In this paper, the extended model of data Envelopment analysis (DEA), that is, the non-expected output super efficiency SBM model, is used for calculation. The efficiency measurement of the traditional DEA model is not affected by the units of input and output indicators. Because it does not consider the problem of relaxation variables and the actual situation that the input and output will appear redundant, the calculation results will be biased and not accurate enough. Therefore, on the basis of traditional DEA, Tone proposed a SBM model considering the non-radial Angle of relaxation variables. This model directly introduced all relaxation variables into the objective function in a non-ray mode of action, and the evaluation results of efficiency value were more accurate. In order to solve the problem that the efficiency value of many DMU in the results is equal to 1 and its real size cannot be measured, Tone [23] et al. introduced the super efficiency SBM model, the formula is shown in (3-1).

min ρ = 1 − 1 m ∑ i = 1 m s i − x i k 1 + 1 e 1 + e 2 ( ∑ r = 1 e 1 s r + y r k + ∑ t = 1 e 2 s t b − b t k ) ∑ j = 1 , j ≠ k n x i j λ j − s i − ≤ x i k ∑ j = 1 , j ≠ k n y r j λ j − s r + ≥ y r k ∑ j = 1 , j ≠ k n b t j λ j − s t b − ≤ b t k i = 1 , 2 , ⋯ , m ; r = 1 , 2 , ⋯ , e 1 ; t = 1 , 2 , ⋯ , e 2 ; j = 1 , 2 , ⋯ , n ( j ≠ k ) (3-1)

ρ represents the carbon emission efficiency value in the formula. There are m inputs, e₁ expected outputs, e₂ non-expected outputs. x represents input, y represents expected output, b represents non-expected output. s = ( s i + , s r − , s t b − ) represents the relaxation of input, expected output and unexpected output, λ represents the weight vector.

This paper measures the carbon emission efficiency of China’s pharmaceutical manufacturing industry from the perspective of input-output. The input-output indicators are shown in Table 1.

The basic input factors include capital factors and labor factors. The fixed asset investment of pharmaceutical manufacturing enterprises is used as the replacement index of capital factors, and the GDP index is deflated with 2010 as the base period. The average number of employees of pharmaceutical manufacturing enterprises is used as the replacement index of labor factors. Different from ordinary efficiency, energy consumption should also be included in the input index of carbon emission efficiency for analysis. The energy consumption of pharmaceutical manufacturing industry in various provinces is converted through the coefficient relationship between different energy consumption and standard coal. The main business income is used as an alternative indicator of economic benefit, and the GDP index is deflated based on 2010. The annual CO₂ emission of pharmaceutical manufacturing industry in 30 provinces was taken as the index of undesirable output.

The panel data of pharmaceutical manufacturing industry in 30 provinces of China except Hong Kong, Macao, Taiwan and Xizang from 2010 to 2019 were used as research samples. The original data of each index came from the official website of CEADs, China High-tech Industry Statistical Yearbook, China Investment Statistical Yearbook, China Statistical Yearbook, China Industrial Statistical Yearbook and local statistical yearbooks. For individual missing values, interpolation method was used to fill in the data.

MATLABR2022b software is used to calculate the carbon emission efficiency of 30 provinces in China from 2010 to 2019, and the carbon emission efficiency is calculated separately in the eastern, central and western regions. The results are shown in Table 2. Nationally, the carbon emission efficiency of pharmaceutical manufacturing industry showed a fluctuating upward trend from 2010 to 2014, and reached the highest point of 0.936 in 2014. It showed a downward trend from 2015 to 2018, and recovered an upward trend from 2018 to 2019, which may be related to the rapid and vigorous development of generic drugs in pharmaceutical manufacturing industry in recent years. In the process of development, pharmaceutical enterprises pay more attention to economic benefits and ignore the innovation of green technology, thus the energy utilization efficiency began to decline. From the perspective of three regions, the carbon emission efficiency of pharmaceutical manufacturing industry in eastern region is higher than that in western region, and western region is higher than that in central region. The mean carbon emission efficiency of pharmaceutical manufacturing industry in eastern China was 0.931, higher than the national average of 0.914; the mean carbon emission efficiency of pharmaceutical manufacturing industry in western China was 0.924, also higher than the national average; and the mean carbon emission efficiency of pharmaceutical manufacturing industry in central China was 0.879, lower than the national average. The carbon emission efficiency of the pharmaceutical manufacturing industry in the eastern and central regions

shows a W-shaped change trend; The carbon emission efficiency of the pharmaceutical manufacturing industry in the western region shows an overall N-shaped trend. According to the average carbon emission efficiency of the pharmaceutical manufacturing industry in each province in the past ten years, the average carbon emission efficiency of Ningxia Hui Autonomous Region, Hainan Province, Beijing City, Guizhou Province and Shaanxi Province ranks in the top five. Xinjiang Uygur Autonomous Region, Shanxi Province and Fujian Province ranked the bottom.

The calculation result of DEA model is technical efficiency. Since the production frontier referenced by DMU at different time points is different, it represents a relative efficiency and cannot dynamically analyze the change of productivity. Swedish economist Sten Malmquist [24] first proposed the Malmquist index in 1953, which is used to dynamically analyze the changes of productivity and the respective roles of technical efficiency and technological progress in productivity changes. Among them, the changes of production technology reflect the changes of production frontier. Changes in technical efficiency reflect the extent of movement to the forefront of production. Due to the existence of the undesired output problem, a modified Malmquist index appeared again. Chung et al. [25] applied the directional distance function containing the undesired output to the Malmquist model and called the resulting Malmquist index the Malmquist-Luenberger index. While the traditional Malmquist index is calculated based on the output distance function, the Malmquist-Luenberger index is calculated based on the directional distance function, which aims to increase the desired output while reducing the undesired output. Under the assumption of constant returns to scale (CRS), ML index can be decomposed into technical efficiency change index (MLEC) and technological progress index (MLTC) [26] . The calculation formulas are shown in (3-2) to (3-5).

ML ( x t + 1 , y t + 1 , z t + 1 , x t , y t , b t ) = E t ( x t + 1 , y t + 1 , b t + 1 ) E t ( x t , y t , b t ) E t + 1 ( x t + 1 , y t + 1 , b t + 1 ) E t + 1 ( x t , y t , b t ) (3-2)

MLEC = E t + 1 ( x t + 1 , y t + 1 , b t + 1 ) E t ( x t , y t , b t ) (3-3)

MLTC = E t ( x t + 1 , y t + 1 , b t + 1 ) E t + 1 ( x t , y t , b t ) × E t ( x t + 1 , y t + 1 , b t + 1 ) E t + 1 ( x t + 1 , y t + 1 , b t + 1 ) (3-4)

ML = MLEC × MLTC (3-5)

MATLABR2022b software was used to calculate the ML index and decomposition index of carbon emission efficiency in China from 2010 to 2019, and the three regions were divided into eastern, central and western regions. The results are shown in Table 3. From the perspective of the whole country, the ML index

of the whole study period is relatively stable, with three periods less than 1, and the ML index of other periods greater than 1, indicating that the overall trend is rising from 2010 to 2019. The technical efficiency index can promote the improvement of carbon emission efficiency, and the average growth rate of the technical efficiency index is 1.6%, while the technical progress index is less than 1. It has an inhibitory effect on the improvement of carbon emission efficiency, with an average inhibitory rate of 1.5%. From a regional perspective, the technological progress and efficiency in the eastern region are both less than 1, and the technological progress is slightly higher than the technological efficiency, which means that the eastern region should pay attention to improving the technological progress and efficiency at the same time. It is suggested that the eastern region should further strengthen the resource allocation management and factor use efficiency and accelerate the technological progress at the same time; The technical efficiency of the central region has promoted the improvement of carbon emission efficiency. The average growth rate of technical efficiency is 4.3%, while the technical efficiency of the central region is less than 1, which indicates that the central region should pay more attention to technological progress; The technological efficiency of the western region plays a role in promoting the carbon emission efficiency, while the technological progress index of the western region is less than 1, indicating that the western region needs to further develop innovative technologies.

Due to the non-negative truncation of carbon emission efficiency, the Tobit model is used for regression in this paper. The model construction is shown in (4-1).

EFF i t = α + β 1 FDI i t + β 2 CR i t + β 3 ER i t + β 4 NE i t + β 5 Inno i t + ε i t (4-1)

In the formula, i represents different regions, t represents different years, and EFF is interpreted as a variable and represents the carbon emission efficiency of the pharmaceutical manufacturing industry. The explanatory variables were the level of foreign investment (FDI), the level of industrial agglomeration (CR) and the intensity of environmental regulation (ER). The unit of economic energy consumption (NE), scientific and technological innovation level (Inno), α is the constant term, ε_it is the error term.

The explained variable is the carbon emission efficiency (EFF) of the pharmaceutical manufacturing industry, which is calculated from the above. Others are explanatory variables. The level of foreign investment (FDI) is measured by the utilization of foreign investment in fixed assets of the whole society, and the GDP index is deflated with 2010 as the base period. Introducing foreign investment will increase the investment in scientific and technological innovation of enterprises, and may introduce foreign advanced pollution treatment technology to improve production efficiency and reduce carbon emissions. The degree of industrial agglomeration (CR) is measured by location entropy method. With high degree of industrial agglomeration, rapid technological exchange and diffusion, and vigorous development of technological intermediary market, resource utilization efficiency and technological innovation level are further improved, so as to improve carbon emission efficiency. Environmental regulation intensity (ER) is expressed by the proportion of the completed investment in pollution control in GDP. Environmental regulation can force enterprises to carry out scientific and technological innovation activities. Innovation and creativity will enable enterprises to improve the production mode, gradually enhance the competitive advantage, eliminate the increased input cost due to environmental control, and improve the efficiency of carbon emission. The level of scientific and technological innovation (Inno) is expressed by the number of patent applications of pharmaceutical manufacturing industry. The ratio of energy consumption per unit of economic energy consumption (NE) to the main business income of the pharmaceutical manufacturing industry indicates that the less energy consumed per unit of economy, the higher the carbon emission efficiency.

The descriptive statistics of variables are shown in Table 4, and the regression results of the national Tobit model are shown in Table 5. It can be seen from Table 5 that industrial agglomeration, environmental regulation intensity and technological innovation level have a positive impact on national carbon emission efficiency. The higher the unit economic energy consumption, the lower the carbon emission efficiency. The level of foreign investment negatively affects carbon emission efficiency, but not significantly. The intensity of environmental regulation is the main influencing factor.

In order to ensure the validity and robustness of the empirical results, this paper takes the period from 2010 to 2018 as the research object and conducts Tobit regression again by shortening the time window method. The results are shown in Table 6. The results of each variable are still significant, which is consistent with

Note: *, ** and *** indicate the significance level under the conditions of 10%, 5% and 1% respectively.

Note: *, ** and *** indicate the significance level under the conditions of 10%, 5% and 1% respectively.

the conclusions above, indicating the robustness of the results.

From the perspective of input and output, the carbon emission efficiency of the pharmaceutical manufacturing industry in 30 provinces in China from 2010 to 2019 was calculated using the expected output super-efficiency SBM model. The ML index and its decomposition index model are used to explore the changing trend and driving factors of carbon emission efficiency values in China, eastern, central and western regions, and Tobit model is used to explore the influencing factors of carbon emission efficiency. It is concluded that the green development of China’s pharmaceutical manufacturing industry has been effective and the carbon emission efficiency of China’s pharmaceutical manufacturing industry has been steadily improved. The pharmaceutical manufacturing industry is gradually transforming from resource factor type to ecological target type. Technical efficiency can promote the improvement of national carbon emission efficiency, and technological progress and development deserve more attention. The carbon emission efficiency of the eastern part of China is higher than that of the western part, and that of the western part is higher than that of the central part. The central and western parts are dominated by technological efficiency, and technological progress and technological efficiency need to be further improved. Among the influencing factors, the level of environmental regulation, the level of scientific and technological innovation, and the degree of industrial agglomeration have positive effects on carbon emission efficiency. Unit economic energy consumption negatively affects carbon emission efficiency. The level of foreign investment has no significant effect on carbon emission efficiency.

Based on the conclusions, this paper puts forward the following suggestions: 1) strengthen the intensity of environmental regulation, strengthen the assessment of ecological environmental protection, improve the environmental accountability mechanism, and promote enterprises to tackle the key core pollution treatment technologies by collecting environmental tax. Use market instruments such as emission trading system to encourage enterprises to carry out environmental innovation. 2) To strengthen scientific and technological innovation, the government should implement the science and technology training based development plan, build the ability of source innovation and set up a special fund to support enterprises to develop green and environmental protection technologies. 3) To speed up the elimination of backward production capacity, the government should scientifically and reasonably set the rectification standards for high-consumption and low-efficiency enterprises that meet the actual situation of the pharmaceutical manufacturing industry, and carry out the transformation, upgrading and merger and reorganization of substandard enterprises. Accurately analyze the equipment operation and energy consumption data of the enterprise, optimize the different nodes in the production process by virtue of intelligent control equipment and internal systems, and reduce the unit energy consumption while helping the factory to improve its capacity. 4) Increase the scale of industrial agglomeration, use diversified media to promote the flow of knowledge elements, and use the effect of scale economies to promote the technological progress of pharmaceutical manufacturing industry. While pursuing the scale advantage, we should beware of the problems of agglomeration but not excellent and high level of overcapacity. 5) Implement the policy of opening to the outside world, raise the threshold of environmental access for pharmaceutical manufacturing enterprises while expanding the opening to the outside world in an orderly manner, and create a negative list system for high-quality foreign investment access. 6) Jointly formulate regional green innovation policies, promote the coordinated development of regional green economy. We will comprehensively use various means such as administration, science and technology, the rule of law, and the market to improve the carbon emission efficiency of the pharmaceutical manufacturing industry and achieve carbon peak and carbon neutrality as soon as possible.