This paper selects the data of 30 provinces in China from 2012 to 2021 (based on data availability, except Xizang) as sample observations. The data mainly comes from the “China Rural Statistical Yearbook”, “China Statistical Yearbook”, “China Social Statistical Yearbook”, “China Education Statistical Yearbook”, national data, and EPS database. The missing data is supplemented with Excel and linear interpolation method.

By referring to a large number of literatures and combining the principles of data availability and scientificity, this paper uses the data of 30 provinces in China (except Xizang) from 2012 to 2021 to build an evaluation system for indicators of poverty alleviation through education and rural revitalization, and the attribute of each indicator and the weight value of each secondary indicator determined by the entropy weight method are shown in Table 1.

The core explanatory variables are education poverty alleviation (Epa) and rural revitalization (Rr). To reduce the impact of subjective factors, education poverty alleviation and rural revitalization were calculated using the entropy weight method, as detailed in Table 1.

The controlling variables in the education poverty alleviation equation include education input (Lfee), education level (Edl), urbanization level (Ur), and local economic development level (LnPgdp). Among them, education poverty alleviation is expressed by the proportion of local financial education expenditure and local financial general budget expenditure; the average number of years of education = (population aged 6 and above who have not attended school * 1 + primary school population aged 6 and above * junior high school population aged 6

and above * population of junior high school aged 6 and above * population of 9 + high school population aged 6 and over 6 years old * population of high school aged 6 and above * population of 12 + population aged 6 and above of college and above * 16)/total population sampled; The level of urbanization is expressed by the ratio of the number of permanent urban residents at the end of the year to the total permanent population of the region. The level of local economic development is expressed logarithmicly by per capita GDP. Pennia [1] showed that education investment has achieved remarkable results in education poverty alleviation, and Yan Zhonglian [2] concluded through empirical research that education level and local economic development level promote the process of education poverty alleviation, and urbanization level inhibits education poverty alleviation development.

The controlling variables in the rural revitalization equation include wage level (LnWl), human capital (Hc), cultural construction (Pclh), and the total fixed asset investment of rural households (LnGd). The wage level is a logarithmic treatment of the average wages of employees in private units in agriculture, forestry, animal husbandry and fishery towns; Human capital is the ratio of the number of self-employed people in rural areas to the number of rural population; The per capita possession of public library collections is expressed by the per capita public library holdings of the region; The total fixed asset investment of rural farmers is expressed by the logarithmic total fixed asset investment of rural farmers in the region. Qu Yanchun et al. [10] believe that the rural revitalization strategy should further promote the structural reform of agricultural supply side and increase farmers’ wage income. Zhao Dandan et al. [11] based on dynamic panel data of 31 provinces in China prove that human capital has a promoting effect on rural revitalization. Rural style civilization occupies a core position in the rural revitalization strategy, cultural construction is an important measure to improve spiritual civilization, rural farmers’ fixed asset investment is of great significance to rural economic development, therefore, it is of great significance to study the effect of per capita library collection and rural farmers’ fixed asset investment on rural revitalization. The clear definition and calculation method of variables are shown in Table 2, and the descriptive statistics of variables are shown in Table 3. It can be seen from Table 3 that the mean value of rural revitalization is 0.28304, the standard deviation is 0.08216, the maximum value is 0.53631, the minimum value is 0.12879, and there is a certain distance between the maximum value and the minimum value, indicating that there are regional differences in rural revitalization in various provinces in China. The mean value of education poverty alleviation was 0.23888, the standard deviation was 0.06542, the maximum value was 0.44659, and the minimum value was 0.10192.

To avoid false regression or correlation, and to make the research results more effective and reliable, panel data stationarity tests were conducted on all variables in the article. According to the method of unit root test for panel data given by Chen Qiang [12] , this article uses four methods, LLC, IPS, ADF-Fisher, and Breitung, to conduct panel unit root tests. The test results are shown in Table 4, and it is believed that the variables in this article are stationary, which can further establish a spatial panel simultaneous equation model for analysis.

Note: ***, **, and * respectively indicate significance at the 1%, 5%, and 10% significance levels, the same below.

The purpose of this study is to explore the interactive effect between education poverty alleviation and rural revitalization. In order to make the research results more robust and reliable, three different spatial weight matrices are constructed to achieve the research purpose. The first type is the adjacency space weight matrix (W₁). Based on the adjacency concept of spatial weight matrix, this article selects the queen adjacency weight matrix. If two adjacent provinces i and j have a common edge or vertex, it is adjacency, with a value of 1, otherwise it is 0. The second type is the geographic distance spatial weight matrix (W₂). Using the reciprocal form of distance W 2 = 1 / d i j , d i j is calculated from the longitude and latitude of provinces i and j. The third type is the Economic Geographic Distance Weight Matrix (W₃). The reciprocal of the absolute value of the difference between the GDP of two provinces in 2019 during the sample period and the product of the geographical distance spatial weight matrix W₂ are used.

Using the adjacency space weight matrix, the education poverty alleviation and rural revitalization in 30 provinces of China from 2012 to 2021 were calculated using Moran index statistics, as shown in Table 5. The results show that the global Moran index of rural revitalization (Rr) is greater than 0, and all of them pass the spatial correlation test at a significance level of at least 5%, indicating

that there is a significant positive spatial correlation in rural revitalization; Except for the global Moran index of education poverty alleviation (Epa) in 2021, which is equal to 0 and there is no spatial autocorrelation, the global Moran index of all other years is greater than 0, basically passing the 10% significance level test, indicating that there is also a positive spatial autocorrelation in education poverty alleviation.

Introducing spatial effects into the simultaneous equation system, while considering the interactive impact between education poverty alleviation and rural revitalization, a spatial panel simultaneous equation model is established to model the interactive effect, spatial spillover effect, and mechanism between the two. The expression is as follows:

{ E p a i t = α 0 + α 1 W i j E p a i t + α 2 R r i t + α 3 W i j R r i t + ∑ k = 1 k 1 α k A k , i t + ε i t               ( 1 ) R r i t = β 0 + β 1 W i j R r i t + β 2 E p a i t + β 3 W i j E p a i t + ∑ k = 1 k 2 β k B k , i t + τ i t             ( 2 )

Equation (1) is the education poverty alleviation equation, Equation (2) is the rural revitalization equation, where i and t represent the region and year, E p a i t represents the education poverty alleviation in the t-th year of region i, R r i t represents the rural revitalization in the t-th year of region i, and e and t are random perturbation terms. A k , i t is the control variable group that affects education poverty alleviation, and B k , i t is the control variable group that affects rural revitalization.

In order to conduct in-depth research on the interactive relationship and spatial spillover effects between education poverty alleviation and rural revitalization, this article adopts three different spatial weight matrices and estimates the spatial panel simultaneous equation model using the generalized spatial three-stage least squares method proposed by Kelejian and Prucha (2004) [13] . The detailed results are shown in Table 6. It can be seen that the rural revitalization equation

and education poverty alleviation equation are all greater than 0.95 under three different weight matrices. At the same time, the estimated values of the coefficients of the variables have hardly changed, proving that the equation fits well and the empirical results of the model are relatively robust and reliable. Next, a detailed discussion will be conducted based on the economic geographical distance weight matrix.

The equation for rural revitalization in Table 6 shows that the estimated coefficient of the spatial lag term for rural revitalization (W · Rr) is 0.5053, which is significant at the 1% level, indicating that there is a significant spatial spillover effect in rural revitalization, that is, the implementation effect of rural revitalization will be positively driven by neighboring areas with good economic performance. The estimated coefficient of poverty alleviation through education (Epa) is 0.20731, which positively promotes rural revitalization at a significance level of 1%. Compared with the lagged term of education poverty alleviation in the adjacency matrix and geographic matrix, the lagged term of education poverty alleviation has a significant promoting effect on rural revitalization and has a less significant inhibitory effect. The estimated coefficient of human capital (Hc) is 0.1209, which significantly promotes the positive development of rural revitalization policies at the 1% level. The estimated coefficient of the total fixed assets investment of rural households (LnGd) is 0.03201, which promotes rural revitalization at the significance level of 1%, meaning that increasing the total fixed asset of rural households will play a good role in promoting rural revitalization. The per capita possession of public library collections (Pclh) is estimated to significantly promote rural revitalization and development at the 1% level with a coefficient of 0.03. The estimated coefficient of wage level (LnWl) is 0.04198, which significantly promotes rural revitalization at a level of 1%. It can be seen that an increase in the average wage level of urban private sector employees in agriculture, forestry, animal husbandry, and fisheries can improve people’s livelihoods and promote rural economic development.

The equation for poverty alleviation through education in Table 6 shows that the estimated coefficient of rural revitalization is 0.25692, which is significant at the 1% level, indicating that the implementation of rural revitalization strategy also has a positive impact on education poverty alleviation policies. The estimated coefficient of the spatial lag term in rural revitalization is 0.61754, which improves the effectiveness of education poverty alleviation at a significance level of 1%. The spatial lag of education poverty alleviation significantly inhibits the implementation of education poverty alleviation at a level of 1%, possibly because surrounding economically underdeveloped cities will reduce the support for education poverty alleviation in economically prosperous areas. The coefficient sign of the local economic development level (LnPgdp) is positive, and the estimated coefficient of 0.07868 significantly promotes education poverty alleviation. The level of urbanization (Ur) has a negative impact on education poverty alleviation at a level of 1%. The regression coefficient of education investment (Lfee) is 0.42824, which promotes the effectiveness of education poverty alleviation at a significance level of 1%. This means that increasing the proportion of local financial education expenditure in local general budget expenditure will have a significant positive promoting effect on education and poverty alleviation. The impact of education level (Edl) on education poverty alleviation is not significant, but in the context of adjacency spatial weight matrix, education level has a positive promoting effect on education poverty alleviation at a significance level of 1%.