1Has the free (or virtually free) nature of pre-elementary, elementary, secondary, and higher education contributed to decreasing inequality? If there is no doubt about the answer in relation to compulsory education (up to age 16 in France), there is a recurring debate about the redistributive character of higher education, where the ratio of students from modest backgrounds remains relatively low. Free higher education would thus seem to bring about a transfer of funds from the poorest households, who pay taxes but do not benefit from public expenditures, toward better-off households, who benefit (or have benefited) from increased public spending on higher education. It is possible to imagine that taxpayers as a whole, including low-income households, finance the education of the most affluent households. Accordingly, the argument that the system of free higher education is regressive is regularly invoked as a justification for the demutualization of its funding.
2This paper considers the redistributive impact of public spending on education with financing taken into account. But how should we measure this redistributive impact? The answer to this question, while apparently simple, depends upon methodological and normative choices. The aim of this paper is to clarify the various difficulties related to definitions and the measurement of redistributive impact and to produce a redistributive balance sheet for cohorts emerging from the educational system in 2001 and 2002. To this end, we adopt a life-cycle perspective in accordance with which individuals benefit initially from education spending in their youth and then contribute to education financing when they become active and able to do so. In order to isolate questions of inequality and intra-generational redistribution, we hypothesize that each cohort should finance its own educational costs. In this way, we control for inter-generational effects. Another perspective would involve parents paying all (or part) of the cost of education, a view we would characterize as dynastic, in opposition to the individualist approach analyzed here, which was adopted for similar purposes in other papers (see, for instance, Hugounenq 1998). Finally, we work within a static framework and do not treat the question of the effect of financing upon length of study.
3In a first section, we discuss methodological questions and demonstrate how our approach relates to the literature about the redistributive impact of educational expenditures and the various techniques for modeling career paths and the life cycle. In a second section, we present our data, the academic paths of the cohorts we followed, and the public investments from which the individuals in our sample could have benefited. In a third section, we simulate a number of professional careers for each individual and we estimate a steady income so as to allow us to measure each individual’s contribution to educational financing as a function of his or her future income. However, this estimation of steady income is not purely deterministic as we add to the deterministic component of projected salaries a risk function calibrated to reproduce the salary dynamics measured from French panel data, using for this purpose the results of Magnac and Roux (2009).  In a final section, we present the principal results of our study, specifically the intra-generational transfers brought about by educational costs and financing.
4Given the various possible understandings of inequality, there is no single method for estimating the redistributive effects of spending. Calculating redistributive impact requires: (1) assessing the value of what is transferred; (2) assigning this value to individuals or groups of individuals (families, cohorts, etc.); and (3) classifying individuals and groups in order to compare the distribution of the transfer with an initial distributive hierarchy, for example in terms of income or standard of living. If the least advantaged individuals receive more or contribute less than the most favored in relative terms (absolute), we will conclude that the measure is progressive (or redistributive), but in the contrary case, that it is regressive (or anti-redistributive).
Evaluating Gross Spending on Education: Transfer or Investment?
5Every estimate of the redistributive impact of education spending initially assumes an evaluation of the whole of public education spending. This approach to the problem is rather similar to the evaluation of adjusted disposable incomes, which consists of adding to household disposable incomes the transfers in kind provided by public services such as healthcare, education, or housing (see Amar et al. 2008). But what value should be assigned to public services and to education in particular? A first approach, which is adopted here as in most of the studies that evaluate adjusted disposable incomes, involves measuring the value of these services at cost (Smeeding et al. 1993; Hugounenq 1998; Marical et al. 2006; Callan and Keane 2008). Another solution would be to measure the value of services in terms of their utility to consumers. Concerning education expenditures, this utility depends on individual differences in return on these expenditures. This brings us closer to the models inspired by Becker (1964, 1967, 1981), in which education expenditures should not be considered a pure transfer but rather an investment that can have a high rate of return. Lastly, another option is to measure the value of education as a service in terms of what its market price would be if it were provided by private entities. The difficulty here is to generate this counterfactual data.  Lacking supplemental information, we adopt a quantifiable logic in which the value of education is measured at 100% of nominal cost. A related hypothesis is that spending has an equivalent return, whatever its nature may be. This simplification allows us to give a value to cultural expenditures whatever the return might be in terms of salary and to treat each course of study equally without applying a discount for this or that kind of educational path. In this kind of model, educational expenditures are thus equivalent to a monetary transfer. This approach is instructive and could be implemented through a dynamic approach in which education is considered an investment and not simply a transfer.
To Assign and Categorize: A Familial or Individual Approach?
6There next arises the question of the distribution of this stock of human capital among individuals, groups, or families, taking one or several generations as the focus of study. Here again, several approaches are possible. Education expenditures can be attributed to families (parents) and measured according to the standard of living in the parental home. The underlying idea is that in the case of the demutualization of educational expenses, it would be families that would take charge of these expenditures. According to this logic, there is a perfect substitutability between public and familial transfers, and it is therefore the parents who benefit from public education spending. Hugounenq (1998) takes this approach to analyzing the French data. 
7Hugounenq also departs from the principle that education costs are equivalent to a transfer. Households are classified by standard of living percentile, taking into account the number of consumption units per household.  However, in this kind of approach, redistributive effects depend in large part on the size of the household. All else being equal, a household with two children will receive twice as much educational funding as a household with one child. Since households with many children generally have lower standards of living than households with few or no children, just as with other forms of spending targeted toward children, education spending is thus highly redistributive. Finally, this method measures the drop in standard of living that comes along with children rather than the redistributive character of education expenditures. For example, according to this method, the lower the family’s funds are, the more education spending benefits poor households, and the more it appears to be redistributive. If this method can be instructive, equally so is the analysis according to household size. One answer to this problem lies in comparing only households of the same size.
8Another option consists of attributing expenditures to individuals (public school and university students) and not to their families. Working with the French data, Albouy, Bouton, and Roth (2002) take this kind of individualist approach. The authors categorize individuals according to the standard of living of their parental household of origin. However, this approach is risky because the parental household’s standard of living depends on the number of children, and some of the siblings may or may not have already left home. Moreover, the age of leaving the parental home depends heavily upon the length of the children’s studies. The analysis of Albouy et al. relies on meticulous efforts to exhaustively reassign to each household the children who have left home, producing a more accurate view of the original standard of living.
Net Financing of Education Spending
9Like Albouy et al., we adopt an individualist approach. However, our aim is to complement this approach by taking account of the financing of education spending in order to calculate net educational expenditure. Accordingly, we rely on a life-cycle perspective in which individuals benefit from spending at the beginning of their life and then finance these transfers during their professional career. The implicit counterfactual to such an approach relies on the idea that in the absence of public financing of education, it would be the individuals themselves who would assume educational costs, for example through loans or parental financing, serving as anticipated deductions from the transmission of intra-familial capital.
10Our approach has a number of points in common with inter-generational accounting (Auerbach, Gokhale, and Kotlikoff 1991, 1994; Gokhale, Page, and Sturrock 1999; Chojnicki and Docquier 2007). In their two papers, Auerbach, Gokhale, and Kotlikoff are interested in the net contribution of a generation to the financing of public services and transfers dispensed by the US government. The task here is mainly to measure for a given generation the difference between transfer payments received and taxes paid within a life-cycle perspective for that generation. The aim is to measure the debts handed by one generation to succeeding ones. If the estimated difference between the net value of expenditures provided by the government and the taxes that contemporary generations are expected to pay is lower than the government’s net effective assets, there necessarily exists a financial need that future generations must cover through their taxes. The authors then calculate a permanent tax rate per generation (the average rate a member of a generation will have to pay throughout the course of his or her life) to determine whether certain generations, owing to budgetary choices made by their elders, will be forced to deal with higher tax rates than others. However, Auerbach et al. do not attribute the value of public education to its beneficiaries, that is, to the younger generations, even though human capital is transferred to them. Moreover, the authors recognize the perfectible character of this choice of model by admitting that there really is a transfer of assets taking place from active or working generations to those still in school. We can thus conclude that their estimate of an eventual average tax rate increase of 25 points by comparison to generations born at the start of the 1990s is largely overvalued. Moreover, it is this intuition that leads Chojnicki and Docquier (2007) to follow the logic of measuring inter-generational inequalities by relying upon and developing in a more complex manner an earlier model created by Gokhale, Page, and Sturrock (1999). The estimates of Chojnicki and Docquier lead to more modest values for the amount transmitted to future generations, estimating that an increase of 1.4 points in the average tax rate would be sufficient to sustain US public finances. The difference between the studies of Chojnicki and Docquier and earlier analyses stems from the fact that the former take into account the underlying increase in educational level, which offers hope for a downward trend in social transfers. Then again, in the three approaches cited, education paid for by working generations for those in school is never capitalized and passed down.
11The approach we propose is inspired by the ideas of Auerbach et al., notably that educational equity must be appreciated by means of the analysis of a complete life cycle by subtracting taxes paid from transfers received. Nevertheless, apart from this generational compatibility, our analysis is interested in intra-generational, not inter-generational transfers. In fact, we might speak of intra-generational compatibility. Just as with generational compatibility, our approach requires us to have a prospective vision that allows us to integrate an educational financing mechanism for the cohorts that stand to benefit. If this hypothesis is first and foremost a thought experiment that allows us to distinguish intra-generational from inter-generational effects, it has a theoretical justification in that it is customary and relevant to divide the investment cost over a period of use (through loans or amortization, for instance).
12We account for the financing of educational expenditures by estimating a permanent income for all of the individuals concerned, based on a cross-section. This necessitates understanding the salary dynamic at the heart of a cohort. To do this, we rely on models established through longitudinal data. Income inequalities can be broken down into permanent and temporary features. If inequalities are due to temporary shocks, permanent income inequalities will be weaker than the inequalities observed in a momentary cross-section. Here we are particularly interested in the connection between educational qualification and permanent income. In this context, a significant share of temporary features will have the effect of reinforcing the connection between qualification and permanent income. Conversely, if inequalities have a permanent character (for example, because they are tied to unobserved individual features, lasting accidental effects, or the initial choice of job sector), then the connections between qualifications and permanent income will be lower. The connection between qualification and permanent income has an impact on both the financial side and the classification of individuals.  The stronger the ties, the more the individuals who benefit from education spending will be those who finance it. At the extreme, if qualification and permanent income were perfectly correlated and the tax rates allowing for the financing of educational expenditures were equal to the apparent return on supplemental educational spending,  then education spending would have a zero redistributive impact as spending would then be financed according to a contributive logic.  Similarly, the stronger the links between qualification and permanent income, the more those individuals with the highest permanent standards of living would benefit from education spending, indicating an apparently regressive effect of gross education spending. Conversely, if the links are weak, a significant part of education spending would then benefit individuals with a lower permanent standard of living, and this would appear more progressive when individuals are classified according to permanent standard of living.
13Thus the establishment of a pattern for career dynamics and the temporary or permanent character of changes play a significant role in a life-cycle approach. Many studies have estimated these salary dynamics from longitudinal data, both French and foreign (Abowd and Card 1989; Lollivier and Verger 1999; Koubi 2003). Lillard and Willis (1978) generate a salary equation from Mincer (1974) and incorporate into the model the error term that includes a permanent proportion due to unobserved individual differences (talent, effort level, physical capacity) and a temporary proportion based on autoregressive model of order 1 representing the more or less lasting impact of accidents. The authors conclude that 73% of the logarithmic salary variance relates to permanent differences, 4% is tied to serial correlations, and 23% is purely stochastic. Using the same method applied to French data, Colin (1999) estimates that 62% of the residual variance is due to permanent individual differences and that serial correlations represent a nearly null portion of variance. Magnac and Roux (2009) assess several ARMA (Autoregression and Moving Average) models authorizing auto-correlations up to order 4. According to the models tested, the permanent portion of variance varies between 60% and 63%. In the model retained by Magnac and Roux and which we take up in this paper, namely ARMA (4.2), the proportion of variance due to constant heterogeneity is 61%. The authors conclude that there are few differences between qualifying groups.
14The weak link between educational qualification and permanent income may be due to individual choices, for example if it results from choices between more or less remunerative fields, or to greater or lower effort levels on the part of those who graduated. In this case, the redistribution effected by education spending hardly seems justified. At the same time, the weak link between qualification and permanent income may be due to external factors (such as the lasting impact of an accident, discrimination, or the role of social capital in the determination of positions). In this case, redistribution would seem justified. Since our study does not aim to distinguish between these two mechanisms, we will not be in a position to offer normative conclusions.
Contributions of the Study
15The chief contribution of our work does not bear specifically upon the description of public spending in relation to original standard of living (the conclusions of studies focusing on France converge on this point, and this in spite of the different periods under consideration). Rather, it stems from the association between this descriptive study and a model of permanent income for those leaving the education system, which then allows for a prospective calculation. This enables us to integrate the financing of education into our analysis. The calculation of a transition matrix between quantiles allows us to additionally provide an original estimate of social mobility in terms of income. The literature on this subject (Shea 2000) effectively demonstrates not only that parental income is correlated to their children’s accumulation of human capital but also that the permanent income of parents is correlated to that of their children (with a coefficient of 0.4 in Shea’s study), which suggests, for example, that credit constraints restrict the children of the poorest families in the pursuit of studies to their fullest natural potential over and above any transmissions of social or human intra-familial capital.
Characteristics of the 2001 and 2002 Cohorts
16We utilize the data from the 2003 Taxable Income Survey (Enquête Revenus Fiscaux – ERF). This survey matches individuals from the Employment Survey from the 4th quarter of 2003 with their tax return. The ERF has many advantages. The sample is representative of the French population, the fiscal component gives us reliable information about household incomes, and the employment component gives us information about educational qualifications and age at completion of study for individuals over 15 years of age.
17Our sample is comprised of 1,872 individuals who completed their initial schooling in 2001 and 2002, the last two full yearly cohorts included in ERF 2003. This sample is representative of 1,341,888 individuals. We define our cohorts by the last year of study of the individuals in our sample. We thus compare individuals who are confronted with the same economic conditions throughout their active work life. Another solution would have been to undertake the same analysis for birth cohorts, that is, individuals who were born in the same year. However, the decision to use end-of-study cohorts was made for methodological reasons. In order to estimate the educational expenditures relative to individuals of the same generation, we have to wait until all of the individuals have finished their initial schooling, which necessitates the choice of an older generation. Unfortunately, the older the generation, the more fragile its connections to family origin (because of lower rates of cohabitation). Using the 2001 and 2002 cohorts thus appeared to strike a good compromise from a methodological standpoint: we have complete information about qualifications, family origin for sampled individuals still living with their parents, and entry into the job market for the entire sampled population. This allows us to describe net educational transfers according to the status of the parents but also according to estimated permanent salaries.
Educational Characteristics of the 2001 and 2002 Cohorts
18Tables 1 to 3 present the educational paths of the individuals in our sample. While 51.4% of middle-class children obtained a higher education degree, only 11.2 % of working-class children and 23% of the children of salaried workers reached this level, which confirms the extent of the inequalities of access to higher education cited at the outset.
Highest Degree Earned, Frequency, Weighted Frequency, and Percentage
Highest Degree Earned, Frequency, Weighted Frequency, and PercentageDomain: Initial schooling, classes of 2001 and 2002.
19Table 2 supports the theoretical possibility that the most-modest social classes finance the education of the children of the most-well-off classes, taking into account the inequality of access to long-term studies. However, it is useful to distinguish between compulsory education, the cost of which is by nature progressive provided that financing is positively correlated with income, and post-compulsory education, in which case social selections creates a potentially anti-redistributive scenario.
Highest Degree Earned, by Father’s Socio-professional Status
Highest Degree Earned, by Father’s Socio-professional StatusDomain: Initial schooling, classes of 2001 and 2002.
20To better describe the social situation of each individual beyond simply the socio-professional status (SPS) of the father of the family, we construct for each former student from the 2001 and 2002 cohorts a classification that reflects the family’s standard of living at age 16 (the original standard of living), and then calculate a permanent income that corresponds to the value of that person’s actual salary averaged over the course his or her professional career. Next, we calculate the educational expenditures and net financial transfers for all of the individuals in our sample in order to measure the redistributive nature of the school system.
Classification according to Original Standard of Living
21Of the 1,872 individuals in our survey, 933 (49.8%) are still members of their parents’ household. As a first step, we estimate a parental standard of living for these cohabitants at 16 years of age. Then building upon these estimates, we assign a parental standard of living for all the individuals in the sample (cohabitants and former cohabitants, i.e., those who were [or no longer were] living together according to their parents’ socio-professional status [SPS]).
22In practice, we calculate an initial parental income by subtracting from the initial household income any wages or unemployment benefits of the children. Next, we divide this initial income by the number (units of account) of adult spouses in the household (1 if the child lives with one parent without spouse, 1.5 if the child lives with one of the parents or with the parents as a couple). We adjust this standard of living according to the age of the individuals in order to reflect the original household situation for the individual at age 16.  Thus the parents of older graduates enjoy a higher initial income thanks to greater professional experience on average.
23For all of the individuals in the sample, we predict the parental standard of living using a regression analysis that links the standard of living of the cohabitants with the SPS of the father and mother. The predicted parental standard of living is 12% higher for former cohabitants compared to cohabitants. It can be observed that the former cohabitants on average come from better-off households, which indicates that cohabitation may also be a response to limited familial resources. Table 3 shows higher education levels attained according to quintile of parental standard of living. In accord with intuition, higher education degrees are more accessible to children from better-off homes, with children from the richest 20% of households having four times the likelihood of earning a higher education degree than do children from less-well-off households.
Highest Degree Earned by Quintile of Parental Standard of Living
Highest Degree Earned by Quintile of Parental Standard of LivingDomain: Initial schooling, classes of 2001 and 2002.
Estimation of Permanent Professional Income
24Our next stage of analysis involves estimating a permanent professional income for the individuals in our sample. Here, we estimate an equation for annual salaried income for non-students and non-retired individuals in the Taxable Income Survey (ERF) with up to 40 years of experience. We proceed separately for men and women in order to eliminate problems of heteroscedasticity linked to gender.
25Our salary equations take the following form:
27where REVSALi is the annual salaried income (including payments, wages, and unemployment allowances, agricultural, industrial, and commercial and non-commercial income) of the individual i; FR a dichotomous (binary) variable indicating whether or not the individual is of French nationality; TU5 the urban unit grouping divided into five segments measuring a region’s population density; CSPP the SPS of the father, in five segments; DIPL the graduation status, in fifteen categories; EXP the number of years since completion of initial schooling; EXP01 a variable of value 1 for individuals with only one year of experience and 0 for others (as the effect of experience is not linear in the first year, with income growing rapidly at career start); and r the remainder. We use a quadratic specification that allows for an increase in productivity in the early years after a year of experience and then for a decrease before becoming negative at career end. The cross-variable EXP x DIPL refers to the productivity of experience depending on graduation status. The variance in salaried income thus explained is relatively weak (adjusted R2 is 0.42 for men and women), which underlines the importance of unobserved variables in the determination of salaried incomes along with the risk that surrounds the probability of employment for each worker.
28We estimate not potential salary but expectation of salaried income, taking into account periods of unemployment and inactivity. One shortcoming of this method is the retrospective nature of the data we use with prospective intent as this poses a problem when it comes to describing career end for the 2001 and 2002 cohorts. In effect, we attribute to these cohorts a career profile similar to that of the generation currently at career end, which rules out interpretation of certain intergroup differences when the job market situation has changed a great deal during that period (especially when comparing men and women).  We therefore make the implicit assumption that the outcomes of education are constant. Yet the outcomes of an educational degree for career end could significantly change thirty years on from now as a result, for example, of technological innovations capable of increasing the return on education. Conversely, the broadening of higher education might reduce the gap between variously educated populations. We must therefore keep in mind the hybrid character of our method: if it is based on a prospective calculation, we must rely upon education expenditures and returns observed today cross-sectionally.
29Because of the relatively weak variance explained by the salary equation, the reconstitution of salaried careers starting with a cross-sectional salary equation requires the formulation of hypotheses about the remainder of the salary equation. In our salary predictions, to suppose that the remainder is null would amount to constructing a deterministic model of salaried careers and would give too much weight to explanatory variables (especially to the educational diploma) and underestimate salary mobility. Moreover, salaries being estimated logarithmically, it is important that projected salaries have a variance that conforms to what is observed in real data in order not to create bias through the logarithmic operation.
30We reconstitute real variance in projected salaries with the most parsimonious model possible. The salary of individual i with experience t has two components: one deterministic component equal to the prediction of the salary equation (1), and a stochastic component (ui + vit) such that:
32where xitβ is equal to the prediction of the salary equation (1); ui is a stochastic variable representing the constant individual component; and vit is a variable component (noise). The variables ui and vit are independent of each other and of regressors xit.
33Next, we need to understand the role of variance due to the constant heterogeneity of the total variance of the remainders: α = σ2u /(σ2u + σv). This role depends on the significance of unobservable individual characteristics (i.e., the professional talents of the individuals, the enduring aspect of their commitment to professional life, their willingness to exert effort, etc.) in relation to salary dynamics along with the persistence of shock events. As this parameter is not observable in a cross-section, we must estimate it with longitudinal data. As a central scenario, we use the estimate of the proportion of the variance due to constant heterogeneity from Colin (1999) and Magnac and Roux (2009) based on French data, or around 60%. We also test the robustness of our results as this parameter varies.
34In practice, we calculate the deterministic component of salaries for each individual and each of the 40 years of that individual’s professional career. The variance of the stochastic component (ui + vit) was deducted from the variance of the remainders of the salary equation (σ2r). We draw an individual random effect ui in a normal distribution with zero mean and with a deviation (variance) of σ2u = α * σ2r. Next, we draw for the 40 years of professional career a variable for vit with zero mean and deviation of σ2v = (1-α) * σ2r. These remainders are added to the individual random effect as well as to the deterministic component of salary.
35The permanent income for each individual i is then equal to the average of that individual’s actual salary estimated over a career span of 40 years. We keep the following parameters in projecting salaries and incorporating the flux of future taxation, that is, an average salary growth of 1.0% based on real structural growth in Gross Domestic Product (GDP) of 1.8%, as observed over the past 20 years, while lessening this growth to account for demographic effects of 0.5% per year, the increase in the average standard of education, and finally from the aging of the working population. All of these factors lead us to predict an individual growth in productivity and salary lower than the change in GDP observed retrospectively.
36We actualize the changes in real interest rates (net of inflation) from 3, the average of rates without risk at different maturities over time in recent years. We use the same rates of actualization for income and taxes.  By using the same actualization rates for all individuals and for the state, we abandon trying to distinguish a rate of time preferences for individuals. At this stage, we consider this option acceptable in the absence of solid analysis of different rate of time preferences or of their lasting effect at the age when studies are completed. To the extent that our income projections are made over 40 years, we cannot claim to be able to model a rate of time preferences for all of the individuals in a generation across the whole of their working lives.
37Our results are not very sensitive to the chosen actualization rate to the extent that we are interested here in intra-generational inequalities and therefore in the differences between individuals in terms of actualized income. The estimated actualized income level of our individuals depends heavily on the rate of actualization but not the relative incomes of the individuals of the same cohort. We used an equal rate (still 3%) to actualize the costs of education assigned to students over the course of their studies by supposing that the costs of learning change in sync with GDP (in conformity with a Baumol effect, which is equivalent to hypothesizing a stable relative buying power on the part of the students) and that the amount borrowed from the state is constant in the long term. Once again, a relaxation of these hypotheses would have only a minor impact on the measurement of intra-generational inequalities. The last section presents our sensitivity calculations. Figure 1 presents average salary progression by degree level, and Table 4 presents average permanent income for individuals by qualification level. These two illustrations suggest the existence of clear returns on education, in particular the highly remunerative nature of higher education even after just two years of post-secondary education.
Average Salary Progress by Degree level
Average Salary Progress by Degree level
Actualized Permanent Income (in euros) by Degree
Actualized Permanent Income (in euros) by Degree
38Table 5 illustrates the limits of social mobility in France since the average permanent annual income of the individuals from the 1st quintile of parental income is €7,000 lower than for those in the 5th quintile. Over the course of a professional career (40 years), the difference comes close to €300,000 (€287,960). This confirms the persistence of inequalities between “family dynasties” as young adults from backgrounds below the median income level have a future salary expectation that is clearly inferior to that of young adults from more advantaged backgrounds. Moreover, this demonstrates (if there were need to do so) that unequal access to higher education and especially to the most remunerative degree programs as well as the weakness of social networks at the lowest levels create a great deal of inertia.
Actualized Permanent Income by Quintile of Parental Income
Actualized Permanent Income by Quintile of Parental Income
39Table 6 represents the transition matrix between original standard of living and permanent income. The domain used is individuals who were between five and fifteen years beyond initial schooling. These groups are both close to the cohorts studied and have been on the job market long enough for their SPS information to be gathered.
Social Mobility Matrix in Terms of Income – Quintile of Permanent Income by Quintile of Parental Standard of Living
Social Mobility Matrix in Terms of Income – Quintile of Permanent Income by Quintile of Parental Standard of LivingKey: 5.3% of individuals are in the 1st permanent income quintile and come from the 1st quantile of parental standard of living; 26.0% of individuals coming from the 1st quintile of parental standard of living are in the 1st quintile of permanent income; 26.9% of individuals from the 1st quintile of permanent income come from the 1st quintile of parental standard of living.
Domain: Individuals 5 to 15 years beyond initial schooling and with professional experience.
40The distribution of individuals in this matrix can serve to measure social mobility. For example, the more individuals fall on the diagonal of the matrix, the weaker the social mobility since these individuals have the same relative standard of living as their parents. A first measure of social mobility consists therefore in determining the number of persons on the diagonal of the matrix, with 25.3% of individuals being immobile from the standpoint of permanent income while 33.6% are immobile from the standpoint of social categories. The number of individuals expected to fall on the diagonal of the monetary matrix is 20% (= 5 x 0.2 x 0.2). The surplus of monetary immobility is thus 5.3%.
41It is interesting to note, as shown in Table 6, the asymmetry between the probability of being poor when one is born poor (26%) and the probability of remaining rich when one is born rich (33.8%). This is possible only because the middle classes (3rd quintile) are at greater risk of social descent than of rise. Moreover, individuals from the 2nd quintile have less than a one-in-two chance of moving upward by even one quintile in spite of an already favorable position, which might explain the general sense of weak social mobility.
Gross Education Spending and Net Transfers by Student
42In order to measure the net financial contribution of each individual in the education system, we next assign each individual in our sample an educational expenditure as a function of that individual’s age at completion of studies and scholarly path as reported in the Taxable Income Survey (ERF). Educational expenditure is the sum of the notional cost of a course of study and a repeat cost (for repeated years). Table 7 shows the average annual spending by high school student and by university student in 2002. Higher-education spending depends heavily on the course of study chosen. Spending per student in preparatory classes at the Grandes Écoles (€11,910) is 75% higher than spending per university student, except for those studying in Institutes of Technology (IUT) and engineering (€6,840).
Average Annual Spending (in euros) by School and University Student in 2002*
Average Annual Spending (in euros) by School and University Student in 2002** sts: Sections de Techniciens Supérieurs; cpge: Classes Préparatoires aux Grandes Écoles; iut: Institut Universitaire de Technologie; bep: Brevet d’Études Professionnelles; bts: Brevet de Techniciens Supérieur; deug: Diplôme d’Études Universitaires Générales.
43Table 8 presents the cost of several kinds of schooling. The total costs of education are actualized at the rate of 3%, as justified in the central scenario above. For repeating students, we assign a cost for each repeated year equal to the average annual cost of one year of that individual’s schooling.
Average Educational Expense (in euros) by Degree Level
Average Educational Expense (in euros) by Degree Level
44Table 8 also shows the assigned spending for education beyond compulsory schooling. On average, students who obtain a higher-education degree are seen to have been assigned total educational expenditures nearly twice as large as those of students who leave the education system without graduating. The educational cost of studying beyond 16 years of age is more than three times greater for students who graduate compared to those who receive a Professional Aptitude Certificate (CAP) (€95,716) or a Junior Secondary Education Certificate (BEP) (€30,370).
45Next, we attribute to each individual a financing cost for educational spending. In our central scenario, we hypothesize financing proportional to the individual’s permanent income by supposing that each generation finances its own educational expenses and that the financing of education is evenly distributed. The hypothesis of proportional financing corresponds to the simplified form of taxation curve in France for most households, taking into account Supplemental Social Security Contributions (CSG) and Value Added Tax (VAT).  In the central scenario, the proportional tax rate is equal to the sum of educational expenditures divided by the sum of salaried income actualized across the whole of the professional career, or 18.1%. This rate may seem significant and appears to exceed the budgeted costs for education. However, let us note that education is financed by salaries alone (and not by the total revenue of the economy).
46Tables 9a and 9b present net education spending (total spending and non-compulsory educational spending) financed according to degree level. They show that on average, workers with a higher-education degree finance the educational expenses of other workers thanks to their higher salaried incomes. However, if we focus on non-compulsory studies, the situation is reversed. The net contribution of individuals without a degree is around €15,000 (or close to €20,000 in the case of the General Education Certificate (Brevet du Collège), whereas higher-level students benefit from a transfer subsidy of around €4,000 (or €8,000 for graduates of short-term post-secondary studies). This table illustrates the problem of equity between individuals who completed their studies and those who did not. If we consider education as a private good (or a benefit in kind), the educational system and its financing operate as a transfer between those who study in the short term and those who study over the long term. Some workers who pursued short-term study but earn high incomes thus subsidize individuals who pursued long-term studies from which the monetary payoff is less than the average (for example some types of teachers and the cultural professions as well as individuals who fall victim to discrimination in the job market).
Net Transfers by Educational Level; Proportional Financing
Total Spending** (in euros)
Total Spending** (in euros)Key: A negative sign indicates a net contribution.
Educational Spending (in euros) beyond Age 16**
Educational Spending (in euros) beyond Age 16**Key: A negative sign indicates a net contribution.
Net Transfers by Educational Level; Proportional Financing
47Workers obtaining only a General Education Certificate also seem to be net contributors to the educational system thanks in particular to the lower amount of educational expenditures involved as well as to their incomes being equivalent to those with a Professional Aptitude Certificate (CAP) or a Junior Secondary Education Certificate (BEP). Nonetheless, the weight of this specific aspect of our results is put into perspective by taking into account the weak numbers in this population category.
Redistributive Impact of Education Spending and Its Financing
48Tables 10a and 10b represent the net average transfer resulting from total education expenditures. Given the weight of compulsory schooling, the expenditures naturally appear redistributive. The weight of these transfers in relation to average permanent income is therefore not negligible.
Actualized Net Transfers (Total Education Expenditures) by Parental Standard of Living (in euros and as % of Average Permanent Income)**
Actualized Net Transfers (Total Education Expenditures) by Parental Standard of Living (in euros and as % of Average Permanent Income)**Key: A negative sign indicates a net contribution.
Actualized Net Transfers (Total Education Expenditures) by Permanent Standard of Living (in euros and as % of Average Permanent Income)**
Actualized Net Transfers (Total Education Expenditures) by Permanent Standard of Living (in euros and as % of Average Permanent Income)**Key: A negative sign indicates a net contribution.
49Tables 11a and 11b are more revealing in that they concern educational expenditures past the age of compulsory schooling (16 years) by quintile of parental standard of living and by quintile of lifelong individual income. Table 11a shows that net of financing, education spending is neither significantly distributive nor significantly anti-redistributive. Table 11b reveals another facet of the situation, namely that in the life-cycle approach: it is really the wealthiest individuals that finance the education of the less advantaged. Throughout the life cycle, the net contribution of individuals from the first quintile is around €27,000, while the less-well-off benefit from an actualized net transfer equal to around €13,000, which corresponds to 4.2% and 2.0% (respectively) of average permanent income.
Actualized Net Transfers (Education Spending past 16 years of age) by Parental Standard of Living (in Euros and as % of Average Permanent Income)**
Actualized Net Transfers (Education Spending past 16 years of age) by Parental Standard of Living (in Euros and as % of Average Permanent Income)**Key: A negative sign indicates a net contribution.
Actualized Net Transfers (Education Spending past 16 years of age) by Permanent Standard of Living (in euros and as % of Average Permanent Income)**
Actualized Net Transfers (Education Spending past 16 years of age) by Permanent Standard of Living (in euros and as % of Average Permanent Income)**Key: A negative sign indicates a net contribution.
50This reflects (among other things) the fact that with financing proportional to incomes, individuals with the strongest incomes finance for equal educational expenditures those with lower incomes. Possession of a degree is not the only factor explaining income differences, which are also affected by effort levels, choice of job sector, professional talent that may not be reflected in the degree itself, regional inequalities, job market discrimination, social networking, and even luck. Compared to a mode of financing proportional to income, the financing of an individual’s educational expenses would thus be unfavorable for those who make the least effort, who choose a job sector where the monetary reward is lower, and who are less talented, but also those who face discrimination in the job market, who have less social capital, or are the most unlucky. The judgment as to the just or unjust character of such a reform will therefore depend on the way in which inequalities take shape in the job market (in terms of choice and effort versus luck and social reproduction).  Loan systems that make repayment contingent upon income allow us to take account of the individual cost of studies pursued as well as the incomes achieved by former students in the job market (see, for example, Trannoy 2006).
51It will be noted that the two modeling options adopted here have a notable impact on the results. We supposed above that each student receives for the same kind of scholastic career an education of the same value regardless of that student’s original social status. Yet we might argue that students from privileged backgrounds actually benefit from a costlier and higher-quality education at the elementary, secondary, and/or post-secondary levels.
Robustness of the Results
52It should also be noted that if from the life-cycle perspective, it is those who are the most economically successful who ultimately finance the studies of the rest, this outcome depends on the modeling of social and economic life variables we simulate here in parameter α. Had we not simulated these variables (unequal distribution of talent and abrupt changes in temporary income, or shocks, such as loss of employment), then the children of more affluent households, because they are clearly more educated and earn more degrees on average, would still be the net beneficiaries of the education system. Table 12 presents the results that would have emerged with different choices for parameter α.
Net Transfer (Educational Spending beyond 16 Years of Age) by Quintile of Permanent Income as a Function of Choice of Projected Salary Variable in the Models
Net Transfer (Educational Spending beyond 16 Years of Age) by Quintile of Permanent Income as a Function of Choice of Projected Salary Variable in the ModelsKey: A negative sign indicates a net contribution.
53The table shows that our results are relatively robust in the choice of modeling for the variable for a relatively wide range of alpha (α). Indeed, the conclusions would not be very different if we used the estimate of Lillard and Willis (1978) for US data (α approximately equal to 0.75).
54Table 13 presents our results in light of a more progressive taxation scenario than simply proportional taxation. A taxation curve close to that of France (Column 1), that is, lightly progressive, does not substantially modify our results as the public financing of non-compulsory education remains barely progressive but becomes so if individuals are classed according to their permanent income. On the other hand, more progressive taxation (Columns 2 and 3) allows for appropriate redistributive effects, whatever perspective is adopted.
Net Transfer (Education Expenses after 16 years of age) by Quintile of Permanent Revenue as a Function of Adopted Fiscal Structure
Net Transfer (Education Expenses after 16 years of age) by Quintile of Permanent Revenue as a Function of Adopted Fiscal StructureKey: A negative sign indicates a net contribution.
55Intuitively, factoring in the weight of compulsory schooling, overall education spending appears progressive. In particular, it reduces inequalities linked to social origins (Table 10a). In this paper, we demonstrate that in terms of life-cycle logic and taking financing into account, non-compulsory educational spending constitutes a net transfer from the highest segments to the lowest segments of the population when the income strata is defined in terms of actualized income across a whole life span (Table 11b). If individuals are grouped according to their permanent income, we readily perceive that those with higher incomes finance the studies of those with lower incomes. Let us recall that the perspective adopted here is inter-generationally balanced, with each generation reimbursing ex post the initial cost of its studies. In actuality, it is possible that inter-generational balance sheets are imbalanced and that one generation leaves a deficit to those that follow. If parents participated in the financing of studies, we would be able to see other redistributive effects, to the detriment of childless families. The perspective we adopt here allows us to highlight individual inter-generational inequalities other perspectives (inter-generational or inter-familial) would have kept hidden.
56Another question concerns equity between individuals who pursue studies and those who do not. Here, too, education spending constitutes a transfer between graduates and non-graduates (Table 9b). If education is considered an investment that profits chiefly those who receive it, the transfer resulting from non-compulsory education spending could be considered unjust. Those who have high incomes but did not receive much education finance the studies of others, the more so as these are drawn out and as their beneficiaries ultimately have more modest incomes. Conversely, if education is characterized in terms of important social benefits, a large part of it becomes a public good, the just financing of which can be based on incomes and not on the costs of education to individuals.
57In the case of non-compulsory education, many uncertainties remain, to the extent and in the sense that supplementary hypotheses might modify our conclusions, for instance by showing that children from privileged households also benefit from higher-quality education (through the selection of better teachers, a peer effect), or by supposing that they are less exposed to risks in their professional life. In both of these cases, higher education and its financing could be revealed as regressive, life-cycle perspective included. Nevertheless, whatever the adopted modeling hypothesis, the transfers resulting from such a public spending schema connected to financing produces fairly weak effects, which might justify at most a few hundred euros per year of tuition for students from the two most affluent quintiles. In a general sense, financing a public service through taxation even when the service is rather unevenly distributed and the tax is not progressive produces redistributive effects when we adopt a life-cycle perspective. Transfers in kind financed by a proportional tax can thus lessen inequalities even when these are not aimed at the poorest segments of the population.
58To conclude, as a matter of fairness, priority should be given to policies that favor equal access and equal success (given identical talent) in matters concerning higher education. It is essential to reduce the differences in scholastic and professional career achievement as a function of one’s original social environment. According to our calculations, the net actualized difference in the value of expected income for a full-time job is nearly €300,000 for an individual from a home in the first quintile versus someone from an upper-income home (Table 7).  Clearly, a portion of this discrepancy is tied to the greater interest in (private) education on the part of the better-off. Yet even in this case, it is difficult to defend the situation entirely. Net transfers resulting from educational expenses beyond 16 years of age are one-hundredth (or €2,500) of the difference between the first and the last quintile of parental standard of living (see Table 10) and therefore negligible. Moreover, the sum involved in the difference in net transfer between higher education graduates and non-graduates, at less than €20,000 (Table 9b), is less than one-tenth of the difference in terms of access to education. The question of fairness in relation to raising tuition rates thus risks being transformed into a veil that masks—intentionally or not—a major inequality: that of unequal access to spaces that are already unequal. Moreover, an increase in tuition and a move toward the private financing of higher education would become significant levers of social exclusion to the extent that credit constraints would in all likelihood weigh most heavily upon those who are already the most disadvantaged. Although loan repayments made contingent upon professional success respond to this problem as well as to the inequality of education financing that exists between students and non-students, it seems that the base financing of higher education must rest upon traditional financing through taxation (of incomes), whether proportional or progressive. The main objective must thus be to reduce the gap education today opens up between individuals from different social backgrounds.
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The authors would like to thank their colleagues at OFCE as well as two anonymous referees for their suggestions and critiques. The authors are responsible for the opinions expressed in this paper and for any errors that may remain.
Magnac and Roux (2009) estimate a dynamic for salaries of the ARMA (4.2) type. In our projection, which extends over 40 years, only the permanent component of variance not explained by observed variables is relevant. In this paper, redistributive effects come only from the net actual value (NAV) of permanent income, and yearly shocks in relation to the general trajectory, even when correlated, have no significant impact on our results when added and actualized over 40 years.
Although the question is complex, it is possible to imagine that for the same quality of education, the tuition charged by Institut Henry IV in Paris would be higher than that of an institution in (underprivileged) La Courneuve. Private institutions would probably pick up a portion of the revenue tied to peer effects. Moreover, if current teachers in highly regarded schools were perceived as being better, they would command higher salaries in a competitive market. Finally, tuition should reflect the difference between property values in central Paris and in (suburban) La Courneuve.
The study relies upon the Budget des Ménages 1994 (Household Budget) survey (INSEE).
This assumes the use of an equivalence scale. The general scale used, which we retain here, is the Oxford scale: 1 unit of consumption for the first adult, 0.5 for the second member of the household, and 0.3 per person from the third, and so on.
This is the case when these individuals are classed by decile of permanent standard of living. We propose alternativer classifications, namely parental standard of living and graduation status.
We can define this as the return value of a supplemental euro of education spending (Se) in terms of permanent income (Ip): ΔIp/ΔSe.
In this case, if the apparent rate of return for supplemental spending on education is lower than the tax rate, the spending would be regressive; if it is higher, the spending would be progressive.
As an actualization factor, below we use the relative coefficient of experience in the estimated salary equation but across the totality of our sample and thus obtain a value of 1.0164, which is very close to the growth in productivity.
Let us also note that we use a cross-section where effects of experience and cohort are combined in order to estimate a longitudinal profile.
We tested many actualization rates. Our results are only minimally susceptible to this rate due to the hypothesis of the self-financing of educational costs by each cohort.
We tested other financing possibilities that are more progressive and that lead mechanically to making the public financing of education more redistributive. Two variants are presented in the section entitled Robustness of the Results.
Such a reform should also be assessed according to its incentivizing and dis-incentivizing effects, as suggested by Heckman, Lochner, and Taber (1988).
The permanent income of an individual whose parents are part of the most-well-off 20% is €895,000 (or 22,370 x 40) as opposed to €607,000 (or 15,171 x 40) for individuals whose parents are from the least-well-off 20%.