(cid:87)(cid:87)(cid:87)(cid:46)(cid:74)(cid:65)(cid:81)(cid:77)(cid:46)(cid:82)(cid:79) (cid:74)(cid:74)(cid:79)(cid:79)(cid:85)(cid:85)(cid:82)(cid:82)(cid:78)(cid:78)(cid:65)(cid:65)(cid:76)(cid:76) (cid:79)(cid:79)(cid:70)(cid:70) (cid:65)(cid:65)(cid:80)(cid:80)(cid:80)(cid:80)(cid:76)(cid:76)(cid:73)(cid:73)(cid:69)(cid:69)(cid:68)(cid:68) (cid:81)(cid:81)(cid:85)(cid:85)(cid:65)(cid:65)(cid:78)(cid:78)(cid:84)(cid:84)(cid:73)(cid:73)(cid:84)(cid:84)(cid:65)(cid:65)(cid:84)(cid:84)(cid:73)(cid:73)(cid:86)(cid:86)(cid:69)(cid:69) (cid:77)(cid:77)(cid:69)(cid:69)(cid:84)(cid:84)(cid:72)(cid:72)(cid:79)(cid:79)(cid:68)(cid:68)(cid:83)(cid:83) (cid:86)(cid:111)(cid:108)(cid:46)(cid:32)(cid:49)(cid:48) (cid:81)(cid:117)(cid:97)(cid:110)(cid:116)(cid:105)(cid:116)(cid:97)(cid:116)(cid:105)(cid:118)(cid:101)(cid:32)(cid:77)(cid:101)(cid:116)(cid:104)(cid:111)(cid:100)(cid:115)(cid:32)(cid:73)(cid:110)(cid:113)(cid:117)(cid:105)(cid:114)(cid:101)(cid:115) (cid:78)(cid:111)(cid:46)(cid:32)(cid:49) (cid:83)(cid:112)(cid:114)(cid:105)(cid:110)(cid:103) (cid:50)(cid:48)(cid:49)(cid:53) (cid:73)(cid:83)(cid:83)(cid:78)(cid:32)(cid:49)(cid:56)(cid:52)(cid:50)(cid:8211)(cid:52)(cid:53)(cid:54)(cid:50) Editorial Board JAQM Editorial Board Editors Ion Ivan, Bucharest University of Economic Studies, Romania Claudiu Herteliu, Bucharest University of Economic Studies, Romania Gheorghe Nosca, Association for Development through Science and Education, Romania Editorial Team Cristian Amancei, Bucharest University of Economic Studies, Romania Catalin Boja, Bucharest University of Economic Studies, Romania Radu Chirvasuta, Imperial College Healthcare NHS Trust, London, UK Ştefan Cristian Ciucu, Bucharest University of Economic Studies, Romania Irina Maria Dragan, Bucharest University of Economic Studies, Romania Eugen Dumitrascu, Craiova University, Romania Matthew Elbeck, Troy University, Dothan, USA Nicu Enescu, Craiova University, Romania Bogdan Vasile Ileanu, Bucharest University of Economic Studies, Romania Miruna Mazurencu Marinescu, Bucharest University of Economic Studies, Romania Daniel Traian Pele, Bucharest University of Economic Studies, Romania Ciprian Costin Popescu, Bucharest University of Economic Studies, Romania Aura Popa, YouGov, UK Marius Popa, Bucharest University of Economic Studies, Romania Mihai Sacala, Bucharest University of Economic Studies, Romania Cristian Toma, Bucharest University of Economic Studies, Romania Erika Tusa, Bucharest University of Economic Studies, Romania Adrian Visoiu, Bucharest University of Economic Studies, Romania Manuscript Editor Lucian Naie, SDL Tridion I Advisory Board JAQM Advisory Board Luigi D’Ambra, University of Naples “Federico II”, Italy Kim Viborg Andersen, Copenhagen Business School, Denmark Tudorel Andrei, Bucharest University of Economic Studies, Romania Gabriel Badescu, Babes-Bolyai University, Romania Catalin Balescu, National University of Arts, Romania Avner Ben-Yair, SCE - Shamoon College of Engineering, Beer-Sheva, Israel Ion Bolun, Academy of Economic Studies of Moldova Recep Boztemur, Middle East Technical University Ankara, Turkey Constantin Bratianu, Bucharest University of Economic Studies, Romania Ilie Costas, Academy of Economic Studies of Moldova Valentin Cristea, University Politehnica of Bucharest, Romania Marian-Pompiliu Cristescu, Lucian Blaga University, Romania Victor Croitoru, University Politehnica of Bucharest, Romania Gurjeet Dhesi, London South Bank University, UK Cristian Pop Eleches, Columbia University, USA Michele Gallo, University of Naples L'Orientale, Italy Angel Garrido, National University of Distance Learning (UNED), Spain Anatol Godonoaga, Academy of Economic Studies of Moldova Alexandru Isaic-Maniu, Bucharest University of Economic Studies, Romania Ion Ivan, Bucharest University of Economic Studies, Romania Adrian Mihalache, University Politehnica of Bucharest, Romania Constantin Mitrut, Bucharest University of Economic Studies, Romania Mihaela Muntean, Western University Timisoara, Romania Peter Nijkamp, Free University De Boelelaan, The Nederlands Bogdan Oancea, Titu Maiorescu University, Romania Victor Valeriu Patriciu, Military Technical Academy, Romania Dan Petrovici, Kent University, UK Gabriel Popescu, Bucharest University of Economic Studies, Romania Mihai Roman, Bucharest University of Economic Studies, Romania Satish Chand Sharma, Janta Vedic College, Baraut, India Ion Smeureanu, Bucharest University of Economic Studies, Romania Nicolae Tapus, University Politehnica of Bucharest, Romania Timothy Kheng Guan Teo, University of Auckland, New Zeeland Daniel Teodorescu, Emory University, USA Dumitru Todoroi, Academy of Economic Studies of Moldova Nicolae Tomai, Babes-Bolyai University, Romania Pasquale Sarnacchiaro, Unitelma Sapienza University, Italy Vergil Voineagu, Bucharest University of Economic Studies, Romania II Contents Page Quantitative Methods Inquires Emanuela RAFFINETTI, Isabella ROMEO Evaluating Social Tracking in the Primary School: Evidence from the Lombardy 1 Region (Italy) Smaranda CIMPOERU A Logistic Model on Panel Data for Systemic Risk Assessment – Evidence from 15 Advanced and Developing Economies Silvia DEDU, Florentin SERBAN Stochastic Optimization using Interval Analysis, with Applications 30 to Portfolio Selection Adriana AnaMaria DAVIDESCU Bounds Test approach for the Long Run Relationship between Shadow Economy 36 and Official Economy. An Empirical Analysis for Romania Kalyan MONDAL, Surapati PRAMANIK The Application of Grey System Theory in Predicting the Number of Deaths of 48 Women by Committing Suicide- A Case Study Ion PARTACHI, Vitalie MOTELICA Methods of Measuring Core Inflation in Inflation Targeting Countries 56 Angel-Alex HAISAN, Vasile Paul BRESFELEAN Connections between Will to Emigrate and Attachment 67 Theory – A Data Mining Approach Diana-Silvia ZILISTEANU, Ion Radu ZILISTEANU, Mihai VOICULESCU A Study of Survival Modelling in Dialysis Patients 85 Applying Different Statistical Tools Eva MILITARU The Redistributive Effect of the Romanian Tax-Benefit 93 System: A Microsimulation Approach Eduard Gabriel CEPTUREANU Survey Regarding Resistance to Change in Romanian 105 Innovative SMEs from IT Sector III Quantitative Methods Inquires EVALUATING SOCIAL TRACKING IN THE PRIMARY SCHOOL: EVIDENCE FROM THE LOMBARDY REGION (ITALY)1 Emanuela RAFFINETTI2 PhD, Post-Doc Research Fellow, Department of Economics, Management and Quantitative Methods Università degli Studi di Milano, Italy E-mail: [email protected] Isabella ROMEO3 PhD, Post-Doc Research Fellow, Department of Statistics and Quantitative Methods University of Milano-Bicocca, Italy E-mail: [email protected] Abstract Recently, the Italian schools were deeply affected by the “social tracking” phenomenon, intended as the process of segregating students into socio-economic classes. Typically, this phenomenon occurs within the lower secondary school. In such a perspective, the study reported in the paper is innovative, since addressed to investigate the actual presence of the social tracking phenomenon as an event starting from the primary school. For this purpose, we considered data provided by Invalsi (Istituto Nazionale per la Valutazione del Sistema di Istruzione e Formazione) with regard to students of the fifth grade of primary schools in the Lombardy region (Italy). The study was carried out following two different approaches. First, a preliminary descriptive analysis of the segregation phenomenon was carried out by computing the Gini coefficient of the the socio-economic status average at class level. Second, due to the usual hierarchical structure of educational data, multilevel models were considered with the aim of partitioning the pupils’ socio-economic status variability within the student, class and school level. In this way, school and class social segregation indicators were obtained. Subsequently, a conditional multilevel model including school and class social segregation indicators as explanatory variables was built. Results underline that even though in general social tracking is not an actual threat for the Lombardy primary schools, a remarkable socio-economic heterogeneity among classes appears especially in some provinces of the Lombardy region. Key words: social tracking phenomenon, class heterogeneity, Gini coefficient, segregation indices, multi-level modeling, Invalsi data 1 Quantitative Methods Inquires 1. Introduction Interest in evaluating the Italian education systems is manifest in a large number of recent publications and in the diffusion of standardized tests (e.g., Haladyna, 1991; Ballard and Bates, 2008). Typically, the content of these contributions focuses on the main pupils and schools’ determinants affecting the learning levels of students. If on one hand the educational research field stresses the impact of such factors on the students’ attainments, on the other hand only a few works addressed the issue of equal opportunity in education (i.e. each state must provide the same opportunities for everyone who attends school regardless of gender, race or nationality). Even though the Italian law imposes the “equity principle” which should be preserved by composing the most possible heterogeneous classes, recent studies highlight that the practice of segregating students with similar features is particularly widespread, especially in the lower secondary schools (e.g. Ferrer-Esteban, 2011). Such a sociological issue falls under the name of “formal tracking” phenomenon. In some cases, school staff may generate a great deal of selection by assigning children with similar achievement to the same classroom, in order to minimize teaching difficulty, or by placing all of the “problematic” students in a certain teacher’s class because he is good at dealing with them. However, the segregation phenomenon can be generated in several ways and at different levels. Specifically, the increasing participation of the pupils’ parents to the dynamics of the school is leading to a kind of “informal tracking” phenomenon, allowing families to influence the classroom composition in order to better respond to their social features, such as for instance their socio-economic status (e.g. Dupriez et al., 2008). Social tracking gives rise to homogeneity within classes (social segregation) that in turn may come out in inequality of education opportunities (e.g., Checchi and Flabbi, 2007; Hindriks et al., 2010). Children with different family background, race and ability will have different access to knowledge. It was proven (for example, Loveless, 1999) that whether the curriculum is adjusted to better match ability level of students, while high ability students may receive a boosted achievement, low ability students may suffer from assignment to lower tracks. Thus, homogeneity within classes negatively affects disadvantages students. Classroom environment is then really important for student achievement, as stated by Hill and Rowe (1996): “How much a student learns depends on the identity of the classroom on which the student is assigned”. Indeed, a student’s innate ability can affect his peers, not only through knowledge spillovers but also through his behavior. On the contrary, a student who has not learned self-discipline at home may bother the classroom. The study presented in this paper is innovative since it attempts to explore the actual presence of the social segregation phenomenon in Italy as an event starting from the primary schools. Indeed, to the best of our knowledge, no research contributions illustrating the existence of an informal tracking phenomenon in the Italian primary schools are currently provided in literature. More precisely, our research question is the following. Since primary schools represent the first education compulsory stage after the kindergarten, the segregation process of kids can probably be encouraged by parents on the basis of their socio-economic features. Kindergarten has a relevant role in the process of contact among the families of kids. Thus, the pupils' families may wish that their children were kept together with their kindergarten friends, when accessing to the primary school. The analysis was carried out on data provided by the National Evaluation Committee (Istituto Nazionale per la Valutazione del Sistema di Istruzione e Formazione, 2 Quantitative Methods Inquires henceforth Invalsi). In Italy the National Evaluation Committee has been established with the specific aim of evaluating the Italian schools through the analysis of the students’ achievement at different levels of education; second and fifth year of the primary school (age 7 and 10, respectively), first and third of the lower-secondary (age 11 and 13), second and fifth of the upper-secondary (age 15 and 18). The collection of such data started from the school year 2008-2009 and represents the first time that a law imposes a national evaluation by using standardized tests in all students population. Here, we considered a unique dataset that tracks the performance in Reading of students of the fifth grade of primary schools in the Lombardy region for the school year 2009-2010. On the statistical point of view, our proposal was pursued through two different approaches. First, a preliminary investigation of the social tracking phenomenon was provided by resorting to a descriptive inequality index, the Gini coefficient, which is widely used for studying inequality in education attainments (e.g., Leckie et al., 2012). The Gini coefficient was computed by taking into account the class average value of the variable representing the socio-economic status (henceforth denoted by SES) over all the classes in every province of the Lombardy region. Second, to shed light on how the heterogeneity of the students’ performance and SES are portioned out between school and class level, different multilevel models were considered both to properly take into account the hierarchical structure of data with pupils nested in classes and schools (e.g., Snijders and Bosker, 1999) and to define social segregation indices at school and class level. Finally, a conditional multilevel model with even the social segregation indices is performed. The remainder of the paper is organized as follows. In Section 2 the examined Invalsi dataset is illustrated and some descriptive statistics provided. In Section 3 a preliminary analysis of the social tracking phenomenon is introduced by resorting to a descriptive approach based on the Gini coefficient. In Section 4 an overview of the proposed multilevel methodology is presented. In Section 5 school and class level social segregation indices are computed and commented. Section 6 is devoted to the discussion of the obtained results. Finally, Section 7 concludes. 2. Data Our proposal is based on data coming from the survey led by Invalsi at the end of the school year 2009-2010 and referring to students of the fifth grade (students of about 11 years old). Coherently with our research scope, the variable under study is here detected by the pupils school achievement in Reading, expressed as the proportion of correct answers provided in the administered test by each student. Such data cover the whole population (it is not a sample) made up of 77.200 students belonging to 4.488 classes that in turn belong to 1.050 primary schools located in different provinces of the Lombardy region. The administered test is built on 41 multiple-choice items and is composed by two parts: the former is related to the comprehension of two texts and the latter is related to the grammar issues. The testing time is of one hour. The test reserves even a set of questions concerning the students’ personal information (e.g. gender, ethnicity, grade retention and so on). Further information about the social, economic and cultural conditions of students are collected through additional questionnaires filled by the School Principals and students' parents. Variables considered for the analysis are enlisted below and include:  demographic variables: i.e. gender, ethnicity, year of birth; 3 Quantitative Methods Inquires  sociocultural variables: in this case, a synthetic index, named SES is made directly available by Invalsi. It is computed analogously to the OECD’s procedure, that is by considering the parents’ occupation and education, possession of some kinds of goods such as, for instance, the availability of an encyclopedia or an Internet connection, the number of books at home and so on (Campodifiori et al., 2010);  school variables: school size (number of students), type of school administration (private or public), number of female students, number of students repeating one or more grades and number of students belonging to ethnic minorities;  geographical area of the school, specified in the provinces of the Lombardy region: Bergamo (BG), Como (CO), Lecco (LC), Lodi (LO), Milano (MI), Pavia (PV), Varese (VA), Brescia (BS), Cremona (CR), Mantova (MN) and Sondrio (SO). A note about the type of school administration (private or public) is needed. For private school we mean schools with private involvement in managing and funding. Here, we only focused on private schools following the ministerial program and thus considered equivalent to the public ones. Before proceeding to the construction of the statistical model, an analysis of missing data was done for all the variables that potentially may be included in it. The reference dataset is characterized by variables which present missing values at random. However, the main trouble appears with the pre-school (i.e. kindergarten attendance) variable whose lack of information is consistent, since missing values amount to the 10.4%. In such a context, the problem of missing data was easily solved by directly deleting the pre- school variable from the model. This is because, the ejection of the pre-school variable from the model found reason in its low contribution in explaining the Reading scores variability. In order to provide more interpretable parameters, all the variables were standardized and a reference level was defined (e.g., Snijder and Bosker, 1999). Furthermore, to better clarify the role of the categorical variables included into the model and concerning the demographic characteristics of pupils (i.e. gender, ethnicity, and grade retention) and the school features (public or private status), a related description is presented in Table 1, where the corresponding reference categories are reported. Table 1. Description of the pupil and school categorical variables Variables Description Demographic Gender Male (reference category); Female Ethnicity Italian (reference category); Ethnic minorities of first or second generation Student that has not repeated a year (reference category, pupils born in Grade Repetition 1998); Student that has reapeated at least a year (grade repetition) Educational School Administration Public (reference category); Private With regard to class and school level, we considered variables representing the proportion of students being female, repeating one or more grades and belonging to ethnic minorities. These variables were already available in the dataset at school level and relate to students belonging to all grades in the school. On the contrary, variables at class level were derived as aggregation of individual covariates at class level. Thus, the latter are related only to students participating to the survey of the fifth grade. Moreover, the school and class average of the students’ SES index were computed as aggregation of individual SES index. 4 Quantitative Methods Inquires The main key statistics about variables at class and school level are displayed in Table 2. It is worth noting that variables at school level were centered on the grand mean and variables at student level were centered on the school average. As shown in Table 2, the average score4 amounts to 73.20 with a standard deviation equal to 16.63, the average percentage of female is the 49% at class level and the student SES average is 0.03 at class level and 0.04 at school level. In addition, almost the 9% of schools are private, the average percentage of ethnic minority students amounts to the 13% both at class and school level, while the average percentage of students repeating the year is the 3% at class level and smaller than the 1% at school level. Table 2. Descriptive Statistics Number of units Mean St Dev Min Max Score in Reading 77,200 73.20 16.63 0.00 100.00 % Ethnic Minorities 4,466 0.13 0.55 0.00 1.00 Class mean SES 4,487 0.03 2.17 -2.05 2.16 Class % Females 4,485 0.49 0.51 0.00 1.00 % Student Repeating the year 4,487 0.03 0.23 0.00 1.00 Class size 4,488 20.00 10.00 6.00 28.00 % Ethnic Minorities 1,050 0.13 0.18 0.00 0.83 School mean SES 1,050 0.04 0.86 -1.28 2.04 % Females 1,050 0.48 0.07 0.00 1.00 % Student Repeating the year 1,050 0.003 0.01 0.00 0.03 School size 1,050 532.00 428.00 28.00 1,338 School Administration: Public 74,265 91.17 School Administration: Private 7,191 8.83 Province: BG 10,020 12.30 Province: BS 11,401 14.00 School Province: CO 4,869 5.98 Province: CR 2,833 3.48 Province: LC 2,867 3.52 Province: LO 1,923 2.36 Province: MN 3,477 4.27 Province: PV 3,991 4.90 Province: SO 1,558 1.91 Province: VA 7,412 9.10 Province: MI 31,105 38.19 3. Preliminary Analysis: the Gini coefficient In the literature, a wide range of indices are proposed for assessing the actual presence of the social tracking phenomenon. As deeply discussed by Leckie et al. (2012), Hutchens (2004) and Reardon and Firebaugh (2002), researchers typically resort to descriptive indices such as, for instance dissimilarity and square root indices (e.g., Duncan and Duncan, 1955; Jenkins et al., 2008), in order to detect possible scenarios of inequality in education opportunity. Since our aim is not limited to detect the presence of inequality in opportunity but to measure its extent, within the large set of available descriptive indices, the Gini coefficient was considered (e.g., Gini, 1921). More in detail, the idea here is to provide a measure of the heterogeneity between classes in term of the socio economic status of students. For this purpose, we propose to consider as variable of interest the average SES at class level. For all the classes within each school and each province of the Lombardy region, 5 Quantitative Methods Inquires we computed the average value of the students’ SES index. We remark that for every single student, the SES index ranges between -3 and +3. Thus, it is reasonable to believe that the average SES at class level may take even negative values. In such a context, the reliability of the classical Gini coefficient may come less since requiring the considered variable to be characterized by non-negative values. Indeed, in case of negative values, the Gini coefficient may violate the normalization principle and thus take values greater than one. A solution to this problem was recently provided by Raffinetti et al. (2014), who introduced a new Gini coefficient adjusted for the presence of negative values. The new Gini coefficient, expressed as the ratio between the absolute mean difference (cid:4666)1⁄(cid:1840)(cid:2870)(cid:4667)∑(cid:3015) ∑(cid:3015) |(cid:1851) (cid:3398)(cid:1851)| and (cid:4666)2/(cid:1840)(cid:4667)∑(cid:3015) |(cid:1851)|, fulfills the normalization principle. This allows us (cid:3036)(cid:2880)(cid:2869) (cid:3037)(cid:2880)(cid:2869) (cid:3036) (cid:3037) (cid:3036)(cid:2880)(cid:2869) (cid:3036) to provide a measure of inequality in opportunity which can occur as a consequence of the class composition process conditioned to the pupils’ socio-economic status. Indeed, if the Italian schools actually respected the legislative principle of “equal-heterogeneity” in the composition of classes, the Gini coefficient should be close to zero. This does not happen, as shown by results in Table 3, where the Gini coefficient of the average SES at class is reported for every province. Table 3. Gini coefficient of the average SES at class level per province Province BG BS CO CR LC LO MI MN PV SO VA Gini coefficient 0.65 0.67 0.71 0.69 0.72 0.71 0.72 0.63 0.73 0.69 0.70 The Gini coefficient is greater than 0.60 in all the provinces. More precisely, over the 50% of the provinces presents a Gini coefficient greater than 0.70. The province of PV has the higher heterogeneity between classes with a Gini coefficient equal to 0.73. Such findings are made more evident by the boxplots in Figure 1 which show a remarkable variability of the average SES at class level in every province of the Lombardy region. Even though these descriptive statistics seem to confirm the presence of the social tracking phenomenon, they are obtained without taking into account the hierarchical structure of classes nested in schools. Thus, the high heterogeneity between classes at province level may reflect the high heterogeneity between schools within the province. For this reason, one may assume this variability to be explained by the gaps across the territorial areas where schools are located. Indeed, schools located in more disadvantaged areas catch more disadvantaged students. Further investigations were carried out by distinctly computing the Gini coefficient of the SES average at class level within each school across all the provinces. Also in this case, the Gini coefficient reaches very high values, leading us to believe that heterogeneity between classes is a real threat for the equality in opportunity in the Italian primary schools. In order to validate such a conclusion, the multilevel modeling approach (e.g., Goldstein, 2011) was considered to take into account the complexity of the educational systems organized in school and class level. First, we assessed how the variability of SES portions out among the different considered levels in order to define segregation status indicators at class and school level, as suggested by Ferrer-Esteban (2011). Subsequently, we analyzed the partition of the variability of the scores in the Reading test among the different levels. Finally, a conditional multilevel model was built in order to evaluate the effects of both the SES index and segregation status indicators, after controlling for the aforementioned variables, with the purpose of detecting the actual presence of the social tracking phenomenon across the Lombardy primary schools. 6