to the result for domestic sourcing in Figure 5. The U.S. comparativeadvantage in the service sector dominates its comparative disadvantage in stage 2, whichmakes it more likely to source both stages of the service sector from itself.

Table 6: Counterfactual Changes in the Share of Stage 1 within Sectors (%)
Agriculture

MiningManufacturing

Service

China

-10.9

-94.3

-57.4

-91.4

USA

-5.0

13.7

19.5

2.2

ROW

-43.8

15.8

-8.6

19.9

The changing sector- and stage-level specialization patterns change the relative demand
for labor and finally change the skill premium. Our model implies that decline in China’s
40

trade costs leads to an increase the skill premium in all three countries, China, U.S., andROW, by 0.25%, 0.94%, and 1.09%, respectively. This parallel increase in skill premia isconsistent with the previously mentioned skill upgrading story in the literature.
The increase in the U.S. is driven by sector-level and stage-level specialization forces,
both of which go in the same direction. The U.S. has a comparative advantage in the service
sector. Moreover, highly educated workers in the U.S. have a comparative advantage in theservices sector. Hence, the sector level channel leads to an increase in the skill premium. The
U.S. also has a comparative advantage in stage 1 production. Stage 1 production in the U.S.
is high-skilled occupation intensive; moreover, higher educated workers have a comparativeadvantage in high-skilled occupations. Hence, the stage-level channel also leads to an increasein the skill premium.
The increase in the skill premium in China reflects two offsetting forces. At the sector
level, China has a comparative advantage in manufacturing. Less educated workers in China
have a comparative advantage in the manufacturing sector. Hence, the sector level leads toa decrease in the skill premium in China. On the other hand, at the stage level, China has
a comparative advantage in stage 2 production. Stage 2 production in China is high-skilledoccupation intensive; moreover, higher educated workers have a comparative advantage inhigh-skilled occupations. Hence, the stage level channel leads to an increase in the skill
premium. The skill upgrading story in the literature holds through stage-level specialization
introduced by our GVC structure. Overall, our model predicts that the stage-level specialization dominates the sector level specialization, leading to an increase in China’s skill
premium.
In addition, the magnitude of the skill premium change should depend on the exact levelof the GVC intensity, because our calibration results for γ s show that sectors differ in GVC
intensity. Therefore, how strongly the skill upgrading story holds under the context of GVC
depends on how much each sector depends on GVCs.
According to our calibrated model, the U.S. has a comparative advantage in stage 1
and in the service sector. However, compared to agriculture and manufacturing sectors, theservice sector is where stage 1 has relatively lower weight. Therefore, the increase of theskill premium is limited in magnitude in the U.S. Similarly, because γ s is relatively small inthe manufacturing sector, where China has a comparative advantage, the fact that stage 2
uses high-skilled occupations more intensively does not drive up the labor demand for better
educated workers very much. This limits the increase in China’s skill premium. The actual
GVC structure calibrated to the data translates only a part of specialization effects into
wage responses, thus it limits the magnitude of distributional effects of the China shock.
In order to better understand the role of our GVC structure, we run the same coun41

terfactual exercise with γ s = 0.999 for all s.7 This extreme case shuts down the GVC
channel because all value-added comes from stage 2. In this case, there is only sector-levelcomparative advantage through the Ricardian channel, and better educated workers havea comparative advantage in the service sector through the Roy channel. In this exercise,
our model implies that the skill premium increases by 0.17% in the U.S., and it decreases
by 1.16% in China. This result highlights the importance of the GVC as a transmission
mechanism increasing the skill premium in both countries.
Combining our calibration results with the counterfactual results, we conclude that in
the absence of the GVC channel, the skill upgrading in both China and the U.S. could notoccur. Both countries specialize in relatively high-skilled-occupation-intensive production
stages through GVCs, and therefore, the skill premium increases in both countries. However,conditional on the GVCs, our calibrated values of the GVC intensity show that there is lower
intensity, or weight, on each country’s comparative advantage stage and sector combination.
This limits the magnitude of the increases in the skill premium for both countries. If there
was a larger weight on each country’s comparative advantage sector and stage combination,then the GVC effect on the skill premium would be even larger. We discuss this alternative
case in the next subsection.
Our model also shows the labor reallocation patterns within each worker type in responseto the China trade integration shock. Figure 6 shows the labor reallocation across sectors
and occupations for high school dropouts and workers with advanced degrees in the U.S.
and China. Each country’s comparative advantage across sectors is a major factor that
determines workers’ reallocation across sectors. In the U.S., both worker types are likely tomove to the service sector. In China, both types tend to reallocate into the manufacturingsector. While sector-level reallocation is similar between worker types, different worker types
tend to choose different occupations even when they are moving into the same sector. This
occupation-level labor reallocation is determined by the relative magnitude of Tts,o acrossoccupations. For example, in the U.S., even though both worker types are likely to moveinto the service sector, low-skilled workers are going there for low-skill service occupations,while better educated workers are much more likely to have managerial and professional
occupations in the service sector. Lastly, our model predicts more reallocation within lesseducated worker types, which is related to their larger labor allocation elasticity θt from ourestimation.
7

We keep the calibrated values for the other parameters the same without re-calibrating the model tofocus only on the mechanism. Results from the re-calibrated model are discussed in the next section, Section
5.2.

42

Figure 6: Within-worker-type Reallocation of Labor(a) China, high school dropouts(b) China, advanced degrees
4

2

3

Changes in employment share (pp)Changes in employment share (pp)

1.5
1
0.5
0
-0.5
-1
-1.5
-2
-2.5

Low-skill services
Assemblers
Production/Crafters
Admin/Clerk/SalesManagers/Prof/Tech

1
0
-1
-2
-3
-4

-3
Agriculture

MiningManufacturing

Agriculture

Services(c) U.S.A, high school dropouts

MiningManufacturing

Services(d) U.S.A, advanced degrees

3

2

1.5

2

Changes in employment share (pp)Changes in employment share (pp)

2

1

0

-1

-2

1

0.5

0

-0.5

-1

-3

-1.5
Agriculture

MiningManufacturing

Services

Agriculture

MiningManufacturing

Services

We conduct sensitivity analysis with respect to two key elasticities, the elasticity of substitution (σ) and the common part of the trade elasticity (ν.) We first run the same counterfactual with σ = 1 (Cobb-Douglas) and σ = 4, respectively.8 The skill premium increases
in both China and the U.S. with these alternative parameter values, and the magnitudes
are very similar to the baseline result–0.34% and 0.16% for China, and 0.94% and 0.94% for
the U.S., respectively. We then run the counterfactual with ν = 5.5 and ν = 8.28 (EK),
respectively. The signs again remain unchanged, but the skill premium increases more withthese alternative common trade elasticities which are larger than the baseline value ν = 4.
The skill premium increases by 2.04% and 3.62% in China and by 1.42% and 2.10% in the8

For these exercises, we did not recalibrate the other parameters.

43

U.S. for each ν = 5.5 and ν = 8.28. Overall, we conclude that varying these two elasticities
does not change the results by much.

5.2

Alternative Counterfactuals with Different GVC Intensities

In order to investigate the role of the GVC intensities on the distributional impacts of the
China shock, we run the same counterfactual exercise (50% decline in bilateral trade costswith China) with alternative values of γ s . We conduct two alternative counterfactuals.
In the first alternative counterfactual, we put extreme weights on each country’s comparative advantage sector and stage. We set γ s = 1 for the manufacturing sector and γ s = 0 for
the service sector. This puts the maximum weight on stage two for manufacturing, which is
China’s comparative advantage, and the maximum weight on stage 1 for the services sector,
which is the U.S. comparative advantage. We set γ s = 0.5 for the remaining two sectors, sothat both stages are equally important in those sectors. We keep the values of the occupation intensity βij,o from our baseline calibration. Given these values, we then re-calibrate theRicardian productivity Asi and the value-added share αis .9
In response to the China trade integration shock, the skill premium in China and the
U.S. increase, as before. However, the magnitude of the increase is almost twice as high as in
the baseline exercise – 0.58% increase in China and 1.47% increase for the U.S. This result
suggests that if GVC intensities are weighted towards each country’s comparative advantage
sector and stage, then changes in labor demand based on the relative occupation intensity
will be larger. And these larger changes in labor demand will translate into larger wagechanges, especially for the highly educated workers in both countries, and ultimately largerchanges in the skill premia. Our result mirrors our second simulation of the simple 25 case.
In the simulation, when we put larger weights on each country’s comparative advantage
sector and stage (by varying the gap between γ s across two sectors), the effect of decline intrade costs on the skill premium is larger.
In the second alternative counterfactual exercise, we consider the case where the GVC
channel is shut down by setting γ s = 0.999 for all sectors s. In the previous subsection, we
studied this alternative specification without re-calibrating the model. Now, we re-calibrate
the Ricardian productivity Asi and the value-added share αis (and keep the values of βij,o fromthe baseline calibration). All value-added comes only from stage 2 production, country-levelcomparative advantage is defined only across sectors based on the relative magnitude of Asi .
Hence, when the China integration shock occurs, China specializes in the manufacturingsector, and the U.S. specializes in the service sector. Because occupation intensities vary by
9

We re-calibrated these parameters to match the same set of moments as in the baseline calibration.

44

stage, not by sector, the sector-level specialization changes the fundamental wage variable
wis,o primarily across sectors. The Roy channel of our model shows that better-educatedworkers have a comparative advantage in the service sector. Therefore, increased labordemand in the service sector in the U.S. increases the skill premium in the U.S. (+0.02%.)
In contrast, higher labor demand in the manufacturing sector of China decreases the skill
premium in China (-0.39%,) without the GVC channel.
The key role of of the GVC channel in our model is that each country’s specialization in
relatively high-skilled production operates through GVCs. If the GVC mechanism does notoperate, the skill upgrading argument in the literature does not hold. The skill premium in
the U.S. still increases in response to the China shock even in the no-GVC counterfactual but
by a much smaller amount, because GVCs add one more layer of country-level comparativeadvantage across production stages based on stage-specific occupation intensities.
In summary, two alternative counterfactual exercises show that the GVC channel makes
the skill upgrading mechanism work by making each country specialize in production stages
that are relatively intensive in high-skilled occupations. Given that the GVC channel isoperative, the actual GVC intensity governs how much of the specialization effect translates
into changes in relative wages. The baseline and alternative counterfactuals show that theskill premium in each country responds more the greater the value-added in each country’s
comparative advantage sector originating from its comparative advantage stage.

6

Conclusion

The increasing prevalence of vertical specialization through global value chains has attracted
a lot of attention in the literature. However, the role of GVCs as a propagating mechanismof distributional impacts of trade shocks has been surprisingly understudied. In this paper,
we provide new insight on the effect of GVCs on aggregate outcomes, such as trade flows
and prices, and more importantly, on the skill premium, by introducing a new quantitative
general equilibrium model of GVCs with Ricardian and Heckscher-Ohlin motives for trade,
and with Roy heterogeneous worker mechanisms.
Our model shows how country-level comparative advantage and worker-level comparative advantage interacts with each other through GVCs. When trade shocks are transmitted
through GVCs, countries specialize in sectors and stages where they have a comparativeadvantage. Different sectors depend differently on each production stage, and different production stages have different occupation intensities. Therefore, the effect on relative labordemand varies by sector and occupation. Workers respond to this change in labor demand byreallocating their labor based on their own comparative advantage in sector and occupation.
45

We calibrate our model to the U.S., China, and the rest of the world in 2000, and study
the effect of a decline in trade costs with China, to capture China’s entry into the WTO.
The trade shock leads each country to specialize in stages where high-skilled occupations
are used more intensively. As a consequence, the relative demand for high-skilled occupations for which high-skilled workers have a comparative advantage increases in all countries.
Therefore, the skill premium increases everywhere. The skill upgrading argument in the
trade literature operates in our model through GVCs.
The GVC channel governs the direction of changes in the skill premium, and also its
magnitude. Our model shows that the sector-specific GVC intensity determines how muchof the specialization effect from trade liberalization translates into relative wage responses.
Our calibrated model shows that each country’s comparative advantage sector and stage infact has a relatively small contribution to the entire value chain, and therefore the increasein the skill premium from the trade shock is not large.
Our model can serve as a good toolkit to quantify the distributional impacts of changes
in trade environment through global value chains. While our model features a rich interaction between country-level comparative advantage, worker-level comparative advantage,and global value chains, it does not have varying length of value chains across sectors or amore general sectoral input-output linkage structure for the composite intermediate good.
We leave these two features for future research.

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50

A

Tables and Figures

Table A1: Calibrated γ s , αis , and Asi for the Year 2000(a) GVC Intensity, γ sγsAgriculture

MiningManufacturing

Service

0.12130.50070.39990.4475(b) Roundabout Intensity, αis
Agriculture

MiningManufacturing

ServiceChina0.28930.51400.37470.5405

U.S.A.

0.23470.27880.3847

0.4668ROW

10.82720.59000.5001(c) Ricardian Productivity, Asi
Agriculture

MiningManufacturing

ServiceChina36.74866.96894.98263.733

U.S.A.

44.03152

51.938162.62

ROW

74.875150.38199.97100

51

Table A2: Calibrated βij,o for the Year 2000(a) China
Low-skill
Service
Jobs

Assemblers
MachineOperators

Precision
Production
Crafters

Admin
ClerksSales

Managers
Professionals
TechniciansStage 10.42710.13910.13900.15490.1389

Stage 20.29690.28710.12503.27E-170.2900(b) U.S.A.
Low-skill
Service
Jobs

Assemblers
MachineOperators

Precision
Production
Crafters

Admin
ClerksSales

Managers
Professionals
TechniciansStage 1

0.55810.07030.03510.05050.2851

Stage 20.62501.53E-06

0.06250.31301.53E-06(c) ROW
Low-skill
Service
Jobs

Assemblers
MachineOperators

Precision
Production
Crafters

Admin
ClerksSales

Managers
Professionals
TechniciansStage 10.8398

1.53E-06

1.53E-06

0.1602

1.53E-06

Stage 2

5.55E-170.27880.1332

1.91E-04

0.588952