How to evaluate the efficiency of rural preschool education resources and its regional differences in China

Abstract

Rural preschool education is an integral part of rural society, and improving the efficiency system of evaluation of rural preschool education resource allocation is an important strategy for the implementation of the rural revitalization. This paper uses an input-oriented three-stage DEA model to analyze the efficiency of rural preschool education resource allocation in 30 provinces in China from 2012 to 2020. The results show that external factors such as the level of urbanization, birth rate, and the scale of kindergarten impacts the efficiency of rural preschool education resource allocation significantly. Without regard to the influence of environmental and random factors, the overall trend of the average efficiency of rural preschool education resource allocation in China has improved, showing a regional pattern of “central > eastern > western.” Therefore, based on the relevant policies, this paper puts forward rational suggestions for the improvement of rural preschool resource allocation efficiency in China from the perspectives of human, financial and material resources.

Introduction

Nowadays, the strategic importance of education for national development is beyond doubt. However, there is considerable debate over what policies should be adopted to develop education. The neoliberal education policies that emerged in the 1980s, characterized by the industrialization and marketization of education, and school performance competition, have been criticized. Similarly, state welfare education policies with high welfare characteristics have been challenged amid the gloomy economic globalization and an uncertain global economic outlook. Balancing government education policies between those focused on public well-being and those promoting employment and economic growth, and negotiating between state welfare education policies and neoliberal education policies, have become focus and challenges for public education policies in various countries today.

From a worldwide perspective, since the industrialization revolution, the need for specialists in socialized mass production has forced countries around the world to pay more attention to and vigorously develop education. The emergence of pre-school education, in particular, has made the state gradually become the largest provider and investor in education. This situation is more prominent in some undeveloped rural areas, and governments at all levels have consciously taken the development of rural pre-school education as one of the important strategy in the process of implementing poverty alleviation policies and accomplishing the task of poverty alleviation.

The origin of the concept of rural preschool education efficiency can be traced back to welfare economics, and the core of its research focuses on input-output ratio, equity and the relationship between them. Based on the utility ordinal theory, Pareto optimization and other western economic theories, Oh, Chang-Yeong regarded “the human, material and financial resources occupied, used and consumed by the education process as a measure of the efficiency of resource allocation in rural preschool education¹. And theories such as Pareto improvement, Sitovsky criterion, and Kador-Hicks function are developed. High quality and balanced development is also the long-term goal of China’s preschool education development. China’s “urban-rural dualistic” pattern has not only brought about uneven social and economic development, but also made the development of preschool education present a “dualistic” situation. In the face of the reality of insufficient resources in rural pre-school education, an objective analysis of the situation and effectiveness of rural pre-school education resource allocation in recent years has become a fundamental basis for further promotion of the quality and balanced development of rural pre-school education in China.

The paper is structured as follows. Section “Literature review” reviews previous research results. Section “Research design” presents the indicator system and data sources. Section “Research method” describes the research methodology, followed by the research findings in section “Empirical analysis”. Section “Conclusion and recommendation” demonstrates the conclusions, including the limitations and prospects of the study.

Literature review

In terms of research perspectives, researchers pay more attention to the influence of the government on the performance of preschool education resource input at macro level. Scholar Izard has studied the government’s monopoly on preschool education resource allocation, and believes that this monopoly will lead to inefficiency and waste of resources². Wu Guangzhi verified and pointed out in his empirical study that there are three criteria to effectively measure the effect of the operation of the financial system: the effective issue of education resource allocation, the adequacy of education services, and the fairness of the allocation of education resources³. Liu Fengqin empirically investigated the impact of measures for education reform on the impoverished population in African countries from the perspective of education resource allocation, and demonstrated the direct impact of government investment in education on anti-poverty policies⁴. Guo Yuanzhi suggested in his study that resource allocation should be included to poor areas and schools as a way of solving the dilemma of the gap between different regions in resource allocation⁵.

At the level of research methods, empirical method is the main method to measure the efficiency of educational resource allocation, mainly including marginal analysis, structural analysis, capacity analysis, mathematical statistics, parametric analysis and non-parametric analysis. Among them, Data Envelopment Analysis (DEA) is a non-parametric production frontier surface model, which has been widely used by researchers in the measurement of production efficiency. In the field of production efficiency measurement research, western scholar Farrell firstly proposed the prototype of DEA⁶, and then Fu Zhiyu⁷ and Fiedler⁸ researched the efficiency of preschool education resource allocation in many countries with the help of this model, while Zheng⁹ considered the efficiency of preschool education resource allocation under the constraints of environment, resources and population.

In terms of research content, researchers have begun to pay attention to the efficient allocation of resources among different levels and types of education at the micro level. Using comparative analysis, de Figueiredo examined the allocation of school resources in three different regions, namely urban, suburban and rural, and tried to measure the efficiency of resource allocation among different levels of education with the results¹⁰. Bhardwaj et al. used the DEA method to explore the efficiency of preschool education resource allocation in India¹¹. Thanassoulis et al. further analyzed the cost structure, efficient allocation of resources and productivity of different types of kindergartens in the United Kingdom¹². Duong measured the resource allocation efficiency of preschool education based on the Malmquist index model, and found that the overall level of technical efficiency of preschool education resources was high, while the lower technical efficiency was mainly in the western region, centrally due to the lack of scale¹³. In addition, Lauver tried to analyze the preschool education resource allocation efficiency in Pennsylvania in the context of urbanization, and found that urbanization has a positive positive effect on improving the preschool education resource allocation efficiency, and proposed that the future preschool education resource allocation focus should be transferred on rural counties¹⁴.

Taking an overview of previous research results, the research on rural preschool education resource allocation has the following four main characteristics. Firstly, from the research object, most of the researches take kindergartens as the unit of education supply to study the interactive relationship between supply and demand, but the problems of the overall layout of the preschool education facilities are ignored. Secondly, from the content of the study, it is mostly based on the balanced measurement model of preschool education resource allocation, with less regard to the geospatial distribution characteristics of education resources. Thirdly, from the characteristics of the data, it is mostly based on sample data or questionnaire data as the main object of the study, but lacks large-sample data. Lastly, from the research scale, it is mostly based on the research of a single scale of the provincial, municipal, or county areas, and lacks of an overall comparison on a national scale. Based on this, this paper attempts to break through the research limits above and takes the large-sample data of 30 provinces and cities in China as the basis to explore the efficiency of resource allocation in rural preschool education and regional differences, and puts forward specific strategies to optimize resource allocation in rural preschool education.

Research design

In order to scientifically analyze the regional differences in the efficiency of resource allocation and strategies of optimizing rural preschool education in China, this study will select the most mature analytical model in the field of efficiency evaluation - Data Envelopment Analysis (DEA), and analyze the level of efficiency, regional differences, and specific improvement strategies by collecting the relevant data of rural preschool education to form the Technical Road map (see Fig. 1).

Fig. 1 [Images not available. See PDF.]

Research technical road map.

Index construction

Any educational resources that can promote the effect of teaching and learning can be defined as quality resources, covering all aspects of human, material and financial resources needed to carry out educational activities. Funding input, teacher qualification and hardware facilities configuration are the main basis for measuring whether the allocation of educational resources is balanced or not¹⁵. Input indicators of the effectiveness of preschool education resource allocation include per captita pupils’ expenditure on education, the proportion of teachers graduating from colleges or above, per capita pupils’ area of school buildings, and the number of books per captita pupils; and the output indicators include the number of kindergarten graduates and the number of people who have received preschool education as a proportion of the total enrollment in elementary school.

The rationality of the selected indicators is further verified by examining the “isotropy” of the input and output indicators of rural preschool education resource allocation in different provinces and municipalities. As can be seen from Table 1, the Pearson correlation coefficients of the input and output indicators of all provinces and municipalities from 2012 to 2020 are all positive, and the significance testing is qualified, which is in line with the hypothesis of “isotropy” of the research model.

Table 1. Pearson correlation coefficient.

	Education expenditure per student	Proportion of college graduates or above	School building area per student	Number of books per student	Number of kindergarten graduates	Proportion of primary school enrolment with pre-primary education
Education expenditure per student	1	− 0.0575	− 0.3002	− 0.4892	− 0.2596	− 0.4553
Proportion of college graduates or above	0.3635	1	0.4343	0.3603	0.107	0.2217
School building area per student	0.7411	0.4204	1	0.6652	0.3286	0.5267
Number of books per student	0.5267	0.3286	0.6652	1	0.4204	0.7411
Number of kindergarten graduates	0.2217	0.107	0.3603	0.4343	1	0.3635
Proportion of primary school enrolment with pre-primary education	− 0.4553	− 0.2596	− 0.4892	− 0.3002	− 0.0575	1

As shown in Table 2, previous research has found that environmental variables will directly affect the performance of preschool education resource input¹⁶, so it is necessary to further consider the integrity of environmental variables to carry out the second stage of the similarity regression analysis. The environmental variables indicators, including the level of urbanization, the birth rate of the local population and the number of kindergartens are selected.

Economic factors (gdp). The level of economic development affects the allocation efficiency of rural preschool education resources, and regions with higher levels of economic development invest more in education and sustainable development issues, so that the performance of preschool education investment is higher. This paper selects the urbanization rate of each province, region and city as a measure of economic development level.

Population factor (born). The influence of education investment on the population is implicit, and good education investment will have a great impact on future development of education. This paper selects the proportion of births in each province and region as a measure of the birth rate of the population.

Scale factor (scale). The aggregation effect of kindergartens will affect the efficiency of preschool education investment. In this paper, the number of kindergartens in each region is chosen as a measure of development scale.

Table 2. Three stage DEA model index system.

Destination layer	Criteria layer	variable
The input variables	Financial input	Average education expenditure
	Human input	Proportion of college graduates or above
	Material input	School building area per student
		Number of books per capita
The output variables	Output quality	Number of kindergarten graduates
	Output quantity	Proportion of primary school enrolment with pre-primary education
The external variable	Economic factors	Urbanization rate
	Demographic factors	Fertility rate
	Scale factors	Number of kindergartens

Data source

The foundational data for the above indicator system are mainly based on the China Rural Education Development Report, the China Education Expenditure Statistical Yearbook, the China Education Statistical Yearbook, the China Population and Employment Statistical Yearbook, as well as provincial statistical yearbooks and statistical bulletins on national economic and social development. In order to compared between regions, the provinces covered in this study are divided into three major regions, namely, eastern, central and western regions, respectively.

Research method

Data envelopment analysis (DEA for short) is an efficiency analysis method that can be used to evaluate decision-making units with multiple inputs and outputs, first proposed by Charnes et al.¹⁷. As there exists the defect of inputs and outputs being scaled up and down in the same proportion the traditional DEA model, Fried tried to add the interference of environmental factors and random noise in the model and proposed the famous three-stage DEA model. Compared with the traditional DEA model, the three-stage DEA model can eliminate the influence of external environment, random interference and other factors, and the efficiency value obtained is closer to the practice.

First stage: traditional BCC model

In this study, the BBC model with changeable returns to scale is adopted, taking into account the differences in the scale of pre-school education inputs across provinces and cities. The raw input-output data are brought into the DEAP 2.1 software to calculate the combined, pure technical and scale efficiencies for each decision unit and the slack values for each input indicator. At the same time, research will be focused on how to minimize the amount of inputs while keeping outputs constant. Thus, an input-oriented research methodology is adopted, and scientific preschool education input decision-making suggestions are aimed to be proposed through systematic analysis and empirical research.

The second stage: stochastic frontier SFA model

The slack variables in the first stage are combined with the SFA model to eliminate the influence of environmental and random factors. Through FRONT 4.1 software, the slack variables for each input indicator are modeled and analyzed separately. The slack variable is the difference between the actual production and operational inputs in each region and the inputs at peak efficiency, reflecting the magnitude of environmental variables, random error terms, and managerial inefficiencies. At the second stage, the input slack variables obtained in the first stage are used to construct the SFA model:

1

represents the relaxation value of the nth input for the ith decision unit; denotes the environmental variable with as its coefficient. The term encompasses a composite error, where signifies a random disturbance term following a normal distribution , and represents managerial inefficiency following a normal distribution . In Eq. (1), the efficiency values include the effects of external environmental indicators and the mixing error term , which need to be corrected in the next step in order to exclude these effects.

Through the regression analysis of the SFA model, the effect of external environmental factors and random interference is excluded, and the revised input volume is obtained, as shown in Eq. (2) :

2

where represents the actual input value; represents the adjusted input value; means that all decision units belonging to the same level. is an adjustment for environmental factors.

The third stage: the model is replaced again after adjustment

When measuring the actual efficiency of a decision-making unit (DMU), adjustments for input variables and raw output variables are combined. By eliminating the interference of environmental and random factors, adjusted input and output variables to are used to measure them, efficiency values can be produced more objectively and accurately to reflect the true level than unadjusted data (see Fig. 2).

Fig. 2 [Images not available. See PDF.]

Logical framework diagram of the three-phase DEA methodology.

Empirical analysis

The first stage: traditional DEA model

According to the index system constructed in Table 2, with select input variables and output variables, the variable BBC model of returns to scale is used to measure the initial efficiency of resource allocation efficiency of rural preschool education from 2012 to 2020 in 30 provinces in China. The results are shown in columns 3 and 4 of Table 3.

Table 3. Average efficiency levels of rural preschool education resource allocation in each province from 2012 to 2020.

Region	Province	First stage		Third stage
		Efficiency value	Rank	Efficiency value	Rank
Eastern	Beijing	0.438	29	0.818	18
	Tianjin	0.528	5	0.852	15
	Hebei	0.584	22	0.91	5
	Liaoning	0.567	14	0.855	14
	Shanghai	0.425	7	0.783	22
	Jiangsu	0.474	16	0.828	17
	Zhejiang	0.524	2	0.775	23
	Fujian	0.712	28	0.918	4
	Shandong	0.547	10	0.87	13
	Guangdong	0.66	26	0.936	1
	Hainan	0.613	23	0.791	20
Central	Shanxi	0.56	9	0.881	11
	Jilin	0.531	17	0.761	25
	Heilongjiang	0.504	20	0.764	24
	Anhui	0.617	30	0.904	7
	Jiangxi	0.706	15	0.897	10
	Henan	0.762	21	0.908	6
	Hubei	0.771	19	0.933	2
	Hunan	0.715	18	0.903	8
Western	Inner Mongolia	0.486	13	0.722	28
	Chongqing	0.727	1	0.901	9
	Sichuan	0.636	6	0.804	19
	Guangxi	0.773	25	0.923	3
	Guizhou	0.58	24	0.785	21
	Yunnan	0.589	3	0.754	26
	Shanxi	0.552	8	0.732	27
	Gansu	0.373	27	0.647	30
	Qinghai	0.549	11	0.717	29
	Ningxia	0.561	12	0.852	16
	Xinjiang	0.629	4	0.88	12

On a national scale, without removing the impact of environmental factors and random variables, the average efficiency values for most provinces from 2012 to 2020 have consistently been less than 1 (see Fig. 3). This indicates that the initial efficiency of rural preschool education resource allocation in China exhibits varying degrees of inefficiency. However, there is a general downward trend these years. The continuous decline in the efficiency of rural preschool education resource allocation is closely related to the failure to fully implement preschool education funding mechanisms. In some provinces, there has been no gradual increase in education funding, and the growth rate of preschool education financial allocations has been lower than the growth rate of regular fiscal income. Additionally, there are issues of delayed allocation, misappropriation, and diversion of education funds in some regions. The average efficiency value has never reached 1, indicating that the efficiency of rural preschool education resource allocation in China remains far from ideal, with significant room for improvement.

Fig. 3 [Images not available. See PDF.]

Average efficiency value changes in the first stage from 2012 to 2020.

From an inter-provincial comparison: There are significant inter-provincial differences in the efficiency levels of rural preschool education resource allocation. Chongqing has the highest education efficiency level, ranking first with an efficiency value of 0.727. While Anhui has the lowest efficiency level, ranking last with an efficiency value of 0.617. The efficiency value difference between the two is as high as 0.11. The resource allocation efficiency of economically developed provinces is not as high as expected. For example, Beijing ranks 29th, Shanghai ranks 7th, and Guangdong ranks 26th. Conversely, some less developed provinces rank relatively high in governance efficiency, such as Yunnan, Xinjiang, and Sichuan, which ranks third, fourth, and sixth, respectively. This indicates that provinces with better development levels do not necessarily have high rural preschool education resource allocation efficiency, while those with slightly lower development levels do not necessarily have low governance efficiency. Various factors influence the efficiency levels of rural preschool education resource allocation in different provinces.

From 2012 to 2020, there were significant regional differences in the efficiency levels of rural preschool education resource allocation in China. Among the three major regions, the central region had the highest efficiency value, with an average efficiency of 0.646. The western region followed, with an average efficiency of 0.587. The eastern region had the lowest efficiency level, with an average of 0.552 (see Fig. 4). By comparing the data, it can be concluded that the efficiency values of the central and western regions are relatively close and rank high, while the eastern region ranks low in efficiency value.

Fig. 4 [Images not available. See PDF.]

Changes in the efficiency of the eastern, central, and western regions from 2012 to 2020 in the first stage.

The second stage: SFA model analysis

In the first stage, the slack variables of each input variable are derived, and in this part, using the slack variables as the explanatory variables and the environmental variables as the explanatory variables, the SFA regression results can be obtained in the second stage by using Frontier4.1 software, as shown in Table 4. From the log likelihood function value (log likelihood) and likelihood ratio test (LR test) in the SFA regression results, it can be seen that the estimation effect is good, and most of the coefficients of each environmental variable on the input variables can pass the significance test, which indicates that there is a significant effect of external environmental variables on the redundancy of each input variable. The γ value of each preschool education input slack variable is as high as 0. 93, indicating that management factors dominate the role, and it is necessary to remove the environmental and random factors for analysis.

Table 4. Second stage stochastic frontier regression results.

SFA	Average education expenditure		Proportion of junior college graduates or above
	Coefficient	T-test	Coefficient	T-test
Constant	− 11058.949***	− 7.347	− 40.0445***	− 5.3338
Economic development level	− 148.7481***	− 8.7075	− 0.5714***	− 7.7583
Fertility rate	328.4179***	4.0097	1.6779***	6.0715
Number of kindergartens	22.0921***	4.7116	0.0591***	2.7535
Sigma-squared	45677218.000***	44920183.000	563.7199***	3.5383
Gamma	0.9467***	216.9742	0.9605***	79.9264
Eta	− 0.1190***	17.4526	− 0.0532***	− 5.4779
Log likelihood function	− 2460.1853		− 857.5451
LR unilateral check value	404.94053***		251.48481***

SFA	School building area per student		Number of books per capita
	Coefficient	T-test	Coefficient	T-test
Constant	− 6.5198***	− 6.3126	− 3.2989***	− 3.4626
Economic development level	− 0.0841***	− 8.3366	− 0.0306***	− 3.0681
Fertility rate	0.2918***	5.7613	0.0800*	1.7043
Number of kindergartens	0.007378**	1.9957	0.014057***	3.7654
Sigma-squared	13.480098***	3.4100	45.1852***	4.0748
Gamma	0.9369***	46.3585	0.9854***	246.1957
Eta	− 0.1004***	− 7.3819	− 0.1526***	− 12.6317
Log likelihood function	− 405.34502		− 389.02262
LR unilateral check value	171.6597***		446.04416***

∗∗∗, ∗∗, and ∗ shows significance at the 1% level, 5% level, and 10% level, respectively.

Level of economic development (gdp). The regression coefficients of the slack variables of the economic development level and the input variables such as education expenditure per pupil, the proportion of the number of teachers graduated from specialized courses or above, school building floor space per pupil, and books per pupil all pass the significance test and are all negative. And the increasing level of urbanization reduces the redundancy values of these several inputs, making the performance of preschool education resource inputs increase. This also verifies the findings of Huybrechts¹⁸.

Birth rate (born). The birth rate and the average per capita expenditure on education, the proportion of the number of teachers who graduated with a specialized degree or higher, the average per capita floor space of school buildings, the average per capita books (books) and other input slack variables of the birth rate can pass the test of significance, which indicates that the higher the birth rate is, the more redundant the preschool education inputs are. It makes the performance of the preschool education resource inputs lower, which is consistent with the findings of Elgen¹⁹. This indicates that the higher the birth rate, the more investment that the government inputs to guarantee the development of preschool education in rural areas.

Number of kindergartens (scale). The regression coefficients of the number of kindergartens with the slack variables of the four inputs are positive, significant at 1% level and all pass the test of significance, which is not conducive to the realization of efficient allocation of resources. This is consistent with the empirical findings of Greier²⁰. This suggests that the aggregation of young children does not directly affect the performance of pre-school education resource inputs, but rather increases the slack variable. It indicates that blindly expanding the scale of pre-school education operations have the potential to lead to the crude development of pre-school education.

The third stage: adjusted DEA empirical results

Based on the Stochastic Frontier Analysis (SFA) calculations in the second stage, the raw input indicator data values were adjusted and substituted into the first stage DEA model for calculations to produce more accurate and realistic efficiency values. The results are displayed in columns 5 and 6 of Table 3. The changes in the adjusted efficiency values in Stage 3 compared to Stage 1 are significant.

From a national perspective, the efficiency values adjusted in the third stage show significant changes compared to the first stage, indicating that external environmental factors and random factors significantly underestimated the efficiency of rural preschool education resource allocation in China. As shown in Fig. 5, the adjusted average efficiency of rural preschool education resource allocation in China increased significantly from 0.590 in the first stage to 0.834 from 2010 to 2020, a growth of 41.3%. In the third stage, the efficiency value of Guangdong Province reached 0.936, indicating that there has been some success in the efficiency of rural preschool education resource allocation in China over the past decade, which is a commendable accomplishment.

From the perspective of each province, the gap in the efficiency of rural preschool education resource allocation among the provinces has narrowed. Among the 30 provinces studied, the efficiency rankings of 29 provinces, except Liaoning Province, have changed, accounting for 96.6% of all provinces. In the first stage, Chongqing ranked first in the efficiency of rural preschool education resource allocation, but after adjustment, it ranked ninth; Fujian Province’s efficiency ranking increased by 24 places, an increase of 85.7%. Yunnan Province dropped from third place in the first stage to 26th, with an efficiency decrease of 88.4%. This indicates that the development conditions, economic factors, scale, and population of different provinces affect the efficiency of rural preschool education resource allocation. In practice, despite efficiency gaps among provinces in rural preschool education resource allocation, these gaps are not as large as they were in the first stage.

From a regional analysis perspective, unlike the significant fluctuations in the first stage efficiency values, the changes in efficiency values in different regions from 2012 to 2020 after adjustment show smooth fluctuations. This indicates that the influence of random factors and environmental variables increased the actual efficiency values. As shown in Fig. 6, the efficiency ranking of the central region rose, surpassing the eastern region to rank first, with an average efficiency value of 0.868; the eastern region ranked second with an average efficiency value of 0.848; and the western region ranked third with an average efficiency value of 0.793. Despite the previously higher rural preschool education resource allocation efficiency in the central and western regions, the efficiency decreased after considering economic, social, and population factors. In contrast, the eastern region invest more in rural preschool education, with its advantageous social resources and the government’s policy of prioritizing the development of the eastern region, resulting in improved efficiency in resource allocation.

Fig. 5 [Images not available. See PDF.]

Changes in average efficiency values in the third stage from 2012 to 2020.

Fig. 6 [Images not available. See PDF.]

Changes in the efficiency of the eastern, central, and western regions from 2012 to 2020 in the third stage.

Conclusion and recommendation

This paper evaluates and analyzes the efficiency of rural preschool education resource allocation in China from 2012 to 2020 using a three-stage DEA model, and draws the following conclusions and suggestions:

Conclusions

First, random factors and environmental variables indeed underestimate the efficiency of preschool education resource allocation in rural areas. If the influences of external environmental factors and random factors are not isolated, it is prone to draw incorrect research conclusions, which may to some extent lead to inappropriate development decisions, resulting in resource redundancy and waste.

Second, the level of economic development is positively correlated with the efficiency of preschool education resource allocation in rural areas. The level of economic development affects the government’s fiscal spending and the amount of disposable educational resources, thereby influencing the efficiency level of preschool education resource allocation in rural areas. Moreover, economically developed regions are generally at the forefront of educational reform, with more mature preschool education systems compared to underdeveloped areas. Therefore, their well-established preschool education systems may also be an important foundation for promoting the efficiency of preschool education resource allocation.

Third, the number of kindergartens shows a negative correlation with the efficiency of preschool education resource allocation in rural areas. Although the scope of kindergartens gradually expands and concentrates, government support keeps difficult to benefit children in rural and remote areas, causing the number of beneficiary children to decrease year by year. The increase in the number of kindergartens thus impedes the efficiency of preschool education resource allocation in rural areas.

Fourth, the birth rate shows a negative correlation with the efficiency of preschool education resource allocation in rural areas. The more school-age children in a region, the greater the competition for preschool education. When supply reaches a certain level of saturation, opportunities for preschool education in rural areas will consequently decrease.

Suggestions

In summary, to improve the efficiency of rural preschool education resource allocation in various provinces and cities, and to further deepen the reform of preschool education in China, multiple measures should be adopted to ensure the effective allocation of educational resources.

First, from the perspective of human resource input, the critical to effective allocation of rural preschool education resources is to promote balanced teacher allocation in rural areas. To begin with, unified standards for urban and rural preschool teacher staffing should be improved. Based on local birth rates and population mobility, the number of teachers required for various levels and subjects in urban and rural areas should be regularly calculated to determine the adjustment of teacher staffing. For rural small-scale schools with less than 100 students, existing policies should be followed to ensure that each teaching point has an adequate number of full-time teachers with a balanced structure. Next, innovative reward mechanisms for rural teachers should be implemented. Teachers’ basic salaries should be legally guaranteed to be no less than the average salary of local civil servants. Special government allowances should be set up for rural teachers in underdeveloped counties. On the basis of raising basic living allowance standards, a “reward instead of subsidy” system should be implemented. Graduated rewards should be given to teachers who have been rooted in rural areas for a long time and have made various contributions to rural education, ensuring that their monthly subsidies and rewards exceed the average salary of urban teachers. Finally, the policy of exchange and rotation between urban and rural teachers should be further implemented. The whole society should create a social atmosphere and strengthen public opinion guidance. Education administrative departments and schools at all levels should increase publicity and mobilization efforts to normalize teacher exchange program. The construction of exchange incentive mechanisms should be improved. Teachers exchanged to rural areas should receive the same salary treatment as they did in their original schools, and should also receive living and transportation allowances. They should be given priority consideration in evaluations, promotions, and training opportunities under the same conditions.

Second, from the perspective of financial input, a “compensatory” education fund transfer payment system should be established. To start with, implementing differentiated fiscal input policies with appropriate inclination towards rural areas. The central and provincial governments should increase fiscal transfer payments to underdeveloped rural areas to reduce financial pressure on these regions. Next, the funding mechanism for rural preschool education should be guaranteed, strengthening supervision over rural preschool education funds and severely punishing illegal behaviors such as fund interception and misappropriation. The “school finances managed by the finance bureau” model should be fully implemented in rural kindergartens, strengthening the management of special funds. Lastly, governments at all levels should distribute fiscal inputs well and clearly guarantee the direction of preschool education fiscal use. They should avoid the phenomenon of funds and resources surplus in urban schools. Instead, the weaker structure such as standardized construction of small-scale rural schools and rural boarding schools and the implement of fully functional classroom should be highlighted. This would promote “precise poverty alleviation” in rural kindergarten finances, narrowing the urban-rural gap.

Third, from the perspective of material input, a standard and comprehensive material resource management system should be constructed. First, a long-term mechanism for the informatization of investment in preschool education should be improved, with the establishment of special funds to promote the construction of preschool education informatization standards. This would achieve full coverage of the informatization of teaching equipment and full network access in urban and rural areas, accelerating the construction of digital campuses and strengthening the management of informatized terminal equipment and software. Second, the characteristic development of kindergartens should be integrated with the construction of kindergarten-based curricula. In the construction of characteristic schools, attention should be paid to support the construction of kindergarten-based curriculum. The development of kindergarten-based curricula should also responds to the overall characteristic development of the school, promoting a systematic development of education. Finally, cooperation between rural schools and rural communities should be strengthened, effectively responding to and sharing the cost of preschool education services. For example, through strategies such as rent exemption for kindergarten premises, policy preferences, and the transfer for land use rights, the quality of preschool education services can be improved, forming a virtuous cycle of “high input—high quality—high input”.

Research limitations and outlook

This study employs an input-oriented three-stage DEA model to analyze the efficiency of rural preschool education resource allocation in 30 provinces in China from 2012 to 2020. Due to the limited research capabilities and time, there are still some shortcomings in this study that need further improvement. First, this paper uses data envelopment analysis for empirical research, but future researchers can use projection pursuit models and Theil index for further discussion. Second, this paper focuses on measuring regional equalization differences and does not address urban-rural equalization measurements, which also deserves further research. Finally, due to data unavailability, some indicators, such as the enrollment rate of rural kindergartens, were not included in the evaluation indicator system. In the future, it is hoped that a scientific, reasonable, and multi-dimensional evaluation indicator system for rural preschool education resources can be established.

Author contributions

M.M.T.: conceptualization, writing—review and editing, methodology, and manuscript revision. Z.Z.: prepare Figs. 1, 2, 3, 4, 5 and 6; Tables 1, 2, 3 and 4. Q.L.: reference management, funding acquisition, and manuscript revision critically. All authors contributed to the article and approved the submitted version.

Data availability

The original contributions presented in the study are included in the article/Supplementary Material, and further inquiries can be directed to the corresponding author.

Declarations

Competing interests

The authors declare no competing interests.

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