Private vs. Public Schooling: The role of school composition

Elke Claes, Léonard Moulin

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Elke Claes, Léonard Moulin. Private vs. Public Schooling: The role of school composition. International Journal of Educational Research, 2026, 135, pp.102863. 10.1016/j.ijer.2025.102863. hal-05441797

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# Private vs. Public Schooling: The role of school composition

Elke Claes<sup>a, b, ∗</sup>, Léonard Moulin<sup>b, c, †, ∗</sup>

## ARTICLE INFO

Keywords:

Private school

School composition

Educational achievement

Propensity score matching

Lower secondary education

## ABSTRACT

Publicly funded private schooling is a common feature of many education systems, yet its implications for educational equity and effectiveness remain contested. While private schools often exhibit higher student achievement, the sources of this advantage are not well understood. In particular, differences in student composition—especially in terms of socioeconomic status (SES)—are likely to play a key role. This paper examines how school-level SES composition contributes to achievement differences between public and private schools. Using propensity score matching (PSM) on data from 22,441 French ninth-grade students, we find that private school students outperform their public school peers in mathematics and French, with especially large effects for low-SES students, an underrepresented group in private schools. While school composition explains only part of these effects, it accounts for a substantial share of the performance gap among high-SES students, rendering the adjusted effect statistically indistinguishable from zero. These findings highlight which students benefit most from private schooling and point to the need for further research into the mechanisms underlying performance differences across school sectors.

## 1. Introduction

Schools play an important role in shaping academic outcomes, but they are not all alike. Since Coleman et al. (1982) demonstrated private schools' academic superiority and their role in desegregation, research has increasingly focused on differences between private and public schools. However, students in private schools differ from those in public schools due to selection; as they typically come from privileged families, with better-educated parents and stronger academic skills (Thapa, 2015). This complicates an assessment of the effect of private schooling on student performance. Nevertheless, several studies have addressed this effect using varying methodologies such as an IV approach, exploiting lottery systems, fixed-effects estimation, or propensity score matching.<fnref n="1" /> Regardless of how selection bias is addressed, it seems evident that attending charter schools can have a positive impact on students' test scores in the U.S. (e.g., Abdulkadiroğlu et al., 2011; Angrist et al., 2016, 2010, 2013). Private schools, moreover, tend to

<footnote><sup>a</sup> Research Centre for Education and the Labour Market (ROA) - Maastricht University, Netherlands</footnote>

<footnote><sup>b</sup> Institut national d'études démographiques (INED), F-93300 Aubervilliers, France</footnote>

<footnote><sup>c</sup> Associate Researcher at Érudite, Université Paris-Est Créteil, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail addresses: e.claes@maastrichtuniversity.nl (E. Claes), leonard.moulin@ined.fr (L. Moulin).</footnote>

<footnote n="1">¹ First, several studies use an IV approach, mainly in assessing the impact of Catholic schooling. They instrument the choice of attending Catholic school by instruments such as Catholic region (Evans & Schwab, 1995), school attendance in a predominantly Catholic area (Evans & Schwab, 1995), and Catholic schools per square mile (Neal, 1997). Second, the impact of a type of schooling could be assessed by exploiting lottery systems, mostly used to examine the effect of charter schools in the U.S. (e.g., Chabrier et al., 2016). As highlighted by Spees and Lauen (2019), the applicability of these studies is however limited, as their results are relevant only to charter schools where the number of applicants exceeds the available spots. Third, fixed-effect estimation with longitudinal data can offer valuable insights, but its application is limited to students who change between different types of schools (e.g., Epple et al., 2016). Last, propensity score matching, which relies on the assumption that all relevant confounders are observed (selection on observables), is also used to assess the effect of private schooling on student performance (Epple et al., 2016).</footnote>
outperform public schools (e.g., Anand et al., 2009; Azam et al., 2016; Cox & Jimenez, 1990; Lefebvre et al., 2011; Thapa, 2015; Wamalwa & Burns, 2018).<fnref n="2" />

While private schooling has generally been shown to have a positive impact on student achievement internationally, the unique structure of private schools in France warrants separate consideration. Private schools in France differ significantly from those in other countries. Most private lower secondary schools are under contract with the state, receiving substantial public funding for teachers' salaries and operating costs. These schools, often referred to as government-dependent schools, follow the same curriculum as public schools and are highly dependent on state support, resembling charter schools in the U.S. or free schools in the U.K. However, unlike charter and free schools, private schools in France require certified teachers, can select students, and must adhere to the national curriculum. Several studies have examined the effect of private schooling on student performance in France, generally reporting positive effects (e.g., Bertola, 2017; Caille, 2004; Cayouette-Remblière & Moulin, 2019; Langouët & Léger, 1990). However, others find more mixed or even negative results, particularly regarding grade retention and long-term academic outcomes (e.g., Tavan, 2004; Valdenaire, 2011). While most of these studies rely on relatively weak identification strategies, more recent research using causal inference methods provides more robust insights. Fougère et al. (2017), focusing on primary education, use the distance between the nearest private and public schools as an instrument—a strategy that raises concerns due to potential socioeconomic sorting, as school proximity may influence the composition of families in the area. In contrast, Moulin (2023), applying propensity score matching, finds a significant positive effect of private schooling on ninth-grade test scores.

While nearly all studies examining the effect of private schooling on student performance account for students' individual socioeconomic backgrounds, none—to our knowledge—explicitly consider the socioeconomic composition of schools. Yet, school composition plays a crucial role in shaping learning environments, as it can influence peer effects, teaching strategies, and overall academic expectations. This paper aims to fill this gap by investigating whether school SES composition drives the observed differences in student performance between private and public schools. More specifically, we consider French and mathematics scores of French ninth-grade students. Furthermore, we examine heterogeneity at student-level SES. We assess whether the effects of private schooling differ between low- and high-SES students, and whether school SES composition plays a different role for both groups.

We use French data from the Direction de l'Évaluation, de la Prospective et de la Performance (DEPP) of 22,441 ninth-grade students. The data include students' ninth-grade performance in mathematics and French, complemented with information about their parental, family, and scholastic background. They contain information about the school SES, measured as the proportion of students of high-SES (see Table A.1 in Appendix) within the school and the student SES, measured by the socio-occupational category of householder.<fnref n="3" />

To estimate the effect of school SES composition on student achievement while addressing selection bias, we apply propensity score matching (PSM), a method that allows us to compare students with similar observable characteristics across school types. We find that school composition explains only a small portion, approximately 15%–23%, of the private school advantage. Notably, private schooling proves especially beneficial for students from low socioeconomic status (SES) backgrounds, though their limited representation in private schools restricts access to these advantages. For high-SES students, initial performance gains associated with private schooling diminish when differences in school composition are taken into account, suggesting that these advantages are substantially attenuated once peer composition is taken into account.

Given the established performance differences between public and private schools, the question consequently arises of why these differences between schools exist. We argue that these differences could stem from the composition of their student bodies, based on the work of Dronkers and Robert (2008). Using PISA data from 22 countries, they examine whether the academic advantage associated with private schooling can be partly explained by school composition. They distinguish private government-dependent from private independent schools in their analyses, and conclude that private schools outperform public schools. Dronkers and Robert (2008) focus in their work, among others, on how school composition might explain achievement differences between public and private schools. Using a cross-national multilevel analysis, they demonstrate that school composition explains a large part of the achievement difference between private government-dependent and public schools. School climate differences are mentioned as an important explanation for this achievement difference. For the difference between private-independent schools and public schools, they find that the initial positive effect of private schools on student achievement reverses and becomes negative once school composition is considered. These findings align with results from PISA 2022, which show that, across OECD countries, students in private schools initially appear to outperform their peers in public schools in mathematics. However, once both student- and school-level socio-economic composition are taken into account, this apparent advantage not only disappears but reverses: public school students perform 11 points better than students in private schools, and 14 points better than those in government-dependent private schools (OECD, 2023).<fnref n="4" /> Similar conclusions are reached by Lubienski and Lubienski (2006), who analyze data from the 2003 U.S. National Assessment of Educational Progress (NAEP) in mathematics. Using multilevel modeling, they show that the initial achievement advantage observed in private schools largely reverses or disappears after controlling for both student-level variables and school-level factors.

<footnote n="2">² In contrast, some studies have found that attending charter or private schools offers no clear advantage, and in some cases, may even have a negative impact on student achievement (e.g., Abdulkadiroğlu et al., 2018; Bettinger, 2005; Bifulco & Ladd, 2006; Chudgar & Quin, 2012; Newhouse & Beegle, 2006; Ni & Rorrer, 2012).</footnote>

<footnote n="3">³ These proportions are calculated by the DEPP from exhaustive administrative registers, and thus reflect the actual composition of each school and classroom.</footnote>

<footnote n="4">⁴ A similar pattern holds in France, where the adjusted performance gap also turns in favor of public schools. Public school students score 21 points higher than their counterparts in fully private schools, and 23 points higher than those in government-dependent private schools.</footnote>
We contribute to the literature on private schooling in two ways. The first contribution of this paper to this strand of literature is that we examine whether school composition with regard to SES can explain performance differences between private and public schools. While private schools often attract students from higher SES backgrounds, the extent to which their benefits persist when accounting for school SES composition remains underexplored. While this question has received some attention, most existing studies either rely on international assessments that do not allow for detailed country-level analysis, or examine particular sectors within the U.S. system, such as charter schools. These approaches offer useful perspectives but are not directly applicable to the French context. We address these limitations by using propensity score matching to reduce selection bias and by conducting a focused analysis within the French education system. In France, private schooling is a widely debated policy issue, yet little is known about the factors that shape its impact on student performance. One such factor could be the school SES. Several studies examine the relationship between school SES composition and students' outcomes (e.g., Early et al., 2020; Kim, 2019; Kim et al., 2019; Sirin, 2005; Tan et al., 2023). Tan et al. (2023), for instance, conclude in their meta-analysis on a strong association between school SES composition and student outcomes. Perry and Mcconney (2010), who examine this association using PISA data from more than 12,000 students from Australia, add that there is no heterogeneity in this regard to individual SES. Sirin (2005) concludes in his meta-analysis that school SES composition significantly impacts academic achievement, beyond the individual SES of students.

There are several reasons to suspect that school SES composition is a mechanism in the effect of private schooling on student performance. First, high-SES schools might have access to greater financial and material resources, enabling them to invest in better facilities, advanced technology, and enriched extracurricular opportunities. These resources might directly enhance the quality of education and indirectly support students' development. Second, the school climate might differ in schools with a low or high social composition. Schools with a higher SES composition might foster a culture of academic engagement, peer support, and aspirational learning norms. Students in such environments benefit from exposure to peers who model positive academic behaviors and attitudes, as Hanushek et al. (2003) show that peers significantly affect student performance. Third, teachers matter for academic achievement (e.g., Clotfelter et al., 2007) and the way in which teachers are appointed differs among private and public schools. Furthermore, teachers and teaching might differ among schools with varying school SES compositions. Schools with higher SES might be more attractive for teachers, as these schools typically consist of an 'easier' student population. Teachers in higher SES schools might maintain higher expectations for their students, which is important for academic performance (Rosenthal & Jacobson, 1968). Timmermans et al. (2016) show that teacher experiences differ depending on student characteristics and behaviors (e.g., the student's self-confidence, social behavior in classroom, work habits etc.). And last, higher SES schools might benefit from greater parental involvement as parents choose for their students to attend private school, making them interested in schooling.

The second contribution to the understanding of private and public schooling relates to heterogeneity. We investigate whether the effect of private schooling on student performance varies between low- and high-SES students, not previously addressed in the existing literature. Previous literature on heterogeneity in the effects of private schooling shows that private schools tend to be more beneficial for initially low-performing students (e.g., Abdulkadiroğlu et al., 2011; Angrist et al., 2016, 2010, 2013; Chabrier et al., 2016; Moulin, 2023) compared to their peers. It is, however, interesting to know whether the effect of private and public schooling differs between low-SES and high-SES students, despite this already established heterogeneity. While there is often a relationship between socioeconomic status and academic performance, they are distinct factors that may interact differently with school type. So, examining SES heterogeneity could help policymakers and educators better target interventions and resources to support students from different socioeconomic backgrounds, regardless of their current academic performance.

This paper proceeds as follows: Section 2 presents the institutional background, the data, and descriptive statistics. Section 3 details the estimation strategy. Section 4 reports the results. Section 5 offers a discussion and concludes.

## 2. Institutional background, data, and descriptive statistics

### 2.1. Private schools in France

The French education system comprises four levels: *maternelle* (kindergarten, 3 years), *primaire* (primary school, 5 years covering 1st to 5th grades), *collège* (lower secondary school, 4 years covering 6th to 9th grades), and *lycée* (upper secondary school, 3 years covering 10th to 12th grades). Private education plays a significant role in France, especially at the lower secondary level, where 21.5% of students in collège were enrolled in private schools in 2019 (Moulin, 2023). A distinction is made between students in private lower secondary schools under contract with the state (*collèges privés sous contrat*) and independent private lower secondary schools (*collèges privés hors contrat*). The former represents the largest portion of the students (98%). Private schools under contract with the state operate under government regulation and receive state funding. Therefore, these schools must adhere to the national curriculum, pursue the same pedagogical objectives, and maintain equivalent academic standards as public schools. In Catholic lower secondary schools, tuition fees average €849 per year (Cour des comptes, 2023).<fnref n="5" /> In contrast, the small percentage of students in independent private schools attend institutions with greater autonomy, but these schools receive no government funding and charge higher fees.

Private schools under contract with the state, which we focus on in this paper, mainly differ from public schools in terms of student and teacher assignment. Public schools enroll students based on strict residential zoning rules, whereas contract private

<footnote n="5">⁵ In France, Catholic schools account for 91% of government-funded private lower and upper secondary schools (source: based on the author's calculations using Cour des comptes, 2023).</footnote>
schools have the autonomy to select their students based on academic achievement and motivation. Admission decisions are made at the discretion of the school head, and there are no standardized entrance exams. In addition, teachers in private schools under contract with the state are recruited through national competitive examinations and are funded by the state. Nevertheless, unlike their public school counterparts, they are neither civil servants nor assigned to the school through a strict administrative procedure. These two points of flexibility allow private schools to cultivate distinct educational environments, which may contribute to greater cohesion among teaching staff and students.

## 2.2. Data

We use French data from the Direction de l'Évaluation, de la Prospective et de la Performance (DEPP), a department within the French Ministry of National Education and Higher Education. The data consist of information on a balanced random sample of 34,986 students, i.e. 1/22 of sixth-grade students from 2007, tracked through 2013. They include detailed socioeconomic and educational records, complemented by family surveys conducted in 2008 and 2011 to capture additional socioeconomic details. The sample was carefully designed to represent the broader population using comprehensive data on students and schools.

The Panel 2007 was implemented by the French Ministry of Education using a balanced random sampling procedure. While the selection remained probabilistic, available information on students and schools was used to ensure that the sample faithfully reproduced the distribution of key population characteristics (Caille, 2017). Out of the 7,004 collèges open at the beginning of the 2007 school year, 6,857 (98%) had at least one student represented in the panel, with an average of five students per collège. The Panel 2007 was also the first French education panel to be drawn from an exhaustive national database (the academic student registers), which reinforced its robustness and representativeness. Further details on the survey methodology are available in the official documentation (DOI: 10.13144/lil-0955).

The total data consist of information about 34,986 students. We restrict the sample to students who were expected to take the *brevet* examination in 2011 or 2012 (n = 30,161). Among students who entered grade 6 in 2007, 84% progressed to grade 9 and sat for the general *brevet* four or five years later, while the remainder followed vocational pathways or experienced delays due to grade repetition (Cayouette-Remblière & Moulin, 2019). We exclude students who do not have standardized test scores in either mathematics or French from sixth-grade (n = 23,958). This constitutes the largest source of attrition and reflects the structure of the DEPP database. We also exclude those without reported scores in either subject in grade 9 (n = 22,454), which mainly corresponds to students absent from the standardized ninth-grade assessments or for whom scores were not recorded in the DEPP database. Finally, we only consider students enrolled in either public schools or government-funded private schools in grade 9, resulting in a final sample of 22,441 students. This restriction is required by our research design, since our treatment variable compares outcomes between public and private (government-dependent) schools. Students enrolled in other types of institutions (e.g. fully independent private schools or vocational tracks) are therefore outside the scope of our analysis.

It is important to note that attrition is not random. Appendix Table A.2 shows that excluded students are disproportionately from disadvantaged backgrounds. For instance, 43.57% of excluded students are classified as low-SES, compared with 32.39% among those retained, while 24.20% of included students are high-SES versus only 15.96% among those excluded. Similarly, parents of excluded students are less likely to hold tertiary education (17.88% vs. 30.26% for mothers; 14.96% vs. 24.79% for fathers). Excluded students are also more likely to have repeated a grade in primary school (25.60% vs. 8.25%), and their mean grade 6 test scores are substantially lower (-0.767 SD vs. 0.211 SD in mathematics; -0.784 SD vs. 0.222 SD in French). Attrition also affects the measurement of school and class composition: excluded students tend to come from schools and classes with a higher proportion of low-SES peers and a lower proportion of high-SES peers. For instance, the average proportion of low-SES students in class is 39.59% among excluded students, compared with 33.88% among those retained, while the average proportion of high-SES students in school is 18.96% for excluded students versus 21.55% for those retained. Exclusions are also slightly more prevalent among students from private schools, both at the primary level (17.32% vs. 16.29%) and in grade 6 (21.86% vs. 19.89%). As a result, the low-SES students who remain in the analytical sample are positively selected relative to the broader low-SES population. In other words, the most disadvantaged students are underrepresented in our analyses.

Although our data refer to the 2007 cohort, we believe the results remain relevant today. Since then, the French and mathematics curricula and the *diplôme national du brevet* have been revised (notably in 2016-2018), yet the exam continues to assess core competencies in these subjects through national written tests. Likewise, grade-6 national assessments remain focused on the same foundational skills. The institutional framework governing public and government-dependent private schools has remained broadly stable since the 2000s. What is expected to reshape the landscape in the coming years is not new selection rules but demographic decline: lower-secondary enrollments started to decrease in 2023 and are projected to fall by about 7% by 2030 and 22% by 2038 (Charousset et al., 2025). This demographic shock may, in the future, reconfigure the balance between public and private provision and reshape patterns of social composition.

## 2.3. Descriptive statistics

We investigate whether school composition plays a role in student performance differences between students in public and private school. To do so, we consider the ninth-grade score of students on mathematics and French, which we standardize to have a mean of zero and a standard deviation of one.<fnref n="6" /> The test scores stem from the French national exam at the end of lower secondary

<footnote n="6">⁶ We standardize the mathematics and French score over the years 2011 and 2012, to make scores between the two years comparable. We have test scores for both years to account for students who repeated a grade and were therefore in grade 9 in 2012 instead of 2011.</footnote>
<figure><img src="image_7.png" /><figcaption>Fig. 1. Distribution of the ninth-grade test scores.</figcaption></figure>

Notes: This figure presents the distribution of ninth-grade test scores in mathematics (left) and French (right). The black line represents the distribution of scores for students in private schools, while the gray line corresponds to students in public schools. In addition, the figure differentiates the score distributions based on SES, highlighting results for both low- and high-SES students.

Source: Panel 2007.

Although the official brevet final grade combines standardized exams with continuous assessment, our analyses use only the nationwide standardized exam scores. Continuous assessment grades are not included. As can be seen from the first row in Fig. 1, ninth-grade performance differs between students in public and private schools, with students in private schools outperforming students from public schools.<fnref n="7" />

Furthermore, Fig. 1 presents a distinction between students from low- and high-SES backgrounds. To make this distinction, we consider the socio-occupational category of the students' householder. We use the PCS (Professions and Socio-professional Categories) classification that organizes individuals into four socio-professional tiers based on their occupations and social standing (see Table A.1 in Appendix). This four-group classification follows the convention used by the Ministry of Education in its official statistics (Rocher, 2016) and is widely employed in research on French education (Bonneau & Grobon, 2025; Breda et al., 2023). First, the highly favored group, which we refer to as high-SES group, includes roles like business owners with ten or more employees, liberal professionals, senior civil servants, and engineers. Second, the favored group, referred to as middle-high-SES, encompasses intermediate professions in health and social work, clergy, technicians, and supervisors. Third, the average group, which we translate to the middle-low-SES group, features occupations such as farmers, craftsmen, sales employees, and police officers. And fourth, the disadvantaged group includes skilled and unskilled workers, agricultural laborers, and unemployed individuals who have never worked, with a separate category for those whose status is unknown or irrelevant. We refer to this last category as low-SES category. For our analyses, we focus on the two extreme categories to explore the differences in student SES groups. Fig. 1 illustrates that students from both low- and high-SES backgrounds attending private schools outperform their counterparts in public schools in mathematics and French.

Table 1 presents descriptive statistics for all variables used in the PSM estimation, distinguishing between public and private schools, with t-statistics shown in the final column. First, we control for sex, distinguishing male and female students, who are equally represented in both school types. High-SES students are proportionally more represented in private (37.14%) than in public school (20.93%). In contrast, low-SES students are more represented in public (35.81%) than in private school (18.86%). Next, parental education is categorized into five levels: (1) tertiary education, (2) general upper secondary education, (3) technical or vocational upper secondary education, (4) vocational education, and (5) no qualification or not reported (NR). Furthermore, significantly fewer students in public schools have fathers with tertiary education (21.77%) compared to private schools (36.73%). Conversely, fathers without qualifications are more prevalent in public schools (32.70%) than in private schools (20.48%). A similar pattern is observed for maternal education. Additional variables include parenthood, immigration background, and number of siblings, all of which show

<footnote n="7">⁷ Students in public schools achieve an average mathematics score of -0.09 SD, compared to 0.41 SD in private schools. A t-test confirms that this difference is statistically significant ($p < 0.001$). Similarly, the average French score for public school students is -0.04 SD, while private school students score 0.40 SD on average. This difference is also statistically significant ($p < 0.001$).</footnote>
<caption>**Table 1**

Descriptive statistics by school type.</caption>

Source: Panel 2007.

<table><thead><tr><th>Variables</th><th>Public school (%)</th><th>Private school (%)</th><th>p-value</th></tr></thead><tbody><tr><td><strong>Socioeconomic characteristics</strong></td><td></td><td></td><td></td></tr><tr><td>Gender</td><td></td><td></td><td></td></tr><tr><td>Girl</td><td>51.51%</td><td>50.93%</td><td>0.500</td></tr><tr><td>Boy</td><td>48.49%</td><td>49.07%</td><td>0.500</td></tr><tr><td>Socioeconomic status</td><td></td><td></td><td></td></tr><tr><td>High-SES</td><td>20.93%</td><td>37.14%</td><td>0.000</td></tr><tr><td>Middle-high-SES</td><td>17.36%</td><td>16.85%</td><td>0.423</td></tr><tr><td>Middle-low-SES</td><td>25.90%</td><td>27.15%</td><td>0.095</td></tr><tr><td>Low-SES</td><td>35.81%</td><td>18.86%</td><td>0.000</td></tr><tr><td>Mother's educational attainment</td><td></td><td></td><td></td></tr><tr><td>Tertiary education</td><td>27.09%</td><td>42.79%</td><td>0.000</td></tr><tr><td>General upper secondary education</td><td>6.47%</td><td>6.81%</td><td>0.430</td></tr><tr><td>Technical or vocational upper secondary</td><td>11.17%</td><td>12.11%</td><td>0.088</td></tr><tr><td>Vocational education</td><td>25.48%</td><td>19.60%</td><td>0.000</td></tr><tr><td>No qualification or not reported (NR)</td><td>25.80%</td><td>13.31%</td><td>0.000</td></tr><tr><td>Father's educational attainment</td><td></td><td></td><td></td></tr><tr><td>Tertiary education</td><td>21.77%</td><td>36.73%</td><td>0.000</td></tr><tr><td>General upper secondary education</td><td>3.81%</td><td>4.15%</td><td>0.314</td></tr><tr><td>Technical or vocational upper secondary</td><td>7.95%</td><td>8.51%</td><td>0.235</td></tr><tr><td>Vocational education</td><td>29.78%</td><td>24.75%</td><td>0.000</td></tr><tr><td>No qualification or NR</td><td>32.70%</td><td>20.48%</td><td>0.000</td></tr><tr><td>Family type</td><td></td><td></td><td></td></tr><tr><td>Two parents</td><td>69.56%</td><td>75.92%</td><td>0.000</td></tr><tr><td>Single mother</td><td>13.59%</td><td>9.51%</td><td>0.000</td></tr><tr><td>Single father</td><td>1.53%</td><td>1.11%</td><td>0.025</td></tr><tr><td>Blended family</td><td>7.03%</td><td>5.32%</td><td>0.000</td></tr><tr><td>Other situations (including NR)</td><td>2.44%</td><td>1.97%</td><td>0.051</td></tr><tr><td>Number of siblings</td><td>1.931</td><td>1.722</td><td>0.000</td></tr><tr><td>Immigration background</td><td></td><td></td><td></td></tr><tr><td>Parents born in France</td><td>79.84%</td><td>85.19%</td><td>0.000</td></tr><tr><td>At least one foreign-born parent</td><td>20.16%</td><td>14.81%</td><td>0.000</td></tr><tr><td><strong>School characteristics</strong></td><td></td><td></td><td></td></tr><tr><td>Size of the urban area</td><td></td><td></td><td></td></tr><tr><td>Rural</td><td>24.98%</td><td>21.38%</td><td>0.000</td></tr><tr><td>&lt; 5,000 inhab.</td><td>7.82%</td><td>7.18%</td><td>0.148</td></tr><tr><td>[5,000; 10,000] inhab.</td><td>5.96%</td><td>5.97%</td><td>0.979</td></tr><tr><td>[10,000; 20,000] inhab.</td><td>5.26%</td><td>5.19%</td><td>0.843</td></tr><tr><td>[20,000; 50,000] inhab.</td><td>6.28%</td><td>5.91%</td><td>0.354</td></tr><tr><td>[50,000; 100,000] inhab.</td><td>6.65%</td><td>7.16%</td><td>0.245</td></tr><tr><td>[100,000; 200,000] inhab.</td><td>5.59%</td><td>5.07%</td><td>0.163</td></tr><tr><td>[200,000; 2,000,000] inhab.</td><td>22.18%</td><td>26.54%</td><td>0.000</td></tr><tr><td>Paris agglomeration</td><td>15.17%</td><td>15.53%</td><td>0.557</td></tr><tr><td><strong>Educational characteristics of the student</strong></td><td></td><td></td><td></td></tr><tr><td>Sector in primary education</td><td></td><td></td><td></td></tr><tr><td>Public</td><td>89.39%</td><td>38.56%</td><td>0.000</td></tr><tr><td>Private</td><td>6.29%</td><td>55.86%</td><td>0.000</td></tr><tr><td>Grade repetition primary education</td><td></td><td></td><td></td></tr><tr><td>No</td><td>90.99%</td><td>94.78%</td><td>0.000</td></tr><tr><td>Yes</td><td>9.01%</td><td>5.22%</td><td>0.000</td></tr><tr><td>6th-grade test score in mathematics</td><td>0.162</td><td>0.406</td><td>0.000</td></tr><tr><td>6th-grade test score in French</td><td>0.171</td><td>0.420</td><td>0.000</td></tr></tbody></table>

Notes: The table presents the weighted summary statistics of our sample. The table presents these statistics for observations in public (left) and private (right) schools. The last column shows the p-value for the difference between both school types.

significant differences between school types. Locality size of the student's school is also considered. Last, the analysis includes the student's primary educational trajectory, distinguishing those who attended public versus private primary schools and accounting for grade repetition in primary education. We also control for sixth-grade performance in mathematics and French, assessed via a standardized national test. Table 1 shows private school students significantly outperforming public school students, with average mathematics scores of 0.162 SD and 0.406 SD, respectively, and French scores of 0.171 SD for public schools versus 0.420 SD for private schools.

Next, we present the school composition variable that we consider: the proportion of students from high-SES backgrounds in the school as a proxy for school SES. In addition, we consider a similar variable in the classroom to inspect whether our findings also hold at the classroom level. Fig. 2 illustrates the distribution of both variables in public as well as private schools. This figure
<figure><img src="image_8.png" /><figcaption>Fig. 2. Distribution of the school and classroom composition variables.</figcaption></figure>

Notes: This figure presents the distribution of school composition (left) and class composition (right). The black line represents the distribution of scores for students in private schools, while the gray line corresponds to students in public schools.

Source: Panel 2007.

shows that the composition of both school types differs significantly, with a more advantaged composition in private than in public schools.<fnref n="8" />

As a final part of the descriptive analysis, we visualize the performance of public and private school students on the standardized ninth-grade test score. Fig. 3 illustrates students' test scores in relation to the percentage of students from a high-SES background within their school. It shows a positive relationship between students' test scores and the percentage of high-SES students within the school for public and private school students. The figure also suggests that this relationship is stronger for students in public schools than for those in private schools, although the differences appear minimal.

## 3. Estimation strategy

### 3.1. Propensity score matching

To evaluate the causal effect of private school attendance on academic achievement, we rely on the well-established potential outcomes framework, originally developed by Roy (1951) and later formalized by Rubin (1974). Since school choice is not random, simple comparisons of mean outcomes between private and public school students may be biased due to selection on observable characteristics. In this context, PSM provides a robust strategy to estimate causal effects by comparing treated and untreated individuals with similar covariate profiles, in the absence of randomized assignment.<fnref n="9" />

Let $D_i \in \{0, 1\}$ denote the treatment indicator, equal to 1 if student $i$ is enrolled in a private school and 0 otherwise. For each student, we define two potential outcomes: $Y_i(1)$, the outcome under private schooling, and $Y_i(0)$, the outcome under public schooling. The observed outcome is thus: $Y_i = D_iY_i(1) + (1 - D_i)Y_i(0)$ and the individual-level treatment effect is: $\tau_i = Y_i(1) - Y_i(0)$. Since it is not possible to observe both outcomes for the same student, our objective is to estimate the average treatment effect on the treated (ATT):

$$ \text{ATT} = E[Y(1) | D=1] - E[Y(0) | D=1]. \qquad (1) $$

<footnote n="8">⁸ The proportion of students from a high-SES background within a school is, on average, 19.75% for public schools, whereas this is 35.92% in private schools. A t-test confirms that this difference is statistically significant ($p < 0.001$). Similarly, the average proportion of high-SES students within a class is 22.64% in public schools, while this is 37.99% in private schools. This difference is also statistically significant ($p < 0.001$).</footnote>

<footnote n="9">⁹ PSM has been widely applied in education research, especially in studies assessing the impact of private schooling (e.g., Anand et al., 2009; Azam et al., 2016; Chudgar & Quin, 2012; Nguyen et al., 2006; Sass et al., 2016; Vandenberghe & Robin, 2004; Wamalwa & Burns, 2018). The approach is particularly useful as students are not randomly assigned to private schools and when numerous covariates must be controlled for (Caliendo & Kopeinig, 2008). It addresses selection on observables by accounting for variables that influence both private school enrollment and outcomes, thereby aiming to reduce potential bias due to unobserved factors (Epple et al., 2016; Spees & Lauen, 2019).</footnote>
<figure><img src="image_9.png" /><figcaption>Fig. 3. School SES composition and average standardized grade 9 test scores.</figcaption></figure>

Notes: The figure compares standardized test scores between public and private lower secondary schools as a function of the share of students from high socioeconomic status (SES) backgrounds. Each dot represents a school-by-sector average. The outcome uses only standardized final exam scores in mathematics and French; continuous assessment is excluded. Public schools are shown in gray, private schools in black.

Source: Panel 2007.

Identification of the ATT relies on two standard assumptions. First, the conditional independence assumption (CIA) requires that, conditional on a set of pre-treatment covariates, potential outcomes are independent of treatment status. It is captured by the following expression: $Y(0), Y(1) \perp D | X$, and implies that all relevant determinants of selection into private schooling are captured by observed covariates. In practice, this means that the propensity score specification must include all variables that jointly influence both treatment assignment and academic outcomes. Second, the common support assumption ensures that for each treated individual, there exists at least one untreated individual with a similar combination of covariates: $0 < \Pr(D = 1 | X) < 1$. Provided that the conditional independence and common support assumptions hold, the ATT can be identified as the average difference in expected outcomes between treated and control students with the same propensity score. Formally:

$$ \tau_{ATT} = E[Y(1) | p(X), D=1] - E[Y(0) | p(X), D=0]. \qquad (2) $$

The estimation proceeds in two steps. First, we estimate the propensity score using a logistic regression model, where private school attendance is regressed on a comprehensive set of pre-treatment characteristics. These include gender, students' socioeconomic background, mother's and father's educational attainment, family structure, number of siblings, parents' countries of birth, size of the school's urban area, prior enrollment in a private primary school, grade retention during primary education, and academic performance in sixth-grade mathematics. This step captures the selection process into private schools based on observable characteristics. Second, treated students (i.e., those enrolled in private schools in grade 9) are matched with control students using kernel matching, based on the estimated propensity scores. Consistent with standard practice in the literature, we employ an Epanechnikov kernel with a bandwidth of 0.06. The matching is restricted to the region of common support, defined as the overlapping range of propensity scores between treatment and control groups.

The empirical strategy adopted in this paper—propensity score matching—reflects a pragmatic choice in the absence of exogenous variation in school assignment. While PSM offers a transparent and flexible framework for adjusting for observable confounders, it is less robust to unobserved heterogeneity than designs leveraging natural experiments or credible instruments. In the context of school choice, instrumental variable approaches have often relied on religious proximity (e.g., distance to Catholic schools) or historical school density, particularly when evaluating Catholic or government-dependent schools. However, the exclusion restriction underlying such instruments is often questionable: residential location, religious affiliation, or urban
density may themselves be correlated with unobserved determinants of achievement. Lottery-based admission designs, though highly credible in terms of identification, typically apply to charter school systems with oversubscription, and are thus limited in external validity. In the French setting, no large-scale lotteries or sharp assignment rules exist, and distance-based instruments are also problematic due to strong spatial sorting along socioeconomic lines. Our use of PSM is therefore well-suited to the institutional context and the available data, and is strengthened by the inclusion of detailed pre-treatment characteristics, prior test scores, and family-level variables. Still, we acknowledge the trade-offs involved, and we complement our main estimates with bounding techniques and sensitivity analyses to probe the robustness of our findings.

While PSM provides a transparent and intuitive approach to address selection on observable characteristics, it relies on strong identifying assumptions, particularly the CIA. The potential presence of unobserved factors that simultaneously influence school choice and academic performance may still compromise identification. A key limitation of our analysis is that it does not explicitly model the selection process into school types. Even conditional on prior achievement and family background, families make differentiated schooling choices—reflecting not only observed characteristics but also important unobserved dimensions. Although our dataset includes rich administrative and survey-based information, it does not capture all relevant factors that may influence both school choice and student outcomes. In particular, key aspects such as parental aspirations, perceptions of school quality, or informal support networks remain unobserved. These limitations are especially salient in a context of active school choice, where families differ not only in socio-demographic traits but also in values, expectations, and levels of involvement. These factors are central to educational outcomes yet difficult to measure empirically. This includes the possibility that low-SES students attending private schools may be more academically driven, ambitious, or better supported than their peers in public schools. For instance, their enrollment in private school may be driven by parental aspirations or support mechanisms that are not fully captured by our observable controls. While our analysis controls for prior achievement and detailed family background, such motivational or aspirational differences remain difficult to observe and could still play a role in explaining the residual advantage observed for low-SES students in private schools.<fnref n="10" /> As such, while we account for a broad set of observables and prior achievement through matching, we cannot fully rule out selection on unobservables. Moreover, parents themselves—who actively choose between public and private options—are a critical input into the education production function and may contribute differently across sectors. Although we cannot integrate these dimensions directly into our empirical framework, acknowledging their role is essential for interpreting our results and their generalizability. To assess the robustness of our estimates to this threat, we implement two complementary robustness checks (see Section 4.3). First, we use Rosenbaum and Rosenbaum (2002) bounds, which quantify the strength of unobserved confounding required to overturn the statistical significance of our results. Second, we rely on a simulation-based method proposed by Nannicini (2007), which allows us to evaluate the sensitivity of the estimated effects under different scenarios of unobserved heterogeneity, by modeling the bias using an observed proxy variable.

## 3.2. Propensity score estimation

In Table 2, we present the results of the propensity score logit estimation as the first step in the PSM. This estimation calculates the propensity score, which represents the probability of attending a private school given the covariates. The table indicates that several covariates are significantly associated with the probability of attending a private school. Low-SES students are less likely to attend private schools compared to their high-SES peers, as are students with less-educated parents, those from non-two-parent households, and those with more siblings. Conversely, girls are more likely to attend private schools. Additionally, students who attended private primary schools or achieved higher test scores in primary education are more likely to attend private school in grade 9. The propensity score is estimated on the subset of students with non-missing values for all covariates. This complete-case restriction yields 20,309 observations (out of 22,441 in the main sample).

## 3.3. Propensity score balance and matching quality

We assess balance and matching diagnostics to verify the validity of the propensity score matching process. These diagnostics confirm whether the matching has effectively balanced covariates between treated and control groups, reducing confounding bias.

First, we look at the density balancing plot presented in Fig. 4, which visualizes the distribution of the propensity scores before and after matching. The left graph shows that the density score distribution between the treatment and control group visibly differs before the matching procedure. The graph suggests students in the treatment group have on average a higher probability of enrolling in private school, before matching. On the right graph can be seen that this density score distribution is similar for both groups after executing the matching procedure.

Once the matching procedure is performed, it is essential to validate its quality. Table 3 presents various covariate balance indicators before and after matching. Two key metrics are particularly informative. First, the number of statistically significant differences in means between the treatment and control groups, at the 1% significance level, dropped from 18 before matching to 0 after matching. This reduction indicates a substantial improvement in covariate balance. Second, the mean absolute standardized bias decreased significantly, from 15.49% before matching to 2.03% after matching, well below the threshold of 35% suggested

<footnote n="10">¹⁰ At the beginning of grade 6, low-SES students enrolled in private schools score 0.16 SD higher in mathematics and 0.20 SD higher in French than their counterparts in public schools. While these differences are modest in size, they are statistically significant and justify the inclusion of prior achievement as a matching variable in our analysis.</footnote>
<caption>Table 2</caption>

Propensity score logit estimation.

Source: Panel 2007.

<table><thead><tr><th></th><th></th></tr></thead><tbody><tr><td>Socioeconomic characteristics</td><td></td></tr><tr><td>Girl</td><td>0.101*<br>(0.044)</td></tr><tr><td>Socioeconomic status</td><td></td></tr><tr><td>High-SES (ref.)</td><td>-</td></tr><tr><td>Middle-high-SES</td><td>-0.295***<br>(0.071)</td></tr><tr><td>Middle-low-SES</td><td>-0.084<br>(0.070)</td></tr><tr><td>Low-SES</td><td>-0.532***<br>(0.079)</td></tr><tr><td>Mother's educational attainment</td><td></td></tr><tr><td>Tertiary education (ref.)</td><td>-</td></tr><tr><td>General upper secondary education</td><td>-0.211*<br>(0.094)</td></tr><tr><td>Technical or vocational upper secondary education</td><td>-0.045<br>(0.074)</td></tr><tr><td>Vocational education</td><td>-0.221***<br>(0.065)</td></tr><tr><td>No qualification or NR</td><td>-0.457***<br>(0.073)</td></tr><tr><td>Father's educational attainment</td><td></td></tr><tr><td>Tertiary education (ref.)</td><td>-</td></tr><tr><td>General upper secondary education</td><td>-0.125<br>(0.114)</td></tr><tr><td>Technical or vocational upper secondary education</td><td>-0.120<br>(0.090)</td></tr><tr><td>Vocational education</td><td>-0.062<br>(0.073)</td></tr><tr><td>No qualification or NR</td><td>-0.207**<br>(0.077)</td></tr><tr><td>Family type</td><td></td></tr><tr><td>Two parents (ref.)</td><td>-</td></tr><tr><td>Single mother</td><td>-0.410***<br>(0.078)</td></tr><tr><td>Single father</td><td>-0.136<br>(0.218)</td></tr><tr><td>Blended family</td><td>-0.377***<br>(0.105)</td></tr><tr><td>Other situations (including NR)</td><td>-0.071<br>(0.149)</td></tr><tr><td>Number of siblings</td><td>-0.085***<br>(0.019)</td></tr><tr><td>At least one foreign-born parent</td><td>-0.206**<br>(0.065)</td></tr><tr><td>School characteristics</td><td></td></tr><tr><td>Size of the urban area</td><td></td></tr><tr><td>Rural</td><td>-0.782***<br>(0.105)</td></tr><tr><td>&lt; 5,000 inhab.</td><td>-0.629***<br>(0.093)</td></tr><tr><td>[5,000; 10,000] inhab.</td><td>-0.507***<br>(0.096)</td></tr><tr><td>[10,000; 20,000] inhab.</td><td>-0.204*<br>(0.096)</td></tr><tr><td>[20,000; 50,000] inhab.</td><td>0.060<br>(0.093)</td></tr><tr><td>[50,000; 100,000] inhab.</td><td>0.115<br>(0.095)</td></tr><tr><td>[100,000; 200,000] inhab.</td><td>0.019<br>(0.102)</td></tr><tr><td>[200,000; 2,000,000] inhab.</td><td>0.062<br>(0.072)</td></tr></tbody></table>

(continued on next page)
<table><caption>**Table 2 (continued).**</caption><tr><td>Paris agglomeration (ref.)</td><td>-</td></tr><tr><td><em>Educational characteristics of the student</em></td><td></td></tr><tr><td>Enrolled in a private primary school</td><td>3.030<sup>***</sup><br>(0.048)</td></tr><tr><td>No grade retention in primary school</td><td>0.137<br>(0.099)</td></tr><tr><td>6th-grade test score</td><td>0.158<sup>***</sup><br>(0.030)</td></tr><tr><td>Constant</td><td>-1.586<sup>***</sup><br>(0.127)</td></tr><tr><td>Number of observations</td><td>20,309</td></tr></table>

*Notes:* Reported coefficients are derived from a logit model estimating the probability of attending a private school in grade 9. 6th-grade test score in the table specifically refers to the mathematics test score. Standard errors are reported in parentheses. Significance levels are indicated as follows: \*\*\* $p < 0.001$, \*\* $p < 0.01$, \* $p < 0.05$.

<figure><img src="image_10.png" /><figcaption>**Fig. 4.** Density balancing plot.</figcaption></figure>

*Notes:* This figure illustrates the density score distributions for the treatment and control groups before and after the matching procedure.

*Source:* Panel 2007.

by Caliendo and Kopeinig (2008). This confirms the high quality of the matching procedure in balancing the covariates across groups. Additionally, other indicators reinforce the success of the matching. The pseudo-$R^2$ value from the propensity score estimation decreased dramatically from 0.297 before matching to 0.003 after matching, indicating a near-complete elimination of the relationship between the covariates and the treatment assignment. Similarly, the $p$-value for the joint significance test of the covariates changed from highly significant ($p < 0.001$) before matching to non-significant ($p = 0.370$) after matching, demonstrating that the covariates no longer explain treatment assignment, indicating successful balancing between the treatment and control groups. Thus, our matching procedure successfully reduced differences in the observed variables between the treatment and control groups, providing confidence in the robustness of the estimates derived from the matched sample.
<caption>**Table 3**</caption>

Matching quality.
Source: Panel 2007.

<table><thead><tr><th></th><th>Before matching</th><th>After matching</th></tr></thead><tbody><tr><td>Number of variables with<br>significant differences in means</td><td></td><td></td></tr><tr><td>At 1%-level</td><td>18</td><td>0</td></tr><tr><td>At 5%-level</td><td>2</td><td>3</td></tr><tr><td>At 10%-level</td><td>1</td><td>0</td></tr><tr><td>Number of variables with<br>absolute standardized bias</td><td></td><td></td></tr><tr><td>&lt;1%</td><td>2</td><td>6</td></tr><tr><td>1% until &lt;3%</td><td>6</td><td>17</td></tr><tr><td>3% until &lt;5%</td><td>3</td><td>4</td></tr><tr><td>5% until &lt;10%</td><td>4</td><td>2</td></tr><tr><td>10% until &lt;15%</td><td>5</td><td>0</td></tr><tr><td>≥ 15%</td><td>9</td><td>0</td></tr><tr><td>Mean absolute standardized bias<br>in %</td><td>15.49</td><td>2.03</td></tr><tr><td>Median absolute standardized bias<br>in %</td><td>8.44</td><td>1.73</td></tr><tr><td>Pseudo-R<sup>2</sup> for propensity score<br>estimation</td><td>0.297</td><td>0.003</td></tr><tr><td>p-value of joint significance test</td><td>0.000</td><td>0.370</td></tr><tr><td>Total number of variables</td><td>29</td><td>29</td></tr><tr><td>Treated students off support</td><td>8</td><td>8</td></tr></tbody></table>

Notes: The propensity score is estimated using a logit model that includes the following variables: gender, students' socioeconomic background, mother's and father's educational attainment, family structure, number of siblings, parents' countries of birth, size of the school's urban area, prior enrollment in a private primary school, grade retention during primary education, and academic performance in sixth-grade mathematics. The logit model results for the propensity score estimation are displayed in Table 2.

<caption>**Table 4**</caption>

Main effect of private school attendance on standardized test scores (grade 9).
Source: Panel 2007.

<table><thead><tr><th></th><th></th><th colspan="2">Mathematics</th><th colspan="2">French</th></tr></thead><tbody><tr><td>ATT</td><td>0.214***</td><td>0.176***</td><td>0.182***</td><td>0.170***</td><td>0.131***</td></tr><tr><td>Standard error</td><td>(0.022)</td><td>(0.025)</td><td>(0.024)</td><td>(0.020)</td><td>(0.025)</td></tr><tr><td>School composition</td><td>No</td><td>Yes</td><td>No</td><td>No</td><td>Yes</td></tr><tr><td>Classroom composition</td><td>No</td><td>No</td><td>Yes</td><td>No</td><td>No</td></tr><tr><td>Treated students off support</td><td>8</td><td>0</td><td>35</td><td>1</td><td>0</td></tr><tr><td>Number of observations</td><td>20,309</td><td>20,259</td><td>18,699</td><td>20,309</td><td>20,259</td></tr></tbody></table>

Notes: The average treatment effects on the treated (ATT) are estimated using PSM with an Epanechnikov kernel and a bandwidth of 0.06. Standard errors are reported in parentheses, and both *p*-values and standard errors are obtained through bootstrapping with 5,000 replications. The variables included in the logit model for estimating the propensity score encompass socioeconomic, school and educational characteristics. The full set of variables used in the propensity score estimation, along with the corresponding logit model coefficients, are presented in Table 2. When estimating the ATT for mathematics, sixth-grade mathematics test scores are included as a control variable, and for French, sixth-grade French test scores are used similarly. Significance levels are indicated as follows: *** *p* < 0.001, ** *p* < 0.01, * *p* < 0.05.

# 4. Results

## 4.1. Main results

We first estimate the average treatment effect on the treated in Table 4, as presented in the first row of the table. The table shows that ninth-grade private school students, on average, score 0.214 SD higher in mathematics compared to their public school counterparts. Similarly, they score 0.170 SD higher in French than their peers in public school.

In the second column of Table 4, we include school composition in the model to examine whether performance differences between students in private and public school can be explained by the difference of school composition between both school types. We observe that, after including this school composition measure, private school students outperform their counterparts in public school with, on average, 0.176 SD and 0.131 SD in mathematics and French, respectively.<fnref n="11" /> This suggests that considering differences

<footnote n="11">¹¹ For interpretability, after controlling for school composition, these estimates correspond to 0.76 points in mathematics (mean scores: 11.17 and 10.41 in private and public schools, respectively) and 0.42 points in French (mean scores: 11.87 and 11.45, respectively) on the 0-20 point *brevet* scale among low-SES students.</footnote>
<caption>**Table 5**
Heterogeneity by SES.</caption>

Source: Panel 2007.

<table><thead><tr><th rowspan="2"></th><th colspan="4">Mathematics</th><th colspan="4">French</th></tr><tr><th colspan="2">High-SES</th><th colspan="2">Low-SES</th><th colspan="2">High-SES</th><th colspan="2">Low-SES</th></tr></thead><tbody><tr><td>ATT</td><td>0.094*</td><td>0.070</td><td>0.288***</td><td>0.244***</td><td>0.110**</td><td>0.092</td><td>0.265***</td><td>0.197***</td></tr><tr><td>Standard error</td><td>(0.040)</td><td>(0.042)</td><td>(0.040)</td><td>(0.051)</td><td>(0.038)</td><td>(0.047)</td><td>(0.040)</td><td>(0.054)</td></tr><tr><td>School composition</td><td>No</td><td>Yes</td><td>No</td><td>Yes</td><td>No</td><td>Yes</td><td>No</td><td>Yes</td></tr><tr><td>Treated students off support</td><td>2</td><td>0</td><td>2</td><td>3</td><td>2</td><td>0</td><td>2</td><td>3</td></tr><tr><td>Number of observations</td><td>4,863</td><td>4,849</td><td>6,680</td><td>6,658</td><td>4,863</td><td>4,849</td><td>6,680</td><td>6,658</td></tr></tbody></table>

Notes: The average treatment effects on the treated (ATT) are estimated using PSM with an Epanechnikov kernel and a bandwidth of 0.06. Standard errors are reported in parentheses, and both *p*-values and standard errors are obtained through bootstrapping with 5,000 replications. The variables included in the logit model for estimating the propensity score encompass socioeconomic, school and educational characteristics. The full set of variables used in the propensity score estimation, along with the corresponding logit model coefficients, are presented in Table 2. When estimating the ATT for mathematics, sixth-grade mathematics test scores are included as a control variable, and for French, sixth-grade French test scores are used similarly. Significance levels are indicated as follows: *** *p* < 0.001, ** *p* < 0.01, * *p* < 0.05.

in school composition between private and public school only minimally alters the achievement advantage of private school students compared to their public school peers, indicating that other important mechanisms are at play in explaining this effect. We also perform a similar analysis with classroom composition in column 3 and derive a comparable conclusion from this analysis.

These findings are broadly consistent with previous research on the impact of private schooling in France. Moulin (2023) similarly identifies a significant positive effect of private school attendance on ninth-grade test scores using a propensity score matching approach. His results indicate an effect size ranging from 0.203 to 0.222 SD for boys and from 0.138 to 0.198 SD for girls, depending on the subject (mathematics or French), which aligns closely with our estimates. Importantly, by introducing school and classroom composition into the model, our analysis extends this discussion by demonstrating that differences in peer group characteristics only marginally alter the estimated effect of private schooling. This suggests that beyond compositional factors, institutional differences—such as school organization, pedagogical strategies, or resource allocation—may play a central role in explaining the observed performance gap.

These findings can be related to recent international evidence, and in particular to the latest PISA results for France, which report that the private-sector advantage disappears once students' and schools' socio-economic background is taken into account. Two elements help explain why our estimates may differ. First, PISA relies on an international assessment that is external to the national curriculum (Pulkkinen & Rautopuro, 2022), while our analysis uses national standardized tests and the national diploma. Curriculum-aligned outcomes capture performance within the French education system, and private schools may prepare students more effectively for these specific examinations than for international tests. Second, our empirical strategy controls for several pre-existing differences that PISA cannot observe. We include sixth-grade achievement, grade repetition, and prior attendance in private primary schools, as well as detailed family background variables, thereby reducing selection bias into private schooling. For these reasons, our findings should be viewed as complementary to PISA, offering a within-country perspective based on curriculum-aligned outcomes and richer controls for students' prior trajectories.

## 4.2. Heterogeneous effects by student socioeconomic status

We next explore heterogeneity in our main result by comparing low- and high-SES students. To ensure that our analysis remains unbiased, we employ a sample-split approach rather than relying on interaction terms (Feigenberg et al., 2023). We present the average treatment effects for low- and high-SES students in Table 5. The first four columns present the results for mathematics, while the last four columns display the results for French.

For mathematics, private school students with a low-SES background score, on average, 0.288 SD higher in mathematics compared to their public school counterparts. This differs remarkably from the difference between private and public school students with a high-SES background, which is only 0.094 SD. This suggests that low-SES students benefit the most from attending private schools, yet they remain the most underrepresented group in these schools (cf. Table 1). Table 5 shows a similar finding for French. Low- and high-SES students in private schools outperform their counterparts in French in public schools with 0.265 SD and 0.110 SD, respectively.<fnref n="12" />

While the effect for low- and high-SES students differs, the role of school composition also tends to vary for both groups. When taking into account school composition, performance differences between private and public school students with a low-SES background remain (from 0.288 to 0.244 SD in mathematics and from 0.265 to 0.197 SD in French). However, the performance differences between high-SES students from private and public schools are substantially reduced once school composition is taken into account (from 0.094 to 0.070 SD in mathematics and from 0.110 to 0.092 SD in French). While these estimates remain similar in relative

<footnote n="12">¹² As noted in Section 2.2, sample selection is not random: students excluded from the final analytical sample are disproportionately from disadvantaged backgrounds. Exclusions are also slightly more prevalent among those from private schools, both at the primary level and in grade 6. This implies a stronger positive selection of the remaining private-school students. As a result, the estimated private-public advantage for low-SES students may be upward-biased and should be interpreted as an upper bound.</footnote>
terms to the reductions observed for low-SES students, they become statistically insignificant, partly due to smaller subgroup sample sizes and higher standard errors.<fnref n="13" /> This suggests that, for high-SES students, the private school advantage is largely explained by social composition.<fnref n="14" /> In other words, after accounting for school composition, high-SES students in private schools no longer significantly outperform their peers in public schools. Low-SES in private schools keep their lead over those in public school. This pattern suggests that attending private schools is especially beneficial for low-SES students, whereas the initial advantage observed among high-SES students primarily reflects their greater exposure to socially advantaged peers within the private sector.

These findings complement previous research on heterogeneity in the effects of private schooling, which shows that private schools tend to be particularly beneficial for initially low-performing students (Abdulkadiroğlu et al., 2011; Angrist et al., 2016, 2010, 2013; Chabrier et al., 2016; Moulin, 2023). Our results extend this literature by showing that students from low-SES backgrounds—a group often less likely to attend private schools—benefit significantly more from private schooling than their high-SES peers. This suggests that private institutions may offer a particularly supportive environment for students facing social disadvantage, not only academic difficulty. The fact that school composition fully accounts for the private school effect among high-SES students, but not among low-SES students, underscores the importance of contextual factors. While high-SES students may already benefit from substantial educational support outside of school, low-SES students appear to experience a real added value from private schooling, potentially through greater academic expectations, discipline, or pedagogical support. These results also raise the question of whether similar gains could be achieved through targeted interventions in the public sector. One key aspect to consider is the role of teachers, which differs significantly between the two sectors. Private schools have more flexibility in shaping their teaching teams, allowing them to ensure better alignment between pedagogical practices and institutional expectations. In contrast, public schools operate within more rigid administrative constraints, which may limit their ability to foster a cohesive and adaptive teaching environment. Granting public schools greater autonomy in the management of their teaching staff—while maintaining rigorous qualification standards—could help create learning conditions that are more conducive to student success.

### 4.3. Robustness checks

We verify the validity of our results through multiple robustness checks. First, we assess whether our findings depend on the definition of socio-economic status. Because socio-economic background can be operationalized in different ways using household occupational categories, it is essential to check that our conclusions are not driven by a specific classification. Second, we employ the bounding approach (Rosenbaum & Rosenbaum, 2002), which evaluates the robustness of the estimated effects against potential unobserved biases. Third, we use the simulation approach (Nannicini, 2007), which assesses the sensitivity of the estimated effects to unobserved heterogeneity simulated from observable characteristics.

Our baseline heterogeneity analysis (Table 5) compares students from the most and least advantaged socio-economic backgrounds, using the proportion of high-SES students as the measure of school composition. We performed additional robustness checks to ensure that our results are not driven by this particular definition. Table 6 replicates the heterogeneity analysis using the proportion of low-SES students instead of the proportion of high-SES students as the measure of social composition within schools, while Table 7 uses a linear index of social composition constructed from the distribution of students across all four SES categories. Specifically, we define the centered index as: $SES_{index} = 1.5 \times p_{high} + 0.5 \times p_{middle-high} - 0.5 \times p_{middle-low} - 1.5 \times p_{low}$, where $p_{high}$, $p_{middle-high}$, $p_{middle-low}$, and $p_{low}$ denote the proportions of students in each SES category within the school. Higher values of this index indicate a more advantaged social composition. In both cases, the estimated treatment effects are very close to those reported in Table 5. When replacing the proportion of high-SES students with the proportion of low-SES students as the measure of school composition (Table 6), private school students from low-SES backgrounds still score about 0.248 SD higher for mathematics than their public school peers once school composition is taken into account, whereas the initial advantage for high-SES students becomes statistically insignificant. A similar pattern holds for French: the private school effect persists for low-SES students (0.189 SD) but becomes statistically insignificant for high-SES students. Similarly, when using the centered linear index of social composition (Table 7), the private school advantage persists for low-SES students (0.262 SD in mathematics, 0.197 SD in French) but becomes insignificant for high-SES students. Appendix Table A.3 extends the heterogeneity analysis to the two intermediate SES categories, showing that effects weaken but remain statistically significant, again indicating that the disappearance of private school advantages is specific to the most advantaged group.

The sensitivity analysis using the bounding approach, based on the work of Rosenbaum and Rosenbaum (2002), evaluates the robustness of estimated effects in the presence of potential biases caused by unobserved factors that simultaneously influence treatment assignment and outcomes. This methodology quantifies the level of bias a model can tolerate before the estimated effects lose statistical significance. The results presented in Table 8 show that the estimated effects for mathematics and French are generally similar in terms of robustness. However, for high-SES students, the effects appear more sensitive to unobserved biases, as reflected by the slightly lower critical values ($\Gamma$) for this group (1.15–1.20 at the 1% significance level in mathematics, compared to 1.70–1.75 for low-SES students). This increased sensitivity can partly be explained by the fact that, as shown in Table 5, the initial effects for high-SES students were smaller and showed relatively weak statistical significance ($p < 0.05$ in mathematics and $p < 0.01$ in French), suggesting that they were more susceptible to being explained away by differences in school composition. The results, at

<footnote n="13">¹³ Results for the middle-high and middle-low-SES groups (see Table A.3 in the Appendix) show much smaller reductions after adjusting for school composition, indicating that the attenuating role of peer effects is particularly pronounced at the extremes of the socioeconomic spectrum.</footnote>

<footnote n="14">¹⁴ For interpretability, after controlling for school composition, the ATT for low-SES students corresponds to 1.04 points in mathematics (mean scores: 9.61 and 8.58 in private and public schools, respectively) and 0.63 points in French (mean scores: 10.80 and 10.17, respectively) on the 0-20 point brevet scale.</footnote>
<caption>**Table 6**</caption>

Heterogeneity by SES (low-SES share as composition).

Source: Panel 2007.

<table><thead><tr><th rowspan="2"></th><th colspan="4">Mathematics</th><th colspan="4">French</th></tr><tr><th colspan="2">High-SES</th><th colspan="2">Low-SES</th><th colspan="2">High-SES</th><th colspan="2">Low-SES</th></tr></thead><tbody><tr><th>ATT</th><td>0.094*</td><td>0.052</td><td>0.288***</td><td>0.248***</td><td>0.110**</td><td>0.100</td><td>0.265***</td><td>0.189**</td></tr><tr><th>Standard error</th><td>(0.041)</td><td>(0.052)</td><td>(0.040)</td><td>(0.068)</td><td>(0.037)</td><td>(0.064)</td><td>(0.040)</td><td>(0.064)</td></tr><tr><th>School composition</th><td>No</td><td>Yes</td><td>No</td><td>Yes</td><td>No</td><td>Yes</td><td>No</td><td>Yes</td></tr><tr><th>Treated students off support</th><td>2</td><td>15</td><td>2</td><td>13</td><td>2</td><td>16</td><td>2</td><td>18</td></tr><tr><th>Number of observations</th><td>4,863</td><td>4,848</td><td>6,680</td><td>6,666</td><td>4,863</td><td>4,848</td><td>6,680</td><td>6,666</td></tr></tbody></table>

Notes: The average treatment effects on the treated (ATT) are estimated using PSM with an Epanechnikov kernel and a bandwidth of 0.06. Standard errors are reported in parentheses, and both *p*-values and standard errors are obtained through bootstrapping with 5,000 replications. The variables included in the logit model for estimating the propensity score encompass socioeconomic, school and educational characteristics. The full set of variables used in the propensity score estimation, along with the corresponding logit model coefficients, are presented in Table 2. This specification uses the proportion of low-SES students as the measure of school composition. When estimating the ATT for mathematics, sixth-grade mathematics test scores are included as a control variable, and for French, sixth-grade French test scores are used similarly. Significance levels are indicated as follows: *** *p* < 0.001, ** *p* < 0.01, * *p* < 0.05.

<caption>**Table 7**</caption>

Heterogeneity by SES (centered SES index as composition).

Source: Panel 2007.

<table><thead><tr><th rowspan="2"></th><th colspan="4">Mathematics</th><th colspan="4">French</th></tr><tr><th colspan="2">High-SES</th><th colspan="2">Low-SES</th><th colspan="2">High-SES</th><th colspan="2">Low-SES</th></tr></thead><tbody><tr><th>ATT</th><td>0.094*</td><td>0.058</td><td>0.288***</td><td>0.262***</td><td>0.110**</td><td>0.096</td><td>0.265***</td><td>0.197**</td></tr><tr><th>Standard error</th><td>(0.041)</td><td>(0.045)</td><td>(0.040)</td><td>(0.056)</td><td>(0.037)</td><td>(0.053)</td><td>(0.041)</td><td>(0.059)</td></tr><tr><th>School composition</th><td>No</td><td>Yes</td><td>No</td><td>Yes</td><td>No</td><td>Yes</td><td>No</td><td>Yes</td></tr><tr><th>Treated students off support</th><td>2</td><td>0</td><td>2</td><td>3</td><td>2</td><td>0</td><td>2</td><td>2</td></tr><tr><th>Number of observations</th><td>4,863</td><td>4,846</td><td>6,680</td><td>6,656</td><td>4,863</td><td>4,846</td><td>6,680</td><td>6,656</td></tr></tbody></table>

Notes: The average treatment effects on the treated (ATT) are estimated using PSM with an Epanechnikov kernel and a bandwidth of 0.06. Standard errors are reported in parentheses, and both *p*-values and standard errors are obtained through bootstrapping with 5,000 replications. The variables included in the logit model for estimating the propensity score encompass socioeconomic, school and educational characteristics. The full set of variables used in the propensity score estimation, along with the corresponding logit model coefficients, are presented in Table 2. This specification uses a centered linear index of school composition, constructed from the distribution of students across all four SES categories. When estimating the ATT for mathematics, sixth-grade mathematics test scores are included as a control variable, and for French, sixth-grade French test scores are used similarly. Significance levels are indicated as follows: *** *p* < 0.001, ** *p* < 0.01, * *p* < 0.05.

<caption>**Table 8**</caption>

Sensitivity analysis—bounding approach.

Source: Panel 2007.

<table><thead><tr><th rowspan="2"></th><th colspan="4">Mathematics</th><th colspan="4">French</th></tr><tr><th colspan="2">High-SES</th><th colspan="2">Low-SES</th><th colspan="2">High-SES</th><th colspan="2">Low-SES</th></tr></thead><tbody><tr><th>1.00</th><td>0.000</td><td>0.000</td><td>0.000</td><td>0.000</td><td>0.000</td><td>0.000</td><td>0.000</td><td>0.000</td></tr><tr><th>1.25</th><td>0.127</td><td>0.492</td><td>0.000</td><td>0.000</td><td>0.040</td><td>0.251</td><td>0.000</td><td>0.000</td></tr><tr><th>1.50</th><td>0.968</td><td>0.999</td><td>0.000</td><td>0.012</td><td>0.890</td><td>0.990</td><td>0.000</td><td>0.103</td></tr><tr><th>1.75</th><td>0.999</td><td>1.000</td><td>0.018</td><td>0.305</td><td>0.999</td><td>0.999</td><td>0.077</td><td>0.688</td></tr><tr><th>2.00</th><td>1.000</td><td>1.000</td><td>0.271</td><td>0.839</td><td>1.000</td><td>1.000</td><td>0.527</td><td>0.978</td></tr><tr><th colspan="9">Critical values</th></tr><tr><th>1%</th><td>1.15–1.20</td><td>1.05–1.10</td><td>1.70–1.75</td><td>1.45–1.50</td><td>1.20–1.25</td><td>1.10–1.15</td><td>1.60–1.65</td><td>1.35–1.40</td></tr><tr><th>5%</th><td>1.20–1.25</td><td>1.10–1.15</td><td>1.80–1.85</td><td>1.55–1.60</td><td>1.25–1.30</td><td>1.15–1.20</td><td>1.70–1.75</td><td>1.45–1.50</td></tr><tr><th>10%</th><td>1.20–1.25</td><td>1.15–1.20</td><td>1.85–1.90</td><td>1.60–1.65</td><td>1.25–1.30</td><td>1.20–1.25</td><td>1.75–1.80</td><td>1.45–1.50</td></tr><tr><th>School composition</th><td>No</td><td>Yes</td><td>No</td><td>Yes</td><td>No</td><td>Yes</td><td>No</td><td>Yes</td></tr></tbody></table>

Notes: Results were obtained using (Rosenbaum & Rosenbaum, 2002) bounds to evaluate sensitivity to unobserved heterogeneity. The top part of the table displays the probabilities at which estimated effects lose statistical significance as the level of unobserved bias (Γ) increases. The bottom part lists the critical Γ thresholds at which effects become non-significant at the 1%, 5%, and 10% levels. Higher Γ values indicate greater robustness, meaning that stronger unobserved bias would be required to invalidate the results. The variables included in the logit model for estimating the propensity score encompass socioeconomic, school, and educational characteristics. The full set of variables used in the propensity score estimation, along with the corresponding logit model coefficients, are presented in Table 2. When estimating the ATT for mathematics, sixth-grade mathematics test scores are included as a control variable, and for French, sixth-grade French test scores are used similarly.

least for low-SES students, seem fairly robust to unobserved heterogeneity. Furthermore, the inclusion of school composition in the models appears to make the estimates more sensitive to unobserved biases, as indicated by the reduction in critical values (Γ) in the sensitivity analysis. This may be explained by the fact that school composition acts as a proxy for unobserved factors, such as the educational environment, which influence both treatment assignment and outcomes.

We employ the simulation approach inspired by Nannicini (2007), which assesses the robustness of estimated effects in the presence of unobserved heterogeneity. This method assumes that an unobserved variable, potentially correlated with both the
<caption>**Table 9**
Sensitivity to unobserved heterogeneity—simulation approach.</caption>

Source: Panel 2007.

<table><thead><tr><th rowspan="2"></th><th colspan="4">Mathematics</th><th colspan="4">French</th></tr><tr><th colspan="2">High-SES</th><th colspan="2">Low-SES</th><th colspan="2">High-SES</th><th colspan="2">Low-SES</th></tr></thead><tbody><tr><td>No confounder</td><td>0.094</td><td>0.070</td><td>0.288</td><td>0.244</td><td>0.110</td><td>0.092</td><td>0.265</td><td>0.197</td></tr><tr><td>Gender - Girl</td><td>0.124</td><td>0.091</td><td>0.342</td><td>0.295</td><td>0.135</td><td>0.117</td><td>0.310</td><td>0.242</td></tr><tr><td>Mother's educational attainment - Tertiary education</td><td>0.116</td><td>0.080</td><td>0.329</td><td>0.284</td><td>0.123</td><td>0.103</td><td>0.295</td><td>0.230</td></tr><tr><td>Father's educational attainment - Tertiary education</td><td>0.121</td><td>0.086</td><td>0.342</td><td>0.295</td><td>0.129</td><td>0.109</td><td>0.311</td><td>0.242</td></tr><tr><td>Family types - Two parents</td><td>0.119</td><td>0.086</td><td>0.332</td><td>0.288</td><td>0.131</td><td>0.112</td><td>0.302</td><td>0.238</td></tr><tr><td>Parents born in France</td><td>0.123</td><td>0.090</td><td>0.322</td><td>0.279</td><td>0.134</td><td>0.115</td><td>0.292</td><td>0.229</td></tr><tr><td>Size of the urban area - Paris agglomeration</td><td>0.126</td><td>0.094</td><td>0.334</td><td>0.287</td><td>0.133</td><td>0.115</td><td>0.305</td><td>0.238</td></tr><tr><td>Enrolled at least once in a private primary school</td><td>0.131</td><td>0.072</td><td>0.305</td><td>0.211</td><td>0.170</td><td>0.115</td><td>0.307</td><td>0.211</td></tr><tr><td>Grade repetition in primary school</td><td>0.121</td><td>0.089</td><td>0.335</td><td>0.287</td><td>0.132</td><td>0.113</td><td>0.301</td><td>0.233</td></tr><tr><td>School composition</td><td>No</td><td>Yes</td><td>No</td><td>Yes</td><td>No</td><td>Yes</td><td>No</td><td>Yes</td></tr></tbody></table>

Notes: The reported results represent the ATT, estimated using a simulation approach (see Nannicini, 2007). The number of replications is 5,000. The variables included in the estimation encompass socioeconomic, school and educational characteristics (see Table 2). When estimating the ATT for mathematics, sixth-grade mathematics test scores are included as a control variable, and for French, sixth-grade French test scores are used similarly.

treatment and the outcomes, shares the same distribution as a specific observed variable. Table 9 thus presents results based on the sensitivity of the effects to such an unobserved variable, simulated from observed characteristics such as gender, parental education level, or family structure. Our ATT estimates remain relatively stable regardless of the type of observed variable used to simulate an unobserved one, and this holds true across the subject studied (mathematics or French) and whether the school composition is included in the model. For instance, for mathematics and low-SES students, the ATT varies only slightly between 0.342 and 0.305 in models without the inclusion of school composition. Similarly, for high-SES students, the ATT fluctuates between 0.124 and 0.131 depending on the variable. Importantly, the estimated effects are consistently close to the baseline results under the “no confounder” assumption. For example, in mathematics, the ATT for low-SES students without school composition is 0.288, which is close to the range of 0.305–0.342 when unobserved heterogeneity is simulated. This stability in results, regardless of the subject and model specification (with or without accounting for school composition), strengthens confidence in the robustness of the estimated effects, suggesting they are extremely insensitive to the influence of unobserved heterogeneity with a distribution similar to that of the observed variables.

## 5. Conclusion

Previous research has consistently demonstrated the positive impact of private schooling on student performance, a finding that is also supported by our study. In this paper, we examine whether school composition helps explain these effects. We find that it accounts for only a limited share of the private school advantage—about 15-23% according to our estimates. In addition, we examine SES heterogeneity and find that private schooling is particularly beneficial for students from low-SES backgrounds. However, the low representation of these students in private schools limits their access to these benefits. For high-SES students, we observe initially positive effects, but these are largely explained by the higher concentration of advantaged peers, as the adjusted effects become small and statistically indistinguishable from zero once school composition is taken into account.

Taken together, these findings suggest that the benefits of private schooling are not evenly distributed: low-SES students stand to gain the most, yet they are least likely to attend private schools. In contrast, the initial advantage observed for high-SES students appears to be driven primarily by school composition, rather than by any intrinsic quality of private education itself.

To better understand the heterogeneous effects of private schooling across socioeconomic groups, we propose two complementary mechanisms that are consistent with our findings. First, the disappearance of the initial advantage for high-SES students once school composition is controlled for suggests that the performance gap is largely driven by peer effects rather than by intrinsic features of private schools. High-SES students may benefit not so much from private schooling per se, but from being enrolled in socially homogeneous environments where academic engagement is widely shared. Such settings may foster achievement by reinforcing academic norms, reducing classroom disruptions, and creating a climate of high expectations. In this case, the observed advantage reflects selection into more favorable peer groups, not institutional quality. Second, the fact that the private school advantage persists for low-SES students even after controlling for school composition points to other mechanisms beyond peer environment. Private schools may provide a more structured and supportive learning environment that is particularly beneficial for students with limited academic support at home. This may reflect greater organizational autonomy, particularly in the recruitment and management of teachers. Unlike public schools, where teachers are assigned by the central administration, private school principals have the authority to recruit their teaching staff directly. This allows them to build pedagogical teams that are more cohesive in terms of professional commitment, instructional approach, and alignment with the school’s educational mission. Such coherence may facilitate the implementation of consistent classroom practices and clearer behavioral expectations, which in turn may help disadvantaged students better engage with the academic and disciplinary framework of the school. These interpretations are consistent with empirical findings from other contexts. Using PISA data from multiple countries, Hanushek et al. (2013) show that student performance is positively associated with school autonomy—particularly in high-income countries where accountability
systems are stronger. Autonomy in areas such as staff recruitment, curriculum, and budgeting is linked to better student outcomes, suggesting that institutional flexibility can enhance school effectiveness. Verschelde et al. (2015), focusing on Belgium, also finds that schools with greater autonomy in personnel management tend to perform better. Finally, Hahn et al. (2018) shows that in the Korean context, the superior performance of private school students is largely explained by greater autonomy in personnel decisions. These findings lend empirical support to the idea that institutional autonomy—particularly in staffing—can contribute to more effective learning environments. While we cannot directly observe these mechanisms in our data, our results are consistent with this interpretation, especially for low-SES students who may benefit most from structured and cohesive pedagogical settings.

Although our analysis focuses on the French context—where private schools under contract with the state operate within a tightly regulated framework—the mechanisms we uncover are likely to resonate more broadly. Our findings show that performance gains from private schooling persist for low-SES students even after accounting for peer composition, whereas for high-SES students, these gains appear to reflect the advantaged social composition of their schools rather than a distinct educational value-added. This asymmetry suggests that institutional features of private schools—such as greater autonomy in teacher recruitment, more cohesive pedagogical teams, or stronger school-level governance—may offer particular benefits to disadvantaged students, who typically lack academic support at home. In contrast, the advantages observed among high-SES students appear to reflect social stratification rather than school-specific value-added. These mechanisms are not unique to France and are likely relevant in other systems combining public funding with parental choice.

From a policy perspective, our findings raise important considerations regarding the accessibility of private education for disadvantaged students. If private schools contribute to reducing academic inequalities for low-SES students, mechanisms to support their enrollment—such as targeted scholarships or financial aid—could be explored. However, rather than focusing solely on expanding access to private schools, it is also crucial to investigate whether certain institutional features of private education—such as pedagogical practices, teacher management, or school-level autonomy—could be adapted within the public sector. Future research should examine these mechanisms more closely, including specific instructional approaches, differences in school climate, or variations in teacher expectations, and assess whether similar effects can be replicated through targeted reforms in public schools. Such efforts could provide valuable insights into how to foster educational equity without relying exclusively on private school expansion.

### CRediT authorship contribution statement

Elke Claes: Writing – original draft, Conceptualization. Léonard Moulin: Writing – review & editing, Writing – original draft, Methodology, Formal analysis, Conceptualization.

### Declaration of generative AI in scientific writing

During the preparation of this work the authors used generative AI to improve the clarity of the writing. After using this tool/service, the authors reviewed and edited the content as needed and take full responsibility for the content of the publication.

### Funding sources

This research received no external funding.

### Declaration of competing interest

The authors report there are no competing interests to declare.

### Appendix

See Tables A.1–A.3

### Data availability

Data are available to researchers via Quetelet Progedo Diffusion.
<caption>Table A.1</caption>

Nomenclature for socio-professional categories.

Source: DEPP—MESR.

<table><thead><tr><th>PCS</th><th>PCS Code</th></tr></thead><tbody><tr><td><strong>High-SES</strong></td><td></td></tr><tr><td>Business owner with ten or more employees</td><td>23</td></tr><tr><td>Liberal profession</td><td>31</td></tr><tr><td>Senior civil servant</td><td>33</td></tr><tr><td>Teacher and equivalent</td><td>34</td></tr><tr><td>Information, arts, and entertainment professional</td><td>35</td></tr><tr><td>Administrative and commercial manager in a company</td><td>37</td></tr><tr><td>Engineer - technical manager in a company</td><td>38</td></tr><tr><td>Primary school teacher and equivalent</td><td>42</td></tr><tr><td><strong>Middle-High-SES</strong></td><td></td></tr><tr><td>Intermediate profession in health and social work</td><td>43</td></tr><tr><td>Clergy, religious personnel</td><td>44</td></tr><tr><td>Intermediate administrative profession—public sector</td><td>45</td></tr><tr><td>Intermediate administrative and commercial profession—private sector</td><td>46</td></tr><tr><td>Technician</td><td>47</td></tr><tr><td>Foreman, supervisor</td><td>48</td></tr><tr><td>Retired executive or intermediate profession</td><td>73</td></tr><tr><td><strong>Middle-Low-SES</strong></td><td></td></tr><tr><td>Farmer</td><td>10</td></tr><tr><td>Artisan</td><td>21</td></tr><tr><td>Shopkeeper and equivalent</td><td>22</td></tr><tr><td>Civil employee, service agent—public sector</td><td>52</td></tr><tr><td>Police officer and military personnel</td><td>53</td></tr><tr><td>Administrative employee in a company</td><td>54</td></tr><tr><td>Sales employee</td><td>55</td></tr><tr><td>Personal service worker</td><td>56</td></tr><tr><td>Retired farmer</td><td>71</td></tr><tr><td>Retired artisan, shopkeeper, or business owner</td><td>72</td></tr><tr><td><strong>Low-SES</strong></td><td></td></tr><tr><td>Skilled worker</td><td>61</td></tr><tr><td>Unskilled worker</td><td>66</td></tr><tr><td>Agricultural worker</td><td>69</td></tr><tr><td>Retired employee or worker</td><td>76</td></tr><tr><td>Unemployed person who has never worked</td><td>81</td></tr><tr><td>Person without professional activity</td><td>82</td></tr><tr><td>Not specified (unknown or not applicable)</td><td>99</td></tr></tbody></table>
<caption>Table A.2</caption>

Descriptive statistics by missingness status.

Source: Panel 2007.

<table><thead><tr><th>Variables</th><th>Non-missing (%)</th><th>Missing (%)</th><th>p-value</th></tr></thead><tbody><tr><td><strong>Socioeconomic characteristics</strong></td><td></td><td></td><td></td></tr><tr><td>Gender</td><td></td><td></td><td></td></tr><tr><td>Girl</td><td>51.39%</td><td>44.21%</td><td>0.000</td></tr><tr><td>Boy</td><td>48.61%</td><td>55.79%</td><td>0.000</td></tr><tr><td>Socio-economic status</td><td></td><td></td><td></td></tr><tr><td>High-SES</td><td>24.20%</td><td>15.96%</td><td>0.000</td></tr><tr><td>Middle-high-SES</td><td>17.26%</td><td>12.64%</td><td>0.000</td></tr><tr><td>Middle-low-SES</td><td>26.15%</td><td>27.83%</td><td>0.001</td></tr><tr><td>Low-SES</td><td>32.39%</td><td>43.57%</td><td>0.000</td></tr><tr><td>Mother's educational attainment</td><td></td><td></td><td></td></tr><tr><td>Tertiary education</td><td>30.26%</td><td>17.88%</td><td>0.000</td></tr><tr><td>General upper secondary</td><td>6.54%</td><td>4.63%</td><td>0.000</td></tr><tr><td>Technical or vocational upper secondary</td><td>11.36%</td><td>7.56%</td><td>0.000</td></tr><tr><td>Vocational education</td><td>24.30%</td><td>24.44%</td><td>0.768</td></tr><tr><td>No qualification or NR</td><td>23.28%</td><td>35.46%</td><td>0.000</td></tr><tr><td>Father's educational attainment</td><td></td><td></td><td></td></tr><tr><td>Tertiary education</td><td>24.79%</td><td>14.96%</td><td>0.000</td></tr><tr><td>General upper secondary</td><td>3.88%</td><td>3.13%</td><td>0.000</td></tr><tr><td>Technical or vocational upper secondary</td><td>8.06%</td><td>5.59%</td><td>0.000</td></tr><tr><td>Vocational education</td><td>28.77%</td><td>25.77%</td><td>0.000</td></tr><tr><td>No qualification or NR</td><td>30.23%</td><td>40.50%</td><td>0.000</td></tr><tr><td>Family type</td><td></td><td></td><td></td></tr><tr><td>Two parents</td><td>70.84%</td><td>51.96%</td><td>0.000</td></tr><tr><td>Single mother</td><td>12.77%</td><td>14.36%</td><td>0.000</td></tr><tr><td>Single father</td><td>1.44%</td><td>1.85%</td><td>0.006</td></tr><tr><td>Blended family</td><td>6.69%</td><td>7.54%</td><td>0.004</td></tr><tr><td>Other situations (including NR)</td><td>2.34%</td><td>3.15%</td><td>0.000</td></tr><tr><td>Number of siblings</td><td>1.889</td><td>2.212</td><td>0.000</td></tr><tr><td>Immigration background</td><td></td><td></td><td></td></tr><tr><td>Parents born in France</td><td>80.92%</td><td>78.99%</td><td>0.000</td></tr><tr><td>At least one foreign-born parent</td><td>19.08%</td><td>21.01%</td><td>0.000</td></tr><tr><td><strong>School characteristics</strong></td><td></td><td></td><td></td></tr><tr><td>Size of the urban area</td><td></td><td></td><td></td></tr><tr><td>Rural</td><td>9.38%</td><td>5.04%</td><td>0.000</td></tr><tr><td>&lt; 5,000 inhab.</td><td>11.25%</td><td>5.04%</td><td>0.000</td></tr><tr><td>[5,000; 10,000] inhab.</td><td>9.82%</td><td>5.71%</td><td>0.000</td></tr><tr><td>[10,000; 20,000] inhab.</td><td>8.34%</td><td>4.81%</td><td>0.000</td></tr><tr><td>[20,000; 50,000] inhab.</td><td>8.83%</td><td>6.63%</td><td>0.000</td></tr><tr><td>[50,000; 100,000] inhab.</td><td>8.08%</td><td>6.11%</td><td>0.000</td></tr><tr><td>[100,000; 200,000] inhab.</td><td>6.79%</td><td>5.22%</td><td>0.000</td></tr><tr><td>[200,000; 2,000,000] inhab.</td><td>22.31%</td><td>13.65%</td><td>0.000</td></tr><tr><td>Paris agglomeration</td><td>15.20%</td><td>9.70%</td><td>0.000</td></tr><tr><td><strong>Educational characteristics of the student</strong></td><td></td><td></td><td></td></tr><tr><td>Sector in primary education</td><td></td><td></td><td></td></tr><tr><td>Public</td><td>79.14%</td><td>71.96%</td><td>0.000</td></tr><tr><td>Private</td><td>16.29%</td><td>17.32%</td><td>0.018</td></tr><tr><td>Sector in grade 6</td><td></td><td></td><td></td></tr><tr><td>Public</td><td>80.10%</td><td>78.03%</td><td>0.000</td></tr><tr><td>Private</td><td>19.89%</td><td>21.86%</td><td>0.000</td></tr><tr><td>Grade repetition primary education</td><td></td><td></td><td></td></tr><tr><td>No</td><td>91.75%</td><td>74.40%</td><td>0.000</td></tr><tr><td>Yes</td><td>8.25%</td><td>25.60%</td><td>0.000</td></tr><tr><td>6th-grade test score in mathematics</td><td>0.211</td><td>-0.767</td><td>0.000</td></tr><tr><td>6th-grade test score in French</td><td>0.222</td><td>-0.784</td><td>0.000</td></tr><tr><td>School composition</td><td></td><td></td><td></td></tr><tr><td>% Students from high-SES</td><td>21.55%</td><td>18.96%</td><td>0.000</td></tr><tr><td>% Students from middle-high-SES</td><td>14.18%</td><td>12.90%</td><td>0.000</td></tr><tr><td>% Students from middle-low-SES</td><td>27.47%</td><td>27.14%</td><td>0.001</td></tr><tr><td>% Students from low-SES</td><td>34.09%</td><td>37.89%</td><td>0.000</td></tr></tbody></table>

(continued on next page)
<table><caption>Table A.2 (continued).</caption><thead><tr><th>Variables</th><th>Non-missing (%)</th><th>Missing (%)</th><th>p-value</th></tr></thead><tbody><tr><td>Class composition</td><td></td><td></td><td></td></tr><tr><td>% Students from high-SES</td><td>23.74%</td><td>21.74%</td><td>0.000</td></tr><tr><td>% Students from middle-high-SES</td><td>14.94%</td><td>13.77%</td><td>0.000</td></tr><tr><td>% Students from middle-low-SES</td><td>28.39%</td><td>28.24%</td><td>0.279</td></tr><tr><td>% Students from low-SES</td><td>33.88%</td><td>39.59%</td><td>0.000</td></tr></tbody></table>

Notes: The table reports weighted summary statistics. Column “Non-missing” includes observations kept in the analytic sample. Column “Missing” includes observations excluded in the final sample. The last column shows the *p-value* for equality of means between both groups.

<caption>Table A.3
Heterogeneity by SES (middle-high and middle-low-SES groups).</caption>

Source: Panel 2007.

<table><thead><tr><th rowspan="2"></th><th colspan="3">Mathematics</th><th colspan="3">French</th></tr><tr><th colspan="2">Middle-high-SES</th><th colspan="2">Middle-low-SES</th><th colspan="2">Middle-high-SES</th><th colspan="2">Middle-low-SES</th></tr></thead><tbody><tr><td>ATT</td><td>0.259***<br>(0.047)</td><td>0.252***<br>(0.050)</td><td>0.268***<br>(0.040)</td><td>0.260***<br>(0.040)</td><td>0.245***<br>(0.047)</td><td>0.215***<br>(0.048)</td><td>0.125***<br>(0.037)</td><td>0.110**<br>(0.037)</td></tr><tr><td>Standard error</td><td>No</td><td>Yes</td><td>No</td><td>Yes</td><td>No</td><td>Yes</td><td>No</td><td>Yes</td></tr><tr><td>School composition</td><td>2</td><td>1</td><td>18</td><td>36</td><td>2</td><td>3</td><td>33</td><td>25</td></tr><tr><td>Treated students off support</td><td>3,501</td><td>3,498</td><td>5,265</td><td>5,256</td><td>3,501</td><td>3,498</td><td>5,265</td><td>5,256</td></tr><tr><td>Number of observations</td><td colspan="3"></td><td colspan="3"></td><td colspan="2"></td></tr></tbody></table>

Notes: The average treatment effects on the treated (ATT) are estimated using PSM with an Epanechnikov kernel and a bandwidth of 0.06. Standard errors are reported in parentheses, and both *p-values* and standard errors are obtained through bootstrapping with 5,000 replications. This specification replaces the high- and low-SES groups from Table 5 with the two intermediate SES categories (middle-high and middle-low). When estimating the ATT for mathematics, sixth-grade mathematics test scores are included as a control variable, and for French, sixth-grade French test scores are used similarly. Significance levels are indicated as follows: *** *p* < 0.001, ** *p* < 0.01, * *p* < 0.05.

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