Proceedings of International Workshop on Policy Integration Towards
Sustainable Urban Energy Use for Cities in Asia, 4-5 February 2003 (East West Center, Honolulu, Hawaii)
© 2003 Institute for Global Environmental Strategies All rights reserved.
Developing a Computable General Equilibrium Model:
Case Studies on Beijing and Shanghai
Hirofumi Nakayama*a, Shinji Kaneko b
1. Introduction
In order to analyze the quantitative relations of economic growth and environmental issues in China at a future point,
we need detail data on socio-economic and environmental situations in past a few decades to present and a forecasting
model that extracts these complicated causes and effects. China’s old statistical data are, however, sometimes not
reliable or even do not exist. This data limitation makes it difficult that researchers conduct a forecasting analysis with a
complicated model. This study employs a forecasting model based on General Equilibrium theory which can determine
important parameters for the model from a single (the latest) year’s data. The target cities are Beijing and Shanghai,
each of which are categorized into urban and rural areas and a CGE (Computable General Equilibrium) model which
explains market trading of goods, services, labor and capital in the two areas forecasts the economic growth, changes in
industrial structure.
This model forecasts four items; GDP in urban areas, industrial structure, household income and population
urbanization rate, which are used as the background data for the energy consumption forecast in private sector in this
research project.
2. Analysis framework
2.1 Model structure
Structural overview of the model is shown in figure 1. This model is a sequential equilibrium type GE model which is
mostly based on the GE model developed by Ichioka. In the CGE model in this study industries input labor, capital and
intermediate goods as production factors and produce goods and services. Here in the production function, Leontief
model is employed for intermediate input structure and Cobb-Douglas model for inputs of capital and labor, and
constant returns to scale is expected. Industrial behaviors are formulated as being cost minimizing to production amount.
On consumption side, on the other hand, households are divided into two; urban and rural, and they behave in order to
maximize their utilities under budget constraints. This study employs Cobb-Douglas model for household utility
function. And in this analysis the government has its annual revenue from indirect tax, labor tax and capital tax from
firms and income tax from households and government’s final consumption is regard as the annual expenditure, and the
balance of the revenue and expenditure is kept for savings.
* Corresponding author. Tel: +81-92-642-4092, Fax: +81-92-642-3848, E-mail: [email protected]
a Research Associate, Institute of Environmental Systems(IES), Faculty of Engineering, Kyushu University, 6-10-1, Hakozaki, Higashi-ku, Fukuoka,
812-8581 Japan.
b Associate Professor, Graduate School for International Development and Cooperation (IDEC), Hiroshima University, 1-5-1 Kagamiyama,
Higashi-Hiroshima 739-8529 Japan.
2.2 Categorization of industries and households in urban and rural areas
This study analyzes Beijing City and Shanghai City. Cities in China’s administrative categorization includes large
rural areas and hold large rural population. Comparison between urban and rural areas tells us that household income
level and consumption structure are quite different between the two areas, and also in industrial sector there are
technological gaps even in the same industry. For instance, the scale of production facilities, production methods and
technological levels in small-scale firms in rural areas are totally different from those in the firms in urban areas. The
industrial structures are also largely different; labor-intensive light industry is popular in rural areas and
capital-intensive heavy chemical industry is dominant in urban areas. Therefore in order to take these facts in China into
consideration, the analysis model needs to distinguish urban and rural areas.
The industrial sectors are three; agriculture, industry and services and they are distinguished by urban and rural
industries except for the first one, which make five sectors; agriculture, urban industry, rural industry, urban services
and rural services. Household sector is also divided into urban and rural areas so that the model can describe the
differences of income level and consumption structure.
Total Population
Capital Stock
Price Block
Labor Price, Capital Price
Labor Demand per
Unit Value Added
Capital Demand
per Unit Value
Added
Household (Urban, Rural) Block
Government Block
Labor & Capital Supply
Household Income
Household
Consumption
Household
Savings
Government Planned
Tax Income
Labor productivity,
Capital productivity
Income Tax
Government
Consumption
Government
Savings
Prices of Goods
Total Consumption
GRP
Macro Economic Structure
Total Investment
Industry Block
(Urban, Rural
and by Sector)
Urbanization Ratio
Import & Export
Final Demand by
Goods
Total Production by
Sector
Value Added by Sector
Income (Urban, Rural)
Production Tax
Government Tax
Income
Equilibrium
Labor & Capital Demand by Sector
Final output
Figure 1. Basic model sructure
2.3 Urbanization
The CDE model can calculate production factor demand. Production factors consist of the three factors of labor,
capital and intermediate inputs. Since this model can extract labor demand in rural and urban areas respectively, it can
also calculate the number of labor population migration between rural and urban areas. This model, however, has its
own limitation that the amount of migration is only about labor population because there are a lost of driving forces for
migration other than working such as study, marriage and so on..
3. Model formulization
(1) Industrial production
Each industry produces the products under the cost-minimizing principle from the two production factors of capital
and labor and from production goods in other industries as intermediate goods according to the production patterns
shown in the Input-Output (I-O) table. In the model the production function of jth industry is formulated as follows.
Q j = Q j (L j , K j , X 1 j , m , X nj )
[
= min VA j (L j , K j ) / a 0 j , X 1 j / a1 j , m , X nj / a nj
(
)(
)
]
･･･(1)
n
s.t.　p j Q j = pK K j + pL L j 1 + t0 j + ¦ a ji X ji
i =1
･･･(2)
where Qj indicates production amount of jth industry (jth production goods), Xij indicates ith production goods inputs
(intermediate consumption), aij (i≠0) indicates input parameter, Vaj indicates value added, t0j indicates net indirect tax
rate composed of indirect tax and subsidy, and a0j indicates value-added ratio which explains value added per
production unit. Each industry expectedly needs constant a0j of value added per production unit. The value added is
calculated by the following Cob-Douglas function with labor (Lj) and capital (Kj) as production factors.
α
(1−α j )
VA j = γ j L j j K j
･･･(3)
γj: scale parameter, αj: share parameter
(2) Household utility
Household utility U in this model is formulated as Cob-Douglas function regarding composite commodity of
consumption goods i, and utility maximization is described as follows.
n
max U = ∏ (CH i )λi
i =1
s.t.　INC − SH = CH
･･･ (4)
･･･ (5)
where CHi indicates the purchase amount of the household’s ith consumption goods, λi indicates the share of ith
goods in the total amount of consumption goods purchase, INC and SH describe disposable income and savings amount
of households respectively. INC here is formulated as the balance of factor income from labor and capital and income
tax (tax rate: tH).
(1 − tH )
INC = ( pL L + pK K )　･･･ (6)
SH in equation (5) is derived by multiplying disposable income by savings rate rH as equation (7) shows.
SH = rH INC
･･･(7)
(3) Government
The government does government consumption SG and savings CG from its tax revenue TAX (sum of income tax
from households and net indirect tax from industry).
n
(
)
TAX = ( pL L + pK K )　t H + ∑ pL L j + pK K j t0 j
j =1
TAX − SG = CG
･･･ (8)
･･･ (9)
The purchase amount of ith consumption goods in the government consumption is fixed to the share by commodity
(ωi ) at the standard year for the future forecast also. It is calculated by the following equation.
CG i = ω i CG
･･･ (10)
Also, government savings rate rG is formulated as household savings rate rH is.
SG=rGINCG
･･･ (11)
(4) Investment
Investment is determined after savings as the following equation shows.
INV = pINV I = SH + SG
･･･ (12)
pINV and I indicate the price of investment goods and actual investment respectively in equation (13). pINV is
calculated from the price of production goods by industry (pi) and investment goods share by industry (bi) by the
following equation.
n
p INV = ∑ p i ⋅ bi
i =1
･･･ (13)
(5) Fixed capital stock
Fixed capital stock KSt is calculated by adding actual investment It to the balance of the fixed capital stock in the
previous year (KSt-1) minus depletion.
KSt = (1 − δ t )KSt −1 + I t
･･･ (14)
(6) Conditions of general equilibrium
Equilibrium in this model is described by the following three equations.
n
∑ Lj = L*
j =1
･･･ (15)
n
¦ Kj = K*
j =1
n
･･･ (16)
¦ X ij + CH + CG + I + ¦ j =1
n
j =1
n
EX − IM
= ¦Qj
pj
j =1
TAX=TAX*
･･･ (17)
･･･ (18)
where L* and K* indicate the initial labor holdings by households and the initial capital holdings, and T* indicate the
government expected tax revenue. Equations (17) to (18) describe the equilibrium in labor market, capital market,
market of goods and services , and government tax revenue and expenditure respectively.
4. Dataset
It is most essential for building a CGE model that formulation of economic actors’ behaviors is done by
microeconomic theory and overall and comprehensive microeconomic dataset of economy and tax system is prepared.
Taking the year which the dataset comes from as the standard year, it is expected that general and benchmark
equilibrium is observed which gives benchmarks to the model. And also, the data in the dataset indicate equilibrium
value of each economic parameter.
This study takes year 1997 as the standard year since I-O tables in Beijing City and Shanghai City are available for
that year. China Statistical Yearbook 1998, which covers major macroeconomic data for 1997, is used to adjust the
microeconomic data from a variety of data sources. Other important data sources are as follows; China Statistical
Yearbook on Industry and Economy, China Statistical Yearbook on Household Income and Expenditure in Urban Cities,
China Labor Statistical Yearbook, China Yearbook of Town and Village Enterprizes, China Fixed Assets Investment
Yearbook, Beijing Statistical Yearbook, Shanghai Statistical Yearbook.
(1) Capital stocks
Since China does not have reliable data on capital stocks, this study conducts estimation. Overall capital stocks in
1997 are estimated from capital stocks by province in 1995 estimated by Esaki et al. and average growth rate of capital
stocks from 1991 to 1995 (11.67%). In this study Esaki’s estimation is converted to 1997 price from original 1995 price
by investment price index of fixed assets.
(2) Dividing urban and rural areas of the I-O table
This study divides industries into the two areas except for agriculture. As the data on the total production amount and
production amount in rural areas are available, they are used in this analysis for input and production, and the input and
production amount in urban areas is derived by extracting the amount in rural areas from the total amount. The
production amount in rural areas is adopted from Small-scale Industry Yearbook.
Intermediate inputs are allocated to urban and rural areas from total inputs according to the input ratio. The value
added in rural areas is calculated by multiplying total rural inputs by value-added ratio in the areas, and the value added
in urban areas is derived from the balance of total value added and rural one. Fixed assets depletion in the two areas is
extracted from the total depletion and the fixed assets stock ratio. Net production tax and operating surplus are derived
in the same manner from the total net production tax and the total input ratio, and the total operating surplus and fixed
assets stock ratio in the two areas respectively. Labor earnings are derived by extracting fixed assets depletion, net
production tax and operating surplus from total value added. The total production ratio in urban and rural areas adjusts
intermediate use, final use, export, import, etc.
5. Simulation
5.1 Sensitivity aalysis
The results of sensitivitiy analysis that indicate sensitivity to the change in GDP affected by the improvement of labor
and capital productivity, share change in the investment, taxation to value added of industrial sector are shown in Fig 2
to 6.
1.20
B eijing
urban
rural
1.15
C hange in G R P
(year 2020 /base year )
C hange in G R P
(year 2020 /base year )
1.20
1.10
1.05
1.15
1.10
1.05
1.00
1.00
0.0
0.2
0.4
0.6
0.8
0.0
1.0
0.2
0.4
0.6
0.8
1.0
grow th rate of labor productivity(%)
grow th rate of labor productivity(%)
1.20
1.20
B eijing
C hange in G R P
(year 2020 /base year )
C hange in G R P
(year 2020 /base year )
S hanghai
urban
rural
urban
rural
1.15
1.10
1.05
urban
rural
1.15
S hanghiai
1.10
1.05
1.00
1.00
0.0
0.2
0.4
0.6
0.8
1.0
grow th rate of capital productivity(%)
0.0
0.2
0.4
0.6
0.8
1.0
grow th rate of capital productivity(%)
Change in GRP (base case =1.0)
1.02
1.01
Beijing
Shanghai
1.00
0.99
0.98
0.0
1.0
2.0
3.0
4.0
5.0
production tax rate (%)
Figure 2-6. Results of sensitivity analyses
Firstly, with regard to the result of labor productivity and capital productivity, sensitivity [ as opposed to change of the
capital productivity of GDP ] is high in Beijing and Shanghai. The reason why Shanghai’s sensitibity is higher than that
in Beijing is considered that Shanghai has more capital intensive industrial structure. Secondly, regading tax levy on
manufacturing sector, sensitivity of Shanghai. This is considered to be due to the fact that in Shanghia, the share of
manufacturing secotr is relatively higher than that in Beijing.
5.2 Forecast by the CGE model
Here, the economic forecasts from 1997 in Beijing and Shanghai to 2020 are performed using a CGE model. The
items to be forecasted are GRP, industrial structure, and urbanization ratio.
(1) Base case
First, the future value of exogenous variables required for projection of basic case was set, as shown in Table 1. Those
value are following the BaU case where the past trend is followed. The result of calculation for future value, using the
exogenous-variables set for a standard case from 1997 to 2000 are shown in figure 7-11.
Table 1. Exogenous variables
urban
household
1997-2005
population growth rate
growth rate of labor
productivity
growth rate of capital
profitability
-
-
2.0%
2005-2010
1.0%
2010-2020
0.5%
1997-2005
3.0%
3.0%
-
2005-2010
2.0%
2.0%
-
2010-2020
1.0%
1.0%
-
1997-2005
0.0%
0.0%
-
2005-2010
0.0%
0.0%
-
2010-2020
0.0%
0.0%
-
agriculture
changes in value added
ratio
rural
total
household
urban
industry
rural
industry
rural
service
1997-2005
0.50%
1.50%
0.50%
1.50%
0.50%
2005-2010
0.50%
0.50%
0.50%
0.50%
0.50%
2010-2020
0.50%
0.25%
0.50%
0.25%
0.50%
agriculture
industry
service
1997-2005
0.00%
-1.00%
1.00%
changes in consumption
2005-2010
share (urban house hold)
0.00%
-0.75%
0.75%
2010-2020
0.00%
-0.50%
0.50%
1997-2005
-0.25%
-0.75%
0.75%
changes in consumption
2005-2010
share (rural house hold)
-0.13%
-0.50%
0.50%
2010-2020
0.00%
-0.50%
0.50%
1997-2005
0.0%
-2.0%
2.0%
2005-2010
0.0%
-1.0%
1.0%
2010-2020
0.0%
-0.5%
0.5%
changes in investment
share
urban
service
million yuan, const.'97
8,000
7,000
6,000
5,000
4,000
3,000
2,000
1,000
0
1990
1995
2000
2005
2010
2015
2020
2015
2020
2015
2020
%
Fig.7　GRP
16
14
12
10
8
6
4
2
0
1990
1995
2000
2005
2010
Fig.8　GRP growth rate
60
50
%
40
30
20
10
0
1990
1995
2000
2005
2010
Fig.9　share of secondary industry
70
60
%
50
40
30
20
10
0
1990
1995
2000
2005
2010
2015
Fig.10　share of tertiary industry
2020
100
80
%
60
40
20
0
1990
1995
2000
2005
2010
2015
2020
Fig.11　urbanization ratio
(2)Scenarios
Here, as opposed to the BAU scenario, service industry promotion scenario (scenario A) and industrialization
promotion (scenario B) was set. In Case A, rather than a standard case, 1%, the investment market share rate of increase
to tertiary industry is set up highly, and imposes a tax to an industrial section further. This assumes an environmental tax.
Although it should formulize so that a tax may originally be imposed to the amount of discharge of a contaminant, it has
set up here for simplification so that a products tax may be increased 5%. On the contrary, in Case B, it is the scenario
which promotes industrialization and the investment market share to a farm village industrial sector is espaially
expanded. In this scenario, the investment market share rate of increase to a city industrial section and the investment
market share rate of increase to farm village industry are set up higher than the standard scenario, 1% and 2%
respectively.
(3) Future projection result : example of Beijing case
Figure 12-14 illustrates the prediction result of GRP of Beijing in 2020, industrial structure, and the rate of
urbanization according to a scenario. First, on GRP, the scenario A which promoted service industries is the lowest, and
the scenario B of industrialization is conversely high. This is obtained although it does not solve as a result of reflecting
the scale of industrial likage of an in several sector, as mentioned above. However, in this analysis, there are five few
sectors, and since industrial urban industrial structure may not be reflected correctly, it is necessary to compare with the
calculation result at the time of expanding the number of sections. On the other hand, in view of urbanization rate,
Scenario A shows the highest value. The service industry of Shanghai is because most exists in the city, and this is
because population moved to the city from the farm village by labor demand expansion of a city service industry.
However, the rate of urbanization here is defined only by labor movement between a city area and a farm village area,
and the urbanization by the increase in population density of the farm village itself needs to care about the point which
is not taken into consideration.
GRP (million yuan, const.'97)
8,000
6,000
4,000
2,000
0
Base scenario
scenario A
scenario B
Figure12. Future GRP in different scenarios
100%
75%
50%
tertiary
secondary
25%
primary
0%
Base scenario
scenario A
scenario B
Figure 13. Future industrial structure in different scenarios
urbanization ratio (%)
100
75
50
25
0
Base scenario
scenario A
scenario B
Figure 14. Future urbanization ratio in different scenarios
6. Conclusion
In order to forecast the future economy and industrial structurre of Beijing and Shanghai, the simple CGE model was
built and some simple projection was performed. The result of this calculation is a projection value under the conditions
limited by model structure, and also has the portion with which neither original economy nor the situation of industry is
necessarily expressed. In order to perform more accurate future projection, it is necessary to solve the issues listed
below. (1) an improvement of the utility function of household’s demand system, especially the income elasticity and
the price elasticity should be included in this model (2) expansion of the sectors (This time, study is confined to the
rural, urban industry, urban agfriculture, urban serivice industry, and rural service industry), (3) environmental tax of
the number of parameter estimation. (4) Parameter estimation of export and import expansion (village, city industry,
farm village industry, city service industry, and farm village service industry) (5) Improvement in calculation method.
I received help in Mr. Shirakawa of Hiroshima University in carrying out this research. It describes here and gratitude
is expressed.