Education as a dimension of human development: A Provincial-level Education Index for Ecuador

RESEARCH ARTICLE Education as a dimension of human development: A Provincial-level Education Index for Ecuador Marta Guijarro-Garvi1,2, Bele´n Miranda-EscolarID2,3*, Yira Tatiana Cedeño-Mene´ ndez4, Pedro Benito Moyano-PesqueraID2,3 1 Department of Economics, University of Cantabria, Santander, Spain, 2 Economics and Public Policy Research Group, University of Valladolid, Valladolid, Spain, 3 Department of Applied Economics, University of Valladolid, Valladolid, Spain, 4 Faculty of Economics, University Eloy Alfaro of Manabı´, Manta, Ecuador * belen@eco.uva.es Abstract This article deepens in the differences in educational development between the Ecuadorian provinces and in their evolution over time by estimating the Provincial-level Education Index. This index is built using the micro-databases of the two latest rounds of the Ecuador‘s Living Standards Measurement Survey (2005–2006 and 2013–2014). The results show an overall increase in the educational development of the Ecuadorian provinces, as well as a slight reduction in inequality. However, differences between them continue to exist. Underly- ing our results, which are consistent with the provincial production structure and socioeco- nomic context, some public policies seem to affect the educational sector, as their impact has been evidenced during the period covered in this research. Introduction In its first report on the Human Development Index, published in 1990, the United Nations Development Programme (UNDP) considered health, education, and income as the three key

dimensions of human development. Also, the Human Development Index (HDI) as a “more genuine measure of socioeconomic progress” [1] was presented in said report. As does the human capital approach [2–7], the human development approach considers that education enhances the capital incorporated into the production process. In addition, educated individu- als obtain a greater monetary return, since, due to the close link between real capital and the formation of human capital, education increases productivity [8]. Generally, more years of schooling leads better paid jobs, lower risk of material deprivation, and higher levels of subjec- tive well-being [9]. Furthermore, education can be related to health through three interacting pathways: acquired health knowledge and its application in daily life; employment and income, and social and psychological factors, including sense of control and social status [10]. In general, people that have received more years of education have longer life expectancy and better PLOS ONE PLOS ONE | https://doi.org/10.1371/journal.pone.0270932 July 8, 2022 1 / 27 a1111111111 a1111111111 a1111111111 a1111111111 a1111111111 OPEN ACCESS Citation: Guijarro-Garvi M, Miranda-Escolar B, Cedeño-Mene´ndez YT, Moyano-Pesquera PB (2022) Education as a dimension of human development: A Provincial-level Education Index for Ecuador. PLoS ONE 17(7): e0270932. https://doi. org/10.1371/journal.pone.0270932 Editor: Simona Lorena Comi, University of Milano– Bicocca: Universita degli Studi di Milano-Bicocca, ITALY Received: January 16, 2022 Accepted: June 21, 2022

Published: July 8, 2022 Copyright: © 2022 Guijarro-Garvi et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability Statement: All relevant data are within the article and its Supporting Information files. Funding: “Programa de Perfeccionamiento del Personal Acade´mico de la Universidad Laica Eloy Alfaro de Manabı´ ULEAM de Ecuador” (Development Programme for Academic Staff of the Eloy Alfaro Lay University at Manabı´ ULEAM in Ecuador) to take the Interuniversity Doctorate Programme in Economics at the Universities of

health, as they adopt healthier lifestyles −such as regular physical exercise, refraining from smoking, and undergoing regular medical check-ups [11, 12]. Education is also a right which was established in 1948 by the United Nations Universal Declaration of Human Rights [13]. Moreover, it is a key factor for improving people’s qual- ity of life. In addition, amongst other targets, the fourth Sustainable Development Goal (SDG) seeks to ensure that every child completes free primary and secondary education by the year 2030. This goal also aims to provide equal access to attainable technical training, eliminating gender or income-related disparities, and achieving universal access to quality higher education. Furthermore, education is behind the accomplishment of many other SDG, such as eradicating poverty–given that one of its many expressions concerns the diffi- culty of access to basic services such as education–and reducing inequality through greater investment in education [14]. As a result, education is widely recognized as an instrument which can help people to overcome poverty [15], improve their well-being and curb their dependence on social protection programs [16–18]. Income and work status depend on the level of schooling achieved, so breaking the continuing income inequality is essential to reduce inequality in education. It is therefore necessary to promote more equal access to the quantity and quality of education [7]. The Buen Vivir (Good Living) approach is grounded on the paradigm of human develop-

ment [19]. Indeed, it goes further by placing collective well-being above individual well-being (see, e.g., [20]). Most of its many meanings agree that the origin of Buen Vivir lies in the culture of the indigenous peoples and that equality and environmental sustainability are core princi- ples [21]. Buen Vivir–or sumak kawsay (in kichwa)–is a multidimensional concept [22] enshrined in the 2008 Ecuadorian Constitution [23], with equity being one of its principles [19]. The Ecuadorian policies of Buen Vivir are reflected in the Planes Nacionales de Desarrollo (National Plans for Good Living), which are the principal mechanisms of national political management [24–26]. These policies are geared towards bolstering individuals’ capabilities and potential by considering access to education as one of the central dimensions of well- being [27, 28]. The values of the Human Development Index (HDI) in Ecuador and, more specifically, those related to its education index increased between the years of the study (from 0.600 in 2006 to 0.695 in 2014) [29]. Thereby, they evidenced an improvement in educational well- being in Ecuador over the period analyzed. However, both the HDI and its dimension indices are national averages and therefore mask inequalities in the level of well-being within a coun- try [1]. Interterritorial inequalities are related to factors that heighten the inequalities between individuals or social groups, and they might also be linked to social conflicts. This is especially

true in the presence of weak political regimes [30], with the consequent deterioration of social cohesion [31]. This justifies the exploration of such inequalities at the subnational level [32]. Our work is in the line of research adopted by works that have estimated HDI values for differ- ent population subgroups [33–38]. Furthermore, understanding these differences will serve as a starting point for the achievement of SDG 10, i.e. the reduction of inequality within and between countries. In Ecuador, the “horizontal” inequalities between groups that have been established for cultural reasons [39] only exacerbate the risk of poverty and social exclusion. This is partic- ularly remarkable amongst the indigenous and Afro-descendant populations [40–42], as well as between the different areas of the country. Ecuador has four regions, three of which are continental (Costa, Sierra, and Amazonia). In contrast, the fourth region, the island region of the Galapagos archipelago, is on the Pacific Ocean. In turn, the regions are divided into provinces, which are the first-level political-administrative units. The geographical location of the population may stifle the academic achievement of children and youngsters, PLOS ONE Education as a dimension of Human development PLOS ONE | https://doi.org/10.1371/journal.pone.0270932 July 8, 2022 2 / 27 Valladolid, Salamanca, and Burgos (Spain). Research project 061/092242 of the Fundacio´n General de la Universidad de Valladolid (General Foundation of the University of Valladolid). The funders had no role in study design, data collection

and analysis, decision to publish, or preparation of the manuscript.” Competing interests: The authors have declared that no competing interests exist.

leading them to fall behind or leave school early, since not all the provinces are able to offer the same educational quality (poorly qualified teachers) or adequate school infrastructures (difficulties regarding access, electricity, drinking water or sanitation). Moreover, the situa- tion of child labor in those provinces whose productive specialization and the nature of the local labor market increase the opportunity costs of education must be considered. Finally, ethnic and linguistic fragmentation–which is unequally distributed throughout the various provinces–is a major challenge for the Ecuadorian education system, as it is results in a need to take account of the idiosyncrasy of children in the different areas of the country and to guarantee education in indigenous languages, as a first language, and in Spanish, as the language of intercultural relations [43, 44]. Given that one of the priorities of Buen Vivir is the reduction of inter-territorial inequalities [45], the analysis of these inequalities will provide a key tool for decision-making [46]. Thus, this paper provides information on the educational dimension of human development in the Ecuadorian provinces and its evolution over the period covered by the last two rounds (2005– 2006 and 2013–2014) of the Ecuadorian Encuesta de Condiciones de Vida (Living Standards Measurement Survey, or LSMS). For this purpose, a Provincial-level Education Index (PEI) is calculated by using the micro-databases from these two latest rounds of the LSMS. The Ecua-

dorian LSMS is a household survey that offers a multidimensional concept of individual well- being which is in line with the human development paradigm underlying the HDI. However, data provided by a LSMS must be converted into information [47]. In the context of this research, measuring a country’s educational development requires the interpretation of data based on its educational reality. Thus, to carry out this measure, we must consider the struc- ture of the national education system of Ecuador in its latest reforms, focusing on the period covered in the two rounds of the LSMS. Furthermore, for a correct interpretation of provincial differences, we need to explore our understanding of Ecuador’s educational reality within the territorial context of the country. To obtain the PEI, we first estimate the variables mean years of schooling and expected years of schooling for each Ecuadorian province. Secondly, we combine these indicators fol- lowing the UNDP method for obtaining the education component of the HDI. The result is a comparable index that provides insight into the level of educational development of Ecuador- ian provinces. In particular, the PEI allows us to situate this level of educational development in the context of Latin American and Caribbean (LAC) countries with an upper-middle income level such as Ecuador. Finally, we estimate the level of Ecuadorian educational inequal- ity in 2006 and 2014, as well as the contribution of each component of the PEI and of each Ecuadorian province to this inequality.

Although our results indicate an increase in the educational development of Ecuadorian provinces and a slight reduction in inequality, there are still differences between provinces. Our findings are consistent with the provincial socio-economic context and show the effects of certain education policies. Given that the methodological structure of the Ecuadorian LSMS has remained unchanged since its first round, it is to be hoped that the procedure put forward to estimate the PEI might be replicated in future rounds. Thereby it will enable us to extend current knowledge on the distribution of education in Ecuador at a provincial level and thus help public authorities to take more effective education policy decisions. It is worth noting that LAC countries conduct continuous household surveys that provide information on different aspects of the country’s well-being and some of them conduct LSMS on a continuous basis. Therefore, the present research could be used as a guide for obtaining educational development indices at the subna- tional level in other LAC countries. PLOS ONE Education as a dimension of Human development PLOS ONE | https://doi.org/10.1371/journal.pone.0270932 July 8, 2022 3 / 27

2. Ecuador in the context of Latin American and Caribbean education policies Most of the education policy reforms that have been implemented in LAC countries in recent decades have revolved around three axes [48–51]: (i) institutional reforms aimed at causing changes in the management and functioning of the education system, promoting decentraliza- tion in decision-making, granting more autonomy to schools, and encouraging local and fam- ily participation in educational activities; (ii) improvements in quality and equity,–mainly in schools and social sectors with lower incomes and academic performance–, through free text- books, school materials and uniforms, investments in school infrastructure and teaching mate- rials, and improvements in teacher qualification and training, and (iii) new funding sources aimed at improving the efficiency and effectiveness of public spending on education: educa- tion vouchers, special funds for the allocation of resources based on academic achievement and/or the number of students enrolled, and grants for children coming from vulnerable fami- lies with scarce socioeconomic resources. Despite the efforts made, diagnoses of the educational situation in the region show that there are still problems that need to be solved in terms of quality, equity, and efficiency. Although decentralization has improved educational coverage and allowed greater participa- tion of parents and local communities in the functioning of school life, learning outcomes are much less encouraging [48, 50, 52]. These shortcomings may lie behind the absence of

accountability policies and standards-based reforms, which introduce elements that have tra- ditionally existed in other education systems–such as school inspection and external evalua- tion of learning outcomes, from which guidelines for school improvement can be derived–, especially in Europe and North America [53]. Although these processes have been in place for years in some LAC countries, such as Colombia and Chile [54, 55], the lack of reliable information and appropriate indicators has limited their widespread incorporation. To this should be added the consequences associated with the procedures that aim to achieve higher quality in teaching by assigning rewards and sanctions based on individual performance. However, given the large differences in educa- tional resources and in student composition (different ethnicities) between schools (rural vs. urban), as well as the complex nature of the educational process itself, it is very difficult to determine the net effect in each case. Therefore, rewards and sanctions can often be unfair, affecting not only the equity but also the productivity of the mechanism itself [56]. Neverthe- less, many of the education reforms that have been implemented in the region in recent years have moved in this direction. Ecuador’s educational problems are no different from those of other LAC countries, with high repetition and dropout rates as two characteristics of the education systems in the region [56, 57]. Also, poor academic achievement should be added to these phenomena [40–42].

These problems were behind the successive educational reforms implemented by Ecuador in recent decades. Among them, the 1983 Ley Orgánica de Educación (Education Act, or LOE) [58] should be highlighted. This Act, together with the Reglamento General de la Ley Orgánica de Educación (General Rules of the Education Act) in 1985 [59], set out the structure of the non-university education (S1 Table). In the belief that education is one of the most effective means of preventing hereditary pov- erty, the Ecuadorian government designed and promoted the first Plan Decenal de Educación (Ten-Year Education Plan) 2006–2015. The reforms stemming from the Ten-Year Education Plan were first conducted in 2009, modifying the levels of general basic education and, subse- quently in 2011, with the first curricular reform of the general unified Baccalaureate. These reforms were consolidated through the approval of the Ley Orgánica de Educación Intercultural PLOS ONE Education as a dimension of Human development PLOS ONE | https://doi.org/10.1371/journal.pone.0270932 July 8, 2022 4 / 27

Bilingüe (Intercultural Bilingual Education Act, or LOEI) in 2011 [60]–last amended in 2021 [61]–which is currently in force. Schooled education consists of three levels: Initial Education, General Basic Education, and Baccalaureate (S2 Table). The major changes which the LOEI brought into non-university education were that Primary Education (six years) and Lower Sec- ondary (three years), from the previous system, became the ten-year General Basic Education by also including one further year, corresponding to Basic Preparatory Education. This latter educational level ceased to be optional after the approval of the LOEI and, in turn, Diversified Secondary Education (three years) came to be known as Baccalaureate (S1 and S2 Tables). In the field of university education, reforms were set out in the Leyes Orgánicas de Educa- ción Superior (Higher Education Acts, or LOES) of 2000 and 2010 [62, 63]. More recently, in 2018,–although outside the period analyzed in this paper–the Ley Orgánica Reformatoria a la Ley Orgánica de Educación Superior (Reform Act) was approved [64]. These reforms have mainly affected institutions that conform the national higher education system, in an effort to bolster it and ensure equal opportunities for students. Moreover, the duration of studies was also extended, now ranging from two years for full-time students in the High-level Technician Degree (increasing the number of teaching hours from 1,950 to 3,200) to six years for the Degree in Human Medicine. Postgraduate studies (Master’s Degrees) have a minimum dura-

tion of one and a half years (three semesters or other periods equivalent to 48 weeks) and they may entitle admission to a doctoral program. The PhD programs lasts a minimum of six semesters and a maximum of fourteen, plus two grace periods. Along with these reforms, other policies that may have contributed to the improvement of Ecuador’s educational development, such as the Bono de Desarrollo Humano (BDH), should be considered. The BDH is a conditional cash transfer (CCT) program whose origin lies in the Bono Solidario of 1998 [65, 66]. CCT programs were implemented by LAC countries at the request of international organizations between the end of the past century and the start of the 21st century. One of its main tools was the payment of a cash transfer conditional upon univer- sal access to social services in health and education [67, 68]. These programs, which were key symbols in poverty reduction [69], consider education as a vital factor in human development [70]. The BDH is part of the poverty eradication policy foreseen in the National Plans for Good Living, acting in close collaboration with the Ten-Year Education Plans. In fact, the BDH’s objectives included fostering school reinsertion and ensuring continued school attendance of children and adolescents [71]. Initially, co-responsibility in education was applied to selected families with children between the ages of 6 and 16. Throughout its over twenty years of existence, the BDH has undergone several changes which have affected,

among other things, criteria for selecting beneficiaries and the amount of the transfer. The lat- est reform of the BDH in 2019 adds to the fixed amount of USD 50 per month transferred to the heads of beneficiary households in extreme poverty, an additional variable component depending on the number and age of children under 18 years old. In this vein, the maximum amount that the monthly cash transfer can reach by adding the fixed and variable components is USD 150 [72]. This is the line followed by some studies that consider that a differentiated cash transfer according to the level of poverty (higher for the poorest), the age of the children (lower for the youngest) and the ethnic group (higher for indigenous and Afro-Ecuadorian children) is essential [41]. Data and methods Data: The Ecuadorian Living Standards Measurement Survey Since the 1990s, there has been a considerable increase in the availability and robustness of national household surveys in LAC countries. Moreover, the subnational nature of many of PLOS ONE Education as a dimension of Human development PLOS ONE | https://doi.org/10.1371/journal.pone.0270932 July 8, 2022 5 / 27

fesional (Professional Training Service), whilst the following rounds were implemented by the Instituto Nacional de Estadística y Censos (National Department of Statistics and Census, or INEC). Since its first round in 1994, the LSMS was designed to gain an insight into the distri- bution of the population’s well-being and to glean information on the impact of the measures of macroeconomic adjustment and government programs aimed at reducing poverty. In fact, the general objectives of the Ecuadorian LSMS are aligned with the logic of Buen Vivir, provid- ing the necessary tools to implement policies that contribute to the elimination of population inequalities. Furthermore, due to its methodological design, the LSMS is a fundamental statis- tical instrument in the study of the living conditions of the Ecuadorian population [78]. As the aim was to also obtain an updated baseline to measure compliance with the United Nations Millennium Development Goals [79], the LSMS provide information concerning the different aspects and dimensions of well-being in Ecuadorian households, which constitute the units of information (the methodology used in this survey may be seen in [78]). The multidi- mensional concept of individual well-being offered by the Ecuadorian LSMS in line with the human development concept of the HDI and its intermediate indexes makes it the most suit- able household survey for the study of educational development in the Ecuadorian provinces. To measure Ecuadorians’ quality of life, the variables considered in the LSMS are classified

into sections. In particular, the section devoted to the educational dimension of human devel- opment aims to ascertain the level of literacy among the population, the level of non-atten- dance or household spending on education, among other aspects. The micro-databases of the fifth round (2005–2006) and the sixth round (2013–2014) of the Ecuadorian LSMS used in this paper contain information on 55,666 and 109,694 individuals, respectively [80, 81]. The two rounds of the LSMS adopt a similar methodology in terms of the structure of the questionnaire, the variables used, and the treatment given to the information by the executing entity, which endows the results obtained with a high degree of reliability. Both surveys offer national, regional, and provincial representativeness [78, 82]. Their method- ology is based on the expansion factor of each individual surveyed, defined as the inverse of the probability of choosing a household and its members in each province [78, 82]. This method allows the indicators derived from their use to be generalized to the population repre- sented in the survey [78] and avoids the problem of missing values in certain household sur- veys (see, for example, [83]). PLOS ONE Education as a dimension of Human development PLOS ONE | https://doi.org/10.1371/journal.pone.0270932 July 8, 2022 6 / 27

Educational development in Ecuador’s provinces: The Provincial-level Education Index and its components Our use of the micro-databases of the two rounds of the Ecuadorian LSMS was established on a selection of identification and education variables of the population surveyed. This enabled us to estimate the indicators that make up the PEI for Ecuadorian provinces, following the method for the education index of the HDI applied by the UNDP since 2010. These indicators, which respectively reflect a population’s levels of both current and future education, are mean years of schooling (MY) and expected years of schooling (EY) [84]. Based on the UNESCO definitions [85], both indicators are felt to be of interest by the INEC within the educational dimension of well-being [86]. Thus, for each province, we obtained the MY indicator as an average of school years studied by the population aged 25 or over: MY ¼ X j j � nj N where nj is the number of individuals with j years of education out of a total of N individuals aged 25 and over. Undoubtedly, this indicator was the most difficult to estimate given that different education systems have existed (still exist) in Ecuador at the same time, due to the enactment, withdrawal and, on occasions, intertwining of successive reforms. It should therefore be remembered that those people surveyed might have gone through one education system, another, or indeed both. This complex scenario is further compounded by the fact that neither of the two rounds of the LSMS offers a direct question addressing the number of years an individual has spent in

the education system, forcing us to merge various answers from each respondent to obtain the required information. S3 and S4 Tables sum up the main aspects of the procedure undertaken to estimate the mean years of schooling indicator for each province using the fifth and sixth round of the LSMS, respectively. The first column of each table specifies the possible answers to the ques- tion in the questionnaire concerning the “highest level of education attended or completed” which, together with the “highest year of education passed” (second column of both tables), provided us with a base from which to obtain the number of years of schooling of the respon- dent. The third column sets out the maximum number of years an individual attended school, according to the level of education indicated in their answer to the previous questions. The last column contains the rest of the questions used, in addition to some of the technical issues we considered when interpreting certain answers. Finally, to estimate the mean years of schooling indicator, we multiplied the number of years of schooling of each individual by the expansion factor. To estimate the EY indicator for each province, we followed the definition proposed by the INEC to calculate this indicator at a national scale [78, 82]. To do this, we added the atten- dance (or enrolment) rates for each age between 5 and 17, together with the corresponding gross attendance (or enrolment) rate for the 18–22 aged group multiplied by five: EY ¼ X 17 j¼5 uj vj þ X 22 j¼18 uj X 22 j¼18 vj � 5 PLOS ONE

Education as a dimension of Human development PLOS ONE | https://doi.org/10.1371/journal.pone.0270932 July 8, 2022 7 / 27

where uj is the number of individuals of age j enrolled out of a total of vj individuals. Finally, we applied the expansion factor to each individual enrolled in each age group. We estimated the PEI for the provinces of the regions: Sierra (Azuay, Bolı´var, Cañar, Carchi, Cotopaxi, Chimborazo, Imbabura, Loja, Pichincha, and Tungurahua); Costa (El Oro, Esmeraldas, Guayas, Los Rı´os and Manabı´), and Amazonia (Morona Santiago, Napo, Pastaza, Zamora Chinchipe, Sucumbı´os and Orellana). We did not take into consideration the single- province region of Galapagos due to a lack of representativeness in both LSMS [78, 82]. Although the fifth round of the LSMS is only representative at the regional level for Amazonia, we estimated the PEI for its provinces for this round as well. Sometimes it is not possible to find representative samples of the population, which raises the dilemma between the desire to obtain more accurate results–whose reliability could be statistically evaluable–, and the prac- tice of calculating less accurate results [87]–which allow us to approach the reality to be ana- lyzed–. In this study, we critically evaluated this particular context [88] and opted for the second option. Therefore, we were cautious in interpreting the results for these Amazonian provinces when they referred to the fifth round of the survey. Processing the information at a provincial level involved identifying the codes of the coun- try’s territorial divisions. This was by no means a trouble-free procedure, as in 2007 the prov-

ince of Santo Domingo de los Tsachilas (hereafter Santo Domingo) and in 2008 the province of Santa Elena were created, which did not exist in the fifth round of the LSMS, and whose populations belonged to Pichincha and Guayas, respectively [89]. The creation of new politi- cal-administrative units affects the construction of chronological series of socioeconomic indi- cators for the various spatial levels. These new units, which tend to be established based on a grouping of smaller units, as is the case here, change the previously existing boundaries and make spatial standardization of the time series even more difficult. Consequently, with a view to drawing comparisons between the PEI values for 2006 and 2014, it was necessary to calcu- late a “combined” value of the estimations for each of the education indicators. These estima- tions were made using the micro-databases from the sixth round for Pichincha and Santo Domingo, on the one hand, and for Guayas and Santa Elena, on the other. In order to obtain these values, we used the means estimation procedure in the stratified sampling, taking the ini- tial estimations of the values of indicators in the four provinces and using, for this case, the weightings determined by the corresponding population ratios obtained from the 2014 popu- lation forecasts [90]. To validate our results, we compared our provincial estimations of the mean years of schooling indicator, in 2014, to the information offered by the Secretaría Nacional de Planifica-

ción y Desarrollo (National Department of Planning and Development, or SNPD) [91] on this variable at a provincial level for said year, which was also obtained from the microdata of the sixth round of the LSMS. This is the only information from official statistics for Ecuador that may be deemed “homogeneous” vis-à-vis drawing comparisons. In any case, the mean years of schooling provided by the SNPD was estimated on the population aged 24 and over, which does not allow comparisons with UNDP data, unlike the methodology proposed in this paper. Given that the estimations were conducted on different population groups, we used the Spear- man´s rank correlation coefficient to compare the classifications determined on the provinces both by our estimations and by those from the SNPD in order to assess the validity of our results. Moreover, and bearing in mind that the SNPD statistics offer data for Santo Domingo and Santa Elena, we included the estimations of the indicator for these provinces in said analy- sis. The estimated value of the coefficient equal to 0.99 and statistically significant at the 1% level is indicative of near perfect concordance between the classifications given by the two indi- cators and therefore evidences the consistency of our estimations. Furthermore, there are no official statistics for the expected years of schooling indicator at a provincial level in Ecuador. PLOS ONE Education as a dimension of Human development PLOS ONE | https://doi.org/10.1371/journal.pone.0270932 July 8, 2022 8 / 27

Having estimated the education indicators for each province, we transformed both indica- tors into normalized indices between 0 to 1 by the UNDP goalposts used since the 2014 Human Development Report: minimum of 0 years for both indicators, and maximum of 15 and 18 years for mean years of schooling and expected years of schooling, respectively [92]: MYSi ¼ MYi 0 15 0 EYSi ¼ EYi 0 18 0 where MYSi and EYSi are the mean years of schooling and the expected years of schooling nor- malized indices for province i, respectively. For each province, i, we calculated its PEIi as the arithmetic mean of the normalized education components (i.e., (MYSi + EYSi) / 2). This is the methodology used by UNDP to obtain the education index of the HDI since 2014 [92]. PEIi ranges from 0 (minimum level of educational development) to 1 (maximum level of educa- tional development). Applying the same method of estimating the PEI that the UNDP uses to construct the educational component of the HDI allowed us to “situate” the level of educa- tional development of Ecuadorian provinces in the international context. More specifically, it enabled us to compare Ecuador‘s educational well-being to that of LAC countries with similar socioeconomic characteristics. In this sense, to illustrate the spatial distribution of Ecuadorian educational development, we took as a reference the classification by quartiles corresponding to the PEI of Ecuadorian provinces in 2014. We used the quartile ranking because it is the procedure adopted by UNDP

to rank countries according to their level of human development based on their HDI values (low, medium, high, and very high) [93]. It should be mentioned that the HDI is meant to order geographic units, allowing comparisons between countries and between different time periods. Therefore, what is important is not so much the value of the HDI in a given country, but its rank or order number in relation to the rest of the countries. This is equally valid for each of the intermediate indexes that compose the HDI, such as the education index. To complete the above information, we determined the level of educational development of each province compared to that of the countries with available information for 2014 in the UNDP database [29] Thus, following the aforementioned UNDP methodology for its HDI, we calculated the first, second and third quartiles, respectively, of the HDI education index distri- bution for 2014. These quartiles are the thresholds that allowed each province to be classified according to its level of educational development. Statistical analysis of Ecuadorian educational inequality across provinces We explored whether the provinces with the lowest educational development in 2006 were the ones that grew the most between 2006 and 2014. To see whether this convergence process occurred, we estimated the Spearman‘s rank correlation coefficient, ρ, between the ranking of the provinces determined by their PEI in 2006 and that given by the annual mean variation of the PEI between 2006 and 2014 [94, 95], and we replicated this analysis for the two compo-

nents of the PEI. To analyze the significance of the results we used the statistic t ¼ r � ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðN 2Þ= 1 r2 ð Þ p , where N is the number of provinces; assuming no concordance between rankings, this statistic follows a t-distribution with N—2 degrees of freedom. To quantify the inequality in Ecuador’s educational development across provinces and to gain an insight into its evolution over the period analyzed and the contribution of each compo- nent of the PEI makes to overall educational inequality, we used the square of the coefficient of PLOS ONE Education as a dimension of Human development PLOS ONE | https://doi.org/10.1371/journal.pone.0270932 July 8, 2022 9 / 27

variation, CV2. This choice is due to the simplicity of this measure in terms of calculation and interpretation and because it offers the desired properties of a measure of inequality (for a review of measures of inequality and their properties, see e.g. [96]), one of which is the possi- bility of its additive decomposability by factors [97]. As is well known, the square of the coefficient of variation of PEI, CV2 PEI, is equal to s2 PEI=m2 PEI where s2 PEI and m2 PEI are, respectively, the variance and the square of the mean of the PEI. The closer the value of CV2 PEI is to zero, the lower the educational development inequality. Conversely, since this coefficient is not upper bounded, the larger its value, the greater the inequality. Considering that PEI = (MYS + EYS) / 2 and following Shorroks’s methodology [97], the “natural” decomposition of the square of the coefficient of variation is CV2 PEI ¼ 1 4 � m2 PEI s2 MYS þ sMYS;EYS � þ 1 4 � m2 PEI ðs2 EYS þ sMYS;EYSÞ where s2 MYS, s2 EYS, and sMYS;EYS are the variances of MYS and EYS, and the covariate between these education indices, respectively. This decomposition implies that the interaction term, 2 � sMYS;EYS, is allocated in the same way for both indices. Thus, ðs2 MYS þ sMYS;EYSÞ=4 � s2 PEI and ðs2 EYS þ sMYS;EYSÞ=4 � s2 PEI are the proportions of overall educational inequality contributed by MYS and EYS, respectively. Finally, given that the numerator of CV2 PEI is the variance of PEI, simple calculations leaded us to see that the contribution of province i to overall inequality is equal to PEIi mPEI ð Þ2=n � s2

PEI, where n is the number of provinces. Empirical results Fig 1 shows the spatial distribution of the PEI in Ecuador for 2006 and 2014 (education indica- tors data, and PEI and its components data available in S5 and S6 Tables). The Ecuadorian map illustrates the PEI distribution in 2014 taking the classification by quartiles as reference. It can be seen how provinces with a large urban population, such as Pichincha (whose capital is Quito, an eminently metropolitan area), Loja or Guayas, evidenced the highest levels of educa- tion, whereas the lowest levels corresponded to provinces with a greater concentration of rural population, such as Chimborazo, Cotopaxi, Los Rı´os, and Orellana. Pastaza is an interesting case, as it was the only province in the Amazonia that was among the group of Ecuadorian provinces which displayed the highest level of educational development. Although no regional pattern is evident–since the provinces exhibiting the highest and lowest PEI values were spread around the three regions considered in the study–, what did emerge is that provinces located in the southwest part of the country, such as Guayas, El Oro, and Loja, displayed greater devel- opment in education. Meanwhile, Sucumbı´os and Orellana–located to the north-east–were two of the provinces lagging furthest behind in the education dimension of well-being. Table 1 complements the information provided in Fig 1. This table shows the Ecuadorian provinces classified according to their level of educational development in 2014. To conduct

this classification, firstly, we considered the values of the education index calculated by UNDP for all countries with available information in 2014 [29]. Secondly, following the aforemen- tioned UNDP methodology for its HDI, we calculated the values 0.500, 0.664 and 0.784, corre- sponding to the first, second and third quartiles, respectively, of the HDI education index. These quartiles were the thresholds that determined the level of educational development of each province: low, if its PEI was less than 0.500; medium, if its PEI was greater than or equal to 0.500 and less than 0.664; high, if the PEI was greater than or equal to 0.664 and less than PLOS ONE Education as a dimension of Human development PLOS ONE | https://doi.org/10.1371/journal.pone.0270932 July 8, 2022 10 / 27

0.784; and, finally, very high, if the PEI was greater than or equal to 0.784. Since all the Ecua- dorian provinces had a PEI between 0.606 and 0.751 (see Fig 1), their level of educational development in 2014 was medium or high. Fig 2 illustrates the dynamics of the PEI distribution and its components, MYS and SYS, for 2006 and 2014, thereby furthering the description provided by Fig 1. All the distributions shifted to the right, with an increase in the mean values of the distributions between the years of the study. This evidences a positive evolution, both in PEI and in MYS and SYS between 2006 and 2014. The figure also shows a slight reduction in the disparity between provinces for the education index and its components between the years in the study, which will be analyzed later. The bimodal nature of the PEI distribution, which was only hinted at in 2006, was more evident in 2014, and reflects the concentration of a group of provinces with an educational Fig 1. Provincial-level Education Index by quartiles in 2014 and annual mean variation. 2006 and 2014. Notes: the Galapagos region was removed since it was not subject to analysis; the provinces of Santo Domingo and Santa Elena are included in Pichincha and Guayas, respectively; approximate results for the provinces of Amazonia in 2006 due to lack of representativeness in the survey. PEI = Provincial-level education index; AMV = annual mean variation; AMV = (PEI(2014)–PEI(2006))/(2014–2006). https://doi.org/10.1371/journal.pone.0270932.g001

Table 1. Ecuadorian provinces according to their level of educational development (2014). Educational development level Region Provinces Medium a Costa Esmeraldas; Los Rios; Manabı´ Sierra Bolı´var; Cañar; Carchi; Cotopaxi; Chimborazo Amazonia Morona Santiago; Zamora Chinchipe; Sucumbios; Orellana High b Costa El Oro; Guayas Sierra Azuay; Imbabura; Loja; Pichincha; Tungurahua Amazonia Napo; Pastaza Notes: a Medium: Provincial-level education index greater than or equal to 0.500 and less than 0.664. b High: Provincial-level Education Index greater than or equal to 0.664 and less than 0.784. https://doi.org/10.1371/journal.pone.0270932.t001 PLOS ONE Education as a dimension of Human development PLOS ONE | https://doi.org/10.1371/journal.pone.0270932 July 8, 2022 11 / 27

level that was above the distribution mean (equal to 0.599, in 2006, and 0.659, in 2014). It is also worth highlighting the different behavior of the distributions of the PEI components. The slight bias to the right of the 2006 MYS distribution virtually disappeared in 2014 and with it so did the number of provinces displaying MYS values below the respective mean value (equal to 0.482, in 2006, and 0.541, in 2014). Regarding the EYS distribution, Fig 2 indicates that most provinces were concentrated around the mean value (equal to 0.715, in 2006, and 0.776, in 2014) for both years of the study. It can also be seen that the density linked to lower values of this indicator tended to decrease in 2014. Despite this, there was a second mode for this indicator in said year, which is related to a group of provinces with below mean values. The graphs above reflect the general time evolution of the PEI distributions and their com- ponents, and, therefore, do not show any changes that have occurred at a provincial level between the years in the study. Any change in the general distribution of a variable may be the consequence of multiple combinations of changes at a provincial level [98]. As a result, it is necessary to look at the annual mean variations distribution for each index. The mean values of the distributions (0.0074, for MYS and 0.0076, for EYS) as well as the standard deviations (0.0044, for MYS and 0.0041, for EYS) were virtually the same in both distributions. However, Fig 3 shows that the growth patterns differed by index, being more moderate in the case of

MYS. There was also a group of provinces with a negative mean variation in the distribution of this component. Despite there was an overall improvement in PEI values between 2006 and 2014, certain provinces which had a poorer educational development in 2006, such as Cañar or Bolı´var and, particularly, Esmeraldas, were seen to be those which had improved most (annual mean varia- tion [AMV] equal to 0.0099, 0.0108, and 0.0112, respectively), whereas others who exhibited greater initial educational development, such as El Oro or Guayas, had made less progress (respective AMV values equal to 0.0052 and 0.0041) (Fig 1). In this regard, our estimation of the Spearman’s rank correlation coefficient between the classification of Ecuadorian provinces as determined by the PEI in 2006 and the other defined by the AMV of the PEI was negative (-0.493). This fact indicated that the provinces which most increased their values between 2006 and 2014 were those that lagged furthest behind in 2006 with a lower PEI. This therefore pointed to a process of convergence in education amongst Ecuadorian provinces. Based on the provincial estimations of the education components of the PEI (S6 Table), the convergence between provinces was greater for the EYS index, since the absolute value of the Spearman’s rank correlation coefficient was closer to one (-0.734) and was extremely weak for the MYS index (-0.182) (Table 2). Table 3 provides the CV2 values of the PEI and of its components for 2006 and 2014. These values give useful information on the degree of educational inequality among Ecuadorian

Fig 2. Distribution of the Provincial-level Education Index and its components. Notes: Each line represents the density function of the corresponding distribution. MYS = mean years of schooling index; EYS = expected years of schooling index: PEI = Provincial-level Education Index. https://doi.org/10.1371/journal.pone.0270932.g002 PLOS ONE Education as a dimension of Human development PLOS ONE | https://doi.org/10.1371/journal.pone.0270932 July 8, 2022 12 / 27

provinces, particularly on its variation over time, as well as on the weight of each component in this inequality. Therefore, extending the previous results, we saw that the distributions of the PEI components reduced in inequality over the period studied. Nevertheless, the MYS dis- tribution, which displayed the greatest level of inequality in the two years (CV2 equal to 0.0125, in 2006, and 0.0118, in 2014), was also the one to reduced said inequality less. In con- trast, the CV2 values of the EYS in the two years showed that there was substantial homogene- ity amongst Ecuadorian provinces in terms of this educational component, particularly in 2014, in which the CV2 presented a value close to zero. Nevertheless, the distribution of this indicator reduced its inequality across provinces between 2006 and 2014 by over 50%. In addi- tion, overall educational inequality across provinces also fell between 2006 and 2014, according to the CV2 of the PEI in these years. As regards the contribution to overall inequality for the two years, the contribution of MYS was greater than that of EYS and was almost three times higher in 2014. To complement the information provided by the normalized education indices, it is worth- while looking at the indicators behind them–mean years of schooling and expected years of Fig 3. Provincial distribution of the annual mean variation between 2006 and 2014 of the mean years of schooling and the expected years of schooling indices.

Notes: Each line represents the density function of the corresponding distribution. MYS = mean years of schooling index; EYS = expected years of schooling index. https://doi.org/10.1371/journal.pone.0270932.g003 PLOS ONE Education as a dimension of Human development PLOS ONE | https://doi.org/10.1371/journal.pone.0270932 July 8, 2022 13 / 27

schooling–, which allows us to understand the full meaning of the analysis. Table 4 shows the most common descriptive statistics in data analysis for these indicators. The mean value of the mean years of schooling indicator increases by slightly less than one year between 2006 and 2014 (0.885), while the increase is slightly more than one year for the mean of the expected years of schooling indicator (1.095). From the statistical point of view, normalization implies a change of scale in the variable: a transformation with respect to which CV2 is invariant, as shown in the table. However, it is worth noting the values taken by the coefficient of variation (square root of CV2) for each of the indicators. Thus, for the mean years of schooling indicator, the dispersion represents 10.8% of its mean value in 2014, while, in the case of the expected years of schooling indicator, the variability represents only 3.4%. Despite the reduction in educational inequality among Ecuadorian provinces, the range of the variable mean years of schooling in 2006 is around 3.4 years (from 5.902 in Bolivar to 9.285 in Pichincha), while, in 2014, this range reaches 4.1 years (from 6.144 in Chimborazo to 10.248 in Pichincha). However, when not considering Pichincha, the range is reduced to 3.1 years (from 6.144 in Chimborazo to 9.205 in Guayas). In the case of the expected years of schooling indicator, the range goes from 2.7 years in 2006 to 1.8 in 2014 (S5 Table). Data in Fig 4 show that the provinces with the greatest or lowest educational development

drive inequality the most, whereas the lowest weight corresponded to provinces whose PEI val- ues were closer to the mean value of the corresponding PEI distribution. Specifically, in 2006, the provinces of Pichincha and Guayas (with the highest PEI values) contributed most, in per- centage terms, to overall educational inequality in Ecuador (27% and 10.4%, respectively), fol- lowed by Bolivar, with 9%, and Cañar, with 7.3% (provinces that evidenced a lower level of educational well-being in said year). In 2014, Pichincha (32.1%) and Chimborazo (10.5%) were the provinces with the highest and lowest PEI value, respectively, and which contributed most to educational inequality in Ecuador. Table 2. Provincial-level Education Index and its components: Spearman´s rank correlation coefficient between the index in 2006 and its annual mean variation (2006–2014). ρ p PEI -0.493 0.011 � MYS -0.182 0.215 EYS -0.734 0.000 �� Notes: PEI = Provincial-level Education Index. MYS = mean years of schooling index; EYS = expected years of schooling index: ρ = Spearman’s rank correlation coefficient; p = p-value from the one-tailed t-test; � indicates statistical significance at the 5% level; �� indicates statistical significance at the 1% level. https://doi.org/10.1371/journal.pone.0270932.t002 Table 3. Inequality in educational development and contribution of education indicators. 2006 2014 MYS EYS PEI MYS EYS PEI CV2 0.013 0.002 0.004 0.012 0.001 0.003 % Contribution 63.18% 36.82% 77.31% 22.69%