Efficiency in education: primary and secondary schools in Italian regions

ABSTRACT

By using stochastic frontier analysis, single- and multiple-output methods, this paper empirically investigates the efficiency of Italian regions in providing public primary and secondary education for the period 2011–18. The analysis detects strong interregional differences, outlining a clear North–South geographical pattern. To single out the reasons for the poor performance of Southern regions, context variables (per capita gross domestic product, poverty, institutional quality, adult education) are considered and shown to be highly relevant in shaping regional efficiency. Finally, when interregional disparities in socio-economic factors are accounted for, no residual geographical pattern in regional efficiency emerges.

KEYWORDS:

• efficiency
• education
• stochastic frontier analysis
• Italy

JEL:

• H52
• H75
• I21

ACKNOWLEDGEMENTS

We thank Mariarosaria Agostino and two anonymous referees for their comments. We also thank the participants in the XLI annual Scientific Conference of the Italian Association of Regional Sciences (online conference, 2–5 September 2020) and the Workshop of the cMET05 University Centre for Applied Economic Studies (Prato, Italy, 9–10 September 2020) for discussing an earlier version of this paper.

DISCLOSURE STATEMENT

No potential conflict of interest was reported by the authors.

Notes

1. At school level there are, of course, many other factors possibly leading to different educational outcomes, for example, school ownership, that is, private or public (Barbetta & Turati, 2003), degree of competition (Agasisti, 2013), teachers’ age (Bryson et al., 2020) and status, that is, tenured or not (Di Giacomo & Pennisi, 2015), share of disabled students (Agasisti & Vittadini, 2012), etc. Since these variables take on similar values in all Italian regions, they are not explicitly considered in the following analysis.

2. Per capita public expenditure on education is calculated as the ratio of public expenditure to the population aged 3–18 years.

3. The reference to macro-regions is common in the literature on the Italian geographical divide. Macro-regions are North-West (including Piedmont, Aosta Valley, Lombardy, Liguria), North-East (Veneto, Trentino-Alto Adige, Friuli Venezia Giulia, Emilia-Romagna), Centre (Tuscany, Umbria, Marche, Latium), South (Abruzzi, Molise, Campania, Apulia, Basilicata and Calabria) and Islands (Sicily and Sardinia).

4. PISA is the OECD Program for International Student Assessment launched in 2000. The PISA test measures and compares the skills in reading, mathematics and science of 15-year-old students. In 2018, mean scores in reading ranged from 340 (Philippines) to 555 (China), while mean scores in mathematics were included between 325 (Dominican Republic) and 591 (China).

5. The Istituto Nazionale per la Valutazione del Sistema educativo di Istruzione e di formazione (INVALSI) is the government agency charged with the assessment of the Italian educational system. Every year in spring, the mathematics and Italian language skills of all students are evaluated through a standardized test including multiple-choice questions and open-response items. INVALSI data refer to school and class average marks (for multiple-choice questions) and overall ability scores.

6. Including the 2018 wave allows attenuating concerns of data reliability connected to the possibility of score manipulation due to student and teacher cheating, which can occur mainly through dishonest transcription of students’ responses on machine-readable answer sheets (Bertoni et al., 2013). Indeed, from 2018 answers from secondary schools’ students are collected and processed through an automatized and centralized process, ruling out any kind of influence by teachers and local administrators (INVALSI, 2018). Comparing regional scores in 2018 and previous years, we find that rankings remain basically unaltered and data variability across regions is even reduced, which seems to exclude the possibility that dishonest behaviour was significantly more widespread in the South than other areas.

7. The polar coordinates $\theta$ are recursively obtained by:

${\theta }_m\left(y\right)={\mathrm{c}\mathrm{o}\mathrm{s}}^{-1}\left(y_m/\parallel y\parallel \prod _{j=0}^{m-1}\mathrm{s}\mathrm{i}\mathrm{n}{\theta }_j\right)$ $\mathrm{f}\mathrm{o}\mathrm{r}m=1,\dots ,M$.

8. For a single-output technology, $p\left(\theta \right)=1$, and the ray production function, $f\left(x,\theta \right)$ simplifies to the single-output production function $f\left(x\right)$.

9. The polar coordinates $\theta$ are not in logarithmic form (Henningsen et al., 2015).

10. A model with $m$ outputs includes $m-1$ polar coordinates. For example, considering the output vector $y=\left(y_1,y_2,y_3\right)$, the polar coordinates are ${\theta }_1$ when measuring the angle between $y_1$ and the plane spanned by $y_2$ and $y_3$; and ${\theta }_2$ when measuring the angle between $y_2$ and $y_3$.

11. This amounts to considering the largest output that educational institutions are able to achieve with available resources as a benchmark, and deriving a measure of the inefficiency of those producing less.

12. The key idea is that disturbance terms ${ϵ}_{rt}$ in equation (9) are assumed to be – conditional on $z_{rt}$ – independently truncated normally distributed, with a two-sided truncated normal distribution (left-truncation at $-\gamma z_{rt}$ and right truncation at $1-\gamma z_{rt}$). Since this distributional assumption on ${ϵ}_{rt}$ is not appropriate for panel data, equation (9) is estimated on the pooled dataset. We are aware that a residual problem of separability (Badin et al., 2014) may exist, even if in our case the context variables may not impact on the teaching/learning technology.

13. The regional public expenditure on education is divided by population ages 3–18 years, that is, the share of the population that possibly benefits from that expenditure. Since INVALSI tests are administered in spring, we use one-year lagged values of EXP because scores are likely to be affected by expenditure of time t – 1 rather than current time. Data on public expenditure on education at a regional level are collected by the Italian Regional Public Accounts System (CPT, 2020).

14. In particular, the infrastructure endowment $STRU$ is proxied by the share of schools providing specific services to disabled pupils (e.g., access ramps, elevators, standard stairs, etc.). Schools supplying better instruments to ease access to education are assumed to improve students’ results and school efficiency.

15. As the level of difficulty of INVALSI tests is not constant over time, we standardize annual scores by subtracting the national mean and dividing by the standard deviation. As a result, a part of our data assume negative values, which induce us to employ the SRPF model when allowing for multiple outputs.

16. The EQI proposed by Charron et al. (2013) is based on a large survey of about 34,000 European citizens living in 172 NUTS-1 and NUTS-2 regions within 18 European countries. Respondents are asked about their own experiences about and perceptions of the quality, impartiality and corruption of public services. We employ EQIs for 2010, 2013 and 2017 published by Charron et al. (2019); missing values are imputed by interpolation of the closest observations.

17. When evaluating the impact of context variables, the TFE model, as well as the distance function model, estimates the effects of regressors on inefficiency (not on efficiency). This implies that a positive (negative) sign of the estimated coefficient means that a variable negatively (positively) impacts the efficiency of the regional educational system.

18. The special status is acknowledged to islands (Sardinia and Sicily) and Northern border regions with relatively large linguistic minorities (i.e., Aosta Valley, Trentino-Alto Adige and Friuli Venezia Giulia).

19. According to CPT (2020), for the period 2011–18, regional per student real expenditure on primary and secondary schools was higher than the national average by 1.65 times in Trentino-Alto Adige, 1.19 times in Aosta Valley, 1.17 times in Sardinia and 1.14 times in Friuli Venetia Giulia.

20. For simplicity, and to facilitate comparison with Figure 2, here TFE estimated inefficiency $\widehat{u_{rt}}\ge 0$ is expressed through a logarithmic transformation as an efficiency index $1/e^{\widehat{u_{rt}}}$ included between 0 and 1.

21. These additional estimations are not shown in Table 3 and are available from the authors upon request.

22. Alternatively, a Tobit regression is also used, yielding results similar to those obtained by the Simar and Wilson method. In addition, to take possible changes in technology into account, we also include time effects; however, the hypothesis that the coefficients of year dummies are jointly equal to 0 is never rejected. Both Tobit and time-effect regressions are not reported, but are available from the authors upon request.

23. In Table 4, the estimated values of coefficients measure the impact of regressors on efficiency, rather than inefficiency. Thus, here the expected signs of the coefficients are opposite to those of Tables 2 and 3.

24. Robustness is confirmed by inspection of the kernel density of efficiency scores obtained by Simar and Wilson and TFE models (data not shown, but they are available from the authors upon request). The shape of probability distributions of efficiency derived from the two estimation methods are pretty similar, with a large part of the scores being concentrated in the interval 0.75–0.95 and, especially in the Simar and Wilson case, very few scores < 0.4.

25. We also regressed Simar and Wilson residuals on regional dummies to test whether geographical determinants affect residual inefficiency (i.e., inefficiency not due to the context variables employed in estimation). The results (available from the authors upon request) corroborate the hypothesis that when the socio-economic peculiarities of Southern regions are appropriately accounted for, the North–South geographical pattern of inefficiency vanishes or is strongly attenuated.