Productivity Improvement in the Specialized Industrial Clusters:
The Case of the Japanese Silk-Reeling Industry∗
Yutaka Arimoto†

Kentaro Nakajima‡

Tetsuji Okazaki§

December 13, 2012

Abstract
We examine two sources of productivity improvements in specialized industrial clusters.
Agglomeration improves the productivity of each plant through positive externalities, shifting
plant-level productivity distribution to the right. Selection expels less productive plants
through competition, truncating distribution on the left. By analyzing the data of the earlytwentieth century Japanese silk-reeling industry, we ﬁnd no evidence conﬁrming a right-shiftof the distribution in clusters or that agglomeration promotes faster productivity growth.
These ﬁndings imply that the plant-selection eﬀect was the source of higher productivity in
the Japanese silk-reeling clusters.

Keywords: Economic geography; Heterogeneous ﬁrms; Selection; Productivity
JEL classiﬁcation: R12; O18; L10∗This is a much revised version of a paper released in the CEI discussion paper series #2010-11. The former
title was ”Agglomeration or selection? The Case of the Japanese Silk Reeling Industry in 1908–1915.” We are
grateful to Toshihiro Matsumura, Noriaki Matsushima, and Yasusada Murata for kindly providing invaluablecomments and suggestions. We also thank Janet Hunter, Ryo Horii, Ryo Kambayashi, Daiji Kawaguchi, Takashi
Kurosaki, Masaki Nakabayashi, Kaoru Sugihara, Tomohiro Machikita, Raﬀaele Paci, Osamu Saito, Ryuhei Wakasugi, Kazuhiro Yamamoto and participants of the meetings of Socio-Economic History Society at Hiroshima
University, ARSC at Kushiro Public University of Economics, JEA at Kyoto University, NARSC at San Francisco, WEHC at Utrecht University, and seminars at Hitotsubashi University, KISER, Kyushu University, Nihon
University, RIETI, Tohoku University, the University of Tokyo, and University of Tsukuba for comments and discussions. Authors gratefully acknowledge ﬁnancial support from the Japan Society for the Promotion of Science(#21330064 and #22223003). Arimoto gratefully acknowledges ﬁnancial support from the Japan Society for the
Promotion of Science (#1810041). Nakajima gratefully acknowledges ﬁnancial support from the Japan Society
for the Promotion of Science (#21730181). The usual disclaimer applies.
†
Institute of Economic Research, Hitotsubashi University, 2-1 Naka, Kunitachi, Tokyo 186-8603, Japan. Tel:
+81-42-580-8346. E-mail: arimotoy@ier.hit-u.ac.jp‡
Faculty of Economics, Tohoku University, 27-1 Kawauchi Aobaku, Sendai 980-8576, Japan.Tel/Fax: +81-22795-6305. E-mail: nakajima.kentaro@gmail.com§
Faculty of Economics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan. E-mail:okazaki@e.u-tokyo.ac.jp1

1

Introduction

Plants located in industrial clusters are more productive than those not located in clusters.
Indeed, a positive association between the spatial concentration of economic activities and productivity has been empirically conﬁrmed in the literature. For example, labor density is known
to have a positive eﬀect on productivity in the U.S. (Ciccone and Hall, 1996) and in the EU
countries (Ciccone, 2002) at the regional level. This also holds true at the plant-level in the
U.S. high-tech industry (Henderson, 2003). Excellent reviews of the existing studies on spatialconcentration and productivity can be found in Rosenthal and Strange (2004) and Melo et al.
(2009).
The higher productivity of plants in industrial clusters has long been explained through agglomeration eﬀects, which refer to positive localized externalities: transferring knowledge andinnovating ideas among densely agglomerated workers, alleviating matching through thick labor markets, or reducing transaction costs by transacting with proximate ﬁrms. These positive
externalities directly improve plant-level productivity in the form of “bonuses” in the agglomeration.
At the same time, recent theoretical developments in international trade and spatial economics with heterogeneous ﬁrms have suggested plant selection as another factor that could
improve productivity (Melitz, 2003; Melitz and Ottaviano, 2008; Behrens et al., 2009; Baldwin
and Okubo, 2006). That is, in clusters, intensiﬁcation of competition expels less productiveplants, and consequently, only the relatively productive plants survive. Thus, clusters havehigher average regional productivity, even though they do not actually improve the productivity of each plant. Empirically, Syverson (2004) ﬁnds that higher plant density truncates the
productivity distribution in the lower tail in the ready-mixed concrete industry, implying that
low-productivity producers are less likely to survive under increased competition. Corcos et al.
(2010) have identiﬁed the selection eﬀect induced by trade policy.
Recent studies attempt to identify which of these two eﬀects are in place. A pioneering
work by Combes et al. (2012) developed an innovative method to measure the magnitudes of
the two eﬀects and found that agglomeration eﬀects could mostly explain higher productivity
in French metropolitan areas. Following Combes et al. (2012), Accetturo et al. (2011) too
found the existence of agglomeration eﬀects in most of the industries, and selection eﬀects ina few industries in Italian metropolitan areas. These two studies suggest a stronger impact of2

agglomeration eﬀects in urban metropolitan clusters.
However, there remains a question of whether such agglomeration eﬀects can also be foundin specialized industrial clusters. Since urban metropolitan clusters typically consist of many
diverse industries and that Combes et al. (2012) and Accetturo et al. (2011) applied labor
density in all sectors as the source of externalities, the detected agglomeration eﬀects containboth industry-speciﬁc externalities (Marshall-Arrow-Romer (MAR) externalities) and externalities through diversity (Jacobs externalities) as termed by Glaeser et al. (1992).1 In contrast,
specialized industrial clusters of plants within the same industry, such as the high-tech clusterin the Silicon Valley (U.S.), automobile clusters in Detroit (U.S.), and Toyota (Japan) typicallyconcentrate on a smaller number of related industries, thereby, lacking the beneﬁts from thediversity of industry. Moreover, given that agglomerated plants produce similar products, competition is likely to be ﬁercer. However, identifying the agglomeration eﬀects or selection eﬀects
in specialized industrial clusters is problematic since many of these clusters are also localized in
few areas, thus reducing the size of the observation.
In this paper, we aim to identify the sources of productivity improvement in the specialized
industrial clusters of silk-reeling in Japan during the period from 1908 to 1915. The Japanesesilk-reeling industry then possessed two key characteristics necessary for the purposes of thiswork. First, silk-reeling clusters, by the nature of the industry, were formed in mountainous,
peripheral areas with few plants other than those for silk-reeling. For example, in Suwa County
in Nagano Prefecture, one of the largest silk-reeling clusters in that period, 36,814 out of 37,161
total manufacturing workers (or 99.1%) belonged to the silk-reeling sector. Further, in countylevel aggregation, the average and median shares of silk-reeling workers in total manufacturing
workers is 87% and 94% respectively, in Nagano Prefecture. Therefore, the silk-reeling industry
formed specialized clusters with limited interactions between diverse industries, allowing us tofocus solely on MAR externalities. Second, besides the clustered plants, there existed numerous
silk-reeling plants across Japan, which enable us to exploit suﬃcient regional variations for
empirical analysis. In fact, more than half of the counties in Japan (354 of 680) had more than
one silk-reeling plant in 1919.
To frame our empirics, we develop a model of agglomeration and selection through com1

Henderson (2003) ﬁnds using micro data in the U.S. machinery and high-tech industries that the plant densityof the same sector signiﬁcantly improves plant-productivity. While he attributes the bonus to agglomerationeﬀects, it could be explained by selection eﬀects.

3

petition among plants over input procurement. The literature mostly relied on monopolisticcompetition in the output market to model agglomeration or selection. However, the silk-reelingplants in our study were takers of price determined in the international market. Instead of competing in the output market, the plants aggressively competed over input procurement (cocoon).
To take this feature into account, we modify Syverson’s (2004) selection model on competition
over the sales of homogeneous output, to competition over input procurement. While Syverson(2004) relies on demand density as the source of selection, we show that a regional diﬀerence
in entry cost can generate industrial clusters endogenously through selection. Following Fujita
and Ogawa (1982) and Lucas and Rossi-Hansberg (2002), we then introduce an agglomeration
economy into the model as done in Combes et al. (2012). We obtain theoretical predictions identical with Combes et al. (2012), which enable a distinction between agglomeration and selectioneﬀects by examining the characteristics of plant-level productivity distributions. Intuitively, theagglomeration eﬀect will shift the distribution to the right by improving the productivity of allplants in a region but keep the shape of the distribution unchanged. However, the selectioneﬀect will left-truncate the distribution by expelling less productive plants from the market.
By using this theoretical identity in the characteristics of the distribution, we follow Combes
et al. (2012)’s estimation method to estimate the agglomeration and selection eﬀects from theproductivity distribution.
Our main empirical conclusion is that selection improves productivity in clusters in theJapanese silk-reeling industry. We ﬁnd strong evidence of the existence of selection eﬀect. On theother hand, we do not ﬁnd any evidence of the existence of agglomeration eﬀect. These results arealso supported by exploiting prefectural variations. We ﬁnd that the width of the distribution forclusters was narrower and more severely left-truncated than that for non-clusters. However, we
ﬁnd no clear evidence of the right-shift of the distribution for clusters. Furthermore, we support
this ﬁnding with the evidence that the extent of agglomeration did not aﬀect the productivity
growth rate. If the agglomeration eﬀect is in place, we should observe higher productivity
growth among plants in clusters. These results suggest that productivity improvements took
place through selection before operation rather than through agglomeration economies after
entry. Contrary to the results of Combes et al. (2012) and Accetturo et al. (2011), whichemphasize the role of the agglomeration eﬀect in urban metropolitan areas, our results suggest
the importance of the selection eﬀect in specialized industrial clusters.

4

The rest of this paper is organized as follows. The next section overviews the Japanese silkreeling industry during the period from 1908 to 1915. Section 3 provides a theoretical explanationof industrial clusters and plant-level productivities. Section 4 describes the estimation strategy,
and Section 5 describes the data. Section 6 provides our main results. Section 7 discusses therobustness of our ﬁndings by using a summary statistics approach and focusing on the timingof the cluster eﬀects. Finally, Section 8 concludes the paper.

2

Overview of the Japanese silk-reeling industry

The silk-reeling industry was one of the major industries in pre-war Japan2 . For example, in
1908, this industry employed 24.4% of the total factory workers in Japan,3 and its product,
raw silk, occupied 26.6% of the total export (Ministry of International Trade and Industry,
1962; Toyo Keiizai Shinposha, 1927). A distinctive feature of the silk-reeling industry was that
it was composed of numerous small and medium-sized plants. For example, in 1908, Japan
had more than 3,200 silk-reeling plants. Even the largest plant accounted for only 4.3% of thetotal silk production in 1908, and the median value of the market share was 0.058% (Ministryof Agriculture and Commerce, 1910). In this sense, the market structure of the silk-reelingindustry was very competitive.
These silk-reeling plants formed several clusters, of which those in the Nagano, Aichi, andGifu prefectures in the central region of Japan were the largest; 37.5% of the silk-reeling plants
in Japan were located in these three prefectures in 1908. These silk-reeling clusters were highly
specialized. According to the Census of Manufacturing in 1919, in Suwa County of Nagano
Prefecture, the largest silk-reeling cluster in terms of employment, the share of the silk-reelingindustry in the total manufacturing employment was a whopping 99.1%. In addition, in ShimoIna County, the second-largest cluster, and in Kami-Ina County, the third-largest cluster, theshares of silk-reeling employment were 98.5% and 96.7%, respectively.
Of these clusters, the cluster in Suwa County in Nagano Prefecture was the largest (Ministryof Agriculture and Commerce 1910). In 1930, to document the history of Hirano Village, thecenter of the Suwa silk-reeling cluster, the assigned editors conducted a survey of the major plant2
Of the many studies on the development of the silk-reeling industry in Japan, Ishii (1972) and Nakabayashi(2003) are basic references.
3
The denominator is the number of total factory workers in 1909 (Ministry of International Trade and Industry,1962).

5

owners on the reasons behind the development of the silk-reeling industry in the village; one of
the most common answers was that they could not secure their living only through agriculture
as their land holdings were small and the soil was not fertile. Some respondents also cited thelack of good alternative occupations as a reason (Hirano Village Oﬃce 1932, pp.560–562). These
answers imply that the opportunity cost for entering the silk-reeling industry was lower owing
to the natural conditions in Suwa District. These ﬁrst-nature characteristics were importantcauses that facilitated silk-reeling start-ups.
It is also notable that besides the large clusters, silk-reeling plants also operated in otherareas, that is, in non-clusters. Figure 1 is the map of Japan, indicating the density of silk-reelingplants in 1908. The dark colored areas represent the prefectures where silk-reeling plants weredensely located.

= Figure 1 =The silk-reeling industry emerged in Japan in the Tokugawa Era, but its growth was accelerated by the opening of the economy in 1859. Under the free trade regime, the export of raw silk
experienced a boom. Initially, raw silk was produced using the traditional hand-reeling technology (zaguri -reeling), but in the 1870s, a new technology, machine-reeling (kikai -reeling), wasdeveloped, which modiﬁed the imported European technology. While hand-reeling production
stagnated owing to competition with Chinese products in the 1870s, machine-reeling production
experienced growth in this period (Nakabayashi 2003, pp.66–68). Machine-reeling production
exceeded hand-reeling production in 1894, and the latter witnessed a decline in 1900.
According to Nakabayashi (2003), the basic market condition was factored by the growthof the silk weaving industry in the U.S. The U.S. silk-weaving industry introduced its mass
production system in the 1860s and preferred homogeneous raw silk in large lots; meeting thisdemand was a challenge for the traditional silk-reeling industries in both Japan and China. Using
the machine-reeling technology, the emerging silk-reeling industry in Japan met the demand of
the U.S. silk-weaving industry and thereby grew rapidly.4 In the U.S. market, each silk-reelingplant in Japan, which as mentioned above, was very small, was basically a price-taker, and it
could sell as much raw silk as it wanted to at the market price in Yokohama, the main exportingport.
4

For example, in 1908, the ratio of export to production was 98.9% with respect to machine-reeled raw silkand the share of export to U.S. was 74.0% (calculated from the statistics in Nakabayashi, 2003, pp.468–462).

6

According to Duran (1913), the typical machine-reeling process during that period was asfollows. A silk-reeling plant purchased cocoons from sericulture peasants. Cocoons were boiled
to unwind the cocoon ﬁlaments. Then, from a group of boiled cocoons, unwound ﬁlaments werebundled and reeled onto a small moving reel that was powered by water, steam, electricity, orgas. Young female workers played a key role in this production process. Each female worker
was in charge of one reeling machine, and her ability and level of eﬀort substantially aﬀected
the productivity and quality of the raw silk.
Owing to its relatively simple production process, the productivity and survivability of asilk-reeling plant essentially depended on the procurement and management of the two basic
inputs, cocoons and labor. It is notable that competition in these input markets—the cocoonand labor markets—was substantially diﬀerent.
In the cocoons market, competition for procurement was very severe in clusters, raising
input prices not only in the clusters but also in the adjacent prefectures or prefectures farther
away (Hirano, 1990; Ishii, 1972, ch.4; Matsumura, 1992). The competition was ampliﬁed by the
temporal and technological constraint that raw cocoons had to be transported quickly or dried
appropriately to ensure that their quality and condition were maintained, because they perishedin moist environments. Drying was also necessary to prevent the metamorphosis of the pupa.
As Kajinishi ed. (1964) states, “As the silk-reeling industry developed in Suwa, competition
for raw materials and work force became harsh among plants, while loss due to transportation
cost and damage of cocoons increased” (pp.304–306). Indeed, in March 1908, the price of spring
cocoons per koku (180.39 liters) was 50 yen in Matsumoto City (close to Suwa), whereas it was
42 yen in Nagano City (Nagano Prefecture 1910, p.213). To relax competition, silk-reeling plants
attempted (and often failed) to arrange cartels for the joint purchase of cocoons and production
reductions, or engaged in vertical integration (tokuyaku torihiki) in the form of contract farmingby concluding direct prior agreements with cocoon farmers with regard to price and quantity.
On the labor side, most silk-reeling workers were young women. As the enormous labordemand in clusters forced plants to hire those workers from rural areas around them, the plants
would pay a ﬁxed cost for boarding, food, and even education, which increased unit laborcost. Moreover, because silk-reeling required some experience and skill, recruiting and training
new workers was expensive for the plants. Therefore, poaching trained workers from otherplants was prevalent in clusters, and the practice gradually proliferated throughout the country7

(Kambayashi, 2001; Nakabayashi, 2003; Tojo, 1990). In spite of this background, wages of silkreeling workers did not largely increase on average, because of the abundant supply of young
unemployed women in the agricultural areas around the clusters. Nakabayashi (2003) reports
the basic statistics of worker-level wage at a plant in Suwa from the late nineteenth century
to the early twentieth century. For example, the sample mean and median of wage per day
in 1908 were 0.24 and 0.25 yen, respectively (p.259). Meanwhile, the average daily wage offemale agricultural workers was 0.23 yen in the same year (Statistics Bureau, Management andCoordination Agency 1988, p.228). These data imply that unit labor cost for an average femalesilk-reeling worker in the largest cluster was approximately the same as that of the average
agricultural worker, and there is little diﬀerence among regions.

3

Theoretical model and empirical strategy

We ﬁrst develop a theoretical framework to model plant selection in the context of the Japanesesilk-reeling industry by modifying Syverson’s (2004) selection model. Then, we incorporate theagglomeration eﬀect.

3.1

Market structure

We consider the entry and production decisions of silk-reeling plants that procure cocoons fromfarmers, reel silk, and sell the ﬁnal product. Output is sold in the export market (Yokohama)at an exogenous price p set by the international market. Plants are price-takers and they cansell as much as they wish in Yokohama.
We assume that the production of qi silk by plant i entails labor cost hi qi , input purchasecost w(Q)qi for cocoons, and ﬁxed cost f . Silk production relied heavily on female workers
who reeled unwound cocoon ﬁlaments, and their skill and eﬀort were crucial determinants ofplant-level productivity.
While workers’ individual reeling skills would be inherently diﬀerent, we assume that allplants faced the same skill distribution regardless of the plant’s location. Thus, we ignore
the heterogeneity of workers’ productivity and rely solely on plant-side heterogeneity (i.e., thecapability of the machines, management and incentive systems, training, etc.) to explain theplant-level productivity diﬀerence.5
5

While workers’ inherent skills at the individual level may be diﬀerent, there is no reason to assume that its

8We let hi denote the eﬀective labor required to produce one unit of output (raw silk).
This variable can be considered as the plant’s productivity: a higher hi implies greater labor
requirement, and hence, lower productivity. Following the discussion on the female labor market
in that period in Section 2, we can normalize the cost of unit eﬀective labor to unity.
Input purchase price w(Q) can be considered an aggregate inverse supply function, where∑
Q = qi is the total output in the region (or, in other words, factor demand). We assume thatw(Q) increases with Q because greater silk production requires a higher demand for cocoons.
Therefore, unlike the plants modeled in Syverson (2004), for which demand density is the key
variable of focus, plants in our model do not compete over output sales but rather over input
purchases (cocoons).
The proﬁt of a plant can be represented as
πi = pqi − hi qi − w(Q)qi − f

For simplicity, we assume the linear marginal input purchase price as w(Q) = wQ:
πi = pqi − hi qi − wQqi − f.

(1)

This model has two stages. In stage one, each potential plant decides whether to pay a sunk
entry cost s to enter the market. After the payment, a plant draws labor unit requirement hi
from distribution g(h) with support [0, h], where h is an arbitrary upper bound. In stage two,each plant decides its level of production qi given its productivity parameter hi , forming an
expectation of the total output in a region, E(Q).
The expected proﬁt of an entrant plant at stage two isE(πi ) = (p − hi )qi − wE(Q)qi − f.

(2)

The ﬁrst-order condition with respect to qi is∂E(πi )
= p − hi − wqi − wE(Q) = 0,
∂qi

(3)

distribution diﬀered across regions. Moreover, regional migration based on reeling skill was unlikely except forexperienced, top-ranked reelers who mostly engaged in training, which should be considered as the plant’s eﬀort
for productivity improvement.

9and as such, the optimal output of a plant with marginal cost hi isqi ∗ (hi ) =p − hi − wE(Q)
.
w

(4)

Inserting qi ∗ back into the expected proﬁt yields

E[πi (hi )] =[p − hi − wE(Q)]2
− f.
w

(5)

The expected proﬁt decreases with hi . Therefore, a critical labor unit requirement draw ĥ exists
such that entrants drawing hi > ĥ choose not to produce. This cutoﬀ labor unit requirementdraw can be solved by setting E(πi ) = 0:ĥ(E(Q)) = p − wE(Q) −Inserting p − wE(Q) = ĥ +

√

√

wf .

(6)

wf obtained from (6) into E(πi ) yields operating proﬁt,

conditional on hi ≤ ĥ:(√ )2]ĥ − hi + wf
− f.
E πi (hi |hi ≤ ĥ) =
w
[

(7)

We assume a free-entry condition so that plants enter the market (i.e., pay s and draw ci ) until
the expected value of entry is equal to zero:
∫ ĥ
Ve =
0

(

√ )2
ĥ
−
h
+
wf


− f  g(h)dh − s = 0

w

(8)

Equilibrium ĥ is the value that solves this expression, and it is a function of g(h) and parameters
w, f , and s.

3.2

Entry cost, selection eﬀect, and emergence of clusters

We now consider regions that are symmetric except for entry cost s. On the basis of thehistorical information in Section 2, we assume that s varies across regions owing to the ﬁrst
nature or opportunity costs of starting-up a new business. We show that a region with a lower s
imposes ﬁercer competition (i.e., lower cutoﬀ unit labor requirement) but retains a large number
10

of operating plants, resulting in the formation of a cluster.
We ﬁrst consider the eﬀect of entry cost s on the cut-oﬀ marginal unit labor requirement ĥ.
The implicit function theorem implies thatdĥ−(∂V e /∂s)
w
=
= ∫ (
> 0.
√ )
ĥ
ds
∂V e /∂ ĥ2ĥ − h + wf g(h)dh(9)

0Implication 1 (Selection eﬀect). Regions with a lower start-up cost have a lower cutoﬀ labor
unit requirement ĥ. This relationship implies that competition is more severe: high-cost (lowproductivity) plants are not proﬁtable in regions with a lower start-up cost.

Next, we investigate the eﬀect of s on the number of plants in a region. Let Ne denotethe number of entrant plants that had paid s and drawn hi , and let Np denote the number of
producing plants with hi 6 ĥ. Then,∫ ĥ
Np = Neg(h)dh = Ne G(ĥ).

(10)

0

By applying (4), the total production in a region can be represented as∫ ĥ
Q = Neqi∗ g(h)dh = Ne

0

∫ ĥ
0

p−h
g(h)dh − Ne E(Q)G(ĥ).
w

Since Q = E(Q) in the equilibrium, we can represent Q as a function of Ne and ĥ:Q(Ne , ĥ) =

∫ ĥ

Ne
1 + Ne G(ĥ)0p−hg(h)dh.
w(11)

Additionally, rearranging (6) yields
p − ĥ −
Q=
w

√

wf

.

(12)

By applying (11) and (12), we can represent Ne as a function of ĥ and g(·), and parameters{p, w, f }:Ne = ∫√
p − ĥ − wf
.
√
ĥ
(
ĥ
−
h
+
wf
)g(h)dh011(13)

Partial diﬀerentiation with respect to ĥ yields∫ ĥ√√− 0 (p − h)g(h)dh − (p − ĥ − wf ) wf g(ĥ)
=
< 0.
[∫
]2
√
ĥ
∂ ĥ
0 (ĥ − h + wf )g(h)dh

∂Ne

(14)

Therefore, a lower ĥ (ﬁercer selection) entails more entry.
Now, since Np = Ne G(ĥ), the eﬀect of the entry cost on the number of producing plants isexpressed bydNp
dNe dĥdĥ=G(ĥ) + Ne g(ĥ) .
ds
dsdĥ ds(15)

The eﬀect of s on Np consists of two eﬀects. The ﬁrst eﬀect represented by the ﬁrst term isthe entry eﬀect, which is negative. That is, a lower s entails that more plants will enter themarket. The second eﬀect represented by the second term is the competition eﬀect, which is
positive because ddsĥ > 0 from (9). Because lower s induces severe competition, the number ofplants that can produce after entry will be smaller. The aggregate eﬀect of a low entry coston the number of producing plants depends on the relative magnitude of the (positive) entry
eﬀect and the (negative) competition eﬀect. However, we can show that the entry eﬀect always
dominates the competition eﬀect. Substituting (13) and (14) into (15) yields
[
]
dNp
dNe
dĥ
=
G(ĥ) + Ne g(ĥ)
ds
ds
dĥ
[
] [
]∫
∫ ĥ
√
ĥ
−(p − ĥ) G(ĥ)2 − g(ĥ) 0 G(h)dh − G(ĥ) + wf g(ĥ) 0 G(h)dh dĥ
< 0.
=
[∫
]2
√
ds
ĥ
0 (ĥ − h + wf )g(h)dh

(16)

[
]
∫ ĥ
This value is negative because G(ĥ)2 − g(ĥ) 0 G(h)dh is positive because G(ĥ) ≥ G(h) forall h ∈ [0, ĥ], G(ĥ) > g(ĥ), and ddsĥ > 0 from (9).
Implication 2 (Endogenous clusters). A lower entry cost s entails that more plants will enter
the market (entry eﬀect), but it imposes ﬁercer competition after entry and reduces the numberof producing plants (competition eﬀect). The former always dominates the latter, and therefore,
the number of producing plants is greater in a region with a lower s.

12

3.3

Agglomeration eﬀect and productivity distributions

Following Combes et al. (2012), we now introduce the agglomeration eﬀect, which improves
plants’ productivities through the interaction between adjacent operating plants. We model
this eﬀect by assuming that when a plant interacts with Np plants, the eﬀective units of labor
supplied by an individual worker during their unit time becomes a(Np ), where a(0) = 1, a′ > 0,
and a′′ < 0. Then, a plant with unit labor requirement hi reduces the number of workers tol(hi ) = qi hi /a(Np ) at a total cost of a(Np )l(hi ) = qi hi . Thus, each plant’s maximization problem
is unchanged.
Given this agglomeration eﬀect, the logarithm of a plant’s productivity φi can be derived asfollows:
φi = ln

[q ]
i

l

[

]
qi
= ln
= ln[a(Np )] − ln(hi )qi hi /a(Np )(17)Then, the density function of the log productivities is as follows:f (φ) =
 0for φ < φ̂ ≡ A − ln(ĥ),

A−φ
A−φ

 e g(e )for φ > φ̂,

G(ĥ)

(18)

where A ≡ ln[a(Np )].
As discussed above, each plant’s maximization problem is unchanged regardless of the presence of the agglomeration eﬀect. Thus, plugging the equilibrium cut-oﬀ unit labor requirementĥ obtained from eq. (8) into eq. (18) yields the equilibrium distribution of plant productivities.
From this productivity density function and the assumption of a′ > 0, it is clear that the increasein the number of operating plants shifts the distribution rightwards while maintaining its form.

Implication 3 (Agglomeration eﬀect). An increase in the number of operating plants in aregion Np shifts the productivity distribution to the right.

Fortunately, the result of our model with respect to the productivity distribution is identicalto that of Combes et al. (2012), although the theoretical set up is diﬀerent. Thus, we can apply
their novel empirical strategy. To do so, we introduce additional notations.
Now we introduce regions into the model explicitly using the index of r. Let F (φ) be the13corresponding cumulative density function of f (φ). The proportion of ﬁrms that cannot survive
in region r is deﬁned as Sr ≡ 1 − G(h̄r ), where h̄r is the cutoﬀ productivity in region r. Let
Ar ≡ ln[a(Npr )] be the agglomeration eﬀect in region r, where Npr is the number of producing
plants in region r. The underlying cumulative density function of log productivities in all regions
when there are no selection or agglomeration eﬀects (h̄r → ∞ and Ar = 0, ∀i) can be deﬁned
as follows:F̃ (φ) ≡ 1 − G(e−φ ),(19)because φ = 0, and if Ar = 0, then, h = e−φ and there is a change of variables. Then, thecumulative density function of log productivities for survival ﬁrms in region r can be deﬁned asfollows:{F̃ (φ − Ar ) − Sr
Fr (φ) = max 0,
1 − Sr}.

(20)

Because the results of productivity distribution from our model are identical to those of
Combes et al. (2012), we can consider the following four polar cases with respect to the channels
of productivity improvement, as in the Combes et al. (2012) model. For simplicity, we consider
two regions r = c (clusters) and r = n (non-clusters).
Case 1 (Only the selection eﬀect matters). When there is no agglomeration eﬀect, only selectionaﬀects productivity. In this case, a(Np ) = 1 holds for any value of Np . However, selection implies
that hˆc < hˆn , where hˆc (hˆn ) is the cutoﬀ unit labor requirement in region c (n). This raises thelog productivity cut-oﬀ in the clusters: φˆc > φˆn . This case is represented in Figure 2(a). The
solid line represents the log productivity distribution in clusters, while the dashed line represents
that in non-clusters. The log productivity distribution in clusters is left-truncated.
Case 2 (Only the agglomeration eﬀect matters). In this case, only the agglomeration eﬀect
improves plants’ productivity. To eliminate the selection eﬀect, we impose sc = sn = s, wheresc (sn ) is the startup cost in region c (n). Then, the intention of the selection is the same in theboth clusters and non-clusters, and therefore, hˆc = hˆn and Npc = Npn , where Npc (Npn ) is thenumber of plants in region c (n). To establish clusters and non-clusters, we assume Nc > Nn byexogenous reasons that are outside the scope of our model. Only ﬁrms in clusters beneﬁt fromlarger worker interactions, ln[a(Npc )] > ln[a(Npn )]. Thus, log productivity simply shifts to theright while maintaining its distribution form. This case is shown in Figure 2(b).

14Case 3 (Both the selection and agglomeration eﬀects matter ). In this case, the ﬁxed entry
costs are diﬀerent between clusters and non-clusters, sc < sn , and the concentration of workers
improves their productivity, a′ > 0 and a′′ < 0. Thus, both left-truncation by selection andright-shift by agglomeration occur in clusters. This case is shown in Figure 2(c).
Case 4 (Neither eﬀect matters). In this case, the ﬁxed entry costs are the same for all regions
and the concentration of workers does not improve their productivity, a(Np ) = 1. Then, thelog productivity distribution is common across regions. Thus, there is no diﬀerence in the
productivities across regions. This case is shown in Figure 2(d).

= Figures 2(a) to 2(d) =Intuitively, these four cases are distinguished by two measures that characterize the productivity distributions. The ﬁrst measure is the interquartile range of the distribution, which wasused by Syverson (2004). If no selection eﬀect exists (cases 2 and 4), the shape of the distribution
should be the same for clusters and non-clusters, and thus, the interquartile range should haveno diﬀerence. However, if a selection eﬀect exists (cases 1 and 3), the productivity distribution
should be left-truncated in clusters and the interquartile range should be smaller than that for
non-clusters. Hence, by comparing the interquartile range between clusters and non-clusters, wewould be able to detect the presence of the selection eﬀect.6
The second measure consists of the percentiles of the distribution. Because selection lefttruncates the distribution, we should observe a rise in the lower percentile points rather thanthe higher percentile points of the log-productivity distribution. However, the agglomerationeﬀect aﬀects every percentile point of the distribution because it shifts the whole distribution
rightwards. Thus, if the agglomeration eﬀect is in place, both the higher and lower percentile
points of the distribution should increase.
The above discussions are summarized in Table 1.

= Table 1 =6

Of course, variance is also an informative measure of truncation. However, empirically, the interquartile range
is more robust for outliers.

15

The table represents the direction of the shift for each measure of distribution in clusters
relative to non-clusters for the four cases.
The next section describes the formal estimation strategy based on the theory.

4

Empirical strategy

As we have shown in the previous chapter, our theoretical results in the plant-level log of productivity distribution are identical to the Combes et al. (2012)’s results, although the theoretical
set up is diﬀerent. Thus, we can apply their quantile approach for quantitatively measuring
selection and agglomeration eﬀects. This section brieﬂy describes the empirical strategy. For
more detail, please see Combes et al. (2012).
Before describing the estimation strategy, we address the concern that the impact of theagglomeration eﬀect varies by plant. For example, high-productivity plants would tend to more
rapidly beneﬁt from agglomeration economies. To include this eﬀect, we redeﬁne the agglomeration economies by introducing heterogeneity in the beneﬁts from an agglomeration economy.
By introducing heterogeneity, agglomeration economy a(Np ) can be rewritten as a(Np )h−(Dr −1) ,where Dr ≡ ln[d(Np )], d(0) = 1, d′ > 0, and d′′ < 0. Then, the log productivity of a ﬁrm withunit cost h in region r is denoted by(φr (h) = ln

qr (h)lr (h))= Ar − Dr ln(h).

(21)

Then, we can write the cumulative density function of the log of productivity in a survival ﬁrm
in region r as{
Fr (φ) = max 0,rF̃ ( φ−A
Dr ) − S r

1 − Sr}.

(22)

This implies that the agglomeration eﬀect not only shifts the distribution to the right by Ar ,but also dilates the distribution by Dr ; however, selection drops a fraction Sr of entrants. It
is worth noting that the heterogeneity also allows for the case wherein low-productivity plants
beneﬁt more than high-productivity plants from the agglomeration economy. In this case, Dr
takes a negative value.
Based on the extended model, we describe the estimation strategy. As in the previous section,
we consider two regions, r = c (clusters) and r = n (non-clusters), and the cumulative density

16

functions in each region as{
Fc (φ) = max 0,

and{Fn (φ) = max 0,cF̃ ( φ−A
Dc ) − S c}(23)

1 − ScnF̃ ( φ−A
Dn ) − Sn}(24)

1 − SnNow, we introduce the following relative parameters:
D≡

Dc
,
Dn

A ≡ Ac − DAn ,S≡

Sc − Sn.
1 − Sn(25)

Combes et al. (2012)’s method does not separately estimate Ar , Dr , and Sr in each region;
instead, it estimates the relative strength of each variable: A = Ac − DAn , D = Dc /Dn ,and S = (Sc − Sn )/(1 − Sn ). Accordingly, we estimate the relative strength of selection andagglomeration in specialized clusters as compared to non-clusters. Intuitively, if we obtain A > 0,
there is a larger right-shift in clusters than in non-clusters. Dilation by agglomeration is captured
by D. If we obtain D > 1, clusters have larger dilation of the distribution than non-clusters.
Selection is captured by S. If S > 0, there is more elimination of entrants in clusters than in
non-clusters.
By introducing these parameters, we can express cumulative density functions Fc (φ) andFn (φ) in terms of the other expression in such a way that clariﬁes their relationship. If Sc > Sn ,Fc can also be obtained from Fn by dilating D, shifting by A, and left-truncating a share of S
as follows:{

Fn ( φ−AD )−SFc (φ) = max 0,
1−S

}
.

(26)

1
A
If Sc < Sn , Fn can also be obtained from Fc by dilating D, shifting by − D, and left-truncating−Sa share of 1−S
as follows:{
Fn (φ) = max 0,−S
Fc (Dφ + A) − 1−S−S
1 − 1−S}.

(27)

Then, to estimate relative parameters A, D, and S, we rewrite the cumulative density
functions into quantiles, and combine them. If S > 0, (26) can be rewritten in the quantile form17

as
λc (u) = Dλn (S + (1 − S)u) + A,

(28)

where λc (u) ≡ Fc−1 (u) is the uth quantile of Fc and λn (u) ≡ Fn−1 (u) is the uth quantile of Fn .
Further, if S < 0, (27) can be rewritten as

λn (u) =

1
λc
D

(

u−S
1−S

)
−

A
.
D

(29)

By combining these two equations and using change of variable u → rS (u), where rS (u) =−S−Smax(0, 1−S) + [1 − max(0, 1−S)]u, we can obtain following expression:

λc (rS (u)) = Dλn (S + (1 − S)rS (u)) + A.

(30)

This equation implies how the quantiles of the productivity distribution in clusters relates tothat in non-clusters through relative parameters A, D, S. Then, we deﬁne mθ (u) = λc (rS (u)) −Dλn (S + (1 − S)rS (u)) + A, where θ = (A, D, S). Finally, we can obtain the estimator of θ byminimizing the mean-square error on mθ , as(∫ 1θ̂ = arg minθ

)2[m̂θ (u)] du ,

(31)

0

where m̂θ (u) is the empirical counterpart of mθ (u), obtained by replacing λc and λn with theirestimators.7 However, this implementation compares the two distributions asymmetrically. Thatis, we compare the quantiles of actual region c’s productivity distribution to the quantiles of
the truncated, dilated, and shifted distribution of region n. Combes et al. (2012) took one more
step to obtain a robust estimator to consider a way to symmetrically treat the quantiles of thetwo distributions. Combining (28) and (29) into one equation and using change of variableu → r̃S (u), where r̃S (u) = max(0, S) + [1 − max(0, S)]u, we obtain another equality condition:1m̃θ (u) = λn (r̃S (u)) − λcD(r̃S (u) − S
1−S

)
+

A
.
D

(32)

By using this condition, Combes et al. (2012)’s estimator θ̂ = (Â, D̂, Ŝ) that we actually estimate

7

See Combes et al. (2012) for details on obtaining these estimators.

18

in this paper is described as follows:∫ 1θ̂ = arg min M (θ),
θ

where

∫ 1
[m̂θ (u)]2 du +M (θ) =0ˆ θ (u)]2 du,
[m̃

(33)

0

ˆ θ (u) is the empirical counterpart of m̃θ (u) obtained by replacing the true quantiles, λcwhere m̃and λn by their estimators. The standard errors for the estimated parameters are obtained by
200 bootstrap iterations, including re-estimating TFP.

5

Data, and measures of plant-level productivity

5.1

Data

We compiled the silk-reeling industry census data, Zenkoku Seishi Kojo Chosa, for the two data
points 1908 and 1915. The data include plant-level information: plant name, location, year offoundation, number of pots, number of workers, number of business days per year, types of power
used, and output. This data set covers both hand-reeling and machine-reeling plants. Here,
we focus on machine-reeling plants because hand-reeling and machine-reeling are completely
diﬀerent techniques. We matched plants over two periods and constructed an unbalanced panel
data set by using plant name, location, and year of foundation. The number of machine-reelingplants in 1908 was 2385 and that in 1915 was 2263. The number of plants that existed in 1908and survived until 1915 was 910. The extent of agglomeration is measured by regional plantdensity, computed as the number of plants per km2 . Information regarding the regional area at
the prefecture or county level was obtained from the Geographical Information System (GIS)
data for 1937, from “Taisho-Showa Gyoseikai Data.”8

5.2

Measures of plant-level productivity

As discussed in the previous section, we focus on the shape of the productivity distributions to
distinguish the channels of productivity improvement eﬀects. For this purpose, we ﬁrst estimate
the productivity of each plant. We use TFP as the primary measure of plant-level productivity.

8

The data are published by Yuji Murayama,
Division of Spatial Information Science, Graduate School of Life and Environmental Sciences, University of Tsukuba, URL:
http://giswin.geo.tsukuba.ac.jp/teacher/murayama/data map.html

19In order to estimate TFP, we specify the ﬁrm-level production function as follows:

yit = βk kit + βl lit + βm mit + δZit + ωit + ϵit ,(34)

where yit is the log of output, kit is the log of capital input (number of pots), lit is the logof labor inputs (number of female workers), mit is the log of intermediate input (quantityof cocoons used), Zit is the vector of plant i’s observable characteristics, and ωit and ϵi areproductivity terms unobservable to econometricians. While ϵit is also unobserved by ﬁrms
before they make their input decisions, ωit is observable. We assume that ωit = ωi ; that is,observable productivity for plants does not change through the study period (7 years). As plant
i’s observable characteristics, we include the log of plant age, a dummy variable indicating thatthe plant used water power, and a dummy variable indicating that the plant used steam power.
Given this assumption, we estimate this production function by ﬁxed eﬀects model.9
The estimation results are reported in Table 2.

= Table 2 =The coeﬃcients of ln(capital) and ln(worker) have expected signs and magnitudes with highstatistical signiﬁcance. The coeﬃcient of ln(intermediate) is positive, but not signiﬁcantly different from zero. We interpret yit − βˆk kit − β̂l lit + βˆm mit − δ̂Zit as the TFP of plant i in periodt. We also use output per pot (capital productivity) and output per worker (labor productivity)
as alternative measures of plant-level productivity. In the Japanese silk-reeling industry, output
per pot and output per worker were conventionally used as measures to evaluate plant-levelproductivity.

6

Main results

We now show the estimation results and distinguish the relative size of agglomeration andselection eﬀects.

9

An alternative way of estimating TFP is the structural approach proposed by Levinsohn and Petrin (2003)
that relaxes the assumption of ωit = ωi is potentially useful, but the limitation of our data set is that the two
periods are seven years apart, making it diﬃcult for the application of the method of Levinsohn and Petrin (2003).

20

We use a prefecture as a unit of observation of regional productivity density to obtain
suﬃcient observations. All prefectures in Japan are classiﬁed into two groups on the basis ofregional plant densities (number of plants per km2 in a region). We sorted prefectures according
to the density of silk-reeling plants, and picked up the prefectures from the top until these
prefectures had more than half of the total plants in Japan. We regard those prefectures withhigh plant density as clustered prefectures, and the other prefectures as non-clustered prefectures.
There were 47 prefectures in total in Japan at that time, and of these, ﬁve are identiﬁed asclustered prefectures in each period (Aichi, Yamanashi, Nagano, Gifu, and Kyoto for 1909,
while Gumma instead of Kyoto for 1916). The other 42 prefectures are regarded as non-clusteredprefectures. Plant density in each prefecture in 1909 is illustrated in Figure 1. For instance,
Nagano prefecture, the largest cluster, had over 18 plants per km2 .
First, we estimate the kernel density functions10 of plant-level productivity for each groupof prefectures. Figure 3 represents the kernel densities.

= Figure 3 =The solid line refers to the density of clustered prefectures and the dashed line refers to thedensity of non-clustered prefectures. In every ﬁgure, the estimated density in the lower tailof the distribution is lower for clustered prefectures than for non-clustered prefectures, while
density in the higher tail of distributions is similar for the two prefecture groups. Moreover,the shapes and positions of the two distributions seem to be similar except for the lower tails.
There is no clear sign that the distribution of clustered prefectures shifts to the right. Given
the predictions summarized in Table 1, these features of the two distributions suggest that aselection eﬀect existed but an agglomeration eﬀect did not.
These observations are also conﬁrmed by the descriptive statistics of the productivity distributions shown in Table 3.

= Table 3 =10

We estimate the density functions by using the Epanechnikov kernel with optimal bandwidth.

21

Panel A represents the statistics for 1908 and Panel B represents those for 1915. The mean
productivities are signiﬁcantly higher in clusters for every productivity measure and period,
indicating that plants located in industrial clusters were indeed more productive than those in
non-clusters.
Our conventional predictions in Table 1 suggest that the interquartile range is informativein detecting selection eﬀects. If the productivity distribution is truncated by selection, we
should observe a shorter interquartile range. We can also examine the existence of selection andagglomeration eﬀects by looking at the percentiles of distribution at the lower and higher tails:
while selection aﬀects only the lower tail, agglomeration aﬀects every support of the distribution
because agglomeration shifts the whole distribution rightwards. Hence, if the agglomerationeﬀect exists, both the lower and higher tails of the distribution should shift to the right.
Table 3 reveals that the interquartile range of the distribution in clustered prefectures issmaller than that in non-clustered prefectures. This suggests the truncation of the distribution
implied by plant selection. This interpretation is further supported by the percentiles of the
distribution. In the lower tails (the 10th and 25th percentiles), percentiles in clusters are muchhigher than in non-clusters. For example, in 1908, while the 10th percentile in cluster is –0.21, the same percentile in non-clusters is –0.33, and the diﬀerence is 0.1. However, in higher
tails, the percentiles in both clusters and non-clusters are quite similar (the 90th percentile inboth clusters and non-clusters are 0.18). These ﬁndings are consistent with Case 1 in Table
1: productivity distribution is left-truncated but no right-shift is observed. According to ourtheoretical prediction, this implies the existence of plant selection and non-existence of theagglomeration eﬀect.
The estimation results are shown in Table 4.

= Table 4 =These results are for three measures of productivities and for two periods. Column (1) in Table
4 reports our results for TFP in 1909. The point estimate of A is negative but not signiﬁcantly
diﬀerent from zero, while that of D is greater than one but not statistically diﬀerent from one.
These values suggest that there is no larger rightwards shift of the distribution and dilations insilk-reeling clusters compared to non-clusters. However, the point estimate of S is positive andstatistically diﬀerent from zero, suggesting that there is more elimination of the distributions22

in clusters compared to non-clusters. These results strongly suggest that the selection eﬀect inclusters is larger compared to in non-clusters, while the agglomeration (and dilation) eﬀect isnot. That is, the higher plant-level productivity in silk-reeling clusters can be explained only by
the selection eﬀect. This result is the exact opposite of the result of Combes et al. (2012) that
focuses on urban metropolitan areas.
This result is robust for the measure of productivities and periods. In every column, thepoint estimate of S is positive and statistically diﬀerent from zero. However, the point estimateof A is negative but not signiﬁcantly diﬀerent from zero, while that of D is greater than one but
not statistically diﬀerent from one with the exception of column (3). These results suggest therobustness of our conclusion: the higher plant-level productivity in silk-reeling clusters can be
explained only by the selection eﬀect.
In sum, robustly, the selection eﬀect was larger in specialized silk-reeling clusters than in the
non-clusters, while there were no agglomeration or dilation eﬀects. These results suggest thatthe higher plant-level productivity in silk-reeling clusters can be explained only by the selectioneﬀect.
Why were there no agglomeration economies in the silk-reeling clusters? One possible reason
is that the major innovative knowledge for improving productivity had already spread by thisperiod. Nakabayashi (2003) showed that the productivity of a silk-reeling plant in prewar Japan
was principally determined by machines and the mode of labor management, and that substantial innovation occurred in the latter in Suwa District in the 1900s. That is, a sophisticatedperformance-based wage system was devised to provide appropriate incentives to female workers. In this system, the performance of each female worker was evaluated by several measures
including labor productivity, cocoon productivity, and product quality, which were strategic forthe competitiveness and proﬁtability of a plant (pp.241-288). Notably, this wage system wasﬁrst devised in Suwa, but had widely diﬀused in Japan by the early 1910s (Ishii, 1972, p.300).
In this sense, there was little room for productivity improvement through learning in the 1910s.

23

7

Robustness checks

7.1

Prefectural variations

In the previous section, we found by the method developed by Combes et al. (2012) that there waslarger selection but no agglomeration in silk-reeling clusters than in non-clusters. This method
is theoretically and statistically rigorous, but it cannot fully utilize regional variations because
the method compares two distributions of the log of productivities. However, our method todistinguish the agglomeration eﬀect and the selection eﬀect by the summary statistics of thelog of productivity distribution as was done in Syverson (2004) and as described in Table 1 was
not rigorously developed but can fully utilize the prefectural variations. Although the summary
statistics approach cannot purely distinguish the agglomeration eﬀect and the selection eﬀect,
it yields a useful approximation. This section adopts the summary statistics approach to checkthe robustness of the previous results.
Based on Table 1, we ﬁrst investigate the eﬀect of plant densities on the interquartile rangeof the productivity distribution. We index each prefecture by p and estimate the following
equation:
IQRpt = α + β ln(Dpt ) + yeart + εpt(35)

where IQRpt refers to the interquartile range of the plant-level productivity distribution in
prefecture p in period t, Dpt is the plant density and yeart is the year ﬁxed eﬀects. Under
the presence of selection eﬀects, an increase in plant density will truncate the distribution andshorten the interquartile range; thus, we expect a negative sign for β. We estimate this equation
by pooled OLS with year ﬁxed eﬀects. Because this estimation focuses on the productivity
distribution and requires a certain number of observations (plants) in each prefecture, we restrict
samples to prefectures that had more than 20 plants. The results are shown in columns (1) to(3) in Table 5.

= Table 5 =In every result (columns 1–3), the coeﬃcients of plant density are negative and statisticallysigniﬁcant. This suggests the truncation of productivity distributions, which is consistent withthe existence of the selection eﬀect.
24

Next, we examine the role of the agglomeration eﬀect by focusing on the percentiles of the
productivity distribution. We estimate the following equation:

Pupt = α + β ln(Dpt ) + yeart + εpt ,(36)

where Pupt is the u-th percentile of the log productivity distribution in prefecture p for period t.
The equation is estimated by pooled OLS.
The results are shown in Table 6.

= Table 6 =Columns (1) to (4) use TFP as a measure of productivity while columns (5) to (8) and (9)to (12) use output per pot and output per worker, respectively. Regardless of the measure of
productivity, the coeﬃcients of plant density are positive and signiﬁcant for the lower tail, thatis, the 10th and 25th percentiles (columns 1, 2, 5, 6, 9, and 10). This result is consistent withboth the agglomeration and selection eﬀects. However, every coeﬃcient of plant density is notstatistically diﬀerent from zero at the 75th or 90th percentiles (columns 3, 4, 7, 8, 11, and 12).
This implies that higher plant density had no eﬀect on the productivity distribution shifting
rightwards. The evidence runs contrary to the existence of the agglomeration eﬀect.
These results indicate that the increase in plant density truncated the log productivity distribution in the lower tail but had no eﬀect in shifting the distribution rightwards. This isconsistent with the existence of the selection eﬀect and the non-existence of the agglomerationeﬀect (Case 1 in Table 1). The results obtained in this section strongly support our main resultthat the higher plant-level productivity in silk-reeling clusters can be explained only by theselection eﬀect.

7.2

Productivity growth after operation

According to the results obtained in the previous sections, there is no agglomeration eﬀect in
the clusters. Did the concentration of the plants actually have no positive externality to theplants located there? For the ﬁnal robustness check, we examine the timing of the productivity
growth.
Our strategy is as follows. If the agglomeration eﬀect is in place and learning from leading25

plants improves plant-level productivities, we would observe faster productivity growth in clusters than in non-clusters after the plants are operational.11 Thus, we check the productivity
growth after commencement of operations by comparing the productivity growth rates between
plants in clusters and non-clusters.
Descriptive statistics of the productivity growth rate from 1908 to 1915 for three diﬀerent
productivity measures are shown in Table 7.

= Table 7 =Younger plants might tend to learn and improve their productivities faster than older plants.
We report descriptive statistics for start-up plants separately. We deﬁne start-up plants as plants
with age less than ﬁve years.
For every productivity measure, the average productivity growth rate is similar for clusters
and non-clusters. Rather, the average growth rate in clusters is smaller than in non-clusters.
We test the diﬀerence in the average productivity growth rate between clusters and non-clusters
using a t-test, but the null hypothesis that the mean diﬀerence in the growth rates between
clusters and non-clusters is zero is not rejected at the conventional levels of statistics for every
measure of productivity. Furthermore, this relationship also holds even if we restrict samples
to start-up plants. Overall, start-up plants grew faster than older plants in terms of every
productivity measure. Meanwhile, the average productivity growth rate of start-up plants inclusters is again lower than in non-clusters, and we also cannot reject the null hypothesis thatthe mean diﬀerence in the growth rates between the clusters and non-clusters is zero in every
measure of productivity. Thus, there is no evidence that plants learned faster in clusters thanin non-clusters.
To control plant-level diﬀerences, we econometrically test the learning eﬀects in clusters, by
estimating the following equation:

1908
1908
GrowthRateicp = α + βDcp
+ δZicp+ γProductivity1908
icp + prefp + εicp ,

11

(37)

Such dynamics of productivity growth is not introduced into our theoretical model. However, technologicalexternality does occur gradually rather than instantaneously. In a sense, this section considers the agglomeration
economies separately from our baseline model.

26where GrowthRateicp is the productivity growth rate of plant i located in county c in prefecture1908 is the plant density at the county level in 1908, and Z 1908 is the vector
p from 1908 to 1915, Dcp
icp

of plant-level control variables (number of pots, number of workers, age, steam power dummy,
and water power dummy) in 1908. To control low-productivity plants’ faster learning and growth(catch-up), we include the initial productivity in 1908. Finally, prefp denotes prefectural ﬁxed
eﬀects. Table 8 reports the results.

= Table 8 =Again, we use three measures for plant-level productivity. Column (1) gives the baseline
result. Even after controlling for plant-level variables, the coeﬃcient of plant density is notstatistically diﬀerent from zero. That is, plants in clusters did not improve their productivities
faster than plants in non-clusters. Column (2) controls initial productivity in 1908. Interestingly,
the coeﬃcient of initial productivity in 1908 is negative and signiﬁcant, suggesting a catch-up
by low-productivity plants. However, the coeﬃcient of plant density is still not statisticallydiﬀerent from zero. Low-productivity plants did learn and catch-up, but their speed was not
signiﬁcantly diﬀerent for clusters and non-clusters. This result is robust to the alternative
measures of productivity (columns 3–6) or the restricted sample of start-up plants (columns
7–12). The coeﬃcient of initial productivity in 1908 is signiﬁcantly negative but plant density
is not statistically diﬀerent from zero. In sum, these results do not support the presence oflearning implied by the agglomeration eﬀect. Low-productivity plants did catch up, but we ﬁnd
no evidence that plants in clusters improved their productivity faster than did their counterpartsin non-clusters. The concentration of plants did not have any productivity growth eﬀect in these
periods. This result also supports our main result that the higher plant-level productivity insilk-reeling clusters can be explained only by the selection eﬀect.

8

Concluding remarks

This paper attempted to distinguish the two channels through which industrial clusters improve
plant-level productivity, focusing on the Japanese silk-reeling industry in the period from 1908
to 1915. On the basis of a nested model of selection and agglomeration, we considered the27

agglomeration eﬀect, which improves the productivities of all plants in a region, and the plantselection eﬀect, which raises the average regional productivity by expelling less-productive plants
through intense competition.
Using plant-level data, we distinguished the channels of productivity improvement by theestimation method proposed by Combes et al. (2012). We found on one hand that there was lefttruncation of the log of the productivity distribution in clusters relative to non-clusters, and on
the other hand, that there was no rightwards shift and dilation of the distribution. These ﬁndings
suggest that the higher plant-level productivity in the silk-reeling clusters can be explained onlyby the selection eﬀect. These main ﬁndings were robust for the alternative method to detect thoseeﬀects via prefectural variations and summary statistics of the distribution. The observation isfurther supported by the ﬁnding that there was no diﬀerence in the productivity growth rate ofindividual plants between clusters and non-clusters. This result implies that productivity growththrough learning suggested by the agglomeration eﬀect was not evident. We suspect that thepossible reason for this lack of agglomeration eﬀect is that the major innovative knowledge for
improving productivity (i.e., performance-based wage system) had already spread by this period.
We therefore conclude that in the Japanese silk-reeling industry, higher average productivity
in clusters was not caused by the agglomeration eﬀect but through selection; that is, the intensiﬁcation of competition in clusters expelled low-productivity plants, and consequently, only
relatively more productive plants survived.
Our ﬁnding is contrary to that of Combes et al. (2012) and Accetturo et al. (2011), which
ﬁnd agglomeration eﬀects in French and Italian metropolitan areas, respectively. The diﬀerence
implies that the source of productivity improvement may be diﬀerent in urban metropolitan areasand specialized industrial clusters. In particular, plants in specialized industrial clusters are lesslikely to enjoy the beneﬁts of “Jacobs externality,” while facing severe competition comparedto those in urban metropolitan clusters. Further investigation of the diﬀerence between urban
metropolitan clusters and specialized industrial clusters remains for future research.

References
Accetturo, A., V. Di Giacinto, G. Micucci, and M. Pagnini (2011), Local Productivity Diﬀerences
through Thick and Thin: Market Size, Entry Costs and Openness to Trade, mimeo.

28

Baldwin, R., T. Okubo (2006), Heterogeneous Firms, Agglomeration and Economic Geography:
Spatial Selection and Sorting, Journal of Economic Geography 6, 323–346
Behrens, K., G. Mion, Y. Murata, and J. Südekum (2009), Trade, Wages, and Productivity,
CEPR Discussion Paper Series, #7369.
Ciccone, A. (2002), Agglomeration Eﬀects in Europe, European Economic Review 46, 213–227.
Ciccone, A., R. Hall (1996), Productivity and the Density of Economic Activity, American
Economic Review 86, 54–70.
Combes, P., G. Duranton, L. Gobillon, D. Puga, and S. Roux (2012), The Productivity Advantages of Large Cities: Distinguishing Agglomeration from Firm Selection, Econometrica,
forthcoming.
Corcos, G., M. Del Gatto, G. Mion, and G. Ottaviano (2010), Productivity and Firm Selection:
Quantifying the “New” Gains from Trade, mimeo.
Duran, L. (1913) Raw Silk: A Practical Hand-Book for the Buyer. Silk Publishing Company,
New York.
Eguchi, Z., and Y. Hidaka eds. (1937) Shinano Sanshigyo Shi (History of the Silk-Reeling Industry in Nagano Prefecture). Dainihon Sanshikai Shinano Shikai. (in Japanese).
Fujita, M., and H. Ogawa (1982), Multiple Equilibria and Structural Transition of Nonmonocentric Urban Conﬁgurations, Regional Science and Urban Economics 12, 161–196.
Glaeser, E., H. Kallal, J. Shainkman, and A. Shleifer (1992), Growth in Cities, Journal of
Political Economy 100, 1126–1152.
Henderson, V. (2003), Marshall’s Scale Economies, Journal of Urban Economics 53, 1–28.
Hirano, Y. (1990) Kindai Yo-san-gyo no Hatten to Kumiai Seishi (Development of Modern
Sericulture and Cooperative Silk-reeling). University of Tokyo Press, Tokyo. (in Japanese).
Ishii, K. (1972) Nihon Sanshigyo-shi Bunseki (Analysis of Japanese Silk industry). University ofTokyo Press, Tokyo. (in Japanese).
Jacobs, J. (1969) The Economy of Cities. Vintage, New York.

29

Kambayashi, R. (2001) Tokyu Chingin Seido to Ko-jo Toroku Seido,” (Grade Wage System
and Registration System of Female Factory Workers) in T. Okazaki (ed.) Torihiki Seido no
Keizai-shi (Governing Business Transactions: A Historical Perspective), University of Tokyo
Press, Tokyo. (in Japanese).
Levinsohn, J., and A. Petrin (2003), Estimating Production Functions using Inputs to Control
for Unobservables, The Review of Economic Studies 70, 317–341.
Lucas, R., and E. Rossi-Hansberg (2002), On the Internal Structure of Cities, Econometrica 70,
1445–1476.
Matsumura, S. (1992) Senkan-ki Nihon Sanshigyo-shi Kenkyu (Historical Study of JapaneseSilk-reeling in the Inter-war Period). University of Tokyo Press, Tokyo. (in Japanese).
Melitz, M. (2003), The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry
Productivity, Econometrica 71, 1695–1725.
Melitz, M., and G. Ottaviano (2008), Market Size, Trade, and Productivity, Review of Economic
Studies 75, 295–316.
Melo, P., D. Graham, and R. Noland (2009), A Meta-Analysis of Estimates of Urban Agglomeration Economies, Regional Science and Urban Economics 39, 332–342.
Nagano Prefecture (1910), Naganoken Tokeisho (Statistical Yearbook of Nagano Prefecture),
1908 issue, Nagano Prefecture. (in Japanese).
Nakabayashi, M. (2003), Kindai Shihonshugi no Soshiki: Seishigyo no Hatten ni Okeru Torihiki
no Tochi to Seisan no Kozo (An Orgazation of Modern Capitalism: The Governance of Tradeand the System of Production in the Development of the Silk Reeling Industry). University ofTokyo Press, Tokyo. (in Japanese).
Rosenthal, S., and W. Strange (2004), Evidence on the Nature and Sources of Agglomeration
Economies, in V. Henderson and J. Thisse (eds.) Handbook of Regional and Urban Economics,
Vol. 4., North-Holland, Amsterdam, 2119–2171.
Syverson, C. (2004), Market Structure and Productivity: A Concrete Example, Journal of
Political Economy 112, 1181–1222.

30

Tojo, Y. (1990), Seishi Domei no Joko Toroku Seido (Worker Registration System of Silk-reeling
Association). University of Tokyo Press, Tokyo. (in Japanese).

31

Table 1: Measures of distribution in clusters relative to non-clusters
Cases
Case 1: Selection
Case 2: Agglomeration
Case 3: Selection & agglomeration
Case 4: Neither eﬀect

Mean
+
+
+
0

Interquartile range–
0–0

Lower percentile+++0

Higher percentile
+
++
++
0

Table 2: Estimation result of plant-level productivityln(capital)
0.152**(0.056)ln(labor)
0.153**(0.074)ln(intermediates)
0.719**(0.076)ln(age)0.056**(0.022)

Water power
dummy
0.053*(0.032)

Steam power
dummy
0.004
(0.035)Constant
2.170 **
(0.134)

No. obs.
4479

R2
0.955

Note: The dependent variable represents the log of output: The capital represents the number of pots, labor
represents the number of workers, and intermediates represents the quantity of cocoons. Estimated by the ﬁxed
eﬀects model.
Robust standard errors in parentheses.
* Signiﬁcant at the 10 percent level.
** Signiﬁcant at the 5 percent level.

32

Table 3: Descriptive statistics of plant-level productivity
Panel A: 1908
Measure of
productivity

Clusters vs.
Non-clusters

Obs.

Mean

Interquartile
range

10th
Percentile

25thPercentile

50thPercentile

75thPercentile

90thPercentile

All
Clusters
Non-clusters

2232
1119
1113

-0.03
-0.002-0.05(4.288)

0.22
0.19
0.26

-0.27
-0.21
-0.33

-0.14
-0.09
-0.18

-0.01
0.01
-0.04

0.09
0.1
0.08

0.18
0.18
0.18

All
Clusters
Non-clusters

2233
1119
1114

3.95
4.07
3.82
(10.031)

0.71
0.57
0.82

3.2
3.44
2.96

3.62
3.82
3.43

4.03
4.07
3.92

4.33
4.39
4.25

4.57
4.57
4.56

All
Clusters
Non-clusters

2234
1119
1115

3.92
4.04
3.8
(10.113)

0.66
0.55
0.79

3.16
3.44
2.96

3.63
3.81
3.44

4.00
4.06
3.93

4.29
4.35
4.23

4.51
4.54
4.47

Clusters vs.
Non-clusters

Obs.

Mean

Interquartile
range

10th
Percentile

25thPercentile

50thPercentile

75thPercentile

90thPercentile

All
Clusters
Non-clusters

2247
1263
984

0.03
0.04
0.004
(3.218)

0.28
0.24
0.34

-0.27
-0.2
-0.34

-0.1
-0.07
-0.15

0.06
0.07
0.05

0.18
0.18
0.19

0.29
0.28
0.29

All
Clusters
Non-clusters

2263
992
1271

4.17
4.26
4.05
(7.180)

0.87
0.79
1.04

3.22
3.53
2.93

3.78
3.87
3.59

4.29
4.34
4.19

4.65
4.66
4.63

4.93
4.93
4.94

All
Clusters
Non-clusters

2263
992
1271

4.14
4.23
4.02
(7.581)

0.83
0.77
0.94

3.24
3.49
2.91

3.76
3.85
3.62

4.26
4.31
4.18

4.6
4.61
4.56

4.86
4.88
4.83

TFP

Output per pot

Output per Worker

Panel B: 1916
Measure of
productivity
TFP

Output per pot

Output per Worker

Note: TFP is estimated by the ﬁxed eﬀects estimation. The t-values of the t-test are presented in parentheses.
The null hypotheses of the t-test is that average productivity is the same for clusters and non-clusters.

33

Table 4: Main estimation results

(1)
TFP
1908

(2)
TFP
1916

(3)
Output per pot
1908

(4)
Output per pot
1916

(5)
Output per worker
1908

(6)
Output per worker
1916

A (relative agglomeration)–0.016[0.159]–0.029[0.140]–0.603∗∗[0.177]–0.071[0.232]–0.192[0.253]–0.153[0.203]D (relative dilation)

1.023[0.069]1.012[0.057]1.200∗∗[0.044]1.042[0.053]1.089[0.063]1.073[0.046]S (relative selection)

0.024∗∗[0.003]0.013∗∗[0.003]0.022∗∗[0.003]0.024 ∗∗
[0.004]0.018 ∗∗
[0.004]0.027 ∗∗
[0.003]Observations
R2

2232
0.649

2247
0.576

2233
0.338

2263
0.439

2234
0.509

2263
0.457

Measure of productivity
Year

Note: Estimation method proposed by Combes et al. (2012) is used. Standard errors are calculated by 200
bootstrapping iterations. TFP is estimated by the ﬁxed eﬀects estimation.
Bootstrapped standard errors in square parentheses.
**: for A and S signiﬁcantly diﬀerent from 0 at the 5 percent level, for D signiﬁcantly diﬀerent from 1 at the 5
percent level.

Table 5: Plant density and interquartile range of productivity distribution
(1)
TFP

(2)
Output per pot(3)
Output per workerln(density)-0.0276∗(0.0151)-0.129∗∗(0.0453)-0.130∗∗(0.0539)

Constant

0.256∗∗(0.0280)0.860∗∗(0.0876)

0.811∗∗(0.104)

Observations
Adjusted R2

45
0.071

45
0.111

45
0.102

Measure of productivity

Note: The dependent variables are the interquartile range of the productivity distribution at the prefectural level.
TFP is estimated by the ﬁxed eﬀects estimation.
Robust standard errors in parentheses.
* Signiﬁcant at the 10 percent level.
** Signiﬁcant at the 5 percent level.

Table 6: Plant density and percentiles of productivity distribution
(1)

(2)

(3)

(4)

TFP
10th

TFP
25th

TFP
75th

ln(density)

0.0506∗(0.0290)0.0430∗(0.0243)

Constant
Year ﬁxed eﬀect-0.286∗∗(0.0509)
yes

Observations
Adjusted R2

45
0.031

Measure of
productivity
Percentiles

TFP
90th

(5)
Output per
pot
10th

(6)
Output per
pot
25th

(7)
Output per
pot
75th

(8)
Output per
pot
90th

(9)
Output per
worker10th(10)Output per
worker25th(11)
Output per
worker75th(12)Output per
worker90th

0.0154(0.0155)

0.0189(0.0141)0.197∗∗(0.0772)0.181∗∗(0.0764)0.0527(0.0560)

0.0546(0.0475)

0.191∗∗(0.0801)0.169∗∗(0.0804)

0.0387(0.0535)

0.0672(0.0473)-0.168∗∗(0.0422)yes

0.0875∗∗(0.0254)yes

0.166∗∗(0.0224)
yes

3.122∗∗(0.139)yes

3.432∗∗(0.136)yes

4.292∗∗(0.0901)
yes

4.557∗∗(0.0788)yes

3.138∗∗(0.147)yes

3.453∗∗(0.145)yes

4.264∗∗(0.0825)
yes

4.473∗∗(0.0724)
yes

45
0.046

45
0.145

45
0.292

45
0.115

45
0.117

45
0.202

45
0.318

45
0.075

45
0.087

45
0.227

45
0.385

Note: Dependent variables are percentile points of the productivity distribution at the prefectural level. TFP is
estimated by the ﬁxed eﬀects estimation.
Robust standard errors in parentheses.
* Signiﬁcant at the 10 percent level.
** Signiﬁcant at the 5 percent level.

34

Table 7: Plant-level productivity growth rate, 1909 to 1916
Panel A. Measure of productivity: TFP
All plants
Clusters vs. Non-clusters

Obs.

Mean

Standard
deviation

Clusters
Non-clusters
AllDiﬀerence(Clusters/Non-clusters)

448
461
909

0.279
0.311
0.295
–0.032

0.680
1.053
0.888
0.059

Start-up plants
t-value

Obs.

Mean

Standard
deviation

t-value

115
83
198

0.417
0.640
0.510
–0.223

0.829
1.842
1.350
0.194

–1.148–0.535

Panel B. Measure of productivity: Output per pot
All plants
Clusters vs. Non-clusters

Obs.

Mean

Standard
deviation

Clusters
Non-clusters
AllDiﬀerence(Clusters/Non-clusters)

448
461
909

0.471
0.494
0.482
–0.023

1.011
1.568
1.323
0.088

Start-up plants
t-value

Obs.

Mean

Standard
deviation

t-value

115
83
198

0.676
1.053
0.834
–0.377

1.219
3.014
2.163
0.311

–1.213–0.265

Panel C. Measure of productivity: Output per worker
All plants
Clusters vs. Non-clusters

Obs.

Mean

Standard
deviation

Clusters
Non-clusters
AllDiﬀerence(Clusters/Non-clusters)

448
461
909

0.459
0.489
0.474
–0.030

1.049
1.551
1.327
0.088

Start-up plants
t-value–0.337

Obs.

Mean

Standard
deviation

t-value

115
83
198

0.652
1.009
0.802
–0.357

1.198
2.973
2.131
0.307

–1.164

Note: TFP is estimated by the ﬁxed eﬀects estimation. The t-value columns show the results of the t-test. The
null hypotheses of the t-test is that average productivity growth is not diﬀerent for clusters and non-clusters.

35

36

-0.511∗∗(0.134)-0.133∗∗(0.0431)-0.552∗∗(0.183)-0.0783∗(0.0415)

0.0531(0.0791)-0.0316(0.0811)ln(cocoon) in 1908ln(age) in 1908

Steam power dummy in 1908

Water power dummy in 1908

909
0.157

Observations
Adjusted R2

909
0.265

Yes

1.337∗∗(0.350)-1.100∗∗(0.203)-0.0732(0.0764)

909
0.160

Yes

2.567∗∗(0.737)-0.0214(0.128)0.0720(0.114)-0.128∗(0.0714)-0.962∗∗(0.309)-0.391(0.652)

1.435∗∗(0.585)-0.0138(0.0410)

All

909
0.219

Yes

5.179∗∗(1.142)-1.221∗∗(0.273)-0.00273(0.127)0.122(0.111)-0.121∗(0.0691)-0.0380(0.200)-0.130(0.644)0.300(0.634)-0.00820(0.0389)All(4)
Output per
pot

909
0.159

Yes

2.781∗∗(0.757)0.00137(0.131)

0.101(0.120)-0.132∗(0.0721)

909
0.226

Yes

5.554∗∗(1.175)-1.296∗∗(0.277)0.0212(0.129)0.154(0.115)-0.124∗(0.0697)-0.0282(0.194)0.732∗∗(0.318)1.751∗∗(0.466)-1.009∗∗(0.317)-0.600∗∗(0.229)0.0165(0.0370)All(6)Output per
worker-0.691∗∗(0.259)0.0105(0.0391)All(5)
Output per
worker
TFP

(7)

198
0.534

Yes

2.870∗∗(1.225)0.671∗∗(0.339)0.701∗(0.355)

198
0.574

Yes

2.401∗∗(1.114)-1.114∗∗(0.483)0.370(0.257)-0.231(0.206)-1.297∗∗(0.479)-0.806(0.573)2.240∗∗(0.432)-0.0911(0.0832)

Start-up

TFP

(8)

0.398
(0.262)-0.182(0.222)-1.472∗∗(0.554)-0.816(0.638)2.393∗∗(0.438)-0.0589(0.0919)

Start-up

Table 8: Estimation of growth eﬀects(3)
Output per
pot

198
0.405

Yes

5.301∗∗(2.489)1.395∗∗(0.692)0.542(0.418)-0.437(0.400)-2.535∗∗(1.113)-0.914(1.129)3.552∗∗(0.605)-0.119(0.151)

Start-up(9)
Output per
pot

198
0.435

Yes

8.077∗∗(3.413)-1.587∗(0.822)

1.437∗∗(0.687)0.508(0.413)-0.417(0.369)-1.144(0.953)-0.657(1.101)1.989∗∗(0.950)-0.165(0.145)

Start-up(10)
Output per
pot

198
0.401

Yes

5.433∗∗(2.499)

198
0.435

Yes

8.279∗∗(3.382)-1.627∗∗(0.780)1.465∗∗(0.687)0.653(0.403)0.688∗(0.407)1.421∗∗(0.692)-0.477(0.368)-0.981(0.912)0.700(0.924)0.346(0.439)-0.142(0.143)

Start-up(12)
Output per
worker-0.498(0.398)-2.407∗∗(1.114)2.063∗(1.076)0.322(0.436)-0.0949(0.147)

Start-up(11)
Output per
workerNote: The dependent variables represent the growth rate of the plant-level productivity from 1909 to 1916. TFP is estimated by the ﬁxed eﬀects estimation. A start-up
is a plant with age less than ﬁve years.
Robust standard errors in parentheses.
* Signiﬁcant at the 10 percent level.
** Signiﬁcant at the 5 percent level.

Yes

Prefectural FEs

Constantln(Output per worker) in 1908ln(Output per pot) in 1908

1.370∗∗(0.420)-0.274(0.389)-0.340(0.418)ln(worker) in 1908

ln(TFP) in 1908

0.877∗∗(0.377)0.968∗∗(0.393)ln(pot) in 1908

0.0933(0.0753)-0.00968(0.0258)

All

TFP-0.0148(0.0284)

All

Samples(2)ln(density) in 1908

TFP

Dependent: Measure of
productivity growth(1)Plant Density
0.000000
0.000001 - 1.473488
1.473489 - 2.410958
2.410959 - 3.881675
3.881676 - 9.191416
9.191417 - 18.085370

Figure 1: Map of Japan and the density of silk-reeling plants in 1909

37

0.5
0.0

0.1

0.2

Density

0.3

0.4

0.5
0.4
0.3
Density
0.2
0.1
0.0
-4

-2

0

2

4

-4

-2

Case 1

0

2

4

2

4

Case 20.4
0.3
Density
0.2
0.1
0.0

0.0

0.1

0.2

Density

0.3

0.4

0.5

(b) Agglomeration

0.5(a) Selection

-4

-2

0

2

4

-4

Case 3-20Case 4(c) Both selection and agglomeration(d) Neither eﬀect

Figure 2: Four considerable cases of cluster eﬀects

38

TFP 1916

0

0

.5

Density1
2

Density
1 1.5

2

3

TFP 1909

−3

−2

−1

0

1

2

−2

−1

0
TFP 1916

TFP 1909
ClusteredNon−clustered

1

Clustered3

Non−clustered

Output per pot 1916

0

0

.2

.2

Density.4.6

Density.4 .6 .81.8Output per pot 1909

2

0

2

4
Output per pot 1909
Clustered

6

8

0

2

Non−clustered4
Output per pot 1916
Clustered8

Non−clustered

Output per worker 1916

0

0

.2

.2

Density.4.6

Density.4 .6 .81.8Output per worker 1909

6

0

2

4
Output per worker 1909
Clustered680Non−clustered2

4
Output per worker 1916
ClusteredFigure 3: Kernel densities of plant-level productivity

39

6
Non−clustered

8

A

Mathematical Appendix (not for publication)

A.1

Derivation of ddsĥ (eq.(9))

The implicit function theorem implies thatdĥ−(∂V e /∂s)=.
ds
∂V e /∂ ĥ−(∂V e /∂s) = 1 is immediate from eq.(8). The denominator is
(

√

)2



√ ]
∫ ĥ [ĥ − h + wf ĥ − ĥ + wf
− f  g(ĥ) + 2
g(h)dh
=
w
w
∂ ĥ
0
√ ]
∫ ĥ [ĥ − h + wf
=2
g(h)dh > 0.
w
0

∂V e

Therefore,dĥ−(∂V e /∂s)
w
=
= ∫ (
> 0.
√ )
e
ĥ
ds
∂V /∂ ĥ2ĥ − h + wf g(h)dh0A.2

Derivation of Ne (eq.(13))

Total production in a region is∫ ĥ
Q = Neqi∗ g(h)dh.

0Inserting qi∗ from eq.(4) yields∫ ĥ
Q = Neqi∗ g(h)dh

0

∫ ĥ
0

p − h − wE(Q)g(h)dhw0p−hg(h)dh − Ne E(Q)G(ĥ).
w

= Ne
∫ ĥ
= Ne

Since Q = E(Q) in the equilibrium, we can write Q as a function of Ne and ĥ:Q(Ne , ĥ) =

∫ ĥ

Ne
1 + Ne G(ĥ)

40

0

p−h
g(h)dh.
w

Further, by rearranging eq.(6) (ĥ = p − wQ −√wf ), we get another expression ofp − ĥ −
Q=
w

√

wf

.

As such, we have
∫ ĥ

Ne

p−h
p − ĥ −g(h)dh =
w
w

√

wf

1 + Ne G(ĥ) 0
∫ ĥ
√
⇒ Ne
(p − h)g(h)dh = [1 + Ne G(ĥ)](p − ĥ − wf )
]
[0∫
ĥ
√
√
⇒ Ne
(p − h)g(h)dh − (p − ĥ − wf )G(ĥ) = p − ĥ − wf
0

[∫
⇒ Ne

ĥ

(p − h)g(h)dh −

0

[∫
⇒ Ne

∫ ĥ
0

ĥ

(ĥ − h +√]√√(p − ĥ − wf )g(h)dh = p − ĥ − wf]wf )g(h)dh = p − ĥ −

√

wf ,

0

and henceA.3√
p − ĥ − wf
Ne = ∫.
√ĥwf)g(h)dh
(
ĥ
−
h
+
0

e
Derivation of ∂N
∂ ĥ

[√
]
∫ ĥ
∫ ĥ
√
√
−
(
ĥ
−
h
+
wf
)g(h)dh
−
(p
−
ĥ
−
wf
)
wf
g(
ĥ)
+
g(h)dh
0
0
∂Ne
=
]2
[∫
√
ĥ
∂ ĥ
0 (ĥ − h + wf )g(h)dh
∫ ĥ
∫ ĥ
√
√
√
√
− 0 (ĥ − h + wf )g(h)dh − 0 (p − ĥ − wf )g(h)dh − (p − ĥ − wf ) wf g(ĥ)
=
]2
[∫
√
ĥ
(
ĥ
−
h
+
wf
)g(h)dh0∫ ĥ
√√− 0 (p − h)g(h)dh − (p − ĥ − wf ) wf g(ĥ)
=
< 0.
[∫
]2
√
ĥ
(
ĥ
−
h
+
wf
)g(h)dh0

A.4

Derivation of dNp /ds

Since Np = Ne G(ĥ),[]
dNpdNe dĥ
dĥ
dNe
dĥ
=
G(ĥ) + Ne g(ĥ)=.
G(ĥ) + Ne g(ĥ)
dsdsdsdĥ dsdĥ

41

By using eqs.(13) and (14), and letting

ξ≡

∫ ĥ

(ĥ − h +√wf )g(h)dh,0

the term in the brackets is
∫ ĥ
√
√
√
−G(ĥ) 0 (p − h)g(h)dh − (p − ĥ − wf ) wf g(ĥ)G(ĥ)(p − ĥ − wf )g(ĥ)G(ĥ) + Ne g(ĥ) =
+
[∫
]2
∫ ĥ
√
√
ĥ
dĥ
(ĥ − h + wf )g(h)dh
(
ĥ
−
h
+
wf
)g(h)dh
0
0
∫ ĥ
√
√
√
−G(ĥ) 0 (p − h)g(h)dh − (p − ĥ − wf ) wf g(ĥ)G(ĥ) + (p − ĥ − wf )g(ĥ)ξ
=
[∫
]2
√
ĥ
(
ĥ
−
h
+
wf
)g(h)dh
0
[√
]
∫ ĥ
√
−G(ĥ) 0 (p − h)g(h)dh − (p − ĥ − wf )g(ĥ) wf G(ĥ) − ξ
=
]2
[∫
√
ĥ
wf
)g(h)dh
(
ĥ
−
h
+
0
[√
]
∫ ĥ
∫ ĥ
√
√
−G(ĥ) 0 (p − h)g(h)dh − (p − ĥ − wf )g(ĥ) wf G(ĥ) − 0 (ĥ − h + wf )g(h)dh
=
.
]2
[∫
√
ĥ
wf
)g(h)dh
(
ĥ
−
h
+
0

dNe

Let J denote the numerator:
J = −G(ĥ)∫ ĥ(p − h)g(h)dh − (p − ĥ −

√

[

∫ ĥ
√
√
wf )g(ĥ)
wf G(ĥ) −(ĥ − h + wf )g(h)dh0= −G(ĥ)∫ ĥ

0∫ ĥ ()√(p − h)g(h)dh + (p − ĥ − wf )g(ĥ)
ĥ − h g(h)dh0= −G(ĥ)∫ ĥ

0(p − h)g(h)dh + (p − ĥ −√wf )g(ĥ)ĥG(ĥ) − (p − ĥ −√∫ ĥwf )g(ĥ)= −G(ĥ)0(p − h)g(h)dh + (p − ĥ −√wf )g(ĥ)ĥG(ĥ) − (p − ĥ −√wf )g(ĥ) ĥG(ĥ) −0= −G(ĥ)∫ ĥhg(h)dh
[

0

∫ ĥ

]

G(h)dh0(p − h)g(h)dh + (p − ĥ −0

= −pG(ĥ) + G(ĥ)
2

√

∫ ĥ
wf )g(ĥ)G(c)dh0∫ ĥ√hg(h)dh + (p − ĥ − wf )g(ĥ)
(
)
∫

∫ ĥ

0

ĥ

= −pG(ĥ)2 + G(ĥ) ĥG(ĥ) −G(h)dh+ (p − ĥ −G(h)dh0√∫ ĥwf )g(ĥ)

0= −pG(ĥ) + ĥG(ĥ) − G(ĥ)
2

∫ ĥ

2

G(h)dh0G(h)dh + (p − ĥ −√∫ ĥwf )g(ĥ)0G(h)dh0∫ ĥ
] ∫ ĥ
G(h)dh + (p − ĥ)g(ĥ)G(h)dh= −(p − ĥ)G(ĥ) − G(ĥ) + wf g(ĥ)
0
0
[
]
∫ ĥ
[
] ∫ ĥ
√2= −(p − ĥ) G(ĥ) − g(ĥ)G(h)dh − G(ĥ) + wf g(ĥ)G(h)dh.
2

[

√

0

0

42

]

∫ ĥ

Therefore, we have
[
]
dNp
dNe
dĥ
=
G(ĥ) + Ne g(ĥ)
ds
ds
dĥ
[
] [
]∫
∫ ĥ
√
ĥ
−(p − ĥ) G(ĥ)2 − g(ĥ) 0 G(h)dh − G(ĥ) + wf g(ĥ) 0 G(h)dh dĥ
=
< 0.
[∫
]2
√
ds
ĥ
0 (ĥ − h + wf )g(h)dh

(38)

[
]
∫ ĥ
This is negative because G(ĥ)2 − g(ĥ) 0 G(h)dh is positive, since G(ĥ) ≥ G(h) for all h ∈ [0, ĥ]and G(ĥ) > g(ĥ).

43