Cécile Bonneau
email: ce-cile.bonneau@psemail.eu.

Sébastien Grobon
email: sebastien.grobon@cor-retraites.fr.

Parental Income and Higher Education Patterns: Evidence From France

Keywords: H52, I2, J62 Higher Education, Parental Income, Expenditures, Human Capital, Resource Allocation, France

In this paper, we present new stylized facts on inequality of enrollment in higher education by parental income in France. On average, an increment of 10 percentiles in the parental income distribution is associated with a 5.8 percentage-point increase in the proportion of children entering higher education. This overall degree of inequality is surprisingly close to that observed in the United States. We identify potential explanatory factors driving comparable levels of inequality in the two countries with markedly different institutional contexts. Finally, we explore a consequence of enrollment disparities by assessing the distribution of public spending on higher education.

Introduction

Since the 1960s, the number of university students has soared throughout the developed world. In France, for instance, it increased eight-fold from 310,000 in 1960 to 2,551,000 in 2015(MESRI-SIES, 2021). Is this increase in enrollment in higher education due to mass schooling actually a sign of equal opportunity? In this paper, we reassert the persistence of marked inequality in higher education attendance patterns, observing it from an innovative perspective, namely according to parental income.

Despite the extensive documentation of inequalities based on social origin (e.g. parents' education or occupation), since pioneering work in sociology in the 1960s in France [START_REF] Bourdieu | Les héritiers: les étudiants et la culture[END_REF]; Boudon (1973)), as well as in the United States [START_REF] Blau | The American Occupational Structure[END_REF], surprisingly few studies have addressed the strictly economic dimension of these inequalities. This perspective has been adopted in recent studies in the United States (Chetty et al. (2014), [START_REF] Chetty | Income Segregation and Intergenerational Mobility Across Colleges in the United States[END_REF]), Norway [START_REF] Bütikofer | Status Traps and Human Capital Investment[END_REF], and Germany [START_REF] Dodin | Social Mobility in Germany[END_REF] but remains rare in most countries.

Inequality according to parental income provides a continuous measure of the effect of social background, which is more suitable for international comparisons. However, enrollment in higher education is rarely studied in relation to parental income for two main reasons. The first is lack of administrative data on parental income in education data and the presence of significant biases in self-reported income [START_REF] Moore | Income Measurement Error in Surveys: A Review[END_REF], which complicates the interpretation of survey results; the second is the uneven representativeness of the surveys themselves. In fact, the specific situation of young adults raises difficult issues of survey design, such as multiple residences. This concern is important, because unrepresentative samples are subject to homogeneity bias and may underestimate the relationship between parental income and child outcomes [START_REF] Solon | Intergenerational Income Mobility in the United States[END_REF].

In this article, we use an innovative survey design 2 where young adults are surveyed regardless of housing status (parents' home, own apartment, student housing), and parental income is retrieved from administrative tax data. This produces novel descriptive estimates of inequalities in attendance patterns in higher education by parental income in France. To the best of our knowledge, this is the first comparison between the United States and a European country of the degree of inequality in enrollment in higher education according to parental income, with a representative sample of the whole population and a reliable measure of parental income. We organize our analysis into three parts.

The first part presents new statistics on attendance patterns in higher education by parental income in France. Following the literature, we use the percentile rank of parental pre-tax household income 3 to study relative attendance in higher education. We find large differences in enrollment as a function of parental income: at the bottom of the income distribution, around 35 percent of individuals aged 19-24 enroll in higher education, compared with a more than 90 percent at the top. Enrollment in master's degree and selective programs is even more unequal. In the bottom 40 percent of the income distribution, under 10 percent of children do enroll in master's degree programs and under 5 percent to selective programs, compared with about 50 percent at the very top of the income distribution. We then compare our estimates with those obtained in the United States by [START_REF] Chetty | Income Segregation and Intergenerational Mobility Across Colleges in the United States[END_REF]. We find that the degree of inequality in France is only marginally lower than in the United States, despite the important institutional differences between the two countries. Specifically, a 10-percentile increase in the parental income rank is associated with a 5.8 percentage-point (p.p.) increase in participation in higher education in France and a 6.1 p.p. increase in the United States. However, the functional form is different: in the U.S. the effect of income on enrollment in higher education is linear, whereas in France it is much greater in the upper than in the lower half of the parental income distribution: a 10-percentile increase in rank is associated with a 4.9 p.p. increase in attendance in higher education in the lower half of the income distribution and 8.6 p.p. in the upper half.

In the second part of the paper, we scrutinize the variations in institutional contexts between France and the United States to shed new light on the surprising similarity in their levels of higher education inequality. We present descriptive statistics comparing the two countries to examine the hypothesis that the comparable level of inequality in higher education attendance patterns in both France and the United States results from a mix of different institutional factors exerting opposing influences on educational disparities. The higher cost of attending higher education as well as greater income inequalities in the United States would suggest stronger higher education inequalities. The paradox of a similar level of inequalities in France can be reconciled if we consider the strong correlation between academic performance of parents socio-economic background, as well as the existence of early tracking.

In the third section, we compare the distribution of higher education spending in France and in the United States. We also combine our estimates of attendance inequality with new data on higher education spending to assess the redistributive profile of higher education public spending in France. While disaggregated data for the most expensive elite programs are unfortunately lacking, we find substantial differences in higher education spending along the parental income distribution. On average, children in the bottom third of the income distribution (percentiles 0-30, or P0-P30) receive around e9,000 worth of investment in higher education over six years of studies, compared with e32,000 for those in the top 10 percent -broken down into e21,000 of public investment and e11,000 of private investment through the tuition paid by their parents. In France, attendance disparities are the main contributor of public spending inequalities by parental income, while differences in annual cost and duration of studies have a more limited role.

Our paper is structured as follows. We begin in Section 2 by presenting the related literature. Section 3 describes the institutional context of the French higher education system. Section 4 describes the data and the main variables of our analysis. In Section 5, we present the main results in terms of enrollment in higher education according to parental income. Section 6 delves into a comparison of institutional factors in France and the United States, examining how they might contribute to the observed similarities in higher education inequalities between the two countries. Section 7 examines the redistribution that occurs through public spending on higher education, related to these attendance inequalities in higher education. Section 8 concludes.

Related Literature

Our paper builds on several strands of the literature. First, it relates to the extensive work on intergenerational mobility reviewed by [START_REF] Black | Recent Developments in Intergenerational Mobility[END_REF]. Ensuring broad and equitable enrollment in higher education can be seen as a corollary of Rawls' theory of justice [START_REF] Rawls | A Theory of Justice[END_REF]) and his second principle, namely equality of opportunity, which means that the assignment of individuals to a place in the social hierarchy is not fixed by birth. There is currently no consensus on the level of social mobility in France compared to other countries. 4Given this ambiguity, it is crucial to compare how enrollment in higher education -a known driver of social mobility [START_REF] Blau | The American Occupational Structure[END_REF][START_REF] Chetty | Income Segregation and Intergenerational Mobility Across Colleges in the United States[END_REF] -varies by parental income in France relative to other countries.

Our paper refers more directly to the literature directed to estimating the elasticity of educational attainment with respect to parental income [START_REF] Taubman | Role of Parental Income in Educational Attainment[END_REF], [START_REF] Haveman | The Determinants of Children's Attainments: A Review of Methods and Findings[END_REF], [START_REF] Mayer | What Money Can't Buy: Family Income and Children's Life Chances[END_REF], [START_REF] Blau | The Effect of Income on Child Development[END_REF]). 5 Our estimate of the impact of parental income on enrollment in higher education in France contributes in two ways. First, the vast majority of studies on this issue refer to the U.S., whereas in most European countries the effect of income on university attendance has not been assessed. And yet, the magnitude of the effect could depend at least partly on country-specific institutional factors such as higher education cost, the diversity of higher education programs, information dissemination about the returns to higher education, existing public aid or the relationship between students' academic performance and their parents' educational attainment. Second, our results span the entire distribution of parental income and apply to a representative sample of all young adults aged 19-24 in France. This makes them complementary to the studies that seek to measure the causal effect of income on educational attainment using an instrument whose validity is by definition local -i.e. at a specific point in the parental income distribution [START_REF] Shea | Does Parents' Money Matter?[END_REF], [START_REF] Acemoglu | Changes in the Wage Structure, Family Income, and Children's Education[END_REF], [START_REF] Maurin | The Impact of Parental Income on Early Schooling Transitions: A Re-Examination Using Data over Three Generations[END_REF], [START_REF] Løken | Family Income and Children's Education: Using the Norwegian Oil Boom as a Natural Experiment[END_REF], [START_REF] Hilger | Parental Job Loss and Children's Long-Term Outcomes: Evidence from 7 Million Fathers' Layoffs[END_REF]).

Our research also aims to contribute to comparative studies on how the characteristics of education systems influence educational inequalities in different countries. We focus on France and the United States, which offer stark contrasts in their higher education systems. Key differences include the cost of higher education, the proportion of expenses subsidized by state funding, and the extent of student debt. Based on these criteria alone, one might anticipate significantly higher enrollment inequality in the United States. However, a thorough understanding of the relationship between higher education participation and parental income requires considering additional country-specific factors. These include the correlation between parental socio-economic status and academic performance, the variety of educational pathways available, and how resources are distributed [START_REF] Causa | Equity in Student Achievement across OECD Countries: An Investigation of the Role of Policies[END_REF], [START_REF] Chmielewski | Patterns of Cross-National Variation in the Association Between Income and Academic Achievement[END_REF]). From a policy perspective, fostering a higher education system capable of accommodating and educating the largest possible number of individuals is crucial for development and productivity in both the medium and long term, as exemplified by the Morrill Act in the United States [START_REF] Ehrlich | What Accounts for the US Ascendancy to Economic Superpower by the Early Twentieth Century? The Morrill Act-Human Capital Hypothesis[END_REF]). Nevertheless, comparative research in this domain remains scarce.

The stylized facts developed here also contribute to the literature on the mechanisms explaining the link between parental income and educational attainment. Two main channels have been identified in this literature. The first is parents' direct investment in children's education. Traditional models of human capital investment [START_REF] Becker | An Equilibrium Theory of the Distribution of Income and Intergenerational Mobility[END_REF] emphasize the importance of credit constraints in explaining low-income families' relative lack of enrollment in higher education. In France, tuition fees in public programs are set at a very low level (see Section 3); however, there may still be credit or budget constraints related to the cost of student living, especially since most universities are located in large cities where the cost of living is high, plus the opportunity cost incurred by students when they opt for education over immediate employment. The second channel consists in long-run factors associated with parental income (parents' education and occupation, transmission of aspirations or risk aversion, etc.), including the intergenerational transmission of academic skills or abilities. 6 Although our data do not allow us to to isolate the specific causal pathways through which parental income affects educational outcomes, the comprehensive nature of the survey facilitates a thorough descriptive examination of multiple contributing factors, including prior academic credentials and as-pirations. Such an analysis can shed light on potential underlying mechanisms that lead to similar levels of educational inequalities in both France and the United States, despite their distinct institutional frameworks in higher education.

Lastly, our paper contributes to the literature on the redistributive impact of public higher education spending. The empirical question of the degree of regressivity of spending on higher education has been the subject of intense methodological debate since the 1970s. The first empirical studies, conducted in the United States starting in 1969, gave rise to a controversy between [START_REF] Hansen | The Distribution of Costs and Direct Benefits of Public Higher Education: The Case of California[END_REF], who find higher education spending in California to be regressive -individuals at institutions with the least subsidies being less wealthy on averageand Pechman et al. (1970), who claim that higher education spending in California is progressive -wealthy people paying more in taxes than they receive in subsidies compared with the less affluent. The issue of redistribution via in-kind transfers has also recently received renewed attention in distributional accounts research [START_REF] Piketty | Distributional National Accounts: Methods and Estimates for the United States[END_REF], [START_REF] André | A Broader Approach to Inequality and Redistribution in France with a Monetary Valuation of Public Services[END_REF]). Table A1 in the Appendix reviews the findings on the redistributivity of educational spending in different institutional settings and based on different methodological choices. Our study updates and extends the work of [START_REF] Albouy | Communication préparée pour le séminaire "les effets redistributifs de l'éducation : les enseignements d'une approche monétaire statique" organisé par le Cerc[END_REF] on higher education spending, allowing several contributions to this literature. First, it addresses the lack of recent results in the U.S. or Europe (Johnson (2006)) and includes an unprecedented comparison of the distribution of higher education spending between France and the United States. Then, it explores a specific context of a European country with low tuition fees yet high levels of educational inequality; and uses data that, for the first time in France, disaggregates the costs of different higher education programs and fields.

Institutional Background

The French Higher Education System. The French higher education system is characterized by significant institutional differentiation and academic hierarchy among tracks. Higher education is divided into three main tracks: technical and vocational, non-selective academic (university) and selective academic, i.e. preparatory programs and elite graduate schools (Grandes écoles). Among first-year students in 2014-2015, 35% were on the technical and vocational track, 45% on the university track, and 20% on the selective academic track [START_REF] Menesr-Depp | Repères et références statistiques -Édition[END_REF]. The coexistence of two academic tracks is a specificity of the French system. Until 2018, university attendance was formally available to anyone holding the high school graduation exam (Baccalauréat), 7 but enrollment in elite graduate schools was highly selective, admission being based on performance in competitive national exams, and candidates being required to take an intensive 2-3-year preparatory course (Classes Préparatoires aux Grandes Écoles) for eligibility to take the exams. Attending these preparatory courses after high school is already selective.8

Tracking. The stratification of the French education system begins as early as the 10th grade when students must decide between a vocational track and a general or technological track in high school. This stratification continues with the choice of majors within the academic or technological tracks (before 11th grade). The STEM major is the most prestigious and the one that most often leads to selective programs in higher education, while the vocational track is the least likely to lead to enrollment in higher education.

The Financing of Higher Education. Most French higher education institutions are publicly funded, with tuition set at a very low level. In 2014-2015, tuition in public universities were e184 for undergraduate students, e256 for master's students, e391 for Ph.D. students, and e610 for most engineering schools. 9 The private sector accounted for 18% of total enrollment in higher education [START_REF] Menesr-Depp | Repères et références statistiques -Édition[END_REF]. All universities are public, and the private sector consists mainly of business schools, a third of engineering schools, plus other specialized schools (journalism, paramedical, social, cultural and artistic, etc.). Tuition at business schools generally ranges from e9,000 to e15,000 a year, for private engineering schools around e7,000.

Data and Variable Definition

In this section, we first describe our data and the construction of our main sample, present summary statistics, and define the key variables and concepts. SEE). This survey targeted a representative subset of young adults between the ages of 18 and 24, as well as their respective parents. The sample is smaller than in studies based on administrative or census data, but these data offer the advantage of combining detailed questions about young adults' educational background and the resources they have to live on, with the reliability of administrative data on parental income, on a representative sample of the young adult population. 10 The parental income data within the ENRJ is sourced directly from admin-istrative tax records of the surveyed parents. The final sample includes 5,776 young adults and 6,304 parents. Out of these, in 5,197 instances, responses were received from both the young adult and at least one parent. Survey weights are used to account for nonresponse bias.

The Data

Survey of Young

Higher Education Cost Data in France. The final section of our analysis incorporates supplementary data on higher education expenditure. In national accounts and in earlier studies focused on France, higher education expenditures are typically grouped into just three categories, irrespective of the specific track or field of study (MESRI-SIES, 2021). Our research utilizes additional data from the "Cost Awareness" project. 11 This project, conducted from 2016 to 2019 across 65 higher education institutions (representing about one-third of all French students), provides a more detailed breakdown of costs across various programs and fields. Notably, it enables the calculation of the instructional expenditures in higher education, excluding research costs that are present in more aggregated data sources.

We use the information contained in the main survey (ENRJ) on the studies undertaken by individuals to match the two data sources at the level of each track and field of study. 12 The link with the ENRJ survey data also makes it possible to gauge private investment in higher education through tuition fees paid by parents, a distinction not generally made in the literature on France.

Higher Education Cost Data in the United States. For the United States, the data is sourced from IPEDS 2015 (Integrated PostSecondary Education Data System). IPEDS is a comprehensive survey of higher education institutions that covers areas such as college finance, enrollment, admissions, completions, graduation rates, outcomes, and institutional characteristics. To ensure consistency with the data on France, which only includes instruction expenditure, we compute per student spending for instructional expenditure. This is derived by dividing the total instructional expenditure 13 by the total fall enrollment of the institution.

Sample Definition

The main sample includes young adult respondents to the survey and aged between 19 and 24 (n=3,947). We exclude 18-year-olds, as individuals in this age group are likely to still be in high school. When the parents are still living together, only one was interviewed and answered other aspects of parental background, like education or occupation. Census data, such as those used by [START_REF] Dodin | Social Mobility in Germany[END_REF] and [START_REF] Hilger | Parental Job Loss and Children's Long-Term Outcomes: Evidence from 7 Million Fathers' Layoffs[END_REF], partly address these limitations by offering large samples. Nevertheless, a significant drawback is that they predominantly cover children still living with their parents. This is a potential bias, especially concerning enrollment in higher education-a crucial juncture when an important share of students moves out, with these departures potentially correlating with parental income.

11 Connaissance des coûts des activités des établissements d'enseignement supérieur et de recherche, DGESIP 2016-2019 [START_REF] Boiteau | Le projet de connaissance des couts des activités des établissements d'enseignement supérieur et de recherche : retour d'expérience[END_REF].

12 See Appendix B.2.2.3 for more details on these new higher education cost data and Table B5 for annual public spending per student, broken down by field of study and track, the level of disaggregation that we are using. 13 This expense category includes expenses of the colleges, schools, departments, and other instructional divisions. It covers costs related to general academic instruction, occupational and vocational instruction, community education, preparatory and adult basic education, and regular, special, and extension sessions. questions about their partner. 14 When parents are separated (26% of our sample young adults), both were interviewed in 46% and only one in 54% of the cases, in which case we have no information about the non-responding parent. In analysing spending on higher education, we restrict ourselves to individuals aged 22-24, who are the most advanced in their education in our sample and we infer the educational trajectories until 24 for individuals aged 22 and 23.

Descriptive Statistics

Table 1 presents some descriptive statistics of our sample of young adults aged 19-24, by quintile of parental pre-tax income. On average, they are 21.5 years old, and 49 percent are female. The average pre-tax income of parents -the sum of father's and mother's household income, divided by two when there are two distinct households -ranges from e9,400 per year in the bottom quintile to e92,700 in the top quintile, with a mean of e41,900. The parents of students or former students are more affluent on average, with an annual pre-tax income of e50,900. A bit more than 10 percent of all the parents have a bachelor's or graduate degree, compared with over 20 percent of the parents of students or former students. The higher income quintiles tend to have a greater proportion of parents of high socio-economic status (SES) and with advanced degrees: more than 55 percent of individuals in the top quintile have a father of high SES, compared with 3 percent in the bottom quintile. About two thirds of the parents are still living together and a quarter are separated. The father is unknown or deceased in 7 percent of cases, the mother in 2 percent. As to geographic origin, 17 percent of the individuals in our sample have at least one parent living in the Paris region and another 29 percent in an urban center of at least 100,000 inhabitants (excluding Paris). The proportion of individuals in the Paris region or other large urban centers is greater at the top of the income distribution.

A concern here could be that the top deciles of the distribution concentrate the oldest parents and accordingly also the oldest young adults in our sample, which would bias the estimate of inequality in enrollment in higher education. However, this is not the case: neither the age of the young people nor that of their parents is statistically different across income groups.

[place Table 1 here]

Definitions of the Variables

In this section, we define the key variables used to measure enrollment in higher education by parental income.

Enrollment in Higher Education. We define individuals -aged 19-24 in our sample -as having enrollment in higher education if they meet any of the following criteria in the year of the survey: they are enrolled in a higher education program, they have already obtained a higher education degree, or they have reached a higher education level without obtaining the corresponding degree. To be considered as enrolling in higher education, an individual must therefore have been enrolled for at least one year in higher education. Similarly, we define attendance in a specific program (master's degree, medical school, selective higher education, etc.) as being currently enrolled in, having graduated from, or having reached some level in one of these programs without necessarily graduating.

Selective Higher Education. We define selective programs as preparatory courses, elite graduate schools, medical school and Ph.D. programs. The degree of selectivity of each of these programs can be assessed by ranking all students on the basis of their performance on the high school graduation exam. In 2016-2017, the median percentile rank of non-medical students in university was 50.2, that of students in medical studies was 68.1, that of students in preparatory courses was 84.9, and that of students in elite graduate schools was 72.8 [START_REF] Bonneau | Quelle démocratisation des grandes écoles depuis le milieu des années 2000 ?[END_REF].

Parent Income. Following Chetty et al. (2014) and [START_REF] Chetty | Income Segregation and Intergenerational Mobility Across Colleges in the United States[END_REF],15 our preferred specification uses the percentile of parental pre-tax income, defined as the sum of the father's pre-tax household income and the mother's pre-tax household income, divided by two when we have both parents' household income. 16 Parental income retrieved from income tax returns corresponds to individual income (before transfers) from wages, unemployment benefits, pensions, alimony, disability pensions, life annuities, agricultural income, industrial and commercial income, and noncommercial income. Capital income (property income, rent, finance, and securities) is not included. Taking property and capital incomes into account would mainly affect rankings within the top decile and only marginally those in the rest of the distribution.

To further assess the representativeness of our sample, we compare the distribution of pretax incomes of parents in the ENRJ sample and individuals aged 42-62 in the ERFS, another survey with a much larger sample (n=50,096) where income data are taken from tax sources as well. Overall, pre-tax income are quite similar in the two samples (Table B3). Parents of young adults (ENRJ sample), exhibited a slightly higher disposable income and a slighlty reduced standard of living when compared to the individuals in the general population (ERFS sample), due to the presence of children. Table B4 shows that the average parental income in France is lower than in the United States, being $53,000 compared to $97,000. Moreover, the standard deviation for France is considerably smaller, at $46,000, as opposed to $353,000 in the U.S. (all amounts in 2012 dollars).

Parent Tax Income Versus Self-Reported Income. Our data show that self-reported income is correlated quite weakly with parental income obtained from tax administrative sources. The deciles obtained with the two datasets coincide for only 34 percent of the youths, and the cor-relation coefficient of the two variables is only 0.67. The gap in enrollment in higher education is significantly underestimated when self-reported income is used instead of administrative income -by 5 to 12 percentage points, depending on the specification -due to underestimation of enrollment rates at the top of the distribution.

Parents' Occupation.

For occupations, we rely on the Department of Education's statistical service17 classification, which classes them in four groups by socio-economic status (SES). High SES encompasses professionals, managers, CEOs, teachers, professionals and artists. Uppermiddle SES corresponds to intermediate occupations, technicians, foremen and supervisors. Lower-middle SES refers to farmers, artisans, shopkeepers and white-collar employees. Low SES is defined as blue-collar workers and non-working people. Table B2 in the Appendix details the four SES categories and the corresponding occupations.

Parents' Diploma. The data contains information on the highest degree obtained by parents. We define six categories: elementary school certificate or less, middle school certificate, high school diploma or equivalent, two-year university degree, bachelor's or master's degree, and M.D. or Ph.D.

Socio-Economic Position Index.

For some analyses, we rely on a composite index of economic, social and cultural status (ESCS), based on OECD PISA 2015 and 2018 data. This index integrates a range of resources available to students. These resources are derived from the education and occupations of their parents, as well as an index summarizing numerous household possessions that serve as proxies for material wealth or cultural capital (OECD (2016)).

Unequal Enrollment in Higher Education by Parental Income

This section sets out our main findings on income-related disparities in enrollment in higher education and to different programs in France. We then explore the interplay between attendance disparities, which are linked to parental income, and other parental background characteristics, such as education and occupation. Following this, we compare the correlations between parental income and children's enrollment in higher education in France and the United States.

Inequalities in Higher Education Enrollment by Parents' Income

The proportion of 19-24-year-olds enrolled in higher education rises sharply with parental income (Figure 1): around 35 percent of those whose parents are in the bottom income quintile (P0-P20) are or have been students, compared with more than two times as many -around 90 percent -in the top decile.

[place Figure 1 here] Enrollment in master's degrees and selective programs -preparatory courses, elite graduate schools, medical school and Ph.D. -is more unequal still (Figure 2). Up to the 5th income decile for master's degrees and the 9th for selective programs, under 10% of individuals enter these studies. On the other side of the distribution, around 50 percent of individuals whose parents are in the top 2 percent of the income distribution (P98-P100) reach the master's level or enter a selective program between the ages of 19 and 24. These results confirm the problem of a dual system of higher education in France, in which enrollment in the most prestigious courses of study remains highly dependent on parental income.

[place Figure 2 here] Robustness Checks. A first concern is the possible mis-estimation due to the fact that our parental income is calculated for a single year and so could well be affected by transitory fluctuations [START_REF] Solon | Intergenerational Income Mobility in the United States[END_REF]. To test this, we use an alternative measure of parental income: the parents' household taxable income. This administrative variable is available in our sample at the household level for years t and t -2. We then compare the attendance differential between these two years, as shown in Table C6. Higher education attendance rates by decile of parental household taxable income in year t and in year t-2 do differ slightly, but the difference is never statistically significant. These results are consistent with the finding that the measure of social mobility is little affected by the number of years for which parental income is measured. 18A second concern is that the household measure of income, which we use for consistency with Chetty et al. (2014) and [START_REF] Chetty | Income Segregation and Intergenerational Mobility Across Colleges in the United States[END_REF], increases with cohabitation. We thus perform a robustness check with individual parental income -the sum of the individual incomes of the mother and father, regardless of marital status -in Appendix C.3.2. Figures C1 shows that overall, the results in terms of enrollment in higher education are very close to our main specification. The non-linearity of the effect of parental income on enrollment in higher education, discussed in a subsequent section, is nevertheless more pronounced when using individual parental income.

Complementarity of Inequalities Related to Parents' Income, Education and Occupation

Enrollment in higher education is often evaluated based on social background factors like parents' educational degree or occupation, rather than purely economic criteria. Our analysis delves into the connections among parental income, education, and occupation in relation to higher education attendance. We document descriptively that a significant portion of the higher education attendance gap based on parental income is associated with parental education or occupation, though not the entirety.

The heatmap in Figure 3 highlights disparities associated with parental income and occupation (Panels a and b) as well as parental education (Panels c and d). It depicts a staircase pattern, suggesting links between these factors. Specifically, within a given parental income bracket, there's an observed association between higher parental occupation or educational qualifications and increased enrollment in higher education -and the reverse is also true. This stair-step trend is notably evident when observing parental occupation. When considering parental educational attainment, there are pronounced discontinuities based on the number of years of education. Interestingly, this marked shift occurs at the 14-year education mark. This corresponds to the point where parents have attained a higher education degree themselves. For instance, 87 percent of individuals whose mother has a higher educational degree -14 years of education or more -have enrollment in higher education between the ages of 19 and 24, as against 47 percent of those whose mother does not. This observation aligns with a pattern where offspring of parents with higher education qualifications are often found in higher education themselves. Notably, this gap is even more pronounced when looking at the mother's education level, underscoring its pivotal role in a child's educational prospects. This is in line with some previous findings in the literature [START_REF] Currie | Mother's Education and the Intergenerational Transmission of Human Capital: Evidence from College Openings[END_REF], [START_REF] Sacerdote | How Large are the Effects from Changes in Family Environment? A Study of Korean American Adoptees[END_REF], [START_REF] Chevalier | The Impact of Parental Income and Education on the Schooling of their Children[END_REF], [START_REF] Lundborg | On the Family Origins of Human Capital Formation: Evidence from Donor Children[END_REF]).

[place Figure 3 here] More formally, we explore the complementarity of the different dimensions of inequality by observing the evolution of the regression coefficient of parental income on enrollment in higher education by successively adding various parental background controls (Table 2).19 These descriptive regressions do not aim to establish a causal impact of parental income on higher education enrollment but rather to illustrate the complementarity among inequalities stemming from parental income, occupation, and education. For a given occupation and educational degree, the higher the percentile rank of parental income, the greater the proportion of individuals enrolling in higher education and different programs. For example, those whose mother's highest degree is a high school diploma -12 years of education or less -have a 36 percent rate of enrollment in higher education between the ages of 19 and 24 when their parents are in the bottom income quintile and 77 percent when they are in the top quintile. Conversely, for a given level of parental income, the more privileged the parents' occupation or the higher their educational degree, the higher the proportion of children entering higher education.

Our most comprehensive regression controls not only for parents' education and occupation, but also for other observable characteristics likely to be linked to participation in higher education: family structure, and size of residential area. After controlling for all these factors, a residual significant effect of parental income remains, albeit only at the lower end of the parental income distribution. This descriptive analysis does not show a causal effect of parental income on higher education enrollment; rather, it simply indicates that the correlation between parental income and higher education enrollment cannot be fully explained by these observable characteristics alone.

[place Table 2 here] We have examined how the differences in enrollment in higher education by parental income, can partly overlap with inequalities related to other factors, such as parental education and occupation, but remains significant while controlling for these observable factors. In the next section, we compare the higher education attendance inequalities in France and the United States.

Comparison With the United States

Very few works have studied enrollment in higher education in relation to parental income on a nationally representative basis. One exception to this is [START_REF] Chetty | Income Segregation and Intergenerational Mobility Across Colleges in the United States[END_REF] in the United States, which studies college enrollment between the years individuals turn 19 and when they turn 22, using extensive administrative data. We compare these estimates with our sample, which is representative of individuals aged 19-24.

Surprisingly, given the differences in institutional contexts, the inequality appears to be almost as pronounced in France as in the United States (Figure 4). In the U.S., an increase of one decile in parental income is associated with an increase of 6.1 p.p. in the proportion of young people entering higher education, compared to 5.8 p.p. in France. We cannot reject that the coefficient in France is similar to the coefficient in the U.S. 20 In both countries, the proportion of individuals in higher education at the bottom of the income distribution is around 35 percent and that at the top is around 90 percent.

[place Figure 4 here] Linearity of the Income Effect. Although the relationship between parental income and children enrollment in higher education is broadly similar between the two countries, its functional form differs. The link is linear in the United States, but much higher in the upper as in the lower half of the distribution in France, where an increase of one decile in parental income is associated with an increase of 4.6 p.p in the proportion of young people entering higher education in the lower half of the income distribution and 9.6 p.p. in the upper half. Although attendance rates are quite similar at the two extremes of the income distribution, these non-linearities imply that the enrollment rate to higher education is lower in the middle of the income distribution in France than in the U.S.

Table 2 shows in more details the non-linear association in France between income and enrollment in higher education. Students with parents in the top income quintile are observed to attend college 30 percentage points more frequently than those in the middle quintile. Conversely, students with parents in the bottom quintile are observed to attend college 18 percentage points less often than those in the middle quintile. The stronger correlation between parental income and children's higher education attendance in the upper half of the income distribution is somewhat counterintuitive. If this effect were related to credit constraints, one would expect a larger impact at the lower end of the spectrum, where households are typically more financially constrained. This suggests that the income gradient in higher education attendance might be linked to other parental characteristics that correlate with parental income. However, when accounting for parental characteristics, a notable association between parental income and higher education enrollment emerges primarily in the lower half of the income distribution (Table 2). This descriptive pattern suggests that financial constraints might play a more significant role for individuals with lower incomes, while disparities linked to incomecorrelated characteristics could be more prevalent in the upper half of the distribution. This provides only suggestive evidence on the matter, as these associations are merely descriptive.

In this section we have set out novel estimates of inequality in enrollment in higher education according to parental income in France -using reliable income data from administrative tax sources -and compared our estimate to that observed in the United States. We find similar levels of inequality in France and the United States, which may seem surprising given the very different higher education contexts between the two countries. In the following section, we present some potential explanations for the similar levels of enrollment inequalities observed between the two countries.

Institutional Factors Related to Education Inequality in France and the U.S.

We analyze institutional differences between France and the United States to understand their similar levels of higher education inequality. Specifically, we explore education costs, early tracking and education disparities before entering higher education. The arguments presented here suggest that the similar levels of inequality in higher education enrollment observed between France and the United States can be attributed to different institutional factors. Atten-dance disparities in the U.S. are associated with a higher cost of higher education and more pronounced income inequalities. In France, enrollment in higher education could be hindered by early tracking and academic results that highly correlate with social origin.

Cost of Studies and Income Inequalities

We emphasize the institutional factors related to the cost of education and income inequalities in the two countries, which might suggest a lower level of higher education enrollment disparities in France compared to the United States.

First, higher education is much more expensive in the United States. In 2014-2015, average tuition in the United States was $9,139 at public four-year colleges for in-state students and $31,231 at private nonprofit institutions (The College Board, 2014), incomparably more than the cost of between e184 and e610 for most programs in France (see Section 3 for more details).

Second, income inequality is more pronounced in the U.S. than in France, with greater disparities between the top and bottom deciles. 21 Greater income inequalities means that the top and bottom income deciles are more different in the United States than in France. Moreover, higher income inequalities could exacerbate skill inequalities [START_REF] Causa | Equity in Student Achievement across OECD Countries: An Investigation of the Role of Policies[END_REF]). Some studies also indicate that countries or regions with higher income inequality often exhibit greater educational inequality [START_REF] Duncan | Increasing Inequality in Parent Incomes and Children's Schooling[END_REF], [START_REF] Workman | Inequality Begets Inequality: Income Inequality and Socioeconomic Achievement Gradients Across the United States[END_REF]).

Ultimately, greater income inequality has a knock-on effect on educational inequality through the returns to higher education. The latters are greater in the United States -estimated to about 14% as against 10% in France ( [START_REF] Psacharopoulos | Returns to Investment in Education: a Decennial Review of the Global Literature[END_REF]. Given the significant relationship between parental and child education, countries with higher returns to education are likely to have a stronger link between parental income and children's educational outcomes.

This section addresses a notable paradox: France and the United States exhibit similar levels of income-related educational inequality, despite stark contrasts in their educational and economic landscapes. In the United States, higher education costs substantially more, income inequality is greater, and the financial returns to education are higher compared to France. The next two sections will examine institutional factors in France that could explain the similar levels of enrollment inequalities in higher education. These include the strong correlation between parents' socio-economic status and children's academic achievement, as well as early tracking.

Unequal Academic Performance Before Higher Education

The unequal participation in higher education in France likely reflects an accumulation of inequalities from earlier schooling. The link between the parents' socio-economic status and PISA results in math, reading, and science at age 15 is stronger in France than in the U.S.

(Figure 5 (a)). According to the 2015 PISA survey, 20 percent of the variation in science performance is explained by socio-economic status in France, as against only 11 percent in the United States and an OECD average of 13 percent (OECD, 2018b). France is one of the OECD countries where educational performance is most closely correlated with social background. Socio-economic disparities in school performance are observed in both primary and secondary education [START_REF] Barhoumi | Les élèves sortent de l'enseignement secondaire de plus en plus diplômés mais au terme de parcours scolaires encore socialement différenciés[END_REF]; [START_REF] Barasz | Scolarités. Le poids des héritages[END_REF]).

[place Figure 5 here]

We employ Das [START_REF] Gupta | Decomposition of the Difference Between Two Rates and its Consistency when more than Two Populations Are Involved[END_REF] decomposition method to examine the contribution of prior credentials on the higher education attendance gap between the top and bottom income deciles (Table 3). 22 The middle school certification gap accounts for 21 percent of the total higher education enrollment disparity, while the high school certification gap among middle school graduates contributes 50 percent. These degrees thus explain 71% of the gap in higher education attendance; the remaining 29% being unexplained by prior credentials. In the United States, disparities in high school graduation rates based on parental income are less pronounced. We compare our data with the analysis conducted by Ziol-Guest and Lee (2016) for the U.S.: the proportion of high school graduates in France is substantially lower in the bottom half of the income distribution than in the U.S., with a gap of at least 20 percentage points. Furthermore, in France, the percentage of high school graduates increases with parental income in the top half of the income distribution. In contrast, in the United States, the proportion of high school graduates remains consistently above 90% across all income levels in the upper half of the distribution. 23[place Table 3 here] Inequalities likely encompass both academic/cognitive skills and social-behavioral/noncognitive skills. The disparity between students from high and low socio-economic status, especially in terms of perceived self-efficacy, is more pronounced in France than in the U.S. France also exhibiting a considerably lower average perceived self-efficacy score (Figure 5 (b)). France's lag in incorporating social and behavioral skills in its educational system [START_REF] Algan | Économie du savoir-être[END_REF]) might be a factor exacerbating these socio-economic-based inequalities.

Early Tracking and School Segregation

Early Tracking. Early tracking in France might enhance the strong correlation between socioeconomic status and academic performance. From the 10th grade onwards, students and their parents have to make key decisions about their school careers. These decisions are highly correlated with socio-economic status: [START_REF] Herbaut | Inequalities in Access to Higher Education in France. Cumulative Advantage and Compensatory Advantage over the Course of Secondary Education[END_REF] found that 92% of students with parents holding a higher education diploma choose the general and technological track in high school over the vocational track. In contrast, only 52% make the same choice among students whose parents have just a high school diploma. The authors also show that such decisions significantly impact educational and career trajectories. These differences in orientation according to social origin are only partially explained by differences in previous academic achievement: for the generation entering 6th grade in 1995, Ichou and Vallet (2012) observed that half of the academic track attendance gap between the working classes and the upper classes was due to differences in educational outcomes, while the other half was not explained by previous academic performance.

When comparing educational systems between countries, earlier tracking leading to separate pathways is generally associated with a higher level of educational inequality (Van de Werfhorst ( 2019)). The French "republican elitism" [START_REF] Baudelot | L'élitisme républicain: l'école française à l'épreuve des comparaisons internationales[END_REF]) stems from the Napoleonic system, in which schools were expected first and foremost to train the nation's elite. Until the 1970s, both secondary and higher education catered mainly to an upper-class minority. 24 This socio-economic divide persisted after primary school until the 1975 introduction of an unified middle school (collège unique, [START_REF] Merle | La démocratisation de l'enseignement[END_REF])). 25 In the United States, tracking is much less marked up to high school [START_REF] Brunello | Does School Tracking Affect Equality of Opportunity? New International Evidence[END_REF]).

Countries with early tracking also tend to exhibit more pronounced disparities in educational aspirations based on socio-economic status (OECD (2017)). Our sample of young adults in France shows notable variations in educational aspirations along the parental income distribution. Among 18-19-year-olds,26 those in the top income decile predominantly aim for advanced degrees (master's or Ph.D.) -nearly 80%. In contrast, only about 35% from the bottom quintile express the same aspiration (Figure 6 (a)). When comparing the aspirations of highachieving students using PISA data, a significantly higher proportion of disadvantaged French students do not expect to succeed in tertiary education compared to their U.S. counterparts (Figure 6 (b)). 27[place Figure 6 here] Students on vocational tracks in France are significantly less likely to enroll in higher education than students from academic tracks. Addressing this issue by ensuring that high-ability students from low socio-economic backgrounds have better access to high school academic tracks present an interesting prospect for increasing their enrollment in higher education.

School Segregation. The wider use of private schools in France also accentuates socioeconomic segregation at school [START_REF] Boutchenik | How Do Urban Segregation and High School Choice Contribute to School Segregation?[END_REF]), potentially reinforcing income-based inequalities. In 2018, only 80% of 15-year-old French pupils attended public schools, compared to 93% in the United States (OECD, 2020). Moreover, the socio-economic disparity between students in public and private institutions in France has been growing since the early 2000s [START_REF] Guillerm | Évolution de la mixité sociale des collèges[END_REF].

In this section, we have outlined institutional factors that could explain the similarly observed levels of enrollment inequality in higher education in both France and the U.S. In France, the pronounced correlation between a student's academic performance and their parents' socioeconomic status could be mitigated by the lower cost of attending higher education, while in the U.S., these factors might interact in the opposite direction. The following section provides a more detailed analysis of the distribution of higher education spending in France and in the U.S.

Unequal Public Expenditure for Young Adults

In this last section, we analyze the implications of the unequal enrollment in higher education based on parental income by assessing the redistributive profile of higher education expenses. 28First, we analyze the distribution of public higher education spending for all individuals, regardless of parental income. We also compare the annual distribution of higher education instruction expenditures between France and the United States. Then, we examine the distribution of spending across full higher education trajectories in France. We eventually assess the rank-rank correlation between higher education spending and parental income and examine in more detail the distribution of higher education spending by parental income in France. This approach enables us to decompose descriptively the role of three factors -attendance disparities, duration of studies, and annual costs -on the inequality in public spending for higher education among individuals from the lowest and highest parental income deciles.

Table A1 in the appendix presents a review of the literature on the redistributivity of education spending in different institutional settings and applying different methodologies. Usually, spending on K-12 education tends to be redistributive and that on higher education regressive. The table shows that the various studies are based on key methodological choices, such as how to take into account the socio-economic status of parents, whether or not to take taxes into account, 29 and in some cases the use of a life-cycle approach, although most of the studies are estimated in cross-section. This also points out the lack of recent estimates for France and the United States, and the need to supplement this literature.

Distribution of Spending on Higher Education in France and the United

States

We begin by examining the distribution of spending on higher education in France an in the United States, without connecting it to parental income. Spending on higher education is highly concentrated in both countries, as illustrated in Figure 7. In both cases, the bottom half of the distribution of higher education expenditure is marginal, mainly due to the fact that an important share of individuals do not pursue higher education and thus have zero spending for higher education. In France, the lower 50% of individuals account for 4.1 percent of the total spending, while in the United States, they account for 3.4 percent. However, the concentration of spending at the upper end is more pronounced in the U.S. Specifically, in the U.S., the top 10 percent of individuals who receive the highest spending on higher education account for 44.9 percent of the total expenditure. In contrast, in France, this figure stands at 28 percent. Similarly, the top one percent in the U.S. receives 16 percent of the total higher education spending, whereas in France, they receive 5 percent.

For France, we are able to map out comprehensive higher education trajectories, focusing on individuals aged 22 to 24 in our sample. This provides insights into the distribution of higher education expenditures over the span of 6 years, from ages 18 to 24. As presented in Figure D2 in the Appendix, approximately 40 percent of individuals -specifically those who do not pursue higher education -accrue no educational expenditures. Merely 10 percent incur an educational cost exceeding e30,000 during their studies. Furthermore, the top 1 percent accrue e71,000 over their 6-year educational journey. This is 2.4 times the expenditure faced by those at the 90th percentile and 9 times that of the median, which stands at e7,800.

In the subsequent section, we delve deeper into the breakdown of public and private higher education expenditures in relation to parental income in France.

[place Figure 7 here]

Inequality in Spending on Higher Education by Parental Income in France

We find strong inequalities in educational spending according to parental income, suggesting a strong link with the inequalities in participation highlighted above (Figure 8). Those in the bottom 50 percent receive e8,000 to e11,000 worth of investment in higher education between the ages of 19 and 24, compared with e32,000 -of which e21,000 in public funds -for those in the top 10 percent (Figure 8a). The differences in private investment in higher education are also quite substantial: parents at the bottom of the income distribution pay an average of e200 in tuition for their child over six years, compared with more than e10,000 for those at the top. The ratio of higher education spending between the top and bottom income deciles (D10/D1) is equal to 4.0:1, while that of public investment alone is 2.7:1. In Appendix D.4.4, we discuss how taking into account parental taxes to fund public higher education would alter these findings.

Another way of gauging inequalities in public spending for higher education is to consider the correlation between the percentile rank of parental income and that of public spending on higher education (Figure D3). On average, a 1-percentile increase in parental income is correlated with a 0.4-percentile increase in the distribution of public spending on higher education. Individuals whose parents are in the lowest decile of pre-tax income are on average in the 30rd percentile of public spending for higher education, while those whose parents are in the top decile are in the 68th percentile.

Decomposition of Inequalities in Public Spending

The observed disparities in higher education public spending based on parental income can arise from three potential factors: variations in enrollment rates in higher education, unequal duration of studies, or differential spending across distinct higher education programs, considering existing enrollment disparities. The aim of this section is to delineate the influence of these underlying determinants.

In France, the inequalities in public spending appear to derive primarily from differences in higher education attendance: inequality is much less pronounced when only higher education students are considered (Figure 8b). Students whose parents are in the highest deciles receive only a slightly higher public investment between the ages of 18 and 24 (about e24,000 in the top third, compared to e20,000 in the lowest two third). Those at the very top of the distribution, however, still benefit from a much larger private investment in higher education: about e11,000 over 6 years on average in the top 10%, compared with e500 for those at the bottom of the income distribution and between e1,000 to e3,000 in the rest of the distribution.

We use Gupta's rate decomposition method (Das [START_REF] Gupta | Decomposition of the Difference Between Two Rates and its Consistency when more than Two Populations Are Involved[END_REF] to further decompose public expenditure inequalities between an extensive margin -enrollment in higher education -and an intensive margin related to the duration of studies and differences in annual cost. 30 Inequalities in enrollment account for about 67 percent of the disparity in spending between the top and bottom income deciles (Table 4 and Figure D5). The remainder is almost entirely explained by differences in the duration of studies -students at the bottom of the income distribution pursuing higher education for an average of 3.3 years, compared with 4.5 years for students at the top (Figure D4). 31 In our main specification, there is almost no difference in annual public spending between students whose parents are at the top and the bottom of the income distribution. This is primarily because, although high-income students are largely overrepresented in selective programs (Figure 2), low-income students more often enroll in vocational programs, which also benefit from a much higher endowment than university programs (Table B5).

[place Table 4 here] Robustness Check: Matching Richer Individuals to Better-Endowed Programs. One concern about this finding of equal annual public spending for higher education students may be limited ability to match students with the specific program in which they are enrolled and to disaggregate spending on some of the most selective programs (elite graduate schools in particular). The contribution of enrollment disparities to inequality in public spending would then be overestimated.

We simulate a variant of public spending on higher education to predict how a more uneven distribution of public spending within each track and field might alter this result (Table 4). Positing that within a particular field of study and track, the most affluent consistently benefit from the most expensive programs and from the most expensive elite graduate schools (column 2),32 the contribution of the attendance gap declines significantly but still accounts for about half of the total difference in public spending for higher education between the poorest and richest individuals.

In this section, we have determined that the discrepancies in higher education spending in France largely result from disparities in enrollment rates, rather than from differences in funding across programs. In contrast, in the United States, disparities in educational spending seem to be primarily associated with differences in funding across programs. Bonneau (2020) posits that, given the variance in spending within a particular educational level in the United States, the degree of educational spending inequality would persist nearly unchanged even if everyone reached the same level of educational attainment. To draw more conclusive remarks on these topics, further research would be needed for a more comprehensive comparison between the two countries.

Conclusion

Using a detailed survey of young adults together with administrative data on their parents' income, this study examines inequality of enrollment in higher education and selective programs according to parental income. On average, a 10-percentile increase within the parental income distribution is associated with a 5.8-percentage-point increase in the proportion of children enrolling in higher education. The level of attendance inequality according to parental income in France is very similar to that in the United States despite much lower tuition fees and income inequalities in France. This is a new result that we interpret by the importance of intergenerational transmission of educational outcomes and early tracking in France. In France, spending on higher education is regressive. This is primarily due to the inequalities in participation that we have highlighted, even though the concentration of resources among higher education institutions is less uneven than in the United States.

Our analysis reveals a disparity in the prerequisites for higher education enrollment, calling for earlier and more robust skill support of low-income students. Specifically, policies aiming at reducing the attendance gap in high school academic tracks based on socio-economic background could be a beneficial strategy to enhance higher education enrollment of low-income students. Additionally, the significant disparities in enrollment rates for selective programs among high school graduates highlight the importance of giving disadvantaged students targeted, transparent, and clear information about the various higher education programs available. The effectiveness of need-based scholarships [START_REF] Fack | Improving College Access and Success for Low-Income Students: Evidence from a Large Need-Based Grant Program[END_REF] as well as marked differences in parental transfers among students [START_REF] Grobon | Combien coûte un jeune adulte à ses parents?[END_REF], indicate a need for more comprehensive need-based scholarships to adequately cover higher education expenses. This need is particularly acute for students in the middle-income bracket, who benefit the least from the combination of public support and parental tax deductions.

Our research identifies a key divide in higher education enrollment inequalities based on parental income. In some countries, these inequalities could arise primarily due to financial barriers to entry, while in others, they could result from earlier disparities in the accumulation of human capital. Applying this perspective to European or developing countries could be insightful. In Europe, a crucial question is how to align this divide with the differences between social democratic and liberal welfare state regimes, as outlined by [START_REF] Willemse | Three Worlds of Educational Welfare States? A Comparative Study of Higher Education Systems across Welfare States[END_REF], and the contrast in social mobility between Nordic and liberal countries. For developing countries, this divide should be considered in relation to the level of public funding for higher education systems. This funding could affect income inequalities through an increase in human capital, as discussed by Ehrlich and Kim (2007).

This need for international comparison of inequality in enrollment in higher education calls for educational data to be further enriched with reliable data on parental income. Detailed comparative data on spending differentials in higher education, especially for selective programs, would further contribute to the public debate by allowing more systematic estimation of the redistribution occurring through higher education public spending. B2 for more details on this variable). We measure parental education with six diploma categories -primary school or less (9 years of education), middle school diploma (10 years of education), high school diploma (12 years of education), two-year higher education degree (14 years of education), Bachelor's or master's degree (17 years of education), and M.D. or Ph.D. (20 years of education). 2020)). In both countries, the parental income used is the sum of the pre-tax income of the father's household and the mother's household, divided by two when there are two different households. In the U.S., these figures represent the proportions of individuals who enrolled in higher education at least once between the ages of 18 and 21. In France, we consider individuals aged 19-24 currently enrolled in or having graduated from higher education as these individuals are most likely to have entered higher education between the ages of 18 and 21. We exclude the youngest (18-year old individuals) from our sample in order to limit the minor bias stemming from the fact that some are still in high school. We do not include property and capital incomes in the estimate for France because it is not possible to identify them independently of the incomes of all household members, thus also including the incomes of cohabiting young adults. Taking property and capital incomes into account would mainly affect rankings within the top decile and only marginally those in the rest of the distribution. [START_REF] Chetty | Income Segregation and Intergenerational Mobility Across Colleges in the United States[END_REF] study cohorts born between 1980 and 1982 in the United States, whereas the survey used in our study focuses on cohorts born between 1990 and 1996 in France.33 ) is defined as the degree to which individuals believe in their own ability to perform specific tasks and engage in activities, particularly in adverse circumstances [START_REF] Bandura | Self-Efficacy: Toward a Unifying Theory of Behavioral Change[END_REF]). In 2018, PISA asked students about their general sense of efficacy or competence, especially in challenging situations. These figures are sourced from the PISA 2015 and 2018 database (OECD (2018a), OECD ( 2021)). Notes: These figures display the disparities in public and private spending on higher education, by parental income. Panel (a) shows the total amount of public and private investment in higher education for all individuals until 24, as a function of parental income. Panel (b) shows total public and private investment in higher education for students or former students until 24, by parental income. For a complete analysis of educational pathways up to age 24, we restrict the sample to 22-to 24-year-olds and the length of study for 22-and 23-year-olds is extended by parental income decile based on the continuation rates observed in the sample. Private spending corresponds to tuition paid by the parents and expanded over the 6-year period, taking into account the number of years of education completed by each individual. The parental income used is the sum of the pre-tax income of the father's household and the mother's household, divided by two when there are two different households. Deciles are based on this definition (x-axis). We use the "Cost Awareness" project and MESRI-SIES (2021) data for higher education spending.

Figures

Notes:

The sample is constructed from the ENRJ survey. It includes only individuals for whom a young adult and at least one parent responded to the questionnaire. The number of observations is not equal for all parental income quintiles because in creating the parental income ranks we apply the survey weights for assessing non-response bias. The mother's occupation is missing for 4 percent of the observations and the father's for 9 percent. The mother's diploma is missing for 4 percent of the observations and the father's for 17 percent. When the parents are separated, both were questioned in 46 percent and only one in 54 percent of the cases. When the two parents do not live in the same city, we use the larger urban center. Notes: This table presents the estimates of the effect of parental income on enrollment in higher education (1), successively adding controls for parental occupation ( 2), parental education ( 3), and all these controls simultaneously with family status and urban center size (4). Parental income used is the sum of the pre-tax income of the father's household and the mother's household, divided by two when there are two different households. Quintiles are based on this definition. We omit the third quintile. The coefficients should thus be interpreted as the difference from the baseline probability of higher education enrollment for individuals with parents in the third income quintile. The potential financial transfer variable represents what young adults would have received from their parents if they were studying, based on their characteristics (indicators for parents' income decile, number of siblings, father's degree, mother's degree, father's occupation, mother's occupation, parents' marital status, and size of urban center where the young adult lives). Parents' occupation is introduced in dummy variables for each of the Notes: This table presents the contribution of different credentials -middle school graduation, high school graduation for those who passed the middle school graduation exam, higher education attendance gap for those who passed the high school graduation exam -to the total difference in enrollment in higher education, selective programs, and master's degrees between individuals in the top and bottom 10 percent of the parental income distribution (in percent). To decompose the contribution of different factors, we rely on Gupta's decomposition methods [START_REF] Gupta | Decomposition of the Difference Between Two Rates and its Consistency when more than Two Populations Are Involved[END_REF]. See Appendix B.2.3 for more details on this decomposition method. Notes: This table shows the contribution of different factors -enrollment in higher education, differences in duration of study for students, differences in annual public spending for students -to the total difference in public higher education spending between individuals in the top 10 percent and the bottom 10 percent of the income distribution (in percent). Parental income used is the sum of the pre-tax income of the father's household and the mother's household, divided by two when there are two different households. Deciles are based on this definition. For a complete analysis of educational pathways up to age 24, we restrict the sample to 22-to 24-year-olds and the length of study for 22-and 23-year-olds is extended by parental income decile based on the continuation rates observed in the sample. To decompose the contribution of different factors, we rely on Das [START_REF] Gupta | Decomposition of the Difference Between Two Rates and its Consistency when more than Two Populations Are Involved[END_REF] decomposition method. See Appendix B.2.3 for more details on this decomposition method.

Column (1) represents our main specification. Column (2) presents a simulation designed to address potential underestimation of inequalities in public spending on higher education in our data. This counterfactual approach involves associating the most expensive courses in the respective field with the most affluent students and adding consideration for increased spending on elite graduate schools. More specifically each combination of tracks and fields, we assign the 10th (or 25th) percentile of the distribution of student-weighted costs -or the next higher percentile when we do not have enough observations for the 10th or 25th percentile -to individuals whose parents are in the bottom 10 percent (or 25 percent) of the income distribution and the 75th percentile (or 90th percentile) -or the next lower percentile -to those whose parents are in the top 25 percent (or 10 percent) of the income distribution. Concerning elite graduate schools, individuals in the top 5 percent of the income distribution are assumed to enroll in schools with endowments three times the typical endowment and those in the next 5 percent to enroll in schools with endowments twice the typical endowment. See Appendix C.3.3 for more details on these simulations.

B.2 Variables, Data and Methods

B.2.1 Grouping of Parental Occupations

B.2.2.3 Data on Public Spending on Higher Education in France

Cost of Studies by Track and Field of Study. In the French national accounts, higher education expenditures are generally classed in one of just three categories,34 regardless of the track or field of study (MESRI-SIES, 2021). Our study draws additional data from a survey of higher education institutions, the "Cost Awareness" project (Connaissance des coûts des activités des établissements d'enseignement supérieur et de recherche, DGESIP 2016-2019 [START_REF] Boiteau | Le projet de connaissance des couts des activités des établissements d'enseignement supérieur et de recherche : retour d'expérience[END_REF]) designed to assess the expenditures of different higher education institutions. This survey was conducted between 2016 and 2019 at 65 higher education institutions that enroll approximately one-third of all French students. Not all public institutions have been surveyed, but the sampled institutions are representative of all public higher education institutions under the Ministry of Higher Education [START_REF] Bennani | Les coûts des formations dans l'enseignement supérieur français: déterminants et disparités[END_REF]). These data allow for a detailed breakdown of costs across various tracks and fields of study.

Elite Graduate Schools and Variance in Spending Within Tracks and Fields of Study.

Despite their quality, these new higher education cost data still have some limitations. We are not able to differentiate public spending among elite graduate schools. 35 We therefore attribute the average cost of engineering schools to the other public elite graduate schools, which might lead us to underestimate inequalities in public spending. Some of these schools indeed have very high per-student expenditures (for example, Berné and Métivier (2015) found that some specific elite graduate schools have expenditures of e60,000 per student per year) and an attendance rate that remains very uneven [START_REF] Bonneau | Quelle démocratisation des grandes écoles depuis le milieu des années 2000 ?[END_REF]). More generally, public spending still varies greatly within tracks and fields, which we do not take into account because we cannot link students to the exact university in which they are or were enrolled. We address these issues by simulating two variants of public spending on higher education to predict how a more uneven distribution of public spending within each program and field might alter this result (see Appendix C.3.3). Unlike university programs, we cannot break down the costs of vocational programs and preparatory courses by field because we do not have detailed expenditure data for these programs, which are located in specific high schools. Since both are national programs and the course load, student/teacher ratio, and teacher salaries are set by the state, we can assume that there is little disciplinary variation in these programs. In the same way that we remove the costs of research in university programs, here we consider only the costs of training: 85.3 percent of total costs for preparatory courses and 86.7 percent for vocational programs [START_REF] Bennani | Les coûts des formations dans l'enseignement supérieur français: déterminants et disparités[END_REF].

Integration of Survey and Cost Data.

Our study integrates two key datasets: cost data from the "Cost Awareness" survey and survey data on young adults (ENRJ survey). The cost data presents expenditures for each track and field within public programs. The survey data details individual registrations across these tracks and fields. To ensure a comprehensive analysis, we matched these datasets based on their respective track and field descriptors, creating a consolidated "track × field" data. For a specific breakdown of the cost data granularity used in our analysis, refer to Table B5.

Construction of Educational Spending Over the Entire Educational Trajectory.

To study inequality along the higher education trajectory, we restrict ourselves to individuals aged 22 to 24, who are the most advanced in their studies in our sample. The length of study for 22-and 23-year-olds is extended by parental income decile based on the continuation rates observed in the sample. We retain the higher cost between the highest degree obtained, the highest level of education attained, or ongoing studies. We partially account for reorientations. For example, someone who is enrolled in a master's program but has an engineering degree has the cost of the full engineering school program plus the cost of one year of a master's degree in their field. In the absence of complete information on individual trajectories in the data, we do not consider individuals who repeat in the same program. It is likely that this approximation leads us to underestimate the cost of university students who repeat: 27 % of first-year students (MESRI-SIES, 2020) but also students in preparatory courses who often repeat the second year of the program -9.1 % in economic preparatory courses, 20 % in humanities preparatory courses and 22.1 % in scientific preparatory courses.36

Parents' Private Spending on Higher Education. We account for private investment in higher education through tuition paid by parents. We average tuition amounts declared by young adults and their parents to limit measurement error. Because our cost data represent the full training cost and not public spending, in cases where tuition paid is less than e650, we subtract the tuition paid by parents from the total cost to get the net public cost. When the tuition is above e7,500, we consider it to be private education and the net public cost is set at 5 % of the tuition paid. Between these two extreme limits, which we must set by convention, we consider the public cost data as the public cost and the tuition as the private cost. For individuals who have already graduated from college (16% of individuals in our sample and 29% of those aged 22-24), we cannot know whether they were enrolled in a public or private program because we do not have information on the tuition paid by their parents. We assume that all these individuals were enrolled in public programs, which represents the vast majority of programs in

France. The private sector indeed accounted for 18% of total enrollment in higher education (?) in 2014. Notes: This table presents the annual spending on higher education, for different tracks, degrees and fields. These data come from MESRI-SIES (2021) for vocational programs and preparatory courses, from the Commission d'évaluation des formations et diplômes de gestion (CEFDG) for business schools (https://www.cefdg.fr/fr/ecoles-et-formations-visees) and calculated from the "Cost Awareness" project (DGESIP 2016(DGESIP -2019) ) for all other courses. In calculating the average annual cost per student, we weight each program surveyed by the number of students enrolled.

B.2.3 Gupta Decomposition Method

We decompose both the enrollment gap in higher education and the differences in the cost of public higher education between individuals from the top income decile (T ) and those from the bottom decile (B) using a standard rate decomposition method developed by Das [START_REF] Gupta | Decomposition of the Difference Between Two Rates and its Consistency when more than Two Populations Are Involved[END_REF]. When the outcome is defined as a product of other variables of interest, the method defines a way to calculate the contribution of each of the latter to the total gap in the outcome variable between two subpopulations.

We denote the outcome variable of interest as r and the k explanatory factors as x 1 , . . . , x k such that

r(x 1 , . . . , x k ) = k n=1 x i .
When k = 2, the contribution of each factor C(x 1 ) and C(x 2 ) can be written as:

   C(x 1 ) = 1 2 (x T 2 + x B 2 )(x T 1 -x B 1 ) C(x 2 ) = 1 2 (x T 1 + x B 1 )(x T 2 -x B 2 ) (1)
In the general case where k ≥ 3, the contribution of each factor C(x i ) can be expressed as:

C(x i ) = k-1 j=1 R(j -1, i) k k-1 j-1 (x T i -x B i ) (2)
where R(j, i) is the sum of all possible values of the product of k -1 factors (excluding x i ), of which j factors are from population T and all other factors from population B [START_REF] Li | Rate Decomposition for Aggregate Data Using Das Gupta's Method[END_REF].

For instance, when k = 3, the contribution of the first factor to inequalities between individuals from top (T ) and bottom (B) income deciles is obtained with:

C 1 = x B 2 × x B 3 3 + x B 2 × x T 3 + x B 3 × x T 2 6 × (x T 1 -x B 1 )
In our framework, we initially break down the disparity in higher education participation between individuals whose parents are positioned at the top of the income distribution (denoted T ) and those with parents at the income distribution's lower end (denoted B) by examining prior degree attainment.

The rate of participation in higher education for each group G (where G ∈ (B, T )) is computed as:

HE G = M SC G × HSC G M SC × HE G HSG (3)
Here, 'HE G ' denotes the rate of higher education participation for individuals in group G. M SC G represents the rate at which individuals in group G achieve the middle school certificate. Furthermore, HSC G M SC indicates the rate of obtaining a high school certificate among those in group G who have previously achieved the middle school certificate. Lastly, HE G HSG specifies the rate of higher education participation for those in group G who hold a high school certificate.. Refer to Table 3 for results derived from this decomposition technique.

Second, we decompose differences in public spending on higher education between individuals in the top (T ) and bottom (B) income deciles based on differences in enrollment in higher education, duration of study, and spending on each year of higher education. Formally, public spending on higher education for individuals in the G group (with G ∈ (B, T )) can be defined as follows:

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P S G = HE G × LS G student × AC G student
With P S G public spending on higher education for individuals in the G group, HE G participation rate in higher education of individuals in the G group, LS G student average duration of study of students in the G group, and AC G student average annual public cost of students in the G group. The results of the contribution of each of these factors to differences in higher education costs are presented in Table 4. Notes: Our main analyses are based on a single year of parental income: the survey year (2014). In this table we present the sensitivity of our results to using multiple years of parental income. The parental income used in our main specification is the sum of the father's household and the mother's household pre-tax income, divided by two when two parental households are identified. To perform this robustness check between year t and t-2, we use a slightly different concept of income, parents' household taxable income that is available for both year t and t-2.

C.3 Robustness Checks

The regression coefficients part reports estimates of a regression of parental income percentile on enrollment in higher education. They should be interpreted as the average change in the participation rate in higher education for an increase of 10 percentile ranks (i.e., one decile) in the parental income distribution. The differences in estimation between our main concept of parental income and this taxable income concept are due to better imputation of missing responses in our main concept and the fact that some types of income (alimony, retirement savings, and special allowances) are deducted from taxable income. Standard deviations (Panel A) and standard errors (Panel B) in parentheses.

C.3.2 Using Parents' Individual Income Instead of Parents' Household Income

The parental income variable used in our main analysis is the sum of the father's household and the mother's household pre-tax income, divided by two when two parental households are identified. In this Appendix, we present the main results of our analysis with respect to a slightly different concept of parental income, the sum of the father's pre-tax income and the mother's pre-tax income, regardless of marital status. This variant differs from our main specification in that it does not take into account the incomes of the spouses of separated and reunited parents, consistent with the fact that income pooling is less frequent in re-partnered couples (Burgoyne and Morison (1997), [START_REF] Ponthieux | La mise en commun des revenus dans les couples[END_REF]). When parents are separated (concerning 26% of our sample of young adults), both were interviewed in 46% and only one in 54% of the cases. To prevent this nonresponse from biasing our income variable, we impute the income of the nonresponding parent using the responses of the separated parents who both responded to the survey, controlling for the gender and income decile of the responding parent. Notes: This figure displays the proportion of individuals aged 19 -24 who are currently enrolled, have enrolled in higher education without necessarily obtaining a degree, or already hold a higher education degree, by parental individual pre-tax income. The parental income used is the sum of the father's pre-tax individual income and the mother's pre-tax individual income, regardless of marital status. Deciles are based on this definition. We further decompose the top 10 percent of the distribution (x-axis). The black line represents the standard errors.

C.3.3 Matching Richer Individuals to Better-Endowed Programs

There is still variance in within-field and within-track spending that we cannot account for because we are not able to link students to the exact university in which they are enrolled. This could lead to a downward bias in the observation of the redistribution occurring through higher education spending if wealthier individuals are able to attend better-endowed programs.

We thus perform a robustness check by assigning, for each combination of tracks and fields, the 10th (respectively 25th) percentile of the distribution of student-weighted costs -or the nearest higher per-centile when we do not have enough observations to observe the 10th or 25th percentile -to individuals whose parents are in the bottom 10 percent (respectively 25 percent) of the income distribution and the 75th percentile (respectively 90th percentile) -or the nearest lower percentile -to those whose parents are in the top 25 percent (respectively 10 percent) of the income distribution. Our main results are relatively close to those found with this assumption of extreme concentration of wealthier individuals in more expansive programs, meaning that there is not much variation in costs within programs enrolling a large portion of the student body. In our main specification, individuals in the top decile of the income distribution receive 2.7 more public investment in higher education than those in the bottom decile (Table C7). When richer programs are associated with richer individuals, individuals in the top 10 percent of the income distribution benefit 3.7 times more than those in the bottom decile.

One of the other limitations of the cost data used is that we are not able to differentiate public spending among the most selective elite graduate schools, which could lead us to underestimate inequities in public spending. Indeed, some of these schools have very high per-student expenditures -for example, Berné and Métivier (2015) found that specific elite graduate schools have expenditures of e60,000 per student per year -and an participation rate that remains very unequal [START_REF] Bonneau | Quelle démocratisation des grandes écoles depuis le milieu des années 2000 ?[END_REF]. In a final specification, we assume both that wealthier individuals attend better-endowed university programs, as previously and that individuals from the top decile of the income distribution, when they enter elite graduate schools (engineering schools, institutes of political studies, or other specialized schools), attend better endowed schools. Individuals in the top decile of the income distribution account for about 30 percent of elite graduate school enrollment in our sample. We assume that individuals in the top 5 percent of the income distribution attend schools with endowments three times the typical endowment and that those in the next 5 percent of the income distribution enroll in schools with endowments twice the typical endowment. In this latter specification, which is the most comprehensive and included in the main body of the paper, we find that individuals at the top of the income distribution benefit from 4.5 times as much as individuals at the bottom of the income distribution.

In our main specification, enrollment inequality explains about 70 percent of the inequality in public spending on higher education between individuals in the top and bottom income deciles. When we allocate better-endowed programs to wealthier individuals, the contribution of enrollment inequality to public spending inequality decreases mechanically but remains equal to about half of total spending differences (Table C8). Notes: This table presents public spending on higher education by parental income decile under different assumptions. The parental income used is the sum of the pre-tax income of the father's household and the mother's household, divided by two when there are two different households. Deciles are based on this definition. For a complete analysis of educational pathways up to age 24, we restrict the sample to 22-to 24-year-olds and the length of study for 22-and 23-year-olds is extended by parental income decile based on the continuation rates observed in the sample. Column (1) represents our main specification. Column (2) represents the results obtained by assigning wealthier individuals to programs that are better endowed in their track and field of study. In this simulation, we assign for each combination of programs and fields, the 10th (respectively 25th) percentile of the distribution of student-weighted costs -or the nearest higher percentile when we do not have enough observations to observe the 10th or 25th percentile -to individuals whose parents are in the bottom 10 percent (respectively 25 percent) of the income distribution and the 75th percentile (respectively 90th percentile) -or the nearest lower percentile -to those whose parents are in the top 25 percent (respectively 10 percent) of the income distribution. Column (3) represents the same simulation as in column [START_REF]Enrollment in Higher Education, by Parents' Pre-Tax Income Quintile[END_REF] with additional assumptions about the cost of highly selective elite graduate schools. We assume that individuals from the top decile of the income distribution, when they enter elite graduate schools (engineering schools, institutes of political studies, or other specialized schools), enroll in better endowed schools. We assume that individuals in the top 5 percent of the income distribution attend schools with endowments three times the typical endowment and that those in the next 5 percent of the income distribution enroll in schools with endowments twice the typical endowment. Notes: This table shows the contribution of different factors -enrollment in higher education, differences in duration of study for students, differences in annual public spending for students -to the total difference in public higher education spending between individuals in the top 10 percent and the bottom 10 percent of the income distribution (in percent). Parental income used is the sum of the pre-tax income of the father's household and the mother's household, divided by two when there are two different households. Deciles are based on this definition. For a complete analysis of educational pathways up to age 24, we restrict the sample to 22-to 24-year-olds and the length of study for 22-and 23-year-olds is extended by parental income decile based on the continuation rates observed in the sample. To decompose the contribution of different factors, we rely on Das [START_REF] Gupta | Decomposition of the Difference Between Two Rates and its Consistency when more than Two Populations Are Involved[END_REF] decomposition method. See Appendix B.2.3 for more details on this decomposition method.

Column (1) represents our main specification. Column (2) represents the results obtained by assigning wealthier individuals to programs that are better endowed in their track and field of study. In this simulation, for each combination of tracks and fields, we assign the 10th (or 25th) percentile of the distribution of student-weighted costs -or the next higher percentile when we do not have enough observations for the 10th or 25th percentile -to individuals whose parents are in the bottom 10 percent (or 25 percent) of the income distribution and the 75th percentile (or 90th percentile) -or the next lower percentile -to those whose parents are in the top 25 percent (or 10 percent) of the income distribution. Column (3) represents the same simulation as in column [START_REF]Enrollment in Higher Education, by Parents' Pre-Tax Income Quintile[END_REF] with additional assumptions about the cost of highly selective elite graduate schools. We assume that individuals from the top decile of the income distribution, when they enter elite graduate schools (engineering, institutes of political studies, or other specialized schools), enroll in better endowed schools. More specifically, individuals in the top 5 percent of the income distribution are assumed to enroll in schools with endowments three times the typical endowment and those in the next 5 percent to enroll in schools with endowments twice the typical endowment. Notes: This table reports the estimates of the effect of parental income percentile, potential financial transfers, parents' education, parents' occupation, family status and urban center size on enrollment in higher education. Parental income used is the percentile rank calculated from the sum of the father's household and the mother's household pre-tax income, divided by two when two parental households are identified. The potential financial transfer variable represents what young adults would have received from their parents, if they were studying, based on their characteristics (indicators for parents' income decile, number of siblings, father's degree, mother's degree, father's occupation, mother's occupation, parents' marital status, and size of urban center where the young adult lives). For parent's education we define six categories: elementary school certificate or less, middle school certificate, high school diploma or equivalent, two-year degree, bachelor's or master's degree, and M.D. or Ph.D. The mother's degree is missing for 4 percent of observations and the father's for 17 percent. For occupations, we rely on the Department of Education's statistical service grouping into four socio-economic statuses (SES). High SES includes professionals, managers, CEOs, teachers, professionals and artists. Upper-middle SES corresponds to intermediate occupations, technicians, foremen and supervisors. Lower-middle SES refers to farmers, artisans, shopkeepers and employees. Low SES is defined as blue-collar workers and nonworking people. Table B2 details the four SES categories and the corresponding occupations. The mother's occupation is missing for 4% of the observations and the father's for 9%. When the two parents do not live in the same city, we use the larger of the two.

D.4.2 Distribution of Higher Education Public Spending on Young Adults

In this section we present the distribution of public expenditures dedicated to young adults and their parents, regardless of parental income.

Figure D2 shows the distribution of public spending on higher education aggregated over studies (until 24). About 40% of individuals have zero spending because they did not enter higher education.

Only 10% of individuals receive more than e30,000 of investment in higher education during their education. The 1% of individuals with the highest public expenditure on higher education receive on average e70,500 over 6 years of study. They receive 2.4 times more spending than individuals at the 90th percentile of higher education spending and 8.5 times more spending than individuals at the median of public spending on higher education (e70,500 versus e8,300 on average).

Figure D3 shows the correlation between the percentile rank of parental income and the percentile rank of public spending on higher education. A significant correlation between parental income and public spending on higher education is observed. On average, a one percentile increase in parental income is correlated with a 0.4-percentile increase in the distribution of public spending on higher education. On average, individuals whose parents are in the lowest decile of pre-tax income are in the 30th percentile of public spending on higher education, while those whose parents are in the highest decile are in the 68th percentile of public spending.

Percentile of Public Spending

Notes: This figure shows the average public spending on higher education over 6 years (until 24), by public spending percentile. 42% of 22-24 year olds have zero spending because they did not enter higher education. Unlike the rest of our analyses, we do not consider parental income in calculating this distribution. For a complete analysis of educational pathways up to age 24, we restrict the sample to 22-to 24-year-olds and the length of study for 22-and 23-year-olds is extended by parental income decile based on the continuation rates observed in the sample. Notes: This figure plots the correlation between the percentile rank of parental income and the percentile rank of public spending on higher education. The red line is the linear regression of the percentile rank of parental income on the percentile rank of public spending on higher education. The parental income used is the sum of the pre-tax income of the father's household and the mother's household, divided by two when there are two different households. The percentiles are calculated based on this definition. For a complete analysis of educational pathways up to age 24, we restrict the sample to 22-to 24-year-olds and the length of study for 22-and 23-year-olds is extended by parental income decile based on the continuation rates observed in the sample. Notes: This figure shows the decomposition of inequality in public spending on higher education between an extensive margin -differences in enrollment in higher education -and an intensive margin -differences in spending on higher education for those who enroll, related to both inequality in duration of study and inequality in annual spending. We restrict the sample to 22-to 24-year-olds and the length of study for 22and 23-year-olds is extended by parental income decile based on the continuation rates observed in the sample. The dark curve represents the current level of inequality in public spending on higher education (corresponding to Figure 8a). The left curve represents the level of inequality that would result if all individuals enrolled in higher education with the current level of spending inequality. The right-hand curve represents the level of inequality that would result if all individuals had the same expenditure on higher education with the current level of inequality in participation. The parental income used is the sum of the pre-tax income of the father's household and the mother's household, divided by two when there are two different households. Deciles are calculated based on this definition (x-axis).

D.4.3 Decompositions of Inequalities in Public Spending on Higher Education

D.4.4 Accounting for Parental Taxes in Higher Education Spending Distribution

One common objection to the finding of regressive government spending is that wealthier parents contribute more to the funding of higher education through their taxes. We thus estimate a net benefit measuring the degree of redistribution of public spending on higher education, net of the share of the taxes paid by parents that must be allocated to finance this expenditure. Given our data, we consider a static framework in which young adults' higher education is funded by a contribution from all taxpayers, including their parents. Alternative methods might adopt a lifecycle approach, wherein individuals repay through taxes the benefits they received during their studies. We first outline the accounting method devised to incorporate parents' taxes into the evaluation of higher education spending's redistributivity, followed by a presentation of our findings.

D.4.4.1 Methodology

We assess the redistribution that takes place through public spending on higher education and propose a method of accounting for the taxes paid by parents and used to finance this particular public expenditure. This section details and motivates the assumptions concerning the scope of higher education spending, the duration of study or the taxes considered that underlie our calculation of the degree of redistribution of public spending on higher education, once parental tax contributions are taken into account.

Scope of Public Spending on Higher Education. We restrict our analysis to higher education expenditures only. We draw upon data from the "Cost Awareness" project37 , designed to assess the expenditures of various higher education institutions. Conducted between 2016 and 2019 at 65 institutions enrolling roughly one-third of French students, this survey enables us to segregate costs by program and field of study and to discern the cost of higher education net of research costs, which are included in more aggregated data. We use the main survey's (ENRJ) information on individual studies to match the two data sources at the level of each track and field of study. 38 Consequently, this data facilitates a more precise estimation of public spending on higher education per individual compared to highly aggregated data. For all programs, we focus solely on instructional expenditure.

Period Considered. Our main sample comprises young adults aged 19 to 24, spanning a 6-year period. This range encapsulates the majority of student trajectories. However, expenditures on those continuing their education post-24 are omitted. We also project fiscal contributions over a 6-year timeframe by multiplying the annual parental contribution by 6. For the purpose of assessing public spending on higher education, our focus is on individuals aged 22 to 24, representing the most advanced in their academic journey within our dataset. The study duration for individuals aged 22 and 23 is extended based on continuation rates observed in the sample, stratified by parental income decile.

Taxes Paid by Parents. Our database incorporates administrative records of parents' income tax payments. We calculate the proportion of income allocated to VAT, corporate income tax, and other indirect taxes for each standard-of-living decile based on results from national accounts [START_REF] André | A Broader Approach to Inequality and Redistribution in France with a Monetary Valuation of Public Services[END_REF]). We use standard-of-living deciles to match the figures in the referenced study. This is a deviation from the rest of the article, where the deciles pertain to the pre-tax household income of parents. The derived tax rates for each standard-of-living decile, presented in Table D10, are subsequently applied to the pre-tax income of parents in our database, based on the respective standard-of-living decile to which they belong. Notes: This table presents the proportion of pre-tax income that is allocated to various taxes (VAT, energy and excise taxes, corporate taxes, and income taxes) based on the standard-of-living decile of the entire population. For instance, households in the first standard-of-living decile expend 17% of their total pre-tax income (which includes public support) on VAT. The percentage of income allocated to VAT, corporate income tax, and other indirect taxes for each decile is determined by dividing the tax revenue sourced from that decile by its collective income, inclusive of public support for VAT and excise duties computation. The results are derived from the distributed national accounts [START_REF] André | A Broader Approach to Inequality and Redistribution in France with a Monetary Valuation of Public Services[END_REF]). It's important to note that the table's standard-of-living deciles pertain to the broader population to maintain consistency with the figures in the referenced studies. This approach differs from the rest of the article where the deciles are based on pre-tax parental income. For the income tax data, we rely on the administrative variable provided in our survey.

Net Benefit From Public Spending on Higher Education. We then apply the predetermined share of taxes calculated above, which amounts to 4%, dedicated to the public funding of higher education, to the unallocated taxes paid by parents. This calculation yields the estimated portion of taxes from parents that is allocated to higher education. To ascertain their net benefit, we subtract this tax amount from the higher education spending received by their child. This net benefit can be understood as the advantage parents gain from the public funding of higher education after accounting for the taxes they have paid and dedicated to such funding.

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The mean net benefit for each parental income decile d is therefore calculated as follows:

N et_Benef it d = 1 n d n d i=1 S HE i -(0.04 × T axes i × 6) (7)
Where:

• N et_Benef it d denotes the average net benefit for the d th parental income decile;

• n d represents the number of individuals in decile d;

• S HE j is the higher education spending over a 6-year period for the i th individual;

• T axes i refers to the taxes paid by the i th individual's parents;

• The factor of 0.04 represents the 4% share of taxes dedicated to higher education, defined above as Share_T axes HE ;

• Multiplication by 6 adjusts the tax amount over the relevant period under study for higher education expenses.

This equation does not need to account for the number of children parents have. This is due to the specifics of our survey data. We establish deciles based on the parents' income of surveyed young adults, who are representative of individuals aged 18 to 24. In cases where a demographic group has a larger number of children on average, these offspring will naturally cover a broader spectrum of the parental income distribution. While it's not universally accurate that one child aged 18-24 equates to one parent's observation, this assumption is valid in our survey data, given the sampling method (1 young adult = 1 parental household (or 2 in case of separated parents)). Therefore, in the equation for computing the redistribution of higher education public spending, net of parental tax contributions, we can assume that 1 parental household accounts for 1 young adult, with the survey weights adjusting for any overrepresentation or underrepresentation of certain demographics. This approach would be different in comprehensive administrative data, where all young individuals and their parents are accounted for, allowing multiple young adults in the 18-24 age bracket to be linked to the same parents.

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D.4.4.2 Results

In this section, we discuss the redistributive effects of public funding for higher education, considering the taxes paid by parents specifically for this purpose, as elaborated in the preceding methodology section.

The data reveals that, on average, parents receive a net benefit of e9,600 over a six-year period, as depicted in Figure D6 and Table D11. Interestingly, parents benefit from horizontal solidarity since 76% of the higher education expenses for their young adults are funded by taxpayers who do not have young adults. However, this average masks variations among households. Households with young adults enrolled in higher education experience a net benefit that is nearly double at e18,100, while those without young adults in higher education see a negative value of e1,900, as they participate in higher education funding without benefiting from it.

When examining the impact of taxes used to fund higher education, it becomes apparent that while this spending remains regressive, there is a noteworthy shift at the top of the income distribution. Specifically, the net benefit is roughly twice as high in the upper third of the distribution compared to the lower third (e13,900 versus e6,900). This benefit rises with parental income, particularly in the upper half of the distribution (from P50 to P90), peaking at about e17,000, as evidenced in Table D11 and Figure D6.

Yet, the top decile, due to higher taxation and even with their increased enrollment in higher education, has a net benefit of only two-thirds that of the ninth decile (e11,600 compared to e17,000). Nonetheless, this figure exceeds the net benefit seen in the bottom decile (e6,800). Notes: This figure plots the distribution of higher education public expenditures on young adults over a 6-year period, by pre-tax parental income, taking into account parents taxes funding higher education. The solid line shows public spending on higher education until 24.

Analysis for educational pathways up to age 24 targets the 22-24 age bracket, extending study periods for 22-and 23-year-olds based on observed continuation rates by parental income deciles in the sample. This corresponds to the dark grey bars in Figure 8. The dash line with empty dots shows the same variable, net of 4 percent of parental tax contribution -corresponding to the share of all taxpayers' unallocated taxes needed to fund public higher education. Parental income used is the sum of the pre-tax income of the father's household and the mother's household, divided by two when there are two different households. Deciles are based on this definition (x-axis). We use the "Cost Awareness" project and MESRI-SIES (2021) data for higher education spending. Notes: This table outlines the distribution of higher education public expenditures on young adults against the fiscal contributions of their parents, categorized by pre-tax parental income. Parental income used is the sum of the pre-tax income of the father's household and the mother's household, divided by two when there are two different households. Deciles are based on this definition (x-axis). We use the "Cost Awareness" project and MESRI-SIES (2021) data for higher education spending. Values are rounded to the nearest 100 euros. Column (1) details public spending on higher education until 24. Analysis for educational pathways up to age 24 targets the 22-24 age bracket, extending study periods for 22-and 23-year-olds based on observed continuation rates by parental income deciles in the sample. Column (2) represents 4% of taxes contributed by parents over six years, reflecting the portion of unallocated taxes from all taxpayers needed to finance public higher education. This figure is derived from a representative dataset of all taxpayers (ERFS), with imputations for indirect and corporate tax sourced from the distributed national account [START_REF] André | A Broader Approach to Inequality and Redistribution in France with a Monetary Valuation of Public Services[END_REF]). Column (3) displays the net benefit from higher education, calculated by subtracting the parental tax contribution from the total public expenditure on higher education.

D.4.5 Predicted Lifetime Earnings

Disparities in higher education enrollment based on parental income lead to differences in educational attainment. These educational achievements, in turn, result in disparities in lifetime income, which likely contribute to the relatively low social mobility observed in France (Kenedi and Sirugue (2023)). This

Appendix offers a descriptive analysis, specifically examining the implications of our main findings in terms of predicted lifetime earnings.

Educational Attainment Disparities. The disparities in higher education attendance, highlighted in this study, directly lead to significant disparities in educational achievement. For instance, around 45% of 22-to 24-year-olds41 whose parents are within the top 5% of the income distribution have obtained a bachelor's degree. In stark contrast, only about 10% of individuals from the bottom 10% income bracket have achieved this level of education. This pronounced disparity is further illustrated in Figure D7. Prediction of Lifetime Earnings Based on Educational Attainment. To predict lifetime earnings, we combine the educational attainment of 22-24 year-olds observed in our sample with the first empirical measure of lifetime earnings for France, recently produced by Garbinti et al. (2023). 42 In their estimation of lifetime earnings, they use a granularity of six distinct educational levels. Lifetime earnings, as defined in the study, represent the average earnings across 31 working years, from age 25 to 55, focusing on the cohort born in 1962. 43 Additionally, we included a differential in lifetime earnings between Master's degree holders and elite graduate school graduates, as calculated by ? using self-reported earnings data.

Estimated lifetime earnings by gender and education level, which form the basis of our analysis, are depicted in Figure D8. Underlying Hypothesis. In our analysis, we correlate the educational attainment of individuals aged 22 or older with their corresponding average lifetime earnings. This approach allows us to explore how differences in educational achievement relate to variations in lifetime incomes, under specific conditions outlined below. First, these estimates are based purely on educational attainment levels, ignoring individual variations in earnings within each attainment level. Secondly, these estimates draw on data from much earlier cohorts who have completed their careers. Thirdly, we do not account for variations in educational returns influenced by parents' socio-economic backgrounds, due to the lack of substantial evidence for such effects in France (Courtioux (2011)). Lastly, the ambition of this analysis is purely descriptive. We describe variations in predicted lifetime earnings among young adults with certain characteristics, rather than attempting to ascertain causal relationships.

Lifetime Earnings Gap According to Higher Education Participation and Parental Income. Based on the assumptions previously outlined, we find that young adults who have enrolled in higher education are predicted to have lifetime earnings approximately 33% higher than their counterparts who did not pursue higher education. This figure considers both the direct causal effect of higher education and the selection factors involved into higher education attendance. The disparities in enrollment in higher education outlined in our study suggest a discrepancy of 1.27 between predicted lifetime earnings of young adults whose parents are in the bottom 10% income bracket and those whose parents are in the top 10%. Additionally, there is a disparity of 1.19 in predicted lifetime earnings between the lowest 30% and the highest 30%.

Bridging the Gap Between the Bottom and the Middle of Parental Distribution. As highlighted in our main analysis, there is a notable disparity in higher education participation based on parental income. Specifically, participation rates for young adults from the bottom 30% of the parent income distribution are, on average, 15 percentage points lower than those from the middle income bracket (P50-P60). Considering the varying lengths of study correlating with parental income among those enrolled

  Adults and Their Parents. The main dataset used in our work is the National Survey of Youth Resources (Enquête Nationale sur les Ressources des Jeunes, ENRJ) from 2014, collaboratively administered by the Direction de la Recherche, des études, de l'évaluation et des Statistiques (DREES) and the Institut National de la Statistique et des études économiques (IN-

[

  place Figure 8 here]

Figure 1 :

 1 Figure 1: Proportion of Individuals Enrolling in Higher Education, by Parents' Pre-Tax Income

Figure 2 :

 2 Figure 2: Proportion of Individuals Enrolling in Master's Degree or Selective Programs, by Parents' Pre-Tax Income (a) Master or Higher Degree

Figure 3 :

 3 Figure 3: Higher Education Attendance by Parents' Pre-Tax Income, Occupation, and Diploma (a) Father's Occupation

Figure 4 :

 4 Figure 4: Enrollment in Higher Education in France and in the United States, by Parents' Pre-Tax Income

Figure 5 :

 5 Figure 5: Correlations Between Academic Skills, Behavioral Skills and Socio-Economic Status in France and in the United States (a) Impact of Socio-Economic Index Increase on Academic Skills Score

Figure 6 :

 6 Figure 6: Educational Aspirations in France and the United States (a) Educational Aspirations in France, by Parents' Pre-Tax Income

Figure 7 :

 7 Figure 7: Distribution of Higher Education Spending Over One Year in France and in the United States

Figure 8 :

 8 Figure 8: Inequalities in Public and Private Spending on Higher Education in France

C. 3 . 1

 31 Using Multiple Years of Parental Income 52 Documents de travail du Centre d'Economie de la Sorbonne 2022.05RR (Version révisée)

Figure C1 :

 C1 Figure C1: Proportion of Individuals Enrolled in Higher Education, by the Sum of Individual Pre-Tax Income of Both Parents

59

  Documents de travail du Centre d'Economie de la Sorbonne 2022.05RR (Version révisée)

Figure

  Figure D2: Distribution of Public Spending for Higher Education

Figure

  Figure D3: Rank-Rank Correlation

Figure

  Figure D4: Duration of Study

Figure

  Figure D5: Extensive and Intensive Margins

68

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Figure D6 :

 D6 Figure D6: Spending for Higher Education, Net of Parental Taxes Funding Higher Education

Figure

  Figure D7: Highest Degree Earned by Parents' Pre-Tax Income

Figure

  Figure D8: Lifetime Earnings by Gender and Educational Level

Table 1 :

 1 Descriptive Statistics

	Quintile of income	P0-P20	P20-P40	P40-P60	P60-P80	P80-P100	Total	Students or
								former students
		n= 760	n= 796	n= 838	n= 820	n= 733	n= 3,947	n= 2,353
	Age of young adults	21.5 (1.7) 21.6 (1.7) 21.4 (1.7) 21.5 (1.7)	21.3 (1.7)	21.5 (1.7)	21.5 (1.7)
	Age of fathers	55.5 (6.6) 54.5 (6.8) 53.3 (5.5) 53.0 (5.6)	53.6 (5.9)	53.9 (6.1)	53.9 (5.8)
	Age of mothers	50.6 (6.2) 49.9 (5.6) 49.7 (5.0) 50.3 (4.6)	51.0 (4.4)	50.3 (5.3)	50.8 (5.0)
	Female	0.53	0.47	0.50	0.49	0.47	0.49	0.53
	Pre-tax household	9,360	24,050	36,050	49,690	92,690	41,904	50,869
	income of parents	( 6,280)	( 3,320)	( 3,490)	( 4,770)	(60,550)	(39,173)	(46,298)
	Father's occupation
	Low SES	0.33	0.40	0.41	0.28	0.06	0.30	0.21
	Lower-middle SES	0.35	0.28	0.22	0.22	0.14	0.24	0.24
	Upper-middle SES	0.05	0.11	0.20	0.27	0.21	0.17	0.20
	High SES	0.03	0.04	0.06	0.19	0.56	0.17	0.26
	Mothers's occupation
	Low SES	0.27	0.20	0.19	0.13	0.04	0.17	0.10
	Lower-middle SES	0.58	0.60	0.56	0.45	0.28	0.50	0.44
	Upper-middle SES	0.05	0.11	0.13	0.27	0.30	0.17	0.23
	High SES	0.02	0.04	0.07	0.11	0.37	0.12	0.19
	Father's dipoma
	Primary School or less	0.21	0.22	0.20	0.08	0.02	0.15	0.10
	Middle School degree	0.03	0.05	0.04	0.06	0.04	0.04	0.04
	High-School degree	0.23	0.43	0.51	0.54	0.29	0.40	0.38
	Two-year degree	0.04	0.04	0.06	0.13	0.19	0.09	0.13
	Bachelor or Master degree	0.03	0.02	0.04	0.11	0.32	0.10	0.16
	M.D. or Ph.D.	0.00	0.01	0.01	0.01	0.10	0.02	0.04
	Mother's dipoma
	Primary School or less	0.44	0.29	0.19	0.10	0.02	0.21	0.12
	Middle School degree	0.07	0.10	0.09	0.08	0.03	0.07	0.07
	High-School degree	0.33	0.44	0.50	0.48	0.31	0.41	0.39
	Two-year degree	0.04	0.08	0.09	0.19	0.24	0.13	0.19
	Bachelor or Master degree	0.04	0.04	0.08	0.12	0.31	0.12	0.18
	M.D. or Ph.D.	0.00	0.00	0.01	0.01	0.06	0.02	0.03
	Marital status of parents
	Parents live together	0.37	0.55	0.70	0.81	0.87	0.65	0.70
	Parents are separated	0.44	0.35	0.23	0.17	0.12	0.26	0.23
	Father unknown or deceased	0.16	0.09	0.05	0.02	0.01	0.07	0.05
	Mother unknown or deceased	0.03	0.02	0.02	0.01	0.01	0.02	0.02
	Parents unknown or deceased	0.00	0.00	0.00	0.00	0.00	0.00	0.00
	Biggest urban center
	of parent's residence
	Parisian area	0.14	0.14	0.12	0.15	0.30	0.17	0.20
	More than 100,000 inhabitants	0.33	0.29	0.28	0.27	0.29	0.29	0.29
	Less than 100,000 inhabitants	0.51	0.56	0.59	0.57	0.41	0.53	0.49

Table 2 :

 2 Enrollment in Higher Education, by Parents' Pre-Tax Income Quintile

	Enrollment in higher education	(1)	(2)	(3)	(4)
	Baseline proba. of enrollment	0.57	0.57	0.57	0.57
	Parents' income quintile
	Parents' income quintile=1	-0.18 * * *	-0.15 * * *	-0.041 -0.087 * * *
	Parents' income quintile=2	-0.073 * * * -0.067 * * * -0.035	-0.048 *
	Parents' income quintile=3	0	0	0	0
	Parents' income quintile=4	0.12 * * *	0.057 * * 0.064 * * *	0.040
	Parents' income quintile=5	0.30 * * *	0.091 * * * 0.12 * * *	0.032
	Control variables included
	Father Occupation (26 categories)		X		X
	Mother Occupation (26 categories)		X		X
	Father Diploma (6 categories)			X	X
	Mother Diploma (6 categories)			X	X
	Family situation				X
	Urban center size				X
	Observations	3,947	3,616	3,066	3,019

* p < 0.1, * * p < 0.05, * * * p < 0.01

Table 3 :

 3 Decomposition of Higher Education Participation Rate Differences by Prior Credentials

	Contribution of previous credentials	Higher	Selective	Master's
	to enrollment disparities (in percent)	education	programs	degrees
	Middle school graduation	21	9	10
	High school graduation	50	21	24
	Enrollment in higher education	-	12	15
	Residual differential enrollment	29	58	51

Table 4 :

 4 Decomposition of Differences in Public Spending on Higher Education

		(1)	(2)
		Main specification Wealthier individuals
			attend more costly
			programs and elite
			graduate schools
	Enrollment in higher education	67	49
	Duration of study	23	17
	Annual public spending	10	33

  TableB2below details the four SES categories and the corresponding occupations. The mother's occupation is missing for 4% of the observations and the father's for 9% of the observations.

44 Documents de travail du Centre d'Economie de la Sorbonne 2022.05RR (Version révisée)

Table B2 :

 B2 Grouping of Occupations

	Socioeconomic statuses (SES)	Corresponding occupations
	High SES
	23	Entrepreneurs with 10 or more employees
	31	Liberal professions
	33	Public service executives
	34	Professors, scientific professions
	35	Information, arts and entertainment professions
	37	Administrative and commercial executives of companies
	38	Engineers and technical company executives
	42	Teachers and assimilated
	73	Former executives
	Upper-middle SES
	43	Intermediate professions in health and social work
	44	Clergy, religious
	45	Administrative intermediary professions of the public service
	46	Administrative and commercial intermediary professions of companies
	47	Technicians
	48	Foremen, supervisors
	74	Former intermediary professions
	Lower-middle SES
	11	Smallholder farmers
	12	Farmers on medium farm
	13	Large-scale farmers
	21	Craftsmen
	22	Traders and assimilated
	52	Civilian employees and civil servants
	53	Police and military
	54	Administrative employees of companies
	55	Commercial employees
	56	Staff in direct personal services
	71	Former farmer operators
	72	Former craftsmen, traders, business leaders
	75	Former employees
	Low SES
	62	Skilled industrial type workers
	63	Skilled artisan type workers
	64	Drivers
	65	Skilled workers in handling, warehousing and transport
	67	Unskilled industrial workers
	68	Unskilled artisan type workers
	69	Agricultural workers
	76	Former workers
	80	Inactive

Notes: This table details the occupations corresponding to the four socio-economic status used in our analyses. This grouping corresponds to the official grouping of the Department of Education's statistical service (Direction de l'évaluation, de la prospective et de la performance (DEPP)).

B.2.

2 Data B.2.2.1 Representativeness of the SampleTable B3 :

 B3 Comparison of Income Distributions in ENRJ and ERFS Samples This table compares the distribution of different income variables for parents in our database (ENRJ) and individuals aged 42 to 62 in another tax survey with a much larger sample (ERFS). 99% of parents of young adults aged 18-24 are in the age range 42-62 in our ENRJ data. The two samples are relatively close in terms of pre-tax income. Individuals in our sample (parents of young adults) have slightly higher disposable incomes and a slightly lower standard-of-living than individuals in the ERFS sample, due to the presence of children.

		ENRJ (2014)	ERFS (2014)
		(Parents of	(One member of
		young adults) the household between)
			43-62 years old)
	Mean age	51.5 (5.8)	51.6 (6.9)
	Pre-tax income
	Mean	41,904	43,022
	Median	35,514	35,240
	P10	9,955	9,470
	P90	77,556	78,010
	P99	162,021	188,190
	Disposable income
	Mean	48,047	41,401
	Median	42,849	34,690
	Standard-of-living
	Mean	22,692	24,408
	Median	19,712	20,915
	Number of observations	3,947	20,293

Notes:

B.2.

2.2 Comparison of Parental Income Distribution in France and the United StatesTable B4 :

 B4 Parental Income Distribution in France and the United States This table compares the distribution of parental income in France and the United States. The U.S. data come from Table III in the online Appendix ofChetty et al. (2014). In both cases, family income is pre-tax household income, divided by two when both the father's and mother's household incomes are available. All amounts are in 2012 dollars. We do not include property and capital incomes in France because it is not possible to identify them independently of the incomes of all household members, thus also including the incomes of cohabiting young adults. In any case, taking property and capital incomes into account would mainly affect rankings within the top decile and only marginally those in the rest of the distribution. In the United States, family income is the average household income from 1996 to 2000 becauseChetty et al. (2014) studies cohorts born between 1980 and 1982. In France, family income is 2014 because the survey we use was conducted in 2014.

	Income Distribution United States France
	Mean	87,219	52,030
	Std. Deviation	353,430	46,400
	Median	60,129	44,580
	Observations	9,867,736	3,947

Notes:

Table B5 :

 B5 Per Student Annual Public Spending

	Track	Field of study	Public cost
			over one year
			(in euros)
	Vocational Track (BTS)		12,400
	Preparatory Courses (CPGE)		13,400
	Bachelor Degree (Non Vocational) (Licence)	Humanities, Arts, Languages	3,400
		Markets & Organizations	3,000
		Math, Engineering, Computer science	5,300
		Law	2,500
		Material, Earth and Universe Sciences	6,200
		Social Sciences	3,500
		Life Sciences	4,900
		Various	3,600
	Bachelor Degree (Vocational) (Licence professionnelle)	Humanities, Arts, Languages	4,900
		Markets & Organizations	5,400
		Math, Engineering, Computer science	7,700
		Law	5,400
		Material, Earth and Universe Sciences	9,400
		Social Sciences	5,300
		Life Sciences	7,000
		Various	6,400
	Technical Training (IUT)	Markets & Organizations	7,500
		Math, Engineering, Computer science	11,300
		Law	7,000
		Material, Earth and Universe Sciences	11,700
		Social Sciences	7,500
		Life Sciences	10,100
		Various	9,500
	Master Degree	Humanities, Arts, Languages	5,400
		Markets & Organizations	4,800
		Math, Engineering, Computer science	7,300
		Law	4,000
		Material, Earth and Universe Sciences	8,900
		Social Sciences	4,700
		Life Sciences	6,500
		Various	5,300
	Engineering Schools	Math, Engineering, Computer science	10,400
		Material, Earth and Universe Sciences	12,000
		Social Sciences	11,300
		Life Sciences	11,900
		Various	10,600
	First Year of Medical Studies (PACES)	Medicine	2,400
	Medical Studies (Except First Year)	Medicine	4,400
	Paramedical Trainings	Medicine	2,700
	Institute of Political Studies (IEP)		4,000
	Business Schools		400
	Other Elite Graduate Schools (Grande école)		10,600

Table C6 :

 C6 Sensitivity of Results to Using Multiple Years of Parental Income

		Access rate to higher education
			Parental income variable used:
		Household	Household	Average of household
		taxable income	taxable income	taxable incomes
		in year t	in year t-2	in years t and t-2
	Panel B. Parental income decile
	P0-P10	0.40	0.48	0.42
		(0.49)	(0.50)	(0.49)
	P10-P20	0.42	0.35	0.40
		(0.49)	(0.48)	(0.49)
	P20-P30	0.43	0.43	0.43
		(0.50)	(0.50)	(0.50)
	P30-P40	0.52	0.55	0.53
		(0.50)	(0.50)	(0.50)
	P40-P50	0.53	0.48	0.53
		(0.50)	(0.50)	(0.50)
	P50-P60	0.57	0.54	0.50
		(0.50)	(0.50)	(0.50)
	P60-P70	0.61	0.62	0.64
		(0.49)	(0.49)	(0.48)
	P70-P80	0.65	0.65	0.66
		(0.48)	(0.48)	(0.47)
	P80-P90	0.76	0.80	0.77
		(0.43)	(0.40)	(0.42)
	P90-P100	0.85	0.86	0.86
		(0.36)	(0.35)	(0.35)
	Panel B. Regression coefficients
	Full sample	0.46	0.46	0.48
		(0.03)	(0.03)	(0.03)
	Lower half	0.31	0.16	0.32
		(0.07)	(0.07)	(0.07)
	Upper half	0.72	0.81	0.85
		(0.07)	(0.07)	(0.07)

Table C7 :

 C7 Sensitivity of Results to the Student-Program Matching

			(1)	(2)	(3)
		Decile of parental	Main specification	Association of	Assumption (2) +
		household income		wealthier individuals	assumptions on the cost of
				to better-endowed programs	elite graduate schools
	All individuals	D1	7,800	6,200	6,200
		D2	7,600	6,400	6,400
		D3	8,800	7,800	7,900
		D4	9,100	8,500	8,600
		D5	10,000	9,400	9,500
		D6	12,500	11,200	11,400
		D7	12,200	11,200	11,300
		D8	16,800	16,200	16,700
		D9	21,300	21,700	22,200
		D10	21,400	22,900	27,900
		D10/D1 Ratio	2.7	3.7	4.5
	Students or	D1	22,200	17,500	17,600
	former students	D2	19,200	16,100	16,200
		D3	18,900	16,700	16,900
		D4	19,900	18,600	18,700
		D5	18,500	17,300	17,400
		D6	21,300	19,000	19,400
		D7	23,200	21,300	21,500
		D8	21,300	20,600	21,200
		D9	26,700	27,200	27,800
		D10	23,500	25,100	30,500
		D10/D1 Ratio	1.1	1.4	1.7

Table C8 :

 C8 Decomposition of Differences in Public Spending on Higher Education: Three Vari-

	ants of Spending
		(1)	(2)	(3)
		Main specification	Association of	Assumption (2) +
			wealthier individuals wealthier individuals
			with better-endowed	attend more costly
			programs	elite graduate schools
	Enrollment in higher education	67	52	49
	Duration of study	23	18	17
	Annual public spending	10	30	33

Table D9 :

 D9 Enrollment in Higher Education Based on Parents' Income, Occupation and Diploma p < 0.1, * * p < 0.05, * * * p < 0.01

		(1)	(2)	(3)	(4)	(5)	(6)
	Parent's income percentile rank	0.58 * * *	0.55 * * *	0.22 * * *	0.27 * * *	0.14 * * *	0.100 * *
	Log of potential financial transfers		0.0097 * * *				0.0028
	Father Primary school			-		-	-
	Father Middle School			0.00035		-0.027	-0.029
	Father High School			0.051 * *		0.032	0.040 *
	Father Two-year degree			0.19 * * *		0.13 * * *	0.13 * * *
	Father Bachelor or Master degree			0.23 * * *		0.16 * * *	0.15 * * *
	Father M.D. or Ph.D.			0.26 * * *		0.18 * * *	0.19 * * *
	Mother Primary school			-		-	-
	Mother Middle School			0.14 * * *		0.12 * * *	0.13 * * *
	Mother High School			0.16 * * *		0.13 * * *	0.14 * * *
	Mother Two-year degree			0.37 * * *		0.30 * * *	0.31 * * *
	Mother Bachelor or Master degree			0.31 * * *		0.20 * * *	0.21 * * *
	Mother M.D. or Ph.D.			0.35 * * *		0.22 * * *	0.21 * * *
	Father Low SES				-	-	-
	Father Lower-middle SES				0.13 * * * 0.099 * * * 0.095 * * *
	Father Upper-middle SES				0.16 * * *	0.11 * * *	0.11 * * *
	Father High SES				0.24 * * *	0.14 * * *	0.15 * * *
	Mother Low SES				-	-	-
	Mother Lower-middle SES				0.095 * * * 0.061 * * * 0.062 * * *
	Mother Upper-middle SES				0.24 * * *	0.13 * * *	0.14 * * *
	Mother High SES				0.28 * * *	0.17 * * *	0.18 * * *
	Parents live together						-
	Separated parents						-0.077 * * *
	Parisian area						-
	Urban unit of more than 100,000 inhabitants						-0.032
	Urban unit of less than 100,000 inhabitants						-0.055 * *
	Observations	3,947	3,947	3,066	3,329	3,046	3,013
	R 2	0.114	0.116	0.196	0.176	0.214	0.221

*

Table D10 :

 D10 Taxes as a Proportion of Pre-Tax Income, by Overall Population Standard-of-Living

		Distributional national accounts at ENRJ administrative
			the macro level	data
		VAT	Energy and excise taxes	Corporate tax	Income tax
	D1	0,17	0,06	0,02	0,01
	D2	0,14	0,05	0,01	0,03
	D3	0,12	0,04	0,01	0,02
	D4	0,12	0,04	0,01	0,03
	D5	0,11	0,04	0,01	0,03
	D6	0,11	0,03	0,01	0,04
	D7	0,11	0,03	0,01	0,04
	D8	0,10	0,03	0,02	0,05
	D9	0,10	0,03	0,02	0,08
	D10	0,08	0,01	0,11	0,13
	Total	0,11	0,03	0,04	0,04
	Public support
	included in pre-tax	Yes	Yes	No	/
	parental income

Table D11 :

 D11 Average Public Spending and Fiscal Contribution on Young Adults Over 6-Year Period, by Parents' Pre-Tax Household Income (in Euros)

		(1)	(2)	(3)
		Public spending for higher education (A)	4% of fiscal contribution of parents over 6 years (B)	Net benefit for higher education (A)-(B)
	P0-P10	7,800	1,000	6,800
	P10-P20	7,600	1,300	6,300
	P20-P30	8,800	1,600	7,200
	P30-P40	9,100	1,800	7,300
	P40-P50	10,000	1,900	8,200
	P50-P60	12,500	2,400	10,100
	P60-P70	12,200	2,500	9,700
	P70-P80	16,800	2,800	14,000
	P80-P90	21,300	4,200	17,100
	P90-P100	21,400	9,800	11,600
	Average	12,500	2,800	9,600

The National Survey of Youth Resources or Enquête Nationale sur les Ressources des Jeunes, DREES-INSEE, 2014.

We rank young adults aged 18-24 in 2014 by parents' pre-tax income. The rank specification is used more commonly than the log of income to measure intergenerational mobility because it yields more stable estimates(Chetty et al., 2014). 2 Documents de travail du Centre d'Economie de la Sorbonne 2022.05RR (Version révisée)

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Some studies, like those by[START_REF] Lefranc | Intergenerational Earnings Mobility in France: Is France More Mobile than the US?[END_REF] andAlesina et al. (2018), suggest that France has a moderate to high level of social mobility, falling between the U.S. and Nordic countries or even paralleling Sweden. However, other research, such as by[START_REF] Corak | Inequality from Generation to Generation: The United States in Comparison[END_REF] and Perez-Arce et al. (2016), suggests that France has lower social mobility than one might expect, especially given its moderate income inequality. This inconsistency challenges the commonly accepted "Gatsby curve," which typically shows a negative relationship between social mobility and income inequality. Recent findings byKenedi and Sirugue (2023) and[START_REF] Sicsic | Who Climbs Up the Income Ladder? An Analysis of Intergenerational Income Mobility in France[END_REF] also highlight the persistence of income across generations in France, mirroring trends seen in the U.S. byChetty et al. (2014).

This literature has not yet produced a consensus on the magnitude of this effect.[START_REF] Taubman | Role of Parental Income in Educational Attainment[END_REF] finds that the elasticity of educational attainment with respect to parental income ranges from 3 to 80 percent, and[START_REF] Mayer | What Money Can't Buy: Family Income and Children's Life Chances[END_REF] reports that the average effect of a 10 percent increase in parental income on years of schooling ranges from 0.024 to 0.104 years. In France,[START_REF] Ben-Halima | Skill Premia and Intergenerational Education Mobility: The French Case[END_REF] show an increase in the effect of father's income on educational outcomes between 1993 and 2003 using a parental income variable estimated on the basis of other observable characteristics (father's occupation and education). We update and extend this work with a survey matched with tax administrative data, which allows direct study of the relationship between parental income and children's education, with no need to estimate parental income. 4 Documents de travail du Centre d'Economie de la Sorbonne 2022.05RR (Version révisée)

The importance of this transmission has been confirmed in France by recent studies (OECD (2018b),[START_REF] Herbaut | Inequalities in Access to Higher Education in France. Cumulative Advantage and Compensatory Advantage over the Course of Secondary Education[END_REF],[START_REF] Barhoumi | Les élèves sortent de l'enseignement secondaire de plus en plus diplômés mais au terme de parcours scolaires encore socialement différenciés[END_REF]). An important debate in this literature concerns the relative significance of nature and nurture in the intergenerational transmission of abilities. In a study of donor children in Denmark,[START_REF] Lundborg | On the Family Origins of Human Capital Formation: Evidence from Donor Children[END_REF] find that net of genetic skill transfers, only the mother's education matters in explaining the children's school performance. 5 Documents de travail du Centre d'Economie de la Sorbonne 2022.05RR (Version révisée)

Of students with a high school diploma (academic, technical or vocational) 75% enrolled in higher education; among those with an academic diploma, 99%. 6 Documents de travail du Centre d'Economie de la Sorbonne 2022.05RR (Version révisée)

These students account for just 3.4 percent of total enrollment in higher education[START_REF] Menesr-Depp | Repères et références statistiques -Édition[END_REF]. In 2014-2015, 39% of the students in preparatory courses had passed their high school graduation exam with highest honors -a GPA of 16/20 or better -compared with 3% of technical/vocational students and 6% of university students[START_REF] Bonneau | Quelle démocratisation des grandes écoles depuis le milieu des années 2000 ?[END_REF].

Order of August 12, 2014, setting tuition rates for public higher education institutions under the authority of the ministry of higher education (https://www.legifrance.gouv.fr/loda/id/ JORFTEXT000029409760/).

As highlighted by Dodin et al. (2021), administrative datasets, despite their vast sample sizes and the ability to link parents with their children, are often constrained by a paucity of variables, typically lacking insights into 7 Documents de travail du Centre d'Economie de la Sorbonne 2022.05RR (Version révisée)

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Some 67% of the young adults in the sample have their parents still living together. In 68% of these cases, the mother answered the parents' questionnaire.

The authors show that using a rank specification provides much more stable estimates of intergenerational mobility than using the logarithm of parental income and allows for the inclusion of zeros in parental income.

This household measure of income increases with cohabitation, to ensure that this feature does not generate bias, we present in Appendix C.3.2 a robustness test of our main results based on the sum of individual parental income -sum of the father's and mother's pre-tax income, regardless of marital status. 10 Documents de travail du Centre d'Economie de la Sorbonne 2022.05RR (Version révisée)

Direction de l'évaluation, de la prospective et de la performance (DEPP).

See Figure III Panel B of Chetty et al. (2014). 12 Documents de travail du Centre d'Economie de la Sorbonne 2022.05RR (Version révisée)

See table D9 in the Appendix for the details of all the coefficients on the control variables.13 Documents de travail du Centre d'Economie de la Sorbonne

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The 95% confidence interval for the coefficient of parent's income percentile rank on enrollment in higher education in France is[5.3 ; 6.3].

Table B4 details parental income distribution in both countries. In 2012 dollars, the standard deviation of parental household income is $353,430 in the U.S. compared to $45,640 in France. In 2014, the top income decile accounted for 46% of total income in the U.S. and 33% in France, respectively(https://wid.world/data/). 16 Documents de travail du Centre d'Economie de la Sorbonne 2022.05RR (Version révisée)

See Appendix B.2.3 for more details on this decomposition method.

Refer to table 2, p.5, in Ziol-Guest and Lee (2016) for detailed data.

In 1930, less than 7% of children aged 11-17 pursued education beyond primary school[START_REF] Isambert-Jamati | Crises de la société, crises de l'enseignement[END_REF]

One track catered to the upper classes (secondary education), while another track, established in the late 19th century, targeted the intermediate classes (upper primary education). Notably, restricted higher education participation remained, despite the late 19th-century educational laws and the 1930 provision for free secondary education.

We focus on the youngest to minimize the influence of completed schooling on aspirations.

The important correlation between lower aspirations and later educational inequalities has been documented in France by[START_REF] Guyon | Biased Aspirations and Social Inequality at School: Evidence from French Teenagers[END_REF].

Unequal enrollment in higher education is also associated with inequalities in lifetime earnings, which we approximate using recent estimates ofGarbinti et al. (2023) and differences in the degrees attained by young adults aged 22 or over in our sample. This other implication of the unequal enrollment is explored in Appendix D.4.5.

When taxes are not taken into account, the authors generally find that higher education spending is regressive.19 Documents de travail du Centre d'Economie de la Sorbonne 2022.05RR (Version révisée)

Conversely, when all the taxes paid by households are taken into account, the authors generally conclude that higher education spending is progressive, because wealthy people pay more in taxes than they receive in subsidies for public higher education. 20 Documents de travail du Centre d'Economie de la Sorbonne 2022.05RR (Version révisée)

See Appendix B.2.3 for more details on this decomposition method. 21 Documents de travail du Centre d'Economie de la Sorbonne 2022.05RR (Version révisée)

To match the public spending on higher education of those in the middle-income bracket (P50-P60), the enrollment rate for students from the bottom third of parental income distribution would need to rise by 19 percentage points. This required increase is only slightly higher than the current enrollment gap of 15 percentage points.

 32 This specification can be seen as an upper bound of inequalities in educational expenditure. See Appendix C.3.3 for more details on the assumptions made in this counterfactual scenario associating the wealthiest individuals with the best-endowed programs.

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A previous version of our study (see the French Council of Economic Analysis focus https://www.caeeco.fr/enseignement-superieur-un-acces-inegal-selon-le-revenu-des-parents) used older data from Chetty et al. (2014). The update of Chetty et al. (2020) including Pell Grant recipients who were not counted in the 1098-T data used for Chetty et al. (2014) makes the estimates of higher education attendance by parental income in France and the United States even more similar. 26 Documents de travail du Centre d'Economie de la Sorbonne 2022.05RR (Version révisée)

categories of occupation (TableB2), separately for father and mother. Parents' education is introduced in dummy variables for each of the 6 categories of degree (elementary school certificate or less, middle school certificate, high school diploma or equivalent, two-year degree, bachelor's or master's degree, and M.D. or Ph.D.), separately for father and mother. The family situation is introduced in 5 categories: parents together, separated, father unknown, mother unknown or parents unknown. Urban center size is introduced in three categories: Paris metropolitan area, urban center of more than 100,000 inhabitants, urban center of under 100,000 inhabitants. When the two parents do not live in the same urban center, we use the larger of the two.

In 2014-2015, on average, vocational programs cost e14,150 per student, preparatory courses e15,620 and university programs e10,980.

The survey is representative of institutions under the supervision of the Ministry of Higher Education and Research, although some institutions, notably certain engineering schools, are under the supervision of other ministries (Ministry of the Economy, Ministry of the Army, Ministry of Agriculture, etc.). Business schools are not included in the survey either. We therefore supplement this survey with specific data on the costs of business school students (https://www.cefdg.fr/fr/ecoles-et-formations-visees). On average, public funding covers about 5 percent of student costs for these private programs.

Bulletin officiel de l'éducation nationale n°18, 3 May 2012 (https://www.education.gouv.fr/pid285/ bulletin_officiel.html?pid_bo=26454)

Connaissance des coûts des activités des établissements d'enseignement supérieur et de recherche, DGESIP 2016-2019[START_REF] Boiteau | Le projet de connaissance des couts des activités des établissements d'enseignement supérieur et de recherche : retour d'expérience[END_REF]).

Refer to Appendix B.2.2.3 for more details on these new higher education cost data and TableB5for annual public spending per student, divided by field of study and track, the level of disaggregation we use.

For this analysis, we restrict our sample to individuals aged 22 to 24, who are the most advanced in their studies within our sample.

We would like to thank Bertrand Garbinti and Vladimir Pecheu for sending us custom data on lifetime earnings by gender and educational attainment.

 43 This older cohort was selected for its complete labor market trajectory, providing a comprehensive view of lifetime earnings, a perspective not yet available for our younger cohort (aged 19-24 in 2014).

Acknowledgements

This work was supported by the French National Research Agency Grant ANR-17-EURE-0001. We would like to thank Gabrielle Fack for most helpful and relevant feedback throughout this project, as well as Jérôme Gautié, Julien Grenet, Thomas Piketty and François-Charles Wolff for valuable comments. This paper also benefited from useful suggestions from Guillaume Allègre, Mathias André, Elvire Guillaud, Elise Huillery, Xavier Joutard, Gustave Kenedi, Chloé Lallemand, David Margolis, Michaël Sicsic, Louis Sirugue and Sander Wagner. We would also like to thank participants in the Applied Economics Lunch Seminar and PSIPSE Seminar at PSE, INSEE Internal Seminar, INED Coffee Seminar, IPP Internal Seminar as well as participants in the 69th Congress of the French Economic Association, the World Inequality Lab Conference #2, the 2022 LESE Conference, the 2022 Doctorissime Conference, the 2022 JMA Conference and the 2022 LAGV Conference for useful remarks. We would like to thank Bertrand Garbinti and Vladimir Pecheu for sending us custom data on lifetime earnings by gender and educational attainment. Lastly, we thank the French Council of Economic Analysis and the Ministry of Higher Education and Research for giving us access to data on higher education spending, and in particular Madeleine Péron, Hamza Bennani and Gabriele Dabbaghian for formatting the data and helping to interpret them.

(Institut National de la Statistique

Restrictions apply to the availability of these data, which were used under license for this study. Data are available from ADISP (Archives de Données Issues de la Statistique Publique) for the main databases (ENRJ 2014 and ERFS 2014 surveys), from INSEE

Appendix

Notes: This table summarizes the results of the empirical literature on the progressivity or regressivity of educational expenditures, obtained in various countries and institutional contexts. The "parental background" column specifies which parental social origin variable is used in the analysis (education level, occupation or income). The column "taxes taken into account" indicates whether or not the authors deduct the taxes paid by the parents (either partially or entirely) or not. The "higher education only" column specifies whether the analysis is devoted solely to higher education spending or to all education spending. Documents de travail du Centre d'Economie de la Sorbonne 2022.05RR (Version révisée)

The aggregate public spending on higher education is given by:

Where:

• y represents the total number of young adults in our sample;

• S HE j denotes the expenditures on completed higher education over 6-year period for the j th young adult;

• W eight j is the sampling weight allocated to the j th young adult in the ENRJ survey;

• n j=1 W eight j = Y ensures that Y corresponds to the total number of young adults in the broader population Taxes Financing Higher Education. The literature on distributed national accounting takes into account all taxes and redistribution that occurs through direct public support and indirect in-kind transfers (e.g., public financing of education or health). In our case, the way in which taxes are taken into account to study the redistribution of the public financing system of higher education is complicated by the fact that we are only interested one specific expenditure item, higher education expenditure. In contrast to what has generally been done previously in the literature, where taxes are considered as a whole, we decide to consider only unallocated taxes (those that participate in the financing of higher education) and only to the extent that they finance higher education. Deducting only the taxes needed to cover the expenditures under consideration, but extending the contributors to all taxpayers, is more consistent with the fact that: (i) parents of young adults are not the only taxpayers funding higher education, and that (ii) not all of their taxes are allocated to higher education. In contrast to life-cycle approaches focused on an individual, we consider a state that balances its higher education budget annually with unallocated tax funds.

We assume that higher education is funded by households through direct and indirect taxation and by firms through corporate taxes but not through direct contributions (as is the case, for example, with apprenticeships); nor is it funded by public debt. The taxes most likely to contribute to the financing of higher education are income tax, VAT, corporate taxes that are allocated to households, and other indirect taxes -tax on energy products (TICPE) and excise duties. We do not take into account social contributions, nor taxes dedicated to the financing of social security (CGS and CRDS). We also do not take into account local taxes, which contribute only marginally to the financing of higher education.

Our sample consists of parents of young adults. Since these individuals are not the only ones involved in financing higher education, we need to estimate the share of taxes to be considered out of sample. We use the 2014 Tax and Social Income Survey, 39 a representative sample of all taxpayers in France, for this purpose. 39 Enquête sur les revenus fiscaux et sociaux (ERFS), 2014

We calculate the total amount of unallocated taxes paid over six years by French taxpayers as follows:

Where:

• T axes all represents the total amount of unallocated taxes paid by all taxpayers over a six-year period, that will be contributing to the financing of 6-years of higher education;

• n is the total number of observations in the survey;

• IT i is the income taxes paid by i;

• V AT i the value added taxes by i;

• CT i the corporate taxes paid by i;

• E i the energy and excise taxes paid by i;

• W eight i the weight assigned to individual i in the ERFS survey;

• n i=1 W eight i = N ensures that N corresponds to the total number of taxpayers in the general population.

The total unallocated taxes paid by all French taxpayers over six years amounts to e1.50 trillion.

Proportion Needed To Fund Higher Education Expenditures. We calculate the share of unallocated taxes needed to fund public spending on higher education with the following ratio:

Share_T axes HE = S HE all T axes all (6)

Where:

• Share_T axes HE represents the share of taxes devoted to public spending on higher education for young adults;

• S HE all is the sum of total public spending on higher education devoted to individuals until 24 as derived in equation 4;

• T axes all is the sum of all unallocated taxes paid by all taxpayers over six years as derived in equation 5.

In total, 4% of all unallocated taxes paid by taxpayers must be devoted to funding the cost of higher education. This proportion is consistent with official data from national accounts. 40 40 The 2021 Finance Bill indicates an amount of e220 billion for the sum of the taxes we are considering here (VAT, income tax, corporate tax and domestic consumption tax on petro-leum and energy products) and e10 billion (4.5% of the tax revenue considered) for higher education excluding university research (see https://www.budget.gouv.fr/budget-etat/ for unallocated tax amounts and https://www.budget.gouv.fr/budget-etat/ministere?annee=118&loi_finances=50&type_ budget=all&ministere=34726&programme=30340&type_donnee_budget=ae&op=Valider for higher education spending). We cannot report these figures for 2014, the year of the survey, because government spending was not displayed broken down by spending item at that time.

in higher education, the participation rate for the bottom third would need to increase by an additional 19 percentage points to achieve a level of public spending on higher education equivalent to that for the middle income group.

We descriptively simulate the extend to which increasing higher education participation among the most disadvantaged would affect our lifetime earnings prediction. This simulation operates under the significant assumption that individuals from the most disadvantaged group, upon increased participation, would achieve the same level of educational attainment as current students from the bottom 30% of the income distribution. 44 Under this assumption, our findings suggest that the predicted lifetime incomes for this disadvantaged group would increase by 5.7%, and by 1.6% for young adults as a whole.

Consequently, the earnings gap between the wealthiest 30% and the least well-off 30% would decrease from a factor of 1.19 to 1.12. It is important to note that this estimate does not account for general equilibrium effects and assumes that the financial return to higher education would remain constant even with expanded participation. 44 Expanding access through a shift in early orientation could make this hypothesis more plausible. Ichou and Vallet (2012) found that students from less privileged backgrounds would have a 21 percentage point higher enrollment rate in academic and technical high school tracks if they had the same inclination to choose these tracks as upper-class students, after controlling for prior academic ability.

Appendix References