Kyoto University,
Graduate School of Economics
Research Project Center Discussion Paper Series

Trade Patterns and International Technology Spillovers:
Theory and Evidence from Patent Citations

Naoto Jinji
Xingyuan Zhang
Shoji Haruna

Discussion Paper No. E-10-006

Research Project Center
Graduate School of Economics
Kyoto University
Yoshida-Hommachi, Sakyo-ku
Kyoto City, 606-8501, Japan

October 2010

Trade Patterns and International Technology Spillovers:
Theory and Evidence from Patent Citations∗
Naoto Jinji†

Xingyuan Zhang‡

Shoji Haruna§This version: March 28, 2011

Abstract
In this paper, we develop a two-country model of monopolistic competition with quality differentiation by extending the model of Melitz and Ottaviano (2008) and examine the relationshipbetween the bilateral trade structure and international technology spillovers. We show that bilateral trade patterns and the extent of technology spillovers will change, depending on the technology
gap between two countries. We then test predictions of the model by using bilateral trade data
among 44 countries and patent citation data at the U.S., European, and Japanese Patent Oﬃces.
We use patent citations as a proxy for spillovers of technological knowledge. Trade patterns are
categorized into three types: one-way trade (OWT), horizontal intra-industry trade (HIIT), andvertical intra-industry trade (VIIT). Each of OWT and VIIT is further divided into two subcategories, based on the direction of trade. We ﬁnd that intra-industry trade plays a signiﬁcantrole in technology spillovers. In particular, HIIT is associated with larger technology spillovers
than VIIT, which conﬁrms the predictions of the model.
Keywords: technology spillovers; patent citations; intra-industry trade; ﬁrm heterogeneity.
JEL classification: F12; O31; O33.

∗ We would like to thank Lee Branstetter, Shuichiro Nishioka, Nobuhito Suga and seminar and conference partici-

pants at Kyoto University, Hokkaido University, Otaru University of Commerce, University of Pittsburgh, Yokohama
National University, APTS 2010, Fall 2010 Meeting of Midwest International Economics, Korea International Economic
Association meeting 2010 for their helpful comments and suggestions on earlier versions of the paper. We alone areresponsible for any remaining errors. We acknowledge ﬁnancial support from the Japan Society for the Promotion of
Science under the Grant-in-Aid for Scientiﬁc Research (B) No. 19330052 and the Murata Science Foundation.
† Corresponding author. Faculty of Economics, Kyoto University, Yoshida-honmachi, Sakyo-ku, Kyoto 606-8501,
Japan. Phone & fax: +81-75-753-3511. E-mail: jinji #at-mark# econ.kyoto-u.ac.jp.
‡ Faculty of Economics, Okayama University, 3-1-1 Tsushima-Naka, Kita-Ku, Okayama 700-8530, Japan.
§ Faculty of Economics, Okayama University, 3-1-1 Tsushima-Naka, Kita-Ku, Okayama 700-8530, Japan.

11Introduction

The issue of international technology diﬀusion has been attracted great attention in economics.1 Thisis because international technology diﬀusion is an important factor to determine the speed at which
the world’s technology frontier expands. It also contributes to income convergence across countries.
For example, Eaton and Kortum (1996) estimate innovation and technology diﬀusion among 19
OECD countries to test predictions from a quality ladders model of endogenous growth with patenting.
They ﬁnd that each OECD country other than the United States (U.S.) obtains more than half of
its productivity growth from technological knowledge originated abroad. They also ﬁnd that morethan half of the growth in every OECD country is derived from innovation in the U.S., Japan, andGermany. Eaton and Kortum (1999) ﬁt a similar model to research employment, productivity, andinternational patenting among the ﬁve leading research economies, i.e., the U.S., Japan, Germany, theUnited Kingdom (U.K.), and France. They ﬁnd that research performed abroad is about two-thirds aspotent as domestic research. In particular, technological knowledge from Japan and Germany diﬀuses
most rapidly, while France and Germany are the quickest to exploit knowledge. They also show that
the U.S. and Japan together contribute to over 65 percent of the growth in each of the ﬁve countries.
Previous studies have identiﬁed international trade as a major channel of international technology
spillovers.2 Coe and Helpman (1995) examine R&D spillovers among OECD countries and ﬁnd large
spillover eﬀects from foreign R&D capital stocks to domestic productivity that is measured by totalfactor productivity (TFP). They also show that countries exhibit higher productivity levels by importing goods from countries with high levels of technological knowledge, which supports the existenceof trade-related international R&D spillovers. However, Keller (1998) provides a ﬁnding that casts
doubt on Coe and Helpman’s result by employing a Monte-Carlo-based robustness test. He ﬁnds that
estimated international R&D spillovers among randomly matched trade partners turn out to be large(and even larger than those among actual trade partners). Xu and Wang (1999) estimate that about
half of the return on R&D investment in 7 OECD countries spilled over to other OECD countries andthat trade in capital goods is a signiﬁcant channel of R&D spillovers. More recent study by Acharya
and Keller (2009) ﬁnd that the diﬀusion of technological knowledge is strongly varying across countrypairs. They show that imports are crucial for technology diﬀusion from Germany, France, and the
U.K., while non-trade channels are relatively more important for the U.S., Japan, and Canada.
1 See Keller (2004) for a survey of the literature.
2 Trade works as a channel of technology spillover because, for example, ﬁrms can obtain information on advanced

technology by reverse engineering of imported goods. International trade also provides channels of cross-border communication that facilitates learning of production and organizational methods and market conditions (Grossman andHelpman, 1991). Another major channel is foreign direct investment (FDI). Technological spillovers through FDI are
empirically conﬁrmed by a number of studies (Branstetter, 2006; Haskel, Pereira, and Slaughter, 2007; Javorcik, 2004;
Keller and Yeaple, 2009), while some studies do not ﬁnd signiﬁcant spillovers (Aitken and Harrison, 1999; Haddad andHarrison, 1993).

2

Although a number of studies have investigated technological knowledge spillovers through trade,none of the existing studies have paid attention to the relationship between bilateral trade patterns andtechnology spillovers. However, it is expected that technology spillovers through imports will diﬀer,
depending on whether a country exports products with similar quality or with diﬀerent quality in thesame industry as imports or the country does not export products in the same industry. Therefore, inthis paper we examine the relationship between the bilateral trade structure and technology spillovers
from both theoretical and empirical points of view. Here, by the term “technology spillovers” we refer
to “the process by which one inventor learns from the research outcomes of others’ research projects
and is able to enhance her own research productivity with this knowledge without fully compensating
the other inventors for the value of this learning” (Branstetter, 2006: 327–328). In this sense, we
distinguish technology spillovers from imitation or technology adoption.
Empirical studies on intra-industry trade categorize bilateral trade ﬂows into one way trade(OWT), or inter-industry trade, and two-way trade, or intra-industry trade (IIT). IIT is further
decomposed into horizontal intra-industry trade (HIIT) and vertical intra-industry trade (VIIT) (e.g.,
Fontagné and Freudenberg, 1997; Greenaway, Hine, and Milner, 1995; Fukao, Ishido, and Ito, 2003).
The diﬀerence between HIIT and VIIT reﬂects the diﬀerences in quality of products in the same
category traded between two countries. In HIIT, horizontally diﬀerentiated products (i.e., productswith similar quality but diﬀerent varieties) are traded, whereas vertically diﬀerentiated products (i.e.,
products with diﬀerent qualities) are traded in VIIT.3 On data HIIT and VIIT can be distinguishedby using unit values (i.e., total value of import or export in one product category divided by quantityof import or export in that product category) under the assumption that unit values are increasing
in product quality.
The theoretical literature on intra-industry trade has been separated into two branches for a long
period. As is well known, trade models with monopolistic competition could explain HIIT (e.g., Krugman, 1979, 1980; Helpman, 1981; Eaton and Kierzkowski, 1984). However, in these models, productvarieties are symmetric and not diﬀerentiated in quality. Trade models with vertical diﬀerentiation, on
the other hand, could explain VIIT but could not explain HIIT (e.g., Falvey, 1981; Shaked and Sutton,
1984; Falvey and Kierzkowski, 1987; Flam and Helpman, 1987; Lambertini, 1997; Motta, Thisse, andCabrales, 1997; Herguera and Lutz, 1998). Given the fact that HIIT and VIIT arise in continuous
phenomena, this divergence in the theory would not be acceptable. More recently, a number of studies
have attempted to introduce quality diﬀerentiation into the monopolistically competitive trade model.
Some studies use a quality-augmented type of Dixit-Stiglitz demand speciﬁcation in the framework
3 Note that in the literature the terms of HIIT and VIIT are sometimes used in diﬀerent meanings. In an alternative

deﬁnition, HIIT means trade of ﬁnal goods in the same industry across countries, while VIIT involves trade of intermediate goods with ﬁnal goods in the same industry (Yomogida, 2004). Since we do not consider the distinction between
intermediate goods and ﬁnal goods in this paper, this alternative deﬁnition of HIIT and VIIT is not applicable.

3

of Melitz (2003)4 with the assumption that higher quality is associated with higher marginal cost
(Baldwin and Harrigan, 2007; Gervais, 2008; Helble and Okubo, 2008; Johnson, 2010; Kugler andVerhoogen, 2010; Mandel, 2010).5 On the other hand, Antoniades (2008) introduces quality diﬀerentiation into the quasi-linear utility with a quadratic subutility speciﬁcation in the framework of
Melitz and Ottaviano (2008) and considers endogenous quality upgrading by heterogeneous ﬁrms. He
shows that ﬁrms with higher productivity choose higher qualities and charge higher prices. However,his model faces some limitations when extended to the case of two-country trade. In this paper, we
also introduce quality diﬀerentiation into the framework of Melitz and Ottaviano (2008). We employ
a diﬀerent approach from Antoniades (2008). We assume that ﬁrms randomly draw their productquality so that ﬁrms with identical productivity are heterogeneous in product quality. This reﬂects
the stochastic nature of product R&D. This formulation of quality diﬀerentiation turns out to be
tractable. Then, we show that our model can explain OWT, HIIT, and VIIT in one uniﬁed framework. Using this framework, we examine how international technology spillovers are associated withbilateral trade structure.
For empirical analysis of international technology spillovers, we use data on patent citations as aproxy for spillovers of technological knowledge. There is a relatively small but growing literature on
empirical analysis of knowledge ﬂow based on patent citations (e.g., Jaﬀe, Trajtenberg, and Henderson,
1993; Jaﬀe and Trajtenberg, 1999; Hu and Jaﬀe, 2003; MacGarvie, 2006; Mancusi, 2008; Haruna, Jinji,
and Zhang, 2010).6 In the literature, patent citation data are used as a direct measure of technology
spillovers (Hall, Jaﬀe, and Trajtenberg, 2001). Hu and Jaﬀe (2003) use data on patents granted in
the U.S. and examine patent citations by inventors residing in Korea, Japan, Taiwan, and the U.S.
to infer the pattern of technological knowledge ﬂows from the U.S. and Japan to Korea and Taiwan.
They ﬁnd that Korean patents are much more likely to cite Japanese patents than U.S. patents, while
Taiwanese patents cite both Japanese and U.S. patents evenly. Mancusi (2008) estimates technologicalknowledge diﬀusion within and across sectors and countries by using European patents and citationsfor 14 OECD countries. She ﬁnds that international knowledge diﬀusion is eﬀective in increasing
innovative productivity in technologically laggard countries, while technological leaders (the U.S.,
Japan, and Germany) are a source rather than a destination of knowledge ﬂows. Using French ﬁrms’
patent citations and ﬁrm-level trade data, MacGarvie (2006) ﬁnds that the patents of importing ﬁrms
4 Originally, Melitz (2003) mentions that diﬀerences in productivity may be interpreted as diﬀerences in productquality at equal cost.
5 Sugita (2010) also uses a quality-augmented type of Dixit-Stiglitz demand and considers matching between intermediate good producers and ﬁnal good producers. He shows that improvements in matching due to trade liberalization
result in improvements in product quality.
6 However, Jaﬀe, Trajtenberg, and Henderson (1993) admit that patent citation is a coarse and noisy measureof knowledge ﬂow, because not all inventions are patented and not all knowledge ﬂows can be captured by patentcitations. Based on a survey of inventors, Jaﬀe, Trajtenberg, and Fogarty (2000) suggest the validity of patent citations
as indicators of technology spillovers, despite the presence of noise.

4are signiﬁcantly more likely to be inﬂuenced by technology in the exporting country than are thepatents of ﬁrms that do not import. In contrast, she ﬁnds no signiﬁcant evidence of exporting ﬁrms’
citing more patents from their destination countries. Moreover, in our previous work (Haruna, Jinji,
and Zhang, 2010), we investigate whether the trade structure plays an important role as a channelof technological knowledge diﬀusion between Asian economies (Korea, Taiwan, China, and India)
and G7 countries including the U.S. and Japan. In that paper, we use a modiﬁed version of theBalassa’s index of Revealed Comparative Advantage (RCA), which represents the share of country iin sector j relative to the country’s export (or import) share for all sectors. Then, we ﬁnd that trade
specialization, especially import specialization, has a direct eﬀect on knowledge diﬀusion.
In this paper, we take our study one step further and investigate the relationship between bilateral
trade patterns and international knowledge ﬂow in more detail. In order to accomplish this task,
we develop a two-country model of monopolistic competition with quality diﬀerentiation, in whichinter- and (horizontal and vertical) intra-industry trade patterns endogenously arise, depending on
the conditions of trading countries. Our model is an extension of the model developed by Melitz andOttaviano (2008). In our model, ﬁrms are heterogeneous in product quality rather than in productivity.
Then, after deriving hypotheses from the model, we test them by using data on bilateral trade among
44 countries and patent citations at the U.S., European, and Japanese Patent Oﬃces.
The main results in this paper are as follows. Our model predicts that the bilateral trade pattern
is HIIT when the two countries have access to a similar level of technology, while it is VIIT when
there is technological diﬀerence between them. Moreover, if the technological diﬀerence is suﬃciently
large, the bilateral trade pattern becomes OWT. Our model also predicts that technology spillovers
are highest when the bilateral trade pattern is HIIT, followed by VIIT and OWT. Our estimation
results basically conﬁrm those predictions of the model. We ﬁnd that an increase in the share of intraindustry trade in the bilateral trade has a positive eﬀect on the number of patent citations between
the two countries. HIIT has a larger eﬀect than VIIT. On the other hand, the eﬀects of OWT on thenumber of citations are much weaker than those of IIT.
The remainder of the paper is organized in the following way. Section 2 sets up a closed-economy
model of monopolistic competition with quality diﬀerentiation. Section 3 extends the model to thecase of two-country trade and derives testable implications from the theoretical model. Section 4
conducts an empirical analysis. Section 5 concludes this paper.

5

2

The Basic ModelIn this section, we describe the basic structure of the model in a closed economy. Then, we extend
the basic model to the case of two-country trade in the next section.
Consider an economy with two sectors: a homogenous agricultural sector and a diﬀerentiatedmanufacturing sector.7

2.1

DemandWe introduce quality diﬀerentiation into the quasi-linear (instantaneous) utility with a quadratic
subutility, which is developed by Ottaviano, Tabuchi, and Thisse (2002) and Melitz and Ottaviano(2008).8 There are L consumers in the economy. Preferences are identical across consumers anddeﬁned over a continuum of diﬀerentiated varieties indexed by i ∈ Ω and a homogenous numeraire
good. The representative consumer maximizes an additively separable intertemporal utility functionof the form,U= ∞u(t)e−ρt dt,(1)0

where ρ is the common subjective discount rate and u(t) is the instantaneous utility given by

2


1
1
c
c
c 2
c
u(t) = q0t +αit qit di − γ(q ) di − η
qit di ,2 i∈Ωt it
2
i∈Ωt
i∈Ωt

(2)

c
c
and qitare the individual consumption levels of the numeraire and variety i at time t andwhere q0t

αit > 0 measures the product quality of variety i at time t.9 The parameter γ > 0 measures thedegree of horizontal diﬀerentiation, or the substitutability between varieties and the parameter η > 0
captures the degree of substitution between the diﬀerentiated varieties and the numeraire.
We assume that consumers have positive demands for the numeraire. The inverse demand forvariety i at time t is then given bycpit = αit − γqit
− ηQct ,c> 0, where Qct =as long as qit


i∈Ωt

(3)

qit di is the total consumption level over all varieties. Let Ω∗t ⊂ Ωtbe the subset of varieties that are actually consumed. Then, from Eq. (3), the market demand forvariety i ∈ Ω∗t can be expressed asc=qit ≡ Lqit
7 In this

L
ηLNt
L
ηLNt
αit −
ᾱt − pit +p̄t ,γγ(ηNt + γ)γγ(ηNt + γ)

(4)section, we develop a simple two-sector model. The analysis can be extended to a model with many

diﬀerentiated manufacturing sectors to ﬁt the empirical study in the next section. However, such an extension will notchange qualitatively the main results in this section.
8 The quadratic utility is also widely employed for the analysis of oligopoly. See, for example, Dixit (1979), Singh andVives (1984), and Vives (1985). Quality-augmented versions of the quadratic utility function are developed by recent
studies of Häckner (2000) and Symeonidis (2003a, 2003b).
9 Häckner (2000) provides the same treatment of product quality in a discrete version of quadratic utility.

6
where Nt is the measure of consumed varieties in Ω∗t , and ᾱt = (1/Nt ) i∈Ω∗ αit di and p̄t =t

(1/Nt ) i∈Ω∗ pit di are their average quality and price, respectively.
t

2.2

SupplyIn both sectors, labour, which is inelastically supplied in the competitive labour market, is the only
production factor. One unit of labour is required to produce one unit of the homogenous agricultural(numeraire) good. Thus, the wage rate w is equal to one.
In the diﬀerentiated manufacturing sector, each ﬁrm produces a diﬀerent variety. Every productvariety has generations (or versions), depending on the date of development. For simplicity, we assume
that each generation of a product variety loses its consumption value after one period. Thus, eachﬁrm must engage in product R&D to develop a new generation of the product variety in every period.
While the cost of product R&D, f (measured in units of labour), is identical for all manufacturingﬁrms, the outcome of product R&D, αit , is stochastic.10 Since R&D actually involves uncertainty in
its outcome, it would be quite natural to model R&D as a stochastic process. To simplify the analysis,
we model product R&D in the following way. Let αMt be the maximum product quality that could beobtained by the current technology in the economy, or the frontier of the current technology, at timet. Firm i randomly draws the degree of successfulness of R&D, ait , from a time-invariant common(and known) probability density function g(a) with support on [a, 1], where 0 < a. We assume thatg  (a) < 0 so that the probability of higher degree of success is lower. Then, ﬁrm i’s product quality
is given by αit = ait αMt . This implies that the product R&D can be equivalently expressed as arandom draw from a cumulative distribution function Gt (α) with support on [αt , αMt ] at time t,where αt = aαMt . As is explained below, Gt (α) shifts as time passes. We normalize that αM0 = 1.
That is, let the maximum quality of the ﬁrst generation of the product be one.
Each ﬁrm must decide whether to spend the cost of R&D before knowing its outcome. If a ﬁrm
does not conduct R&D at time t, it does not enter the market in that period.
The market competition in the manufacturing sector takes a form of three-stage game. In stage
one, all potential entrants decide whether to engage in product R&D (by paying the cost of f ). In
stage two, those ﬁrms conducted R&D in the previous stage know the outcome of R&D and thendecide whether to stay in the market or exit. In stage three, the ﬁrms that stay in the market choose
prices to maximize their own proﬁts.11
A variety of the manufacturing good is produced under constant-returns-to-scale at unit labour
requirement c, which is identical across all ﬁrms and independent of the product quality αit .12 Since
10 As is evident, the cost of product R&D f serves as a ﬁxed entry cost. Since ﬁrms pay a ﬁxed entry cost and draw

their productivity parameter in Melitz (2003) and Melitz and Ottaviano (2008), ﬁrms engage in stochastic process R&D
in their cases. In our model, on the other hand, ﬁrms engage in stochastic product R&D.
11 In the two-country model in Section 3, each ﬁrm chooses price in each market independently.
12 We assume identical productivity across all ﬁrms to simplify the analysis. Our model can be extended to incorporate7w = 1 as long as the numeraire good is produced in the economy, c is the (constant) marginal cost.
Since the R&D cost is sunk, ﬁrms that can cover their marginal costs survive and supply manufacturing
goods to the market. All other ﬁrms exit. Surviving ﬁrms maximize their proﬁts in each period bytaking the average quality level ᾱ, the average price level p̄, and the number of ﬁrms N in that
period as given.13 Given the market demand for variety i (Eq. (4)), it is easily seen that the priceelasticity of demand, εi ≡ −(∂qi /∂pi )(pi /qi ), does not tend to inﬁnity as N goes to inﬁnity. Thus,
the manufacturing sector is characterized by monopolistic competition.14 Let pmax (α) be the priceat which demand for a variety with quality α is driven to 0. Eq. (4) yields thatpmax (α) ≡ α −ηN(ᾱ − p̄).
ηN + γ(5)Then, any i ∈ Ω∗ satisﬁes pi ≤ pmax (αi ). Given Eq. (4), ﬁrm i’s gross proﬁt is given by πi = pi qi −cqi .
From the ﬁrst-order condition (FOC) for proﬁt maximization, we obtainq(α) =

L[p(α) − c],γ(6)where q(α) and p(α) are proﬁt-maximizing output and price for the product with quality α. Let αD
be the quality level for the ﬁrm that earns zero proﬁt due to p(αD ) = pmax (αD ) = c. Using Eq. (5),it yields thatαD =ηN(ᾱ − p̄) + c.
ηN + γ(7)Then, substitute Eq. (4) into Eq. (6) and use Eq. (7) to obtainp(α) =

α − αD+ c.
2(8)This implies that ﬁrms with positive demands (i.e., αi > αD ) charge prices above the marginal cost
and that the prices are increasing in product quality. Note that the average price p̄ is given byp̄ =ᾱ − αD
+ c.
2

(9)

Then, (7) and (9) yield the mass of surviving ﬁrms
N=

2γ(αD − c).
η(ᾱ − αD )

(10)

α
Note that the average product quality of surviving ﬁrms ᾱ is expressed as ᾱ = [ αDM αdGt (α)]/[1 −Gt (αD )] and that the mass of entrants is given by NE = N/[1 − Gt (αD )].
Although we do not use a speciﬁc parametrization for the distribution Gt (α), we assume thefollowing condition:
heterogeneous productivity among ﬁrms, like Melitz (2003) and Melitz and Ottaviano (2008).
13 Hereafter, we omit the time index unless necessary.
14 In contrast to the standard model of monopolistic competition with constant elasticity of substitution (CES) demand
developed by Dixit and Stiglitz (1977), the price elasticity of demand is not uniquely determined by the degree of
product diﬀerentiation in this quasi-linear utility with quadratic subutility speciﬁcation. Behrens and Murata (2007)
and Zhelobodko, Kokovin, and Thisse (2010) also investigate implications of relaxing the CES assumption in themonopolistic competition.

8

Assumption 1 0 < dᾱ/dαD < 1.
This condition means that an increase in the cut-oﬀ quality increases the average quality of products
supplied in the market but the extent of the increase in the average quality is smaller than theincrease in αD . This condition restricts the shape of the distribution Gt (α). We need this assumption
to obtain an unambiguous eﬀect of a change in the cut-oﬀ product quality on the size of productvarieties, which will be shown below. Note that in Melitz and Ottaviano (2008) a similar property
holds for the relationship between the cut-oﬀ productivity and the average productivity by assuminga Pareto distribution for the distribution of cost draws.
Following Melitz and Ottaviano (2008), let μ(α) = p(α) − c, r(α) = p(α)q(α), and π(α) = r(α) −q(α)c be the absolute mark-up, revenue, and proﬁts of a ﬁrm that produces a product with quality α.
Then, these performance measures can be written asα − αD,(11)2
L(α − αD )q(α) =
,
(12)
2γ

L 
(α − αD )2 + 2c(α − αD ) ,(13)r(α) =
4γL(α − αD )2 .
(14)π(α) =
4γ
αSince the expected proﬁt prior to entry at time t is given by αDM π(α)dGt (α) − f , the equilibriumμ(α)=

free entry condition is given by
 αM

L αM
π(α)dGt (α) =(α − αD )2 dGt (α) = f.
4γ
αD
αD

(15)

The ﬁrst equality is obtained by using Eq. (14). From Eqs. (10) and (15), we obtain the following
lemma:
Lemma 1 (i) Given Gt (α), αD and ᾱ are both decreasing in f (R&D cost) and γ (the degree ofhorizontal diﬀerentiation) and increasing in L (the market size).
(ii) Under Assumption 1, for a given Gt (α), a higher αD leads to a higher N (more varieties) and ahigher NE (more entrants).
Proof. The ﬁrst part is directly obtained from Eq. (15). For the second part, diﬀerentiate Eq. (10)with respect to αD to yield
2γ(αD − c) d(ᾱ − αD )
2γ
dN
−
=
> 0.
dαD
η(ᾱ − αD ) η(ᾱ − αD )2dαD
Assumption 1 ensures that the right-hand-side is positive. Then, since NE = N/[1 − Gt (αD )], a higher
αD and a higher N lead to a higher NE .

9

This lemma shows that the eﬀects of parameters on the cut-oﬀ quality and the average quality
in our model are similar to the eﬀects of parameters on the cut-oﬀ productivity and the average
productivity in Melitz and Ottaviano (2008).

2.3

Technology spillovers

The individual ﬁrm’s technological knowledge spillovers to other ﬁrms in the manufacturing sector.
In the spirit of Romer (1990) and Grossman and Helpman (1990, 1991), we assume that technologicalknowledge has a public-good nature. That is, individual ﬁrm’s R&D output contributes to “generalknowledge” in the economy and all ﬁrms equally have access to the general knowledge without any
costs. We capture technology spillovers by the expansion of the technology frontier, αMt . Morespeciﬁcally, we assume that αMt changes in the following way:α̇Mt = λKt αMt ,(16)

where λ > 0 and Kt is the knowledge ﬂow at time t. Assuming that knowledge ﬂow is proportional
to the number of varieties actually produced, we have
K t = Nt(17)

by choosing units for Kt . Note that Nt is the mass of surviving ﬁrms that produces quality levelα ≥ αDt .
Since technology spillovers shift the distribution G(α) to the right without changing its shape, it
has the following properties:
Lemma 2 An upward shift of G(α) leaves μ(α), q(α), r(α), and π(α) unchanged and increases N
and NE .
Proof. Let G0 (α0 ) and G1 (α1 ) be the distributions before and after the change, respectively. Let
α0M and α1M be the upper bound of G0 (α0 ) and G1 (α1 ), respectively, and set α1M = α0M + k withk > 0. Then, since α1 = α0 + k holds for any α0 and α1 that take the same relative position in each
distribution, Eq. (15) for G0 (α0 ) can be transformed to that for G1 (α1 ). Thus, Eqs. (11) to (14) areunchanged. However, since ᾱ − αD is unchanged and α1D = α0D + k, Eq. (10) yields a higher N andhence a higher NE .
This lemma implies that as long as all ﬁrms equally have access to the general knowledge, technology improvement in the sense of an upward shift of G(α) increases the absolute levels of productquality for all varieties but keeps their relative positions in the industry unchanged. However, Lemma
2 also implies that there are more varieties in the economy with advanced technology than in theeconomy with lagged technology.
10

3

Trade between Two Countries

3.1

A two-country setting

Now, we consider two countries, Home and Foreign with LH and LF consumers in each country.
Consumers in both countries share the same preferences given by Eqs. (1) and (2). We assume thatthe markets in the two countries are segmented, while ﬁrms can produce in one location and supply
their products to the market in the other country by incurring a per-unit trade cost.
Manufacturing ﬁrms in the two countries have the same marginal cost c but draw product qualitiesFHH
αH and αF from their domestic distributions GH
t (α) and Gt (α) with support on [αt , αMt ] andF[αFt , αMt ], respectively.

Following Melitz and Ottaviano (2008), we assume that ﬁrms in country h must incur the unit
cost of τ l c with τ l > 1 to deliver one unit of their products to the market in the country l. We also
assume that the homogenous numeraire good is always produced in each country after opening up to
trade, so that the wage rate is equal to one in both countries.
The price threshold for positive demand in market l is given byplmax (α) ≡ α −ηN l(ᾱl − p̄l ),ηN l + γ(18)where N l is the mass of ﬁrms selling in country l, which includes both domestic ﬁrms in country land exporters from country h, and ᾱl and p̄l are respectively average quality and price across bothlllocal and exporting ﬁrms in country l. Let ND
and NX
denote the mass of ﬁrms producing in countryl that supply products to the domestic market and the other country’s market, respectively. Then,lh
N l = ND
+ NX
holds (l, h = H, F, l = h).

Firms maximize their proﬁts earned from local and export sales independently (due to the assumptions of segmented market and constant-returns-to-scale technology). Let αlD and αlX be the quality
levels for the ﬁrm producing in country l that earns zero proﬁts from local sales and export sales,
respectively. From p(αlD ) = plmax (αlD ) = c and p(αlX ) = phmax (αlD ) = τ h c, we obtain
αlD

=

αlX

=

ηN l
(ᾱl − p̄l ) + c,
ηN l + γηN h(ᾱh − p̄h ) + τ h c.
ηN h + γ

(19)
(20)

Thus, it holds thatαhX = αlD + (τ l − 1)c.

(21)

l
l
l
l
(α) = [plD (α) − c]qD(α) and πX(α) = [plX (α) − τ h c]qX(α) be the maximized value of proﬁts
Let πDfor a ﬁrm with quality α producing in country l from domestic sales and export sales, respectively,
where plD (α) and plX (α) are proﬁt-maximizing prices for domestic and export sales, respectively,ll
and qD(α) and qX(α) are corresponding quantities. From the ﬁrst-order conditions, it holds that

11

l
l
qD
(α) = (Ll /γ)[plD (α) − c] and qX(α) = (Lh /γ)[plX (α) − τ h c]. Then, use the same procedure to derive(9) and (12) in the closed economy to yield the optimal prices and outputs for domestic and export
sales, respectively:plD (α)=plX (α)=α − αlD
Ll (α − αlD )l(α) =+ c, qD,22γ
α − αlX
Lh (α − αlX )l+ τ h c, qX
.
(α) =
2
2γ

(22)
(23)

Then, the maximized proﬁts from domestic sales and export sales are respectively given by
l
πD
(α)

=

l
(α)
πX

=

Ll
(α − αlD )2 ,4γ
Lh(α − αlX )2 .
4γ

(24)
(25)

The equilibrium free entry condition in country l at time t is given by αlM tαlDtlπD(α)dGlt (α) + αlM tαlXtlπX(α)dGlt (α) = f.

(26)

Substitute (21), (24), and (25) into this to yield two equilibrium free entry conditions:
LH
LF

 αH
Mt
αH
Dt

 αFM t
αF
Dt


2
F
dGH
α − αHDtt (α) + L2Hα − αFdGF
Dtt (α) + L

 αH
Mt
αF
+(τ F −1)cDt αFM t2FHα − αFDt − (τ − 1)c dGt (α) = 4γf,(27)αH+(τ H −1)cDtHα − αH− 1)c
Dt − (τ2dGFt (α) = 4γf,(28)which jointly determine the cut-oﬀ qualities for domestic sales in the Home and Foreign at time t,FαH
Dt and αDt . We then assume the following: αlM
Assumption 2

αl

l
πD
(α)dGl (α) +

 αlM
αl

l
πX
(α)dGl (α) > f .

Under Assumption 2, there are always some ﬁrms that exit the market in country l even if no ﬁrm
enters the market in country h.
Since the mass of ﬁrms selling in country l at time t is still determined by (10), Ntl is given byNtl =2γ(αlDt − c),η(ᾱlt − αlDt )where ᾱlt is the average quality of products sold in country l at time t, which is given by αlM tᾱlt =

α dGlt (α) + αhM tα dGht (α)αlDt +(τ l −1)c.
2 − Glt (αlDt ) − Ght (αlDt + (τ l − 1)c)αlDt

Similar to Assumption 1 in the case of the closed economy, we assume
Assumption 3 0 < dᾱl /dαlD < 1.

12

(29)

l
Let NEt
be the mass of entrants producing in country l at time t, which is determined by
H
H
F
F
F
H
[1 − GHt (αDt )]NEt + [1 − Gt (αXt )]NEt = Nt ,

(30)

F
F
H
H
H
F
[1 − GF
t (αDt )]NEt + [1 − Gt (αXt )]NEt = Nt ,

(31)

l
l
l
l
where [1 − Glt (αlDt )]NEt= NDt
and [1 − Glt (αlXt )]NEt= NXt. The equilibrium free entry conditionsl(27) and (28) will hold so long as there is a positive mass of entrants NEt> 0 in country l at time t.
lOtherwise, NEt= 0 and country l specializes in the numeraire good.

In this two-country setting, knowledge spills over both within a country and across countries. As
was the case in the closed economy (Eq. (16)), knowledge ﬂow expands the technology frontier ofcountry l in the following way:α̇lMt = λKtl αlMt ,l = H, F.

(32)

We assume that knowledge spillover is perfect within a country but imperfect across countries.
Instead of Eq. (17), knowledge ﬂow in country l is given bylh+ φl (αlMt , αhMt )NXt,
Ktl = NDt

where
φl (αlMt , αhMt )⎧⎪⎨ = 1,

l = H, F, h = l,

if αlMt = αhMt ,⎪⎩ ∈ (0, 1),

(33)

(34)

otherwise,

which controls the degree of international knowledge spillovers, depending on the technology gap
between two countries. We assume ∂φl /∂αlM > 0 for αlM < αhM .
In Eq. (33), our primary interest is in technology spillovers from country h to country l at time t,
Slh , which are measured byhSlht = φl (αlMt , αhMt )NXt,

l = H, F, h = l.

(35)

As is evident, we consider international technology spillovers only through imports.15 We assume
that international technology spillover is proportional to the number of varieties actually imported.
However, the degree of international technology spillovers is reduced unless the two countries share the15 Thus,

we ignore the “learning-by-exporting” eﬀect.

Some empirical studies ﬁnd the existence of learning-by-exporting (Aw et al., 2007; De Loecker, 2007; Salomon and Shaver, 2005), while Bernard and Jensen (1999) and
Lileeva and Treﬂer (2007) ﬁnd only limited evidence and Clerides, Lach, and Tybout (1998) and Damijan and Kostevc(2006) fail to ﬁnd conclusive evidence of such an eﬀect. See Greenaway and Kneller (2007) for a survey of the literature.
The majority of the studies in this literature consider productivity improvements by exporting as learning-by-exporting,which is beyond the scope of technology spillovers in our deﬁnition. The only exception is Salomon and Shaver (2005),
who ﬁnd that exporters increase their product innovations and patent applications subsequent to exporting. However,evidence from patent citations data is much less supportive. MacGarvie (2006) ﬁnds no signiﬁcant evidence of exportingﬁrms’ citing more patents from their destination countries. Haruna, Jinji, and Zhang (2010) ﬁnd that the eﬀect of export
specialization on knowledge diﬀusion is relatively weak.

13

same technology level. When country l has a higher technology than country h, knowledge spilloverfrom h to l is reduced because a country with advanced technology (country l) beneﬁts less fromknowledge of the technological lagger. When country l has a lower technology than country h, on theother hand, knowledge spillover from h to l may be again reduced because a country with inferior
technology (country l) only has lower absorptive capacity. The relative size of φl and φh underαlM = αhM is generally ambiguous, unless the functional form of φl (·) is speciﬁed.

3.2

Trade patterns and technology spillovers

We now investigate the relationship between trade patterns and international technology spillovers
and derive testable hypotheses.
Consider ﬁrst the case in which the two countries share the same technology at a given time t:
F
H= LF
that is, αH
Mt = αMt . If the size of the market and the trade barrier are symmetric (i.e., Land τ H = τ F ), then the countries have the same average quality and the same average price of export
goods. Thus, the trade pattern between the two countries is characterized by HIIT. In this case,international technology spillovers occur in both directions by the same degree because φH = φL = 1
HF
and NXt= NXt.

We then examine how trade patterns and technology spillovers between the two countries willchange if there is a technology gap between the home and foreign countries. Without loss of generality,
we assume that the home country is technologically superior to the foreign country at a given time.
We continue to assume that the market size is the same in the two countries (i.e., LH = LF ). We
compare the (symmetric) case in which GH (α) and GF (α) are identical with the (asymmetric) case inwhich GH (α) remains the same but GF (α) is distributed over the interval with some smaller values.
Comparing the overall distribution of product qualities (of domestic products plus imported products)
in each market in these two cases, the distribution in the asymmetric case ﬁrst-order stochasticallydominates that in the symmetric case in either market. This implies that competition in each market
Fis less intensive in the asymmetric case than in the symmetric case. Consequently, αH
D and αD areboth lower in the asymmetric case and hence from Eq. (29) N H and N F are both smaller in theasymmetric case under Assumption 3, which also implies that the mass of entrants in each countryF(i.e., NEH and NEF ) is also smaller in the asymmetric case. The lower values of αH
D and αD imply thatHαF
X and αX are also lower in the asymmetric case. As a result, the mass of varieties exported fromH
F
each country (i.e., NX
and NX) is smaller in the asymmetric case.

In order to investigate the structure of trade patterns, we need to know the average quality andprice of goods exported from each country. The average quality and price of goods exported from14

country l at time t, ᾱlXt and p̄lXt , are respectively given by αlM t
ᾱlXt

=

p̄lXt

=

αlXt

α dGlt (α)

1 − Glt (αlXt )ᾱlXt − αlXt
+ τ h c.
2

(36)
(37)

Then, in the asymmetric case, because of the transport cost, the overall distribution of product qualities in the market of the (technologically inferior) foreign country ﬁrst-order stochastically dominatesthat in the market of the (technologically advanced) home country.16 It implies that competition isF
more intensive in the home market than in the foreign market, and hence αH
D is higher than αD andH
HF
αF
X is higher than αX . However, αM > αM holds and this diﬀerence is larger than the diﬀerence inHαF
X and αX unless the tranport cost is highly asymmetric. Consequently, with regard to the averageFHFquality and price of exports, from Eqs. (36) and (37) it yields that ᾱH
X > ᾱX and p̄Xt > p̄Xt . That is,

the home country exports varieties with higher quality on average at higher price on average. Since
the two countries trade products in the same industry with (on average) diﬀerent quality with eachother, the trade pattern becomes VIIT when the gaps in the average quality and in the average priceare suﬃciently large.
Recall that the size of technology spillovers from country h to country l,Slh , is measured by Eq.
(35), which consists of φl (a parameter that controls the degree of international knowledge spillovers)hand NXt(the mass of varieties exported from country h to country l). Then, as for technology

spillovers under VIIT, φH and φF are both smaller in the asymmetric case than in the symmetricH
Fcase and NX
and NX
are also both smaller in the asymmetric case, Thus, we obtain the following

hypothesis:
Hypothesis 1 Compared to the case in which the trade pattern is HIIT, the size of technology
spillovers is lower in either direction when the trade pattern is VIIT.
F
H
Moreover, the size of technology spillovers is asymmetric under VIIT. Since αH
D > αD and ᾱX >ᾱF
X , the mass of varieties exported from the home country is greater than that exported from theHFforeign country. That is, NX> NX. However, this does not necessarily imply that the size oftechnology spillovers is larger from the home country to the foreign country than in the opposite
direction. The reason is that φH < φL may hold and that it may cause SHF > SF H to hold in Eq.
(35). Thus, the following hypothesis is obtained:
Hypothesis 2 When the trade pattern is VIIT, the relative size of technology spillovers from thehome country to the foreign country and in the opposite direction is ambiguous.

16 Note that if τ H = τ L = 1, then the overall distribution of product qualities is identical in the two markets.

15

We next consider the case in which the technology gap between the two countries is widenedFfurther, so that αF
M < αX holds or the free entry condition in the foreign country (Eq. (28)) becomesLF αFM t
αF
Dt


2
H
dGF
α − αFDtt (α) + L

 αFM tαH+(τ H −1)c
Dt


2
H
− 1)c dGF
α − αH
Dt − (τt (α) < 4γf.

In the former case, some foreign ﬁrms may still enter the manufacturing sector but no foreign ﬁrm
F= 0 holds and thecan export goods to the home country. In the latter case, on the other hand, NEtforeign country is specialized in the numeraire good. In either case, the trade pattern is characterizedby pure OWT, or pure inter-industry trade. International technology spillovers still occur from thehome country to the foreign country but no spillovers in the opposite direction. As is evident fromthe above discussion on the case of VIIT, a widened technology gap between the two countries causesFF
HαH
D and αD to be lower under OWT than under VIIT. Then, αX and αX are also lower under OWT
Hthan under VIIT, which implies that the mass of varieties exported from the home country (i.e., NX)
F
H
is smaller under OWT. Moreover, since the gap between αH
M and αM is widened, the values of φ

and φF decrease. Therefore, we obtain the following hypothesis:
Hypothesis 3 Compared to the case in which the trade pattern is VIIT, the size of technology
spillovers is lower when the trade pattern is OWT.
As will be argued in the next section, OWT does not necessarily mean that the trade pattern iscompletely inter-industry. In the empirical analysis, a small amount of intra-industry trade that is
below some critical value is categorized as OWT. Thus, the direction of technology spillovers in thecase of OWT is not necessarily one-way.
From the theoretical investigation, we obtained three testable hypotheses on the relationship between trade patterns and international technology spillovers. In the next section, we empirically test
these three hypotheses.

4

Empirical Analysis

In the previous section, we have shown that technology spillovers across countries may be related withpatterns of bilateral trade. In this section, we empirically test predictions of the theoretical model byusing bilateral trade data and patent citation data.

4.1

Estimation framework

We ﬁrst explain the method of categorizing bilateral trade ﬂows. In the previous studies, trade patterns
are usually categorized into three types, namely, one-way trade (OWT), horizontal intra-industry trade(HIIT), and vertical intra-industry trade (VIIT) (e.g., Fontagné and Freudenberg, 1997; Greenaway,16

Hine, and Milner, 1995; Fukao, Ishido, and Ito, 2003). The standard method of categorization is given
by Fontagné and Freudenberg (1997), which is summarized in Table A.2.17 This method is basedon the assumption that the gap between the unit values of imports and exports for each commodity
reﬂects the qualitative diﬀerences of the products exported and imported between two countries. We
extend the standard method to take the direction of trade into account and categorize bilateral trade
ﬂows into ﬁve types.
Let Xijk and Mijk be the values of country i’s exports to and imports from country j of productk, respectively. Then, the trade pattern in industry k is one-way trade with importing (OWTM ) ifmin(Xijk , Mijk )≤θmax(Xijk , Mijk )and Xijk < Mijk

hold and one-way trade with exporting (OWTX ) ifmin(Xijk , Mijk )≤θmax(Xijk , Mijk )and Xijk > Mijk

hold. The trade pattern in industry k is two-way trade, or intra-indutry trade (IIT), if
min(Xijk , Mijk )>θmax(Xijk , Mijk )XMholds. IIT is further divided into three types. Let U Vijk
and U Vijk
be average unit values of country

i’s exports to and imports from country j of product k. Then, the trade pattern in industry k ishorizontal intra-industry trade (HIIT) if
1−ξ ≤X
U VijkM
U Vijk≤1+ξ

holds (This condition is the same as that in the standard method). The trade pattern in industry k
is vertical intra-industry trade with importing higher-quality products (VIITM ) if
X
U Vijk<1−ξM
U Vijkholds and vertical intra-industry trade with exporting higher-quality products (VIITX ) if
X
U Vijk>1+ξ

M
U Vijk17 There is another method of categorizing trade patterns proposed by Greenaway, Hine, and Milner (1994, 1995),

which is based on a decomposition of Grubel–Lloyd index. In their method, intra-industry trade in industry k ismeasured by
IITk = 1 −  nnz − Mz ||Xknkn

z + Mz )
(Xkn
kn

,

where n refers to products and z denotes HIIT or VIIT. In order to disentangle total IIT into HIIT and VIIT, they also
use the ratio of unit values. Fontagné, Freudenberg, and Gaulier (2006) investigate the diﬀerence between these two
methods. They argue that, while the two methods diverge on the deﬁnition of IIT, they rely on the same assumption
regarding the relationship between unit values and the quality of traded products.

17

holds. Then, the share of each trade pattern is deﬁned byz(X z + Mijk)
k ijk
,
(X
+
M
ijk
ijk )
k
where z denotes one of the ﬁve trade types, i.e., OWTM , OWTX , HIIT, VIITM , and VIITX . In
the above conditions, the choice of θ and ξ is to a large extent arbitrary. Altough Fontagné and
Freudenberg (1997) and some other studies use ξ = 0.15, Fontagné, Freudenberg, and Gaulier (2006)
report the sensitivity of the relative importance of HIIT to total intra-industry trade and argue thatdeﬁning θ as 0.1 and ξ as 0.25 is quite reasonable. Fukao, Ishido, and Ito (2003) also employ θ = 0.1
and ξ = 0.25. They argue that a 25% threshold would be reasonable because of the possible eﬀects of
exchange rate ﬂuctuations on the value recorded in trade statistics and noise in the measurements ofunit values at 6-digit level of trade statistics. Thus, we also use θ = 0.1 and ξ = 0.25 in our analysis.
We then use patent citations to measure technology spillovers. The use of patent citations inmeasuring technology spillovers has been pioneered by Jaﬀe, Trajtenberg, and Henderson (1993), in
which patent citations are used to measure the extent of technology spillovers within the U.S. Every
U.S. patent applicant is required to disclose any knowledge of the “prior art” in his or her application.
Hall, Jaﬀe, and Trajtenberg (2001) point out that the presumption for using patent citations as aproxy for learning technology is that the citations to the “prior art” are informative of the causal
links between those patented innovations, because citations made may constitute a “paper trail” fordiﬀusion, i.e., the fact that patent B cites patent A may be indicative of knowledge ﬂowing from A to
B. This logic is also practicable to the case of the patent citations between countries.
On the other hand, the patent citations between the two countries may be associated with thepast records of patenting in both the cited and the citing countries. The number of patents ﬁled by
the citing country is related to the scale of human resource in this country, and reﬂects the indigenous
capacity to absorb foreign technology. The number of patents in the cited country implies a potential
opportunity of citations for the citing country. Based on the reasoning above, our regression model isdeﬁned as follows:
log c∗ijt=

β  xijt + ijt=

β1 Shareijt (OW TM , OW TX , HIIT, V IITM , or V IITX ) + β2 log Pit × Pjt + uij + eijt

where c∗ijt is the number of patent citations made by patents ﬁled by country i (the citing country)
to country j (the cited country) in year t, Shareijt is bilateral OWTM , OWTX , HIIT, VIITM , or
VIITX share between country i and j in year t, Pit and Pjt are the number of patent applications
ﬁled by country i and j respectively in year t.18 Thus, we use c∗ijt as a proxy for technology spillovers
from country j to country i. The term Pit × Pjt is included to control the eﬀect of the citing country’s
absorptive capacity of technology and the cited country’s potential opportunity of citations.
18 The stochastic nature of product R&D assumed in our theoretical model is not directly reﬂected in our estimation

framework. As we have shown in the previous sections, however, the average quality and the distribution of quality

18

Since patent citations are rarely happened among some countries, there are substantial zero valuesin c∗ijt . We then use a random-eﬀects panel Tobit model to deal with this issue. In that case, thedependent variable is now a latent variable, where⎧⎨ log c∗ijt
log cijt =⎩0

if c∗ijt > 0,otherwise,

andijt = uij + eijt ,u ∼ N ID(0, σu2 ),e ∼ N ID(0, σe2 ),

ρ=

σu2
.
σu2 + σe2

In general independence between the u and e is assumed. On the other hand, there is neither
a convenient test nor estimation method for test of random versus ﬁxed-eﬀects of Tobit model aswell as for estimation of a conditional ﬁxed-eﬀects model.19 In order to assess the robustness of theestimated results by the random-eﬀects Tobit model, we try to use a ﬁxed-eﬀects negative binomial
model proposed by Hausman, Hall, and Griliches (1984) for our same sample.

4.2

Data

4.2.1

Trade data

There are several kinds of datasets for empirical analysis on international trade such as International
Trade Commodity Statistics (ITCS–SITC) released by OECD, and Personal Computer Trade Analysis
System (PC–TAS) published by the United Nations Statistical Division. As indicated by Gaulier andZignago (2008), the empirical analysis is suﬀered from the two diﬀerent ﬁgures for the same tradeﬂow, because the import values are generally reported in CIF (cost, insurance and freight) and export
values in FOB (free on board). To reconcile the two ﬁgures, Gaulier and Zignago (2008) develop a
procedure to estimate an average CIF cost and remove it from the declarations of imports to provide
FOB import values for bilateral trade ﬂows drawn on United Nations COMTRADE data. In thispaper, we utilize this reconstructed trade dataset called as BACI. The BACI dataset covers morethan 200 countries and 5,000 products between 1995 and 2007.20
4.2.2

Patent citation data

The data of patents and patent citations used in this paper consist of two sources, i.e., EPO Worldwide
Patent Statistical Database (PATSTAT) and the Institute of Intellectual Property (IIP) dataset. We
collect the patent statistics of the United States Patent and Trademark Oﬃce (USPTO) and European
among actually supplied products in an industry are invariant for a given distribution Gt (α). Since we use the industry
average to determine the bilateral trade patterns, we think that our empirical framework is consistent with the theoreticalmodel in the previous sections.
19 Honore (1992) has developed a semiparametric estimator for ﬁxed-eﬀect Tobit models.
20 Please see the website of CEPII (http://www.cepii.fr) for the details of BACI dataset.

19Patent Oﬃce (EPO) from the former, and these of Japanese Patent Oﬃce (JPO) from the latter. The
two datasets include the dates of patent applications, International Patent Classiﬁcation (IPC), theinformation of citation and the country names both of citing and cited patent applicants.
Unlike the patent application in the USPTO, patent applicants in JPO have no legal duty to list
the patents that he/she cites in the front-page of document, although some referenced information
provided by the applicants lies scattered across the patent body text. The information of citations in
the front-page is usually added by the examiners in JPO as well as in EPO (Hall, Thoma, and Torrisi,2007). According to Goto and Motohashi (2007), about two thirds of JPO citations are decided by
the examiners since 1990s.
Although the decision regarding which patents to cite ultimately depends on the patent examiner,
implying that the inventors may have been unaware of the cited patents, the presumption that thecitations are relevant as the indicator of technology links between the citing and the cited is widely
recognized in many empirical studies such as Jaﬀe, Trajtenberg, and Henderson (1993), Jaﬀe andTrajtenberg (1996, 1999), and Hall, Jaﬀe, and Trajtenberg (2001) for the U.S. patents, Maurseth andVerspagen (2002), and MacGarvie (2006) for the European patents.
4.2.3

Sample selection

We start to select our sample from top 60 trade countries in 2008, according to the quantity of theirimport and export in the world. Because crude oil makes up the most of trade in some top trade
countries such as Saudi Arabia, Nigeria, Russia and Venezuela, we exclude these countries from oursample. At the same time, we also exclude countries such as Kazakhstan, Peru and Vietnam, since
they rarely made or received patent citations in USPTO, JPO or EPO. As a result, we obtain a sample
which covers 44 countries across advanced, emerging and developing economies in the world.21
The patent statistics used in this paper are classiﬁed according to the IPC, which is based either on
the intrinsic nature of the invention or on the function of the invention. Schmoch et al. (2003) provide
a concordance between technical ﬁelds and industrial sectors. This concordance table refers to IPC
for patents, and international classiﬁcations, namely European Union’s Classiﬁcation of Economic
Activities within the European Communities (NACE), the United Nations’ International Standard
Industrial Cassiﬁcation (ISIC) and the U.S. Standard Industrial Classiﬁcation (SIC) with 44 industrial
sectors. The empirical analyses in Schmoch et al. (2003) show that this concordance with 44 industrial
sectors (or technical ﬁelds) has a reasonable level of disaggregation, because the economic data forinternational comparisons are not available in the ﬁner diﬀerentiation. Thus, we use their concordancetable to allocate the patents statistics into 44 industrial sectors.22 Since the number of citations is very
limited in some sectors, especially for products in some light manufacturing sectors such as textiles,
21 See the list of sample countries in Table A.3.
22 See Table A.4 for the details of the 44 industrial sectors.

20

wearings, and paints, we focus our analysis on ﬁve ﬁelds, i.e., non-metal products, metal products,
machinery, ICT relation equipments, and motor vehicle. The ﬁve ﬁelds correspond with Sectors 17
and 18, Sector 20, Sectors 21-25, Sectors 28 and 34-38, and Sector 42 in Schmoch et al. (2003).
In order to match the data for trade with patents, we map the 6-digit Harmonized System (HS6)and the ISIC rev. 3 according to the industrial concordance table provided by Jon Haveman.23 Then,
we use the method explained above to measure the shares of OWT, HIIT and VIIT for our sample
countries in the ﬁve ﬁelds discussed above for the periods of 1995-1996, 1997-1998, 1999-2000, 20012002, and 2003-2004 (i.e., ﬁve periods). The descriptive statistics for the shares of OWT, HIIT and
VIIT, and the number of citations are presented in Table A.1. On one hand, there are substantial
citations between some developed countries, especially between the U.S. and Japan. For instance, theU.S. patents belonged to Sector 28 made more than 56,300 citations to Japanese patents during theperiod of 2003 and 2004. On the other hand, among about four ﬁfths of observations citations are not
identiﬁed in our sample period.
Table 1 describes the shares of OWT, HIIT and VIIT for some selected sample countries averagely across ﬁve ﬁelds and ﬁve periods. From the table, we ﬁnd that the remarkable bilateral IIT(HIIT+VIIT) intensities are observed among European countries. More than 91% of trade is IIT for
the trade between Germany and France, 79% for France and Belgium–Luxembourg, 92% for Netherlands and Belgium–Luxembourg. These ﬁgures largely coincide with those reported by Fontagné,Freudenberg, and Gaulier (2006) for the same country pairs (86.2%, 80.4% and 85.0%, respectively),
based on trade statistics of year 2000.
Table 2 presents how patent citations have been made by the patents of some selected countries
ﬁled to USPTO, JPO and EPO respectively. Although the scale of citations is diﬀerent across thepatent oﬃces, the patterns of citations between the selected countries are similar across the patentoﬃces. For example, the U.S., Japan and Germany are the largest targets of citations not only forother countries, but also for each other, while citations are relatively less received as well as made by
Chinese patents yet.

4.3

Estimation results

Table 3 summarizes the results for full ﬁelds, estimated based on the patent citations in USPTO,
JPO and EPO respectively. We added dummy variables to control for the ﬁelds and time periods,
and, as we expected, the coeﬃcients estimates of the number of patents hold by citing and citedcountries are positively signiﬁcant. To assess the robustness of the estimated results in Table 3 at thesame time, we also apply an alternative regression technique, namely, a ﬁxed-eﬀects negative binomial
model proposed by Hausman, Hall, and Griliches (1984), to the same sample. Table 4 summarizes
23 See http://www.macalester.edu/research/economics/page/haveman/trade.resources/tradedata.html

21

the ﬁxed-eﬀects negative binomial estimates, where the number of citations is used as a dependent
variable.
In Tables 3 and 4, we see that all coeﬃcient estimates for HIIT and most of those for VIIT
are signiﬁcant and positive, implying that intra-industry trade plays a signiﬁcant role in technology
spillovers. The coeﬃcients for HIIT are estimated as 1.92, 2.38 and 2.21 in Table 3, which are evidently
larger than those for VIIT, when the two variables are used in the same regression for the three diﬀerent
patent statistics. This pattern remains true also in Table 4. Compared with the vertical intra-industry
trade, the horizontal intra-industry trade shows a dominant eﬀect on technology spillovers.
Unlike the intra-industry trade, the estimations for the relationship between OWT and the number of citations reveal somewhat mixed results. In Table 3, the estimated coeﬃcients of OWT aresigniﬁcantly positive. However, the magnitudes of the coeﬃcients are quite smaller than those for
HIIT and VIIT. In Table 4, the estimated coeﬃcients of OWT are weakly signiﬁcant or insigniﬁcantin the cases of JPO and EPO, while they are signiﬁcantly negative in the case of USPTO. These
results imply that the eﬀect of OWT on technology spillovers is much weaker than that of IIT andmay be negligible.

5

Conclusions

In this paper, we have examined how technology spillovers across countries would diﬀer according to
the bilateral trade patterns. We ﬁrst developed a two-country model of monopolistic competition withquality diﬀerentiation by extending the model of Melitz and Ottaviano (2008). In our model, qualityof each product in the manufacturing sector is diﬀerentiated and stochastically determined by ﬁrms’
engaging in product R&D. The structure of our model is quite similar to that of Melitz and Ottaviano(2008), except for that ﬁrms are heterogeneous in the product quality rather than in productivity. We
then introduced technology spillovers in our model as the process of expanding the technology frontierof the industry. We assumed that, in a given sector, all ﬁrms in the same country equally have accessto the “general knowledge” without paying any cost. However, technology spillovers are imperfectacross countries. In particular, the degree of international technology spillovers falls as the technology
gap between the two countries increases. We then showed that in our model the trade pattern is
intra-industry when the technology gap between the two countries is small, while it is inter-industry
when the technology gap is suﬃciently large. Since products are diﬀerentiated in quality in our model,
both horizontal and vertical intra-industry trade patterns also emerge endogenously.
From the model, we derived three testable hypotheses. The ﬁrst hypothesis was that technology
spillovers are larger when the trade pattern between the two countries is horizontal intra-industry
trade (HIIT) than when it is vertical intra-industry trade (VIIT). The second hypothesis was thatwhen the trade pattern is VIIT, the relative size of technology spillovers from the country exporting22

high quality products on average to the country exporting low quality products on average and in the
opposite direction is ambiguous. The third hypothesis was that technology spillovers are lower when
the trade pattern is inter-industry trade, or one-way trade (OWT), than when it is VIIT.
We then empirically tested those hypotheses obtained from the model by using bilateral trade data
among 44 countries at 6-digit level patent citations data at the U.S., European, and Japanese Patent
Oﬃces. Following Jaﬀe, Trajtenberg, and Henderson (1993) and other recent studies on technology
spillovers, we measure international technology spillovers by patent citations among countries.
Our estimation results basically conﬁrmed the predictions of our model. That is, we found that anincrease in the shares of HIIT and VIIT has a signiﬁcantly positive eﬀect on international technology
spillovers. Our estimation results showed that HIIT has a larger eﬀect on spillovers than VIIT does.
On the other hand, the relative magnitudes of technology spillovers between the country exporting
high quality products and the country exporting low quality products on average under VIIT aregenerally ambiguous. We also found that the eﬀect of OWT on technology spillovers tends to be much
weaker than that of other trade patterns. Therefore, we concluded that intra-industry trade plays asigniﬁcant role in technology spillovers.
In this paper, we primarily focused on technology spillovers through international trade and did
not take the eﬀects of foreign direct investment (FDI) into account. As argued in the introduction,
however, a number of existing studies have empirically conﬁrmed that FDI is also a major channel forinternational technology spillovers. In our estimations, we found that an increase in the share of OWT
has a signiﬁcantly positive eﬀect on technology spillovers in some cases, in particular in the cases of
JPO and EPO. The positive eﬀect of OWT with exporting the good in question even exceeds thatof HIIT and/or VIIT in some cases in Table 4, which contradicts the predictions by our theoreticalmodel. This may be due to FDI. Thus, it is our future research to incorporate the eﬀects of FDI into
our framework.

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29

30

Korea
0.58
0.05
0.29
0.42
0.12
0.37
0.58
0.06
0.35
0.42
0.06
0.50
0.51
0.06
0.26
0.53
0.07
0.21
0.46
0.03
0.18
0.58
0.03
0.28
0.35
0.06
0.23
0.57
0.02
0.15

(1) The upper, middle and lower ﬁgures are for OWT, HIIT and VIIT respectively.
(2) The sum of OWT, HIIT and VIIT could be less than 1.0 due to unavailability for the unit value in some cases.
(3) Luxembourg is included in Belgium.

CanadaBelgium(3)U.K.

Netherlands

Italy

France

Japan

U.S.

China

Germany

Table 1. Shares of OWT, HIIT and VIIT for Selected Countries(1) (2)
China
U.S. Japan
France
Italy
Netherlands
U.K. Belgium Canada
0.63
0.25
0.36
0.08
0.19
0.11
0.12
0.16
0.52
0.03
0.20
0.21
0.51
0.31
0.48
0.37
0.40
0.09
0.25
0.54
0.42
0.41
0.50
0.40
0.51
0.43
0.29
0.63
0.50
0.59
0.53
0.64
0.63
0.50
0.63
0.04
0.07
0.04
0.04
0.02
0.03
0.02
0.01
0.30
0.39
0.23
0.34
0.19
0.25
0.18
0.16
0.48
0.28
0.41
0.36
0.21
0.44
0.08
0.12
0.19
0.08
0.09
0.24
0.12
0.28
0.40
0.52
0.51
0.52
0.53
0.41
0.28
0.51
0.48
0.57
0.44
0.59
0.67
0.15
0.10
0.04
0.13
0.02
0.04
0.28
0.33
0.30
0.40
0.22
0.12
0.19
0.20
0.08
0.11
0.34
0.37
0.28
0.45
0.42
0.10
0.43
0.51
0.47
0.47
0.42
0.29
0.26
0.32
0.50
0.13
0.26
0.28
0.05
0.55
0.47
0.39
0.28
0.14
0.07
0.37
0.25
0.42
0.07
0.60
0.50
0.38
0.20
0.32
0.26
0.11
0.53
0.51
0.45
0.03
0.22

31

Citing Country

57
31886
12040
1324
578
741
1024
120
890
1327

18
3855
32394
737
322
451
435
55
143
457

6
940
1121
247
136
76
70
40
20
77

Germany
China
U.S.
Japan
France
Italy
Netherlands
U.K.
Belgium
CanadaKorea
Germany
China
U.S.
Japan
France
Italy
Netherlands
U.K.
Belgium
CanadaKorea
Germany
China
U.S.
Japan
France
Italy
Netherlands
U.K.
Belgium
CanadaKorea

Germany

Table 2. Patent Citations for Selected Countries(1)Cited Country
China
U.S.
Japan
France
Italy
Netherlands
Citations in USPTO
15
19905
16403
1772
554
513
529
359
20
1
10
323
151745
14808
3077
6464
66
89969
4278
1084
1935
6
7444
4719
143
252
0
1633
1207
184
37
5
6936
4343
250
59
4
6201
2824
450
88
137
1
584
435
86
8
17
5
8147
3385
365
65
125
38
18312
26438
810
222
526
Citations in JPO
8
5834
63171
835
350
499
127
1550
21
3
3
21
177390
1729
463
1277
173
108506
10506
2939
7545
0
2371
19458
102
207
0
490
4327
152
33
0
2374
23097
166
58
1
1560
10452
169
35
108
0
188
1844
33
5
8
0
483
3608
43
9
27
6
3790
67141
284
84
229
Citations in EPO
1
2041
2221
323
220
160
48
62
9
0
0
9
4581
513
247
300
10
6809
517
245
474
1
1046
862
68
81
0
303
318
58
16
1
301
314
58
15
1
381
281
41
12
22
0
135
138
25
6
16
1
226
117
14
4
9
3
678
1357
59
12
54
11
6
35

295
4
538
478
117
34
23

24
50
150

578
3
1457
7001
213
35
172

24
353
399

1238
16
13030
3069
397
111
211

U.K.

2
5

34
0
99
126
11
5
2
9

4
18

85
0
182
1296
25
2
22
14

28
57

107
3
1087
445
27
11
27
28

Belgium

24

41
9
129
109
37
2
5
7
3

77

117
6
400
1870
48
21
23
41
8

355

416
27
7701
1432
242
23
87
142
14

Canada

39
3
178
395
49
14
17
8
3
9

317
15
1369
15195
162
19
231
56
16
21

1212
126
17794
13404
547
137
567
217
21
442

Korea

Table 3: The Random-Eﬀects Panel Tobit Estimates for Patent Citation(1)Coeﬃcient
USPTO citations
JPO citations
HIIT
2.049∗∗∗ (2)2.027∗∗∗
1.706∗∗∗
2.615∗∗∗
2.699∗∗∗
2.290∗∗∗(17.0)(3)(16.8)(13.8)(15.3)(15.7)(13.1)V IITM
1.836∗∗∗
1.801∗∗∗
1.821∗∗∗
2.338∗∗∗
2.420 ∗∗∗
2.548 ∗∗∗
(17.0)(16.7)(16.1)(15.3)(15.7)(16.0)
1.697∗∗∗
1.675∗∗∗
1.687∗∗∗
2.399∗∗∗
2.466∗∗∗
2.580∗∗∗V IITX(15.0)(14.8)(14.3)(15.1)(15.4)(15.7)
OW TM
0.729∗∗∗
0.758 ∗∗∗
0.378∗∗∗
1.268∗∗∗
1.600∗∗∗
1.037 ∗∗∗
(8.4)
(8.0)
(4.2)
(10.0)(11.7)(8.0)
OW TX
0.606∗∗∗
0.666∗∗∗
0.293∗∗∗
1.498∗∗∗
1.737∗∗∗
1.180∗∗∗
(7.0)
(7.1)
(3.3)
(11.8)(12.9)(9.2)
0.310∗∗∗
0.312∗∗∗
0.318 ∗∗∗
0.325∗∗∗
0.152∗∗∗
0.151∗∗∗
0.153∗∗∗
0.158∗∗∗
log Pi × Pj
(48.1)(48.3)(48.0)(48.3)(33.6)(33.3)(33.7)(33.9)
P eriod1
0.120 ∗∗∗
0.120∗∗∗
0.104 ∗∗∗
0.132∗∗∗
1.430∗∗∗
1.438 ∗∗∗
1.389 ∗∗∗
1.401∗∗∗
(3.7)
(3.7)
(3.2)
(4.0)
(20.8)(20.8)(20.1)(20.3)
P eriod2
0.198∗∗∗
0.196∗∗∗
0.175∗∗∗
0.211∗∗∗
1.323∗∗∗
1.324∗∗∗
1.257∗∗∗
1.296∗∗∗
(6.1)
(6.1)
(5.4)
(6.5)
(19.0)(18.9)(18.0)(18.5)
0.411∗∗∗
0.410∗∗∗
0.388∗∗∗
0.440∗∗∗
1.472∗∗∗
1.477∗∗∗
1.417 ∗∗∗
1.479∗∗∗
P eriod3(12.8)(12.7)(11.9)(13.6)(21.1)(21.1)(20.3)(21.1)
P eriod4
0.433∗∗∗
0.430∗∗∗
0.397∗∗∗
0.434∗∗∗
1.355∗∗∗
1.357∗∗∗
1.292 ∗∗∗
1.352∗∗∗(12.3)(12.1)(11.0)(12.0)(19.1)(19.1)(18.2)(18.9)
F ield2
0.096
0.098
0.077
0.209∗∗∗-0.326∗∗∗-0.338∗∗∗-0.384∗∗-0.244 ∗∗∗
(1.2)
(1.2)
(0.9)
(2.6)
(-2.9)(-3.0)(-3.4)(-2.1)-0.025-0.026-0.079-0.0440.184∗
0.195∗∗
0.128
0.178 ∗
F ield3(-0.4)(-0.4)(-1.1)(-0.6)
(1.9)
(2.0)
(1.3)
(1.8)
F ield4-0.107-0.106-0.214 ∗∗∗-0.0980.295∗∗∗
0.286 ∗∗∗
0.121
0.310∗∗∗(-1.5)(-1.5)(-3.1)(-1.4)
(3.0)
(2.9)
(1.2)
(3.2)
F ield5
0.148∗
0.154 ∗∗
0.136∗
0.122-0.190∗-0.210∗-0.251∗∗-0.254∗∗
(1.9)
(2.0)
(1.8)
(1.6)
(-1.8)(-1.9)(-2.3)(-2.3)
1.338∗∗∗
1.337∗∗∗
1.357∗∗∗
1.382 ∗∗∗
1.991∗∗∗
1.992∗∗∗
2.000∗∗∗
2.044∗∗∗
1/σu(54.8)(54.8)(53.7)(53.2)(53.2)(53.1)(52.8)(52.2)
1/σe0.870∗∗∗
0.872∗∗∗
0.877∗∗∗
0.875∗∗∗
1.064∗∗∗
1.063∗∗∗
1.066∗∗∗
1.066∗∗∗(86.7)(86.7)(85.4)(84.7)(74.3)(74.2)(73.8)(72.6)
ρ
0.703
0.702
0.706
0.714
0.778
0.778
0.779
0.786
(0.7)
(0.7)
(0.7)
(0.7)
(0.8)
(0.8)
(0.8)
(0.8)
46764
46764
46764
46764
46764
46764
46764
46764
No. of obs.
Log likelihood-15143-15154-15261-15356-13169-13148-13201-13324
Ward test(Prob4>chi2 )
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
LR test(Prob>chi2 ) (4)(1) The regression is based on full sample and includes constant term.
(2) “***”,“**” and “*” denote 1%, 5% and 10% signiﬁcant levels, respectively.
(3) The values in the parentheses are t-statistics.
(4) Likelihood ratio test for RE model vs. pooled model.

32

0.076∗∗∗(24.5)-0.793∗∗∗(-16.5)-0.764∗∗∗(-15.4)-0.709∗∗∗(-14.1)-0.602∗∗∗(-11.9)-0.416∗∗∗(-4.4)
0.208∗∗∗(2.6)
0.565 ∗∗∗
(7.4)
-0.070(-0.8)
1.379∗∗∗(46.0)
0.718∗∗∗(60.6)
0.787
(0.8)
46764
-8099
0.0
0.0

2.434∗∗∗(18.9)
2.137 ∗∗∗
(17.7)
2.183∗∗∗(17.5)
1.116∗∗∗(11.0)EPO citations
2.433∗∗∗(18.8)
2.100 ∗∗∗
2.107∗∗∗(17.5)(16.8)
2.195∗∗∗
2.169∗∗∗(17.6)(16.8)
1.205∗∗∗(11.1)
1.128∗∗∗
1.214∗∗∗(11.0)(11.1)
0.076∗∗∗
0.081∗∗∗(24.4)(25.3)-0.791∗∗∗-0.857∗∗∗(-16.5)(-17.6)-0.762∗∗∗-0.843∗∗∗(-15.5)(-16.8)-0.709∗∗∗-0.787∗∗∗(-14.1)(-15.4)-0.599∗∗∗-0.679∗∗∗(-11.9)(-13.2)-0.417∗∗∗-0.428∗∗∗(-4.4)(-4.6)
0.214∗∗∗
0.143∗(2.7)(1.8)
0.574 ∗∗∗
0.426 ∗∗∗
(7.5)
(5.6)
-0.060-0.085(-0.7)(-1.0)
1.387∗∗∗
1.414∗∗∗(45.8)(46.4)
0.715 ∗∗∗
0.720∗∗∗(60.6)(59.4)
0.790
0.794
(0.8)
(0.8)
46764
46764
-8099
-8218
0.0
0.0
0.0
0.0

0.754∗∗∗(7.6)
0.781∗∗∗(7.7)
0.081∗∗∗(25.1)-0.811∗∗∗(-16.8)-0.787∗∗∗(-15.8)-0.712∗∗∗(-14.1)-0.617∗∗∗(-12.1)-0.319∗∗∗(-3.4)
0.194∗∗(2.5)
0.569 ∗∗∗
(7.5)
-0.120(-1.4)
1.443∗∗∗(46.8)
0.712 ∗∗∗
(58.1)
0.804
(0.8)
46764
-8338
0.0
0.0

1.974∗∗∗(15.2)

33

0.252∗∗∗(27.7)
0.193∗∗∗
(6.8)
0.409
(14.9)
0.726∗∗∗(26.1)
1.019∗∗∗(29.6)

0.779∗∗∗ (2)(7.7) (3)0.510∗∗∗(5.4)
0.689∗∗∗(7.1)
0.253∗∗∗(2.7)

No. of obs.
11874
11874
11874
11874
8900
Log likelihood-15538-15542-15562-15559-11335
0.0
0.0
0.0
0.0
0.0
Ward test(Prob4>chi2 )(1) The regression is based on full sample.
(2) “***”,“**” and “*” denote 1%, 5% and 10% signiﬁcant levels, respectively.
(3) The values in the parentheses are t-statistics.

P eriod4

P eriod3

P eriod2

P eriod1

log Pi × Pj

OW TX

OW TM

V IITXV IITM

Coeﬃcient
HIIT

8900
-113110.0

8900-113270.0

8900-113320.0

Table 4: Fixed-eﬀects Negative Binomial Estimates for Patent Citation(1)USPTO citations
JPO citations
0.673∗∗∗
0.350∗∗∗
0.400∗∗∗
0.871∗∗∗
0.343∗∗
(6.5)
(3.8)
(2.6)
(5.8)
(2.5)
0.400∗∗∗
0.111
0.130
0.609∗∗∗
0.235∗
(4.2)
(1.2)
(0.9)
(4.3)
(1.7)
0.580∗∗∗
0.291∗∗∗
0.493∗∗∗
0.974∗∗∗
0.598∗∗∗
(5.9)
(2.9)
(3.4)
(6.6)
(4.1)
-0.108-0.147∗-0.259∗-0.110-0.248∗(-1.1)(-1.7)(-1.8)(-0.8)(-1.8)-0.038-0.292∗∗∗-0.329∗∗∗0.968∗∗∗
0.657∗∗∗
0.514 ∗∗∗(-0.4)(-3.1)(-3.8)
(7.2)
(4.8)
(4.1)
0.251∗∗∗
0.256∗∗∗
0.257∗∗∗
0.058∗∗∗
0.056∗∗∗
0.058∗∗∗
0.058∗∗∗(27.4)(27.8)(28.1)(12.2)(11.8)(12.1)(12.2)
0.194∗∗∗
0.193∗∗∗
0.198∗∗∗
2.373∗∗∗
2.402∗∗∗
2.370∗∗∗
2.374∗∗∗
(6.8)
(6.7)
(6.9)
(31.0)(31.3)(30.9)(30.9)
0.412
0.415
0.417
2.385
2.406
2.378
2.382
(15.0)(15.0)(15.1)(30.8)(31.0)(30.6)(30.7)
0.730∗∗∗
0.733∗∗∗
0.736∗∗∗
2.567∗∗∗
2.581∗∗∗
2.564∗∗∗
2.570∗∗∗(26.2)(26.0)(26.2)(33.2)(33.3)(33.0)(33.2)
1.025∗∗∗
1.029∗∗∗
1.026∗∗∗
2.608∗∗∗
2.618∗∗∗
2.602∗∗∗
2.607∗∗∗(29.8)(29.4)(29.4)(33.3)(33.4)(33.2)(33.3)
6110
-6216
0.0

0.024∗∗∗(6.5)-0.181∗∗∗(-3.2)-0.039(-0.7)
0.119∗∗(2.0)
0.318∗∗∗(5.4)

0.469∗∗
(2.4)
0.295
(1.5)
0.598∗∗∗
(3.0)
0.235
(1.2)

6110
-6212
0.0

6110
-6217
0.0

EPO citations
0.636∗∗∗(3.2)
0.459∗∗
0.219
(2.3)
(1.2)
0.773∗∗∗
0.518∗∗∗
(3.8)
(2.8)
0.192
(1.0)
0.608∗∗∗
0.407∗∗(3.1)(2.1)
0.024∗∗∗
0.024∗∗∗
(6.5)
(6.6)
-0.183 ∗∗∗-0.188∗∗∗(-3.2)(-3.3)-0.047-0.048(-0.8)(-0.8)
0.113∗
0.119∗∗(1.9)(2.0)
0.307∗∗∗
0.313∗∗∗
(5.2)
(5.3)

6110
-6220
0.0

0.052
(0.3)
0.264
(1.5)
0.023∗∗∗(6.5)-0.172∗∗∗(-3.0)-0.032(-0.6)
0.138 ∗∗
(2.3)
0.329∗∗∗
(5.6)

0.234
(1.4)

Table A.1: Descriptive Statistics
Variable
HIIT
V IIT
OW T
USPTO citations
Pi in USPTO
Pj in USPTOJPO citations
Pi in JPO
Pj in JPO
EPO citations
Pi in EPO
Pj in EPO

No. of Obs
46764
46764
46764
47300
47300
47300
47300
47300
47300
47300
47300
47300

Mean
0.05
0.17
0.28
14.9
412.0
412.0
14.5
2382.71527.8
0.9
275.1
275.1

34

StdDev
0.10
0.19
0.24
400.0
2803.62803.6419.0
19395.311114.7
18.3
1273.51273.5

Min
0.00
0.00
0.00
0
0
0
0
0
0
0
0
0

Max
1.00
1.00
1.00
56342
59160
59160
39332
279823233511
1614
16533
16533

Table A.2: Fontagné and Freudenberg’s (1997) Decomposition

Type of Trade (z)Trade Overlap

One-way trade (OWT)

min(Xijk ,Mijk )max(Xijk ,Mijk ) ≤ θ

Shares of Types

UV X

 z
z
k (Xijk +Mijk )1 − ξ ≤ UVijk
M ≤ 1 + ξ

Horizontal intra-industry trade (HIIT)
Vertical intra-industry trade (VIIT)

Unit Valueijkmin(Xijk ,Mijk )max(Xijk ,Mijk ) > θorIntra-industry tradenon-allocated (IITna)

X
UVijk
M
UVijk
X
UVijk
M
UVijk

>1+ξ
<1−ξ

Unit value not available

35k(Xijk +Mijk )Table A.3: Sample Countries
No
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22

Country
Germany
China
United States
Japan
France
Italy
Netherlands
United Kingdom
Belgium-Luxembourg
CanadaKorea
Singapore
MexicoSpain
Taiwan
Malaysia
SwedenSwitzerland
BrazilAustria
Thailand
India

36

No
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44

Country
Australia
NorwayPolandCzech Republic
IrelandIndonesia
TurkeyDenmark
Hungary
Finland
South Africa
Chile
Slovak Republic
Argentina
IsraelPhilippines
Portugal
UkraineRomania
Colombia
New Zealand
Slovenia

Table A.4: Correspondence derived by Schmoch et al. between technical ﬁelds and ISIC industrial
classiﬁcations1
Field No.
Sector
ISIC ver. 3
1
food
15
tobacco16
2
3
textiles17
4
wearing18
leather
19
5
6wood products
20
7
paper
21
publishing
22
8
9
petroleum23
10
basic chemicals
241
11
pesticides
2421
12
paint
2422
13
pharmaceuticals
2423
14
soaps
2424
15
other chemicals
2429
man-made ﬁbres
243
16
17
plastic products
25
18
mineral products
26
basic metals
27
19
20
metal products
28
21
energy machinery
2911, 2912, 2913
non-speciﬁc machinery
2914, 2915, 2919
22
23
agricultural machinery
2921
machine-tools
2922
24
25
special machinery
2923, 2924, 2925, 2926, 2929
26
weapons
2927
domestic appliances
293
27
28
computers
30
29
electrical motors
311
electrical distribution
312, 313
30
31accumulators
314
32
lightening314
other electrical
315
33
34
electronic components
321
35
telecommunications
322
television
323
36
37
medical equipment
3311
38
measuring instruments
3312
industrial control
3313
39
40
optics332
watches333
41
42
motor vehicles
34
43
other transport
35
consumer goods
36
44
1 Tables 3-1 and 3-5 in Schmoch et al. (2003).

37