Technological Externalities and Economic
Distance: A Case of the Japanese Automobile
Suppliers∗
Yosuke Takeda†and Ichihiro Uchida‡
August 29, 2009

Abstract
This paper in the spirit of Marshall(1920) raise a question of how economic distance aﬀects the firms’ productivities, focusing upon roles of idea
in sharing technological knowledge or information between firms. In order to quantify the degree of knowledge spillover or information sharing,
we take production function approach. Assuming core-periphery structure around automobile assemblies surrounded with auto-parts suppliers,
we estimate plant-level production functions of the Japanese auto-parts
suppliers, where productivity function depends upon economic distancemeasuring information sharing with both geographic plant location andmembership of technological cooperation associations. We take econometric issues of cross-sectional dependence of productivities and a simultaneity problem between inputs, applying methods to the standard OLS and
GMM estimators. Positive technological externalities(i.e. agglomerationeﬀects) are seen in general or for independent plants, the fact which is robust to specifications of the production functions. Agglomeration eﬀects
are rarely observed for relation-specific or cooperative plants. Some ofthem cost the auto-parts plants substantial negative externalities. Once asimultaneity problem is econometrically considered, instead of increasing
returns, decreasing returns to scale emerge in cases of total materials. Agglomeration, if any, could be brought about not by increasing returns toscale, but by productivities spillover among proximate suppliers aroundautomobile assemblies.
∗ This paper was formerly entitled as ”Agglomeration or Congestion? Productivity andEconomic Distance of the Japanese Automobile Suppliers.” We are grateful to Mika Sato,
Maki Yamaguchi and Manami Fujishiro for devoted assistance of data construction, to Iichiro
Uesugi and Toshiyuki Matsuura for helpful suggestions on data accessibility and handling, toMasahisa Fujita, Shin-ichi Fukuda, Takatoshi Tabuchi, and Toyoharu Takahashi for encouraging comments, and to numerous participants in 2009 Far Eastern and South Asia Meeting of
the Econometric Society and the Research Institute of Economy, Trade and Industry, Japan,
Nagoya University, and Nanjing University. We also appreciate financial support from grantin-aid for scientific research(#19530254), Ministry of Education, Culture, Sports, Science andTechnology.
† Correspondence: Faculty of Economics, Sophia University. y-takeda@sophia.ac.jp‡ Faculty of Economics, Aichi University.

11

Introduction

Spatial and growth economics look to the productivities of firms as a primarydriving force of economic development. Consequently, productivity analysis investigates how to quantify the unobservable stuﬀ and capture the eﬀects upon
economic development. However, while the measurements of productivities arewell understood, relatively little is known about how economic distance aﬀects
the productivities and firms’ growth, although the old issue raised by Marshall(1920) is modernity.
For instance, Toyota Motor Corporation is famous for its ’just-in-time’ production system, where the make-to-order system aims to reduce goods-in-process
inventories of automobile parts provided by the Japanese circumvoluting suppliers. The domestic production system supported mainly by the suppliers sitedin Mikawa Area at the center of Aichi Prefecture, however, has changed in aform of step-up overseas production. From 1999 to 2008, the total automobile
production rose more than 17 times in a decade, while there were then gradualdecreases from 659% to 489% in domestic production ratio of the manufactured automobiles. Will the decentralization of the Toyota’s producer regions
make the Japanese giant producer more globally competitive as well as in domestic markets? Will the domestic R&D jointly involving the vicinity suppliers
be replaced with arm’s-length patent license granted across the borders? The
answers to these questions could hinge upon distributions of the productivities
shared by auto suppliers on the periphery of automobile assembly plants. If
the productivity distributions agglomerate into a mass or group, then the organizational decentralization would deteriorate the competitiveness. Otherwise if
the distributions reveal congestion in the neighbourhood of the core assemblies,
then the replacement of R&D with granted patent license would enhance theproductivities.
In this paper, we estimate production functions of the Japanese automobileparts plants, specifying relation between the productivities and some measured
economic distance. The estimations take into account some econometric issues.
Our main results are as follows:
1. In 2003, the number of membership companies with associations for technology cooperation is so limited. Most of the auto-parts corporations are
independent of the memberships.
2. Locations of the general or independent plants is distributed in positively
skewed way. On the other hand, the relation-specific or cooperative plants
show diﬀerences in locations between the automobile assembly groups or
the association memberships for technology cooperation.
3. The general or independent plants could benefit from positive technological externalities. Agglomeration eﬀects of relation-specific or cooperativeplants are rarely noticed for the Japanese automobile corporations and2their technology cooperation associations. A few of them cost the autoparts plants or the member companies substantial negative externalities
in productivity.
4. Qualitative results concerning agglomeration or congestion vary between
the standard OLS or GMM and an estimator with cross-sectional dependence(Conley, 1999). However, general, a relationship group or independent plants still achieve agglomeration eﬀect upon the auto-parts plants.
The agglomeration eﬀect of general and independent locations is also robust to specifications of production function in material variables and incross-sectional dependence of productivities.
5. Once a simultaneity problem associated with unobservable productivities
is econometrically considered, decreasing returns to scale emerge insteadof increasing returns. Material variables also lose significance in estimatingproduction functions. The rejection of constant returns to scale leads toagglomeration, if any, brought about not by increasing returns to scale, but
by productivities spillover among proximate suppliers around automobile
assemblies.
The paper is organized in the following Sections. Section 2 presents a brief
overview upon roles of economic distance in economic theory and management
science. Based upon the definitions of economic distance detailed in Appendix,
we then construct some distance variables from data on plants’ location andmemberships with associations for technology cooperation. In Section 3, theproduction functions augmented with the productivity function are estimatedwith OLS and GMM estimators. The specification of the productivity function nests some types of agglomeration and congestion eﬀects. Section 4 takes
a few econometric issues associated with either cross-sectional dependence of
productivities or a simultaneity problem between inputs. Finally, we conclude
in Section 5.

2

Economic Distance in Theory and Practice

2.1

Related Literatures

In order to explain why we raise a question ”agglomeration or congestion?”in terms of productivity, in economic theory and management science among
related literatures, we briefly view roles of economic distance. Economic distancecan be so broadly interpreted in several meanings of geographical, industrial,social/sociological, organizational, or legal context. Literatures covered froma view point of economic distance, however, are confined to economic growththeory, spatial economics, industrial organization, productivity analysis, andmanagement science.

3Marshall(1920) emphasized advantages of proximity for production in entrepreneurship, with provident yet immature view upon industrial agglomeration through three channels of goods, people and ideas.
When an industry has thus chosen a locality for itself, it is likely tostay there long: so great are the advantages which people following
the same skilled trade get from near neighborhood to one another.
The mysteries of the trade become no mysteries; but are as it were in
the air, and children learn many of them unconsciously. Good work
is rightly appreciated, inventions and improvements in machinery,in processes and the general organization of the business have their
merits promptly discussed: if one man starts a new idea, it is taken
up by others and combined with suggestions of their own; and thus
it becomes the source of further new ideas. And presently subsidiary
trades grow up in the neighborhood, supplying it with implements
and materials, organizing its traﬃc, and in many ways conducing to
the economy of its material.(IV, X, 7, Marshall, 1920)
Among ”externalities” through the three channels, as Scitovsky(1954) pointed
out, there is a distinction of technological externalities and pecuniary ones.
The former externalities deal with non-market interactions directly aﬀected byproduction function of a firm, while the latter ones refer to interactions throughmarket mechanisms. For the sake of this paper, our interest is in ’technologicalexternalities’ in production function caused by proximity to ’source of further
new ideas’.
The Marshallian externalities have been often addressed in the economic
growth theory(for instance, Romer, 1986). Monopoly rights to ’lean’ production technology associated with superior world knowledge, become barriers tointernational transferability of technology to proximate countries in technological closeness, delaying economic development(Parente and Prescott, 1994;
Schmitz, 1989). In the cross-sectional empirical studies following Barro andSala-i-Martin(1997), using some spatial econometric methods, spatial externalities of technological interdependence are analyzed in the convergence equation(Ertur and Koch, 2007) or the costs of transporting physical capital between countries are taken into account to reevaluate the Barro-regression’s results(Conley and Ligon, 2002).
More directly in the regional and spatial economics, including economic agglomerations within congested ’cities’(Fujita and Thisse, 1996) or industrial
agglomerations from increasing returns(Krugman, 1991), a variety of social interactions are analyzed. Among them, there is a model of social distance, where
correlated with social distance between agents, such social decisions as educational attainment or childbearing may reproduce social ’class’ stability(Akerlof,
1997). Some indexes for plants’ geographic concentration and ’coagglomeration’are constructed based upon a model of location choice, in cases of the US manufacturing industries(Ellison and Glaeser, 1997) and the UK data(Durantonand Overman, 2005). Input-output relations also provide an economic distance4

measure that is used to characterize interactions between sectors(Conley andDupor, 2003).
In the field of industrial organization, empirical studies on production(Ackerberg,
Benkard, Berry and Pakes, 2006) address such market outcomes as industry
dynamics of firms’ entry and exit(Olley and Pakes, 1996), industry dynamics
from product switching(Bernard, Redding and Schott, 2008), R&D spillover
through patents(Griﬃth, Harrison and van Reenen, 2006; Bloom, van Reenen
and Schankerman, 2007), or spillover eﬀects of opening ”million dollar plants”
on incumbent plants(Greenstone, Hornbeck and Moretti, 2008). These analyses suggest that the degree of proximity in industries, products or inputs isa key factor to industry dynamics or technological spillover. In a series of papers by van Biesebroeck(2002, 2003) on productivity in the automobile assemblyplants in the North America, technology choice or switch between heterogeneousmass or lean(flexible) production accounts for diﬀerences between the US andJapanese automobile producers in complementarities of productivity(Milgrom
and Roberts, 1990; van Biesebroeck, 2007).
In the management science literature, complementarities in production aremathematically represented in supermodular function(Topkis, 1995). As evidence of the complementarities, firms locating near one another at Silicon
Valley learn innovations(Saxenian, 1996). Another case study on Toyota Motor Corporation(Nishiguchi and Beaudet, 1998) elaborates a fire accident andrapid recovery from production stoppage, in 1997 at Kariya Plant of Aisin Seiki
Co., Ltd., the Toyota’s exceptionally major supplier of an auto-part ’p-valve’1 .
The disaster was followed by collegial eﬀorts of reproducing the same partsas the Aisin’s products by corporations aﬃliated with Toyota. The corporations included member companies belonging to Kyoho-kai, Toyota’s association
for technology cooperation described in Appendix. The episode reminds the
management researchers of sociological ”small worlds” framed by Watts(1999),
where horizontal bypass between suppliers is usually eﬀective in hierarchicalcluster structures(Aoki, 1986; Rajan and Zingales, 2001).
In practice, the most prominent activity between proximate firms may beresearch collaboration. The collaboration network has typical forms of either’joint ventures and research corporations’ or ’joint R&D and technology exchange’(Hagedoorn, 2002). The former collaboration is set up in a distinct new
firm which is based upon equity investment jointly contributed by concerned
firms. For instance, Toyota Motor Co., Ltd. and Panasonic Corporation established a firm, Panasonic EV Energy Co., Ltd., on December 1996 at Kosai,
Shizuoka Prefecture, Japan. It is within 18 from a Toyota’s major assembly,
Tahara Plant as the crow flies. The new firm develops, manufactures and sells
Nickel metal hydride and Lithium ion rechargeable batteries for HEVs(hybrid
electric vehicles) and PEVs(pure electric vehicles), the profits of which are dis1 There was another accident visiting Riken Corporation, located at Niigata Prefecture in
Japan that the Mid Niigata Prefecture Earthquake directly hit in 2007. Riken Co. thenshared near a half the market of an automobile engine part, piston ring. Not only Toyota but
also all the other Japanese motor corporations had to stop their productions, but the breakperiod was up to one week.

5

tributed in proportion to the investments(Toyota 60% and Panasonic 40%). The
latter form of research collaboration, R&D partnerships, however has relatively
dominated over joint ventures of declining importance, especially in industries
such as pharmaceuticals or information technology2 .
Among the comprehensive literatures, the closest approach to this paper
is ones estimating some forms of productivity functions. Griﬃth, Harrison andvan Reenen(2006) assume that productivities depend upon the number of patentcitations. van Biesebroeck(2002, 2003) emphasizes diﬀerences in productivities
between ’lean’ and ’mass’ production systems. Henderson(2003) also identifies local information spillover in plant-level production functions for the US
machinery and high-tech industries.

2.2

Data Construction

We construct some measures of economic distance  applied to each plant
. We assume core-periphery structure around automobile constructors surrounded with auto-parts suppliers. In the structure, technological information
can be shared through both locating plants with geographic closeness and joining technological cooperation associations organized by auto-assemblies.
Our data source of geographic distance is Current Survey of Production,
conducted by Ministry of Economy, Trade and Industry, Government of Japan.
We use cross section in the fiscal year 2003, when the Japanese macro economy
had recovered from a severe deflationary episode. We pick up two broad items forauto-parts: automotive body and concomitant of an industrial subclassification
3012; and automotive component and accessory of 3013. We choose as theautomobile constructors the following 10 companies, listed in an alphabeticorder: Daihatsu, Hino, Honda, Isuzu, Matsuda, Mitsubishi, Nissan, Subaru,
Suzuki, and Toyota. As described in Appendix, our data excludes automobile
assemblies, a 4-digit industrial subclassification 3011, but the real constructor orgroup names are stipulated to be confidential in utilizing the plant-level data.
Note that a subscript  denoting automobile production companies does notcorrespond to the order above.
The other data source of us is The Japanese Auto Parts Industries, published by Japan Auto Parts Industries Association. It contains membership ofeach auto-parts company belonging to 8 technological cooperation associationsorganized by 8 constructors(Daihatsu; Hino; Isuzu; Matsuda; Nissan; Subaru;
Suzuki; Toyota) and company names of business partners with Honda and Mitsubishi.
We integrate both data sources to construct four measures of economic distance with the following definitions:Definition 1 General: Minimum distance of a plant  measured from any au2 The evidence is from Hagedoorn(2002), which presents some international evidence using
the MERIT-CATI database, an extensive survey on inter-firm allianaces starting in 1960.

6tomobile construction plants aﬃliated with major 10 production companies.
 for a plant (1)Definition 2 Relationship: Minimum distance of a plant  from any plants ofeither automobile production company above  = 1 2 3 4 5 6 7 8 9or 10 for a plant  and a company (2)where consequently,  = min .


Definition 3 Cooperation: Measured with the following product term: ≡  × (1 −   ) for a plant  and a company (3)where   is a dummy variable consisting of a value 1 in case of each company joining a technology cooperation association organized by an automobile
production company above  = 1 2 3 4 5 6 7 8 9or 10, or a value 0 otherwise.
If two suppliers join the same association organized by a constructor, then they
can share the technological information, so that the minimum distance of theplants from the constructor’s establishment should be zero.
Definition 4 Independence: A measure for non-aﬃliating companies or plants
with any specific automobile production companies.
 ≡  ×  −

(4)where a dummy variable  − denotes technologically independent plants without cooperative relationships with any production companies  = 1 2 3 4 5 6 7 8 9or
10.
Concerning the economic distance measures summarized in Table 12, there
are a few characteristics to mention. First, we plot plants locations of our sample
on the virtual globe software Google Earth, longitude and latitude of which arecoded with the geographical information software ArcGIS. Figure 1 indicateslocation information on plants joining any technology cooperation associationsorganized by either automobile assembly corporation, that is plants with zero
value of  . Compared with Figure 2 of independent companies’ locations, wefind that the number of member companies of the associations is so limited.
Second, some histograms indicate that distribution of the general or independence distance measure is positively skewed(Figure 3 and Figure 4). The
relationship or cooperation distance measures show diﬀerences between the automobile assembly corporations(as typical cases, Figure 5 and Figure 7), or
between the groups for technology cooperation(similarly, Figure 6 and Figure
8).

7

3

Production Functions EstimatedThis paper estimates the Cobb-Douglas type of production function measuring
gross revenue  with an i.i.d. component  ,ln  =

0+ ln  +ln  +ln  +   +

(5)where capital stocks  , labour inputs  , and intermediate materials  are
the production factors. Productivity of a plant  is then measured with theb  . Note that the Cobb-Douglas type of production function
estimates b0 + 
satisfies the supermodularity formulated by Topkis(1995).
We decompose the serially correlated component of productivity   into twoparts,
 =  + ˜(6)where   denotes distance-dependent productivity, and  ˜means the residual
productivity independent of economic distance. We assume that the distancedependent productivity  is exogenous, in that location choice of each plant
or corporation is predetermined ahead of production decisions including input
choices. We recognize that plant location is another choice variable for corporations, as market entry and exit are endogenous decisions. However, as in
the above citation from Marshall(1920), ”When an industry has thus chosena locality for itself, it is likely to stay there long: so great are the advantages
which people following the same skilled trade get from near neighborhood to
one another,” the location choice is probably associated with sunk costs. The
assumption is also appropriate for us, since this paper analyzes cross-sectional
data.

3.1

Specification of Productivity Function

We approximate  with a third-order polynomial in distance  .
  = 1  + 2 ( )2 + 3 ( )3(7)

where a distance measure  is one among the 4 types of economic distanceabove. Our simplified specification of the productivity function draws upon the
Silicon Valley hypothesis of Saxenian(1996) that nearby firms learn innovations.
Note that in the polynomial function, the distance measures and either input
variables should be independent of each other. The constant predetermined
locations cannot be state variables determining endogenous production inputs.
The distance measures are also in cases results of location choices by parents
companies, which is out of scope for each plant.
Applying the specification of productivity function, we define agglomerationeﬀect and congestion one. Agglomeration(congestion) has the same meaning8as positive(negative) technological externalities defined by Scitovsky(1954). We
evaluate the externalities in a neighbourhood of core automobile assemblies,that is when  → +0. In our interpretation, congestion eﬀect for instance indicates ’lock-in-eﬀect’ preventing suppliers from getting access to more advanced
technology provided by more remotely located constructors.
Definition 5 The agglomeration eﬀect on productivity in the sphere of any
core assemblies, is measured with signs of the estimates in the following cases:
A.1 Linear agglomeration:(  ) |→+0 =(  ) |→+0£¤

c1 + 2cc1  02 ( ) + 3c
3 ( )2 = 

A.2 Quadratic agglomeration:


£
¤


c1 + 2cc1 = 0∧2 ( ) + 3c
3 ( )2 = (  ) |→+0 = (  ) |→+0 (  ) |→+0 =

2 + 6c3 ( )] = 2c
2  0(  ) |→+0 [2cA.3 Cubic agglomeration:






£
¤

c1 + 2cc1 = 0∧2 ( ) + 3c
3 ( )2 = (  ) |→+0 =(  ) |→+0

(  ) |→+0 =2 + 6c3 ( )] = 2c
2 = 0∧(  ) |→+0 [2c









3  0(  ) |→+0 = 6c
Definition 6 The congestion eﬀect is also measured in the following cases:
C.1 Linear congestion:(  ) |→+0 =(  ) |→+0

C.2 Quadratic congestion:






£
¤

c1 + 2cc1  02 ( ) + 3c
3 ( )2 = £¤
c1 + 2cc1 = 0∧2 ( ) + 3c
3 ( )2 = (  ) |→+0 =(  ) |→+0

(  ) |→+0 =2 + 6c3 ( )] = 2c
2  0(  ) |→+0 [2c







C.3 Cubic congestion:






£
¤

c1 + 2cc1 = 0∧2 ( ) + 3c
3 ( )2 = (  ) |→+0 =(  ) |→+0

(  ) |→+0 =2 + 6c3 ( )] = 2c
2 = 0∧(  ) |→+0 [2c









3  0(  ) |→+0 = 6c

9

3.2

OLS and GMM Estimates

We estimate the production functions augmented by the economic distance measures with OLS and GMM. The GMM estimator instruments the first lagged
variables of endogenous production inputs, labour, capital stocks and materials.
The instrument data is supplemented by the year 2002 sample. We alternate
either variable of total materials including raw materials, fuel, electricity andoutsourcing costs, or raw materials. Heteroskedasticity robust standard errors
are ones proposed by Davidson and MacKinnon(2004).
Since some of the Japanese auto-parts suppliers at least probably maintainpricing power in their auto-parts markets, productivity term in estimated production function might contain changes in market demand for auto-parts. In
order to control the market demand, we include in production function the products dummy variables, which are equal to 1 if each auto-parts supplier list eachproduct; or 0 otherwise. We cover total 28 items subordinate to the 2 broad
items of auto-parts.
We first show estimation results when excluding any distance variable in the
explanatory variables. Evidently in Table 1, the fit is well with 2 at least 088.
All the estimated coeﬃcients on production inputs are significant, though therelative magnitude is diﬀerent between two cases with total or raw materials as
an explanatory variable. The null hypothesis of constant return to scale(CRTS)+= 1 is strongly rejected in all the cases, which implies increasing
 +returns to scale in the Japanese automobile-part plants.
We proceed to estimating each equation augmented by productivity functionof each economic distance variable one by one. The magnitude and significanceof the coeﬃcients on inputs remain almost the same as in the production function without distance. The increasing returns to scale is also accepted. Resultson the coeﬃcients in the productivity function are in Table 2 for OLS estimatesand Table 3 for GMM. Qualitative results of OLS are very similar to those ofGMM. We make some remarks about the GMM results.
In a case of total materials, few of the economic distance measures are significant except for general distance, and independence distance. In the estimatedproductivity functions of the two distance variables, we find the agglomerationeﬀect of a type 1 defined above. On the other hand, the other case of raw
materials generates more coeﬃcients in the productivity polynomial which aresignificant with a significance level of 10%. There are not only seven equationsof the 1 agglomeration including general, relationship  = 1 and independence
distance, and one equation of the 2 agglomeration eﬀect, but also six of the1 congestion eﬀect for the automobile assembly corporation  = 3. The remaining estimated equations also suggest neither agglomeration nor congestioneﬀect.
The results imply that general and independence distances do matter withpositive technological externalities of plant location. Agglomeration eﬀects ofrelationship and cooperation distances on productivity are only noticeable forsome of the Japanese automobile corporations and their technology cooperation
associations. A few of them cost the auto-parts plants or the member companies

10substantial negative externalities in productivity.

4

Econometric Issues

Estimates of productivity have been resulted in by numerous analyses on estimation of production functions, especially influenced by Griliches and Mairesse(1998)
which pointed out econometric problems associated with estimation of production functions with micro data. There are broadly two problems, cross-sectional
dependence(Conley, 1999; Conley and Ligon, 1995) and simultaneity problem(Olley and Pakes, 1996; Levinsohn and Petrin, 2003; Bond and Sőderbom,
2005)3 . We take the two econometric issues in the estimation.

4.1

Cross-Sectional Dependence

We are concerned about possibilities of interdependence among unobservableproductivities in the plants and its possible econometric influences upon the
OLS estimates above. We draw upon a non-parametric covariance matrix estimators proposed by Conley(1999). Conley(1999) applies the time series methodof Newey and West(1987) or White and Domowitz(1984) to cross-sectional datawith possible spatial dependence characterized by economic distance. The covariance matrix estimators based upon GMM estimator are shown to be consistent even when economic distances are measured with errors. The key component reflecting the cross-sectional dependence lies in a weight matrix associatedwith spatial autocovariances, where the weights are used to calculate weighted
averages of the spatial autocovariance terms. Considering roles of economic distance in ideas or knowledge, we suppose the weights as being zero for plants
located farther apart than some cutoﬀ levels  and  at longitude and latitude, respectively. More concretely, instead of truncated estimator of White andDomowitz(1984), we take the following weight function   ( ) of a Bartlett
window(Newey and West, 1987), where a square regular lattice spaces each plantin square at longitude  and latitude  for ||   , ||   ,||
) for a plant in square at longitude  and latitude (1 − || )(1 − 0otherwise.
(8)
In setting the cutoﬀ levels  and  in the weight function, we take into
account geographical information on territory of Japan. Prefecture Hokkaido islocated at the northernmost extreme, with eastern end at longitude 148 ◦ 53 0 42 00
and northern one at latitude 45 ◦ 33 0 28 00 . At the southernmost extreme of the  ( ) = {3 The reflection problem is also related to the estimation of production functions(Manski,1993), in case that endogenous social or peer eﬀects are considered in production process.
There are the cases of endogenous social eﬀects of technology or location choice. Anotherpossible problem is group eﬀects on individual response variables in cluster sample(Moulton,
1990; Wooldridge, 2003). The Marshallian externalities in aggregate physical capitals are an
example of the cluster eﬀects.

11continental Japan(excluding small-island shaped Okinawa Prefecture), Prefecture Kagoshima has western end at longitude 128 ◦ 23 0 43 00 and southern one
at latitude 27 ◦ 01 0 07 00 . Considering the diﬀerences of the rectangular national
land in longitude and latitude as well as the histograms displayed in Figure 3
to Figure 8, cutoﬀ levels for either longitude or latitude are set in the Conley(1999) method, at sample means of each distance measure multiplied with
45−27
45−27
)) + 0743294 or sin(arctan( 148−128)) + 0668965, respeccos(arctan( 148−128
tively.
The results are shown in Table 4 for total materials and Table 5 for raw
materials for OLS estimations of an equation without the productivity function.
The OLS estimates are the same values whether with or without cross-sectional
dependence. The spatial standard errors are of almost the same order as theheteroskedasticity robust standard errors for most of the variables, remaining
the significance of the coeﬃcients unchanged in both cases of material variables.
Incorporating the productivity function in the equation, we examine changes
in significance of the coeﬃcients in the productivity function to check out
whether there is agglomeration or congestion. Results are presented in Table 6 for total materials case and Table 7 for raw materials. Qualitative results
concerning agglomeration or congestion are so diﬀerent from the OLS estimatesdisregarding cross-sectional dependence. At a significance level of 10% in eachcase of total or raw materials, there are six or ten functions of productivity
with 1 type of congestion, while general, relationship  = 1 and independence distances still achieve agglomeration eﬀect upon the auto-parts plants.
The agglomeration eﬀect of general and independent locations is thus robust to
specifications of production function in material variables or in cross-sectional
dependence of productivities.

4.2

Simultaneity

The GMM estimates above took into account endogeneity of the explanatory
input variables in the production function. However, there are no concerns
about simultaneity problem between the input variables. Since Marschak andAndrews(1944) among the literature on productivity estimates, there has been
known that a simultaneity problem is serious for estimating production function.
The simultaneity problem occurs when there is contemporaneous correlation
between unobservable productivity and production inputs. The simultaneity
makes it diﬃcult for econometricians to gain unbiased and consistent estimates.
If capital stocks and labour input are positively correlated and correlation withproductivity shocks is higher for labour than for capital stocks, then an OLS
estimate of a coeﬃcient on labour input would be overestimated and one of a
coeﬃcient on capital stocks be underestimated.
In order to address the simultaneity problem, we follow a partially-linear
semi-parametric model of Levinsohn and Petrin(2003) with firm’s intermediate inputs a proxy variable for unobservable productivity4 . Since we assume
4 A seminal paper in the literature, Olley and Pakes(1996) present an identification method12that plants’ location choices are predetermined, an economic distance term of
productivities’ determinant can be separable from an unobservable technology
component ˜ . In the estimating equation ln  = 0 +  ln −1 + ln  +3P
ln  + ( ) + ˜ +  at a period  augmented by a third-order
=1polynomial in an exogenous distance-variable, we assume a demand function
 of a firm  for intermediate inputs ln  ,ln  =  (˜  ln −1 )(9)which proxies for productivity ˜ at the current period and depends upon astate variable of capital stocks ln −1 at the end of the previous period 5 . It isalso assumed that the demand function  is monotonic in the productivity ˜
for all the capital stocks ln −1 . The monotonicity of the intermediate inputs
demand makes it possible to gain an inverse function  ˜ =  ˜ (ln   ln −1 ),which replaces the productivity term in the estimating equation:ln  =ln  +3P

=1

 ( ) +  (ln   ln −1 ) +



(10)

ln  +  ˜ (ln   ln −1 ).
where  (ln   ln −1 ) ≡ 0 +  ln −1 +The monotonicity assumption leads to dropping from our data some samples
with zero value of either material variable. The number of zero zero-value is 9
in a case of total materials or 48 in the raw material case, in either year of 2002
or 2003.
The computational procedure is as follows. The first step of the Levinsohn
and Petrin(2003) procedure with an application of a third-order polynomial
3 3−
P
P
  (ln −1 ) (ln  ) to the function  (ln   ln −1 ), is to consis=0 =0

on labour input ln  and coeﬃcients    = 1 2
tently estimate a coeﬃcientand 3 on distance variables  in Equation (10). Using the consistent estimates ( b  c )  = 1 2 and 3 the second step is to identify another coeﬃcients) on capital stocks and intermediate inputs in Equation (10). Using the
( 
d
˜
c
ln 
estimates c
 gained in the first step, we define   ≡  −  ln −1 −for any value of (  ). Assuming a first-order Markov process of producd
˜ | ˜tivity  ˜ , we also define (−1 ) as predicted values from a regressionof production function estimated, which is an application of a partially linear semi-parametricmodel of Robinson(1988). Olley and Pakes(1996) use investment variables as a proxy for correlation between production inputs and unobservable productivity. Levinsohn and Petrin(2003)
point out practical uselessness of the method, however, since the Olley and Pakes(1996)’s
identification relies upon the monotonic inverse relation between investment and productivity. In practice, there are so many observations of investment variable with a zero value inwhatever plant-level data. The zero-values break the monotonic condition, upon which theidentification of Olley and Pakes(1996) crutially depends.
5 As described in Appendix, the timing of our capital variable is diﬀerent from that in Levinsohn and Petrin(2003). Their timing assumption makes them use as instruments ”presentperiod capital and the first lag of the proxy variable”.

13

d
˜
2
˜
3
˜ =  +  ˜
01 −1 +  2 ( −1 ) +  3 ( −1 ) . The residual for the estimationis +   = ln  −\b ln  − P c ( ) −3

=1

 ln −1 −d˜ | ˜ln  − (−1 )
(11)d
˜ | ˜where an innovation to productivity   ≡  ˜ − (
).
We
use
as
−1

instruments the first lagged capital stocks ln −2 and the first lag of theproxy variable ln −1 . Two moment conditions (  +   | ln −2 ) and(  +  | ln −1 ) lead to just identified estimates ( c  c ). Following Levinsohn and Petrin(2003), we use the Newton’s method as a default solution to aminimization problem of the GMM criterion function, or when we obtain diﬃculties in convergence, we instead apply the grid search. The covariance matrixof the parameters is also calculated with the Stata’s bootstrap command.
To examine whether the simultaneity problem aﬀects the estimates gainedin Section 3.2, we compare the GMM estimates with those from Levinsohn
and Petrin(2003) method. Estimation results without productivity function are
shown in Table 8 for total materials and in Table 9 for raw materials. The result
suggests that, without consideration of simultaneity between inputs, the OLS
and GMM estimators generate overestimates of coeﬃcients on labour inputs
and underestimates of capital stocks coeﬃcients in the production function. It
implies the case where both production inputs are positively correlated andcorrelation with productivity shocks is higher for labour than for capital stocks.
Estimations also reject a null of constant returns to scale, but once thesimultaneity problem is considered, decreasing returns to scale emerge instead ofincreasing returns. Magnitude of the estimated coeﬃcients totally changes, yetstill significant except for material variables. The rejection of constant returns toscale is also confirmed in a case with value-added outputs the dependent variablein the production functions without any material input variables. The result
leads to agglomeration, if any, brought about not by increasing returns to scale,but by productivities spillover among proximate suppliers around automobile
assemblies.
Finally, we estimate the production function with productivity function with
the Levinsohn and Petrin method. Evidently in Table 10 for total materials andTable 11 for raw materials, the qualitative results are similar to ones with crosssectional dependence. There are a lot of congestion eﬀects of type 1 or 2
but we find robustly qualified agglomeration eﬀects for some specific distancesof general, relationship  = 1 and independence in cases of raw materials. For areference to the estimations, we plot the estimates of productivity that is definedd˜ | ˜as a sum of the predicted productivity term (−1 ) and the economic3Pc ( ) in the typical cases of cooperation distance for  = 3
distance terms
=1

probably with congestion eﬀect and independence distance with agglomerationeﬀect, as is evident in Figure 9 and Figure 10 respectively.

14

5

Conclusion

This paper in the spirit of Marshall(1920) raised a question of how economic distance aﬀects the firms’ productivities, focusing upon distributions of the productivities shared by auto-parts companies on the periphery of automobile assemblyplants. We estimated production functions of the Japanese automobile-parts
plants, with special attention to productivity function of measured economic
distance. We took econometric issues of cross-sectional dependence of productivities and a simultaneity problem between inputs, as well as the standard OLS
and GMM estimators.
It turned out that the number of membership companies with associations
for technology cooperation is so limited. The rest of the auto-parts corporations
are independent of the memberships. The general or independent plants gain
positive technological externalities, the fact which is robust to specifications of
the production functions. Agglomeration eﬀects are rarely observed for relationspecific or cooperative plants. Some of them cost the auto-parts plants or themember companies substantial negative externalities. Once the simultaneity
problem is considered, decreasing returns to scale emerge instead of increasing
returns. Material variables loses significance in the production functions. The
rejection of constant returns to scale leads to agglomeration, if any, brought
about not by increasing returns to scale, but by productivities spillover amongproximate suppliers around automobile assemblies.
In future work, we hope to incorporate into another econometric issue thegroup eﬀects on individual response variables in cluster sample following Wooldridge(2003).

15

References[1] Ackerberg, Daniel & Lanier Benkard, C. & Berry, Steven & Pakes, Ariel,
2007. ”Econometric Tools for Analyzing Market Outcomes,” Handbook of
Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 63 Elsevier.
[2] Akerlof, A. George. ”Social Distance and Social Decisions.” Econometrica
vol.65, no.5, pp.1005-1027.
[3] Aoki, Masahiko, 1986. ”Horizontal vs. Vertical Information Structure of
the Firm,” American Economic Review, American Economic Association,
vol. 76(5), pages 971-83, December.
[4] Barro, Robert J & Sala-i-Martin, Xavier, 1997. ” Technological Diﬀusion,
Convergence, and Growth,” Journal of Economic Growth, Springer, vol.
2(1), pages 1-26, March.
[5] Andrew B. Bernard & Stephen J. Redding & Peter K. Schott, 2006. ”MultiProduct Firms and Product Switching,” NBER Working Papers 12293,
National Bureau of Economic Research, Inc.
[6] Nicholas Bloom & Mark Schankerman & John Van Reenen, 2007. ”Identifying Technology Spillover and Product Market Rivalry,” NBER Working
Papers 13060, National Bureau of Economic Research, Inc.
[7] Stephen Bond & Mans Soderbom, 2005. ”Adjustment Costs and the Identification of Cobb Douglas Production Functions.” Economics Papers 2005W04, Economics Group, Nuﬃeld College, University of Oxford.
[8] Conley, G. Timothy. ”GMM Estimation with Cross Sectional Dependence.”
Journal of Econometrics vol 92, pp. 1-45.
[9] Timothy G. Conley & Bill Dupor, 2003. ”A Spatial Analysis of Sectoral
Complementarity,” Journal of Political Economy, University of Chicago
Press, vol. 111(2), pages 311-352, April.
[10] Conley, Timothy G & Ligon, Ethan, 2002. ” Economic Distance and CrossCountry Spillover,” Journal of Economic Growth, Springer, vol. 7(2), pages
157-87, June.
[11] Russell Davidson and James G. MacKinnon. Econometric Theory andMethods. Oxford University Press (New York) in October, 2003 with a2004 copyright.
[12] Duranton, Gilles & Overman, Henry G., 2005. ”Testing for Localization
Using Micro-Geographic Data,” Review of Economic Studies, Blackwell
Publishing, vol. 72(4), pages 1077-1106, October.

16[13] Ellison, Glenn & Glaeser, Edward L, 1997. ”Geographic Concentrationin U.S. Manufacturing Industries: A Dartboard Approach,” Journal of
Political Economy, University of Chicago Press, vol. 105(5), pages 889-927,
October.
[14] Cem Ertur & Wilfried Koch, 2007. ”Growth, technological interdependence
and spatial externalities: theory and evidence,” Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(6), pages 1033-1062.
[15] Fujita, Masahisa & Thisse, Jacques-Francois, 1996. ”Economics of Agglomeration,” Journal of the Japanese and International Economies, Elsevier,vol. 10(4), pages 339-378, December.
[16] Griliches, Zvi, and Jacques Mairesse. 1998. ”Production Functions: The
Search for Identification.” in Econometrics and Economic Theory in the
Twentieth Century: The Ragnar Frisch Centennial Symposium(Cambridge
University Press), pp.169-203.
[17] Michael Greenstone & Richard Hornbeck & Enrico Moretti, 2008. ”Identifying Agglomeration Spillover: Evidence from Million Dollar Plants,” NBER
Working Papers 13833, National Bureau of Economic Research, Inc.
[18] Rachel Griﬃth & Rupert Harrison & John Van Reenen, 2006. ”How Special
Is the Special Relationship? Using the Impact of U.S. R&amp;D Spillover
on U.K. Firms as a Test of Technology Sourcing,” American Economic
Review, American Economic Association, vol. 96(5), pages 1859-1875, December.
[19] Henderson, J. Vernon, 2003. ”Marshall’s Scale Economies.” Journal of Urban Economics, Elsevier, vol.53(1), pages 1-28, January.
[20] Krugman, Paul, 1991. ”Increasing Returns and Economic Geography,”
Journal of Political Economy, University of Chicago Press, vol. 99(3), pages
483-99, June.
[21] James Levinsohn & Amil Petrin, 2003. ”Estimating Production Functions
Using Inputs to Control for Unobservables,” Review of Economic Studies,Blackwell Publishing, vol. 70(2), pages 317-341, 04.
[22] Marschak J., and Andrews, W.. 1944. ”Random Simultaneous Equations
and the Theory of Production.” Econometrica vol. 12, pp. 143-205.
[23] Marshall, Alfred. 1920. Principles of Economics. London: Macmillan.
[24] Milgrom, Paul & Roberts, John, 1990. ”The Economics of Modern Manufacturing: Technology, Strategy, and Organization,” American Economic
Review, American Economic Association, vol. 80(3), pages 511-28, June.
[25] Newey, Whitney K & West, Kenneth D, 1987. ”A Simple, Positive Semidefinite, Heteroskedasticity and Autocorrelation Consistent CovarianceMatrix,” Econometrica, Econometric Society, vol. 55(3), pages 703-08, May.
17

[26] Nishiguchi, Toshihiro, and Alexandre Beaudet. 1998. ”The Toyota Groupand the Aisin Fire.” Sloan Management Review, Vol. 40, No. 1, pp. 49-59.
[27] Olley, G Steven & Pakes, Ariel, 1996. ”The Dynamics of Productivity in
the Telecommunications Equipment Industry,” Econometrica, EconometricSociety, vol. 64(6), pages 1263-97, November.
[28] Parente, Stephen L & Prescott, Edward C, 1994. ”Barriers to Technology
Adoption and Development,” Journal of Political Economy, University of
Chicago Press, vol. 102(2), pages 298-321, April.
[29] Raghuram G. Rajan & Luigi Zingales, 2001. ”The Firm As A Dedicated Hierarchy: A Theory Of The Origins And Growth Of Firms,” The Quarterly
Journal of Economics, MIT Press, vol. 116(3), pages 805-851, August.
[30] Robinson, Peter M, 1988. ”Root- N-Consistent Semiparametric Regression,” Econometrica, Econometric Society, vol. 56(4), pages 931-54, July.
[31] Romer, Paul M, 1986. ”Increasing Returns and Long-run Growth,” Journalof Political Economy, University of Chicago Press, vol. 94(5), pages 100237, October.
[32] Saxenian, AnnaLee. 1996. Regional Advantage Culture and Competition in
Silicon Valley and Route 128, Harvard University Press.
[33] Schmitz, James A, Jr, 1989. ”Imitation, Entrepreneurship, and Long-run
Growth,” Journal of Political Economy, University of Chicago Press, vol.
97(3), pages 721-39, June.
[34] Tibor Scitovsky, 1954. ”Two Concepts of External Economies,” Journal of
Political Economy, University of Chicago Press, vol. 62, pages 143.
[35] Topkis Donald M., 1995. ”Comparative Statics of the Firm,” Journal of
Economic Theory, Elsevier, vol. 67(2), pages 370-401, December.
[36] Johannes van Biesebroeck, 2002. ”The Eﬀect of Technology Choice on Automobile Assembly Plant Productivity,” The Economic and Social Review,
Economic and Social Studies, vol. 33(1), pages 65-73.
[37] Johannes van Biesebroeck, 2003. ”Productivity Dynamics with Technology
Choice: An Application to Automobile Assembly,” Review of Economic
Studies, Blackwell Publishing, vol. 70(1), pages 167-198, January.
[38] Johannes van Biesebroeck, 2007. ”Complementarities in automobile production,” Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol.
22(7), pages 1315-1345.
[39] Watts, D. J.. 1999. Small Worlds: The Dynamics of Networks Between
Order and Randomness. Princeton University Press.

18[40] White, Halbert & Domowitz, Ian, 1984. ”Nonlinear Regression with Dependent Observations,” Econometrica, Econometric Society, vol. 52(1), pages
143-61, January.
[41] Wooldridge, M. Jeﬀrey. ”Cluster-Sample Methods in Applied Econometrics.” American Economic Review Papers and Proceedings, May 2003,
pp.133-138.

19

Appendix: Variables used and their construction• Observations: Current Survey of Production, conducted by Ministry of
Economy, Trade and Industry, Government of Japan. The scope of thissurvey covers establishments or enterprises that produce manufactured
goods and mineral products (including processed products) set forth by
the ministerial ordinance. Survey items consist of minerals, steel andiron, non-ferrous metals, metal products, general machinery, electric machinery, transport machinery, precision machinery, ceramics, stone andclay products, manufactured chemical products, oil and coal products,
plastics, pulp and paper, paper and paper processed goods, manufactured
textile products, rubber products, leather products, and other manufactured products.
We use cross-sectional data from the survey in a fiscal year 2003, accompanied with the year 2002 data as a supplemental sample in panel data.
We confine sample into plants with more than 30 employees. This paper
covers two items: automotive body and concomitant of a 4-digit industrial subclassification 3012; and automotive component and accessory of aclassification number 3013. We exclude automobile(including two-wheeledvehicle) of a classification 3011, since the automobile sector contains plants
of motor corporations, operating as core system of the whole automobile
industry with probably diﬀerent technologies than acquired by the constructors of automotive parts belonging to two classifications 3012 and3013. The year 2002 and 2003 data is matched with a STATA program
identifying ’firm ID’ distributed among the sample plants, the work which
resulted in the sample of 2346 observations. The location on maps browsedwith the Google Earth, is displayed separately in Figure 1 for ’cooperation’plants defined with a dummy variable   = 1 for either  = 1 · · · or 10
or in Figure 2 for ’independent’ plants with a dummy  − = 1. Construction of these dummy variables are described in a list of ’cooperation
distance’ below.
• Output: We construct nominal output as a sum of total shipment value,and changes in manufactured products and semifinished goods in inventory
at the beginning and the end of the year in the Current Survey of Production. The real term is the nominal values divided by industry organization(IO) deflators in the Japan Industrial Productivity Database 2006 (JIP
2006 database, available in http://www.rieti.go.jp/en/database/d05.html).
The JIP database has been complied in a collaboration between the Research Institute of Economy, Trade and Industry(RIETI) as part of its”Study on Industry-Level and Firm-Level Productivity in Japan” research
project and Hitotsubashi University as part of its Hi-Stat (21st-Century
COE Program, ”Research Unit for Statistical Analysis in the Social Sciences”) project. The original version of the JIP Database (ESRI/Hi-Stat
JIP Database 2003) was compiled through collaboration between the Economic and Social Research Institute (ESRI), Cabinet Oﬃce, Government20

of Japan as part of its research project on ”Japan’s Potential Growth” andthe Hitotsubashi University Hi-Stat project. The JIP 2006 contains annual data on 108 sectors from 1970-2002 that can be used for total factor
productivity (TFP) analyses. The database includes detailed information
on sectoral capital service input indices and labor service input indices, including information on real capital stocks and the nominal cost of capitalby type of capital and by industry, annual nominal, and real input-output
tables, as well as some supplementary tables, such as statistics on trade,inward and outward FDI, and Japan’s industrial structure. All real values
are based on 1995 prices. The database is currently updated to 2008 andpublicly on a website.
• Labour input: We construct labour input as a product of total numberof full-time employees in the Current Survey of Production and industrial
person-hours in the JIP2006 database.
• Capital stock: We calculate market values of tangible fixed assets by multiplying tangible fixed assets held at the beginning of the year in the Current
Survey of Production and ratio of market to book values compiled in the
JIP2006 database. The each plant ’s market values  at the beginningof year  + 1 are constructed following an equation
 = −1 (1 − ) + (A.1.)

where  is an annual industrial depreciation rate in the JIP2006 and is acquisition values of tangible fixed assets in the Current Survey of Production. Note that the timing of our capital variable is diﬀerent from thatin Levinsohn and Petrin(2003). They ”assume investment occurring inthis period enters capital in this period”, instead of assuming that ”investment reported last period enters the production function as capital inthis period”(p. 324, Levinsohn and Petrin, 2003), as not only Olley andPakes(1996) but also this paper does.
• Intermediate inputs or materials: We use total materials including raw
materials, fuel, electricity and outsourcing costs, as well as raw materials
used. The deflator is the IO deflators in the JIP2006 database.
• Products dummy: As variables controlling demand eﬀects in production
functions, we include products dummy variables which are equal to 1 if
plants list each product or 0 otherwise. Products cover 28 items subordinate to the 2 broad classifications of auto-parts: Fabricated textile products, n.e.c., including knitted ones; Fabrication of plastic film, sheets, floor
coverings and synthetic leathers (cutting, jointing, painting, evaporationand plating, buﬃng, etc.); Aluminum machinery parts, without machine
finishing; Stamped and pressed machinery parts, without machine finishing; Piston rings; Charging generators; Starter generators; Miscellaneous
auxiliary equipment for internal combustion engines; Parts, attachments
21and accessories of auxiliary equipment for internal combustion engines;
Radio applied equipment; Passenger car bodies; Bus bodies; Truck bodies;
Special-use car bodies; Trailers, including trailer chassis and bodies; Gasoline engines for motor vehicles; Diesel engines for motor vehicles; Internal
combustion engines for motorcycles and motor scooters; Parts, attachments and accessories of internal combustion engines for motor vehicles;
Parts of driving, transmission and operating units; Parts of suspension
and brake systems; Parts of chassis and bodies; Car air-conditioners; Car
heaters; Finished seats; Miscellaneous parts of motor vehicles, including
parts of motorcycles; KD sets (passenger cars, buses and trucks); KD sets
(motorcycles).
• General economic distance: As described in Section 2.2, we construct three
types of economic distance measures: general; relationship; cooperation;or independence. In making these measures, we require to transform into
latitude and longitude address information of each plant listed in the Current Survey of Production. On a basis of the lat/long information, we use
the ArcGIS software to calculate minimum distance  of plant  from any
automobile construction plants aﬃliated with major 10 motor corporations. The distance measure is ’general’ in that technology is potentiallyaccessible for any plants located within a sphere of another plant.
• Relationship distance: We also measure another distance of plants fromeither core plant of motor corporations, Daihatsu(Head Oﬃce and Ikeda
Plant, Kyoto Plant, Shiga Plant, or Machinery Engineering Division(Tada
Plant)), Hino(Head Oﬃce and Hino Plant, Hamura Plant, or Nitta Plant),
Honda(Saitama Plant, Suzuka Plant, Kumamoto Plant, Hamamatsu Plant,or Tochigi Plant), Isuzu(Tochigi Plant, or Fujisawa Plant), Matsuda(Plant
complex in Head Oﬃce, Plant complex in Ujina District, Miyoshi Plant,
Hofu Plant(Nishinoura District and Nakanoseki District)), Mitsubishi(Okazaki
Plant, Kyoto Plant, Shiga Plant, Mizushima Plant, or Pajero Manufacturing Co., Ltd.), Nissan(Tochigi Plant, Oppama Plant, Kyushu Plant, Nissan Body Shonan Plant, Yokohama Plant, or Iwaki Plant), Subaru(Gunma
Main Plant, Gunma Yajima Plant, Gunma Ota North Plant, Gunma
Oizumi Plant, or Isesaki Plant), Suzuki(Head Oﬃce and Takatsuka Plant,
Iwata Plant, Osuka Plant, Kosai Plant, or Sagara Plant), or Toyota(HeadPlant, Motomachi Plant, Kamigo Plant, Takaoka Plant, Miyoshi Plant,
Tsutsumi Plant, Myochi Plant, Shimoyama Plant, Kinu-ura Plant, Tahara
Plant, Teiho Plant, Hirose Plant, Toyota Motor Hokkaido, Inc., or Toyota
Motor Tohoku Co., Ltd.). The measure  for a plant  and a motor
corporation  is called ’relationship’ distance, since technology is accessible for plants establishing transactional relationships with either motor
assembly company.
• Cooperation distance: The third measure of economic distance is ’cooperation’ distance  , since we focus upon memberships with associations
for technological cooperation aﬃliated with the major 10 motor assem22

bly corporations. According to the Japanese Auto Parts Industries(Japan
Auto Parts Industries Association), there are some associations for technological cooperation aﬃliated with major assembly companies: Daihatsu
Kyoyu-kai; Hino Kyoryoku-kai; Isuzu Kyowa-kai; Nishi-Nihon Youko-kai,
Kanto Youko-kai, and Kansai Youko-kai(all for Matsuda Motor Corporation); Nissho-kai(For Nissan); Subaru Yuhi-kai; Suzuki Kyoryoku-kyodokumiai; and Kyoho-kai(for Toyota). A representative association of Toyota, Kyoho-kai says on the website,”The objective of KYOHOKAI is, together with Toyota Motor Corporation and its member companies, to make world economic and social
contributions through activities based upon a global and open partnership. To aim for further sharing of information and the enhancement of
2-way communication with Toyota Motor Corporation based on the policy of Toyota Motor Corporation to ”Create solid footing and build astronger foundation”. The member companies shall develop meeting activities for the purpose of mutual study and exchange to strengthen our
global competitive edge and to continue growth by focusing on the ”Pursuit of quality”. To further enhance and improve the eﬃciency of meeting
activities”.
In the year 2003 sample, the number of member companies is so limited,
as is evident from the number of zero values shown in summary statistics
of Table 12. In addition to member companies of the associations, theJapanese Auto Parts Industries contains information on business partners
with the Honda Motor Co., Ltd. and Mitsubishi Motors Co.. We construct
10 dummy variables    = 1 · · ·  10 for each plant that take a value of
1 if it is a member company, or a value 0 otherwise. Product terms of thedummy variable 1−  and the relationship distance  indicate sharedtechnological knowledge among the associated technological cooperation,so we call the distance ’cooperation through relationship’.
• Independence distance: We also construct the other dummy variable  −
representing neither membership of the 10 major assembly corporations.
Product term of the independence dummy  − and the general distance is a distance measure  for independent companies. The independentcompanies are the majority of the 2003 sample shown in Table 12.

23

Materials

Distance orderTotal
3rd 3

1st 1

2nd 2-.006***(.001).00008***(.00002)-.0004(.0007)-.0003(.0005).0003(.0002).0003(.0002).0001(.0003)-.0005*(.0003).0002(.0002).0001(.0002)-.0007(.0005).0002(.0003)-.001(.0007)-.0003(.0004).0003(.0002).0003(.0002).0001(.0003)-.0005*(.0003).0002(.0002).0001(.0002)-.0007(.0005).0002(.0002)

Raw materials
3rd 3CRTS

1st 1

2nd 2-3.01e-07***(7.31e-08)

54.16
(0)

-.007***(.002).00009***(.00002)-3.47e-07***(8.63e-08)

90.14
(0)

9.10e-07(4.99e-06)
1.52e-06(1.93e-06)-4.94e-07(4.32e-07)-7.92e-07(5.69e-07)-6.86e-07(8.07e-07)
7.59e-07(7.67e-07)-7.26e-07(5.83e-07)-5.55e-07(5.61e-07)
1.72e-06(2.26e-06)-1.34e-06(8.85e-07)-5.58e-10(1.03e-08)-1.87e-09(2.15e-09)
1.32e-10(2.45e-10)
5.54e-10(4.18e-10)
4.01e-10(5.60e-10)-3.18e-10(6.14e-10)
5.46e-10(4.26e-10)
4.35e-10(4.18e-10)-1.34e-09(2.26e-09)
9.87e-10(7.31e-10)

55.57
(0)
55.63
(0)
55.58
(0)
55.68
(0)
55.92
(0)
56.17
(0)
55.87
(0)
55.82
(0)
56.03
(0)
56.11
(0)

-.001
(.0008).0003(.0005).0006**(.0003).0005*(.0003).0004(.0003)-.001***(.0003).0005*(.0003).0003(.0002)-.001**(.0006).0002(.0003)4.66e-06(6.14e-06)-6.44e-07(2.07e-06)-9.58e-07**(4.87e-07)-1.31e-06*(7.14e-07)-1.65e-06*(8.92e-07)
1.93e-06**(8.34e-07)-1.57e-06**(7.30e-07)-1.16e-06*(7.03e-07)
3.56e-06(2.56e-06)-1.55e-06(1.02e-06)-5.34e-09(1.26e-08)-1.98e-10(2.23e-09)
2.82e-10(2.69e-10)
8.87e-10*(5.20e-10)
1.04e-09*(6.13e-10)-9.95e-10(6.58e-10)
1.12e-09**(5.32e-10)
8.48e-10(5.23e-10)-2.75e-09(2.53e-09)
1.20e-09(8.08e-10)

92.07
(0)
95.30
(0)
93.82
(0)
95.30
(0)
94.37
(0)
89.80
(0)
95.38
(0)
95.72
(0)
97.29
(0)
95.16
(0)

5.94e-06(5.28e-06)
1.37e-06(1.91e-06)-4.96e-07(4.28e-07)-8.30e-07(5.66e-07)-6.19e-07(8.00e-07)
7.58e-07(7.67e-07)-7.79e-07(5.81e-07)-5.63e-07(5.61e-07)
1.53e-06(2.22e-06)-1.32e-06(8.81e-07)-9.27e-09(1.07e-08)-1.75e-09(2.13e-09)
1.32e-10(2.44e-10)
5.78e-10(4.16e-10)
3.60e-10(5.56e-10)-3.17e-10(6.14e-10)
5.81e-10(4.25e-10)
4.43e-10(4.19e-10)-1.17e-09(2.23e-09)
9.66e-10(7.28e-10)

56.51
(0)
55.52
(0)
55.65
(0)
55.67
(0)
55.90
(0)
56.17
(0)
55.83
(0)
55.84
(0)
55.93
(0)
56.04
(0)

-.001*(.0008).0004(.0005).0006**(.0002).0005*(.0003).0004(.0003)-.001***(.0003).0005**(.0003).0003(.0002)-.001**(.0006).0001(.0003)5.91e-06(6.12e-06)-8.51e-07(2.04e-06)-9.58e-07**(4.81e-07)-1.34e-06*(7.09e-07)-1.51e-06*(9.02e-07)
1.93e-06**(8.34e-07)-1.64e-06**(7.26e-07)-1.06e-06(7.06e-07)
3.28e-06(2.52e-06)-1.52e-06(1.01e-06)-7.44e-09(1.26e-08)-1.78e-11(2.21e-09)
2.80e-10(2.67e-10)
9.11e-10*(5.17e-10)
9.42e-10(6.17e-10)-9.93e-10(6.58e-10)
1.16e-09**(5.30e-10)
7.94e-10(5.24e-10)-2.49e-09(2.50e-09)
1.18e-09(8.04e-10)

91.49
(0)
95.53
(0)
94.38
(0)
95.57
(0)
94.57
(0)
89.80
(0)
95.59
(0)
95.99
(0)
96.62
(0)
94.93
(0)

-3.49e-07***(8.55e-08)

89.42
(0)

CRTS

GeneralRelationship
j=1
2
3
4
5
6
7
8
9
10
Cooperation
j=1
2
3
4
5
6
7
8
9
10
Independence-.006***.00008***-3.03e-07***53.98-.008***.00009***(.001)(.00002)(7.27e-08)(0)(.002)(.00002)
Note:  statistics and p-value in a parenthesis for constant-returns-to-scale(CRTS).
* refers to significance at 10%, ** at 5%, and *** at 1% level.

Table 2: OLS estimations with distance24Materials

Distance orderTotal
3rd 3

1st 1

2nd 2-.006***(.001).00008***(.00002)-.0004(.0007)-.0003(.0004).0003(.0002).0003(.0002).0001(.0003)-.0005*(.0003).0002(.0002).0002(.0002)-.0008(.0005).0002(.0002)-.001(.0007)-.0003(.0004).0003(.0002).0003(.0002).0001(.0003)-.0005*(.0003).0002(.0002).0001(.0002)-.0007(.0005).0002(.0002)

Raw materials
3rd 3CRTS

1st 1

2nd 2-2.96e-07***(7.19e-08)

54.52
(0)

-.007***(.002).00009***(.00002)-3.36e-07***(8.43e-08)

106.02(0)

8.16e-07(4.97e-06)
1.51e-06(1.91e-06)-4.92e-07(4.30e-07)-7.58e-07(5.65e-07)-6.80e-07(8.02e-07)
7.50e-07(7.61e-07)-7.08e-07(5.80e-07)-5.24e-07(5.57e-07)
1.86e-06(2.25e-06)-1.36e-06(8.80e-07)-3.67e-10(1.03e-08)-1.87e-09(2.13e-09)
1.32e-10(2.44e-10)
5.29e-10(4.14e-10)
3.99e-10(5.56e-10)-3.12e-10(6.10e-10)
5.32e-10(4.23e-10)
4.12e-10(4.15e-10)-1.47e-09(2.25e-09)
1.00e-09(7.27e-10)

55.31
(0)
54.83
(0)
55.23
(0)
55.04
(0)
55.38
(0)
55.60
(0)
55.14
(0)
55.11
(0)
55.42
(0)
55.78
(0)

-.001
(.0008).0003(.0005).0006**(.0002).0004*(.0003).0004(.0003)-.001***(.0003).0005*(.0003).0003(.0002)-.001**(.0006).0002(.0003)4.20e-06(6.09e-06)-6.06e-07(2.06e-06)-9.03e-07*(4.86e-07)-1.24e-06*(7.07e-07)-1.62e-06*(8.83e-07)
1.90e-06**(8.25e-07)-1.50e-06**(7.27e-07)-1.10e-06(6.96e-07)
3.67e-06(2.54e-06)-1.57e-06(1.00e-06)-4.70e-09(1.26e-08)-2.21e-10(2.22e-09)
2.56e-10(2.69e-10)
8.37e-10(5.15e-10)
1.00e-09*(6.07e-10)-9.91e-10(6.48e-10)
1.06e-09**(5.29e-10)
8.01e-10(5.17e-10)-2.87e-09(2.51e-09)
1.20e-09(7.98e-10)

109.31(0)112.86(0)111.40(0)112.49(0)111.66(0)106.93(0)112.78(0)112.84(0)114.36(0)
113.01(0)5.74e-06(5.24e-06)
1.36e-06(1.89e-06)-4.98e-07(4.27e-07)-7.99e-07(5.62e-07)-6.21e-07(7.94e-07)
7.49e-07(7.61e-07)-7.63e-07(5.78e-07)-5.34e-07(5.57e-07)
1.65e-06(2.21e-06)-1.34e-06(8.76e-07)-8.89e-09(1.06e-08)-1.74e-09(2.11e-09)
1.34e-10(2.43e-10)
5.56e-10(4.13e-10)
3.63e-10(5.52e-10)-3.11e-10(6.10e-10)
5.68e-10(4.23e-10)
4.22e-10(4.15e-10)-1.28e-09(2.21e-09)
9.86e-10(7.24e-10)

55.98
(0)
54.73
(0)
55.27
(0)
54.99
(0)
55.45
(0)
55.60
(0)
55.07
(0)
55.11
(0)
55.41
(0)
55.74
(0)

-.001*(.0008).0003(.0005).0006**(.0002).0004*(.0003).0004(.0003)-.001***(.0003).0005*(.0003).0003(.0002)-.001**(.0006).0002(.0003)5.61e-06(6.10e-06)-8.16e-07(2.03e-06)-9.06e-07*(4.80e-07)-1.28e-06*(7.02e-07)-1.46e-06(8.93e-07)
1.89e-06**(8.25e-07)-1.56e-06**(7.23e-07)-9.90e-07(6.98e-07)
3.38e-06(2.50e-06)-1.55e-06(9.99e-07)-7.07e-09(1.26e-08)-3.77e-11(2.20e-09)
2.55e-10(2.66e-10)
8.65e-10*(5.12e-10)
9.07e-10(6.11e-10)-9.89e-10(6.48e-10)
1.11e-09**(5.27e-10)
7.43e-10(5.19e-10)-2.60e-09(2.48e-09)
1.18e-09(7.94e-10)108.80(0)113.11(0)111.98(0)112.74(0)111.98(0)106.94(0)112.97(0)
113.02(0)113.58(0)112.80(0)-3.37e-07***(8.35e-08)

105.13(0)

CRTS

GeneralRelationship
j=1
2
3
4
5
6
7
8
9
10
Cooperation
j=1
2
3
4
5
6
7
8
9
10
Independence-.006***.00008***-2.98e-07***54.37-.007***.00009***(.001)(.00002)(7.15e-08)(0)(.002)(.00002)
Note:  statistics and p-value in a parenthesis for constant-returns-to-scale(CRTS).
* refers to significance at 10%, ** at 5%, and *** at 1% level.

Table 3: GMM estimations with distance25

Distance
GeneralOrder
1st 1
2nd 2
3rd 3
1st 1
2nd 2
3rd 3
1st 1
2nd 2
3rd 3
1st 1
2nd 2
3rd 3
1st 1
2nd 2
3rd 3
1st 1
2nd 2
3rd 3
1st 1
2nd 2
3rd 3
1st 1
2nd 2
3rd 3
1st 1
2nd 2
3rd 3
1st 1
2nd 2
3rd 3
1st 1
2nd 2
3rd 3
1st 1
2nd 2
3rd 3
1st 1
2nd 2
3rd 3
1st 1
2nd 2
3rd 3
1st 1
2nd 2
3rd 3
1st 1
2nd 2
3rd 3
1st 1
2nd 2
3rd 3
1st 1
2nd 2
3rd 3
1st 1
2nd 2
3rd 3
1st 1
2nd 2
3rd 3
1st 1
2nd 2
3rd 3
1st 1
2nd 2
3rd 3

OLS estimate
White S.E.
-.006
.001***.00008.00002***-3.007e-07
7.31e-08***
Relationship j=1-.0004.0007
9.102e-07
4.99e-06-5.585e-10
1.03e-08
j=2-.0003.0005
1.515e-06
1.93e-06-1.872e-09
2.15e-09
j=3
.0003
.0002
-4.944e-07
4.32e-07
1.317e-10
2.45e-10
j=4
.0003
.0002
-7.921e-07
5.69e-07
5.537e-10
4.18e-10
j=5
.0001
.0003
-6.863e-07
8.07e-07
4.009e-10
5.60e-10j=6-.0005.0003*
7.593e-07
7.67e-07-3.180e-10
6.14e-10
j=7
.0002
.0002
-7.264e-07
5.83e-07
5.464e-10
4.26e-10
j=8
.0001
.0002
-5.546e-07
5.61e-07
4.347e-10
4.18e-10j=9-.0007.0005
1.722e-06
2.26e-06-1.341e-09
2.26e-09
j=10
.0002
.0003
-1.344e-06
8.85e-07
9.866e-10
7.31e-10
Cooperation j=1
-.001
.0007
5.944e-06
5.28e-06-9.273e-09
1.07e-08
j=2-.0003.0004
1.370e-06
1.91e-06-1.748e-09
2.13e-09
j=3
.0003
.0002
-4.961e-07
4.28e-07
1.316e-10
2.44e-10
j=4
.0003
.0002
-8.299e-07
5.66e-07
5.783e-10
4.16e-10
j=5
.0001
.0003
-6.193e-07
8.00e-07
3.596e-10
5.56e-10j=6-.0005.0003*
7.575e-07
7.67e-07-3.168e-10
6.14e-10
j=7
.0002
.0002
-7.786e-07
5.81e-07
5.810e-10
4.25e-10
j=8
.0001
.0002
-5.629e-07
5.61e-07
4.428e-10
4.19e-10j=9-.0007.0005
1.528e-06
2.22e-06-1.165e-09
2.23e-09
j=10
.0002
.0002
-1.315e-06
8.81e-07
9.662e-10
7.28e-10
Independence-.006.001***.00008.00002***-3.029e-07
7.27e-08***
Note: * refers to significance at 10%, ** at 5%, and *** at 1% level.

Spatial S.E.
.002***.00002***
8.785e-08***.00005***3.629e-07**
7.281e-10.00003***
1.395e-07***1.735e-10***.00001***2.530e-08***1.600e-11***.00001***2.312e-08***1.512e-11***.00002***4.793e-08***
3.966e-11***.00002***
6.968e-08***6.605e-11***.00001***2.568e-08***
1.549e-11***.00001***2.290e-08***
1.514e-11***.00006***3.015e-07***3.035e-10***.00002***9.401e-08***
8.532e-11***.0008
5.780e-06
1.148e-08.0005
2.077e-06
2.268e-09.0002
4.395e-07
2.541e-10.0002
6.064e-07
4.445e-10.0003
8.697e-07
6.006e-10.0003*
8.289e-07
6.428e-10.0002
6.309e-07
4.610e-10.0002
5.999e-07
4.498e-10.0006
2.404e-06
2.366e-09.0002
8.972e-07
7.474e-10.0003***
5.350e-06***
2.135e-08***

Table 6: Cross-sectional dependence(2-1): Total materials

26

Variable(name)Coeﬃcient(standard error)GMM.87***(.02).70***(.05).88***(.02).03***(.007).01**(.006).03***(.007)

OLS

Labour(lnobe2).68***(.04).01***(.006)
Capital(lkstock2)
Materials
Total materials(lmtotal2).41***(.03)—.41***(.03)
Raw materials(lzairyo2)—.24***(.01)—-2.38***(.27)-3.12***(.23)-2.52***(.30)
Const.
0
Returns to scale*
55.84(0)97.63(0)55.04(0)
2
.92
.89
.92
# of obs.
2346
Note:  statistics and p-value in a parenthesis for constant-returns-to-scale.
Table 1: OLS and GMM estimations without distance

Variable(name)OLS estimate White S.E. Spatial S.E.
Labour(lnobe2).68.04***.04***.01.006***.004***
Capital(lkstock2)
Materials.41.03***.03***(lmtotals)-2.38.27***.26***
Const.
0# of obs.
2346
Note: * refers to significance at 10%, ** at 5%, and *** at 1% level.
Table 4: Cross-sectional dependence(1-1): OLS estimates(total materials)

Variable(name)OLS estimate White S.E. Spatial S.E.
Labour(lnobe2).87.02***.03***.03.007***.007***
Capital(lkstock2)
Materials.24.01***.01***(lzairyo2)-3.12.23***.27***
Const.
0# of obs.
2346
Note: * refers to significance at 10%, ** at 5%, and *** at 1% level.
Table 5: Cross-sectional dependence(1-2): OLS estimates(raw materials)

27—.25***(.01)-3.23***(.22)
114.69(0).89Distance
GeneralOrder
1st 1
2nd 2
3rd 3
1st 1
2nd 2
3rd 3
1st 1
2nd 2
3rd 3
1st 1
2nd 2
3rd 3
1st 1
2nd 2
3rd 3
1st 1
2nd 2
3rd 3
1st 1
2nd 2
3rd 3
1st 1
2nd 2
3rd 3
1st 1
2nd 2
3rd 3
1st 1
2nd 2
3rd 3
1st 1
2nd 2
3rd 3
1st 1
2nd 2
3rd 3
1st 1
2nd 2
3rd 3
1st 1
2nd 2
3rd 3
1st 1
2nd 2
3rd 3
1st 1
2nd 2
3rd 3
1st 1
2nd 2
3rd 3
1st 1
2nd 2
3rd 3
1st 1
2nd 2
3rd 3
1st 1
2nd 2
3rd 3
1st 1
2nd 2
3rd 3
1st 1
2nd 2
3rd 3

OLS estimate
White S.E.
-.007
.002***.00009.00002***-3.474e-07
8.63e-08***
Relationship j=1
-.001
.0008
4.658e-06
6.14e-06-5.342e-09
1.26e-08
j=2
.0003
.0005
-6.443e-07
2.07e-06-1.980e-10
2.23e-09
j=3.0006.0003**-9.580e-07
4.87e-07**
2.823e-10
2.69e-10
j=4.0005.0003*-1.307e-06
7.14e-07*
8.865e-10
5.20e-10*
j=5
.0004
.0003
-1.655e-06
8.92e-07*
1.035e-09
6.13e-10*
j=6-.001.0003***
1.933e-06
8.34e-07**-9.955e-10
6.58e-10j=7.0005.0003*-1.573e-06
7.30e-07**
1.118e-09
5.32e-10**
j=8
.0003
.0002
-1.160e-06
7.03e-07*
8.482e-10
5.23e-10j=9-.001.0006**
3.561e-06
2.56e-06-2.748e-09
2.53e-09
j=10
.0002
.0003
-1.548e-06
1.02e-06
1.196e-09
8.08e-10
Cooperation j=1-.001.0008*
5.906e-06
6.12e-06-7.437e-09
1.26e-08
j=2
.0004
.0005
-8.511e-07
2.04e-06-1.778e-11
2.21e-09
j=3.0006.0002**-9.581e-07
4.81e-07**
2.800e-10
2.67e-10
j=4.0005.0003*-1.344e-06
7.09e-07*
9.112e-10
5.17e-10*
j=5
.0004
.0003
-1.508e-06
9.02e-07*
9.420e-10
6.17e-10
j=6-.001.0003***
1.929e-06
8.34e-07**-9.931e-10
6.58e-10j=7.0005.0003**-1.639e-06
7.26e-07**
1.162e-09
5.30e-10**
j=8
.0003
.0002
-1.061e-06
7.06e-07
7.944e-10
5.24e-10j=9-.001.0006**
3.277e-06
2.52e-06-2.488e-09
2.50e-09
j=10
.0001
.0003
-1.522e-06
1.01e-06
1.176e-09
8.04e-10
Independence-.008.002***.00009.00002***-3.487e-07
8.55e-08***
Note: * refers to significance at 10%, ** at 5%, and *** at 1% level.

Spatial S.E.
.002***.00003***1.016e-07***.00007***4.295e-07***7.847e-10***.00003***
1.487e-07***1.743e-10.00001***2.289e-08***
1.391e-11***.00001***3.232e-08***
2.383e-11***.00002***
6.397e-08***
5.099e-11***.00002***
7.194e-08***6.460e-11***.00002***
3.495e-08***
2.332e-11***.00001***
3.407e-08***2.476e-11***.00007***3.675e-07***3.656e-10***.00003***
1.157e-07***9.953e-11***.0008*
6.255e-06
1.299e-08.0005
2.168e-06
2.328e-09.0002***
4.860e-07**
2.798e-10.0003*
7.203e-07*
5.316e-10*.0004
9.410e-07
6.429e-10.0003***
8.304e-07**
6.564e-10.0003**
7.479e-07**
5.507e-10**.0002
7.132e-07
5.384e-10.0006**
2.585e-06
2.551e-09.0003
1.020e-06
8.180e-10.0004***
6.961e-06***
2.775e-08***

Table 7: Cross-sectional dependence(2-2): Raw materials

28

Figure 1: Plants’ locations joining any technology cooperation association organized by either automobile assembly company  = 1 · · ·  10.

29

Coeﬃcient(standard error)
Variable(name)
GMM
LP
Labour(lnobe2).70***(.05).31***(.02).01**(.006).10**(.04)
Capital(lkstock2).41***(.03).08(.29)
Materials(lmtotal2)-2.52***(.30)
Const.
0
Returns to scale*
55.04(0)3.49(.06)
2.92# of obs.
2346
2337
Note: 2 statistics and p-value in a parenthesis
for constant-returns-to-scale.
Table 8: Simultaneity(1-1): Total materials

Coeﬃcient(standard error)
Variable(name)
GMM
LP
Labour(lnobe2).88***(.02).40***(.02).03***(.007).06(.04)
Capital(lkstock2).25***(.01).12(.30)
Materials(lzairyo2)-3.23***(.22)
Const.
0
Returns to scale*
114.69(0).87(.35)
2.89# of obs.
2346
2306
Note: 2 statistics and p-value in a parenthesis
for constant-returns-to-scale.
Table 9: Simultaneity(1-2): Raw materials

30Distance
GeneralRelationship
j=1
2
3
4
5
6
7
8
9
10
Cooperation
j=1
2
3
4
5
6
7
8
9
10
Independence

Distance

Labour

Input
CapitalMaterials

1st order

2nd

3rd

Returns
to scale.31***(.02).31***(.02).31***(.02).31***(.02).31***(.02).31***(.02).31***(.02).31***(.02).31***(.02).31***(.02).31***
(.02)

.10**
(.04)
.10**
(.04)
.10**
(.05)
.10**
(.04)
.10**
(.05)
.10**
(.05)
.10**
(.05)
.10**
(.05)
.10**
(.05)
.10**
(.05)
.10**
(.05)

.08
(.29)
.08
(.26)
.08
(.31)
.08
(.27)
.08
(.30)
.08
(.29)
.08
(.30)
.08
(.30)
.08
(.30)
.08
(.28)
.08
(.29)

-.0006(.0008).0006(.0005)-.00008(.0003).0002(.0002).0004***(.0001)-.0002(.0002)-.0003(.0002).0004***(.0001).0003**(.0001).00003(.0003)-.0001(.0002).00001(.00001)-4.48e-06(3.53e-06)
8.01e-07(1.30e-06)-2.23e-07(3.24e-07)-1.02e-06**(4.07e-07)
4.88e-07(5.75e-07)
6.18e-07(5.69e-07)-1.00e-06**(4.06e-07)-8.93e-07**(3.75e-07)-3.49e-07(1.55e-06)
3.22e-07(6.29e-07)-6.50e-08(4.99e-08)
8.08e-09(7.41e-09)-1.26e-09(1.61e-09)
4.46e-11(1.95e-10)
6.99e-10**(2.99e-10)-3.75e-10(4.18e-10)-4.08e-10(4.88e-10)
7.02e-10**(3.05e-10)
6.34e-10**(2.85e-10)
1.42e-10(1.64e-09)-3.25e-10(5.48e-10)

4.26
(.04)
4.22
(.04)
4.24
(.04)
4.90
(.03)
4.46
(.03)
4.56
(.03)
4.12
(.04)
4.40
(.04)
3.99
(.05)
5.47
(.02)
4.41
(.04)

.31***(.02).31***(.02).31***(.02).31***(.02).31***(.02).31***(.02).31***(.02).31***(.02).31***(.02).31***(.02).31***
(.02)

.10**
(.05)
.10**
(.05)
.10**
(.05)
.10**
(.04)
.10**
(.04)
.10**
(.04)
.10**
(.04)
.10**
(.04)
.10**
(.05)
.10**
(.04)
.10**
(.04)

.08
(.29)
.08
(.30)
.08
(.33)
.08
(.31)
.08
(.29)
.08
(.28)
.08
(.27)
.08
(.25)
.08
(.30)
.08
(.29)
.08
(.29)

.0005
(.0004)-.00008(.0003).0001(.0001).0004***(.0001)-.0002(.0002)-.0003(.0002).0004***(.0001).0003**(.0001).00007(.0003)-.0001(.0002)-.0006(.0008)-4.20e-06(3.26e-06)
8.03e-07(1.27e-06)-2.16e-07(3.17e-07)-1.04e-06***(3.44e-07)
5.22e-07(5.40e-07)
6.17e-07(5.28e-07)-1.01e-06***(3.82e-07)-9.01e-07**(3.76e-07)-5.09e-07(1.45e-06)
3.32e-07(6.35e-07).00001(.00001)

7.64e-09(6.98e-09)-1.27e-09(1.54e-09)
4.15e-11(1.99e-10)
7.11e-10***(2.53e-10)-3.96e-10(3.97e-10)-4.07e-10(4.55e-10)
7.05e-10**(2.81e-10)
6.41e-10**(2.85e-10)
2.86e-10(1.53e-09)-3.32e-10(5.33e-10)-6.52e-08(4.72e-08)

3.72
(.05)
4.35
(.04)
3.94
(.05)
3.88
(.05)
3.79
(.05)
4.38
(.04)
5.81
(.02)
4.80
(.03)
4.76
(.03)
4.56
(.03)
4.12
(.04)

31
Table 10: Simultaneity(2-1): Total materials

Distance
GeneralRelationship
j=1
2
3
4
5
6
7
8
9
10
Cooperation
j=1
2
3
4
5
6
7
8
9
10
Independence

Distance

Labour

Input
CapitalMaterials

1st order

2nd

3rd

Returns
to scale.41***(.02).41***(.02).40***(.02).40***(.02).40***(.02).41***(.02).41***(.02).40***(.02).40***(.02).41***(.02).41***
(.02)

.06
(.04)
.06
(.04)
.06
(.05)
.06
(.04)
.06
(.05)
.06
(.04)
.06
(.04)
.06
(.05)
.06
(.05)
.06
(.05)
.06
(.05)

.12
(.28)
.12
(.28)
.12
(.32)
.13
(.33)
.13
(.30)
.12
(.31)
.13
(.30)
.13
(.29)
.13
(.30)
.13
(.29)
.12
(.30)

-.002**(.001)-.0009(.0006).0004(.0003).0006***(.0002).0007***(.0002)-.00005(.0002)-.0007***(.0002).0007***(.0002).0006***(.0002)-.0006(.0004)-.0002(.0002).00003*(.00002)3.61e-06(3.90e-06)-8.70e-07(1.36e-06)-7.98e-07**(3.47e-07)-1.99e-06***(4.20e-07)-2.57e-07(6.46e-07)
1.04e-06*(6.18e-07)-2.18e-06***(4.60e-07)-1.83e-06***(4.36e-07)
4.59e-07(1.69e-06)
1.63e-07(6.67e-07)-1.15e-07*(6.21e-08)-5.78e-09(7.43e-09)-6.39e-11(1.59e-09)
2.16e-10(1.96e-10)
1.32e-09***(2.91e-10)
1.12e-10(4.71e-10)-5.35e-10(5.07e-10)
1.49e-09***(3.29e-10)
1.27e-09***(3.16e-10)-1.32e-10(1.78e-09)-1.71e-10(5.52e-10)

.93
(.33)
.74
(.39)
.91
(.34)
.58
(.44)
.60
(.44)
.94
(.33)
.68
(.41)
.74
(.39)
.66
(.42)
.75
(.39)
.84
(.36)

.41***(.02).40***(.02).40***(.02).40***(.02).41***(.02).41***(.02).40***(.02).40***(.02).41***(.02).41***(.02).41***
(.02)

.06
(.04)
.06
(.04)
.06
(.04)
.06
(.04)
.06
(.04)
.06
(.04)
.06
(.05)
.06
(.04)
.06
(.04)
.06
(.04)
.06
(.04)

.12
(.30)
.12
(.27)
.13
(.30)
.13
(.28)
.12
(.29)
.13
(.31)
.13
(.29)
.13
(.31)
.13
(.25)
.12
(.30)
.12
(.31)

-.001*(.0006).0004(.0003).0005***(.0002).0007***(.0002)-.0002(.0002)-.0007***(.0002).0007***(.0002).0005***(.0002)-.0005(.0003)-.0003(.0002)-.002**(.001)

3.83e-06(3.90e-06)-7.82e-07(1.38e-06)-7.39e-07**(3.39e-07)-1.98e-06***(4.62e-07)
6.58e-09(6.44e-07)
1.04e-06*(5.98e-07)-2.16e-06***(4.49e-07)-1.62e-06***(4.45e-07)
2.90e-07(1.59e-06)
2.42e-07(7.76e-07).00003**(.00001)-6.11e-09(7.36e-09)-1.55e-10(1.63e-09)
1.88e-10(1.96e-10)
1.32e-09***(3.35e-10)-5.40e-11(4.63e-10)-5.34e-10(4.95e-10)
1.47e-09***(3.21e-10)
1.14e-09***(3.22e-10)
1.99e-11(1.65e-09)-2.26e-10(6.19e-10)-1.18e-07**(5.53e-08)

.64
(.43)
1.05
(.31)
.62
(.43)
.62
(.43)
.64
(.43)
.73
(.39)
.67
(.41)
.75
(.39)
.61
(.43)
.75
(.39)
.87
(.35)

32
Table 11: Simultaneity(2-2): Raw materialsName# of obs.

Unit

Mean

S.D.

Min.

Max.

OutputVariable

lpoutput2

2346

Ten thousand yen(ln, real)

12.46

1.44

9.01

17.99

# of zero0

Labourlnobe22346

Man-hours(ln)

14.40

.95

12.78

18.93

0
75

Capitallkstock2

2346

Ten thousand yen(ln, real)

11.09

2.62

0

16.56

Materials

lmtotal22346

Ten thousand yen(ln, real)

11.70

1.95

0

17.73

9

lzairyo22346

Ten thousand yen(ln, real)

11.16

2.56

0

17.72

40

ttdis

2346

km

28.91

36.22

0

231.56

11

km
km
km
km
km
km
km
km
km
km

143.89106.620359.735

180.83124.150775.292

540.38245.81.441454.530280.62242.8401116.711

272.62179.42.40

1193.000

214.86200.1201105.541

269.98248.08.521117.140267.19247.40.591112.02

0

92.08

97.85

0

857.941

174.41160.3101102.841

143.49106.800359.7319

180.22124.360775.2912538.22247.6401454.5311

279.85243.2801116.7112272.14179.8701193.007

214.86200.1301105.543

269.40248.3601117.149266.19247.6501112.02

11

91.59

98.07

0

857.9420

173.67160.5301102.84

14

28.66

36.26

0

231.5649

Distance
GeneralRelationship
j=1

tdis1

2346

2

tdis2

2346

3

tdis3

2346

4

tdis4

2346

5

tdis5

2346

6

tdis6

2346

7

tdis7

2346

8

tdis8

2346

9

tdis9

2346

10

tdis102346

Cooperation
j=1

pdis1

2346

2

pdis2

2346

3

pdis3

2346

4

pdis4

2346

5

pdis5

2346

6

pdis6

2346

7

pdis7

2346

8

pdis8

2346

9

pdis9

2346

10

pdis10

2346

km
km
km
km
km
km
km
km
km
km

pdis112346

km

Independence

Table 12: Summary statistics(year 2003)

33

Figure 2: Locations for plants independent of any technology cooperation association organized by either automobile assembly company  = 1 · · ·  10.

34

.04
.03
Density
.02
.01
0
0

50

100
150
General distance(km)Figure 3: Histogram of ’general’ distance

35

200

250

.04
.03
Density
.02
.01
0
0

50

100
150
Independence distance(km)Figure 4: Histogram of ’independence’ distance

36

200

250

.004
.003
Density
.002
.001
0
0

200

400
600
800
Relationship distance(j=6, km)

Figure 5: Histogram of ’relationship’ distance( = 6)

37

1000

.004
.003
Density
.002
.001
0
0

200

400
600
800
Cooperation distance(j=6, km)

Figure 6: Histogram of ’cooperation’ distance( = 6)

38

1000

.01
.008
Density
.006
.004
.002
0
0

200

400
600
Relationship distance(j=9, km)

Figure 7: Histogram of ’relationship’ distance( = 9)

39

800

.01
.008
Density
.006
.004
.002
0
0

200

400
600
Cooperation distance(j=9, km)

Figure 8: Histogram of ’cooperation’ distance( = 9)

40

800

Sum of predicted productivity and estimated residual
0
500
1000
1500
0

500
1000
Cooperation distance (km)Figure 9: Productivity estimates(cooperation distance, j=3) with quadratic
polynomial predictions

41

1500

Sum of predicted productivity and estimated residual
0
500
1000
1500
2000
0

50

100
150
Independence distance (km)Figure 10: Productivity estimates(independence distance)

42

200

250