Measurement of Higher Education Competitiveness Level and Regional Disparities in China from the Perspective of Sustainable Development

2.2.1 Evaluation Methods for Higher Education Competitiveness

In order to present the current status and competitiveness of higher education in China scientifically and reasonably, the selection of measurement models is crucial. On the one hand, scholars have employed qualitative analysis methods to measure the level of higher education competitiveness (Chang & Liu, 2019; Stoimenova, 2019). Li and Yu (2013) assessed the competitiveness level of universities using the expert rating method. Bileviciute et al. (2019) used Mykolas Romeris University as an example to investigate both the level of higher education competitiveness and modern innovative management methods in universities. Alfaro Bernedo et al. (2021) conducted research showing that the Unified Enterprise Architecture model is a powerful tool for supporting organizational management, which helps improve the functional competitiveness of universities and their overall competitiveness. Yang et al. (2020) analyzed the international sustainable competitiveness of Chinese higher education based on the Diamond Model theory and proposed effective approaches to enhance China’s sustainable competitiveness in the international education service market. However, qualitative analysis methods often rely on the experience and intuition of the analysts, which can be subjective, so the evaluation of the research subject needs to be scientifically assessed from an objective perspective.

Additionally, scholars have conducted quantitative data analysis by constructing evaluation models to explore the development of higher education. Estrada-Real and Cantu-Ortiz (2022) analyzed the competitiveness of higher education institutions using data from the QS World University Rankings. They constructed models using statistical and machine learning algorithms from the library of R Studio software tool to predict the rankings of global universities and forecast the competitiveness level of world universities for the next decade. Moskovkin et al. (2023) identified two indicators: the total number of universities in a country and the average ranking of these universities over a period of time. They normalized and weighted these indicators and used them to analyze the competitiveness level of universities in a country through case studies. Kelly (2016) introduced the Herfindahl index to analyze the competitiveness level of certain disciplines within the UK higher education system. The evaluation indicators mentioned in previous studies may not fully cover multiple factors in the system, neglecting comprehensive indicators and dynamic development. Some scholars have used higher education efficiency as a representation of higher education competitiveness (Sun et al., 2023). For example, using the multi-level frontier analysis, Naderi evaluated the competitiveness of faculties, colleges, and universities by analyzing the efficiency scores of two groups of departments at a university in Iran (Naderi, 2022). Tran et al. calculated the efficiency of 172 higher education institutions in Vietnam during the inclusive period from 2012 to 2016 using the data envelopment analysis method. They examined the competitiveness level of higher education institutions from aspects such as disciplinary distribution, autonomy, and internationalization (Tran et al., 2023). However, higher education efficiency mostly presents the level of competitiveness from the perspectives of input and output, without providing a comprehensive depiction of the development of the higher education system from a sustainable development perspective.

2.2.2 DPSIR Model

The Driving-force–Pressure–State–Impact–Response (DPSIR) framework model is an evaluation model proposed by the European Environment Agency (EEA) in 1993. It organizes relevant indicators based on causal relationships and has been widely used in environmental system assessments, gradually becoming an effective tool for assessing the state of environmental systems and causal relationships regarding environmental issues (Duan et al., 2021). This model evolved from a combination of the Pressure–State–Response (PSR) model and the Driving–State–Response (DSR) model, incorporating their respective advantages (Yousafzai et al., 2022).

The DPSIR model enables a more comprehensive and systematic analysis and evaluation of the continuous feedback mechanisms between indicators. Existing research has predominantly focused on the application of the DPSIR model in environmental assessments (Liu et al., 2022), resource management (Zhao et al., 2023), and other related areas. In the DPSIR model, concerning environmental issues, the driving forces (D) primarily consist of economic and social development, as well as population growth, which exert a series of negative pressures (P) on the ecological environment. These pressures lead to the deterioration of the ecological state (S), resulting in various adverse impacts (I) on human society. In response, corresponding measures (R) are taken to improve the current ecological environment, seeking harmonious development between humans and nature. Despite being an important theoretical framework widely used in environmental governance (Wan et al., 2018; Zhao et al., 2021), there has been limited research applying the DPSIR model to the selection of evaluation indicators for higher education competitiveness. Since the 1930s, scholars have been applying the principles of ecological sustainability from the field of ecology to the domain of education, introducing concepts such as “educational ecology” (Yanli, 2020). In recent years, with the development of higher education in China, many scholars have started examining the current state of higher education from a sustainable development perspective (Wang & Zhou, 2023). However, only a few studies have recognized the DPSIR model as an important guiding framework for exploring sustainable development initiatives (Kelly, 2016), demonstrating the model’s completeness and effectiveness (Zhao et al., 2021). In the field of higher education competitiveness research, the DPSIR model also holds strong applicability. Firstly, the DPSIR model allows for a comprehensive construction of an evaluation indicator system for higher education competitiveness, incorporating the five subsystems of driving forces, pressures, state, impact, and response. This offers a new analytical framework for investigating the competitiveness of Chinese higher education. Second, the higher education system exhibits characteristics of complexity and dynamism. This study introduces the “Driving-force–Pressure–State–Impact–Response” framework, which not only reflects the multi-level nature of the evaluation elements of higher education competitiveness but also captures the cyclical nature of system dynamics.

3.1.1 The Entropy Weight TOPSIS Measurement Method

In this study, the entropy weight TOPSIS method was employed to measure the competitiveness level of higher education in China (Abdel-Basset et al., 2018). This method offers high precision and reliability. It not only effectively avoids the influence of subjective preferences on indicator weights but also overcomes the limitations of principal component analysis, such as susceptibility to outliers (Ren, 2020). The specific steps are as follows:

Step 1: Standardize the indicators using the range method.

In the formula, X i j , Z i j represents the jth original value of the higher education competitiveness indicator for the i province, and represents the standardized value after normalization, respectively.

Step 2: Calculate the information entropy E j for each indicator Z i j in the higher education competitiveness indicator system.

Step 3: Calculate the weights for each indicator.

Step 4: Calculate the weighted index for each indicator of higher education competitiveness level.

Step 5: Calculate the distances D i + and D i − between each measured object and the best object S j + and worst object S j − , respectively.

In the formula, S j + = max ( R i 1 , R i 2 , … , R i m ) , S j − = min ( R i 1 , R i 2 , … , R i m ) .

Step 6: Calculate the relative closeness degree Ci between each measured object and the ideal object.

The relative closeness degree C i , as represented in the formula, ranges between 0 and 1. A higher value of Ci indicates a higher level of competitiveness in higher education for province i . Conversely, a lower value of C i indicates a lower level of competitiveness in higher education for province i .

3.1.2 Kernel Density Estimation

3.1.3 Markov Chain Analysis Method

The Markov chain analysis method is a special stochastic process with discrete time and state. It involves discretizing the data into n types and calculating the corresponding changes and probability distributions over time to approximate the entire process of evolution (Li et al., 2021). The Markov chain method is primarily used to describe the probabilities of transitioning from one state to another for the subject of study. By analyzing the probability transition matrix, the dynamic evolution process of the subject can be studied. In this study, the Markov chain method is employed to analyze the dynamic evolution process of higher education competitiveness. The basic model setup is as follows:

In the formula, the sequence { X t } represents the Markov chain, and X t denotes that the state in period t + 1 is only dependent on the state in period t .

In this study, higher education competitiveness is divided into n state. Through the Markov chain model, the probability p a b is calculated to transition the measured higher education competitiveness level from state a in period t to state b in period t + 1 . The calculation formula is as follows:

In the formula, n i j represents the number of provinces transitioning from state a at time period t to state b at time period t + 1 ; n i represents the total number of provinces in state a at time period t . p a b forms a n × n dimensional Markov chain transition probability matrix, where the elements on the diagonal represent the probability of the higher education competitiveness level remaining stable in the current state. The larger the probability, the less fluid the mobility of higher education competitiveness level. The elements off the diagonal represent the probability of transitioning between different states of higher education competitiveness level. The larger the probability, the less stable the level of higher education competitiveness.

3.1.4 Dagum Gini Coefficient

Compared to the traditional Gini coefficient and Theil index, the Dagum Gini coefficient not only handles the issue of cross-overlapping between sample data but also characterizes regional disparities in Higher Education Competitiveness Level and decomposes the sources of overall regional disparities (Mai et al., 2023). Therefore, this study employs the Dagum Gini coefficient to analyze regional disparities in Higher Education Competitiveness Level and their sources (Zeng et al., 2022). The Dagum Gini coefficient and its decomposition formula are as follows:

First, calculate the overall Gini coefficient for all provinces.

In the formula, j and h represent different regions, i and r represent different provinces, Q represents the total number of provinces, k also represents the total number of provinces, Q j ( Q h ) represents the number of provinces within the region j ( h ) , T j i ( T h r ) represents the higher education competitiveness level of the province i ( r ) within the region j ( h ) , and T ¯ represents the average higher education competitiveness level of all provinces.

Secondly, decompose the Gini coefficient G into within-region disparity G w , between-region disparity G n b , and supervariation density G t using the subgroup decomposition method.

In the formula, G j j represents the Gini coefficient within region j , and G j h represents the Gini coefficient between region j and region h .

In the formula, U j = Q j / Q , V j = Q j T j ¯ / Q T ; D j h represents the mutual influence of Higher Education Competitiveness Level between region j and region h . The calculation formula is as follows:

In the formula, d j h represents the difference in Higher Education Competitiveness Level between region j and region h . F j ( F h ) represents the cumulative distribution function of Higher Education Competitiveness Level in region j ( h ) .

4.2.1 Kernel Density Estimation of China’s Higher Education Competitiveness Level

First, unconditional Kernel density estimation is used to investigate the changing trend of China’s higher education competitiveness level from year t to t + 3; second, the static Kernel density estimation method under spatial conditions is used to reveal the spatial correlation relationship between the higher education competitiveness level of each province and that of its neighboring provinces during the same period; finally, considering the time span on the basis of spatial dynamic Kernel density estimation method, the impact of neighboring provinces’ higher education competitiveness level in year t on the higher education competitiveness level of the province in t + 3 years is analyzed. In the Kernel density estimation under spatial conditions, this article selects the binary adjacency matrix to investigate the spatial correlation between provinces. In the Kernel density graph, the x-axis and y-axis represent the higher education competitiveness level, and the z-axis represents the density of each point in the X–Y plane. In the density contour map, both the x-axis and y-axis represent the higher education competitiveness level, and the density contour lines represent different density values. The closer the contour lines are to the center, the higher the density value, and the more densely packed the contour lines, indicating a larger density change and a steeper corresponding Kernel density graph shape.

4.2.2 Unconditional Kernel Density Estimation of China’s Higher Education Competitiveness Level

In Kernel density graphs and density contour maps, the positive 45° diagonal line is usually used as a marker for changes in the evolution trend of higher education competitiveness level. In unconditional Kernel density estimation, the x-axis represents the higher education competitiveness level of the province in year t, the y-axis represents the higher education competitiveness level of the province in t + 3 years, and the z-axis represents the probability density. If the probability mass tends to be near the positive 45° diagonal line, it indicates that the trend of higher education competitiveness level from t to t + 3 years is relatively stable; if the probability mass tends to be near the negative 45° diagonal line, it indicates a significant change in the higher education competitiveness level from t to t + 3 years; if the probability mass concentrates near a specific scale on the y-axis and parallel to the x-axis, it indicates a converging trend of higher education competitiveness level. According to Figure 3, the unconditional Kernel density estimation probability of the competitiveness level of higher education in China is mainly distributed around the positive 45° diagonal line. This suggests that without considering spatial conditions, the competitiveness level of higher education in each province of China demonstrates strong continuity.

Figure 3

Unconditional Kernel density graph and density contour lines of China’s higher education competitiveness level. (a) Unconditional Kernel density, (b) unconditional Kernel density contour lines.

In addition, there are four peaks in the probability mass, which are distributed near the x-axis at 0.2, 0.5, 0.7, and 0.9. The peak near 0.9 is slightly lower than the 45° diagonal line, indicating that under unconditional assumptions, provinces with a higher education competitiveness level above 0.9 tend to experience a decline in the growth rate of higher education competitiveness level after 3 years.

4.2.3 Spatial Static Kernel Density Estimation of China’s Higher Education Competitiveness Level

Figure 4 reports the results of Kernel density estimation under spatial static conditions, that is, the evolution of the higher education competitiveness level of a province considering the impact of neighboring provinces’ Higher Education Competitiveness Level. In Figure 4, the X-axis represents the higher education competitiveness level of neighboring provinces in year t, the Y-axis represents the higher education competitiveness level of the province in year t, and the Z-axis represents the probability density of Y under X condition. If China’s higher education competitiveness level shows a provincial convergence trend, and there is a positive spatial correlation between neighboring provinces’ Higher Education Competitiveness Level, that is, high-level provinces cluster with high-level provinces, and low-level provinces cluster with low-level provinces, then the probability mass will tend to be near the positive 45° diagonal line.

Figure 4

Kernel density map and contour lines of China’s higher education competitiveness level under spatial static conditions; (a) spatial static Kernel density, (b) spatial static Kernel density contour lines.

According to Figure 4, the evolution trend of China’s higher education competitiveness level under spatial static conditions exhibits a “discontinuity” phenomenon. Specifically, with 0.6 as the dividing line for the higher education competitiveness level of neighboring provinces, the evolution trends are quite different. When the higher education competitiveness level of neighboring provinces on the X-axis is below 0.1, the probability body is parallel to the X-axis, indicating that being adjacent to provinces with a level below 0.1 does not significantly improve the higher education competitiveness level of the province. When the higher education competitiveness level of neighboring provinces on the X-axis is between 0.1 and 0.6, the probability body tends to be close to the positive 45° diagonal line, indicating that the spatial positive correlation is more significant at this time. The flow of educational resources, technology, and human capital between neighboring provinces contributes to the coordinated development and mutual improvement of Higher Education Competitiveness Level across provinces. When the higher education competitiveness level of neighboring provinces is above 0.6, the probability body significantly deviates downward, concentrating at 0–0.2 on the Y-axis, indicating that being adjacent to high-level provinces does not significantly affect the improvement of the higher education competitiveness level of the province. When there is a significant gap between the Higher Education Competitiveness Level of neighboring provinces and the province, the flow of elements related to higher education tends to be more concentrated in the more developed provinces, causing a siphoning effect in neighboring provinces.

4.2.4 Kernel Density Estimation of China’s Higher Education Competitiveness Level under Spatial Dynamic Conditions

Figure 5 reports the Kernel density estimation results under spatial dynamic conditions, which consider both spatial factors and the time span, further examining the dynamic changes in the future development level of higher education competitiveness in a province due to its neighboring provinces in the current period. In Figure 5, the X-axis represents the higher education competitiveness level of neighboring provinces in year t, and the Y-axis represents the higher education competitiveness level of the province in year t + 3. Compared with spatial static conditions, the overall probability body distribution under spatial dynamic conditions is similar but with some differences, indicating that the time factor can affect the interaction between provinces in the development of China’s higher education competitiveness. Similar to Figure 4, Figure 5 also uses 0.6 as the dividing line for the higher education competitiveness level of neighboring provinces. When the higher education competitiveness level of neighboring provinces in year t is between 0 and 0.6, the probability body tends to be close to the positive 45° diagonal line, indicating that the higher education competitiveness level between provinces shows a spatial positive correlation. Compared to Figure 4, the probability body distribution in the Y-axis direction in Figure 5 presents a more dispersed trend, indicating that the spatial correlation of Higher Education Competitiveness Level between provinces is weakened under the condition of time lag. When the higher education competitiveness level of neighboring provinces on the X-axis is above 0.6, the 3-year lag period does not show significant differences. Overall, for neighboring provinces with higher Higher Education Competitiveness Level, the time condition has not played a significant role in promoting the upward transfer of the province’s higher education competitiveness level. However, for neighboring provinces with low and medium Higher Education Competitiveness Level, extending the time span can significantly reduce the spatial correlation effect between provinces.

Figure 5

Kernel density map and contour lines of China’s higher education competitiveness level under spatial dynamic conditions: (a) Spatial dynamic Kernel density, (b) contour lines of spatial dynamic Kernel density.

4.2.5 The Markov Chain Analysis method of China’s Higher Education Competitiveness Level

This study uses the Markov chain analysis method to explore the direction and transition probability of Higher Education Competitiveness Level in different regions and further explain the dynamic evolution trend of China’s higher education competitiveness level based on the Kernel density estimation analysis. This article divides China’s provinces’ Higher Education Competitiveness Level (HECL) into four levels using the equal division method: low level (0 < HECL ≤ 25%), medium-low level (25% < HECL ≤ 50%), medium-high level (50% < HECL ≤ 75%)), and high level (75% < HECL). The Markov transition probability matrix of China’s higher education competitiveness level state transition for 2008–2020 is then calculated with a time lag of 1 year, 2 years, 3 years, and 4 years, as shown in Table 2.

Table 2 shows that regardless of the time span, the probability values on the diagonal are higher than the probability values in other positions. Except for the medium-low level at t = t + 4, the other diagonal probability values are greater than 0.5, indicating that when not considering the impact of spatial factors, the trend of Higher Education Competitiveness Level in various provinces of China is relatively stable, with low mobility but strong persistence. It is difficult for provinces at different levels to achieve level transitions. This result is consistent with the unconditional Kernel density estimation result. As the time span increases, the probability values on the diagonal decrease, and the convergence trend of Higher Education Competitiveness Level in various provinces weakens with the delay of time, and the stability gradually decreases. Second, the state transition of Higher Education Competitiveness Level in provinces usually occurs at adjacent level intervals. Under different time spans, the transition probabilities of each level are almost zero, indicating that the transition speed of Higher Education Competitiveness Level in various provinces is slow. As the time span increases, the probability of low-level to medium-high level transitions increases year by year, suggesting that provinces with lower Higher Education Competitiveness Level may achieve faster development in a certain period in the future, while other provinces may have difficulty achieving leapfrog development.

Table 3 presents the Markov transition probability matrix considering spatial lag terms. As shown in Table 3, regardless of the time span, the probability values on the diagonal are greater than those in other positions, indicating that when considering both time and space factors, the mobility trend of Higher Education Competitiveness Level in adjacent provinces is significantly enhanced.

When the higher education competitiveness of adjacent provinces is at medium-low and medium-high levels, the probability values on the diagonal are lower than those when the higher education competitiveness of adjacent provinces is at low and high levels. When the higher education competitiveness of adjacent provinces is at a medium level, the Higher Education Competitiveness Level of various provinces begin to show a significant positive spatial correlation, which is consistent with the conclusions drawn from the Kernel density estimation analysis under the spatial conditions mentioned earlier. Secondly, under various time spans, the probability values not directly adjacent to the diagonal values are also mostly zero or close to zero, indicating that as the time span extends, it becomes challenging for provinces to achieve leapfrog development in higher education competitiveness, regardless of the level of higher education competitiveness of adjacent provinces.

The traditional Markov chain analysis shows that the development trend of higher education in each province of China is relatively stable. With the extension of time span, the stability of each province’s higher education competitiveness level is gradually weakened. Spatial Markov chain analysis shows that after considering the spatial factor, the level of higher education competitiveness of each province remains unchanged. Whether considering the spatial factor or not, the level of higher education competitiveness of each province is difficult to achieve a leap forward improvement.