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Citation: Xu R, Wu Y, Chen M, Zhang X, Wu W, Tan L, et al. (2019) Calculation of the contribution rate of China’s hydraulic science and technology based on a feedforward neural network. PLoS ONE 14(9): e0222091. https://doi.org/10.1371/journal. pone.0222091
Editor: Baogui Xin, Shandong University of Science and Technology, CHINA
Received: March 21, 2019 Accepted: August 21, 2019 Published: September 11, 2019
Copyright: © 2019 Xu et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability Statement: All relevant data are within the manuscript and its Supporting Information files.
Funding: This work was supported by the National Key Research and Development Program of China (No. 2017YFC0405805, 2017YFC0405803) and Basic Research Projects of the Central Research Institute in Nanjing Hydraulic Research Institute (No. Y516031, Y517013, Y517015, Y519001). The funder provided support in the form of salaries for authors R.R Xu, Y.X Wu, G.X. Wang, X. Zhang, W.
RESEARCH ARTICLE
Calculation of the contribution rate of China’s hydraulic science and technology based on a feedforward neural network
Rongrong XuID1, Yongxiang Wu1,2*, Ming Chen1, Xuan Zhang3, Wei Wu1, Long Tan4, Gaoxu Wang1, Yi Xu1, Bing Yan1, Yuedong Xia5
1 Hydrology and Water Resources Department, Nanjing Hydraulic Research Institute, Nanjing, China,
2 State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineer, Nanjing, China, 3 Hydrology and Water Resources College, Hohai University, Nanjing, China, 4 Sina Com Technology (China) Co. LTD, Beijing, China, 5 Water Conservancy Bureau of Pinghu, Jiaxing, China
* yxwu@nhri.cn
Abstract
Quantitative analysis of the contribution rate of China’s hydraulic science and technology and analysis of the underlying reasons behind changes provide an important foundation upon which the government can formulate water policies. This paper abandons the assump- tion of a scale economy and separates the changes of benefits brought about by the scale from scientific and technological progress, thus changing the C-D production function from linear to nonlinear. Based on a feedforward neural network, it calculates the coefficient of the output elasticity, the economic contribution rate of China’s hydraulic science and tech- nology and the scale economies for each year using relevant data from 1981 to 2016. The results show that (1) the average contribution rate of capital investment from 1981 to 2016 was 47.3%, and the average contribution rate of labor from 1981 to 2016 was 9.1%. It is not obvious that the significant increase in the labor force has contributed to the growth of Chi- na’s water conservancy industry. (2) The average contribution rate of scale economies in 1981–2016 was 26.7%, and the contribution rate of scale economies is negatively corre- lated with the capital contribution rate. (3) The average contribution rate of China’s hydraulic science and technology was 43.6% from 1981 to 2016, and the average contribution rate of the total factor productivity after removing scale economies from 1981 to 2016 was 16.9%. During the period of the 6th Five-Year Plan(1981~1985), the contribution rate of water con- servancy science and technology was relatively high. Since that time, it has remained at 40%. In recent years, as water conservancy reforms in key areas have made positive prog- ress, scientific and technological progress has increased the growth of water conservancy benefits annually.
1 Introduction
In recent years, water resources in China have faced practical problems of flooding, droughts, water quality pollution, and soil loss [1], and the government of China has stated that the
PLOS ONE | https://doi.org/10.1371/journal.pone.0222091 September 11, 2019 1 / 22
Wu, but did not have any additional role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript. The specific roles of these authors are articulated in the ‘author contributions’ section. Sina Com Technology (China) Co. LTD didn’t play a role in this study.
Competing interests: The authors have declared that no competing interests exist and have approved submission to the journal. Author Long Tan is an employee of Sina Com Technology (China) and Sina Com Technology (China) does not alter the authors’ adherence to PLOS ONE policies on sharing data and materials.
proportion of research and development investment in these sectors of the economy will increase to more than 2.5% of GDP by 2020, while the contribution rate of science and tech- nology will reach more than 60% [2]. Quantitative analysis of the contribution rate of China’s hydraulic science and technology can provide valuable information on the investment benefits of China’s water conservancy projects [3]. However, accurately and scientifically measuring the contribution rate of science and technology has been a relatively complex theoretical prob- lem that has not been well solved [4]. In particular, the benefits of water conservancy projects are significantly affected by the climate of each year, so they have strong uncertainty [5]. This paper evaluates the total factor productivity of water conservancy science and technology in China over the past 40 years.
The total factor productivity, as an important concept by which to measure economic effi- ciency, is an important tool for use in analyzing the sources of economic growth [6,7]. In par- ticular, it is an important basis upon which the government can formulate policies for long- term sustainable development [8]. Many countries have proposed various methods to measure the total factor productivity, including the Cobb–Douglas production function [9], the Solow residual model [10], data envelopment analysis [11], and the frontier production function [12]. Cobb and Douglas [13] established mathematical models of inputs and outputs and cal- culated the contribution of technological progress to the increase in the total output value. Abramovitz [14] stated that in addition to the growth in outputs from production factors, other factors also contribute to total output value growth. Solow [15] proposed a production function that incorporates scientific and technological progress and quantitatively separates the role of scientific and technological progress in economic growth, Jorgenson [16] broke down production factors into capital and labor and further improved the Solow model.
Since the mid-1980s, a group of economists including Paul M.Romer and Lucas [17] have begun to break through the analysis framework of neoclassical growth theory and put forward new ideas on economic growth. Romer [18] constructed a model to explain the economic growth with increasing returns with scale and the externality of knowledge, proving that under the above assumptions, the economy may have a competitive equilibrium and that the social optimal competitive equilibrium is generally socially suboptimal. Lucas [19] put forward the assumption of perfect competition and began to build models under the framework of monop- oly competition.
The total factor productivity has quite extensive applications in economics. It can be used to calculate the impacts of different inputs in an economy on the total factor productivity. Wu et al. [20] established a dynamic spatial regression model using provincial panel data and found that corruption directly reduces the total factor productivity of a region. Christiano
et al. [21] estimated a New Keynesian model supposed that a firm is faced with price rigidity and found that the decline of the total factor productivity and rising operating costs played big roles during the Great Depression. The concept of total factor productivity has also been applied to climate change [22,23]. Zhong et al. [24] used data envelopment analysis to build a data model embedded with climate change information and calculated the total factor pro- ductivity of Chinese agriculture. Moore et al. [25] implemented empirical estimates of the temperature effects on GDP growth rates in the DICE model through two pathways: total factor productivity growth and capital depreciation. Dellink et al. [26] developed storylines of the shared socioeconomic pathways (SSPs), and predicted the factors affecting the GDP per capita, which are the total factor productivity, population, capital and energy. The con- cept of total factor productivity has also been applied to the study of carbon dioxide emis- sions [27,28]. Li et al. [29] used stochastic frontier functions to analyze the relationship between carbon dioxide and production technologies in China. Fan et al. [30] used the global Malmquist-Luenberger index method that consider carbon dioxide emission to study the
Calculation of the contribution rate of China’s hydraulic science and technology
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Calculation of the contribution rate of China’s hydraulic science and technology
improvement of the total factor CO2 emission performance relationship through scientific and technological progress. The production function and water price [31,32] have also been studied, and it has been shown that different production functions should be selected to bet- ter reflect reality [33].
The current method for measuring the contribution rate of water conservancy science and technology in a monopoly industry is mainly based on the C-D production function and the Solow residual value method [34,35]. Kong [36] used solow model to calculate the contribu- tion rate of water conservancy science and technology in China, and predicted the future development of hydraulic technology [37]. The values of the capital-output elasticity coeffi- cient α and the labor output elasticity coefficient β in the model strongly influence the final result of the contribution rate of water conservancy science and technology [38]. At present, there are some disadvantages to estimating model parameters using the empirical value method [39] or the neoclassical growth theory, the empirical value method is subjective, and the neoclassical growth theory lacks a solid foundation in reality [40]. The neoclassical growth theory has two core assumptions: one is exogenous technology, and the other is the constant return of the scale of production. Therefore, if there is a scale economy effect, the result of
the water conservancy science and technology contribution rate will be distorted [41]. In
this paper, we abandon the second assumption of the neoclassic growth theory, and separate the changes in benefits brought about by the scale from scientific and technological progress, thus changing the model from linear to nonlinear. Based on the partial derivative of the feed- forward neural network output function, the partial derivative is used to fit the production function.
There are some limitations in using a multilayer feedforward network. The number of hidden layer nodes in neural network is related to the complexity of mapping relation. The fewer the number of hidden layer nodes, the more difficult the network is to describe com- plex problems. However, too much number will lead to the increase of training time of neu- ral network, and too many networks will overfit. Therefore, when using neural network to calculate the contribution rate of water conservancy science and technology in China, it is necessary to choose the appropriate network structure to get the ideal result. Another defect of neural networks is local optimum, Most of the current algorithms can be divided into
two categories: gradient descent and numerical computation. It is difficult to compare which algorithm is better in the actual situation, and researchers are often required to conduct sim- ulation experiments.
Generally speaking, neural network is more complex than traditional solow residual method, and the network and algorithm need more elaborate design. However, through the neural network algorithm, the production function can be made more flexible, and the effect of economies of scale on the overall return can be well calculated. We abandon the unreason- able assumptions in the model and make the model closer to reality. In this paper, we design an algorithm to overcome. From this algorithm, the output elasticity of production factors is calculated, and the contribution rate of water conservancy science and technology is estimated for each year. The deep-seated reasons behind the changes are analyzed to provide a reference for the government to use when formulating water conservancy policies and long-term control measures.
This paper was organized as follows: Section 2 described the data and calculation method in detail. Section 3 set the key parameters of the neural network and described calculation results. Section 4 compared the results to those using another production function, and then discussed the development direction of water conservancy technology in China, summarized the concept and calculation method of the total factor productivity, and presented the future prospects for research on this topic.
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Calculation of the contribution rate of China’s hydraulic science and technology
2 Data and methodology
2.1 Data source and processing
2.1.1 Calculation of the annual water conservancy benefits in China. The scope of the water conservancy benefits includes six major benefits: the irrigation benefit, hydropower ben- efit, flood control benefit, water supply benefit, soil and water conservation benefit, and water logging control benefit.
The irrigation benefit is mainly reflected in the increase in the yield and output of agricul- tural products due to irrigation. The increased agricultural output is the result of a combina- tion of irrigation and agricultural measures and is deduced by the apportion coefficient of the water conservancy irrigation benefit.
The direct financial benefit of hydropower is obtained by multiplying the electric energy production (after deducting factory power consumption and line losses) by the electricity price. It is calculated by multiplying the hydroelectric energy production in China by the national average electricity price for water conservancy systems annually.
The benefits of new flood protection projects that reduce flood damage include the sum of the direct economic losses of various sectors of the national economy, including industry, agriculture, commerce, transportation, construction, and property in inundated areas. The flood control benefit is obtained by multiplying the area experiencing disaster reduction due to the flood prevention project by the total loss in terms of the Mu unit price.
The water supply benefit refers to the urban water supply benefits from water conser- vancy projects. After utilizing the input-output coefficient obtained from the weighted average of the water supply investment and water supply benefits over the years, the water supply benefits can be calculated according to the national annual investment in water sup- ply projects.
The soil and water conservation benefits mainly include direct income from agriculture, forestry, animal husbandry, and fishing in addition to other social and economic benefits.
Waterlogging control benefits refer to the increased production of primary crops after building a waterlogging control project. This benefit generally reflects the national waterlog- ging control benefit, which is calculated according to the annual waterlogging control area and the waterlogging control benefit per acre.
The retail price index is selected for analysis, the economic benefits of China’s water conser- vancy system are shown in Table 1.
2.1.2 Input data estimation. Capital stock estimation: This paper selects the fixed
capital formation from the “China Water Conservancy Statistical Yearbook” as the investment
flow indicator in the current year. Assuming that the output and capital stock have the
same average growth rate over a given period, the average growth rate of the capital stock
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
is g 10 Y1990=Y1980 1⁄4 0:0665; I1980 = 2.707 billion; the average asset depreciation
1⁄4I �ð1þgÞg g1⁄414:86%;andthebaseperiodcapitalstockK =I /(g+d)=12.58484
0 ~I 1980 1980
billion. The capital stock of the water conservancy industry in each year was converted to the 1980 price level, as shown in Table 2.
Labor input estimation: The contribution of labor to the water conservancy system, excluding labor by those engaged in work with earth and stone, should be attributed to the labor input. According to the relevant data from the “China Water Conservancy Statistical Yearbook” for past years, the annual labor input of the national water conservancy system is calculated by taking the average between the beginning and ending dates of the year, as shown in Table 2.
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Calculation of the contribution rate of China’s hydraulic science and technology
零售物价指数
Table 1. Benefits from the water conservancy system from 1979 to 2016.
Retail Price index
Flood control
Waterlogging control
Irrigation
Hydropower
Water supply
Soil and water conservation
94.34
213.69
92.66
196.58
50.37
2.55
270.38
100.00
211.23
93.163
198.95
58.38
2.356
274.023
102.40
187.22
93.417
197.778
65.736
3.146
277.319
104.35
169.05
94.444
198.035
74.615
3.536
275.754
105.91
146.11
95.007
197.558
86.608
7.418
282.366
108.88
120.64
96.045
196.964
87.036
8.216
297.136
118.46
108.01
97.008
195.062
92.642
8.448
308.922
125.56
114.25
97.931
194.818
94.754
8.814
319.016
134.73
118.49
98.961
195.2
100.52
8.97
329.797
162.35
117.14
99.514
195.257
109.494
9.045
341.923
192.39
116.49
100.377
196.709
118.643
9.154
347.283
196.43
126.34
100.937
196.92
127.068
10.216
352.723
214.67
141.42
102.209
199.207
125.162
11.86
371.814
247.51
165.48
103.198
201.294
131.781
14.7
390.439
313.35
191.85
103.792
202.821
151.137
18.267
407.871
345.93
229.93
102.722
203.223
185.336
25.337
426.696
397.13
269.47
104.69
205.154
187.342
29.48
445.174
421.35
310.17
105.855
208.198
187.442
33.759
461.595
424.72
363.12
107.145
212.707
195.165
42.239
481.045
413.68
464.96
107.953
217.311
204.893
50.513
499.556
401.27
566.52
108.777
221.242
81.487
59.072
518.241
395.25
693.55
109.566
223.876
94.775
71.313
539.103
392.09
620
109.731
225.926
104.109
95.329
542.952
386.99
955.69
110.127
227.314
113.688
140.479
568.728
386.60
1037.09
110.337
227.487
121.119
176.41
657.317
397.43
1107.14
110.654
228.918
123.257
215.373
612.636
400.61
1113.5
111.395
230.181
151.739
250.084
630.282
404.62
1162.01
111.584
232.281
164.075
312.116
649.173
419.99
1189.61
111.808
235.145
180.422
401.836
665.021
444.77
1470.79
111.836
237.951
222.744
506.475
676.448
439.43
1600.16
112.67
241.165
200.58
690.521
696.144
453.06
2479.34
113.231
245.585
270.282
909.856
711.16
475.26
506
113.387
251.013
258.147
1152.65
730.231
484.76
892
114.095
254.305
343.494
1533.1
685.543
491.55
2358
114.543
258.303
369.168
1849.29
711.772
498.92
379
116.768
262.646
422.331
2155.86
743.182
506.91
422
118.562
268.07
441.426
2962.66
769.091
517.55
2354
120.41
274.423
466.546
3732.8
801.72
Year Total
1979 826.23
1980 838.102
1981 824.616
1982 815.434
1983 815.067
1984 806.037
1985 810.092
1986 829.583
1987 851.938
1988 872.373
1989 888.656
1990 914.204
1991 951.672
1992 1006.89
1993 1075.74
1994 1173.24
1995 1241.31
1996 1307.02
1997 1401.42
1998 1545.19
1999 1555.34
2000 1732.18
2001 1698.05
2002 2116.03
2003 2329.76
2004 2397.98
2005 2487.18
2006 2631.24
2007 2783.84
2008 3226.24
2009 3541.24
2010 4729.45
2011 3011.43
2012 3822.53
2013 5661.08
2014 4079.79
2015 4981.81
2016 7749.89
unit: 100 million yuan
https://doi.org/10.1371/journal.pone.0222091.t001
2.2 Production function selection
Among the many production functions, the most commonly used production functions are the Cobb-Douglas production function, linear production function, Leontief production func- tion[42], constant elasticity of substitution production function[43] and translog production function[44], as shown in Table 3.
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固定资产投资价格指数 Y
Table 2. Capital and labor input to the water conservancy system over time. Year
K
L
Labor force
Calculation of the contribution rate of China’s hydraulic science and technology
Fixed asset investment price index
Fixed assets formation (current prices)
Fixed assets formation (1980 prices)
Capital stock of fixed assets (1980 prices)
100.00
27.07
27.07
125.85
103.00
13.57
13.14
120.32
106.00
17.48
16.54
118.93
108.00
21.13
19.52
120.82
113.00
20.68
18.36
121.17
121.00
20.16
16.69
119.82
129.00
22.86
17.79
119.74
135.00
27.08
20.03
122.01
154.00
30.65
19.96
123.78
167.00
35.55
21.33
126.67
180.36
48.72
27.72
134.86
192.00
64.87
33.71
148.61
222.00
97.17
43.80
170.29
281.00
124.93
44.48
189.45
310.00
168.74
54.42
215.73
328.29
206.32
62.83
246.52
341.42
238.51
69.84
279.74
347.23
315.41
90.81
329.01
346.53
467.56
134.89
415.05
345.15
499.15
144.58
497.99
348.94
612.94
175.61
599.65
350.34
560.97
160.08
670.66
351.04
819.22
233.31
804.37
358.76
743.41
207.17
892.06
378.85
790.31
208.55
968.10
384.91
827.39
214.89
1039.20
390.69
932.72
238.68
1123.51
405.92
1026.52
252.81
1209.44
442.05
1604.09
362.78
1392.59
431.44
1702.69
394.55
1580.31
446.97
2707.61
591.07
1951.25
476.47
3452.1
732.39
2385.80
481.81
4117.2
854.53
2885.80
483.26
3954.0
818.19
3275.16
485.67
4345.1
894.65
3683.126
476.93
5452.2
1143.18
4278.99
488.85
6113.99
1250.69
4929.77
1980 102.49
1981 102.43
1982 102.315
1983 101.775
1984 104.18
1985 107.98
1986 111.15
1987 118.645
1988 128.805
1989 134.745
1990 136.88
1991 140.8
1992 144.25
1993 147.95
1994 149.98
1995 151.625
1996 156.55
1997 158.405
1998 155.705
1999 151.11
2000 143.455
2001 134.77
2002 130.16
2003 125.865
2004 120.525
2005 114.33
2006 109.815
2007 107.965
2008 106.165
2009 104.655
2010 105.215
2011 104.58
2012 102.935
2013 103.7
2014 100.55
2015 95.9
2016 93.6
Unit: 100 million yuan, 10,000 persons
https://doi.org/10.1371/journal.pone.0222091.t002
The main differences between the production functions lie in the assumption of elasticity of substitution, and the values of the elasticity of substitution of these production functions are shown in Table 4.
According to the characteristics of each production function, we can obtain some conclusions:
1. Thelinearproductionfunctiondescribesaproductionmodelwithaconstantreturnon scale, which can be used in economic analysis, including constant economies of scale. In
PLOS ONE | https://doi.org/10.1371/journal.pone.0222091 September 11, 2019 6 / 22
Calculation of the contribution rate of China’s hydraulic science and technology
Table 3. Commonly used form of the production function. Production function name
Cobb-Douglas production function
Linear production function
Leontief production function
Constant elasticity of substitution production function(CES) Translog production function
Production function form
YN y1⁄4b xbn
0n n1⁄41
y 1⁄4 b0 þ XN XM
XN bnxn
y 1⁄4
y 1⁄4 b 0 ð
n1⁄41 bnmðxnxmÞ0:5
n1⁄41 m1⁄41
XN m
b n x nr Þ = r bnInxn
n1⁄41
y 1⁄4 expðb0 þ
XN n1⁄41
þ 12
XN XM n1⁄41 m1⁄41
bnm lnxn lnxm Þ
https://doi.org/10.1371/journal.pone.0222091.t003
this paper, we abandon the assumption that the economies of scale of the CD production function are constant.
2. Theconstantelasticityofthesubstitutionproductionfunction(CES)improvestheelasticity
of substitution of the Cobb-Douglas production function. For different research objects or
different sample intervals of the same research object, the elasticity of substitution is differ-
ent because of the difference in sample values. The substitution elasticity of the constant
elasticity of the substitution production function is 1 , while the substitution elasticity of 1þr
the Cobb-Douglas production function is 1, and this makes the constant elasticity of the substitution production function more realistic than that of Cobb-Douglas production function.
3. TheelasticityofsubstitutionoftheLeontiefproductionfunctioniszero,andthisshows that there is no substitution between input factors.
4. Thetranslogproductionfunctioncanbeconvertedtoanyformofsecond-orderTaylor approximation of the production function, and it can be used to test whether the elasticity of substitution is constant. The translog production function has good mathematical prop- erties, but it requires complete panel data, so the transcendental logarithm function is not used for comparison in this paper.
Based on the data in this article, we used a more general C-D production function that con-
siders scale economy effects for analysis, and we also used CES production functions to com- pare the results of the C-D production function. The methods of CES production functions are shown in the S1 File.
Table 4. Commonly used forms of production functions.
Production function name
Cobb-Douglas production function
Linear production function
Leontief production function
Constant elasticity of substitution production function Translog production function
https://doi.org/10.1371/journal.pone.0222091.t004
Elasticity of substitution
1
1
0 Constant Variable
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Calculation of the contribution rate of China’s hydraulic science and technology
The C-D production function and Solow residual value method assume that the sum of the output elasticities of production factors is 1. If there is no scale economy, this assumption will attribute the changes in benefits brought about by the scale change to scientific and technologi- cal progress. The C-D production function and Solow residual method do not consider the impacts of scale economies, which will lead to errors in the results of the contribution rate of scientific and technological progress.
This paper does not assume scale economies. The production function:
QðtÞ 1⁄4 AtKaLb ð1Þ
Let capital productivity P1 = Y/K and labor productivity P2 = Y/L, Convert Eq (1) to:
QðtÞ 1⁄4 Pa� Pb� Ka� Lb� ð2Þ
12
InEq(2),α� =α/(α+β),β� =β/(α+β),α� +β� =1.
Lety1⁄4DQðtÞ; k1⁄4DK; l1⁄4DL; a1⁄4dlnAt.ChangeEq(1)toadifferentialform:
QðtÞ K L dt
yt 1⁄4at þatkt þbtlt 1⁄4at þ1⁄2ðat at 1Þkt þðbt bt 1Þlt�þat 1kt þbt 1lt
1⁄4at þ1⁄2ðat at 1Þkt þðbt bt 1Þlt þðat 1 a�t 1Þkt þðbt 1 b�t 1Þlt�þða�t 1kt þb�t 1ltÞ ð3Þ 1⁄4at þ1⁄2ðat a�t 1Þkt þðbt b�t 1Þlt�þða�t 1kt þb�t 1ltÞ:
αt and βt are the output elasticities of capital and labor in year t. The first item in Eq (3) is the Solow residual value produced after eliminating the scale economy. The second item is the output change (st) brought about by the scale economy effect. The sum of the first two items constitutes the total factor productivity (TFP). The third item is the output changes brought about by the change in production factors. Through this method, the increased output brought by scale economies can be removed from the TFP.
2.3 The C-D production function calculation method
2.3.1 The challenges of the C-D production function calculation in a multilayer feedfor- ward network. Next, the effect of the scale economy on the output growth must be calculated based on the Eq (3). When using multivariate regression analysis, which requires a longer time series, it is easy to miss changes in capital, labor, and technology for the current year. Addition- ally, in this paper, if α and β are constants, the output change (st) brought about by the scale economy effect will be equal to zero, which will be contrary to the original intention of this paper. Therefore, ordinary least squares(OLS) cannot be used.
A multilayer feedforward network can describe extremely complex nonlinear systems and handle the random characteristics of the original data. A multilayer feedforward network is a universal approximator that can automatically simulate a system when there is sufficient train- ing time.
In the structural design of a feedforward network, the node scale should be reduced as much as possible to reduce the system complexity and learning time while still meeting the requirements. The number of nodes is related to the complexity of the object to be expressed in the model. If the number is too small, the model struggles to describe real problems. If the number is too large, however, the degree of nonlinearity becomes higher, the training time increases, and the model becomes prone to the “overlearning” phenomenon. As a result, the ability of the model to generalize deteriorates. Therefore, the principle used to select the num- ber of nodes in this paper is based on the correct reflection of the relationship between the
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input and output, and fewer hidden layer nodes are used to make the network structure as sim- ple as possible.
The multilayer feedforward network uses a single-track multilayer structure in which each layer contains several nodes. The nodes in the same layer are not connected and the informa- tion between the layers is transmitted in only one direction. A single-layer feedforward net- work can only distinguish linearly separable modes while a multilayer feedforward network can be used for any classification problem. In addition, a multilayer feedforward network can be used as a general function approximator. A two-layer feedforward network can approxi- mate any complex continuous function as long as there are enough nodes in its hidden layer with an s-shaped activation function of the hidden layer and a linear activation function of the output node. Therefore, this paper selects a two-layer feedforward network with a hidden layer as the research method.
In the research process, we find that there are two main problems of the BP algorithm: the slow convergence speed and the local minimum point of the function. To resolve the slow con- vergence speed, a network pruning algorithm is used to delete redundant input nodes. At the same time, based on the sensitivity analysis, we analyze the influence of parameters on the system, the influence of small disturbances in the parameters on the network output, and the importance of the network parameters. When the function has a local minimum point, the adaptive variable step length algorithm is selected, which means that the learning compensa- tion adjusts with the variation in the error surface.
2.3.2 The solutions of the C-D production function calculation.
1) Sensitivity Analysis
Sensitivity analysis is also called perturbation analysis. It is an analytical method used to deter- mine the sensitive factors and their degree of influence.
The sensitivity function S (yi, xj) indicates how the change in the system input xj affects the system output yi. There are four calculation methods, as follows:
Normalized sensitivity:
S yi; xj Seminormalized sensitivity by yi:
� �
S yi; xj Seminormalized sensitivity by xi:
Unnormalized sensitivity:
jjij
� �
@yi=yi xj @yi
1⁄4 @x =x 1⁄4 y @x ð4Þ
@yi @yi
1⁄4 @x =x 1⁄4 xj @x ð5Þ
jjj
@yi=yi 1 @yi
Syi;xj 1⁄4@x1⁄4y@x ð6Þ
jij
� � @yi
Syi;xj 1⁄4@x ð7Þ
j
2) Configuration Optimizing Theory
� �
Sensitivity analysis is used to define the sensitivity of nodes, and then the relative total sensi- tivity is defined. The relative total sensitivity index is used to characterize the influence degree
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of the parameters on the model output. The input node, hidden layer node, and connection weight are selected using the relative total sensitivity index, and then the parameters with little or no effect can be deleted.
Definition 1 For mode u, xðuÞ represents the input of the j th input node, and yðuÞ represents ji
the output of the i th output node. The sensitivity of the network output function F(x, w) with respect to the input node can be defined as:
@yðuÞ=yðuÞ @yðuÞ xðuÞ sðuÞ1⁄4i i1⁄4i j
ij @xðuÞ=yðuÞ @xðuÞ yðuÞ iiji
ð8Þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P ðsðuÞ Þ2 is
This is referred to as the sensitivity of output i to input j for mode u. tsðuÞ 1⁄4
j ij
the total sensitivity of the input vector to input j. qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Definition 2 For a given training set, AS 1⁄4 PðsðuÞÞ2=s is the average sensitivity of ij ij
output i to input j, and RSI 1⁄4 ASij is the relative sensitivity index of output i to input j. The ij ASij
weight of each output variable in the system is not exactly the same: ASij must be weighted. qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
P
TSij 1⁄4
X
ðlijASijÞ2 ð9Þ
λij istheweightofASij,andsatisfies∑j λij =1,λij �0,i=1,2,…,n.
In the training process, some nodes have a strong network correlation but represent
small proportions. The average sensitivity ASij calculation method may delete nodes. Further, by using the average calculation method, training will be reduced, but a stronger correlation will be suppressed. Therefore, we need to calculate the variance of the node to be deleted
s2 1⁄4Varððtsð1Þ;tsð2Þ;…;tsðsÞÞTÞtomakefurtherjudgments.
jjjj
3) Sensitivity Calculation
To carry out sensitivity analysis, (1) ~ (3):
@yðuÞ i @xj
needs to be calculated. Take the derivative of Eqs
� ðuÞ� � !ðuÞ�
1⁄4 k1⁄41 f2 yi � wik � f1 hi � wkj ð10Þ
The training set instance x(u) can calculate the partial derivative of the network output func- tion F(x, w) with respect to the input x. If u = l, 2, . . ., s, s partial derivative matrixes can be obtained by repeated calculations, and the elements in the matrix will be partial derivatives that are shaped like formula (10). If expressed by a matrix symbol, Eq (10) can be written as:
JðuÞ 1⁄4 G0 W2G0 W1 ð11Þ x21
@yðuÞ Xl i0!201
@x
j
JðuÞ is the Jacobian matrix of the network output function F(x, w) at x(u);
x
W1 is the connection weight matrix of the first layer;
W2 is the second-level connection weight matrix;
� � !ðuÞ� � !ðuÞ� � !ðuÞ��
G01 is a diagonal matrix diag f10 h1 ;f10 h2 ;…;f10 hi ;
����� ���
0 0 !ðuÞ 0 !ðuÞ 0 !ðuÞ
G2 is a diagonal matrix diag f2 y1 ;f2 y2 ;…;f2 yn ;
The sensitivity of the hidden layer node, relative sensitivity, and partial derivative can be similarly obtained.
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Calculation of the contribution rate of China’s hydraulic science and technology
4) Calculation of the output elasticity coefficient
The econometric model of a multilayer feedforward network can be expressed as:
yðtÞ 1⁄4fðxðtÞ;xðtÞ;…;xðtÞÞ ð12Þ i12m
It can be obtained from Eq (12):
dyðtÞ i
dxðtÞ
1⁄4 sðtÞ 1
dxðtÞ þ sðtÞ 2 i2 ðtÞ
dxðtÞ
þ � � � þ sðtÞ m ð13Þ
sðtÞ is defined as the Eq (4) normalized sensitivity. ij
Suppose that:
i1 ðtÞ
yi x1 x2 xm
ðtÞ
0@yðtÞ @yðtÞ 1 B1���1C
im ðtÞ
B @x1 @xm C JðtÞ1⁄4B. . .C
B. .. .C B@@yðtÞ @yðtÞ CA
n���n @x1 @xm
dyðtÞ 1⁄4ðdyðtÞ;dyðtÞ;…;dyðtÞÞT 12n
dxðtÞ 1⁄4ðdxðtÞ;dxðtÞ;…;dxðtÞÞT 12n
dyðtÞ 1⁄4 JðtÞdxðtÞ ð14Þ
Eq (14) can be expressed as:
dyðtÞ yðtÞ
1⁄4 SðtÞ
dxðtÞ xðtÞ
ð15Þ
S(t) is a normalized sensitivity matrix.
Inthispaper,yðtÞ 1⁄4fðxðtÞ;xðtÞ;…;xðtÞÞ1⁄4AKaLb,whereA,α,andβareparametersthat
i12mtt 5) Key parameters of production function fitting
The input data are normalized to speed up the network convergence. Three datasets are
selected as the test set, and the remaining 33 datasets are used as the training set. The initial
network structure can be taken as n-l-m, and when the RTSIj of a hidden layer node is smaller
than a 1⁄4 1 (where l is the number of hidden layer nodes), the node should be deleted. The 10l
training goal is to achieve a mean square error (MSE) of 10−6, which can ensure the robustness of the model. The code can be found in S2 File.
3 Results
3.1 Parameter settings of the neural network
This paper establishes a multilayer feedforward network model. After training MATLAB’s neural network toolbox, the output function is obtained in the form of Q(t) = AtKαLβ.
The input data are normalized to speed up the network convergence. Three datasets are selected as the test set, and the remaining 33 datasets are used as the training set. The
change with time.
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Calculation of the contribution rate of China’s hydraulic science and technology
training goal is to achieve a mean squared error (MSE) of 10−6. The maximum number of cycles is 5000.
The initial network structure is taken as 5-10-1, and when the RTSIj of a hidden layer node is smaller than a 1⁄4 1 (where l is the number of hidden layer nodes), the node should
10l
be deleted. The network structure optimization algorithm is applied to obtain the simplest
network structure 3-4-1. The MSEs of the training set and the test set are 1.0264×10−6 and 1.0057×10−6. The connection weight matrix and threshold are W1 = [-1.0245–2.9913] W2 = [-1.6944–9.2483] b1 = -0.1367 b2 = -6.9678.
When the multilayer feedforward network fits the production function, because the input and output data are normalized, the partial derivative needs to be multiplied by a correspond- ing coefficient to obtain the estimated value of the partial derivative of the potential function. Then the output elasticities α and β of the production factors are found, as shown in the S3 File.
To determine the contribution rate of scientific and technological progress, the following indicators need to be calculated.
First, the average annual growth rate y, k, l should be calculated. Because the scope of flood
disaster reduction and the extent of disasters in water conservancy projects are also random
variables affected by climatic factors, benefits such as flood control and water logging control
show greater volatility interannually. Therefore, the horizontal method is used to calculate the
qffiffiffiffi
output. Taking the output as an example: y 1⁄4 t Yt 1, where Yt is the output efficiency of the
Y0
According to Eq (3), the contribution rate of the Solow residual value to the total output
water system during period t. growth rate EAt is:
EAt 1⁄4 at � 100% ð16Þ yt
yt
The contribution of the capital input to the total output EKt is:
EKt 1⁄4a�t 1kt �100% ð18Þ yt
The contribution rate of the labor input to the total output ELt is:
ELt 1⁄4b�t 1lt �100% ð19Þ
yt
The calculation results are shown in the S3 File.
3.2 The growth of benefits of water conservancy according to the input factor
The contributions of different input factors to the economic benefits of water conservancy over the years show different trends. The water conservancy industry is a traditional infra- structure industry. The average contribution rate of capital input from 1981 to 2016 was 47.3%, and the average contribution rate of labor input from 1981 to 2016 was 9.1%.
The contribution of the scale economy to the total output growth ESt is:
ESt 1⁄4 st � 100% ð17Þ
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Calculation of the contribution rate of China’s hydraulic science and technology
Fig 1. Trend of the input factor contribution rate.
https://doi.org/10.1371/journal.pone.0222091.g001
During the process of reform and opening up, the scale of capital input was relatively small, but as time passed, the water conservancy investment gradually increased. From 1981 to 1993, the contribution rate of capital investment rose from 14.0% to 60.8%, and then it declined slowly. After the outbreak of the international financial crisis in 2008, the central government of China implemented a proactive fiscal policy and increased water conservancy infrastructure construction. As a result, the contribution rate of capital investment rose again and then declined, and the capital contribution rate was 37.1% in 2016.
As shown in Fig 1, the contribution rate of the labor input remained relatively stable between 1981 and 2016. It is not obvious that the significant increase in the labor force con- tributed to the growth of China’s water conservancy industry because laborers in China are not productive. Taking a long-term perspective, China’s economy must enter an intensive growth period and policy makers should pay attention to the utilization of human resources.
3.3 The growth of the benefits of water conservancy based on the scale economy
The average contribution rate of the scale economy from 1981 to 2016 was 26.7%. As shown in
Fig 2, the scale economy contribution rate has a negative correlation with the capital contribu- tion rate.
From 1981 to 2007, the scale economy contribution rate was relatively stable. After the reform and opening up, the invisible hand of the market economy gradually played a role, and the scale economy contribution rate has increased; thus, the capital investment can bring
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Calculation of the contribution rate of China’s hydraulic science and technology
Fig 2. Trends of the scale economy and capital contribution rate.
https://doi.org/10.1371/journal.pone.0222091.g002
multiple investment returns, and there has been less water conservancy industry duplicate construction during this period. After the implementation of the proactive fiscal policy in 2008, the central government of China implemented a large amount of investment in water conservancy construction, which led to a certain amount of duplication of construction, and the scale of the economic contribution declined and then returned to normal levels.
3.4 Scientific and technological progress in the growth of water conservancy
The average rate of the scientific and technical contribution to water conservancy from 1981 to 2016 was 43.6%. After excluding the economies of scale, the average contribution rate of the TFP was 16.9%.
During the period of the 6th Five-Year Plan (1981~1985), although the scale of capital investment was small, the national scientific and technological research plan within the 6th Five-Year Plan heavily subsidized water conservancy. The implementation of the “Study of the South-to-North Water Diversion Project,” “Technology development of large-scale hydro- power stations”, “Studies on the Development and Utilization of Water Resources and Com- prehensive Evaluation in East China” and other projects quickly compensated for technical problems in traditional infrastructure construction and became the main impetus promoting the growth of water conservancy benefits in the early stages of reform and opening up.
Since then, the contribution rate of water science and technology has remained at 40%. With the implementation of strict water resource management systems and the construction
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Fig 3. Trend of the contribution rate of scientific and technological progress.
https://doi.org/10.1371/journal.pone.0222091.g003
of large-scale water conservancy projects, water conservancy reforms in key areas have made positive progress. Scientific and technological progress has increased the growth of water conservancy benefits annually. In 2015, the contribution rate of science and technology was 53.6%, compared with 55.7% in 2016.
As shown in Fig 3, Solow’s residual value has been decreasing since 1981. The growth of water conservancy emphasizes the formation of physical capital. If the capital allocation is not reasonable, the high capital accumulation rate will compensate for the economic operation inefficiency. The Chinese economy has shown extensive features over a period of time, but
in the last ten years, the TFP has again increased, and economic growth has shifted from the extensive mode to the intensive mode.
4 Discussion
4.1 Comparison of the results of the CES production function
There is no research on the contribution rate of water conservancy science and technology in China, so we choose the calculation results of the CES production function for a comparative analysis.
As shown in the S3 File, ρ is approximately equal to zero, and this proves that selecting the Cobb-Douglas production function can basically meet the research needs. Then we compare the contribution rates of the capital, labor, total factor productivity, economies of scale and
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Calculation of the contribution rate of China’s hydraulic science and technology
Fig 4. Comparison of the contribution rates calculated by the CES production function and the Cobb-Douglas production function.
https://doi.org/10.1371/journal.pone.0222091.g004
Solow residual value as calculated by the Cobb-Douglas production function and the constant elasticity of substitution(CES) production function.
As shown in Fig 4, the capital contribution rate of the CES production function is relatively stable compared with that of the Cobb-Douglas production function. However, the capital contribution rate of the CES production function from 2008 to 2011 was higher than that
of Cobb-Douglas production function. The labor contribution rate of the CES production function is consistent with that of the Cobb-Douglas production function. The total factor pro- ductivity of the CES production function has the same trend as that of the Cobb-Douglas pro- duction function, but it is lower than that of the Cobb-Douglas production function from 2008 to 2011. The contribution rates of capital and the total factor productivity as calculated by the CES production function are still inversely proportional.
As shown in Fig 5, the scale economy contribution rates and Solow residual values calcu- lated by the CES production function and Cobb-Douglas production function are quite differ- ent in some years. The scale economy contribution rate of the CES production function was negative from 2008 to 2012. Although the scale economy contribution rate of the Cobb-Doug- las production function also declined in 2008, the decline was not as significant as the scale economy efficiency of the CES production function. Because the CES production function has a scale economy coefficient m, it has an advantages over the Cobb-Douglas production func- tion in calculating the contribution rate of the scale economy. From 1981 to 2007, the scale
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Calculation of the contribution rate of China’s hydraulic science and technology
Fig 5. Comparison of the scale economy contribution rates and Solow residual values.
https://doi.org/10.1371/journal.pone.0222091.g005
economy contribution rates calculated by the Cobb-Douglas production function and the CES production function were roughly the same. Because the two production functions have differ- ent ways to calculate the scale economy contribution rate, the two Solow residual values have some deviations, and this results in a certain deviation of the two Solow residuals calculated by the two production functions. Especially after 2008, the Solow residual value of the CES pro- duction function fluctuated greatly, which is quite different from the case for that of the Cobb- Douglas production function.
4.2 Prospects for the development of water conservancy science and technology in China
The development of water conservancy science and engineering technology come from the needs of the survival and development of human society. Its goal is to understand the laws of nature and to manage and allocate water resources artificially through a variety of technical and engineering measures. However, water security in China is still facing a serious situation, which is highlighted in the serious shortage of water resources, water pollution, the threat
of water disasters, water ecological degradation and other aspects. At the same time, super- strong earthquake, excessive flooding huge geological disasters and other factors threaten
the long-term safe operation of hydropower stations[45]. These problems endanger the downstream people’s lives and property safety. In terms of science and technology, there are still many major problems that need to be solved. 1) Water resources security[46]: the pre- diction of the supply and demand of water resources affected by climate change in the future; the inter-basin spatial and temporal allocation of water resources; and the strictest water resources management technology. 2) Watershed water, sediment and environmental ecol- ogy[47]: the prediction of future river water, sediment, and ecological environment changes under the conditions of industrial and agricultural development, urbanization and large- scale water conservancy project construction; the interaction of the fluxes of river water and sediment with the ecological environment; the hydrodynamics of river systems; the balance and regulation of geomorphology and biodiversity. 3) Hydropower energy development and long-term safe operation guarantee[48]: the effects of extreme disaster factors such as super earthquakes, excessive flooding, and complex geological conditions on the hazard chain risk of the high dam junction group of hydropower stations. 4) Flood and drought disaster pre- vention[49]: the disaster mechanism and risk control of river flood, urban floods, mountain
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Fig 6. Trends of total factor productivity and capital contribution rate.
https://doi.org/10.1371/journal.pone.0222091.g006
mudslides, storm surges, and drought under the influence of extreme meteorological condi- tions and human activities.
The first, second, and third scientific and technological problems require the construction of a large number of water conservancy facilities such as dams, water diversion channels and so on. The fourth scientific question is inclined to the study of earth system science and the water circulation mechanisms. As shown in Fig 5, the efficiency of the scale economy in
China declined significantly in 2008. As shown in Fig 2, there is a certain inverse relationship between capital and scale economies. As shown in Fig 6, the contribution rate of capital and the science and technology of water conservancy in China are basically the same, and in recent years, the contribution rate of science and technology has risen slowly. The policy of the Chi- nese government has gradually shifted from building water conservancy to harmonious co- existence between man and nature. This policy will minimize the construction of large water conservancy projects. It is expected that the future investment in water resources will gradually turn into the mechanical study of the water cycle, in which technology will play a further lead- ing role.
4.3 The concept of the total factor productivity
The concept of the total factor productivity in this paper is Solow residual value, which uses the output growth rate after deducting each input factor growth rate to measure the total factor productivity. There is another definition of the total factor productivity, which refers to the ability to achieve the maximum output under a given input or the ability to minimize the
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Calculation of the contribution rate of China’s hydraulic science and technology
Table 5. Comparison of different methods for estimating the total factor productivity.
Cobb-Douglas production function
Data envelopment analysis(DEA)
Yes
No
Cross-section data
Cross-section data, Panel data
Yes
No
Entirety
Decision-making unit
No
Yes
Whether to assume a functional form Data type
Whether price data is needed Research object
Whether to support multiple output indicators
https://doi.org/10.1371/journal.pone.0222091.t005
Stochastic frontier analysis
Yes Cross-section data, Panel data No Decision-making unit Yes
input under a given output. This scenario is considered an example of Pareto optimality[50]. Under this definition of the total factor productivity, we use the DEA[51] and other methods [52] for the calculation. The calculation method and sphere of application are summarized in Table 5.
The calculation method of the DEA or SFA is often used to compare the total factor produc- tivities of different departments, which requires complete panel data. The C-D production function is used to calculate the total factor productivity of the entirety. The two types of calcu- lation methods have different definitions of the total factor productivity. However, both meth- ods can reflect the efficiency of the research object’s use of input factors. In follow-up study, we can combine a non-parametric method (DEA, SFA) with a parametric method, and unify the definition of the total factor productivity. At the same time, we can consider pollution emission from different section to further expand the comprehensiveness of the total factor productivity.
5 Conclusions
This paper establishes a C-D production function that considers scale economy effects and uses a feedforward neural network to fit the potential production function with historical data. It calculates the coefficient of the output elasticity and then determines China’s TFP from 1981 to 2016. The conclusions are as follows:
1. Thecontributionsofdifferentinputfactorstotheeconomicoutputofwaterconservancy over the years have shown different trends. The average contribution rate of the capital input from 1981 to 2016 was 47.3%, and the average contribution rate of the labor input was 9.1%. During the process of reform and opening up, capital investment in water con- servancy increased from 14.0% to 60.8% between 1981 and 1993 and then declined slowly. After the international financial crisis in 2008, China implemented a proactive fiscal policy and increased water conservancy infrastructure construction, leading the contribution rate of capital investment to rise again and then fall. The contribution rate of capital in 2016 is 37.1%. It is not obvious that the significant increase in the labor force has contributed to the growth of China’s water conservancy industry, because the laborers in China are not productive.
2. Theaveragecontributionrateofthescaleeconomyfrom1981to2016was26.7%,andthe scale economy contribution rate was negatively correlated with the capital contribution rate. From 1981 to 2007, the contribution rate of the economies of scale was relatively sta- ble. After the implementation of the proactive fiscal policy in 2008, the contribution rate of economies of scale decreased, and the efficiency of capital utilization fell further before returning to normal levels.
3. Theaveragerateofthescientificandtechnicalcontributionofwaterconservancyfrom 1981 to 2016 was 43.6%. After excluding economies of scale, the average rate of the total
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Calculation of the contribution rate of China’s hydraulic science and technology
factor contribution from 1981 to 2016 was 16.9%, and the contribution rate of water conservancy technology in 2016 was 55.7%. During the period of the 6th Five-Year Plan (1981~1985), the contribution rate of water conservancy science and technology is rela- tively high. Since that time, it has remained at 40%. In recent years, as water conservancy reforms in key areas have made positive progress, scientific and technological progress has gradually increased the growth of water conservancy benefits.
Supporting information
S1 File. The CES production function.
(DOCX)
S2 File. Implementation process and the MATLAB code.
(DOCX)
S3 File. Results of the contribution rate.
(XLSX)
Acknowledgments
The authors are grateful to anonymous reviewers for their detailed comments, which have sig- nificantly improved the presentation of this work. Readers can also contact the first author via
Author Contributions
Conceptualization: Rongrong Xu.
Data curation: Yuedong Xia.
Formal analysis: Rongrong Xu, Long Tan.
Funding acquisition: Yongxiang Wu, Ming Chen, Gaoxu Wang. Investigation: Rongrong Xu.
Methodology: Rongrong Xu.
Project administration: Yongxiang Wu, Wei Wu. Resources: Rongrong Xu.
Software: Bing Yan.
Supervision: Yongxiang Wu.
Visualization: Xuan Zhang, Wei Wu.
Writing – original draft: Rongrong Xu, Xuan Zhang. Writing – review & editing: Rongrong Xu, Yi Xu.
References
1. Sun S, Fang C, Lv J (2017) Spatial inequality of water footprint in China: a detailed decomposition of
inequality from water use types and drivers. Journal of Hydrology 553.
2. Zheng SL, Ren-Hai WU, Wen-Gang R (2010) A Tentative Inquiry into Indicator System of Planning EIA Based on Low Carbon and Circular Economy. Environmental Science & Technology 33: 199–204.
3. Du K, Lin B (2017) International comparison of total-factor energy productivity growth: A parametric Malmquist index approach. Energy 118: 481–488.
PLOS ONE | https://doi.org/10.1371/journal.pone.0222091 September 11, 2019 20 / 22
Calculation of the contribution rate of China’s hydraulic science and technology
4. Long X, Zhao X, Cheng F (2015) The comparison analysis of total factor productivity and eco-efficiency in China’s cement manufactures. Energy Policy 81: 61–66.
5. Wu CS, Yang SL, Lei YP (2012) Quantifying the anthropogenic and climatic impacts on water discharge and sediment load in the Pearl River (Zhujiang), China (1954–2009). Journal of Hydrology 452–453: 190–204.
6. Molinos-Senante M, Maziotis A, Sala-Garrido R (2017) Assessment of the Total Factor Productivity Change in the English and Welsh Water Industry: a Fa ̈ re-Primont Productivity Index Approach. Water Resources Management 31: 2389–2405.
7. Tang D, Tang J, Zheng X, Ma T, Bethel BJ (2017) Environmental regulation efficiency and total factor pro- ductivity—Effect analysis based on Chinese data from 2003 to 2013. Ecological Indicators 73: 312–318.
8. Zhao X, Liu C, Yang M (2018) The effects of environmental regulation on China’s total factor productiv- ity: An empirical study of carbon-intensive industries. Journal of Cleaner Production 179: 325–334.
9. Jia S, Long Q, Wang RY, Yan J, Kang D (2016) On the Inapplicability of the Cobb-Douglas Production Function for Estimating the Benefit of Water Use and the Value of Water Resources. Water Resources Management 30: 3645–3650.
10. Burda MC, Severgnini B (2014) Solow residuals without capital stocks. Journal of Development Eco- nomics 109: 154–171.
11. Asmild M, Balezˇentis T, Hougaard JL (2016) Multi-directional productivity change: MEA-Malmquist. Journal of Productivity Analysis 46: 109–119.
12. Wang Q, Su B, Sun J, Peng Z, Zhou D (2015) Measurement and decomposition of energy-saving and emissions reduction performance in Chinese cities. Applied Energy 151: 85–92.
13. Cobb CW, Douglas PH (1928) A Theory of Production. American Economic Review 18: 139–165.
14. Abramovitz M (1956) Thinking about growth: Resource and output trends in the United States since
1870. Nber Chapters 46: 5–23.
15. Solow RM (1957) TECHNICAL CHANGE AND THE AGGREGATE PRODUCTION FUNCTION. Review of Economics & Statistics 39: 554–562.
16. Jorgenson DW, Griliches Z (1967) The Explanation of Productivity Change. Review of Economic Stud- ies 34: 249–283.
17. Romer PM (1987) Growth Based on Increasing Returns Due to Specialization. American Economic Review 77: 56–62.
18. Romer PM (1989) Endogenous Technological Change. Nber Working Papers 98: 71–102.
19. Lucas RE (1999) On the mechanics of economic development. Quantitative Macroeconomics Working
Papers 22: 3–42.
20. Wu S, Li B, Nie Q, Chen C (2017) Government expenditure, corruption and total factor productivity. Journal of cleaner production 168: 279–289.
21. Christiano LJ, Eichenbaum MS, Trabandt M (2015) Understanding the great recession. American Eco- nomic Journal: Macroeconomics 7: 110–167.
22. Feng C, Wang M, Liu G, Huang J (2017) Sources of economic growth in China from 2000–2013 and its further sustainable growth path: A three-hierarchy meta-frontier data envelopment analysis. Economic Modelling 64: 334–348.
23. Yuan B, Xiang Q (2018) Environmental regulation, industrial innovation and green development of Chi- nese manufacturing: Based on an extended CDM model. Journal of cleaner production 176: 895–908.
24. Zhong Z, Hu Y, Jiang L (2019) Impact of Climate Change on Agricultural Total Factor Productivity Based on Spatial Panel Data Model: Evidence from China. Sustainability 11: 1516.
25. Moore FC, Diaz DB (2015) Temperature impacts on economic growth warrant stringent mitigation pol- icy. Nature Climate Change 5: 127.
26. Dellink R, Chateau J, Lanzi E, Magn E B (2017) Long-term economic growth projections in the Shared Socioeconomic Pathways. Global Environmental Change 42: 200–214.
27. Zhang N, Zhou P, Kung C (2015) Total-factor carbon emission performance of the Chinese transporta- tion industry: A bootstrapped non-radial Malmquist index analysis. Renewable and Sustainable Energy Reviews 41: 584–593.
28. Amri F (2018) Carbon dioxide emissions, total factor productivity, ICT, trade, financial development, and energy consumption: testing environmental Kuznets curve hypothesis for Tunisia. Environmental Science and Pollution Research 25: 33691–33701. https://doi.org/10.1007/s11356-018-3331-1 PMID: 30276690
29. Li W, Wang W, Yu W, Ali M (2018) Historical growth in total factor carbon productivity of the Chinese industry—a comprehensive analysis. Journal of Cleaner Production 170: 471–485.
PLOS ONE | https://doi.org/10.1371/journal.pone.0222091 September 11, 2019 21 / 22
Calculation of the contribution rate of China’s hydraulic science and technology
30. Fan M, Shao S, Yang L (2015) Combining global Malmquist—Luenberger index and generalized method of moments to investigate industrial total factor CO2 emission performance: a case of Shanghai (China). Energy Policy 79: 189–201.
31. Xin B, Sun M (2018) A differential oligopoly game for optimal production planning and water savings. EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 269: 206–217.
32. Xin B, Li Y (2013) Bifurcation and Chaos in a Price Game of Irrigation Water in a Coastal Irrigation Dis- trict. DISCRETE DYNAMICS IN NATURE AND SOCIETY.
33. Ackerberg DA, Caves K, Frazer G (2015) Identification properties of recent production function estima- tors. Econometrica 83: 2411–2451.
34. Molinos-Senante M, Sala-Garrido R, Herna ́ ndez-Sancho F (2016) Development and application of the Hicks-Moorsteen productivity index for the total factor productivity assessment of wastewater treatment plants. Journal of Cleaner Production 112: 3116–3123.
35. Li B, Wu S (2016) Effects of local and civil environmental regulation on green total factor productivity in China: A spatial Durbin econometric analysis. Journal of Cleaner Production 153: S1991399945.
36. Kong D, Yuan R (2010) The contribution rate of solow model to water conservancy science and technol- ogy. Science & Technology and Economy 23: 59–62.
37. Yuan R, Kong D (2009) Measurement of contribution rate of hydraulic Science and technology in 30 years of China’s reform and opening up. Forum on Science and Technology in China: 20–24.
38. Hossain MM, Basak T, Majumder AK (2013) Application of Non-Linear Cobb-Douglas Production Func- tion with Autocorrelation Problem to Selected Manufacturing Industries in Bangladesh. Open Journal of Statistics 333019: 173–178.
39. Asche F, Guttormsen AG, Nielsen R (2013) Future challenges for the maturing Norwegian salmon aquaculture industry: An analysis of total factor productivity change from 1996 to 2008. Aquaculture 396: 43–50.
40. Balk BM (2014) Measuring and Relating Aggregate and Subaggregate Productivity Change Without Neoclassical Assumptions. Statistica Neerlandica 69: 21–48.
41. Byerlee D, Murgai R (2015) Sense and sustainability revisited: the limits of total factor productivity mea- sures of sustainable agricultural systems. Agricultural Economics 26: 227–236.
42. Antoci A, Borghesi S, Sodini M (2017) Water resource use and competition in an evolutionary model. Water Resources Management 31: 2523–2543.
43. Zha D, Zhou D (2014) The elasticity of substitution and the way of nesting CES production function with emphasis on energy input. Applied energy 130: 793–798.
44. Lu H, Xie H, He Y, Wu Z, Zhang X (2018) Assessing the impacts of land fragmentation and plot size on yields and costs: A translog production model and cost function approach. Agricultural Systems 161: 81–88.
45. Shan ZG, Yan P (2010) Management of rock bursts during excavation of the deep tunnels in Jinping II Hydropower Station. Bulletin of Engineering Geology & the Environment 69: 353–363.
46. Al-Saidi Mohammad (2017) Conflicts and security in integrated water resources management. Environ- mental Science & Policy 73: 38–44.
47. Wang X, Shang S, Yang W, Clary CR, Yang D (2010) Simulation of land use—soil interactive effects on water and sediment yields at watershed scale. Ecological Engineering 36: 328–344.
48. Yu ̈ ksel I (2010) Hydropower for sustainable water and energy development. Renewable & Sustainable Energy Reviews 14: 462–469.
49. Qiang Z, Zhang W, Chen YD, Jiang T (2011) Flood, drought and typhoon disasters during the last half- century in the Guangdong province, China. Natural Hazards 57: 267–278.
50. He Z, Yen GG, Zhang J (2014) Fuzzy-Based Pareto Optimality for Many-Objective Evolutionary Algo- rithms. IEEE Transactions on Evolutionary Computation 18: 269–285.
51. Tang D, Tang J, Xiao Z, Ma T, Bethel BJ (2017) Environmental regulation efficiency and total factor pro- ductivity—Effect analysis based on Chinese data from 2003 to 2013. Ecological Indicators 73: 312– 318.
52. Shao S, Luan R, Yang Z, Li C (2016) Does directed technological change get greener: Empirical evi- dence from Shanghai\”s industrial green development transformation. Ecological Indicators 69: 758– 770.
PLOS ONE | https://doi.org/10.1371/journal.pone.0222091 September 11, 2019 22 / 22