# Centrality in Production Networks and International Technology Diffusion111
I thank Naoto Jinji, Keiko Ito, Sawako Maruyama, and participants of the
Japanese Economic Association, the Japan Society of International Economics,
and the Kansai Branch workshop of the Japan Society of International Economics
for their helpful comments and suggestions on earlier versions of the paper.

Rinki Ito Graduate School of Economics, Kyoto University, Yoshida Honmachi,
Sakyo-ku, Kyoto (Email: itou.rinki.73r@st.kyoto-u.ac.jp).

###### Abstract

This study examines whether the structure of global value chains (GVCs)
affects international spillovers of research and development (R&D). Although
the presence of “hub” countries in GVCs has been confirmed by previous
studies, the role of these hub countries in the diffusion of the technology
has not been analyzed. Using a sample of 21 countries and 14 manufacturing
industries during the period 1995-2007, I explore the role of hubs as the
mediator of knowledge by classifying countries and industries based on a
“centrality” measure. I find that R&D spillovers from exporters with High
centrality are the largest, suggesting that hub countries play an important
role in both gathering and diffusing knowledge. I also find that countries
with Middle centrality are getting important in the diffusion of knowledge.
Finally, positive spillover effects from own are observed only in the G5
countries.
JEL-Classification: F14, L60, O33, O47
Keywords: Production networks, Centrality, International R&D spillovers,
Technology diffusion

##  Introduction

Where do the R&D spillover effects come from? Starting with Coe and Helpman
(1995), the study of international R&D spillovers has developed over the last
three decades, both theoretically and empirically, and have shown that trade
is an important channel in the propagation of knowledge. Although several
previous studies have confirmed that countries adopt foreign technologies
through trade, and this affects productivity, it only investigates the overall
effects from abroad. The export is, at best, classified as G7 countries. After
all, previous studies do not answer Keller’s (1998) question about the
possibility that the country from which technology is imported is
inconsequential. To answer his question, we need to dig deeper into the
connections between the countries.
Trade has increased over the years. However, it has not increased evenly in
each country, and has been concentrated in a few countries alone (Criscuolo
and Timmis, 2018a). Additionally, a structure exists whereby many countries
trade with the hub in their respective regions, and the hubs trades with the
hubs in other regions. Therefore, it is obvious that there would exist a
difference in the spillover effects produced between the hubs and the non-
hubs. This is because the hub country is responsible for transmitting the
technology of other countries, and the indirect effects are likely to be
larger than those in the non-hub countries. Although no study has identified
and examined the centrality of the export side, I consider that the hubs,
which distort the network structure in trade, are important for the diffusion
of knowledge.
In fact, recent studies in macroeconomics have found that the manner of
interaction of a firm or industry with others in the production network is
important for the transmission of shocks. In particular, the presence of large
hubs in production networks facilitates the propagation of shocks that are
considered localized disturbances (e.g., Gabaix, 2011; Acemoglu et al., 2012;
Carvalho, 2014; Acemoglu et al., 2016; Boehm et al., 2019; Carvalho et al.,
2021). This is because the hub firm trades with several firms. However,
conversely, it means that transaction with such firms indirectly benefits from
the technology of other firms.
Motivated by these episodes, I ask the following research questions: How does
the structure of the GVCs affect the international spillover effect of
knowledge? In particular, are the international R&D spillover effects from
trading with high centrality countries greater than trading with peripheral
countries? Are the central countries important in technology diffusion? In
addition, are there any differences in the spillover effects due to the
differences in properties on the import side? To explore the role of the
central country in the diffusion of technology, I use the World Input-Output
Database (WIOD) that is the global input-output table, and identifies
countries that are central in both the backward and forward linkages (i.e.,
key buyer and key supplier), following Criscuolo and Timmis (2018a).222
Centrality computed here is not an absolute measure, but rather a relative
measure; relative to other country-industries in the network. An advantage of
this is that the centrality metric has a consistent unit of measurement over
time. However, as Criscuolo and Timmis (2018a) say, it does require care to
interpret changes in centrality over time, meaning increasing/decreasing
influence relative to others in the network. For example, increasing
centrality could, in principle, be because you are more influential in
absolute terms or because peers in the network have become less influential.
Since the key buyer can be considered important in gathering knowledge from
other countries, and the key supplier can be considered important in diffusing
knowledge to other countries, I consider that a country that has both the
characteristics is important for diffusing other countries’ technology.
Therefore, any country benefits more by trading with a high centrality country
rather than a low centrality country. Lumenga-Neso et al. (2005) show that
indirect effects are as important as direct effects in international
spillovers. Thus, I consider that the trade with hub countries, which generate
more indirect demands due to trade with several countries, will have large
spillover effects than peripheral countries. Additionally, I consider that the
importers are more likely to benefit from the spillover effect if they are in
an environment that facilitates trade with a hub country, while countries with
high technological capabilities are less susceptible to spillover effects from
abroad. However, since the hub country of this study is central in terms of
both “imports” and “exports, ” it is considered to have certain technological
capabilities.333 This is probably because high productivity is required for
exports (Bernard and Jensen, 1999; Clerides et al., 1998; Melitz, 2003).
Therefore, for the latter, trade with high centrality may generate spillover
effects.
In my empirical analysis, I examine the hypothesis using a sample of 21
countries and 14 manufacturing industries from 1995 to 2007. Following
Nishioka and Ripoll (2012), I decompose the R&D contents into domestic and
foreign. I also analyze the relationship between international R&D spillovers
and the structure of the GVCs by splitting my sample as follows. First, I
decompose the importer into two categories based on geographical and
technological aspects (All samples, European countries, and North American
countries; G5444France, Germany, Japan, the U.K, and the U.S. and non-G5
countries). Second, to explore the difference in the effects between the
exporter’s centrality, I divide the countries into three categories: high,
middle, and low. The top 33% countries are high centrality, the next top 33%
countries are middle centrality, and the rest are low centrality in each
sector in each year, respectively. Finally, I focus on the difference of
centrality in each industry, and further split exporters. Centrality is
computed as a relative value across all trades, thus, even if a country
belongs to the high centrality group, it could not be considered a hub in
overall trade. If the trade volume of the industry is small, its centrality
will naturally be small, and its importance in knowledge diffusion will be
reduced. Therefore, to distinguish, I classify the 14 industries into two
categories: “Group A” and “Group B (more centralized industry)”.
The main findings of my empirical analysis are as follows: First, the impacts
of foreign R&D contents from high centrality exporters are the highest, and
positively significant. These exporters are important as mediators in
gathering and diffusing knowledge. Second, trade with middle centrality
exporters also have significantly positive effects on domestic total factor
productivity (TFP). In particular, the increase in direct and indirect demand
from middle centrality countries since 2002 is believed to have contributed to
the results. Finally, it seems that only technologically-advanced countries
(G5) are affected by the spillover effect from own. Additionally, looking at
the share of domestic and foreign R&D contents, the share of domestic content
is much higher in the G5 countries than in the other countries. This result
suggests that the proportion of the R&D contents flowing into a country is
important for R&D spillovers.
This study proceeds as follows. In Section 2, I discuss the conventional
research and issues of the impact of international R&D spillovers. In Section
3, I explain the data, variables, and classifications that I use in the
empirical analysis. Section 4 illustrates the empirical strategy. The results
of the estimations and the robustness check are reported in Section 5. Section
6 concludes the study.

##  Literature Review

There has been a long history of study on the impact of foreign R&D on
productivity through trade. It has been studied from both theoretical and
empirical perspectives, especially in the empirical study, pioneered by Coe
and Helpman (1995) (henceforth, CH). They find that a country’s TFP depends on
its domestic R&D stock and on the R&D stock of the foreign countries. They
decipher this by using the import-weighted sums of the trade partners’
cumulative R&D expenditure. The framework for several analysis of subsequent
R&D spillover studies at country or industry levels has been estimated
according to CH’s model (e.g., Xu and Wang, 1999; Coe et al., 2009).555 Keller
(2002a, b) use Non-linear Least Squares (NLS). He examines the geographical
effect on spillovers, and the link between productivity, and domestic and
foreign R&D at the industry level, respectively. Fracasso and Vittucci
Marzetti (2015) modify Keller’s NLS model to apply threshold regression. To
answer Keller’s (1998) question, they study whether the spillovers are
relatively stronger (though not necessarily in a proportional way) where trade
relations are relatively more intense666 Acharya and Keller (2009) use value-
added as independent variable, and labor and capital as dependent variables
instead of using the TFP measure. Although there are some studies that follow
this specification (e.g., Badinger and Egger, 2016), the import share is still
used for the foreign R&D variable. To augment CH’s approach, some studies
point out that the foreign R&D variable used in a lot of studies captures only
the current-period bilateral trade, and that indirectly generated demand must
also be taken into account (e.g., Lumenga-Neso et al., 2005; Franco et al.,
2011; Nishioka and Ripoll, 2012; Poetzsch, 2017). For example, it is possible
that country A benefits from country C, D, and E’s technology without
importing from these sources, if country C, D, and E export to country B,
which, in turn, exports to country A. This analysis uses the idea of Leontief
inverse matrix to account for indirect demands, and suggests that these
indirect trade-related spillovers are as important as the direct ones. It also
strengthens the view that trade does matter for the international transmission
of R&D. Therefore, the introduction of indirect foreign R&D spillovers into
CH’s approach seems to have resolved the doubts raised by Keller (1998)
suggested the possibility that it does not matter from which a country imports
on CH’s approach.
There have been some studies on the effects of participation in the GVCs since
the development of the global input-output table (e.g., Piermartini and
Rubinova, 2014; Badinger and Egger 2016; Foster-McGregor et al., 2016; Poschl
et al., 2016; Tajoli and Felice, 2018). However, these studies (including the
above-mentioned studies) mostly investigate the overall use-driven R&D
spillover effects, and do not answer the question of which countries are
important to trade with. In other words, these studies only examine the
overall effects from abroad. In an attempt to answer this question, Keller
(2002a) investigates the degree of localization of technology, using the
distance between the G5 and other countries. He finds that for every
additional 1200-km from the G5 countries there is a 50% drop in technology
diffusion. In this study, I analyze the geographical aspect, in terms of how
the countries are connected, rather than the distance between them. A trade
structure has long been confirmed that many countries trade with the hub in
their region, and the hub trades with the hubs in other regions. Therefore, I
classify the export side by “centrality”, and understand the countries with
whom it is important to.

##  Data, Variables, and Classifications by Centrality

###  Data

This study uses data from 14 manufacturing sectors and 21 countries777 The
countries are Belgium (BEL), Canada (CAN), Czech Republic (CZE), France (FRA),
Germany (DEU), Greece (GRC), Hungary (HUN), Ireland (IRL), Italy (ITA), Japan
(JPN), Mexico (MEX), Netherlands (NLD), Poland (POL), Portugal (PRT), Romania
(ROM), Russia (RUS), Spain (ESP), Slovenia (SVN), Turkey (TUR), the United
Kingdom (GBR), and the United States of America (USA). for the years between
1995-2007 for the main analysis. This is because the business R&D data at the
industry level can be obtained only for 21 countries under the conditions of
the interpolation of unreported data.888 Data on R&D expenditures is also
available for Korea and Australia, however, I exclude them from my sample in
this analysis. Japan is included in the data set because it is a G5 country,
and its R&D expenditures are considerably high. However, Korea and Australia
are far from the other countries in the region, and their R&D expenditure is
not very high, therefore, their influence on the results is considered to be
small. In addition, these two countries are excluded from the data set because
including them in the centrality classification (see Section 4.2.3 for
details) may cause bias in the results. The global financial crisis of 2008
had a considerable impact on trade, therefore, including that year in the
analysis is likely to bias the results. However, since I cannot collect much
data after 2009, and the oldest global input-output table available dates to
1995, I test my hypothesis with data from 1995 to 2007.
Internationally comparable figures on employment, capital stocks, labor
compensation, output, and value-added on the industry level come from the WIOD
Socio Economic Accounts (WIOD SEA) for the years 1995-2007. To convert the
nominal values to the real values, I use the industry-level value-added
deflators, GDP deflators,999 I use GDP deflator for only four countries
(Ireland, Russia, Romania, and Turkey) because these countries are not
reported in the STAN database., and constant 1995 dollars at purchasing power
parity (PPP) rates. The value-added deflators and the GDP deflators are
obtained from the OECD STAN database, and the World Bank’s World Development
Indicators, respectively. Data on sample countries’ business R&D come from the
OECD ANBERD database, and the global input-output linkages data are obtained
from the WIOD for the years 1995-2007.
An advantage of using the WIOD is that it provides socio-economic accounts,
which include annual data such as employment and capital at the industry
level. The OECD-ICIO is also available as an international input-output table,
however, if this is used, it will be necessary to separately collect the
variables used in the calculation of the TFP. It will also be necessary to
convert them from nominal to real values.

###  Definition of the variables

####  3.2.1 Industry-level TFP

I follow Caves et al. (1982) for constructing the industry-level TFP indexes.
It is defined as:

$\displaystyle\ln\mathrm{TFP}_{iht}=$ $\displaystyle\Bigl{[}\ln
Y_{iht}-\frac{1}{N}\sum_{i}\ln
Y_{iht}\Bigr{]}-\frac{1}{2}\Bigl{(}\sigma_{iht}+\frac{1}{N}\sum_{i}\sigma_{iht}\Bigr{)}\Bigl{[}\ln
L_{iht}-\frac{1}{N}\sum_{i}\ln L_{iht}\Bigr{]}$
$\displaystyle-\Bigl{[}1-\frac{1}{2}\Bigl{(}\sigma_{iht}+\frac{1}{N}\sum_{i}\sigma_{iht}\Bigr{)}\Bigr{]}\Bigl{[}\ln
K_{iht}-\frac{1}{N}\sum_{i}\ln K_{iht}\Bigr{]},$

where $i$ is the country index, $h$ is the industry index, and $t$ is the time
index. $Y$ is the real value-added, $\sigma$ is the labor compensation shares,
$L$ is the total employment, $K$ is the real capital stock, and $N=21$ is the
number of countries. Following Hall (1990), I use cost-based factors for labor
shares since these are more robust than the revenue-based factor shares in the
absence of a constant return to scale. Labor compensation shares are
calculated as nominal labor compensation divided by nominal value-added.
However, some of the obtained values of the labor shares exceed one.101010
This is because the value of capital compensation is negative. To control
this, I use the smoothing procedure according to Harrigan (1997) such that the
labor shares are obtained by regressing the following equation:

$\sigma_{iht}=\alpha_{i}+\alpha_{h}+\alpha_{t}+\phi_{h}\ln(K_{iht}/L_{iht}),$

where $\alpha_{i},\alpha_{h},$, and $\alpha_{t}$ are country, industry, and
year fixed effects, respectively. I use the point estimates as the labor cost
shares and the normalization of other variables for constructing the TFP,
which should help reduce simultaneity issues (Keller 2002b).

Table 1: Summary statistics of TFP | All observations
---|---
| Obs. | Min | Max | Mean | Std. dev.
Food, Beverages, and Tobacco | 273 | -0.55 | 0.44 | -0.01 | 0.17
Textiles and Textile Products | 273 | -0.53 | 0.37 | -0.01 | 0.21
Leather, Leather and Footwear | 273 | -0.7 | 0.55 | -0.01 | 0.25
Wood and Products of Wood and Cork | 273 | -0.5 | 0.39 | -0.01 | 0.18
Pulp, Paper, Printing, and Publishing | 273 | -0.32 | 0.64 | -0.01 | 0.18
Coke, Refined Petroleum, and Nuclear Fuel | 273 | -1.88 | 0.94 | -0.02 | 0.47
Chemicals and Chemical Products | 273 | -0.56 | 0.75 | -0.01 | 0.24
Rubber and Plastics | 273 | -0.35 | 0.28 | -0.01 | 0.15
Other Non-Metallic Mineral | 273 | -0.47 | 0.24 | -0.01 | 0.14
Basic Metals and Fabricated Metal | 273 | -0.4 | 0.28 | -0.01 | 0.15
Machinery, Nec | 273 | -0.73 | 0.32 | -0.01 | 0.23
Electrical and Optical Equipment | 273 | -0.58 | 0.58 | -0.01 | 0.2
Transport Equipment | 273 | -0.47 | 0.33 | -0.01 | 0.18
Manufacturing, Nec; Recycling | 273 | -0.38 | 0.52 | -0.01 | 0.16
Note : Author’s calculation. This table is constructed using all observations. |

Table 1 reports, for each industry, the summary statistics for the TFP for all
the observations and the growth rate obtained by dividing the value for 2007
by the value for 1995. Across all the samples, the mean is almost the same for
all the industries, except for “Coke, Refined Petroleum, and Nuclear Fuel”
where the maximum value is higher than the others while the minimum value is
much smaller, indicating that there is a large difference in the technical
competence in that industry.

####  3.2.2 Industry-level R&D stocks

Next, I explain the computation of domestic R&D stock. In this study, I use
only the manufacturing R&D, and I set non-manufacturing R&D as zero.111111
Non-manufacturing sectors’ R&D are quite noisy, and there are a lot of
unreported values. The domestic R&D stock $S_{iht}$ for industry $h$ in the
country $i$ at the time $t$ is computed using the perpetual inventory methods
as follows:

$S_{iht}=(1-\delta)S_{ih,t-1}+R_{iht},$

where $\delta$ is the depreciation rate of knowledge obsolescence, assumed to
be 0.15 following Coe and Helpman (1995), and $R_{iht}$ is the real business
R&D expenditure. To obtain the initial value of the real business R&D stock, I
compute:

$S_{ih0}=\frac{R_{ih0}}{\delta+g_{ih}},$

where $g_{ih}$ is the annual average logarithmic growth rate of real business
R&D expenditures for industry $h$ in the country $i$ for the entire period for
which data are available. Real business R&D expenditures are obtained from the
OECD ANBERD database; however, the values are deflated by country-level GDP
deflators. To reduce the possibility of results being induced by common
deflators, I use the value-added deflators at the industry level reported in
the STAN database.
Using domestic R&D stock and the WIOD, I calculate the R&D contents of the
final goods in equation (1) for 40 countries and RoW.121212 The other
countries, in addition to the previously-mentioned 21 countries, were
Australia (AUS), Austria (AUT), Bulgaria (BGR), Brazil (BRA), China (CHN),
Cyprus (CYP), Denmark (DNK), Estonia (EST), Finland (FIN), India (IND),
Indonesia (IDN), Korea (KOR), Latvia (LVA), Lithuania (LTU), Luxembourg (LUX),
Malta (MLT), Slovakia (SVK), Sweden (SWE), and Taiwan (TWN)  After
calculation, I selected the 21 countries since I could not obtain the domestic
R&D contents for the other countries.

####  3.2.3 The R&D contents of the final goods

Following Nishioka and Ripoll (2012), I introduce the R&D content of the
“final goods,” which focuses on the R&D embodied in trade volume, and
considers both direct and indirect input flows. I first explain the definition
of R&D contents for the “intermediates” used, and proceed to show how to
change it to the final goods.
Nishiokan and Ripoll (2012) follow Trefler and Zhu (2010), and use a diagonal
matrix, $Q$, of dimension $NG\times NG$ where the element $Q_{i}(h)$ is the
amount of industry $h$’s output in the country $i$. They also use a global
intermediate input coefficients matrix, $B$, of dimension $NG\times NG$ where
the element $B_{ji}(g,h)$ is the amount of intermediate input $g$ made in the
country $j$ to produce one unit of gross output of country $i$’s good $h$. If
$a_{ji}(g,h)$ is the value of goods shipped from industry $g$ in country $j$
for intermediate use by industry $h$ in country $i$, $B_{ji}(g,h)$ is
calculated by $a_{ji}(g,h)/Q_{i}(h)$. Now consider the demand of intermediate
inputs, including indirect effects, using these matrixes. Let $Z_{i}$ be a
$NG\times 1$ vector with the $i$th element representing global consumption of
goods from country $i$, while all the remaining elements are zero. The
production of $Z_{i}$ requires intermediate inputs given by $BZ_{i}$. Further,
since the production of these intermediate inputs requires the use of other
intermediate inputs given by $B^{2}Z_{i}$, if I consider it as a recursive
algorithm, the matrix of intermediate inputs, directly and indirectly,
required for the production of $Z_{i}$ is given by
$\sum_{n=1}^{\infty}B^{n}Z_{i}$. Thus, the total requirements needed to
deliver $Z_{i}$ is given by

$Z_{i}+\sum_{n=1}^{\infty}B^{n}Z_{i}=\sum_{n=0}^{\infty}B^{n}Z_{i}=(I-B)^{-1}Z_{i},$

where $I$ is the identity matrix, and $(I-B)^{-1}$ is known as the Leontief
inverse matrix. This equation allows me to calculate the direct and indirect
effects on the demand for intermediate goods. Nishioka and Ripoll (2012) use
$BQ$ instead of $Z_{i}$ in their analysis. Next, let $S_{j}$ be a $1\times G$
vector whose $g$th element is the real business R&D stock to produce $g$ in
country $j$, and let $D_{j}$ be a $1\times G$ vector whose $g$th element is
the ratio of the R&D stock to good $g$ in country $j$. Thus, the direct R&D
requirements are defined as $D_{j}Q_{j}=S_{j}$. Nishioka and Ripoll (2012)
define the R&D content of intermediate inputs $F$ as:

$F=D(I-B)^{-1}BQ.$

They also define $(I-B)^{-1}B=A$, and select the elements of $D$ and $A$ for
capturing the various effects. For example, to calculate the total (domestic
and foreign) effects of trading with the same industries, I compute
$\sum_{j}D_{j}(h)A_{ji}(h,h)Q_{i}(h)$, and if the trades are between different
industries, I calculate $\sum_{j}\sum_{g\neq h}D_{j}(g)A_{ji}(g,h)Q_{i}(h)$.
Using these disaggregations, they analyze similar investigation as Keller
(2002b) in the years 1995, 2000, and 2005. They find that the R&D knowledge
spillovers through trade in intermediate inputs are only among high R&D
industries, and it is statistically significant for trade between the same
industries, however, it is insignificant for trade between different
industries. Thus, their results suggest that the effects of R&D on
productivity with intermediate trade are limited, and these points are
different from Keller’s (2002b).
In this study, I modify their model. Although Nishioka and Ripoll (2012) use
the intermediate goods matrix ($BQ$) for $Z_{i}$, the methodology of Trefler
and Zhu (2010) correspond to the equilibrium output model in the input-output
analysis. Therefore, the final demand matrix should be used for $Z_{i}$. In
the first place, the number of columns is different between the two ($BQ$ and
$Z_{i}$). Therefore, I use the final demand and calculate the R&D contents
embodied in the final demand in my analysis.
To reconstruct the R&D content of the final goods, I use a diagonal matrix of
the sum of exports to global final demand of country $j$, $f_{j}$, of
dimension $G\times G$:

$f\equiv\left[\begin{array}[]{cccc}f_{1}&0&\ldots&0\\\ 0&f_{2}&\ldots&0\\\
\vdots&\vdots&\ddots&\vdots\\\ 0&0&\ldots&f_{N}\end{array}\right].$

Thus, the R&D content of the final goods for the final demand is defined as
follows:

$\displaystyle V=D(I-B)^{-1}f.$ (1)

###  Classifications by Centrality

####  3.3.1 Centrality in production networks

The concept of centrality is originally used in sociology, and various
centrality measures have been used to capture a person’s centrality, power,
prestige, and influence. Among several measures of centrality, those used to
identify the influence of individuals within an organization are called the
“Degree centrality” and the “Eigenvector centrality,” as defined by Bonacich
(1972), and the “Katz-Bonacich eigenvector centrality,” as defined by Katz
(1953) and Bonacich (1987). In these measures, high centrality indicates that
a person is important to the organization. These centrality measures have been
used in sociology to identify individuals who have a significant influence on
their surroundings within organizations.131313 For example, Alatas et al.
(2016) examine the influence of network structure on information aggregation,
using the social structure of Indonesian villages, and find that the presence
of central households with an easy access to information and connections with
others play an important role in increasing the efficiency of knowledge
diffusion. Additionally, Acemoglu et al. (2014) show that overall learning
efficiency is achieved by the presence of a person who is the hub of the
information.
Using this idea, a similar analysis can be performed for economics by
regarding the organization as a production network in economic activity, and
the individuals as firms, industries, or countries. In fact, the existence of
hubs in production network is also confirmed through data141414 Bernard et al.
(2007) identified the existence of hubs at the firm level, using customs data,
and Criscuolo and Timmis (2018a) identified the same at the industry and
country level, using global input-output table., and research regarding the
importance of hubs has also been conducted, using these centrality measure.
For example, the study of propagation of shocks in macroeconomics used the
idea of centrality (Acemoglu et al., 2012; Carvalho, 2014; Acemoglu et al.,
2016; Boehm et al., 2019; Carvalho et al., 2021). These studies used firm-
level data. However, Criscuolo and Timmis (2018a) used the global input-output
table to conduct macro-level analysis. They examined the change of centrality
in a country and an industry both in backward and forward linkages. They found
that in 1995, a small number of central hubs, such as Japan, Germany, and the
United States, dominated each regional value chain, and that in 2011, the
central hub of Asia changed from Japan to China. In addition, Criscuolo and
Timmis (2018b) examined the effects of the changes in the GVC structures on
firm productivity, taking into account centrality in production networks. They
found that increasing centrality was important for improving the productivity
of smaller or non-frontier firms, and this trend has been witnessed post-2004
in firms in the EU-member or small countries.
I have discussed the importance of the presence of central countries,
industries, and firms in a production network. However, there is no study on
the existence of hubs for the diffusion of knowledge through trade. Currently,
most research are regarding the propagation of shocks. Previous studies of
international R&D spillover effects have focused on direct and indirect
relationships, however, no analysis has as yet incorporated the idea of
centrality into their study.

Figure 1: Overview of trade network

I consider that the central countries in GVCs are connected to various
countries and, thus, are important as mediators in gathering the technologies
in trade from other countries. For example, Figure 1 shows an overview of an
industry in Country B2 that imports the final goods from Country B1. Country
B1 imports intermediate goods not only from the same region, but also from
other regions. The hubs in other regions (Country A1 and Country C1) also
import intermediate goods from those regions, and export to Country B1.
Therefore, the sector in Country B2 receives the knowledge of the countries in
other regions via the hub sector, Country B1, in the same region. In other
words, I consider that the central countries in the GVCs have large spillovers
in the surrounding countries through large indirect demands. Figure 1 shows
the effect of the countries that are central to the “imports,” however, I am
interested in the spillover effects of the countries that are also central to
knowledge diffusion, or “exports.” By estimating the effects of the countries
that are central to both imports and exports, I confirm the effect of
knowledge gathering, and the extent of its diffusion. Therefore, in the next
subsection, I identify the centrality of the countries and the industries,
using the centrality measure.

####  3.3.2 Centrality Measures

In this study, I use the Katz-Bonacich eigenvector centrality.151515This
measure has been widely used in literature refarding the propagation of
shocks. This measure can rank the influence of each node to evaluate its
importance in more detail. For example, Figure 1 shows that a simple
production network and the size of each node denotes centrality. It is worth
noting here that A has the highest centrality, not C. B and C exist as a hub
for G and H, and D, E, and F, respectively, and A exists as a hub that
connects B and C. In the Katz-Bonacich eigenvector centrality, it is important
whether a shock is likely to propagate significantly across the whole, not
simply the number of connections with others.

Figure 2: Katz-Bonacich eigenvector centrality

Source: Criscuolo and Timmis(2018a)
Note: The size of each node denotes centrality. This measure of centrality
represents a node as a central hub if it can easily influence the whole. Thus,
A, the hub of B and C, is the central hub.

As discussed above, other metrics, i.e, “degree centrality” and “eigenvector
centrality” are popular in sociology, however, there are reasons why they are
not suitable for this study. First, the degree centrality is defined as the
sum of the number of outdegree or indegree,161616 Outdegree represents the
edges directed out from a vertex in a network, while indegree represents the
edges directed toward a vertex. In trade, we can think of the vertex as a
country or an industry. however, it captures only direct connections. This
measure results in several industries with the same centrality in trade,
making it difficult to group them by the degree of their centrality. Second,
although the eigenvector centrality captures both direct and indirect effects,
however, if either the number of outdegree or indegree is zero, then the
centrality becomes zero. In trade, since several industries only import or
export,171717 This problem is seen in all sectors: agriculture, manufacturing,
and services. this measure is not suitable for this analysis.
On the other hand, the Katz-Bonacich eigenvector centrality solves the above-
mentioned problems. However, this measure denotes the nodes that trade more
with the central node also as important nodes, even if the total trade value
of the node is smaller than the others. Nevertheless, this is not a concern in
this analysis because those nodes (i.e., countries or industries) can be
considered important transmitters of the central node’s knowledge.
By using the world input-output table, I compute the centrality of each sector
in each country. It is important to note that a centrality obtained by
calculation does not represent centrality within the same industry alone, but
rather all the other industries. Furthermore, since the effects on
productivity of trading with central industries in exports and imports,
respectively, are likely to be different, I distinguish between forward
linkages and backward linkages in my analysis. Following Criscuolo and Timmis
(2018a), I calculate forward ($\mathrm{Centrality}_{iht}^{fwd}$) and backward
($\mathrm{Centrality}_{iht}^{back}$) centrality that are defined as:

$\displaystyle\mathrm{Centrality}_{iht}^{fwd}$ $\displaystyle=$
$\displaystyle\eta(\mathbf{I}-\lambda\mathbf{W})^{-1}\mathbf{1},$
$\displaystyle\mathrm{Centrality}_{iht}^{back}$ $\displaystyle=$
$\displaystyle\eta(\mathbf{I}-\lambda\mathbf{W^{\top}})^{-1}\mathbf{1},$

where $W$ represents input-output linkages matrix, and $\eta=1-\lambda$ is the
baseline centrality level. The parameter, $\lambda$, reflects the average
share of intermediate inputs in production, as shown theoretically by Acemoglu
et al. (2012) and Carvalho (2014). I use $\lambda=0.5$. When I calculate
forward and backward centrality, I assume $\sum_{i}w_{ji}=1$ and
$\sum_{j}w_{ji}=1$, respectively. If $a_{ji}(g,h)$ is the value of goods
shipped from sector $g$ in country $j$ for intermediate use by sector $h$ in
country $i$, the elements of matrix $W$ are defined as
$w_{ji}(g,h)=a_{ji}(g,h)/\sum_{i}a_{ji}(g,h)$ in forward linkages, while
$w_{ji}(g,h)=a_{ji}(g,h)/\sum_{j}a_{ji}(g,h)$ in backward linkages.
There are two things to note in the measurement of centrality used in this
study. First, when I calculate centrality, I exclude RoW in the WIOD (i.e., I
use 40 countries). The Katz-Bonacich eigenvector centrality reflects that
nodes with relationships with larger nodes are also large. Since the RoW is a
collection of various countries, it can be a large node. Therefore, due to the
existence of a huge node called RoW, the centrality of the other countries may
not be reflected well. For example, even if a country is not central by
nature, but conducts a lot of trade with the RoW, its centrality will
increase. Second, I also exclude the internal transactions in a country from
the input-output table. In this study, I aim to investigate the impact of the
industries that are in important positions of the GVCs. If I include the
internal transactions of a country in the calculation, a country’s centrality
in the GVCs will be higher if the internal transactions are considerably more
active than those with the other countries. However, the high centrality
industries are not considered important in the GVCs, and it deviates from the
objective of this study. Thus, I exclude the internal transactions from the
input-output table. These notations indicate that the higher the value of the
forward centrality, the greater the supply of the industry to similar and
other industries in trade. Additionally, the higher the value of the backward
centrality, the greater the demand from the industry from similar and other
industries in trade. Therefore, it can be said that industries with high
centrality exist as the hubs in trade. Under these notations, after the
calculation of centrality for 40 countries, I selected 21 countries.
Table 2 displays the summary statistics for backward and forward centrality
for each industry in 21 countries. Table 2 shows that the maximum value of
centrality is so difference among industries. As discussed above, the degree
of centrality represents the importance in trade. For example, the maximum
value of backward centrality for Transport Equipment is 11.26, which is quite
high, and the country with this centrality imports from many countries and
industries when the final demand per unit occurs. The maximum value of forward
centrality for Chemicals and Chemical products is also quite high at 18.77.
The country with this centrality supplies the most when the final demand for
each industry occurs. For industries with small maximum values, the values of
centrality of industries are generally small, indicating that they are not
important in trade. On the other hand, for industries with large maximum
values, it is considered that there are countries that are hubs in trade,
i.e., countries with high centrality, such as Transport Equipment and
Chemicals and Chemical products. The maximum values of forward centrality
within industry are larger than that of backward centrality, but this may be
because exports are concentrated in some countries because exports have higher
hurdles than imports (Bernard and Jensen, 1999; Clerides et al., 1998; Melitz,
2003; Helpman et al, 2004).

Table 2: Summary statistics of backward and forward centrality | Backward centrality | Forward centrality
---|---|---
| Obs. | Min | Max | Mean | Std. dev | Obs. | Min | Max | Mean | Std. dev
Food, Beverages, and Tobacco | 273 | 0.59 | 5.13 | 1.89 | 1.13 | 273 | 0.51 | 2.21 | 0.89 | 0.48
Textiles and Textile Products | 273 | 0.55 | 3.15 | 1.16 | 0.62 | 273 | 0.51 | 4.60 | 1.22 | 0.87
Leather, Leather and Footwear | 273 | 0.51 | 2.41 | 0.74 | 0.34 | 273 | 0.51 | 2.55 | 0.69 | 0.40
Wood and Products of Wood and Cork | 273 | 0.53 | 1.84 | 0.79 | 0.32 | 273 | 0.52 | 2.25 | 0.86 | 0.37
Pulp, Paper, Printing, and Publishing | 273 | 0.56 | 3.97 | 1.21 | 0.76 | 273 | 0.52 | 6.02 | 1.58 | 1.33
Coke, Refined Petroleum, and Nuclear Fuel | 273 | 0.51 | 2.00 | 0.86 | 0.35 | 273 | 0.52 | 5.70 | 1.34 | 1.04
Chemicals and Chemical Products | 273 | 0.57 | 4.97 | 1.46 | 1.02 | 273 | 0.64 | 18.77 | 4.14 | 4.16
Rubber and Plastics | 273 | 0.55 | 2.32 | 0.88 | 0.41 | 273 | 0.51 | 3.16 | 1.28 | 0.72
Other Non-Metallic Mineral | 273 | 0.53 | 2.11 | 0.81 | 0.29 | 273 | 0.52 | 2.10 | 0.87 | 0.40
Basic Metals and Fabricated Metal | 273 | 0.59 | 5.57 | 1.54 | 1.10 | 273 | 0.61 | 12.9 | 2.77 | 2.46
Machinery, Nec | 273 | 0.56 | 5.37 | 1.25 | 1.03 | 273 | 0.55 | 8.97 | 1.86 | 1.96
Electrical and Optical Equipment | 273 | 0.56 | 5.19 | 1.58 | 1.15 | 273 | 0.50 | 12.6 | 2.86 | 3.06
Transport Equipment | 273 | 0.54 | 11.26 | 2.42 | 2.49 | 273 | 0.50 | 10.07 | 2.14 | 2.22
Manufacturing, Nec; Recycling | 273 | 0.53 | 2.55 | 0.96 | 0.47 | 273 | 0.51 | 2.06 | 0.82 | 0.35
Note : Author’s calculation. This table is constructed using all observations. |  |  |  |  |  |

####  3.3.3 Classification of exporters

To explore which country has the high centrality, I divided the industries
into three categories: high, middle, and low. I defined the top 33% as high
centrality, the next top 33% as middle centrality, and the remaining as low
centrality in each sector, in each year, respectively.
In this study, I am interested in countries that have both a “gathering” and
“diffusing” nature of knowledge, therefore, I further classify the sample
countries by total centrality that was defined by using both backward and
forward centrality. Countries that are “high” in both backward and forward
linkages are considered “High”, those that are “low” in both are considered
“Low”, and the remaining are categorized as “Middle. ”181818 Although
Criscuolo and Timmis (2018a) define total centrality as the average of the
backward and forward centrality, I categorize the countries in this way
because only one of them may have a large value, and even if the total
centrality is large, it may not necessarily have the properties of both
knowledge aggregation and diffusion.191919 There are a total of seven
combinations of Middle: high (in backward)-middle (in forward); high-low;
middle-high; middle-middle; middle-low; low-high; low-middle. High, Middle,
and Low account for about 27%, 47%, and 26% of the total, respectively.202020
In Middle’s seven categories, high-middle accounts for 11.4%, high-low for
1.8%, middle-high for 12.6%, middle-middle for 45.9%, middle-low for 13.2%,
low-high for 0.7%, and low-middle for 14.4%, on an average, from 1995 to 2007.
I divide a country into which classification it belongs in each industry, but
also divide the industry itself into two groups. This is because, as Table 2
shows, there is a clear difference in the maximum value of centrality across
industries. For example, the maximum value for “Wood and Products of Wood and
Cork” is 1.84 and 2.25 in backward and forward linkages, respectively, while
for “Transport equipment” it is 11.26 and 10.07, respectively. Since,
centrality is computed as a relative value across all the trade, therefore,
even if a country is defined as a high group in the “Wood and Products of Wood
and Cork” category, it cannot be called a hub in the overall trade. Based on
this, I classify the top seven industries with maximum values of centrality as
“Group B”, and the rest as “Group A”.

##  Empirical Strategy

###  Basic model

Following Nishioka and Ripoll (2012), the benchmark model used in the
literature to investigate the spillover effects of R&D on industry
productivity through trade in the final goods is:

$\displaystyle\ln\mathrm{TFP}_{iht}=\alpha_{ih}+\alpha_{t}+\beta\ln
V_{iht}+\epsilon_{iht},$ (2)

where indexes $i$, $h$, and $t$ denote country, industry, and year,
respectively. $\mathrm{TFP}_{iht}$ measures the productivity of country $i$ in
industry $h$ in the year $t$. $\alpha_{ih}$ and $\alpha_{t}$ are country-
industry and time-fixed effects, respectively. $V$ is the R&D content of the
final goods in the for final demand, and this is defined in equation (1).
$\epsilon_{iht}$ is the error term. In this equation, I use the R&D content of
the final goods, $V$, instead of $F$, as defined by Nishioka and Ripoll
(2012). Following Bertrand et al. (2004), I address the potential serial
correlation and heteroskedasticity issues by calculating the standard errors
clustered at the industry level. I avoid the simultaneity issues in two ways.
First, I employ the TFP index of Caves et al. (1982). Although this method
requires more variables, and is more difficult to construct than the method of
Coe and Helpman (1995) and Coe et al. (2009), it reduces the simultaneity
problems. Second, I use industry-specific value-added deflators for almost all
the countries. The real R&D expenditures reported in the OECD ANBERD are
deflated by the GDP deflators, however, the impact of the common deflator is
reduced by using industry-level value-added deflators.
The analysis in this study deepens the study of the effects of R&D on
productivity through trade by incorporating data that was excluded from
previous studies, and by considering new ideas of centrality that further
elucidate the structure of the GVCs.

###  Model with classification by centrality

In the empirical analysis, I decompose equation (2) into domestic and foreign
R&D inputs, and analyze the spillover effects from foreign R&D contents,
including centrality.
First, I use the two industry groups, and the three categories (High, Middle,
and Low) for centrality, as described above, to investigate whether the
centrality of the exporting country affects the spillover effects, both in
more centralized industries and others. Since countries with high centrality
have strong relationships with various countries, they are expected to produce
larger effects than countries with middle or low centrality. I also focus on
the importing country’s region in this analysis. This is because there are
more hubs in Europe than in the other regions, and European countries are more
likely to be involved with other hub countries, therefore, a larger effect is
expected. To observe this effect, I divided the sample on the import side into
three regions: All (ALL), Europe (EUR), and North America (NA).212121 I don’t
separate sample in Asia because Japan is the only Asian country in my sample.
For the importers to I make ALL, EUR, and NA sets of all the sampled
countries, only European countries in the sample, and only North American
countries in the sample, respectively, and make A and B sets of Group A and
Group B, respectively. For the exporters, I also make High, Middle, and Low
sets of industries included in the High, Middle, and Low centrality
categories, respectively. I estimate the following specifications:

$\displaystyle\ln\mathrm{TFP}_{iht}=\>\>$
$\displaystyle\alpha_{ih}+\alpha_{t}+\beta\ln\Bigl{[}\sum_{g}D_{it}(g)T_{iit}(g,h)\Bigr{]}$
$\displaystyle+\rho_{1}\ln\Bigl{[}\sum_{j\neq
i,i\in\mathrm{ALL}\;\mathrm{or}\;\mathrm{EUR}\;\mathrm{or}\;\mathrm{NA},\;j\in\rm{High}}\sum_{\;g\in\;\mathrm{A}\;\mathrm{or}\;\mathrm{B}}D_{jt}(g)T_{jit}(g,h)\Bigr{]}$
$\displaystyle+\rho_{2}\ln\Bigl{[}\sum_{j\neq
i,i\in\mathrm{ALL}\;\mathrm{or}\;\mathrm{EUR}\;\mathrm{or}\;\mathrm{NA},\;j\in\rm{Middle}}\sum_{\;g\in\;\mathrm{A}\;\mathrm{or}\;\mathrm{B}}D_{jt}(g)T_{jit}(g,h)\Bigr{]}$
$\displaystyle+\rho_{3}\ln\Bigl{[}\sum_{j\neq
i,i\in\mathrm{ALL}\;\mathrm{or}\;\mathrm{EUR}\;\mathrm{or}\;\mathrm{NA},\;j\in\rm{Low}}\sum_{\;g\in\;\mathrm{A}\;\mathrm{or}\;\mathrm{B}}D_{jt}(g)T_{jit}(g,h)\Bigr{]}+\epsilon_{iht},$
(3)

where the first term in brackets ($\beta$) captures the effect of domestic R&D
contents, and the second to fourth terms
($\rho_{1},\>\rho_{2},\>\mathrm{and}\>\rho_{3}$) capture the effect of the
foreign R&D contents. Additionally, $j$ and $g$ are subscripts, indicating the
exporter.

###  Comparison of the effects between G5 and non-G5 countries

Next, I estimate the effect, which classifies importers on technological
aspects instead of geographical aspects, like equation (3). I categorize
importers into G5 and non-G5. The share of domestic and foreign R&D contents
in all the sample countries indicates that there is a large difference between
G5 and non-G5. For example, the share of domestic R&D contents in Japan is
about 96-97.5%, the United States is about 92-93%, and Germany, France, and
the U.K. are about 70-80%. The share of foreign R&D contents in Germany,
France, and the U.K. is relatively high compared to Japan and the United
States, probably because they are in the EU. Nevertheless, the gap with non-G5
countries is large. Therefore, as an assumption, it is expected to be affected
from within in the case of high technology countries. I estimate the
specification as follows:

$\displaystyle\ln\mathrm{TFP}_{iht}=\>\>$
$\displaystyle\alpha_{ih}+\alpha_{t}+\beta\ln\Bigl{[}\sum_{g}D_{it}(g)T_{iit}(g,h)\Bigr{]}$
$\displaystyle+\upsilon_{1}\ln\Bigl{[}\sum_{j\neq
i,i\in\mathrm{G5}\;\mathrm{or}\;\mathrm{nonG5},\;j\in\rm{High}}\sum_{\;g\in\mathrm{A}\;\mathrm{or}\;\mathrm{B}}D_{jt}(g)T_{jit}(g,h)\Bigr{]}$
$\displaystyle+\upsilon_{2}\ln\Bigl{[}\sum_{j\neq
i,i\in\mathrm{G5}\;\mathrm{or}\;\mathrm{nonG5},\;j\in\rm{Middle}}\sum_{\;g\in\mathrm{A}\;\mathrm{or}\;\mathrm{B}}D_{jt}(g)T_{jit}(g,h)\Bigr{]}$
$\displaystyle+\upsilon_{3}\ln\Bigl{[}\sum_{j\neq
i,i\in\mathrm{G5}\;\mathrm{or}\;\mathrm{nonG5},\;j\in\rm{Low}}\sum_{\;g\in\mathrm{A}\;\mathrm{or}\;\mathrm{B}}D_{jt}(g)T_{jit}(g,h)\Bigr{]}+\epsilon_{iht}.$
(4)

##  Estimation Results

###  Main results

In this part, I explain the results of estimating equation (3), which
classifies importers on geographical aspects, and considers the scale of the
industries and exporters’ centrality in trade.

Table 3: The results of exporters’ centrality effects

| Group A | Group B
---|---|---
| (1) | (2) | (3) | (4) | (5) | (6)
| All | Europe | North America | All | Europe | North America
domestic, $\beta$ | -0.019 | -0.028 | $0.045^{**}$ | -0.025 | -0.032 | $0.045^{**}$
| (0.015) | (0.019) | (0.023) | (0.015) | (0.020) | (0.021)
exporter’s |  |  |  |  |  |
centrality: |  |  |  |  |  |
High, $\rho_{1}$ | $0.027^{*}$ | 0.014 | 0.014 | $0.040^{**}$ | $0.063^{***}$ | 0.013
| (0.015) | (0.021) | (0.028) | (0.019) | (0.019) | (0.054)
Middle, $\rho_{2}$ | 0.027 | 0.050 | -0.031 | $0.034^{**}$ | $0.036^{**}$ | -0.061
| (0.019) | (0.028) | (0.028) | (0.014) | (0.015) | (0.040)
Low, $\rho_{3}$ | 0.015 | 0.010 | 0.004 | $0.015^{*}$ | 0.008 | -0.003
| (0.012) | (0.016) | (0.017) | (0.008) | (0.011) | (0.025)
$\mathrm{constant}$ | 0.105 | 0.132 | -0.134 | -$0.110^{*}$ | -$0.150^{*}$ | -0.009
| (0.096) | (0.123) | (0.159) | (0.061) | (0.070) | (0.241)
$N$ | 3819 | 3091 | 546 | 3819 | 3091 | 546
$R^{2}$ | 0.867 | 0.855 | 0.957 | 0.870 | 0.860 | 0.958
Country- |  |  |  |  |  |
Industry FE | Yes | Yes | Yes | Yes | Yes | Yes
Year FE | Yes | Yes | Yes | Yes | Yes | Yes

2121footnotetext: Note: This table shows the results for using the
classification of centrality and the two industry groups ”All” includes 21
countries. Standard errors in parentheses, * $p<0.1$, ** $p<0.05$, ***
$p<0.01$

Columns (1) to (3) in Table 3 show the results for Group A, an industry with
relatively low centrality, and columns (4) to (6) show the results for Group
B, an industry with relatively high centrality. First, Table 3 shows that
industries in Group A are hardly statistically significant. This is probably
because these industries are less important and less active in trade,
therefore, less susceptible to foreign influences. Second, in Group B for All
and Europe, the impact of foreign R&D contents from high centrality exporters
is positively significant, and the largest. That is, trade with countries with
high centrality generates the largest spillovers. Since these countries are
defined as central to both imports and exports, the results suggest that they
are mediators of knowledge gathering and diffusion. Third, the results show
that countries with middle centrality are also important in the spillover
effect. This result is discussed in detail in Section 5.3 (Discussion) and
Appendix. Finally, in contrast to the other country groups, the result is
positively significant for domestic R&D contents in North America.

###  Difference in the results between G5 and non-G5 countries

In the previous subsection, Table 3 showed that the results for All samples
and European countries were consistent with the hypothesis, while only North
American countries obtained spillover effects from domestic R&D contents.
However, since North America has only three countries, it may strongly reflect
the influence of the U.S., an economic superpower. Next, I describe the
results of estimating equation (4), which classifies importers on
technological aspects instead of geographical aspects, like equation (3).

Table 4: G5 and non-G5 results

| Group A | Group B
---|---|---
| (1) | (2) | (3) | (4)
| G5 | Non-G5 | G5 | Non-G5
domestic, $\beta$ | $0.102^{**}$ | -0.021 | $0.095^{***}$ | -$0.029^{*}$
| (0.043) | (0.015) | (0.036) | (0.016)
exporter’s |  |  |  |
centrality: |  |  |  |
High, $\upsilon_{1}$ | -0.019 | 0.029 | $0.058^{**}$ | $0.060^{**}$
| (0.023) | (0.021) | (0.021) | (0.020)
Middle, $\upsilon_{2}$ | 0.021 | 0.033 | -0.013 | $0.039^{**}$
| (0.023) | (0.026) | (0.020) | (0.018)
Low, $\upsilon_{3}$ | -0.035 | 0.011 | -$0.039^{*}$ | 0.001
| (0.026) | (0.015) | (0.023) | (0.009)
$\mathrm{constant}$ | -$0.755^{**}$ | 0.076 | -$0.789^{***}$ | -$0.231^{***}$
| (0.350) | (0.110) | (0.295) | (0.067)
$N$ | 910 | 2909 | 910 | 2909
$R^{2}$ | 0.910 | 0.860 | 0.909 | 0.866
Country- |  |  |  |
Industry FE | Yes | Yes | Yes | Yes
Year FE | Yes | Yes | Yes | Yes

2121footnotetext: Note : This table shows the effects, which classifies
importers on technological aspects: G5 and Non-G5. Group A is the worst seven
of the 14 manufacturing industries in terms of the MAX value of centrality.
Group B is the other 7. Standard errors in parentheses, * $p<0.1$, **
$p<0.05$, *** $p<0.01$

The results are reported in Table 4. The results for non-G5 countries are
similar to those for Europe. The effect from high centrality countries is the
highest, and the effect from middle centrality countries is also significant.
On the other hand, G5 countries are positively significantly affected by the
R&D contents from their home countries. It is confirmed that the effect from
the domestic R&D contents is not the nature of North America, but the nature
of G5 countries with high technological capabilities. The results are
generally consistent with the assumption, however the international spillover
effects from high centrality countries are also observed in G5. Therefore, a
country with high technological capability will benefit from the spillover
effects if the trading country too has some extent of high level of
technological. In addition, there is no common significant effects in Group
A’s industries between G5 and non-G5 countries.

###  Discussion

Based on the results (Table 3 and 4), I discuss the relationship between the
spillover effects and centrality. In regards with the scale of the industries
and exporters’ centrality, the results in Table 3 show that there is a large
difference in the international spillover effects between two group
industries. First, in relatively low centrality industries (Group A), there
are statistically insignificant effects from the foreign R&D contents across
all the classifications. Second, in more centralized industries (Group B),
European countries have strong significance effects from exporters with high
centrality because many countries participate in the EU, making it easy to
trade within the EU, and the large number of hubs make trade more active.
Further, I find that it is significant in countries with middle centrality as
well. In Appendix, I further investigate the significance of Middle. I find
that the demand from countries with middle centrality is on the rise, with a
large increase in 2002 (Figure 3). In fact, the interaction term of the Middle
centrality classification, with the dummy variable equal to 1, is positively
significant after 2002 (Table 8). Specifically, the effects of the Middle
categorization suggest that countries with middle centrality in imports and
high centrality in exports are important (Figure 4), and there is a growing
presence of mediators in trade. Finally, only North America shows different
results in Table 3 that I further investigate. Instead of classifying the
importers by geography, I now classify them by technology, i.e., G5 and
non-G5. It turns out that G5 countries are positively significantly affected
by R&D contents from their home countries. The international spillover from
countries with high centrality is also observed in G5 (Table 4).
In the next section, I conduct robustness checks for the results in Table 4,
and explain the method and results of the robustness checks.

###  Robustness checks

In this section, I conduct two robustness checks for the results reported in
Table 3. First, I use the other classification of centrality to show that the
results do not vary with the centrality classification used in this study.
Second, I use one-year lagged explanatory variables for capturing the effects
that are not reflected immediately after the trade.
In the analysis, since I use the classification of centrality categorized at a
rate of 33%, and examine the effects of each, I classify the centrality in the
other classification, and investigate if the same results can be obtained. I
define the top five countries as high centrality, the next top five countries
as middle centrality, and the remaining countries as low centrality.

Table 5: Other centrality classification results

| Group A | Group B
---|---|---
| (1) | (2) | (3) | (4) | (5) | (6)
| All | Europe | North America | All | Europe | North America
domestic | -0.023 | -0.027 | $0.052^{**}$ | $-0.026^{*}$ | -0.033 | $0.033^{**}$
| (0.014) | (0.018) | (0.024) | (0.014) | (0.020) | (0.015)
exporter’s |  |  |  |  |  |
centrality: |  |  |  |  |  |
High | 0.006 | 0.024 | -0.055 | $0.037^{**}$ | $0.061^{**}$ | -0.066
| (0.012) | (0.021) | (0.047) | (0.016) | (0.020) | (0.058)
Middle | 0.041 | 0.070 | $0.042^{*}$ | $0.028^{*}$ | $0.030^{*}$ | -0.031
| (0.033) | (0.060) | (0.024) | (0.015) | (0.016) | (0.033)
Low | 0.025 | 0.026 | -0.001 | 0.016 | 0.008 | 0.072
| (0.017) | (0.025) | (0.020) | (0.014) | (0.014) | (0.043)
$\mathrm{constant}$ | 0.124 | 0.142 | -0.168 | -$0.133^{**}$ | -$0.179^{**}$ | 0.258
| (0.080) | (0.101) | (0.145) | (0.060) | (0.065) | (0.179)
$N$ | 3819 | 3091 | 546 | 3819 | 3091 | 546
$R^{2}$ | 0.868 | 0.856 | 0.954 | 0.870 | 0.859 | 0.959
Country- |  |  |  |  |  |
Industry FE | Yes | Yes | Yes | Yes | Yes | Yes
Year FE | Yes | Yes | Yes | Yes | Yes | Yes

2121footnotetext: Standard errors in parentheses, * $p<0.1$, ** $p<0.05$, ***
$p<0.01$

The results are reported in Table 5, and show that the significance is almost
the same. Only the significance of exporters with high forward centrality
disappears in G5, but the other significances remain. Therefore, I find that
changing the classification of centrality does not affect the results.
Next, the technology of the trading partners is not immediately reflected in
their own industry, but may affect productivity across time. To account for
this effect, a one-year lag is given to the explanatory variables in the
analysis.

Table 6: 1 year lagged results

| Group A | Group B
---|---|---
| (1) | (2) | (3) | (4) | (5) | (6)
| All | Europe | North America | All | Europe | North America
domestic, lagged | -0.014 | -0.017 | $0.044^{**}$ | -0.018 | -0.020 | $0.044^{**}$
| (0.012) | (0.016) | (0.021) | (0.013) | (0.016) | (0.018)
exporter’s |  |  |  |  |  |
centrality: |  |  |  |  |  |
High, lagged | $0.026^{*}$ | 0.012 | 0.011 | $0.026^{*}$ | $0.032^{*}$ | 0.022
| (0.013) | (0.020) | (0.027) | (0.014) | (0.018) | (0.055)
Middle, lagged | 0.018 | 0.037 | -0.031 | 0.025 | $0.029^{*}$ | -0.078
| (0.017) | (0.025) | (0.021) | (0.014) | (0.016) | (0.063)
Low, lagged | 0.006 | 0.001 | -0.004 | 0.011 | 0.002 | 0.000
| (0.010) | (0.012) | (0.013) | (0.008) | (0.011) | (0.022)
$\mathrm{constant}$ | 0.053 | 0.057 | -0.180 | -0.082 | -$0.137^{*}$ | 0.013
| (0.077) | (0.097) | (0.160) | (0.063) | (0.076) | (0.231)
$N$ | 3525 | 2853 | 504 | 3525 | 2853 | 504
$R^{2}$ | 0.883 | 0.872 | 0.963 | 0.885 | 0.875 | 0.964
Country- |  |  |  |  |  |
Industry FE | Yes | Yes | Yes | Yes | Yes | Yes
Year FE | Yes | Yes | Yes | Yes | Yes | Yes

2121footnotetext: Standard errors in parentheses, * $p<0.1$, ** $p<0.05$, ***
$p<0.01$

The results are reported in Table 6, and show that the significance is almost
the same, and the effects are smaller. Therefore, I find that using the one-
year lagged variable does not produce significantly different results from the
hypothesis.

##  Conclusion

In this paper, I examine the relationship between the international R&D
spillovers and the structure of the GVCs by using 21 countries and 14
manufacturing industries as samples for the period of 1995 to 2007. To this
end, I identify the centrality of each industry in the GVCs in each year,
using the world input-output table, and categorize the countries as per high,
middle, and low centrality. Further, I classify the industries into two
categories. Based on these, I examine the difference in the effects of
exporters’ centrality. I obtain the following results. First, I find that
trading with high centrality countries have positively significant, and the
highest effects, on domestic TFP. This result suggests that the high
centrality countries have a greater role in transmitting knowledge, and
diffusing effects. Second, I find that the exporters with middle centrality
are also statistically significant. In particular, the increase in direct and
indirect demand from countries with middle centrality since 2002 is believed
to have contributed to the results. It is suggested that countries with middle
centrality in imports and high centrality in exports are important for this
result. Finally, it seems that only technologically-advanced countries (G5)
are affected by the spillover effect from own. Looking at the share of
domestic and foreign R&D contents, the share of domestic content is much
higher in the G5 countries than in the other countries. This result suggests
that the proportion of the R&D contents flowing into a country is important
for R&D spillovers.
This study is the first to consider, and empirically analyze, the position of
the exporters in the GVCs for international R&D spillovers. In contrast to the
claims of Keller (1998), these findings suggest that the identity of both the
importing and the exporting country is important in the international
spillover effects. However, the impact of the final goods from domestic trade
is significant only in the countries with a high share of domestic R&D
contents. In this study, I have only included Japan from the Asian countries
due to data limitations, however, South-east Asia has built a strong
production network, and I consider it possible to analyze the relationship
between centrality and international spillover effects from a different
perspective than that of Europe and North America. In addition to South-east
Asia, there are many other countries, such as China and India, that have an
important position in the GVCs, and if they can be included in the analysis,
it will be possible to elucidate the relationship between the international
R&D spillover effects and the GVCs in more detail.

## Appendix: Decomposition of the R&D contents into direct and indirect
demands

I decompose the foreign R&D contents into direct and indirect, demands, and
try to better understand the results in Table 4. Following Lumenga-Neso et al.
(2005), I decompose it as follows:

$\displaystyle V^{f}=$
$\displaystyle\>\>V^{f\\_\rm{direct}}+V^{f\\_\rm{indirect}}$ $\displaystyle=$
$\displaystyle\>\>DB^{F}f\hskip 6.54413pt+D[(I-B)^{-1}-(I+B)]^{F}f$

Table 7 displays the percentage of flows from countries in each centrality
category for 1995 (panel (a)) and 2007 (panel (b)), respectively. As these
panels indicate, most of them are from the High category (about 85% and 73% in
panels (a) and (b), respectively). Although only 27% of the countries are
classified as High, we can see the importance of this category in the
spillover effect. In addition, high indirect demand is common across
categories. In “Food, Beverages, and Tobacco,” for example, there is a
difference of about 50-60%. Therefore, in the results of Table 4, we can see
that indirect effects also account for a large part of the spillovers, and the
results indicate that countries with High centrality are important as
mediators of knowledge. On the other hand, comparing 1995 and 2007, it turns
out that High has decreased and Middle has increased. To follow the trend in
further detail, I analyze the time series change in the ratio of direct and
indirect demands, respectively. As Figure 3 shows, the direct and indirect
demands from countries with Middle centrality is on the rise, especially since
2001.222222 Although this figure shows the share in “Electrical and Optical
Equipment, ” the trend is basically the same for other industries as well.
This is one of the reasons why the effects from a country with Middle
centrality are statistically significant.

Table 7: The shares of the R&D contents

| Direct ($V^{f\\_\rm{direct}}$)(%) | Indirect ($V^{f\\_\rm{indirect}})$
---|---|---
classification |  |  |  |  |  |
of centrality: | High | Middle | Low | High | Middle | Low
(a) 1995: |  |  |  |  |  |
Food, Beverages, and Tobacco | 12.7 | 2.3 | 0.1 | 71.1 | 13.3 | 0.5
Textiles and Textile Products | 30.2 | 3.9 | 0.3 | 54.7 | 10.6 | 0.3
Leather, Leather, and Footwear | 24.3 | 3.8 | 0.3 | 59.5 | 11.8 | 0.4
Wood and Products of Wood and Cork | 21.5 | 3.7 | 0.2 | 62.2 | 11.8 | 0.5
Pulp, Paper, Printing, and Publishing | 25.6 | 4.3 | 0.2 | 58.5 | 11 | 0.4
Coke, Refined Petroleum, and Nuclear Fuel | 21.1 | 5.8 | 0.3 | 57.3 | 15.3 | 0.3
Chemicals and Chemical Products | 48 | 6.9 | 0.5 | 36.9 | 7.3 | 0.3
Rubber and Plastics | 45.5 | 6.1 | 0.5 | 39.8 | 7.8 | 0.3
Other Non-Metallic Mineral | 28.4 | 5.2 | 0.3 | 55.2 | 10.6 | 0.4
Basic Metals and Fabricated Metal | 26.1 | 4.5 | 0.3 | 57.7 | 10.9 | 0.5
Machinery, Nec | 38.3 | 4.2 | 0.2 | 49.1 | 7.8 | 0.3
Electrical and Optical Equipment | 50.7 | 4 | 0.2 | 39.8 | 5.1 | 0.2
Transport Equipment | 42.5 | 7.1 | 0.1 | 42.2 | 7.9 | 0.2
Manufacturing, Nec; Recycling | 27 | 4.1 | 0.3 | 57.2 | 10.9 | 0.4
(b) 2007: |  |  |  |  |  |
Food, Beverages, and Tobacco | 11.9 | 4 | 0.2 | 60.4 | 22.5 | 1
Textiles and Textile Products | 27.9 | 9.2 | 0.4 | 44 | 17.9 | 0.6
Leather, Leather, and Footwear | 22.9 | 7.5 | 0.6 | 49 | 19.3 | 0.7
Wood and Products of Wood and Cork | 19.3 | 7.8 | 0.5 | 51.8 | 19.8 | 0.8
Pulp, Paper, Printing, and Publishing | 22.3 | 8.5 | 0.5 | 49.2 | 18.8 | 0.7
Coke, Refined Petroleum, and Nuclear Fuel | 16.1 | 6.3 | 0.5 | 52.9 | 23 | 1.1
Chemicals and Chemical Products | 40.3 | 15.5 | 1 | 30.1 | 12.7 | 0.4
Rubber and Plastics | 37.1 | 13.3 | 0.7 | 34.1 | 14.3 | 0.5
Other Non-Metallic Mineral | 23.9 | 7.8 | 0.5 | 48.9 | 18.2 | 0.7
Basic Metals and Fabricated Metal | 21.8 | 6.3 | 0.4 | 52.3 | 18.4 | 0.8
Machinery, Nec | 35.2 | 7.9 | 0.5 | 40.7 | 15.2 | 0.5
Electrical and Optical Equipment | 39.7 | 12.4 | 0.4 | 32.9 | 14.4 | 0.3
Transport Equipment | 40.2 | 6.5 | 0.3 | 39.5 | 13.1 | 0.4
Manufacturing, Nec; Recycling | 24.9 | 8 | 0.5 | 47.4 | 18.4 | 0.7

2222footnotetext: Note: Author’s calculation. This table shows the average
percentage of foreign R&D contents in the the final goods imported by each
industry. The share is calculated as the average of the percentage of the
total, including both direct and indirect demand.

Figure 3: The average R&D contents share in Electrical and Optical Equipment

Source: Originally created by the author, using WIOD
Note: The y-axis represents the ratio of the foreign R&D contents. The shares
are calculated using direct and indirect demand, respectively, and as the
average of all the sample countries.

Next, I add the dummy variable, that is equal to 1, for the years 2002-2007
($Year^{02-07}$) as interaction term with centrality term, and estimate the
change in the effect since 2002. Table 8 shows the results of the additional
analysis, and rows 5-7 indicate the newly-added variables. The effects from
the countries with Middle centrality are positive and significant post-2002.
This result indicates that countries with Middle centrality are also important
in the spillover effects since 2002. On the other hand, in all the samples,
the effect from the countries with High centrality is negatively significant.
These results correspond to the trend in Figure 3. In North America, there are
no significant effects from the foreign R&D contents, and it is affected only
by the domestic R&D contents.

Table 8: The results after adding the dummy variable

| Group A | Group B
---|---|---
| (1) | (2) | (3) | (4) | (5) | (6)
| ALL | EUR | NA | ALL | EUR | NA
domestic, $\beta$ | -0.022 | -0.032 | $0.040^{**}$ | -$0.030^{*}$ | -$0.042^{*}$ | $0.046^{**}$
| (0.015) | (0.020) | (0.020) | (0.017) | (0.020) | (0.021)
exporter’s |  |  |  |  |  |
centrality: |  |  |  |  |  |
High, $\rho_{1}$ | $0.037^{**}$ | 0.029 | -0.030 | $0.056^{**}$ | $0.059^{**}$ | -0.002
| (0.015) | (0.024) | (0.024) | (0.021) | (0.023) | (0.048)
Middle, $\rho_{2}$ | 0.022 | 0.020 | -0.017 | 0.015 | $0.028^{*}$ | -0.046
| (0.019) | (0.027) | (0.025) | (0.013) | (0.015) | (0.069)
Low, $\rho_{3}$ | 0.014 | 0.010 | 0.008 | $0.018^{*}$ | 0.013 | 0.001
| (0.012) | (0.015) | (0.024) | (0.009) | (0.011) | (0.044)
High * $Year^{02-07}$ | -0.016 | -0.019 | 0.048 | -$0.024^{**}$ | 0.021 | 0.039
| (0.010) | (0.019) | (0.041) | (0.011) | (0.028) | (0.111)
Middle * $Year^{02-07}$ | $0.026^{*}$ | 0.028 | 0.043 | $0.040^{**}$ | $0.045^{**}$ | -0.050
| (0.012) | (0.021) | (0.037) | (0.015) | (0.023) | (0.130)
Low * $Year^{02-07}$ | -0.006 | -0.007 | -0.044 | -0.015 | -$0.031^{*}$ | -0.004
| (0.007) | (0.008) | (0.033) | (0.009) | (0.015) | (0.039)
$\mathrm{constant}$ | 0.105 | 0.133 | -0.140 | -$0.144^{**}$ | -$0.192^{**}$ | 0.018
| (0.094) | (0.120) | (0.140) | (0.064) | (0.081) | (0.214)
$N$ | 3819 | 3091 | 546 | 3819 | 3091 | 546
$R^{2}$ | 0.868 | 0.856 | 0.960 | 0.872 | 0.861 | 0.958
Country- |  |  |  |  |  |
Industry FE | Yes | Yes | Yes | Yes | Yes | Yes
Year FE | Yes | Yes | Yes | Yes | Yes | Yes

2222footnotetext: Standard errors in parentheses, * $p<0.1$, ** $p<0.05$, ***
$p<0.01$

Furthermore, I identify the Middle categories that impact the results. In
Table 7, I checked the respective percentages of the R&D contents in High,
Middle, and Low, however, here I will focus on Middle alone. I do not
distinguish between direct and indirect demand, and consider the total demand.
In “Electrical and Optical Equipment,” the time-series change in each category
of Middle, averaged over the sample countries, as shown in Figure 4.

Figure 4: The average R&D contents shares in Electrical and Optical Equipment
in Middle classification

Source: Originally created by the author, using WIOD
Note: The y-axis represents the ratio of the foreign R&D contents. The shares
are calculated using the total demand, and the average of all the sample
countries. For each category, for example, “high-middle” means that countries
with high centrality in backward and middle centrality in forward.

As Figure 4 indicates, “middle-high” and “middle-middle” account for most of
the Middle classification (about 80%-97%). In addition, while “middle-middle”
is on a downward trend, “middle-high” is on an upward trend.232323 Although
this figure shows the share in “Electrical and Optical Equipment,” the trend
is the same for the other industries.

Therefore, when combined with the results in Table 8, we see that countries
with middle centrality in imports but high centrality in exports also play an
important role in the foreign R&D spillovers as mediators. They are also
important in the diffusion of knowledge because of their high centrality in
exports.

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