Research on Input-output Table and Analysis
Method in Western China
Qiu Piqun
XI’AN Statistics Institute, Department of Information 6#
Xiaozhai East Road #64, XI’AN City, China
E-mail: peiqunqiu@yahoo.com.cn
Liu Yin
York University
Toronto City, Canada
E-mail: liu_yin2001@yahoo.com
Western development is the major strategy of Chinese economic construction in the
21st century. During western development, recognizing the present state and
development potential of society, economy, resources and environment in western
area is the precondition to carrying out “develop towards west” scientifically and
effectively. It is very necessary to use input-output technique to analyze the economic
linkage, resources supply and environmental protection in the ten western provinces
and autonomous regions. By working out the total input-output table, this paper
researches and analyzes input-output relationship, environment and resources
occupation in western China.
The ten western provinces and autonomous regions include: Xinjiang, Gansu, Qinghai,
Ningxia, Shaanxi, Sichuan, Chongqing, Guizhou, Yunnan and Xizang.
1. The structure of total input-output table in western China
The total input-output table (Table 1) in western China is a model, which includes
product, labor force flow, pollution and pollution control, and resources occupation of
the ten western provinces and autonomous regions. The structure of Table 1 includes
9 quadrants: Ⅰ . Middle use, which reflects the middle flux of each production
department in various regions; Ⅱ. Middle input of pollution control departments,
which reflects product consumption of each department in pollution control process;
Ⅲ. Final use, which reflects the direction and structure of final use in each department;
Ⅳ. Initial input, which reflects the initial input of each production department in
various regions; Ⅴ. Initial input of pollution control departments, which reflects the
pollution control cost of each department; Ⅵ. Pollution formation, which reflects the
pollution formation status of each department in middle use; Ⅶ. This quadrant reflects
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the pollution formation amount in decontamination; Ⅷ . This quadrant reflects
pollution formation status in final use; Ⅸ. Resources occupation, which reflects the
occupation of land, water, mine and other natural resources.
Middle input
Table 1. The total input-output table in western China
Middle use
Pollution
Final use
control
dept.
12…n
12…m
1
2
…
Ⅰ
n
Ⅱ
Ⅲ
Total output
Initial input
Ⅳ
Ⅴ
Ⅶ
Total input
Pollution-creating
dept.
1
2
…
m
Ⅵ
Resources
occupation
Land
Water
Mine
Others
Ⅸ
Ⅷ
The total table (Table 1) is designed by modularization method, and the 9 quadrants
are regarded as 9 modules. The following three different input-output models can be
obtained by combining the modules.
2. The regional input-output model and analysis in western China
The regional input-output table in western China can be obtained by combining the
Ⅰ, Ⅲ, Ⅳ modules of the total table (Table 1) and dividing the Ⅰ quadrant into
composite groupings. Ten regions are divided under the middle use and the middle
input, and n departments are divided under each region. Table 2 is the regional
input-output table in western China. The first part of Table 2, that is the Ⅰ quadrant
of Table 1, is a regional flux matrix. The flux is xijpq , which expresses the product
consumption of department j, department j is in region q; the product is supplied by
department i, department i is in region p. The second part of Table 2, that is the Ⅲ
quadrant of Table 1, is divided into 11 regions under the final use. The eleventh region
reflects the total of midland and eastern area.
The final use is expressed as Yi pq .
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11
The sum of ranks is Yi p , Yi p   Yi pq .
q 1
10
The sum of lines is Yi q , Yi q   Yi pq .
p 1
Table 2. The regional input-output table in western China
Middle use
Region2 … Region10
Dept.
Dept.
12…n … 12…n
Region1
Dept. 1
Dept. 2
…
Dept. n
Region2
Dept. 1
Dept. 2
…
Dept. n
…
…
Region10
Middle input
Region1
Dept.
12…n
Final use
Region
1
Region
2
xijpq
…
Region
10
Midland
East
Yi pq
Total
output
X ip
Dept. 1
Dept. 2
…
Dept. n
Initial input
N qj
Total input
X qj
In the third part of Table 2 (that is the Ⅳ quadrant of Table 1), the initial input is
expressed as N qj , which includes depreciation, labor rewards, and interest tax, etc.
The total output is expressed as X ip , and the total input is expressed as X qj .
The equilibrium relationship in Table 2 is:
10
Line:
n
 x
q 1 j 1
10
Rank:
pq
ij
 Yi p  X ip
n
 x
p 1 i 1
pq
ij
 N qj  X qj
( pi  11,,22......10n )
( qj11,,22......10n )
The direct consumption coefficient of partition product is:
aijpq 
xijpq
X qj
( pi,,qj  11,,22......10n )
(1)
The total consumption coefficient of partition product is:
B pq  ( I  A pq ) 1  I
(2)
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 
where, A pq  aijpq
nn
.
Substituting aijpq in the equilibrium relationship, and the equilibrium equations are:
10
 a
q 1 j 1
10
pq
ij
X qj  Yi p  X ip
( pi  11,,22......10n )
pq
ij
X qj  N qj  X qj
( qj11,,22......10n )
n
n
 a
p 1 i 1
Its matrix representation is:
10
A
X q Y p  X p
( p=1,2…10 )
C q X q  N q  X q
( q=1,2…10 )
pq
q 1
10

p 1

10 n
10 n
 10 n

pq
where, C q  diag   aipq
,
a

ainpq 

1  i 2
p 1 i 1
p 1 i 1
 p 1 i 1

set
 
A  A pq
1010 ,




C  diag (C 1 C 2 C 10 ) ,
Y  (Y 1Y 2 Y 10 ) T, X  ( X 1 X 2  X 10 ) T, N  ( N 1 N 2  N 10 ) T
get
AX  Y  X

CX N X
then
the line model is:
X  ( I  A) 1 Y
(3)

the rank model is:
X  ( I  C ) 1 N
(4)
According to formula (1) and (2), the direct consumption coefficient and the total
consumption coefficient can be figured out. They can be used to analysis the
consumption relationship between regional product and labor force, and the relation
of regional manufacturing technique. According to formula (3) and (4), the regional
economic development in western China can be forecasted.
3. The environmental protection input-output model and analysis in western
China
The environmental protection input-output model in western China can be obtained
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by combining the Ⅰ , Ⅱ , Ⅲ , Ⅵ , Ⅶ , Ⅷ modules of the total table (Table 1).
Considering the environmental protection model is complicated, the form of regional
input-output model is not used again. The model is a substance-value model. To
production departments, it use value unit to link up with the total table; to
pollution-creating matters, it use unit in kind to get data easily; to consumable of
pollution control departments, it use value unit to establish equations set easily.
The number of pollution-creating departments and pollution control departments is
assumed corresponding equal. They all include m types, such as drain water, and
exhaust gas, waste residue, garbage, etc. The production departments include n types.
In the first part of the model, the middle flux of production departments is expressed
as X ij ; in the second part of the model, the middle input flux of pollution control
departments is expressed as Eij ; in the third part of the model, the final use of
production departments is expressed as Yi ; in the fourth part of the model, the
pollution-creating flux in production process is expressed as Fij ; in the fifth part of
the model, the pollution-creating flux in pollution control process is expressed as K ij ;
in the sixth part of the model, the pollution-creating amount in final use is expressed
as Ri ; and the total output of production departments is expressed as X i , the total
pollution is expressed as Gi , the decontaminated pollution is expressed as S i .
According to the environmental protection input-output table, the following economic
parameters can be worked out.
① The pollution-creating coefficient of production departments
f ij 
Fij
Xj
( ij 11,,22......mn )
(5)
② The pollution-creating coefficient of pollution control departments
k ij 
K ij
Sj
( i,j =1,2…m )
(6)
③ The direct consumption coefficient of pollution control departments
eij 
E ij
Sj
( ji  11,,22......nm )
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(7)
④ Decontamination ratio
λi =
Si
Gi
( i =1,2…m )
(8)
The measurement unit of the numerator and the denominator is not the same in
formula (5) and (7). The former represents pollution amount created by production
department j in the process of manufacturing one value unit of products, the latter
represents the consumption values of product manufactured by department i in
decontaminating one unit of pollution j.
According to formula (5), (6), (7), (8), pollution-creating coefficients and pollution
control coefficients can be worked out to calculate the pollution-creating amount and
measure the condition of decontamination, and analyses the relationships between
environmental protection and economic development.
4. The resources occupation input-output model and analysis in western China
The resources occupation input-output model in western China can be obtained by
combining theⅠ, Ⅲ, Ⅳ, Ⅸ modules of the total table (Table 1) and dividing the Ⅰ
quadrant into n departments. The Ⅰ quadrant becomes a flux matrix, which includes
n  n departments. The table is also a substance-value input-output table, the first
part (middle use), the second part (final use) and the third part (initial input) of the
table all use value unit to agree with the unit of the total table (Table 1); the fourth
part (natural resources occupation quadrant) of the table uses unit in kind to do natural
resources occupation analysis in western China and get data easily. Natural resources
are divided into 4 types, that is land, water, mine, and other resources. Each type is
divided into several resources; the total number is s. Natural resources occupation is
expressed as Z ij , i is the number of the resources types, j is the production department,
and the total amount of resource i is expressed as Wi .
According to the fourth part of the resources occupation input-output table, the
following economic parameters can be worked out.
① The direct resources occupation coefficient
s ij 
Z ij
Xj
( ij  11,,22......sn )
② The total resources occupation coefficient
S *  S ( I  A) 1
where, S  sij sn , A  aij nn ,
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a ij is the direct product consumption coefficient, the formula doesn’t
consider the consumption of fixed assets, it is a simplified formula.
③ The distribution coefficient of direct occupation
t ij 
Z ij
Wi
( ij  11,,22......sn )
④ The distribution coefficient of total occupation
T *  T ( I  H ) 1
where, T  t ij sn ,
H  hij nn ,
hij is product distribution coefficient.
⑤ The output coefficient of unit occupation
rij 
Xj
Z ij
( ij  11,,22......sn )
According to the above economic parameters, we can analyze the direct occupation,
the total occupation, the direct distribution, and the total distribution of various
natural resources during economic development of western China. According to the
output coefficient of unit occupation, we can analyze the relationships between
resources input, occupation, and economic benefits of output, and research the
relationships between resources occupation and regional output.
References
[1] W.Leontief, Input-output Economics, New York Oxford University Press, 1966
[2] Li Qiang, The Experience and Research on Input-output in Contemporary China, Chinese
Statistic Press, 1999
[3] Cheng Xikang, The Demonstration and Innovation of Input-output in Contemporary China,
Chinese Statistic Press, 1995
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