Rural–Urban Educational Inequalities and Their Spatial Variations in China

Existing discussions of rural–urban education inequality focus primarily on education investment and/or attainment, with little attention being paid to the opportunities or potential that an area has to achieve better educational outcomes. This study presents a new analytical framework based on Amartya Sen’s capability approach for a better understanding of rural–urban education disparity. In addition, the rural–urban definitions for educational research are clarified and the effects of a wide range of Central Government policies aimed at reducing the rural–urban educational gap are assessed. The results suggest: inadequate investment (e.g., funding and high-quality teaching resources) in rural education in some regions, especially middle and high schools; inappropriate partitioning of the national territory by the Government for policy implementation; and negative effects resulting from the school consolidation policy. The latter will influence the ability of some rural areas to match the educational achievements of their urban counterparts. This research also reveals that the existing rural–urban gap will be unlikely to narrow under the current policy regime. A conventional approach based on investment and outcomes alone in rural–urban disparity research and policy may overlook the important interactions and conversion processes that are important for mitigating rural–urban disparities.


Introduction
Education is one of the fundamental pillars of development, raising individuals' productivity and promoting their life opportunities (OECD, 2016). Recent evidence suggests that, while most nations are likely to achieve near-universal primary education in the next decade, large inter-regional disparities in rates of secondary-school completion will persist (Friedman et al., 2020). There have been repeated attempts to reform education in countries around the world to reduce inequalities, nowhere more so than in China, where Notifications of the Reform of the Funding Guarantee System for Rural Compulsory Education (NR) (December 24, 2005) were issued in 2005, a Law of Compulsory Education was introduced in 2006, and a National Medium and Long-term Educational Reform and Development (NMLERD) Plan Outline (2010-2020) was published in 2010 (Sun, 2012;The State Council of China, 2010). One of the main targets of these associated policies is to redress the imbalance in education between urban and rural areas.
Due to the shift from a planned to a market-oriented economy, the policies in the 1980s and 1990s were focused on mobilising additional government and non-government resources to enhance the efficiency of education funding. In this period, most of the funds for education were required to be provided by local government, while Central Government had little responsibility for financing basic education (Hu, 2012, Zhu & Peyrache, 2017. As a result, the primary responsibility to guarantee funding for education (i.e., education facilities, school building construction, teacher salaries) was transferred to local authorities. The availability of educational resources and potential for education development was, therefore, closely related to local economic circumstances (Hannum, 2003). The funding for primary, junior secondary and senior secondary school education in rural areas was mainly provided by local authorities at village, township and county levels (Sun, 2010;Tsang, 1996). Due to the uneven economic development between rural and urban areas in China, rural and urban areas had varying abilities and resources to invest in education. Local authorities in rural areas relied heavily on charging students informal levies (extra-budgetary sources) to compensate for their insufficient educational budgets (Tsang, 1996;Wang, 2014). Tuition fees, miscellaneous fees, and rural educational surtax paid by parents became the major sources of funding for compulsory education in rural areas between 1990 and 2000 (Fu & Ren, 2010). Consequently, the policy of decentralisation of educational funding led to an excessive financial burden for rural residents who were already suffering from urban-centric development (Fu & Ren, 2010;Wang, 2014).
Education equality between rural and urban areas is an important part of education equality per se. Since 2000, important adjustments by the Central Government have been implemented to improve the unequal relationship between urban and rural areas. Over the past 20 years, the Chinese Government has been constantly increasing the funding for rural education through, for example, making transfer payments, reforming the funding system, investing in special projects, Rural-Urban Educational Inequalities and Their Spatial… e.g., Project Hope (Li & Liu, 2014), and reducing the financial burden of rural residents. Rural-urban educational inequality has been an important topic for policymakers and academics in China (Fu & Ren, 2010;Qian & Smyth, 2008;Rao & Ye, 2016;Zhang, 2017).
However, empirical research has only paid attention to rural-urban education disparities at a national/aggregated level from the perspective of the whole economy or public policy and has tended to ignore the importance of spatial variations of rural-urban disparity, i.e., a geographical perspective. In addition, there remains a lack of research that measures spatial variation in rural-urban educational inequalities in China over time, and that monitors the impact of policies and evaluates their effects. Furthermore, common measurements of rural-urban education disparity lack important theoretical justification. The performance of education in rural and urban areas is discussed only in monetary terms, such as per-pupil educational expenditure (PPEE) or educational attainment. The link between educational investment and attainment is missing in the discourse on rural-urban educational inequalities.
Accordingly, this research proposes an analytical framework based on Sen's capability approach (Sen, 1992) to assess educational inequalities, which fills the current theoretical gap. Capability refers to the level of freedom or the ability of an agency (i.e., responsible individuals or groups) to achieve or choose something that the agency has reason to value doing or being (Sen, 2001;Walker, 2005). Compared to other human well-being evaluation approaches, it offers a more comprehensive and multi-dimensional analytical framework to evaluate real well-being, including education advantage or disadvantage and can be very meaningful from a policy perspective. A key question for this research is whether rural-urban inequalities in education have decreased under the policy changes that have been implemented in China. The aim of this paper is to address this question by examining the so-called rural-urban education gap in China using Sen's analytical framework and identifying how the spatial variations in gap indicators have changed as new policy regimes have been put in place since 2000.
The paper is structured as follows: a new analytical framework for analysing education inequality based on Amartya Sen's capability approach has been proposed in the following section; a short synopsis of the education policies related to rural areas and the definition of what constitutes 'rural' in China has been clarified thereafter; the sections that follow illustrate how the rural-urban attainment gap has deepened over time by using selected indicators and the capability approach; the policy implications are discussed before conclusions are drawn in the final section.

Capability Approach and Education Inequality Evaluation
In this section, we begin by setting out an alternative analytical framework based on Sen's capability theory to evaluate education disparities. The major theme of the capability approach is how to measure development and human wellbeing (Sen, 1992). It rests on a critique of other theories that focus on the distribution of resources (or commodity) or utility (or outcome). Capabilities refer to opportunities or levels of freedom that people have to achieve what they consider valuable (Sen, 1992). In order to introduce the capability approach to education inequality assessment, some of its core ideas are explained in the following sub-sections.

Equality of What?
Inequality is inevitable and pervasive in our world. In order to offer a fair basis for regulating education inequality, it is very crucial to define what education equality is (Baker et al., 2016b). The core question for different egalitarian theories (Baker et al., 2016a;Hare, 1952;Rawls, 1971) is 'equality of what?' (Sen, 1979). The answer to this question determines what to assess and what equality we prioritise. According to Sen's theory, what we should prioritise or equalise is not just resources (i.e., per-pupil educational expenditure) or outcomes (i.e., education attainment), but human capabilities (i.e., educational opportunities that people have or what people are able to obtain from being educated) (Walker, 2005).

Functioning and Capability
The distinction between functioning and capabilities is one of the core ideas in the capability approach (Sen, 1979). 'Functioning' refers to achieved outcomes of education, that is, educational attainment (e.g., getting high grades at high school). 'Capabilities' are the potential or opportunities to achieve these outcomes or functioning (e.g., having been given high-quality education). Thus, the difference between the two concepts is that one is about actual achievement while the other emphasises the opportunities to achieve.
Whilst previous educational evaluations have primarily focused on 'functioning', evaluations based on outcomes ignore information about the context and process associated with achieving outcomes. Equal achievement may mask different stories or capability sets. However, these differences are germane to reveal equality related policy implications and to propose effective new measures (Terzi, 2007). The advantage of the capability approach is that it emphasises the potential or real freedom that students have to achieve their valued functioning from education, thus providing a method to evaluate real education advantage and disadvantage.

Agency and Regional Context
'Agency' is another central concept in the capability approach that requires further elucidation. It refers to responsible individuals or groups who shape their own valued lives (Walker & Unterhalter, 2007). In education, the students are the agents of learning. However, whilst 'agency' in the capability approach not only applies at the individual level, it also relates to the regional context (Koo & Lee, 2015). Educational disadvantages in a region can have considerable impacts on individuals who live in these areas to pursue what they want to become and what they want to achieve from their education. For example, children in lagging/remote rural areas without quality schools will have a lower chance to receive education of a standard that enables them to achieve what they want. In other words, individuals' freedom or choices in education are constrained due to regional education inequalities. Therefore, efforts to reduce regional (e.g., rural-urban) educational disparities are closely related to the objectives of enhancing individuals' capabilities. This research applies the capability approach to the analysis of rural-urban educational disparity. Accordingly, all the residents within targeted areas are considered as a single agent.

Conversion Factors and the Importance of Context
'Conversion' is also a crucial concept of Sen's capability approach and differentiates it from resource-based approaches. Sen argues that providing equal resources will not necessarily offer people equal freedom of choice, as there are substantial variations in their abilities to convert resources into freedom. At the individual level, these include personal differences, such as enthusiasm for academic study, environmental differences and social differences (Walker, 2005). For an area or a region, its ability to convert its 'capability' into 'functioning' (e.g., education attainment) is restricted by its educational foundation, e.g. previous education attainment or current educational infrastructure/teaching quality and policy circumstances. These restrictions can work as conversion factors that determine the extent to which urban or rural areas can generate capability from the resources provided (Walker, 2005).
Apparently, the number of disposable resources will greatly influence the opportunities of the 'agency' to achieve specific 'functioning'. Thus, resource-based approaches are used in many studies involving the evaluation of inequalities. The assumption lying behind the resources-based approach is that people will be equally 'well off' (or achieve the same educational attainment) when given the same amount of resources (Sen, 1992). However, this assumption does not consider the substantial variations in their ability to convert resources into the functioning combinations they value (Koo & Lee, 2015). In terms of education, the areas with the same educational investment may achieve different levels of attainment because of their varied education foundations. Therefore, just considering available resources, like educational provision, is inadequate. In addition, Sen regards education itself as a basic capability, which affects the development, expansion and conversion of other capabilities and expands human freedom.

Analytical Framework and Data
Accordingly, rural-urban educational inequalities can be conceptualised by using the above capability approach (Fig. 1). Firstly, economic context (i.e., like global/ national/regional economic conditions and fiscal policy) and social context (i.e., educational policies) will significantly impact educational provision in targeted rural and urban areas. Educational provision, as measured by per-pupil educational expenditure (PPEE) and high-quality teaching resources, is important for enabling an area to have the freedom/opportunities to achieve better educational outcomes. Thus, the quantity and quality of the educational provision will impact the capability of an area to achieve the desired functioning.
In this research, the capabilities of an area to achieve better education attainment is the focus of the assessment of rural-urban educational inequalities. The relationships between educational provision and capability sets are influenced by conversion factors, achieved functioning or existing educational foundations (achieved educational attainment), as well as economic and social contexts. The areas with different educational foundations and fiscal policies may have varied abilities to convert educational resources into capabilities. Choices made by an area link capability (i.e., what this area can achieve in education) and functioning, (i.e., what this area has achieved in education). The effective choices an area can make are determined by social contexts, involving educational policy, the law of compulsory education, and social norms and traditions. Sen's capability approach provides theoretical justification for the multidimensional and comprehensive framework to evaluate and assess the spatial and temporal rural-urban educational comparisons in this research.
Using this analytical framework, three dimensions of rural-urban education inequality in China have been investigated: the economic and policy context, the achieved functioning or conversion factors and the educational provision. The latter two dimensions have been evaluated using the selected indicators shown in Table 1. The data used in this research and summarised in Table 1 have been extracted from the Chinese Census and the relevant Statistical Yearbooks.

Economic and Policy Contexts
Over the past 40 years, the growth of China's GDP has averaged nearly 10% per year and succeeded in lifting 850 million people out of poverty (The World Bank, 2020). However, the rapid growth led by labour-and resource-intensive manufacturing has reached its limits and China still lags behind in human capital and labour productivity. To ensure a sustainable growth path, many reforms are required and institutional problems need to be addressed. Education is recognised as the most important and efficient way to reduce inequalities in the economy and free the rural poor from the rural poverty trap (Zhang, 2017). Although nine years of compulsory education has been confirmed by the Decision on the Reform of the Education System (Central Committee of the Communist Party of China, 1985) and the Compulsory Education Law of the People's Republic of China in 1986, inadequate investment in rural education due to the decentralised funding system has caused the rural-urban education gap to widen (Wang, 2014). Also, extra financial burdens (e.g., educational surcharges and levies) were imposed on rural families to make up for insufficient local authority education budgets. At the same time, there has been an enormous influx of rural migrants into urban areas to search for better employment opportunities, supporting China's rapid economic growth. However, these rural to urban migrants are left disadvantaged in urban areas by the household registration system (hukou) which is implemented in China to restrict the mobility of the rural population and their access to public services (including education) and benefits (Xiang et al., 2018(Xiang et al., , 2020Zhao & Howden-Chapman, 2010). Given various administrative and financial barriers based on the hukou system, the children of rural migrants cannot enjoy equal access to educational resources in urban areas. There are substantial education inequalities between urban and rural children (including those of migrants) (Zhang et al., 2015) that force the rural population into a poverty trap (Zhang, 2017) which, over time, influences the development of the whole country.
Accordingly, a series of taxation reforms, financial support policies and other educational related policies have been implemented by the Central Government to reduce rural-urban education disparities and promote education equality. Two important aspects of the policy background are tax reform and financial support policies for rural areas and the suspension of 'school consolidation' in rural areas.

Taxation Reforms and Financial Support Policies for Rural Areas
Since 2001, Central Government has initiated a series of rural taxation reforms to relieve the excessive fiscal burden on rural residents. "Tax-For-Fee" was implemented as the first stage with all fees collected previously in villages and townships, including education surcharges, being abolished and replaced by agricultural taxes and related surcharges (Wang, 2014;Wang & Zhao, 2014). In 2004, the rural taxation reforms moved to the second stage as Central Government decided to phase out the agricultural tax and abolish it entirely in 2006. The implementation of rural taxation reforms not only reduced previous financial burdens on rural families but also led to the establishment of a new financing mechanism for rural education with the provincial governments and Central Government playing an increasingly important role (Wang, 2014).
In addition, the "Two Waivers and One Subsidy" policy was introduced to further reduce the educational fiscal burdens on rural residents with financial difficulties in 2001. Under this policy, Central Government provided poor pupils in rural areas with free textbooks, exemption from miscellaneous fees (e.g., administrative fees) and a living cost subsidy for boarding pupils with financial difficulties (Rao & Ye, 2016;Wang, 2014). In 2004, a 'one-charge system' was initiated nationwide, allowing schools to collect a standard charge from pupils which was set by provincial governments.
However, these policies had limited influence because of the enactment of the Notifications of the Reform of the Funding Guarantee System for Rural Compulsory Education (NR) in 2005, which extended the targets of the "Two Waivers and One Subsidy" policy from rural families with financial difficulties to all rural residents. The funding guarantee system confirmed by this policy was executed based on a partitioning of national territory into three macro-economic zones (Fig. 2). The eastern areas are all coastal areas with flat terrain and each plays a leading role in China's economic development, like Beijing and Shanghai. The main grain production areas and 80% of coal resources are in the central area. The topography and environment of the western areas, like Inner Mongolia and Tibet, are very diverse, with plateaus, basins, deserts and prairies. Their economic development has come much later than the eastern areas (Tan & Huang, 2008). According to this partitioning, rural residents in the western region were relieved from paying tuition and miscellaneous fees in 2006, while those in rural areas in central and eastern areas became exempt from these fees in 2007. Central Government improved its redistributive capability in educational resources and enhanced its power to play an equalising role in the new funding guarantee system for rural areas; 80% of funds for providing free compulsory education (i.e., no tuition and miscellaneous fees) and basic public funds for education were offered by Central Government in rural areas in the western region. The Central Government proportion of education funding was 60% in the central region, whilst in the eastern region (comparatively developed areas) the proportion was determined by their financial conditions. All the funds for offering free textbooks and 50% of building renovation expenses for rural compulsory education are now provided by Central Government in western and central regions, while these funds are provided by the local governments in eastern areas. Teachers' salaries are still covered by local governments, but transfer payments are enhanced by provincial-level governments to ensure that teachers' income in rural areas is stable and sufficient.
In 2006, a Compulsory Education Law also confirmed that pupils in compulsory education are exempt from tuition and miscellaneous fees and proclaimed that all funding must be guaranteed by public funds from Central Government and local authorities (Standing Committee of the National People's Congress, 2006). The main funding source was transferred from township to county in 2001 (Wang & Zhao, 2012) and then to the provincial government in 2006, ensuring adequate education spending in rural areas, while the administrative responsibility for education was moved to county or higher-level government according to the Compulsory Education Law. Furthermore, reducing rural-urban educational disparities and achieving more accessible and equal basic public education for everyone was emphasised by the National Medium and Long-term Educational Reform and Development (NMLERD) Plan Outline (2010-2020) in 2010. The funding of public schools in rural areas had shifted from local rural inhabitants to being a public-run education system, which was deemed beneficial to the long-term development of rural education (Rao & Ye, 2016).

Suspension of School Consolidation in Rural Areas
In the initial period of the establishment of the People's Republic of China (PRC), the number of primary and middle schools had increased dramatically in rural communities from 1949 (Rao & Ye, 2016). A principle of 'at least one primary school in each village, and one middle school in each town or township' was established in rural areas (Mei et al., 2015). In addition, plenty of education departments at the county level stipulated that schools should be built within 2.5 kms of a village, thus allowing pupils in rural areas to attend schools located near to their homes (Rao & Ye, 2016).
Since the 1980s, the number of school-age children in rural areas had decreased sharply due to the strict one-child policy, which was implemented in 1980 and ended in 2016, and the rapid urbanisation process (Rao & Ye, 2016). Due to a loosening of internal migration controls, many surplus rural labourers flooded into urban areas searching for work, often accompanied by their children seeking opportunities to study. Moreover, affluent rural families tended to send their children to urban schools to receive better education (Zhao & Parolin, 2014). Correspondingly, the Decision on the Reform and Development of Compulsory Education was issued by the State Council (2001), explicitly requiring that school plans and educational resources should be adjusted and integrated to improve the education quality of rural schools (Mei et al., 2015;Rao & Ye, 2016). After that, a policy of 'school consolidation', also referred to as Rural School Mapping Adjustment (Rao & Ye, 2016), was implemented by local authorities in 2001. The village-level schools which were Rural-Urban Educational Inequalities and Their Spatial… considered to be costly and inefficient were withdrawn or amalgamated and boarding schools were promoted in rural areas; accordingly, the location of primary schools shifted from within villages to townships and the locations of secondary schools changed from townships to counties (Rao & Ye, 2016). Simultaneously, there was more investment in merged schools to improve the teaching and physical conditions of these schools (Wang & Zhao, 2012).
The main objectives of school consolidation were to save costs, enhance administrative efficiencies and improve education quality in sparsely populated rural areas (Zhao & Parolin, 2014). However, a lot of problems transpired due to unreasonable school mergers and poor educational planning, such as wasted rural educational resources, oversized schools, long commuting distances for pupils and increased education-related financial burdens on rural families. In 2012, the school consolidation policy was suspended by the Ministry of Education (Mei et al., 2015).

Rural-Urban Classification
Before undertaking any analysis of rural and urban inequalities, the definition of what constitutes rural and urban education needs clarification. According to regulations about rural and urban divisions stipulated by the National Bureau of Statistics of the PRC, there are three area categories: urban; town (or county); and rural. The statistical definition adopted by the China Statistical Bureau (1999) indicates that 'urban' and 'town' both belong to the 'urban' category (Fu & Ren, 2010;Zhao & Parolin, 2014).
The maps in Fig. 2 display the spatial distribution of the proportion of the urban population in each provincial-level unit in 2005 and 2014. As the data for 2004 are not available from the China Statistical Yearbook, the data for 2005 are used for comparison with those for 2014. The proportion of the national population that was urban by the end of 2005 was 43% (Fig. 2a); by 2014, the national percentage had increased to 54.8% (Fig. 2b). However, this proportion varied significantly among different regions and decreased from coastal to inland areas. The urban population of Shanghai and Beijing accounted for 89.1% and 83.6% of their total populations respectively in 2005 and 2014, while that of Tibet was only 20.9% in 2005. By 2014, the proportion of the urban population in most regions was more than 40%, except for Tibet, where it remained relatively low at 25.7%.
However, the scope of rural education used in most of the official educational development reports, such as the Educational Statistics Yearbook, the report on national education development (Ministry of Education of PRC, 2016) and the Statistical Indicator System of China's Educational Monitoring and Evaluation (Ministry of Education of PRC, 2015), does not exactly coincide with the definition of rural areas based on the above rural and urban division. In these official education statistics, rural education refers to the education of 'big rural' areas, which includes education in rural areas and towns. Rural education is defined from the perspective of the service object; as only some of the primary schools are located in rural areas, the middle schools and high schools which also provide education to rural population are mainly located in towns or counties 1 even before school consolidation (Mei et al., 2015).
Secondly, due to a large number of village-level primary schools that were withdrawn or merged under the school consolidation policy, the location of a large number of primary schools moved from within villages to townships and secondary schools moved from townships to counties (Rao & Ye, 2016). Table 2 illustrates that the total number of primary and middle schools had decreased by 61.8% and 53.5% respectively in rural areas between 2004 and 2014, while the number of primary and middle schools in towns increased by 38.9% and 44.5% respectively. The number of high schools decreased both in rural areas and towns. Furthermore, the total rural primary school, middle school and high school pupil percentages were 32.3%, 17.1% and 3.3% respectively in 2014 (using the rural-urban division). These proportions of rural pupils are significantly lower than the percentage of the rural population (45.2%), which means many rural pupils were not studying in rural areas but in towns or urban areas. Consequently, rural education is regarded as education in rural areas and towns (counties) in this research, which is consistent with the rural-urban education division used by most educational statistics. 2

Education Attainment: Conversion Factors
As no time-series data are available on education attainment for rural and urban areas in each provincial-level unit in the Educational Statistics Yearbooks, the data used for assessing rural and urban education attainment disparities are derived from the fifth (2000) and the sixth (2010) population censuses. Given that only national-level data are available for use in comparing rural and urban education attainment in 2000, the temporal variation can only be compared at the Rural-Urban Educational Inequalities and Their Spatial… national scale. As mentioned in the above section, the data for 'rural' and 'town' are also combined to give values for rural areas. Figure 3 displays the composition of the population living in rural and urban areas in 2000 and 2010 according to academic qualifications. It is clear that there exists a large gap in educational attainment levels between rural and urban areas in both years. For example, in 2000, those who received education at senior secondary school (high school and vocational secondary school) and above (college, undergraduate and postgraduate) accounted for 36.1% in urban areas and only 9.3% in rural areas. Owing to the implementation of the Compulsory Law in 2006 and the Two Waivers and One Subsidy policy of NR (2005), the proportion of people with middle school and above qualifications had increased significantly in rural areas by 2010. However, the educational attainment in rural areas was still significantly lower than that of urban areas in 2010 and even lower in 2000. The supply of high-quality labour in rural areas remains insufficient; for example, only 4.1% of rural residents had achieved a college or graduate education in 2010, while the proportion was 21.5% for urban areas.
Another measure used to quantify the gap between rural and urban areas is the average years of schooling (AYS). In the 2000 and 2010 Census data, the average education duration was assumed as five years for those completing primary school ( p ), eight years for middle school ( m ), 10.5 years for high school and vocational secondary school ( h ), 14 years for college ( c ), 15 years for undergraduate ( u ) and 19 years for those completing postgraduate study ( po ). Pop i refers to population aged six and over in area i.The AYS in area i,V i , is calculated by the formula modified from Qian and Smyth (2008) as follows: (1)  The national AYS gap for rural-urban areas was 2.20 (urban: 8.31; rural: 6.11) in 2000, increasing to 2.39 (urban: 9.39; rural: 7.00) in 2010. Although many policies were introduced to try to narrow this attainment gap, the conclusion is that these policies failed to narrow the gap entirely between rural and urban areas. The provincial distribution of AYS in rural (Fig. 4a) and urban areas (Fig. 4b) together with the rural-urban AYS gap (Fig. 4c) follow a familiar pattern: educational attainment levels in provincial-level units to the north-east of the dotted line, which distinguishes north-east from southwest provinces, are generally better than those in provinces to the southwest of the line. Figure 4c reveals that the southeast coastal areas and the area to the north of Beijing have the smallest gap of AYS (e.g., 1.69 years in Fujian), while the less developed western inland areas have a relatively larger gap (e.g., 3.56 years in Tibet). When comparing maps in Fig. 4c with those in Fig. 2, the provinciallevel units with higher proportions of the urban population normally have a lower rural-urban education attainment gap and vice versa, except for Beijing and Shanghai. Although the AYS in rural Beijing in 2010 was the highest among all rural areas, for example, the rural-urban gap was still very high at 2.51 years.

Educational Provision
An examination of the differences in rural-urban education provision has been conducted from three perspectives: firstly, the financial resources committed to education by government measured by the per-pupil educational expenditure (PPEE) indicator; secondly, relative access of pupils to teachers for which the teacher-pupil ratio (TPR) is the indicator used; and thirdly, education quality as measured by teachers' professional ranks.

PPEE Variation between Rural and Urban Areas
As there are no separate PPEE data for urban areas, the rural and urban PPEE disparities will be revealed by comparing average PPEE for rural areas with the aggregate (i.e., average PPEE for all pupils in each provincial-level unit). Moreover, these data are only accessible for primary and middle school education; there are no rural PPEE data available for high school education. In 2004, the national ratio of the average PPEE for rural areas to that for all areas was 0.82 for primaries and 0.73 for middle schools. From 2004 to 2014, the PPEE ratio increased to 0.97 and 0.96 respectively; i.e., the PPEE of rural areas was only marginally lower than that of the national average in 2014. Thus, the gap in overall education investment between rural and urban areas was narrowing. Maps a-d in Fig. 5 3, 4 show the spatial and temporal variations of rural-urban educational gaps in PPEE. It is apparent that the PPEE in the majority of rural areas has increased dramatically from 2004 to 2014 owing to more investment from Central Government since 2001 and NR policy in 2005. The PPEE for primary and middle school education is higher than that of urban areas (rural-urban average) in most the provincial level units in 2014, while their educational fiscal investment in rural areas was significantly lower than urban areas in 2004.
However, there are still some rural areas with comparatively lower PPEE compared to urban areas (rural-urban average), which has been identified by dashed circles in maps 5b and 5d. The geographical patterns of the PPEE ratio for primary schools and middle schools show certain differences. PPEE ratios for primary schools were lower in some central areas in 2014, while the areas to the southwest of the dotted line still have lower ratios (map 5d) for middle schools in 2014. This may lead to rural education lagging further behind in these areas, which means more financial support is required for middle schools in the southwestern rural areas and for primary schools in the central areas.
Although PPEE ratios were very low in some developed areas, like Beijing and Shanghai, the rural PPEE in these areas was already greatly higher than the national PPEE (maps e-h in Fig. 5). For example, the ratio for primary schools was only 0.78 in Shanghai in 2014, however, the PPEE in rural areas of Shanghai was already 2.23 times that of the national average PPEE in rural areas (computed from data in the China Educational Finance Statistical Yearbook of 2014). This is because the local authorities in these developed areas normally had more funds for investment in urban education. Even though there was already quite a lot of educational investment in these rural areas, the PPEE remained relatively low compared to the extremely high urban PPEE. However, we find that most of the areas with lower PPEE in rural areas are also areas with lower rural-urban PPEE ratios in 2014 (dashed circles in maps 5f and 5 h). This indicates that more financial support is required in these rural areas.

Comparing Teacher-Pupil Ratios between Rural and Urban Areas
The teacher-pupil ratio (TPR) is a familiar indicator of education provision calculated by dividing the number of pupils by the number of teachers. 5 A higher TPR indicates that each pupil can expect more attention from teachers. Rural-urban TPR (RUTPR) is obtained by dividing the teacher-pupil ratio of rural areas by that of urban areas. In 2004, the RUTPR for primary (0.97), middle (0.85) and high schools (0.93) were lower than one, indicating that the TPR was higher in urban than rural areas in 2004. However, by 2014, the RUTPR values for primary (1.18) and middle schools (1.10) were higher than one, suggesting a higher TPR in rural areas. However, the RUTPR for high school remained below one (0.93) in both periods.
Maps a-d in Fig. 6 show that the RUTPRs have increased significantly in almost all provincial-level units from 2004 to 2014 for primary and middle schools. Most provincial-level units had a RUTPR of more than one in 2014 for primary and middle schools; that is, rural TPRs were higher than urban TPRs in these areas. However, the ratios in certain provincial-level units, such as Tibet for middle schools (0.88), were lower than one, which means significantly lower TPRs in the rural parts of these areas.
The change between 2004 and 2014 in the RUTPR for high schools is minimal and the values in most areas are still lower than one (map 6f) in 2014, although the TPRs in rural areas have been improved in most areas (maps 6k and 6l). The RUTPR in some provincial-level units like Tianjin, Shanghai and Ningxia decreased over the ten-year period. The lower TPR for high schools indicates that there is still a lack of sufficient input in terms of teachers for rural high school education. The most likely reason why the RUTPR for high school education is different from that of compulsory education (primary and middle school education) is that the children of migrants to the cities are not allowed to attend university entrance examinations locally (due to hukou restrictions) and are therefore forced to return to their hometowns to receive high school education.

Quality of Teaching
The quality of teaching can be measured using either the qualifications 6 obtained by school teachers or by their professional ranking. 7 A higher percentage of qualified teachers or of those with higher ranked professional titles indicates better educational quality, given that teachers' professional rank is based on the assessment of their educational background, teaching skills and professional accomplishments. Compared to teacher qualifications, teacher rank is a more comprehensive indicator and is also influenced by experience and years of working. Accordingly, the rural-urban higher professional rank ratio (RUPR) is used in this research to compare the proportion of teachers with higher professional rank in rural areas with that in urban areas.
The national RUPR values for primary, middle and high schools were 0.80, 0.64 and 0.79, indicating that there were significant rural-urban disparities for teaching quality in 2004, especially for middle schools. By 2014, these values have been increased to 0.93, 0.88 and 0.87 respectively for primary, middle and high schools. It demonstrates that the gap between rural and urban areas is shrinking, but the gaps are still considerable.
The maps in Fig. 7 show that the RUPR varies spatially for each education stage. Although the RUPR has increased from 2004 to 2014 for all provincial-level units. It is apparent that the high-quality education resources gap between rural and urban areas was still significant in the majority areas at all educational stages in 2014, especially in western regions indicated by the areas in dashed circles in the maps 7b, 7d and 7f.
Maps 7g-l exhibit the spatial variations in the percentage of qualified teachers in rural areas. These maps demonstrate that the high-quality teaching resources in western rural areas are relatively insufficient compared to central and eastern areas. In order to improve rural education in western areas, more efforts are required to increase the proportion of qualified teachers in these areas.

Discussions Based on Capability Approach and Policy Implications
From the reported results we find that the rural-urban education attainment gap has not been narrowed. This situation has occurred despite the fact that the overall PPEE and teaching quality in rural areas have increased significantly and the rural-urban gaps of PPEE and teachers' quality have narrowed considerably. Why has the educational gap between rural and urban areas not closed? Whereas it is hard to explain this using outcome-based or resources-based approaches, the analytical framework presented in this paper provides a feasible interpretation.
According to our analytical framework, education in each area is not only influenced by the available education resources (education provision) but also depends on conversion factors (Sen, 2001;Xiang et al., 2020). These conversion factors are crucial for educational capability, which will greatly impact the conversion effectiveness of education provision. As the educational foundation (attainment) in rural areas was lower in 2004, the conversion ability in rural areas will be lower than in urban areas even if the same amount of educational resource is provided. Thus, so as to reduce the rural-urban educational gap and allow people in rural and urban areas to enjoy the same chance of success in education, more resources should be allocated to rural areas compared to urban areas. If the Central Government continues to offer the same or a similar amount of resources to rural areas, the existing rural-urban gap cannot be narrowed. However, the overall educational provision, in terms of PPEE, teachers' qualification and teachers' rank in rural areas, is still slighter lower than that in urban areas in 2014. Moreover, there is still a long way to go to improve teaching quality in less developed rural areas. More measures should be conducted to improve the teachers' teaching skills and the teaching quality of existing teachers.
Except for the above implications, based on analyses in the above sections, more needs to be done to make further improvements and there are a number of other points for consideration.

High PPEEs and TPRs May Not Always Mean Improvement
It is worth noting that the high PPEE and TPR in rural areas may not always indicate education improvement in these areas. The increases in TPRs in rural areas for primary and middle school education may have occurred for various reasons including increased wages for rural teachers, the movement of pupils away from rural areas as part of the urbanisation process, and the large rural-urban gap in education quality which has encouraged more pupils to go to urban areas to receive education. If rural schools are losing students while the number of teachers and related expenses, like salaries, have not changed, this can also lead to higher PPEE.
The PPEE can be divided into three parts: personnel expenditure (e.g., teaching staff salaries and benefits, student subsidies and scholarships), public expenditure (e.g., official expenses, equipment purchases and repairs) and construction expenditure. Take Inner Mongolia as an example, the rural-urban PPEE ratio was 1.5 for primary schools in 2014. The ratios for the three parts were 1.64, 1.11 and 0.86 respectively. It is apparent that the high PPEE for Inner Mongolia primary school education occurs mainly because of high personnel expenditure; however, the construction costs in rural area are still lower than that in urban areas. In addition, the proportion of pupils living in rural areas decreased from 48% in 2004 to 14% in 2014 and a large number went to schools in towns or urban areas. So, the high PPEE for Inner Mongolia primary education may well be due to pupil decline rather than education improvement. Further analyses are needed to reveal the real stories behind the high PPEE.
In addition, although the PPEE has increased significantly in rural areas, a large proportion of government funding was spent on establishing and supporting boarding schools (e.g., accommodation costs). The extra spending on boarding schools in rural areas will decrease the investments associated with other aspects of rural education, which will greatly influence the efficiency of the conversion of educational inputs.

Increasing Accessibility to School
It is acknowledged that the economic context, the social context (including parents' cultural perspective on education), policies (e.g., school consolidation policy) and environmental factors (e.g., accessibility to schools) also affect the conversion of educational provision into valued capabilities. For example, due to school consolidation, the accessibility of education for rural pupils was considerably reduced. Additional costs of living and transportation, caregiving, and children's mental health problems were imposed on rural residents, and the economically disadvantaged groups in rural areas were even more vulnerable to these changes. Unreasonable consolidation led to a huge waste of existing education resources in some villages whereas certain merged schools were overburdened. A large part of the funds from the Central Government was used to adjust school layouts and to construct or extend boarding middle schools for rural pupils (Rao & Ye, 2016). The boarding schools have separated pupils from their parents and the local community, exacerbating disadvantage in rural areas, and more pupils from poverty-stricken families may have dropped out of education due to the growing inconvenience (Mei et al., 2015;Wang & Zhao, 2012). Although the State Council suspended the school consolidation policy in 2012, it is extremely hard to mitigate the negative impact of current school layouts on rural areas. Small rural schools play a very important role in delivering education in rural areas in China (Zhao & Parolin, 2014), therefore they should be retained and equipped with appropriate facilities to fulfil their roles. In addition, local rural residents should have more chances to participate in the decision-making process involving school consolidation.

Implementing Policies based on Macro-Economic Zones is not Reasonable
The financial support policies reported earlier were aimed at enthusing the redistributive capability of Central Government and playing an equalizing role. In general, the support policies of the Central Government have greatly improved educational provision with decreasing rural-urban differentials in expenditure per pupil. However, their policies are based on a crude area partitioning.
This research demonstrates for the first time the spatial variations in the rural-urban educational gap and their temporal evolution following the implementation of Central Government support policies. These patterns are different from the Government's crude area partitioning; it seems inappropriate to implement policies and allocate resources simply based on dividing China into three macro-regions; the specific developmental level of each area should be evaluated and the different needs of each area should also be identified. In addition, the development of different education stages also varies and therefore funding support should also take the specific developmental level of each education stage into consideration.

Providing Support for Neglected High School Education
In addition, neglected rural high school education will be one of the major obstacles to reducing rural-urban education in China. The funding and policy support from the Central Government only focuses on rural compulsory education, while high school education is not part of compulsory education in China. The results of the comparison of TPRs and RUPRs (quality of teaching) also reveal that provision of high school education in most rural areas is still lower than in urban areas. This indicates that the educational gap in high school education between majority rural and urban areas will be wider. Given that high school education is the bridge between compulsory and higher education, the rural-urban educational difference cannot be narrowed without eliminating/reducing the big gap in high school education.

Conclusion
This paper has reported the utilisation of an analytical framework for understanding and analysing rural-urban education inequalities. Compared to outcome-based evaluations, which ignore related context and the process, and resource-based approaches, which assume the same educational attainment will be achieved given the same amount of resources, the new analytical framework developed in this paper is a more comprehensive method to evaluate and explain education advantage and disadvantage. We suggest that this framework has a wider relevance for educational inequalities and assessment of other capability sets and our contributions are targeted at a wide-ranging audience including researchers, policy makers and practitioners and researchers. The paper has examined spatial variations of educational inequalities between rural and urban areas over time and evaluated the policies aimed at reducing rural-urban disparities. The rural-urban educational gap reflects the historical rural-urban socio-economic development differences, partly due to urban and efficiency priority strategies. Although the PPEE, TPR and teacher rank gaps between rural and urban areas have been reduced in this period, the overall rural-urban attainment gap has not been narrowed from 2000 to 2010. According to the capability-based analysis framework, the previous comparatively low education performance (education foundation), and the disadvantageous natural physical and social environment (e.g. parents' cultural perspective) in rural areas has led to low conversion rates in rural areas. Thus, even given the same education provision, rural areas will probably still achieve lower education attainment than urban areas. This suggests that only more investment in the education of children in rural areas can, de facto, eliminate the rural-urban gap.
Although the overall rural-urban educational gap in China has not been reduced, there are significant spatial variations in the rural-urban educational gap in terms of PPEE. The higher PPEE in rural areas in some provincial-level units has probably narrowed the rural-urban educational gap in these areas and vice versa. Therefore, the allocation of financial resources should be based on the specific developmental level of each area and the stage of education that each area has reached. Policy makers and researchers should use the two indicators, TPR and PPEE, with caution when assessing educational investment in rural areas. In addition, more attention should be paid to high school education in rural areas. Moreover, some of the closed rural schools or teaching posts should be returned to service to reduce the negative effects caused by the school consolidation policy. In summary, although some success has been achieved by the previous policies that have been implemented, more adjustments are needed to realise educational equity between rural and urban areas in China.