HIAS-E-76

Fragmentation and Gains from Trade
Edwin L.-C. LAI(a) and Han (Steﬀan) QI(b)(a) Department of Economics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon,
Hong Kong(b) Department of Economics, Hong Kong Baptist University, Kowloon Tong, Kowloon, Hong Kong

October, 2018

Hitotsubashi Institute for Advanced Study, Hitotsubashi University
2-1, Naka, Kunitachi, Tokyo 186-8601, Japan
tel:+81 42 580 8604
http://hias.ad.hit-u.ac.jp/
HIAS discussion papers can be downloaded without charge from:http://hdl.handle.net/10086/27202
https://ideas.repec.org/s/hit/hiasdp.html

All rights reserved.

Fragmentation and Gains from TradeEdwin L.-C. LAI†andHan (Stean) QI‡

This draft: 22 October 2018

Abstract
In this paper, we estimate the competitiveness of countries in intermediate goods and in
ﬁnal goods. We ﬁnd that China’s competitiveness in both intermediate goods and ﬁnal goods
increased exceptionally rapidly during 1995-2011. We also ﬁnd that the gains from trade ofcountries with strong comparative advantage in ﬁnal goods can be substantially under-estimatedif we do not separately take into account trade ﬂows in intermediate goods and ﬁnal goods. We
also ﬁnd that, during 1995-2011, the average increase in gains from intermediate goods tradeacross all countries in our sample is distinctly higher than the average increase in gains fromﬁnal goods trade. This suggests that gains from trade due to international fragmentation of
production is becoming more important over time relative to gains from trade in ﬁnal goods.

JEL Classiﬁcation codes: F10, F11, F14, F17
Keywords: fragmentation, gains in trade, global value chain, global sourcing,W

We would like to thank Samuel Kortum, Jonathan Eaton, Fernando Parro, Zhi Wang and participants in HKUSTInternational Economics Conference 2017, Seminar at Fudan University, Shanghai in 2017, SAET Annual Conference
2018 (Taipei), Asia-Paciﬁc Trade Seminars 2018 (Hong Kong) for their helpful comments.
†
CESifo Research Network Fellow. Department of Economics, Hong Kong University of Science and Technology,
Clear Water Bay, Kowloon, Hong Kong. Phone: (852) 2358-7611; Fax: (852) 2358-2084; Email: elai@ust.hk or
edwin.l.lai@gmail.com‡
Department of Economics, Hong Kong Baptist University, Kowloon Tong, Kowloon, Hong Kong. Email: steffan@hkbu.edu.hk

0Fragmentation and Gains from Trade1

Introduction

Production of goods is increasingly fragmented internationally. The intermediate goods used in the
production of a ﬁnal good in a country are often carried out in dierent countries. This phenomenon
is variously termed fragmentation, vertical specialization, global sourcing, and so on. This has been
documented and analyzed extensively in the literature, including the notable work of Hummels,
Ishii and Yi (2001), Baldwin and Venables (2013), Costinot, Vogel and Wang (2013), Grossman
and Rossi-Hansberg (2008), Johnson and Noguera (2012), Kee and Tang (2016), Koopman, Wang
& Wei (2014), Antras and Gortari (2017), to name just a few. One implication of this phenomenon
is that trade in intermediate goods accounts for a larger and larger fraction of total trade in theworld. Therefore, in order to better understand the comparative advantage of countries and moreaccurately calculate their gains from trade, we must estimate the competitiveness of each country
in intermediate goods and ﬁnal goods separately as well as calculate the market share of homesupplied intermediate goods and ﬁnal goods separately. The tradable intermediate goods (TIG)
model is a convenient short cut to approximately account for trade ﬂows in intermediate goods
as part of total trade ﬂows. However, it does not separately make use of the data of trade ﬂows
in intermediate goods and ﬁnal goods. The TIG model assumes that, in any given market, acountry’s market share in ﬁnal goods is the same as its market share in intermediate goods. Thus,a country’s competitiveness in ﬁnal goods is the same as that in intermediate goods. However,
the existence of countries that serve as major assembly centers / export platforms that importintermediate goods for ﬁnal assembly and export ﬁnal goods to the rest of the world means that acountry’s competitiveness in exporting intermediate goods can be signiﬁcantly dierent from thatin exporting ﬁnal goods. Therefore, in any given market, a country’s market share in ﬁnal goods
can be substantially dierent from its market share in intermediate goods. Figure 1, which plots
the market share of home-supplied intermediate goods and services of country n ( qq ) against
the market share of home-supplied ﬁnal goods in n (e qq ), illustrate the above point clearly.1 For
eqq  0=91, while for Great Britain,  qq  0=68 and 
eqq  0=48.
example, for China,  qq  0=61 and  qq across countries justiﬁes our investigation into the above issues.2
Such large variation in  qq @e?Figure 1 is about hereA

Arkolakis, Costinot and Rodriguez-Claire (2012) (hereinafter ACR) develop a formula that
relates the gains from trade of a country to the expenditure share of home-supplied goods. The
paper does not deal with the distinction between trade in intermediate goods and trade in ﬁnal
goods until the “Tradable Intermediate Goods Extension” section of the paper, where they adopt
1
2

Throughout this paper, “intermediate goods and services” are also called “intermediate goods” for short.
The data for Figure 1 are derived from the TiVA data set as described in Appendix A.

1

Figure 1:  qq : Home share in intermediate goods (y-axis) vs. 
eqq : Home share in ﬁnal goods (x-axis) as of 2011

the TIG approach to address the issue of intermediate goods trade. As we explained above, one
shortcoming of the TIG approach is that the market share of home-supplied intermediate goods
is assumed to be the same as that for ﬁnal goods, which is not true in general. In this paper, we
modify ACR’s formula and make use of the data of home market shares in intermediate goods andﬁnal goods separately for calculating the overall gains from trade. Using our approach, the gains
from trade in intermediate goods and ﬁnal goods can be computed separately.
In this paper, we modify the TIG model of Eaton and Kortum (2002) (hereinafter referred
to as the TIG model) and derive gravity equations for trade in intermediate goods and trade in
ﬁnal goods separately. Although the gravity equations in this paper are derived from the approachof Eaton and Kortum (2002) (hereinafter referred to as EK), they can be micro-founded by amore general model. As shown in Head and Mayer (2014), the gravity equation can be microfounded from demand-side derivation, e.g. Armington (1969), or from supply-side derivation, e.g.
EK or Chaney (2008) based on the Melitz (2003) approach. We also verify the generality of thegravity equations in this paper by deriving them from an alternative model (Armington) shown in
Online Appendix G.1. Based on these gravity equations, we estimate countries’ competitiveness2

in intermediate goods and in ﬁnal goods. The levels of competitiveness of countries are estimatedusing the ﬁxed-eect approach popularized by EK instead of the non-linear least squares estimation
approach of Anderson and van Wincoop (2003). As argued in Head and Mayer (2014), the ﬁxedeect approach gives a consistent estimation of the general structural gravity equation, yet it has
the advantage of imposing less structure in the estimation process.
We then go on to calculate the gains from trade of countries based on an equation that explicitly
accounts for gains from trade in intermediate goods and in ﬁnal goods separately. We then compare
our gains from trade results with those obtained by using the TIG model, which does not accountfor trade in intermediate and ﬁnal goods separately. We ﬁnd that, across countries, the ratio ofdomestic market share in ﬁnal goods (e qq ) to that of intermediate goods ( qq ) is signiﬁcantly andpositively correlated with the ratio of competitiveness in ﬁnal goods to that of intermediate goods.
We argue that the countries with high 
eqq @ qq ratios have comparative advantage in ﬁnal goods

versus intermediate goods. This dimension of comparative advantage has not been captured by
the TIG approach. It turns out that this dimension of comparative advantage is closely tied towhere a country is positioned on the global value chain. As explained above, we ﬁnd that a country
that has comparative advantage in ﬁnal goods tends to have a higher import penetration rate inintermediate goods relative to that in ﬁnal goods. This further implies that it gains relatively
more from trade in intermediate goods than trade in ﬁnal goods. Most interestingly, its total gains
from trade can be substantially under-estimated had we not separately accounted for these twocomponents of gains from trade. The intuition for this result is that the structure of manufacturing
production dictates that the gains from trade in intermediate goods are substantially larger thanthose from trade in ﬁnal goods even for the same import penetration rate in both types of goods.
The reason is as follows. The cost share of intermediate goods in manufacturing production (ofboth intermediate and ﬁnal goods) is greater than 2/3 in most countries (which implies that thecost share of value-added is less than 1/3 in most countries). This implies that intermediate goods
are very important in producing both intermediate and ﬁnal goods. This in turn implies that thegains from trade in intermediate goods contributes substantially more than gains from trade in
ﬁnal goods to the overall gains from trade even if the import penetration rate in the two types ofgoods are the same.
Those countries that have strong comparative advantage in ﬁnal goods gain signiﬁcantly morefrom trade than other countries as they actively participate in the global value chain by importing alarge share of intermediate goods (thus having high import penetration rate in intermediate goods),
and then add factor inputs to produce ﬁnal goods, which are mostly exported. They typically havemuch lower import penetration rates in ﬁnal goods. One policy implication of this ﬁnding is thatremoving barriers to trade in intermediate goods contributes more to welfare than that in ﬁnal
goods, as for the same increase in import penetration rate for intermediate and ﬁnal goods, thepercentage increase in gains from trade generated from liberalization of intermediate goods trade3

is on average more than twice that from ﬁnal goods trade. A real world example is the large
volume of intermediate goods imported by China that helped to produce ﬁnal goods cheaply bothfor domestic consumption and exporting (to pay for the imported intermediate goods). This helped
to provide manufacturing employments and lift the living standards of tens of millions of Chinese
citizens, signifying large gains from trade.
Our ﬁndings indicate that understanding this dimension of comparative advantage is very important in understanding the large gains from trade of many less developed countries that participate
actively in the global value chain. It turns out that a large fraction of the gains from trade ofthese countries is attributed to trade in intermediate goods. The TIG approach tends to seriously
underestimate the gains from trade of these countries, as explained above. In sum, we ﬁnd that thedegree of under-estimation of the gains from trade of a country by the TIG model increases withthe strength of comparative advantage of the country in ﬁnal goods versus intermediate goods.
We also ﬁnd that, during 1995-2011, the average increase in gains from intermediate goods tradeacross all countries in our sample is distinctly higher than the average increase in gains from ﬁnal
goods trade. This suggests that gains from trade due to international fragmentation of production
are becoming more important over time relative to gains from trade in ﬁnal goods.
We begin our analysis with a one-sector model, on which sections 2, 3 and 4 are based. To
check the robustness of our results, we carry out an extension based on a multi-sector setting withinter-sectoral input-output linkage. This extension is motivated in part by Costinot and RodriguezClare (2014) and Caliendo and Parro (2015), both of whom calculate gains from trade based on amulti-sector setting with input-output linkage. We ﬁnd that the most important results based on
the one-sector setting are robust to the multi-sector extension.
We are not the ﬁrst paper to estimate separate gravity equations for intermediate goods tradeand ﬁnal goods trade. One notable work is Baldwin and Taglioni (2013), who estimate tradeelasticities for intermediate and ﬁnal goods separately. But they are inconclusive about whether
the two elasticities are signiﬁcantly dierent. In this paper, we run the gravity regressions in orderto establish that a country’s competitiveness in ﬁnal goods is in general dierent from that inintermediate goods. We ﬁnd that when a country has higher competitiveness in ﬁnal goods relative
to that in intermediate goods, it tends to have higher gains from trade in intermediate goods
relative to that in ﬁnal goods, and higher overall gains from trade. Concerning the geography of
the “upstreamness” of a country in the global value chain, Antras and Gortari (2017) predict that
more centrally-located countries tend to produce goods with lower average “upstreamness”. In
this paper, stronger comparative advantage in ﬁnal goods versus intermediate goods means greater
specialization in the downstream (ﬁnal) goods as opposed to the upstream (intermediate) goods,
implying lower average “upstreamness”. However, unlike Antras and Gortari (2017), we do not havea theory about the origin of this comparative advantage. ACR adopt the TIG approach to address

4the issue of intermediate goods trade in a later section of their paper. In this paper, we show that,in order to more accurately calculate the gains from trade, the formula has to be modiﬁed to makeuse of data on both home market shares in intermediate goods and in ﬁnal goods if these data are
available.
In Section 2, we present our model of fragmentation. In Section 3, we derive the gravity
equations for trade in intermediate goods and trade in ﬁnal goods based on our model. Estimatingthese equations yields the competitiveness of each country in intermediate goods and ﬁnal goodsin each year. We discuss the rapid rise in competitiveness of China in both intermediate goods
and ﬁnal goods during 1995-2011 and explain the underlying causes. In Section 4, we calculate thegains from trade of each country as of 2011, and the change in gains from trade during 1995-2011,by separately making use of data on home market shares in intermediate goods and ﬁnal goods ineach country. In section 5, we carry out a multi-sector extension of the one-sector model used in
sections 2, 3 and 4. Section 6 concludes.

2

A Model of Fragmentation

In this section, we describe a model of production and trade of intermediate goods and ﬁnal goods
by extending the Ricardian model of EK. We use this model to derive and estimate two gravity
equations. The gravity equations obtained, and the main results of this paper, however, are notdependent on this speciﬁc model. They can be derived from a more general model. In Online
Appendix G.1, we describe how the same gravity equations can be obtained by an alternative
approach, thus verifying the generality of the gravity equations that we estimate in the main bodyof this paper.
The Setting. There are Q countries in the world, indexed by q = 1> ===> Q . Country q haslabor endowment Oq , which serves as the only primary input in production of all kinds of goods.
Labor is fully mobile across sectors within the same country, but not mobile across countries. Labor
wage in country q is denoted by zq . The production of an intermediate or ﬁnal good requires theconversion from a composite input called an input bundle, which is a combination of labor andthe entire set of intermediate goods (which is called an composite intermediate good). There are
multiple varieties of ﬁnal goods and multiple varieties of intermediate goods. We assume that all
countries have the capability to produce all varieties of intermediate goods and all varieties of ﬁnal
goods. All goods are tradeable but there are trade costs.
A typical country imports intermediate goods from all over the world (including itself), then
combines the entire set of intermediate goods with domestic labor to form input bundles, and thenproduces either intermediate goods or ﬁnal goods from the input bundles. The goods are thenexported to destinations all over the world. In equilibrium, all countries export some intermediate5

goods and some ﬁnal goods to all other countries and to themselves. Markets for both intermediate
and ﬁnal goods are assumed to be perfectly competitive.
Whenever an intermediate or ﬁnal good is shipped from country q to country p, an iceberg
trade cost  pq is incurred. That is,  pq A 1 units of good are shipped from the origin for one unit
to arrive at the destination. We assume  qq = 1 for all q.
Preferences. In each country a representative household maximizes utility by choosing a consumption bundle of ﬁnal goods, indexed in the interval [0, 1], subject to the budget constraint. The
utility function of the representative household in country n is given by½Z 1 hi ¾
e q (l) gl
ln T
Xq = exp(1)0eq (l) is the consumption of ﬁnal good of variety i by the representative household in country
where Tn.

Technology and Comparative Advantage. For each country, each ﬁnal good or intermediate
good is converted from the input bundle, but the e!ciency of conversion for each variety of goodis stochastic. Denote the e!ciency of country o in converting the input bundle into a ﬁnal goodof variety l 5 [0> 1] by ]eo (l), and denote the e!ciency for converting the input bundle into anintermediate good of variety m 5 [0> 1] by ]o (m). The production function of an input bundle incountry q is given by:|q = (Pq )13 q (oq ) q , where 0 ?  q ? 1,

(2)

where |q is the quantity of input bundle produced in country q; Pq is the corresponding quantityof the composite intermediate good (which is deﬁned in equation (3) below); oq is the corresponding
labor input.
Due to perfect competition, ﬁrms in country q will import the intermediate good of variety jwith the lowest competitive price in q across all sources. The quantity of composite intermediate
good produced by q is determined by the following function:½Z 1¾
ln [Tq (m)] gm ,Pq = exp(3)0

where Tq (m) is the quantity of intermediate good of variety j used by country q.
We follow EK by assuming that ]o (m) follows the Fréchet distribution, with the cumulative
density function given by
Pr[]o (m) ? }] = h3[Wo ]}3

;m 5 [0> 1]

where Wo is country o’s technology stock for producing intermediate goods and 1@ is positively
related to the variance of the distribution of ]o (m) ;m 5 [0> 1]. When  is smaller, there is more roomfor gains from trade due to dierences in comparative advantage across varieties of intermediate6

goods among countries. The parameter Wo reﬂects country o’s absolute advantage in producing
intermediate goods, which can be viewed as a summary measure of the (broadly deﬁned) technology
stock of country o for the production of intermediate goods, e.g. technology embodied in machines,
human capital, infrastructure, how well-developed is the domestic supply network, etc.
Following this, the competitive price of intermediate good of variety j exported from o to q is
given bysqo (m) =
where

fo
 qo
]o (m)¶13 o µ ¶ o
So
zo
fo =
(4)
1  oois the unit cost of an input bundle corresponding to equation (2), with So being the unit price ofµthe composite intermediate good, the production function of which is given by equation (3). It canbe easily shown that
Sq = (
where
q 

31
q)  >(5)PQ

3
p=1 Wp (fp  qp )is deﬁned as country q’s global access to intermediate goods.3
It is straightforward to show that the market share of intermediate goods imported from country
o in country q is given by qo =Wo (fo  qo )3=q

Go ( qo )3
Gq + Iq

(6)

ih
i
h
where Go  Wo (fo )3 = Wo · ( o )13 o (zo )3 o  (1   o )13 o ( o ) o is deﬁned as country o’s comP
petitiveness in supplying intermediate goods, and Iq  p6=q Gp ( qp )3 is deﬁned as country
q’s access to foreign intermediate goods. Thus, the competitiveness of a country in intermediate

goods can be high because of three factors: low wage, large technology stock for the production ofintermediate goods, or favorable access to foreign intermediate goods. Note that the set of unit costs
of input bundles {fo } and set of unit prices of composite intermediate goods {So } for o = 1> 2> ===Q

are interrelated throughequations (4) and (5). When the set of trade-costs-adjusted technology¯
3 ¯
stocks { Wp ( op ) ¯ o> p = 1> ===> Q } and set of labor costs { zp | p = 1> ===> Q } are known, we cansolve for the { fo | o = 1> ===> Q } and { So | o = 1> ===> Q } from the sets of equations given by (4) and(5).

eo (l) follows the Fréchet distribution, with the cumulative density function
We assume that ]given by3heo (l) ? }] = h3[Wo ]}
Pr[]

3h


;l 5 [0> 1]

Here we assume the elasticity of substitution between each pair of varieties of intermediate goods to be equal

to one (the Cobb-Douglas case). If we assume a constant elasticity of substitution 0 6= 1 instead, we will have thel 1 0k 1
01(xq )3  instead, as shown on p.1749 of EK. The same logic applies to ﬁnal goods.
Sq = K +137

where Weo is country o’s technology stock for producing ﬁnal goods and 1@e is positively related toethe variance of the distribution of ]o (l) ;l 5 [0> 1]. Again, the parameter Weo reﬂects country o’s

absolute advantage in producing ﬁnal goods, e.g. technology embodied in machines, human capital,
infrastructure, how well-developed is the domestic supply network, etc.

The competitive price of ﬁnal good of variety i that can potentially be exported from o to q is
given byseqo (l) =where fo is given in (4).

fo

 ,eo (l) qo]

Similar to (6), the market share of ﬁnal goods imported from country o in country q is given byhe o ( qo )3hWeo (fo  qo )3
G

eqo =
=
e q + Ieq
fq
G

(7)

PQ f
3h

where fq 
is deﬁned as country n’s global access to ﬁnal goods, Ieq 
p=1 Wp (fp  qp )P
h3eis deﬁned as country q’s access to foreign ﬁnal goods, and
p6=q Gp ( qp )hihihfo  Weo (fo )3h = Weo · ( o )13 o (zo )3 oh (1   o )13 o ( o ) o is deﬁned as the competitivenessGof country o in supplying ﬁnal goods. Sinceo = Go + Io , a country is more competitive in ﬁnal

goods because of four factors: it has large technology stock for production of ﬁnal goods, large
technology stock for production of intermediate goods (as Wo raises Go , which in turn raiseso ),low wage or favorable access to foreign intermediate goods.
It can be easily shown that the exact price index of the entire set of ﬁnal goods as indicated in
the utility function (1) is given by³ ´31@h.
Seq = fq

(8)

Let us deﬁne country o’s strength of comparative advantage in ﬁnal goods versus intermediate
fo @Go if  = e
. Thus, if  is approximately equal to e
, thengoods as Weo @Wo . Note that Weo @Wo = G

fo @Go . Therefore, if country o has stronger comparative advantage
Weo @Wo is approximately equal to G
fo @Go .
in ﬁnal goods versus intermediate goods, it also has larger G

3

Empirical Estimation

In this section, we use the data of global trade in both intermediate goods and ﬁnal goods from theunderlying inter-country input-output (ICIO) tables used in the construction of the Trade in Value
Added (TiVA) data set to carry out estimation of the gravity equations for trade in intermediate
goods and trade in ﬁnal goods respectively. The data set is described in Appendix A.

8

3.1

Gravity Equation for trade in Intermediate Goods

One of our goals is to estimate the competitiveness of a country in exporting ﬁnal goods and thatin exporting intermediate goods. To do that, we turn to the gravity equation. The total value ofintermediate goods exported from o to q is given by[qo =  qo [q;q> o = 1> ===> Q(9)where [q is country n’s total expenditure on intermediate goods. Equations (6) and (9) imply that
[qo
 qo
Go 3
=
=

[qq
 qq
Gq qo
¶
µ
[qo
= ln Go  ln Gq   ln  qo
=,
ln
(10)
[qq
which we call the gravity equation for trade in intermediate goods. The parameter ln Go is estimatedas the coe!cient for the indicator variable which takes on a value of 1 if country o is an exporting
country and -1 if country o is an importing country and zero otherwise. To be consistent with themodel, in the rest of the paper, whenever we estimate the competitiveness of countries based on
country ﬁxed eects, we impose the restriction that the importer ﬁxed eect when a country is an
importer is equal to the exporter ﬁxed eect when the country is an exporter. We also impose theP
restriction that Q
q=1 ln Gq = 0 so that the estimated competitiveness of each country is relative
to the mean of all countries.4 In estimating equation (10), we proxy the bilateral trade cost byln  qo = gn + e + o + Ohjdo + FX + Fro + pq ,(11)

a combination of commonly used bilateral trade cost measurements, including distance gn , sharedborder e, shared language o, shared legal system Ohjdo, shared currency FX , historical colonial
linkage Fro, and the overall destination ﬁxed eect pq . Here, as in EK, gn is the distance eect
between q and o lying in the nth interval, with the six intervals being [0, 375); [375, 750); [750,1500); [1500 3000); [3000, 6000); and [6000, maximum) miles. The choice of the other right handside variables is based on Head, Mayer and Ries (2010).
We then estimate Equation (10) using aggregated data for intermediate goods (from sixteen
2-digit manufacturing sectors) and services (from sixteen 2-digit service sectors) that are used to
produce goods in the sixteen 2-digit manufacturing sectors, for each of the following seven years:
1995, 2000, 2005 and 2008-2011. These sectors are listed in Appendix A. Note that we haveexcluded all inputs from the primary sector (e.g. resources and agricultural goods) as intermediate
goods when we calculate [qo for running the regressions, but we include intermediate services forthe production of manufactured goods. We report the result in Table 1. ?Table 1 about hereA
Table 1 shows that other than shared currency, all the coe!cients have the expected sign in all
years. When we use the logarithm of distance rather than the discrete distance measures for gn and
4This normalization is also adopted by EK.

9Variable

1995

2000

2005

2008

2009

2010

2011

-4.06***-3.94***-3.77***-3.62***-3.74***-3.73***-3.75***(0.36)(0.16)(0.16)(0.16)(0.16)(0.16)(0.16)-5.31***-4.99***-4.81***-4.68***-4.77***-4.71***-4.72***(0.36)(0.12)(0.12)(0.12)(0.12)(0.12)(0.12)-5.86***-5.48***-5.32***-5.19***-5.27***-5.22***-5.21***(0.35)(0.11)(0.101)(0.11)(0.11)(0.11)(0.11)-6.28***-5.81***-5.65***-5.54***-5.60***-5.57***-5.54***(0.35)(0.11)(0.11)(0.10)(0.11)(0.11)(0.11)-6.92***-6.48***-6.31***-6.17***-6.26***-6.22***-6.18***(0.36)(0.12)(0.11)(0.11)(0.11)(0.11)(0.11)-7.67***-7.18***-7.10***-6.93***-7.05***-7.03***-7.00***(0.35)(0.11)(0.11)(0.10)(0.11)(0.11)(0.10)

0.43***

0.44***

0.37***

0.33***

0.33***

0.32***

0.30***(0.076)(0.073)(0.073)(0.071)(0.072)(0.072)(0.071)

0.23***

0.24***

0.22***

0.19***

0.17***

0.18***

0.17***(0.052)(0.049)(0.049)(0.048)(0.049)(0.049)(0.048)0.36***

0.30***

0.26***

0.27***

0.28***

0.26***

0.24***(0.029)(0.028)(0.028)(0.027)(0.027)(0.027)(0.027)-0.35-0.18**-0.18***-0.16**-0.14**-0.16**-0.17***(0.34)(0.072)(0.068)(0.066)(0.067)(0.067)(0.066)

0.40***

0.35***

0.34***

0.30***

0.34***

0.34***

0.36***(0.074)(0.071)(0.071)(0.069)(0.070)(0.070)(0.069)Dest. FE

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Observations

3,595

3,600

3,600

3,600

3,600

3,600

3,600

g1
g2
g3
g4
g5
g6
Shared Border
Shared Language
Shared Legal
Shared Currency
Colonial Linkage

WWW indicates 1% signiﬁcance level, WW indicates 5% signiﬁcance level

Table 1: Gravity Equation for trade in Intermediate Goods and Services for Manufacturing Sectors

10re-run Equation (10), we obtain Table 11, shown in Online Appendix G.2. The coe!cients of thecomponents of bilateral trade cost other than distance are quite similar there to the ones in Table
1. Table 2 shows the competitiveness in exporting intermediate goods as obtained in regression(10) subject to (11). ?Table 2 about hereA
Country

1995

Country

2005

Country

2011

USA

4.11

USA

3.79

USA

3.66

Japan

3.65

Japan

3.19

China

3.26

Germany

3.33

Germany

2.98

Germany

2.79

Italy

2.50

China

2.73

Japan

2.75

France

2.49

Korea

2.23

Russia

2.04

UK

2.46

Italy

2.20

Korea

2.03

Korea

2.37

UK

2.18

Italy

1.96

Taiwan1.85

France2.17

France1.90

Russia1.85

Russia

1.85

UK

1.90

Canada1.70

Taiwan

1.66

India

1.67

Netherlands

1.61

Spain

1.43

Brazil

1.58

Switzerland

1.53

Canada1.43

Canada1.49

Sweden1.50

Brazil

1.38

Spain

1.45

China

1.47

India

1.27

Taiwan

1.35

Spain

1.33

Netherlands

1.22

Australia

1.18

Table 2: Competitiveness in exporting Intermediate Goods and Services

3.2

Gravity Equation for Trade in Final Goods

The total value of exports of ﬁnal goods from o to q is given byeq
eqo = eqo [[;q> o = 1> ===> Q(12)

eq is the total expenditure of country n on ﬁnal goods. Thus, (7) and (12) imply that
where [

=,

eo h
eqo

eqo
G
[
=
=
 3
eqq
e q qo

eqq
[
G
Ã
!
eqo
[
eq  ee o  ln Gln
 ln  qo
= ln Geqq[(13)

e o is estimated aswhich we call the gravity equation for trade in ﬁnal goods. The parameter ln G

the coe!cients for the indicator variable which takes on a value of 1 if country o is an exporting

country and -1 if country o is an importing country and zero otherwise; ln  qo is given by (11). We
report the estimation result for the regression of each year in Table 3. ?Table 3 about hereA
11

Variable

1995

2000

2005

2008

2009

2010

2011

g1

-2.89***-3.12***-2.98***-2.90***-3.06***-3.05***-2.97***(0.69)(0.28)(0.27)(0.26)(0.26)(0.26)(0.25)-4.73***-4.68***-4.48***-4.41***-4.52***-4.47***-4.38***(0.68)(0.22)(0.20)(0.20)(0.20)(0.20)(0.19)-5.34***-5.26***-5.06***-4.99***-5.05***-5.04***-4.91***(0.67)(0.19)(0.18)(0.17)(0.17)(0.18)(0.17)-5.90***-5.74***-5.58***-5.52***-5.54***-5.49***-5.38***(0.67)(0.19)(0.18)(0.17)(0.17)(0.17)(0.17)-6.65***-6.62***-6.36***-6.22***-6.31***-6.32***-6.10***(0.68)(0.20)(0.19)(0.18)(0.18)(0.18)(0.18)-7.77***-7.65***-7.41***-7.30***-7.38***-7.40***-7.20***(0.67)(0.19)(0.18)(0.17)(0.17)(0.17)(0.17)

0.31**

0.31**

0.28**

0.28**

0.30***

0.29**

0.30***(0.14)(0.13)(0.12)(0.12)(0.12)(0.12)(0.12)

0.26***

0.34***

0.41***

0.32***

0.31***

0.35***

0.30***(0.098)(0.085)(0.082)(0.079)(0.078)(0.079)(0.078)0.52***

0.43***

0.36***

0.38***

0.42***

0.43***

0.40***(0.055)(0.048)(0.046)(0.044)(0.044)(0.045)(0.044)-0.26-0.36***-0.19*-0.24**-0.22**-0.31***-0.18(0.65)(0.13)(0.11)(0.11)(0.11)(0.11)(0.11)

0.50***

0.42***

0.43***

0.38***

0.34***

0.35***

0.38***(0.14)(0.12)(0.12)(0.11)(0.11)(0.11)(0.11)

Dest. FE

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Observations

3,561

3,579

3,582

3,590

3,587

3,589

3,585

g2
g3
g4
g5
g6
Shared Border
Shared Language
Shared Legal
Shared Currency
Colonial Linkage

WWW indicates 1% signiﬁcance level, WW indicates 5% signiﬁcance level,
W indicates 10% signiﬁcance level

Table 3: Gravity Equation for Trade in Manufactured Final Goods (Equation (13))

12There is nonlinearity in the distance eect, as shown in Tables 1 and 3. When the distance issmall (d1 and d4, i.e. less than 3000 miles), distance is a higher barrier to trade in intermediate
goods than to trade in ﬁnal goods. But when the distance is large (d6, i.e. larger than 6000 miles),the reverse is true.
When we use the natural logarithm of distance rather the discrete distance measures and re-run
Equation (13), we obtain Table 12, shown in Online Appendix G.2. In that table, the coe!cientsof the bilateral trade cost components other than distance and shared border are quite similar tothe ones in Table 3.
Comparing Tables 11 and 12, we see that, on average, distance elasticity for trade in ﬁnal goods(from Table 12) is larger than the distance elasticity for trade in intermediate goods (Table 11).
That is, distance is a lower barrier to trade in intermediate goods than to trade in ﬁnal goods.
Baldwin and Taglioni (2013) found that distance elasticity is larger in magnitude when trade ﬂow
is dominated by intermediate goods, but then they found that the result is not robust.
From running Equation (13), we obtain the countries’ competitiveness in supplying ﬁnal goods.
The results are given in Table 4. ?Table 4 about hereA
Country

1995

Country

2005

Country

2011

USA

4.64

USA

4.09

China

4.26

Japan

4.17

China

3.72

USA

4.02

Germany

3.74

Japan

3.54

Germany

3.25

Korea

3.16

Germany

3.37

Japan

3.04

Italy

3.00

Korea

2.94

Korea

2.85

UK

2.84

Italy

2.58

Italy

2.48

France2.80

France2.54

France2.36

Taiwan

2.64

UK

2.16

UK

2.09

China

2.44

Taiwan

2.10

India

2.07

Sweden1.99

Brazil

1.98

Taiwan1.85

Canada

1.90

Thailand

1.79

Thailand

1.83

Thailand1.88

Malaysia

1.74

Brazil

1.83

Singapore

1.80

Spain

1.70

Spain

1.63

Switzerland

1.78

Sweden

1.46

Malaysia

1.45

Netherlands

1.78

Canada1.44

Canada1.39

Table 4: Competitiveness in Exporting Final Goods
Comparing Tables 2 and 4, we see that a country’s competitiveness (relative to the average) inintermediate goods and in ﬁnal goods can dier signiﬁcantly. For example, China’s competitivenessin intermediate goods in 1995, 2005 and 2011 are 1.47, 2.73 and 3.26 respectively, while its ﬁnal
13

goods competitiveness are 2.44, 3.72 and 4.26 respectively. Thus, China was signiﬁcantly morecompetitive in ﬁnal goods compared with intermediate goods in those years. This result indicatesthat China has strong comparative advantage in ﬁnal goods versus intermediate goods.
Comparative Advantage
fo @Go is positively correlated with Figure 2 shows that G
eoo @ oo for all country o. Thus, acountry that has comparative advantage in ﬁnal goods versus intermediate goods tends to have ahigh ratio of domestic share in ﬁnal goods to domestic share in intermediate goods. This result
makes sense. Intuitively, as a country that has comparative advantage in a set of goods shouldhave a large domestic market share in those goods. In the context of our model, given that   e
,fo @Go 2 
eoo @ oo across countries if fo 2G

5 6o across countries, which turns out to be true. , ?Figure

2 about hereA

3.3

China’s CompetitivenessComparing Tables 2 and 4, we see that the competitiveness of China in intermediate goods andﬁnal goods rose very rapidly during the period 1995-2011, while those of other highly competitive
countries mostly fell continuously during this period. For example, the competitiveness of the
US in intermediate goods in 1995, 2005 and 2011 are 4.64, 4.09 and 4.02 respectively, while its
ﬁnal goods competitiveness are 4.11, 3.79 and 3.66 respectively. The rise of China is one of themost important developments in international trade during this period. What explains the highcompetitiveness of China in the most recent year? What explains the rapid rise of competitivenessof China? The data indicates that the reason is the same for both intermediate goods and ﬁnal
goods competitiveness. Thus, we only focus on explaining intermediate goods competitiveness here
and relegate the explanation concerning ﬁnal goods to Online Appendix G.4. Recall that, in Section
2, we state that the competitiveness of a country in intermediate goods depends on three factors:
wage, technology stock for intermediate goods, and access to foreign intermediate goods. Table 5
veriﬁes empirically this theoretical prediction. The three factors together on average account for
94% of the intermediate goods competitiveness and 96% of the ﬁnal goods competitiveness of acountry. ?Table 5 is about hereA
The mean of each dependent and independent variable in Table 5 is normalized to zero.
5

h q vs. xq , which shows that x
h q is strongly correlated withSee Figure 11 in Online Appendix G.3 for a plot of x

xq , with a correlation coe!cient equal to 0.9715.
6
The method of estimating Wq , xq and Iq is as follows. First, note that qq , , zq and  q are either data or
estimated elsewhere in the literature. Second, Gq is estimated from (10). This in turn allows us to estimate xq from1

ln xq = ln Gq 3 ln  qq . Then we estimate Sq from Sq = (xq )3  . This in turn allows us to estimate fq from (4).
h q and
Then we estimate Wq from Gq = Wq (fq )3 . We can estimate Iq from 1 3  qq = Iq @xq . The variables Whq , x

hqq , h, zq ,  q and equation (13). We use  = h
 = 4=0, following Simonovska and
Ihq are similarly estimated, using 
Waugh (2014).

14

e q : ln (comp. in interm. goods/comp. in ﬁnal goods) (y-axis) vs.  qq @eFigure 2: ln Gq  ln G qq : home share ininterm. goods / home share in ﬁnal goods (x-axis). For the estimated slope and statistical signiﬁcance of each ﬁtted line, refer
to Appendix C.

In the case of China, we want to ﬁnd out the relative importance of each of these factors indetermining the high competitiveness of China. We answer this question by referring to Figures 3,
4 and 5 concerning the competitiveness in intermediate goods. ?Figures 3, 4, 5 about hereA
In Figure 3, we see that there is a very strong and positive correlation between competitivenessin intermediate goods and access to foreign intermediate goods. Figure 4 shows that the correlation
between intermediate goods competitiveness and technology stock in intermediate goods production
is weaker than the correlation shown in Figure 3 though the correlation coe!cient is still positiveand signiﬁcant. Figure 5 shows that the correlation between intermediate goods competitivenessand wage is statistically insigniﬁcant. We can understand China’s rise by comparing it with the US.
China is clearly an outlier in the plot of intermediate goods competitiveness against intermediate
goods technology stock – its technology stock is much lower than that of the US during 1995-2011.
On the other hand, its access to foreign intermediate goods rose rapidly from 1995 (much belowthat of the US) to 2011 (overtaking that of the US). Moreover, China’s wage was much lower than15

Competitiveness

Competitivenessin intermediate goods

in ﬁnal goods

0.905WWW

0.903WWW(0.048)(0.032)-1.767WWW-1.788WWW(0.101)(0.064)0.419WWW

0.443WWW(0.034)(0.032)

Q

385

385

U2

0.94

0.96

Technology Stockln(wage)Access to foreign intermediate goods

Table 5: Determinants of Competitiveness in Intermediate Goods and Final Goods
that of the US during 1995-2011, sustaining its high competitiveness. Based on these diagrams,
we argue that the main factors that determine China’s competitiveness are its favorable accessto foreign intermediate goods and low wage, and not its technology stock. (The corresponding
plots for ﬁnal goods competitiveness are very similar. They are put in an Online Appendix G.4.)
What explains the rise in China’s access to foreign intermediate goods? We speculate that it is
its large volume of processing trade (with very low trade costs in importing intermediate goods)
and increasingly active participation in the global value chain during 1995-2011 (especially after
accession to WTO in 2001), playing the role of a major global assembly center.
What explains China’s rapid rise of competitiveness during 1995-2011 relative to other countries? As discussed above, China’s competitiveness in 2011 (relative to other country’s) is mainly
due to its relatively favorable access to foreign intermediate goods and relatively low wage and not
because of its technology stock, which is mediocre. Ironically, however, the increase in China’s
competitiveness from 1995 to 2011 in fact relied on a large part from the increase in its technology
stock (even though its technology stock is still not that high compared with the US in 2011), while
the increase in China’s wage during this period in fact lowers its competitiveness. The increasein access to foreign intermediate goods (which was already quite high in 1995) only contributedmodestly compared with technology stock in the increase in competitiveness of China during thisperiod. This is shown in Table 6. ?Table 6 about hereA
CompetitivenessCompetitivenessContribution of

in intermediate goods

in ﬁnal goods

Technology Stock156.2%

154.8%

ln(wage)-84.8%-84.5%

Access to foreign intermediate goods

35.7%

37.1%

Table 6: The change in China’s competitiveness from 1995 to 201116

Figure 3: Gq : Comp. in interm. goods (y-axis) vs. Iq : Access to foreign interm. goods (x-axis). For the estimated slope
and statistical signiﬁcance of each ﬁtted line, refer to Appendix C.

The numbers in Table 6 are computed based on the regression coe!cients in Table 5 and thechange in China’s technology stock, wage and access to foreign intermediate goods during 19952011.

4

Gains from Trade

In this section, we calculate the gains from trade of a country by making use of data on both homemarket shares in intermediate goods and ﬁnal goods. Under our framework, we can separately
calculate the gains from trade in ﬁnal goods and intermediate goods. When a country imports more
ﬁnal goods, the consumers there can directly beneﬁt from it through the cheaper imported goods.
This is the source of the gains from trade in ﬁnal goods. When a country imports more intermediate
goods, the composite intermediate good becomes cheaper as cheaper imported intermediate goods(i) substitute for home-supplied ones and (ii) lower the costs of home-supplied ones by lowering thecost of the composite intermediate good through a multiplier eect. Thus, the domestic consumers
17

Figure 4: Gq : Comp. in interm. goods (y-axis) vs. Wq : Tech. stock in interm. goods (x-axis). For the estimated slope andstatistical signiﬁcance of each ﬁtted line, refer to Appendix C.

can indirectly beneﬁt from it as a cheaper composite intermediate good in production implies
cheaper ﬁnal goods produced. This the source of the gains from trade in intermediate goods.
Let {b = {0 @{ (where {0 is the new value and { is the old value) denote the change in the value
fq . The followingof {. The welfare of country n, denoted by Zq , is equal to the real wage, zq @S
proposition would guide our welfare analysis in the rest of this section.

Proposition 1 The change in welfare of country n can be expressed as´31@h
³13
3  q
d
d
q
=

e
(d

)
Z
q
qq
qq

d
The gains from trade is deﬁned as Zq  1.
Proof:

18(14)

Figure 5: Gq : Comp. in interm. goods (y-axis) vs. ln zq : ln (wage) (x-axis). For the estimated slope and statisticalsigniﬁcance of each ﬁtted line, refer to Appendix C.

According to (4) and (5), the percentage change in unit cost of the input bundle is given byg ln fq =  q g ln zq + (1   q ) g ln Sq¶µ
1  qg ln q .
=  q g ln zq From this and (8), we obtain the percentage change in the welfare (i.e. real wage) of country q as
¶
µ
µ ¶
1
1  q1
f
g ln e qg ln q +g ln fq +g ln Zq = g ln zq  g ln Sq =
e
q
 q

¶
µ
µ ¶h
i
1  q1 e
g ln fq + g ln e q(g ln fq + g ln q ) +
=
e
 q

µ
¶
µ ¶
1  q1(15)
g ln  qq= g ln 
eqq 
e
 q


where the ﬁrst term in the last line of (15) comes fromg ln fq  g ln e q (based on (7))
g ln 
eqq = e19

while the second term in the last line of (15) comes fromg ln  qq = g ln fq  g ln

q (based on (6))

Integrating equation (15) between the initial and new equilibria leads to (14). ¥4.1

Estimates of Gains from Trade

Denote welfare under autarky by ZqD . Equation (14) implies that the gains from trade (startingfrom autarky) is given byh3dD  1  Zq  1 = (e qq )31@ ( qq )
Z
q
D
Zq

h



13
3  qwhen [(e qq)31@1][( qq )3or [( qq )

13 q
 q

q

13 q
 q





13 q
3

h

 1  (e )31@  1 + ( qq ) q| qq {z|}{z 1 (16)}

gains from tradegains from trade inin ﬁnal goods

intermediate goodsh1] is su!ciently small, which would be true when [(e qq )31@ 1]

 1] is su!ciently small, which holds for all the cases we consider in this paper.

We then compare it to the gains from trade based on the TIG model:
eqq
Zq[qq + [
31@( q )

1
=
(
)

1
with


qq
qq
eq
ZqD
[q + [

where  qq and  are variables/parameters corresponding to the TIG model, which pools trade inintermediate and ﬁnal goods together. There is no consensus in the literature concerning whether
the trade elasticity in intermediate goods trade is dierent from that in ﬁnal goods. Simonovska
and Waugh (2014) estimate that the point estimate of the elasticity of trade should be around4.0. Eaton and Kortum (2012) also adopt such a number. Therefore, following these authors, we = 4=0. The gains from trade in 2011 based on the our model and the TIG
assume that  =  = emodel respectively are shown in Table 8 in Appendix D.

Because we separately account for the gains from trade in intermediate goods and those fromﬁnal goods, the level of gains from trade based on our model is in general dierent from thatobtained from the TIG model, as long as 
eqq is not equal to  qq . According to the data, for about

80% of the observations,  q  0=333.7 Hence, the following corollary holds for a vast majority ofthe observations in our sample.

Corollary 1 As long as  q  0=333 (which is true of about 80% of the observations) and  ==e = 4=0 (approximation based on the literature), the gains from trade of country q is under-

estimated by the TIG model if the ratio of the domestic share in ﬁnal goods (e qq ) to the domestic
7

Out of 434 observations, only 94 have  q A 0=333.

20

share in intermediate goods ( qq ) is great than one. The higher (lower) is this ratio (e qq @ qq ),the greater (smaller) is the degree of under-estimation.
Proof: See Appendix E.
The intuition that the TIG model under-estimates the overall gains from trade when 
eqq A  qqis that the gains from trade in intermediate goods are substantially larger than those from trade
in ﬁnal goods even when 
eqq =  qq . The reason is that since  q  0=333 for about 80% of theobservations, 1   q , the cost share of intermediate goods in manufacturing production, is very
likely to be greater than 0.667 (with the rest being the cost share of factor inputs such as labor andcapital) in any country, which implies that intermediate goods are very important in producing
both intermediate and ﬁnal goods. This in turns implies that any given import penetration rate
in intermediate goods contributes substantially more to gains from trade than the same importpenetration rate in ﬁnal goods. Mathematically, referring to (16), given that  = e
 = 4=0 and
³
´
13 q
 q  0=333, we see that the exponent of  qq , which is equal to   , is more than twiceq
the magnitude of the exponent of 
eqq , which is equal to 1@e. Thus, the gains from trade inintermediate goods carry a much higher weight than those from trade in ﬁnal goods in determining
the overall gains from trade. Therefore, if 
eqq @ qq A 1 (import penetration rate of ﬁnal goods

is low and import penetration rate of intermediate goods is high) and one does not distinguishbetween intermediate goods and ﬁnal goods in calculating the market share, the under-estimationof the gains from trade in intermediate goods would be so high as to lead to under-estimation ofh3

the overall gains from trade. Hence, (e qq )31@ ( qq )

13 q
 q

would be greater than ( qq )31@( q ) .

fq @Gq also
Figures 6 and 7 verify Corollary 1. They show that countries with high 
eqq @ qq and G

tend to be those whose gains from trade are underestimated by the TIG model, and degree of underfq @Gq , both of which measure the strength of comparative
estimation increases with 
eqq @ qq or G

advantage of the country in ﬁnal goods. In these diagrams, JI WqW LJ @ JI WqOT denote the ratioof gains from trade based on the TIG model and those based on the model in this paper. Figuree q . Figure 7
6 shows that JI WqW LJ @ JI WqOT is signiﬁcantly and positively related to ln Gq  ln G

eqq . ?Figures 6 andshows that JI WqW LJ @ JI WqOT is signiﬁcantly and positively related to  qq @ 

7 about hereA

Table 7 gives the breakdown of total gains from trade into those from trade in intermediate
goods and those from trade in ﬁnal goods as of 2011. ?Table 7 about hereA
In fact, within the entire sample of countries, the average gains from trade in intermediate
goods is 8.38% while the average gains from trade in ﬁnal goods is 3.65%. Within the OECD
(non-OECD) countries, they are 5.28% (10.21%) and 3.07% (3.99%) respectively. Thus, within thesample countries, the gains from trade in intermediate goods is more than twice of those from ﬁnal
21

Country

WelfareCountry

WelfareCountry

WelfareInterm.

Final

Interm.

Final

Interm.

Final

Goods

Goods

Goods

Goods

Goods

Goods

Argentina

3.02%

1.78%

Germany

4.68%

2.70%

Norway

4.50%

2.37%

Australia

1.95%

2.33%

Greece

3.66%

2.85%

Philippines

4.45%

2.13%

Austria

5.53%

3.77%

Hong Kong

11.58%

11.33%

Poland

10.13%

3.27%

Belgium

10.27%

2.33%

Hungary

20.68%

4.90%

Portugal

8.04%

3.27%

Brazil

2.65%

1.03%

Iceland

5.18%

3.73%

Russia

2.79%

1.87%

Brunei

3.65%

14.98%

India

7.50%

1.09%

Saudi Arabia

2.38%

5.25%

Bulgaria

13.35%

4.99%

Indonesia

2.10%

1.53%

Singapore

6.32%

1.72%

Cambodia21.81%

5.98%

Ireland

6.48%

3.45%

Slovak

17.52%

5.96%

Canada

4.58%

2.87%

Israel

3.26%

2.88%

Slovenia

9.03%

5.80%

Chile

1.62%

4.20%

Italy

5.17%

2.16%

South Africa

4.96%

2.97%

China

16.96%

0.82%

Japan

1.56%

0.79%

Spain

5.08%

2.54%

Columbia

2.94%

2.18%

Korea

11.75%

1.58%

Sweden

5.28%

3.34%

Costa Rica

8.37%

4.82%

Latvia

7.56%

5.42%

Switzerland

3.57%

5.12%

Croatia

4.75%

2.92%

Lithuania

6.71%

4.08%

Taiwan17.29%

3.13%

Cyprus

5.12%

5.42%

Luxembourg

13.71%

13.90%

Thailand

19.23%

2.52%

Czech

17.37%

3.63%

Malaysia

39.59%

3.64%

Tunisia

14.83%

4.56%

Denmark

2.76%

1.64%

Malta

3.43%

2.83%

Turkey14.30%

2.31%

Estonia11.34%

5.22%

Mexico

8.91%

3.21%

UK

3.40%

3.16%

Finland

7.32%

2.56%

Netherlands

4.33%

0.75%

USA

1.71%

1.28%

France

5.76%

2.59%

New Zealand

3.56%

2.79%

Viet Nam

36.42%

5.93%

Table 7: Breakdown of the Gains from Trade into those from Trade in Intermediate Goods andthose from Final Goods as of 2011

22

e q:
Figure 6: JI WqW LJ @ JI WqOT : Gains from trade under TIG / Gains from trade in this paper (y-axis) vs. ln Gq ln G
ln (comp. in interm. goods/comp. in ﬁnal goods) (x-axis). For the estimated slope and statistical signiﬁcance of each ﬁtted
line, refer to Appendix C.

goods. Moreover, not only did the developing countries gain a lot more from trade, they also gainsigniﬁcantly more from trade in intermediate goods than from trade in ﬁnal goods.

4.2

Change in gains from trade

Next, we compute the change in gains from trade for each country q during a period by calculating
the dierence between the gains from trade in the beginning year and the ending year. The changes
in gains from trade over each of the four periods 1995-2000, 2000-2005, 2005-2011 and 1995-2011
are given in Tables 9 and 10 in Appendix D.
From Table 9, we see that during 1995-2011, for the OECD countries, the average change ingains from trade in intermediate goods is 1.18% while the average change in gains from trade in
ﬁnal goods is 0.08%. This implies that, on average, for the OECD countries, the contribution offragmentation (i.e. trade in intermediate goods) to the total gains from trade has increased during
23

Figure 7: JI WqW LJ @ JI WqOT : Gains from trade under TIG / Gains from trade in this paper (y-axis) vs.  qq @ 
eqq :home share in interm. goods / home share in ﬁnal goods (x-axis). For the estimated slope and statistical signiﬁcance of eachﬁtted line, refer to Appendix C.

1995-2011. More importantly, it can be seen that the change in gains from trade in intermediate
goods are not proportional to the change in gains from trade in ﬁnal goods. In some countries,
they are of dierent signs. This distinction is what we would like to highlight in this paper so as todemonstrate that the TIG model over-simpliﬁes the picture, as the TIG model would imply thatthe change in gains from trade in intermediate goods is proportional to that in ﬁnal goods.
From Table 10, it can be seen that for the non-OECD countries the average change in gains fromtrade in intermediate goods is 2.99% while the average change in gains from trade in ﬁnal goods is-0.09%. This again implies that for the non-OECD countries the contribution of fragmentation to
the total gains from trade has increased during 1995-2011.
From Tables 9 and 10, we see that, during 1995-2011, the average increase in gains from intermediate goods trade for all countries in the sample, 2.32%, is distinctly higher than the averageincrease in gains from ﬁnal goods trade, -0.03%. This suggests that gains from trade due to frag24

mentation is becoming more important over time for both developed and less developed countries.
Figure 8 summarizes the results in Tables 9 and 10 diagrammatically. It plots the change in gains
from trade in ﬁnal goods during 1995-2011 (y-axis) against the change in gains from trade inintermediate goods during 1995-2011 (x-axis). ?Figure 8 about hereA

Figure 8: GFT in Final Goods 1995-2011 (y-axis) vs. GFT in Intermediate Goods 1995-2011 (x-axis)

5

Extension: Gains from Trade under a Multi-sector Model

So far, we have been using a one-sector model, though we make use of data of trade ﬂows in intermediate goods and ﬁnal goods separately in our empirical work. As Costinot and Rodriguez-Clare(2014) point out, the gains from trade calculated using a multi-sector model can be substantiallydierent from that calculated using a one-sector model, as the parameters for dierent sectors canbe quite dierent. Furthermore, in a multi-sector setting, ﬁnal goods in one sector are produced using intermediate goods from other sectors, i.e. there are input-output linkages across sectors,which
can also lead to a dierent estimated value of the gains from trade. Such kind of input-output
linkages have been analyzed by, for example, Caliendo and Parro (2015). However, Caliendo and25

Parro (2015) adopt a multi-sector version of the TIG model, and so they do not separately makeuse of the data of trade ﬂows in intermediate goods and ﬁnal goods in their empirical analysis.
In their empirical work, trade ﬂows in the two types of goods are lumped together. Here in thisextension, we introduce input-output linkages across sectors and, in contrast to the TIG model, we
separately make use of the data of trade ﬂows in intermediate goods and ﬁnal goods in our empiricalanalysis. We want to see whether our results concerning gains from trade are robust to switchingfrom a one-sector analysis to a multi-sector analysis. Speciﬁcally, under the multi-sector setting,
we would like to know whether and how the extent to which the gains from trade calculated basedon our model deviates from the TIG model is related to the strength of comparative advantage inintermediate goods versus ﬁnal goods. Furthermore, we would like to know if the average increasein gains from trade in intermediate goods is distinctly greater than those in ﬁnal goods during theperiod 1995-2011.

5.1

The ModelThis section states the main features of the model and the major results. For the detailed calculation, refer to Appendix F. There are N sectors, indexed by v. Sectors v = 1> 2> ===> P are
manufacturing sectors, v = P + 1> P + 2> ===> N are service and primary (hereinafter referred to as
S&P) sectors. Hereinafter, “goods” refers “goods and/or services”. We deﬁne the utility functionof the representative household in country q as
½N¾
Z
P v 1 h fv iq
ln Tq (l) gl
Xq = exp
v=1

for q = 1> 2> ===> Q

(17)

0

eq (l) is the quantity consumed of variety i of sector-v ﬁnal good by the representative
where Thousehold in country n, and vq is the expenditure share of sector-v ﬁnal goods in country n. Thus,NPvq = 1. We are only interested in gains from trade in ﬁnal manufactured goods and trade in

v=1

intermediate manufactured and S&P goods used to produce manufactured goods. Thus, we assume

that ﬁnal S&P goods as well as intermediate manufactured and S&P goods used to produce S&P
goods are non-tradable.
fv (l)
A ﬁnal good or an intermediate good is produced by conversion from an input bundle. ]odenotes the e!ciency of country o in converting a sector-v input bundle into a sector-v ﬁnal goodof variety l 5 [0> 1], and ]ov (m) denotes the e!ciency for converting a sector-v input bundle into a
sector-v intermediate good of variety m 5 [0> 1]. The production function of a sector-v input bundle
in country q is given by:vv|qv = (Pqv )13 q (oqv ) q , where 0 ?  vq ? 1 for v = 1> 2> ===> N(18)

where |qv is the quantity of sector-v input bundle produced in country q; Pqv is the corresponding
quantity of the sector-v composite intermediate good (which is deﬁned in equation (19) below); oqv
26

is the corresponding labor input. The quantity of sector-v composite intermediate good producedby q is determined by the following production function:½N¾
Z
P vu 1vvu
qln [Tq (m)] gm
for v = 1> 2> ===> N>
Pq = exp
u=1

(19)

0

where Tvu
q (m) is the quantity of variety m of sector-u intermediate good used by country q in the pro-duction of the sector-v composite intermediate good,  vu
q is the cost share of intermediate goods fromNP
sector u used to produce the sector-v composite intermediate good in country q. Thus,
 vu
q =1
u=1

for all v. The random variable ]ov (m) follows the Fréchet distribution, with the cumulative density

function given byv

Pr[]ov (m) ? }] = h3[Wo ]}3v;m 5 [0> 1] for v = 1> 2> ===> N>(20)

where Wov is country o’s technology stock for producing sector-v intermediate goods and 1@v is
positively related to the variance of the distribution of ]ov (m) ;m 5 [0> 1].
fv (l) follows the Fréchet distribution, with the cumulative density function
We assume that ]ogiven byiv

fv (l) ? }] = h3[Wo ]}
Pr[]
o

i
v
3

;l 5 [0> 1] for v = 1> 2> ===> N>(21)

fv is country o’s technology stock for producing sector-v ﬁnal goods and 1@ev is positively
where Wo
fv o (l) ;l 5 [0> 1].
related to the variance of the distribution of ]The variables fvo , svqo ,  vq , Sov ,vv ,  v , [ v , [ and eev , Sev , e v , ev e
fvo , sevqo , 
q
q
o
qo
qo
o
o eqo , [qo , [q are all

similarly deﬁned as in the one-sector model except that they are speciﬁc to the sector v.
Gains from Trade

Taking the model to the data, as we are interested only in gains from trade in manufactured
ﬁnal goods and trade in intermediate manufactured and S&P inputs used to produce manufactured
goods, the total gains from trade is given by
v Q
v  vu
P QN
v 3 hqv
u 3 quqdD  1 = QP (e

)
(
)
1
Z
q
v=1
¸ u=1 qq¸
 v=1 qqv
v vuQP QN
QPv 3 hvq
u 3 quq
(e

)

1
(
)

1
·

qq
qq
v=1
v=1
u=1
|
{z
} |
{z
}
gains from tradegains from trade

in ﬁnal goods

in intermediate goods(22)

where  vu
q is the row v column u element of the Leontief inverse matrix minus the identity matrix
as described in Appendix F.
If we lump together the trade ﬂows of intermediate goods and ﬁnal goods in each sector, thehome market share in sector s of country n is given by vqq = evqq =  vqq =

v +[
v
eqq
[qq
for v = 1> 2> ===> N.
eqv[qv + [

27

Now, suppose we adopt a multi-sector TIG model as described in Coli endo and Parro (2015).
Under such a model, the gains from trade (starting from autarky) for the multi-sector TIG model
is given by

¯
d
D ¯¯
Z
q

W LJ

1=

QP QN
v=1

u 3
u=1 ( qq )

vu
vu
v
q ( q +1 )
u

1

(23)

where 1vu is a indicator variable which is equal to 1 i v = u and 0 otherwise.
We also estimate the sectoral gravity equations for trade in intermediate goods (used to produce
manufactured goods)
ln

µ

v
[qo
v
[qq

¶

= ln Gov  ln Gqv  v ln  vqo for v = 1> 2> ===> N>and sectoral gravity equations for trade in ﬁnal goods
Ã
!
ev
v
[
qo
e qv  ee v  ln G ln  vqo for v = 1> 2> ===> P>ln= ln Gove[qq

with ln  vqo = gvn + ev + ov + Ohjdov + FX v + Frov + pvq , to obtain the sectoral competitivenessin intermediate goods (used to produce manufactured goods) ln Gov for v = 1> 2> ===> N and sectorale v for v = 1> 2> ===> P . Like in the one-sector model, we assume
competitiveness in ﬁnal goods ln Gvov

 =  = 4=0 for all v. The deﬁnitions of the variables that are not yet deﬁned so far arethat v = e

the same as in the one-sector model.

The aggregate competitiveness in intermediate goods and ﬁnal goods are deﬁned in Appendix
n o
e v respectively.
F. They are expenditure-weighted averages of the estimated values of {Gv } and G
o

5.2

o

Empirical results

Our empirical ﬁndings are summarized by Figures 9 and 10.
1. Figure 9 plots the ratio of gains from trade under multi-sector TIG to the gains from tradeunder our multi-sector model against the ratio of the multi-sector aggregate competitiveness inintermediate goods to the multi-sector aggregate competitiveness in ﬁnal goods. This diagram isto be compared with Figure 6 under the one-sector model. ?Figure 9 about hereA
2. Figure 10 plots the gains from trade under multi-sector TIG to gains from trade under our
multi-sector model against the ratio of home share in intermediate goods to home share in ﬁnal
goods. This diagram is to be compared with Figure 7 under the one-sector model. ?Figure 10
about hereA
Recall that under the one-sector setting, the TIG model (which does not separately make useof data of trade ﬂows in intermediate goods and ﬁnal goods respectively) under-estimates the gains
from trade of only those countries with su!ciently large 
eqq @ qq (e.g. when the ratio is greater
28









6$8
&+/
&2/
,65 $86&5,
*5&
/9$
+59
%51
125
7+$ ,6/+.*
/78
%*5
)5$
86$
*%5
$87
'(8
&$1%5$
3+/
781+81
'1.
%(/
1/'
0<6
63
-31
&+(
6*3
32/
,7$
357 (
),1
&=(
7:1
0/7.+0 &<3,'1
69..25
(67
/8;
6:(
0(;
,5/ 910 691
,1'

785
+59
*5&
/9$
,65 *%5$8612586$
357
%(/
$87
)5$
(63
.25
%*5
+.*
'1.
&<3
781 &=(32/
,7$
&+/
7+$
1/'
%5$
),1&$1'(8,1',6/ &5,
0<6
6*3
69.
0/7
(67910/8;&2/+81 691
6:(
1=/
,5/
,'1
0(;
&+(



1=/





$86
1=/
*5&
%51
%*5
*%586$
+59
781
,65
6*3
-31
/78 %(/
125
/9$
)5$
,1'
357(67
7+$
(63
7:1
.25
'1.
&$1
,7$%5$&5,$87
910
,'1
),1
691
&+/
3+/
69.
'(8
32/
6:(
1/'
0(;
&=(
,5/
6$8
,6/ &2/&<3 785+81&+1/8;
0/7
+.*
&+(



-31

&+1

&+1

.+0

$86 &2/
1=/
3+/
,'1
*5&
,65
(63
&+/ -31125/78357)5$86$%(/
691 .25
7:1
*%5
+59
$87
(67
&5,
&$1
7+$ 69.6*3%5$,7$ 0/7
%51
'1.
'(8
,5/
),1
785
+81
%*5
910
&=( 32/6:(
1/'0(;
&<3
&+(
/8;
/9$
781 &+1
,6/
+.*

6$8





6$8













UHOFRPUHOZHO)LWWHGYDOXHV*UDSKVE\\HDU

Figure 9: JI WqW LJ @ JI WqOT : Gains from trade under multi-sector TIG / Gains from trade under the multi-sector
e q : multi-sector aggregate competitiveness in intermediate goods / aggregate
model in this paper (y-axis) against ln Gq ln G

multi-sector competitiveness in ﬁnal goods (x-axis). For the estimated slope and statistical signiﬁcance of each ﬁtted line, refer
to Appendix C.

than 1). It is interesting to note that, under the multi-sector setting, the TIG model underestimates the gains from trade for almost all countries, as shown in Figure 10. The reason is thatthe gains from trade in intermediate service inputs are greatly under-estimated by the TIG model
as all countries have home-bias in ﬁnal services relative to intermediate services. This follows fromthe fact that the home-supplied market shares of ﬁnal services are set to one for all countries as
ﬁnal services are assumed to be non-tradable. (This assumption is not too far from the fact.)8
Just like in the one-sector model, for a country that has high ratio of home share in ﬁnal service
to home share in intermediate service, the TIG model can greatly under-estimate the gains from8

For example, for the year 2011, in China, the domestic share in ‘’Post and telecommunications” as ﬁnal goods is0.994, in ‘’Real estate activities” is 0.995, in ‘’Computer and related activities” is 0.988, in ‘’R&D and other businessactivities” is 0.995, in ‘’Public admin. and social security” is 0.999, in ‘’Education" is 0.994, in ‘’Health and social
work" is 0.997,

29









6$8
&2/ &+/,65/9$ $86*5&&5,+59
125 $87
7+$
%*5
)5$
/78
86$
*%5
'(8
,6/
&$1 '1.
3+/ 781
1/'
%(/
%5$
(63
-31
&+(
+81
32/
,7$
.25
357
),16*3&=(
0/77:1
,'1
69.
(67
910
6:(
691
0(;
,5/
,1'

0<6

1=/



6$8
+59
*5&
125
86$,65*%5-31.+0$86 $87
357
%(/
)5$
(63
.25 781
%*5
,7$
&+/
7+$
%5$
1/'
32/
,1'
&5, '1.
&=(),1'(8910 0/7 &2/ 69.&$1(67 691+81,'1 ,5/ 1=/ 6:(
0(;
785

&+1

&+1






$86
*5&

.+0

$86
&2/
1=/
3+/
,'1
*5& ,65-31 86$
(63
.25
125
)5$
/78
%(/6*3 +59
357
691
7:1
*%5
$87
(67
&5,
&$1
7+$
%5$
586
0/7
,7$
'(8'1.
.+0),1,5/ 69.
785+81910%*5 6:(
&=(
1/'
32/
0(;
&+1
781
,6/





1=/
%*5
86$
*%5
+59
781
,65
6*3 -31 125 /78)5$ (67,1' %(/
7+$ .257:1(63357$87'1.
,7$&$1&5,
910 ,'1586%5$),1691&+/
3+/ 0(; 1/' 32/'(8
6:(69.
&=( ,5/785 +81
&+1
&2/
0/7
&+(





 





UHOSL
UHOZHO)LWWHGYDOXHV*UDSKVE\\HDU

Figure 10: JI WqW LJ @ JI WqOT : Gains from trade under multi-sector TIG / Gains from trade under the multi-sector
model in this paper (y-axis) vs.  qq @e qq : home share in intermediate goods / home share in ﬁnal goods (x-axis). For theestimated slope and statistical signiﬁcance of each ﬁtted line, refer to Appendix C.

intermediate service trade. The overall gains from trade is equal to the sum of the gains from tradein manufacturing goods and intermediate service and primary inputs. But the cost of intermediate
primary goods only account for a small share of the total cost of intermediate service and primary
goods on average. Thus, if the under-estimation of gains from trade in intermediate service inputs
is su!ciently large in all countries, then the overall gains from trade is under-estimated by the TIG
model for almost all countries, even those with small 
eqq @ qq .

Nonetheless, the positive relationship between the relative gains from trade and comparativeadvantage depicted in Figures 6 and 7 continue to hold in the multi-sector setting. In other words,
it is still true that the TIG model under-estimates the gains from trade to a larger extent for
countries that have stronger comparative advantage in ﬁnal goods versus intermediate goods. For
example, in 2000, China’s gains from trade are under-estimated by more than 30% by the TIG
model (China is the country most under-estimated by the TIG model), and China is one of the30

countries with the strongest comparative advantage in ﬁnal goods. On the other hand, the gains
from trade for the US are almost not under-estimated by the TIG model at all, and the US is oneof the countries with the strongest comparative advantage in intermediate goods.
We next examine the change in the gains from trade in intermediate goods (i.e. the changev  vu
QNQu )3 quq  1), and change in gains from trade in ﬁnal goods (i.e.
(in the value of P
qq
v=1
u=1
v
Q
v 3 hqv
the change in the value of P(e) 1), from 1995 to 2011 for each country. Like in theqq
v=1
one-sector model, countries gain distinctly more from intermediate goods trade than from ﬁnal

goods trade. The average increase in gains from intermediate goods trade for all countries in thesample is 1.18% and average increase in gains from ﬁnal goods trade for all countries in the sample
is 0.48%. To show how individual countries behave, we plot 4GFT in Final Goods 1995-2011(y-axis) vs. 4GFT in Intermediate Goods 1995-2011 (x-axis) for the multi-sector model in the





following diagram.

910



6$8
/9$





&<3
&+/%51 691
781,6/&+(32/
/8;
528
&5,
69.
=$)
0(;
(63
+8178 5
$5*
)5$
&2/
*%5
6:(
),1
'(8
86$
,7$
-31
,1'
52:
,65
$86
&$1
&%5$
+1357
/78
125
&=(
+59
$87
,5/ 586
%*5
*5&
7+$
3+/
,'1
1=/ %(/
1/ '1.
'

7: 1

.25

6*3

0<6
0/7



(67








GZHOBLQWHUGZHOBILQDO





GZHOBLQWHU

In sum, the most important results concerning gains from trade are robust to switching from a
one-sector to a multi-sector analysis.

31

6Conclusion and Remarks

The availability of inter-country input-output tables in recent years has enabled us to disaggregatebilateral total trade ﬂows into bilateral trade ﬂows in intermediate goods and ﬁnal goods respectively. Separately making use of the data of bilateral trade ﬂows in intermediate goods and ﬁnal
goods yields interesting results and insights. It enables us to estimate a country’s competitiveness inintermediate goods and that in ﬁnal goods separately and to estimate the strength of comparativeadvantage of a country in ﬁnal goods versus intermediate goods. It also enables us to get a moreaccurate estimation of the gains from trade of a country and to link it to the country’s strength ofcomparative advantage in ﬁnal goods versus intermediate goods.
In this paper, we modify the Eaton-Kortum model and derive separate gravity equations for
trade in intermediate goods and trade in ﬁnal goods. Based on these equations and the data on
actual bilateral trade ﬂows in intermediate goods and ﬁnal goods, we estimate countries’ competitiveness in intermediate goods and in ﬁnal goods. We then go on to calculate the gains from tradeof countries based on an equation that separately accounts for both gains from trade in intermediate goods and that in ﬁnal goods. We then compare our results with those obtained by using thetradeable intermediate goods model. We ﬁnd that, across countries, the ratio of domestic market
share in ﬁnal goods to that in intermediate goods is positively correlated with the ratio of competitiveness in ﬁnal goods to that in intermediate goods. We argue that when this ratio is higher, thecountry has stronger comparative advantage in ﬁnal goods versus intermediate goods. The TIG
model tends to underestimate the gains from trade more for countries with stronger comparativeadvantage in ﬁnal goods, due to the fact that the gains from trade in intermediate goods contribute
substantially more than the gains from trade in ﬁnal goods to the overall gains from trade of acountry.
We also ﬁnd that, during 1995-2011, the average increase in gains from intermediate goods tradeacross all countries in our sample is distinctly higher than the average increase in gains from ﬁnal
goods trade. This suggests that gains from trade due to international fragmentation of production
is becoming more important over time relative to gains from trade in ﬁnal goods.
We ﬁnd that the above results concerning gains from trade are robust to generalization to a
multi-sector model with inter-sectoral input-output linkage. For future research, we can make useof this multi-sector model to explore other issues, such as how and why changes in foreign tradeshares in intermediate goods over time dier across countries and across sectors.

32

References[1] Anderson, James E. and Eric van Wincoop: Gravity with Gravitas: A Solution to the Border
Puzzle, American Economic Review, 93(1), 170-192 (2003)[2] Antras, Pol and Alonso de Gortari: On the Geography of Global Value Chains, NBER working
paper no. 23456 (2017)[3] Arkolakis, Costas, Costinot, Arnaud and Andres Rodriguez-Clare: New Trade Models, SameOld Gains?, American Economic Review, 102(1), 94—130 (2012)[4] Baldwin, Richard E. and Daria Taglioni: Gravity Chains: Estimating Bilateral Trade Flows
when Trade in Components and Parts Is Important, in Aaditya Mattoo, Zhi Wang and ShangJin Wei (eds.) Trade in Value Added: Developing New Measures of Cross-Border Trade, Centre
for Economic Policy and World Bank (2013)[5] Baldwin, Richard E., and Anthony Venables: Spiders and snakes: Oshoring and Agglomeration in the Global Economy, Journal of International Economics 90(2), 245—254 (2013)[6] Chaney, Thomas: Distorted Gravity: The Intensive and Extensive Margins of International
Trade, American Economic Review, 98(4), 1707—1721 (2008)[7] Caliendo, Lorenzo and Fernando Parro. 2015. “Estimates of the Trade and Welfare Eects of
NAFTA.” Review of Economic Studies.
[8] Costinot, Arnaud and Andres Rodriguez-Clare. 2014. “Trade Theory with Numbers: Quantifying the Consequences of Globalization.” in Handbook of International Economics Volume 4,edited by G. Gopinath, E. Helpman, and K. Rogo.
[9] Costinot, Arnaud; Jonathan Vogel, and Su Wang. 2013. “An Elementary Theory of Global
Supply Chains.” Review of Economic Studies 80, 109—144 (2013)[10] Eaton, J. and Kortum, S.: Technology, Geography and Trade, Econometrica 70(5), 1741—1779(2002)[11] Eaton, J. and Kortum, S. 2012. “Putting Ricardo to Work.” Journal of Economic Perspectives
26(2), Spring, 65-90.
[12] Grossman, Gene M., and Esteban Rossi-Hansberg: Trading Tasks: A Simple Theory of Oshoring, American Economic Review 98(5): 1978-1997 (2008)[13] Head, Keith and Thierry Mayer. 2014. “Gravity Equations: Workhorse, Toolkit, Cookbook.”
Handbook of International Economics Vol. 4, Elsevier Publisher, pp.131-195.

33

[14] Head, Keith, Thierry Mayer, and John Ries. 2010. “The erosion of colonial trade linkages after
independence.” Journal of International Economics.
[15] Hummels, D., Ishii, J., Yi, K., The nature and growth of vertical specialization in world trade,
Journal of International Economics 54, 75—96 (2001)[16] Johnson, R.C. and G. Noguera: Accounting for intermediates: Production sharing and tradein value added, Journal of International Economics 86 224—236 (2012)[17] Kee, Hiau Looi and Heiwai Tang: "Domestic Value Added in Exports: Theory and Firm
Evidence from China." American Economic Review, 106(6): 1402-36. (2016)[18] Koopman, R., Zhi Wang, and Shang-Jin Wei: Tracing Value-added and Double Counting in
Gross Exports, American Economic Review 104(2): 459-494 (2014)[19] Simonovska, Ina and Michael Waugh. 2014. “The Elasticity of Trade: Estimates and Evidence.”
Journal of International Economics, 92(1), 34-50.

34

A

Data Description

To carry out our empirical work, we use data from various sources. Here is a summary of the data
we use in the paper• Bilateral value of trade of intermediate goods and ﬁnal goods are obtained from the underlying
inter-country input-output (ICIO) tables of the November 2015 version of Measuring Tradein Value Added (TiVA) data set, an OECD-WTO joint project to calculate the value added
by a country in the production of any good or service that is exported to the destination
country. This data set was ﬁrst released in late May 2013, and was updated in June 2015
and November 2015. We only use the November 2015 version of the data set.
• The data for bilateral trade costs come from the GeoDist dataset of CEPII, which is also usedby Head, Mayer and Ries (2010).

• We adopt all the above data without any modiﬁcation, in order to avoid any possible bias
caused by inappropriate treatment.

• In the underlying ICIO table of the TiVA dataset, we can directly observe the value ofintermediate goods sourced from sector u of country o to be used in the production of goods
vu , as well as the value of sector-v ﬁnal goods exported from country
in sector v of country q, [qoe v , together with the sectoral value-added of country q in sector v, Yqv . The
o to country q, [qo

sectoral output for manufacturing sector v of country q, \qv (v = 1> ===> P), can be written as
\qv =
=

PQ PN
o=1

PQ

p=1

vu
v
u=1 [qo + Yq (total value of intermediate goods used plus value-added)

PQ
nv
ev
n=1 [pq +p=1 [pq (total value of intermediate and ﬁnal goods produced)

PN

In the one-sector model, we carry out the following aggregation. (Note that the source sectorsof intermediate goods do not include primary sectors.)
[qo =

PP PN
v=1

vu
u=1 [qo ,eqo = PP [ev[
v=1 qo >[qwith  q = PPv
v=1 \qP[q = Qo=1 [qoP
eq = Q [e[o=1 qoh

For the TIG model,  qq = [qq +[hqq .
[q +[qIn the multi-sector model, we carry out the following aggregationu[qo=with  vq =PNvu
v=1 [qo ,
v
[q
\qv

35

[qu =

PQ

v
o=1 [qoCountries in the Sample for Estimations
Argentina

Australia

Austria

BelgiumBrazilBrunei Darussalam

Bulgaria

Cambodia

Canada

Chile

China

Columbia

Costa Rica

Croatia

CyprusCzech Republic

Denmark

Estonia

FinlandFranceGermany

GreeceHong Kong, China

Hungary

Iceland

India

Indonesia

IrelandIsrael

Italy

Japan

Korea

LatviaLithuania

Luxembourg

Malaysia

Malta

MexicoNetherlands

New Zealand

NorwayPhilippines

PolandPortugal

Russian Federation

Saudi Arabia

Singapore

Slovak Republic

Slovenia

South Africa

Spain

SwedenSwitzerland

TaiwanThailandTunisia

TurkeyUnited Kingdom

United States

Viet Nam

SectorType

SectorType

Agriculture, hunting and ﬁshingPrimary

Manufacturing nec; recycling

Manufacturing

Mining and quarrying

Primary

Electricity, gas and water supply

Service

Food products and beverages

Manufacturing

Construction

Service

Textiles products and footwear

Manufacturing

Wholesale and retail trade

Service

Products of wood and cork

Manufacturing

Hotels and restaurants

ServicePulp, paper products and printing

Manufacturing

Transport and storage

ServiceCoke, reﬁned petroleum products

Manufacturing

Post and telecommunications

Service

Chemicals and chemical products

Manufacturing

Financial intermediation

Service

Rubber and plastics products

Manufacturing

Real estate activities

Service

Other mineral products

Manufacturing

Renting of machinery & equipment

Service

Basic metals

Manufacturing

Computer and related activities

Service

Fabricated metal products

Manufacturing

R&D and other business activities

Service

Machinery and equipment, nec

Manufacturing

Public admin. and social security

Service

Computer, Electronic equipment

Manufacturing

Education

ServiceElectrical machinery and apparatus

Manufacturing

Health and social work

Service

Motor vehicles and trailers

Manufacturing

Other services

Service

Other transport equipment

Manufacturing

Private households employment

Service36

B

Variables used in the diagrams in this paper

Pi_nn: Country n’s home-supplied market share in intermediate goods used in the production of
manufactured goods
S_nn: Country n’s home-supplied market share in manufactured ﬁnal goods
Com_inter: ln (Competitiveness in exporting intermediate goods used in manufactured goods
production) (relative to the mean)
Com_ﬁnal: ln (Competitiveness in exporting manufactured ﬁnal goods) (relative to the mean)
Com_EK: ln (Competitiveness in exporting manufactured goods under the TIG model) (relative
to the mean)
wel_EK: Gains from trade relative to autarky under the TIG model
wel_LQ: Gains from trade relative to autarky under our modelsdwel_ﬁnal: Cumulative change in gains from trade in manufactured ﬁnal goods during 1995 —2011
sdwel_inter: Cumulative change in gains from trade in intermediate goods used in the production of manufactured goods during 1995 — 2011
relpi: Pi_nn / S_nn
relcom_fnl: Com_ﬁnal - Com_EK
T_ﬁnal: ln(Technology stock in producing manufactured ﬁnal goods) (relative to the mean)
T_interm: ln(Technology stock in producing intermediate goods used in the production of
manufactured goods) (relative to the mean)
relT: T_interm - T_ﬁnal
relcom: Com_inter - Com_ﬁnal
relwel: wel_EK / wel_LQ
foreignaccess: Access to foreign intermediate goods
lw: ln (wage)

37

C

Slopes and statistical signiﬁcanceThe slopes and statistical signiﬁcance of the ﬁtted lines in the ﬁgures are given below.
Figure

1995

2000

2005

2011

Figure 2

0.70W (0=38)

1.25WWW (0=25)

1.62WWW (0=20)

1.57WWW (0=24)

Figure 3

1.04WWW (0=05)

1.05WWW (0=05)

1.04WWW (0=05)

1.01WWW (0=04)

Figure 4

0.63WWW (0=08)

0.61WWW (0=08)

0.65WWW (0=09)

0.69WWW (0=10)

Figure 5

0.83WW (0=34)

0.60W (0=33)

0.41 (0.34)

0.36 (0.38)

Figure 6

0.18WWW (0=05)

0.24WWW (0=05)

0.36WWW (0=06)

0.36WWW (0=07)

Figure 7

0.66WWW (0=13)

0.57WWW (0=10)

0.98WWW (0=10)

1.13WWW (0=13)

Figure 12

1.28WWW (0=06)

1.29WWW (0=06)

1.25WWW (0=06)

1.23WWW (0=06)

Figure 13

0.74WWW (0=07)

0.74WWW (0=08)

0.78WWW (0=09)

0.84WWW (0=09)

Figure 14

0.86W (0=43)

0.49 (0.41)

0.21 (0.42)

0.13 (0.46)

Figure 90.10WW (0=04)

0.14WWW (0=05)

0.04 (0=06)

0.06 (0=05)

Figure 10

0.14WWW (0=05)

0.18WWW (0=05)

0.08W (0=04)

0.09WW (0=05)

WWW

indicates 1% signiﬁcance level, WW indicates 5% signiﬁcance level, W indicates 10% signiﬁcance level

Standard errors are in parentheses.

D

Tables 8, 9 and 10?Tables 8, 9, and 10 about hereA

E

Proof of Corollary 1
h



13
3  q

Step 1. First we want to prove that if 
eqq A  qq and  q ? 0=333 then (e qq )31@ ( qq )31@( q )( qq ).

qA

Let d = expenditure on home-supplied ﬁnal goods; e = total expenditure on ﬁnal goods; f =expenditure on home-supplied intermediate goods; g = total expenditure on intermediate goods.
Thus, eqq = de ;  qq = gf and  qq = d+fe+g , where 0 ? d ? e and 0 ? f ? g.

According to the data, for more than 78% of the observations,  q ? 0=333.9 To be conservative, = 4=0, following Simonovska andwe assume that  = 0=333. We also assume that  =  = eqWaugh (2014). Thus,
9

340 out of a total of 434 observations have  q ? 0=333.

38

Country

Gains from trade
Our

Country

Gains from trade
Our

TIG

Country

TIG

Our

Model

Model

Gains from trade
TIG

Model

Argentina

4.85%

6.42%

Germany

7.51%

9.37%

Norway

6.97%

8.01%

Australia

4.33%

7.76%

Greece6.62%

10.09%

Philippines

6.69%

8.11%

Austria

9.51%

11.95%

Hong Kong

24.23%

31.58%

Poland13.73%

12.63%

Belgium

12.84%

9.82%

Hungary

26.59%

21.69%

Portugal

11.57%

11.71%

Brazil

3.70%

3.86%

Iceland

9.11%

9.94%

Russia

4.71%

5.87%

Brunei19.18%

55.82%

India

8.67%

5.22%

Saudi Arabia

7.76%

18.35%

Bulgaria

19.01%

18.52%

Indonesia

3.67%

5.77%

Singapore

8.15%

6.57%

Cambodia

29.09%

24.67%

Ireland10.16%

12.39%

Slovak

24.53%

20.91%

Canada

7.58%

9.61%

Israel

6.24%

8.30%

Slovenia

15.35%

17.22%

Chile

5.89%

10.77%

Italy

7.44%

7.89%

South Africa

8.07%

10.15%

China

17.92%

7.04%

Japan

2.37%

2.92%

Spain

7.75%

8.74%

Columbia

5.18%

8.14%

Korea

13.52%

9.22%

Sweden8.80%

10.28%

Costa Rica

13.59%

17.39%

Latvia13.39%

16.20%

Switzerland

8.87%

12.48%

Croatia

7.81%

10.73%

Lithuania

11.07%

13.73%

Taiwan20.95%

15.09%

Cyprus10.82%

19.09%

Luxembourg

29.52%

30.54%

Thailand

22.24%

16.71%

Czech

21.63%

17.38%

Malaysia

44.67%

23.32%

Tunisia

20.07%

18.99%

Denmark

4.44%

5.20%

Malta

6.35%

9.84%

Turkey16.95%

10.29%

Estonia17.15%

17.64%

Mexico12.41%

14.33%

UK

6.67%

9.58%

Finland10.07%

9.37%

Netherlands

5.12%

3.83%

USA

3.01%

4.44%

France

8.50%

8.67%

New Zealand

6.45%

8.64%

Viet Nam

44.50%

27.23%

Table 8: Gains from Trade as of 201139

Country

Intermediate Goods

Final Goods

Total

95-00

00-05

05-11

95-11

95-00

00-05

05-11

95-11

95-11

Australia-0.12%-0.09%

0.53%

0.31%

0.03%

0.56%

-0.14%

0.45%

0.77%

Austria-0.11%

0.81%

1.02%

1.72%

0.81%

-0.70%-0.24%-0.13%

1.65%

Belgium

0.09%-0.78%

2.17%

2.37%

-0.56%-0.31%-0.49%-1.36%

0.93%

Canada1.41%-0.59%-0.53%

0.29%

0.47%

-0.65%-0.38%-0.57%-0.29%

Denmark-0.17%

0.33%-0.33%-0.16%-0.04%-0.23%-1.27%-1.54%-1.75%

Finland

0.91%

0.37%

2.49%

3.76%

0.10%

0.24%

0.02%

0.37%

4.24%

France

1.59%

0.01%

1.05%

2.65%

0.56%

0.04%

0.21%

0.81%

3.55%

Germany

1.37%

0.17%

1.09%

2.63%

0.74%

-0.12%

0.16%

0.78%

3.50%

Greece-0.01%-0.20%

0.49%

0.28%

0.72%

0.02%

-0.71%

0.03%

0.32%

Ireland-0.43%-2.11%-0.98%-3.52%-0.58%-0.83%-0.16%-1.56%-5.36%

Iceland

0.99%

0.86%

0.81%

2.66%

0.81%

-0.17%-0.51%

0.13%

2.89%

Israel-0.73%

1.42%-0.94%-0.25%-0.22%

0.33%

0.18%

0.29%

0.05%

Italy

0.86%

0.16%

0.64%

1.66%

0.42%

-0.17%

0.21%

0.46%

2.17%

Japan

0.15%

0.39%

0.40%

0.94%

0.15%

0.13%

0.08%

0.37%

1.32%

Korea

1.66%

-0.53%

3.88%

5.01%

0.01%

-0.42%

0.23%-0.18%

4.90%

Luxembourg

1.70%

1.14%

1.88%

4.72%

4.28%

-2.87%

0.53%

1.95%

7.50%

Netherlands-0.40%-1.16%

1.00%-0.56%-0.81%-0.83%-0.08%-1.72%-2.37%New Zealand-0.22%-0.28%

0.87%

0.37%

-0.76%

1.24%-0.32%

0.15%

0.54%

Norway0.21%-0.55%-0.21%-0.55%

0.37%-0.66%-0.24%-0.52%-1.12%

Portugal-0.64%

0.10%

0.50%

-0.04%

0.48%-0.35%-0.09%

0.05%

0.01%

Spain

2.22%

-0.70%-0.89%

0.63%

1.07%

-0.30%

0.08%

0.85%

1.54%

Sweden1.42%-0.18%-0.01%

1.23%

0.75%

-0.39%

0.06%

0.42%

1.71%

Switzerland

1.04%

0.38%

-0.82%

0.59%

2.12%

-1.42%-0.58%

1.28%

1.95%

UK

-0.07%-0.49%

0.98%

0.42%

0.31%

-0.13%

0.44%

0.62%

1.08%

USA

0.10%

-0.11%

0.23%

0.22%

0.29%

0.09%

0.03%

0.41%

0.64%

Table 9: Change in Gains from Trade for OECD (i.e. Developed) Countries

40

Country

Intermediate Goods

Final Goods

Total

95-00

00-05

05-11

95-11

95-00

00-05

05-11

95-11

95-11

Argentina

0.19%

1.61%

0.17%

1.97%

0.27%

0.49%

0.06%

0.82%

2.83%

Brazil

0.93%

0.23%

-0.06%

1.10%

0.22%

-0.13%

0.24%

0.32%

1.44%

Bulgaria-4.09%

3.65%

0.32%

-0.11%

0.50%-0.11%

0.08%

0.48%

0.42%

Chile

-0.10%-0.36%-0.16%-0.62%-0.37%

0.12%

0.61%

1.44%

0.82%

China

-0.79%

2.11%-1.32%

0.00%

0.02%

0.30%

-0.40%-0.07%-0.08%

Croatia-0.03%

0.19%-0.62%-0.46%

0.91%-0.21%-1.10%-0.41%-0.91%

Colombia-0.15%

0.10%

0.47%

0.42%

-0.18%-0.01%

0.75%

0.56%

1.00%

Cyprus0.45%-2.13%

0.74%-0.94%

1.08%-1.72%

0.12%-0.52%-1.54%

Czech

1.64%

3.77%

2.11%

7.52%

-0.32%

0.45%-0.49%-0.36%

7.39%

Estonia

9.07%-5.35%-6.71%-2.99%

0.60%-1.34%-1.77%-2.50%-6.01%

Hungary

13.96%-6.56%

1.67%

9.07%

0.36%

0.13%

-0.76%

0.90%

10.52%

Indonesia

0.37%-2.03%—0.48%-2.15%-0.15%-0.31%

0.11%-0.36%-2.55%

India-0.39%

1.99%

3.23%

4.83%

-0.21%

0.49%

0.16%

0.45%

5.34%

Lithuania-0.72%-0.41%

2.05%

0.93%

0.73%

-0.03%

0.00%

0.70%

1.71%

Latvia

1.31%

2.39%

0.18%

3.89%

4.28%

-2.87%

0.54%

1.95%

6.19%

Mexico2.20%-0.59%-0.38%

1.23%

0.72%

-0.09%

0.28%

0.92%

2.26%

Malaysia

33.00%

26.53%-29.66%29.87%-3.53%-0.83%-0.03%-4.39%

26.13%

Philippines-3.98%

5.17%-9.31%-8.13%-1.00%

0.06%

0.06%

-0.88%-9.29%

Poland

2.53%

1.95%

2.49%

6.97%

1.06%

0.33%

0.34%

1.74%

8.99%

Romania-0.56%

0.37%-1.52%-1.71%

0.52%

0.50%

0.52%

1.54%

-0.16%

Russia-0.14%

0.46%

0.50%

0.82%

-0.93%

0.22%

0.12%

-0.59%

0.24%

Slovakia

7.33%-0.59%

1.51%

8.24%

2.87%

0.63%

-1.52%

1.98%

10.90%

Slovenia

2.35%-1.16%

0.72%

1.91%

0.98%

-1.26%

0.24%-0.04%

1.98%

Thailand

3.08%

4.28%

3.30%

10.66%-1.06%-0.01%

0.14%-0.93%

9.91%

Turkey

0.56%

9.80%

2.58%

12.95%

0.48%-0.60%

0.75%

0.63%

12.88%

Taiwan

0.94%

1.87%

5.00%

7.82%

1.14%

-0.62%

0.03%

0.55%

8.67%

Viet Nam

7.27%

17.70%

4.91%

29.88%

0.82%

1.74%

1.35%

3.90%

35.80%South Africa

1.94%

0.68%

-0.97%

1.65%-0.06%

0.25%

0.70%

0.89%

2.62%

Table 10: Change in Gains from Trade for non-OECD (i.e. Developing) Countries41µ ¶ µµ ¶¶11
1  q1
1  q= 0=5 and== 0=75.
= 0=25 and

e
e
 q
 q
 q



Note that 
eqq A  qq +, dg A ef. Moreover, we assume that 2de + ef  fg A 0, which holds

for more than 95% of the observations.10 Thus, we have(dg  ef) (2de + ef  fg) A 0(dg  ef) [2 (de + ef)  (ef + fg)]¶µ
dg  ef2
ef + fg¶µ
dg  ef1+2
ef + fgµ¶
dg + fg 2=,
ef + fgA 0
dg  efA
de + efdg  efde + dg
A 1+=, which is great than one, since dg A ef,
de + efde + efA

de + dgde + ef

dg + fg
dg  ef
and 1 + { =since (1 + {)2 A 1 + 2{ where { =ef + fg
ef + fg
¶2
¶
µ
µ
d e+g
d+f g
·
·
A
/
e+g f
e d+f
¶ 13q¶1µµd + f g q
d e + g h
·
·
/
A
e+g f
e d+f




¶3 1 3 13qµ
³ d ´3 1 ³ f ´3 13q
h
 q

d
+
f
h
 q

/
A
e
g
e+g

/

h



13
3  q(e qq )31@ ( qq )qA ( qq )31@( q )Therefore, for at least 73% [which comes from 78%  (100%  95%)] of the observations, eqq A qq implies that the TIG model under-estimates the gains from trade. 73% is considered a very large
fraction of the observations su!cient to deliver statistically signiﬁcant correlation in the sample.

¸ h

i
13 q
h
3
@ ( qq )31@( q ) , we want to prove that
Step 2. Next, deﬁning U  (e
 qq )31@ ( qq ) q

an increase in 
eqq @ qq leads to an increase in U. That is, the curve of U on the y-axis against
eqq @ qq on the x-axis has a positive slope.

ln  qqln U = 0=25 ln 
eqq ¶0=5 ln  qq +µ0=75 ¶
µ
 qq

eqq
 0=75 ln= 0=25 ln
 qq
 qq
µ ¶
 µ
¶¸
dg
f e+g
= 0=25 ln 0=75 ln
.
ef
g d+f

10

413 out of a total of 434 observations have 2de + ef 3 fg A 0.

42

(24)

Note that dg A ef and 2de + ef  fg A 0 imply that
2d2 eg + defg A egf2/

eg (2d  f) (d + f) A 0/

2d A fFirst we examine the case when 
eqq A  qq . From (24), we haveg ln U
0=25
0=75
=
+
A0
gd
d
d+f

since 2d A f.

That is, given that 
eqq A  qq , an increase in 
eqq @ qq (caused by an increase in d) leads to arise in U. (Note that changes in d while keeping e unchanged would still capture all possible d@eratios. Thus, it is enough to just consider changes in d.)Second, we examine the case when 
eqq ?  qq . In that case, we have, ef A dg and 2de + ef A fg.

If we add the two inequalities, we have

2de + 2ef A dg + fg/

2e (d + f) A g (d + f)/

2e  g A 0

From (24), we haveg ln U
0=25
0=75
=

?0
ge
e
e+g

since 2e A g.

That is, given that 
eqq ?  qq , an increase in 
eqq @ qq (caused by a decrease in e) leads to arise in U as well. (Note that changes in e while keeping d unchanged would still capture all possible
d@e ratios. Thus, it is enough to just consider changes in e.) ¥F

Multi-sector extension: Detailed calculation

From (20), we can infer that the competitive price of variety m of sector-v intermediate goods (usedto produce manufactured goods) exported from o to q is given by
svqo (m) =
where
fvo =

ÃQ

fvo
 v for v = 1> 2> ===> N>]ov (m) qoNuvu  vuou=1 (So @ o )v
1  o!13 vo µ
43

zo
 vo

¶ vo

for v = 1> 2> ===> N>(25)

is the unit cost of an input bundle whose production function is given by equation (18) (with q
set to o), with Sov being the unit price of the sector-v composite intermediate good, the production
function of which is given by equation (19) (with q set to o). It can be easily shown that
Sqv = (
wherev 3 1v
q)

for v = 1> 2> ===> N>

PQ
3
v
v
v v
q 
p=1 Wp (fp  qp )(26)

for v = 1> 2> ===> N>which is deﬁned as country q’s global access to the sector-v intermediate goods.
The market share of the sector-v intermediate goods (used to produce manufactured goods)
imported from country o in country q is therefore given byv vqo =v[qo
Wov (fvo  vqo )3Gov ( vqo )3
=
=
v
v
[qv
q
q

v

for v = 1> 2> ===> N>(27)

v is the imports of sector-v intermediate goods from country o to country q, [ v is thewhere [qoqtotal expenditure on sector-v intermediate goods in country q, and Gov  Wov (fvo )3 is country o’s

competitiveness in supplying sector-v intermediate goods.

From (21), we can infer that the competitive price of variety l of sector-v ﬁnal goods that canpotentially be exported from o to q is given by
sevqo (l) =fvo
 v for v = 1> 2> ===> P ,fv (l) qo]owhere fvo is given in (25). Note that sevqo (l) = 4 for v = P + 1> P + 2> ===> N and q 6= o, as we
assume that ﬁnal S&P goods are non-tradable.

Similar to (27), the market share of sector-v ﬁnal goods imported from country o in country q
is given byv
fv (fv  v )3hv
fv ( v )3h
ev
W
G
[
v
o qo
qo
qo
o
o
=
=

eqo =
eqv
fvq
fvq
[

for v = 1> 2> ===> P>

e v is the imports of sector-v ﬁnal goods from country o to country q, [eqv is the total
where [
qo
P
v
h
Q
3

v v
v
is deﬁned as country
expenditure on sector-v ﬁnal goods in country q, fvq Wfp (fp  qp )
p=1

fv (fv )3hv is the competitiveness of country o in
fv  Wn’s global access to sector-v ﬁnal goods, and Gooosupplying sector-v ﬁnal goods. Note that 
evqo = 0 for v = P + 1> P + 2> ===> N and q 6= o as ﬁnal
S&P goods are non-tradable.

R1
0

The
h exact
i price index of the sector-v composite ﬁnal good captured by the subutility expressionvfln Tq (l) gl in the utility function (17) is given by³ ´31@hv
fqv = fvq
for v = 1> 2> ===> N.
S
44

(28)

Gains from Trade
Welfare of country q, Zq , is deﬁned as the real wage of q. The percentage change in real wage
in country q is given byg ln Zq = g ln zq 

N
P

v=1

fqv
vq g ln S

µ
¶
1
v
f
g ln zq + v g ln q
=
e
µ
¶
PN
g ln evqqvv=v
v=1 q g ln zq  g ln fq 
e

PN

v
v=1 qv

where the last equality follows from g lnhhv qq = g ln fvq  h1v g ln fvq .
According to (25) and (26), the percentage change in the unit cost of the input bundle is givenbyg ln fvq =  vq g ln zq + (1   vq )
=

,

PN

vu
u
u=1  q g ln SquPvu g ln q.
 vq g ln zq  (1   vq ) Nu
u=1 q

for v = 1> 2> ===> N>µ¶g ln uqvuglnz
for v = 1> 2> ===> N>

+
q
u=1 q
u

¸
P
g ln  uqqvuu
= (1   vq ) N


g
ln
f
)

(g
ln
z
(29)
q
q
u=1 q
u

g ln zq  g ln fvq = (1   vq )PN

where the last equality follows g ln  uqq = u g ln fuq  g ln

u.
q

v

For country q, deﬁne cq  {d ln wn  d ln csn }, which is a N  1 vector, q { g lnv qq }, whichis also a N  1 vector, Bq is deﬁned as a diagonal matrix with the vth diagonal element being  vq ,q { vu
q } is the N  N input-output matrix of country q. Thus, (29) can be rewritten as
cq = (I  Bq ) q (cq +  q ),cq = [I (I  Bq ) q ]31 (I  Bq ) q q= {[I (I  Bq ) q ]31  I} q

where [I (I  Bq ) q ]31 is a typical Leontief inverse matrix. Deﬁne  vu
q as the row v column uelement of [I (I  Bq ) q ]31  I, theng ln Zq¶g ln 
evqq PN vu g ln  uqq= 
+ u=1  q
v
e
u

P
evqq PN PN
g ln  uqqv g ln =  N
 v=1 u=1 vq  vuv
qv=1 qeuPNv
v=1 qµThus the gains from trade (starting from autarky) of country n is given by
v

QN QN
v 3 hqv
u 3 quqdD  1 = QN (eZ1qv=1  qq )v=1
u=1 ( qq )v  vu

45(30)

In the special case of q = I (no inter-sectoral input-output linkage), we have I (I  Bq ) q =vvvu
Bq ,  vv
q = (1   q ) @ q and  q = 0 for v 6= u. The gains from trade will be reduced to


¸vq
13 v
1
q
v 3 hv
v 3 v  vq
dD  1 = QN (e
Z

)
(
)
 1.
qq
q
qq
v=1

dD is the weighted geometric mean of the sectoral welfare
In this case, the overall change in welfare Z
q
31

13 v

3 v  vq

change (e vqq ) hv ( vqq )qfor all v, with welfare change in each sector being equal to that in the

one-sector case.

Taking the model to the data, as we are interested only in gains from trade in manufactured
ﬁnal goods and trade in intermediate manufactured and S&P goods used to produce manufactured
goods, the total gains from trade is given by (22), and we compare it to the total gains from tradeof the multi-sector TIG model given by (23).
We also deﬁne the aggregate competitiveness of country q in ﬁnal goods as
eq =
log G

PP

v
ev
v=1 q ln Gq

and the aggregate competitiveness of country q in intermediate goods as
PP PN
v
v
vu
u
u=1 q (1   q )  q ln Gq
log Gq = v=1 PPvv
v=1 q (1   q )both of which are the expenditure share weighted average of the levels of sectoral competitiveness.

G

Online Appendix

G.1

An Alternative ModelIn this appendix, we put forward a model which assumes that ﬁnal and intermediate goods aredierentiated according to the country of origin. We use this model to illustrate that the gravity
equations that we derive can arise from many dierent settings. Thus, the gravity equations weobtain in the main body of the paper can arise from a rather general model.
The Setting. There are Q countries in the world, indexed by q = 1> ===> Q . Country q has laborendowment Oq , which serves as the only primary input in production of all kinds of goods. However,
we can interpret labor metaphorically as a composite factor input that includes labor, capital, andland. Labor is fully mobile across sectors within the same country, but not mobile across countries.
Labor wage in country q is denoted by zq . The production of an intermediate or ﬁnal good requires
the conversion from a composite input called an input bundle, which is a combination of labor andthe entire set of intermediate goods (which is called an composite intermediate good). We assume46

that all countries have the capability to produce a variety of intermediate good and a variety ofﬁnal good. All goods are tradeable but there are trade costs.
A typical country imports intermediate goods from all over the world, then combine the entire
set of intermediate goods with domestic labor to form input bundles, and then produces either
intermediate goods or ﬁnal goods from the input bundles. The goods are then exported to destinations all over the world. In equilibrium, all countries export some intermediate goods and someﬁnal goods to all other countries and to themselves. Markets for both intermediate and ﬁnal goods
are assumed to be perfectly competitive.
Preferences. In each country a representative household maximizes utility by choosing a consumption bundle of ﬁnal goods, subject to the budget constraint. The utility function of therepresentative household in any country is given by¸ 
 Q31 31P(etp ) 
X=

,

(31)

p=1

where tep is the consumption of the ﬁnal good produced by country p, and  A 1 is the elasticity of
substitution between each pair of ﬁnal goods. The utility function of the representative consumer
is the same for all countries.

Technology. Each ﬁnal good or intermediate good is converted from the input bundle. Denotethe e!ciency of country o in converting the input bundle into a ﬁnal good by Weo , and denote the

e!ciency for converting the input bundle into an intermediate good by Wo . The production functionof an input bundle in country q is given by:|q = (Pq )13 q (oq ) q , where 0 ?  q ? 1,(32)

where |q is the quantity of input bundle produced in country q; Pq is the corresponding quantity of
the composite intermediate good (which is deﬁned in equation (33) below); oq is the corresponding
labor input.
The quantity of composite intermediate good produced by q is determined by the following
function:
Pq =

 Q
P

(tp )

 0 310

p=10¸ 031;q,(33)where tp is the use of the intermediate good produced by country p, and  0 A 1 is the elasticity
of substitution between each pair of intermediate goods.
The competitive price of ﬁnal good exported from o to q is given by

where
fo =

µ

seqo =So1  ofo
 qo ,
Weo¶13 o µ

47

zo
o

¶ o

is the unit cost of an input bundle corresponding to the production function (32), with So being
the unit price of the composite intermediate good, the production function of which is given byequation (33).
The competitive price of intermediate good exported from o to q is given by
sqo =

fo
 qo .
Wo

Gravity equation for ﬁnal goods trade. With the utility function (31), we can derive agravity equation for trade in ﬁnal goods:
e e
epq = Gq [p ( pq )13[ep

epq is the exports of country q ﬁnal good to country p, G
e q is the competitiveness of
where [
ep is the total expenditure on ﬁnal goods in country p,
country q in exporting its ﬁnal good, [
P
Q
13
ep =
e
is the global access of ﬁnal goods by country p, and 1 is the elasticity of
o=1 Go ( po )trade in ﬁnal goods. In fact, the same gravity equation can be obtained under many other models,such as dierent types of utility functions. The parameter corresponding to the elasticity of trade
in ﬁnal goods can vary across dierent model settings.
e q = Weq (fq )13 , where fq is the unit cost of an input bundle in country q,
We assume that G
and Weq here stands for the technology level of country q in producing ﬁnal good. The parametercorresponding to this technology term can vary across dierent model settings.
Thus, the market share of ﬁnal good is given byepq =e q ( pq )13G
ep

which is the similar to (7) in the main text. From this, we can derive a similar gravity equation as(13).
Gravity equation for intermediate goods trade. With the production function for thecomposite intermediate good (33), we can derive a gravity equation for trade in intermediate goods:
[pq =

Gq [p

( pq )130pwhere [pq is the exports of country q intermediate good to country p, Gq is the competitivenessof country q in exporting its intermediate good, [p is the total expenditure on intermediate goods
P
130
is the global access of intermediate goods by country p,
in country p, p = Q
o=1 Go ( po )and 1   0 is the elasticity of trade in intermediate goods. Again, the same gravity equation canbe obtained under many other models. The parameter corresponding to the elasticity of trade inintermediate goods can vary across dierent model settings.
48

0

We assume Gq = Wq (fq )13 , where fq is the unit cost of an input bundle in country q, and Wq
here stands for the technology level of country q in producing intermediate good. The parametercorresponding to this technology term can vary across dierent model settings.
Thus, the market share of intermediate good is given by pq =Gq ( pq )130pwhich is the similar to (6) in the main text. From this, we can derive a similar gravity equation as
(10).

G.2

Use of continuous distance for the gravity model

Comparing Tables 11 and 12, we see that the magnitude of the distance elasticity of trade inintermediate goods is smaller than that of trade in ﬁnal goods.
?Tables 11 and 12 are about hereA
Variable

1995

2000

2005

2008

2009

2010

2011

ln(Dist)-0.90***-0.82***-0.82***-0.80***-0.81***-0.81***-0.81***(0.015)(0.010)(0.010)(0.010)(0.010)(0.010)(0.010)0.45***

0.48***

0.46***

0.43***

0.42***

0.42***

0.38***(0.065)(0.061)(0.062)(0.059)(0.061)(0.061)(0.060)0.18***

0.22***

0.22***

0.19***

0.17***

0.19***

0.18***(0.050)(0.047)(0.048)(0.046)(0.047)(0.047)(0.047)0.31***

0.25***

0.20***

0.21***

0.22***

0.19***

0.18***(0.028)(0.027)(0.027)(0.026)(0.027)(0.027)(0.027)-0.86***-0.36***-0.34***-0.33***-0.32***-0.34***-0.35***(0.15)(0.068)(0.065)(0.063)(0.064)(0.064)(0.063)0.44***

0.35***

0.34***

0.30***

0.33***

0.33***

0.35***(0.071)(0.069)(0.070)(0.067)(0.069)(0.069)(0.068)

Dest. FE

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Observations

3,595

3,600

3,600

3,600

3,600

3,600

3,600

Shared Border
Shared Language
Shared Legal
Shared Currency
Colonial Linkage

WWW indicates 1% signiﬁcance level, WW indicates 5% signiﬁcance level,
WWW indicates 1% signiﬁcance level

Table 11: Gravity Equation for Trade in Intermediate Goods and Services

49

Variable

1995

2000

2005

2008

2009

2010

2011

ln(Dist)-1.16***-0.96***-0.92***-0.91***-0.92***-0.92***-0.90***(0.030)(0.018)(0.017)(0.017)(0.017)(0.017)(0.017)0.44***

0.67***

0.64***

0.64***

0.63***

0.64***

0.63***(0.13)(0.11)(0.10)(0.10)(0.10)(0.10)(0.10)

0.24**

0.42***

0.49***

0.41***

0.40***

0.45***

0.39***(0.096)(0.084)(0.081)(0.078)(0.078)(0.079)(0.078)0.45***

0.33***

0.27***

0.28***

0.33***

0.34***

0.31***(0.055)(0.048)(0.046)(0.045)(0.045)(0.045)(0.044)-2.98***-0.91***-0.60***-0.65***-0.62***-0.73***-0.57***(0.29)(0.12)(0.11)(0.11)(0.11)(0.11)(0.11)

0.52***

0.39***

0.40***

0.36***

0.30***

0.31***

0.34***(0.14)(0.12)(0.12)(0.11)(0.11)(0.12)(0.11)

Dest. FE

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Observations

3,561

3,579

3,582

3,590

3,587

3,589

3,585

Shared Border
Shared Language
Shared Legal
Shared Currency
Colonial Linkage

WWW indicates 1% signiﬁcance level,WWindicates 5% signiﬁcance level,

W indicates 10% signiﬁcance level

Table 12: Gravity Equation for Trade in Manufactured Final Goods

G.3

e q against xq
Plotting x

The strong correlation between e q (global access to ﬁnal goods) andq (global access to interme-

diate goods) is shown in Figure 11. ?Figure 11 about hereA

G.4

Unpacking the determinants of China’s ﬁnal goods competitiveness

Figures 12, 13 and 14 show that China’s rapid rise in competitiveness in ﬁnal goods is mainly due
to its rise in access to foreign intermediate goods and its low wage, but not due to its technology,
which is quite low relative to the mean. ?Figures 12, 13 and 14 are about hereA

50

Figure 11: e q : Global access to ﬁnal goods (y-axis) vs.

51

q : Global access to intermediate goods (x-axis)

e q (y-axis) vs. Iq : access to foreign intermediate goods (x-axis). For the estimated slope and statisticalFigure 12: G
signiﬁcance of each ﬁtted line, refer to Appendix C.

52

e q (y-axis) vs. Weq (x-axis). For the estimated slope and statistical signiﬁcance of each ﬁtted line, refer toFigure 13: G
Appendix C.

53

e q (y-axis) vs. ln zq (x-axis). For the estimated slope and statistical signiﬁcance of each ﬁtted line, refer toFigure 14: G

Appendix C.

54