Journal of Robotics, Networking and Artificial Life, Vol. 1, No. 2 (September 2014), 150-154

An Empirical Examination of Inter-firm Capital Relationships in Mazda’s Yokokai using theIDE Spatial Model
Makoto Sakamoto*, Satoshi Ikeda

Dept. of Computer Science and Systems Engineering, University of Miyazaki, 889-2192 Japan
Takao Ito

Graduate School of Engineering, Hiroshima University, Higashi-Hiroshima, 739-8527 Japan
Rajiv Mehta

School of Management, New Jersey Institute of Technology, 07102-1982 U.S.A
Seigo Matsuno, Shinya Tagawa

Dept. of Business Administration, Ube National College of Technology, Yamaguchi, 755-8555 JapanVictor D. Berdonosov

Faculty of Computer Science, Komsomolsk-on-Amur State University of Technology, 691013 Russia*Corresponding author, E-mail: sakamoto@cs.miyazaki-u.ac.jp
Tel: +81-985-58-7392, Fax: +81-985-58-7392

Abstract
Just as workflow and transactional linkages, inter-firm capital relationships are similarly known to have an impact
on corporate performance. Because of the superior performance of Japanese networks known as Keiretsu, many
companies have begun to recognize the importance of capital linkages whereas other companies have placedemphasis on improving coordination of managerial resources. In this paper, we review the literature on networkorganizations with a lens focused on examining the capital relationships in Yokokai, the Mazda’s Keiretsu.
Employing regression analysis, three significant indices, influence, degree, and efficiency, were selected from nineindices, including others that include dyadic redundancy, dyadic constraint, effective size, constraint, hierarchy, anddensity. We propose a new approach, called IDE spatial model, to calculate the strength of the inter-firm’srelationships. In order to ascertain the rational inter-firm relationships, network indices and corporate performance
are analyzed. Therefore, this research suggests a new perspective to examine the rational inter-firm relationship thatcan be used in any network organization.
Keywords: influence, degree, efficiency, the IDE spatial model, Keiretsu.

1. Introduction
Just as workflow and transactional linkages, inter-firm
capital relationships are similarly known to have animpact on corporate performance. Because of thesuperior performance of Japanese networks known as
Keiretsu, many companies have begun to recognize theimportance of capital linkages whereas other companies

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M. Sakamoto et al.

have placed emphasis on improving coordination ofmanagerial resources. In this paper, we propose a newapproach, called IDE spatial model, to calculate thestrength of the inter-firm’s relationships. In order toascertain the rational inter-firm relationships, network
indices and corporate performance are analyzed.
Therefore, this research suggests a new perspective toexamine the rational inter-firm relationship that can beused in any network organization.
This paper is organized as follows. In Section 2, webriefly review some relevant literature of quantitative
approaches of Keiretsu. Section 3 introduces the IDE
spatial model. Section 4 shows the results, and discusses
the implications of the results. Finally in Section 5 weconclude by a summary of this paper.
2. Background
One of the important factors in structural analysis, astrong tie and/or weak tie is popular way to describe thedifferent strength of a relationship.
However, quantitative approaches are required to
discover the determinants of corporate performance.
Relationships among firms based on distances between
their locations and the frequency of face-to-facecommunication among engineers in the automobile
industry has been examined [1]. Moreover, Fukuoka etal. reported a new finding on relationships among
member firms in Nissan’s using transactions and crossshareholdings [2]. Recently Ito et al. applied graphtheory to network organization analysis, and identified
some characteristics such as centrality, size of network
as being important facets of relationships [3].
Transactional inter-firm’s relationships are the keyconcepts in these studies. In a Keiretsu, capital interfirm’s relationship is known as cross shareholding. To
the best of our knowledge, only a few studies haveexamined cross shareholdings from an organizational
network vantage point; therefore this investigation
attempts to shed light on one of the most advanced
quantitative analysis using data gathered from Mazda’s
Yokokai Keiretsu.

suitable for the analysis of capital network. In order to
identify the factors that impact corporate performance,
we employed regression analysis using three significant
indices, influence, degree, and efficiency, were selectedfrom nine indices. The others six are dyadic
redundancy, dyadic constraint, effective size, constraint,hierarchy, and density. We propose a new approach,called IDE spatial model, to calculate the strength of theinter-firm’s capital relationships.
3.1. Outline of the IDE spatial model
Generally influence means one kind of power to affectpersons or events, or causing something without any
direct or discernible effort. Influence reflects the power
to influence or have an impact on other member firms
directly and indirectly in a network. Consequently,influence will be divided into two parts: direct influenceand indirect influence. Suppose that A is the matrix ofthe direct network, and An means the indirect influence
from one firm to another firm by n steps. Then influenceis calculated as follows.

T = A + R = A + A 2 + A3 + ⋅ ⋅ ⋅ + A n= A( I − A) −1
where
T: Total influence;
A: direct influence;
R: indirect influence;
I: Identity matrix.
An integral index known as centrality has many facetsthat include degree, closeness, and betweenness. Degree
expresses a firm’s potential communication activity. In
cross shareholding network, degree includes two
categories: in-degree and out-degree, because crossshareholding networks are considered to be asymmetricorganizations. In-degree refers to a firm accept
investment from other member firms, whereas outdegree reflects a firm that only buy stocks of other firms
within the network. Degree is calculated as below.
nCD ( pk ) == ∑ a( pi , pk )i =1

i = 1,2,⋅ ⋅ ⋅, n; k = 1,2,⋅ ⋅ ⋅, n3. Method
Many spatial paradigms, such as the IDCBI model andthe DEC spatial model have been developed to discern
the relationship between network indices and corporate
performance. One of the key questions of thisinvestigation is to determine if all these models arewherea(pi, pk)=1; if and only if pi and pk are connected by alinea(pi, pk)=0; otherwise

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An Empirical Examination of Inter-firm Capital Relationships

In this paper, percent data of inter-firm’s transactions
are collected from Yokokai.
Efficiency is another important index. Effective size ofthe network is the number of alters that ego has, minus
the average number of ties that each alter has to otheralters. Suppose that A has ties to three other actors.
Further, suppose that none of these three has ties to anyof the others. Thus the effective size of ego's network isthree. Alternatively, suppose that A has ties to threeothers, and that all of the others are tied to one another.
A's network size is three, but the ties are "redundant"
because A can reach all three neighbors by reaching any
one of them. The average degree of the others in thiscase is 2 (each alter is tied to two other alters).
Therefore, the effective size of the network is its actualsize, i.e., 3, reduced by its redundancy, i.e., 2, to yieldan efficient size of 1. Efficiency expresses the effective
size of ego's network by its actual size. That is, what
proportion of ego's ties to its neighborhood is “nonredundant”? Thus, efficiency tells us how much impact
ego is getting for each unit invested in using ties. A firm
can be effective without being efficient; and an actor
can be efficient without being effective.

3.2. Data collection and visualization
In order to measure influence, degree, and efficiency ofeach firm in Yokokai, cross shareholding data in theYokokai Keiretsu in 1997 and 2004 have been collectedfrom our interviews and the publications of the Japan
Auto Parts Industries Association and Automotive Parts
Publishing Company [4].
In 1997, 53 financial institutions, 190 parts suppliers,and 11 carmakers are included in Yokokai. The detailed
information of the numbers of financial institutions,parts-supplies, and carmakers in Mazda’ crossshareholdings network in 1997 and 2004 are shown in
Table 1.
In this paper, a singleton, which can be found in any
network, is defined as a firm that exists independently,
without any relationship with other firms. Therefore, asingleton generally is an isolated firm in a givennetwork. In 1997, 132 singletons including 26 financialinstitutions, 105 parts-suppliers, and 1 carmaker havebeen found. In 2004, 1 financial institution, 120 partssuppliers, and 2 carmakers are singletons. All of thesingletons have been removed in this paper because thenumber of singletons has no any impact on thecalculation results.
Table 1 Numbers of financial institutions, parts
suppliers and carmakers in Yokokai in 1997 and 2004
19972004
Financial Institutions

5336

Parts-suppliers
Carmakers

190
11177
11Total

254

224

The cross shareholdings relationships among thecompanies were identified through three dimensionalmodeling. A bar shows the percentage of the transaction
between each pairs of firms. The three dimensional
capital inter-firm relationships in Yokokai are depicted
in Figure 1 and 2 respectively.
The cross shareholdings relationships among thecompanies were identified through three dimensionalmodeling. A bar shows the percentage of the transaction
between each pairs of firms. The three dimensional
inter-firm capital relationships in Yokokai are shown in
Figure 1 and 2 respectively.
Compared with Figure 1, we find that the interactivity
between financial institutions and parts-suppliers islower, whereas the interactivity between parts suppliers
is higher. The reason is that the interactive relationshipamong financial institutions, suppliers and carmakers
changed rapidly with the varying of economicenvironment. For suppliers, the control from carmakers
is becoming looser than before. Now suppliers can moreeasily forge a new capital relationship with other firms.

Figure 1 Inter-firm’s capital network in 1997

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M. Sakamoto et al.

4.2. Data collection and visualization
We calculated partial correlation coefficient of the nine
indices in multiple regression model, and found density,
effective size and other 4 indices are not significant.
Thus we removed those 6 variables and re-estimated theregression model. The results in 1997 are shown inTable 2.

Table 2 Results of the variance analysis

Figure 2 Inter-firm’s capital network in 2004

Sum ofSquares

Degree ofFreedom

Mean
SquareTotal

4.239E+1161

Regression

2.777E+113

9.257E+10

Prob.

Residual

1.462E+1158

2.521E+09

0.000

F Test36.721

Coefficient of determination: 0.65510
Multiple correlation coefficient: 0.80938
Adjusted R-square: 0.79829
AIC: 1,521.98
DW ratio: 2.5382

As shown in Table 1, the coefficient of determination is0.65510, and DW ratio is 2.5382, and the probability is0.000. Therefore, the regression model is significant.
The estimation of regression coefficients is shown in
Table 3.
Table 3 Estimation of regression coefficients
Figure 3 Out-degree and in-degree in 1997 and 2004.
4.

Results and discussions

4.1. Centrality changes
In an asymmetric network, degree can be divided into
two parts: out-degree and in-degree. The result of theout-degree and in-degree of the whole crossshareholdings is shown in Figure 3.
The out-degree in 2004 is lower than that in 1997 but
the in-degree in 2004 is higher than that in 1997. Lower
centrality means that much more companies invest theirmoney to buy parts suppliers they interested. In otherword, parts supplier can accept much more different
companies’ investment without permission from the top
firm of their Keiretsu. Especially the dramaticallychange between out-degree and in-degree inflects thestructure changes happened in Yokokai.

Partialregression
coefficientStandard
coefficient
T value
Degree ofFreedom
Prob.
Correlation
coefficientPartialcorrelation
coefficient

Influence

DegreeEfficiency

Intercept

4.17 E+7-7.300E+4

5.575E+5-5.509E+582.896-82.398

0.289

0.000

8.536

-8.4873.465-3.455

58

58

58

58
0.001

0.000

0.000

0.001

0.47560.470-0.0180.746-0.744

0.414

The estimation of regression coefficients in 2004 has
been calculated also. Based upon Table 2 and thecalculation of 2004, influence, degree, and efficiency
are significant. Degree is negative, while influence andefficiency are positive. Degree is an index of number ofstockholdings, and influence is an index of structuralpositions, then the hypothesis of “better structural
position, higher performance” is upheld.

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An Empirical Examination of Inter-firm Capital Relationships

The number of influence is decreasing. And the numberof degree and efficiency are increasing. It means that theimportance of structural position is still effective, but
the capital relationship with other firms and themanaging cost of investment is becoming more andmore important because of the membership keiretsu isloosening..

5. Conclusion and future works
In this paper, the new approach of IDE analysis isproposed, and its validity is proved. We ascertained that(1) the centrality of Keiretsu is becoming low, (2) not
all network indices, only influence, degree, andefficiency has an impact on profits. (3) The importanceof influence is becoming lower, and the degree andefficiency is becoming higher due to the trend in theloosening of Keiretsu. However, additional research
advocated developing our knowledge on rational capital
relationships with other parts suppliers.
Acknowledgment: This research was partially
supported by the Japan Society for the Promotion ofScience, Grant-in-Aid for Scientific Research (C)24510217.

References
1. Dyer H. J. (1996) “Specialized Supplier Networks as a
Source of Competitive Advantage: Evidence from theAuto Industry”, Strategic Management Journal, Vol. 17,271-291
2. Fukuoka S., Ito T., Passerini K. and Sakamoto M. (2006)
An Analysis between Transaction and Cross
Shareholdings in the Keiretsu of Nissan, Managing
Information in the Digital Economy Issues & Solutions,163-169, IBIMA International Conference, BonnGermany
3. Ito T., Tagawa S., Matsuno S., Uchida Y., Sakamoto M.,Ikeda S., Mehta R. (2013) An Analysis of Network
Structure in Mazda’s Yokokai using the DEC Spatial
Model, Proceedings of the 2013 International Conference
on Business Administration, Marketing, and Economics(MAME 2013), Recent Advances in Business
Administration, Marketing and Economics, pp.77-81,
September 28-30, 2013, Venice, Italy
4. JAPIA&APPC (1997, 2004), Japanese Automotive Parts
Industry, Automotive Parts Publishing Company,(Japanese Edition)

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