Firm Agglomeration in Knowledge
Intensive Business Service Sectors
Shinya Fukui
June, 2020
Discussion Paper No.2008

GRADUATE SCHOOL OF ECONOMICS
KOBE UNIVERSITYROKKO, KOBE, JAPANFirm Agglomeration in Knowledge
Intensive Business Service Sectors*
Shinya Fukui†Research Fellow, Graduate School of Economics, Kobe University, Japan
Senior Researcher, Osaka Prefectural Government, Japan
June, 2020
Abstract
We observe dense agglomerations of Knowledge-Intensive Business Services (KIBS) inlarge cities such as Tokyo and Osaka. Such urban features of KIBS stem from the factthat the main customers for KIBS are corporate headquarters (HQs), and KIBS’s main
input is highly skilled labor. We adhere to the model proposed by Redding and
Venables (2004) and present a monopolistic competition model. Our results indicatethat improving access to the agglomeration of HQs and KIBS and knowledge
agglomeration will strengthen market access and supply access and that KIBS firms will
be even more inclined to establish locations in those municipalities.
Keywords: Knowledge-Intensive Business Service; Headquarters; Monopolisticcompetition model; Japan; Municipalities
JEL classification: R12; L84; C21*

I would like to thank, Nobuaki Hamaguchi, Yoichi Matsubayashi, Naoya Sueishi, Keijiro Otsuka,

Chian-Yue Wang, Masahisa Fujita, Asao Ando, Keisuke Kawata, Dao-Zhi Zeng, Kentaro Nakajima,
Yasuharu Ukai, Nobuo Kobayashi, Norihiro Kasuga, and Tatsuya Asami for helpful comments. Allremaining errors are my own responsibility.
†

Address: Graduate School of Economics, Kobe University, 2-1 Rokkodai-cho, Nada- ku, Kobe 657-

8501, Japan. E-mail address: s_fukui@people.kobe-u.ac.jp

1 Introduction
In the last few decades, the business service sector has expanded enormously ineconomically developed economies, including Japan (Ministry of Economy, Trade andIndustry 2002, OECD 2005a). The business service sector has become important forJapanese economic performance (Ministry of Economy, Trade and Industry 2017).
One prominent feature of business service activity is its high knowledge intensity.
The OECD (2005b) classifies post and telecommunications, finance and insurance,business activities (not including real estate), education, and health as a knowledgeintensive business services (KIBS) at the two-digit ISIC/NACE level. Miles et al. (1995),
who used the term KIBS originally, defined KIBS as
1. Relying heavily upon professional knowledge
2. Being themselves primary sources of information and knowledge, using theirknowledge to produce intermediary services for their clients’ production processes
3. Having competitive importance and supplied primarily to business.
Based on those earlier studies and the industrial classification used in the“Economic Census” of the Statistics Bureau, Ministry of Internal Affairs andCommunications (MIC), our definition of KIBS corresponds to the following.
F: Finance and insurance
IT: Information services, Services incidental to the internet, Content industries,
producing video picture information, sound information, character
information production and distribution
P: Professional services, for which qualifications are needed, Professional
services,

providing design

services andbusiness consultants,

Advertising
T: Technical services, such as commodity inspection and non-destructive
testing services, engineering and architectural services, and mechanicaldesign services
Following Miles et al. (1995), over the last few decades, the concentration,
activity, and evolution of KIBS have garnered growing attention from numerous authors:
Den Hertog (2000), Muller and Zenker (2001), Keeble and Nachum (2002), Wood (2002),
Miles (2006), Koch and Stahlecker (2006), Wood (2006), Freel (2006), Doloreux andMuller (2007), Shearmur and Doloreux (2008), Johansson and Klaesson (2011), Doloreux
and Shearmur (2012), Jacobs et al. (2014), Meliciani and Savona (2015), and Klaesson
and Norman (2015).
2

The products of KIBS are characterized as intermediate supplier services rather
than final goods for consumption. They supply services that are provided mainly to theother sectors. Additionally, KIBS is characterized as a knowledge-intensive sector.
Therefore, the main customers for this sector are some pivotal corporate functions
including headquarters (HQs). These customers tend to be agglomerated in larger cities(Fukui and Matsushita, 2018). Whereas KIBS demands highly skilled labor as input,
highly skilled workers tend to reside in larger cities (Glaeser, 1999; Kox and Rubalcaba,
2007a, 2007b; Karlsson et al., 2009; and Schricke et al., 2012).
For instance, 37.9% of the KIBS labor force is in the 23 wards of Tokyo andOsaka city, the share of employees working for HQs in the 23 wards of Tokyo and Osaka
city throughout Japan is approximately 10% (“Economic Census for Business Activity
2012” (Keizai sensasu katsudo chousa, Statistics Bureau, MIC, hereafter ECBA2012)).
Additionally, the 23 wards of Tokyo and Osaka city have approximately 12% of all
university graduates of all of Japan (“National Census 2010” from Statistics Bureau,
MIC). That importance notwithstanding, the surface area of the 23 wards of Tokyo andOsaka city accounts for only about 0.2% of the entirety of Japan.
To analyze the KIBS market structure, we propose a monopolistic competition
model. A wide variety of KIBS firms provide a diverse range of differentiated services
demanded by HQs. This broad, various supply of services enables the production of ahomogeneous set of services used by HQs. In addition, KIBS rely on highly skilledworkers.
In a competitive market with free entry, higher wages attract laborers who work
to provide KIBS. In fact, according to ECBA2012, 359,326 enterprises provide KIBS,
whereas the total number of enterprises in KIBS with fewer than five employees is203,179, with the share of 56.5%. Therefore, the market can be regarded as competitive,
due to a large degree of small firms.
As a salient feature of KIBS, firms tend to locate in core cities such as Tokyo
and Osaka, rather than in periphery cities. This agglomeration tendency is particularly
stronger for KIBS than for other sectors such as manufacturing or retail sales. Therefore,
KIBS is an important driving force of the economy in large cities (Ottaviano and Thisse,
2004; Proost and Thisse, 2017). This paper is designed to elucidate the causes of KIBS
agglomeration.
Industrial agglomeration is a main subject of economic geography (e.g., Fujita
et al. 1999; Fujita and Thisse, 2002). Larger cities tend to show agglomeration of firms
and facilities because higher market potential or market accessibility associated with3

larger cities generates scale economies, thereby enabling firms to obtain greater profits.
A Few empirical investigations of the location of KIBS firms can be found in theurban economics and economic geography literature. Jacobs et al. (2014) test the relations
between location of birth of KIBS and multinational enterprises (MNEs). Meliciani and
Savona (2015) examine the determinants of specialization of business service across EU27. Klaesson and Norman (2015) explore the relation between spatial distribution and thegrowth of KIBS and market potential.
It is unsatisfactory, however, that all of these empirical studies are based on adhoc reduced-form equations but are not derived explicitly from a theoretical model ofspatial economics. For instance, although Klaesson and Norman (2015) use market
potential calculated using the size of the economy in the region as an explanatory variable,consideration of the actual situation calls for a calculation of KIBS’ market potential
based explicitly on the distribution of demand for agglomerated HQs and KIBS firms.
Johansson and Klaesson (2011) present an empirical model that uses the demand function
and pricing equation under the setting of increasing returns to scale. In spite of their
explicit reference to the spatial economics theory, their analytical model is not derived
from a clear description of the structural form.
Davis and Henderson (2008) and Strauss-Kahn and Vives (2009) examine thedeterminant factors affecting HQ location choice. Business services are used as one
important factor to ascertain the HQ location. However, our study analyzes causality inthe opposite direction: the demand by HQs to induce the location of KIBS firms.
From a theoretical perspective, Duranton and Puga (2005) explain the relations
between trade cost and urban specialization in HQs and business services. They conclude
that if the transmission cost of headquarter services is sufficiently low, then firms locate
their headquarters away from their production plants and closer to other business service
firms. This result is attributable to low intra-firm operating costs between HQs and the
production site, while locating HQs proximate to concentrated business services in thecity. Nevertheless, no empirical investigation has used this theoretical form.
In spite of the increasing importance of KIBS in economically developed
countries, no research in the relevant literature describes a theory-based empirical study
conducted to identify the agglomeration factor of KIBS. In fact, ours is the first study toestimate the agglomeration forces of KIBS derived from the spatial economic model
setting.
As described herein, we seek the determinants of agglomeration of KIBS using
data for Japan. Given that large cities such as Tokyo and Osaka represent the driving force4

of the Japanese economy and given that they maintain great agglomerations of KIBS,
investigating how KIBS agglomeration is created in the Japanese economy is important.
The remainder of the paper proceeds as follows. Following the Introduction,
Section 2 outlines the related literature. Section 3 presents an explanation of thetheoretical founding of our analysis. Section 4 presents a description of the empiricalmodel and the data used in our estimation. Section 5 provides results and discussion.
Section 6 presents conclusions.
2 Related literature
Several empirical studies have been conducted based on the theoreticalbackground of economic geography. Redding and Venables (2004) are the first to suggest
a structural framework of market access. They find the relation between per-capita
income and distance to markets and supply access. The wage equation à la Fujita et al.
(1999) plays a central role in their analysis. Hanson (2005) states that a strong relation
exists between wages and market access across U.S. counties. Head and Mayer (2004,
2006) examine the link between the wage equation and market potential. Related to these,with increasing returns to scale and transport costs, some studies test the existence ofhome market effects (Davis and Weinstein, 1996, 1999, 2003).
Building on Helpman’s research (1998), Redding and Sturm (2008) derivetheoretically that the population increases with greater market access. They use thedivision of Germany after World War II as a natural experiment to examine the role playedby market access. Amiti and Cameron (2007) estimate agglomeration benefits attributableto market access effects for firms in Indonesia. Hering and Poncet (2010) explain that
individual wage differences arise from the geography of market access of Chinese cities.
Another line of study based upon a natural experiment is that of Nakajima (2008) forJapan.
Several researchers examine the sectoral concentration of KIBS based on
economic geography. Jacobs et al. (2014) test the relations between the location of birthof KIBS and multinational enterprises (MNEs) in Amsterdam in the Netherlands. Afterthey assume the profit function of a firm, they conclude that KIBS tend to locate close to
MNEs due to agglomeration externalities. Although they point out that HQs of MNEs areimportant for KIBS-birth, for the roles HQs play such as “command and control activities”
and “concentrations of human capital and knowledge spillover,” their inspection is notcomprehensive: they only specifically examine MNEs. Meliciani and Savona (2015)5

examine the determinants of specialization of business service across EU-27 using
explanatory factors such as agglomeration economy, intermediate demand, andinnovation in services. They treat the manufacturing sector and neighboring businessservices as intensive users of business services and treat information and communication
technologies (ICTs) as an important determinant factor for specialization in businessservices. Klaesson and Norman (2015) explore the relation between spatial distribution
and growth of KIBS and market potential in Sweden. The market potential of their paper
is measured as in the total number of jobs in area. They find positive relations between
the growth of KIBS and market potential.
3 Theoretical backgroundIn this section, to derive our estimable specification form, we follow the model
presented by Redding and Venables (2004), which is built on the spatial economic theory
à la Fujita et al. (1999).
The economy consists of two sectors, HQs (sector H) and KIBS (sector K) andthere are 𝑖, 𝑗 = 1, ⋯ , 𝑅 cities.
First, we describe the demand side of the economy. H sector in city 𝑗 has the
production function in producing homogeneous HQ services represented as
2
234

56

9

234
𝐻) = *+ , 𝑘.) (𝑧) 2 𝑑𝑧:.

72
234 234= ;+ 𝑛. 𝑘.)2 =
,
.
9

(1)

where 𝑘(𝑧) denotes the varieties of KIBS services with 𝑧 ∈ [0, 𝑛. ], 𝑛. represents therange of varieties produced in city 𝑖, and 𝜎 > 1 stands for the constant elasticity of
substitution. The second equality holds because all services produced in city 𝑖 behave ina symmetric way. The price index for these HQs to purchase all variety of KIBS is defined
as

9

56

4
432

𝑃) = *+ , 𝑝.) (𝑧)432 𝑑𝑧:.

9= ;+ 𝑛. 𝑝.) 432 =

4
432

,

(2)

.

7

where 𝑝.) (𝑧) denotes the price of variety 𝑧 produced in city 𝑖 and sold in city 𝑗. 𝑧
6can be dropped by assuming symmetry.
Using Shephard’s lemma to the KIBS service price index, demand for a KIBS
service in city 𝑗 produced in city 𝑖 is𝑘.) = 𝑝.) 32 𝐸) 𝑃) (234) ,(3)

5

where 𝐸) = 𝐻) 𝑞) + ∫7 M 𝑘) (𝑧)𝑝) (𝑧)𝑑𝑧 represents the total expenditure on KIBS and HQs
in city 𝑗 and 𝑞) expresses the price for the HQ service.
The profit function of a sector K firm in city 𝑖 is
9

9
R
P R
𝜋. = + 𝑝.) 𝑘.) − 𝑃. 𝑤. 𝑐 + 𝑘.) 𝑇.) − 𝑃.P 𝑤. 𝐹,
)
)

(4)

where 𝑐 represents a composite of KIBS and skilled labor required for one unit of K
R

production, whereas fixed input is 𝐹 and 𝑃.P 𝑤. gives a unit price of the composite
input. Each KIBS firm employs all varieties of KIBS as input with price index 𝑃 andhighly skilled labor with wage 𝑤, subject to input shares 𝛼 and 𝛽, where 𝛼 + 𝛽 = 1.
For this study, 𝑇.) > 1 represents the iceberg type transport cost and 𝑇.) − 1 denotes
the proportion of loss of service output produced in city 𝑖 to arrive in city 𝑗. This
expression implies that 𝑘.) 𝑇.) amount of service must be produced to sell a service tocity 𝑗 that is produced in city 𝑖. Consequently, ∑9) 𝑘.) 𝑇.) represents the total output ofa sector K firm at city 𝑖 to attend to demand from all regions.
The price for each city where the service product is sold is 𝑝.) = 𝑝. 𝑇.) . With
profit maximization, the f.o.b. price 𝑝. has a constant markup as𝑝. =𝜎
× 𝑢𝑛𝑖𝑡 𝑐𝑜𝑠𝑡,
𝜎−1

(5)

R

where 𝑢𝑛𝑖𝑡 𝑐𝑜𝑠𝑡 = 𝑃.P 𝑤. 𝑐. Substituting equation (5) in (4), the profit of sector K in eachcity 𝑖 becomes9𝑝.
𝜋. = *+ 𝑘.) 𝑇.) − (𝜎 − 1)𝐹 :.
𝜎
)

7

(6)

The free entry market equilibrium requires that 𝜋. = 0. It follows from equation (6) that9𝑘b = + 𝑘.) 𝑇.) = (𝜎 − 1)𝐹 ,(7))

where 𝑘b represents equilibrium output of a sector K firm that is constant irrespective of
the market size. Substituting the demand equation (3) to ∑9) 𝑘.) 𝑇.) , then using equation(5), the equation becomes
9

2
𝜎
R
𝑘b de
f 𝑃.P 𝑤. 𝑐g = + 𝐸) 𝑃) (234) 𝑇.) (432) .
𝜎−1

(8)

)

Solving the equation (8) for 𝑤. , the equation is rewritten as
9R2
𝑤. = e𝜎 32 32 34 3P2
f 𝑐 𝑘b 𝑃.
+ 𝐸) 𝑃) (234) 𝑇.) (432) ,
𝜎−1
)

4/R2

9
3P/R

𝑤. = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 × 𝑃.

*+ 𝐸) 𝑃) (234) 𝑇.) (432) :

,

(9)

)

2

where 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 = e234f

34/R

𝑐 34/R 𝑘b 34/R2 . This calculation is the wage equation

proposed by Fujita et al. (1999). The right-hand side (RHS) of the equation shows the“market access”: the summation of market capacities under consideration of transportcost. The left-hand side (LHS) of the equation is the wage at which each firm in city 𝑖can pay with zero profit.
We now turn to the supply side, where access to supply is measured as 𝑛. 𝑝.) 432 ,where 𝑛. signifies the number of firms, and where 𝑝.) (432) stands for the price inwhich the trade cost is included.
From the demand equation (3), total service sold from city 𝑖 to city 𝑗 is8

5M

𝑛. 𝑝. 𝑘.) = 𝑛. 𝑝. 432 𝑇.) (432) l𝑞) 𝐻) + , 𝑘) (𝑧)𝑝) (𝑧)𝑑𝑧m 𝑃) (234) .

(10)

7

This equation represents transaction between cities. The RHS of equation (10) gives both5

the market capacity 𝑚) ≡ p𝑞) 𝐻) + ∫7 M 𝑘) (𝑧)𝑝) (𝑧)𝑑𝑧q𝑃) (234) and the supply capacity𝑠. ≡ 𝑛. 𝑝. 432 associated with trade cost 𝑇.) (432) between cities. Here, 𝑚) denotes thecapacity of total sales in city 𝑗, which expresses the amount that the services sector K incity 𝑖 can sell. Here, 𝑠. represents the capacity of production, which consists of thenumber of firms 𝑛. and service price in sector K in city 𝑖.
Using 𝑝.) = 𝑝. 𝑇.) , the price index becomes

9432𝑃) = ;+ 𝑛. p𝑝. 𝑇.) q

4
432

=

4
432

9

= ;+ 𝑠. 𝑇.) (432) =

.

.

(11)

.

The price index shows how severe the competition is in city 𝑗.
From equation (10), the market access of each city 𝑖 and the supply access ofeach city 𝑗 is defined as
95M

𝑀𝐴. ≡ + l𝑞) 𝐻) + , 𝑘) (𝑧)𝑝) (𝑧)𝑑𝑧m 𝑃) (234) 𝑇.) (432) ,
)

(12)

7
9

𝑆𝐴. ≡ + 𝑛. 𝑝. (432) 𝑇.) (432) .

(13)

)

In those expressions, 𝑀𝐴. signifies market access, which is the distance-weighted sumof the market capacities of all partner cities. Also 𝑆𝐴. denotes supply access, which isthe distance-weighted sum of supplier capacities of all partner cities.
Finally, from equations (9), (10), (11), (12) and (13), we have the estimablefunction of

9

3P/R

𝑤. = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 × 𝑃.

4/R2

5M

9

*+ l𝑞) 𝐻) + , 𝑘) (𝑧)𝑝) (𝑧)𝑑𝑧m 𝑃) (234) 𝑇.) (432) :)7
P/R(234)= 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 × 𝑆𝐴)

4/R2

𝑀𝐴.

,

(14)

where 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 is the same as that in equation (9).
-Parameters are 𝜎 > 1, 𝛼 < 1, 𝛽 < 1. Therefore, the following are true.
5
High demand p𝑞) 𝐻) + ∫7 M 𝑘) (𝑧)𝑝) (𝑧)𝑑𝑧q in city 𝑗 leads to high market access.

-If the price index 𝑃) increases, then sector K in city 𝑖 can sell much more of
their services. This improvement corresponds to increased market access.

-

Reduction in transport cost leads to increased market access.

-An increase in the number of firms 𝑛. and a decline of the price 𝑝.) (432)increase the supply access.

-Increased supply access reduces the price index, so the cost reduction in KIBS
leads to reduced service production cost in city 𝑖 (from equation (11)).

-

Similarly, reduction in transport costs will lead to an increase in supply access.
Market access expresses the benefit of proximity to a large market. Supply accessindicates the benefit of proximity to suppliers. All in all, the higher the market access andhigher the supply access, the higher a wage payment can be afforded.
4 Data description and econometric model
4.1 Data description
The logarithm of equation (14) will be

ln 𝑤. = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 + x

1
𝛼y ln 𝑀𝐴. + x
y ln 𝑆𝐴. .
𝛽𝜎𝛽 (𝜎 − 1)
4

(15)

P

When defining parameters as 𝑏4 ≡ dR2g , 𝑏{ ≡ dR(234)g, this formation will be estimable.
We use a municipal unit of data for Japan for estimation because the inspectionof spatial interaction is appropriate in such a small unit of aggregated data. Because wage
data of KIBS are not available in municipal units, we substitute wages with share of thenumber of KIBS employees in municipality to the number of employees belonging to all10

industries in that municipality. This substitution is plausible because it is more profitablefor firms to locate in city 𝑖, which has a higher wage. The KIBS share corresponds tolocation probability, in a sense.
As defined by Nakajima (2008), we replace “market access” 𝑀𝐴. with “market
potential”: 𝑀𝑃. . We follow Head and Mayer (2004) and use Harris (1954) type market
potential in municipality 𝑖: 𝑀𝑃. . Here, 𝑀𝑃. is derived as
9𝑀𝑃. = +
.

𝑌)
,
𝑑.)

𝑖 ≠ 𝑗,(16)

where 𝑌) denotes the size of the economy of the other municipality 𝑗 and 𝑑.)expresses the distance from municipalities 𝑖 to 𝑗. Distance is calculated according to the
Euclidean distance between municipalities 𝑖 and 𝑗 . 1 We use the number of theemployees of HQs plus KIBS in municipalities for 𝑌) . For that reason, the variable isexpressed as 𝑀𝑃(𝐻𝑄𝑠 + 𝐾𝐼𝐵𝑆). .
On the supply side, we replace “supply access” (𝑆𝐴. ) with “supply potential”
and use specifications for market potential type. The equation for supply potential (𝑆𝑃. )is as follows
9

𝑆𝑃. = +
.

𝐿)
,
𝑑.)

𝑖 ≠ 𝑗,(17)

where 𝐿. is the number of highly skilled laborers in municipality 𝑗 and 𝑑.) continues
to express the distance from municipalities 𝑖 to 𝑗.
For the KIBS share, we use ECBA2012 for the data of KIBS employees inmunicipalities. The KIBS share of municipality 𝑖 is calculated as the share of the numberof KIBS employees in municipality 𝑖 to the number of employees belonging to allindustries in municipality 𝑖. The numbers of HQ employees and KIBS employees are
Define longitude and latitude of municipality 1 for 𝑥4, 𝑦4, longitude and latitude of municipality 2 for𝑥{, 𝑦{, and calculate the Euclidean distance as 𝑑 = 6378.137 × cos34 (𝑠𝑖𝑛𝑦4 𝑠𝑖𝑛𝑦{ +𝑐𝑜𝑠𝑦4 𝑐𝑜𝑠𝑦{cos (𝑥{ − 𝑥4 )). Longitude and latitude are computed using a “Geocoding Service” provided
by the Center for Spatial Information Science of The University of Tokyo. When we input the names ofmunicipalities, “Geocoding Service” returns the longitude and latitude of city offices of themunicipalities. Therefore, we use these data.
1

11

taken from ECBF2009 for calculating market potential. As a proxy for highly skilledlabor, the population of university graduates is taken from the “National Census 2010”
from Statistics Bureau, MIC.
We use some controls for municipalities. Population density (𝑃𝑂𝑃𝑑𝑒𝑛𝑠𝑒. ) is a
proxy for congestion. This setting of the proxy is in line with a procedure used in an
earlier study: Jacobs et al. (2014) state that population density represents crowding effects.
For calculation of the population density, the population is taken from “Basic Resident
Register (Jyumin-kihon-daicho) 2010” from Statistics Bureau, MIC. The land area ofmunicipalities is from “Statistical reports on the land area by prefectures andmunicipalities in Japan (Zenkoku-todoufuken-sikutyoson-betsu-mennski-no-shirabe)”from the Geospatial Information Authority of Japan.2
Second, the number of enterprises (𝑒𝑛𝑡. ) is used because KIBS also sell theirservices to the other sector, irrespective of HQs and KIBS. Third, the manufacturing shareof municipalities (𝑚𝑎𝑛𝑢 𝑠ℎ𝑎𝑟𝑒. ) is used because municipalities with high manufacturing
shares show different activities for KIBS locations. For instance, Aichi prefecture is
known to have high inclination of manufacturing, with many HQs related to
manufacturing. However, KIBS activity is lower than in other large cities such as Tokyo,
Osaka, or Kanagawa (Fukui and Matsushita, 2018). The number of enterprises and the
manufacturing share based on the number of manufacturing employees in municipalities
to the number of employees of the total sector in municipalities are from ECBA2012.
In addition to these, we use the cross term 𝐾𝑛𝑜𝑤𝑙𝑒𝑑𝑔𝑒. = 𝐿𝑠ℎ𝑎𝑟𝑒. ×
𝑃𝑂𝑃𝑑𝑒𝑛𝑠𝑒. to capture knowledge agglomeration in the municipalities. Population
density is a proxy to the degree of urbanization. Therefore, if the share of highly skilledlabor and population density is simultaneously high, then the concentration of highly
skilled labor is apparent in large cities, so knowledge spillover occurs and agglomerationof knowledge is strong in that municipality. We calculate the market potential forknowledge agglomeration, otherwise knowledge agglomeration potential (𝐾𝑃. ), as
9

𝐾𝑃. = +.

𝐾𝑛𝑜𝑤𝑙𝑒𝑑𝑔𝑒),𝑑.)𝑖 ≠ 𝑗,(18)

where 𝐾𝑛𝑜𝑤𝑙𝑒𝑑𝑔𝑒. = 𝐿𝑠ℎ𝑎𝑟𝑒. × log 𝑃𝑂𝑃𝑑𝑒𝑛𝑠𝑒. and where 𝐿𝑠ℎ𝑎𝑟𝑒. is calculated as
the share of the number of highly skilled laborers in municipality 𝑖 to the number of highly
2

Data for population density have been corrected by Professor Koji Yasuda for the purpose of analysis in anotherwork. He kindly provided me with the correct data, and I appreciate his contribution.

12

skilled laborers in Japan total, and 𝑑.) expresses the distance from municipalities 𝑖 to𝑗.
For cross-section, 1877 municipalities are used. The data pertain to private
sectors (excluding public sector). ECBA2012 and ECBF2009 are exhaustive surveys
about Japanese establishments and enterprises. Single-unit enterprises are excluded: weuse only data of head office of multi-unit enterprises, for HQs because single-unit
enterprises are presumed to demand KIBS in different way compared with head office ofmulti-unit enterprises. Demand for KIBS of head office of multi-unit enterprises ispresumed to be more knowledge-intensive than for single-unit enterprises.
Descriptive statistics are presented in Table 1. The maximum and minimum
values of KIBS share are 0.324 and 0.000, respectively. The Market potential of HQs and
KIBS ranges from 8,466 to 1,376,398, and the coefficient of variation is 1.147.
Additionally, the maximum and minimum values of the Supply potential of highly skilledlabor are 10,154 and 548,180, respectively, and the coefficient of variation is lower thanthat of the Market potential of HQs and KIBS (0.851). The coefficient of variation of
Knowledge agglomeration potential is 0.938. The maximum value of Population density
is 19,444, and the minimum value of Population density is 1.555. Number of enterprises
ranges from 70 to 952,499. Manufacturing share ranges from 0 to 0.678.
Table 1 Descriptive statistics for variables used in estimation for the agglomeration of
KIBS
Standard
Mean

deviation

Coefficient ofMedianMin

Max

variation

KIBS share

0.037

0.030

0.030

0.000

0.324

0.811

Market potential of HQs and KIBS

93231

106926

63426

8466

1376398

1.147

Supply potential of highly skilled labor

105748

89971

77081

10154

5481800.851

Knowledge agglomeration potential

0.048

0.05

0.033

0.004

0.282

0.938

Population density

1483

3003

252

1.555

19444

2.025

Number of enterprises

29731

59128

10868

70

952499

1.989

Manufacturing share

0.206

0.122

0.192

0.000

0.678

0.592

Note: KIBS share is the share of KIBS employees in municipalities, Market potential of HQs and KIBS is
the market potential in municipality 𝑖, which can be calculated via equation (16) using the number of HQ
employees plus the number of KIBS employees in municipalities 𝑖 and 𝑗 as well as the distance between
them, Supply potential of highly skilled labor is determined via equation (17) using the number of highly
skilled laborers in municipality 𝑗, and Knowledge agglomeration potential can be calculated via equation(18) using 𝐾𝑛𝑜𝑤𝑙𝑒𝑑𝑔𝑒. , which is defined as 𝐾𝑛𝑜𝑤𝑙𝑒𝑑𝑔𝑒. = 𝐿𝑠ℎ𝑎𝑟𝑒. × log 𝑃𝑂𝑃𝑑𝑒𝑛𝑠𝑒. . Population
density is the population density in municipality 𝑖, Number of enterprises denotes the number of enterprises,
and Manufacturing share stands for the manufacturing share based on the number of employees of13manufacturing in municipalities to the number of employees of all sectors in municipalities.

4.2 Econometric model
Our specification in estimating agglomeration of KIBS is using the Spatial Error
model (SEM). Meliciani and Savona (2015) use the Spatial Durbin model (SDM) for theestimation of business service specialization. Actually, SDM is a general model thatencompasses SEM or a Spatial Autoregressive model (SAR) (LeSage and Pace, 2009). In
our spatial regression, spatial dependence for the independent variable and dependent
variable are already included in specifications. These are market potentials of KIBS andHQs: 𝑀𝑃(𝐻𝑄𝑠 + 𝐾𝐼𝐵𝑆). and the spatial lag of highly skilled labor share: 𝑊𝐿𝑠ℎ𝑎𝑟𝑒. .
Therefore, in our case, spatial dependence between municipality 𝑖 and 𝑗 is summarized
in the error term. Unobserved spatial dependence might appear in the error term. For
instance, knowledge spillover or office supply in neighboring regions is conceivably
unobserved spatial dependence. These variables are not available.
Specification for the estimation is
𝐾𝐼𝐵𝑆𝑠ℎ𝑎𝑟𝑒. = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 + 𝑏4 ln 𝑀𝑃(𝐻𝑄𝑠 + 𝐾𝐼𝐵𝑆). + 𝑏{ ln 𝑆𝑃. + 𝛾4 ln 𝑃𝑂𝑃𝑑𝑒𝑛𝑠𝑒.
+ 𝛾{ ln 𝑒𝑛𝑡. + 𝛾‘ 𝑚𝑎𝑛𝑢𝑠ℎ𝑎𝑟𝑒. + 𝑢. ,𝑢. = 𝜆𝑊𝑢. + 𝑒. ,(19)

where the 𝐾𝐼𝐵𝑆𝑠ℎ𝑎𝑟𝑒. is the share of the number of KIBS employees in municipalities,
ln 𝑀𝑃(𝐻𝑄𝑠 + 𝐾𝐼𝐵𝑆). is the log of market potential in municipality 𝑖, which is definedin equation (16) using the number of the employees of HQs plus KIBS in municipalities
and distances between municipality 𝑖 and 𝑗. Additionally, 𝑆𝑃. is the log of supply
potential in municipality 𝑖, which is defined in equation (17) using the number of highly
skilled laborers in municipalities 𝑖 and 𝑗 as well as the distance between them.
ln 𝑃𝑂𝑃𝑑𝑒𝑛𝑠𝑒. signifies log of population density in municipality 𝑖, ln 𝑒𝑛𝑡. denotes thelog of the number of enterprises, 𝑚𝑎𝑛𝑢𝑠ℎ𝑎𝑟𝑒. expresses the manufacturing share basedon the number of employees of manufacturing in municipalities to the number of
employees of the total sector in municipalities, 𝑢. is the error component, 𝜆 is a spatial
parameter associated with the spatial weight matrix, and 𝑒. is the idiosyncratic error term.
𝑊 is 𝑅 × 𝑅 spatial weight matrix, where 𝑅 represents the number ofmunicipalities. Diagonal elements of 𝑊 are set to 0; off-diagonal elements are theinverse distance of 1,000 km unit between cities 𝑖 and 𝑗. This connection effect isthought to have distance decay so the off-diagonal elements of 𝑊 can be expressed as a
14

gravity-like model, following Anselin (2002), as

𝑤.) =

1
,
𝑑𝑖𝑠𝑡.){𝑖 ≠ 𝑗,

where 𝑑𝑖𝑠𝑡.) expresses the distance between municipalities 𝑖 and 𝑗. As a convention,
each row of 𝑊 is normalized to 1.
An alternative specification is
𝐾𝐼𝐵𝑆𝑠ℎ𝑎𝑟𝑒. = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 + 𝑏4 ln 𝑀𝑃(𝐻𝑄𝑠 + 𝐾𝐼𝐵𝑆). + 𝑏{ ln 𝐾𝑃. + 𝛾4 ln 𝑃𝑂𝑃𝑑𝑒𝑛𝑠𝑒.
+ 𝛾{ ln 𝑒𝑛𝑡. + 𝛾‘ 𝑚𝑎𝑛𝑢𝑠ℎ𝑎𝑟𝑒. + 𝑢. ,𝑢. = 𝜆𝑊𝑢. + 𝑒. ,(20)

where ln 𝐾𝑃. is the log of knowledge agglomeration potential in municipality 𝑖, which
is defined in equation (18) using the share of the number of highly skilled laborers inmunicipality 𝑖 to the number of highly skilled laborers in Japan total and log of population
density in municipalities 𝑖 and 𝑗 as well as the distance between them.
Correlation coefficients are presented in Table 2. High correlation coefficients(over 0.5) are apparent between KIBS share and Market potential of HQs and KIBS
(0.549), KIBS share and Number of enterprises (0.681). The correlation coefficients of
KIBS share and Supply potential of highly skilled labor, as well as of KIBS share andKnowledge agglomeration potential, are relatively low – 0.412 and 0.422, respectively –but positive. The correlation coefficients of explanatory variables are as follows: Market
potential of HQs and KIBS and Supply potential of highly skilled labor (0.889), Market
potential of HQs and KIBS and Knowledge agglomeration potential (0.897), Market
potential of HQs and KIBS and Population density (0.781), Supply potential of highly
skilled labor and Knowledge agglomeration potential (0.999), Supply potential of highly
skilled labor and Population density (0.799), Knowledge agglomeration potential and
Population density (0.808). Negative correlations are seen among Manufacturing shareand all other variables.
Consequently, we can expect positive causality between our examined variables:
KIBS share, Market potential of HQs and KIBS, Supply potential of highly skilled labor,
and Knowledge agglomeration potential. Here, estimations have been conducted using
the spatial generalized moments (GM) estimator proposed by Kelejian and Prucha (1999).

15

Table 2 Correlation coefficients of variables used to estimate the agglomeration of
KIBS
KIBS share

MarketSupplypotential ofpotential of

HQs andhighly skilled

KIBS

labor

Knowledge
agglomerati
on potential

Population

Number ofdensityenterprises

Market potential of HQs and KIBS

0.549

Supply potential of highly skilled labor

0.412

0.889

Knowledge agglomeration potential

0.422

0.897

0.999

Population density

0.493

0.781

0.799

Number of enterprises

0.681

0.664

0.466

0.472

0.481

Manufacturing share-0.280-0.092-0.048-0.066-0.2110.808-0.167

Note: KIBS share is the share of KIBS employees in municipalities, Market potential of HQs and KIBS is
the market potential in municipality 𝑖, which can be calculated via equation (16) using the number of HQ
employees plus the number of KIBS employees in municipalities 𝑖 and 𝑗 as well as the distance between
them, Supply potential of highly skilled labor is determined via equation (17) using the number of highly
skilled laborers in municipality 𝑗, and Knowledge agglomeration potential can be calculated via equation(18) using 𝐾𝑛𝑜𝑤𝑙𝑒𝑑𝑔𝑒. , which is defined as 𝐾𝑛𝑜𝑤𝑙𝑒𝑑𝑔𝑒. = 𝐿𝑠ℎ𝑎𝑟𝑒. × log 𝑃𝑂𝑃𝑑𝑒𝑛𝑠𝑒. . Population
density is the population density in municipality 𝑖, Number of enterprises denotes the number of enterprises,
and Manufacturing share stands for the manufacturing share based on the number of employees ofmanufacturing in municipalities to the number of employees of all sectors in municipalities.

5 Results and discussion
This section presents our estimation results. As in Redding and Venables (2004),
correlation coefficients between Market potential of HQs and KIBS, which represents
market access in equation (14), Supply potential of highly skilled labor, which represents
supply access in equation (14), and Knowledge agglomeration potential, which is anotherform of supply access, are high. In Table 2, the correlation coefficient of Market potentialof HQs and KIBS and Supply potential of highly skilled labor is 0.889, and that of Market
potential of HQs and KIBS and Knowledge agglomeration potential is 0.897. The
situation results in multicollinearity when we estimate using these two key explanatory
variables simultaneously.
Because we adhere to the work of Redding and Venables (2004), first of all, we
estimate using market access only; thus, we examine the Market potential of HQs and
KIBS. The results of this estimation are presented in Table (3). The estimated coefficientsare all found to be significant with magnitudes of about 0.01 to 0.02. If the Market
potential of HQs plus KIBS increases 1%, then the KIBS share increases by 0.0001 points.
16

Next, we estimate the explanation for the KIBS share using our key explanatory
variables, Supply potential of highly skilled labor and Knowledge agglomeration
potential. Implied parameters for Market potential of HQs and KIBS are calculated using
structural parameter values. Derived from equation (15), the estimated parameters are

𝑏4 = x1
𝛼y , 𝑏{ = xy𝛽𝜎𝛽 (𝜎 − 1)and the relationship between them is as follows

𝑏4 = 𝑏{

𝜎−1
.
𝛼𝜎

(21)

In keeping with the work of Redding and Venables (2004), we set input share at 𝛼 = 0.5
and constant elasticity of substitution at 𝜎 = 10.
Results are displayed in Table 4 and the implied parameters of Market potentialof HQs and KIBS are listed. Specification (1), which specifies that only structuralvariables are employed, demonstrates a significant and positive coefficient for Supply
potential of highly skilled labor; however, under specifications (2)-(5), the coefficient of
key variable Supply potential of highly skilled labor is not significant. Under
specifications (6)-(10), which dictate an alternative variable for supply access, Knowledge
agglomeration potential, the results change completely and key coefficients of estimation
are all significant and positive. Coefficients range from 0.1 to 0.3; if Knowledge
agglomeration potential increases 1%, then the KIBS share increases by 0.001 to 0.003
points. Additionally, implied parameters display values from 0.2 to 0.6, so if theKnowledge agglomeration potential increases 1%, then the KIBS share increases by 0.002
to 0.006 points. The values change drastically from the results shown in Table 3.
The results support our model. If the agglomeration of HQs and KIBS is strong
in municipalities, then the market access will be high. If easy access to knowledge
agglomeration increases, then supply access will increase in kind. Therefore, KIBS will
be located in those municipalities. When we employ Supply potential of highly skilledlabor for the structural variable supply access, the estimation results are insignificant.
However, if we use Knowledge agglomeration potential for supply access, the results are
all plausible. Therefore, the existence of knowledge agglomeration is more important than
the share of highly skilled labor in municipalities.
17

Table 3 Estimation results of the agglomeration forces of KIBS
(the effects of Market Access)Dependent variable: KIBS share(1)Market potential of HQs and KIBS (log)(2)

0.0168 ***(0.0018)(3)0.006 ***
(0.0018)

Population density (log)Number of enterprises (log)Manufacturing share

Lambda(0.0020)0.005 ***
(0.0019)0.00040.0061 ***(0.001)(0.0006)(0.0005)

0.0085 ***0.0087 ***0.0089 ***(0.0005)(0.0004)(0.0005)-0.064 ***-0.063 ***-0.068 ***(0.0049)(0.005)-0.151 ***-0.104 ***-0.110 ***-0.044 **(0.020)(0.018)(0.021)(0.020)0.673 ***

Estimation method(0.0016)(5)0.005 ***

0.0004(0.0049)
Intercept(4)

0.0071 ***Spatial GM

0.620 ***
Spatial GM

0.630 ***
Spatial GM

0.690 ***
Spatial GM

0.648 ***
Spatial GM

Note: Parentheses show the standard error. The number of observations is 1877. *, **, and *** indicate
statistical significance at the 10, 5, and 1 percent levels, respectively. “Lambda” corresponds to the spatial
parameter in equations (19) and (20).

Table 4 Estimation results of the agglomeration forces of KIBS
(the effects of Market Access and Supply Access)Dependent variable: KIBS share(1)Market potential of HQs and KIBS (log, implied)
Supply potential of highly skilled labor (log)(2)-0.0040.0114 ***0.000

0.0022-0.002-0.002(0.0019)(0.0016)(0.0021)(0.0021)

Number of enterprises (log)Manufacturing share

0.0016 **0.0073 ***(0.001)(0.0007)(0.0005)

0.0084 ***0.0092 ***0.009 ***

(0.0005)(0.0004)(0.001)-0.062 ***-0.038 *-0.061 ***-0.0290.032(0.020)(0.017)(0.023)(0.022)(6)Knowledge agglomeration potential (log)0.647 ***
Spatial GM
(7)

(9)

0.261

0.310

0.3216 ***0.147 ***

0.1447 ***0.172 ***

Number of enterprises (log)Manufacturing share(0.0291)(0.0258)(0.0321)0.669 ***
Spatial GM
(10)
0.179
0.100 ***
(0.0330)-0.0002-0.0006

0.0060 ***(0.001)(0.0006)(0.0005)

0.0087 ***0.0086 ***0.0091 ***(0.0005)(0.000)(0.0005)-0.061 ***(0.0049)

Lambda(8)0.705 ***
Spatial GM

0.264

Population density (log)

Estimation method

0.646 ***
Spatial GM

0.579(0.0285)

Intercept-0.067 ***(0.005)-0.095 ***0.710 ***

Market potential of HQs and KIBS (log, implied)-0.062 ***(0.0049)(0.023)
Spatial GM

Dependent variable: KIBS share-0.0040.0015 **(0.0049)

Lambda(5)

0.004

Population density (log)

Estimation method

(4)

0.000

(0.0021)

Intercept

(3)

0.020

***

-0.0610 ***-0.067(0.0049)(0.005)0.020 ***

-0.038 ***-0.038 ***-0.053 ***0.012 ***

(0.002)(0.004)(0.004)(0.004)(0.003)0.616 ***
Spatial GM

0.588 ***
Spatial GM

0.610 ***
Spatial GM

0.629 ***
Spatial GM

0.630 ***
Spatial GM

Note: Parentheses show the standard error. The number of observations is 1877. *, **, and *** indicate
statistical significance at the 10, 5, and 1 percent levels, respectively. “Lambda” corresponds to the spatial
parameter in equations (19) and (20).

6 Conclusion

18

With the increasing importance of the knowledge-intensive business service
sector (KIBS) in Japan, we can observe dense agglomerations of KIBS in large cities suchas Tokyo and Osaka. We attempt to identify the cause for dense agglomeration of KIBS.
We take “market access” and “supply access” (Redding and Venables, 2004) as causes
for agglomeration in KIBS because higher market access and higher supply access makehigher wage payments for KIBS affordable. No study—building on spatial economic
theory—has specifically examined the agglomeration force of KIBS.
We estimate several regression equations using Japanese municipal unit data. We
use the KIBS share as the independent variable. The market potential for HQs and KIBS
is used as a proxy for market access. Also, the population of university graduates is used
as a proxy for supply access, highly skilled labor. Additionally, we use a cross term, theproduct of highly skilled labor share and log of population density, to express knowledge
agglomeration potential in the municipalities.
We propose our monopolistic competition model for describing theagglomeration force of KIBS built on Redding and Venables (2004). A reduced form,
based on the structural form, is driven. We conduct estimation for the whole KIBS sector.
Results obtained using the GM method proposed by Kelejian and Prucha (1999)
demonstrate that knowledge agglomeration potential, which represents supply access in
our model, displays significant and positive results. The results support our model. If theagglomeration of HQs and KIBS is strong in municipalities, then the market access will
be high. If access to knowledge agglomeration increases, then supply access will increase
as well. Therefore, KIBS will be located in those municipalities. Additionally, themagnitude of highly skilled labor agglomeration is relatively low, according to ourempirics. This implies that improving access to the agglomeration of HQs and KIBS andknowledge agglomeration will strengthen market access and supply access and that KIBS
firms will be even more inclined to establish locations in those municipalities. Thus, theeffects of knowledge agglomeration on municipalities and neighboring municipalities arestrongly supported by research.
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