**2. Literature**

Previous studies on industrial production efficiency, such as the one conducted by [7], used the SDG-9 index to assess the degree of industrialization of countries, as well as social inclusiveness, less use of natural resources and environmental impact. Ref. [8] using the DEA method, discusses the relationship between the American manufacturing industry

and environmental performance. The unintended output is reported as SOx, NOx, Co, etc. It is found that air pollution is mainly a by-product of manufacturing activities. The share of the manufacturing industry in the total amount of state-owned products and the share of the polluting industry in the total amount of manufacturing activities are two important factors determining the intensity of pollution. Using DEA, Ref. [9] discuss the energy conservation and carbon reduction efficiency of China's industrial production from 2006 to 2010. The input variables are labor, capital and energy consumption, and the output variables are SO2, wastewater and GDP. It is found that the energy conservation and emission reduction efficiency in East China is the best. Ref. [10] using the DEA method, evaluated the environmental efficiency of 46 countries in 2002, 2007 and 2011. The input variables are labor, capital and energy use, and the output variables are GDP, CO2 and NOx. The study found that the energy efficiency of countries rich in oil and natural gas resources is relatively poor. Ref. [11] using the DEA method, discuss the analysis of the energy and environmental efficiency of two petrochemical plants in China from 2012 to 2013, and divide the output into expected output and unexpected output. It was found that by analyzing the energy efficiency and environmental efficiency of the ethylene production process in complex chemical processes, the energy saving and emission reduction potential of ethylene plants can be obtained, and the efficiency performance of DMU can be improved by improving energy efficiency and reducing carbon emission. Research on energy efficiency by [11] evaluated the efficiency of the water, food and energy (WEF) relationship in 30 provinces and municipalities in China from 2005 to 2017. Inputs were labor force, water resource use, energy use, food consumption and other variables, and outputs were social benefits, wastewater discharge and solid discharge. The researchers analyzed the weight of the WEF relationship, and put forward the strategy of sustainable resource management. Ref. [12] discussing the research results of DEA application in the field of energy and environment from the 1980s to 2010, found that the development process will produce various pollutants to air, water and other types of pollutants which are related to health and climate change. Therefore, it is necessary to strike a balance between economic growth and pollution mitigation. Ref. [13] using the DEA method to explore the impact of U.S. economic growth on the environmental efficiency of the power sector, found that there is a stable n-shape relationship between environmental efficiency and regional economic growth, while in the case of local pollutants, there is an inverted n-shape relationship between environmental efficiency and regional economic growth. For policymakers, climate change needs to consider the relationship between economy, environment and society at the same time. On the research related to water use efficiency, Ref. [14] evaluated the efficiency of SDG-6 and a serious water shortage in the Medjerda Basin in Tunisia. Ref. [15] used the DEA method to explore the water use efficiency of 10 cities in the Minjiang River Basin in China in 2018. The research found that the input of social water and economic water are different, and the output of GDP and unintended wastewater are the factors affecting water use efficiency. Ref. [16] using TFP and Tobit models, discuss the water use efficiency of 30 provinces and municipalities in China from 2006 to 2015. The study found that the efficiency of water use in the administrative regions of provinces and cities is low, so we should establish the awareness of water conservation from the investment of education, so as to balance economic development and water use efficiency. Ref. [17] used the DEA method to explore China's regional ecological efficiency from 2003 to 2014. The input variables were labor force, water consumption, energy consumption, etc., and the output variables were GDP, SO2, smoke and dust, industrial wastewater, household waste, etc. The study found that the efficiency and progress rate of the eastern region are better than other regions, and there is still room for improvement in China's overall environmental efficiency. Ref. [18] used DDF to evaluate the water resources and wastewater discharge efficiency of China's industrial sector. The input variables were labor, capital and industrial water consumption, and the output variables were industrial output value, chemical oxygen demand, etc. The study found that the eastern region has made progress in science and technology, and the

pollutants discharged by industrial production in the western region are more serious. Ref. [19] using the DDF model, evaluated the efficiency of administrative water removal in 31 provinces and cities in China from 2011 to 2015. The study found that there were significant differences between the efficiency performance and technology gap in Eastern, Central and Western China. Ref. [20] evaluating the relationship between China's industrial water efficiency and regional differences from 2005 to 2015, found that the industrial water efficiency values of administrative regions in 31 provinces and cities are less than 1, among which the per capita water resources, R&D investment, regulation formulation, GDP and industrial structure will affect the industrial water efficiency. Ref. [5] using the SBM model, studied the economic production and sewage treatment efficiency of 30 provinces and cities in China from 2011 to 2017. The input variables were labor force, domestic and industrial water, investment in sewage treatment projects and the number of sewage treatment plants. The output variables were GDP, chemical oxygen demand of wastewater discharge and heavy metal pollution. The study found that there are great differences in inefficiency in different regions of China. The efficiency in the economic production stage is significantly higher than that in the sewage treatment stage. The sewage treatment efficiency is the main drag factor of the overall efficiency. Ref. [21] assessed the regional differences of China's provincial air pollution efficiency from 2006 to 2015. The study found that there were significant differences in air pollution emission efficiency in various regions. Air pollution emission efficiency was significantly positively correlated with economic development level, industrial structure optimization, technological innovation and foreign direct investment (FDI), and negatively correlated with energy consumption structure. Ref. [22] used DEA and regression analysis to explore China's energy efficiency performance from 2001 to 2013. Input variables included labor, capital and energy use, and output variables were GDP, industrial wastewater, solid waste and air pollutants. The study found that technological innovation has a positive impact on TFEE. The government should pay attention to technological innovation, which will be conducive to the effectiveness of energy conservation and emission reduction and environmental pollution prevention and control. Research on pollution control costs, such as [23], discusses the efficiency of China's iron and steel industry and pollution control. It is found that the production efficiency of China's iron and steel industry is low and causes serious pollution to the environment. Enterprises must improve the overall efficiency by increasing environmental protection investment, introducing foreign advanced technology and strengthening the R&D of pollutant management.

As for the discussion on energy consumption and pollution control technology, for example, in a paper by [24], it is estimated that Beijing, China, will improve its air quality by adjusting its industrial structure, controlling pollutant emissions, controlling vehicle pollution emissions and other measures and regulations due to rapid industrialization, urbanization and motorization, the continuous growth of energy consumption and the resulting emissions of a variety of pollutants. Ref. [25] assessing the impact of foreign investment on greenhouse gas emissions in developing countries, found that foreign investment enabled technology transfer, improved labor, reduced greenhouse gas emissions, improved energy efficiency and achieved sustainable development goals.

As mentioned above, most previous studies focused on industrial production efficiency, energy efficiency, pollutant emission and control. Therefore, this study uses the DDF method to explore the impact of pollution control on the production efficiency of 31 provinces and municipalities in the Yellow River Basin and Non-Yellow River Basin in China from 2013 to 2017, and uses TGR to measure the change in the technology gap. We objectively evaluate the efficiency difference of pollution control in different provinces and cities to provide an effective reference basis for policy formulation and budget control.

The main contributions of this study are as follows:

(1) Different from the previous literature results, this study uses the parallel method and takes the industrial production department and the pollution control department as input variables to objectively evaluate the impact of pollution prevention and control funds on industrial production efficiency in 31 provinces and municipalities in China;

(2) This study compares the changes in industrial production efficiency and the technology gap between the Yellow River Basin and Non-Yellow River Basin, which is conducive to mastering the situation of pollution control and production efficiency in 31 provinces and municipalities in China, and provides objective suggestions as a reference for SDG-6- and SDG-9-related policy making.

## **3. Research Method**

Ref. [26] first put forward the concept of a deterministic nonparametric front in 1957. It is used to measure the production level of a decision-making unit. Then, Ref. [27] proposed the CCR model. Ref. [28] proposed the BCC model. Over time, Ref. [29] (1996) proposed the directional distance function (DDF). In addition, Ref. [30] introduced the VRS super-efficiency Nerlove–Luenberger (N–L) model to solve the unreasonable problem. This method can adjust the input and output levels in the same proportion, and the efficiency value obtained under the VRS super-efficiency of DDF can be used for ranking all DMUs. The directional distance function model under variable return to scale (VRS) and the calculation method of efficiency values used in this study are as follows:
