The construction and development of economic education model in universities based on the spatial Durbin model

3.1 An economic education model according to the SDM

The study used geographical econometrics models to empirically assess the spatial effects of master’s degree programs on technological development. The SDM, among others, takes into account spatial autocorrelation and may handle missing data. In addition, the SDM quantifies cross-regional spillover effects. A variation of the recognized specification known as the SDM in the econometric of spatial research is shown in Eq. (1).

where z represents the technical advancement X indicates the explanatory factors. β output elasticity of the explanatory factors W = ∑ j = 1 n w ij is spatial of the weight matrix (n × n) often used in spatial economics to represent spatial interactions observing between WC θ reflects the influence of explanatory factors from other regions; ρ is the autocorrelation in related to spatial; and ε is the phrase for unexpected error.

Designing a weight matrix of spatial is an essential step in spatial economic research. Matrix-based geographic characteristics are often used in spatial metrics research. Economic as well as regional factors have an impact on innovation in technology as a systematic activity from inputs to output. As a result, this research created spatial matrices of weights based on the topographical and economic features of the province.

Three spatial weight matrices are specified in the research. The first definition of W1 is as follows:

The adjacent matrix is depicted as U 1 . U 1 represents the neighbouring matrix. W ij = 0 indicates that province j is not geographically within to state i, whereas W ij = 1 indicates the opposite.

Based on economic factors, the U 2 spatial load medium was created. This definition of the economic matrix (EM) U 2 is as follows:

where m i denotes the province as the sample period average GDP per person. Conventionally, elements W ij on the primary diagonal is zero, whereas those W ij utilize a decreasing function of economic distance.

The weighing matrix is normalized and it equals the combined value of each item in the first row to equalize the impact of the outside world on each region.

The third spatial weight matrix, U 3 , was created using geographic and economic factors. The definition of the geographical EM U 3 is as follows:

where v ij is the distance between regional capitals on a geographical basis. The convention designates that the essentials W ij primarily reside on the main diagonal with a value of zero, signifying a reference to the same entity or location. Meanwhile, the off-diagonal components W ij depict a gradual decrease in value as the geographical and economic distances between the entities that they represent to increase. These W ij components are determined based on a diminishing relationship that takes into account for both geographical and economic factors.

3.2 Spatial autocorrelation analysis

3.2.1 Spatial autocorrelation index (SAI)

We should check for spatial autocorrelation, or resemblance in the immediate region, to see if a spatial panel’s model may be used to study innovations in technology. Figure 1 depicts the spatial autocorrelation flowchart. The principal test for identifying spatial autocorrelation is the SAI, which is calculated as follows:

(5) I = ∑ i = 1 n ∑ i = 1 n W ij ( c i − c ̅ ) D 2 ∑ i = 1 n ∑ j = 1 n W ij ,

where D 2 = ∑ i = 1 n ( c i − c ̅ ) 2 n is the difference, W ij is the weight matrix of the spatial, c i is provincial observational value, and c ̅ is the mean.

(6) c ̅ = 1 n ∑ i = 1 n c j ; n = 31 .

Figure 1

Flowchart of spatial autocorrelation.

3.2.3 Spatial distribution of postgraduates

The SAI of postgraduates is shown in Table 2. SAI statistics in the adjacent matrix are favorable. Matrix-based statistics are U 2 and U 3 and are favorable and noteworthy at the rate of 1% each year. Compared to matrix W 1 , the SA index statistics in matrices U 2 and U 3 are greater and highly significant. This research takes postgraduates’ information from 2017 as an instance and computes local autocorrelation to expand on the province distribution of postgraduates. The SAI scatter diagram, which is split into four quadrants, is used to examine spatial preferences of postgraduates. The initial quadrant indicates a higher value region accompanied by other performance-valued regions; the next diagram displays a lower value territory accompanied by a higher value region; the third map displays lower value regions accompanied by other lower value regions; and a higher value region is shown in the fourth. Figure 2 displays the geographic of postgraduates.

Table 2

Moran’s I Postgraduate Index from 2015 to 2022

Matrix	2015	2016	2017	2018	2019	2020	2021	2022
U 1	0.237	184	0.182	0.16	0.184	0.172	0.165	0.172
U 2	0.352	0.424	0.441	0.427	0.423	0.435	0.443	0.441
U 3	0.324	0.482	0.414	0.482	0.125	0.525	0.515	0.511

Figure 2

Chinese province postgraduate education local Moran distribution.

Hypothesis 1

Technological innovation in an area is positively correlated with postgraduate education.

Hypothesis 2

The impact of graduate study on technical innovation is multiplied.

4.1 Spatial Durbin model’s result

The economic, neighboring, and socioeconomic-geographical matrix structures are used in SDM 1, 2, and 3. In addition, these models exhibit strong goodness of fit, as seen by expected coefficients for sigma 2 and R, and substantially positive spatial autocorrelation coefficients ( b < 0.01 ) in every model. Indicating that a change in a particular area linked to any given explanatory variable has an impact on the province itself and may have an indirect impact on neighboring provinces, spatial autocorrelation coefficients differ significantly from zero. Tables 3–5 list the three different types of matrices that are used to examine direct, indirect, and total impacts. The term “direct effect” describes how explanatory factors affect a province’s innovation. The term “indirect effect,” also known as “spatial spillover effect,” describes how excellence factors affect the technological innovation of other regions.

Let’s discuss the direct effect. Postgraduate students’ coefficients were considered positive in each model ( b < 0.05 ) , proving that technical innovation was favorably encouraged by Chinese postgraduate education and so validating Hypothesis 1. Population efficiency was positive, and trade efficiency was significantly positive, showing that global commerce encouraged technological progress. The significant negative coefficients for UR showed that the high rate of unemployment did not promote technological innovation. Independent power producer (IPP) had positive and significant coefficients at the 1% level. IPPs encouraged technical innovation. Figure 3 and Table 3 depict the direct effects of the SDM model.

Figure 3

Direct effects of SDM.

The variable “Postgraduate” has a positive correlation of 0.5613, showing that better economic growth (technology innovation) is correlated with an increase in the distribution of postgraduates. This shows that PG education significantly and favorably affects economic development in the areas examined. A positive correlation of 0.3419 for the variable “Population” indicates that areas with more people likely to have more rapid economic growth. The positive coefficient of 0.2014 for the variable “Trade” indicates that areas with greater trade operations have better levels of economic development. Higher urbanization rates are linked to more economic growth, as shown by the variable “Urbanization Rate” with a positive correlation of 1.0202. A positive correlation of 0.1147 for the variable “IPP” indicates that areas with greater industrial output levels also often have better economic growth. In the framework of the geographical model, coefficients indicate the corresponding factors’ direct influence on economic growth. The particular dataset, model parameters, and analytic controls may also have an impact on the relevance and interpretation of these coefficients. Now let’s examine direct and indirect effects. The postgraduate education coefficients in models 2 and 3 were significantly positive ( b < 0.01 ) and thus supporting Hypothesis 2. Substantially enhancing postgraduate education encouraged innovation in neighboring provinces with comparable economic features, demonstrating geographical spillover effects. The indirect result of the PG study was much greater than the direct effect, according to matrices U 2 and U 3 . Figure 4 and Table 4 show the indirect effects of the SDM model. These findings show that postgraduate migration diminishes the postgraduate education’s ability to stimulate local innovation while increasing the spillover impact.

Figure 4

Comparison of indirect effects.

Education at the “Postgraduate” level has an indirect impact of 0.2933. This translates to the idea that the presence of postgraduates in one location has a good impact on the economic development of other regions, which in turn encourages technical innovation there. The indirect impact of “Population” is 0.5422. This shows that locations with higher populations have a beneficial spillover impact on the economic growth of nearby regions, encouraging innovation in such areas. The indirect impact of “Trade” is 0.3371. It suggests that via knowledge transfer and economic relationships, trade activities in one location may have a favorable influence on the economic improvement of nearby regions. The indirect impact of “Urbanization Rate” is 1.64364. This suggests that greater rates of urbanization in one location have large positive spillover effects on the economic development of neighboring places, most likely as a result of the concentration of economic resources and activity in urban areas. The indirect impact of “IPP” is 0.1721. This shows that places with greater industrial output levels might have a little beneficial impact on the economic expansion of nearby section. In the total effect, postgraduate education coefficients ranged from 0.85 to 1.08 and were significantly positive ( b < 0.01 ) . Postgraduate education efficiency ratios were greater than IPP and those for trade, reflecting the significance of master’s degree education for innovative activities. Figure 5 and Table 5 denote the total effects of SDM.

Figure 5

Total effects of SDM.

Results from the use of neighboring, economic, and EGMs are reported by Models 1, 2, and 3 in Table 6. The short-run indirect and direct effects of postgraduate education were constructive in all models. Long-run effects were constructive but not significant, whereas short-run overall effects were significantly favorable. Long-run effects have greater coefficients than short-run effects. According to the findings in Tables 3–5, the indirect effects of postgraduate education were greater than their direct effects. The results demonstrated that China’s technological innovation activities could be explained by the spatial panel model and that there was an important positive spatial autocorrelation for technological innovation. In addition, there was nonequilibrium and geographic autocorrelation in the distribution of postgraduates. In addition, the postgraduate study contributed favorably to the advancement of technological innovation. Better than that commerce and postgraduate education has a geographical spillover effect on technical improvement. Postgraduate education has the potential to not only encourage technical innovation in the province that serves as its focal point but also to spread to other provinces. The spatial spillover effect of postgraduate education was greater than its direct effect in economic and geographical economic matrices. The dynamic panel of SDM is represented in Figure 6 and Table 6.

Figure 6

Comparison of dynamic SDM panel.

The current work employs the SDM with individual permanent effects as its reference model. The fundamental benefit of the dynamic panel of this model is that it can be used to observe the potential for both short- and long-term endogenous and exogenous interaction effects in education.