1. Introduction

2. Materials and Methods

2.1. The Construction of the Indicator System

Surface validity is a primary goal when constructing an indicator system. Therefore, the evaluation system for research efficiency in Chinese universities must reflect the actual situation of higher education in China and the broader social context. The indicator system is designed from an input-output perspective, considering data continuity and availability, while ensuring scientific rigor. The system adheres to principles of adaptability to social development, scientific rigor, guidance, representativeness, and objectivity, drawing on mature experiences from related studies (Song et al, 2022; Wang et al, 2023).

The main selected research indicators for evaluating research efficiency are as follows (Dagum, 1997; Valero, 2019; Nabil et al, 2020; Liu et al, 2022): (1) research inputs, including university R&D personnel, university R&D funds, and full-time equivalent of university R&D personnel. (2) research outputs, which comprises domestic and international aspects. Domestic research output encompasses both economic and social benefits and includes indicators such as the number of university R&D projects, income from patent ownership transfer and licensing, and the establishment of national or industry standards. Foreign research output indicators consist of the number of scientific papers published in international journals and the inclusion of Chinese scientific papers in major international databases (SCI, EI, CPCI-S).

Table 1. Indicator System for Evaluating Research Efficiency in China.

Table 1. Indicator System for Evaluating Research Efficiency in China.

Primary Indicators	Secondary Indicators	Tertiary Indicators	Unit	Attribute
Research Inputs(A1)	Personnel(B1)	Proportion of Faculty with Doctoral Degrees（C1）	%	+
		Number of Full Professors among Full-time Faculty（C2）	Person	+
		University R&D Personnel（C3）	Person	+
	Financial Resources(B2)	University R&D Funding（C4）	Ten Thousand Yuan	+
		Assets of Teaching and Research Instruments and Equipment（C5）	Ten Thousand Yuan	+
	Time(B3)	Full-time Equivalent of University R&D Personnel（C6）	Person-Year	+
Research Output(A2)	Domestic Research Output(B4)	Publication of Scientific Papers（C7）	Articles	+
		Publication of Technological Works（C8）	Projects	+
		Number of Patent Applications（C9）	Projects	+
		Income from Patent Ownership Transfer and Licensing（C10）	Articles	+
		Number of R&D Projects in Higher Education Institutions（C11）	Categories	+
		Establishing national or industry standard figures.（C12）	Categories	+
	International Research Output(B5)	Number of Scientific Papers Published Abroad（C13）	Articles	+
		Inclusion of Chinese Scientific Papers (SCI) in Major Foreign Indexing Tools（C14）	Articles	+
		Inclusion of Chinese Scientific Papers in Major Foreign Indexing Tools (EI)（C15）	Articles	+
		Inclusion of Chinese Scientific Papers in Major Foreign Indexing Tools (CPCI-S)（C16）	Articles	+

2.3. Model

2.3.1. BCC-DEA Model

Classic DEA models mainly include CCR, BCC, FG, and ST, among others. The CCR (Charnes, Cooper, and Rhodes) model assumes constant returns to scale (CRS) and measures the overall efficiency of Decision Making Units (DMUs). In contrast, the BCC (Banker, Charnes, and Cooper) model is an extension of the CCR model, accommodating variable returns to scale (VRS).

The BCC model can be further divided into Input (I) and Output (O) models: (1) The Input model assumes constant outputs and focuses on how to adjust inputs to achieve efficiency. (2)The Output model assumes constant inputs and focuses on improving and increasing outputs.

The model used in this article is the BCC (O) model, which emphasizes improving and increasing outputs while holding inputs constant. This approach is particularly suitable for evaluating research efficiency in universities, where enhancing the quality and quantity of research outputs is often a primary objective.

BCC Model and Its Properties: Envelopment Form

BCC Model and Its Properties: Dual Form

Introducing non-Archimedean factors, the BCC model can be formulated in its envelopment form：

Its dual form

In the formula, $x_0$, $y_0$ represent the input and output indicators of the evaluated unit respectively; $\lambda$ denotes the unit combination coefficient; $\epsilon$ stands for the non-Archimedean infinitesimal, typically assumed to be a very small positive number, such as 10-6, in practical applications. In the formula, $e^T$ represents the unit row vector, $s^{-}{s}^{+}$ denotes the slack (redundant) variables, and $\theta$ stands for the efficiency evaluation index. If $\theta$=1, and $s^{-}=0$ and $s^{+}=0$, then DMU0 is BCC efficient; otherwise, DMU0 is BCC inefficient.

2.3.2. Malmquist-DEA Model

The Malmquist index, based on panel data analysis, facilitates dynamic assessment by comparing efficiency between a given period and the previous period or base period. Its results provide a dynamic comparison of input-output efficiency between the current period and the previous one.

$${\mathrm{M}}_0({\mathrm{x}}_{\mathrm{t}},{\mathrm{y}}_{\mathrm{t},}{\mathrm{x}}_{\mathrm{t}+1},{\mathrm{y}}_{\mathrm{t}+1})=\frac{{\mathrm{D}}_{\mathrm{t}+1}({\mathrm{x}}_{\mathrm{t}+1},{\mathrm{y}}_{\mathrm{t}+1})}{{\mathrm{D}}_{\mathrm{t}}({\mathrm{x}}_{\mathrm{t}},{\mathrm{y}}_{\mathrm{t},})}\times \sqrt{\frac{{\mathrm{D}}_{\mathrm{t}}({\mathrm{x}}_{\mathrm{t}+1},{\mathrm{y}}_{\mathrm{t}+1})}{{\mathrm{D}}_{\mathrm{t}+1}({\mathrm{x}}_{\mathrm{t}+1},{\mathrm{y}}_{\mathrm{t}+1})}\times \frac{{\mathrm{D}}_{\mathrm{t}}\left(\right({\mathrm{x}}_{\mathrm{t}},{\mathrm{y}}_{\mathrm{t},})}{{\mathrm{D}}_{\mathrm{t}+1}({\mathrm{x}}_{\mathrm{t}},{\mathrm{y}}_{\mathrm{t},})}}$$

$$M_0\left(x_t,y_t,x_{t+1},y_{t+1}\right)=\frac{D_{t+1}\left(x_{t+1},y_{t+1}\right)}{D_t\left(x_t,y_t\right)}\times \sqrt{\frac{D_t\left(x_{t+1},y_{t+1}\right)}{D_{t+1}\left(x_{t+1},y_{t+1}\right)}\times \frac{D_t\left(x_t,y_t\right)}{D_{t+1}\left(x_t,y_t\right)}}$$

(1)

${\mathrm{D}}_{\mathrm{t}}({\mathrm{x}}_{\mathrm{i}},{\mathrm{y}}_{\mathrm{i}})$ refers to the distance function for period t, and ${\mathrm{D}}_{\mathrm{t}+}({\mathrm{x}}_{\mathrm{i}},{\mathrm{y}}_{\mathrm{i}})$ refers to the distance function for period t+1, where x represents inputs and outputs. When M0​>1, it indicates efficiency growth, and when M0​<1, it indicates efficiency decline.

2.3.3. Calculation of Redundancy Ratio

The calculation of redundancy ratio, based on the BCC-DEA model, enables the study of input redundancy for DMUs.

$${\mathrm{I}}_{\mathrm{m}\mathrm{i}}={\mathrm{S}}_{\mathrm{j}\mathrm{m}\mathrm{i}}^{~}/{\mathrm{X}}_{\mathrm{m}\mathrm{i}}$$

${\mathrm{I}}_{\mathrm{m}\mathrm{i}}$ represents the input redundancy ratio, ${\mathrm{S}}_{\mathrm{j}\mathrm{m}\mathrm{i}}^{~}$ denotes the redundancy amount of the m-th input for the i-th DMU, and Xmi​ indicates the m-th input quantity for the i-th DMU.

3. Results

4. Discussion

Table 7. Redundancy Amount and Ratio of Research Input in 8 Provinces and Municipalities of China from 2012 to 2022.

Table 8. A Comparison of Research Input-Output Shortage Variables in 8 Provinces and Cities in China from 2012 to 2022.

5. Conclusions

Table 9. Summary of Static and Dynamic Analysis Results of Research Efficiency in 31 Provinces and Cities in China from 2012 to 2022.

Table 10. Key Points of Evaluation for Different Types of Universities in China in the New Era.

References

1. Abbott, M., & Doucouliagos, C.(2003). The efficiency of Australian universities: a data envelopment analysis. Economics of Education Review, 32(1),89-97. [CrossRef]
2. Adhi, I. H., Diana, S., Muhammad, A. I. M., & Kurnia, A.(2024). Efficiency of research in various fields: Evidence from Indonesia. Research Evaluation, 2024, rvae001. [CrossRef]
3. Antreas, D. A., & Estelle, S.(1997). Assessing the Comparative Efficiency of Higher Education Institutions in the UK by the Means of Data Envelopment Analysis.Education Economics,5(2),117-134.
4. Bhutto, A., Rashdi, P. I., Abro, Q. M.(2012).Indicators for science and technology policy in Pakistan: Entering the science, technology and innovation paradigm. Science and Public Policy,39(1):1-12. [CrossRef]
5. Cai, S. F., Zhang, G. Q., &Wang, W.(2023). Evaluation of Innovation Performance of University Knowledge Economic Circles Based on Data Envelopment Analysis. Journal of Tongji University (Natural Science Edition),51(05), 682-686.
6. Charnes, A., Clark, C. T. Cooper, W. W. & Golany, B. (1984)..A developmental study of data envelopment analysis in measuring the efficiency of maintenance units in the U.S. air forces. Annals of Operations Research,2(1),95-112. [CrossRef]
7. Charnes, A, Cooper, W.W., Golany, B., Seiford, L., & Stutz, J.(1985). Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical production functions. Journal of Econometrics, 30(1-2): 81-107. [CrossRef]
8. Charnes, A., Cooper, W.W., & Rhodes, E.(1978). Measuring the efficiency of decision making units. European Journal of Operational Research,,2(6):429-444. [CrossRef]
9. Dagum, C.(1997). A new approach to the decomposition of the Gini income inequality ratio. Empirical Economics, 22(4), 515-531. [CrossRef]
10. Griliches, Z. (1979). Issues in Assessing the Contribution of Research and Development to Productivity Growth. The Bell Journal of Economics,1979,10(1):92-106. [CrossRef]
11. Li, K., & Fan, Y. J. (2022). Evaluation of Research Efficiency of First-Class Universities under the "Double First-Class" Goal. Research Management, 43(09), 41-47. [CrossRef]
12. Jiang, H., Yang, Y., & Wang, P. J. (2022). Research on Evaluation of Research Output of Universities Based on DEA and SFA Efficiency Value Method - Taking Analysis of Data from 52 "Double First-Class" Universities as an Example. Modern Education Management, (04), 40-49 . [CrossRef]
13. Li, Y., & Zhang, P.(2022). Research on Efficiency of Scientific and Technological Innovation in Production, Learning and Research Based on Network DEA and Shapley Value. Research in Science and Technology Management, 42(05), 93-103.
14. Liu, C. B., Dai, W., Yu, L. A., & Yang, J. A.(2022). Research on Prediction of Evaluation of University Scientific Research Platform Based on GCA-DEA-MSVC Method. Chinese Journal of Management Science, 2022,30(03): 240-247. [CrossRef]
15. Liu, Z. W., & Liu, H. M.(2023). Research on Enhancing the Performance Evaluation of Regional Scientific and Technological Resources in Universities with "Double High" Construction Schools: Based on the DEA-Malmquist Model. Science and Technology Management Research, 43(09), 82-89.
16. Ma, L.(2021) Promoting Differentiated Innovation in the Evaluation of Universities in the New Era. Ethnic Education Research, 32(06), 5-10. [CrossRef]
17. Madria, W. F., Miguel, A. S., & Li, R. C.(2019). Quality-Oriented Network DEA Model for the Research Efficiency of Philippine Universities.International Conference on Industrial Engineering and Engineering Management, 596-600. [CrossRef]
18. Nabil, A., Mehdi, R., & Norrin, H.(2020).Assessing the research efficiency of Canadian scholars in the management field: Evidence from the DEA and fsQCA. Journal of Business Research,115, 296-306. [CrossRef]
19. Qi, T.(2023). Retrospective Study on the Research Efficiency of Various Types of Universities in China during the "Thirteenth Five-Year Plan" Period Based on Data Envelopment Analysis. Research in Science and Technology Management, 43(06), 114-122.
20. Song, Z. Y., & Sun, B. C.(2022). Research on Input-Output Efficiency and Its Influencing Factors in Chinese Ordinary Universities: A Stochastic Frontier Analysis Based on Provincial Panel Data from 2009 to 2018. Journal of Lanzhou University (Social Sciences Edition), 50(06),128-137. [CrossRef]
21. Valero, A., & Reenen, J. V.(2019). The Economic Impact of Universities: Evidence from Across the Globe.Economics of Education Review,68(1), 53-67. [CrossRef]
22. Wang, X. Z., & Jiang, Z. H.(2019). Analysis of Innovation Efficiency and Environment of Universities in China: A Perspective of Value Types. Research Management,,40(10), 25-36. [CrossRef]
23. Wang, Z., Lv, N. H., Wu, M. Y. (2023). Evaluation of Research Efficiency of Humanities and Social Sciences in "Double First-Class" Construction Universities Based on Three-Stage DEA. China's Higher Education of Science and Technology, Z1, 26-30. [CrossRef]
24. Yang, M., Fei, X. Y., Wei, Y. Q., & Liang L. (2022).Two-Stage DEA Evaluation Method Based on Resource Sharing and Subsystem Interaction - Evaluation of Research Performance of "First-Class Universities" in China. Chinese Journal of Management Science, 30(02), 256-263. [CrossRef]
25. Shi, Y. K., Wang, D. C., & Zhang, Z.M. (2022). Categorical Evaluation of Scientific Research Efficiency in Chinese Universities: Basic and Applied Research. Sustainability, 14(8), 4402. [CrossRef]
26. Zhang, H. Q., & Shang, T. T.(2015). Comparative Analysis of Research and Innovation Efficiency in Universities: Based on Panel Data from 30 Provinces Nationwide. Research Management, 36(S1),181-186. [CrossRef]
27. Zhang, X. M., & Zhao, G. D.(2023). Spatial-Temporal Pattern and Evolution of Efficiency in the Allocation of Graduate Education Resources in China - Supply-Side Analysis Based on Provincial Panel Data from 2003 to 2018. Journal of East China Normal University (Educational Sciences Edition),,41(06), 59-77. [CrossRef]
28. Zhou, J. X., & Gao, S. H.(2022). Evaluation of Scientific and Technological Innovation Efficiency in the Construction of First-Class Universities - A Dual Perspective Based on School Types and Regional Differences. China's Higher Education of Science and Technology, (09), 8-15. [CrossRef]