# Dynamic Evaluation and Internal Driving Factors of Water Resources Green Efficiency in China
## 3 Materials and Methods
### Total Factor Productivity Index Model
#### 3.3.2 Expected Output Indicators  
The expected output indicators for water resources green efficiency included economic development and social development indicators. (1) Indicator of economic development  
Economic development is an important evaluation index to measure the economic efficiency of water resources. The gross domestic product of each province was adopted as the economic development indicator and the price was adjusted based on the prices in year 2000. (2) Social development index  
High-quality economic development and construction of an ecological civilization require China's social and economic development to follow the modern ideas of innovation, coordination, \"greenness\", openness and sharing to meet the residents' desire for a better quality of life. Water Resources Utilization also needs to realize \"economy-society-ecology\" win-win goals. However, social development indicators have been used rarely to assess water efficiency according to the existing research literature. Therefore, against the background of ecological civilization construction, social development factors should be reflected in the process of water resources utilization. Social development includes economy, culture, education, medical care, etc. The present situation of social development is the result of the joint action of various factors. Therefore, in this study, social development was regarded as the expectedoutput of water resources utilization. The indicators listed in Table 1 were selected as elements in the indicator system for measuring the social development index. Components of the social development evaluation index were defined as follows. 1. Population growth refers to the ratio of the natural increase in the population (the number of births minus the number of deaths) for within a certain period of time (i.e., one year) to the average number (or the number of people in the current period). 2. The proportion of the population aged 65 and over refers to the proportion of the population aged 65 and over in the sample survey during a certain period in each region. 3. Engel's coefficient refers to the proportion of total food expenditure in the total personal consumption expenditure. 4. Urbanization rate refers to the proportion of permanent urban residents at the end of a year. 5. Proportion of financial expenditures on education and science and technology refers to the education expenditure and science and technology expenditure in the general public budget expenditure in each region. 6. Medical resources refer to the number of health technicians per 10,000 population. The above indicator data were derived from the 2001-2017 China Statistical Yearbook and the statistical yearbooks of the provinces. Relevant price data were adjusted based on prices in the year 2000. The original data were all normalized before being used in the evaluation. Drawing on existing research [54], Equation (5) was developed for calculating the social development index:  
\[G_{t}^{s}=\sum X_{it}/n \tag{5}\]  
In Equation (5), \(G_{t}^{s}\) is the t-year social development index of a certain province. The greater the G value, the better the social development conditions. N indicates the number of indicators. \(X_{it}\) represents the unstructured quantitative value of the original data of a provincial social development evaluation indicator in year t (This paper uses the normalization method to dimensionlessly quantify the original data of indicators). The analysis of the indicators listed in Table 1 showed that reasonable improvement of the population growth, urban development level, financial input in science and education, and medical resources had a positive effect on social development. Each of these four indicators was defined as a high quality indicator. In contrast, increases in the proportion of population aged 65 and above,