International testing, such as TIMSS and PISA, has made the comparison of countries’ academic performance an integral part of determining national educational policies (Long 2014). However, some authors argue that the country’s international rating may overshadow spatial differences in academic outcomes within the country that could be significant. For example, the score difference in PISA-2015 among US states corresponds to several years of schooling (Carnoy, Garcia, and Khavenson 2015). 
On the one hand, the difference in academic performance between regions in the country can be explained by their access to educational resources: curricula, human resources (HR), funding. For example, even within one US state, the differences among schools regarding their funding and teachers’ experience can result in a significant difference in academic performance (Jimenez-Castellanos 2010). On the other hand, unequal access to resources can correlate with regional socio-economic inequality. For instance, in Chile, most children in less urbanized communities, with a lower SES and lower density attend municipal schools, whereas students from more privileged regions largely enroll in private schools, which provide better quality education (Larrañaga, Peirano, and Falck 2009).
Although regional differences could overcome the international ones, the spatial dimension has not become a focus of sociological concepts aimed at explaining education attainment and outcomes. In our paper, we examine the concepts of Maximally Maintained Inequality (MMI) and Effectively Maintained Inequality (EMI). Both of them were worked out to explain inequality in access to education on different levels. However, inequality is attributed to social factors such as cultural, economic, or social capital (Raftery and Hout 1993; Hout 2006; Lucas 2001, 2009, 2017). We contribute to the literature testing whether regional differences in access to education and educational outcomes could be explained by these theories. Thus we add a spatial dimension to EMI and MMI concepts.
Our second contribution relates to examining the MMI and EMI theories on the case of Russia as a federal country with a large number of regions. Russian data are of special interest to the sociology of education as they allow us to study how educational resource distribution at the regional level correlates with significant socio-economic and demographic inequality. In Russia, socio-economic differences between regions are comparable to international ones. For example, the GRP per capita in the richest Russian regions is 17 times higher compared to the poorest ones (World Bank, 2018). In terms of economic development, some regions are comparable to Singapore and the Netherlands, while others are similar to Bolivia and Honduras (ibid). These and other significant differences make it interesting to assess the relationship between them and students’ choice of educational track and academic performance in different regions.
This paper investigates the ways in which regional differences in socio-economical and demographic indicators are related to access to educational resources, as well as how these characteristics relate to a share of students who have chosen the academic track after completing lower secondary school and to a regions' average scores in school graduation tests. For these aims, we have collected the unique dataset of Russian regions’ socio-demographic and economic characteristics, and indicators of school systems for 83 Russian regions. We focus on the cohort of upper secondary school graduates (11th-graders) of 2016.
Our third contribution to the literature relates to the research methodology. In our paper, we compare the traditional approach with spatial econometrics analysis which we apply to control for potential neighbor effects on the track choice and academic results. Altogether such a comparison allows us to gain more accurate estimates.

The analysis is done in three steps. First, we analyze how characteristics of regional school resources correlate with socioeconomic and demographic indicators using a series of Pearson pair correlations. Second, we assess the relationship of educational resources and the socio-demographic context in the regions with the share of students that chose the academic track after completing the 9th grade in 2014. Third, we analyze the relationship between regional characteristics and regional average USE scores in Mathematics and in Russian after students finished upper secondary school in 2016. In steps two and three, we apply regression analysis and spatial econometrics analysis. Earlier studies while taking into account spatial characteristics of education attainment usually use variables that denote the type of settlement (e.g. Gerber 2000; Khavenson and Chirkina 2018; Hao, Hu and Lo 2014) or distance to the nearest college, school, or regional center (Francesconi, Slonimczyk, and Yurko 2019). However, this approach to the analysis with regional data assumes potential estimation biases for neighbor effects and spillovers (Manski 1993). Using regions with certain borders and locations in space as observation units demands to apply spatial econometric analysis which helps to reduce potential biases and thus to gain more accurate estimates (Anselin 2013; Hillman 2017). Taking this into account, in our research we compare traditionally used Ordinary Least Squares (OLS) estimates with the results of spatial econometrics analysis - Spatial Autoregressive Model (SAR) and Spatial Error Model (SEM). Our analysis imposes some limitations on the interpretation of the results. In particular, our research aim is to analyze inequality at the regional level. The variance of indicators within regions is out of our focus. Another limitation is related to the endogeneity problem. Regression coefficients provide unbiased causal estimates under a strict assumption that there are no unobserved characteristics that correlate with both our predictors and outcomes. We control for socio-demographic characteristics of the regions that help to reduce endogeneity bias.

Our results can be explained by both MMI and EMI theories. The choice of the academic track after grade 9 mostly depends on regional indicators for human capital and the level of urbanization, rather than on institutional educational resources. Altogether this is consistent with the findings of other studies that show that in Russia, the choice of education largely depends on students’ social background. From MMI perspectives, our findings might mean that demand for upper secondary school is still not saturated for higher SES families which are unevenly distributed in Russian regions. MMI and EMI are equally applicable here. However, MMI regards the choice of the vocational track as an option equal to drop out from education while EMI considers the transition to academic or vocational tracks as the attainment of education of different types (or qualities) and thus is more preferable. The spatial approach to EMI and MMI theories sheds light on the other side of educational transitions. We don’t have significant spatial lag for an academic track choice means that enrollment in upper secondary vs vocational schools does not depend on a region’s location. In other words, this choice is being made based on social but not spatial characteristics. Spatial inequality here is explained by social factors. Contrary to a track choice, we find significant spatial lags for USE scores. This proves the existence of groups of regions with shared borders (or neighboring regions) with similar performance. It could be regarded as a sort of stratification of regions by educational outcomes. Spatial inequality here exists as an independent dimension, which could not be explained only with social characteristics or resource distribution. As USE outcomes are used to distribute students to more or less selective universities (qualitative dimension of education), this conclusion supports EMI.

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