2.1 Model building
To understand the influence of increased water resources on Beijing’s economic development, we will first calculate the water consumption input–output table of all sectors using the input–output table of Beijing. This is followed by an analysis of the additional output of all key industrial sectors in Beijing resulting from the increased water volume, by calculating the direct value-added output coefficient and total value-added output coefficient of water consumption in all sectors. Lastly, we summarize the total benefit of South-to-North Water Diversion on Beijing’s economy.
Based on the above consideration, the direct economic influence (GDP
D) of South-to-North Water Diversion on Beijing is calculated in the following ways:
$${\mathbf{GDP}}_{\varvec{D}} = {\mathbf{\mu W}}$$
(1)
where
μ = ρ
θA/2 refers to the row vector of water consumption direct value-added output coefficient. Element
μ
i
refers to the value-added per unit water usage of sector
i and reflects the direct economic benefit of sectional production.
ρ refers to the water production elasticity, that is, the quantitative increment correlated with the increase of 1 m
3 total output of water consumption.
θ is the row vector of water consumption value-added of all sectors, wherein the element
θ
i
refers to the unit water consumption value-added of sector
i and
A refers to the direct consumption coefficient matrix of water resources.
W refers to the column vector of water consumption of South-to-North Water diverted to all industrial sectors.
When considering the economic relation between sectors, the contribution made by increased water supply to GDP from the perspective of the whole economic system needs to be examined, or the total economic influence (GDP
T) of the South-to-North Diversion Water needs to be calculated, as shown in Eq. (
2):
$${\mathbf{GDP}}_{\varvec{T}} = {\varvec{\gamma} \mathbf{W}}$$
(2)
where
γ = ρ
θB/2 refers to the row vector of the water consumption total value-added output coefficient and the element
γ
i
is the quantitative change value of the whole system value-added correlated with an increase or decrease of 1-unit water consumption in a certain sector. The definitions of
ρ,
θ and
W are the same as above, and
B refers to the complete consumption coefficient matrix of water resources.
2.2 Parameter estimation
Next, we calculate the water consumption of all sectors in Beijing and the values of ρ, θ, A and B based on the actual situation in Beijing. This is followed by the calculation of water consumption direct value-added output coefficient and complete value-added output coefficient of Beijing.
Firstly, to calculate the water consumption of all sectors in Beijing, this paper considers the water consumption of all sectors and the availability of water consumption data based on the sector category in Beijing 42 * 42 input–output table in 2007 and 2010. All related sectors are merged and the total value of the industrial sectors after treatment is 30. The principles for the merger of all sectors are as follows: (1) Primary industries are merged into one sector. (2) For secondary industries, handiwork and other manufacturing industries as well as waste products and materials are integrated into “other industries,” with 23 sectors in total. (3) For tertiary industries, this research divides the service sector into the following categories: transportation, storage and post, wholesale and retail, hotels and catering services, renting and leasing business services, management of water conservancy, environment and public facilities, education, health, social security and social welfare, culture, sports and entertainment, public management and social organization and other service industries (including postal services, information transmission, computer service and software industry, financial industry, real estate, research and development industry, synthesis technique service industry, neighborhood services and other service industries). Classification is based on the water consumption data of the tertiary industrial sectors provided by the Beijing Water Authority.
Using the total water consumption of Beijing and the water consumption of all sectors as control data, and with the assumption that the water consumption structure of Beijing industrial sectors is identical to that of the whole country, we adjust and calculate the water consumption of industrial sectors in Beijing from 2008 to 2013 based on the
China’s Statistic Yearbook,
Beijing Water Resources Bulletin (2008–2013), Research Group of China Input–Output Association (
2007) and the data and research conclusion of Wang et al. (
2008). Based on the water consumption of all industrial sectors in Beijing, we find that water consumption differs greatly for different industrial sectors. In particular, the water consumption of the agricultural sector, which had been consistently high, now shows a downwards trend (reduced from 1.2 billion cubic meters in 2008 to 0.909 billion cubic meters in 2013). The increment of the agricultural production value shows the increased water consumption efficiency of the agricultural sector. The total water consumption of industrial sector is reduced year on year, since Beijing readjusts the industrial structure every year and shuts down industries which consume a lot of water and energy. The annual water consumption of the service sector is relatively stable and water consumption efficiency is increasing year on year. Sectors can be categorized into high-water-consumption sectors (direct water consumption of more than 30 million tons), medium-water-consumption sectors (direct water consumption between 8 and 30 million tons) and low-water-consumption sectors (direct water consumption below 8 million tons) according to the actual water consumption of the sector; see Table
1.
Table 1
Categorization of water consumption sector (take 2013 as the example)
High-water-consumption sector | Agriculture, manufacture of foods and tobacco, processing of petroleum, coking, processing of nuclear fuel, chemical industry, smelting and rolling of metals, production and processing industry of electric and thermal power, construction, wholesale and retail trades, hotels and catering services, management of water conservancy, environment and public facilities, education and public management and social organization |
Medium-water-consumption sector | Coal mining and washing, metal separation, manufacture of textile, papermaking and stationery manufacturing, manufacture of communication equipment, computer and other electronic equipment, culture, sports and entertainment, renting and leasing business services, health, social security and social welfare |
Low-water-consumption sector | Extraction of petroleum and natural gas, mining of nonmetal ores, manufacture of garment/feather/down feather and other fiber products, processing of timbers and manufacture of furniture, manufacture of nonmetallic mineral products, manufacture of metal products, manufacture of general purpose and special purpose machinery, manufacture of transport equipment, manufacture of electrical machinery and equipment, manufacture of measuring instruments and machinery for cultural activity and office work, production and distribution of gas, production and distribution of water, other industries, transport, storage and post |
Secondly, the decomposition of inputs into capital (
K), labor (
L), energy (
E) and intermediate materials (
M) was applied by Jorgenson et al. (
1987). In this paper, in order to calculate the output elasticity
ρ of water, we use water as an intermediate material, which as the capital and the labor force of the Cobb–Douglas production function, so as to calculate the output elasticity of water. To be specific, the three-element production function can be calculated as follows:
$$Z = AK^{\alpha } L^{\beta } W^{1 - \alpha - \beta }$$
(3)
where
Z,
L and
K represent output, labor force and capital, respectively.
W represents water resource and
A represents coefficient of technical efficiency.
α and
β represent output elasticity of the labor force and that of the capital, respectively. After linearization to the above equation through natural logarithm, we attain:
$$\ln \left( {\frac{Z}{W}} \right) = \ln A + \alpha \cdot \ln \left( {\frac{K}{W}} \right) + \beta \cdot \ln \left( {\frac{L}{W}} \right)$$
(4)
Using Eq. (
4), we conduct regressive calculation of Beijing’s data from 2002 to 2013 and estimate
α and
β.
1 The data are sourced from the
Statistical Yearbook of Beijing over the years.
Water output elasticity
ρ over the years can be determined using Eq. (
5), the results of which is shown in Table
2:
$$\rho_{t} = {\raise0.7ex\hbox{${\left\{ {\ln \left( {Z_{t} } \right) - \ln A - \alpha \ln \left( {K_{t} } \right) - \beta \ln \left( {L_{t} } \right)} \right\}}$} \!\mathord{\left/ {\vphantom {{\left\{ {\ln \left( {Z_{t} } \right) - \ln A - \alpha \ln \left( {K_{t} } \right) - \beta \ln \left( {L_{t} } \right)} \right\}} {\ln \left( {W_{t} } \right)}}}\right.\kern-0pt} \!\lower0.7ex\hbox{${\ln \left( {W_{t} } \right)}$}}$$
(5)
Table 2
Water output elasticity over the years
Thirdly, we calculate the unit water output coefficient
θ
it
of industrial departments. Coefficients of various industrial departments’ water output are their unit water outputs, which can be considered as the reciprocal of the water consumption volume per RMB 10,000 GDP. This can be calculated by dividing various industrial departments’ water consumption volumes using their added value through the input–output table, as shown in Eq. (
6):
$$\theta_{it} = {\raise0.7ex\hbox{${\overline{{{\text{GDP}}_{it} }} }$} \!\mathord{\left/ {\vphantom {{\overline{{{\text{GDP}}_{it} }} } {\overline{\text{TW}}_{it}^{\text{Beijing}} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${\overline{\text{TW}}_{it}^{\text{Beijing}} }$}}$$
(6)
As the government of Beijing only published the input–output table for the year of 2007 and 2010, various departments’ added value in other years can be derived using the following method: (1) For the year of 2007 and 2010, the data in the input–output table are used directly. (2) Various departments’ added value in 2008, 2009, 2011, 2012 and 2013 are derived through adjustment from relevant data in the Statistical Yearbook of Beijing. Unit water output coefficients of various departments can be derived with the help of their individual water consumption volumes.
In addition, the water’s direct consumption coefficient matrix is derived on the basis of the ordinary value type input–output table. Sector
j produces the unit product by direct consumption of sector
i’s product volume, which is referred to as sector
j’s direct consumption coefficient to sector
i, represented by
a
ij
:
$$\varvec{a}_{{\varvec{ij}}} = \frac{{\varvec{X}_{{\varvec{ij}}} }}{{\varvec{X}_{\varvec{j}} }}\varvec{ }\quad \left( {i,j = 1, \, 2, \, 3, \ldots ,30} \right)$$
(7)
where
X
j
is sector
j’s added value and
X
ij
is sector
i’s input of added value to sector
j. Direct consumption coefficient matrix
A is the 30-order matrix comprised of various departments’ direct consumption coefficients. The water’s complete consumption coefficient is the sum of the total direct consumption coefficient and the total indirect consumption coefficient. Based on the direct consumption coefficient matrix, the water’s complete consumption coefficient matrix
B is calculated through the Leontief matrix.
Lastly, based on the foregoing built model, the water direct value-added output coefficient and the water complete value-added output coefficient of Beijing’s various industrial departments are derived as shown in Table
3.
Table 3
Water direct and water complete value-added output coefficients (RMB/m3)
AFA | 27.56 | 103.55 | 133.54 | 519.74 |
MWC | 42.78 | 161.43 | 229.29 | 946.33 |
PNG | 91.54 | 120.03 | 225.46 | 507.62 |
MMO | 44.44 | 79.27 | 137.13 | 691.85 |
MNO | 85.24 | 334.74 | 267.51 | 1018.79 |
MFT | 51.37 | 136.36 | 191.18 | 663.34 |
MAT | 40.35 | 96.4 | 159.62 | 582.65 |
TFC | 41.66 | 101.75 | 148.13 | 564.2 |
TMF | 76.29 | 164.72 | 252.84 | 745.3 |
PPA | 48.97 | 106.93 | 190.09 | 552.72 |
PCN | 85.96 | 183.17 | 316.48 | 719.51 |
CHI | 38.19 | 127.03 | 161.48 | 658.81 |
NMP | 65.47 | 215.39 | 254.73 | 892.11 |
SRM | 29.6 | 109.83 | 191.58 | 813.92 |
MMP | 45.36 | 110.79 | 209.62 | 725.8 |
GSM | 160.19 | 237.83 | 369.02 | 822.06 |
MTE | 157.46 | 379.79 | 454.27 | 1237.95 |
EME | 136 | 247.17 | 350.35 | 859.63 |
CCO | 171.59 | 164.61 | 545.74 | 864.8 |
MCO | 243.32 | 254.76 | 526.91 | 816.43 |
PEH | 20.22 | 114.8 | 116.84 | 725.89 |
PDG | 26.28 | 313.87 | 73.76 | 892.56 |
PDW | 95.88 | 193.11 | 259.57 | 810.98 |
OTI | 35.11 | 124.98 | 195.15 | 726.01 |
CON | 67.67 | 187.36 | 242.69 | 825.63 |
TSP | 94.29 | 381.09 | 265.63 | 1081.56 |
WRT | 57.33 | 187.98 | 163.23 | 573.46 |
HCS | 37.74 | 129.44 | 144.38 | 607.38 |
RLB | 89.77 | 231.42 | 257.52 | 790.51 |
WEP | 45.4 | 143.78 | 172.88 | 655.91 |
EDU | 41.76 | 91.05 | 142.34 | 380.57 |
HSS | 34.15 | 79.96 | 156.98 | 544.21 |
CSE | 61.9 | 155.41 | 193.21 | 584.71 |
PMS | 58.88 | 173.1 | 173.7 | 661.86 |
OTS | 82.65 | 186.36 | 244.65 | 619.55 |
Based on the water direct value-added output coefficients of Beijing’s various industrial departments, the water output effect of different industrial departments varies significantly. If the water direct value-added output coefficient is used as a basis for classification, then we can categories the industrial departments into: high-output departments (output coefficient above 200 yuan/m
3), medium-output departments (output coefficient between RMB 100–200/m
3) and low-output departments (output coefficient below RMB 100/m
3). The categories reflect the efficiency of various industrial departments in terms of direct water consumption. Table
4 describes the direct water consumption efficiency of various industrial departments in 2013.
Table 4
Various industrial departments’ direct water consumption efficiency (for the year 2013 as an example)
High-output departments | Mining and separating of nonmetal ores and other ores, manufacturing of nonmetallic mineral products, manufacturing of general purpose and special purpose machinery, manufacturing of transport equipment, manufacturing of electronic machinery and apparatus, manufacturing of measuring instruments and machinery for cultural activity and office work, production and distribution of gas, other industrial, scientific and technical services |
Medium-output departments | Mining and washing of coal, extraction of petroleum and natural gas, mining of metal ores, manufacturing of foods and tobacco, processing of timbers and manufacturing of furniture, processing of petroleum, coking, processing of nuclear fuel, chemical industry, smelting and rolling of metals, manufacturing of metal products, manufacturing of communication equipment, computer and other electronic equipment, production and supply of electric power and heat power, production and distribution of water, construction, commercial services, hotels and catering services, public management, other services |
Low-output departments | Agriculture, manufacture of textile, textile/garment/shoe/hat/feather and their manufacture, papermaking, printing and manufacture of articles for culture, education and sports activities, education and sport activities |