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Heterogeneity, school-effects and the North/South achievement gap in Italian secondary education: evidence from a three-level mixed model


With the aim of assessing the extent of the differences in the context of Italian educational system, the paper applies multilevel modeling to a new administrative dataset, containing detailed information for more than 500,000 students at grade 6 in the year 2011/2012, provided by the Italian Institute for the Evaluation of Educational System. Data are grouped by classes, schools and geographical areas. Different models for each area are fitted, in order to properly address the heteroscedasticity of the phenomenon. The results show that it is possible to estimate statistically significant “school effects”, i.e., the positive/negative association of attending a specific school and the student’s test score, after a case-mix adjustment. Therefore, the paper’s most important message is that school effects are different in terms of magnitude and types in the three geographical macro areas (Northern, Central and Southern Italy) and are dependent on specific students’ and schools’ characteristics.

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  1. 1.

    Indeed, we are aware that the quality of schools is characterized by a wider set of dimensions (such as non-cognitive achievements, school climate, cognitive test scores in additional subjects, teachers’ satisfaction, etc.). Thus, while the formulation “schools with higher tests” is somehow less intuitive, it is definitely more adequate for describing the real aspect that we are monitoring in this research. However to ease notation we use the word quality in the text.

  2. 2.

    A recent paper (Agasisti and Falzetti 2013) also showed that schools in the South practice a within-school segmentation (e.g., between classes) stronger than their counterparts in the North. In this paper, we explore between-schools differences, but we are aware that similar mechanisms (that is to say, differential effects on achievement between classes of the same school) are also operating within schools.

  3. 3.

    An interesting example of study of longitudinal data at student level in Italy is presented in Bartolucci et al. (2011).

  4. 4.

    While the distribution of \(b_j\) is checked later, its characteristics of being exogenous (in the sense of Steele et al. 2007) is not empirically verifiable in this setting.

  5. 5.

    Let us remind that the number of schools is much lower in Central Italy because the administrative classification of North, Centre and South used does not separate the country in three equal parts; instead, Central Italy only includes four regions out of twenty (Tuscany, Lazio, Marche, Umbria).


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This work is within FARB—Public Management Research: Health and Education Systems Assessment, funded by Politecnico di Milano. The authors are grateful to Invalsi for having provided the original dataset, and P. Falzetti for the statistical assistance in building the specific database used in this paper.

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Correspondence to Francesca Ieva.



As suggested by an anonymous referee, we report the estimates of model (1), fitted discarding the CMS5, for each geographical areas, in two cases: the entire database and the reduced one. We report only the estimates of fixed effects to ease comparison between the two cases (see Table 7). This enforces us in relying the listwise deletion approach, despite the discrepancies highlighted in Sect. 2.2.

Table 7 ML estimates of fixed effects (with SEs) for model (1) without CMS5, fitted both to entire dataset (ED) and to reduced one (RD) of Northern, Central and Southern area

There are no significant differences in the two cases, so we can claim that the large proportion of missing data is not a big problem.

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Agasisti, T., Ieva, F. & Paganoni, A.M. Heterogeneity, school-effects and the North/South achievement gap in Italian secondary education: evidence from a three-level mixed model. Stat Methods Appl 26, 157–180 (2017).

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  • Child development
  • Multilevel models
  • School effectiveness
  • Value-added model
  • Contextual effects
  • Education