duranton-overman (res05) のk密度アプローチ - kyoto u...1 duranton-overman (res05)...

1

Duranton-Overman (RES05) のK密度アプローチ

データ：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

• 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）

cf. 地域ベースの集積度指標(e.g., EG(97), MNS(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

2

K密度関数(事業所立地ベース）

K̂(d) =1

n(n− 1)h

n−1∑

i=1

n∑

j=i+1

f

(d− di,j

h

)

{f(u) = 1√

2πexp

(−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

{∫ ∞

0K̂(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

EGと同様に集積の定義に関する問題

EGの場合と同様e.g., 分散分布 ≈ 　　事業所数(/雇用者数)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

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

5

6

(c) Other agricultural and forestry machinery

(SIC2932)

(d) Machinery for textile, apparel and

leather production (SIC2954)

6

Distance (km) Distance (km)


K(d)

K(d)

K(d)

K(d)

ランダムパターンの局所的信頼区間(95%)

ランダムパターンの大域的信頼区間(95%)[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)


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

Γi(d) = max{

K̂i(d)−K(d), 0}

Ψi(d) =

{max

(K(d)− K̂i(d), 0

)if

∫ 1800 Γi(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

Γ(d) =∑

i

Γi(d)

Ψ(d) =∑

i

Ψi(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.

#{Γglobal(d) > 0

}

#{Γlocal(d) > 0

}

#{Ψlocal(d) > 0

}

#{Ψglobal(d) > 0

}

※ 個々の集積範囲の違い？　集積の数の違い(1 vs 2)?

13


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

1009080706050403020100

0 20 40 60 80 100Distance (km)

120 140 160 180

(b) Global dispersion

1009080706050403020100

0 20 40 60 80 100Distance (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

Γ(d)

一般的な集積範囲 ≈ 都市圏

15

各産業の集積度／分散度

Γi =∫ 1800 Γi(x)dx

Ψi =∫ 1800 Ψi(x)dx

52%の4桁製造業：ある距離レベルで集積

産業分布※ 全が集積無しの基準となっていることに注意

16


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

17

K̂emp(d) =

∑n−1i=1

∑nj=i+1 e(i)e(j)f

(d−di,j

h

)

h∑n−1

i=1

∑nj=i+1 e(i)e(j)

K密度関数(雇用者立地ベース）

事業所 i の雇用者数

（同一事業所内の雇用者間距離は無視）

※ 43% (vs 事業所ベース52%)の産業が集積

18


(a) Number of localized industries

100908070605040302010

00 20 40 60 80 100

Distance (km)120 140 160 180

(b) Index of global localization

0·260·240·220·200·180·160·140·120·100·080·060·040·020·00

0 20 40 60 80 100Distance (km)

120 140 160 180

FIGURE 7

Global localization when weighting establishments by their employment

industries in Electrical machinery show localization in the initial results whereas only one still

shows localization when weighting establishments by employment. In two other branches, Food

and beverages (SIC15) and Other non-metallic mineral products (SIC26), the exact opposite

happens. For instance, only one food industry in the baseline shows localization while five do

when weighting by employment.

These findings are fully consistent with those obtained when censoring for smaller firms.

Furthermore findings reported in Holmes and Stevens (2002) allow a comparison with U.S.

manufacturing although we note that his comparison should be interpreted with caution given

differences in the methodologies employed. Holmes and Stevens (2002) examine the location

patterns of large plants in U.S. manufacturing using the EG index. They find that large plants

tend to be more localized than their whole industry. In broad agreement with this tendency, we

observe an increase in our index of localization, !(d), for the U.K. when censoring for small

plants. However, in contrast with U.S. findings, localization in the U.K. is driven by large firms

in only some industrial branches.

More generally, it must be emphasized that taking plant size into account reinforces the

four main conclusions obtained so far.17 Localization is detected in at most half of the industries.

Deviations still occur at a scale of 0–50 km. There is still a lot of cross-industry heterogeneity

with respect to localization and dispersion. This is compounded by cross-industry differences in

location patterns between small and large establishments. Finally we observe broad patterns of

clustering of small vs. large establishments by industrial branch.

Before turning to a detailed comparison between our approach and the EG index, it

must be noted that the two approaches developed here to examine patterns of localization by

establishment size could be further refined. Instead of considering only one threshold, we could

consider finer classes of establishment sizes in each industry. The counterfactuals could also

be modified. For instance, imagine that establishment size constrains location choices to a set of

“appropriate” sites. Then, we could construct counterfactuals that only allow large firms to locate

on large sites and small firms to locate only on sites currently occupied by a small firm. These

questions as well as broader issues about which type of establishment localize (e.g. independent

17. Interestingly when industries are ranked by decreasing localization the Spearman rank correlation whenweighting by employment with the baseline is 0·77 whereas that with the ranking when censoring for establishmentsize is 0·74.

(a) 集積を示す産業数 (b) 集積度

事業所ベースとは異なる集積範囲※ 個々の集積範囲の違い？　集積の数の違い(1 vs 2)?

# {Γemp(d) > 0}

Γemp(d)

19

異業種事業所間距離のK密度

事業所ペア数

{同一産業：

異業種：

nA(1− nA)/2nAnB

{

K̂(A,B)(d) =1

P (nA, nB)

nA∑

i=1

nB∑

j=1,j !=i

f

(d− dij

h

)

産業AとBの事業所数を固定→非復元無作為抽出

Γ(A,B)(d) = max{

K̂(A,B)(d)−K(A,B)(d), 0}

20

産業ペア数

#{Γ(A,B)(d) > 0

}

都市圏より広域で最大のピーク

21

K̂(d) =1

nmh

n∑

i=1

m∑

j=1

f

(d− dij

h

)

Duranton-Overman (JRS08)

•新規立地事業所 vs 既存事業所•系列事業所 vs 非系列事業所•外資系事業所 vs 内資系事業所•小規模事業所 vs 大規模事業所•投入産出連関した事業所

22

DURANTON AND OVERMAN: MANUFACTURING INDUSTRIES 225

DispersionlabolG(b)LocalizationlabolG(a)

FIGURE 3. Number of Industries in Which Entrants Are Localizedor Dispersed.

CodispersionlabolG(b)ColocalizationlabolG(a)

FIGURE 4. Number of Industries for Which Entries Are Colocalized andCodispersed with Existing Establishments.

(or 9 percent) have entrants that are colocalized with existing establishmentswhereas, interestingly, about twice as many industries, 41 (or 20 percent), arecodispersed. Again, this is consistent with our suggestion that some industriesare changing location over time.

When plotting, in Figure 4, the number of industries by distance for whichentrants are colocalized and codispersed with existing establishments, we findan interesting tendency for colocalization to take place at very short distances(below 20 km). Among the industries for which entrants colocate most closelywith existing establishments, we find various media and publishing indus-tries as well as some high-tech industries suggesting that this colocalizationmay be driven by the creation of spin-offs that tend to locate very close to the

C© Blackwell Publishing, Inc. 2008.

新規立地事業所 vs 既存事業所

23

228 JOURNAL OF REGIONAL SCIENCE, VOL. 48, NO. 1, 2008


FIGURE 6. Number of Industries for Which Establishments of the SameFirms Are Localized and Dispersed.

Manufacture of Bread (SIC1581), Cold Rolling of Narrow Strips (SIC2732), Manu-facture of Rusks and Biscuits (SIC1582), and Other Processing of Iron (SIC2735).This is arguably a very heterogeneous group of industries although they do in-volve either a multistep production process (e.g., producing dough and baking itin bread production) or some form of output differentiation (e.g., maintenanceof tractors along with maintenance of their equipment, tiller or loader, in agri-cultural machinery). Firms in these industries may well be organized aroundspecialized establishments located close to each other. In contrast, among theindustries for which the establishments within firms are most dispersed, wefind industries such as Manufacture of Machinery for Paper (SIC2955), Manufac-ture of Articles of Cork, Straw and Plaiting Materials (SIC2052), or Manufactureof Cordage and Rope (SIC1752). It is likely that these industries involve veryspecialized producers that disperse their establishments to best serve differentmarkets. Remember, however, that this pattern is far less widespread than theclustering of establishments that belong to the same firm.17

As argued above, a natural interpretation is that this within-firm cluster-ing of establishments reflects the organizational strategies of firms that decideto separate their production activities across different establishments locatedclose to each other. The characteristics of the industries with the most localizedsame-firm establishments and the spatial scale at which this clustering takesplace are certainly supportive of this interpretation. However, it may also bethat the firms located in clusters also have more establishments. In this case,the clustering of establishments within the same firm would partly reflect a

17Interestingly there is a significant negative Spearman-rank correlation across industriesbetween same-firm establishment localization and the localization of the industry relative to man-ufacturing. This suggests that the patterns of localization exhibited in Duranton and Overman(2005) are not driven by the clustering of establishments within firms.


系列事業所 vs 非系列事業所

24



FIGURE 7. Number of Industries with Localization and Dispersion of TheirForeign-Owned Establishments.

strong tendency for establishments that belong to the same firms to cluster. Onthe other hand, there is no particular tendency for multiestablishment firms tocluster together or for affiliated establishments to cluster with single plants.

6. FOREIGN VERSUS DOMESTIC OWNED ESTABLISHMENTS

We now turn to questions relating to the location of foreign versus do-mestically owned establishments. The widespread tendency of foreign-ownedestablishments to cluster has been often noted and studied (e.g., Guimaraes,Figueiredo, and Woodward, 2000; Head and Mayer, 2004). The two issues thatwe consider here have received considerably less attention. First, we ask if theclustering of foreign-owned plants is more or less pronounced than that of do-mestic establishments. Then, we turn to the question of whether foreign-ownedestablishments locate near or far from domestic ones. We start by consideringwhether foreign-owned establishments locate closer to each other than any ran-dom pair of establishment in the industry. To do this, we look at the distributionof distances between foreign-owned establishments as opposed to distances be-tween randomly chosen establishments in the industry regardless of ownership.That is, we apply equation (1) to distances between foreign-owned establish-ments (rather than entrants) and generate our counterfactuals by randomlyreallocating foreign ownership of plants within the industry.

To perform our analysis, we retained the 106 industries with at least 10foreign owned establishments. We find that only 11 industries (or 10 percent)exhibit localization of foreign-owned establishments while 24 (or 23 percent)exhibit dispersion. Figure 7(a) plots the number of industries for which foreign-owned establishments localize by distance. There is no clear pattern in terms ofthe distances at which localization occurs in this context aside from a mild ten-dency to localize at shorter distances. Figure 7(b) plots the number of industries


外資系事業所

25



FIGURE 8. Number of Industries with Localization and Dispersion of TheirTop Decile of Largest Establishments.

To shed more light on this issue, we perform a number of exercises usingequations (1) and (2). We start by asking whether the largest establishmentsare clustered within industries. To answer this question, we compare the distri-bution of distances between these large establishments to the same distributionin counterfactual industries obtained by randomly reallocating these large es-tablishments across sites occupied by the industry.

To begin, we defined large establishments as those in the top decile ofemployment in their industry. We considered the 172 industries with at least10 firms in their top decile of employment. We find that large establishmentsare localized in 91 industries (or 53 percent) and dispersed in only 26 (or 15percent). Figure 8 shows that the localization of large establishments has amild tendency to occur at small spatial scales, below 50 km. By contrast, thereis no obvious spatial scale at which dispersions occur.

When looking at the reality that underlies the figures above, we find avery heterogeneous group of industries for which the localization of the largestestablishments is strongest: Reproduction of Video Recordings (SIC2232), Man-ufacture of Ceramics (SIC2621), Manufacture of Hosiery (SIC1771), Manufactureof Locks (SIC2863), and Manufacture of Distilled Potable Beverages (SIC1591).Despite their heterogeneity, what all these industries have in common is the factthat they are, themselves, highly localized relative to overall U.K. manufactur-ing. This finding, however, does not hold more generally: The Spearman-rankcorrelation between the index of localization for the largest establishmentswithin the industry and the index of localization for the entire industry rela-tive to overall manufacturing (as computed in Duranton and Overman 2005) issmall and insignificant.

We replicated the exercise, this time for establishments in the top quartilerather than the top decile. Out of 211 industries (with at least 10 establish-ments in their top quartile), 121 (or 57 percent) have localized top-quartile


大規模事業所の集積(上位10%)

26



FIGURE 9. Number of Industries with Localization and Dispersion of TheirTop Quartile of Largest Establishments.

establishments while 24 (or 11 percent) exhibit dispersion. As shown by Fig-ure 9, the spatial pattern of localization is even more marked than in Figure8. This suggests that the tendency of large establishments to localize is notthe preserve of the very largest establishments. Quite the opposite, the es-tablishments with the strongest tendency to agglomerate tend to be those inthe top quartile but not in the top decile. As for the top decile, the Spearman-rank correlation with the index of localization is insignificant showing thatthe industries where the larger firms localize are not necessarily localizedoverall.

This localization of larger establishments is not the entire story. When weperformed the same exercise, but this time for the decile of smallest establish-ments, we find that 89 industries in 194 (or 46 percent) exhibit localization oftheir smallest establishments while 29 (or 15 percent) exhibit dispersion.23 Verysimilar figures are obtained when looking at the bottom quartile: 99 industriesin 213 (or 46 percent again) experience localization of their bottom quartile es-tablishments whereas 37 (or 17 percent) experience dispersion of their smallerestablishments. Overall these findings suggest that small-establishment alsocluster within their industry, but that this clustering is weaker than the clus-tering tendency of large establishments.

In Figure 10, we plot the number of localized and dispersed industries forestablishments in the bottom decile by distance.24 These two figures differ quite

23The number of industries is not the same as with the top decile because the existence ofmany establishments at the cut-off size allowed us to keep a number of industries with fewer than100 establishments (but with nonetheless 10 or more establishments in their bottom “decile” afterrounding).

24The patterns for the bottom quartile are the same.


大規模事業所の集積(上位25%)

27



FIGURE 10. Number of Industries with Localization and Dispersion of TheirBottom Decile of Smallest Establishments.

a lot from those in Figure 8. More specifically, the pattern for localization inFigure 10(a) is hump-shaped with an increase between 0 and 30 km followedby a decrease before reaching a low plateau. For dispersion, we observe a milddecrease between 0 and 60 km followed by a low plateau in Figure 10(b). Thesepatterns are intriguing. We leave our interpretation until after the examinationof distances between different sizes of establishments.

Distances between Establishments across Size Classes

We analyze the colocation patterns of large and small establishments us-ing equation (2) for distances between establishments in the top quartile andthose in the other three quartiles.25 Again the counterfactuals were constructedby randomly reallocating the actual distribution of establishment employmentacross sites occupied by the industry. Among 211 industries (with more than10 establishments in their top quartile), 59 (or 28 percent) exhibit colocaliza-tion between large and small establishments whereas 43 (or 20 percent) exhibitcodispersion.

These findings and those above concerning the concentration of small es-tablishments are consistent with small establishments often being located closeto large establishments at very short distances (as a result, for instance, ofspin-offs).26 It is only for slightly larger distances that the tendency for small

25Performing the same exercise between top-decile establishments and those in the bottomnine yields similar results.

26This can make them look weakly localized or even dispersed depending on whether largeestablishments are themselves localized or dispersed at these short distances as reflected in Figure10.


小規模事業所の集積(下位10%)

28



FIGURE 12. Number of Colocalized and Codispersed Pairs ofVertically-Linked Industries (Demand Linkages).

as well as Plastic Products.36 On the other hand, among the most codispersedindustries, we have Plastic Products selling to Meat Processing, Fertilizers, andFish and Fruit Processing as well as Other Metal Products selling to AlcoholicBeverages, Insulated Wire and Cable, Fish and Fruit Processing, and AnimalFeeds. These examples suggest that industries may colocalize when they arefundamental to each other and when the final output is easy to transport (likewith Leather and Footwear) whereas codispersion is observed when the clientindustry is only one among several and when the final output (or some otherkey input) is much more costly to transport than the intermediate output (likethe industries above using plastic to package their final goods).

Finally, when plotting the number of pairs of industries that that colocalizeand codisperse in Figures 12(a) and 12(b) some interesting patterns emerge.Starting with Figure 12(b), it is interesting to note that the cases of codis-persion decline when larger distances are considered. Recall that these aresituations for which establishments are closer to other establishments in thesame industry than establishments in the companion vertically-linked indus-try. As industry localization is observed at distances below 60 km (Durantonand Overman, 2005), this graph may not be very surprising and is likely toreflect the tendency of industries to localize at small spatial scales. Put dif-ferently, codispersion between industries at small spatial scales may be thecounterpart of industry localization. The first part of the graph on the left(in Figure 12a) is more interesting because it shows that the colocalizationtends to become more important at larger spatial scales, that is, at the regionallevel.

36These strongly colocalized industries also appear prominently in the mirror analysis usingthe “demand” input–output matrix.


投入産出連関事業所の集積

duranton-overman (res05) のk密度アプローチ - kyoto u...1 duranton-overman (res05)...

Documents