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Students' Resilience and School Efficiency in One of the Most Unequal Countries in the World: Empirical Evidence from Colombia

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Title: Students' Resilience and School Efficiency in One of the Most Unequal Countries in the World: Empirical Evidence from Colombia
Language: English
Authors: Sebastian López-Estrada, Tommaso Agasisti, Víctor Giménez, Diego Prior
Source: Education Economics. 2025 33(2):180-197.
Availability: Routledge. Available from: Taylor & Francis, Ltd. 530 Walnut Street Suite 850, Philadelphia, PA 19106. Tel: 800-354-1420; Tel: 215-625-8900; Fax: 215-207-0050; Web site: http://www.tandf.co.uk/journals
Peer Reviewed: Y
Page Count: 18
Publication Date: 2025
Document Type: Journal Articles
Reports - Research
Descriptors: Foreign Countries, Resilience (Psychology), Efficiency, Public Schools, Private Schools
Geographic Terms: Colombia
DOI: 10.1080/09645292.2023.2298845
ISSN: 0964-5292
1469-5782
Abstract: This article analyzes students' resilience in 7,789 schools in the Colombian educational system and its relationship with educational efficiency between 2014 and 2019. The empirical analysis is carried out in two stages. First, a multilevel model with random intercept and slope is estimated to determine the students categorized as resilient. Then conditional order-m models are used to calculate the efficiency. The results indicate a negative relationship between thenumber of resilient students and schools' inefficiency of up to 33% in public schools and 12% in private schools.
Abstractor: As Provided
Entry Date: 2025
Accession Number: EJ1485623
Database: ERIC
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  Value: <anid>AN0183842092;ede01apr.25;2025Mar21.03:44;v2.2.500</anid> <title id="AN0183842092-1">Students' resilience and school efficiency in one of the most unequal countries in the world: empirical evidence from Colombia </title> <p>This article analyzes students' resilience in 7,789 schools in the Colombian educational system and its relationship with educational efficiency between 2014 and 2019. The empirical analysis is carried out in two stages. First, a multilevel model with random intercept and slope is estimated to determine the students categorized as resilient. Then conditional order-m models are used to calculate the efficiency. The results indicate a negative relationship between thenumber of resilient students and schools' inefficiency of up to 33% in public schools and 12% in private schools.</p> <p>Keywords: Educational inequity; students' resilience; efficiency analyses; schools; conditional order-m</p> <hd id="AN0183842092-2">1. Introduction</hd> <p>Education is a priority and a fundamental right that matters to the government, institutions, and society in general. In this context, the fourth Sustainable Development Goal (SDG 4) aims to 'Guarantee inclusive and equitable quality education and promote lifelong learning opportunities for all' within the framework of the United Nations 2030 agenda. This policyprioritizes inclusion, equity, and giving the same opportunities to all students and is designed to align the main government efforts addressed to the most vulnerable and marginalized population, ensuring that everyone is provided with the same access to and quality of education, regardless of their circumstances (UNDP & UNESCO [<reflink idref="bib69" id="ref1">69</reflink>]).</p> <p>Some studies have focused on those students who, despite coming from relatively disadvantaged socioeconomic and cultural backgrounds, obtain outstanding educational performance (Agasisti et al. [<reflink idref="bib4" id="ref2">4</reflink>]; Cordero and Mateos-Romero [<reflink idref="bib19" id="ref3">19</reflink>]; Gabrielli, Longobardi, and Strozza [<reflink idref="bib35" id="ref4">35</reflink>]; Vicente, Pastor, and Soler [<reflink idref="bib71" id="ref5">71</reflink>]). This stream of research takes into account the multiple positive economic and social externalities that result from higher educational levels (Hanushek [<reflink idref="bib40" id="ref6">40</reflink>]; Hanushek and Woessmann [<reflink idref="bib42" id="ref7">42</reflink>]), and advocates the active promotion of resilience in these students as a potential strategy to raise a country's development levels.</p> <p>In social terms, the concept of resilience originally emergedin the field of psychology (Finn and Rock [<reflink idref="bib33" id="ref8">33</reflink>]; Luthar, Cicchetti, and Becker [<reflink idref="bib48" id="ref9">48</reflink>]), and due to the potential of its definition, interest spread to other areas of research, such as the economics of education (Agasisti and Longobardi [<reflink idref="bib6" id="ref10">6</reflink>]; Cordero and Mateos-Romero [<reflink idref="bib19" id="ref11">19</reflink>]). Resilience has generallybeen defined as the achievement of success in a situation where a person is disadvantaged or facingadversity (Ungar [<reflink idref="bib70" id="ref12">70</reflink>]; Windle [<reflink idref="bib74" id="ref13">74</reflink>]).</p> <p>In general, educational or academic resilience has been defined as the ability of a student to achieve outstanding academic performance despite their disadvantaged background (OECD [<reflink idref="bib55" id="ref14">55</reflink>]). Such students stand out because they develop behavior that goes against expectations. The literature regards resilience as a sign of hope (Clavel, García Crespo, and Sanz [<reflink idref="bib17" id="ref15">17</reflink>]), since it breaks the vicious cycle in which poverty is perpetuated across generations.</p> <p>The growing body of research into educational resilience has mainly focused on student effectiveness (Ye, Strietholt, and Blömeke [<reflink idref="bib75" id="ref16">75</reflink>]). It is therefore important to explore whether those schools that have a higher proportion of resilient students alsoperform efficiently, since a balance between efficiency and effectiveness is of vital importance for educational policies (OECD [<reflink idref="bib54" id="ref17">54</reflink>]).</p> <p>In order to optimize resource allocation, it is essential to understand the relationship between different variables andthe efficiency of the educational system (Agasisti [<reflink idref="bib2" id="ref18">2</reflink>]; Sagarra, Mar-Molinero, and Agasisti [<reflink idref="bib61" id="ref19">61</reflink>]). In this regard, analyzing the relationship between educational inequity and schools' efficiency is critical for designing coherent educational policies. Reducing inequity among students is desirable while maintaining or improving academic performance; however, this process requires physical, human, and/or financial resources. The tradeoff between the additional use of resources and the better performance of resilient students can be analyzed from a policymaker's point of view, where the efficiency of resource management pairs with the difficulties involved in improving this educational process. Departmental and municipal governments are interested in knowing how to improve this relationship and help to empower their students, since it has a positive effect on higher education, job placement, economic and social growth, and development.</p> <p>Research on educational efficiency has recently considered problems related to educational inequality (Arbona et al. [<reflink idref="bib9" id="ref20">9</reflink>]; Giménez et al. [<reflink idref="bib38" id="ref21">38</reflink>]; Giménez, Ayvar-Campos, and Navarro-Chávez [<reflink idref="bib37" id="ref22">37</reflink>]) or inequity (Cordero, Pedraja-Chaparro, and Simancas [<reflink idref="bib20" id="ref23">20</reflink>];Marchesi [<reflink idref="bib50" id="ref24">50</reflink>]; Sicilia and Simancas [<reflink idref="bib62" id="ref25">62</reflink>]). In this type of analysis, themost commonly used variables arethe standard deviation in the results of standardized tests or the number of students who reach minimum standards in these tests. Different behaviors or performance levels are found in educational systems when these types of variables are considered. The current paper isone ofthe first studiesto directly analyze the relationship between educational resilience and efficiency within an educational system, in addition tothe analysis by Sicilia and Simancas ([<reflink idref="bib62" id="ref26">62</reflink>]) for the case of Spain.</p> <p>This paper defines two specific objectivesto analyze resilience in7,789schools in the Colombian educational system and its relationship with educational efficiency between 2014 and 2019. First, it analyzes the schools by considering their performance intwoaspects: the number of resilient students and the schools' relative efficiency. Second, it identifies the differences in this relationship across sectors (public and private schools) and regions.</p> <p>Colombia is a representative case of an emerging country with high social and educational inequalities and inequities. The Programme for International Student Assessment(PISA)results for 2018 show lower performance than OECD countries, withonly 35% of Colombian students obtaining proficiency level 2 in mathematics. In addition, 14% of the variation in reading results is explained by the socioeconomic conditions of the students, which is 2% higher than the OECD average (OECD [<reflink idref="bib58" id="ref27">58</reflink>]). Likewise, as highlighted in a relevant OECD ([<reflink idref="bib57" id="ref28">57</reflink>]) report,the situation in Colombia is one of the most concerning, since it has the worst performance in closing gaps: on average it would take at least 300 years for childrenfrom low-income families to reach the mean.</p> <p>The empirical analysis of this study is carried out in two stages. First, we estimate a multilevel model with random intercept and slope (Vicente, Pastor, and Soler [<reflink idref="bib71" id="ref29">71</reflink>])to define the students categorized as resilient, which takes into account the variance between the different levels of analysis (students withina municipality). Second, we use one of the most robust methods to estimate efficiency, namelyconditional order-m models (Cazals, Florens, and Simar [<reflink idref="bib15" id="ref30">15</reflink>]), which also reduces the influence of atypical and extreme values.</p> <p>To analyze the relationship between resilience and efficiency, we construct a database by integratingtwo sources containing information from 2014[<reflink idref="bib1" id="ref31">1</reflink>] to 2019. The first source is the Colombian Institute for the Promotion of Higher Education (ICFES), which providesthe results in the standardized exams in Colombia at different levels of analysis. Thesecond source is the National Administrative Department of Statistics (DANE), which providesaccess to the inventory of physical and personnel resources of each school.</p> <p>Our main finding is the negative relationship between the inefficiency of schools and the number of resilient students. This negative correlation is strongly heterogeneous among departments and between public and private schools. The innovative contribution of this work to the literature is threefold. First, it contributes to the scarce (Sicilia and Simancas [<reflink idref="bib62" id="ref32">62</reflink>]) literature that analyzes theschools of an educational system based on their resilience and efficiency at the same time. Second, it is one of the first analyses of educational resilience in a developing country. Third, compared to previous applications, this is the first study to be carried out with data other than those from theProgress in International Reading Literacy Study(PIRLS), Trends in International Mathematics and Science Study (TIMSS) or PISA, thus contributing to the analysis of the phenomenon from an alternative empirical perspective. Indeed, the availability of a detailed administrative dataset allows for a much more complete and robust empirical analysis than existing studies based on international samples.</p> <p>The paper is divided into five sections. After this introduction (section 1), a literature review is provided in section 2; the methodological approach is described in section 3 and the empirical aspects related to the databases and variables are explained in section 4. Finally, the results are presented in section 5, and conclusions are drawn in section 6.</p> <hd id="AN0183842092-3">2. Literature review</hd> <p>In recent years, many academic studieshave focused on improving educational achievement as a proxy variable of quality (Evans et al. [<reflink idref="bib30" id="ref33">30</reflink>]). However, this cannot be the only objective; Tsai, Smith, and Hauser ([<reflink idref="bib68" id="ref34">68</reflink>]) highlight that the golden rule in educational policy should beto consider excellence (high performance) and equality (low variability in performance) in the results.</p> <p>This discussion initially became relevant with the Equality of Educational Opportunities report (Coleman et al. [<reflink idref="bib18" id="ref35">18</reflink>]), which revealedthe importance of social and economic components as determinants of educational performance at an international level (Hanushek and Woessmann [<reflink idref="bib43" id="ref36">43</reflink>]). Since then, policymakers have endeavored to reduce inequity, understanding it as the differences in educational performance caused bypeople's social, cultural or economic circumstances. That is, students' educational performance must be a function exclusively of effort and abilities (OECD [<reflink idref="bib55" id="ref37">55</reflink>]), and not focus solely on reducing the difference between students, which is understood as inequality.</p> <p>Although various ways have been proposed to reduce inequity, the debate has focused on different types of strategies. At the international level Hanushek and Ludger ([<reflink idref="bib41" id="ref38">41</reflink>]) refer to the choice between selective (for example, Germany, Hungary, Austria) or comprehensive (for example, Japan, Canada, Norway) systems for grouping students in classrooms. Other studies have analyzed the effects of separating students into tracks early their educational trajectories (Dupriez, Dumay, and Vause [<reflink idref="bib29" id="ref39">29</reflink>]; Hanushek and Woessmann [<reflink idref="bib42" id="ref40">42</reflink>]), grouping of skills and/or performance in the classroom (Hindriks et al. [<reflink idref="bib47" id="ref41">47</reflink>]) and individualized support (Ferrer-Esteban [<reflink idref="bib32" id="ref42">32</reflink>]), alluding to the peer effect as a tool for working on inequity (Betts and Shkolnik [<reflink idref="bib11" id="ref43">11</reflink>]). These approaches reflect options to reduce differences in educational performance caused by people's social, cultural, or economic circumstances, which have been mentioned as essential for evaluating educational systems (Sicilia and Simancas [<reflink idref="bib62" id="ref44">62</reflink>]).</p> <p>In this research, educational resilience is used as a proxy to study inequity in the Colombian educational system. Although this is the first study to analyze educational efficiency and resilience for Colombia jointly, approaches considering efficiency and resilience independently can be found in the literature. While educational efficiency has not been studied as much in Colombia as internationally, some studies in higher education focus on the difference in programs (Melo-Becerra, Ramos-Forero, and Hernández-Santamaría [<reflink idref="bib52" id="ref45">52</reflink>]) and the public and private academic sectors (Moreno-Gómez, Calleja-Blanco, and Moreno-Gómez [<reflink idref="bib53" id="ref46">53</reflink>]). At the international level, Cordero, Santín, and Simancas ([<reflink idref="bib22" id="ref47">22</reflink>]) analyze the efficiency of the educational system of 36 countries participating in PISA 2012, including Colombia. In addition, Arbona et al. ([<reflink idref="bib10" id="ref48">10</reflink>]) examine how contributions from the private sector can affect the efficiency of educational institutions at the secondary level. Finally, only one study (Arbona et al. [<reflink idref="bib9" id="ref49">9</reflink>]) has addressed efficiency in conjunction with a problem close to inequity (differences in the standard deviation of student performance), in which the evolution of the public and private sectors is considered for the period 2014–2019.</p> <p>Educational resilience is a phenomenon where students in a situation of disadvantage or adversity achieve outstanding academic results (Wang and Walberg [<reflink idref="bib73" id="ref50">73</reflink>]). We are not aware of any research on this phenomenonspecifically for the case of Colombia, although a series of studies have highlighted the effects of achieving a more equitable educational system at an international level (Agasisti and Longobardi [<reflink idref="bib6" id="ref51">6</reflink>]; Clavel, García Crespo, and Sanz [<reflink idref="bib17" id="ref52">17</reflink>]; Cordero and Mateos-Romero [<reflink idref="bib19" id="ref53">19</reflink>]; Gabrielli, Longobardi, and Strozza [<reflink idref="bib35" id="ref54">35</reflink>]; OECD [<reflink idref="bib55" id="ref55">55</reflink>]; Vicente, Pastor, and Soler [<reflink idref="bib71" id="ref56">71</reflink>]), some of which use data from Colombia at the country level as a member of or allied to the OECD (Agasisti et al. [<reflink idref="bib3" id="ref57">3</reflink>]; OECD [<reflink idref="bib55" id="ref58">55</reflink>]; Vicente, Pastor, and Soler [<reflink idref="bib71" id="ref59">71</reflink>]).</p> <p>The academic literature has studied educational resilience from two perspectives. The first is the perspective of psychology and sociology, in whichnotable contributions use mainly qualitative methodologies to explore factors such as character, commitment and self-confidence (Borman and Overman [<reflink idref="bib13" id="ref60">13</reflink>]; G. Wang and Walberg [<reflink idref="bib73" id="ref61">73</reflink>]). The second perspective mainly focuses on analyzing the composition of resilient student groups and their determinants, comparing their behavior and proportion between countries (Agasisti et al. [<reflink idref="bib4" id="ref62">4</reflink>]; Clavel, García Crespo, and Sanz [<reflink idref="bib17" id="ref63">17</reflink>]; OECD [<reflink idref="bib55" id="ref64">55</reflink>]; Vicente, Pastor, and Soler [<reflink idref="bib71" id="ref65">71</reflink>]).</p> <p>Following the objective of this study, which analyzes the phenomenon of educational resilience from the second point of view, four factors must be taken into account in the conceptual framework (Ye, Strietholt, and Blömeke [<reflink idref="bib75" id="ref66">75</reflink>]):first, the definition of educational resilience;second, how to measure socioeconomic adversity (composite versus distinct measures of student background);third, how to measure positive academic results (selecting the educational achievement indicator to use as a benchmark); andfourth, thresholds for adversity and academic results, and how to compare students, whether cross-country or within-country.</p> <p>The first factor in the conceptual framework (definition of resilience), has been studied from different disciplines, many related to behavioral sciences. Although there is no universal definition across the disciplines, all academics base their analyses on the concepts of adversity and positive adaptation (Windle [<reflink idref="bib74" id="ref67">74</reflink>]). From this perspective, when resilience is analyzed in the educational context, the consensus in the literature is that students' conditions and experiences must be considered as a measure of adversity, and a greater probability of success in school should be regarded as a measure of positive adaptation (Wang and Walberg [<reflink idref="bib73" id="ref68">73</reflink>]).</p> <p>Regarding the second factor, the studies that analyze educational resilience through international large-scaleassessment (ILSA) data––such as PISA or TIMSS––consider that the effect of students' background on educational achievement is related not only to material goods but also to their social and cultural circumstances. The most commonly used variables to measure adversity in educational resilience research are the PISA socioeconomic status(SES) index and the TIMSS home educational resources (HER) index, the main difference being that the SES index considers parents' occupation while the HER index does not.</p> <p>For the third factor, positive adaptation, cognitive outcomes are generally assessed through standardized tests. The main discussion revolvesaround whether to use only one dimension of the standardized tests (for example mathematics) or tests in different subjects. Broadly, some authors suggest that if a student is resilient in one of the dimensions they will be resilient in the others, although other studies do not find this consistency (OECD [<reflink idref="bib55" id="ref69">55</reflink>]). This debate has motivated work on finding resilient students across different dimensions (Agasisti et al. [<reflink idref="bib3" id="ref70">3</reflink>]).</p> <p>The fourth factor of the conceptual framework considers the thresholds of analysis, and cross-country or within-country comparisons. Both for the variables of adversity (disadvantaged) and those of positive adaptation (high performance in standardized tests) the question is posed as to whether the comparisons should be made in a 'fixed' or a 'relative' way. The most recent studies in this line of research opt for within-country comparison thresholds (relative), since they are more useful for educational policy in a specific context (OECD [<reflink idref="bib55" id="ref71">55</reflink>]; Vicente, Pastor, and Soler [<reflink idref="bib71" id="ref72">71</reflink>]).</p> <p>In their systematic review of the literature on academic resilience, Ye, Strietholt, and Blömeke ([<reflink idref="bib75" id="ref73">75</reflink>])find that different criteria are used to define both the variables of adversity, as well as those of positive adaptation and the thresholds. In general, the studies can be categorized into four groups: (I) fixed background and fixed outcome thresholds, (II) fixed background and relative outcome thresholds, (III) relative background and fixed outcome thresholds, and (IV) relative background and relative outcome thresholds.</p> <p>Based on the above, and in line with the objective of the study, this paper shares the characteristics of the third group, which uses a relative background and fixed outcome thresholds. Within the studies that have followed these characteristics, there are differences in the approaches: some authors use direct threshold approaches (García-Crespo et al. [<reflink idref="bib36" id="ref74">36</reflink>]; OECD [<reflink idref="bib55" id="ref75">55</reflink>]), others use residual methods to calculate thresholds (Agasisti and Longobardi [<reflink idref="bib5" id="ref76">5</reflink>]; [<reflink idref="bib6" id="ref77">6</reflink>]; Agasisti et al. [<reflink idref="bib4" id="ref78">4</reflink>]; Cordero and Mateos-Romero [<reflink idref="bib19" id="ref79">19</reflink>]; Vicente, Pastor, and Soler [<reflink idref="bib71" id="ref80">71</reflink>]) and finally, cross-domain operationalization of educational outcomes are also taken into account (Agasisti et al. [<reflink idref="bib3" id="ref81">3</reflink>]).</p> <p>Research on educational resilience haspaid attention to its determinants, in an attempt toshed light on the phenomenon in order to help close the socioeconomic gaps in the educational system. The current literature focuses on three groups of variables: students' demographics (Agasisti et al. [<reflink idref="bib4" id="ref82">4</reflink>]; Gabrielli, Longobardi, and Strozza [<reflink idref="bib35" id="ref83">35</reflink>]; Martin and Marsh [<reflink idref="bib51" id="ref84">51</reflink>]), family background (Agasisti and Longobardi [<reflink idref="bib5" id="ref85">5</reflink>]; Clavel, García Crespo, and Sanz [<reflink idref="bib17" id="ref86">17</reflink>]; Hill and Tyson [<reflink idref="bib46" id="ref87">46</reflink>]), and school and class factors (Cordero, Pedraja-Chaparro, and Simancas [<reflink idref="bib20" id="ref88">20</reflink>]; Tajalli and Cynthia [<reflink idref="bib63" id="ref89">63</reflink>]).</p> <p>When considering demographic characteristics, theexisting studies draw mixed conclusions on the role of students' immigration status (Gabrielli and Impicciatore [<reflink idref="bib34" id="ref90">34</reflink>]; Gabrielli, Longobardi, and Strozza [<reflink idref="bib35" id="ref91">35</reflink>]), and gender (Agasisti and Longobardi [<reflink idref="bib6" id="ref92">6</reflink>]; Martin and Marsh [<reflink idref="bib51" id="ref93">51</reflink>]). Studies analyzing students' family background focus on the cultural capital of the home (Park [<reflink idref="bib59" id="ref94">59</reflink>]) and the parents' intervention in or commitment to the education of their children (Hill and Tyson [<reflink idref="bib46" id="ref95">46</reflink>]).</p> <p>Likewise, school- and class-related factors were studied because of their potential to close the gaps in the students'backgrounds. In this case, the most analyzed variables are the teachers' strategies in the classroom (Tajalli and Cynthia [<reflink idref="bib63" id="ref96">63</reflink>]), class size (Heinesen [<reflink idref="bib45" id="ref97">45</reflink>]), peer effects (Agasisti, Soncin, and Valenti [<reflink idref="bib7" id="ref98">7</reflink>]), and school academicclimate (Wang et al. [<reflink idref="bib72" id="ref99">72</reflink>]).</p> <p>Regarding the validation of the concept of educational resilience, Ye et al.([<reflink idref="bib75" id="ref100">75</reflink>]) highlight three aspects to consider in future works. First, they suggest taking acountry-specificapproach to measure adversity, since this offersa more pertinent way of informingpublic policies in a country. Second, different assumptions must be tested (thresholds and ways of measuring positive adaptation) to increase robustness in the results. Third, the results should focus not only on the number of resilient students but also on the composition of the groups by gender, type of school, ethnicity, etc.</p> <p>The last part of this literature review highlights the fact that although the number of studies into educational resilience is growing, there are still factors to be explored that are relevant and significant for the elaboration of public policies. Specifically, for the purpose of this study the most important factoris the relationship between resilience and educational efficiency. The OECD ([<reflink idref="bib54" id="ref101">54</reflink>]) emphasizes that there must be a balance between educational efficiency and effectiveness for the development of educational policies. To the best of our knowledge, this is one of the first academic papersthat directly address the relationship between efficiency and educational resilience in an empirical analysis, together with the study by Sicilia and Simancas ([<reflink idref="bib62" id="ref102">62</reflink>]) for the case of Spain.</p> <hd id="AN0183842092-4">3. Methodological approach</hd> <p>This section presents the two methodologies used to carry out the empirical analysis. First, it explains how a student is conceptually categorized as resilient,in order to compute the proportion of resilient students by school. Second, we explain the conditional order-m model, which is a robust methodology for calculating the efficiency of schools. In this regard, Daraio and Simar ([<reflink idref="bib23" id="ref103">23</reflink>]; [<reflink idref="bib24" id="ref104">24</reflink>]; [<reflink idref="bib25" id="ref105">25</reflink>]) recommend using conditional models since they include contextual variables in a single stage, and they are not too sensitive to atypical observations.</p> <hd id="AN0183842092-5">3.1. Defining a student as resilient</hd> <p>The academic literature defines a resilient student as an individual who,despite coming from a disadvantaged socioeconomic background, reaches a relatively high level of academic performance(OECD [<reflink idref="bib55" id="ref106">55</reflink>]). Based on the suggestions of Ye, Strietholt, and Blömeke ([<reflink idref="bib75" id="ref107">75</reflink>]) in their systematic literature review, various factors must be consideredwhen categorizing these students. First, it is necessary to define the indicator or variable to consider a student in a situation of disadvantage or adversity. Second, the criteria to define high performance must be specified. Third, the thresholds and the group with which the comparisons will be made in the process (country, region, department, municipality, and school) should be defined.</p> <p>The main methodology used in this stage is multilevel or hierarchical regression. This type of regression allows researchers to take advantage of the nesting of the data structure, i.e. students within schools within departments. In this study, we follow Vicente et al.([<reflink idref="bib71" id="ref108">71</reflink>]) approach,in which the possible correlation between students from the same school and territory is considered, unlike other studies. For students to be classified as resilient, theymust fall within the 25th percentile of the Socioeconomic Index of their municipality. They must also be disadvantaged and achieve an overall test scoredistributionto be above the 75th percentile. This estimate is made considering the socioeconomic background of the students and taking into account the possible variation of this effect in each of the municipalities. The mathematical function is:</p> <p>Graph</p> <p> <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Globalscore</mi><mo>=</mo><mspace width="thickmathspace" /><msub><mi>α</mi><mrow><mn>00</mn></mrow></msub><mo>+</mo><mspace width="thickmathspace" /><msub><mtext fontfamily="times">β</mtext><mn>1</mn></msub><mi>INS</mi><msub><mi>E</mi><mrow><mi>ij</mi></mrow></msub><mo>+</mo><mspace width="thickmathspace" /><msub><mi>ϵ</mi><mrow><mi>ij</mi></mrow></msub><mo>+</mo><msub><mi>δ</mi><mrow><mn>0</mn><mi>j</mi></mrow></msub></math> </ephtml> (<reflink idref="bib1" id="ref109">1</reflink>)</p> <p>where <emph>i</emph> represents the students and <emph>j</emph> represents the municipalities. In addition, the global score of each student is taken into account considering their Socioeconomic Index and the municipalities in a second level. After performing the estimation, two types of error are obtained, the individual (</p> <p>Graph</p> <p> <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>ϵ</mi><mrow><mi>ij</mi></mrow></msub></math> </ephtml> ) and the cluster (</p> <p>Graph</p> <p> <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>δ</mi><mrow><mn>0</mn><mi>j</mi></mrow></msub><mspace width="thickmathspace" /><mi>and</mi><mspace width="thickmathspace" /><msub><mi>δ</mi><mrow><mn>1</mn><mi>j</mi></mrow></msub></math> </ephtml> );</p> <p>Graph</p> <p> <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>δ</mi><mrow><mn>0</mn><mi>j</mi></mrow></msub></math> </ephtml> is the random part of the intercept, that is, the initial position of each student due to their belonging to a specific municipality according to their Socioeconomic Index;in turn,</p> <p>Graph</p> <p> <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>δ</mi><mrow><mn>1</mn><mi>j</mi></mrow></msub></math> </ephtml> is the random part of the slope, in other words, the effect of the Socioeconomic Index variation within a specific municipality. Note that</p> <p>Graph</p> <p> <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>δ</mi><mrow><mn>0</mn><mi>j</mi></mrow></msub><mrow><mi mathvariant="normal">and</mi></mrow><msub><mi>δ</mi><mrow><mn>1</mn><mi>j</mi></mrow></msub></math> </ephtml> are errors that include all factors that cannot be explained after controlling the student's Socioeconomic Index in relation to the global score.</p> <p>Finally, in order to categorize which students are resilient, equation 1 is estimated to add the individual errors with the clusters</p> <p>Graph</p> <p> <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><msub><mi>ϵ</mi><mrow><mi>ij</mi></mrow></msub><mo>+</mo><mspace width="thickmathspace" /><msub><mi>δ</mi><mrow><mn>0</mn><mi>j</mi></mrow></msub><mo>)</mo></math> </ephtml> , while controlling the effect of the variation of the Socioeconomic Index in each municipality (</p> <p>Graph</p> <p> <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>δ</mi><mrow><mn>1</mn><mi>j</mi></mrow></msub></math> </ephtml> ). Then, the 75th percentile of this sum is calculated, and disadvantaged students above this percentile obtained through estimation errors are categorized as resilient. With this approach, resilient students are used as a proxy to study equity and inequity in the educational system. Indeed, these students are overcoming adversity in a specific environment and obtain a result above what is expected given their individual socioeconomic background.</p> <hd id="AN0183842092-6">3.2. Conditional order-m model for calculating the schools' efficiency scores</hd> <p>The main objective of this study is to analyze the educational efficiency of schools and their relationship with resilient students. In general, the academic literature has used various parametric and non-parametric techniques to measure efficiency. Notable non-parametric techniques includeData Envelopment Analysis (DEA) (Charnes, Cooper, and Rhodes [<reflink idref="bib16" id="ref110">16</reflink>]) and Free Disposal Hull (Deprins, Simar, and Tulkens [<reflink idref="bib27" id="ref111">27</reflink>]). Both techniques are based on mathematical programming and do not require any assumption about the production function; however, the main difference between them is that the Free Disposal Hull removes the assumption of convexity, which implies that the relative efficiency is calculated exclusively with other real units and not linear combinations on the frontier (see De Witte and López-Torres [<reflink idref="bib28" id="ref112">28</reflink>]).</p> <p>A non-parametric approach is adopted in this study as multiple outputs can be used (Thieme, Prior, and Tortosa-Ausina [<reflink idref="bib66" id="ref113">66</reflink>]), which helps to take into account different aspects of the educational process at the same time (quality, capacity, inequity). Within this approach, this study uses conditional order-m models, since unlike the Data Envelopment Analysis and the Free Disposal Hull,it is a more robust way of making efficiency estimates due to the bootstrapping and the inclusion of environment variables in the estimation process (Cazals, Florens, and Simar [<reflink idref="bib15" id="ref114">15</reflink>]).</p> <p>To estimate schools' efficiency, production technology is considered as the students' transformation of a set of inputs <emph>x</emph></p> <p>Graph</p> <p> <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mrow><mi>xϵ</mi><msub><mi>R</mi><mo>+</mo></msub><mrow><mspace width="negativethinmathspace" /><mspace width="negativethinmathspace" /><msup><mspace width="negativethinmathspace" /><mi>p</mi></msup></mrow></mrow><mo>)</mo></math> </ephtml> , such as their socioeconomic index, resources they have at school and their own skills, into a set of outputs <emph>y</emph></p> <p>Graph</p> <p> <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mrow><mi>yϵ</mi><mrow><mspace width="thinmathspace" /><msubsup><mi>R</mi><mo>+</mo><mi>q</mi></msubsup></mrow></mrow><mo>)</mo></math> </ephtml> <emph>,</emph> usually measured through standardized tests. Production technology can be established as the set of possible combinations of outputs and inputs:</p> <p>Graph</p> <p> <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">Ψ</mi><mo>=</mo><mo fence="false">{</mo><mo>(</mo><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow><mo>)</mo><mi>ϵ</mi><msubsup><mi>R</mi><mo>+</mo><mrow><mspace width="thinmathspace" /><mi>p</mi><mo>+</mo><mi>q</mi></mrow></msubsup><mo fence="false">|</mo><mi>x</mi><mspace width="thickmathspace" /><mi>can</mi><mspace width="thickmathspace" /><mi>produce</mi><mspace width="thickmathspace" /><mi>y</mi><mo fence="false">}</mo></math> </ephtml> (<reflink idref="bib2" id="ref115">2</reflink>)</p> <p>Following the probabilistic framework presented by Cazals, Florens, and Simar ([<reflink idref="bib15" id="ref116">15</reflink>]), we develop a conditional model that takes into consideration contextual variables</p> <p>Graph</p> <p> <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Zϵ</mi><msub><mi>R</mi><mo>+</mo></msub><mrow><mspace width="negativethinmathspace" /><mspace width="negativethinmathspace" /><msup><mspace width="negativethinmathspace" /><mi>k</mi></msup></mrow></math> </ephtml> since they have an impact on school performance and efficiency. The objective is to illustrate how a school operating at a specific level (<emph>x, y</emph>) can be compared to another school operating under similar contextual conditions (<emph>Z = z</emph>) using the joint production function</p> <p>Graph</p> <p> <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>H</mi><mrow><mi>XY</mi><mo fence="false">|</mo><mi>Z</mi></mrow></msub></math> </ephtml> , where <emph>Z</emph> represents the set of variables characterizing a particular operational environment. Following Cazals, Florens, and Simar ([<reflink idref="bib15" id="ref117">15</reflink>]) and Daraio and Simar ([<reflink idref="bib23" id="ref118">23</reflink>]; [<reflink idref="bib24" id="ref119">24</reflink>]; [<reflink idref="bib25" id="ref120">25</reflink>]), it can be expressed as:</p> <p>Graph</p> <p> <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>H</mi><mrow><mi>XY</mi><mo fence="false">|</mo><mi>Z</mi></mrow></msub><mo>(</mo><mrow><mi>x</mi><mo>,</mo><mi>y</mi><mrow><mo fence="false">|</mo></mrow><mi>z</mi></mrow><mo>)</mo><mo>=</mo><mo movablelimits="true" form="prefix">Pr</mo><mo>(</mo><mrow><mi>X</mi><mo>≤</mo><mi>x</mi><mo>,</mo><mspace width="thickmathspace" /><mi>Y</mi><mo>≥</mo><mi>y</mi><mrow><mo fence="false">|</mo></mrow><mi>Z</mi><mo>=</mo><mi>z</mi></mrow><mo>)</mo></math> </ephtml> (<reflink idref="bib3" id="ref121">3</reflink>)</p> <p>Furthermore, the equation can be decomposed into two components, namely</p> <p>Graph</p> <p> <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>S</mi><mi>Y</mi></msub><mo>(</mo><mrow><mi>y</mi><mrow><mo fence="false">|</mo></mrow><mi>x</mi><mo>,</mo><mi>z</mi></mrow><mo>)</mo></math> </ephtml> , which signifies the survival function of <emph>Y,</emph> and</p> <p>Graph</p> <p> <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>F</mi><mi>X</mi></msub><mo>(</mo><mrow><mi>x</mi><mrow><mo fence="false">|</mo></mrow><mi>z</mi></mrow><mo>)</mo></math> </ephtml> , which denotes the cumulative distribution function of <emph>X</emph>:</p> <p>Graph</p> <p> <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>H</mi><mrow><mi>XY</mi><mo fence="false">|</mo><mi>Z</mi></mrow></msub><mo>(</mo><mrow><mi>x</mi><mo>,</mo><mi>y</mi><mrow><mo fence="false">|</mo></mrow><mi>z</mi></mrow><mo>)</mo><mo>=</mo><mo movablelimits="true" form="prefix">Pr</mo><mo>(</mo><mrow><mi>X</mi><mo>≤</mo><mi>x</mi><mo>,</mo><mspace width="thickmathspace" /><mi>Y</mi><mo>≥</mo><mi>y</mi><mrow><mo fence="false">|</mo></mrow><mi>Z</mi><mo>=</mo><mi>z</mi></mrow><mo>)</mo><mo movablelimits="true" form="prefix">Pr</mo><mo>(</mo><mrow><mi>X</mi><mo>≤</mo><mi>x</mi><mrow><mo fence="false">|</mo></mrow><mi>Z</mi><mo>=</mo><mi>z</mi></mrow><mo>)</mo><mo>=</mo><msub><mi>S</mi><mi>Y</mi></msub><mo>(</mo><mrow><mi>y</mi><mrow><mo fence="false">|</mo></mrow><mi>x</mi><mo>,</mo><mi>z</mi></mrow><mo>)</mo><msub><mi>F</mi><mi>X</mi></msub><mo>(</mo><mrow><mi>x</mi><mrow><mo fence="false">|</mo></mrow><mi>z</mi></mrow><mo>)</mo></math> </ephtml> (<reflink idref="bib4" id="ref122">4</reflink>)</p> <p>Some non-parametric techniques for estimating efficiency, such as DEA, are prone to sensitivity when dealing with extreme or outlier values. To address these issues, a solution is to employ an order-m frontier evaluation process as defined by Cazals, Florens and Simar ([<reflink idref="bib15" id="ref123">15</reflink>]). This process allows us to calculate conditional estimators</p> <p>Graph</p> <p> <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mo>(</mo><mrow><mi>x</mi><mo>,</mo><mi>y</mi><mrow><mo fence="false">|</mo></mrow><mi>z</mi></mrow><mo>)</mo></math> </ephtml> . Order-m models require the specification of a parameter, denoted as <emph>m</emph>, which signifies the number of units randomly selected from the sample for comparison. Consequently, smoothing techniques are applied to the contextual variables, resulting in the conditional model that can be expressed through the following integral:</p> <p>Graph</p> <p> <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mover><mi>λ</mi><mo>ˆ</mo></mover></mrow><mrow><mi>m</mi><mo>,</mo><mi>n</mi></mrow></msub><mo>(</mo><mrow><mi>x</mi><mo>,</mo><mi>y</mi><mo fence="false">|</mo><mi>z</mi></mrow><mo>)</mo><mo>=</mo><mspace width="thickmathspace" /><munderover><mrow><mo largeop="false">∫</mo></mrow><mn>0</mn><mi mathvariant="normal">∞</mi></munderover><mo>⁡</mo><mo>[</mo><mn>1</mn><mo>−</mo><mo>(</mo><mrow><mn>1</mn><mo>−</mo><msub><mi>S</mi><mrow><mi>Y</mi><mo>,</mo><mi>n</mi></mrow></msub><mo>(</mo><mrow><mi>uy</mi><mrow><mo fence="false">|</mo></mrow><mi>x</mi><mo>,</mo><mi>z</mi></mrow><mo>)</mo><mo>)</mo></mrow><msup><mo>]</mo><mi>m</mi></msup><mi>du</mi><mspace width="thickmathspace" /></math> </ephtml> (<reflink idref="bib5" id="ref124">5</reflink>)</p> <p>Based on Equation 5, efficient schools are on the frontier (efficiency score equal to one); on the other hand, inefficient students can be measured using equation 5 when an output orientation is taken:an inefficient student will obtain an efficiency score greater than one, estimating the potential improvement of the outputs. Importantly, the conditional order-m model also allows us to obtain values less than one, which means that the evaluated school is located above the production frontier, that is, this school can be defined as super-efficient.[<reflink idref="bib2" id="ref125">2</reflink>] Note that the output orientation is used, since the objective of students in all educational systems is generally to obtain the best results with the given resources.</p> <p>The relative efficiency estimation process is defined through the Free Disposal Hull model mentioned above, which removes the assumption of convexity for the estimation of the technological set. Then, conditional order-m is introduced, intuitively explaining the main changes with respect to the Free Disposal Hull and the origin of its robustness.</p> <p>Intuitively this implies that each school can be compared only with other existing schools, and not with convex combinations of them, as in the DEAmodels. To estimate the efficiency model, Cazals, Florens, and Simar ([<reflink idref="bib15" id="ref126">15</reflink>]) propose estimating partial frontiers with</p> <p>Graph</p> <p> <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>(</mo><mrow><mo>≥</mo><mn>1</mn></mrow><mo>)</mo></math> </ephtml> units randomly drawn from the sample. These estimates are repeated <emph>B</emph> times,[<reflink idref="bib3" id="ref127">3</reflink>]obtaining multiple measurements, then the final measurement (</p> <p>Graph</p> <p> <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mover><mi>λ</mi><mo>ˆ</mo></mover></mrow><mrow><mi>m</mi><mo>,</mo><mi>n</mi></mrow></msub></math> </ephtml> ) is calculated with a simple average.</p> <p>This estimator allows comparisons to be made with <emph>m</emph> potential units that have a similar input and contextual level. Note that since we do not use the entire sample, it is less sensitive to outliers and extreme values. Therefore, for higher values of <emph>m</emph>, the estimators of order-m tend tothe values of the Free Disposal Hull.</p> <hd id="AN0183842092-7">4. Data, variables and descriptive statistics</hd> <p>According to the 1991 Constitution and the 1994 Education Law, education is a right to which all people in Colombia have access. The Colombian educational system up to higher education is divided into four stages: preschool, primary education (5 years), basic secondary education (4 years), and middle education (2 years). Higher education is more complex since there are different programs of varying length and with multiple providers. In total, 8,604,145 students are enrolled. The public sector represents 78% and the private sector 19.6%. In recent years, total enrollment has decreased by approximately 23,000 students: in 2014, total enrollment was 8,627,797 students, and by 2019, it had fallen to 8,604,145. However, sector behavior was not homogeneous; the public sector increased by 1.2% (84,797 students) while the private sector decreased by 6.8% (122,938 students).</p> <p>The Colombian Institute for the Evaluation of Education (ICFES) is responsible for evaluating education throughout the country. These evaluations are carried out with multiple standardized exams at the national level, although the most important are Saber 3, 5, and 9, and Saber 11 for middle and high school education. Saber 11 is a standardized exam that students normally between 16 and 17 years old take at the end of secondary education and before entering technical, technological, or university education. In 2019, private sector students (average of 263) outperformed public sector students (average of 241) by 23 points.</p> <p>In line with the objective of the analysis, a database is built from two sources of information, the Colombian Institute for the Promotion of Higher Education (ICFES) and the National Administrative Department of Statistics (DANE). The ICFES offers information on standardized tests (for instance Saber 11, Saber Pro), and general characteristics of the students, their families, and the school. DANE offers information on the schools'physical and human resources. Based on the methodological approach proposed in the previous section, this paper uses a dependent and an independent variable for the multilevel regression. To study the relationship between the resilient students and the estimation of efficiency, it uses two outputs, five inputs and two contextual variables.</p> <p>To estimate resilient students through the multilevel model, students in a disadvantaged situation and those who have outstanding performance must be identified. In this study, students in a disadvantaged situation are selected based on the socioeconomic index calculated by the ICFES, following an item response theory methodology (DeMars [<reflink idref="bib26" id="ref128">26</reflink>]). This index is a comprehensive measure of the students'social, economic, and cultural environment, which includes their parents' education level and occupation, and the household income, among other factors.</p> <p>To define students with outstanding academic performance, the students' global score is used, which is a weighted average of the individual scores of each of the tests that the students take in the exam, divided by the total weight (<reflink idref="bib13" id="ref129">13</reflink>) and multiplied by the number of tests (<reflink idref="bib5" id="ref130">5</reflink>). A weighted average (three points for mathematics, reading, social studies, and natural sciences and one for the English language) is used on the recommendation of multiple authors (Agasisti et al. [<reflink idref="bib4" id="ref131">4</reflink>]; Hauser [<reflink idref="bib44" id="ref132">44</reflink>]), who consider it providesa more general evaluation of the students, and it is also the measure used in Colombian educational policy for accessing higher education.</p> <p>Two outputs are used to estimate the efficiency model:first, the global score <emph>(y1)</emph> explained above as a measure of quality (Cordero, Prior, and Simancas [<reflink idref="bib21" id="ref133">21</reflink>]; Tavana et al. [<reflink idref="bib65" id="ref134">65</reflink>]) of the students; andsecond, the students who pass <emph>(y2)</emph> the school year, as a complement to traditional measures to evaluate educational systems. The five selected inputs have frequently been used in the educational efficiency literature (De Witte and López-Torres [<reflink idref="bib28" id="ref135">28</reflink>]). The number of electronic devices <emph>(x1)</emph> includes tablets, desktop computers, and laptops, reflecting the resources available at their school (Agasisti [<reflink idref="bib1" id="ref136">1</reflink>]; Mancebón, Calero, and Ximénez-de-Embún [<reflink idref="bib49" id="ref137">49</reflink>]). Human capital is measured through teaching directors <emph>(x2)</emph> and teachers in classrooms <emph>(x3)</emph>; these variables provide an approximation of the educational and management personnel that educational institutions have for their operation (Haelermans and Ruggiero [<reflink idref="bib39" id="ref138">39</reflink>]; Tran and Villano [<reflink idref="bib67" id="ref139">67</reflink>]).[<reflink idref="bib4" id="ref140">4</reflink>] The number of students enrolled(<emph>x4</emph>)is one of the most commonly used inputs in the literature (Podinovski et al. [<reflink idref="bib60" id="ref141">60</reflink>]). Finally, the Socioeconomic Index(<emph>x5</emph>), which was also used to categorize resilient students and in the literature on educational efficiency, is one of the main sources of information on the production function (De Witte and López-Torres [<reflink idref="bib28" id="ref142">28</reflink>]). In addition, two categorical environment variables are included to control the context in which they operate: the educational sector <emph>(z1)</emph> and the year of application <emph>(z2)</emph>.</p> <p>Table 1 shows a summary of the descriptive statistics of the variables used in the empirical section, both to estimate resilient students and to measure efficiency. The variables provided by the ICFES through the Saber 11 exam are generalized for the entire school by dividing the sum of the variable by all the students who took the test per school and multiplying it by the number of students enrolled. Table 1 shows high levels of standard deviation in all the variables; in general, this is due to the heterogeneity in the territory where the schools operate and the functioning of the public and private sectors.</p> <p>Table 1. Descriptive statistics of inputs and outputs.</p> <p> <ephtml> <table><thead valign="bottom"><tr><td>Variables</td><td>Description</td><td>Average</td><td>Q1</td><td>Q3</td><td>Standard deviation</td><td>Average public</td><td>Average private</td><td>Source</td></tr></thead><tbody><tr><td><bold>Output</bold></td><td /><td /><td /><td /><td /><td /><td /><td /></tr><tr><td><italic>y1:</italic> global score</td><td>(Sum of the global score / Number of students Saber 11) * Educational institution enrollment</td><td>172,148</td><td>58,529</td><td>239,942</td><td>165,217</td><td>185,329</td><td>141,887</td><td>ICFES</td></tr><tr><td><italic>y2:</italic> successful students</td><td>Number of students who pass the school grade</td><td char=".">597</td><td char=".">217</td><td char=".">820</td><td char=".">558</td><td char=".">648</td><td char=".">477</td><td>DANE</td></tr><tr><td><bold>Input</bold></td><td /><td /><td /><td /><td /><td /><td /><td /></tr><tr><td><italic>x1</italic>: electronic equipment</td><td>Number of tablets, desktops, or laptops in use</td><td char=".">111</td><td char=".">28</td><td char=".">131</td><td char=".">153</td><td char=".">135</td><td char=".">54</td><td>DANE</td></tr><tr><td><italic>x2</italic>: teachers in management roles</td><td>Number of teachers who carry out management, planning, coordination, administration and orientation tasks</td><td char=".">3.7</td><td char=".">3.0</td><td char=".">4</td><td char=".">2.1</td><td char=".">3.6</td><td char=".">3.9</td><td>DANE</td></tr><tr><td><italic>x3:</italic> teachers</td><td>Number of teachers in educational work in classrooms</td><td char=".">30</td><td char=".">15</td><td char=".">38</td><td char=".">23</td><td char=".">31.2</td><td char=".">26.9</td><td>DANE</td></tr><tr><td><italic>x4</italic>: enrollment</td><td>Total number of students enrolled in the educational institution</td><td char=".">672</td><td char=".">238</td><td char=".">938</td><td char=".">624</td><td char=".">746</td><td char=".">500</td><td>DANE</td></tr><tr><td><italic>x5</italic>:socioeco-nomic Index</td><td>(Sum of the socioeconomic and cultural index/ Number of students Saber 11) * Educational institution enrollment</td><td>33,769</td><td>11,164</td><td>47,336</td><td>32,847</td><td>35,579</td><td>29,614</td><td>ICFES</td></tr><tr><td><bold>contextual variables</bold><xref ref-type="fn" rid="fn6" /></td><td /><td><bold>Category</bold></td><td><bold>%</bold></td><td /><td /><td /><td /><td /></tr><tr><td>Sector</td><td>Educational sector where the school operates (public or private)</td><td>Public</td><td char=".">71.96%</td><td /><td /><td /><td /><td>DANE</td></tr><tr><td>Private</td><td char=".">28.04%</td><td /><td /><td /><td /></tr><tr><td>Year</td><td>Current educational year. (2014–2019)</td><td>Each year represents approximately 16.5% of the sample</td><td /><td /><td /><td /><td>ICFES</td></tr></tbody></table> </ephtml> </p> <p>1 Source: the authors.</p> <p>Due to the heterogeneities in educational access and quality among the 32 departments and the educational sectors (public and private) of Colombia, the descriptions and results are presented with this disaggregation. The gaps between educational sectors are worrying, since there is great pressure on household spending to provide access to education for their children, which generates effects on their well-being (OECD [<reflink idref="bib56" id="ref143">56</reflink>]). In addition, there is evidence of the gap generated by the availability of resources between these sectors (Castro Aristizabal [<reflink idref="bib14" id="ref144">14</reflink>]).</p> <p>The global score and the number of resilient students have a significant correlation of 17% in the public sector and 20% in the private sector. The difference in the magnitude of the relationships between variables of the educational sectors should be highlighted, since the private sector has only 28.8% of the schools under analysis and 21.3% of enrolled students.</p> <p>Figure 1 shows the global score and the number of resilient students by department and educational sector. Two aspects stand out from this figure. First, there are significant differences between the sectors. The private sector does not have many resilient students per department, compared to the public sector;note that not all the departments have schools in the private sector (Vichada department has no private sector schools in the sample). Second, part of the heterogeneity in the public sector is explained by the concentration in the departments with the largest populations, whichlogically have a greater number of schools and students. Finally, due to the nature of private sectorfinancing, it is not expected to have many students in a disadvantaged situation, at least in the main cities, where there is a relatively larger educational market.</p> <p>Graph: Figure 1. Global score and resilient students by department and sector. Source: the authors.</p> <hd id="AN0183842092-8">5. Results</hd> <p>This section presents the results of the equity (number of resilient students) and efficiency estimates, as well as the relationship between these measures. First, the results of the multilevel model are shown considering multiple thresholds, followed by the descriptive results of the conditional order-m model. Finally, the relationship disaggregated by the educational sector of these two measures is analyzed.</p> <p>The results obtained in the first stage with the multilevel model identify resilient students for the later stages. Models are estimated with three (20%, 25%, and 33%)[<reflink idref="bib5" id="ref145">5</reflink>] different thresholds to increaserobustness. Table 2 shows the model results as the percentage of resilient students by sector, year, and threshold. On average, between 0.5% and 2.24% of students in the private sector are resilient, whereas in the public sector the range is between 7.36% and 18.48%.</p> <p>Table 2. Percentage of resilient students by schoolsector, year and thresholds.</p> <p> <ephtml> <table><thead valign="bottom"><tr><td>Sector</td><td>Year</td><td>Resilients 20%</td><td>Resilients 25%</td><td>Resilients 33%</td><td>Number of students</td></tr></thead><tbody><tr><td>Public</td><td char=".">2014</td><td char=".">7.95%</td><td char=".">11.86%</td><td char=".">19.76%</td><td char=".">331,643</td></tr><tr><td char=".">2015</td><td char=".">7.74%</td><td char=".">11.72%</td><td char=".">19.85%</td><td char=".">339,026</td></tr><tr><td char=".">2016</td><td char=".">7.57%</td><td char=".">11.32%</td><td char=".">19.07%</td><td char=".">317,061</td></tr><tr><td char=".">2017</td><td char=".">7.07%</td><td char=".">10.54%</td><td char=".">17.62%</td><td char=".">328,675</td></tr><tr><td char=".">2018</td><td char=".">6.90%</td><td char=".">10.27%</td><td char=".">17.23%</td><td char=".">326,181</td></tr><tr><td char=".">2019</td><td char=".">6.96%</td><td char=".">10.32%</td><td char=".">17.36%</td><td char=".">331,143</td></tr><tr><td>Private</td><td char=".">2014</td><td char=".">0.40%</td><td char=".">0.71%</td><td char=".">1.75%</td><td char=".">93,622</td></tr><tr><td char=".">2015</td><td char=".">0.33%</td><td char=".">0.71%</td><td char=".">1.71%</td><td char=".">97,367</td></tr><tr><td char=".">2016</td><td char=".">0.45%</td><td char=".">0.82%</td><td char=".">1.95%</td><td char=".">79,923</td></tr><tr><td char=".">2017</td><td char=".">0.78%</td><td char=".">1.36%</td><td char=".">2.80%</td><td char=".">82,315</td></tr><tr><td char=".">2018</td><td char=".">0.77%</td><td char=".">1.27%</td><td char=".">2.66%</td><td char=".">75,605</td></tr><tr><td char=".">2019</td><td char=".">0.75%</td><td char=".">1.30%</td><td char=".">2.59%</td><td char=".">93,246</td></tr><tr><td>Total</td><td char=".">5.94%</td><td char=".">8.92%</td><td char=".">15.09%</td><td char=".">2,495,807</td></tr></tbody></table> </ephtml> </p> <p>2 Source: the authors.</p> <p>The results of the multilevel model show that there is a significant relationship between the Socioeconomic Index and the globalscore. In addition, the variance participation coefficient justifies the inclusion of the two levels (school and municipality). The correlation between the results when different thresholds are used is significant and high, as can be seen in Annex 1.</p> <p>The efficiency estimates are made following the methodological proposal described in section 4b. To estimate a conditional order-m model, the value of the parameters<emph>m</emph>and <emph>B</emph>must be determined, which is the size of the partial frontier with which the other schools are going to be compared and the number of times this process is repeated. In this case, it is determined as11,000(<emph>m</emph>) and 200 (<emph>B</emph>), since these are the numbers with which there are 10% of super-efficient units in the estimates (Bonaccorsi, Daraio, and Simar [<reflink idref="bib12" id="ref146">12</reflink>]; Felder and Tauchmann [<reflink idref="bib31" id="ref147">31</reflink>]) per year. An orientation toward output is used, since the general objective of students and educational managers is to maximize performance subject to given resources.</p> <p>Table 3 offers an overview of the estimates, where levels greater than one show inefficiency or potential efficiency given the inputs, and the results of models are disaggregated by year and educational sector. General interpretations of the results are made with the average efficiency measure (column 3). The average inefficiency level in 2019 is 1.2151;thismeans that they could increase their test scores and the number of students who pass the exam by 21.51% without using a higher level of inputs. In this regard, public schools have a potential level of efficiency of 22.59%, while for the private sector it is 18.84% in that year. The resultsshowthat on average levels of inefficiency are higher in the public sector than in the private sectorfrom 2016 until 2019.</p> <p>Table 3. Descriptive statistics of the results by sector.</p> <p> <ephtml> <table><thead valign="bottom"><tr><td>Year</td><td>Sector</td><td>Mean</td><td>SD</td><td>Min</td><td>Q1</td><td>Median</td><td>Q3</td><td>Max</td></tr></thead><tbody><tr><td>Total</td><td>Public</td><td char=".">1.2321</td><td char=".">0.1199</td><td char=".">0.9277</td><td char=".">1.1532</td><td char=".">1.2272</td><td char=".">1.3038</td><td char=".">2.0085</td></tr><tr><td>Private</td><td char=".">1.2168</td><td char=".">0.1343</td><td char=".">0.9998</td><td char=".">1.1202</td><td char=".">1.2001</td><td char=".">1.2985</td><td char=".">2.0334</td></tr><tr><td>Total</td><td char=".">1.2278</td><td char=".">0.1243</td><td char=".">0.9276</td><td char=".">1.1436</td><td char=".">1.2204</td><td char=".">1.3025</td><td char=".">2.0334</td></tr><tr><td>2019</td><td>Public</td><td char=".">1.2259</td><td char=".">0.1164</td><td char=".">0.9277</td><td char=".">1.1511</td><td char=".">1.2213</td><td char=".">1.2928</td><td char=".">2.0085</td></tr><tr><td>Private</td><td char=".">1.1884</td><td char=".">0.1223</td><td char=".">1.0000</td><td char=".">1.1040</td><td char=".">1.1701</td><td char=".">1.2504</td><td char=".">1.8325</td></tr><tr><td>Total</td><td char=".">1.2151</td><td char=".">0.1193</td><td char=".">0.9277</td><td char=".">1.1357</td><td char=".">1.2068</td><td char=".">1.2851</td><td char=".">2.0085</td></tr><tr><td>2018</td><td>Public</td><td char=".">1.2280</td><td char=".">0.1136</td><td char=".">0.9336</td><td char=".">1.1548</td><td char=".">1.2260</td><td char=".">1.2996</td><td char=".">1.8383</td></tr><tr><td>Private</td><td char=".">1.2107</td><td char=".">0.1395</td><td char=".">1.0000</td><td char=".">1.1124</td><td char=".">1.1918</td><td char=".">1.2929</td><td char=".">2.0171</td></tr><tr><td>Total</td><td char=".">1.2235</td><td char=".">0.1212</td><td char=".">0.9336</td><td char=".">1.1419</td><td char=".">1.2177</td><td char=".">1.2984</td><td char=".">2.0171</td></tr><tr><td>2017</td><td>Public</td><td char=".">1.2471</td><td char=".">0.1270</td><td char=".">0.9723</td><td char=".">1.1634</td><td char=".">1.2405</td><td char=".">1.3208</td><td char=".">1.9026</td></tr><tr><td>Private</td><td char=".">1.2255</td><td char=".">0.1253</td><td char=".">1.0000</td><td char=".">1.1361</td><td char=".">1.2190</td><td char=".">1.3066</td><td char=".">1.7549</td></tr><tr><td>Total</td><td char=".">1.2412</td><td char=".">0.1269</td><td char=".">0.9723</td><td char=".">1.1560</td><td char=".">1.2346</td><td char=".">1.3182</td><td char=".">1.9026</td></tr><tr><td>2016</td><td>Public</td><td char=".">1.2439</td><td char=".">0.1224</td><td char=".">0.9853</td><td char=".">1.1636</td><td char=".">1.2435</td><td char=".">1.3180</td><td char=".">1.8216</td></tr><tr><td>Private</td><td char=".">1.2208</td><td char=".">0.1402</td><td char=".">1.0000</td><td char=".">1.1176</td><td char=".">1.2060</td><td char=".">1.3049</td><td char=".">1.9343</td></tr><tr><td>Total</td><td char=".">1.2375</td><td char=".">0.1280</td><td char=".">0.9853</td><td char=".">1.1517</td><td char=".">1.2355</td><td char=".">1.3158</td><td char=".">1.9343</td></tr><tr><td>2015</td><td>Public</td><td char=".">1.2501</td><td char=".">0.1273</td><td char=".">0.9695</td><td char=".">1.1622</td><td char=".">1.2504</td><td char=".">1.3339</td><td char=".">1.8265</td></tr><tr><td>Private</td><td char=".">1.2517</td><td char=".">0.1444</td><td char=".">0.9999</td><td char=".">1.1518</td><td char=".">1.2420</td><td char=".">1.3409</td><td char=".">2.0334</td></tr><tr><td>Total</td><td char=".">1.2505</td><td char=".">0.1325</td><td char=".">0.9695</td><td char=".">1.1595</td><td char=".">1.2484</td><td char=".">1.3352</td><td char=".">2.0334</td></tr><tr><td>2014</td><td>Public</td><td char=".">1.1991</td><td char=".">0.1036</td><td char=".">0.9535</td><td char=".">1.1351</td><td char=".">1.1968</td><td char=".">1.2566</td><td char=".">1.9164</td></tr><tr><td>Private</td><td char=".">1.2054</td><td char=".">0.1250</td><td char=".">1.0000</td><td char=".">1.1154</td><td char=".">1.1904</td><td char=".">1.2839</td><td char=".">1.9038</td></tr><tr><td>Total</td><td char=".">1.2009</td><td char=".">0.1103</td><td char=".">0.9535</td><td char=".">1.1291</td><td char=".">1.1953</td><td char=".">1.2626</td><td char=".">1.9164</td></tr></tbody></table> </ephtml> </p> <p>3 Source: the authors</p> <p>Table 4 shows the efficiency levels by educational sector and municipal category. In Colombia these categories are defined according to variables such as economic activity, financial performance and institutional capacity. The municipalities where the greatest development and economic and institutional capacities are found is a special case, with only nine municipalities, mainly the large departmentalcapitals. On the other hand, there are 1,178 municipalities in category F, close to 88% of the total. This table highlights two findings. First, the poorerperformance of public sector institutions is marked by the vast majority of small municipalities with few institutional capacities, since it is the only category where performance is worse in the public sector (1.2544) than in the private one (1.2305). Second, as the municipal category decreases, the levels of inefficiency increase, rising from 1.1972 to 1.2530 on average.</p> <p>Table 4. Efficiency results by educational sector and municipal category.</p> <p> <ephtml> <table><thead valign="bottom"><tr><td>Category</td><td>Public</td><td>Private</td><td>Total</td></tr></thead><tbody><tr><td>Special</td><td char=".">1.1986</td><td char=".">1.1959</td><td char=".">1.1972</td></tr><tr><td>A</td><td char=".">1.1985</td><td char=".">1.2298</td><td char=".">1.2115</td></tr><tr><td>B</td><td char=".">1.1891</td><td char=".">1.2195</td><td char=".">1.2032</td></tr><tr><td>C</td><td char=".">1.2216</td><td char=".">1.2385</td><td char=".">1.2272</td></tr><tr><td>D</td><td char=".">1.2321</td><td char=".">1.2427</td><td char=".">1.2352</td></tr><tr><td>E</td><td char=".">1.231</td><td char=".">1.26969</td><td char=".">1.2422</td></tr><tr><td>F</td><td char=".">1.2544</td><td char=".">1.2305</td><td char=".">1.2530</td></tr><tr><td>Total</td><td char=".">1.2319</td><td char=".">1.2165</td><td char=".">1.2276</td></tr></tbody></table> </ephtml> </p> <p>4 Source: the authors.</p> <p>Table 5 illustrates the levels of correlation between resilient students and efficiency, disaggregated by educational sector and year. There is a negative correlation between the levels of inefficiency (efficiency values greater than the unit) and the number of resilient students. In the public sector there is a negative correlation up to 33 in 2019;thismeans thatthe number of resilient students falls as the level of inefficiency increases. When the total sample and the private sector schools are analyzed, the correlations follow the same trend (−19 and −11 in 2019), but with lower magnitudes. When the relationship between resilient students andeducational efficiency is analyzed, the same consistency is found by sector and year.</p> <p>Table 5. Spearman correlation between resilient students and efficiency estimated by sector and year.</p> <p> <ephtml> <table><thead valign="bottom"><tr><td>Year</td><td>Public sector</td><td>Private sector</td><td>Total</td></tr></thead><tbody><tr><td>2019</td><td char=".">−0.3307***</td><td char=".">−0.1193***</td><td char=".">−0.1988***</td></tr><tr><td>2018</td><td char=".">−0.2941***</td><td char=".">−0.1108***</td><td char=".">−0.2012***</td></tr><tr><td>2017</td><td char=".">−0.3103***</td><td char=".">−0.1209***</td><td char=".">−0.2199***</td></tr><tr><td>2016</td><td char=".">−0.2761***</td><td char=".">−0.0339</td><td char=".">−0.1821***</td></tr><tr><td>2015</td><td char=".">−0.2519***</td><td char=".">−0.1089***</td><td char=".">−0.1969***</td></tr><tr><td>2014</td><td char=".">−0.2281***</td><td char=".">−0.0706**</td><td char=".">−0.1802***</td></tr></tbody></table> </ephtml> </p> <ulist> <item>5 (***): significant at 1% confidence level.</item> <item>6 Source: the authors.</item> </ulist> <p>As mentioned above, the differences between educational departments and sectors in Colombia are significant. Annex 2 reports the efficiency results disaggregated by department to show the social gaps between regions. The highest level of average inefficiency by department is evidenced in 2019 in the private sector: Chocó has an inefficiency level of 83.15%. Likewise, in 2018, the difference between the department with the best and worst performance in the public sector is 26.17%, whereas in the private sector the largest gap is identified in 2019 with a difference of 70.90%. Finally, the results show that in all the years at least 33% of the departments (10 out of 32) have worse behavior in the public sector than in the private sector.</p> <p>We can summarize the results presented in the paper in three main points. First, there is a high correlation when different thresholds are used to estimate resilient students. Second, there is a negative relationship between inefficiency and the number of resilient students in both sectors. Third, there are large differences between educational departments and sectors, in general, with worse performance in the public sector than in the private sector.</p> <hd id="AN0183842092-9">6. Concluding remarks and policy implications</hd> <p>This article uses two complementary methodologies to analyze resilient students and their relationship with educational efficiency. First, a multilevel model with random intercept and random slope is estimated with the students' socioeconomic index as the independent variable and the global score as the dependent variable, considering the municipalities at a second level. Afterwards, a conditional order-m model is used to estimate educational efficiency and analyze the relationship. These models are based onthe global score of Saber 11 and the number ofstudents who pass the year exams as outputs.</p> <p>The main conclusion that can be drawnin this study is the negative relationship between educational inefficiency and the number of resilient students. In addition, three further aspects can be highlighted. First, we found that in most of the years analyzed, the public sector performs worse than the private sector in the models estimated. Second,the negative relationship between resilience and school inefficiency is greater in the public sector than in the private sector in 33% of the departments. Third, there are large gaps in efficiency, up to 70%,between educational departments.</p> <p>Decision makers and policymakers in Colombia should take these findings into account,since as well as traditional ways of evaluating the educational system, complementary evaluations focusing on social mobility are also implemented. It is important to develop specific territorial policies that consider the differences between sectors and departments. A negative relationship is found between the inefficiency of schools and the number of resilient students, that is, as the number of resilient students increases, a lower level of efficiency is found.</p> <p>These conclusions are not ideal for an educational system, although they do coincide with the low levels of social mobility found by the OECD ([<reflink idref="bib57" id="ref148">57</reflink>]). The negative relationship between efficiency and resilience could be associated with problems and costs in educational processes. These costs may be related to the increase in problems of cooperation and coordination of educational processes with students from low socioeconomic levels within the specific environment. In addition, educational institutions and municipalities have limited capacityto efficiently manage inequality within vulnerable contexts.</p> <p>The problems of coordination and cooperation may be compounded by pedagogical problems in the classroom due to the presence of diverse groups, as educational systems have implemented a comprehensive approach to address the difficulties have in dealing with differences among the students. However, in a country as unequal and inequitable as Colombia, a diverse mix of students is both ideal and necessary, since it helps social mobility. This conclusion opens up an interesting line of research, namely to analyze the tradeoff between the decrease in efficiency and the benefits of social mobility due to resilient students.</p> <p>On the other hand, we found that on average there is lower efficiency in municipalities with lower capacities. In general, the results show that the public sector helps social mobility significantly more than the private sector does, but the private sectorhas better levels of efficiency. However, this occurs mainly in municipalities with low institutional capacities. Therefore, the relationship of educational processes within institutions must be analyzed in depth,taking into account the institutional capacities of the municipalities.</p> <p>The main implications of the results concern how the allocation of resources helps to improve the efficiency levels of schools. The relationships found between resilient students and school efficiencysuggest that, if resources are targeted to improve the efficiency performance of resilient students, there is greater potential for improvement in academic performance for the school, as compared to asituation where efforts are focused onstudents with average academic behavior.</p> <p>Educational policymakers should consider severalfactors when studying educational resilience in developing countries with high social inequity. The environments in some municipalities are challenging: they have experienced violence due to armed conflict, inconsistent access to and quality of basic education, and high or extreme rates of poverty. In such contexts, the efficient use of resources is even more crucial. Educational policies should therefore include robust efficiency measures such as the one we present in this study when determining budget allocation, disaggregated by sector, municipality, and even targetingsingle educational institutions.</p> <p>Some lines for future research can be identified. First, the results of Saber 11 are used to represent the whole school; extensions shouldbe made in other stages of the educational cycle. Second, radial distances can be used to analyze how to improve specific outputs as soon as possible, which facilitates a complementary analysis on the allocation of resources to the recipient students (Aparicio et al. [<reflink idref="bib8" id="ref149">8</reflink>]). Third, conditional models can be used to recognize and analyze the relevance of specific contextualvariables. Fourth, approaches that combine quasi-experimental methodologies should be used to help control endogeneity in the process (i.e. self-selection of students across schools) in order to infer causality in the relationship between schools' efficiency and academic resilience.</p> <hd id="AN0183842092-10">Appendices</hd> <p></p> <hd id="AN0183842092-11">Appendix 1. Correlation matrix of resilient students with different thresholds</hd> <p></p> <p> <ephtml> <table><thead valign="bottom"><tr><td>Thresholds</td><td>20%</td><td>25%</td><td>33%</td></tr></thead><tbody><tr><td>20%</td><td char=".">1.0000</td></tr><tr><td>25%</td><td char=".">0.9688***</td><td char=".">1.0000</td></tr><tr><td>33%</td><td char=".">0.9058***</td><td char=".">0.9586***</td><td char=".">1.0000</td></tr></tbody></table> </ephtml> </p> <ulist> <item>7 (***): significant at 1% confidence level.</item> <item>8 Source: the authors.</item> </ulist> <hd id="AN0183842092-12">Appendix 2. Educational efficiency by department, year and sector</hd> <p></p> <p> <ephtml> <table><thead valign="bottom"><tr><td>Department</td><td>2014</td><td>2015</td><td>2016</td><td>2017</td><td>2018</td><td>2019</td></tr><tr><td>Public</td><td>Private</td><td>Public</td><td>Private</td><td>Public</td><td>Private</td><td>Public</td><td>Private</td><td>Public</td><td>Private</td><td>Public</td><td>Private</td></tr></thead><tbody><tr><td>Amazonas</td><td char=".">1.2922</td><td char=".">1.1367</td><td char=".">1.3902</td><td char=".">1.1799</td><td char=".">1.3982</td><td char=".">1.1655</td><td char=".">1.3336</td><td char=".">1.0822</td><td char=".">1.4111</td><td char=".">1.1257</td><td char=".">1.2194</td><td char=".">1.1225</td></tr><tr><td>Antioquia</td><td char=".">1.2031</td><td char=".">1.1904</td><td char=".">1.2526</td><td char=".">1.2292</td><td char=".">1.2510</td><td char=".">1.1971</td><td char=".">1.2387</td><td char=".">1.2158</td><td char=".">1.2359</td><td char=".">1.1919</td><td char=".">1.2349</td><td char=".">1.1824</td></tr><tr><td>Arauca</td><td char=".">1.1843</td><td char=".">1.2374</td><td char=".">1.2193</td><td char=".">1.3325</td><td char=".">1.2202</td><td char=".">1.2488</td><td char=".">1.2108</td><td char=".">1.2373</td><td char=".">1.1692</td><td char=".">1.1941</td><td char=".">1.1623</td><td char=".">1.1684</td></tr><tr><td>Atlántico</td><td char=".">1.2118</td><td char=".">1.2030</td><td char=".">1.2409</td><td char=".">1.2473</td><td char=".">1.2354</td><td char=".">1.2331</td><td char=".">1.2349</td><td char=".">1.2353</td><td char=".">1.2231</td><td char=".">1.2429</td><td char=".">1.2052</td><td char=".">1.2069</td></tr><tr><td>Bogotá, D.C</td><td char=".">1.1328</td><td char=".">1.1767</td><td char=".">1.1751</td><td char=".">1.2301</td><td char=".">1.1639</td><td char=".">1.1842</td><td char=".">1.1731</td><td char=".">1.2016</td><td char=".">1.1723</td><td char=".">1.1845</td><td char=".">1.1885</td><td char=".">1.1723</td></tr><tr><td>Bolívar</td><td char=".">1.2341</td><td char=".">1.1588</td><td char=".">1.2628</td><td char=".">1.1925</td><td char=".">1.2892</td><td char=".">1.1955</td><td char=".">1.2992</td><td char=".">1.1771</td><td char=".">1.2935</td><td char=".">1.1410</td><td char=".">1.2589</td><td char=".">1.1246</td></tr><tr><td>Boyacá</td><td char=".">1.1868</td><td char=".">1.2029</td><td char=".">1.2610</td><td char=".">1.2288</td><td char=".">1.2247</td><td char=".">1.1996</td><td char=".">1.2223</td><td char=".">1.1886</td><td char=".">1.1795</td><td char=".">1.1877</td><td char=".">1.1992</td><td char=".">1.1761</td></tr><tr><td>Caldas</td><td char=".">1.2875</td><td char=".">1.2531</td><td char=".">1.3444</td><td char=".">1.2725</td><td char=".">1.3286</td><td char=".">1.2572</td><td char=".">1.3053</td><td char=".">1.2663</td><td char=".">1.2707</td><td char=".">1.2470</td><td char=".">1.2913</td><td char=".">1.2184</td></tr><tr><td>Caquetá</td><td char=".">1.2272</td><td char=".">1.1743</td><td char=".">1.2731</td><td char=".">1.2191</td><td char=".">1.3009</td><td char=".">1.2768</td><td char=".">1.3080</td><td char=".">1.2448</td><td char=".">1.2775</td><td char=".">1.2492</td><td char=".">1.2697</td><td char=".">1.1312</td></tr><tr><td>Casanare</td><td char=".">1.1799</td><td char=".">1.2435</td><td char=".">1.2285</td><td char=".">1.3216</td><td char=".">1.2019</td><td char=".">1.2316</td><td char=".">1.2314</td><td char=".">1.1958</td><td char=".">1.2049</td><td char=".">1.2297</td><td char=".">1.2070</td><td char=".">1.1942</td></tr><tr><td>Cauca</td><td char=".">1.2156</td><td char=".">1.2560</td><td char=".">1.2801</td><td char=".">1.3248</td><td char=".">1.2881</td><td char=".">1.3574</td><td char=".">1.3024</td><td char=".">1.3161</td><td char=".">1.2520</td><td char=".">1.3070</td><td char=".">1.2426</td><td char=".">1.2598</td></tr><tr><td>Cesar</td><td char=".">1.2110</td><td char=".">1.2829</td><td char=".">1.2455</td><td char=".">1.3160</td><td char=".">1.2320</td><td char=".">1.2979</td><td char=".">1.2438</td><td char=".">1.2746</td><td char=".">1.2285</td><td char=".">1.2680</td><td char=".">1.1965</td><td char=".">1.2366</td></tr><tr><td>Chocó</td><td char=".">1.3356</td><td char=".">1.4203</td><td char=".">1.3552</td><td char=".">1.4351</td><td char=".">1.3954</td><td char=".">1.3794</td><td char=".">1.7158</td><td char=".">1.3856</td><td char=".">1.6051</td><td char=".">1.3249</td><td char=".">1.8315</td></tr><tr><td>Córdoba</td><td char=".">1.1735</td><td char=".">1.2298</td><td char=".">1.2194</td><td char=".">1.2273</td><td char=".">1.2242</td><td char=".">1.2244</td><td char=".">1.2443</td><td char=".">1.2101</td><td char=".">1.2185</td><td char=".">1.2196</td><td char=".">1.2037</td><td char=".">1.1746</td></tr><tr><td>Cundinamarca</td><td char=".">1.1958</td><td char=".">1.2068</td><td char=".">1.2733</td><td char=".">1.2497</td><td char=".">1.2486</td><td char=".">1.2196</td><td char=".">1.2432</td><td char=".">1.2217</td><td char=".">1.2220</td><td char=".">1.2094</td><td char=".">1.2300</td><td char=".">1.1819</td></tr><tr><td>Guaviare</td><td char=".">1.2508</td><td char=".">1.1540</td><td char=".">1.2422</td><td char=".">1.3470</td><td char=".">1.2923</td><td char=".">1.2956</td><td char=".">1.3099</td><td char=".">1.3259</td><td char=".">1.2697</td><td char=".">1.3197</td><td char=".">1.3222</td><td char=".">1.2203</td></tr><tr><td>Huila</td><td char=".">1.1966</td><td char=".">1.2280</td><td char=".">1.2554</td><td char=".">1.2534</td><td char=".">1.2457</td><td char=".">1.2208</td><td char=".">1.2503</td><td char=".">1.2267</td><td char=".">1.2164</td><td char=".">1.2141</td><td char=".">1.2141</td><td char=".">1.1917</td></tr><tr><td>La Guajira</td><td char=".">1.2040</td><td char=".">1.2234</td><td char=".">1.2395</td><td char=".">1.2313</td><td char=".">1.2747</td><td char=".">1.2271</td><td char=".">1.2959</td><td char=".">1.2182</td><td char=".">1.3095</td><td char=".">1.2095</td><td char=".">1.2816</td><td char=".">1.1769</td></tr><tr><td>Magdalena</td><td char=".">1.2439</td><td char=".">1.2623</td><td char=".">1.2669</td><td char=".">1.2894</td><td char=".">1.2875</td><td char=".">1.2989</td><td char=".">1.3140</td><td char=".">1.2872</td><td char=".">1.3027</td><td char=".">1.2898</td><td char=".">1.2629</td><td char=".">1.2457</td></tr><tr><td>Meta</td><td char=".">1.1879</td><td char=".">1.2641</td><td char=".">1.1937</td><td char=".">1.3138</td><td char=".">1.2118</td><td char=".">1.2472</td><td char=".">1.2189</td><td char=".">1.2691</td><td char=".">1.2149</td><td char=".">1.2766</td><td char=".">1.2147</td><td char=".">1.2270</td></tr><tr><td>Nariño</td><td char=".">1.1259</td><td char=".">1.2180</td><td char=".">1.1895</td><td char=".">1.2445</td><td char=".">1.1698</td><td char=".">1.1947</td><td char=".">1.1776</td><td char=".">1.2356</td><td char=".">1.1494</td><td char=".">1.1969</td><td char=".">1.1541</td><td char=".">1.1619</td></tr><tr><td>Norte de Santander</td><td char=".">1.1880</td><td char=".">1.2043</td><td char=".">1.2444</td><td char=".">1.2477</td><td char=".">1.2099</td><td char=".">1.2428</td><td char=".">1.2072</td><td char=".">1.2438</td><td char=".">1.1764</td><td char=".">1.2302</td><td char=".">1.1798</td><td char=".">1.2082</td></tr><tr><td>Putumayo</td><td char=".">1.2268</td><td char=".">1.1257</td><td char=".">1.2340</td><td char=".">1.2712</td><td char=".">1.2432</td><td char=".">1.3179</td><td char=".">1.2447</td><td char=".">1.3003</td><td char=".">1.2069</td><td char=".">1.3094</td><td char=".">1.2333</td><td char=".">1.1980</td></tr><tr><td>Quindío</td><td char=".">1.2095</td><td char=".">1.2510</td><td char=".">1.2709</td><td char=".">1.3071</td><td char=".">1.2718</td><td char=".">1.1973</td><td char=".">1.2653</td><td char=".">1.1896</td><td char=".">1.2459</td><td char=".">1.2045</td><td char=".">1.2360</td><td char=".">1.1824</td></tr><tr><td>Risaralda</td><td char=".">1.1903</td><td char=".">1.2400</td><td char=".">1.2447</td><td char=".">1.2633</td><td char=".">1.2449</td><td char=".">1.2550</td><td char=".">1.2439</td><td char=".">1.2327</td><td char=".">1.2348</td><td char=".">1.2296</td><td char=".">1.2359</td><td char=".">1.1988</td></tr><tr><td>Santander</td><td char=".">1.1887</td><td char=".">1.2236</td><td char=".">1.2313</td><td char=".">1.2732</td><td char=".">1.2061</td><td char=".">1.2281</td><td char=".">1.2086</td><td char=".">1.2118</td><td char=".">1.1746</td><td char=".">1.2144</td><td char=".">1.1835</td><td char=".">1.1824</td></tr><tr><td>San Andres y Providencia</td><td char=".">1.2686</td><td char=".">1.1992</td><td char=".">1.3635</td><td char=".">1.2624</td><td char=".">1.3247</td><td char=".">1.2208</td><td char=".">1.3273</td><td char=".">1.2590</td><td char=".">1.3549</td><td char=".">1.1765</td><td char=".">1.3832</td><td char=".">1.2347</td></tr><tr><td>Sucre</td><td char=".">1.1918</td><td char=".">1.2053</td><td char=".">1.2480</td><td char=".">1.2836</td><td char=".">1.2540</td><td char=".">1.2586</td><td char=".">1.2575</td><td char=".">1.2111</td><td char=".">1.2487</td><td char=".">1.2158</td><td char=".">1.2361</td><td char=".">1.2211</td></tr><tr><td>Tolima</td><td char=".">1.2142</td><td char=".">1.2551</td><td char=".">1.3007</td><td char=".">1.3053</td><td char=".">1.2760</td><td char=".">1.2694</td><td char=".">1.2949</td><td char=".">1.2722</td><td char=".">1.2625</td><td char=".">1.2588</td><td char=".">1.2709</td><td char=".">1.2301</td></tr><tr><td>Valle del Cauca</td><td char=".">1.1982</td><td char=".">1.2186</td><td char=".">1.2473</td><td char=".">1.2857</td><td char=".">1.2527</td><td char=".">1.2563</td><td char=".">1.2599</td><td char=".">1.2701</td><td char=".">1.2589</td><td char=".">1.2293</td><td char=".">1.2566</td><td char=".">1.2086</td></tr><tr><td>Vaupés</td><td char=".">1.2326</td><td char=".">1.3799</td><td char=".">1.2534</td><td char=".">1.2985</td><td char=".">1.2839</td><td char=".">1.3958</td><td char=".">1.2855</td><td char=".">1.2472</td><td char=".">1.2504</td></tr><tr><td>Vichada</td><td char=".">1.2113</td><td char=".">1.2242</td><td char=".">1.2876</td><td char=".">1.3037</td><td char=".">1.2795</td><td char=".">1.2626</td></tr><tr><td>Total</td><td char=".">1.1991</td><td char=".">1.2054</td><td char=".">1.2501</td><td char=".">1.2517</td><td char=".">1.2439</td><td char=".">1.2208</td><td char=".">1.2471</td><td char=".">1.2255</td><td char=".">1.228</td><td char=".">1.2107</td><td char=".">1.2259</td><td char=".">1.1884</td></tr></tbody></table> </ephtml> </p> <p>9 Source: the authors.</p> <ref id="AN0183842092-13"> <title> Notes </title> <blist> <bibl id="bib1" idref="ref31" type="bt">1</bibl> <bibtext> Before 2014, the results of the standardized test for secondary education are not comparable due to methodological changes.</bibtext> </blist> <blist> <bibl id="bib2" idref="ref18" type="bt">2</bibl> <bibtext> This type of result has implications for the average values of the sample studied since it can bring the averages to values close to one. However, this possibility is mitigated by setting <emph>m</emph> to obtain 10% super-efficient units (Tauchmann [64]).</bibtext> </blist> <blist> <bibl id="bib3" idref="ref57" type="bt">3</bibl> <bibtext> The estimates are repeated 200 times, following the trend in this line of research (Thieme, Prior, and Tortosa-Ausina [66]).</bibtext> </blist> <blist> <bibl id="bib4" idref="ref2" type="bt">4</bibl> <bibtext> Two variables are added to measure the human capital because, first, there is a difference in the functions, andsecond, in the public sector budgets are generally allocated according to the number of students in the school, whereas in the private sector this depends on the administrative orientation of the school and its board; these allocationsaffect the number of teachersemployed.</bibtext> </blist> <blist> <bibl id="bib5" idref="ref76" type="bt">5</bibl> <bibtext> After the estimation in Table 2, the baseline scenario described in this section of the paper considers the threshold of 25%.</bibtext> </blist> <blist> <bibl id="bib6" idref="ref10" type="bt">6</bibl> <bibtext> Categorical variables are used to control for the environment in which schools operate. For this reason, descriptive statistics are not presented.</bibtext> </blist> </ref> <ref id="AN0183842092-14"> <title> References </title> <blist> <bibtext> Agasisti, T. 2011. " How Competition Affects Schools' Performances: Does Specification Matter? " Economics Letters 110 (3): 259 – 261. https://doi.org/10.1016/j.econlet.2010.11.035.</bibtext> </blist> <blist> <bibtext> Agasisti, T. 2013. " The Efficiency of Italian Secondary Schools and the Potential Role of Competition: A Data Envelopment Analysis Using OECD-PISA2006 Data." Education Economics 21 (5): 520 – 544.</bibtext> </blist> <blist> <bibtext> Agasisti, T., F. Avvisati, F. Borgonovi, and S. Longobardi. 2018. " Academic Resilience: What Schools and Countries Do to Help Disadvantaged Students Succeed in PISA." OECD Education Working Papers 167 : 1 – 37.</bibtext> </blist> <blist> <bibtext> Agasisti, T., F. Avvisati, F. Borgonovi, and S. Longobardi. 2021. " What School Factors are Associated with the Success of Socio-Economically Disadvantaged Students? An Empirical Investigation Using PISA Data." Social Indicators Research, 157 : 749 – 781.</bibtext> </blist> <blist> <bibtext> Agasisti, T., and S. Longobardi. 2014. " Inequality in Education: Can Italian Disadvantaged Students Close the Gap? " Journal of Behavioral and Experimental Economics 52 : 8 – 20. https://doi.org/10.1016/j.socec.2014.05.002.</bibtext> </blist> <blist> <bibtext> Agasisti, T., and S. Longobardi. 2017. " Equality of Educational Opportunities, Schools' Characteristics and Resilient Students: An Empirical Study of EU-15 Countries Using OECD-PISA 2009 Data." Social Indicators Research 134 (3): 917 – 953. https://doi.org/10.1007/s11205-016-1464-5.</bibtext> </blist> <blist> <bibl id="bib7" idref="ref98" type="bt">7</bibl> <bibtext> Agasisti, T., M. Soncin, and R. Valenti. 2016. " School Factors Helping Disadvantaged Students to Succeed: Empirical Evidence from Four." Italian cities.Policy Studies 37 (2): 147 – 177.</bibtext> </blist> <blist> <bibl id="bib8" idref="ref149" type="bt">8</bibl> <bibtext> Aparicio, J., J. M. Cordero, M. Gonzalez, and J. J. Lopez-Espin. 2018. " Using non-Radial DEA to Assess School Efficiency in a Cross-Country Perspective: An Empirical Analysis of OECD Countries." Omega (United Kingdom) 79 : 9 – 20.</bibtext> </blist> <blist> <bibl id="bib9" idref="ref20" type="bt">9</bibl> <bibtext> Arbona, A., V. Giménez, S. López-Estrada, and D. Prior. 2022. " Efficiency and Quality in Colombian Education: An Application of the Metafrontier Malmquist-Luenberger Productivity Index." Socio-Economic Planning Sciences 79 : 101 – 122.</bibtext> </blist> <blist> <bibtext> Arbona, A., S. López-Estrada, D. Prior, and J. Rialp. 2023. " How Much do Companies Know What Contributes to Education? " Journal of the Operational Research Society 74 : 2593 – 2605.</bibtext> </blist> <blist> <bibtext> Betts, J. R., and J. L. Shkolnik. 2000. " The Effects of Ability Grouping on Student Achievement and Resource Allocation in Secondary Schools." Economics of Education Review 19 : 1 – 15. https://doi.org/10.1016/S0272-7757(98)00044-2.</bibtext> </blist> <blist> <bibtext> Bonaccorsi, A., C. Daraio, and L. Simar. 2006. " Advanced Indicators of Productivity of UniversitiesAn Application of Robust Nonparametric Methods to." Italian data.Scientometrics 66 (2): 389 – 410.</bibtext> </blist> <blist> <bibtext> Borman, G. D., and L. T. Overman. 2004. " Academic Resilience in Mathematics among Poor and Minority Students." Elementary School Journal 104 (3): 177 – 195.</bibtext> </blist> <blist> <bibtext> Castro Aristizabal, G. 2019. " ¿ Por qué los colegios privados en Colombia obtienen mejores resultados académicos? " Lumen Gentium 3 : 9 – 31. https://doi.org/10.52525/lg.v3n1a1.</bibtext> </blist> <blist> <bibtext> Cazals, C., J. P. Florens, and L. Simar. 2002. " Nonparametric Frontier Estimation: A Robust Approach." Journal of Econometrics 106 (1): 1 – 25.</bibtext> </blist> <blist> <bibtext> Charnes, A., W. W. Cooper, and E. Rhodes. 1978. " Measuring the Efficiency of Decision Making Units." European Journal of Operational Research 2 (6): 429 – 444.</bibtext> </blist> <blist> <bibtext> Clavel, J. G., F. J. García Crespo, and S. L. Sanz. 2021. " Rising Above Their Circumstances: What Makes Some Disadvantaged East and South-East Asian Students Perform far Better in Science than their Background Predicts? " Asia Pacific Journal of Education 42 : 1 – 16.</bibtext> </blist> <blist> <bibtext> Coleman, J., E. Campbell, C. Hobson, J. McPartland, A. Mood, F. Weinfeld, y R. York. 1966. Equality of Educational Opportunity. Washington, DC : 1066-5684.</bibtext> </blist> <blist> <bibtext> Cordero, J. M., and L. Mateos-Romero. 2021. " Exploring Factors Related with Resilience in Primary Education: Evidence from European Countries." Studies in Educational Evaluation 70 : 1 – 17.</bibtext> </blist> <blist> <bibtext> Cordero, J. M., F. Pedraja-Chaparro, and R. Simancas. 2015. " Success Factors for Educational Attainment in Unfavourable Socioeconomic Conditions." Revista de Educación 370 : 163 – 187.</bibtext> </blist> <blist> <bibtext> Cordero, J. M., D. Prior, and R. Simancas. 2016. " A Comparison of Public and Private Schools in Spain Using Robust Nonparametric Frontier Methods." Central European Journal of Operations Research 24 (3): 659 – 680.</bibtext> </blist> <blist> <bibtext> Cordero, J. M., D. Santín, y R. Simancas. 2017. " Assessing European Primary School Performance Through a Conditional Nonparametric Model." Journal of the Operational Research Society 68 (4): 364 – 376. https://doi.org/10.1057/jors.2015.42.</bibtext> </blist> <blist> <bibtext> Daraio, C., and L. Simar. 2005. " Introducing Environmental Variables in Nonparametric Frontier Models: A Probabilistic Approach." Journal of Productivity Analysis 24 (1): 93 – 121. https://doi.org/10.1007/s11123-005-3042-8.</bibtext> </blist> <blist> <bibtext> Daraio, C., and L. Simar. 2007a. Advanced Robust and Nonparametric Methods in Efficiency Analysis: Methodology and Applications.</bibtext> </blist> <blist> <bibtext> Daraio, C., and L. Simar. 2007b. " Conditional Nonparametric Frontier Models for Convex and Nonconvex Technologies: A Unifying Approach." Journal of Productivity Analysis 28 (1–2): 13 – 32. https://doi.org/10.1007/s11123-007-0049-3.</bibtext> </blist> <blist> <bibtext> DeMars, C. 2010. Item Response Theory: Understanding Statistics Measurement. Oxford : Oxford University Press.</bibtext> </blist> <blist> <bibtext> Deprins, D., L. Simar, and H. Tulkens. 1984. " Measuring Labor Inefficiency in Post Offices." In The Performance of Public Enterprises: Concepts and Measurements, edited by M. Marchand, P. Pestieau, and H. Tulkens, 243 – 267. Amsterdam : North Holland.</bibtext> </blist> <blist> <bibtext> De Witte, K., and L. López-Torres. 2017. " Efficiency in Education: A Review of Literature and a Way Forward." Journal of the Operational Research Society 68 (4): 339 – 363. https://doi.org/10.1057/jors.2015.92.</bibtext> </blist> <blist> <bibtext> Dupriez, V., X. Dumay, and A. Vause. 2008. " How do School Systems Manage Pupils' Heterogeneity? " Comparative Education Review 52 (2): 245 – 273. https://doi.org/10.1086/528764.</bibtext> </blist> <blist> <bibtext> Evans, D. B., A. Tandon, C. L. Murray, and J. A. Lauer. 2000. " The Comparative Efficiency of National of Health Systems in Producing Health: An Analysis of 191 Countries." World Health Organization 29 (29): 1 – 36.</bibtext> </blist> <blist> <bibtext> Felder, S., and H. Tauchmann. 2013. " Federal State Differentials in the Efficiency of Health Production in Germany: An Artifact of Spatial Dependence? " European Journal of Health Economics 14 (1): 21 – 39. https://doi.org/10.1007/s10198-011-0345-8.</bibtext> </blist> <blist> <bibtext> Ferrer-Esteban, G. 2016. " Trade-Off Between Effectiveness and Equity ? An Analysis of Social Sorting Between Classrooms and between Schools." Comparative Education Review 60 (1): 151 – 183. https://doi.org/10.1086/684490.</bibtext> </blist> <blist> <bibtext> Finn, J. D., and D. A. Rock. 1997. " Academic Success among Students at Risk for School Failure." Journal of Applied Psychology 82 (2): 221 – 234. https://doi.org/10.1037/0021-9010.82.2.221.</bibtext> </blist> <blist> <bibtext> Gabrielli, G., and R. Impicciatore. 2021. " Breaking Down the Barriers: Educational Paths, Labour Market Outcomes and Wellbeing of Children of Immigrants." Journal of Ethnic and Migration Studies 48 : 1 – 19.</bibtext> </blist> <blist> <bibtext> Gabrielli, G., S. Longobardi, and S. Strozza. 2021. " The Academic Resilience of Native and Immigrant-Origin Students in Selected European Countries." Journal of Ethnic and Migration Studies 48 : 2347 – 2368.</bibtext> </blist> <blist> <bibtext> García-Crespo, F. J., G. Begoña, F. A. Rubén, and M. José. 2019. " Resiliencia Educativa en Comprensión Lectora : Educational Resilience in Reading Comprehension." Determinant factors in PIRLS-Europe.Revista de Educacion 384 : 71 – 96.</bibtext> </blist> <blist> <bibtext> Giménez, V., F. J. Ayvar-Campos, and J. C. Navarro-Chávez. 2017a. " Efficiency in the Generation of Social Welfare in Mexico: A Proposal in the Presence of bad Outputs." Omega (United Kingdom) 69 : 43 – 52.</bibtext> </blist> <blist> <bibtext> Giménez, V., C. Thieme, D. Prior, and E. Tortosa-Ausina. 2017b. " An International Comparison of Educational Systems: A Temporal Analysis in Presence of bad Outputs." Journal of Productivity Analysis 47 (1): 83 – 101.</bibtext> </blist> <blist> <bibtext> Haelermans, C., and J. Ruggiero. 2017. " Non-parametric Estimation of the Cost of Adequacy in Education: The Case of Dutch Schools." Journal of the Operational Research Society 68 (4): 390 – 398. https://doi.org/10.1057/jors.2015.68.</bibtext> </blist> <blist> <bibtext> Hanushek, E. A. 1986. " The Economics of Schooling: Production and Efficiency in Public Schools." Journal of Economic Litterature 24 (3): 1141 – 1177.</bibtext> </blist> <blist> <bibtext> Hanushek, E. A., and W. Ludger. 2006. " Does Educational Tracking Affect Performance and Inequality? Differences-in-Differences Evidence Across Countries." The Economic Journal 116 : 63 – 76. https://doi.org/10.1111/j.1468-0297.2006.01076.x.</bibtext> </blist> <blist> <bibtext> Hanushek, E. A., and L. Woessmann. 2008. " The Role of Cognitive Skills in Economic Development." Journal of Economic Literature 46 (3): 607 – 668. https://doi.org/10.1257/jel.46.3.607.</bibtext> </blist> <blist> <bibtext> Hanushek, E. A., and L. Woessmann. 2011. " The Economics of International Differences in Educational Achievement." Handbook of the Economics of Education 3 : 89 – 200.</bibtext> </blist> <blist> <bibtext> Hauser, R. M. 2009. " Quality and Equity in the Performance of Students and Schools." Center for Demography and Ecology 1968 : 570.</bibtext> </blist> <blist> <bibtext> Heinesen, E. 2009. " Estimating Class-Size Effects Using Within-School Variation in Subject-Specific Classes." Economic Journal 120 : 737 – 760.</bibtext> </blist> <blist> <bibtext> Hill, N. E., and D. F. Tyson. 2009. " Assessment of the Strategies That Promote Achievement." Developmental Psychology 45 (3): 740 – 763. https://doi.org/10.1037/a0015362.</bibtext> </blist> <blist> <bibtext> Hindriks, J., M. Verschelde, R. Glenn, and K. Schoors. 2010. "Ability Tracking, Social Segregation and Educational Opportunity: Evidence from Bel- gium." CORE discussion paper, Center for Operations Research and Econometrics, Université Catholique de Louvain-la-Neuve.</bibtext> </blist> <blist> <bibtext> Luthar, S. S., D. Cicchetti, and B. Becker. 2000. " The Construct of Resilience : A Critical Evaluation and Guidelines for Future Work." Child Development 71 (3): 543 – 562.</bibtext> </blist> <blist> <bibtext> Mancebón, M. J., J. C. Calero, and D. P. Ximénez-de-Embún. 2012. " The Efficiency of Public and Publicly Subsidized High Schools in Spain: Evidence from PISA – 2006." Journal of the Operational Research Society 63 : 1516 – 1533.</bibtext> </blist> <blist> <bibtext> Marchesi, A. 2006. " El informe PISA y la política educativa en España." Revista de educación, n. extraordinario 18 : 337 – 355.</bibtext> </blist> <blist> <bibtext> Martin, A. J., and H. W. Marsh. 2006. " Academic Resilience and its Psychological and Educational Correlates: A Construct Validity Approach." Psychology in the Schools 43 (3): 267 – 281.</bibtext> </blist> <blist> <bibtext> Melo-Becerra, L. A., J. E. Ramos-Forero, and P. O. Hernández-Santamaría. 2017. " HigherEducation in Colombia: CurrentSituation and EfficiencyAnalysis." Revista Desarrollo y Sociedad 78 : Páginas 59 – 111. https://doi.org/10.13043/dys.78.2.</bibtext> </blist> <blist> <bibtext> Moreno-Gómez, J., J. Calleja-Blanco, and G. Moreno-Gómez. 2019. " Measuring the Efficiency of the Colombian Higher Education System: A two-Stage Approach." International Journal of Educational Management 34 : 794 – 804.</bibtext> </blist> <blist> <bibtext> OECD. 2006. " Higher Education: Quality, Equity and Efficiency." Programme on Institutional Management in Higher Education, 9 – 66.</bibtext> </blist> <blist> <bibtext> OECD. 2011. Against the Odds - Disadvantaged Students Who Succeed in School. Paris : OECD Publishing.</bibtext> </blist> <blist> <bibtext> OECD. 2016. Education in Colombia, Reviews of National Policies for Education. Paris : OECD Publishing.</bibtext> </blist> <blist> <bibtext> OECD. 2018a. A Broken Social Elevator? How to Promote Social Mobility. Paris : OECD Publishing.</bibtext> </blist> <blist> <bibtext> OECD. 2018b. Colombia - Country Note - PISA 2018 Results.</bibtext> </blist> <blist> <bibtext> Park, H. 2008. " Home Literacy Environments and Children's Reading Performance : A Comparative Study of 25 Countries." Educational Research and Evaluation 14 (6): 489 – 505. https://doi.org/10.1080/13803610802576734.</bibtext> </blist> <blist> <bibtext> Podinovski, V., I. Ismail, T. Bouzdine-Chameeva, and W. Zhang. 2014. " Combining the Assumptions of Variable and Constant Returns to Scale in the Efficiency Evaluation of Secondary Schools." European Journal of Operational Research 239 (2): 504 – 513. https://doi.org/10.1016/j.ejor.2014.05.016.</bibtext> </blist> <blist> <bibtext> Sagarra, M., C. Mar-Molinero, and T. Agasisti. 2017. " Exploring the Efficiency of Mexican Universities: Integrating Data Envelopment Analysis and Multidimensional Scaling." Omega (United Kingdom) 67 : 123 – 133.</bibtext> </blist> <blist> <bibtext> Sicilia, G., and R. Simancas. 2023. " Eficiencia y equidad educativa en España: un análisis comparativo a nivel regional." Hacienda Pública Española 245 : 7 – 33. https://doi.org/10.7866/HPE-RPE.23.2.1.</bibtext> </blist> <blist> <bibtext> Tajalli, H., and O. Cynthia. 2004. " Strategies for Closing the Gap: Predicting Student Performance in Economically Disadvantaged Schools." Educational Research Quarterly 28 (4): 44 – 54.</bibtext> </blist> <blist> <bibtext> Tauchmann, H. 2012. " Partial Frontier Efficiency Analysis." Stata Journal 12 (3): 461 – 478. https://doi.org/10.1177/1536867X1201200309.</bibtext> </blist> <blist> <bibtext> Tavana, M., A. Ebrahimnejad, F. J. Santos-Arteaga, S. M. Mansourzadeh, and R. K. Matin. 2018. " A Hybrid DEA-MOLP Model for Public School Assessment and Closure Decision in the City of Philadelphia." Socio-Economic Planning Sciences 61 : 70 – 89.</bibtext> </blist> <blist> <bibtext> Thieme, C., D. Prior, and E. Tortosa-Ausina. 2013. " A Multilevel Decomposition of School Performance Using Robust Nonparametric Frontier Techniques." Economics of Education Review 32 (1): 104 – 121.</bibtext> </blist> <blist> <bibtext> Tran, C. T., and R. A. Villano. 2018. " Measuring Efficiency of Vietnamese Public Colleges: An Application of the DEA-Based Dynamic Network Approach." International Transactions in Operational Research 25 (2): 683 – 703. https://doi.org/10.1111/itor.12212.</bibtext> </blist> <blist> <bibtext> Tsai, S. L., M. L. Smith, and R. M. Hauser. 2017. " Families, Schools, and Student Achievement Inequality: A Multilevel MIMIC." Model Approach.Sociology of Education 90 (1): 64 – 88. https://doi.org/10.1177/0038040716683779.</bibtext> </blist> <blist> <bibtext> UNDP & UNESCO. 2015. Education 2030: Incheon Declaration and Framework for Action for the implementation of Sustainable Development.</bibtext> </blist> <blist> <bibtext> Ungar, M. 2005. Handbook for Working with Children and Youth: Pathways to Resilience across Cultures and Contexts.</bibtext> </blist> <blist> <bibtext> Vicente, I., J. M. Pastor, and Á Soler. 2021. " Improving Educational Resilience in the OECD Countries: Two Convergent Paths." Journal of Policy Modeling 43 (6): 1149 – 1166. https://doi.org/10.1016/j.jpolmod.2021.09.007.</bibtext> </blist> <blist> <bibtext> Wang, M. T., R. L. Selman, T. J. Dishion, and E. A. Stormshak. 2010. " A Tobit Regression Analysis of the Covariation Between Middle School Students' Perceived School Climate and Behavioral Problems." Journal of Research on Adolescence 20 (2): 274 – 286.</bibtext> </blist> <blist> <bibtext> Wang, G., and H. Walberg. 1994. " Educational Resilience in Inner-City." Educational Resilience in Inner-City America: Challenges and Prospects, 45 – 72.</bibtext> </blist> <blist> <bibtext> Windle, G. 2011. " What is Resilience? A Review and Concept Analysis." Reviews in Clinical Gerontology 21 (2): 152 – 169. https://doi.org/10.1017/S0959259810000420.</bibtext> </blist> <blist> <bibtext> Ye, W., R. Strietholt, and S. Blömeke. 2021. " Academic Resilience: Underlying Norms and Validity of Definitions." Educational Assessment, Evaluation and Accountability 33 (1): 169 – 202. https://doi.org/10.1007/s11092-020-09351-7.</bibtext> </blist> </ref> <aug> <p>By Sebastian López-Estrada; Tommaso Agasisti; Víctor Giménez and Diego Prior</p> <p>Reported by Author; Author; Author; Author</p> </aug> <nolink nlid="nl1" bibid="bib69" firstref="ref1"></nolink> <nolink nlid="nl2" bibid="bib19" firstref="ref3"></nolink> <nolink nlid="nl3" bibid="bib35" firstref="ref4"></nolink> <nolink nlid="nl4" bibid="bib71" firstref="ref5"></nolink> <nolink nlid="nl5" bibid="bib40" firstref="ref6"></nolink> <nolink nlid="nl6" bibid="bib42" firstref="ref7"></nolink> <nolink nlid="nl7" bibid="bib33" firstref="ref8"></nolink> <nolink nlid="nl8" bibid="bib48" firstref="ref9"></nolink> <nolink nlid="nl9" bibid="bib70" firstref="ref12"></nolink> <nolink nlid="nl10" bibid="bib74" firstref="ref13"></nolink> <nolink nlid="nl11" bibid="bib55" firstref="ref14"></nolink> <nolink nlid="nl12" bibid="bib17" firstref="ref15"></nolink> <nolink nlid="nl13" bibid="bib75" firstref="ref16"></nolink> <nolink nlid="nl14" bibid="bib54" firstref="ref17"></nolink> <nolink nlid="nl15" bibid="bib61" firstref="ref19"></nolink> <nolink nlid="nl16" bibid="bib38" firstref="ref21"></nolink> <nolink nlid="nl17" bibid="bib37" firstref="ref22"></nolink> <nolink nlid="nl18" bibid="bib20" firstref="ref23"></nolink> <nolink nlid="nl19" bibid="bib50" firstref="ref24"></nolink> <nolink nlid="nl20" bibid="bib62" firstref="ref25"></nolink> <nolink nlid="nl21" bibid="bib58" firstref="ref27"></nolink> <nolink nlid="nl22" bibid="bib57" firstref="ref28"></nolink> <nolink nlid="nl23" bibid="bib15" firstref="ref30"></nolink> <nolink nlid="nl24" bibid="bib30" firstref="ref33"></nolink> <nolink nlid="nl25" bibid="bib68" firstref="ref34"></nolink> <nolink nlid="nl26" bibid="bib18" firstref="ref35"></nolink> <nolink nlid="nl27" bibid="bib43" firstref="ref36"></nolink> <nolink nlid="nl28" bibid="bib41" firstref="ref38"></nolink> <nolink nlid="nl29" bibid="bib29" firstref="ref39"></nolink> <nolink nlid="nl30" bibid="bib47" firstref="ref41"></nolink> <nolink nlid="nl31" bibid="bib32" firstref="ref42"></nolink> <nolink nlid="nl32" bibid="bib11" firstref="ref43"></nolink> <nolink nlid="nl33" bibid="bib52" firstref="ref45"></nolink> <nolink nlid="nl34" bibid="bib53" firstref="ref46"></nolink> <nolink nlid="nl35" bibid="bib22" firstref="ref47"></nolink> <nolink nlid="nl36" bibid="bib10" firstref="ref48"></nolink> <nolink nlid="nl37" bibid="bib73" firstref="ref50"></nolink> <nolink nlid="nl38" bibid="bib13" firstref="ref60"></nolink> <nolink nlid="nl39" bibid="bib36" firstref="ref74"></nolink> <nolink nlid="nl40" bibid="bib51" firstref="ref84"></nolink> <nolink nlid="nl41" bibid="bib46" firstref="ref87"></nolink> <nolink nlid="nl42" bibid="bib63" firstref="ref89"></nolink> <nolink nlid="nl43" bibid="bib34" firstref="ref90"></nolink> <nolink nlid="nl44" bibid="bib59" firstref="ref94"></nolink> <nolink nlid="nl45" bibid="bib45" firstref="ref97"></nolink> <nolink nlid="nl46" bibid="bib72" firstref="ref99"></nolink> <nolink nlid="nl47" bibid="bib23" firstref="ref103"></nolink> <nolink nlid="nl48" bibid="bib24" firstref="ref104"></nolink> <nolink nlid="nl49" bibid="bib25" firstref="ref105"></nolink> <nolink nlid="nl50" bibid="bib16" firstref="ref110"></nolink> <nolink nlid="nl51" bibid="bib27" firstref="ref111"></nolink> <nolink nlid="nl52" bibid="bib28" firstref="ref112"></nolink> <nolink nlid="nl53" bibid="bib66" firstref="ref113"></nolink> <nolink nlid="nl54" bibid="bib26" firstref="ref128"></nolink> <nolink nlid="nl55" bibid="bib44" firstref="ref132"></nolink> <nolink nlid="nl56" bibid="bib21" firstref="ref133"></nolink> <nolink nlid="nl57" bibid="bib65" firstref="ref134"></nolink> <nolink nlid="nl58" bibid="bib49" firstref="ref137"></nolink> <nolink nlid="nl59" bibid="bib39" firstref="ref138"></nolink> <nolink nlid="nl60" bibid="bib67" firstref="ref139"></nolink> <nolink nlid="nl61" bibid="bib60" firstref="ref141"></nolink> <nolink nlid="nl62" bibid="bib56" firstref="ref143"></nolink> <nolink nlid="nl63" bibid="bib14" firstref="ref144"></nolink> <nolink nlid="nl64" bibid="bib12" firstref="ref146"></nolink> <nolink nlid="nl65" bibid="bib31" firstref="ref147"></nolink>
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  Data: Students' Resilience and School Efficiency in One of the Most Unequal Countries in the World: Empirical Evidence from Colombia
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  Data: <searchLink fieldCode="AR" term="%22Sebastian+López-Estrada%22">Sebastian López-Estrada</searchLink><br /><searchLink fieldCode="AR" term="%22Tommaso+Agasisti%22">Tommaso Agasisti</searchLink><br /><searchLink fieldCode="AR" term="%22Víctor+Giménez%22">Víctor Giménez</searchLink><br /><searchLink fieldCode="AR" term="%22Diego+Prior%22">Diego Prior</searchLink>
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  Data: <searchLink fieldCode="SO" term="%22Education+Economics%22"><i>Education Economics</i></searchLink>. 2025 33(2):180-197.
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  Data: Routledge. Available from: Taylor & Francis, Ltd. 530 Walnut Street Suite 850, Philadelphia, PA 19106. Tel: 800-354-1420; Tel: 215-625-8900; Fax: 215-207-0050; Web site: http://www.tandf.co.uk/journals
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  Data: 18
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  Data: Journal Articles<br />Reports - Research
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  Data: <searchLink fieldCode="DE" term="%22Foreign+Countries%22">Foreign Countries</searchLink><br /><searchLink fieldCode="DE" term="%22Resilience+%28Psychology%29%22">Resilience (Psychology)</searchLink><br /><searchLink fieldCode="DE" term="%22Efficiency%22">Efficiency</searchLink><br /><searchLink fieldCode="DE" term="%22Public+Schools%22">Public Schools</searchLink><br /><searchLink fieldCode="DE" term="%22Private+Schools%22">Private Schools</searchLink>
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  Data: <searchLink fieldCode="DE" term="%22Colombia%22">Colombia</searchLink>
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  Data: 10.1080/09645292.2023.2298845
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  Data: 0964-5292<br />1469-5782
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This article analyzes students' resilience in 7,789 schools in the Colombian educational system and its relationship with educational efficiency between 2014 and 2019. The empirical analysis is carried out in two stages. First, a multilevel model with random intercept and slope is estimated to determine the students categorized as resilient. Then conditional order-m models are used to calculate the efficiency. The results indicate a negative relationship between thenumber of resilient students and schools' inefficiency of up to 33% in public schools and 12% in private schools.
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        Value: 10.1080/09645292.2023.2298845
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      – Text: English
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        PageCount: 18
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      – SubjectFull: Foreign Countries
        Type: general
      – SubjectFull: Resilience (Psychology)
        Type: general
      – SubjectFull: Efficiency
        Type: general
      – SubjectFull: Public Schools
        Type: general
      – SubjectFull: Private Schools
        Type: general
      – SubjectFull: Colombia
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      – TitleFull: Students' Resilience and School Efficiency in One of the Most Unequal Countries in the World: Empirical Evidence from Colombia
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