1

事業所立地点パターン

事業所ペア間距離

(各距離レベルの)集積の有無検定

cf. 地域ベースの集積度指標, e.g., Ellison-Glaeser (JPE 97), Mori et. al (REStat 05)

※ 地域間の空間関係無し → 地域単位を超えた集積/集積パターンは(内生的には)検出不可能

集積の空間範囲の検出

Duranton, G., Overman, H.G. (2005) “Testing for localization using micro-geographic data.” RES 72: 1077-1106.

2

K密度関数(事業所立地ベース）

⌅K(d) =1

n(n� 1)h

n�1⇤

i=1

n⇤

j=i+1

f

�d� di,j

h

⇥

⇤f(u) = 1⇥

2�exp

��u2

2

⇥

u = d�di,j

h

ガウスカーネルによる円潤化

“バンド幅”

事業所 i,j 間距離

n(n� 1)2

事業所ペア数：

各dにおける密度を2倍

�� �

0

⇥K(x)dx = 1

3

ランダム立地パターン（基準分布）

立地可能地点集合 ≈ 全産業事業所立地点集合Ellison-Glaeserと同様に集積の定義に関する問題e.g., 分散分布 ≈ 事業所数の大きい産業の分布

各産業の事業所数所与非復元無作為標本抽出

※ DOによる正当化： “立地可能な地点はほぼ埋め尽くされている → 現状立地がある地点以外を潜在的な立地点として含む余地が無い”

・実現した立地は、都心では密だし郊外では疎。・農地・住宅地は物理的に工業用地に転換できる。

→ 現状の集積地(特に大都市)を過大評価→ 結局、Ellison-Glaeserと同様の問題

}しかし…

4

5

(a) Basic pharmaceuticals (SIC 2441) (b) Pharmaceutical preparations (SIC2442)

! Point patterns of 4-digit industries

4桁産業の事業所立地• 事業所郵便番号の特定(176,106事業所）• UK SIC 3・4桁製造業 (234 4桁産業）

5

6

(c) Other agricultural and forestry machinery

(SIC2932)

(d) Machinery for textile, apparel and

leather production (SIC2954)

6

Distance (km) Distance (km)

(a) Basic pharmaceuticals (SIC 2441) (b) Pharmaceutical preparations (SIC2442)

K(d)

K(d)

K(d)

K(d)

ランダムパターンの局所的信頼区間(90%)

ランダムパターンの大域的信頼区間(90%)�K(d),K(d)

⇥

�K(d),K(d)

⇥

事業所間距離メディアン

集積

K(d)

7

局所的信頼区間(90%) : 各距離 d においてランダムK密度の90％を含む：

：d におけるランダムK密度上位5％ポイント：d におけるランダムK密度下位5％ポイント

K(d)

K(d)

大域的信頼区間(90%) : 全ての距離 d∈[0,180km] においてランダムK密度曲線の90％を含む：

5％のランダムK密度曲線：

⇥d � [0, 180km] s.t. Krand(d) > K(d)⇥d � [0, 180km] s.t. Krand(d) < K(d)

8

Distance (km) Distance (km)

(a) Basic pharmaceuticals (SIC 2441) (b) Pharmaceutical preparations (SIC2442)

相対的に集積

平均的な立地パターンと区別できない

9

9

(c) Other agricultural and forestry machinery

(SIC2932)

(d) Machinery for textile, apparel and

leather production (SIC2954)

If the peaks are only two, fine.Even though South-East region has

dense potential locations,

plants are fairly uniformly distributed.

相対的に分散

2地域に集積(少数集積地域がある場合にはピークが顕著)

10

多数の集積がある場合

個々の集積の空間範囲については平均的な値を検出できる。

集積間隔が一定でも、集積ペア間の距離は多様 → 明確な集積検出ができない

11

�i(d) = max⇥

�Ki(d)�K(d), 0⇤

⇥i(d) =

⇤max

�K(d)� ⇧Ki(d), 0

⇥if

⌅ 1800 �i(x)dx = 0

0 otherwise

産業 i の各距離レベル d における集積／分散度

i.e., 集積していない

全産業の各距離レベル d における集積／分散度

�(d) =�

i

�i(d)

⇥(d) =�

i

⇥i(d)

12

1090 REVIEW OF ECONOMIC STUDIES

TABLE 1

Localization at three thresholds for four-digit industries

Percentage of four-digit industries localized at:

5 km 5 km only 5 and 30 km only 5 and 150 km only 5, 30 and 150 km39·3 6·4 22·6 0·9 9·4

30 km 30 km only 30 and 150 km only38·9 6·0 0·9

150 km 150 km only17·1 6·0

(a) Global localization

100908070605040302010

00 20 40 60 80 100 120 140 160 180

Distance (km)

(b) Global dispersion

100908070605040302010

00 20 40 60 80 100 120 140 160 180

Distance (km)

(c) Local localization

100908070605040302010

00 20 40 60 80 100 120 140 160 180

Distance (km)

(d) Local dispersion

100908070605040302010

00 20 40 60 80 100 120 140 160 180

Distance (km)

FIGURE 3

Number of four-digit industries with local/global localization and dispersion

across distances, but not across the two figures.13 It is immediately apparent that the extent of

localization is much greater at small distances than large distances. As before, dispersion does

not show any marked pattern. The important conclusion we draw here is that localization tends

to take place mostly at fairly small scales.

13. This is because for an industry that exhibits localization the density is unbounded from above whereas thedensity of an industry that exhibits dispersion is bounded from below by zero.

#��global(d) > 0

⇥

#��local(d) > 0

⇥

#��local(d) > 0

⇥

#��global(d) > 0

⇥

※ 個々の集積範囲・集積の数の違いを判別できない

13

1100 REVIEW OF ECONOMIC STUDIES

TABLE 4

Localization at three thresholds for three-digit sectors

Percentage of three-digit sectors localized at:

5 km 5 km only 5 and 30 km only 5 and 150 km only 5, 30 and 150 km35·9 5·8 19·4 1·0 9·7

30 km 30 km only 30 and 150 km only38·8 7·8 1·9

150 km 150 km only19·4 6·8

(a) Global localization

100908070605040302010

00 20 40 60 80 100

Distance (km)120 140 160 180

(b) Global dispersion

100908070605040302010

00 20 40 60 80 100

Distance (km)120 140 160 180

FIGURE 8

Number of three-digit sectors with global localization and dispersion

localization in Pharmaceuticals (SIC244) might be driven mostly by the strong tendency of Basic

pharmaceuticals (SIC2441) to cluster. Alternatively, this finding could be driven by a tendency

for firms across different industries that are part of the same sector to co-localize at this spatial

scale. For instance in Pharmaceuticals (SIC244), firms in Pharmaceutical preparations (SIC2442)

may try to locate close to firms in Basic pharmaceuticals (SIC2441) just like producers of car

parts may seek to locate close to car assemblers.

Hence with regard to the localization of three-digit sectors, we must contemplate three

possible explanations. First, there could be a classification problem where the relevant level of

analysis is three-digit sectors instead of four-digit industries. Previous findings for four-digit

industries would then reflect what happens in sectors. Second, the classification problem may

be in the opposite direction and sectoral localization may just reflect localization of four-digit

industries. In this case, the relevant level of analysis is the four-digit industry since sectoral

localization is driven by localization in one or more industries within the sector. Third, and more

subtly, there may be some location differences between industries in the same sector so that the

relevant level of analysis is still the four-digit industry, but at the same time, there may also be

some interactions happening between these industries leading plants in different industries to opt

for locations close to one another.

To assess these three explanations, we look at the location patterns of industries within

sectors. In the next subsection we show that localization is still strong in four-digit industries

even after controlling for the location of the three-digit sectors. That is, the second and third

3桁産業の場合

※ 0～40km圏内は4桁レベル　 以下で集積

14

�(d)

一般的な集積範囲 ≈ 都市圏

15

各産業の集積度／分散度

�i =� 1800 �i(x)dx

⇥i =� 1800 ⇥i(x)dx

52%の4桁製造業：ある距離レベルで集積※ 全産業の分布が集積無しの基準となっていることに注意

16

1092 REVIEW OF ECONOMIC STUDIES

TABLE 2

Most localized and most dispersed four-digit industries

SIC92 Industry � or ⇥

Most localized

2214 Publishing of sound recordings 0·4701711 Preparation and spinning of cotton-type fibres 0·4112231 Reproduction of sound recordings 0·4031760 Manufacture of knitted and crocheted fabrics 0·3211713 Preparation and spinning of worsted-type fibres 0·3192861 Manufacture of cutlery 0·3141771 Manufacture of knitted and crocheted hosiery 0·2901810 Manufacture of leather clothes 0·2031822 Manufacture of other outerwear 0·1812211 Publishing of books 0·178Most dispersed

1520 Processing and preserving of fish and fish products 0·2003511 Building and repairing of ships 0·1131581 Manufacture of bread, fresh pastry goods and cakes 0·0942010 Saw milling and planing of wood, impregnation of wood 0·0822932 Other agricultural and forestry machinery 0·0671551 Operation of dairies and cheese making 0·0641752 Manufacture of cordage, rope, twine and netting 0·0623615 Manufacture of mattresses 0·0501571 Manufacture of prepared feeds for farm animals 0·0492030 Manufacture of builders’ carpentry and joinery 0·047

industries are also in the same list together with three media-based industries. These highly

localized industries are fairly exceptional. In contrast, the mean industry (after ranking industries

by their degree of localization) is barely more localized than if randomly distributed. It is mostly

food-related industries together with industries with high transport costs or high dependence on

natural resources that show dispersion.

Our main focus in this paper is on the proportion of manufacturing sectors that are localized.

However, it is interesting to notice that a number of industries that appear in Table 2 are fairly

small in terms of overall employment. This raises the question as to whether the percentage of

manufacturing workers employed in localized industries is above or below the percentage of

sectors that are localized. Weighting sectors by their share in manufacturing employment, we

find that 67% of U.K. manufacturing employers work in sectors that are localized. This shows

that localized sectors tend to have a larger share of manufacturing employment. Offsetting this,

however, is the fact that the employment share weighted mean of the index of globalization,

�A, is 30% lower than the unweighted mean of the index. That is, larger sectors tend to be less

strongly localized.

Finally, it is also interesting to notice that for many (two-digit) branches, related industries

within the same branch tend to follow similar patterns. Table 3 breaks down localization

of industries by branches. For instance nearly all Food and Drink industries (SIC15) or

Wood, Petroleum, and Mineral industries (SIC20, 23 and 26) are not localized. By contrast,

most Textile, Publishing, Instrument and Appliances industries (SIC17–19, 22 and 30–33) are

localized. The two main exceptions are Chemicals (SIC24) and Machinery (SIC29). In these

two branches, however, the more detailed patterns are telling. Chemical industries such as

Fertilisers (SIC2415) vertically linked to dispersed industries are also dispersed whereas those

like Basic Pharmaceuticals (SIC2441) or Preparation of Recorded Media (SIC2465) vertically

linked to localized industries are themselves very localized. The same holds for machinery: Other

17Research and Development Services are more likely to representnon-random clustering in Boulder than in Denver.

5. Global p-values

Lower local p-values provide greater evidence that a place spe-cializes in a given industry. However, if we are interested in evi-dence that an industry is specialized in any place, then inferencebased upon local p-values will overstate the amount of specializa-

tion. For example, assume that we define a standard critical local p-value of 0.05, and then perform hypothesis tests for an industryacross all 2601 places in our study area. Even if establishmentswere just randomly distributed across the study area, we wouldstill expect to find 130 places where we reject the null hypothesisof no specialization for a given industry. This result would lead usto naively conclude that all industries are subject to specializationin multiple places. This issue has been termed the multiple hypoth-esis testing problem. Though well established in statistics and bio-statistics, economists have only recently began to recognize and

Fig. 2. Population Kernel.

316 S.B. Billings, E.B. Johnson / Journal of Urban Economics 71 (2012) 312–331

Billings, S.B., Johnson, E.B. “A non-parametric test for industrial specialization.” JUE 71: 312-331 (2012)

個々の集積の空間範囲の特定　　→何らかの “クラスタリング”手法が必要

しかし … 小分類産業の事業所数中央値：1930 ≪立地可能地点数　→シミュレーションによるランダム立地信頼区間の導出は極めて困難

Duranton-Overmanによるランダム立地の大域的信頼区間の応用？

※ Duranton-Overmanの2次元化 → 上記問題の解消　 更に、Billings-Johnsonは “集積”ではなく “特化”を測っていると正しく認識している。