A Study on the Spatial–Temporal Evolution of Innovation Efficiency in Chinese Universities in the Context of the Digital Economy

Abstract

With the rapid development of knowledge and the digital economy, it is a crucial to understand the role of the digital economy in improving the innovation efficiency of universities. Using the panel data of universities in 31 Chinese provinces from 2013 to 2020, this paper measures the regional innovation efficiency of Chinese universities and examines the impact of the digital economy on universities’ innovation by employing the super-efficiency DEA model along with the Malmquist index, kernel density estimation and Theil index. The analysis shows the following: (1) The digital economy has a significant positive impact on the efficiency of university innovation, but there is still much room for improvement. (2) In terms of the dynamic evolution of innovation efficiency, Chinese university performance shows a trend toward declining innovation efficiency, and the issue of inadequate investment in technical innovation is discovered, which urgently needs to be addressed. The findings of this paper offer empirical support for understanding the relationship between digital economy growth and university innovation productivity with important ramifications for the innovative expansion of higher education institutions in emerging nations.

1. Introduction

With the development of knowledge and the digital economy, universities have gradually become an important force of knowledge production and technological innovation in the world. Learning from the universities of other nations, Chinese universities are gradually changing from single-teaching or research-oriented universities to comprehensive universities of talent creation, knowledge innovation and achievement transformation. As an important link in the innovation ecological chain, universities are not only training institutions that output innovative talent but are also incubators and boosters of innovative achievements. The practicality, benefits and sociality of the scientific and technological research and development results of universities are receiving increased attention. The experiences of various nations demonstrate that basic research is the cornerstone of national innovation, and universities, as one of the three primary bodies of basic research, are not only the source of disruptive and cutting-edge results [1,2,3] but are also crucial to fostering the output of creative and innovative results [4]. In light of this, innovation in universities has a broad and profound impact on societal and economic advancement as well as industrial change. It is now urgently necessary to find a solution to the problem of how to increase the rate of innovation and foster the growth of scientific and technological university accomplishments. Additionally, the use of digital technology can help solve issues with information asymmetry and positive externality that arise throughout the innovation process in addition to expanding the frontiers of innovation, reducing the long-term nature of R&D and lowering R&D expenses. New waves of innovation mode transformation are inevitably brought on by the growth of the digital economy, which in turn impact the effectiveness of innovation.

In order to enrich research in the field of innovation efficiency and digital economy development and to identify the spatial and temporal changes to innovation development in Chinese universities, this study focuses on measuring the differences in university innovation efficiency in the context of the digital economy and traditional environment and accurately recognizes the temporal evolution and regional differences of university innovation development under the influence of the digital economy, which are important for the comprehensive and collaborative improvement of innovation efficiency in Chinese universities. This study’s analysis of regional differences may promote the improvement and coordinated development of the innovation efficiency of regional universities and provide recommendations for Chinese universities to improve the efficiency of innovation transformation.

The remaining sections of this study are organized as follows: Section 2 reviews relevant literature in the context of the present study; Section 3 describes the index system and data sources; Section 4 presents the static and dynamic evolutionary analysis results; and Section 5 includes conclusions, limitations and suggestions for future studies.

2. Literature Review

Since the Patent and Trademark Law Amendment Act of 1980 was passed by the U.S. Congress, the government has been legally required to protect the transformation of universities’ scientific and technological accomplishments. Universities have reacted favorably to this Act by creating innovation and technology transformation institutions, which have significantly increased the effectiveness of innovation. Since universities’ ability to innovate is seen as a key factor in the development of a national innovation system, the assessment of universities’ capacity for innovation becomes a crucial component of the current management of university research, and the study of universities’ capacity for innovation seems to be a hot topic in the field of innovation management. The different facets of university innovation activities, such as the inputs and outputs of innovation activities, must be investigated in order to assess the efficiency of university innovation. The majority of academics have assessed the innovation efficiency of universities by examining innovation outcomes, such as patented technologies and academic monographs.

In terms of university innovation efficiency evaluation methods, there are currently two methods commonly preferred by academics: the stochastic frontier method, represented by SFA as the parametric method; and the nonparametric method, represented by data envelopment analysis (DEA). Jill Johnes [5] used data on graduates from various institutions and imported them into a DEA model to assess the efficiency of innovation output in universities. Agasisti T. et al. [6] measured the efficiency of innovation in 58 Italian universities with a DEA model using teaching and research as input variables. In order to understand how local undergraduate universities in Yunnan Province collaborate with external scientific research institutes and enterprises in the development of new scientific and technological innovations, She et al. [7] studied the patent output and social network characteristics of these institutions with a DEA model. In this research, it can be found that DEA as a nonparametric model is able to measure the efficiency of multiple inputs and outputs without requiring the definition of the form of the production function. An SFA model can take into account the effects of random shocks and the inclusion of environmental variables in the model, and it can be tested parametrically. However, the results of SFA are susceptible to the influence of the indicator system and are sometimes not stable. Therefore, many scholars have expanded on the traditional DEA model by further applying models such as the SBM-DEA model, Bootstrap DEA model and super-efficient DEA model to measure innovation efficiency. For example, Chen et al. [8] investigated the scientific and technological innovation performance of top universities in China from 2014 to 2019 based on the super-efficiency DEA model and Malmquist index. A new triple helix-based index which involves a large dataset was introduced by Jovanovi et al. [9] to offer important insight to policymakers.

The aforementioned methods are undoubtedly effective for measuring efficiency across a range of inputs and outputs as well as for static comparative analyses, but they do not adequately capture the dynamic nature of university innovation efficiency. This has led several academics to try to examine the dynamic trend of university innovation efficiency using the DEA-Malmquist model, kernel density estimation and other techniques [10,11]. However, research results are relatively scarce, and these methods need to be further explored.

In terms of the factors influencing innovation, personnel investment and financial investment are considered to be the main factors typically affecting the effectiveness of innovation. In addition, to improve the relevant policy formulation, promote the rational allocation of research resources, enhance the innovation capacity of universities and optimize the efficiency of university innovation inputs and outputs, factors such as government support [12,13], international exchange [14], the institutional environment [15], the degree of market interaction [16], taxation [11,17] and other factors have been analyzed to measure innovation efficiency. Since the digital economy has become a major research hotspot in both academic and practical circles, more and more researchers are trying to ascertain the impact of the digital economy on innovation. Digital economy development effectively enhances the development of value chains [18,19] and the global innovation network [20] and serves as a driver of innovation, which could improve the efficiency of regional innovation [21]. Zhang et al. [21] indicated that digital empowerment brought forth by the digital economy can have a favorable moderating influence on innovation effects through innovation networks and innovation capabilities, hence enhancing innovation performance.

As such, this paper attempts to introduce the digital economy as an influencing factor of innovation to further examine the impact of digital economy development on innovation activities in universities, and the super-efficiency DEA model, Malmquist index, kernel density estimation and Theil index are used in this research framework to illustrate Chinese university innovation efficiency and its temporal and spatial evolution, strengthening the practical guiding significance of policy recommendations and university innovation development.

3. Evaluation Index System and Data Sources

3.1. Evaluation Index Systems

Based on existing studies, this paper takes the Cobb-Douglas (CD) production function as the basis and compiles a university innovation input-output index system (see

Table 1. Digital economy development index.

Dimension I	Dimension II	Specific Indicators
Informationization development	Informationization foundation	Fiber optic cable density
		Density of cell phone base stations
		Percentage of informationization employees
	Informationization impact	Total telecommunication business
		Software business income
Internet development	Fixed internet base	Internet access port density
	Mobile internet base	Mobile internet penetration rate
	Impact of fixed internet broadband	Percentage of internet users
	Mobile internet impact	Percentage of mobile internet users
Digital transaction development	Digital transaction basis	Number of websites per 100 enterprises
		Enterprise use of computers
		Proportion of e-commerce enterprises
	Impact of digital transactions	E-commerce sales
		Online retail sales

). Considering the accuracy and accessibility of data, a super-efficiency DEA model was used to measure and analyze the innovation efficiency of universities in each province of China from 2013 to 2020. Additionally, this paper compares and analyzes universities’ innovation efficiency in the context of the digital economy as well as in the traditional context. The outputs of the innovation efficiency of universities in the traditional context are the sum of technology transfer contracts (thousand yuan) and the number of publications, and the input variables are the full-time equivalent research and development personnel and the internal expenditure of university science and technology activities (thousand yuan). The outputs of university innovation efficiency in the digital economy are the sum of technology transfer contracts (thousand yuan) and the number of papers published, while the regional digital economy development index is added to the input variables of the traditional context.

(1) Output variables. Since the realization of academic accomplishment sharing and economic benefit exchange is the ultimate goal of university innovation initiatives, the transformation output of scientific and technological advancements and intellectual production are two categories of university innovation output. The marketability of scientific and technological advancements is one way to assess how they have transformed society, whereas the quantity of scholarly papers produced by higher education institutions is one way to gauge intellectual output. Therefore, the output indicators of the innovation efficiency of universities in this paper are characterized by the sum of technology transfer contracts (thousand yuan) and the number of academic papers published. Additionally, this paper sets the lag period at one year since there is a temporal lag between the input of innovation and the production of innovation results in university innovation activities. Therefore, the number of academic papers published in universities from 2014 to 2021 and the quantity of technology transfer contracts (in thousand yuan) were noted as the innovation output of universities from 2013 to 2020.

(2) Input variables. The input of innovative factors was the main requirement for obtaining innovation output. According to Montresor and Vezzani et al. [22], internal university expenditure on scientific and technological activities (in thousand yuan) and full-time equivalent research and development personnel were chosen as the characterization indices of human resources and the physical resources input, respectively.

(3) Digital economy factors. Referring to the index system by Liu Jun et al. [23] in a measurement study of China’s digital economy, three primary dimensions, being informationization development, internet development and digital transaction development, and the corresponding eight secondary dimensions were used to construct the digital economy development index system (see Table 1), and the digital economy development index of each province from 2013 to 2020 was calculated.

3.2. Data Sources

In this paper, the panel data of 31 Chinese provinces (excluding Hong Kong, Macao and Taiwan) from 2013 to 2020 were selected as the sample, and the number of sample DMUs was greater than twice the sum of the number of input-output indicators, which meets the measuring efficiency requirement using the DEA model. The innovation-related data of universities in each province were obtained from the Compilation of Science and Technology Statistics of Higher Education Institutions from 2013 to 2021, and data on the digital economy development index calculation were obtained from the 2013–2020 China Statistical Yearbook and public data released by the National Bureau of Statistics of China. The 31 provinces were divided into seven regions: North China (5 provinces), Northeast China (3 provinces), East China (7 provinces), Central China (3 provinces), South China (3 provinces), Southwest China (5 provinces) and Northwest China (5 provinces), and the missing individual data were supplemented by interpolation and imputation methods for completeness. The meanings and descriptive statistics of each variable are shown in

Table 2. Input-output indicators and descriptive statistics of variables.

Variables	Indicators	Meaning	Mean	SD
Output	Technology transfer contract quantity	Technology transfer contract quantity (thousand yuan)	12,816.448	12,816.448
	Number of academic publications	Number of academic papers published	4,283,036.141	4,283,036.141
Input	Research and development staff full-time equivalent	Research and development staff full-time equivalent	0.221	0.221
	Internal expenses for scientific and technological activities in universities	Internal expenses for scientific and technological activities in universities (thousand yuan)	12,816.448	12,816.448
Digital economy factors	Digital economy development index	Digital economy development index by province	4,283,036.141	4,283,036.141

.

4. Research Results and Discussion

4.1. Static Analysis of Innovation Efficiency in Universities

Since the traditional DEA method restricts the range of efficiency values to the interval [0, 1] and cannot further distinguish the relative efficiency gap of the decision unit with an efficiency value of 1, this paper adopts the super-efficiency model to study the innovation efficiency of universities in 31 provinces and uses DEA-solver 5.0 software to calculate the innovation efficiency values of Chinese universities from 2013 to 2020. Based on the division of natural geographical regions, the 31 provinces were divided into seven regions, including North China, Northeast China, East China, Central China, South China, Southwest China and Northwest China. In addition, for the comparative analysis of the innovation efficiency of universities in the context of the digital economy and in the traditional context, this paper uses the same method to measure the university innovation efficiency results in each region from two perspectives, which is shown in

Table 3. Comparison of innovation efficiency of universities in the context of the digital economy.

		2013	2014	2015	2016	2017	2018	2019	2020	Mean	SD
National	Traditional	0.559	0.570	0.588	0.556	0.668	0.532	0.497	0.429	0.550	0.065
	Digital	0.782	0.736	0.737	0.648	0.709	0.577	0.529	0.471	0.649	0.105
North China	Traditional	0.472	0.450	0.466	0.530	0.681	0.492	0.456	0.379	0.491	0.082
	Digital	0.690	0.621	0.600	0.646	0.736	0.551	0.494	0.430	0.596	0.095
Northeast China	Traditional	0.339	0.342	0.371	0.388	0.533	0.438	0.447	0.335	0.399	0.065
	Digital	0.663	0.589	0.577	0.552	0.561	0.535	0.534	0.427	0.555	0.062
East China	Traditional	0.539	0.528	0.648	0.461	0.615	0.452	0.415	0.392	0.506	0.087
	Digital	0.731	0.658	0.839	0.538	0.649	0.484	0.440	0.425	0.595	0.139
Central China	Traditional	0.690	0.705	0.706	0.710	0.856	0.684	0.643	0.472	0.683	0.099
	Digital	1.062	0.923	0.860	0.816	0.908	0.770	0.694	0.540	0.822	0.148
South China	Traditional	0.536	0.557	0.549	0.493	0.462	0.467	0.384	0.403	0.481	0.061
	Digital	0.725	0.737	0.709	0.580	0.531	0.506	0.415	0.437	0.580	0.121
Southwest China	Traditional	0.585	0.584	0.622	0.610	0.681	0.585	0.538	0.460	0.583	0.060
	Digital	0.779	0.750	0.740	0.690	0.721	0.616	0.550	0.476	0.665	0.101
Northwest China	Traditional	0.714	0.797	0.673	0.708	0.809	0.633	0.620	0.548	0.688	0.083
	Digital	0.888	0.922	0.769	0.759	0.828	0.644	0.636	0.579	0.753	0.116

.

(1) Analysis of the overall national innovation efficiency of universities. The mean value of the innovation efficiency of Chinese universities in the context of the digital economy from 2013 to 2020 was 0.649. The overall level of innovation efficiency under the digital economy is low, and there is a large efficiency loss. Furthermore, the innovation efficiency of universities in the context of the digital economy from 2013 to 2020 was far higher than that in the traditional context. This indicates that the development of the digital economy has had a favorable influence on the innovation of universities. In addition, the overall innovation efficiency of universities nationwide showed a decreasing trend in fluctuation during the research period, which indicates that there is a growing redundancy of human and financial investment in the innovation activities of universities in China.

(2) Analysis of the innovation efficiency of universities in each region. Combining the data in Table 3 and

Table 4. Regional comparison of universities’ innovation efficiency.

Region	Province	Digital	Traditional	Region	Province	Digital	Traditional
North China	Beijing	0.649	0.513	Central China	Henan	0.889	0.865
	Tianjin	0.411	0.385		Hubei	0.861	0.609
	Hebei	0.656	0.540		Hunan	0.714	0.575
	Shanxi	0.547	0.432	South China	Guangdong	0.516	0.501
	Inner-Mongolia	0.717	0.585		Guangxi	0.666	0.385
Northeast China	Liaoning	0.510	0.412		Hainan	0.558	0.558
	Jilin	0.581	0.406	Southwest	Chongqing	0.666	0.666
	Heilongjiang	0.572	0.381		Sichuan	0.749	0.656
East China	Shanghai	0.578	0.498		Guizhou	0.726	0.573
	Jiangsu	0.763	0.602		Yunnan	0.689	0.524
	Zhejiang	0.409	0.407		Tibet	0.496	0.496
	Anhui	0.799	0.613	Northwest China	Shaanxi	0.784	0.656
	Fujian	0.397	0.388		Gansu	0.771	0.707
	Jiangxi	0.628	0.555		Qinghai	0.684	0.684
	Shandong	0.595	0.481		Ningxia	0.671	0.662
Mean		0.649	0.550		Xinjiang	0.856	0.729

, it can be observed that, from the fluctuation of regional innovation efficiency under the digital economy of universities and the traditional context except for in the northeast region, the fluctuation of regional innovation efficiency in the context of the digital economy from 2013 to 2020 was higher than that in the traditional context (the standard deviation of innovation efficiency in the context of the digital economy was greater), which indicates that the effective use of the digital economy may be one of the important factors leading to the fluctuation of the innovation efficiency of regional universities. In the context of the digital economy, there were large differences in the innovation efficiency of universities in the seven regions. Among them, the most efficient were those of Central China, with the highest innovation efficiency mean value of 0.822, followed by Southwest, North China, East China, South China and Northeast China in that order. The mean value of the innovation efficiency of universities in Central China, Northwest China and Southwest China is higher than the national level. However, Hainan, Tibet, Chongqing and Qinghai do not show the special digital characteristics of regional innovation efficiency, which indicates that the digital economy does not drive the improvement of innovation efficiency in these provinces. Figure 1 visualizes the changing trends of the innovation efficiency of universities in the seven regions. Although the average value of the innovation efficiency of universities in Central China and Northwest China fluctuated, the overall innovation efficiency was at a high level in these regions. This is mainly due to the unprecedented opportunities brought by the “Belt and Road Initiative” to the innovation development of universities in these regions, which have led to the continuous improvement of their innovation efficiency.

4.2. Dynamic Evolutionary Analysis of Innovation Efficiency Changes in Universities

4.2.1. Analysis of University Innovation Efficiency Based on Malmquist Index

This paper investigated the effectiveness of the innovation efficiency of universities in 31 provinces of China from the static aspect by applying the super-efficiency DEA method and analyzed the regional variability. Next, the Malmquist index was used in the dynamic aspect to explore changes in the innovation efficiency of universities in the context of the digital economy. Using the Deap 2.1 software, a dynamic empirical analysis of the innovation efficiency of universities in 31 provinces of China from 2013 to 2020 was carried out, and the Malmquist index and the mean value of each decomposition term of the universities in each province were obtained. The results are shown in

Table 5. Dynamic efficiency of innovation based on DEA–Malmquist.

Region	Province	effch	techch	pech	sech	tfpch
North China	Beijing	0.972	0.970	0.999	0.973	0.943
	Tianjin	1.044	0.896	1.047	0.997	0.936
	Hebei	0.996	0.901	0.997	1.000	0.898
	Shanxi	1.075	0.932	1.074	1.001	1.002
	Inner-Mongolia	1.001	0.913	1.001	1.000	0.914
Northeast China	Liaoning	1.043	0.911	1.016	1.026	0.950
	Jilin	1.059	0.908	1.079	0.981	0.961
	Heilongjiang	1.035	0.905	1.021	1.014	0.937
East China	Shanghai	1.070	0.973	1.045	1.024	1.042
	Jiangsu	1.000	0.931	1.000	1.000	0.931
	Zhejiang	1.033	0.948	1.007	1.026	0.980
	Anhui	0.945	0.919	0.946	0.999	0.869
	Fujian	0.888	0.961	0.895	0.993	0.853
	Jiangxi	0.995	0.904	0.984	1.011	0.899
	Shandong	1.026	0.904	0.986	1.040	0.928
Central China	Henan	1.000	0.909	1.000	1.000	0.909
	Hubei	1.000	0.895	1.000	1.000	0.895
	Hunan	1.015	0.914	1.015	1.000	0.928
South China	Guangdong	1.095	0.948	1.013	1.081	1.038
	Guangxi	0.976	0.903	0.978	0.997	0.881
	Hainan	0.942	0.953	0.914	1.031	0.898
Southwest	Chongqing	1.017	0.965	1.025	0.992	0.982
	Sichuan	1.011	0.932	1.005	1.006	0.942
	Guizhou	1.010	0.901	1.000	1.010	0.910
	Yunnan	0.984	0.905	0.985	0.999	0.890
	Tibet	0.997	0.931	1.000	0.997	0.929
Northwest China	Shaanxi	1.012	0.929	1.014	0.998	0.941
	Gansu	0.994	0.916	1.016	0.979	0.910
	Qinghai	1.045	1.011	1.000	1.045	1.056
	Ningxia	0.960	0.924	1.000	0.960	0.887
	Xinjiang	1.000	0.954	1.000	1.000	0.954
Mean		1.008	0.928	1.002	1.006	0.935

. From Table 5, it can be observed that the mean value of the Malmquist index of national universities for 2013–2020 was 0.935 (less than 1), the average growth rate was −6.5% and the overall innovation efficiency of universities shows a decreasing trend. From the index decomposition, the technical progress index of the universities in all the provinces except Qinghai province was less than 1 (the overall mean value was 0.928), while the mean values of technical efficiency, pure technical efficiency and scale efficiency were greater than 1, indicating that technical progress is the key factor limiting the growth of their Malmquist index.

4.2.2. Analysis of Temporal Evolution Based on Kernel Density Estimation

To portray the dynamic temporal evolution of the innovation efficiency of Chinese universities from an interprovincial regional perspective in more detail, the kernel density estimation method was used for further analysis, and its rationale is as follows:

Let the density function of the p-dimensional random vector x be f(x) = f_((x_1,…, x_n)), reflecting the distribution of innovation efficiency values in universities. {x_1, x_2,…, x_n} is an independent and identically distributed sample, then the kernel density of f(x) is estimated as:

$$f_n\left(x\right)=\frac{1}{n{h}^p}{\displaystyle \sum }_{i=1}^n[K\frac{x-X_1}{h}]$$

(1)

$K[\frac{x-X_1}{h}]$ is the kernel function, which is a smoothing or weighting function, $h$ is the bandwidth and n is the number of sample observations. According to the method of Silverman [24], $h_0=1.06s_x{n}^{-\frac{1}{5}}$. The key objective of this estimation is to observe the pattern of distribution, location and evolutionary dynamics of innovation efficiency in Chinese universities through the comparison of the distribution curves of the kernel density estimation results. This is carried out to compensate for the fact that previous studies have only been able to pinpoint the trend of efficiency changes in a single region.

The temporal trends of university innovation efficiency in the context of the digital economy from 2013 to 2020 are shown specifically in Figure 2.

From Figure 2, the dynamic trend analysis of the innovation efficiency of universities from 2013 to 2020 can be observed. This reveals the following: (1) The overall innovation efficiency distribution density curve has a tendency to shift continually to the left although the movement range is quite small. This phenomenon indicates that the innovation efficiency as a whole is in a slow-declining trend, which is consistent with the previous conclusion. (2) From the shape of the curve, there is no conspicuous trailing feature, which suggests that the overall development is more typical and that the difference in the comprehensive innovation efficiency of universities across the majority of provinces is not particularly noteworthy. (3) From the change in the kurtosis of the curve, the height of the crest gradually becomes higher and the width of the crest gradually becomes narrower, which indicates that the gap between the innovation levels of Chinese universities gradually narrows. (4) The fundamental feature of the kernel density curve during the sample period is a single-peaked distribution, which suggests that there is no clear polarization in the levels of innovation efficiency across Chinese institutions in different regions. (5) Regarding the overall situation of the evolution of the regional innovation efficiency of universities in the context of the digital economy from 2013 to 2020, the provincial concentration of the innovation efficiency of universities in each region becomes higher and gradually exerts a convergence advantage.

4.2.3. Analysis of Spatial Evolution Based on Theil Index

To further illustrate the spatial evolution of Chinese university innovation efficiency, the Theil index is utilized to identify regional differences. The indicators for measuring regional differences generally include the standard deviation, coefficient of variation, Theil’s index and Gini coefficient, etc. By contrast, Theil’s index is decomposable and can be decomposed into inter-regional differences and intra-regional differences in a “spatial” sense, and the contribution of these two types of differences to the total differences and the magnitude of their effects are clarified. In this paper, region-to-region inequality is measured using the Theil index. The overall differences can be broken down into intra-regional and inter-regional differences in the index, which reflects the magnitude and source of discrepancies [25]. The formulas are provided by:

$$T=T_W+T_B$$

(2)

$$T_P={\displaystyle \sum }_{i=1}^{n_p}\frac{1}{n_p}·\left(\frac{e_i}{\overline{e_p}}\right)·ln\left(\frac{e_i}{\overline{e_p}}\right)$$

(3)

$$T_W={\displaystyle \sum }_{p=1}^m\left(\frac{n_p}{\overline{n}}·\frac{\overline{e_p}}{\overline{e}}\right)·T_P$$

(4)

$$T_B={\displaystyle \sum }_{p=1}^m\frac{n_p}{\overline{n}}\left(\frac{\overline{e_p}}{\overline{e}}\right)·ln\left(\frac{\overline{e_p}}{\overline{e}}\right)$$

(5)

where $T_W$, $T_B$ and T represent the Theil index of university innovation efficiency differences within regions, between regions and of overall regions, respectively; $T_P$ denotes the Theil index of innovation efficiency differences within each region; m is the number of regional groups; and $n_p$ is the number of provinces included in each region. $e_i$, $e_p$ and $\overline{e}$ represent the university innovation efficiency of the $i$th province in each region, the average value of university innovation efficiency in each region and the average value of university innovation efficiency nationwide, respectively; the value of T is between [0, 1], and the larger the value of T, the greater the difference in regional university innovation efficiency.

The spatial trends of university innovation efficiency in the context of the digital economy from 2013 to 2020 are shown specifically in Figure 3 and

Table 6. Decomposition of total regional differences in university innovation efficiency.

Year	Overall Difference	Inter-Regional Differences		Intra-Regional Differences		North	Northeast	East	Central	South	Southwest	Northwest
		Value	Ratio (%)	Value	Ratio (%)
2013	0.033447479	0.010095066	30.18%	0.023352413	69.82%	11.19%	1.36%	19.40%	2.39%	9.85%	16.52%	9.11%
2014	0.040274328	0.013105518	32.54%	0.027168811	67.46%	10.68%	2.06%	18.28%	1.53%	11.09%	11.15%	12.67%
2015	0.104329682	0.009000035	8.63%	0.095329647	91.37%	2.17%	0.71%	70.75%	1.48%	2.06%	9.80%	4.40%
2016	0.023242209	0.010668117	45.90%	0.012574092	54.10%	23.17%	1.62%	15.76%	3.88%	1.21%	5.35%	3.10%
2017	0.036197383	0.012242433	33.82%	0.02395495	66.18%	13.46%	0.93%	19.20%	7.66%	0.04%	9.43%	15.47%
2018	0.026528468	0.010675221	40.24%	0.015853247	59.76%	6.75%	2.15%	23.02%	1.18%	5.11%	4.27%	17.27%
2019	0.029572005	0.013726383	46.42%	0.015845622	53.58%	5.63%	3.56%	25.58%	1.11%	1.78%	3.36%	12.55%
2020	0.03026668	0.007390076	24.42%	0.022876604	75.58%	2.80%	0.08%	31.72%	0.25%	9.05%	12.68%	19.00%

.

Figure 3 shows the trend of the Theil index of Chinese university innovation efficiency from 2013 to 2020. It can be observed that the overall and intra-regional differences show an obvious inverted U-shaped trend from 2013 to 2016, followed by minor highs and lows, and the intra-regional differences have slightly increased since 2019. The inter-regional variation is always relatively stable, but has declined more significantly since 2019. Comparing the intra-regional and inter-regional Theil indices, it is clear that the intra-regional Theil index is larger, accounting for about two thirds of the overall Theil index, and the change trend of the intra-regional Theil index is basically the same as that of the overall index, which indicates that intra-regional university innovation efficiency difference is the main component of overall university innovation efficiency difference in China.

From the contribution rate (see Table 6), it can be observed that intra-regional difference always maintained a high contribution rate, except for in 2015, when it rose significantly to 91.37%; the rest of the years fluctuated between 50% and 70%, which indicates that, even within the same region, the innovation development statuses of universities in each province vary greatly, which is also consistent with reality. In the cross-sectional comparison of regions, the contribution rates of Northeast and Central regions were always the smallest compared with East China, North China and South China, which maintained relatively high contribution levels. During the sample period, the contribution rate of East China remained above 15% in all the measured years and reached a peak of 70.75% in 2015. North China and South China also maintained a high contribution rate in general.

5. Conclusions, Limitations and Suggestions for Future Studies

5.1. Conclusions

Based on panel data from China’s 31 provinces from 2013 to 2020, this study used the super-efficiency DEA model, Malmquist index, kernel density estimation and Theil index analysis method to measure the innovation efficiency of universities in each region in the context of the digital economy. It then described the differences between the traditional innovation efficiency of universities and innovation efficiency in the context of the digital economy.

(1) From 2013 to 2020, the overall innovation efficiency of universities in the context of the digital economy showed characteristics of continuous decline and change, the overall level was low, and there was a large efficiency loss. However, the innovation efficiency of universities in the context of the digital economy from 2013 to 2020 was higher than that in the traditional context, which indicates that the growth of the digital economy has had a favorable influence on university innovation.

(2) At the regional level, except for in the northeast region, the fluctuation of innovation efficiency in each university region in the context of the digital economy for 2013–2020 was higher than that in the traditional context, which indicates the importance of the digital economy for universities’ innovation activities. In addition, the provincial concentration of the innovation efficiency of regional universities in the context of the digital economy in China increased from 2013 to 2020 and gradually exerted the advantage of aggregation.

(3) From the mean value of the Malmquist index and each decomposition term, the average annual decline in the Malmquist index of national universities from 2013 to 2020 was 6.5%, and it was concluded that technological progress is a key factor limiting the growth of the Malmquist index. There were significant differences in the sources of Malmquist index growth across the different provinces.

(4) The temporal and spatial evolutions of university innovation efficiency were systematically analyzed by kernel density estimation and the Theil index. The kernel density curve reflected the overall trend of innovation efficiency as a whole, which revealed a general gradual weakening. Further, the analysis of the regional variation of university innovation efficiency by the Theil index revealed that the year 2015 played an important role in the innovation promotion of universities in China; in fact, the year 2015 was an important time point in China for the overall stimulation of societal creativity via the structural reform of mass entrepreneurship and innovation. The support of various policies and funds has greatly enhanced innovation output. However, a lack of follow-up support makes this innovation effect unsustainable.

Based on the above research findings, this paper makes the following suggestions:

(1) To achieve further innovation mode transformation, the potential of the digital economy must be unleashed, and the digital economy must be gradually cultivated into a new growth pole of innovation activity. University innovation activities should be integrated with the digital economy to fully exploit the role of the digital economy in widening the innovation boundary, reducing innovation activity opportunity costs and reducing information asymmetry.

(2) Currently, there is a widespread issue regarding inadequate investment in technological innovation, and the effectiveness of the resources already committed is low. As a result, universities in cities and provinces must expand their investment in technology innovation. In order to achieve improvement in innovation efficiency, universities must also increase the introduction and cultivation of talent; strengthen technical and economic cooperation with a variety of subjects; introduce advanced technologies for digestion and absorption; accelerate the construction of technological innovation infrastructure; and foster the enthusiasm and creativity of scientific and technological talent. This would offer a solid assurance for the efficient growth and development of innovation activities.

(3) With regard to strengthening the continuity of policy support, it can be observed from these research results that there was a rapid growth in innovation efficiency in Chinese universities in 2015, which is strong proof of the benefit resulting from the 2015 promotion of the mass entrepreneurship and innovation reform; however, the continuity of various positive impacts, such as personnel and funds brought by policy promotion, is not strong enough to fully boost the potential of innovation development. In addition, geographical differences should be further taken into account when investing in innovation development, and investments should strive to focus support on Central and Northeast China, where innovation strength is weaker.

5.2. Limitations and Suggestions for Future Studies

This study has limitations. First, the innovation efficiency measurement in this study uses a super-efficient DEA model combined with the Malmquist index, and its measurement results may suffer unfeasible solutions due to the model settings. The global Malmquist index with an SBM (slacks-based measure) directional distance function can be further adopted to measure innovation efficiency in the future and make results more reliable.

Second, the input and output of the innovation activities of universities have a certain lag time, ranging from 1 to 5 years. In this paper, with reference to scholarly research, the lag time between input and output in the stage of knowledge innovation and result transformation was assumed to be 1 year when measuring the efficiency of knowledge innovation and result transformation in universities. In the future, different lags could be set for different types of innovation results.

Finally, there are various factors that affect the innovation efficiency of universities, such as the digital economy, taxation and policies, etc. This paper focused on considering the influential role of the digital economy in the innovation activities of universities, and further econometric models could be built to explore the other factors affecting innovation efficiency so as to provide more comprehensive policy guidance.