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

: This research presents the spatial Durbin method, which may be used to analyze the relationship between economic educational attainment and economic development in China. The method accounts for regional dependence and variety when calculating the impact of economic education on a province economic development. A pedagogical economic strategy has also taken into account how varied the education model is while implementing it. The study ’ s conclusions, which were based on data from Chinese provinces, showed that China ’ s distribution of postgraduates (PGs) was geographically autocorrelated and unstable. This work contributes to existing in two ways. It quanti ﬁ es the in ﬂ uence of postgraduate education on technical innovation in a big, quickly rising economy. The research assesses direct and indirect impacts to comprehend postgraduate education. Overall, PG education has a big impact on technological innovation. Three geographical weighting matrices were utilized in the research study to assess spatial over ﬂ ow, and it was shown that PG education in nearby provinces greatly boosted innovation. The spatial over ﬂ ow e ﬀ ect of the economic matrix (EM) was stronger than that of the matrix adjacent to it. In both the EM and the economic-geo-graphical matrix, the spatial over ﬂ ow impact of postse-condary education was bigger than its direct in ﬂ uence. This research contributes to an improved considerate of the characteristics and goals of PG training in a rapidly changing market.


Introduction
Economic progress is significantly influenced by education.Research that demonstrates how education and educational expenses impact growth is essential in economic theory.There is a ton of information on this topic [1] accessible.It encounters tremendous challenges and is often acknowledged as among the key phases of development.Thus, the relationship between high-quality education and economic prosperity is always crucial.Most individuals agree that education is important for both long-term sustainability and economic prosperity [2].The causation that we recognize runs from economic development to education.A boost in education might sometimes have a favorable impact on gross domestic product (GDP) growth and sometimes a negative one.Nonlinearities become more significant in the examination of the link between economic growth and education since the effects of education might vary at various periods of the economic cycle.In particular, we postulate that a nation's economic development performance varies according to the development of its human capital and, therefore, on its level of educational success [3].The desire for investment in education has grown since the human element has become one of the most significant productive variables influencing economic development.It is now widely acknowledged that learning spending has a significant role in attaining overall economic and social growth [4].Pedagogical design is the intentional, planned influence of management on specific employees and students to organize their actions, as well as the logical and efficient use of educational organization equipment for the aim of human growth.The purpose of design is to have a focused effect on the establishment of relationships between all participants in the process of learning as objects and managerial subjects [5].Although the relationship between education and growth is frequently studied, many new researches focus on higher levels of education and make an effort to determine how it affects economic development.This is due to the fact that superior education is one of the main forces behind economic development and competitiveness across all nations [6,7].Postgraduates are highly educated workers who have attended professional training and benefit from having quick thinking and a combative mentality.Postgraduate education contributes significantly to technical advancement, knowledge transmission, and creativity [8].Higher education institutions are often seen as economic actors, and their economic activity is examined.Universities may work to promote the social and economic advancement of the communities in which they are located, and as a consequence, they may have a positive impact on economic development [9,10].Most of the static panel data are used to determine the historical influence of infrastructure for transportation on economic development.Its inclusion of the spatial component is one of the article's key qualities.When examining the connection between economic educational attainment and economic growth, the spatial Durbin method (SDM) takes into the importance of geographical closeness and interconnectedness across Chinese provinces.The discoveries are given greater depth and refinement due to the spatial viewpoint, which also gives us a more complete grasp of the processes at work.Recognizing the significance of acknowledging the variations in provincial economic structures and educational initiatives within a specific region holds a substantial value.The research may draw more precise and contextually relevant findings on how economic education affects economic growth in various regions of China by taking these variables into account using the SDM.The inquiry may provide insightful information on how higher education, especially post-graduate (PG) degrees, supports innovation and regional economic development by concentrating on this particular level of education.Highlighting the need of taking into account both direct and indirect effects on nearby regions.The goal of the research is to determine how the distribution of PGs impacts technical advancement and regional economic development.The study aims to decipher the complicated regional patterns of the influence of economic education on economic development by taking into account spatial dependency and heterogeneity.This study also aims to investigate the relationship between graduate study and technical advancement in the Chinese regions.While analyzing the effects of economic educational attainment on economic development, it is necessary to evaluate the geographical interdependence and heterogeneity across areas, to determine and quantify the geographical spillover impacts of PG education on the innovation and economic development of surrounding provinces, and to advance knowledge of the traits and objectives of PG education in the context of China's economy's fast economic transformation.
This study provides to the contribution in two ways: • It provides fresh insight into the variables affecting innovation in a large and quickly expanding economy by measuring the effect of postgraduate education on technical innovation.• In order to better understand the features and purposes of postgraduate education, the study calculates both direct and indirect effects.

Related works
Xiao and Mao [11] used three geographical weight matrices to quantify spatial spillover and found that advanced degrees greatly boosted innovation in neighboring regions.More so than the neighboring matrix, the economic one saw a spatial spillover effect.The regional spillover impact of graduate education was larger in economic and economic-geographical matrices (EGMs) than the direct effect.It may help readers get a more nuanced grasp of the qualities and uses of higher education in a dynamic economy.
Horváth and Berbegal-Mirabent [12] analyzed how factors like the amount of institutions and the share of public universities in a region affect the rate of new knowledgeintensive business service (KIBS) company development in that area.Results from a spatial econometric panel analysis conducted on a sample of 47 Spanish regions (provinces) between 2009 and 2013 provide credence to the claim that areas with a higher concentration of universities and a larger percentage of public institutions are more likely to see the establishment of new KIBS businesses.Xie et al. [13] established a temporal fixed effects SDDM to empirically investigate the features of green finance development and its affecting elements.Spillover effects primarily link the degree of financial development to the degree of green finance development, with the optimization of industrial structure also being correlated.Finally, recommendations and remedies are given to increase the growth of green finance in the Yangtze River Delta.Wang and Wang [14] explained why the SDM was used to examine the regional impacts of green financing and energy expansion on robust economic growth.Concurrently, we use the mediation effect model to examine whether progress in green financing has an impact on high-quality economic growth.It may serve as a policy foundation for achieving high-quality development in the region, which is very relevant for achieving sustainable development objectives in the area.The study by Liu et al. [15] used the SDM to examine the direct and spillover impacts of tourist development on economic growth from the perspectives of domestic and inbound tourism.The findings are contrasted with those of the traditional, static SDM.The findings lend credence to the idea that increased tourism in China has contributed to the country's booming economy.The two types of tourismthose that originate at home and those that originate elsewherecontribute significantly to the economic development.The study by Li and Wu [16] indicated that there is a favorable geographical association between the innovation quality of China's various regions.Subsidies can boost regional innovation quality by increasing input from local direct innovation subjects, luring innovation resources from neighboring areas, and bolstering innovation support from local indirect innovation subjects; they also shed light on how the government can implement R&D funding to advance regional innovation quality.Zhang et al. [17] created a geographic SDM using the panel data of 31 provinces in China; we examined the spatial correlation of economic development under various spatial weights and assessed the impacts of government healthcare spending on economic growth.Compared to the 0-1 spatial weight and the geographical distance spatial weight, the economic remoteness spatial weight has a far larger impact on economic development.Government healthcare spending has both aggregate and direct beneficial impacts that are substantial.Cao et al. [18] applied the SDM to investigate the impact of financial development and technological innovation on green growth (GG) in China.The study finds that the development scale of financial institutions (lnFDS) in the local province has a significantly negative effect on local GG, but has a significantly positive effect on GG in the surrounding provinces.The geographical impact, transmission mechanism, and regional variability of new-type urbanization on air pollution are also discussed in the study by Zhao and Wang [19], which presents the SDM and the spatial mediating model.It becomes shown that high agglomeration and low agglomeration dominate the geographical structure of air pollution in China, with some spatial oscillations occurring.Zhu et al. [20] using spatial Durbin models demonstrated that the growth of the digital economy has a significant positive impact on increasing urban resilience; the promotional effect of the digital economy on urban resilience varies greatly across different regions; the promotional effect of the digital economy on urban resilience exhibits a typical double-threshold characteristic as a result of the different stages of digital financial inclusion and the growth of the digital economy.

Proposed method
In this section, we detail the construction of an economic education model based on the spatial Durbin mode.

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 is spatial of the weight matrix (n × n) often used in spatial economics to represent spatial interactions observing between WCθ reflects the influence of expla- natory 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 construction and development of an economic education model  3 The adjacent matrix is depicted as U 1 .U 1 represents the neighbouring matrix.= W 0 ij indicates that province j is not geographically within to state i, whereas = W 1 ij 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 geo- graphical 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.

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: where is the difference, W ij is the weight matrix of the spatial, c i is provincial observational value, and c ̅ is the mean.

Testing for technological innovation using spatial autocorrelation
The outcomes of the SAI for creation from 2015 to 2022 are depicted in Table 1.For all years in the neighboring matrix U 1 , SAI statistics are accurate and pass the significant test.
Data are significant at the 1 percentage level every year, and SA index statistics in matrices U 2 and U 3 vary between 0.354 and 0.637.Overall results show that creativity in one field has an impact on development in another.As a result, a spatial econometric model may be used to assess the geographical autocorrelation in China's technological improvement.

Spatial distribution of postgraduates
The SAI of postgraduates is shown in Table 2. SAI statistics in the adjacent matrix are favorable.Matrix-based statistics areU 2 andU 3 and are favorable and noteworthy at the rate of 1% each year.Compared to matrixW 1 , the SA index statistics in matrices U 2 andU 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 performancevalued 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.The construction and development of an economic education model  5 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 Results and discussion

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 auto- correlation 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.
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 matricesU 2 andU 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.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.
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   The construction and development of an economic education model  7 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.
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.

Conclusions
The influence of higher education on technical innovation was the main topic of this research.The research utilizes spatial econometric techniques to quantify the direct, spillover, and overall effects of postgraduate education because geographical characteristics have an impact on technological innovation.The study uses spatial weight matrices to analyze the impact of complex spatial connections on research findings.These matrices take into account proximity, economic features, and economic-geographical aspects.The geographical autocorrelation in SAI innovation statistics indicated that there may be technological diffusion among the provinces.Spatial autocorrelation and nonequilibrium were evident in postgraduates' SAI statistics.The SDM was used to study how higher study affects innovation, which is the major focus of this research.Our estimate findings indicated both a favorable direct effect and an indirect effect, indicating spillover from neighboring provinces.The geographical spillover effect was more pronounced in the EM than in the neighboring matrices.The spatial spillover effect of postgraduate education was greater than its direct effect in economic and geographical economic matrices.In summary, using the SDM in this study, examining the connection between educational success and economic growth enables a more thorough understanding of the intricate geographical dynamics at work.Direct and indirect impacts, geographical spillovers, and dynamical panels are identified, which aids in the making of well-informed policy choices targeted at advancing both educational attainment and economic growth across various areas.
The analysis takes into account how economic educational attainment affects economic growth, paying particular attention to PG education.While this method offers insightful information, it could fall short of capturing the nuanced and complicated nature of education's role in economic development.Although their impacts may not be completely taken into account in this model, other educational levels, such as elementary, secondary, and university education, might potentially play significant roles in determining economic growth.There are presumptions and restrictions with the SDM.It is important to thoroughly check assumptions like linearity and homoscedasticity since any possible breaches might affect how reliable the findings are.Even though the panel SDM offers insightful geographical information on the relationship between economic educational attainment and economic improvement in China, it is compulsory to consider the limits of the methodology.Future studies might address these flaws and make use of complementary approaches to provide a more thorough knowledge of the dynamics and complexity of this connection in the setting of a market that is changing quickly.
Funding information: This work was supported by Guizhou provincial modification project of teaching content and

Figure 2 :
Figure 2: Chinese province postgraduate education local Moran distribution.
The 31 Chinese provinces' sample data from 2004 to 2018 were utilized in this research.The following justifications support the use of Chinese province statistics.First, China has made incredible technological advancements over the last 20 years.From being one of the world's poorest nations to taking the lead among nations just beginning to industrialize,

Table 1 :
Moran's I of technical innovation from 2015 to 2022

Table 2 :
Moran's I Postgraduate Index from 2015 to 2022

Table 3 :
Direct effects of SDM

Table 4 :
Numerical outcomes of indirect effects

Table 6 :
The findings of dynamic SDM panel

Table 5 :
Total effects of SDM