Beside the core educational goods and services, schools have provided also peripheral education goods and services. In Italy, public schools have provided services such as school meals, transports from and to school to a population of students with different socio-economic characteristics and, it has required more responsibility on the transfers of resources to schools. This study estimates the impact of school inputs such as school meals and public transports from and to schools, within 15 Italian regions with ordinary statues. Three research questions are:

• Is there variability of students’ achievements among municipalities after we control for students and schools’ characteristics?
•  Is there variability of the efficiency level among municipalities in providing services to schools?
• Does the variability among municipalities’ efficiency in producing ancillary services explain the variability of the students’ achievements

The analysis of efficiency among municipalities is conducted using order-m while Data Envelopment Analysis approach (DEA) is proposed for robust analysis. Geographical differences in test scores within the country have emerged in studies by Bratti et al. (2007), Agasisti and Vittadini (2012) and they provide an excellent backdrop for analysing the magnitude and variability of the efficient use of resources among regions and the variability of students’ outcomes across regions. The literature regarding the effect of ancillary services as a whole is scarce. The first study that empirically discussed how transport from and to school affect students’ outcomes is by Lu and Tweeten (1973). Other few studies are used qualitative analysis showing that students who spend more time on the bus are more likely to have lower test score compared to their peers (Henderson 2009). The effect of school meals on students’ performance are plentiful for the USA and the UK but there are also studies from other developed and developing countries. Figlio and Winicki (2005) focus on a random sample of school districts in Virginia finding that schools that increased the nutritional content of school meals for students, saw an improvement on students’ performance. The positive effect of breakfast on students’ test score is found in the work by Imberman and Kugler (2014). Belot and James (2011) present evidences from an experiment produced in Greenwich, U.K. where some schools changed the meals offered to students, from low nutritional content to more healtier food. Different conclusions are obtained by a Danish study by Sørensen et al. (2015) with no effect on mathematics outcomes.

Researchers have also questioned the distribution of resources within schools. Over the past three decades, there is not a unique consensus regarding the link between school resources and students’ performance. In his studies on the EPF around the world, Hanushek (1981, 1989, 1991) has concluded that there is not a strong or consistent relation between resources and student achievement. Other further studies (Hanushek, 1997; Hakkinen et al. 2003) find that educational resources of schools do not have an effect on academic achievement of students. Greenwald et al. (1996) found that “broad range of resources were positively related to student outcomes, with effect sizes large enough to suggest that moderate increases in spending may be associated with significant increases in achievement”. A study for the U.S. by Lafortune et al. (2016) who investigates a post-1990 school finance reforms, also shows that more resources to schools have a large effect on educational achievement.

In order to determine the efficiency scores of municipalities in producing ancillary services for education, the efficient production frontier is defined in the input-output space as the locus of the maximal attainable level of outputs corresponding to given levels of inputs considering the efficiency of production units (maximization of output) or the minimum level of inputs corresponding to given level of output (minimization of inputs), referred to as decision-making units (DMUs). In this study, the order-m approach is the main empirical models adopted, using 1 input and 2 outputs (meals and transports) with input orientation (Cazals et al. 2002). Order-m is a generalization of DEA and FDH and it adds a layer of randomness to the computation of efficiency scores. The main idea is to benchmark the DMUs by the expected best performance in a sample of m peers instead of benchmarking a DMU by the best-performing peer as in DEA and FDH. Order-m performs better in mitigating the impact of (potential) outlier behaviour and allowing for uncertainty in the observed sample. For the goal of this paper in investigating the efficiency scores at municipalities level, the baseline model uses the order-m setting m=100, bootstrap is D=3000. The efficiency scores derived in the nonparametric model are tested then, as an explanatory factor for the variability of test scores between municipalities – which is analysed with a three-level multilevel model. Multilevel modelling is used for studying the determinants of pupils’ test scores, given the nested structure of the database with pupils nested within school and schools nested within municipalities. The aim is to estimate the relationship between a response variable and a set of explanatory variables where units of observation at different levels and, as the within-cluster dependence violates the assumption of ordinary regression models that responses are conditionally independent given the covariates, the issue of incorrect standard errors is overcome by using multilevel models (Bryk and Raudenbush 1992). This paper adopts a three-level multilevel approach with random intercept with pupils nested within school-units and school-units nested within municipalities and it is the appropriate model to investigate the impact of municipalities’ resources on services taking into account pupils and schools’ characteristics and the hierarchical structure of the database (Snijders and Bosker 2012; Goldstein 2011). Three-levels are indicated with pupils at Level 1, school-unit at Level 2 and municipalities at Level 3.

Results demonstrate that local governments have different efficiency levels. Findings also show that the test scores’ variability between students in different municipalities is not explained by different efficiency of local government in producing the ancillary services.

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