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Determinants of Bilateral Trade in Manufacturing and Services: A Unified Approach

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Gravity models have been extensively used as workhorse models to study the determinants of international trade. While most of the literature has focused on trade in manufacturing, a recent literature has emerged that uses gravity models to study international trade in services. Despite showing that gravity equations are well suited to studying trade in services, there is little research on the systematic differences and specificities when using gravity models for each type of trade. This paper addresses this by studying the determinants of aggregate bilateral trade in services vis-à-vis manufacturing. The main objective is to understand the systematic differences between services and manufacturing trade that are borne out empirically. In doing so, we derive a joint theory that brings out "systematic" differences in response to scale and trade cost variables between trade in manufacturing and services. We build a unified theoretical framework that incorporates a demand bias towards services and a difference in national product differentiation between the two sectors. The demand bias yields larger income elasticities for trade in services compared to trade in manufacturing, and differences in national product differentiation produce a higher elasticity of bilateral trade in manufactures for the exporting country's size than in services. We show that the model predictions find support on traditional gravity equation estimates using various specifications and estimation approaches. We also investigate the role of virtual proximity and internet infrastructure in international trade in manufactures and services. We find that virtual proximity is a strong predictor of aggregate trade in services and manufacturing.
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Determinants of Bilateral Trade in Manufacturing and Services:
A Unified Approach
Satya P. Das
satyadas@usf.edu
Vinicios P. Sant’Anna
santann2@illinois.edu
October 5, 2021
Abstract
Gravity models have been extensively used as workhorse models to study the determinants of
international trade. While most of the literature has focused on trade in manufacturing, a recent
literature has emerged that uses gravity models to study international trade in services. Despite
showing that gravity equations are well suited to studying trade in services, there is little research
on the systematic dierences and specificities when using gravity models for each type of trade.
This paper addresses this by studying the determinants of aggregate bilateral trade in services
vis-`a-vis manufacturing. The main objective is to understand the systematic dierences between
services and manufacturing trade that are borne out empirically. In doing so, we derive a joint the-
ory that brings out ”systematic” dierences in response to scale and trade cost variables between
trade in manufacturing and services. We build a unified theoretical framework that incorporates a
demand bias towards services and a dierence in national product dierentiation between the two
sectors. The demand bias yields larger income elasticities for trade in services compared to trade
in manufacturing, and dierences in national product dierentiation produce a higher elasticity
of bilateral trade in manufactures for the exporting country’s size than in services. We show that
the model predictions find support on traditional gravity equation estimates using various specifi-
cations and estimation approaches. We also investigate the role of virtual proximity and internet
infrastructure in international trade in manufactures and services. We find that virtual proximity
is a strong predictor of aggregate trade in services and manufacturing.
Keywords: Trade in Services, Trade in Manufacturing, Gravity Model, National Product Dier-
entiation, Non-Homothetic Tastes, Internet, Virtual Proximity
JEL Classification: D11, D43, F12, F19, L80
Comments from Dan Bernhardt, Greg Howard, and seminar participants at University of Illinois at Urbana-Champaign,
University of South Florida, Winter School 2020, organized by the DelhiSchool of Economics and the Econometric Society,
and Midwest Economics Association 2021 Meeting are appreciated. We thank Christiane Hellmanzik and Martin Schmitz
for kindly sharing the data on bilateral hyperlinks and Anuradha Saha for sharing some calculations. All errors are our own.
Guest Faculty, Department of Economics, University of South Florida; Website: satyapdas.com
Department of Economics, University of Illinois at Urbana-Champaign. Website: vpsantanna.com
1 Introduction
Learning the determinants of bilateral trade by estimating gravity equations is an essential part of
the vast and growing empirical literature on international trade. Most of it study trade in goods or
manufacturing. However, international trade in services has grown faster than trade in manufacturing
in recent decades. The global share of exports of services in total exports has increased from 9% in
1970 to more than 20% in 2014 (Loungani et al.,2017).1Between 2005 and 2016, while total trade
(measured by adding exports and imports) in goods rose from $10 trillion to $16 trillion (i.e., a 60%
increase), that in services increased from $2.5 trillion to nearly $5 trillion, an increase of almost 100%
(UNCTAD,2018). Vis-`a-vis trade in manufacturing, our calculations using our collected sample
of countries yield that, between 2005 and 2017, at 2010 US prices, the total global manufacturing
trade grew at an annual rate of 1.97% while that of commercial services was about 4.14%. During
this period, global trade in services increased by 70% while manufacturing grew by 30%. Figure 1
illustrate these dierences in global international trade between services and manufacturing.
The existing literature on bilateral trade in services is relatively modest compared to the extensive
list of papers that apply gravity models to trade in manufacturing. Besides well-known data limita-
tions on trade in services, there are at least two other reasons for this. First, the increase of the share
of the service sector in international trade is a relatively recent phenomenon—evidently far more re-
cent than the famous paradigm of trade in wine and clothes, stylized by David Ricardo more than
two centuries ago. Second, there is a broad perception that there is no need to distinguish trade in
services from trade in manufacturing: the same general principles and insights derived for trade in
goods should directly apply to services trade.2This is however partially true. There are important
dierences between manufacturing and services, which may reflect in dierent responses of trade
from common determinants. Therefore, a better understanding of the determinants of bilateral trade
in services vis-`a-vis manufacturing is necessary.
Figure 1: Growth of Global Trade: Goods and Manufactures versus Services
10
16
2.5
5
0
2
4
6
8
10
12
14
16
18
2005 2016
Gross Trade (Exports + Imports)
in Trillions of Dollars
Goods Services
1.97
30
4.14
70
0
10
20
30
40
50
60
70
80
Annua l Total
Growth Rate in Percentage
at 2010 Prices: 2005-2017
Globa l Ma nufacturing Trade Globa l Services T rade
(a) UNCTAD (2018) (b) Source: Own Calculations
1Aggregate service trade data typically includes cross-border trade in services only. However, services trade via com-
mercial aliates (Mode 3) constitutes at least half of all trade in services. If we include Mode 3 service trade, the share of
trade in services jumps to more than 40% of total trade (World Trade Organization,2015). Unfortunately, the availability
of Mode 3 service trade data is limited.
2For instance, see Lee and Lloyd (2002) for a detailed discussion about the implications of including international trade
in services to observed levels of total intra-industry trade.
1
The formal empirical literature on the determinants of trade in services began with the estimation
of multilateral trade, e.g., Francois (2001), Freund and Weinhold (2002) and Francois et al. (2003).
While Francois (2001) and Francois et al. (2003) estimated import demand for services with per capita
GDP and population as explanatory variables, Freund and Weinhold (2002) were the first to show the
significance of internet penetration — as a trade cost-reducing agent — in explaining trade in ser-
vices.3Gravity equations of bilateral trade in various sub-sectors of the service sector and the services
sector as a whole have been estimated by authors, including Freund and Weinhold (2002), Gr ¨
unfeld
and Moxnes (2003), Marvasti and Canterbery (2005), Kimura and Lee (2006), Walsh (2008), Head
et al. (2009), Hanson and Xiang (2011), Culiuc (2014), Hellmanzik and Schmitz (2015,2016) and
Anderson et al. (2018). While the literature encompasses dierent samples (dierent sets of countries
or periods), including dierent sets of explanatory variables and estimation techniques, it does not
bring to fore the dierences in how trade in the two categories responds to changes in the explanatory
variables, and, importantly, how to interpret the dierences. The current paper aims to fill this void
(at least partially).
To do this, we first formulate a unified theoretical framework that delivers gravity equations for
the two types of trade flows and allows us to explore and understand systematic dierences between
how various factors aect trade in services vis-`a-vis trade in manufacturing. The model theoretically
distinguishes between manufacturing and service products based on some of their innate characteris-
tics and derive gravity equations, which guide the ensuing empirical specifications and expectations
from them. We explore two dimensions that distinguish services from manufacturing.
Demand Bias: Compared to manufactures, the demand for services is more income-inelastic. This is
standard in the structural-change literature, with a long history and empirical backing, e.g., Kuznets
(1957), Fuchs (1968), Kongsamut et al. (2001), Matsuyama (2009), Boppart (2014), and Comin et al.
(2017). Somewhat surprisingly, however, the general theoretical and empirical implications of this
demand bias towards trade in goods/manufactures vis-`
a-vis services are less analyzed and understood.
Lewis et al. (2019) is an important exception. It examines how such structural change — what we call
demand bias at the global level — has impacted the overall global openness of trade in manufactures
and services. Our endeavor in this paper is oriented towards understanding how the nature of bilateral
trade in the two product categories diers.
Preliminary evidence of how demand bias towards services is reflected in the international trade
basket is depicted in Figure 2. It graphs the simple correlation between per capita GDP and the
manufacturing and services total trade as shares of GDP across the 177 countries in our sample. We
observe that the correlation coecient is positive and statistically significant for trade in services for
every year over 2002-2015. However, for manufacturing trade, the correlation coecients are close
to zero and statistically insignificant.
3Choi (2010) followed up Freund and Weinhold (2002) by working with a much larger data set and a much wider
period and reached the same conclusion that internet penetration is an important determinant of service trade.
2
Figure 2: Cross-country Correlation: Per Capita GDP and the Shares
of International Trade in Manufacturing and Services in GDP
0.559***
0.561***
0.543***
0.521***
0.518***
0.527***
0.521***
0.559***
0.209***
0.129*
0.218***
0.216***
0.233***
0.111
0.0162
0.0026
-0.006
-0.0233
-0.0239
-0.0311
-0.0407
-0.0393
-0.038
-0.0407
-0.0338
-0.0399
-0.0401
-0.038
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015
Correlation Coefficient
Year
Trade in Services (share of GDP) Trade in Manufacturing (share of GDP)
Note: The variables are constructed using our data and sample of countries.
Total trade is calculated as the sum of total exports and imports of each cate-
gory to other countries in the sample.
Statistical Significance: *** p<0.01, ** p<0.05, * p<0.10.
Dierences in National Product Dierentiation: The Armington elasticity of import demand for ser-
vices is smaller than that for manufacturing – equivalent to services being more nationally dierenti-
ated than manufacturing.4Relatively less known notwithstanding, it derives from available empirical
estimates: see Bilgic et al. (2002) and Donnelly et al. (2004).5
What we call Demand Bias is not, per se, new in the gravity literature (see, for instance, Fieler
(2011)). But it has not been brought forth to dierentiate between trade in the two product categories.
It has two theoretical implications. First, per capita income and population size of the importer coun-
try would have dierent impacts on bilateral trade and should enter as separate regressors — instead
of just total income or GDP of the importer country (Markusen,2013). Second, within-country in-
come distribution would matter since the demand for a product basket is not unitarily elastic with
respect to income. Our contribution lies in delineating how these implications may dierentially im-
pact trade in manufacturing and trade in services. Likewise, National Product Dierentiation through
incorporation of Armington elasticity is not new. But, little eort has been made to understand its
implication towards bilateral trade in the two sectors.
We consider pulling these two features together as a theoretical innovation. We find that while
Demand Bias aects the importing-country scale eects on bilateral trade, dierences in National
4We invoke the term “national product dierentiation” a la Head and Ries (2001).
5In their review paper, Bilgic et al. (2002) present dierent regional and national studies that estimate Armington
elasticities in the context of the U.S. for traded commodities and services. For commodities, they range from 1.5 to 3.5,
while for services, they vary between 0.2 and 2.0. Irrespective of the methodology used, services generally have lower
Armington elasticities than manufacturing products. Donnelly et al. (2004) presents Armington elasticities for selected
industries in the U.S. for the USITC and GTAP CGE models. For the former, elasticities average out to be 3.02 and 2.35
for manufacturing and services products, and, for GTAP, these are 2.89 and 2.35, respectively.
3
Product Dierentiation dictate the eects of exporting-country scale eects. More precisely, relative
to bilateral trade in manufactures, that in services is more elastic with respect to per capita income
of the importing country and less elastic with respect to the GDP of the exporting country. These
dierences are derived in section 2.4, and, subsequently supported by our empirical results.
The side-by-side estimation of gravity equations for aggregate trade in manufacturing and that
in services contributes towards understanding and interpreting the similarities and dissimilarities be-
tween them, contrasting with the existing empirical literature that focuses on either manufacturing,
services, or some important segments of them.
In studying the determinants of international trade in services and manufacturing, this paper also
sheds light on the importance of internet penetration and virtual proximity. In the modern internet
era, almost any kind of business dealing with goods or services is likely to have used the internet. It is
natural to speculate that internet use would significantly lower trade costs for both goods and services.
Starting with Freund and Weinhold (2002), internet use has been recognized as an important factor
in reducing trade costs, particularly, for services.6As expected, internet use is found as a significant
determinant of trade in services — particularly that of a country as an exporter, not as an importer
(Freund and Weinhold,2002, Page 240). Instead of using country-wise internet use, in their study of
audiovisual services trade, Hellmanzik and Schmitz (2015) find that the number of bilateral internet
links is a significant determinant of such trade. Following them, we also incorporate this variable and
interpret it as a measure of virtual proximity.
Our empirical section incorporates internet penetration and virtual proximity and we find that, in
particular, virtual proximity is a significant determinant of bilateral aggregate trade in both product
groups. Indeed, it substantially reduces the role of physical distance and scale variables such as GDP
and per capita income. We find suggestive evidence that the elasticity with respect to virtual proximity
is higher for trade in services relative to manufacturing. Our results also show that the exporter
country’s internet penetration is an essential determinant for trade in services even after controlling
for virtual proximity. However, we do not find sucient evidence to support internet penetration as a
determinant of trade in manufacturing. In sum, our empirical analysis implies that virtual proximity
is crucial in understanding trade costs and trade flows in both manufactures and services in modern
times. Its exclusion, we argue, entails a serious omitted-variable issue in estimating gravity relations.
Section 2lays out our theoretical model of trade with non-homothetic preferences that incorpo-
rates demand bias and dierences in national product dierentiation, leading to gravity equations for
aggregate trade in manufacturing and aggregate trade in services in a unified framework. Section 3
describes the data and outlines the empirical strategy. Empirical results are presented in Section 4.
Robustness checks and sensitivity analyses are undertaken in Section 5. Section 6concludes.
2 Theory
The world economy consists of Ncountries and three traded goods: namely, services (s), manufac-
turing (m), and a numeraire good (0). Manufacturing and services are dierentiated and produced by
a primary factor, labor. Each household has a given endowment of good 0, which is homogeneous
and cannot be produced. The presence of a fixed-endowment numeraire good achieves two purposes.
Since these endowments vary (exogenously) across countries, the size of the labor force is not nec-
essarily inversely related to per capita income. Furthermore, such modeling of the numeraire good
6The authors use the number of the top-level domain names in a country as a measure of internet use, whereas Choi
(2010) has used internet penetration (number of users per 100 or 1,000 people) as the measure of the same.
4
implies an endogenous wage rate, which serves two roles in the model. It enables to (a) assess the
eect of the cost of production in the exporter country on the value of bilateral trade and (b) reveal
the role of the Armington elasticity in determining how the total income of an exporter country may
aect bilateral trade. The trading countries are indexed by i,kor r. Country iis endowed with Li
households, each owning one unit of labor.
2.1 Tastes
Households have identical tastes across countries and within countries. For ease of notation and better
exposition, we initially assume that all households in a country have the same endowment of good 0.
This is relaxed in section 2.5.
Demand bias and dierences in national product dierentiation are incorporated via preferences.
A four-tier generalized version of Dixit-Stiglitz specifications reveal these dierences in a transparent
way: outer tier on choice of manufactures-cum-services basket crand the numeraire good, middle-tier
1 over the allocation of crinto the baskets of manufactures (cmr) and services (csr), middle-tier 2 on
the choice of country-specific manufactures (cmir) and services (csir ) and the inner-tier on varieties of
manufacturing (cmir(u)) and services (csir (u)) within the respective country-specific basket. Various
notations are summarized in Table 1.
Table 1: Notations
cr: household consumption in country rof a basket of manufacturing and services
Pr: price of this basket in country r
cmr [csr]: household consumption in country rof the manufactures [services] composite
consisting of varieties produced in all trading countries
Pmr [Psr]: price in country rof the manufactures [services] composite consisting of vari-
eties produced in all trading countries
cmir [csir]: household consumption in country rof the manufacturing [services] compos-
ite consisting of varieties produced in country ionly
Pmir [Psir]: price in country rof the manufacturing [services] composite consisting of va-
rieties produced in country ionly
cmir(u) [csir (u)]: household consumption in country rof a manufacturing [service] variety u
produced in country i
pmir(u) [ psir (u)]: price in country rof a manufacturing [service] variety uproduced in country i
pmi(u) [ psi (u)]: the FOB price of a manufacturing [service] variety uproduced in country i
qmi(u) [qsi (u)] output of a firm in the manufacturing [service] sector of country i
τmir [τsir]: the iceberg transportation/communication cost of shipping or sending a man-
ufacturing [service] variety from country ito country r
mir [sir]: mass of manufacturing [services] varieties which are produced in country i
and sold in country r
¯q0rhousehold endowment of the numeraire good in country r
yr: household income in country r, which includes the value of the numeraire
good endowment.
5
Outer-Tier Tastes: log-linear
Utility Function: vr=β0ln c0r+βln cr, β0>0; β > 0; β0+β=1 (1)
Budget: c0r+Prcr=yr
Demand Functions: c0r=β0yr;cr=βyr
Pr
.(2)
Middle-Tier 1 Tastes; Non-Homothetic CES
Utility Function: X
j(m,s)
c
θjη
η
rc
η1
η
jr =1.(3)
0< θm< θs<1+θm(R1)
η > max (1,θm
1θs+θm)(R2)
Budget: Pmrcmr +Psr csr =erPrcr=βyr(4)
Demand Functions: cjr = Pjr
er!η
[Ξ(Pmr,Psr ,er)]θjη(5)
Expression of cr:cr=Ξ Pmr
,Psr
,er
+!(6)
Expression of Pr:P1η
r=X
j(m,s)
P1η
jr cθj1
r.(7)
Middle-Tier 2 Tastes, Dixit-Stiglitz
Utility Function: cjr =
N
X
i=1
c
j1
j
jir
j
j1
,j=m,s(8)
Budget:
N
X
i=1
Pjircjir =cjr ,j=m,s(9)
Demand Functions: cjir = Pjir
Pjr !j
cjr,j=m,s,where P1j
jr
N
X
i=1
P1j
jir ,j=m,s.(10)
Inner-Tier Tastes, Dixit-Stiglitz
Utility Function: cjir =
Zujir
cjir(u)σ1
σdu
σ
σ1
, σ > 1,j=m,s(11)
Budget: Zujir
pjir(u)cjir (u)=cjir ,j=m,s(12)
Demand Functions: cjir(u)= pjir (u)
Pjir !σ
cjir = pji(u)τjir
Pjir !σ
cjir,j=m,s(13)
where P1σ
jir Zujir
pjir(u)1σdu =Zujir pji(u)τjir 1σdu,j=m,s.(14)
6
Demand bias is introduced in middle-tier 1 preferences. It is modeled a la Fieler (2011), Mat-
suyama (2015) and Comin et al. (2017). Unlike Gorman tastes, the parameter ηmeasures the constant
elasticity of substitution between manufacturing and services. Note that, if θm=θs=1, eq. (3) re-
turns the standard Dixit-Stiglitz function over manufacturing and services.
While θm,θsis a necessary condition for non-homotheticity, (R1) states that the dierence
between them are not supposed to be very large. This ensures normality of both goods (see Appendix
Bfor a proof).7However, the magnitudes of θmand θscan still be large or small: they may exceed or
fall short of unity. (R2) implies η > 1 and (R1) and (R2) together imply
η>θs> θm>0.8
In Appendix Bwe prove that,
Result 1. Both manufacturing and service bundles are normal goods, i.e., given Pjr,dcjr /dcr>0.
Furthermore, the income elasticities of demand for manufacturing and services are respectively less
and greater than unity.
As a corollary of Result 1,
Result 2. At given price indices Pmr and PS r, the quantities demanded for manufacturing and that
for services are respectively a strictly concave and a strictly convex function of income; thus, the
respective Engel curves are strictly concave and strictly convex.
Results 1and 2formally characterize the demand bias towards services. However, an increase
per capita income (yr) has a proportionate eect on the aggregate expenditure on the numeraire good
and that on the manufacturing-services basket.
In middle-tier 2 preference, mand sdenote the respective Armington elasticities that define
national product dierentiation. The critical assumption is that
Assumption 1.
m> s>1,(15)
meaning that services are more nationally dierentiated than manufacturing.
We further assume that the substitutability among within-country varieties exceeds that among
between-country varieties for both manufacturing and services, i.e.,
Assumption 2.
σ>jfor j=m,s.9(16)
To highlight national production dierentiation dierences, we have presumed that substitutabil-
ity between within-country varieties is same between manufacturing and services.10
7Normality of the service bundle is assured under less restrictive assumptions. But normality of manufacturing is not
because, if the demand bias toward services is too large, as nations get larger, they may shift their purchases so heavily
toward services that manufacturing becomes an inferior good.
8If θs1, it is easy to show that η > θs> θm>0.Suppose θs>1. Then (R2) implies ηθs=(θs1)(θsθm)
1+θmθs>0η >
θs> θm>0.
9Ardelean (2009) provides empirical evidence supporting this assumption for manufacturing.
10Otherwise, a more general version of (11) is:
cjir =
Zujir
cjir(u)
σj1
σjdu
σj
σj1
,j=m,s.
7
2.2 The Supply Side
The technology in each production sector obeys increasing returns to scale and is the same across
countries. In terms of the labor requirement, lji(u)=α+qji(u), α > 0, j=m,s, where the units
of manufacturing and services are normalized such that the variable labor coecient is the unity in
both sectors. We abstract from firm heterogeneity — obviously important; but this is kept in mind
for follow-up research. The market structure is monopolistic competition production sectors mand s,
and, perfect competition in the numeraire sector. An individual firm in either production sector faces
constant price elasticity of demand for its variety in each trading country. Hence the price markup
over marginal cost is constant:
pji(u)=σwi
σ1,pjir(u)=σwiτjir
σ1,(17)
implying
Pjir =σwiτjir
σ1·1
σ1
jir ;pjir(u)
Pjir
=
1
σ1
jir ;
Pjr =σ
σ1
N
X
i=1wiτjir1j
1j
1σ
jir
1
1j
Pjir
Pjr
=
wiτjir
1
1σ
jir
PN
i=1wiτjir1j
1j
1σ
jir !1
1j
,
(18)
where ’s are the respective mass of varieties produced and sold. In sector jof country i, the variable
(operating) profit made by firm uin country rhas the expression:
πjir(u)=Lrpjir (u)cjir (u)wiτjir Lrcjir (u)
| {z }
output shipped
to country r
=Lrcjir(u)hpjir (u)wiτjir i=Lrcjir (u)wiτjir
σ1>0.(19)
Since the variable profits are positive in each market, each firm in either sector located in any country
sells in all trading countries:
jir =ji,(20)
where ji is the mass of varieties of jproduced in country i,j=m,s.11 The total variable profit of a
firm that produces variety uis given by the sum of its variable profits made across all Ncountries:
πji(u)=
N
X
r=1
πjir(u)=wiPrLrcjir (u)τjir
σ1=wiqji(u)
σ1.(21)
where, recall that qji(u) is the output of a firm located in sector jof country i. Fixed costs are αwi.
Hence free entry-exit and zero-profits imply qji(u)=α(σ1). Not surprisingly, the equilibrium
firm-level output is constant and the same across all countries, and, it implies lji(u)=ασ.
11This will change if there were firm heterogeneity and positive fixed costs of operating in foreign country.
8
2.3 World Trading Equilibrium
Formally, given the preferences, the endowment of the numeraire good (¯q0r) and the supply of labor
(Lr) for each trading country as well as bilateral trade costs τjir for each pair of trading countries, the
world trading equilibrium is a vector {w
r, Ω
mr, Ω
sr,P
mr,P
sr,c
mr,c
sr,c
r,e
r}, such that
(a) P
r=e
r/c
r; and the vector is consistent with the
(b1) 2Nprice-index expressions (18) for manufacturing and services bundles separately for each
country;
(b2) 2Ndemand functions (A.6) for manufacturing and services bundles separately for each country;
(b3) Ndemand functions
er=β(wr+¯q0r) (22)
for the manufacturing-services basket, one for each country;
(b4) Nexpenditure-share adding up conditions (A.6), one for each country;
(b5) Nfull-employment conditions, one for each country:
ασ (mr +sr)=Lr; (23)
(b6) 2Nworld market-clearing condition for each variety of manufactures and services produced in
each country:
α(σ1) =
wj
iσj
σ1
ji
N
P
r=1wrτjir1j
j1
σ1
jr !j
j1
·
N
X
r=1
Lrcjrτ(j1)
jir j=m,s.(24)
where the left-hand side is the supply for each variety of manufacturing or services (equal to the
equilibrium firm-level output α(σ1)) and the right-hand side is the world demand for it plus the
amount lost in transit.12
We shall now derive expressions for the wage rate and the equilibrium number of varieties pro-
duced in each country, which will be used in deriving the gravity equations — and interpreting them.
Turn to eq. (24) and define
χji PN
r=1Lrcjrτ(j1)
jir
α(σ1) N
P
r=1wrτjir1j
j1
σ1
jr !j
j1
·j=m,s.(25)
Substituting the above back into (24) and rearranging, ji =χjiw
(σ1)j
σj
i.In turn, substitute this into
the full employment condition (23) and obtain:
ασ χmiw(σ1)m
σm
i+χsiw(σ1)s
σs
i!=Liwi=wi χmi
+
, χsi
+
,Li
!.(26)
This is an implicit wage function. Next, using this, we obtain an expression for the equilibrium
number of varieties produced in each country:
ji =χji ·wi(χmi, χsi,Li)(σ1)j
σj.(27)
Eqs. (26) and (27) formalize the following result that is expected:
12Equation (24) is derived in Appendix (C).
9
Result 3. Larger countries are associated with lower wage rate and larger number of varieties.
2.4 Gravity Equations
Following the standard approach in the literature, let the bilateral trade flows be measured by the fob
value of the gross exports at the destination country. Let Xjir denote this, where jis the sector/good
(manufacturing or services), ithe exporting country and rthe importing or the destination country.
We have Xjir =# of varieties of good jproduced in country i×country r’s expenditure on each
variety at the fob price. Various substitutions lead to two expressions of the gravity relation for each
product group mand s:
Xjir = σ1
σ!j1
χ
j1
σ1
ji wi(χmi, χsi,Li)σ(j1)
σj τjir
Pjr !jLrcjr.(28)
=Aj·Lryη
r·
τj
jir
Pηj
jr ·χ
1j
σ1
ji
·wi(χmi, χsi,Li)σ(j1)
σj
Ξ(Pmr,Psr , βyr)ηθj,where Ajβη σ1
σ!j1
.13 (29)
Eq. (29) is closer to a standard-looking gravity equation than is eq. (28).
Worth-emphasizing, a gravity equation like (29) is a cross-sectional relationship, showing how
bilateral exports among various pairs of trading countries are positioned vis-`a-vis one another de-
pending on the equilibrium configuration of global as well as country-specific variables. Following
Anderson and van Wincoop (2003), we can interpret χmi and χsi as multilateral resistance facing the
exporting country i, while Pmr and Psr as those facing the importing country r. It follows directly
from (29) that
Result 4. Bilateral trade in either good depends on multilateral resistance facing the exporting country
and the importing country in both sectors.
Non-homotheticity of tastes implies:
(i) In the right-hand-side of (29), the term Lryrdoes not, on its own, capture the income eect of the
importing country. That is, bilateral trade is not merely a function of total income, divided multi-
plicatively into the population and per capita income (Fieler,2011).
(ii) While bilateral trade is proportional to the size of the population, it is not so with respect to per capita
income.
In view of (28) and Result 1,
Result 5. Bilateral trade of either good is unitarily elastic with respect to the importing country’s
population size, while the importing country per capita income elasticity of bilateral trade in manu-
facturing is less than unity, and that in services exceeds unity.
This follows from the demand bias assumption. Higher income elasticity of demand for services
than for manufactures translates into a higher elasticity of bilateral trade in services with respect to
the per capita income of a country as an importer.
13Expression (28) is derived in Appendix D. Two further substitutions from section 2.1, namely, er=βyrand the
expression of cjr in (5), leads to (29).
10
While non-homothetic tastes form the micro-foundations beneath dierentiating between size
and per capita income of a country as an importer, there is no basis for considering the exporting
country’s size and per capita income as independent determinants of bilateral trade. Only the overall
size matters, represented through the wi(·;Li) function. Since the absolute value of the exponent of wi
in (29) is increasing in jand m> s, it follows that
Result 6. The elasticity of the bilateral trade with respect to the size of the exporting country is greater
for manufacturing than for services.
Hence, bilateral trade is not unitarily elastic with respect to the exporting-country size. Further-
more, the magnitude of the exporting country’s size eect depends on the Armington elasticities.
Multiplying both sides of equation (26) with wi, it can be readily derived that wiis negatively related
to wiLi. Thus, bilateral trade is positively related to total labor income; and, if total labor income is
positively related to total income inclusive of the value of the numeraire good, bilateral trade increases
with total income.
Intuitively, compared to services, lesser national product dierentiation of manufacturing implies
more elastic import demand for it. In equilibrium, manufacturing production and exports are less
governed by world demand and more by the supply side. Therefore, manufacturing trade is more
sensitive to changes in the total endowment of resources of the exporting country, that is, the size of
the exporter country. The dierences in national production dierentiation underpins Result 6. Also,
note in (29) that the elasticity of bilateral trade with respect to trade cost depends on the Arming-
ton elasticity or the national product dierentiation, not the elasticity of substitution between intra-
country varieties. This brings us to the result on trade-cost elasticities, which is a direct implication
of Armington elasticity for manufacturing being higher than that for services.
Result 7. The international trade cost elasticity of bilateral trade is higher, in absolute terms, to man-
ufacturing than is for services.14
2.5 Inequality within Countries
So far, our model has permitted across-country heterogeneity. Because the demand function for each
product category is nonlinear with respect to (per capita) income due to Demand Bias, the income
distribution within the importer country per se would impact the aggregate demand for products from
dierent countries, including its own.
Mitra and Trindade (2005) have articulated a model of trade in food, a necessity, and manufac-
turing, a luxury, (rather than manufacturing and services) with non-homotheticity and a demand bias
toward manufacturing relative to food. However, non-homotheticity is postulated, not on preferences
14We may want to compare the gravity equation (29) to the standard case where tastes are homothetic and there is no
dierence in the national product dierentiation between manufacturing and services. Hence the only dierence between
the two commodities lies in their respective trade costs, while the substitution elasticity among within-country varieties
exceeds that between across-country varieties for both product groups. Accordingly, if θm=θs=1, and, m=s=, the
gravity equations in (29) reduce to
Xjir =A0·(wiLi)·(Lryr)·
χ
1
σ1
ji
ασ Pj(m,s)χji
·
τ
jir
Pη
jr P(η1)
r
,where A0β σ1
σ!1
and Pr
X
j(m,s)
P(η1)
jr
1
η1
.
Notice that bilateral trade of both manufacturing and services are unitarily elastic with respect to size of the importing
country and the exporting country.
11
directly, but in terms of the share of expenditure of food and manufacturing being a function of to-
tal expenditure.15 The theoretical hypothesis is that an increase in income inequality in terms of a
mean-preserving spread of per capita income within a country would increase this ratio. The same
intuition extends to our model. It follows readily from Result 2that, all else the same, as an importer,
a country with a higher income inequality will have less bilateral trade in manufacturing and more
bilateral trade in services.
However, higher or lower income inequality is not synonymous with greater or less spread with
the same mean. In addition to the spread eect, i.e., the per capita income levels remaining the same,
a change in the composition of the population can also result in a change in the average per capita
income or income inequality or both.
More specifically, consider a change in the composition of the population, specifically leading to
a greater polarization, i.e., ‘hollowing out of the middle class,’ while the total or per capita income
remains the same.16 That is, starting from a given composition, let the new composition have a
higher number of relatively richer and a higher number of relatively poorer individuals. How would it
impact on aggregate consumption of manufacturing and services? Depending upon the specifics, the
directional changes can be positive or negative. Table 2presents a numerical example, which is self-
explanatory. Notice from the last column that there is complete polarization in the new composition
of the population, and, hence there is no ambiguity that income distribution has more spread under the
new composition of the population. Straightforward computation shows that the average per capita
income remains the same between the initial and the new situation, while an increase in inequality
in the form of greater polarization leads to an increase in the aggregate manufacturing consumption
and a decrease in services consumption. This is indicative that bilateral trades in manufacturing and
services may respectively fall or increase with an increase in inequality in the importing country. This
is the opposite of the spread eect.
While the notion of mean-preserving spread is often used represent a change in inequality, the
compositional eect is generally neglected. Our example illustrates that the composition eect may
be quite dierent from — and indeed the opposite — of the spread eect. Considering both the
eects, the overall theoretical implication of inequality on bilateral trade is ambiguous.
2.6 A Summary
Our theoretical model predicts that bilateral trades in both manufacturing and services increase with
the exporting country’s GDP while increasing with population and per capita income of the importing
country separately. Moreover, they decline with respect to the bilateral trade costs. These predictions
are hardly surprising. Nonetheless, three main results summarize how our model diers from the
standard gravity model.
(i) The trade elasticity with respect to the exporter GDP is greater for manufacturing than for services.
(ii) The trade elasticity in regard to the importer per capita income is higher for services than for manu-
facturing. Of course, our model yields a more specific result: the importing-country per capita income
15By assumption, the share of manufactures increases and that of food falls with the total expenditure, i.e., income
elasticity of manufacturing and food are respectively higher and lower than unity. In their empirical work, Dalgin et al.
(2008) analyze the eect of income inequality on the ratio of bilateral trade in luxury goods to that in necessary goods
within the category of goods in general without distinguishing between manufactures and food and without the inclusion
of services.
16Income and wealth polarization has been a global phenomenon in recent decades (Hollinger,2012).
12
Table 2: Numerical Example. Increase in Inequality in terms of Greater Polarization and Its Impact
on Aggregate Consumption of Manufacturing and Services
Disposable Share of Share of Initial New
Income Manufactures in Services in Distribution Distribution
in Dollars Manufac-Service Manufac-Service of Population of Population:
Basket Basket Complete
Polarization
200 0.4 0.6 9 10
100 0.6 0.4 6 0
80 0.8 0.2 5 10
Share of Disposable Income Spent on the Manufacturing-Services Basket =0.5
Change in the Aggregate Consumption of Manufactures =$20
Change in the Aggregate Consumption of Services =$20
elasticity of bilateral trade is larger than unity for services and less than unity for manufactures. How-
ever, we should not expect such sharpness of theoretical predictions to be borne out empirically since
some relevant (extraneous) variables, and considerations are absent our model. For instance, our static
model does not incorporate how wealth might aect aggregate consumption and bilateral trade.
(iii) the trade-cost elasticity of trade is larger for manufacturing than for services in absolute terms.
These implications, lending themselves to empirical testing, are intuitively reasoned after Results
6,5and 7respectively. The demand-bias assumption underlies (ii), where (i) and (iii) are driven
by the dierences in the national product dierentiation. Furthermore, within-country inequality in
a country as an importer is a determinant of bilateral trade of both product groups but the direction
of this eect is ambiguous theoretically. Hence, the impact of the importer-country inequality on
bilateral trade is primarily an empirical issue.
Note that openness to trade — which determines products included in the traded basket — may
depend on the size and per capita income of the economy. This is an extensive margin issue, which is
outside of our theoretical model.17
3 Empirical Analysis
This section discusses empirical variables, data sources and our empirical strategy.
3.1 Variables and Data Sources
Aggregate bilateral manufacturing trade flows from 2002 to 2015 are obtained from the U.N. Com-
trade database, United Nations (2018). In compiling the data, preference is given to trade flows
17Furthermore, our theoretical model does not incorporate manufacturing or services as inputs to production. We argue
that the elasticity rankings of bilateral trade with respect to income and per capita income between the two categories of
products are likely to hold even if manufacturing and services were used as inputs to production as long as there are no
significant dierences in factor intensity between the two sectors. There is no compelling reason to suppose that there is a
‘producer-demand bias’ towards manufactures or services, and, that service inputs are less dierentiated than manufactures
inputs.
13
reported by the exporting country. We complement the dataset by mirroring the importer country’s
trade flows whenever the exporter’s report is not available.
For bilateral trade in services, we follow Anderson et al. (2018) and rebuild an integrated dataset
of cross-border services trade from 2002 to 2015. Our primary data source is the “OECD Statistics
on International Trade in Services: Trade in Services by Partner Country and main service category
(EBOPS 2010 classification)”.18 Similar to manufacturing, we accord preference to trade flows as
reported by the exporter country as a more reliable measure of bilateral trade. We used the information
reported by the importer country whenever the exporting country did not report. Even though most
OECD countries already account for a large share of global cross-border service trade, we attempt to
maximize the coverage of global trade flows by augmenting the OECD data with information from
the U.N. Comtrade database. Since the OECD constitutes our preferred data source, the U.N. data
serves to augment the dataset only when the corresponding OECD observation is missing.
The resulting data comprise 177 countries over the period 2002-2015. These countries are listed in
Table 15 in Appendix E. We adopt the following notations and definitions for the included variables.
Xjir: Following the notation from eq. (29), it represents the total aggregate bilateral exports of sector
j=m,sin current US dollars, from country ito country r. This is our dependent variable in the
econometric specifications that follow.
Explanatory variables include GDP, population, per capita GDP, and those aecting trade cost.
In addition, they also include a measure of inequality, even though the theoretical impact on bilateral
trade is ambiguous. It is because if we recognize non-homotheticity, it is only natural to include per
capita income and a measure of inequality.19
GDPi, POPr, gdpr: These represent respectively the total income of the exporting country i, the
population of the destination country r, the per capita GDP (GDP ÷the population) of the destination
country r. This information comes from the World Development Indicators, World Bank (2018).
INQr: This is the income inequality measure. We use the GINI coecient as well as the pre-tax
income share of top 10% and 1%. The respective data sources are Frederick Solt, https://fsolt.
org/swiid/ and World Inequality Database (2019).20
DISTir , BORDERir , LANGir , COLNir : These are the bilateral geographical distance and indi-
cator variables for shared borders, for a common language and colonial relation — usual determinants
of bilateral trade costs. The information on these variables is obtained from the Centre D’Estudes
Prospectives et d’Informations Internationales, CEPII’s gravity database.21
In addition to the above ‘standard’ explanatory variables (perhaps with the exception of income
inequality), we include two variables to capture virtual connectivity between countries, namely, over-
all internet use in a country and the number of bilateral hyperlinks, as determinants of bilateral trade
in both product categories.
18It includes transport (both freight and passengers), travel, communications services (e.g., postal, telephone, and satel-
lite.), construction services, insurance, and financial services, computer and information services, royalties and license fees
for the use of intellectual property, other business services (e.g., merchanting, operational leasing, commercial, technical
and professional services.), cultural, personal and recreational services, and government services.
19As Dalgin et al. (2008, Page 749) write, “At a minimum, the gravity model must be augmented with income per capita
and a measure of the within-country income distribution.
20While GINI is a common measure of inequality, income shares of top 1%, 10%, etc. have also been used; see Leigh
(2007) and Piketty et al. (2019), among others.
21Other bilateral trade cost variables would include, for example, whether the two countries are included in any prefer-
ential trading arrangement like a free-trade bloc. However, we do not incorporate them, although we could, since we believe
it is unlikely to change the nature of our results. It is arguable that bilateral tarilevels may have significant explanatory
power. However, data on it over time is generally lacking (UNCTAD-WTO,2012, Chapter 3).
14
INTPEN: It is a measure of internet penetration in a country: the percentage share of a country’s
population that uses the internet. Annual data is obtained from the World Development Indicators,
World Bank (2018), for 2002-2015. Figure 3shows the rapid growth of internet users globally since
the early 2000s, while there still exists a considerable gap in the usage between high- and low-income
countries. In explaining bilateral trade, internet penetration is viewed as a factor that reduces bilateral
trade costs vis-`a-vis all trading countries.
Figure 3: Internet Penetration by Country Income Group, 2002-2015
0
20
40
60
80
Internet users, % of Population
2000 2005 2010 2015
Year
High income Upper middle income
Lower middle income Low income
Note: This figure, based on annual data, shows the median country’s value
of internet users as a share of total population for each income group. The
income groups are defined as the World Bank classification in 2019.
BLINK: It captures bilateral information flows over the internet, measured by the number of bilateral
inter-domain hyperlinks that internationally connect web pages in two trading countries. In contrast
to DIST indicating physical distance, BLINK measures virtual proximity between two trading na-
tions. The data on inter-domain hyperlinks come from two sources. The information on the bilateral
hyperlinks in 1998 is obtained from the OECD Communications Outlook 1999 report, available for
29 countries. Our second and primary source of hyperlinks data is Chung (2011), who provides in-
formation on bilateral hyperlinks for two years, 2003 and 2009, for 46 and 82 countries, respectively.
This data is also used by Hellmanzik and Schmitz (2015).22
According to the BLINK measure, the U.S.–U.K. is the pair with the highest number of bilateral
hyperlinks for all available years, 1998, 2003, and 2009. Figure 4illustrates the patterns of BLINK
across countries by income level. It presents the average number of hyperlinks between countries of
22Bilateral hyperlinks refer to links from websites with domains from a specific origin country to websites with domains
in another country. An easy way to measure the bilateral hyperlink between two countries is to use country top-level
domains (ccTLD), such as .us for the U.S. or .uk for the U.K. However, determining the host and source countries for
non-national domain names, such as .org,.edu, or .com is a challenging task. Chung (2011) developed an attribution
method that allows for identifying the host country of a .com domain. This feature makes the data much richer and allows
for a more complete and accurate characterization of internet connectivity across countries.
15
Figure 4: Bilateral Hyperlinks, 2003 and 2009
0
.2
.4
.6
.8
1
Average Bilateral Hyperlinks (Million)
H-H H-ML ML-H ML-ML
2003 2009
Note: This figure, shows the average number of Bilateral Hyperlinks from
and to two sets of countries: High Income (H) and Medium-low (ML) income
countries on 2003 and 2009.
dierent income groups in 2003 and 2009. H represents high-income countries, and ML represents
middle or low-income countries. The number of hyperlinks between the two countries is not symmet-
ric. The number of hyperlinks from country A targeting country B is not necessarily the same number
of hyperlinks from country B targeting country A. In Figure 4, H-ML represents the average number
of hyperlinks from high-income countries to middle or low-income countries, while ML-H represents
the average number of hyperlinks from middle or low-income countries to high-income countries. On
average, countries have more hyperlinks targeting high-income countries than middle or low-income
countries. Figure 4shows a growth in the average number of hyperlinks between countries from 2003
to 2009, signifying that the world has increased its virtual proximity. Moreover, the virtual proximity
has increased more between High-Income countries relative to Medium-Low income countries.
In our estimation we only use 2009 BLINK data that are available for 82 countries, which are
listed in Table 16 in Appendix E. We do not use 1998 or 2003 BLINK data since it is available for a
very limited number of countries.
BROAD: It is the number of broadband subscriptions in a country in 2003, a measure of a country’s
information and communication technology infrastructure. It is used as an instrument for BLINK09.
The data source is from the World Development Indicators, World Bank (2018).23
Table 3presents the summary statistics of the variables included in this study. Note, in particular,
that the mean bilateral trade flow in manufacturing goods in our sample is US$ 296.35 million, which
is much larger than the average services flow, US$ 83.3 million. The huge dierence partly reflects
the larger prevalence of barriers to trade in services compared to that in goods and the fact that service
trade data does not include those with commercial presence (Mode 3).
23Table 17 in Appendix Eprovides a summary of all variables included and their sources.
16
Table 3: Summary statistics
N Mean SD Min Max
Trade in manufacturing (US$ Million) 436,128 292.47 3,810.43 0.00 398761.27
Trade in services (US$ Million) 436,128 81.07 1,038.30 0.00 80330.00
GDP (US$ Billion) 2,478 333.04 1,325.81 0.07 18120.71
GDP PPP (US$ Billion) 2,436 467.87 1,589.18 0.14 19820.98
Population (Million) 2,478 37.03 138.36 0.02 1371.22
Internet users (% of population) 2,445 29.96 27.77 0.00 98.20
Broadband Subscriptions in 2003 (Million) 116 86.45 327.92 0.00 2,775.20
Gini index (Disposable income) 1,980 38.64 7.89 23.10 61.60
Top 10th percentile income share 1,463 0.44 0.12 0.22 0.71
Top 1st percentile income share 1,480 0.14 0.06 0.05 0.32
Distance (1000 Km) 31,152 7.93 4.48 0.06 19.90
Shared border (dummy) 31,152 0.02 0.13 0.00 1.00
Common language (dummy) 31,152 0.15 0.36 0.00 1.00
Colonial background (dummy) 31,152 0.01 0.11 0.00 1.00
Bilateral hyperlinks (1998) 794 5,172.62 15,540.01 3.00 212,106.00
Bilateral hyperlinks (2003) 1,824 437,469.96 1,459,996.60 1.00 24,936,200.00
Bilateral hyperlinks (2009) 3,741 593,328.00 2,432,472.77 5.00 48,878,701.00
Notes: This table reports summary statistics for the main variables used in our empirical analyses. The
final sample is composed by 177 countries, over the period 2002-2015. Information for bilateral hyperlinks,
income inequality measures, and Internet users are not available for all countries in our sample.
3.2 Estimation Strategy
The gravity expressions (29) has constant trade elasticities with respect to bilateral trade costs and the
population of the importing country, but not in regard to other determinants. Furthermore, it does not
include within-country inequality. A fully structural estimation would require specifying a functional
form to capture heterogeneity within a country and numerically solving a highly non-linear general
equilibrium system containing across-country and within-country heterogeneities. Instead of this, we
tread along the standard path of assuming a constant-elasticity dependence between the explanatory
variables on the one hand and bilateral trade on the other, on the presumption that the eects of other
higher-order terms are relatively small. In eect, we utilize the theoretical gravity equations (29) as
the basis to parametrically specify the estimable equations, which additionally include a measure of
within-country income inequality.
Our econometric model contains the standard set of variables included in gravity estimations, such
as GDP, per capita GDP, population, and standard bilateral trade cost variables; and, it additionally
includes a measure of income inequality for the importer country and two measures of internet use:
internet penetration and bilateral hyperlinks.
We have a panel data, albeit unbalanced, on bilateral trade, GDP, internet penetration, and other
country-wise characteristics from 2002 to 2015. Thus a fixed-eects panel estimation comes to mind
as a first instinct. There are prominent examples of panel estimation of trade gravity relations in
the literature, e.g., Egger and Pfaermayr (2003) and Baltagi et al. (2014), among others. Indeed,
Yotov et al. (2016) strongly recommend panel estimation of gravity equation whenever panel data is
available. However, we respectfully dier and argue that it is not a preferred strategy, at least in our
context. Our reasons are as follows.
17
Table 4: Variance Decomposition of Time-Varying Variables
Between/Overall Variation (%) Within/Overall Variation (%)
GDP per capita (log) 94.77 5.23
GDP PPP per capita (log) 97.06 2.94
GDP (log) 96.99 3.01
GDP PPP (log) 98.68 1.32
Population (log) 99.83 0.17
Gini Coecient 98.34 1.66
Top 10th percentile (Income) 97.09 2.91
Top 1st percentile (Income) 93.25 6.75
Internet Penetration 71.46 28.54
Notes: This table reports the variance decomposition into between and within variation to the country-
specific and time-varying variables. The data comprises 177 countries over the 2002–2015 period.
(1) The gravity relations in Equation (29) reflect a snapshot of how bilateral trade is aligned in a cross-
sectional equilibrium among trading countries. It is not amenable to a natural interpretation when
there are within-country variations over time of an explanatory variable. For example, there is no
context or a clear interpretation of how a change over time in the importer-country per capita income
would, all else the same, aect its bilateral trade with another country. To paraphrase Head and Mayer
(2014), “All the micro-foundations of gravity that we examined are static models. They provide a
derivation for a cross-section but are questionable bases for panel estimation” [italics added].
(2) The presence of country-specific or country-time-specific fixed eects does not permit the esti-
mation of the marginal impact of observable country-specific variables like GDP, per capita income,
population, or internet use. But, our objective is to estimate and understand the dierences in these
marginal impacts across trade in manufacturing and trade in services. Non-homothetic preferences
do not imply unitary elasticity with respect to scale variables of the exporting or the importing coun-
try. Thus taking size-adjusted trade as the dependent variable is not appropriate. While fixed-eects
panel estimation serves as an attractive filter to isolate the impact of trade costs and the multilateral
resistance — which is important on its own — it is not our sole focus however.
(3) Most compellingly perhaps, in our data set the time-varying explanatory variables have relatively
small within-variation compared to between-variation. Table 4records that within-variation accounts
for a very modest portion of most variables’ total variation, internet penetration being the sole excep-
tion. In the absence of significant within-variations, fixed-eects panel estimates are likely to yield
unreliable estimates.
Therefore, we rely on year-to-year regressions. In any given year, the gravity equations contain
country-specific determinants (e.g., exporting country GDP) and bilateral determinants (e.g., physical
distance and virtual proximity between two countries).
Our primary empirical strategy is a two-step (-stage) approach that uses fixed-eects estimation
in the first step only. This yields estimates of the coecients on bilateral variables. The second-stage
estimation involves the estimates of fixed eects from the first step and the observable country-specific
variables, but it is not a fixed-eects estimation.24 PPML is used in each step. To be clear, a two-stage
24Not using fixed-eects estimation presumes independence between the country-specific observable and unobservable
characteristics. For instance, country-specific policy-induced overall trade restrictions on either manufactures or services
18
estimation of the gravity equation is not new; see, for instance, Head and Ries (2008) and Head and
Mayer (2014). However, we detail our procedure in section 3.3 for the sake of exposition and clarity.
3.3 A Two-Stage PPML Procedure
We begin by translating eq. (29) into the following econometric specification:
Xjir =exp(xji +mjr )·GDPαj
i·Lrβj·gdpγj
r·exp(θjQINQr)·τj
jir +vjir, α j, βj,  j>0,(30)
where vjir’s are the purely bilateral trade error terms. The terms xji and mjr capture the eects of
unobservable exporting-country-specific and importing-country-specific variables, including the mul-
tilateral resistance terms. The other variables are: GDP of the exporting country (GDPi), population
and per capita GDP of the importing country (Lrand gdpr) and trade costs τjir . The population size of
the importing country appears multiplicatively linear in (29), because of the assumption of identical
households in our theoretical model. Once we depart from this assumption, bilateral trade will not be
multiplicatively linear with respect to the population size.
We need to specify the bilateral cost term, τjir as a function of observables. Following the litera-
ture, we adopt a specification that includes traditional variables to characterize bilateral costs such as
geographical distance and shared border, and, in addition, internet penetration and virtual proximity.
Although the last two variables are often neglected in gravity estimation, we show that they play an
important role in predicting trade flows in both manufacturing and services. We define the following
bilateral trade cost function:
τjir =·exp h˜
θjD ln DISTir +˜
θjBBORDERir +˜
θjLLANGir +˜
θjCCOLNir
+˜
θjXI INTPENi+˜
θjM I INTPENr+˜
θjK ln BLINKiri,(31)
One of the main challenges is to deal with the unobservable exporting-country-specific and importing-
country-specific terms xji and mjr . We assume
Exporting Country: xji =Aj+ξji
Importing Country: mjr =Bj+ξjr ,(32)
where ξji and ξjr respectively represent the exporter-country-specific and importer-country-specific
error terms. Substituting (31) and (32) into (30),
Xjir =exp Aj+Bj+ξji +ξjr +αjln GDPi+βjln Lr+γjln gdpr+θjQINQr+θjX I INTPENi
+θjM I INTPENr+θjD ln DISTir +θjK ln BLINKir +θjB BORDERir
+θjLLANGir +θjC COLNir +vjir ,(33)
where θjD ≡ − ˜
θjDj,θj XI ≡ − ˜
θjXI j,θj MI ≡ −˜
θjM I j,θjK ≡ − ˜
θjK j,θjB ≡ − ˜
θjBj,θj L ≡ −˜
θjLj,
θjC ≡ −˜
θjCj. We further represent eq. (33) by separating country-specific terms from bilateral terms.
Xjir =exp Xji +Mjr +θjD ln DISTir +θjK ln BLINKir
— which are not accounted for in our model — may be correlated with observed country-specific variables like GDP or per
capita GDP. Nonetheless, relying solely on the fixed-eects estimator goes too far insofar as not permitting an estimation
of the coecients of country-specific observable variables, which are unquestionably relevant to study.
19
+θjBBORDERir +θj LLANGir +θjC COLNir +vjir ,(34)
where,
Xji Aj+αjln GDPi+θjXI INTPENi+ξji
Mjr Bj+βjln Lr+γjln gdpr+θjQINQr+θj MI INTPENr+ξjr .(35)
Our two-stage technique estimates the parameters in eqs. (34) and (35) separately. In the first
stage, we employ fixed-eects estimation of (34) by using PPML a la Santos Silva and Tenreyro
(2006,2011), a standard approach. The first-stage estimation yields bilateral-trade estimates ˆ
θjD,ˆ
θjK ,ˆ
θjB,ˆ
θjL
and ˆ
θjC as well as [
exp(Xji) and [
exp(Mjr ), where the last two estimates measure the sum of the unob-
servable multilateral resistance eects and the observable country-specific eects. The parameters m
and sare not identified, but whether or not m> scan be verified a la Result 6, i.e., from whether
or not the estimate of αmexceeds that of αs.
Country-specific eects, e.g., estimates of αj,βj,γj, among other parameters, are obtained in the
second stage, where, in view of (35), [
exp(Xji) and [
exp(Mjr ) are separately regressed against country-
specific variables. From their respective definitions,
[
exp Xji=exp Zji +ξji;[
exp Xjr=exp Zjr +ξjr ,where (36)
Zji Aj+αjln GDPi+θjXI ln INTPENi
Zjr Bj+βjln Lr+γjln gdpr+θjQINQr+θj MI ln INTPENr.
We estimate the two equations in (36) by PPML.25 This is dierent from Head and Mayer (2014),
who use generalized least-squares. Both approaches however account for heteroskedasticity issues.
Multilateral resistance terms, adjusted for the constants Ajand Bj, are subsumed in ξji and ξjr ,
whose estimates are [
exp Xji/[
exp Zjiand [
exp Mjr/[
exp Zjrrespectively. Our procedure essen-
tially diers from the (single-stage) random-intercept model in that it identifies and deals with the
exporter and importer-specific eects separately. This is more ecient because the variations in the
bilateral-trade-specific error terms do not directly influence the estimated coecients of observable
country-specific factors.
3.4 Endogeneity Issue with BLINK
For the years 2009 to 2015, we use the BLINK data for 2009 – which we refer to as BLINK09.
However, the number of bilateral hyperlinks may be aected by bilateral trade, an endogeneity issue
due to reverse causality. As shown by Reed (2015), lagging a regressor does not purge the simultaneity
and the endogeneity bias.
25The multiplicative error terms can be easily transformed into additive ones by defining
exp(uji)1+νji
qexp Zjiexp(ujr )1+νjr
qexp Zjr,
where νji and νjr are statistically independent of Zji and Zjr respectively and Eνji=Eνjr =0. The respective conditional
means equal the respective conditional variance and thus the resulting moment equations are equally weighted, which
facilitates the use of PPML estimation. See (Feenstra,2016, Chapter 6) for a lucid treatment of the structure of error term
under which PPML can be applied.
20
Endogeneity is a concern as long as BLINK09 is a regressor. We need to instrument it.26 We
consider two instruments for BLINK09. The first is the number of bilateral hyperlinks in 2003
(BLINK03) as do Hellmanzik and Schmitz (2016,2017). The authors argue that the past values
of bilateral hyperlinks are pre-determined, thus unaected by future shocks to bilateral trade. How-
ever, there might still be concerns that this instrument is correlated with unobserved characteristics
associated with future bilateral trade flows. Moreover, the 2003 bilateral hyperlinks data is available
for only 46 countries, drastically reducing the sample size and potentially raising selection concerns.
We, therefore, consider another instrument, constructed from the number of broadband connections
that the exporter and the importer countries had internally in 2003. We call it BROAD03, which we
interpret as a joint measure of each pair of countries’ pre-existing information and communication
technology infrastructure. The rationale is that the number of bilateral hyperlinks between two coun-
tries would depend, among other factors, on the number of broadband connections in those countries.
We define BROAD03 as the product of the number of broadband connections in the two countries in
2003. This has the intuitive property that its magnitude would be small if the number of broadband
connections in either country is suciently small. Moreover, it is unlikely that BROAD03 would
aect current and future bilateral trade on its own, independent of BLINK09. We thus believe that
BROAD03 meets the exclusion restriction.
4 Results
In this section, we present the results of our estimates of eqs. (34) and (35). First, we apply our
two-stage procedure using data on all 177 countries in our sample for each year in 2002-2015 pe-
riod. In this ‘baseline’ specification, we include all explanatory variables except bilateral hyperlinks,
BLINK09. In Stage 2 there are two dependent variables: the estimated exporter fixed eects and es-
timated importer fixed eects on bilateral trade from stage 1 estimation. Stage 2 estimations recover
the eects of observable country-specific variables. In these regressions, we use nominal GDPs ex-
pressed in US$ and GINI coecient as the measures of size and inequality.27 The results are reported
in Tables 5and 6for service trade and trade in manufactures, respectively.
Next, we estimate the same baseline equations (without the BLINK09 variable), while restricting
the sample to those 82 countries for whom BLINK09 data is indeed available. The goal is to compare
the marginal eects of other variables between the absence and presence of bilateral hyperlinks. The
results are presented in Table 7.
Considering the potential endogeneity issues with BLINK09, we proceed with an instrumental
variable approach. As discussed earlier, the two instruments under consideration are BLINK03 and
BROAD03. To test the validity of our proposed instruments, we first estimate an auxiliary regression
(equivalent to a first-stage regression in a standard 2SLS procedure) by OLS:
BLINK09ir =α+ξi+ξr+β·IV (1)|(2)
ir +γ0·Vir +ir (37)
where ξiand ξrrepresent the exporter and importer fixed eects, respectively; IV(1)|(2)
ir represent the
two considered instruments; Vir is the set of bilateral variables that include the distance, common
border, common language and colonial relationship in the past and ir is the random term. Table 8
26Besides mitigation of endogeneity concerns by instrumenting BLINK09, in the presence of two fixed eects in our
model the concerns of the presence of the incidental parameter problem are alleviated too (see Fern´
andez-Val and Weidner
(2016)).
27Alternative measures of GDP and income inequality are discussed in Section 5.
21
reports the results for BROAD03 (column 1) and BLINK03 (column 2). The coecients on the
instruments are highly significant and the F–statistics for both are large and significant, reducing
concerns for the presence of weak instrument issues.
Between the two instrumental variables, BROAD03 is our preferred choice however. There are
three reasons. First, we have data on BROAD03 for a larger sample of countries. Second, Ta-
ble 8shows a stronger relationship between BLINK09 and BROAD03 than between BLINK09 and
BLINK03. Third, BROAD03 entails less scope for violations of the exclusion restriction relative to
BLINK03. Accordingly, given the coecients from Table 8in Column (1), we calculate the predicted
(log) number of bilateral hyperlinks in 2009. We then estimate the two-stages of the gravity equa-
tions, as described in section 3.3, but replacing the log of BLINK09 by its predicted counterpart from
eq. (37). Table 9reports the results. In what follows, we organize our discussion of results around the
explanatory variables.
4.1 ExportersGDP, ImportersPopulation,and Importers per capita GDP
The second stage results reported in all four tables show that the exporting country’s GDP, the import-
ing country’s population, and per capita income are positively associated with bilateral trade for both
product groups. This is hardly surprising. But note that the estimated coecients on these variables
are consistent with our theoretical model in terms of ranking. The exporter GDP coecients for man-
ufacturing and services are plotted without BLINK09 being included in Figure 5(a) over the period
2002-2015, while the results with BLINK09 included are illustrated in Figure 5(b) for years 2009 to
2015. With some exceptions, the estimated coecients are higher for manufacturing than services.
As these coecients are monotonically related to Armington elasticities, which, in turn, are in-
versely related to the degree of product dierentiation, the ranking of the coecients indirectly sup-
ports one of our basic premises that services are more nationally dierentiated than manufactures.
Figure 5(c) depicts the coecients on importer per capita GDP in the specification without
BLINK09. The numbers are again consistent with the theory: the elasticities of bilateral trade in
services with respect to the importing country per capita GDP are greater, compared to that in man-
ufacturing. Panel (d) depicts the coecients of importing-country per capita GDP for the period
2009-2015, where BLINK is accounted for. The rankings are clear and agree with theory. The ex-
porter GDP elasticity for manufacturing ranges from 0.36 to 0.64, whereas that for services ranges
from 0.38 to 0.57. The importer per capita GDP elasticity for bilateral trade in manufacturing lies in
the range 0.38-0.71, whereas for bilateral trade in services, the range is 0.72-0.98.
A stark finding is that the coecients on exporter GDP, importer population, and per capita im-
porter GDP become significantly lower when BLINK is included in our specifications. All six panels
in Figure 6illustrate this. BLINK tends to increase bilateral trade, and, as Table 10 shows, BLINK09
is positively correlated with all three variables. Thus, the omission of BLINK entails an omitted-
variable problem and leads to an over-estimation of coecients on these variables. This finding
underscores that virtual proximity is an important missing component in the literature, hitherto, on
the estimation of trade costs of bilateral trade in both manufacturing and services.
We can transform the population, and per capita GDP variables of the importing country into the
GDP and the per capita GDP by substituting the log of the population as the log of GDP log of
per capita GDP. Hence, the coecients of importer’s GDP are equal to the coecients on population,
and those of per capita GDP equals the respective coecients in Tables 5-9minus the respective
coecient of the population. Notice that in each set of regression, the coecients on population are
smaller than those on per capita GDP. Hence in the (GDP, per capita GDP) space for the importing
22
Table 5: Trade in Services - PPML estimates Year-by-Year Using the 2-Stage Approach (2002 to 2015)
International Trade in Services (level)
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14)
2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015
First Stage Regressions
Distance (log) –0.66*** –0.65*** –0.64*** –0.64*** –0.67*** –0.69*** –0.68*** –0.69*** –0.64*** –0.61*** –0.62*** –0.63*** –0.66*** –0.64***
(0.04) (0.04) (0.04) (0.04) (0.04) (0.04) (0.04) (0.04) (0.03) (0.03) (0.03) (0.03) (0.03) (0.03)
Common border 0.34* 0.28* 0.32* 0.49*** 0.37** 0.29* 0.27* 0.26* 0.23 0.24* 0.26* 0.28* 0.15 0.10
(0.14) (0.14) (0.13) (0.14) (0.13) (0.13) (0.13) (0.12) (0.13) (0.12) (0.11) (0.12) (0.11) (0.12)
Common language 0.33** 0.39** 0.37*** 0.30* 0.37** 0.38** 0.40*** 0.39*** 0.35*** 0.42*** 0.37*** 0.36*** 0.42*** 0.43***
(0.12) (0.12) (0.11) (0.12) (0.12) (0.12) (0.12) (0.11) (0.11) (0.10) (0.10) (0.10) (0.10) (0.10)
Colony 0.29* 0.22 0.28* 0.17 0.12 0.12 0.15 0.12 0.40*** 0.42*** 0.42*** 0.31** 0.28** 0.24*
(0.14) (0.14) (0.13) (0.13) (0.14) (0.14) (0.13) (0.13) (0.10) (0.10) (0.10) (0.10) (0.11) (0.10)
N 4500 4885 5577 12433 13158 14790 14875 25762 31152 30976 31152 30450 31152 31152
R-sq 0.87 0.85 0.86 0.82 0.82 0.82 0.81 0.82 0.83 0.85 0.85 0.84 0.85 0.85
Exporter and Importer FE XXXXXXXXXXXXXX
Second Stage Regressions
Dependent variable: Exporter Fixed Eects, [
exp(Xji)
Exporter GDP (log) 0.85*** 0.84*** 0.83*** 0.85*** 0.85*** 0.85*** 0.89*** 0.89*** 0.83*** 0.82*** 0.80*** 0.83*** 0.83*** 0.83***
(0.06) (0.06) (0.06) (0.07) (0.06) (0.07) (0.08) (0.07) (0.08) (0.09) (0.09) (0.11) (0.09) (0.09)
Internet Exporter 0.01*** 0.01*** 0.01*** 0.01** 0.01** 0.01** 0.01*** 0.01*** 0.02*** 0.02*** 0.02*** 0.02*** 0.02*** 0.02***
(0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00)
N 35 34 38 77 80 79 80 132 146 136 130 119 108 96
R-sq 0.98 0.98 0.97 0.93 0.94 0.93 0.91 0.90 0.86 0.84 0.85 0.81 0.86 0.88
Dependent variable: Importer Fixed Eects, [
exp(Mjr )
Importer Population (log) 0.55*** 0.53*** 0.53*** 0.67*** 0.67*** 0.70*** 0.73*** 0.72*** 0.73*** 0.73*** 0.73*** 0.75*** 0.72*** 0.70***
(0.04) (0.04) (0.04) (0.07) (0.06) (0.07) (0.07) (0.05) (0.05) (0.05) (0.05) (0.05) (0.05) (0.05)
Importer GDP percap (log) 1.34*** 1.28*** 1.23*** 1.18*** 1.29*** 1.24*** 1.16*** 1.26*** 1.06*** 1.08*** 1.10*** 1.31*** 1.33*** 1.28***
(0.12) (0.12) (0.09) (0.12) (0.12) (0.13) (0.13) (0.12) (0.11) (0.11) (0.12) (0.12) (0.09) (0.08)
Internet Importer –0.00 –0.00 –0.00 0.01 0.00 0.00 0.01 0.01 0.02* 0.02** 0.02** 0.01 0.01 0.00
(0.01) (0.00) (0.00) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.00) (0.00)
Importer Gini 0.06*** 0.06*** 0.06*** 0.02 0.02 0.02 0.02 0.02 0.05** 0.04** 0.04* 0.04* 0.05*** 0.04**
(0.01) (0.02) (0.02) (0.02) (0.02) (0.02) (0.02) (0.02) (0.02) (0.02) (0.02) (0.02) (0.01) (0.01)
N 35 34 38 77 80 79 80 132 146 136 130 119 108 96
R-sq 0.99 0.98 0.97 0.96 0.95 0.94 0.94 0.95 0.95 0.95 0.96 0.95 0.97 0.98
Notes: Robust standard errors are in parentheses. Statistical significance: *** p<0.01, ** p<0.05, * p<0.10.
23
Table 6: Trade in Manufacturing - PPML estimates Year-by-Year Using the 2-Stage Approach (2002 to 2015)
International Trade in Manufacturing
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14)
2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015
First Stage Regressions
Distance (log) –0.70*** –0.73*** –0.74*** –0.77*** –0.76*** –0.76*** –0.76*** –0.76*** –0.76*** –0.76*** –0.73*** –0.76*** –0.75*** –0.74***
(0.03) (0.03) (0.03) (0.03) (0.03) (0.03) (0.03) (0.03) (0.03) (0.03) (0.03) (0.03) (0.03) (0.03)
Common border 0.70*** 0.61*** 0.62*** 0.57*** 0.55*** 0.53*** 0.51*** 0.52*** 0.52*** 0.51*** 0.57*** 0.55*** 0.56*** 0.56***
(0.09) (0.10) (0.10) (0.09) (0.09) (0.09) (0.09) (0.09) (0.10) (0.10) (0.10) (0.09) (0.09) (0.09)
Common language 0.23** 0.24** 0.23** 0.23* 0.23** 0.30*** 0.29*** 0.26** 0.23** 0.24** 0.22* 0.27** 0.25** 0.23**
(0.09) (0.08) (0.09) (0.09) (0.09) (0.08) (0.08) (0.09) (0.08) (0.09) (0.08) (0.08) (0.08) (0.08)
Colony –0.02 0.01 0.02 0.08 0.07 0.12 0.15 0.16 0.17 0.21 0.17 0.15 0.11 0.08
(0.11) (0.12) (0.12) (0.12) (0.12) (0.11) (0.11) (0.12) (0.12) (0.12) (0.11) (0.11) (0.11) (0.11)
N 30800 30800 30800 30800 30800 30800 30800 30800 30800 30800 31152 31152 31152 31152
R-sq 0.90 0.89 0.89 0.89 0.88 0.88 0.87 0.87 0.88 0.87 0.88 0.89 0.89 0.90
Exporter and Importer FE XXXXXXXXXXXXXX
Second Stage Regressions
Dependent variable: Exporter Fixed Eects, [
exp(Xji)
Exporter GDP (log) 0.80*** 0.81*** 0.80*** 0.85*** 0.88*** 0.90*** 0.91*** 0.88*** 0.90*** 0.91*** 0.90*** 0.92*** 0.91*** 0.89***
(0.06) (0.07) (0.09) (0.09) (0.09) (0.11) (0.10) (0.10) (0.11) (0.10) (0.10) (0.10) (0.09) (0.09)
Internet Exporter –0.00 –0.00 –0.00 –0.01 –0.01 –0.01 –0.01 –0.00 –0.00 –0.00 –0.00 –0.01 –0.01 –0.00
(0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01)
N 148 148 148 153 154 157 156 150 146 136 130 120 108 96
R-sq 0.90 0.87 0.81 0.78 0.78 0.75 0.76 0.75 0.71 0.72 0.75 0.76 0.77 0.77
Dependent variable: Importer Fixed Eects, [
exp(Mjr )
Importer Population (log) 0.79*** 0.80*** 0.80*** 0.80*** 0.80*** 0.79*** 0.77*** 0.78*** 0.78*** 0.78*** 0.78*** 0.79*** 0.77*** 0.74***
(0.05) (0.05) (0.06) (0.05) (0.05) (0.05) (0.04) (0.04) (0.05) (0.05) (0.05) (0.04) (0.04) (0.03)
Importer GDP percap (log) 0.91*** 0.82*** 0.81*** 0.85*** 0.85*** 0.81*** 0.80*** 0.80*** 0.82*** 0.86*** 0.90*** 1.08*** 1.11*** 1.10***
(0.07) (0.07) (0.06) (0.06) (0.06) (0.06) (0.06) (0.08) (0.11) (0.13) (0.12) (0.12) (0.11) (0.09)
Internet Importer 0.01 0.01* 0.01* 0.01 0.01 0.01 0.01* 0.01 0.01 0.01 0.00 –0.01 –0.01 –0.00
(0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01)
Importer Gini 0.04*** 0.05*** 0.05*** 0.05*** 0.05*** 0.04*** 0.05*** 0.05*** 0.05*** 0.04*** 0.05*** 0.04*** 0.05*** 0.05***
(0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01)
N 148 148 148 153 154 157 156 150 146 136 130 120 108 96
R-sq 0.97 0.97 0.96 0.96 0.96 0.96 0.96 0.95 0.94 0.93 0.94 0.96 0.97 0.98
Notes: Robust standard errors are in parentheses. Statistical significance: *** p<0.01, ** p<0.05, * p<0.10.
24
Table 7: PPML estimates Year-by-Year Using the 2-Stage Approach only the countries with BLINK information but without BLINK09 as a
Regressor
Services Manufacturing
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14)
2009 2010 2011 2012 2013 2014 2015 2009 2010 2011 2012 2013 2014 2015
First Stage Regressions
Distance (log) –0.65*** –0.63*** –0.60*** –0.61*** –0.59*** –0.63*** –0.62*** –0.69*** –0.68*** –0.68*** –0.68*** –0.68*** –0.68*** –0.67***
(0.04) (0.03) (0.03) (0.03) (0.04) (0.03) (0.03) (0.03) (0.03) (0.03) (0.03) (0.03) (0.03) (0.03)
Common border 0.32** 0.29* 0.33** 0.36** 0.36** 0.23* 0.18 0.61*** 0.63*** 0.64*** 0.68*** 0.69*** 0.68*** 0.69***
(0.12) (0.13) (0.12) (0.12) (0.12) (0.12) (0.12) (0.10) (0.10) (0.10) (0.10) (0.09) (0.09) (0.09)
Common language 0.38** 0.30** 0.36*** 0.31** 0.36*** 0.42*** 0.42*** 0.23* 0.18 0.18 0.18 0.17 0.16 0.14
(0.12) (0.11) (0.10) (0.10) (0.11) (0.11) (0.10) (0.10) (0.10) (0.10) (0.09) (0.09) (0.09) (0.09)
Colony 0.05 0.36*** 0.33*** 0.34** 0.25* 0.22* 0.18 0.09 0.10 0.15 0.12 0.08 0.04 0.02
(0.13) (0.11) (0.10) (0.10) (0.11) (0.11) (0.11) (0.12) (0.12) (0.12) (0.11) (0.11) (0.11) (0.11)
N 3724 3741 3741 3741 3741 3741 3741 3696 3696 3696 3741 3741 3741 3741
R-sq 0.83 0.84 0.86 0.86 0.85 0.86 0.87 0.89 0.90 0.90 0.91 0.92 0.92 0.93
Exporter and Importer FE XXXXXXX XXXXXXX
Second Stage Regressions
Dependent variable: Exporter Fixed Eects, [
exp(Xji )
Exporter GDP (log) 0.90*** 0.85*** 0.84*** 0.82*** 0.85*** 0.85*** 0.85*** 0.85*** 0.87*** 0.86*** 0.88*** 0.89*** 0.89*** 0.88***
(0.08) (0.09) (0.09) (0.10) (0.10) (0.08) (0.07) (0.11) (0.12) (0.11) (0.11) (0.11) (0.10) (0.09)
Internet Exporter (log) 0.01*** 0.01*** 0.01*** 0.01*** 0.02*** 0.02*** 0.02*** –0.00 –0.00 –0.00 –0.00 –0.00 –0.00 –0.00
(0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01)
N 80 82 82 81 82 82 82 81 81 81 81 82 82 82
R-sq 0.90 0.86 0.84 0.84 0.83 0.88 0.90 0.71 0.67 0.69 0.72 0.73 0.75 0.76
Dependent variable: Importer Fixed Eects, [
exp(Mj r)
Importer Population (log) 0.73*** 0.73*** 0.73*** 0.74*** 0.75*** 0.72*** 0.70*** 0.76*** 0.78*** 0.78*** 0.78*** 0.78*** 0.77*** 0.74***
(0.06) (0.05) (0.06) (0.05) (0.06) (0.05) (0.05) (0.05) (0.06) (0.06) (0.06) (0.05) (0.05) (0.04)
Importer GDP percap (log) 1.19*** 1.01*** 1.01*** 1.04*** 1.25*** 1.25*** 1.21*** 0.80*** 0.79*** 0.82*** 0.89*** 1.05*** 1.08*** 1.06***
(0.12) (0.11) (0.12) (0.11) (0.12) (0.10) (0.08) (0.10) (0.13) (0.14) (0.14) (0.13) (0.12) (0.10)
Internet Importer 0.01 0.02* 0.02** 0.01* 0.00 0.00 0.00 0.01 0.01 0.01 0.00 –0.01 –0.01 –0.00
(0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.00) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01)
Importer Gini 0.03 0.05** 0.05*** 0.04** 0.04* 0.05*** 0.04** 0.04** 0.05** 0.04** 0.04** 0.04** 0.04** 0.05**
(0.02) (0.02) (0.01) (0.01) (0.02) (0.01) (0.01) (0.02) (0.02) (0.02) (0.01) (0.01) (0.02) (0.01)
N 75 76 73 72 70 69 61 76 76 73 72 70 69 61
R-sq 0.96 0.95 0.95 0.96 0.95 0.97 0.98 0.94 0.93 0.93 0.93 0.96 0.96 0.97
Notes: Robust standard errors are in parentheses. Statistical significance: *** p<0.01, ** p<0.05, * p<0.10.
25
Table 8: Instrumental Variable Validation: First-Stage Regressions
Dependent Variable:
BLINK09 (log)
(1) (2)
BROAD03 (log) 0.63***
(0.02)
BLINK03 (log) 0.32***
(0.01)
Distance (log) –0.35*** –0.20***
(0.02) (0.02)
Common border 0.50*** 0.26***
(0.08) (0.06)
Common language 0.61*** 0.17***
(0.05) (0.05)
Colony 0.20** 0.06
(0.07) (0.06)
N 3,037 1,580
R-sq 0.95 0.96
F-statistic 390.01 435.18
Exporter and Importer FE X X
countries, the coecients on per capita GDP remain positive. This is, in essence, similar to Dalgin et
al. (2008).
Notice also that, given Table 9, the elasticity of bilateral trade in both manufacturing and services
with respect to the size variables, i.e., exporter GDP, importer GDP, and importer GDP per capita, are
less than unity. This is consistent with Santos Silva and Tenreyro (2006, page 650), who also noted
GDP or per capita GDP elasticity for manufacturing trade to be less than one and argued that this may
be due to larger countries tending to be less open. We note another possible reason: the absence of
wealth variables that can also aect aggregate consumption and bilateral trade.
4.2 Income Inequality in the Importer Country
As argued in Section 2.5, theoretically, the eect of inequality on bilateral trade is ambiguous. Hence,
it is primarily an empirical issue. The coecient on GINI is positive for both manufacturing and
services, i.e., bilateral trade in both product categories is positively associated with income inequality.
In Table 9, the coecients on GINI are positive and nearly identical between manufacturing and
services but statistically insignificant for many of the sample years. In sum, our empirical analysis
implies that importer-country inequality is not a strong predictor of bilateral trade.
4.3 Overall (Unobservable-) Trade-Cost Elasticity
Our empirical model does not yield point estimates of the overall trade-cost elasticities for either
product group. However, the magnitudes of these elasticities are monotonic with respect to the Arm-
ington elasticities that rank the elasticities of bilateral trade with respect to the size of a country as an
exporter, whose point estimates are indeed available: see Table 9and Figure 5.
26
Table 9: Two-stages PPML estimates with BLINK09 instrumented by BROAD03
Services Manufacturing
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14)
2009 2010 2011 2012 2013 2014 2015 2009 2010 2011 2012 2013 2014 2015
First Stage Regressions
Distance (log) –0.53*** –0.51*** –0.48*** –0.49*** –0.47*** –0.50*** –0.49*** –0.60*** –0.59*** –0.58*** –0.52*** –0.58*** –0.58*** –0.58***
(0.04) (0.03) (0.03) (0.03) (0.03) (0.03) (0.03) (0.02) (0.03) (0.03) (0.03) (0.03) (0.03) (0.03)
Common border 0.15 0.08 0.13 0.15 0.16 0.04 –0.00 0.48*** 0.50*** 0.50*** 0.46*** 0.56*** 0.55*** 0.56***
(0.13) (0.14) (0.12) (0.12) (0.13) (0.12) (0.12) (0.10) (0.10) (0.10) (0.10) (0.10) (0.10) (0.10)
Common language 0.20 0.10 0.17 0.11 0.16 0.19 0.20 0.08 0.03 0.02 –0.08 0.01 –0.00 –0.01
(0.13) (0.11) (0.10) (0.10) (0.11) (0.11) (0.11) (0.10) (0.10) (0.10) (0.10) (0.10) (0.10) (0.10)
Colony –0.05 0.25* 0.22* 0.23* 0.15 0.11 0.08 0.00 0.01 0.03 –0.05 –0.05 –0.07 –0.07
(0.13) (0.10) (0.10) (0.10) (0.11) (0.11) (0.10) (0.12) (0.12) (0.12) (0.11) (0.11) (0.11) (0.11)
BLINK09 (log) 0.32*** 0.35*** 0.34*** 0.35*** 0.36*** 0.37*** 0.36*** 0.24*** 0.26*** 0.27*** 0.43*** 0.27*** 0.26*** 0.26***
(0.03) (0.03) (0.02) (0.03) (0.03) (0.03) (0.02) (0.03) (0.03) (0.03) (0.02) (0.03) (0.03) (0.03)
N 3,020 3,037 3,037 3,037 3,037 3,037 3,037 3,037 3,037 3,037 3,037 3,037 3,037 3,037
R-sq 0.83 0.85 0.87 0.86 0.85 0.86 0.87 0.89 0.90 0.90 0.91 0.92 0.92 0.93
Exporter and Importer FE XXXXXXX XXXXXXX
Second Stage Regressions
Dependent variable: Exporter Fixed Eects, [
exp(Xji )
Exporter GDP (log) 0.57*** 0.43*** 0.41*** 0.38*** 0.41*** 0.40*** 0.43*** 0.59*** 0.59*** 0.57*** 0.36** 0.63*** 0.63*** 0.64***
(0.09) (0.10) (0.10) (0.10) (0.11) (0.09) (0.09) (0.10) (0.11) (0.11) (0.11) (0.10) (0.10) (0.09)
Internet Exporter 0.01*** 0.01*** 0.01*** 0.01*** 0.02*** 0.01*** 0.01*** –0.00 0.00 0.00 0.00 –0.00 –0.00 –0.00
(0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01)
N 68 68 68 68 68 68 68 68 68 68 68 68 68 68
R-sq 0.72 0.59 0.57 0.52 0.52 0.55 0.60 0.54 0.49 0.46 0.25 0.58 0.60 0.63
Dependent variable: Importer Fixed Eects, [
exp(Mj r)
Importer Population (log) 0.43*** 0.33*** 0.33*** 0.33*** 0.36*** 0.33*** 0.34*** 0.47*** 0.48*** 0.46*** 0.24*** 0.48*** 0.49*** 0.49***
(0.07) (0.06) (0.06) (0.05) (0.06) (0.06) (0.06) (0.06) (0.06) (0.06) (0.07) (0.06) (0.06) (0.05)
Importer GDP percap (log) 0.98*** 0.82*** 0.72*** 0.77*** 0.88*** 0.90*** 0.97*** 0.54*** 0.51*** 0.47*** 0.38** 0.66*** 0.70*** 0.71***
(0.16) (0.13) (0.12) (0.12) (0.14) (0.16) (0.15) (0.12) (0.12) (0.13) (0.14) (0.17) (0.17) (0.17)
Internet Importer 0.00 0.00 0.01 0.01 0.00 –0.00 –0.01 0.00 0.00 0.00 –0.00 –0.01 –0.01 –0.00
(0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01)
Importer Gini 0.01 0.04 0.04* 0.04* 0.03 0.04** 0.03* 0.04 0.04* 0.03 0.03* 0.03* 0.03 0.04
(0.02) (0.02) (0.02) (0.02) (0.02) (0.01) (0.02) (0.02) (0.02) (0.02) (0.02) (0.02) (0.02) (0.02)
N 64 66 64 63 61 60 55 65 66 64 63 61 60 55
R-sq 0.80 0.75 0.75 0.77 0.74 0.76 0.80 0.80 0.79 0.73 0.42 0.78 0.82 0.85
Notes: Robust standard errors are in parentheses. Statistical significance: *** p<0.01, ** p<0.05, * p<0.10.
27
Figure 5: Coecients on Exporter GDP and Importer per capita GDP
Exporter GDP
(a) No BLINK (b) BLINK09 included
Importer per capita GDP
(c) No BLINK (d) BLINK09 included
The exporting-country GDP elasticity being greater for manufacturing, the Armington elasticity
is higher for manufacturing, implying that the trade-cost elasticity of bilateral trade is higher for
manufacturing than for services. This is consistent with the theoretical prediction in Result 7. As
noted earlier, it indirectly validates our Dierence in the National Product Dierentiation assumption.
4.4 Observable Trade Costs
Internet Penetration Tables 5through Table 9show a positive and statistically significant eect of
internet usage in the exporter country on international trade of services. However, we do not observe
28
Figure 6: Coecients on Exporter GDP, Importer Population and Importer per capita GDP
(a) No BLINK (b) BLINK09 included
Table 10: Correlations with Bilateral hyperlinks
Correlation with BLINK09
2009 2010 2011 2012 2013 2014 2015
Exporter GDP (log) 0.6259*** 0.6278*** 0.6288*** 0.6244*** 0.6223*** 0.6204*** 0.6219***
Importer Population (log) 0.4287*** 0.4270*** 0.4252*** 0.4236*** 0.4219*** 0.4202*** 0.4187***
Importer GDP percap (log) 0.2526*** 0.2678*** 0.2740*** 0.2736*** 0.2667*** 0.2646*** 0.2725***
Note: *** Denotes statistical significance at 1%.
29
a consistent and statistically significant eect of internet usage in the importer country for trade in
services. Moreover, the coecients for internet usage in countries both as exporters and importers
are not statistically significant for trade in manufacturing, suggesting that, at the margin, trade in
manufactures is not aected by the overall internet usage in either country.
Internet usage is likely to be positively and strongly associated with the number of internet web-
sites in a country, which provides essential information on sellers’ products and services in particular.
Typically, the producers advertise their products on their websites, reaching potential consumers at
home and abroad. Thus, internet usage is expected to reduce trade costs for exporting firms. From the
importer country’s perspective, its import behavior is not so much aected by the extent of internet
use in that country as does the internet use in the countries that export their products.
Freund and Weinhold (2002) is among the first to investigate this empirically, and their finding
is somewhat qualified: for trade in services between the U.S. and other countries, internet usage in
other countries positively impacts their exports to the U.S. in specific categories of services. More
generally interpreted, internet utilization is positively associated with bilateral services exports. In
a related paper, Freund and Weinhold (2004) find that internet usage is positively associated with
overall export growth. The authors argue that their findings are consistent with a model in which
internet use reduces market-specific fixed costs of trade, which are likely to enhance export growth.
Our results indicate that the same overall qualitative pattern as in Freund and Weinhold (2002,2004)
hold on average across many countries and years for trade in services.
Bilateral Hyperlinks In contrast to the overall use of internet in a trading country, virtual proximity
– captured by BLINK09 – constitutes a strong trade-cost-reducing agent and exerts positive eects
on bilateral trade for both services and manufacturing. Observe in Table 9that the coecients on
the instrumented BLINK09 are positive and statistically significant. Furthermore, bilateral trade in
services is more sensitive to virtual proximity compared to manufacturing. On average, a 10% in-
crease in bilateral hyperlinks leads, barring the year 2012, to a 2.4 to 2.7% increase in bilateral trade
in manufacturing and 3.2 to 3.7% increase in bilateral trade in services.
Distance, Common Border, Common Language and Colony, and, Substitution Eects The co-
ecients of these standard trade-cost variables bear their expected signs. It is surprising however that
when BLINK09 is included as a regressor, the coecients of common language and colonial relation
generally become statistically insignificant. Moreover, the coecient on the common border is sig-
nificant for manufacturing trade but not for trade in services, while physical distance remain highly
significant for trade in both services and manufacturing. As expected, compared to manufacturing,
bilateral trade in services is less sensitive to physical distance.
It is of interest to know how the coecients on these variables change once we account for the
virtual proximity variable. Comparing Tables 7and 9we observe that, with virtual proximity present
as a regressor, the marginal impacts of distance, common border, and common language on trade in
both services and manufacturing become smaller in magnitude. This is illustrated in Figure 7for
distance and common border.
The estimates for geographical distance imply that virtual proximity partly substitutes physical
proximity. There are two essential points on this finding. First, it does not mean that physical prox-
imity is less important than virtual proximity. Indeed, the absolute value of the coecient on physical
distance exceeds the coecient on virtual proximity for both manufacturing and services.
Second, how does the virtual proximity substitution result relate to the “distance puzzle” a la
30
Brun et al. (2005), Disdier and Head (2008) and Yotov (2012)? Insofar as increasing globalization
includes an increasing flow of information between countries through the internet, we may infer from
Figure 7(a) that there is no distance puzzle since the partial eect of distance has indeed decreased.
The process has presumably begun much before 2009. However, keeping apart the downward shift
of the distance coecient due to virtual proximity, we still see that the physical distance coecient is
remarkably stable from one year to the next. In this sense, the distance puzzle remains. Of course, we
know from Yotov (2012) that the key lies in accounting for internal trade and internal distance eect.
We believe that if these variables are included, the coecients on distance will, with the advent of
virtual proximity, have a decreasing trend over time, combined with a downward shift.
Figure 7: Coecients on Distance and Common Border: BLINK versus No BLINK
(c) Common Border in Services (d) Common Border in Manufacturing
5 Robustness
31
Table 11: Two-stages PPML using PPP GDP (BLINK09 Instrumented by BROAD03)
Services Manufacturing
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14)
2009 2010 2011 2012 2013 2014 2015 2009 2010 2011 2012 2013 2014 2015
First Stage Regressions
Distance (log) –0.53*** –0.51*** –0.48*** –0.49*** –0.47*** –0.50*** –0.49*** –0.60*** –0.59*** –0.58*** –0.52*** –0.58*** –0.58*** –0.58***
(0.04) (0.03) (0.03) (0.03) (0.03) (0.03) (0.03) (0.02) (0.03) (0.03) (0.03) (0.03) (0.03) (0.03)
Common border 0.15 0.08 0.13 0.15 0.16 0.04 –0.00 0.48*** 0.50*** 0.50*** 0.46*** 0.56*** 0.55*** 0.56***
(0.13) (0.14) (0.12) (0.12) (0.13) (0.12) (0.12) (0.10) (0.10) (0.10) (0.10) (0.10) (0.10) (0.10)
Common language 0.20 0.10 0.17 0.11 0.16 0.19 0.20 0.08 0.03 0.02 –0.08 0.01 –0.00 –0.01
(0.13) (0.11) (0.10) (0.10) (0.11) (0.11) (0.11) (0.10) (0.10) (0.10) (0.10) (0.10) (0.10) (0.10)
Colony –0.05 0.25* 0.22* 0.23* 0.15 0.11 0.08 0.00 0.01 0.03 –0.05 –0.05 –0.07 –0.07
(0.13) (0.10) (0.10) (0.10) (0.11) (0.11) (0.10) (0.12) (0.12) (0.12) (0.11) (0.11) (0.11) (0.11)
BLINK09 (log) 0.32*** 0.35*** 0.34*** 0.35*** 0.36*** 0.37*** 0.36*** 0.24*** 0.26*** 0.27*** 0.43*** 0.27*** 0.26*** 0.26***
(0.03) (0.03) (0.02) (0.03) (0.03) (0.03) (0.02) (0.03) (0.03) (0.03) (0.02) (0.03) (0.03) (0.03)
N 3,020 3,037 3,037 3,037 3,037 3,037 3,037 3,037 3,037 3,037 3,037 3,037 3,037 3,037
R-sq 0.83 0.85 0.87 0.86 0.85 0.86 0.87 0.89 0.90 0.90 0.91 0.92 0.92 0.93
Exporter and Importer FE XXXXXXX XXXXXXX
Second Stage Regressions
Dependent variable: Exporter Fixed Eects, [
exp(Xji )
Exporter GDP (log) 0.59*** 0.46*** 0.44*** 0.40*** 0.42*** 0.41*** 0.44*** 0.64*** 0.65*** 0.63*** 0.41*** 0.67*** 0.68*** 0.70***
(0.09) (0.10) (0.10) (0.11) (0.12) (0.11) (0.11) (0.10) (0.11) (0.11) (0.11) (0.10) (0.10) (0.10)
Internet Exporter 0.02*** 0.02*** 0.02*** 0.02*** 0.02*** 0.02*** 0.02*** 0.01* 0.01* 0.01* 0.01* 0.01 0.01 0.01
(0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.01) (0.01) (0.00) (0.00) (0.00) (0.01)
N 68 68 68 68 68 68 68 68 68 68 68 68 68 68
R-sq 0.74 0.61 0.59 0.54 0.50 0.52 0.53 0.57 0.54 0.50 0.29 0.61 0.62 0.63
Dependent variable: Importer Fixed Eects, [
exp(Mj r)
Importer Population (log) 0.47*** 0.38*** 0.36*** 0.37*** 0.41*** 0.36*** 0.38*** 0.50*** 0.51*** 0.48*** 0.27*** 0.51*** 0.51*** 0.52***
(0.06) (0.05) (0.05) (0.05) (0.06) (0.04) (0.05) (0.06) (0.05) (0.06) (0.07) (0.06) (0.05) (0.05)
Importer GDP percap (log) 1.14*** 0.96*** 0.85*** 0.90*** 1.06*** 1.30*** 1.46*** 0.82*** 0.78*** 0.75*** 0.63*** 0.89*** 1.09*** 1.09***
(0.23) (0.18) (0.17) (0.17) (0.21) (0.21) (0.17) (0.16) (0.15) (0.16) (0.16) (0.20) (0.22) (0.24)
Internet Importer 0.01 0.01 0.02** 0.02* 0.01 0.00 -0.00 0.01 0.01 0.00 -0.00 -0.00 -0.00 -0.00
(0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01)
Importer Gini -0.00 0.03 0.03* 0.03* 0.02 0.03** 0.03** 0.03 0.03* 0.03 0.03 0.03 0.03* 0.04*
(0.02) (0.02) (0.01) (0.01) (0.01) (0.01) (0.01) (0.02) (0.02) (0.02) (0.02) (0.01) (0.01) (0.02)
N 64 66 64 63 61 60 55 65 66 64 63 61 60 55
R-sq 0.79 0.76 0.77 0.77 0.72 0.82 0.85 0.84 0.84 0.78 0.48 0.79 0.85 0.86
32
Table 12: Second-Stage Estimates: Alternative Measures of Income Inequality (BLINK09 Instrumented by BROAD03)
Services Manufacturing
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14)
2009 2010 2011 2012 2013 2014 2015 2009 2010 2011 2012 2013 2014 2015
Panel a: Importer Gini Coecient
Importer Population (log) 0.43*** 0.33*** 0.33*** 0.33*** 0.36*** 0.33*** 0.34*** 0.47*** 0.48*** 0.46*** 0.24*** 0.48*** 0.49*** 0.49***
(0.07) (0.06) (0.06) (0.05) (0.06) (0.06) (0.06) (0.06) (0.06) (0.06) (0.07) (0.06) (0.06) (0.05)
Importer GDP percap (log) 0.98*** 0.82*** 0.72*** 0.77*** 0.88*** 0.90*** 0.97*** 0.54*** 0.51*** 0.47*** 0.38** 0.66*** 0.70*** 0.71***
(0.16) (0.13) (0.12) (0.12) (0.14) (0.16) (0.15) (0.12) (0.12) (0.13) (0.14) (0.17) (0.17) (0.17)
Internet Importer 0.00 0.00 0.01 0.01 0.00 –0.00 –0.01 0.00 0.00 0.00 –0.00 –0.01 –0.01 –0.00
(0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01)
Importer Gini 0.01 0.04 0.04* 0.04* 0.03 0.04** 0.03* 0.04 0.04* 0.03 0.03* 0.03* 0.03 0.04
(0.02) (0.02) (0.02) (0.02) (0.02) (0.01) (0.02) (0.02) (0.02) (0.02) (0.02) (0.02) (0.02) (0.02)
N 64 66 64 63 61 60 55 65 66 64 63 61 60 55
R-sq 0.80 0.75 0.75 0.77 0.74 0.76 0.80 0.80 0.79 0.73 0.42 0.78 0.82 0.85
Panel b: Importer Top 10th percentile of income share
Importer Population (log) 0.54*** 0.39*** 0.39*** 0.40*** 0.44*** 0.37*** 0.42*** 0.52*** 0.53*** 0.54*** 0.32*** 0.54*** 0.54*** 0.51***
(0.07) (0.05) (0.05) (0.05) (0.06) (0.06) (0.05) (0.06) (0.05) (0.04) (0.05) (0.04) (0.04) (0.06)
Importer GDP percap (log) 0.91*** 0.85*** 0.74*** 0.77*** 0.77*** 0.89*** 0.98*** 0.57*** 0.55*** 0.51*** 0.30* 0.65*** 0.74*** 0.71***
(0.17) (0.13) (0.12) (0.13) (0.13) (0.15) (0.16) (0.10) (0.12) (0.12) (0.12) (0.13) (0.12) (0.13)
Internet Importer –0.00 –0.00 0.01 0.01 0.01 –0.00 –0.01 0.00 0.00 0.01 0.01 0.00 –0.00 –0.00
(0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.00) (0.00) (0.01) (0.01) (0.01) (0.01) (0.01)
Top 10th percentile of income share –2.53** 1.22 1.73*** 1.64*** 1.42** 1.95*** 2.14*** 2.02** 1.87** 2.18** 3.18*** 2.40*** 2.50*** 2.36**
(0.94) (0.65) (0.46) (0.43) (0.50) (0.40) (0.39) (0.65) (0.63) (0.69) (0.63) (0.65) (0.64) (0.72)
N 48 48 46 46 46 46 43 48 48 46 46 46 46 43
R-sq 0.80 0.75 0.78 0.79 0.77 0.76 0.77 0.83 0.83 0.87 0.70 0.89 0.90 0.79
Panel c: Importer Top 1st percentile of income share
Importer Population (log) 0.54*** 0.37*** 0.36*** 0.37*** 0.42*** 0.34*** 0.40*** 0.51*** 0.52*** 0.51*** 0.26*** 0.51*** 0.51*** 0.48***
(0.07) (0.05) (0.05) (0.05) (0.06) (0.06) (0.05) (0.06) (0.06) (0.05) (0.06) (0.05) (0.05) (0.06)
Importer GDP percap (log) 0.94*** 0.85*** 0.71*** 0.74*** 0.75*** 0.86*** 0.96*** 0.60*** 0.58*** 0.51*** 0.27* 0.62*** 0.69*** 0.64***
(0.17) (0.12) (0.12) (0.13) (0.13) (0.15) (0.16) (0.10) (0.11) (0.12) (0.13) (0.15) (0.14) (0.14)
Internet Importer –0.00 –0.00 0.01 0.01 0.01 –0.00 –0.01 –0.00 –0.00 0.00 0.01 –0.00 –0.00 –0.00
(0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.00) (0.00) (0.01) (0.01) (0.01) (0.01) (0.01)
Top 1st percentile of income share –3.12 2.76** 3.40*** 3.28*** 2.68** 3.60*** 3.89*** 2.87* 2.64* 2.85 5.55*** 3.70* 3.82* 3.25*
(1.80) (1.03) (0.76) (0.77) (0.96) (0.78) (0.81) (1.32) (1.23) (1.51) (1.61) (1.56) (1.52) (1.59)
N 49 49 46 46 46 46 43 49 49 46 46 46 46 43
R-sq 0.80 0.77 0.78 0.80 0.77 0.76 0.75 0.83 0.84 0.84 0.62 0.85 0.87 0.72
33
Table 13: Second-Stage Random Eects PPML (BLINK09 instrumented by BROAD03
Services Manufacturing
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14)
2009 2010 2011 2012 2013 2014 2015 2009 2010 2011 2012 2013 2014 2015
First Stage Regressions
Distance (log) –0.53*** –0.51*** –0.48*** –0.49*** –0.47*** –0.50*** –0.49*** –0.60*** –0.59*** –0.58*** –0.52*** –0.58*** –0.58*** –0.58***
(0.04) (0.03) (0.03) (0.03) (0.03) (0.03) (0.03) (0.02) (0.03) (0.03) (0.03) (0.03) (0.03) (0.03)
Common border 0.15 0.08 0.13 0.15 0.16 0.04 –0.00 0.48*** 0.50*** 0.50*** 0.46*** 0.56*** 0.55*** 0.56***
(0.13) (0.14) (0.12) (0.12) (0.13) (0.12) (0.12) (0.10) (0.10) (0.10) (0.10) (0.10) (0.10) (0.10)
Common language 0.20 0.10 0.17 0.11 0.16 0.19 0.20 0.08 0.03 0.02 –0.08 0.01 –0.00 –0.01
(0.13) (0.11) (0.10) (0.10) (0.11) (0.11) (0.11) (0.10) (0.10) (0.10) (0.10) (0.10) (0.10) (0.10)
Colony –0.05 0.25* 0.22* 0.23* 0.15 0.11 0.08 0.00 0.01 0.03 –0.05 –0.05 –0.07 –0.07
(0.13) (0.10) (0.10) (0.10) (0.11) (0.11) (0.10) (0.12) (0.12) (0.12) (0.11) (0.11) (0.11) (0.11)
BLINK09 (log) 0.32*** 0.35*** 0.34*** 0.35*** 0.36*** 0.37*** 0.36*** 0.24*** 0.26*** 0.27*** 0.43*** 0.27*** 0.26*** 0.26***
(0.03) (0.03) (0.02) (0.03) (0.03) (0.03) (0.02) (0.03) (0.03) (0.03) (0.02) (0.03) (0.03) (0.03)
N 3,020 3,037 3,037 3,037 3,037 3,037 3,037 3,037 3,037 3,037 3,037 3,037 3,037 3,037
R-sq 0.83 0.85 0.87 0.86 0.85 0.86 0.87 0.89 0.90 0.90 0.91 0.92 0.92 0.93
Exporter and Importer FE XXXXXXX XXXXXXX
Second Stage Regressions (Random Intercepts PPML) exp Xji +Mjras dependent variable
Exporter GDP (log) 0.66*** 0.37*** 0.35*** 0.34*** 0.36*** 0.37*** 0.38*** 0.72*** 0.69*** 0.65*** 0.38*** 0.66*** 0.67*** 0.69***
(0.1) (0.09) (0.09) (0.09) (0.09) (0.09) (0.09) (0.08) (0.08) (0.08) (0.09) (0.08) (0.08) (0.08)
Internet Exporter (log) 0.01** 0.01** 0.01** 0.01** 0.02** 0.01** 0.01* 0.01* 0.01* 0.01 0.01* 0.01 0.01 0.01
(0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01)
Importer Population (log) 0.44*** 0.35*** 0.33*** 0.33*** 0.36*** 0.35*** 0.41*** 0.56*** 0.55*** 0.48*** 0.27*** 0.50*** 0.52*** 0.52***
(0.1) (0.09) (0.10) (0.10) (0.11) (0.10) (0.11) (0.09) (0.09) (0.09) (0.10) (0.10) (0.1) (0.11)
Importer GDP percap (log) 0.83*** 0.77*** 0.55* 0.59** 0.66** 0.62** 0.77*** 0.59** 0.52** 0.35 0.22 0.39 0.45 0.46*
(0.27) (0.26) (0.28) (0.28) (0.32) (0.30) (0.30) (0.24) (0.24) (0.26) (0.27) (0.29) (0.28) (0.28)
Internet Importer (log) 0.01 0.00 0.01 0.01 0.01 0.00 0.00 0.00 0.00 0.01 0.01 0.01 0.01 0.00
(0.01) (0.01) (0.02) (0.02) (0.02) (0.02) (0.02) (0.01) (0.01) (0.01) (0.02) (0.02) (0.02) (0.02)
Importer Gini 0.01 0.02 0.03 0.03 0.02 0.02 0.02 0.01 0.01 0.02 0.03 0.03 0.02 0.02
(0.02) (0.02) (0.02) (0.03) (0.03) (0.02) (0.03) (0.02) (0.02) (0.02) (0.02) (0.02) (0.02) (0.02)
Intercept –36.02*** –26.65*** –24.35*** –24.48*** –26.61*** –25.61*** –27.71*** –33.74*** –33.00** –30.12*** –19.93*** –31.44*** –31.68*** –32.32***
(3.88) (3.62) (3.63) (3.60) (3.86) (3.76) (3.80) (3.35) (3.30) (3.35) (3.51) (3.48) (3.48) (3.54)
N 2,932 2,957 2,911 2,885 2,799 2,766 2,639 2,932 2,957 2,911 2,885 2,799 2,766 2,639
Exporters 69 69 69 69 69 69 69 69 69 69 69 69 69 69
Importers 65 66 64 63 61 60 55 65 66 64 63 61 60 55
34
5.1 Alternative Measures of GDP and Income Inequality
Like other gravity models, our theoretical and empirical models do not account for non-tradable
sectors. Keeping this in mind, we consider GDPs measured by PPP. Corresponding estimates are
displayed in Table 11. We notice that the results are similar to those in our baseline model, except for
a weaker evidence of the hypothesis that, compared to bilateral trade in manufacturing, bilateral trade
in services is more sensitive to changes in the per capita income of the importing country.
We also consider alternative measures of income inequality, namely, the pre-tax income share by
the top 10 or 1 percentile of the income distribution. Panels (b) and (c) of Table 12 report the estimates
of the coecients on importer-country specific regressors. (The first-stage estimates and the second-
stage estimates for the exporting-country-specific regressors remain unchanged.) For comparison,
panel (a) reproduces the estimates using GINI, reported earlier in Table 9. Overall, the results are
similar across the dierent measures for within-country income inequality. More inequality is asso-
ciated with more bilateral trade in both manufacturing and services. The estimates of the coecients
on other variables are comparable to our baseline model.
5.2 Random Intercept Model
Although we have argued in favor of our two-stage procedure, for the sake of comparison, we ex-
amined an alternative two-stage approach that relies on the random-intercept PPML estimator in the
second stage, as proposed by (Prehn et al.,2015). That is, we run the first-stage fixed eect PPML
with bilateral explanatory variables only (as earlier), but in the second stage, we estimate the coe-
cients on the observable country-specific regressors of both exporting and importing countries jointly.
The exponential of the sum of the exporter- and importer- fixed eects estimated from the first-stage
regression is the (single) dependent variable in the second-stage estimation. The results are reported
in Table 13. The coecient estimates for the bilateral explanatory variables are the same as in our
baseline results (see Table 9).
Observe additionally that the coecients on country-specific variables are generally close to those
in our baseline approach, except for the marginal impact of importing-country per capita GDP on
bilateral trade in manufacturing. The coecients on some years are not significantly dierent from
zero. Generally speaking, the qualitative patterns remain fairly robust.
5.3 Panel Estimation
In section 3.2, we argued against panel estimation because of the small within-variation of most
country-specific regressors. However, the results from panel estimation might still be of interest,
considering that a significant part of the existing literature has adopted panel estimation for gravity
models (despite the cautionary note by Head and Mayer (2014) on “questionable bases for panel
estimation”). We present the results from the panel covering the years 2009-2015, since we use
BLINK09 for bilateral hyperlinks.
Table 14 presents the results from pooled, random-eects, and various combinations of fixed-
eects specifications. Notice that the predicted patterns on the impact of exporter GDP and importer
per capita GDP are generally borne out from the pooled, exporter-year, importer-year, and country-
pair random eects. Exporter-year and importer-year fixed eects do not yield estimates of country-
specific variables due to perfect multicollinearity. The panel estimation model do not agree with
35
Table 14: PPML Panel Estimates (2009-2015)
Services Manufacturing
Pooled FE RE FE RE Pooled FE RE FE RE
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Distance (log) -0.51*** -0.55*** -0.55*** -0.65*** -0.55*** -0.63*** -0.63*** -0.76***
(0.04) (0.03) (0.01) (0.03) (0.06) (0.03) (0.01) (0.03)
Common border 0.04 0.20 0.21*** 0.09 0.80*** 0.60*** 0.60*** 0.32***
(0.15) (0.11) (0.03) (0.13) (0.22) (0.09) (0.02) (0.12)
Common language 0.64*** 0.19 0.22*** 0.79*** 0.28 0.06 0.06*** 0.47***
(0.13) (0.10) (0.03) (0.10) (0.19) (0.09) (0.02) (0.09)
Colony 0.18 0.21* 0.21*** 0.48*** -0.38* 0.02 0.02 0.09
(0.11) (0.10) (0.03) (0.12) (0.17) (0.11) (0.02) (0.11)
Bilateral hyperlinks (2009) 0.24*** 0.40*** 0.37*** 0.28*** 0.26*** 0.29*** 0.28*** 0.31***
(0.05) (0.05) (0.02) (0.02) (0.05) (0.04) (0.01) (0.02)
Exporter GDP (log) 0.54*** 0.35*** 0.07 0.47*** 0.56*** 0.54*** 0.51*** 0.52***
(0.06) (0.04) (0.12) (0.03) (0.08) (0.04) (0.05) (0.02)
Internet Exporter 0.01*** 0.01*** 0.01*** 0.02*** -0.01* 0.00 -0.00 0.00*
(0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00)
Importer Population (log) 0.44*** 0.34*** 2.28*** 0.42*** 0.48*** 0.45*** 0.70 0.41***
(0.06) (0.05) (0.53) (0.03) (0.08) (0.04) (0.46) (0.02)
Importer GDP percap (log) 0.78*** 0.66*** 0.64*** 0.78*** 0.46** 0.46*** 0.57*** 0.55***
(0.12) (0.11) (0.09) (0.05) (0.17) (0.10) (0.06) (0.03)
Internet Importer 0.01** 0.00 0.01** 0.01** 0.01* 0.01 0.00 0.00
(0.00) (0.01) (0.00) (0.00) (0.00) (0.01) (0.00) (0.00)
Importer Gini 0.05*** 0.03*** 0.01 0.02*** 0.07*** 0.03*** 0.06*** 0.04***
(0.01) (0.01) (0.02) (0.01) (0.02) (0.01) (0.01) (0.00)
N 20454 20454 20454 16746 20454 20454 20410 20454 20324 20454
R-sq 0.69 0.75 0.41 0.80 0.58 0.73 0.85 0.52 0.89 0.67
Exporter–Year FE X X
Importer–Year FE X X
Exporter–Year RE X X
Importer–Year RE X X
Country Pair FE X X
Country Pair RE X X
36
theoretical predictions only when including country-pair fixed eects, in which case the between-
variation vanishes.28
6 Potential Extensions and Concluding Remarks
This paper aims at understanding the dierences and similarities between determinants of aggregate
bilateral trade in manufactures and services and introduces virtual proximity as an essential observ-
able trade-cost-reducing factor for international trade in both sectors. We have articulated a model
where two characteristics dierentiate between manufacturing and services as distinct sectors: non-
homothetic tastes with a demand bias towards services and dierences in the degree of national prod-
uct dierentiation. These considerations imply that bilateral trade in either sector will be influenced,
besides respective trade costs, by the exporting country’s GDP and importing country’s population
and per capita GDP separately.
Although the gravity equations for manufactures and services are separately estimated, they help
us to understand and interpret the similarities and dierences in the magnitudes of the marginal eect
of an explanatory variable across two product groups in light of our theoretical predictions. Compared
to manufacturing, bilateral trade in services is expected to be less sensitive to changes in exporting-
country GDP and more sensitive to variations in the importing country’s per capita GDP. Moreover,
bilateral trade in both categories of products would be dependent on income inequality in the im-
porting country. These predictions are generally supported by the empirical evidence presented. Our
model reveals that trade cost elasticities are functions of the degree of national product dierentia-
tion, not the elasticity of substitution among domestic varieties. Another major finding is that virtual
proximity is an essential factor influencing trade costs of both manufacturing and services, and it
significantly reduces the role of physical distance and language dierences.
Some extensions that have the potential of oering further insights come to mind. First and
foremost, we wish to include data on intra-national trade, which will enable us to estimate border
eects and bilateral trade costs relative to domestic trade costs. We plan to use the International
Trade and Production Database for Estimation (ITPD-E) from Borchert et al. (2020). Second and as
noted earlier, there is considerable firm heterogeneity among service industries in their participation in
international markets (Breinlich and Criscuolo,2011). Recall a key implication of firm heterogeneity
toward the gravity relation, due to Chaney (2008), that is, the elasticity of bilateral trade with respect
to trade cost is governed by the spread of productivity across firms, not the elasticity of substitution
over varieties in consumption. We speculate that both the Armington elasticity and the spread of
productivity will determine the trade cost elasticity. Third, in the light of Hellmanzik and Schmitz
(2015) and Anderson et al. (2018), it will be useful and interesting to analyze bilateral trade flows of
dierent components of both manufactures and services — particularly, the role of trade costs, which,
in part, are impacted by internet use and virtual proximity. Fourth, it will be interesting to model other
attributes that distinguish goods and services. For instance, the proximity between providers and users
is a hallmark of many services. Recognition of this in the context of trade in services will bring into
play the role of FDI in services: Mode 3 of trade in services termed as ‘commercial presence.’ Lastly,
international trade in services conjures up its role, particularly that of business services, in the growth
of national economies. Exploring the link between service exports and growth or per capita income
will be promising.
28The country-pair fixed-eects are a typical solution when the researcher is not interested in the time-invariant variables
that are pair-specific, such as distance and colonial relationship in the past.
37
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Appendices
A Derivation of Demand functions for cr,cjr and Pr: Eqs. (6), (5)and (7)
Letting γand µrdenote the respective Lagrange multipliers, the first-order conditions of Middle tier 1 house-
hold optimization with respect to cr,cmr and csr are:
1+γX
j(m,s)
θjη
ηc
θj2η
η
rc
η1
η
jr =0 (A.1)
γη1
ηc
θmη
η
rc1
η
mr =µrPmr (A.2)
γη1
ηc
θsη
η
rc1
η
sr =µrPsr.(A.3)
Dividing (A.2) by (A.3),
cmr
csr
=c(θsθm)
r Pmr
Psr !η
.(A.4)
Non-homothetic tastes over manufacturing and services imply that this consumption ratio depends on the
overall sub-utility, cr. Given θs> θm, the higher the sub-utility, the higher is the services to manufacturing
consumption ratio, capturing demand-bias towards services. Multiplying (A.2) and (A.3) respectively by cmr
and csr, adding them and using the utility constraint, we obtain
er=γ
µr
·(η1)
η.(A.5)
Substituting this back into (A.2) and (A.3), eliminating γand µr, and defining the price of the manufactures-
services bundle as Prer/crgive the respective demand functions and expenditure shares:
cjr = Pjr
er!η
cθjη
r= Pjr
Pr!η
cθj
r(A.6)
Pjrcjr
er
= Pjr
er!1η
cθjη
r= Pjr
Pr!1η
cθj1
r.(A.7)
Expenditure shares add up to unity, i.e.,
X
j(m,s)
P1η
jr cθjη
r=e1η
r.(A.8)
which implicitly solves cr(eq. (6) in the text).
Plugging back (A.8) into eq. (A.6), we obtain a quasi-reduced-form solution expression of cjr ((5) in the
text). Next, substituting Pr=er/crinto (A.8) yields eq. (7) in the text.
B Results 1and 2
Eqs. (A.6) and (A.8) imply,
ˆcjr =ηˆer(ηθj)ˆcr(A.9)
ˆer=Pjλj(ηθj)
η1·ˆcr,where λj
P1η
jr cθjη
r
e1η
r
(0,1).(A.10)
i