Impact of supply chain network structure on FDI: Theory and evidence*
Ryo Itohi
Kentaro Nakajimaii
June 2013
Abstract: This study investigates how structure of supply chain network of thedomestic market influences FDI of firms embedded in the network. We firstly describea binary choice of firms whether invest or not by a coordination game on fixed networkwith incomplete information on part of firms’ profit, and addressed that the uniqueequilibrium of the game is represented by Katz-Bonacich centrality measure which
captures both direct and indirect effects from the network. We also give empirical tests
for the theoretical hypothesis with a large sized disaggregated data of Japanese firms,
and verified that Katz-Bonacich centrality of each firm has a significantly positive effecton its FDI even when the sector-specific fixed effects and other attributes are controlled,
as our theory anticipated.
Key words: FDI, network game, supply chain, Katz-Bonacich centrality.
JEL Classification: D20, D85, F23.

*

Very preliminary. Authors gratefully acknowledge financial support from the JSPS (nos. 22330073 and25380275). The usual disclaimer applies.
i
Nagoya-city University, Yamanohata 01, Mizuho-ku, Nagoya-city, Aichi-prefecture, Japan. 467-8501.
E-mail: itoh@econ.nagoya-cu.ac.jp
ii
Tohoku University, Kawauchi 27-1, Aoba-ku, Sendai, 980-8576 Japan.
E-mail: knakajima@econ.tohoku.ac.jp

1. Introduction
For the companies considering to establish affiliates in a foreign market, finding good
procurement for materials and sales channels for their products are big issues.
Companies starting new transaction with local companies sometime suffer from various
kinds of frictions like mismatch in design and quality of products and delivery systemof them (e.g. Reid 1995); adjusting them is also difficult because of miscommunication
between firms with different commercial custom and technical basis. Some firms
therefore trade with the affiliates with the same home country to replicate thetransaction partnerships in the domestic market (Hacket and Srinivasan 1998). Such
replication of transaction will yield profit to both sides of transaction not only bysmoothing trades of products but also by exchanging various useful information on themarket and the government. As a result, it is considered that FDI of a firm, including
expect for future investment as well as completed ones, stimulates investment of otherfirms in the same market through a supply-chain network which is a set of whole tradesin the domestic market.
The main concern of the present study is how firms’ FDI to a region is affected by the
supply-chain network in the domestic market. Most of the literature about FDI like
Helpman et al. (2004) focused on attributes of firms like productivity and those ofinvested region like barrier of international trade. Furthermore, a string of studies on
country-of-origin FDI addressed agglomeration of investment from the same homecountries attracts further investment from the country (e.g. Head et al. 1995, Chang andPark 2005, Chung and Song 2004). Specifically, the result of Belderbos and Carree(2002) about influence of group companies (keiretsu) of Japanese firms on FDI is
implying some kinds of supply-chain-network effect. Further, Yamashita et al. (2013)
uses actual transaction relationship data, instead of keiretsu data, and found the positive
influence of transaction relationship on location decision. However, these studies only
capture collective effects of supply-chain-networks and, to the best of the authors’knowledge, few studies have directly focused on the effect of network structure itself.
We contrarily highlight how the decision on FDI of each individual firm is affected bydetailed structure of entire network and its position in that structure. We firstly
investigate this issue with a game-theoretic model, and then provide an empirical test
for the result of it with a disaggregated data of Japanese firms.
 Games with network employed in our study are actively applied to various issues inrecent years, such as for technological choice of firms and education of households. To

describe decision of firms whether they invest or not to a region, a theoretical network
game presented by Bloch and Quérou (2012) is applied for our empirical study on FDI
with some extension. Our model considers a simultaneous choice on a fixed network inwhich a pair of directly linked firms, interpreted as business partners in the domestic
market, have incentives to invest together with each other. Furthermore, part of profit
from FDI is assumed to be private information of each firm that is unobservable to theothers, then decision of each firm relies on an expectation for partners’ uncertain
decision. In our model the stand-alone benefit yielded outside the transaction is
uncertain as Bloch and Quérou (2012) supposed, while we suppose that the benefit oftransaction also differs among firms and is private information.
In our incomplete information game, each firm expects the decision of its direct
partners via expectation for all the indirect partners; i.e. partners of partners and then
their partners, and so on. Through such diffusion of expectation over the network invarious routes and it converges to a strategic equilibrium. Both Bloch and Quérou(2012) and this study demonstrated that under an assumption of uniformly distributed
stand-alone payoffs the game has unique Bayesian-Nash equilibrium in which separated
strategy of each player is characterized by its Katz-Bonacich centrality measure on
network and more “central” players are more likely to invest12. Katz-Bonacich centrality,
denoting how a node is accessible to all others3, is also applied to describe Nashequilibrium of network games by some of our companion papers: Ballester,
Calvó-Armengol and Zenou (2006: hereafter BCZ) and its empirical extension by
Calvó-Armengol, Patacchini and Zenou (2009: hereafter CPZ). This is because themodel of BCZ and ours has similar mathematical forms: a quadratic (expected) payoff
function and hence linear best response function. However, issues of the two studies
differ fundamentally; BCZ consider a continuous choice (e.g. quantity of effort or
money spent for education) while ours considers discrete choice (i.e. whether invest ornot). Since the binary choice like ours cannot be simply explained by BCZ’s model, wethen extend the range of issues to which the Katz-Bonacich centrality is applicable.
Our final destination is to show an empirical evidence of the above theoretical
1

Bloch and Quérou (2012) investigate whether each consumer embedded on network purchases one
unit of indivisible network good or not. On the other hand, In Itoh (2012)’s binary choice modelfirms choose one location point from two (or more) asymmetric regions.
2This measure was firstly proposed by Katz (1953) and generalized by Bonacich (1987), hence
Ballester et. al. (2010) calls the index after their names.
3This index is equivalent to a linear function of centralities of directly linked nodes.

hypothesis. Although the effect of Katz-Bonacich centrality of firms on FDI is therefore
our primary focus, other attributes of firms like productivity is also important for firms’
decision (e.g. Helpman et al. 2004). The incentive for FDI and effect of centrality will
significantly differ among industry despite the entire network consists of firms ofvarious industries. Furthermore, those attributes might correlate to the centrality of the
firm. For example, a high productive or large firm might be also an important firm inthe supply chain network. If so, estimate of the role of the centrality will be distorted if
such variables are omitted in the estimation. Considering these empirical viewpoints, we
extend the basic model with supposing some restricted information of firms so that theeffect of non-network attributes of firms and industry specific influence on FDI are also
tractable as well as Katz-Bonacich centrality4.
We use a disaggregated data of more than 110,000 Japanese firms in manufacturingsector. In addition to various information of each individual firm like number ofaffiliates by country, number of employees, total product and credit ranking,information on main trading partners of each firm is also available for detailed
composition of supply-chain network. This network information allows us to calculate
Katz-Bonacich centrality representing detailed network structure of whole Japanesemanufacturing sector with capturing inter-sectoral effect among small sectors.
Our empirical strategy is regressing firms’ FDI behavior on the Katz-Bonacich
centrality. Because of the computational burden, first, we use the eigenvalue centralitythat is the special case of the Katz-Bonacich centrality, instead of using originalKatz-Bonacich centrality. Then, we calculate original Katz-Bonacich centrality measureand estimate the role of the centrality on the FDI decision by restricting samples to thelarger firms to check the robustness of the results.
Our empirical strategy imposes two critical assumptions. One is the simultaneousdecision-making on the choice of FDI, and we consider the static game situation. The
other one is the exogeneity of the network structure on the FDI decision. That is, the
FDI behavior itself does not matter to the structure of the transaction network. However,these settings are considered to be appropriate for describing FDI of Japanese firms for
4

Despite starting with similar theoretical model with ours, CPZ did not apply Katz-Bonacich
centrality for their empirical tests. This is because effect of the value of error term diffuses via
network in their complete information game and hence the problem of autocorrelation appears. On
the contrary, our incomplete information simultaneous move game can escape such problem and we
can describe the equilibrium probability of FDI by Katz-Bonacich centrality.

some reasons5. First, FDI of Japanese firms have been rapidly growing in these two
decades; specifically in east Asian countries that increased more than twice in thedecade of 1990s. The fact that most of Japanese firms’ FDI concentrates within alimited span means that they have to promptly make their decision for FDI to rapidly
growing markets even partners’ decision might be sometime uncertain. Second, we havealready seen the fact that affiliates have big incentive to replicate the relationship in thehome country rather than starting new trading, and hence what matters for firms’ FDI isthe supply-chain network in the domestic market; such trunk relationship will be
negligibly influenced by investment and is stable at least in the short-run. We therefore
give fixed network although endogeneity problem of network is a considerable problem
for such kind of research.
In the results, we successfully address significantly positive effect of Katz-Bonacich(eigenvalue) centrality on FDI with controlling various individual attributes of firms
including fixed effects of each of four-digit sector6. Further, we confirm the robustnessof the baseline results and the validity of using eigenvalue centrality by conducting
estimation using the original Katz-Bonacich centrality.
The remainder of the paper is structured as follows. Section 2 gives a static coordination
game with network and a theoretical examination for it. Then, section 3 presents data
and framework for empirical analysis. Section 4 discusses about the baseline empiricalresults by using the eigenvalue centrality, and section 5 discusses the robustness of thebaseline analysis by restricting samples to the larger firms. Finally, section 6 concludes
the paper.

2. ModelThis section presents a simultaneous move game with incomplete information todescribe the decision of FDI by firms which prefer coordinated investment with theirtrading partners. Although our theoretical framework is similar to Bloch and Quérou(2012)’s, we consider incomplete information on transaction profit as well as stand5

On the other hand, a few studies analyses dynamic games in which players sequentially change
their choice with observation for others’ choice (Morris 2000, Jackson and Yariv 2007), and suchmodel is also applied for some empirical studies such as of an juveniles’ smoking behavior by
Nakajima (2007).
6
Manski (1993) addressed a detailed methodology for estimate spillover effects on networks while
we simply estimate the influence of calculated centrality based on the theoretical results of ours.

alone profit. In the latter half, we translate their model into an empirically testable form
considering various attributes of individual firms.
2.1 Inter-firm transaction and profit of affiliates
The set N = {1, 2, ..., n} is a finite set of risk-neutral firms which have a nationalityof the home country (i.e. Japan), and an nn matrix G={!ij ! denotes exogenously

given transaction relationship among them: adjacency matrix of the supply-chain
network in the domestic market. The parameter !ij equals one if firms i and j are tradingand equals zero otherwise. We assume G is symmetric and then !ij =!ji holds, andassume !ij = 0 holds for diagonal components.
In the next we denote the set of the domestic firms having an affiliate in a foreign
region r (e.g. eastern Asia) by Nr⊂N. We suppose that the affiliates have the samefacilities as their domestic companies; hence a pair of affiliates can trade to yield apositive profit only if their parent companies are trading in the domestic market7.
Suppose that a firm gains a constant additive profit from transaction with any otherfirms such as through efficient supply and procuration of an intermediate goods orservice. We assume that the additive profit from transaction, denoted by !!" ! !,differs among firms but is never influenced by any other transaction. Therefore,
affiliates i and j must trade if!!! !! ! !! and!!ij >0 hold. At that time, the total profit offirm i gained from all transactions is denoted as !!"!
!!! !!" !!" , where!!" is one whenfirm j has an affiliate in region r or !! ! !! , while zero otherwise.
The total profit of affiliate i in region r is given as follows;Nt! i ("r ; zir ,# ir , G ) = # ir % j =1 " jr$ij + zir

 

(1)

Where !! ! !!!! ! ! ! !!" ! is a vector of investment in region r. Furthermore, zir is astand-alone profit of affiliate i in region r that is independent from transaction (Farrell
and Saloner 1986). Stand -alone profit is influenced from economic condition of regionr and attributes of individual firms, such as investment cost in region r, international
trading costs like tariffs and transportation cost, and demand for firm i’s products byconsumer and firms in r. This study assumes that zir includes any other profit source
7

If firm i invests to region r while its partner j doesn’t, i must give up transaction to j’s affiliate andmust choose whether it trades with j’s affiliate in the home country or finds a new alternative partner
in region r. However, the former case requires tariffs and transportation costs while the latter causes
loss from mismatches. These profits are therefore less than that from trade with the original partners;
this study assumes their additional profit as zero.

except for the transaction on the network. Furthermore, a company gains zero profit ifthey have no affiliate.
We assume that only firm i knows its own !!" and zir; hence marginal transaction profit
and stand-alone profit of each firm are private information. Firms have someprobabilistic information on others’ !!" and zir, which is common knowledge among all
the firms but is not guaranteed to be true because of biased and restricted information
source. This setting gives an incompleteness of information to our model.

2.2 Decision making on FDI
Firms face a binary choice whether they should invest or not to region r to establish anaffiliate there. The decision making on investment to region r must be independent fromthe other investments because the firms can invest to more than one regions and theirprofits are independent each other. All firms make their decision at the same time, hencefirms intend to maximize expected value of the total profit. The present study assumes
that entire network structure G is public information for all firms while only firm iknows its own zir and !!" at the timing of the decision making. In other words, firms
know relationship of all other firms but have no information on their attributes.
Therefore, the other firms only have some probabilistic expectation for the decision ofother firms with given information: distribution functions of zir and !!" . At that time we
suppose that firms expect zir and !!" are independent from each other and any otherobservable variables.
At the timing of the decision making, the expected total profit of firm i’s investment inregion r is denoted as follow;n

E (! ir | p r , G, zir ," ir ) = " ir $ j =1 p jr#ij + zir(2)

where !!" ! !" !!" ! ! !denotes expectation of other firms on j’s probability ofinvesting to r, and !! ! !!! ! ! !!" !is vector of them. Firm i establishes an affiliate
only when !!!!" !!! ! !! !!" ! !!" ! ! ! holds because the firm gains zero profit without
investment. At that time, for given expectation vector !! , each firm has a best-response
threshold !!" with which firms decide investment if and only if !!" !!!" ! !!" holds;
hence denoting best-response strategy of each firm is equivalent to denoting thethreshold. From equation (2), best response threshold of firm i is described as follows.

n!ir = #$ j =1 p jr"ij(3)   This equation implies that higher expectation for partners’ investment decreases !!"and hence increases its own probability to invest. Note that lower threshold means
higher incentive for investment. When firm i is expected to decides according toequation (3), others’ expectation on i’s probability for investment is denoted as follows;+#

pir = Pr( zir / ! ir % "ir ) = & lr (! ir )[1 $ Fr (! ir"ir )]d! if(4)     
Where !! !!! is accumulated distribution function of zir and !! !!! is density function of!!" . All the firms have common knowledge on these distribution functions and are
informed that they are independent, although information of them is unnecessarily true.
$#

When a vector of threshold !r =(!1r ,…,!nr ) is given, we can describe firm i’s best
response threshold to others’ thresholds is denoted as follows from equations (3) and
(4).
+$
n
!ir = %, j =1 & - lr (" jr )[1 % Fr (" jr! jr )]d" jr '#ij
(* %$
)+ 

    (5)By making a system of simultaneous equations consisting of n equations of equation (5)and by solving it by !! , we can derive the equilibrium of strategies of all firms.

2.3 Equilibrium under uniform distribution of random profit
Now we specify distribution of zir in order to derive specific equilibrium. Supposingthat firms expect that zir is uniformly distributed within !!! ! !! ! ! ! !! ! , thedistribution function is denoted as,0
if z < !a + zr"#
Fr ( z ) = %(a ! zr + z ) / 2a if ! a + zr $ z $ a + zr       #
1
if z > a + zr&

(6)where we assume a>0. Expected value of zir denoted by !! can be both positive and!
!
negative. We also suppose !! ! ! ! !!!!and !! ! ! ! !! ! !!!!", where !!"is themaximum value of !!" . These assumptions guarantee the sufficiently wide support of zir
in which the best response threshold is always within !!! ! !! ! ! ! !! ! because!!" ! !!! ! ! !!. It is interpreted that each firm never promises that it definitely makes achoice regardless of its stand-alone profit, even when the firm trading with all others
expects that all the partners choose a choice in probability one. At that time, equation

(5) is rewritten as follows;n"ir = $%

a + zr $ ! r" jr
2a

j =1

#ij

(7)

Where !! is expected value of !!" . We can denote simultaneous equation system of
equation (7) by vector as!r = #!"r G1 + ! G!r(8)

Where 1 is column vector of one, and we denote ! ! !! !!!!! and !! ! !! ! !! !!!!
to simplify the notation. We should note that the above best-response functions denotedby equations (7) and (8) hold only when !! ! !! ! !! !!" ! ! ! !! is satisfied for all i,
but it is promised by the assumption of the sufficiently wide support of zir.
We should note that the above linear best-response function is very similar to that of
BCZ, this is because multiplier of the linear payoff and linear probability yields ourquadratic expected payoff that is similar to the one given in BCZ. Conclusively, thefollowing equilibrium of our model is mathematically identical to that of BCZ, while
the two models start from the different issues.
The equilibrium of the model, denoted as ! r * = (!1*r ,...,! nr* ) , is derived by solving
equation (8) by !r . The system of linear equations represented in equation (8) has
single interior solution if ! is smaller than the inverse of the largest eigenvalue of G8.
Therefore, the strategies of firms necessarily converge to an unique interior equilibrium
because any corner solution (i.e. pi =1 or 0 for any i) can be omitted by the assumptionof sufficiently wide support of zir 9. The equilibrium of the model is derived as follows;!r * = # ! r " G (I # " G ) #11(9)$= # ! r # % k =1 " k G k 1

In equation (9), the equilibrium strategy of each individual firm is described as follows.

!ir* = & " r & bi (G ),%nwhere bi (G ) = ' k =1 ' j =1 # k$ij{k }

 

(10)

When !! diverges because ! is larger than the largest eigenvalue, all firms definitely choose
invest or not are both in equilibrium.
9 The assumption of sufficiently wide support of z promises ! ! !!!! ! !!. This restriction is
ir
actually more restricted than the one that ! is smaller than the largest eigenvalue.
8

We should note that !ij! is ij component of Gk but not k-th power of !ij . The
function !! !!! in equation (10) is identical to a network measure called
Katz-Bonacich centrality or alpha-centrality（Bonachich 1987; BCZ; Ballester andCalvo-Amengol 2009）. This measure is calculated by summing number of all walksof the network (i.e., routes on the network for which links can be traversed morethan once) from i to j with decaying by their length by decaying parameter!!. The
important characteristic of the Katz-Bonacich centrality is considering the influence
from indirect relationship (i.e. the one from partners’ partner) as well as from thedirect partners; then entire network structure feedbacks to each node embedded
there.
Our result represented in equation (10) implies more central players have larger
incentive to invest for the following reason. Under the additively separable profit
function given by equation (1), outgoing firms with many partners can potentiallygain higher profit by FDI, hence other firms expect that such firms are more likely
to invest. Furthermore, the partners of the outgoing firms also have large incentive
to invest because they expect they can trade with the outgoing firms in the foreign
markets with a high probability. When expectation for investment diffuses thoroughany possible path in the network in such way, the more central player embedded in
the hub of network receives larger influences, so called network externality.
Finally, other firms’ expectation on i’s probability for investment in equilibrium isderived from equations (4) and (10) as follows;

pir = 2!"r + ! b(G)                (11)

2.4 Attributes of firm and testable model
The final part of the section discusses how we should consider attributes of individual
firms such as their productivities in our hypothesis, before we go to the empiricalsection. As we have mentioned, zir is independent of network-based profit while
influenced by various attributes of firm i as well as from economic conditions of region
r10. Now we suppose a vector of attributes Xi=(xi1,…,xim) which influences zir, and the10

For example, when product of the sector to which firm i belongs faces a growing demand in marketr, such firm has big incentive to invest to the region. We give further detailed discussion onfollowing equation represents the true relation between zir and Xi’11.
zir =!r +!r Xi '+µir   (12)Where !!" is a random variable independent from Xi’ and i’s position in network,whose cumulative distribution function is denoted by ! ! !!! . !! is vector of
coefficients of each attribute, and !! is a parameter which is interpreted as an synthesis
variable of economic condition of region r giving the equivalent effect to all firms.
Furthermore, we suppose that !!" is actually deterministic and type specific parameter,
and hence we denote !!" ! !!!!!! where t(i) is type of firm i. In particular, we specify
the type of firms by industry and size (large or small) of them in the preceding sections.
Now suppose that there is an observer (i.e. the author(s) of this paper) who can observe
Xi’=(xi1,…,xim) and industry of each firm, and knows distribution of !!" . On the other
hand, we suppose that firms have restricted information on distribution of zir and !!" ,hence firms’ behavior is still represented as equation (10). Firms consider that thesevariables are purely random and ignore influence of attributes12. At this time, firm i’s
probability to invest that the observer prospects is derived as follows from equation (10)and (12);!
!!"! ! !"#$ !!" !!! ! ! ! !!"! ! ! ! ! !!!! ! ! ! !! ! ! !! ! ! !! ! !! !

(13)

Where !! ! ! ! !! ! !! ! ! !! represents a type-specific incentive for investing regionr. In equation (13), probability for investment expected by the observer is described as afunction of centrality and their other attributes of the firms. Note that equation (13) isdifferent from equation (11) which represents the probability expected by firms without
full information on others’ attributes and equation (12). Since !! ! is positive, we canreadily see !!!"! ! !!! !!! ! ! ! from equation (13); hence centrality has positive effect!!!

!!! !!

on probability for investment as well as in equation (11). Further, !!!" ! !! !" !!!"!

!"

attributes of firms in the next section.

One reason for such insufficient information of firms is that they can observe noattribute of others. Although the assumption that zir including unobservable Xi is
uniformly distributed might be failes information, we can justify it by assuming firms’
information on zir is unnecessary true.
12!

represents that attributes with positive effect on stand-alone profit increase probability
for investment, and vise verse.
In the following section we challenge empirical tests for theoretical hypothesis
represented in equation (13).
3. Data and Empirical Strategy
3.1 Data
We use the dataset compiled by a major credit research firm, Tokyo Shoko Research
Incorporated (TSR). The dataset includes 826,169 large and small corporations in Japanand consists of two subsets: a dataset on firms’ characteristics and a dataset on interfirm
relationships. Field researchers of TSR, who not only utilize public sources such as
financial statements, corporate registrations, and public relations documents, but also
implement face-to-face interviews with firms, their customers and suppliers, and banks
that extend loans to them collect necessary information for the dataset. The sub-dataset
on firm characteristics includes information on a firm’s name, address, industry
classification code, products, year of establishment, number of employees, sales,business profit, and credit score. The other sub-dataset on interfirm relationships
includes information on the names of suppliers and customers of a firm. There exists anupper limit of 24 with regard to the number of counterparts each firm can report as its
customers or suppliers. The total number of interfirm relationships is approximately
four million. This dataset covers about half of the total of 1.52 million incorporated
firms in Japan, and it describes actual intefirm relationship in Japan mostcomprehensively. The focus of this paper is manufacturing firm and it reduces sample
size into 142,282.
We also use the dataset on the Japanese manufacturing foreign investments that wascompiled by a major research firm, Toyo Keizai Shimpo sha (TKZ). The dataset
contains information on locations (country and address), year invested, employment,
name of owners and ownership ratio for whole foreign affiliations of Japanese firms.
By connecting those dataset by the name of firm in TSR and the ownership firm in
TKZ, we build a database of Japanese firms FDI activity and their transaction
relationships in Japan. Table 1 shows the summary statistics.
[Table 1 here]Totally, our dataset has 115,111 observations because merging between TSR and TKZ
databases reduces samples. On FDI behavior, 2278 of total manufacturing firms are
conducting FDI in 2010 (i.e, having at least one foreign affiliates at that period), and2070 firms are conducting FDI to the South East Asian country. This suggests that themost of the FDI firms have affiliates in South East Asian countries13.
3.2 Empirical strategy
To test the theoretical prediction presented by equation (13), we estimate the following
equation,
FDI!" ! !! ! !! !"!centrality! ! ! !! ! !!" ! !!" !

(15)

where FDI!" is the FDI dummy that takes one if firm ! is conducting FDI to region r,
and zero otherwise; !"!centrality! ! is the natural logarithm of Katz-Bonacich centrality,! !!" is the other covariates, and !!" is the error term. Equation (15) is also applicablefor pooled FDI data regardless of destination where each coefficient will be weighted
average of corresponding ones in every destination. Further, if we estimate this equation
with separated samples by industry and size of firms, estimated coefficients represent
type-specific effects of centrality and other attributes on FDI.

To estimate this equation, we need to calculate Katz-Bonacich centrality. We calculate
Katz-Bonacich centrality representing detailed network structure of whole Japanesemanufacturing sector with capturing inter-sectoral effect among small sectors. Since,
supply chain network is formed beyond the industry, a firm’s FDI decision depends on
the structure of the whole manufacturing transaction network rather than the network
within the industry to which the firm belongs. For example, the FDI decision of atire-producing firm that is classified to the rubber industry depends on the behavior of
the other firms that belongs not only rubber industry, but also the other industries likemotor vehicle industry.
Considering the network including whole manufacturing firms causes computationaldifficulty in calculating Katz-Bonacich centrality. The calculation of the Katz-Bonacich
centrality requires calculating inverse matrix of the adjacency matrix. If we consider the
Following the model, we assume that all these FDIs are simultaneously establishedin green-fields where there is no prior investor. This assumption is justified by the factthat FDI is rapidly increasing in these two decades.
13

whole manufacturing firms’ transaction network, the adjacency matrix ! has 115,111
115,111 elements. To avoid calculating the large inverse matrix, first, we use theother measure of the centrality instead of using the Katz-Bonacich centrality for theestimation. By assuming the value of the decay parameter ! in eq. (10) by the inverseof the largest eigenvalue of !, we obtain a measure so called eigenvalue centrality as a
special case of the Katz-Bonacich centrality. The eigenvalue centrality does not need
the calculation of the inverse matrix of the adjacency matrix, and is applicable for thehuge network. Thus, in all the estimations of section 4, we use this eigenvalue centrality
as a proxy for the Katz-Bonacich centrality. Then, in Section 5, in order to check thevalidity of using eigenvalue centrality and the robustness of the results, we fully
estimate the empirical model including the decay parameter ! by using a subset ofwhole supply chain network. Hereafter, we present the way of the baseline analysis thatspecifies the decay parameter by the inverse of the largest eigenvalue of the adjacency
matrix of the supply-chain network !.
We estimate eq. (15) by the logit and linear probability model. To assure theconsistency of the estimates, we should argue on the concern of omitted variable bias
and reverse causality.
One most important factor that causes omitted variable problem is the heterogeneity of
the firm productivity. As pointed by Helpman et al. (2004), firm productivity strongly
affects the firm’s FDI decision. Further, the location in the supply chain network might
be correlated to the firm’s productivity. For example, high-productive firm may attracts
many customers and increase the Katz-Bonacich centrality. To deal with this concern,
we introduce labor productivity that is the sales divided by the number of workers, as ameasure of firm-productivity. Other than the productivity, firms’ performances, like
product quality, credibility also might affect both the firms’ FDI decision and theKatz-Bonacich centrality. We include firm age and listed firm dummy that takes one if
the firm is listed firm, and zero otherwise. Further, we include the firm credibility
variable as a measure of the firm’s comprehensive evaluation that captures otherunobserved firm-heterogeneity. The firm credibility is a measure that is created by TSR
originally. Since, TSR is the credit research company, it provides information on afirm’s credibility that represents the total performance of the firm, and is actually usedin the choice of transaction partners by the user companies. The credibility value isranged from zero to 100, and originally generated by TSR by using public sources offirm information and face-to-face interviews. We include this firm credibility into theregression equation to control firms’ unobservable performances.
Network structure to which the agent belongs is one of the most important
identification issues on empirical research of estimating network effect on the agents’behavior. In our case, one may concern about the FDI decision itself may affect thestructure of the transaction network. For example, two firms that have no transaction
relationships between them established their foreign affiliates at the same industry
complex, then, after the establishment, their geographical proximity may facilitatestarting transaction between them. In this case, FDI behavior itself affects the structureof the transaction network. However, newly starting transaction relationship between
foreign affiliates is not so frequently occurred. As Reid (1995) pointed, companies
starting new transaction with local companies sometime suffer from various kinds offrictions like mismatch in design and quality of products and delivery system of them,and then, as Hacket and Srinivasan (1998) pointed, trade with the affiliates with thesame home country to replicate the transaction partnerships in the domestic market.
Foreign affiliates have big incentive to replicate the relationship in the home country
rather than starting new trading, and hence what matters for firms’ FDI is the
supply-chain network in the domestic market; such trunk relationship will be negligibly
influenced by investment and is stable at least in the short-run. Actually, the majority of
the FDI reason is still the request from transaction partners, and the existence of therequest for the transaction partner itself suggests the difficulty of finding newtransaction partners in foreign countries. Further, we take five-year lags between FDI
and network data.
Further, Japanese firms have been conducting FDI to the various countries. In theestimation, first we pool every FDIs that are conducted various countries not only North
American countries, European Unions, and Asian countries but also other small
countries. In this case, the FDI dummy takes one if the firm is conducting FDI inregardless to the destination country, and zero otherwise. However, Baldwin and Okubo(2012) suggested that the foreign affiliations in Japan is making closed supply chain
network within regions, like Southeast Asia, North America. To include those closed
network activity, and then, we separately focus on the FDI behavior by region.
4. Empirical Results
4.1 Baseline results
This section shows the estimation results. First, Figure 1 shows the distribution of thelogarithm of Katz-Bonacich centrality with specifying decay parameter by the inverseof the largest eigenvalue of adjacency matrix; through section 4 we employ thiseigenvalue centrality. The figure clearly shows the difference between FDI and
Non-FDI firms. The distribution is shifted rightward in the FDI firms. This strongly
suggests that the firms that are conducting FDI have higher value of the Katz-Bonacich
centrality.
[Figure 1 here]

Now, Table 2 shows the baseline estimation results using pooled FDI data regardless of
their destinations. Column (1) shows the benchmark result that includes all
manufacturing firms in Japan and estimated by the logit procedure. The coefficient for
the Katz-Bonacich centrality is positively significant. This is consistent to ourtheoretical prediction that the increase of the Katz-Bonacich centrality increases theprobability of conducting FDI. Further, we obtain reasonable coefficients for the othercovariates. The coefficients for worker productivity, credit score, listed firm dummy,
and firm age are positively significant. Those suggest the validity of the model
specification.
Following the discussion of Helpman et al. (2004), firm productivity and its size canaffect to the firm’s FDI decision. We separately estimate equation (15) by the size of the
firm. Column (2) shows the result on the sample that is restricted the number of workers
are less than 100 (smaller firms), and Column (3) shows the result on the sample that is
restricted the number of workers are more than 100 (larger firms). In both columns, thecoefficients for Katz-Bonacich centralities are positively significant. Interestingly, thecoefficient for Katz-Bonacich centrality in larger firms is larger than that in smallerfirms. This is consistent for the prediction of Helpman et al. (2004). Because of thelarge fixed cost for FDI, smaller firms cannot pay for the FDI and are difficult to
conduct FDI in the first place. Network structure has a weaker effect for the FDI
strategy for the smaller firms. On the other hand, constraint of fixed cost for FDI issmaller in the larger firms, and the network structure has larger effect for the decision of
FDI for larger firms.
[Table 2 here]A firm’s FDI decision depends on the products that the firm is producing. To control
such heterogeneity of the products, we include industry fixed effects in the estimation
equation whose results are presented in column (4) to (6). Specifically, we use four-digit
industrial classification in JSIC, and estimate by the linear probability model to reduce
computation time. Column (4) shows the results. Even controlling industry fixed effects,
the coefficient for Katz-Bonacich centrality is still positively significant, and thecoefficient for all of the other covariates are also positively significant. This strongly
supports our theoretical prediction. Column (5) shows the small firm, and Column (6)shows large firm results. Very interestingly, the difference in the coefficient for
Katz-Bonacich centrality between larger and smaller firms becomes much larger. By
controlling industry fixed effects, the difference in the role of the transaction networkon the decision of FDI between large and small firms becomes much more sharp.
In sum, our theoretical prediction is strongly supported by the empirical results.
Katz-Bonacich centrality that represents the firm’s importance in the position in theinterfirm transaction network significantly and positively affects the decision of thefirm’s FDI, and it is robust even in controlling firm’s industry classification.

4.2 Heterogeneity in destination countries
In the above analysis, we include every FDI regardless to their destinations. But as
Baldwin and Okubo (2012) suggested, the purpose of FDI would be different by thedestinations. We, then, focus on the specific destination countries of FDI. Table 3 shows
results.
[Table 3 here]

Column (1) shows results on FDI to Asian countries. In the estimation, dependent
variable is the FDI to Asian country dummy that takes one if a firm conducting FDI to
Asian countries, and zero otherwise, and we estimate it by linear probability model withincluding industry fixed effects. The coefficient for the Katz-Bonacich centrality issignificantly positive, and all of the coefficients for other covariates are also positively
significant. Column (2) shows the small firm, and Column (3) shows large firm results.

In both estimations, the coefficients for Katz-Bonacich centrality and the other variables
are still positively significant. Further, the magnitude of the Katz-Bonacich centrality is
still larger in the result in large firms than in small firms. Column (4) to (6) shows
results of the same estimations on FDI to North America. In the estimation, dependent
variable is the FDI to North America dummy that takes one if a firm conducting FDI to
North America, and zero otherwise. The all firm results represented in Column (4)shows the coefficient for the Katz-Bonacich centrality is significantly positive, and allof the coefficients for other covariates are also positively significant. Column (5) shows
the small firm, and Column (6) shows large firm results. In both estimations, thecoefficients for Katz-Bonacich centrality and the other variables are still positively
significant. Further, the magnitude of the Katz-Bonacich centrality is still larger in the
result in large firms than in small firms. Very interestingly, the magnitude of the
Katz-Bonacich centrality is much smaller than the result in FDI to Asian countries inthe every estimation (baseline, small firms, and large firms). The effect of thetransaction network on the decision of FDI is much more stronger in the FDI to Asian
countries than to the North America.
4.3 Industry heterogeneity
Finally, to examine the industry heterogeneity in the decision of FDI, we estimate theequation by two-digit industry in JSIC. The results are shown in Table 4.
[Table 4 here]
The coefficient of the Katz-Bonacich centrality is significantly positive in every
industry other than Lumber and Wood Industry. This suggests in most industries, thelocation of a firm in the interfirm network significantly affects the firm’s FDI behavior.

5. Robustness
Previous analysis is conducted with using eigenvalue centrality by specifying decay
parameter ! of Katz-Bonacich centrality with the inverse of the largest eigenvalue ofadjacency matrix of the whole supply-chain network !. Now, we check the robustnessof the results without exogenously specifying the decay parameter of Katz-Bonacich
centrality.

To implement the estimation, we need to reduce the size of adjacency matrix of thewhole supply-chain network. We restrict samples by the number of employments. We
extract largest 15000 firms in the number of employments from sample, and conduct
estimation by the following procedure.
First, we provide a candidate value of !, and calculate the Katz-Bonacich centrality
with the given !. Next, we estimate the equation (15) by OLS by using the calculated
Katz-Bonacich centrality, and obtain point estimates of !, and ! and sum of squared
residual, !!". We search the value of ! that minimizes !!", and the minimizers of
the !!" to be point estimates of !, !, and !. The standard errors for the estimatedparameters are obtained by 100 bootstrap iterations.!
The results are shown in Table 5. First of all, the coefficient for the log ofKatz-Bonacich centrality is positively significant at the 1 % level. Katz-Bonacich
centrality still has a positive effect on FDI even without exogenously specifying the
decay parameter. Further, the point estimate of ! is 0.015 and is positively significant.
This implies that the length of the network has a statistically significant decay effect on
the decision of FDI. Furthermore, we cannot reject the null hypothesis that our point
estimate of ! is equal to the inverse of the eigenvalue of adjacency matrix (0.019) atthe conventional level. This strongly suggests the validity of using the inverse of theeigenvalue of adjacency matrix as the decay parameter and the results in the previous
section.

6. Concluding remarks
This paper investigates how structure of supply chain network of the domestic market
influences FDI of firms embedded in the network. We firstly describe a binary choice offirms whether invest or not by a coordination game on fixed network with incomplete
information on part of firms’ profit. This model has a unique equilibrium which isrepresented by Katz-Bonacich centrality measure capturing both direct and indirect
effects from the network when supposing stand-alone profit follows a uniform
distribution with a sufficiently wide support. Following the theoretical results, we give
empirical tests for the theoretical hypothesis with a large sized disaggregated data ofJapanese firms, and verified that Katz-Bonacich centrality of each firm has asignificantly positive effect on its FDI as our theory anticipated. This result is almostrobust even when we consider FDI by destination and industry specific effects on FDI.
These estimations also show us that impact of Katz-Bonacich centrality is relatively
larger for large firms than for small firms. Furthermore, note that most of our estimation
employs specific eigenvalue centrality instead of generalized Katz-Bonacich centrality
and hence our results might depend on such assumption. However, our estimation forthe decay parameter of Katz-Bonacich centrality does not reject the eigenvalue
centrality; hence some robustness of our results is represented.
Finally, in the present model there remained a few problems to be solved althoughpart of them is justified by the existing evidences. First, although we suppose asimultaneous decision making and hence neglect the effect of firms’ observation on
partners’ FDI, an extension to dynamic sequential games considering such observation
will be potentially important issue. Estimation of such dynamic model will enable us to
identify the effect of the expectation from that of observation. Second, we suppose therestricted information of firms for which firms only know structure of network but do
not attributes of others. However, firms’ FDI will be naturally influenced from someeasily accessible information on partners such as industries and scales of them. To
consider such effects on equilibrium decision making, we must apply further extended
centrality measures weighted by attributes of each player such as presented by Ballester
and Calvó-Armengol (2010). However, for these extensions we always face restrictions
both in data availability and burden of computation. The latter is particularly intractablebecause calculating inverse matrices in our large sample data is impossibly difficult in
the present but is essential for estimating network models like ours. Reducing samples
is therefore inevitable for implementing such extended analysis as in section 5 of thispaper, but we must be careful enough to avoid sample bias in such treatment of data.

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-40

-30

-20
ln (Katz-Bonacich centrality)
FDI firms

Figure 1 Distribution of Katz-Bonacich centrality-10

Non-FDI firms0Table 1 Summary statistics

All

All FDIs
FDI firms

Obs.
Mean
SD

Obs.
Mean
SD
Non-FDI firms Obs.
MeanSD
FDI to South East Asia
FDI firms
Obs.
Mean
SD
Non-FDI firms Obs.
MeanSD
FDI to North America
FDI firms
Obs.
Mean
SD
Non-FDI firms Obs.
Mean
SD

Note:

Katz-Bonacich centrality
1151110.0025876
0.0096307

Labor productivity
11511130296.03219833.3

Listed firm dummy
1151110.0089305
0.0940789

Firm age
11511143.60812
22.69696

Credit score
11511151.29483
6.457229

2278
0.0174771
0.052036
1128330.002287
0.0059508

2278
58830.8960254.76
11283329719.94
221838.52278
0.3446005
0.4753422
1128330.0021536
0.0463574

2278
60.97147
25.53022
11283343.25757
22.49865

2278
62.89728
8.021161
11283351.06059
6.2021392070
0.0184025
0.0543769
1130410.002298
0.0059719

2070
59414.82
60716.73
11304129762.81
221649.22070
0.3531401
0.4780613
1130410.0026274
0.0511907

2070
61.14493
25.51585
11304143.28698
22.51522070
63.04928
8.060938
11304151.07958
6.220415

953
0.0280559
0.0776739
1141580.002375
0.0061441

953
64754.1348930.1
11415830008.37
220681.2953
0.5613851
0.4964781
1141580.0043186
0.0655741

953
66.18258
25.5777
11415843.41966
22.57669

953
66.26863
7.871422
11415851.16983
6.296013

Table 2 Baseline results
Dependent: FDI dummyln (Katz-Bonacich centrality)(1)
0.375***(0.0177)(2)0.220***(0.0327)(3)
0.296***(0.0200)(4)0.000797***(0.0000404)(5)0.000216***(0.0000267)(6)0.0125***(0.00140)ln (Labor productivity)

0.603***(0.0335)

0.515***(0.0663)

0.573***(0.0443)

0.00775***(0.000487)

0.00243***(0.000337)

0.0604***(0.00456)

ln (Credit score)

7.212***(0.233)

6.572***(0.477)2.996***(0.287)0.123***(0.00441)

0.0269***(0.00230)

0.298***(0.0286)

Listed firm dummy

3.046***(0.102)

3.639***(0.640)2.373***(0.0908)0.695***(0.0132)

0.323***(0.0912)0.538***(0.0149)ln (Age)0.495***(0.0659)

0.216*(0.111)0.353***(0.0664)0.00717***(0.000650)

0.000916***(0.000347)

0.0323***(0.00546)

Constant-38.57***(0.891)-35.95***(1.754)-19.89***(1.191)-0.581***(0.0186)-0.132***(0.00953)-1.820***(0.123)

Industry FEs

No

No

No

Yes

Yes

Yes

Estimation
Sample

Logit
All

Logit
Small firms

Logit
Large firms

Linear Prob.
All

Linear Prob.
Small firms

Linear Prob.
Large firms

Observations
Adjusted R-squared

11476510391410335

1147650.288

103914
0.019

10335
0.322

Note:
RobustStandard
errors instandard
parentheseserrors in parentheses. ***: 1% level; *: 10% level="* p<0.10** p<0.05*** p<0.01"

Table 3 Results by FDI destinations(1)
Dependent
FDI to South East Asialn (Katz-Bonacich centrality) 0.000734***(0.0000390)(2)
FDI to South East Asia
0.000190***(0.0000257)(3)
FDI to South East Asia
0.0126***(0.00138)(4)
FDI to North America
0.000189***(0.0000196)(5)
FDI to North America
0.0000285***(0.00000680)(6)
FDI to North America
0.00656***(0.000918)

ln (Labor productivity)

0.00713***(0.000467)

0.00207***(0.000316)

0.0576***(0.00451)

0.00239***(0.000268)

0.000438***(0.000115)

0.0241***(0.00311)

ln (Credit score)

0.113***(0.00422)

0.0228***(0.00210)0.300***(0.0280)

0.0543***(0.00293)

0.00474***(0.000941)

0.250***(0.0226)

Listed firm dummy

0.649***(0.0140)0.250***(0.0856)

0.504***(0.0155)

0.495***(0.0154)0.111*(0.0610)0.426***(0.0161)ln (Age)

0.00641***(0.000624)

0.000956***(0.000316)

0.0258***(0.00530)

0.00248***(0.000394)-0.000163(0.000167)

0.0170***(0.00361)

Constant-0.535***(0.0177)-0.113***(0.00883)-1.801***(0.119)-0.247***(0.0124)-0.0226***(0.00392)-1.271***(0.0940)

Industry FEs

Yes

Yes

Yes

Yes

Yes

Yes

Estimation
SampleLinear Prob.
All

Linear Prob.
Small firms

Linear Prob.
Large firms

Linear Prob.
All

Linear Prob.
Small firms

Linear Prob.
Large firms

Observations
Adjusted R-squared

1147650.275

103914
0.016

10335
0.307

1147650.303

103914
0.012

10335
0.316

Note: Robust standard errors in parentheses. ***: 1% level.

Table 4 Results by industry
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
(15)
(16)
(17)
(18)
(19)
(20)
(21)
(22)
(23)
(24)

Industry
Food
Beverages,tobacco and feed
Textile mill products
ApparelLumber and wood products
Furniture and fixtures
Pulp, paper and paper products
Printing
ChemicalPlastic products
Petroleum and Coal
Rubber products
Leather tanning, products and fur skins
Ceramic, stone and clay products
Iron and steel
Non-ferrous metals and products
Fabricated metal products
General machinery
Electrical machinery
Information and communicaion electronics
Electronic parts and devices
Trasportation equipment
Precision instruments and machinery
Miscellaneousln(centrality)
0.349***
0.588***
0.279***
0.0786*0.174
0.389**
0.383***
0.710***
0.251***
0.597***
0.567***
0.296**
0.437***
0.575***
0.431***
0.375***
0.475***
0.397***
0.466***
0.397***
0.438***
0.437***
0.229***
0.149**(0.0668)(0.137)(0.0712)(0.0434)(0.117)(0.172)(0.125)(0.193)(0.0845)(0.217)(0.0903)(0.119)(0.139)(0.0805)(0.0798)(0.101)(0.0515)(0.0376)(0.0679)(0.111)(0.0777)(0.0976)(0.0605)(0.0658)ln(labor productivity)
0.854***
0.426
0.416*
0.730***
0.294
1.212**
0.728**
1.337***
0.319***
0.571*
0.609***
0.969***
0.562
0.649***
0.855***
0.699***
0.745***
0.654***
0.791***
0.613***
0.401***
0.720***
0.260
0.459**(0.151)(0.275)(0.219)(0.177)(0.279)(0.509)(0.291)(0.323)(0.0927)(0.299)(0.129)(0.228)(0.733)(0.230)(0.145)(0.122)(0.133)(0.0820)(0.124)(0.151)(0.106)(0.134)(0.549)(0.196)ln(firm credibility)
6.817***
4.421*
6.389***
5.545***
11.38***
9.678*
5.616***
7.854***
6.641***-1.8836.064***
9.683***
14.71***
7.693***
4.904***
7.689***
7.416***
7.944***
6.879***
6.406***
5.434***
8.898***
9.083***
10.78***(1.199)(2.546)(1.586)(1.246)(2.680)(5.461)(1.389)(2.385)(0.828)(2.463)(0.928)(1.560)(4.627)(1.251)(1.148)(1.201)(0.745)(0.518)(0.847)(1.644)(1.057)(1.086)(1.496)(1.477)

Note: Robust standard errors in parentheses. ***: 1% level; **: 5% level; *: 10% level

listed firm
2.840***
2.160***
3.795***
3.594***
3.028***
2.548**
2.327***
1.916**
3.080***
2.019**
2.906***
2.806***.
3.412***
1.984***
2.716***
2.164***
3.257***
3.444***
2.617***
4.642***
3.548***
3.827***
5.227***(0.333)(0.657)(0.593)(0.826)(0.802)(1.067)(0.596)(0.885)(0.286)(0.925)(0.561)(0.720).
(0.521)(0.448)(0.525)(0.453)(0.276)(0.413)(0.542)(0.774)(0.484)(0.736)(0.968)ln(age)0.297
0.06070.162
0.977***
0.922
0.995**
1.603***-0.127-0.0209
1.873*
0.811**
0.210
3.130***
1.137***
1.109**
0.104
1.113***
0.644***
0.597**
1.090***
0.780***
0.393*
0.126-0.0487(0.242)(0.578)(0.372)(0.354)(0.577)(0.506)(0.501)(0.628)(0.203)(0.967)(0.340)(0.647)(1.193)(0.337)(0.516)(0.326)(0.283)(0.158)(0.250)(0.360)(0.274)(0.223)(0.348)(0.349)Constant-39.77***-22.91**-31.86***-36.66***-56.14***-57.62***-38.59***-45.89***-31.71***-5.168-34.07***-51.14***-77.98***-42.60***-34.02***-39.82***-42.91***-42.43***-39.09***-37.16***-29.86***-45.78***-41.79***-51.20***(5.156)(8.908)(5.988)(5.460)(9.016)(18.70)(6.321)(8.651)(3.521)(10.81)(3.982)(7.165)(16.67)(5.341)(4.984)(4.933)(2.994)(2.014)(3.146)(6.335)(4.308)(4.478)(5.560)(5.452)

Observations
10527
2189
3229
4129
3179
2478
3865
6846
3892
273
6599
1409
708
5114
2420
1826
15395
17832
6560
1461
3270
4038
2489
5036

Table 5: Results in full specificationln(centrality)
0.044***[0.01]ln(labor productivity)
0.039***[0.004]ln(firm credibility)
0.015***[0.003]listed firm
-0.073***[0.002]ln(age)0.237***[0.019]Constant-0.699***[0.095]Gamma
0.015**[0.006]

Observations
15000

Note: Standard errors are calculated by 100 bootstrap iterations. Bootstrapped standard errors in square parentheses. ***: 1% level; **:5% level; *: 10% level