Promoting the efficiency of scientific and technological innovation in regional industrial enterprises: Data-driven DEA-Malmquist evaluation model

2.2.1 DEA-BCC model

The DEA-BCC model has advantages in evaluating the effectiveness of multiple inputs and outputs. Therefore, based on the assumption of variable scale compensation, the DEA-BCC model is proposed to evaluate the efficiency of regional industrial enterprises’ scientific and technological innovation from a static perspective.

Suppose there are n decision units (DMUs)—that is, n evaluation units. θ is the efficiency evaluation value of the decision-making unit; the input variables are α = (α₁, α₂, . . . , α_n) ^T, and the output variable is β = (β₁, β₂, . . . , β_n) ^T where ω represents the combination coefficient of each unit—that is, the weight of each decision-making unit — s^- represents the relaxation variable of the input, and s⁺ represents the relaxation variable of the output. min [ θ - ɛ ( ∑ j = 1 m s j - + ∑ r = 1 s s r + ) ] s . t . { ∑ i = 1 n ω i α i + s j - = θ α i 0 ( j = 1 , 2 , 3 , . . . , m ) ∑ i = 1 n ω i β i - s r + = β _ i 0 ( r = 1 , 2 , 3 , . . . , s ) ∑ i = 1 n ω = 1 ω ⩾ 0 , s r + ⩾ 0 , s j - ⩾ 0 ( 2 )(2)

The above model measures the efficiency of each decision-making unit from the output perspective. The objective function represents the comprehensive efficiency from the perspective of output maximization where comprehensive efficiency = pure technical efficiency × scale efficiency.

If θ = 1, s^- = 0, s⁺ = 0, the DEA of the decision-making unit is effective. Specifically, the input and output of the decision-making unit achieve the optimal state and simultaneously achieve technical efficiency and scale efficiency.

If θ < 1, DMU is DEA invalid, which means that the technical and scale efficiency of the decision-making unit cannot reach the optimal state.

If θ = 1, s^- ≠ 0 or s⁺ ≠ 0, DMU is weakly DEA effective. It indicates that the decision-making unit has not reached the state of technical and scale effectiveness at the same time, and DEA effectiveness can be realized by adjusting input and output.

DEA-BCC model can only measure the relative efficiency value of different decision-making units in the same period but can not measure the change of efficiency value in different periods. Therefore, this study uses the Malmquist index method to measure the total factor productivity index and then studies the dynamic change and internal motivation of scientific and technological innovation efficiency. Compared with other methods [16, 19], this method does not need various research assumptions, and the measurement results are more convincing. On the one hand, this method can clearly understand the dynamic changes of total factor productivity and its decomposition indicators in different periods. On the other hand, this method can also let us clarify the role of operation and management, technological progress, resource allocation, and other influencing factors in different regions on the improvement of total factor productivity, to know how to effectively improve the level of scientific and technological innovation through the decomposition of total factor productivity.

The Malmquist index method can dynamically reflect regional industrial enterprises’ scientific and technological innovation efficiency changes. In this study, (α ^t , β ^t ) and (α^t+1, β^t+1) are used to represent the input-output vector in period t and period t + 1, respectively, and D^t+1 (α^t+1, β^t+1) are used to represent the output distance function of the input-output vector under the technical conditions of reference period t + 1; D^t+1 (α ^t , β ^t ) represents the output distance function of the input-output vector under the technical conditions of reference period t, then the Malmquist index of technology and output angle in period t + 1 is Tfpch = M ( α t + 1 , β t + 1 , α t , β t ) = [ D t ( α t + 1 , β t + 1 ) D t ( α t , β t ) × D t + 1 ( α t + 1 , β t + 1 ) D t + 1 ( α t , β t ) ] 1 2(3)

If M > 1, total factor productivity increases; if M = 1, total factor productivity remains unchanged; if M < 1, it indicates that total factor productivity decreases. The Malmquist index can be divided into two parts: efficiency change (Effch) and technology change (Tech). The specific formula is as follows: Effch = D t ( α t + 1 , β t + 1 ) D t ( α t , β t )(4) Tech [ D t ( α t + 1 , β t + 1 ) D t + 1 ( α t + 1 , β t + 1 ) × D t ( α t , β t ) D t + 1 ( α t , β t ) ] 1 2 .(5)

Efficiency change can be further divided into pure technical efficiency change (Pech) and scale efficiency change (Sech). Thus, the formula of total factor productivity—that is, the efficiency of scientific and technological innovation—is translated into Tfpch = Effch × Tech = ( Pech × Sech ) × Tech .(6)

3.2.1 Construction of index system

SPSS software was used to analyze the correlation of industrial enterprises’ scientific and technological innovation data in Anhui from 2011 to 2019. The correlation coefficient of person detection was greater than 0.5 for the scientific and technological innovation input indexes, the number of R&D personnel, the full-time equivalent of R&D personnel, internal expenditure of R&D funds and scientific and technological innovation output indexes, number of valid invention patents, number of scientific papers published, and sales revenue of new products. At the same time, their significance test also showed a significant correlation at the 0.01 level, meeting the requirements of DEA data analysis. The correlation coefficient matrix is listed in Table 1. Based on this, a multi-input and -output evaluation index system of scientific and technological innovation efficiency of regional industrial enterprises was constructed, as shown in Table 2, providing a reliable index data foundation for subsequent DEA data analysis.

The DEA-BCC model was selected, and DEAP2.1 was used to process the input-output panel data of the scientific and technological innovation of industrial enterprises in 16 cities of Anhui Province from 2011 to 2019 to measure industrial enterprises’ scientific and technological innovation efficiency, as shown in Table 3.

Table 3 reveals that the overall scientific and technological innovation efficiency of industrial enterprises in Anhui Province was not ideal. The average innovation efficiency was below 0.900, showing a fluctuating state, and peaked at 0.934 in 2014. After 2015, industrial enterprises’ average scientific and technological innovation efficiency showed an obvious downward trend. Overall, eight cities or more had a comprehensive technical efficiency index of 1 from 2011 to 2015. In 2016 and 2017, only four and three cities had a comprehensive technical efficiency index of 120. In 2017 and 2018, seven and six cities had a comprehensive technical efficiency index of 1, consistent with the downward trend of the average scientific and technological innovation efficiency of industrial enterprises. This is due to redundancy in scientific and technological innovation input by industrial enterprises in some cities. In particular, the increase in internal expenditure of R&D funds cannot improve the transformation efficiency of scientific and technological achievements of industrial enterprises, resulting in a downward trend in the average value of the pure technical efficiency index. The scale efficiency index is the primary factor affecting the decline in industrial enterprises’ scientific and technological innovation efficiency value. From 2011 to 2019, the number of cities with a scale efficiency index of less than 1 continued to increase, reaching the highest in 2017, and the scale efficiency index of 13 cities was less than 1. Since 2017, the number of cities with a scale efficiency index of less than 1 has decreased, including 8 in 2018 and 10 in 2019. Between 2011 and 2019, the number of pure technical efficiency indexes less than 1 per year was less than that of scale efficiency indexes less than 1. It can be seen that the scale efficiency of scientific and technological innovation of industrial enterprises hinders the improvement of scientific and technological innovation efficiency more than pure technical efficiency.

The Malmquist index can compensate for the deficiency of the DEA-BCC model and measure the dynamic change degree of scientific and technological innovation efficiency of industrial enterprises in 16 prefecture-level cities in Anhui Province. Therefore, DEAP2.1 software was used to analyze industrial enterprises’ scientific and technological innovation data in 16 prefecture-level cities of Anhui Province from 2011 to 2019 to examine the dynamic change and heterogeneity of total factor productivity. Using the Malmquist index, the following results were obtained:

From the perspective of overall efficiency changes, Table 4 and Fig. 3 demonstrate that the average value of industrial enterprises’ scientific and technological innovation efficiency index in Anhui Province from 2011 to 2019 was 1.022, showing an overall upward trend. Total factor productivity was not stable during the study period, sometimes high and sometimes low. The annual total factor productivity index was greater than 1 in 2011–2016 and less than 1 in 2016–2019. The decline was mainly due to the dual impact of reducing technological progress and technical efficiency indices in terms of decomposition, the average technical efficiency index of industrial enterprises’ scientific and technological innovation in Anhui Province increased by 0.2%. The average technical progress index increased by 2% from 2011 to 2019.This indicated that the impact of industrial enterprises’ scientific and technological innovation efficiency in Anhui Province on total factor productivity was stronger than that of the technical efficiency index. The technical progress index played a significant role in improving total factor productivity. The driving effect of the technical efficiency index on total factor productivity was not significant.

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Fig. 3

Malmquist index and its decomposition of scientific and technological innovation of industrial enterprises in Anhui.

Meanwhile, from 2011 to 2019, the average scale efficiency index of industrial enterprise innovation in Anhui Province was 0.997. The average pure technical efficiency index was 1.005, greater than 1, showing an increasing and decreasing trend. During the study period, the scale efficiency index in five years was less than 1, indicating that the scale efficiency index inhibited the improvement of the technical efficiency index. Improving the management level of scientific and technological innovation and using innovative resources in industrial enterprises still has a large space to improve innovation efficiency.

From the difference in efficiency change among cities, it can be seen in Table 5 that, among the 16 cities, seven prefecture-level cities—Bozhou, Bengbu, Fuyang, Chuzhou, Wuhu, Xuancheng, and Huangshan—had higher than the average total factor productivity. The lowest was Huaibei, with a decrease of 6.7%. Except for Hefei, Huainan, Lu’an, and Ma’anshan, the total factor productivity index was less than 1. The other 11 cities were greater than 1, indicating that industrial enterprises’ scientific and technological innovation efficiency in most cities of Anhui Province is constantly improving with a positive development trend. Among them, Wuhu and Bozhou witnessed an increase of more than 10% in the innovation efficiency of industrial enterprises from 2011 to 2019. In terms of increased and decreased motivation, the decline in the technological progress index in Hefei, Huaibei, and Huainan is the main reason for the decline in total factor productivity. The decline in Lu’an’s technical efficiency index leads to a decline in total factor productivity. The decrease in total factor productivity in Ma’anshan is due to the decrease in the technical efficiency index and technical progress index at this stage. The improvement of total factor productivity in Chizhou, Bozhou, and Bengbu benefits from the coordinated growth of the technical efficiency index and technical progress index. The improvement of total factor productivity in Anqing, Huangshan, Suzhou, Xuancheng, Chuzhou, Wuhu, and Tongling benefits from the technical progress index. Their technical efficiency index is less than or equal to 1, which inhibits the improvement of total factor productivity to a certain extent. On the contrary, the improvement in Fuyang total factor productivity benefits from the technical efficiency index, and the technical progress index plays an inhibitory role.

Finally, from the perspective of regional layout, the total factor productivity index of industrial enterprises went from high to low from 2011 to 2019 in southern Anhui, northern Anhui, and central Anhui. The economic growth trend in southern Anhui is good. The innovation efficiency of industrial enterprises is constantly improving, which is consistent with the early economic development of cities in southern Anhui, radiated by “Nanjing metropolitan area,” “Hefei metropolitan area,” and “Hangzhou metropolitan area,” belonging to “Wanjiang urban belt,” and “Yangtze River Delta Urban Agglomeration,” and the remarkable achievements in the innovation and development of industrial enterprises. Northern Anhui has developed from behind, and the pace of development has significantly accelerated. It has become the most dynamic new growth plate in the province. This is consistent with the decision-making strategy of taking the development of Northern Anhui as an important strategic task for the rise of Anhui and placing it in the same important position as the development of areas along the river. The total factor productivity index in central Anhui was the lowest. Hefei is a city in central Anhui. Although it is the political and economic center of the whole province, it is also the second comprehensive national science center after Shanghai. Its innovation strength continues to rise, and major innovation achievements emerge. However, Hefei’s comprehensive strength is insufficient, and its economic radiation ability is weak, leading to an unsatisfactory scientific and technological innovation efficiency index for industrial enterprises in central Anhui.

Using SPSS software, the Malmquist index and its decomposition data of innovation efficiency of industrial enterprises in 16 prefecture-level cities in Anhui Province were clustered. The innovation efficiency level of industrial enterprises in Anhui Province was divided into four categories, as shown in Fig. 4.

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Fig. 4

Cluster pedigree of innovation efficiency of industrial enterprises in 16 cities of Anhui.

The specific classification results were obtained according to the general clustering diagram, as shown in Table 6 and Fig. 5.

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Fig. 5

Map display of scientific and technological innovation efficiency classification of industrial enterprises in Anhui.

As shown in Figs. 4 and 5 and Table 6, from the clustering results, the change in innovation efficiency of industrial enterprises in Anhui Province does not follow the pattern of southern, central, and northern Anhui. The technical efficiency index and technical progress index of Hefei, Suzhou, Bengbu, Chuzhou, Xuancheng, Tongling, Anqing, and Huangshan increase and decrease, placing them in the first category. The technical efficiency of Huaibei, Lu’an, and Ma’anshan has improved, and the total factor productivity has been reduced simultaneously, entering the second category. The innovation efficiency of Bozhou, Wuhu, and Chizhou has improved, and technical efficiency and technological progress have been improved simultaneously; thus, it has entered the third category. The technical efficiency index of Fuyang and Huainan increased, but the technical progress index decreased and entered the fourth category.

In summary, the level of scientific and technological innovation efficiency of industrial enterprises in Anhui Province developed well from 2011 to 2019, which was on the rise as a whole, and decreased in some years, but the range was very small. Although there are some differences in the change range and causes of industrial enterprises’ scientific and technological innovation efficiency in 16 cities, technological progress is the main factor causing the improvement of industrial enterprises’ innovation efficiency in Anhui Province. The unreasonable allocation structure of innovation resources has significantly inhibited the improvement of industrial enterprises’ innovation efficiency, so scale efficiency must be improved.

3.3.1 Improve the scientific and technological innovation management level of industrial enterprises

The empirical analysis results show that the growth rate of pure technical efficiency reflecting the management level is very small at only 0.5%, which shows that enterprises have some deficiencies in scientific and technological innovation management. There is a waste of innovation resources. Effectively using the human, financial, and material resources invested in scientific and technological innovation to maximize the output of scientific and technological innovation is a problem that all industrial enterprises should pay attention to. Industrial enterprises must combine scientific and technological research and development with the transformation of achievements. Therefore, optimizing the allocation structure of scientific and technological innovation investment resources and improving the utilization efficiency of scientific and technological innovation investment resources are important means to improve the efficiency of industrial enterprises’ scientific and technological innovation.

3.3.2 Optimize the scale of investment in scientific and technological innovation of industrial enterprises

The empirical analysis results show that the overall scale efficiency level of Anhui Province from 2011 to 2019 is low, and there is still much room for improvement. All cities should clarify the key points of scientific and technological innovation of industrial enterprises and concentrate on making up for the shortcomings of the innovation and development of industrial enterprises. Specifically, in 2019, Anqing, Maanshan, and Chuzhou were diminishing returns to scale while Bozhou, Suzhou, Bengbu, Lu’an, Xuancheng, Chizhou, and Huangshan were in the stage of increasing returns to scale. Therefore, cities should adjust measures to local conditions, and cities in the stage of diminishing returns to scale should reduce innovation resource investment and unreasonable resource allocation. Cities increasing returns to scale should increase the investment in scientific and technological innovation resources in multiple ways. Increasing the investment scale of industrial enterprises and improving the allocation efficiency of innovation resources to improve industrial enterprises’ scientific and technological innovation efficiency.

3.3.3 Accelerate the transformation of scientific and technological innovation achievements of industrial enterprises

The transformation and application of scientific and technological achievements can inject a strong impetus into regional development. We should actively seek scientific and technological innovation reform; establish a scientific and technological innovation system with industrial enterprises as the main body, market orientation and deep integration of industry, university, and research and promote the transformation efficiency of industrial enterprises’ scientific and technological achievement. At the same time, local governments should speed up the cultivation of market-oriented and professional high-quality scientific and technological innovation service institutions. Scientific and technological innovation service institutions should actively coordinate the effective docking of policy, information, technology, talent, and equipment resources. Establish and improve the whole chain transformation mechanism of basic application research, technology maturation, industrial incubation, enterprise docking, and achievement landing. Shorten the process of scientific and technological industrialization and comprehensively improve the vitality and efficiency of the transformation of scientific and technological achievements in industrial enterprises.

3.3.4 Improve the supporting policies for scientific and technological innovation in industrial enterprises

Government support plays an important role in industrial enterprises’ scientific and technological innovation [66, 67]. The government should clarify its position in the market economy and give full play to its guidance, organization, and support. First, strengthening industrial enterprises’ dominant position and leading role in scientific and technological innovation should optimize the structure of financial investment in science and technology, give play to the role of policy guidance, and give full support to industrial enterprises engaged in basic and key technologies. In addition, the government should continue to implement and strengthen fiscal and tax preferential policies for industrial enterprises, such as low interest and interest-free loans, financial subsidies, tax incentives, and other incentive policies; accelerate the transformation and industrialization of scientific and technological achievements, and boost the high-quality development of industrial enterprises. Finally, it should actively strive for angel investment funds and guidance funds for the transformation of scientific and technological achievements; guide social capital to support the industrialization of scientific and technological achievements; and continue to improve the subsidy and reward policies for relevant institutions and personnel promoting local trading, local transformation, and the local application of scientific and technological achievements.

3.3.5 Promote the scientific and technological innovation synergy of industrial enterprises among cities

Restricted by the administrative boundary, there are many problems in industrial enterprises’ scientific and technological innovation resources in 16 cities of Anhui, such as repeated construction, low utilization efficiency, unreasonable resource allocation, and scattered innovation investment. With China’s industrial economy entering a high-quality development stage, this “separate” industrial innovation development model has been unsustainable. To improve the competitiveness of cities, the “cluster” development model of inter-city industrial innovation has become an inevitable choice. Therefore, the development of Inter-City Industrial Innovation in Anhui should be strategically coordinated, planned, and guided. With the advantages of adjacent regions and similar industries, regional industrial innovation urban agglomerations, such as the Ma’anshan-Wuhu-Tongling industrial innovation urban agglomeration and Bengbu-Huainan industrial innovation urban agglomeration, emerge. Through the scientific and technological innovation cooperation and division of labor of industrial enterprises among cities or mutual borrowing, industrial enterprises among cities can give full play to their comparative advantages and improve the overall innovation competitiveness of industrial enterprises in the whole urban agglomeration. This is a “win-win” situation for a single city or urban agglomeration as a whole. We should actively explore the coordinated development model of scientific and technological innovation of industrial enterprises among urban agglomerations and promote the formation of a new layout of regional industrial-economic innovation and development with complementary advantages and high-quality development to realize the flow and integration of scientific and technological innovation elements of industrial enterprises, such as technology, knowledge, and information, and promote the co-construction and co-sharing of scientific and technological innovation resources of industrial enterprises.