Evaluation of Technological Innovation Efficiency of New Energy Enterprises in the Yangtze River Delta Region—Based on a Two-Stage DEA Optimization Model

Because of the shortcomings of the traditional two-stage DEA model, on the basis that the output of the first stage is completely transformed into the second-stage input. The investment of scientific and technological personnel and capital is added to construct a two-stage DEA optimization model to evaluate innovation efficiency. The model is used to empirically measure the overall efficiency of technological innovation and the efficiency of each sub-stage of the 22 new energy-listed companies in the Yangtze River Delta from 2014 to 2019. An efficiency matrix is proposed. The empirical results show that the overall innovation efficiency of new energy companies in the Yangtze River Delta Region is above the medium level and that there are phenomena such as the incoordination of input and output ratios in the companies’ innovation processes. The technological innovation efficiency of new energy companies has a two-stage nature, and efficiency gaps in different stages within each company are evident. The low eff iciency of technology R&D is a key factor restricting the improvement of the overall innovation efficiency of new energy enterprises. The degree of economic transformation efficiency should be better to fit the overall efficiency.


Introduction
New energy has become a global economic growth factor, and the technological

Index Selection of New Energy Enterprises
In order to analyze the internal characteristics of the technological innovation process of an enterprise, based on Chen's research ideas, this paper decomposes the technological innovation process into the technology R&D stage and the economic transformation stage. The second stage introduces the indicators of scientific and technological capital and scientific and technological personnel input to measure the overall efficiency and sub-stage efficiency of new energy enterprises.
1) The input-output index selection of the technology R&D stage: This process considers the comparability of input-output indexes among enterprises. This paper selects the input indexes of the first stage as R&D personnel input intensity and R&D capital input intensity, respectively. And it selects the technology asset ratio as the output index of the technology R&D stage. In this paper, the technology asset ratio refers to the number of patent applications, new product development projects, and other assets with technology at the core .
2) The input-output index selection in the economic transformation stage: The technical asset ratio, the input intensity of the scientific and technological personnel, and the input intensity of the scientific and technological capital (Wu et al., 2017) are selected as the input indicators for the second stage. The profit rate of the main business and the return on assets Wu et al., 2017) are selected as the output indicators. A two-stage innovation input-output chain is shown in Figure 1.

Construction of the Evaluation Model
There are 22 DMUs (Decision Making Units)  The production technology set is defined as follows: Thus, the proposed model is established to calculate the overall efficiency of R&D innovation as follows: where µ 1 and µ 2 are the first stage input weight coefficients. µ 3 and µ 4 are the second-stage input weight coefficients. υ 1 and υ 2 are the overall output weight coefficients. Equation (1) where m is the first stage output weight coefficient, µ 1 x 10 and µ 2 x 20 are input indexes, and mz 0 is the output index of the first stage. The second stage model is established as follows: where µ 3 w 10 and µ 4 w 20 are the second-stage input indexes, respectively. And υ 1 y 10 and υ 2 y 20 are the output indexes of the second stage, respectively.
Based on the previous research literature, when constructing the total efficiency calculation model of the R&D innovation system, the internal sub-stage process of the R&D innovation system needs to be considered, which meets the two constraints mentioned in (Feng & Chen, 2014;. Therefore, this paper constructs a model to measure the overall efficiency of chain DMU as follows: The first constraint in Equation (4) is shown as follows: The second constraint in Equation (4) is shown as follows: ( ) The third constraint in Equation (4) is shown as follows: It can be concluded that the sum of Equations (6) and (7) is equivalent to Equation (5). Therefore, Equation (4) Suppose that the optimal solution of Equation (8) is as follows: 1 * υ , 2 * υ , 1 * µ , The efficiency of the first stage is shown as follows: The efficiency of the second stage is shown as follows: where η, φ 1 , φ 2 , φ 3 , φ 4 , ϛ 1 , and ϛ 2 are weight. These weights are derived from the DEA model, which is dynamic with different input-output index. Hence, the optimal solution can be obtained.  Table 1.

Descriptive Statistics of Main Input-Output Indicators
Descriptive statistics of the main input-output indicators. According to Table 2, the minimum profit margin of main business is 11.2%, the maximum is 50.0%, and the average is 24.522%; The minimum value of return on assets is 0.6%, the maximum value is 24.3%, and the average value is 4.9338%, indicating that there are certain differences in the economic returns of enterprises. The minimum value of technology asset ratio is 0.5%, the maximum value is 37.7%, and the average value is 3.779%, indicating that the ability of enterprises to develop new patents and new technologies is very different. The minimum input intensity of R&D personnel is 3.1%, the maximum is 39.9%, and the average is 7.336%. The minimum value of R&D capital investment intensity is 0.1%, the maximum value is 11.6%, and the average value is 3.999%. It can be seen that there are great differences in R & D investment among new energy enterprises. The specific descriptive statistical results are shown in Table 2.

Analysis of Innovation Efficiency of New Energy Enterprises in Yangtze River Delta Region
In line with the optimized two-stage DEA model, this paper uses MATLAB to calculate the efficiency of the two-stage input-output chain of technological innovation of new energy enterprises in the Yangtze River Delta region. It uses MATLAB and SPSS 24.0 to analyze the fitting relationship between the sub-stage efficiency and the comprehensive efficiency. It also analyzes the technological innovation efficiency matrix of enterprises, as follows.

Comparative Analysis of Comprehensive Efficiency
In this paper, the effectiveness of the improved model is verified, as compared with the case of not considering the intermediate input (i.e., µ3 = 0 and µ4 = 0) and 0 < µ3 & µ4 ≤ 1. Then, using MATLAB to analyze the sample data of new energy enterprises in the Yangtze River Delta, the specific analysis is as follows.      The sub-stage efficiency in Table 4 indicates that in the technology R&D stage, the R&D efficiency values of Zhengtai Electric, Guodian Nari, and Solar Power are ranked at the bottom for five consecutive years. In the technology R&D stage, they lack the ability to effectively transform the inputs into technological achievements, resulting in a low output rate of technological achievements. We need to optimize the input-output structure to avoid resource redundancy and to improve the efficiency of technology R&D.

Analysis of Sub-Stage Efficiency Level
In   stage, pay less attention to the technology R&D stage, and experience a certain lag in input-output, which lead to technology innovation. The output first shows as low and then a rapid decline. Since 2016, the trend of a rapid rise followed by a slower rise is related to the government's policy of supporting enterprises to achieve R&D innovation. Under government guidance, enterprises increase the introduction of advanced technology, cultivate high-quality R&D talent, and optimize the input-output structure to improve the ability of technology transformation.

Analysis of Fitting Relationship between Sub-Stage Efficiency and Comprehensive Efficiency
The results are shown in Table 5, Figure 5 and Figure 6. R 2 is the Goodness of Fit, and the closer the R 2 is to 1, the better the model is. Table 5 shows that the economic transformation efficiency R 2 is far greater than the technology R&D efficiency R 2 . The distribution of points near the line in Figure 5 is relatively discrete, while the distribution of points near the line in Figure 6 is uniform.
This shows that the fitting degree of economic transformation efficiency to comprehensive efficiency is greater than that of technology R&D efficiency to comprehensive efficiency. Enterprises should coordinate the investment proportion of the two stages to promote overall efficiency. Figure 6 shows that the 22 new energy enterprises are divided into four technological innovation modes: low R&D and high transformation, extensive low efficiency, high R&D and low transformation, and high R&D and high transformation.  Model 2 (θ 2 ) 0.518 21.531 0.720 0.000 *** (0.00039) Note: Standard errors in parentheses; ***p < 0.01, **p < 0.05, *p < 0.1. Source: Computed by the author.

Matrix Analysis of Technological Innovation Efficiency of New Energy Enterprises in Yangtze River Delta Region Based on a Two-Stage DEA Optimization Model
According to the above analysis (Fathi, 2020;Henriques et al., 2020) 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, and 22, respectively. The details are shown in Figure 7. Based on the model and its experiments, there are four types of enterprises: 1) Type 1: Low R&D and high-transformation Nine new energy enterprises, such as Jingsheng Electromechanical Co., Ltd., belong to Type 1, accounting for 40.9%. In the innovation process, there is the phenomenon of low R&D efficiency and high economic transformation efficiency. These enterprises have a strong ability to transform technological achievements into economic benefits, but they lack technology R&D ability. Therefore, enterprises need to pay attention to the investment of related resources at the technology stage. They need to introduce funds and talented personnel to optimize management methods and to find other ways to improve the technology R&D ability, to improve overall innovation efficiency.

4) Type 4: High R&D and high-transformation
Only one new energy enterprise, Space Rainbow, belongs to Type 4, accounting for 4.6%. In this type, the efficiency of technology R&D and the efficiency of economic transformation are both high. Enterprises with high technology R&D ability and economic transformation ability can reasonably adjust the input-output ratio of the two-stage model, which has sufficient personnel training and optimize their policy. The efficiency of the enterprise is significantly ahead of other ones, which makes it a "benchmark" enterprise.

Data Availability
The data used to support the finding of this study is available from the corresponding author upon request.

Funding Statement
The work was supported by National Natural Science Foundation of China un-