2300

AN INTER-REGIONAL FREIGHT DEMAND MODELBY SPATIAL APPLIED GENERAL EQUILIBRIUM ANALYSIS
Shoshi MIZOKAMI
Professor
Dep. of Civil and Environmental Eng.
Kumamoto University
2-39-1, Kurokami, Kumamoto
860-8555 Japan
Tel/Fax: +81-96-342-3541
E-mail: smizo@gpo.kumamoto-u.ac.jp

Ryuji KAKIMOTO
Associate Professor
Dep. of Civil and Environmental Eng.
Kumamoto University
2-39-1, Kurokami, Kumamoto
860-8555 Japan
Tel/Fax: +81-96-342-3537
E-mail: kakimoto@gpo.kumamoto-u.ac.jp

Abstract: As an attempt to express the essential characteristics of inter-regional trade, we propose ademand forecasting model based on the analytical frameworks of inter-regional and inter-industry
linkage analysis and the spatial price equilibrium model. This model seems to be useful in predicting
inter-regional freight demands in conditions of semi-open and middle-term equilibrium, that is to say,1) the final demand except for the household consumption is given by another econometric model
exogenously and 2) it permits change in residential location and differences in production prices andwage rate by zone. At the same time, we explain the kind of data to be considered for practical use,
using a complementary model and an estimation of a model. Furthermore, we show an application of
the results to a motorway improvement project in Japan and to verify the applicability of our model.
Key Words: inter-regional trade, freight demand model, I/O, SCGE

1. INTRODUCTION
Inter-regional trade is a series of physical movements of goods among various industries andwithin certain regions in the process of production activities and commercial transactions. For
example, a product is transported by a producer to other producers as an intermediate product,
and manufactured goods is made of the intermediate products which is turn, shipped towholesalers or retailers, by whom, it is finally distributed to households. Compared withpassenger trips, in interregional trade, there are such unique characteristics as: 1)
indefiniteness in the unit of measurement and transportation; 2) the variety of goods
transported; 3) a change in the appearance of a package in the process of transportation; 4) avariety in transport purposes; and 5) a variety in transport cycles. Nonetheless, in past researchon demand forecasting of the amount of interregional trade, it has been common to apply the
results of research in demand forecasting of person’s trip, which has relatively distinct
characteristics, to its analysis. However, a freight demand analysis should essentially be based
upon a framework that is consistent with economic theories and which is able to cope with theindustrial and economic structure of an economy as well as a change in residential allocation.
Particularly, when there is a business transaction between two regions due to the differentials
in price of the same goods in these regions as seen in developing countries, it is significant toemploy the above-mentioned framework on demand forecasting.
As an attempt to express the essential characteristics of an inter-regional trade, we propose ademand forecasting model based on the analytical frameworks of inter-regional andinter-industry linkage analysis and the spatial price equilibrium model in our study. At thesame time, we explain the kind of data to be considered for practical use, using acomplementary model and an estimation of the model. Furthermore, we show an applicationof the results to a motorway improvement project in Japan to verify the applicability of ourJournal of the Eastern Asia Society for Transportation Studies, Vol.5, October, 2003

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model. Inventory is the important factor in making a fright demand model when the capacityof warehouse is limited in volume. However, this model is only a static and flow estimation
model, so an effect of inventory is not taken into account in our model.
2. REVIEW OF THE MODELS AND OUTLINE OF OUR MODEL
Samuelson (1952) and Takayama et al (1971) developed the spatial price equilibrium modelin which they employed the concept of space separating two markets into an economic model.
The main objective of the spatial price equilibrium model in interregional trade was toformulate mathematical equilibrium values so as to satisfy the condition that interregional
trade takes place only when there is a difference in price, transportation costs included,
providing that there is only one product and two regions (see, for example, Broker, 1988;
Batten et al, 1985). Recently, this model was integrated into network equilibrium models byconsidering traffic systems such as transportation facilities and traffic network as a network.
Harker (1987) and the other scholars have further advanced these models. However, it isunusual that a model is built to describe the inter-regional physical movement of goods, so
called freight demand, itself. We will keep a detailed review and prospects in the field foranother occasion (see, for example, Harker, 1988; Batten, 1992). On the other hand,
Mizokami (1996) proposed a practical inter-regional trade model considering I/O frame andprice equilibrium. In this study, output, price and inter-regional trade pattern were treated as
variables. The model used was based on the framework of general equilibrium analysis, inwhich all the variables are interdependent among all industries and that the supply anddemand of each product are in equilibrium. Although practical, this model seems to be
somewhat weak in economic theories. Both MEPLAN, an integrated model forland-utilization and traffic, developed by Echenique (1986) and econometric models inregional economics (Sasaki, et al, 1987) employ the same concept as ours. However, thesemodels do not seem to deal with demand forecasting of inter-regional trade.
To improve our previous study, we rebuild the demand-forecasting model of inter-regional andinter-industry trade in order to find equilibrium values of the production prices and the amountof shipment, assumed to be equal to the total output of all industries in an intermediate goods
market, by employing the spatial general equilibrium framework of the inter-regional andinter-industry linkage model. The framework of Chenery-Mosesian inter-regional andoutput/selling priceMarket of good (m)output / priceoutput/selling priceMarket of composite good
output / priceinput/buying price

PRIVATE FIRM (n)demand for input nlabors/wage rate
input/buying pricelabors/wage rate
RETAIL (M)demand for input nMarket of laborslabors/wage rate
input/buying priceLand area/land price

HOUSEHOLD (M+1)
demand for composite
good and residential landMarket of residential land
land area/ land pricehouseholds/rentFigure 1.

input/buying pricelabors/wage rate

Mechanism of inter-industrial linkage

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output of n in zone jintermediate demandfor input m in zone j

Inter-regional trade coefficients
based on generalized cost

generalized cost of i-j
output of m in i

generalized cost of 1-j
output of m in 1

Figure 2.

generalized cost of I-j
output of m in I

Mechanism of inter-regional linkage

inter-industry linkage model is used to describe the flow of products, and, thus, theequilibrium condition for supply and demand is satisfied in terms of the quantities. In thesame manner, households are treated as an intermediate sector that provides labos to the othersectors and requires composite goods as well as residential land service. Land service isdecided in its own market mechanism. This market mechanism is shown in Figure 1.
In the normal I/O technique, the prices are usually given and the input coefficients are
generally constant. Our model has a distinct characteristic in its structure as it gives variable
input coefficients. As the production price changes the price of intermediate materials, theoptimum level of inputs will change as a result of rational production behavior in theindustries, and in turn it changes the input coefficients as well. At the same time, asinter-regional trade coefficients change because of the change in the generalized cost, which
consists not only with production and transportation cost but also with non-price factors, thetotal amount of demand will be determined. A brief outline on the inter-regional andinter-industrial linkage system is shown in Figure 2.
Under these situations, the supply and the demand are met according to the framework of theinter-industry linkage model in terms of quantities, and the production prices are adjusted
such that profits in all industries are equal to zero in terms of production prices. Thus, themarket is in equilibrium.
3. MODEL FOR INTER-REGIONAL TRADE AND INTER-INDUSTRY LINKAGE
The structure of the model is briefly shown in Figure 3. We assume that there are two types ofsectors in the economy. They are the private firms and the households which are identified by
m=1,…,M-1 and m=M, respectively. The superscripts m and n denote the shipping andreceiving industries, respectively, and the subscripts i and j (=1,…,I) denote a shipping andreceiving zone, respectively. Land service in terms of additional worth is expressed as m=M+1.
At the same time, we assume that each industry produces only one product.
3.1 The behavior of a private firm

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Final demand
FIRMS (m)HOUSEHOLD(M+1)

Demand for input goods

Demand for composite and land

Input coefficient

Input coefficient

Selling price & generalized price

Selling priceInter-regional trade coefficient
Average buying price

Average buying priceTotal production of goods & labors
Land priceTransport cost

Production prices & wage rate

Figure 3.

Framework of the model

Assuming the logit-type inter-regional trade coefficient model statistically determines thepattern of trade, successively the optimum amount of intermediate products is decisively
determined by the profit-maximization behavior of businesses in their factories. Given that thetentative production price, p = p nj , and the input price c = c mj , the nth industry

{ }

{ }

determines the optimum amount of intermediate product from the mth industry, x mn
j , and the{ }amount of labor input x Mj , under the assumption that it produces the total output, X = X nj

at the equilibrium. Assuming that a Cobb-Douglas production function and linear costfunction, we can set up the following optimization problem:Mmmax : π nj = p nj X nj − ∑ x mn
j cj

(1)

m =1

M

( )

β mn

s.t. ∏ x mn
j
m =1

= X njM(Assuming that ∑ β mn = 1 .)

(2)

m =1

By solving this optimization problem, the optimum amount of intermediate product and thelabor input, x mn
are determined as follows:
j

(

)

x mn
= β mn ⋅ p nj c mj ⋅ X njj

(3)

The input coefficient of intermediate product of the mth industry to be used to produce one
unit of output of the nth industry in the jth zone are given as:a mn= x mn
X nj
j
j

(4)

We consider this value as the inter-regional input coefficient in the Chenery-Mosesianinter-regional and inter-industry linkage table under the tentative production prices.
The sale price, cijm in the jth zone of the output produced by the mth industry in the ith zone is
the sum of the production price, p im , in the ith shipping zone and the transportation margin,sijm between the ith zone and the jth zone such that:
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2304

cijm = p im + s ijm(5)

The generalized sale price, cijm , which includes non-price factor of production, u ijm , such as
the transportation time can be written as:

cijm = cijm + ω muijm = pijm + sijm + ω muijm(6)

where ω m is a value conversion parameter.
The average purchasing price of the mth product in the jth zone, c mj , is the expected value ofthe sale price, cijm , that is a probability function of the interregional coefficient, t ijm , shown as
flows:[ ]c mj = ∑ {Prob xijm ⋅ cijm } = ∑ {t ijm ⋅ cijm }
i

(7)

i

In traditional spatial price equilibrium model, products are bought from the zones where themarginal profits are positive and, thus, the pattern of interregional is endogenously determined.
In our model, due to the fact that there are imperfect information about markets and theexistence of non-price factor of production, the purchase of the mth intermediate product by
the nth producing industry are assumed to be statistically made from all substitutive zones
based on the amount of generalized cost including error terms and also in accordance withlogit-model. The ratio, t ijm , of the amount of intermediate product received from the ithzone to the total amount of intermediate product received by the mth industry in the jth zone isrepresented as a utility function of the generalized sale price cijm and a zone potential uniqueto the ith zone, Wi m which can be obtained by aggregating small zones such that:[ ]t ijm = Prob x ijm =((Wi m ) δ m exp − λ m c ijm()∑ (Wi m ) δ m exp − λ m c ijm
i

)

(8)

This value is considered to be the inter-regional trade coefficient of the Chenery-Mosesianinter-regional and inter-industry linkage model.

3.2 The behavior of a household
Given that the total number of households X Nj , household’s income p Nj , land rent c Mj +1 ,and input price of composite goods c mj , a household attempts to distribute its income, whichis the value for its labor, into the consumption of both the optimal amount of land input(=M+1) and a composite goods (=M-1) from the retail sector. We apply a Cobb-Douglas
utility function and a linear budget constraint to describe the behavior of a household as
follows:(

max: U jN = x Mj −1, N) ⋅ (xα1)

M + 1, N α 2
js.t. p Nj X Nj = c Mj −1 x Mj −1, N + c Mj +1 x Mj +1N (Assume that α 1 + α 2 = 1 )

(9)

(10)

The optimal solution to this problem results that a household allocates the sum of his income
for both inputs in a constant ratio. So, put it that the total amount of consumption of land perhousehold, x Mj +1 X Nj , is fixed in the short term. By solving this optimization problem with

Journal of the Eastern Asia Society for Transportation Studies, Vol.5, October, 2003

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above assumption, the optimum amount of composite goods is determined as:
x mN= ( p Nj X jN − c Mj +1 x Mj +1N ) c mjj

(11)

In consequence, the input coefficient of the composite goods is given as:
a mN= x mNX jN = ( p Nj − c Mj +1 x Mj +1N X jN ) c mj
j
j

(12)

Regarding the land rent, we estimate a land price function in advance. This function has been
introduced based on the equilibrium theory that the supply and the demand of land service are
met in its market within each zone and it is shown as following functional form:
RiM +1 = a + b

X iM
p iM X iMSEc++ d M +i 1
M +1
M +1
Ki
Ki
Ki

(13)

where K iM + 1 is available land space and SE i is the vector of socio-economic attributes in the
ith zone. The land rent ciM +1 is introduced by following transformation:c iM + 1 =µ⋅ RiM + 1t
(1 + µ ) − 1(14)µ is the growth rate of the annual household’s income and t is the term of use.
3.3 Equilibrium conditions(1) Equilibrium condition in terms of the quantities
The equilibrium condition in terms of quantities means that the amount of supply and the*demand are met in every row of the I/O table. A is a diagonal matrix of intra-regional input
coefficient shown as follows:
 A1



A* = 






A2
O
Aj
0



0





O

A J 

(16){ } given in the equations (4)And its jth diagonal element A j is a matrix consisting of a mnj
and (12) which is as follows: a 11
j
 21
aj
 M
A j =  m1
aj

 M
 a M1
 j

(

a 12
j

L a 1njMM
L a mnj

LM
L a MnjL
L a 1N
j

M 
M 

L a mNj
M 
L a MN
j


(17)

)

t

The column vector, Y j = Y j1 ,⋅ ⋅ ⋅, Y jm ,⋅ ⋅ ⋅, Y jM , consists of the final demand Y jm in the jthzone for intermediate product produced by the mth industry, and then it is the jth element oft
the column vector of the final demand, Y * = (Y1 ,⋅ ⋅ ⋅, Y j ,⋅ ⋅ ⋅, YJ ) . Given that
Journal of the Eastern Asia Society for Transportation Studies, Vol.5, October, 2003

2306

(

X i = X i1 ,⋅ ⋅ ⋅, X im ,⋅ ⋅ ⋅, X IM

) , column vector of the total output by zone and industry ist

X * = (X 1 ,⋅ ⋅ ⋅, X i ,⋅ ⋅ ⋅, X I ) . And it can be obtained byt[

X* = I − T* A*

] TY
−1

*

*

(18)

This is just the equilibrium condition in which supply and demand is satisfied in terms of the*quantities under the temporally given production prices. T is a matrix of inter-regional
trade coefficient as follows:
 T11

 T21
 M
T* = 
 Ti1

 M
T
 I1

T12

L T1j
M
M
L Tij
M
L TIj

L
L

L T1J M M 
L TiJ M 
L TIJ (19){ } given in the equation (8)asand its (i,j) element Tij is a diagonal matrix consisting of t ijm
follows:
 t ij1
Tij = 






t

2
ij

O
t ijm

0



0





O

M 
t ij 

(20)(2) Equilibrium condition in terms of the monetary values
The equilibrium condition in terms of the monetary values means that the monetary value of
input and output by each sector are met in every column. The equilibrium condition of private
firm is given as:
p nj X nj = ∑ ∑ xijmn pim + ∑∑ xijmn sijm
i

m

i

(21)

m

The left hand side shows the total amount of products by the nth industry in the jth zone. The
first and second terms of right hand side mean the total production cost of the intermediate
inputs and total transportation cost, respectively. Our model is distinct in its structure as it
regards the unit price of transportation cost as a kind of added value. On the other hand, thebudget constraints shown in the equation (10) corresponds to the equilibrium condition ofhousehold. The household assumes to purchase the composite goods through the retail sector
located in the same zone, so c mj = p mj , and we can rewrite equation (10) as follows:p Nj X Nj = p mj x mN
+ c Mj +1 x Mj +1
j(22)

Equations (21) and (22) are rewritten as follows:
p nj = ∑ ∑ x ijmn X nj ⋅ p im +  ∑ ∑ x ijmn s ijm  X nj
i
m
 i m

N
m
mN
N
M +1
M +1
N
p j = p j ⋅ (x j X j ) + c j ⋅ (x j
Xj )

(

)

(23)
(24)

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2307

The second terms of above both equations are considered to be the vectors of added value, so
we write them as follows:
V jn =  ∑∑ x ijmn s ijm  X nj
 i m

N
M +1
M +1
V j = c j ⋅ (x j
X Nj )

(

(25)
(26)

)

t

The column vector, V j = V j1 ,⋅ ⋅ ⋅, V jn ,⋅ ⋅ ⋅, V jN , consists of the added value V jn in the jth zone
for intermediate product produced by the nth industry, and then it is the jth element of thetcolumn vector of the final demand, V * = (V1 ,⋅ ⋅ ⋅, V j ,⋅ ⋅ ⋅, VJ ) . Given that()

Pi = p i1 ,⋅ ⋅ ⋅, p im ,⋅ ⋅ ⋅, p IM , column vector of the production price is P * = (P1 ,⋅ ⋅ ⋅, Pi ,⋅ ⋅ ⋅, PI ) .
And it can be obtained by
t

t

[ (

P * = I − T* A *

)] V
t −1

*

(27)

This is just as the equilibrium condition in terms of the monetary values under the temporally
given the total amount of production.
Consequently, we can determine the inter-regional and inter-industrial freight flows asfollows:nm
x ijmn = a mn
j ⋅ X j ⋅ t ij

(28)

4. DATA COLLECTION AND MODEL ESTIMATION
4.1 National survey of net flow of freight
The national survey of the net flow of freight seems to be the only usable data in determining
the amount of trade among all industries in the country. It is possible to use the regional

Intermediate demand1
agriculture

2 ……. 25

26
retailFinal demand
27
household1. agriculture0

2. mining

0

28

29
exportOutput3.
0

manufacture
16.

X in

17.
wholesale0

25. warehouse

024.
26. retail00

27. household000Adding Value

Transport

0

Land

Figure 4. I/O framework of the model
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2308

input-output table prepared by the Ministry of Economy, Trade and Industry, which uses thevolume of trade of input instead of the physical amount of inputs as a source of data. Since thefigures in the table are taken from several surveys and statistical data such as data from thenational survey of net flow of freight, it must be considered secondary data. It is better to use
original data for consistency and fewer statistical errors. This national survey of net flow of
freight started in 1970 and has been carried out every five years. While there are a total of
33,002 establishments, the sample covers only 3.5 percent. The total weight of their shipping
covers 41.7% of the total output. Its reliability on weight is considered to be very high. In
accordance with the standard industrial classification of Japan, sampled industries are divided
into 61 sectors. The retail sector is assumed to ship nothing and to only receive goods fromother intermediate sectors. Then the I/O framework of this model results in a kind ofsemi-open type model as shown in Figure 4. The basic spatial unit of regions is a prefecture.
The national survey of the net flow of freight consists both of the annual shipping trend survey(the annual survey) and of the three-days-flow survey (the three-days-survey). From theannual survey, the annual amount of net shipping by zone and industry is obtainable, and the
net flow of inter-regional and inter-industrial over a three-days periods, f ijmn , from thethree-days survey. We can regard the former value as X im , that is to say the total output byzone and sector, and the latter f ijmn as the inter-regional and inter-industrial linkage pattern.
By using the Frator-method, we transfer f ijmn into the annual amount xijmn whose marginal
distribution is consistent with X im and X nj . X nj is not observable from the annual survey,
thus we assume as follows; 
X nj =  ∑ ∑ X im  ⋅  ∑ ∑ f ijmn
 i m
  i m∑∑∑∑ f
i

j

m

n

mn
ij






(29)

In estimating some partial models, which will be represented in the next section, xijmn is abasic data set and the other kinds of datasets are prepared as well. In our empirical study,
intermediate products including the household were reclassified into 27 sectors. The 28th and29th sectors are assigned for the final demand and the export, respectively. The number ofregions is eight except for Okinawa area.
4.2 Model Estimation and Evaluation of Total Test
The partial models which we should estimate in advance are a) Production function ofindustries, b) Inter-regional trade coefficients model, c) Land price function and 3) Utility
function of household. We show the example of estimation results of these models in Table 1
to Table 4, respectively.
A total prediction test of our model, which consists of partial models above mentioned, wasconducted. The iteration is terminated if the relative change in the X im is below 5.0%
together with the production price pim determination procedure. The results ofgoodness-of-fit between estimated and observed on total output X im and production pricepim are shown in Table 5. It is not too much to say that the fit of the model for pim issatisfactory because its correlation coefficient is high and the hypothesis H0: the regression
coefficient is equal to 1.0 is not rejected statistically. On the other hand, X im tends to be

Journal of the Eastern Asia Society for Transportation Studies, Vol.5, October, 2003

2309

Table 1. Example of the Estimation Results for Production Functions
Output sectors (n)Wholesale

Manufacture

Input sectors (m)1 Agriculture
2 Mining
3 Foods
4 Fabrics
5 Woods
6 Paper, Pulp
7 Chemicals
8 Plastic products
9 Ceramics
10 Steel
11 Non-ferrous
12 Metal products
13 Machinery
14 Elect. Machinery
15 Transpn. Machinery
16 Precis. Machinery
17 Textiles
18 Chemicals
19 Metal, Mining
20 Apparel
21 Farm Products
22 Foods
23 Furniture
24 Other
25 Warehouse
26 Retail27 Household

Mining
0.00E+00
5.30E-01
0.00E+00
0.00E+00
0.00E+00
2.66E-06
1.37E-02
3.31E-06
2.67E-03
1.50E-04
4.22E-04
0.00E+00
8.11E-04
1.70E-06
0.00E+00
4.01E-07
0.00E+00
8.87E-07
1.32E-02
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
5.15E-07
0.00E+00
4.39E-01

Manufacture

Wholesale

Ceramics

Steel

Transpn.
Machinery

1.99E-03
4.39E-01
1.15E-06
0.00E+00
4.65E-06
7.47E-06
4.11E-04
1.07E-05
2.68E-01
2.98E-05
2.05E-04
7.11E-04
2.95E-04
8.61E-06
3.95E-05
4.75E-06
0.00E+00
1.14E-04
3.02E-04
0.00E+00
0.00E+00
0.00E+00
7.38E-04
9.95E-05
9.95E-06
0.00E+00
2.88E-01

6.12E-06
4.12E-02
2.38E-07
2.49E-07
9.13E-06
3.51E-05
1.70E-02
7.77E-06
3.03E-02
1.71E-01
9.32E-04
1.66E-02
5.69E-02
2.55E-04
8.80E-03
3.17E-05
0.00E+00
1.07E-03
5.81E-01
1.31E-07
1.66E-06
4.40E-09
2.25E-06
3.53E-04
1.92E-04
0.00E+00
7.46E-02

3.23E-04
2.61E-04
9.17E-05
4.56E-04
7.30E-05
5.93E-03
2.48E-04
4.86E-03
1.48E-02
1.97E-02
3.59E-02
9.38E-03
3.02E-02
2.17E-02
7.85E-01
5.25E-03
1.63E-08
3.88E-03
8.24E-03
1.15E-07
8.67E-09
0.00E+00
9.81E-08
7.59E-03
1.74E-04
0.00E+00
4.58E-02

TextilesChemicals

0.00E+00
0.00E+00
0.00E+00
3.97E-01
4.51E-08
2.14E-04
3.15E-03
4.83E-02
1.86E-06
0.00E+00
0.00E+00
3.61E-06
0.00E+00
8.52E-08
1.52E-07
1.92E-04
4.63E-01
1.20E-04
1.02E-05
5.36E-02
0.00E+00
0.00E+00
1.13E-03
1.08E-02
7.62E-04
0.00E+00
2.10E-02

0.00E+00
0.00E+00
0.00E+00
2.99E-01
2.12E-04
4.64E-03
1.33E-05
8.37E-02
0.00E+00
0.00E+00
0.00E+00
0.00E+00
2.28E-06
1.12E-04
1.75E-06
9.99E-03
6.64E-02
8.39E-04
0.00E+00
4.69E-01
0.00E+00
1.24E-03
6.39E-04
1.82E-02
3.29E-04
0.00E+00
4.56E-02

Warehouse

Retail

0.00E+00
0.00E+00
1.16E-02
2.41E-03
9.82E-05
2.93E-03
1.46E-01
1.97E-02
1.92E-02
4.82E-03
4.88E-05
4.29E-05
1.82E-03
5.64E-03
9.07E-02
1.36E-04
1.33E-03
1.07E-05
7.80E-05
1.06E-04
0.00E+00
1.57E-05
4.87E-03
5.57E-05
2.05E-04
0.00E+00
6.88E-01

3.14E-05
2.07E-03
9.65E-02
8.55E-03
8.00E-03
1.45E-02
1.09E-02
6.25E-03
1.28E-02
6.33E-07
4.69E-05
3.35E-04
1.15E-03
1.47E-03
9.09E-03
7.30E-03
1.06E-02
3.14E-02
1.07E-01
5.35E-02
7.84E-02
9.34E-02
5.69E-02
3.10E-01
4.05E-04
4.40E-03
7.52E-02

Table 2. Example of Estimation Results for Inter-regional Coefficients Models
Sector (n)Manufacture

Agriculture

Mining-1.711(-3.759)-0.877(-2.627)-0.507(-4.413)0.881(3.848)0.050(0.085)-0.179(-0.306)
0.811(1.525)-0.416(-0.500)
0.733(1.272)-0.335(-0.574)-0.478(-0.845)-3.479(-1.609)-4.871(-0.359)-4.521(-3.310)0.115(1.881)
1.123(1.204)1.738(0.524)-0.894(-0.325)
4.210(1.512)1.417(0.504)2.520(0.899)1.406(0.548)0.835(0.302)-2.445(-2.22)-1.475(-1.106)-0.910(-1.725)-0.055(-1.705)
1.215(1.702)-0.256(-0.174)-0.241(-0.174)
2.880(2.266)0.890(0.577)1.998(1.308)0.710(0.553)-0.897(-0.620)-3.336(-2.933)-3.545(-2.933)-2.083(-2.169)-2.731(-2.640)-2.322(-2.425)-2.653(-2.602)-3.273(-3.247)

F-Value

5.778

1.842

6.101

32.483

Multi-Correlation

0.722

0.629

0.757

0.920

Variables
Constant

Production Price( −λ M )Transportation Cost
( −λ M µ M )Transportation Time( −λ M ω M )Zone Potential(δ M )
Zone Dummy

Region-1
Region-2
Region-3
Region-4
Region-5
Region-6
Region-7

Ceramics

Steel-0.697(-2.798)-1.595(-6.191)

WholesaleTranspn.
Machinery

Warehouse

TextilesChemicals-0.005(-1.971)-1.697(-6.284)-1.661(-1.705)-0.008(-1.502)-1.427(-5.882)-4.925(-5.087)-8.137(-2.296)-1.071(-4.204)-3.203(-2.733)

1.717(4.462)-1.532(-1.170)-1.154(-0.853)
2.462(1.866)0.874(0.780)1.809(1.367)0.549(0.440)-2.012(-1.677)

1.657(1.858)0.988(0.831)2.410(2.076)2.633(1.844)
2.195(1.862)2.045(1.607)2.986(2.174)0.652(0.542)7.656

15.081

8.638

4.221

0.778

0.853

0.793

0.666

-0.927(-2.909)-0.015(-1.090)-1.440(-3.076)-0.034(-1.185)0.726(2.495)0.601(0.629)0.857(0.825)-1.217(-1.297)0.659(0.739)-0.719(-0.828)

1.317(3.213)0.979(0.678)-0.699(-0.594)-1.734(-1.664)-1.611(-1.343)

underestimated because the Cobb-Douglas production function, which is homogeneous ofdegree one, lowers the reliability of regional input coefficients. Overall, however, it seems thatthe validity of this model is satisfactory. These empirical results are sufficiently encouraging
to apply the model to practical inter-regional trade demand forecasting.
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Table 3. Estimation Results for Utility Function of Household
Variables
Parameter
Composite goods ( α 1 )0.667

Land service ( α 2 )

0.333

∑

1.0

Table 4. Estimation Results for Land price Function
Variables
Parameters (t-value)
Constant
X
M
i

M
i

p X

K
M
i

4.181 (5.13)

M +1
i

K

-0.0391 (6.20)

M +1i

0.0000199 (12.4)

Multi-correlation

0.99

Table 5. Goodness-of-Fit on Total Test
Evaluation Indices
Correlations Coefficient
0.80m
Total Output( Xi )
Regression Coefficient (t-value)
0.243 (21.9)
Correlations Coefficient
0.99
Production price ( pim )Regression Coefficient (t-value)
0.998 (283.)

5. CASE STUDY FOR MOTORWAY IMPROVEMENT PROJECTS
We applied our model to a case study on two alternative motorway improvement policies
shown in Figure 5. First policy is to improve the motorway connecting Tokyo and Osaka
metropolitan areas, where are the biggest and second biggest cities, by way of Nagaya. This
policy means that the investment will be done into the accessibility improvement between two
metropolitan areas. Second policy is to improve the motorway between rural area and these
two metropolitan areas. This policy encourages the decentralization. We assume that these
improvements can reduce the time length of transportation between all pairs of zones by 10%
and 20%.
Figure 6 shows the economic benefit by region evaluated by the equivalent variation against
both motorway improvement policies. The amount of the equivalent variation per householdis calculated by following equation that is consistent with its utility functional form:α1 c mNj
EV j =  mN  cˆ 
 j α2

 c Mj +1N  cˆ M +1N jpˆ Nj − p Nj

(30)

where ^ of variables means the symbol for the values after projects. We find that
1) For the both policies, benefit of Kanto and Kansai regions, where includes Tokyo andJournal of the Eastern Asia Society for Transportation Studies, Vol.5, October, 2003

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Osaka metropolitan areas, respectively, increases.
2) The benefit of regions where place on the way of improved motorway tends to decrease.
3) The total amount of benefit from second policy is bigger than that from first one. Then thedecentralization policy seems to be maintained only from the viewpoint of economic
benefits.

Policy-1: between two metro areas

SAPPORO
Hokkaido

Policy-2: between rural and metro

Tohoku500km

FUKUOKA Chugoku
Kyushu Shikoku

Chubu
Kansai
Kanto

OSAKA

TOKYO

Figure 5. Alternative motorway improvement policies

Kyushu20% Reduce

Shikoku

10% Reduce

KyushuCyugoku

CyugokuKansaiKansai

Cyubu

Cyubu

Kanto

Kanto

TohokuTohokuHokkaido

Hokkaido

-1000

0

1000

2000

3000-1000

20%Reduce

Shikoku

10%Reduce

0

1000

2000

Benefit (Billion US$)

Benefit (Billon US$)(a) Policy-1(b) Policy-2

3000

Figure 6. Economic benefit for motorway improvement

6. CONCLUDING REMARKSThis model seems to be useful in predicting inter-regional freight demands in conditions ofsemi-open and middle-term equilibrium, that is to say, 1) the final demand except for thehousehold consumption is given by another econometric model exogenously and 2) it permitschange in residential location and differences in production prices and wage rate by zone. The
traditional simple models of transportation demand and land use forecasting originated fromthe analogy of results of other research fields. The most recent models, which combine
behavioral analysis and the equilibrium theory, have undergone improvements. It is certain
Journal of the Eastern Asia Society for Transportation Studies, Vol.5, October, 2003

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that practical inter-regional freight demand forecasting models must trace such a path. In thissense, the model presented in this study may come to mark the first step in this direction. Thismodel, however, can only provide tentative theoretical and practical conclusions. From atheoretical aspect, we must make it consistent with the economic theory on the behavior offirm and general equilibrium analysis in great detail. From a practical point of view, it isnecessary to raise the reliability of our model by improving the database system and individual
partial models. Finally, we have to carry out the feasibility analysis for the intercity highway
construction projects that may change patterns of inter-regional freight flow on a great scale as
far as we evaluate its availability.

REFERENCES
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7) Echenique, M. (1986) MEPLAN Users Manual. Michelle Echenique & Partners Ltd.,
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8) Mizokami, S. (1996) An Inter-Regional Trade Model Considering I/O Frame and Price
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Journal of the Eastern Asia Society for Transportation Studies, Vol.5, October, 2003