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Empirical Analysis of Transport Network and System of Cities:

Case Study of Tohoku Area, Japan

By Se-il Mun

Graduate School of Economics, Kyoto University Yoshida Hon-machi, Sakyo-ku, Kyoto 606-8501, Japan

Fax: +81-75-753-3492 E-mail: mun@econ.kyoto-u.ac.jp

and Komei Sasaki

Graduate School of Information Sciences, Tohoku University Katahira 2 cho-me, Aoba-ku, Sendai 980-8577, Japan

June 2000 Abstract

A general equilibrium model of a multi-region economy with agglomeration effects and transport network is developed and applied to Japanese data. The model determines population distribution (i.e., population in each region), industrial location (i.e., type of industry, level of output in each region), inter-regional trade patterns, wages, prices of goods, land rent, and the utility level of households. Parameters of the model are estimated by using the data of Tohoku region in Japan. It is shown that the model traces the spatial variations of population, wage, and output levels of each industry. By using the model, the effects of transport network improvement on spatial structure are analyzed and welfare of residents is evaluated.

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1. Introduction

In Japan, since the end of World War II, the three largest metropolitan areas (Tokyo, Osaka and Nagoya) have constantly experienced population growth and, in particular, the Tokyo metropolitan area has been attracting positive net population in-migration. In brief, population and economic activities have continued to concentrate in a few of the larger areas. The central government has attempted to alter this tendency of concentration so as to disperse population and economic activities from central metropolitan areas to peripheral, less-dense areas through transportation system improvements, industry-related infrastructure investment, lower taxes and subsidies. Among them, vast amount of money have been spent for investment in transportation infrastructure, expecting to play important roles in reorganizing spatial structure of the economy. However, this effort has not been very successful because such policies have not been effective in modifying the results brought about by market forces. In other words, planners intending to change the spatial structure of the economy need to investigate carefully the market forces prevailing in the existing system of regions. The present research is motivated by this observation.

Urban economists have developed models to explain how the size of each city is determined in a system of cities with emphasis on the role of agglomeration economies (e.g., Abdel-Rahman [1990], Henderson [1987], Kanemoto [1980]). However, they have not taken into account the spatial factors such as the location of cities and distances or transport costs between them. Therefore, such models are not capable of explaining what type of city has developed at each location, how large it is, and how inter-city transport improvements affect its size and scope.

New theories of spatial agglomeration have been developed and flourishing in 1990’s.

Krugman [1991] presented a model of interregional trade with scale economies and investigate the relations between transport cost and industrial concentration. Various extensions of the model have been made recently, e.g., endogenous determinants of cities’ locations (Fujita and Krugman[1995]),

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incorporation of multiple industrial sectors (Fujita, Krugman and Mori[1995]), intra-city land use (Tabuchi[1996], Helpman[1998]), and inter-city transport networks (Mun[1997]). Most models, however, treat only two-city economies or cities locating in a one dimensional space. Furthermore, most of the existing studies cited above have been confined to theoretical analysis or numerical simulation with hypothetical parameters. It has been recognized that the properties of spatial economies with increasing returns are indeed ambiguous. For example, Tabuchi[1996] showed that a reduction in transport cost may cause either a concentration or a dispersion of activities, depending on the initial conditions and parameter values. Thus empirical analysis is needed to know what will happen in reality.

This paper investigates empirically the relations between transport system and urban agglomeration by using a general equilibrium model of multi-region economy in which regions are connected by transport network. The "Tohoku" area (hereafter, the T-area) in the north-eastern part of Japan is chosen as a case study area. For the purpose of this study, T-area is divided into 37 regions, each of which consists of central city and surrounding hinterland. The largest region (whose central city is Sendai) in this area has a population of 1.29 million and the smallest one (central city is Nagai) has 72,500. The average regional population is 263,000 (see Table 1 and Figure 1).

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Region Representative Population Class Code City of Region

1 Aomori 323604 II

2 Hachinohe 352240 II

3 Hirosaki 350603 II

4 Towada 286990 III

5 Goshogawara 169436 IV

6 Morioka 536579 I

7 Ofunato 82689 V

8 Hanamaki 198602 IV

9 Ichinoseki 154389 IV

10 Miyako 190400 IV

11 Kamaishi 106481 IV

12 Mizusawa 147788 IV

13 Sendai 1292282 I

14 Furukawa 223144 III

15 Ishinomaki 237353 III

16 Shiroishi 196143 IV

17 Kesen-numa 114468 IV

18 Tsukidate 185168 IV

19 Honjo 127327 IV

20 Akita 430784 I

21 Noshiro 109635 IV

22 Omagari 165848 IV

23 Kaduno 190946 IV

24 Yuzawa 202938 III

25 Yamagata 465910 I

26 Sakata 161458 IV

27 Yonezawa 180795 IV

28 Shinjo 102214 IV

29 Tsuruoka 166905 IV

30 Nagai 72567 V

31 Obanazawa 108541 IV

32 Fukushima 489514 I

33 Iwaki 433386 I

34 Koriyama 559599 I

35 Aidu-wakamatsu 336785 II

36 Haranomachi 133211 IV

37 Shirakawa 151563 IV

Table 1 37 regions in the T-area

Note: Class division of regions based on population I

II III IV V

) (Ni

Ni

<

400000

400000 300000<Ni

300000 200000<Ni

200000 100000<Ni

100000

i N

(5)
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The subject to be examined in this study is the effects of transportation network change on the distribution of economic activities among regions in the T-area. It is of interest whether improvements in the transportation network of the T-area will disperse economic activities and population among the regions, or will result in the agglomeration in a few regions. This will be examined by simulation analysis. We also evaluate the welfare effects of alternative patterns of network improvements. From this, we could have information concerning which pattern of network improvement is desirable.

The paper is organized as follows. In section 2 the basic theoretical model is presented. Section 3 shows the estimation results of the model, and tests of the model concerning the fitness between estimated and observed values. Section 4 presents the simulation analyses concerning the effects of transport system change on the spatial distribution of economic activities and social welfare.

Concluding remarks are presented in section 5.

2. The model

The theoretical framework for this study is a spatial general equilibrium model, which is based on Mun [1997]. Briefly, this model consists of four markets: commodities, labor, capital and land.

Households and firms are assumed to search for their locations within a multiple-region area (e. g., the T-area) so as to maximize utility and profit, respectively, based upon which spatial equilibrium prices and equilibrium (inter-regional) trade patterns are determined. In an equilibrium, the utility level of a household and the profit of a firm are equal in every region.

2.1 Model assumptions

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The basic assumptions employed in the model are:

1. Firms and households can move freely between regions in the T-area.

2. There is no migration between the T-area and rest of the world. The population in the T-area is fixed (i.e., a large area is closed).

3. Land in each region is used only for households' residences. Residents in a region have equal ownership over the land in that region, so land rental revenue in a region is equally distributed among the residents in that region.

4. M different commodities and services are produced in the T-area by employing labor and capital inputs (intermediate inputs are neglected).

5. In transporting a particular commodity between regions, a certain amount of that commodity is consumed as transport cost (i.e., ice-berg type transport cost is assumed).

6. Capital is mobile between the T-area and rest of the world. The current balance between the T-area and the rest of the world is in equilibrium, so that the difference between the T-area's imports and exports is covered by capital net inflow (or outflows) from (or to) the rest of the world.

7. Every resident in the T-area has equal ownership over a given amount of capital, K , and the capital rent revenue is equally distributed among residents in the T-area.

2.2 Behavior of a firm

A Cobb-Douglas type production function is assumed.

m

m m a

i a m i i m m m

i G N L K

y =δ ( )( ) ( )1 (1) in which the superscript denotes a type of commodity (industrial sector) and the subscript ( ) a particular region. In (1),

) , 1

(m M

m = "

i i=1,"I L and K are, respectively, labor and capital

inputs, and Gm(Ni)expresses agglomeration economies measured as a function of regional

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population, . Agglomeration of population and economic activities in a specific location causes positive externalities for several reasons: cost of materials is lower because of collective purchasing; firms have better access to market trend information relating to the industry; scale economies in related sectors (such as transportation and repair services) work so as to lower the cost incurred by firms; and the search cost of labor is cheaper and the quality of labor higher relative to other regions.

Ni

Under the specification in (1), input demand functions are derived as

m i m i i m m

i q y

w

L = a (2a)

m i m i m m

i q y

r K (1−a )

= (2b) M

m I

i=1," , =1,"

where: qim is the f.o.b. price of commodity m produced in region i ; wi and r are, respectively, wage rate in region and capital cost common in a nation. The maximized profit is zero in a competitive market, and if firms produce positive amounts, then the average cost is equal to the commodity supply price. If the f.o.b. price is lower than the average cost, then output of that commodity is zero in the region. Namely it holds that:

i

≥0

m

yi when qim =Cm(Ni,wi,r) (3a)

=0

m

yi when qim <Cm(Ni,wi,r) (3b) where Cm is the average cost.

2.3 Behavior of a household

The utility function of a household is specified in the following form.

=

+

= M

m

m i m

i x

h U

1

ln

ln β

α (4) where h is residential lot size, and xm is consumption of commodity m. In (4), it is assumed

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that α +

βm =1. Income constraint of a household is

i h i M

m

m i m i i

i h i

i p x p h

N K r N

H

w + p + =

+

=1

(5)

in which is the c.i.f. price of commodity in region (which is different from ), and is the land rent in region . The second and third terms on the LHS in (5) are, respectively, the distributions from land and capital rental revenues. The variables and are, respectively, total land size in region and total population in the T-area.

m

pi m i qim

h

pi i

Hi N

i

A household in region plans consumption bundles so as to maximize (4) subject to (5). Noting that

i

i i

i N

h = H , the following are optimum conditions.

) 1 (

1 N

K w r

x pm i

i m m

i +

= − α

β (6a)

) 1 (

1 N

K w r

h ph i

i

i +

= − α

α (6b)

2.4 Interregional trade

Suppose a consumer has a demand for commodity . He (or she) does not care where that commodity is produced as long as the quality is the same. However, if the supply price of that commodity differs (depending on where it is produced), then he (or she) rationally chooses commodities with the lowest c.i.f. price. In the circumstance of perfect competition, c.i.f. price is the sum of f.o.b. price and transport cost. Thus, in the strict sense, it holds that

m

min mj (1 m ij) (7)

j m

i q t d

p = +

where is the transport cost of commodity per unit per distance, and is the physical distance between regions and . However, in reality, commodities consumed in a particular region are shipped from regions even though the theoretical c.i.f. price from those regions is not the

tm m dij

i j

(10)

lowest. Furthermore, there are many actual patterns of "cross-hauling" between regions although, theoretically, they cannot take place. Such counter-theoretical phenomena are observed mainly because the classification of industrial sectors is not fine enough to ensure the homogeneity of product in a particular sector. Thus, from the standpoint of better explaining as modeling reality, the following probabilistic approach is employed [Footnote1].

It is assumed that, in consuming a commodity, each consumer chooses a firm which produces that commodity on the basis of her own preference towards a particular firm. The choice depends not only on the "theoretical" c.i.f. price level but on each consumer's preference [Footnote2]. The cost incurred by a consumer in region for purchasing a commodity m from a firm in region is expressed as

i f

j

m jf ij m m

jf t d

q (1+ )+ε

In this expression is a consumer specific preference term and varies among consumers in region . Thus is regarded as being distributed among consumers according to a specific density function. In this situation, the probability that a randomly drawn consumer in region chooses firm in region is represented as

m

εjf

i εmjf

i

f j

{

ki kfm

}

m m kf m jf ji m m

jf t d q t d

q (1 ) '(1 ) '

Prob + +ε ≤ + +ε for all k and f' (8) if εmjf obeys the Weibull function with parameters (0,λm), then the probability in (8) is obtained as

+

+

= −

k

ki m m k m m

k

ji m m j m m

jfi n q t d

d t S q

)]

1 ( exp[

)]

1 ( exp[

λ

λ (9)

where is the number of firms in sector in region . Thus, the probability that some firm in region is chosen is

m

nk m k

j

+

+

= −

k

ki m m k m m

k

ji m m j m m

m j

ji n q t d

d t q S n

)]

1 ( exp[

)]

1 ( exp[

λ

λ (10)

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The data on number of firms is not available, so the total regional output is used as a proxy on the presumption that the average size of a firm is the same among regions: i.e.,

m

yi

+

+

= −

k

ki m m k m m

k

ji m m j m m

m j

ji y q t d

d t q S y

)]

1 ( exp[

)]

1 ( exp[

λ

λ (11)

using the estimate of Smji, the shipped quantity of commodity m from region j to region is estimated as

i

{ }

mji

m i m m

i i m

ji N x E S

Z = (1−µ )+ (12) where is the import coefficient (common to all the regions) and denotes the quantity of commodity m exported outside the T-area from region .

µm Eim

i

Finally, the supply purchase price in region is defined as the average of c.i.f. price: i.e., i

+

=

j

ji m m j m ji m

i S q t d

p (1 ) (13) 2.5 Market equilibrium

Equilibrium conditions in this system are represented as follows.

Labor market:

= M =

m

i m

i N

L

1

I

i=1," (14a)

= I =

i

i N

N

1

(14b) Commodity market (at the location of consumption):

=

= +

I

j m ji m

i m m

i

ix E Z

N

1

) 1

( µ i=1,"I m=1,"M (15)

Commodity market (at the location of production):

=

+

= I

j

ij m m ij m

i Z t d

y

1

) 1

( i=1,"I m=1,"M (16) Current balance with the rest of the world (see assumption 6 in section 2-1):

∑∑

∑∑

∑∑

= = = = = =

⎟⎟=

⎜⎜ ⎞

⎛ − I

i M

m

m i i m i m I

i M

m

m i m i I

i M

m m

i K q E p N x

K r

1 1

1 1

1 1

µ (17)

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Households location:

U x x x h

U( i, i1, i2," in)= i=1,"I (18) In this system, the numeraire is the price of capital service, r which is set to utility. Endogenous

variables of the system are: and U. In the subsequent

sections, the models in (1) through (13) are estimated using the cross-section data at 1990; and, on the basis of the estimated structures, the " theoretical value" of each endogenous variable is calculated.

i h i m i m i i m ij m ij m i m i i m

i h y L Z S w q p p N

x , , , , , , , , , ,

3. Estimation of parameters and test of the model

The data required for the subsequent empirical analysis include population, employment, output of each industry, wage, land area, distances between each pair of regions, and interregional trade.

Data on population and employment of each region are obtained from the Population Census. Data on industrial output and wage are obtained from Annual Report on Prefectural Accounts published by each prefecture. Data on land area are obtained from property tax register reports. The distance between each pair of regions was measured as the shortest time path between the central cities of regions along the road network shown in Figure 2.

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3.1 Production function

A statistical model for estimating the production function in (1) is specified in the following way.

m i a

m i

m i i m m m i m

i e

L N K L G

y

m

⎟⎟ +

⎜⎜ ⎞

= ⎛

1

)

δ ( (19)

where Gm(Ni) represents the agglomeration economies, and eim is error term.

There is extensive literature on empirical analysis of agglomeration economies in production (e.g., Sveikauskas[1975], Sasaki[1985], Nakamura[1985], Henderson[1986]). Our hypothesis, distinct from the analysis so far, is that there is some threshold level of regional population above which agglomeration economies start working. That is,

⎪⎩

⎪⎨

<

= ≥

m i m

m i i

i m

N N when N

N N when N N

G

m m

σ σ

)

(

in which Nm is the threshold level of population for industry . In the conventional specification of the agglomeration economics effect, it is implicitly assumed that externality effects work even for small population. However, such benefits as are cited above (e.g., lower purchase cost of materials, lower labor search cost, and better access to information) cannot be realized in a small population, i. e., in a region that is below the threshold.

m

Data on capital stock were not available. Instead, the value of K was estimated in the following way. Under a linear homogeneous production function and a competitive market, the total value added is fully distributed between capital and labor inputs. Then, defining the price of capital service to unity, the amount of capital stock was calculated as K =qywL.

In our model, the threshold level Nm itself is estimated. Estimation was repeatedly performed by changing the value of Nm by 100,000, and the estimated structure with the highest R2 was selected. The value of Nm associated with the selected structure is regarded as the estimate of threshold population level. Such an estimation method is similar to the likelihood maximization approach.

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Industries were classified into 20 sectors as shown in Table 2.

Table 2 Industry classification

Industry Code Industry

1 Lumber & wooden products 2 Textile mill products

Furniture & fixtures Leather & leather products

3 Chemical

Petroleum refining & related products Transport equipment

4 Plastic products Electrical machinery

5 Food products

6 Precision machinery Other manufacturing

7 Stone, clay, and glass products 8 Beverage, feed, & tobacco

Iron & steel Metal products 9 Printing & publishing 10 Apparel & related products

Pulp, paper, & allied products Rubber products

Nonelectrical machinery 11 Nonferrous metal industry 12 Agriculture, forest, & fishery

13 Mining

14 Construction

15 Wholesale & retail

16 Finance, insurance, & real estate 17 Transport, communication 18 Electricity, gas supply

19 Service

20 Government

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0 10 20 30 40 50 60 0.86

0.87 0.88 0.89 0.9 0.91 0.92 0.93

N R2

Figure 3 Estimation of population threshold level (for Industry 7) (10 thousand)

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Table 3 Estimation results of sectoral production function

Industry Code

1 0.3827 (2.635) 0.1738 (6.033) 20 0.4864 (17.110) 0.9001 2 0.1581 (3.171) 0.2561 (5.498) 20 0.8069 (7.363) 0.7898

3 1.0706 (0.148) 0 0.2855 (48.128) 0.9871

4 0.6152 (0.947) 0.1451 (3.522) 20 0.5796 (18.233) 0.9217

5 0.2926 (0.840) 0 0.7489 (10.082) 0.7576

6 0.4932 (1.266) 0.1676 (3.743) 20 0.7087 (13.153) 0.8586 7 0.7755 (1.025) 0.1096 (5.675) 20 0.4118 (17.924) 0.9215 8 0.7032 (1.071) 0.1115 (4.034) 20 0.3589 (27.828) 0.9716 9 0.6071 (0.936) 0.1472 (3.410) 20 0.5914 (12.269) 0.9193 10 0.6242 (1.127) 0.1475 (4.480) 0 0.6029 (15.984) 0.9609

11 1.3145 (0.323) 0 0.5690 (10.977) 0.8959

12 3.9354 0 0.8180

13 2.1510 (22.814) 0 0.2090 (61.345) 0.9823

14 0.6016 (1.512) 0.1389 (5.075) 20 0.5073 (18.8769 0.9309 15 0.1842 (3.561) 0.2429 (6.385) 20 0.8586 (5.780) 0.6869 16 1.0710 (0.695) 0.0339 (5.605) 20 0.1193 (78.872) 0.9957 17 0.5069 (1.836) 0.1573 (5.162) 20 0.5554 (15.139) 0.9118 18 0.9492 (0.782) 0.0333 (6.383) 20 0.0786 (184.520) 0.9990 19 0.4999 (2.130) 0.1646 (6.372) 20 0.6310 (15.747) 0.8885 20 0.5470 (2.261) 0.1226 (5.638) 20 0.2844 (46.106) 0.9860

m N σ

δm am R2

In fifteen of the twenty sectors, the value of R2 reacted to changing Nm in an inverted-U shape, so that a maximum of R2 can be obtained (Figure 3 shows the case of industry 7). The estimation results are shown in Table 3. Goodness-of-fit of the model in (19) is generally high: in thirteen sectors R2 is above 0.9.

Surprisingly and interestingly, the threshold level of population was 200,000 in every sector. This implies that a population concentration of at least 200,000 is a prerequisite for agglomeration economies to work. Therefore it follows that, according to the population size in 1990, agglomeration economies do not occur in twenty-one of the thirty-seven regions in the T-area.

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A general tendency from an industry perspective is that the agglomeration economies do not work in the relative capital-intensive industries such as chemical and nonferrous sectors, and in primary sectors such as mining and agriculture.

As far as the agglomeration economy elasticity, σm, is concerned, it is relatively higher in the textile and wholesale & retail trade sector: that is, the production efficiency in these sectors rises with regional population growth. It might be counterintuitive that the elasticity is relatively lower in the sectors of finance, insurance and real estate (0.0339), and electric and gas utilities (0.0333), since these are typical industries with scale economies in production with average cost declining over a wide range of output. An interpretation of the observed small elasticities in these sectors is that the supply area of those industries is wider than the standard region in this study. So, “true”

agglomeration economies are measured by population size in a large area including the contiguous regions of the region considered. That is, as the specification of is used, in which

is a set of regions in the supply area of firms in region .

Gm

m

Ri

j

Nj σ

⎟⎟⎠

⎜⎜⎝

Ri i

3.2 Trade model

Trade model (11) is rewritten as follows

+

+

= −

k

kj m k m m k m m

k

ij m i m m i m m

m i

ij y q t q d

d q t q S y

ˆ ) exp(

ˆ ) exp(

λ

λ (11)’

where . and in the above equation are unknown parameters to be estimated here.

tm = λmtm λm tˆm

Data of trade flows between regions are obtained from the survey data on inter-regional freight flows, distances between regions are obtained by the shortest time path between the central cities of regions along the road network shown in Figure 2. The f.o.b. prices of commodity

) (Sijm

) (dij

(19)

)

(qim are not obtained from the data directly, but calculated by using the information that f.o.b.

prices are equal to the values of unit cost function in equilibrium,

q C N w r N w r

a a

i

m m

i i

i i

a a

m ma m a

m m m

m m

= =

( , , )

( )

σ

δ

1

1 1

Note that the parameters δ σm, m,am are known after the estimation of production function.

Parameters in the trade model are estimated so that the sum of squared errors between estimated and observed trade flows is minimized. The equation of trade model is non-linear form, but contains only two unknown parameters. So we adopt grid-search method to obtain the parameter values satisfying the above criterion. Table 4 shows the results of estimation.

サンプル数

1 0.000 2.099 0.7498 478

2 0.360 0.606 0.2843 557

3 28.600 1.720 0.7308 1683

4 1.310 1.443 0.7194 1783

5 0.000 2.647 0.8703 2454

6 7.790 0.802 0.3753 300

7 0.000 4.354 0.8575 3147

8 0.000 0.672 0.6833 1829

9 1.990 1.153 0.6620 1077

10 2.620 0.723 0.4965 1530

11 0.000 0.238 0.4297 220

13 19.940 4.140 0.8830 1698

Correlation Coefficient

Number of Observatio ns

Industry Code

Table 4 Estimation results of d

λm tˆm

Simple correlation coefficients representing the goodness-of-fit are generally high except for some sectors with small observations. Note that parameters of trade model in service sectors are not

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obtained here since data on inter-regional trade flows for these sectors are not available. We estimated them by means of ‘calibration’; searching the parameters by operating the simulation model with full equations. This is performed in the step of final test.

3.3 Other parameters

We explain briefly how other parameters were estimated.

The parameters in a log-linear utility function (4) are estimated by the T-area average consumption share of each commodity (or service) in total expenditure. Import coefficients are obtained by input-output table for T-area.

) (βm

3.4 Testing the fitness of the model

A final test was performed to evaluate how well the estimated structures fit the reality. Table 5 shows Mean Absolute Percentage Error (MAPE) of the main endogenous variables.

Table 5. Final test result

Variable Ni wi

qimyim

manufacturing

qimyim

service industry

MAPE(%) 20.69 14.62 45.14 46.79

CORR 0.972 0.797 0.841 0.944

The result indicates that the absolute discrepancy between the actual and predicted values is not small. A main reason is that the structures were estimated using cross-section data for only one year.

In the last row, the simple correlation coefficient between the predicted and actual values is shown for each variable. Correlation coefficients are rather high, which implies that the pattern of actual variance of each variable among regions is better reproduced by the estimated structures. To see

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this, Figure 4 demonstrates the relations between predicted and observed values for populations and wages.

0 500 1000 1500

Observed 0

500 1000 1500

Predicted

(a) Population

1.5 2 2.5 3 3.5 4 4.5

observed 1.5

2 2.5 3 3.5 4 4.5

predicted

(b) Wage rate

Figure 4 Comparison of predicted and observed values

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4. Simulation analysis

4.1 Uniform change in transport cost

Changes in the T-area transportation network will affect the system of regions within the T-area.

A question is whether population and production activities will be more concentrated in some regions or more dispersed across regions. In determining a trend toward concentration or dispersion, two opposing forces operate: agglomeration economies promote more concentration, while relatively lower factor prices such as wage rate and land rent in peripheral regions work to disperse activities.

A simulation analysis is performed making hypothetical changes in the transportation network. In the first simulation, the effect of uniform improvement in the transportation network is investigated.

That is, expressing the new transport cost as tmt0m, where t0m is the initial transport cost, and θ is gradually lowered from 1 to 0. As a measure of interregional disparity, the coefficient of variation of the regional population in the T-area, , was calculated, and is illustrated in Figure 5.

The value of in Figure 5 decreases monotonically as transport cost is lowered (the value of the coefficient of variation in the “actual” distribution where

vp

vp

=1

θ is 1.1252). That is, the dispersion-force rather than the concentration-force prevails in reaction to lowered transportation cost. This implies that the advantages of peripheral or small regions under conditions of lower wage rate and land rent are exploited more than the agglomeration economies of large regions.

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0 0.2 0.4 0.6 0.8 1

θ

1.04 1.05 1.06 1.07 1.08 1.09 1.1 1.11 1.12 1.13

Figure 5 Effect of uniform improvement of transportation network

vP

When transport cost is lowered by half (i.e., θ=0.5), the biggest decrease in population takes place in the Sendai region, i. e., the central region in the T-area. Among the ten largest regions accounting for 59% of the total population of the T-area, only three regions experience population increase due to homogeneous transportation system change. Wage rates are lowered in most larger regions, reflecting a decrease in labor demand. However, the rate of decrease tends to be larger in the smaller of the large regions (see Table 6 and Figure 6).

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V IV III II I

class of region

0.99 0.995 1 1.005

1.01 1.015 1.02

rate of population change

Figure 6 Effect of uniform improvement of transport network(θ=0.5)

Table 6 Effect of uniform improvement of transport network(θ=0.5)

Class of Population Population after-before after/before Number of Increase Decrease

region before change after change regions

I 4403491 4376268 -27223 0.9938 6 3 3

II 1327650 1331318 3668 1.0028 4 2 2

III 1493272 1493725 453 1.0003 6 2 4

IV 1916326 1929687 13361 1.0070 13 9 4

V 597550 607287 9737 1.0163 8 7 1

Coefficient of variation=1.1123

4.2 Effects of network change

In the simulation analysis so far, the transportation network in the T-area was hypothesized to be uniformly improved. However, in reality, some links of the network are improved more than others.

This part of the analysis examines the effects of such non-uniform transportation system change.

In T-area, there exists seven planned road improvement projects, which are labeled as [a] to [g].

Those links to be improved are drawn with thick dotted lines in Figure 2. Regions that are located along each planned road are listed below, where numbers following each road project are region

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code given in Table 1 and Figure 1.

[a]; 13, 25, 29 [b]; 33, 34, 35

[c]; 13, 15, 17, 7, 11, 10 [d]; 11, 8, 22, 20

[e]; 13, 36, 33

[f]; 29, 26, 19, 20, 21 [g]; 1, 4, 2

It is assumed that transport cost is decreased by half along the improved links in the network, while no change occurs along the other links. We conducted seven simulations in each of which one of seven plans is implemented. We further examined the case that all seven plans of road improvements are completed. In each case, inter-regional distance matrix is remade by shortest path search for new network after road improvement. Table 7 summarizes the results. In the table, change in population distribution is represented by the ratio of coefficients of variation with and without road improvement: the ratio with the value greater than unity means that population distribution becomes more uneven after the road improvement, i. e., more concentrated distribution.

The table also shows CV (Compensating Variation) and EV (Equivalent Variation) that are monetary measures of welfare change (= social benefit) caused by road improvements.

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Population distribution

[a] 1.0156 -0.0371 -0.0370

[b] 1.0005 0.0667 0.0667

[c] 0.9941 -0.0528 -0.0527

[d] 0.9897 0.1383 0.1384

[e] 0.9978 0.0383 0.0383

[f] 0.9921 0.0943 0.0943

[g] 0.9949 0.0897 0.0898

All 0.9807 0.3359 0.3353

CV EV

Table 7 Effects of alternative road improvement plans on population distribution and wefare

It is observed from the table that (a) road improvement projects [a] and [b] induce more concentrated population distribution, while other projects induce more dispersion; (b) road projects [a] and [c] have negative benefit values, in other words, residents in T-area are worse off by these road improvements. Those projects improving connections between large city and small peripheral regions tends to have lower social benefits, and cause concentrations. On the other hand, those projects improving connections between peripheral regions, such as projects [d], [f] and [g] have larger benefit values and promote dispersion of economic activities.

Finally we examine the case that all of seven projects are completed (see the last row of Table 7).

It is observed that the variance of population distribution becomes smaller, implying that the assumed transportation system change works to disperse activities within the T-area. We investigated in more detail population changes in each region. Although figures are not shown, findings are as follows. Population decreases in large regions; on the other hand, in some peripheral regions located on the improved links, population increases at a relatively high rate (higher than 10% in some regions). It is generally observed that population increases in the regions located at the end nodes of improved links, and that population decreases in the regions on the non-improved links parallel to the improved links as a consequence of competition between links.

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Also, there is a tendency for the regions between two end nodes of an improved link to lose population. This suggests that regions along the improved road do not necessarily attract population; economic activities tend to concentrate, even in small scale, at fewer locations.

5. Concluding remarks

A general equilibrium model of a multi-region economy with agglomeration effects and transport network is developed and applied to Japanese data. Parameters of the model are estimated by using the data of Tohoku region in Japan. By using the model, the effects of transport network improvement on spatial structure are analyzed and welfare of residents is evaluated.

The major conclusions and related observations are as follows:

1. In estimating the production function, a hypothesis that there is some threshold level of regional population beyond which agglomeration economies start working was tested for each industrial sector. In most sectors, the existence of the threshold level was confirmed, and surprisingly, the threshold level of population was 200,000 in every sector.

2. The model traces well the spatial variations of population, wage, and output levels of each industry, although absolute errors are not small. We can say that the model is useful for predicting qualitative effects rather than quantitative effects

3. As for the effect of transportation network improvement, two opposing forces operate: the concentration effect due to agglomeration economies, in large regions, and the dispersion effect due to lower factor prices in peripheral regions. Our simulation analysis shows that the dispersion-force rather than concentration-force prevails in reaction to lowered transport cost.

4. Among the proposed road improvement plans, those projects improving connections between large city and small peripheral regions tends to have lower social benefits, and cause concentrations.

On the other hand, those projects improving connections between peripheral regions have larger

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benefit values and promote dispersion of economic activities.

References

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Fujita, M., & Krugman, P., “When is the economy monocentric? and Chamberlin unified”, Regional Science & Urban Economics 25, 505-528 (1995).

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Henderson, J. V., “Efficiency of resource usage and city size”, Journal of Urban Economics19, 47-90 (1986).

Henderson, J. V., “System of cities and inter-city trade”, In: Hansen, P. et al. (eds.), System of cities and facility location, Harwood Academic Publishers (1987).

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Sasaki, K., “Regional difference in total factor productivity and spatial feature”, Regional Science and Urban Economics 15, 489-516 (1985).

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Footnotes

1. This is the only difference from the model in Mun[1997].

2. The formulation of “random cost” in this paper is based on Sasaki[1982].

参照

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