A good career or a good marriage: The returns of higher education in France

Economic Modelling 57 (2016) 221–237

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A good career or a good marriage: The returns of higher education in France Pierre Courtioux a,⁎, Vincent Lignon b a b

EDHEC Business School, EDHEC, Paris Campus, 16–18 rue du 4 Septembre, 75002 Paris, France CNAF and Centre d'Economie de la Sorbonne, Université Paris 1 Panthéon Sorbonne, Caisse Nationale des Allocations Familiales, 32 Avenue de la Sibelle, 75685 Paris Cedex 14, France

a r t i c l e

i n f o

Article history: Received 28 October 2015 Received in revised form 18 March 2016 Accepted 15 April 2016 Available online 20 May 2016 JEL classifications: J12 J24 C63 Keywords: Higher education Marriage market Dynamic microsimulation Assorted mating

a b s t r a c t Following human capital theory, investment in education generates two kinds of returns: labour market returns and marriage market returns. Based on a dynamic microsimulation model, this article proposes a decomposition of these two effects for France and discusses the financial incentives of enrolling in higher education. Results show that the incentives stemming from the marriage market are negligible for men. By contrast, for women, the marriage market effect corresponds to almost 1/3 of the median return of higher education. Moreover, the marriage market does play an insurance role concerning the returns on tertiary education. It increases the risk of not capitalizing on higher education for both men and women, because marriage adds the uncertainty of the partner's career to the uncertainty of an individual's career. However, the risks relating to the value of this education investment remain higher for women. Overall, the results in this paper provide evidence for the fact that a family-oriented public policy may affect the educational choices for women. © 2016 Elsevier B.V. All rights reserved.

1. Introduction In economics, education choices are generally analysed as the result of a maximization programme taking into account the financial returns of education over the course of a life time (Becker, 1964). Focusing on the labour market returns, several empirical studies (OECD, 2008; Psacharopoulos and Patrinos, 2004) have shown that due to better job opportunities and higher wages, education is a rather profitable investment: the mean private rate of return on tertiary education is higher than the interest rate in all developed countries. This literature also exhibits significant gender differences in the higher education returns (OECD, 2008; Courtioux et al., 2014) suggesting that the incentives to pursue education at a tertiary level are lower for women than for men. At a first sight, this last result seems at odds with the general trend of increasing participation by women in higher education and in the labour market. Demographic economics complements the analysis of education incentives: education also produces returns on the marriage market. From a theoretical point of view, it is generally argued that it raises the prospects of marriage with an educated partner, thus raising household income within the marriage (Chiappori et al., 2009). Moreover, it seems that national institutional features like divorce law affect the inter-temporal behaviour of married couples (Voena, 2015).

⁎ Corresponding author.

http://dx.doi.org/10.1016/j.econmod.2016.04.011 0264-9993/© 2016 Elsevier B.V. All rights reserved.

As the theoretical implications of this analysis seem well identified, there are very few empirical results on the financial returns of education within the marriage market. This lack of empirical results contrasts with the literature on the choice of partner (Pencavel, 1998; Blossfeld, 2009) which shows up positive “assorted mating”, based on characteristics such as educational level (also known as educational endogamy). The contribution of this article consists in identifying the marriage market effect on tertiary education returns for France and it documents gender differences from this point of view. The empirical literature on education returns has recently been extended in order to take into account the fact that the returns on a particular degree are uncertain, and risk-adverse students or students from low-income families may be reluctant to enrol (Martins and Pereira, 2002; Harmon et al., 2003; Cunha and Heckman, 2007; Courtioux et al., 2014). Our contribution belongs to this growing and prolific literature on the distribution of returns to education: see Dickson and Harmon (2011) for a review. The marriage market effect is estimated by introducing a specific demographic module in a dynamic microsimulation model as developed in Courtioux et al. (2014). This module permits the observed degree of educational endogamy in the marriage market to be modelled, along with the heterogeneity in the union and separation timelines, across genders and diploma. In order to facilitate the comparability of results with this article, we also calibrate our analysis for the cohort born in 1970. The paper is organised as follows: in Section 2, we introduce and discuss the internal rate of return framework and how to take into account

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the potential partner. Section 3 details the original demographic module that is used for the simulation. In Section 4 we present and discuss the results, and Section 5 concludes. 2. A distribution perspective on higher education returns In education economics, following the human capital approach, the choice of pursuing education is analysed based on the financial incentives. Since Becker (1964) the internal rate of return (IRR) has been a key indicator and is obtained by equating the present value of a stream of income when a person invests in human capital to the present value when he/she does not invest. If Y is the stream of income when an agent pursues his/her education and therefore enters the job market later and X is the stream of income when he/she does not pursue higher education and enters the job market directly, then the internal rate of return of this individual (r) solves the following equation: M X Y t −X t t

t¼0

ð1 þ r Þ

¼0

ð1Þ

where t is a time period index and M is the total number of time-period units lived by the individual. The effect of the partner can be analysed by including in the overall stream of income Yt and Xt, both the income of the reference individual i (Yi,t, Xi,t) and the income of the partner p (Yp,t, Xp,t). Y t ¼ Y i;t þ Y p;t

ð1:1Þ

X t ¼ X i;t þ X p;t

ð1:2Þ

At a given point in time (t), if an individual is single then the income of the partner is equal to zero. As far as pursuing higher education tends to postpone the date of union, there is a gap between Yp,t and Xp,t in favour of Xp,t at the beginning of the lifecycle. However, as far as higher education may provide access to a pool of potential better-educated partners (because of educational endogamy) with higher incomes, the difference between Yp,t and Xp,t may change later in the lifecycle. Moreover, we break down each stream of income It (i.e. Yi,t, Yp,t, Xi,t and Xp,t) into five components as follows: I t ¼ W t þ U t þ Rt þ T t :

ð2Þ

Where Wt is the individual net wage at period t, Ut the unemployment benefit, Rt the retirement pension and Tt the individual income tax. For a given point in time, some of these elements may be equal to zero. For instance, if the reference individual or his/her partner is employed in t, the unemployment benefit Ut is equal to zero. If the individual is active in period t, the retirement pension Rt is equal to zero. To produce a distribution of r, we use a stylized birth cohort obtained by dynamic microsimulation. It documents an individual's type of degree; the annual net wage for each age; and the wage of the partner, if the person has a partner. Our methodology differs from that of Deaton (1985): see for instance Cardoso and Gardes (1996) for such an analysis on French data. We do not compute a synthetic cohort based on the observations of a given population for several points in time. Instead, we compute a cohort based on individual datasets, which makes it possible to analyse short-term individual transitions and simulate these implications for the whole lifecycle (see Section 3). To compute our distribution, we work on the assumption that the counterfactual stream of income obtained when not pursuing tertiary education (X) can be estimated by the average earnings by age (t), for individuals who did not obtain a higher education degree: this approach is common and is used, for instance, by the OECD (2008). We also added a specific treatment to take into account the opportunity costs for higher education training which vary with the curriculum followed by an individual. In our view, this is consistent with our non-sequential analytical

framework of higher educational choice. For instance, some students may follow a tertiary education curriculum for only two years and then enter the labour market, whereas others may choose to follow a longer curriculum and therefore face higher opportunity costs. Moreover, some individuals may fail their exams; they then enter the labour force older with higher opportunity costs than the average for individuals with the same level of qualification. To capture this variety in higher education investment that has an impact on the level of returns, we adapt the computation of Xt during the education period of the lifetime to each level of tertiary education (e) already attained by each person. Here, e stands for the degree level and can be ordered from 0 to E. X e;t ¼ X 0;t

if t ≥L

  X e;t ¼ MAX X 0;t ; X 1;t ; :::; X E;t

ð3:1Þ if t b L

ð3:2Þ

where L is the date when the individual in our simulated cohort enters the labour force. In this framework, two individuals with the same diploma entering the labour force at different ages (L) face different opportunity costs. The one who enters the labour force later incurs an additional cost due to the delay period. Opportunity cost estimation depends on the levels of education that could have been attained by a person of the same age: see Eq. (3.2). This means that opportunity costs are increasing with age (t): they take into account the experience premium on wages of persons who enter the labour force earlier, and the education premium of those who have got their degree and are on the labour market – whatever their position – at the given age t. In this framework, a negative individual internal rate of return on education remains possible for educated people: it means that the individual gains associated with a person's highest degree are not sufficient to cover the losses associated with the number of years training, so that the present value of the individual's stream of income remains less than that of the average career of those who do not complete a tertiary diploma. According to Cunha and Heckman (2007), two components should be distinguished in the distribution of returns to education: (i) variability that refers to factors that are unobservable to the econometrician but observable to the agent, and (ii) uncertainty that refers to the share of the distribution which is unpredictable for the econometrician and the agent (luck, unanticipated events, etc.). On this basis, Cunha and Heckman (2007) make a distinction between ex post returns (corresponding to the dispersion of realized returns incorporating both variability and uncertainty) and ex ante returns (referring to dispersion incorporating uncertainty). In other words, ex post returns describe how economies reward schooling, whereas ex ante returns correspond to the distribution observed by the agents, when making their schooling decisions. Following the arguments developed in Courtioux et al. (2014), it is possible to interpret our results as ex ante returns. In order to do this, five assumptions are necessary. 1) There is uncertainty about future earnings an individual will obtain from a wage career distribution; this distribution is conditional on the diploma obtained, (1.1). This uncertainty about future earnings also concerns the potential partner (1.2). 2) 2.1) The student is not aware of his/her own talent/preferences to study and work (2.1.1). Moreover, he/she is not aware of the talent/preferences to work of the potential partner (2.1.2), but knows that these are conditioned by his/her talent/preferences that will be revealed in the future with the diploma obtained (see also assumption 5). 2.2) However, a student thinks that he/she is able to succeed in obtaining a higher education diploma even if the student does not know the level of the higher degree he/she will obtain or the relative quality of the higher education institution attended. 3) The education decision does not concern a marginal year of schooling, but an education track which leads to a diploma.

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4) The individual decision of pursuing higher education is taken at the age when the student can legally enter the labour force — at 16 years old in France. This decision is irreversible. 5) There is uncertainty about the timing of union and potential separation, as well as the education characteristics of the potential partner, but it is conditioned on the diploma obtained (this is the assortative mating assumption). From a general point of view, these assumptions differ from other works (Ge, 2011; Cunha and Heckman, 2007) and refer to a framework with a high level of uncertainty that, in our view, is consistent with some of the key schooling decisions taken at age 16 (assumption 4). Compared to the assumptions of Courtioux et al. (2014), taking into account the effect of a potential partner on the distribution of returns implies adding the assumptions (1.2), (2.1.2), and (5). It is noteworthy that assumptions 2, 3 and 4 are also implicitly made in the construction of OECD indicators of returns to higher education (OECD, 2008). However, the OECD's methodology does not consider the uncertainty of future wages conditional on the diploma. Courtioux et al. (2014) produce a distribution of returns on higher education with the same kind of methodology and indicate that the distribution differs for men and for women: women have a more compressed distribution and a higher share of negative returns. From an economic point of view, this could be the result of a family division of work and may reflect the fact that education may be a means to accessing partners with high returns, rather than having the individual his/herself earning high returns. In this view, interpreting the distribution of returns as an incentive to pursue higher education could be misleading if it does not take into account the fact that education has an impact on the marriage market. In the next section, we present the way we assess this issue and how the distribution of IRR and the effect of the marriage market is computed. 3. Modelling the marriage market: a microsimulation perspective In economics, microsimulation techniques are used for different issues in social policy (for instance Van Sonsbeek and Alblas, 2012), or in transport economics (for example Verikios and Zhang, 2015). In this article, as in Nelissen (1990), we use dynamic microsimulation techniques, and we focus on education.1 Our objective is not to simulate the evolution of the education structure of a population, but rather to simulate life trajectories, given the education structure of a birth cohort. Our modelling simulates dynamic interactions between the labour market and the marriage market, over the course of a life time, and conditional on the highest degree obtained for each individual of our cohort. The distribution of lifecycle trajectories thus produced can be interpreted, as can all the possible states of nature that enter into an individual's calculation of ex ante higher education returns under uncertainty (see Section 2). This distribution is empirically rooted and corresponds to the French case in terms of the education system and marriage market (family laws, degree of endogamy, etc.) that we aim at capturing (the Appendix presents the heterogeneity France's higher education institutions and the degrees available). For econometricians, as well as for the reference individual who calculates this distribution to formulate an education choice, the specification of our microsimulation model is constrained by the data available. On the one hand, we use the French Labour Force Survey (FLFS) for the period 1968–2007, but the definition of the education variable was changed in 2003 and is now more detailed. We chose to use the FLFS 2003–2007 when we need to capture the effect of diploma at a more disaggregated level. The FLFS 2003–2007 is then used to define the determinant of wages conditional on the highest degree obtained (see Section 3.3). It is also used to identify the relative probability of transition into the labour market, conditional on the highest degree obtained 1

See, for instance, Li and O'Donoghue (2013) for a survey of dynamic microsimulation modelling.

223

(see Courtioux et al. 2014, Table 2). This leads us to focus on the simulation of a generation. This is well-represented in the labour force during the years 2003–2007, in order to reduce the cohort-effect bias in our simulation, i.e. the cohort born in 1970. However, the 2003–2007 period is too short to capture time effects, such as the impact of the business cycle on employment, experiences and wages at a disaggregated diploma level, an impact we want to control for individual trajectories. We thus estimate a chronogram of situations in the labour market, conditional to the current unemployment rate with the FLFS 1968–2005 (see Courtioux et al., 2014, Table 1). In the microsimulation, the chronogram is used to calibrate the aggregated trajectory of a whole generation, whereas the wage modelling and the transition in the labour market modelling are used to simulate individual trajectories under this generational constraint. This means that we assume that we can forecast the chronogram of a present generation, based on the observed former generation. Doing so, we potentially miss some cohort effects, that are mainly effective at the end of a career, linked for instance to a rise in the retirement age in France. On the other hand, we are not able to analyse the marriage market on the basis of religion. Religion is generally recognized as an important factor in explaining economic and demographic behaviour (Lehrer, 2004). But religious affiliation, which could be analysed as a stable component of ethnic human capital (Andrén, 2012), is not documented in our datasets. Moreover, religiosity is partially documented but not sufficiently so for it to be disentangled from age and education effects.2 The results presented here are made under the assumption that religion and various degrees of religiosity have homogeneous effects on education, the labour market, and on the marriage market in France. The dynamic microsimulation model used to simulate the careers of a generation has a specification that can be decomposed into four operations3 (for each operation, we explicitly take into account the heterogeneity deriving from the type of tertiary diploma obtained): (1) A simulation of the individual transitions on the labour market conditional on the individual's past trajectory in the labour market; a simulation of the partner's transitions in the labour market on the same basis. (2) A simulation of individual earnings, conditional on the labour market status and the past experience in employment; a simulation of the partner's earnings on the same basis (see Section 3.3). (3) A simulation of the transition in couple status (see Section 3.1) and if this is a new union for the individual, the simulation of the partner's characteristics (see Section 3.2) (4) A simulation of mortality rates over the course of a lifetime conditional on gender and the diploma obtained. The survival functions differentiated by gender and diploma are computed based on the estimates produced by Courtioux et al. (2014).

The very modelling of the marriage market is a two-step process. The first step consists in simulating the timing of a union's formation and dissolution (Section 3.1). The second step concerns the matching process and the calculation of the partner's characteristics (Section 3.2). During the union period, the annual wage of the reference individual and the potential partner are computed on the same basis (Section 3.3). 3.1. Simulating the timing of union formation To simulate union formation and union dissolution, we use two inputs. First, we model an age-specific target to capture the evolution of union behaviour across generations. This modelling leads to estimating the proportion of individuals living with a partner at each age of the lifecycle. We use the estimates to compute the union chronogram of our stylized 1970 birth cohort. Secondly, we model the individual 2 A religiosity variable is available for the years 2008 and 2009, for the French part of the EU-SILC. 3 For a more detailed description of the simulation process see Appendix A.

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probability of entering into different couple statuses. Two statuses are taken into account: being in a relationship or being single. In our analysis, a couple is defined by two individuals living under the same roof and declaring they are living in a relationship. This probability depends on several individual characteristics such as age, sex and diploma. 3.1.1. Modelling aggregated changes across birth cohorts In France, as well as in other countries, family situations have been subject to important changes over the past fifteen years: the age at first union has increased and the proportion of men and women living in union has declined (Sobotka and Toulemon, 2008). The delay in forming a union is mainly due to the lengthening of education (Ní Brohlcháin and Beaujouan, 2012) whereas the decrease in the proportion of individuals living in a relationship is related to the growing instability of unions. Moreover, family situations over the lifecycle differ for men and women (Pailhé et al., 2014). Men tend to form a union later than women but they live more frequently with a partner especially after the age of 40. As noted by Toulemon (2012), when a union is dissolved by a death, it is more often the man who dies than the woman, and in cases of separation, men re-partner more frequently and more rapidly than women. To assess these changes, we use age-specific targets in the simulation. These targets consist in modelling the proportion of union A at each age of the lifecycle for a given generation then producing a chronogram. We use the French Labour Force Survey 1969–2010 to construct segments of the union rate by age and generation. For instance, data available for the generation born in 1950 cover the ages 19 to 60 which constitutes a segment of life, the generation born in 1960 from the age 16 to 50 (this constitutes another segment), the generation born in 1970 from 16 to 40 etc. The model is specified as follows:    Log Agt = 1−Agt ¼ α þ β1 ðt−g Þ þ β2 ðt−g Þ2 þ β3 ðt−g Þ3 þ β4 ðt−g Þ4 ð4Þ þβ5 ðt−g Þ5 þ β6 ðt−g Þ6 þ β7 ðg−1970Þ þ β8 ðg−1970Þ2 þβ9 ðg−1970Þ3 þ β10 ðg−1970Þ4 þ β11 ðut Þ þ εgt where Agt is the union rate of the generation g for the year t, g − 1970 a generational trend (1970 birth cohort as the reference) and ut the unemployment rate of the year t. This model is estimated separately for men and for women. For women, the estimates β9 and β10 are not statistically significant. After verifying that they do not significantly modify Table 1 The modelling of age-specific percentage of individuals in couple.

α β1 β2

(Intercept) (Age) (Age2)

β3

(Age3)

β4

(Age4)

β5

(Age5)

β6

(Age6)

β7

(Generational trend)

β8

(Generational trend2)

β9

(Generational trend3)

β10

(Generational trend4)

β11 R-square N

(Unemployment rate)

Men

Women

−55.67 (1.13) 5.64 (0.16) −2.20E −01 (8.48E −03) 4.45E −03 (3.35E −06) 5.00E −05 (3.35E −06) 2.81E −07 (2.48E −08) −6.00E −10 (7.30E −11) −2.10E −02 (1.33E −03) 3.52E −04 (7.68E −05) 1.55E −05 (2.41E −06) 8.85E −08 (2.16E −08) −2.33 (0.47) 0.94 2646

−45.32 (0.93) 4.89 (0.13) −2.00E −01 (7.40E −03) 4.27E −03 (2.06E −04) −4.83E −05 (3.03E −06) 2.77E −07 (2.27E −08) −6.30E −10 (6.80E −11) −3.78E −02 (9.36E −04) −6.25E −04 (1.34E −05) – – −2.89 (0.32) 0.96 2734

Source: French Labour Force Survey 1969–2010 (Insee); authors' calculations. Note: All estimates are significant at the 1% level; standard errors are in parentheses.

our other estimates, they have been removed from the final estimations. The estimates are reported in Table 1. The results we obtain are consistent with some of the stylized facts we identified (see Appendix A, Fig. A1 for a graphic representation of these targets). First, women enter their initial union earlier than men. For the 1970 generation, the probability of living with a partner at age 25 according to our model was about 60% for women and 37% for men — for the simulation we assume an 8% unemployment rate throughout the period. Secondly, after the age of 40, the union rate of women falls below the men's rate, and tends to decline more rapidly. Regarding our targets, the probability of having a partner is around 80% for men and women at age 40; at the age of 60, this probability is about 74% for men and 63% for women. The specific effect of unemployment rates can also be computed. For instance, according to the estimates reported in Table 1, at age 25, a rise of unemployment rate from 8% to 15% decreases the proportion of women living in with a partner by 5 percentage points (4 percentage points for men). These results are consistent with Sobotka and Toulemon (2008) who show that current unemployment rate is negatively correlated with the proportion of individuals in couple. 3.1.2. Education levels and the timing of unions In addition to age-specific targets, we use an individual's probability of being single/in a relationship at each age of the simulation. The individual probability is computed using binomial logit models, which are estimated on the French part of the EU-SILC (European Union Statistics on Income and Living Conditions) survey, for the 2004 to 2009. The EUSILC survey is a too short to produce estimates from a lifetime perspective: for instance it is not possible to differentiate among singles those who are never-married or those who have experienced marriage and have subsequently divorced. Moreover, from a demographic perspective, it is not possible to know if the children within the household are the children of the couple or the children of only one of the partners, or if there are some other children of one of the partners in another household. As we have already been able to compute the aggregate age-specific target of individuals living in couples for a given birth cohort, our modelling strategy consists in producing the relative probability of being in couple for the individuals of a given birth cohort. We work on the assumption, that demographic and labour market events (i.e. loosing or finding a job, having a small child, etc.) are important in explaining changes in union status a given year. The probability of being in a given state S – defined as a position on the labour market and the marriage market – at the age t is a function f of previous positions and a set of current events (Et): P ðSt Þ ¼ f ðS0 ; S1 ; ::: St−1 ; Et Þ:

ð5Þ

Technically, between age n and age n + 1, four couple transitions are simulated depending on the situation at age n: union formation, union dissolution, remaining single and remaining in a relationship. We estimate two logit models differentiated by sex: a model for singles (union formation the following period versus celibacy) and a model for individuals living with a partner (union dissolution the following period versus no change). The estimates of the first model are presented in Table 2. According to the literature, we introduce into our model several variables that have an impact on union formation such as age, school completion, the presence of children and activity status (Keeley, 1977; Ekert-Jaffé and Solaz, 2001). One has to note that the presence of children in the household is used as a control variable. As far as we do not simulate childbirth, the child effects on labour market or union are not computed during the simulation. To avoid introducing noise in the simulation and after verifying that this does not impact our estimates, we only keep the significant coefficients for the final estimation. First of all, the probability of forming a union is negatively correlated with age. On the one hand, the number of potential partners decreases with age (Ekert-Jaffé and Solaz, 2001). On the other hand, for older singles (who have probably already lived a first relationship) the

P. Courtioux, V. Lignon / Economic Modelling 57 (2016) 221–237 Table 2 Estimates of the probability of being in a couple in n + 1 for single individuals in n (logit).

Intercept Age Age-square Age × end of school Age-square × end of school Activity status year n Employment Unemployment Inactive Not in employment Activity status year n + 1 Employment Unemployment Inactive Not in employment Child age b 3 years old Somers'D Concordant pairs (%) N

Men

Women

−1.8643 (0.0253) −0.0437 (0.0019) 0.0007 (0.0000) 0.0540 (0.0013) −0.0016 (0.0000)

−0.6484 (0.0207) −0.0609 (0.0012) 0.0004 (0.0000) 0.0345 (0.0005) −0.0012 (0.0000)

Ref. 0.1706 (0.0087) −0.0223 (0.0089) –

Ref. – – 0.2598 (0.0061)

Ref. −0.2432 (0.0098) −0.5453 (0.0089) – 1.5848 (0.0162) 0.59 78.4 1841

Ref. – – −0.3199 (0.0060) −0.2724 (0.0086) 0.72 85.0 3424

Source: French SILC 2004–2009 (Insee); authors' calculations. Note: All singles in n. All estimates are significant at the 1% level; standard errors are in parentheses.

probability of forming another union is limited by the previous experience or by the presence of children (Cassan et al., 2001). We control for children under three years old, because the literature shows that in France the employment rate of women with at least a child of 6 years (the age of entering primary school) is very close to the average employment rate for women, whereas it is much lower for women with a child under three years old: more than ten percentage points as reported for instance by Courtioux and Thévenon (2007). Our estimates suggest that the probability of re-partnering is more difficult for women having a young child. In contrast, for men, the presence of a child increases the probability of forming a union which is consistent with Cassan et al. (2001). Moreover, we tested different specifications to model the effect of education. A specification based on the level of diploma was unsatisfactory and we opted for an interaction term between age and the completion of (higher) education. Besides, Ní Brohlcháin and Beaujouan (2012) highlight the importance of age in completing education, in the postponement of union formation. Regarding the estimates of our model, we find that individuals who have not yet completed their studies are more likely to remain single than others. This is consistent with the idea that obtaining a degree is generally a precondition to the formation of a union. Furthermore, the capacity of an individual to find a partner depends on a person's economic situation, i.e. a person's financial contribution to the wealth of the future household: the higher the contribution is, the higher the probability of forming a union will be (Keeley, 1977; Ekert-Jaffé and Solaz, 2001). As having high income is one form of desirable asset, it may increase the prospect of finding a spouse on the marriage market. However, incomes are correlated with education and what we try to estimate with Eq. (5) are the individual differences in the dynamics of union formation: the aggregated age-targets of the individual in a couple for a given cohort are already given by the estimates of Eq. (4). From this view, the effects of the activity status aim at capturing some delay in forming a union, due to delay in finding a job at the end of initial education. Within our simulation, the effect of a spouse as source of income is not captured by this equation but rather by the equation that determines an individual's spouse's diploma and the correlated stream of income during the period corresponding to the period the reference individual is living in a couple with this person (see above Sections 3.2.1 and 3.2.2). Consequently, despite the fact that the annual income is available in the EU-SILC data, it is not used as an explanatory variable to estimate the probability of being in couple.

225

Table 3 Estimates of the probability of being in couple in n + 1 for individuals already in couple in n (logit).

Intercept Age Age-square Human capital (in year) Union duration 0–3 years 4–10 years 11–19 years ≥ 20 years Child aged b3 years old Human capital of the partner (in year) Age differential with the partner Job loss in year n Somers'D Concordant pairs (%) N

Men

Women

1.9239 (0.0394) −0.0056 (0.0022) 0.0004 (0.0000) 0.2810 (0.0072)

3.8468 (0.0282) −0.1738 (0.0016) 0.0021 (0.0000) 0.0470 (0.0012)

Ref. 1.7892 (0.0186) 2.1658 (0.0244) 2.3265 (0.0309) 0.9100 (0.0069) −0.2900 (0.0072) −0.0858 (0.0004) −0.2074 (0.0113) 0.45 68.50 8492

Ref. 2.9012 (0.0138) 3.6100 (0.0165) 4.1500 (0.0218) 0.2000 (0.0054) 0.0300 (0.0012) 0.0716 (0.0005) – 0.46 70.50 8816

Source: French SILC 2004–2009 (Insee) and Survey of Family History 1999 (Insee), authors' calculations. Note: All the individuals aged less than 80, who are in couple in n. Being a widow is not taken into account here. All estimates are significant at the 1% level; standard errors are in parentheses.

An unstable job position also decreases attractiveness on the marriage market, especially for men. Regarding current employment status, we observe that being unemployed or inactive in n and n + 1 decreases the probability of entering into a partnership. This effect is higher for men. However, we note an individual's return to work has a positive effect on union formation. This suggests that an improvement in a person's current economic situation increases the number of potential partners on the marriage market. The estimates of the model for individuals living with a partner are presented in Table 3. Together with union formation, several determinants may explain the dissolution of partnerships (Lyngstad and Jalovaara, 2010). A first explanatory factor is the duration of a union. Computing a Kaplan–Meier duration risk function, Bonnet et al. (2010) show that the risk of union dissolution is important during the first three years of married life and that this risk is more pronounced with younger birth cohorts: i.e. the effect does not exist for the 1957–1961 cohort but is very high for the 1972–1976 cohort. To test this hypothesis with our data, we estimate different functional forms of union duration, but these estimates were not significant when controlling for other factors.4 The reasons may be that Bonnet et al. (2010) do not control for human capital across generations, which has changed dramatically. Nor do they control for employment status during the first years of a union: i.e. there has been an important increase in women's participation in the labour market and an increase in the rate of unemployment since the 1960s in France. To produce a robust estimate of union duration, we decided to pool some years: we first tested a model with an estimate for each of the first 19 years of the union, and one estimate for the following “20 years and more”. As expected, some estimates were not significant, and so we decided to pool the year variables in order to produce robust estimates: a year that does not have a significant estimate is pooled with the contiguous year which has the closer estimate. We thus retain 4 classes of duration (0–3 years, 4–10 years, 11–19 years, 20 years and more). Our model indicates that union dissolution is negatively correlated with the duration of union ceteris paribus. A second key factor of union dissolution is the presence/absence of young children. As advocated for instance by Lillard and Waite (1993), we observe that having a young child reduces the probability of separation. This effect is more important for men than for women. Besides, our model emphasizes a negative effect of age on union dissolution. This result is consistent with

4 These durations stem from the EU-SILC with an imputation based on the Family History Survey 1999, for the duration over three years.

226

P. Courtioux, V. Lignon / Economic Modelling 57 (2016) 221–237

Lyngstad and Jalovaara (2010). The socioeconomic status of partners also plays a role in the probability of separation. In our modelling, we distinguish between current events and more stable socio-economic status. For men, our specification in terms of human capital stock shows that a high level of education is correlated with a lower probability of separation, whereas the education level of the partner has a positive impact. It suggests that the economic independence of women measured by the prospect of having a good career on the basis of her human capital stock increases the probability of union dissolution (Locoh, 2002). For women, the estimated coefficients are positive but low. Regarding activity status, only one estimate is significant. Concerning this issue, Ekert-Jaffé and Solaz (2001) found there is a positive correlation for men between job insecurity and the risk of union dissolution. This is consistent with our estimates which show that when a bad event such as a job loss occurs, the probability of separation increases for men. Based on the estimates reported in Tables 2 and 3, the probability of being in state S for individual i at age a is given by: P ðSit Þ ¼

1  : 1 þ exp −X i;ðt−1Þ  β

ð6Þ

Where β is the column vector of estimates and Xi,t−1 the vector describing the characteristics of individual i at age t − 1.5 The combination of Tables 2 and 3 could then be used in our modelling to compute the union paths taken by individuals from a given birth cohort. Based on the estimates of Table 2, one could easily see that the probability of forming a couple at an early age is higher for those persons who left school early and found a job in the following year. In our simulation of individuals' lifecycles, demographic events interact with the transitions in the labour market (see Appendix A, for a more complete description of the microsimulation process). For instance, being already unemployed at a given age and having a low level of education increase the probability of remaining unemployed in t + 1; as shown in Table 2, this unemployment trajectory has a negative impact on the probability of being in couple. As in our modelling, the transitions from one state to another depend on the variables defined in the past trajectories, such as the duration in unemployment in the labour market or the duration in the union in the marriage market, whereas the current transition probability depends on the past trajectory as defined in Eq. (5). The main interest of retaining such simple modelling that does not differentiate between the current state of being single (for instance between being young and never-married or being a widow) is to produce stylized lifecycles for the individuals of a given cohort which take into account the cumulative effects of events over the course of a life time. However, several interesting preliminary results of a couple's stability and education level can be computed from these tables. Ceteris paribus, these calculations show that the couples' stability is similar and relatively high for partners with the same education level, whatever that level is. For instance the probability of remaining in a couple for a man of 30 with a partner of the same age for less than 4 years is 88% when both partners have invested in 7 years of human capital; the probability is 89% when both partners left the education system at 16. Otherwise there is a dissymmetry between the impact of human capital of men and women on a union's stability: the lack of education for men is factor of instability within the couple. When the same man with a human capital investment of 7 years education is in couple with a woman who left education system at 16, the probability that they will still be together the following year rises to 98%. By contrast, if the man in couple left school at 16, while the women spent 7 more years in education, then the probability of still being together the following year falls to 51%. The magnitude of the human capital matching effect on the couple's stability differs for the estimates for women; this is due to the fact that the effect of a woman's 5 Xi =(xi1, …,xij, …,xin) where xij is equal to 1 if the characteristic j is observed for individual i, and equal to 0 if not. For the intercept, xi =1.

job loss on couple stability is not significant, and cannot be disentangled from the human capital effect in our estimations. 3.2. The characteristics of the potential partner Once we have estimated the probability of transitions to different couple states, we need to determine the characteristics of the partner. Indeed, several works show that the matching process between partners is not random (Blossfeld, 2009; Chiappori et al., 2009; Becker, 1974). Regarding the objective of the paper, two central characteristics of the partner must be taken into account in our simulation: education level and age. Indeed, the education level of the partner determines his/her transitions on the labour market: educational endogamy, for instance, could have a significant impact on income inequality between households. In addition, wages increase with experience: being in a relationship with an older partner could have a positive effect on the total income of the union. To determine the characteristics of the partner, we use the French Labour Force Survey 2003–2010. 3.2.1. Estimating a matching function by type of degree The question of educational endogamy is largely addressed by the literature (see Blossfeld (2009) for a review). In France, According to Vanderschelden (2006a), 56% of unions are composed of individuals with the same education level. Concerning the evolution educational endogamy over time, it seems to have declined since the 1950s. In particular, Bouchet-Valat (2014) shows that this decrease is important for nongraduates. He also notes an exception to this trend: educational endogamy has increased for individuals of France's prestigious Grandes écoles (selective higher education institutions in engineering and business). To simulate educational endogamy, we use couples observed in the French Labour Force Survey 2003–2010 and we estimate matching functions. The Labour Force Survey allows us to focus on detailed diplomas (20 categories), compared to others studies that retain more aggregated categories (Goux and Maurin, 2003; Vanderschelden, 2006a; Greenwood et al., 2014).6 We estimate a matching function m of the following type: ep ¼ mðei ; g ei Þ:

ð7Þ

Where ep is the diploma of the partner and ei the diploma of the reference individual and gei a generational trend in order to capture the change resulting from the evolution of educational levels by potential partners, across generations. The matching function is estimated using a multinomial logit: the partner's diploma is explained by the diploma of the individual and the generational trend. The function is estimated separately for men and women to capture the gender specific change in education across generations. Estimates show that the effect of the generational trend is significant. Moreover, the specification with 20 levels of diploma appears satisfactory, except for the coefficients of the capacité en droit — a one-year higher education degree in law which represents less than 0.1% of the cohort born in 1970. This category is then included in the same class as France's generalist/top highschool diploma (the baccalauréat général). The estimates of our model are presented in Tables 4 and 5. On the basis of these estimates, we compute the matching probabilities by education level. If Xi corresponds to the vector describing the characteristics of individual i (i.e. diploma and birth year) and βj the coefficients vector for partner's diploma j, then the probability of the individual i of forming a union with a partner holding the diploma epj among J possibilities is given by:   P i epj ¼

6

  exp X i β j J

∑e¼1 expðX i βe Þ

; j ¼ 1; 2; …; J:

See Appendix A for a brief presentation of the French education system.

ð8Þ

Table 4 The diploma matching function for men (multinomial logit). e2

e3

e4

e5

e6

e7

e8

e9

e10

e11

e12

e13

e14

e15

e16

e17

e18

e19

Intercept

−0.4548 (0.0005) Ref. 0.8310 (0.0006) 0.4774 (0.0013) 0.6248 (0.0020) 0.8590 (0.0019) 0.8322 (0.0039) 0.7978 (0.0030) 0.8569 (0.0016) 1.0301 (0.0044) 0.8694 (0.0043) 0.6266 (0.0030)

−1.7138 (0.0008) Ref. 0.4213 (0.0010) 2.2103 (0.0013) .0692 (0.0025) 1.2646 (0.0024) 2.5770 (0.0035) .9916 (0.0031) 1.7441 (0.0018) 1.8771 (0.0049) 1.6697 (0.0049) 2.2936 (0.0027)

−2.5187 (0.0014) Ref. 0.7154 (0.0018) 0.8498 (0.0036) 1.5611 (0.0028) 1.0696 (0.0039) 1.5554 (0.0087) 1.5752 (0.0052) 1.5030 (0.0029) 0.6851 (0.0148) 0.5101 (0.0138) 1.5493 (0.0059)

−2.0856 (0.0011) Ref. 0.7897 (0.0013) 1.1842 (0.0024) 1.0917 (0.0029) 2.1025 (0.0024) 1.6733 (0.0062) 1.9563 (0.0038) 1.7923 (0.0022) 1.4024 (0.0081) 1.5621 (0.0068) 1.8612 (0.0041)

−3.6987 (0.0019) Ref. 0.6387 (0.0023) 2.0030 (0.0029) 1.0839 (0.0057) 1.6384 (0.0047) 4.2979 (0.0039) 2.8053 (0.0046) 2.2481 (0.0033) 2.3751 (0.0084) 2.5158 (0.0074) 3.2335 (0.0038)

−3.9633 (0.0026) Ref. 0.9685 (0.0032) 2.0408 (0.0043) 1.6232 (0.0052) 2.2203 (0.0049) 2.9004 (0.0086) 4.2232 (0.0041) 2.5843 (0.0039) 1.6735 (0.0171) 3.0675 (0.0083) 3.0236 (0.0060)

−2.0508 (0.0011) Ref. 0.7632 (0.0014) 1.7725 (0.0020) 1.5807 (0.0025) 1.9302 (0.0025) 2.6194 (0.0046) 2.6996 (0.0031) 2.6751 (0.0019) 2.6293 (0.0054) 2.2204 (0.0055) 2.4034 (0.0035)

−5.0399 (0.0040) Ref. 0.6256 (0.0052) 1.9268 (0.0066) 1.2628 (0.0101) 1.8469 (0.0089) 2.9104 (0.0123) 2.7416 (0.0092) 2.2919 (0.0067) 3.9458 (0.0094) 2.3644 (0.0167) 2.6587 (0.0101)

−2.7081 (0.0013) Ref. 0.7259 (0.0016) 1.6867 (0.0023) 1.4701 (0.0032) 1.8201 (0.0031) 2.7213 (0.0048) 2.7131 (0.0035) 2.2431 (0.0024) 2.6363 (0.0058) 4.4391 (0.0037) 2.9333 (0.0033)

−2.8744 (0.0015) Ref. 0.4018 (0.0020) 2.1960 (0.0023) 1.4662 (0.0034) 1.9586 (0.0033) 3.4341 (0.0044) 3.0668 (0.0035) 2.5079 (0.0025) 2.7087 (0.0064) 2.7530 (0.0058) 4.3490 (0.0027)

−4.4587 (0.0032) Ref. 0.2745 (0.0047) 2.2971 (0.0049) 0.9807 (0.0084) 1.6571 (0.0076) 3.3418 (0.0088) 3.1258 (0.0065) 2.4513 (0.0051) 3.3887 (0.0099) 2.6330 (0.0122) 3.5300 (0.0062)

−3.2570 (0.0018) Ref. 0.4465 (0.0025) 2.4292 (0.0027) 1.3564 (0.0042) 1.9496 (0.0039) 3.7012 (0.0048) 3.0631 (0.0041) 2.7565 (0.0028) 2.9136 (0.0072) 3.1288 (0.0060) 3.9454 (0.0034)

−4.9938 (0.0043) Ref. 0.3546 (0.0061) 2.5719 (0.0061) 1.1927 (0.0099) 1.7034 (0.0097) 3.8810 (0.0094) 2.5882 (0.0103) 2.7471 (0.0061) 3.5413 (0.0122) 2.8474 (0.0146) 3.9026 (0.0072)

−3.9257 (0.0026) Ref. 0.1403 (0.0040) 2.2184 (0.0042) 0.6312 (0.0070) 1.8441 (0.0056) 3.4115 (0.0074) 3.0119 (0.0056) 2.6215 (0.0039) 2.8777 (0.0104) 3.1362 (0.0083) 3.8667 (0.0048)

−5.8782 (0.0068) Ref. 0.3996 (0.0095) 2.8662 (0.0090) 0.0229 ns (0.0249) 1.8002 (0.0146) 3.0168 (0.0209) 4.0430 (0.0099) 2.8091 (0.0093) 4.3894 (0.0137) 3.2613 (0.0191) 3.9354 (0.0111)

−5.5090 (0.0057) Ref. 0.5126 (0.0078) 1.9625 (0.0098) 0.7052 (0.0150) 1.9733 (0.0114) 1.0838 (0.0445) 3.3821 (0.0101) 3.1687 (0.0073) 3.4532 (0.0169) 2.2329 (0.0257) 3.8489 (0.0096)

−5.7435 (0.0060) Ref. −0.0563 (0.0096) 2.4365 (0.0088) −7.7310 (1.1285) 1.6573 (0.0141) 3.3596 (0.0158) 2.8053 (0.0133) 2.1319 (0.0103) 3.7590 (0.0153) 1.9167 (0.0314) 3.9142 (0.0098)

−4.8926 (0.0037) Ref. −0.3857 (0.0066) 2.4108 (0.0054) 0.5694 (0.0126) 1.8278 (0.0084) 3.0883 (0.0109) 2.7229 (0.0088) 2.4228 (0.0060) 3.7434 (0.0097) 4.0294 (0.0081) 3.5766 (0.0068)

0.6446 (0.0038) 0.5870 (0.0036) 0.3217 (0.0078) 0.6544 (0.0052) 0.5591 (0.0059) 0.6752 (0.0026)

2.2371 (0.0035) 2.4452 (0.0031) 2.3540 (0.0062) 2.3316 (0.0047) 2.3463 (0.0050) 2.3381 (0.0023)

1.1361 (0.0102) 1.4590 (0.0069) −0.3594 (0.0342) 1.0568 (0.0100) 0.8259 (0.0172) 1.1396 (0.0070)

1.5371 (0.0062) 2.0554 (0.0044) 1.6265 (0.0103) 1.6674 (0.0067) 1.3194 (0.0102) 1.6980 (0.0041)

2.8696 (0.0055) 3.1577 (0.0046) 3.4050 (0.0081) 2.9947 (0.0070) 2.6916 (0.0086) 2.9337 (0.0038)

3.3565 (0.0069) 3.3268 (0.0060) 3.8439 (0.0094) 3.7831 (0.0067) 3.8980 (0.0081) 3.3433 (0.0051)

3.0370 (0.0039) 2.7409 (0.0036) 2.7836 (0.0071) 3.0015 (0.0047) 3.2013 (0.0055) 3.0723 (0.0027)

4.1766 (0.0073) 2.7273 (0.0111) 3.5623 (0.0149) 3.7759 (0.0098) 3.9317 (0.0111) 3.4024 (0.0071)

2.8562 (0.0043) 3.0638 (0.0037) 3.2998 (0.0067) 3.2736 (0.0050) 3.1629 (0.0057) 3.2438 (0.0028)

3.5234 (0.0040) 4.1174 (0.0032) 4.2296 (0.0059) 3.7956 (0.0048) 3.4594 (0.0060) 3.7052 (0.0028)

5.5522 (0.0047) 3.9995 (0.0059) 4.6818 (0.0085) 4.6634 (0.0063) 4.8716 (0.0071) 4.3012 (0.0048)

4.0841 (0.0041) 4.9434 (0.0033) 4.9247 (0.0059) 4.4264 (0.0047) 4.2789 (0.0056) 4.1566 (0.0031)

4.8159 (0.0069) 4.6179 (0.0065) 6.3358 (0.0073) 5.1192 (0.0070) 5.1030 (0.0084) 4.7358 (0.0057)

4.4210 (0.0052) 4.6014 (0.0044) 5.2024 (0.0068) 5.5387 (0.0049) 4.9139 (0.0063) 4.5386 (0.0040)

5.0334 (0.0100) 4.5506 (0.0100) 4.7553 (0.0156) 5.6923 (0.0092) 7.4732 (0.0083) 5.5795 (0.0078)

4.5996 (0.0096) 4.3478 (0.0090) 5.2562 (0.0115) 4.7199 (0.0096) 4.6536 (0.0126) 6.6388 (0.0062)

4.9133 (0.0090) 4.7718 (0.0085) 5.5032 (0.0110) 5.2446 (0.0090) 4.5675 (0.0133) 5.1103 (0.0073)

4.3092 (0.0067) 4.1020 (0.0064) 4.6174 (0.0096) 4.6949 (0.0070) 4.6727 (0.0082) 4.4297 (0.0051)

0.6499 (0.0073) 0.6487 (0.0051) 0.0382 (0.0000)

2.6374 (0.0059) 2.8067 (0.0040) 0.0369 (0.0000)

1.8385 (0.0168) 1.8002 (0.0132) 0.1339 (0.0001)

2.4082 (0.0090) 1.6538 (0.0088) 0.0807 (0.0000)

3.9669 (0.0069) 3.3280 (0.0061) 0.0310 (0.0001)

4.1386 (0.0100) 3.4575 (0.0096) 0.0847 (0.0001)

3.5493 (0.0065) 3.0229 (0.0056) 0.0951 (0.0000)

3.9899 (0.0140) 3.8412 (0.0109) 0.0551 (0.0001)

4.0377 (0.0058) 4.4929 (0.0038) 0.0515 (0.0000)

4.6500 (0.0057) 3.9810 (0.0048) 0.0673 (0.0000)

5.3402 (0.0079) 4.7773 (0.0071) 0.0788 (0.0001)

5.5540 (0.0055) 4.3296 (0.0052) 0.0789 (0.0001)

6.7184 (0.0073) 4.7083 (0.0095) 0.0864 (0.0001)

5.9499 (0.0065) 4.7915 (0.0067) 0.1137 (0.0001)

6.5524 (0.0108) 5.0898 (0.0132) 0.0958 (0.0001)

6.5013 (0.0097) 4.8810 (0.0125) 0.1055 (0.0001)

8.0305 (0.0079) 5.6684 (0.0094) 0.0749 (0.0001)

5.6648 (0.0077) 7.4150 (0.0050) 0.0589 (0.0001)

e1 No diploma e2 CAP/BEP e3 Bac (general) e4 Bac (profesional) e5 Bac (technical) e6 DEUG (two-year university degrees) e7 DUT/DEUST (two-year University degrees) e8 BTS (two-years degree) e9 Other higher technical diploma (two-year degrees) e10 Paramedical diploma (two-years degrees) e11 Bachelor's degree (three-year university degrees) e12 Other three-years degrees e13 Maîtrise (four-year university degrees) e14 DEA (five-year general university degrees) e15 DESS (five-year profesional university degrees) e16 Business Schools or grande école (five-year degrees) e17 Engineering Schools or grande école (five-year degrees) e18 PhD (medical degree excluded) e19 PhD (medical degree) Generational trenda

P. Courtioux, V. Lignon / Economic Modelling 57 (2016) 221–237

Reference individual/partner diploma

Source: French Labour Force Survey 2003–2010 (Insee); authors' calculations. Note: Men living in couples. All estimates are significant at the 1% level, except ns for non-significant; standard errors are in parentheses. See Appendix A for a brief presentation of the French education system. a The generation trend is captured by the birth year of the reference individual minus 1970.

227

228

Table 5 The diploma matching function for women (multinomial logit). e2

e3

e4

e5

e6

e7

e8

e9

e10

e11

e12

e13

e14

e15

e16

e17

e18

e19

Intercept

−0.3140 (0.0004) Ref. 0.8725 (0.0006) 0.4539 (0.0010) 0.5485 (0.0018)

−2.5816 (0.0010) Ref. 0.4886 (0.0013) 2.2238 (0.0013) 0.7837 (0.0036)

−3.0252 (0.0014) Ref. 0.8770 (0.0020) 1.2378 (0.0025) 1.6916 (0.0028)

−3.1224 (0.0014) Ref. 0.9686 (0.0019) 1.3517 (0.0024) 0.9886 (0.0039)

−5.1459 (0.0029) Ref. 0.8796 (0.0039) 2.6194 (0.0035) 1.4581 (0.0088)

−4.1729 (0.0022) Ref. 0.9526 (0.0030) 2.1273 (0.0031) 1.5316 (0.0052)

−2.7619 (0.0012) Ref. 0.9638 (0.0016) 1.8184 (0.0018) 1.4828 (0.0029)

−5.3940 (0.0036) Ref. 1.0449 (0.0044) 1.8871 (0.0049) 0.5689 (0.0148)

−5.1603 (0.0033) Ref. 0.9355 (0.0043) 1.7271 (0.0049) 0.4326 (0.0138)

−4.3433 (0.0020) Ref. 0.5962 (0.0029) 2.2658 (0.0027) 1.4839 (0.0059)

−5.1097 (0.0027) Ref. 0.6862 (0.0038) 2.2809 (0.0035) 1.0777 (0.0102)

−4.6043 (0.0024) Ref. 0.6349 (0.0036) 2.4944 (0.0031) 1.3679 (0.0069)

−5.1255 (0.0036) Ref. 0.7389 (0.0052) 2.3912 (0.0047) 1.0039 (0.0100)

−5.9116 (0.0039) Ref. 0.5512 (0.0058) 2.3326 (0.0050) 0.8097 (0.0172)

−4.4215 (0.0019) Ref. 0.6977 (0.0026) 2.3622 (0.0023) 1.1754 (0.0070)

−6.8628 (0.0048) Ref. 0.7650 (0.0073) 2.7314 (0.0059) 1.8377 (0.0169)

−6.2518 (0.0035) Ref. 0.7785 (0.0051) 2.9144 (0.0040) 1.7081 (0.0132)

0.7691 (0.0013) 0.6775 (0.0023) 0.9509 (0.0032) 0.7083 (0.0014) 0.6342 (0.0052) 0.7654 (0.0016) 0.4098 (0.0020)

1.1665 (0.0024) 2.0176 (0.0029) 2.0414 (0.0043) 1.7495 (0.0020) 1.9392 (0.0066) 1.6957 (0.0023) 2.2093 (0.0023)

1.3727 (0.0028) 1.3511 (0.0057) 1.9779 (0.0052) 1.8246 (0.0024) 1.4818 (0.0101) 1.7320 (0.0032) 1.6320 (0.0034)

2.1765 (0.0024) 1.7387 (0.0047) 2.3133 (0.0049) 1.9650 (0.0025) 1.9138 (0.0089) 1.9341 (0.0031) 2.0214 (0.0033)

1.6954 (0.0062) 4.3405 (0.0039) 2.9186 (0.0086) 2.6189 (0.0046) 2.9552 (0.0123) 2.7723 (0.0048) 3.4773 (0.0044)

2.0857 (0.0038) 2.9436 (0.0046) 4.3636 (0.0041) 2.7904 (0.0032) 2.8730 (0.0092) 2.8830 (0.0035) 3.2036 (0.0035)

1.8935 (0.0022) 2.3439 (0.0033) 2.7095 (0.0039) 2.7473 (0.0019) 2.3636 (0.0066) 2.3609 (0.0024) 2.5825 (0.0025)

1.3872 (0.0081) 2.3883 (0.0084) 1.6572 (0.0171) 2.5955 (0.0054) 3.9502 (0.0094) 2.6523 (0.0058) 2.7156 (0.0064)

1.5910 (0.0068) 2.5754 (0.0074) 3.0985 (0.0083) 2.2259 (0.0055) 2.4137 (0.0167) 4.5105 (0.0037) 2.8075 (0.0058)

1.8125 (0.0041) 3.2066 (0.0038) 2.9778 (0.0060) 2.3540 (0.0035) 2.6148 (0.0101) 2.8998 (0.0033) 4.3111 (0.0027)

1.5729 (0.0062) 2.9065 (0.0055) 3.3873 (0.0069) 3.0550 (0.0039) 4.2243 (0.0073) 2.9013 (0.0043) 3.5647 (0.0040)

2.0741 (0.0044) 3.2000 (0.0046) 3.3482 (0.0060) 2.7389 (0.0037) 2.7603 (0.0111) 3.1179 (0.0037) 4.1585 (0.0032)

−6.1426 (0.0048) Ref. 0.4149 (0.0078) 2.4401 (0.0062) −0.4195 ns (0.0342) 1.7090 (0.0103) 3.4860 (0.0081) 3.9251 (0.0094) 2.8416 (0.0072) 3.6591 (0.0149) 3.4085 (0.0067) 4.3353 (0.0060)

1.7354 (0.0067) 3.0696 (0.0069) 3.8699 (0.0066) 3.0416 (0.0047) 3.8261 (0.0097) 3.3669 (0.0049) 3.8512 (0.0048)

1.3251 (0.0102) 2.6832 (0.0086) 3.9028 (0.0081) 3.2059 (0.0054) 3.9299 (0.0111) 3.1565 (0.0057) 3.4562 (0.0059)

1.7439 (0.0041) 2.9530 (0.0038) 3.3874 (0.0051) 3.1169 (0.0028) 3.4364 (0.0071) 3.2686 (0.0027) 3.7323 (0.0028)

2.5530 (0.0090) 4.0687 (0.0070) 4.2713 (0.0100) 3.6546 (0.0066) 4.1271 (0.0141) 4.1542 (0.0058) 4.7457 (0.0057)

1.8004 (0.0089) 3.4431 (0.0061) 3.5866 (0.0097) 3.1064 (0.0056) 3.9896 (0.0109) 4.6192 (0.0039) 4.0700 (0.0048)

0.2617 (0.0047) 0.4381 (0.0025) 0.3322 (0.0061) 0.0474 (0.0040) 0.3495 (0.0095) 0.4349 (0.0078)

2.2636 (0.0050) 2.4291 (0.0027) 2.5721 (0.0061) 2.1889 (0.0042) 2.8194 (0.0091) 1.9403 (0.0098)

1.2834 (0.0084) 1.6720 (0.0041) 1.5421 (0.0099) 0.8780 (0.0070) 0.3035 (0.0249) 0.9649 (0.0150)

1.7351 (0.0076) 2.0359 (0.0039) 1.7868 (0.0097) 1.8516 (0.0056) 1.8402 (0.0146) 1.9936 (0.0114)

3.3689 (0.0088) 3.7288 (0.0048) 3.8972 (0.0094) 3.3726 (0.0074) 3.0147 (0.0209) 1.0622 (0.0445)

3.2607 (0.0066) 3.2048 (0.0041) 2.7210 (0.0103) 3.0634 (0.0056) 4.1422 (0.0099) 3.4508 (0.0102)

2.5547 (0.0050) 2.8687 (0.0028) 2.8636 (0.0061) 2.6804 (0.0039) 2.8907 (0.0093) 3.2350 (0.0073)

3.3793 (0.0100) 2.9056 (0.0072) 3.5237 (0.0122) 2.8143 (0.0105) 4.3557 (0.0137) 3.4026 (0.0169)

2.6691 (0.0123) 3.1681 (0.0061) 2.8759 (0.0147) 3.1141 (0.0084) 3.2739 (0.0191) 2.2214 (0.0257)

3.4850 (0.0062) 3.9017 (0.0034) 3.8576 (0.0072) 3.8169 (0.0047) 3.8883 (0.0111) 3.7984 (0.0096)

5.5883 (0.0047) 4.1199 (0.0041) 4.8442 (0.0069) 4.4061 (0.0053) 5.0473 (0.0100) 4.6008 (0.0096)

4.0249 (0.0059) 4.9720 (0.0033) 4.6373 (0.0065) 4.5715 (0.0044) 4.5499 (0.0100) 4.3292 (0.0090)

4.7709 (0.0086) 5.0157 (0.0059) 6.4152 (0.0074) 5.2177 (0.0069) 4.8133 (0.0156) 5.2905 (0.0115)

4.7345 (0.0063) 4.5053 (0.0047) 5.1984 (0.0070) 5.5621 (0.0049) 5.7419 (0.0092) 4.7511 (0.0096)

4.8747 (0.0071) 4.2816 (0.0056) 5.1069 (0.0084) 4.9108 (0.0063) 7.4763 (0.0083) 4.6555 (0.0126)

4.3409 (0.0048) 4.1958 (0.0031) 4.7775 (0.0057) 4.5774 (0.0040) 5.6177 (0.0078) 6.6824 (0.0062)

5.4633 (0.0080) 5.6778 (0.0056) 6.8358 (0.0074) 5.9956 (0.0066) 6.6336 (0.0108) 6.5801 (0.0097)

4.8956 (0.0071) 4.4499 (0.0053) 4.8149 (0.0096) 4.7812 (0.0068) 5.1417 (0.0132) 4.9209 (0.0125)

−0.0259 (0.0096) −0.3344 (0.0066) 0.0283 (0.0000)

2.4558 (0.0088) 2.4360 (0.0054) 0.0104 (0.0000)

−42.5030 ns (51,346,017.) 1.0512 (0.0126) 0.1095 (0.0001)

1.8180 (0.0141) 1.9995 (0.0084) 0.0536 (0.0001)

3.3973 (0.0158) 3.1383 (0.0109) 0.0054 (0.0001)

3.0037 (0.0133) 2.9316 (0.0088) 0.0421 (0.0001)

2.3199 (0.0103) 2.6090 (0.0060) 0.0563 (0.0000)

3.7655 (0.0153) 3.7601 (0.0097) 0.0105 (0.0001)

1.9833 (0.0314) 4.1088 (0.0081) 0.0209 (0.0001)

3.8803 (0.0098) 3.5441 (0.0068) 0.0094 (0.0001)

4.9499 (0.0090) 4.3537 (0.0067) −0.0026 (0.0001)

4.8261 (0.0085) 4.1650 (0.0064) 0.0205 (0.0001)

5.6119 (0.0110) 4.7328 (0.0096) 0.0131 (0.0001)

5.3882 (0.0090) 4.8403 (0.0070) 0.0491 (0.0001)

4.5661 (0.0133) 4.6680 (0.0082) −0.0038 (0.0001)

5.1412 (0.0073) 4.4574 (0.0051) −0.0082 (0.0000)

8.1392 (0.0079) 5.7889 (0.0077) −0.0228 (0.0001)

5.7736 (0.0094) 7.5492 (0.0050) −0.0274 (0.0001)

e1 No diploma e2 CAP/BEP e3 Bac (general) e4 Bac (profesional)

e5 Bac (technical) e6 DEUG (two-year university degrees) e7 DUT/DEUST (two-year University degrees) e8 BTS (two-years degree) e9 Other higher technical diploma (two-year degrees) e10 Paramedical diploma (two-years degrees) e11 Bachelor's degree (three-year university degrees) e12 Other three-years degrees e13 Maîtrise (four-year university degrees) e14 DEA (five-year general university degrees) e15 DESS (five-year profesional university degrees) e16 Business Schools or grande école (five-year degrees) e17 Engineering Schools or grande école (five-year degrees) e18 PhD (medical degree excluded) e19 PhD (medical degree) Generational trenda

Source: French Labour Force Survey 2003–2010 (Insee); authors' calculations. Note: Women living in a couple. All estimates are significant at the 1% level, except ns for non-significant; standard errors are in parentheses. See Appendix A for a brief presentation of the French education system. a The generational trend is captured by the birth year of the reference individual minus 1970.

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Reference individual/partner diploma

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Our results confirm the existence of strong educational endogamy although it appears less important than pointed out in other research (Goux and Maurin, 2003; Vanderschelden, 2006a). Indeed, the definition of a union under endogamy is stricter when the number of education groups increases: as explained above, our estimations are based on a very disaggregated education variable. However, when based on the estimates of Tables 4 and 5, and the distribution of education diploma by birth cohort, it is possible to produce endogamy indicators with a more aggregated education variable.7 With five education groups the share of individuals from the 1970s cohort that are living in couples with someone of the same education level reaches 40–42%. The share decreases to 26–27% when one retains a more disaggregated approach. Furthermore, the results of our modelling confirm a trend to decreasing educational endogamy in France (Vanderschelden, 2006a; Bouchet-Valat, 2014). When we compare the share of unions in endogamy between the 1960 and the 1970 cohorts, there is a decrease for men from 43% to 40% and from 46% to 42% for women. The estimates of the decrease are higher when one retains the most desegregated approach of education possible with our modelling: it decreases by 11 percentage points for the men (from 37% to 26%) and 8 points for women (from 39% to 27%). The result of a decreasing trend in endogamy and of a higher endogamy for women is consistent with the evidence that men are on average older than their spouses, and from this point of view the result anticipates the general trend of marriage endogamy. The results of the calibration for the 1970 birth cohort that are used for the simulations are reported in the Appendix A (Tables A1 and A2). Among the less educated, women without a degree have a 48.8% probability of forming a union with a spouse with the same level of education. This proportion is about 41.4% for men. For the more-qualified men, the degree of educational endogamy is important: it is about 18.8% for business school graduates, 18% for engineering school graduates and 30.1% for doctors. These probabilities are respectively 14.5%, 49.6% and 29.1% for women. 3.2.2. Estimating age differentials between partners To determine the age differential between partners in the simulation, we also use couples observed in the French Labour Force Survey 2003–2010. We estimate the age difference d at the age of union as a function h following:   d ¼ h ei ; ep ; g i ; t i :

ð9Þ

Where ei is the diploma of the reference individual, ep the diploma of the partner (see Eq. (7)), gi a generational trend and ti the age of the reference individual. As shown by Barre and Vanderschelden (2004), Vanderschelden (2006b) and Mignot (2010), the age differential often favours men, but it tends to decline from generation to generation and with the level of education. Furthermore, Mignot (2010) emphasizes the fact that age difference between partners increases with age for men and decreases for women. Therefore, we use specifications that take into account sex, age, educational level and generation.8 The age differential variable is discrete (it is expressed as a number of years) and can take positive or negative values. We suspect that the effects of explanatory variables are homogeneous across genders, and so we run separate estimations for men and women. But we also suspect that the effect of this variable may change across the distribution of d. For instance, following the same curriculum may increase the probability of marrying at the same age for those who fall in love while at university or in higher education. From this point of view, we decide to reject the classical regression model in order to estimate the age differential between partners. More precisely, we use a binomial negative regression. The negative binomial regression can be used 7 It is possible to estimate a proxy of this distribution from the computation of the French Labour Force Survey, for different years. 8 We exclude individuals aged 80 years old and over, in order to control for survival bias.

229

for overly dispersed data, i.e. when the conditional variance exceeds the conditional mean. The problem of this method is that it does not generate negative values. Consequently, we process the data in two steps. First, we estimate the probability of being younger/the same age/older than the partner. Then, we run our negative binomial regression on absolute values. To deal with the first step, we use a cumulative logit.9 The dependent variable can take three values: −1 if the age differential is negative, 0 if it is equal to 0, and 1 if the age differential is positive. Our estimations are differentiated by sex. The explanatory variables are age, agesquared, a generational trend, the education level and an educational endogamy indicator (i.e. interaction between the diploma of the individual and the diploma of his/her partner). The results provided by this model are presented in Table 6. The results of our model are consistent with the literature: the probability of being older than the partner is weaker for women than for men, the age differential decreases over generations, and the probability of having a positive age differential increases with age. The interaction between education level variables is also significant. For instance, being in a relationship with a partner holding a higher education degree is correlated with a high probability of having a negative age differential. The effect of education variables is nevertheless weak, regarding the other variables, including the educational endogamy indicator. The cumulative logit allows us to distinguish five classes: a partner of the same age, a man older than the woman, a man younger than the woman, a woman older than the man and a woman younger than man. For the last four categories, we need to determine the age differential in years. To this end, we use the distribution of the age differential in absolute values and we run a negative binomial regression. We exclude age differential exceeding the 99th percentile of the distribution because it leads to an important over-dispersion that decreases dramatically the explanatory power of the model.10 We then focus on age differential values, ranged between 0 and 14 years for older women and younger men and between 0 and 19 years for older men and younger women.11 The explanatory variables of the model are age, agesquared, education level and an indicator of educational endogamy. The effect of the generational trend is not significant except for women who are younger than their partner. On the basis of these estimates, we can compute the probability of belonging to each age class.12 Given the over-dispersion parameter v, the probability of having an age differential k is equal to:   v−1  k Γ k þ v−1 v−1 expðXβÞ ;k v−1 þ expðXβÞ k!Γðv−1 Þ v−1 þ expðXβÞ ¼ 0; 1; 2; …; n ð10Þ

P ðz ¼ kÞ ¼

where z is the age differential for a given individual, X his/her characteristics and β the corresponding estimates. To determine the age differential between partners in the simulation, we proceed as follows. We first determine the probability of forming a union with a partner who is younger, older or the same age. If the partner is older or younger, we use the coefficients of Table 7 to compute the probability of having an age differential k. We then draw a random variable in a uniform law and we determine the absolute value of the age differential | d | as | d | = z + 1. Finally, we express the age differential as a numerical value and we determine the age of the partners (tc) as tc = t + d (where t is the age of the reference individual when s/he get matched). With the estimates presented in Section 3.2, it is possible to simulate the age and diploma of the partner when the reference individual enters 9 We also tested a multinomial logit model. The results provided by this method do not differ much from the cumulative logit model, especially regarding the generation effect. 10 The results are available from the authors on request. 11 For the estimation, we subtract 1 from each age differential because the negative binomial law includes zero value. As a consequence, in the simulation, we add 1 to each age differential. 12 The formulas presented here are derived from Long and Freese (2001).

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Table 6 Cumulative logit on age differential.

Intercept 1 Intercept 2 Age Age-square Generational trend Somers'D Concordant pairs (%) N

Men

Women

−0.3449 (0.0039) 0.2257 (0.0039) 0.0325 (0.0001) −0.0002 (0.0000) −0.0099 (0.0001) 0.15 56.6 118,423

−3.4292 (0.0039) −2.8566 (0.0039) 0.0582 (0.0001) −0.0004 (0.0000) −0.0016 (0.0001) 0.14 56.4 120,003

Source: French Labour Force Survey 2003–2010 (Insee); authors' calculations. Note: individuals living in couples aged 16–80 years old. The interaction between the diploma of the individual and the diploma of his/her partner is not displayed (see the Appendix Table A1). All estimates are significant at the 1% level; standard errors are in parentheses.

a union. But the simulation process needs some pieces of information about the partner's past trajectory. For instance, one needs the number of years of experience to compute the current wage; the past trajectory vis-à-vis the labour is needed to calculate the probability of transition from one position to another in the labour market, the current entitlement right to unemployment benefit or a retirement pension.13 To compute the new partner's past trajectory, we make the assumption that the person has not been in union before: we only allow the reference individual to have such a possibility. We randomly draw the new partner from the pool composed of the reference individual's lifecycle, conditional on sex and diploma. It is possible to deduce the past trajectory, when knowing the age of the reference individual on entering a union and the age difference between the reference individual and the new partner. Technically, this corresponds to the assumption that the cohort of the partner faced the same labour market conditions as the cohort of the reference individual. This assumption is reasonable if the age difference between partners is not too high at the cohort level: in France, the literature emphasizes that age diffrences have decreased across generations (Vanderschelden, 2006a; Mignot, 2010.) 3.3. Wage estimations of the individual and the potential partner In the simulation, wages are computed the same way for all individuals (reference individual and their partners). To compute the wage at a given age, we use Mincer wage equation differentiated by diploma. The equation has the following form:   Log we;s;i ¼ α e  ei þ βe  xe;i þ δe  xe;i þ ηes  se;i þ μ e  f e;i þ εe;i :

ð11Þ

we,s,i is the monthly wage available in the French Labour Force Survey 2003–2007. For the individual i with the e diploma working in the s industrial sector (seven items), x is the number of experience years, f a dummy indicating if the individual is a public sector employee (fonctionnaire), and εe, a residual conditioned by diploma e — the results of these estimations are presented in Courtioux et al. (2014), Table 3. The Mincer equations presented here are not directly used to compute the internal rate of returns. They aim to produce an estimate of wages at different ages along the lifecycle.14 In education economics, estimates produced with the Mincer equation are generally considered as biased because the residuals of the wage equation are not independent of the number of years schooling. This is due to the endogeneity of education choices: those who pursue their education have intrinsic productivity characteristics (or “talent”) that are also measured in the residual. Our modelling strategy mitigates this endogeneity bias: the estimates are obtained at a very disaggregated level of diploma. At this level, the unobserved heterogeneity is lower than in the usual estimation methods that focus on years of schooling or the level of education. It is reasonable to 13 14

See below Section 3.3. The annual wage is obtained by multiplying the monthly wage by 12.

think that the intrinsic productivity characteristics are captured at the diploma level: the residual εe,i is conditional on the diploma. The empirical distribution of the residuals conditioned on the diploma (εe,i) is pooled and used during the simulation. Insofar as our estimation stands at a very disaggregated level, we interpret the residual as the matching of an individual (and his/her intrinsic characteristics) and a job: the εe,i distribution gives us the empirical law for each diploma. On the basis of a random draw in this law, we impute a residual for every individual conditional on his/her diploma when he/she gets his/ her first job in the lifecycle. When an individual losses a job, a new residual is randomly drawn in the empirical law when he/she gets a new one. From this point of view, the results presented in the next section control for the potential participation bias for women on the labour market, in a lifecycle perspective. The participation equations that are used across the simulation of the lifecycle are calibrated in order to capture the specific aggregated employment pattern for the women of this given cohort and with respect to their relative probability of being in employment at each age. At an individual level, during the simulation ceteris paribus the women who experience unemployment do not increase their experience incrementally, as fast as women who were in employment permanently. The former therefore have lower wages. This modelling strategy faces some limitations in identifying the specific changes of the diploma effect on wages across generations. However, as far as our estimations are based on cross-section pool data (the French Labour Force Survey 2003–2005), it is not possible to differentiate clearly between a career effect and a generation effect: the increasing number of individuals graduating from higher education across generations has an effect on wage increases that we cannot disentangle from a wage decrease effect, due to more competition among tertiary educated workers.15 However, the modelling strategy is correct if the cohort effect generally put forward in the literature (a decrease in the wage premium across cohorts) is mainly due to: (i) a diploma effect (the premium of elite university/school degrees did not change, but the average negative effect is mainly due to an increase in the number of degrees in other types of institutions); and (ii) an exposure effect to a period of high unemployment rate. In the simulation, effect (i) is controlled for, as far as we are working at a very detailed level of education. Effect (ii) is also controlled at the individual level by the impact that the years of unemployment have on a wage career. As shown in Eq. (2), when an individual is not in employment in a given year in the simulation, we need to compute an unemployment benefit (Ut) or a pension (Rt). Unemployment benefit is computed in line with the current rules of the allocation d'aide au retour à l'emploi (ARE). When an individual is out of a job, entitlement to unemployment benefit is calculated according to social legislation: i.e. based on the previous path of the wage career. The three main components of the pension system are simulated. The basic pension is obtained by applying the official formula for the 25 best years of earnings, resulting from the simulation, as well as the complementary pensions. Middle ranking and senior executives (cadres) benefit from specific schemes. Following the common collective labour agreement, we assume that persons with five years of higher education (equivalent to a master's degree) or more are cadres. Complementary pensions are based on payroll taxes actually paid throughout a person's career: we use the current rates. The public sector regime is also simulated. It applies to persons who have worked for more than 41 years in the public sector, and their pension is then a fixed share of their final salary. To compute Tt, (the last element of Eq. (2)), we apply a simplified individual income tax. French income tax is not based on individual income: it is computed at the household level and depends on the number of persons, including children, within the household. This means that T is rather a theoretical individual income tax that is applied to each individual income in the simulation. As a result, this means that the aggregate revenues of income tax are 15 See Guironnet and Peypoch (2007) and Barros et al. (2011) for a discussion of this issue in the French case.

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Table 7 The negative binomial regression on the age differential. Men

Intercept Age Age2 Generational trend Endogamy Over-dispersion parameter

Women

Oldera

Youngera

Older

Youngera

−0.672 (0.045) 0.071 (0.002) −0.001 (0.000) – – 0.581 (0.005)

0.550 (0.090) 0.029 (0.004) 0.000 (0.000) – – 0.953 (0.015)

−2.085 (0.108) 0.105 (0.004) −0.001 (0.000) – −0.073 (0.017) 0.950 (0.015)

1.238 (0.063) 0.014 (0.002) 0.000 (0.000) 0.008 (0.001) – 0.582 (0.005)

Source: French Labour Force Survey 2003–2010 (Insee); authors' calculations. Note: All estimates are significant at the 1% level; standard errors are in parentheses. a Estimates for the education level and an indicator of educational endogamy are not displayed here (see Appendix Table A2).

overestimated, inasmuch as they do not take into account tax breaks (dépenses fiscales) for family circumstances. 4. Results We now turn to the presentation of the results of the IRR distribution obtained by the simulation, for the generation born in 1970. We take the characteristics – gender, diploma and age of entry into the labour force – of the individuals born between 1968 and 1972, as a representative distribution of the characteristics of this generation.16 On the basis of the FLFS 2003–2007, we can distinguish 457 weighted classes. For instance, women with a business school (or Grande école) degree entering the labour force at 25 constitute one of these classes. From these 457 weighted classes we created 34,714 artificial observations. Next we simulated their lifecycle. We then computed from this simulated database an internal rate of return for each individual with a higher education diploma (as explained in Section 2), and hence we obtained a distribution of these returns. In this analysis, we focus on two indicators. First, we compute an indicator of labour market returns: the internal rate of return corresponding to the stream of income of the reference individual (IRRi). It is used as a counterfactual to estimate the net effect of the potential partner along the distribution of returns to higher education. To compute this counterfactual, the values of Yp,t and Xp,t are set to 0 (see Section 2). On the other hand, we compute an indicator mixing labour market and marriage market returns. This is the internal rate of return taking into account the effect of being in couple (i.e. including the potential partner effect), which corresponds to the indicator detailed in Section 2 (IRRc). In so far as the marriage market as well as the timing of the union and the age differential between partners have different features for men and for women, it is interesting to differentiate the results by gender. Courtioux et al. (2014) in particular show that the share of negative higher education returns of a given cohort is driven by women's paths in the labour market. From this point of view, this is interesting to identify how far the marriage market and assorted mating phenomenon lead to changing the assessments concerning the incentives individuals have in pursuing higher education. To address the issue of simulation robustness, which is by definition based on a set of random draws, we simulated 150 stylized 1970 birth cohorts. Each estimate of Tables 8 and 9 corresponds to the mean of the values obtained for these cohorts. This bootstrapping method enabled us to produce standard errors for each of these estimates.17 16 Using the same modelling for another generation is possible but the estimation of the education structure may suffer some bias: for younger generations, individuals who were still in education during the 2003–2007 period (i.e. those with the highest human capital in the cohort) will be underweighted. In contrast, the estimation of an older generation education structure on this basis may suffer survival bias (i.e. the mortality is higher for less educated individuals, especially for men; for the French case see, for example, Courtioux et al. (2014). 17 This is an improvement compared to the microsimulation method proposed by Courtioux et al. (2014). However, in contrast to this previous study, we do not display a density function because with our bootstrapping method by definition, the standard error is not homogeneous across the distribution of returns.

Regarding Table 8, it should be remembered that, as noted by Courtioux et al. (2014), the returns to tertiary education are highly variable across diploma. This is due to the specificity of the French education system: in particular, the very selective Engineering and Business schools (Grandes écoles) lead to the highest returns for both men and women. Table 8 shows that there is a gender gap in the median rates of return to tertiary education, stemming from the individual career (IRRi). This gap in favour of men is consistent with the gap between men and women identified by the OECD (2008). In our simulations, it amounts 3.5 percentage points. This result is mainly due to the welldocumented gender inequalities in the labour market, especially the gender gap in earnings and labour force participation. From this point of view, one can note that the gap in returns between men and women is lower for students who have completed the five-year cycle in Grandes écoles than for other degrees. At this education level, the gender gap is mainly due to wage differentials: individuals with a five-year Grandes écoles degree are relatively protected from unemployment, whatever their sex. One may expect that the gender gap we pointed out is mitigated by the marriage market: women who generally withdraw from the labour force for family reasons may be living with a male “breadwinner” who is focussing on his labour market career. In our analytical framework that stresses uncertainty, one may expect that the partner's career will add to the uncertainty of the reference individual's career. Our results show that this is particularly true for men: there is no significant change in the value of returns, but the standard error is larger. For women also there is an increase in the standard error but the more interesting evidence concerns a significant increase in the value of the median returns. In our simulations this increase is 5.7 percentage points and it leads to a change in the sign of the gap in favour of women. The positive effect of the marriage market for women (including opportunity costs) is thus related to the fact that higher educated women have access to potential partners who are better-paid and less likely to be unemployed during their careers. The magnitude of this effect is not constant across diplomas and reflects the characteristics of the French

Table 8 Median internal rates of return on higher education in percentage points.

All men Two-year degree Five-year degree All women Two-year degree Five-year degree

University School University School University School University School

IRRi

IRRc

15.82 (1.31) 11.53 (1.10) 18.03 (1.51) 13.57 (0.23) 21.02 (1.75) 12.35 (1.03) 9.54 (0.86) 14.33 (1.20) 13.35 (0.21) 19.37 (1.64)

15.98 (3.75) 12.10 (1.12) 17.51 (1.47) 14.37 (0.22) 20.76 (1.73) 18.07 (1.50) 15.07 (1.35) 20.64 (1.73) 18.46 (0.24) 24.63 (2.08)

Source: authors' calculations. Note: tertiary educated, 1970s birth cohort (based on a set of 150 simulations with boostrap); standard errors are in parentheses.

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Table 9 Share of negative internal rates of return on higher education in percentage points.

All men Two-year degree Five-year degree All women Two-year degree Five-year degree

University School University School University School University School

IRRi

IRRc

0.82 (0.12) 2.37 (0.77) 0.70 (0.15) 0.83 (0.25) 0.12 (0.07) 2.24 (0.46) 13.86 (1.37) 5.52 (0.52) 2.97 (0.43) 2.51 (0.47)

1.63 (0.17) 3.17 (0.81) 1.72 (0.21) 1.04 (0.21) 1.10 (0.12) 5.12 (0.58) 10.48 (1.18) 5.79 (0.52) 3.94 (0.42) 3.80 (0.44)

Source: authors' calculations. Note: tertiary educated, 1970s birth cohort (based on a set of 150 simulations with boostrap); standard errors are in parentheses.

education system (see Appendix A). On average, the marriage market produces 32% of the women higher education median returns. But this amount is higher for the two-year university degrees which are the least prestigious segment of the French higher education system. For the most prestigious segment composed of engineering and business schools the effect of the marriage corresponds to 21% of the returns. To illustrate the impact of the potential partner in the valuation risk of tertiary education, it is possible to retain the share of negative returns as reference indicator of extreme risk. In our analytical framework, this indicator could be interpreted as the risk of not capitalizing on higher education, i.e. having a stream of incomes of lower value than the average individual without a (tertiary) degree. Table 9 indicates that the share of negative returns increases significantly for men and for women. This is consistent with the idea that family formation adds uncertainty to a career: some potential partners with the same education level and the same career perspectives get married with some individuals who do not have a tertiary degree. However, the gender gap is also maintained for the valuation risk of tertiary education. In our simulation, the share of negative returns increases by 0.8 percentage points for men but by almost 3 percentage points for women. In this view, the marriage market does not mitigate the labour market effect on the higher risk on higher education return for women in France, identified in Courtioux et al. (2014).

5. Conclusion With a dynamic microsimulation model focusing on a birth cohort leaving of the education system, we estimate the marginal effect of the marriage market on higher education returns. With a dedicated

demographic module, we explicitly control for the heterogeneity of the union timing, as well as the educational endogamy trends. Our results show gender differences. For men, the marriage market effect is not significant on the median returns. By contrast for women, the marriage market effect corresponds to almost one third of these returns. Despite this huge effect for women, however, our results show that the marriage market does not act as an insurance for guaranteeing returns on higher education. The marriage market increases the risk of not capitalizing on tertiary education for both men and women; because it adds uncertainty about a partner's career to the uncertainty an individual faces concerning his/her career. However, this risk remains higher for women than for men. More generally, these results are consistent with the analysis developed by Ge (2011) and Chiappori et al. (2009) which show that the marriage market has important implications for the educational decisions of women. The evidence of an increase in women's participation in tertiary education, despite gender differences in the related career, may be explained by the effect of the marriage market on returns. However, our results also point to the fact that for a given level of risk aversion, women are less likely than men to enrol in tertiary education. It therefore seems important to target incentives to enrol in higher education for women, from a lifecycle perspective, and from this point of view, family-oriented policies may contribute to filling career gender gaps. Such incentive targeting would complement the equal opportunity recommendations put forward by Courtioux et al. (2014), relating to the problem of risk-adverse students who often come from poor family backgrounds. Acknowledgments The estimation of the microsimulation model introduced in this paper was carried out with several data sets: the French Labour Force Survey for 2003–2007, available online (http://insee.fr); the French Labour Force Survey 1968–2002, the French Survey on Income and Living conditions and the Family History Survey produced by INSEE, whose access was provided by the Quetelet centre (http://www.centre.quetelet. cnrs.fr/). The microsimulation model has been developed at EDHEC Business School, where Stéphane Gregoir and Dede Houeto also contributed to the model. A first version of this paper was presented in the Paris Seminar in Demographic Economics and at the 1st RWI Research Network Conference on the Economics of Education (Berlin). The authors wish to thank Hippolyte d'Albis, Carole Bonnet, Bruce Chapman, Edoardo Ciscato, Stéphane Gregoir, Marion Leturcq, Sophie Pennec, Marc Thévenin, Olivier Thévenon and Florence Thibault and two anonymous referees of the review for their comments and remarks. Any remaining errors are the authors' responsibility.

Appendix A. A brief presentation of the French higher education system In France, school is compulsory until the age of 16. There are some mid-school professional certificates for persons who choose to enter the labour force early (usually about 16): the Certificat d'Aptitude Profesionnelle (CAP) and the Brevet d'Etudes Professionnelles (BEP). At the end of high school (lycée) there is an exam, the Baccalauréat, which it is necessary to pass in order to enrol in higher education. There are three main types of Baccalauréat: the general one (with different sets of majors), and two specialized Baccalauréats (one professional/vocational, and the other technical). France is particular it terms of the great heterogeneity of tertiary education paths. This heterogeneity goes beyond the simple fact that scientific programmes of study are generally more costly than other programmes, and relates to the different institutions in charge of higher education paths and their place in the educational system. Traditionally, at the end of high school, students have to choose between two paths: the State universities and France's higher education institutions known as Grandes écoles. The universities are a practically free, whatever the subject area chosen by a student. The Grandes écoles path involves two steps. The first step consists of two years in State-subsidized preparatory classes (Classe préparatoire aux grandes écoles), which are also free of charge. The second step involves three years study in a Grande école. In this second step, a student's choice of subject has financial consequences: engineering schools are subsidized by the State, whereas business schools are much less subsidized and charge their students high fees. Aside from these two main, traditional paths, there are some other specific diplomas: a two-year technical degree known as a

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BTS (Brevet de Technicien du Supérieur) and provided by technical schools, a DUT (Diplôme Universitaire de Technologie) and a DEUST (Diplôme d'Etude Universitaire Scientifique et Technique). The latter two are two-year specialized degrees offered at some universities.

Table A1 French educational groups. Diploma

Aggregates items

e1 e2 e3 e4 e5 e'5 e6

No diploma CAP/BEP Bac (general) Bac (profesional) Bac (technical) Capacité en droit DEUG (two-year university degrees)

e7 e8 e9 e10 e11 e12

DUT/DEUST (two-year University degrees) BTS (two-years degree) Other higher technical diploma (two-year degrees) Paramedical diploma (two-years degrees) Bachelor's degree (three-year university degrees) Other three-years degrees

e13 e14

Maîtrise (four-year university degrees) DEA (five-year general university degrees)

e15 e16 e17 e18 e19

DESS (five-year profesional university degrees) Business Schools or grande école (five-year degrees) Engineering Schools or grande école (five-year degrees) PhD (medical degree excluded) PhD (medical degree)

University two-year degree School two-year degree

University five-year degree School five-year degree

The FLFS contains a variable which identifies the highest diploma obtained. This enabled us to retain twenty classes of diploma. A.1. A brief description of the microsimulation process Based on an input dataset that represents the distribution of a given birth cohort by gender, diploma and the age of entering the labour force, we simulate the evolution of the position of reference individuals using an annual loop. This simulation takes the following steps for every simulated year, t: known, based on a computation using the estimates presented in 1- For each individual outside of the education system, we simulate Table 1. In our simulation, the individuals that are in couple at age their position on the labour market. Based on the estimates of t are those who have the highest individual value. Table B2 we compute an individual's probability of being inactive. 3- If the current partner is a new partner at age t, we determine the This we multiply by a random draw in a continuous law, uniformly person's characteristics. The diploma is simulated by a random distributed between 0 and 1, in order to obtain an individual value. draw in the distribution of partner's diploma, with can be computed The number of individuals of the cohort that are inactive at age t is from Table 5, the sign of the age difference by a random draw in the known, based on a computation using the estimates presented in distribution (Table 6) and the magnitude of the age difference by anTable B1. In our simulation, the individuals that are inactive at age other random draw in the corresponding distribution (Table 7). To t are those who have the highest individual value. The same operacompute the new partner's past trajectory, conditional on sex and tion is reproduced for the other labour market positions. If the referdiploma, we randomly draw on the past trajectory of the partner ence individual is in living in a couple, we carry out the same until the union, using a pool composed of the reference individual's operations for the partner. lifecycle that has been obtained by a simulation without using a de2- For each individual of the cohort we simulate the position in the mographic module (i.e. as done in Courtioux et al., 2014). marriage market. Based on the estimates of Tables 2 and 3, we com4- When in employment, the wage of the reference individual and of pute an individual probability of being in a couple, which we multithe partner are computed from the estimates of Table A3. If they ply by a random draw in a continuous law, uniformly distributed were not in employment at t − 1, a wage residual is randomly between 0 and 1, in order to obtain an individual value. The number drawn, conditional on the diploma. of individuals of the cohort that are living in a couple at age t is

Table A2 Cumulative logit of age differential (interaction between the diploma of the individual and the diploma of his/her partner). Reference individual's diploma

Partner's diploma

Men

Women

e1

e1 e2 e3–e5 e6–e10 e11–e12 e13 e14–e17 e18–e19

Ref. 0.140 0.277 0.140 0.226 0.077 0.440 −0.605

Ref. 0.339 0.497 0.538 0.388 0.585 0.180 0.025

(0.001) (0.001) (0.001) (0.003) (0.004) (0.005) (0.006)

(0.001) (0.001) (0.002) (0.003) (0.005) (0.003) (0.006) (continued on next page)

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Table A2 (continued) Reference individual's diploma

Partner's diploma

Men

e2

e1 e2 e3–e5 e6–e10 e11–e12 e13 e14–e17 e18–e19 e1 e2 e3–e5 e6–e10 e11–e12 e13 e14–e17 e18–e19 e1 e2 e3–e5 e6–e10 e11–e12 e13 e14–e17 e18–e19 e1 e2 e3–e5 e6–e10 e11–e12 e13 e14–e17 e18–e19 e1 e2 e3–e5 e6–e10 e11–e12 e13 e14–e17 e18–e19 e1 e2 e3–e5 e6–e10 e11–e12 e13 e14–e17 e18–e19 e1 e2 e3–e5 e6–e10 e11–e12 e13 e14–e17 e18–e19

−0.090 0.0846 0.2169 0.1937 0.0453 0.2996 0.4881 −0.5036 −0.1177 0.00688 0.1532 0.1709 0.0877 0.1179 0.2912 −0.4019 −0.090 −0.211 0.056 −0.008 0.077 0.071 0.266 −0.023 −0.301 −0.080 0.143 −0.029 0.070 −0.218 0.073 0.122 −0.199 −0.101 0.086 −0.011 0.033 0.082 0.202 0.325 −0.137 −0.142 −0.133 −0.102 −0.005 −0.063 −0.057 −0.349 −0.039 0.287 0.016 −0.040 −0.044 −0.108 0.067 0.049

e3–e5

e6–e10

e11–e12

e13

e14–e17

e18–e19

Women (0.001) (0.001) (0.001) (0.001) (0.003) (0.004) (0.005) (0.009) (0.00131) (0.00148) (0.00124) (0.00148) (0.00242) (0.00305) (0.00383) (0.00584) (0.002) (0.002) (0.002) (0.001) (0.002) (0.003) (0.003) (0.005) (0.003) (0.004) (0.003) (0.002) (0.002) (0.003) (0.004) (0.006) (0.005) (0.006) (0.004) (0.003) (0.003) (0.003) (0.004) (0.008) (0.003) (0.003) (0.002) (0.002) (0.002) (0.003) (0.002) (0.004) (0.006) (0.008) (0.004) (0.003) (0.005) (0.005) (0.004) (0.003)

0.183 0.357 0.600 0.743 0.356 0.528 0.474 −0.192 0.258 0.461 0.522 0.685 0.249 0.425 0.438 0.163 0.398 0.463 0.634 0.734 0.586 0.674 0.667 0.306 0.324 0.661 0.747 0.745 0.544 0.648 0.668 0.315 0.548 0.434 0.703 0.813 0.892 0.569 0.755 0.407 0.292 0.251 0.563 0.651 0.736 0.609 0.923 0.524 1.033 0.977 0.844 0.578 0.324 0.107 0.910 0.293

(0.001) (0.001) (0.001) (0.002) (0.004) (0.006) (0.003) (0.008) (0.00118) (0.00112) (0.00124) (0.00152) (0.00285) (0.00365) (0.00245) (0.00447) (0.001) (0.001) (0.001) (0.001) (0.002) (0.003) (0.002) (0.003) (0.003) (0.003) (0.002) (0.002) (0.002) (0.003) (0.002) (0.005) (0.004) (0.004) (0.003) (0.003) (0.003) (0.003) (0.003) (0.005) (0.005) (0.005) (0.004) (0.003) (0.004) (0.004) (0.002) (0.004) (0.006) (0.009) (0.006) (0.005) (0.006) (0.008) (0.004) (0.003)

Source: French Labour Force Survey 2003–2010 (Insee); authors' calculations. Note: individuals living in couples aged 16–80 years old. All estimates are significant at the 1% level; standard errors are in parentheses.

Table A3 The negative binomial regression on the age differential (interaction between the diploma of the individual and the diploma of his/her partner). Reference individual's diploma

Men older

Men younger

Women younger

Partner's diploma

Partner's diploma

Partner's diploma

e1

e2 e3–e19

−0.04 0.06

(0.01) (0.01)

e2

e1; e3–e19 e2

−0.12 −0.19

(0.01) (0.01)

e2 e3–e5 e6–e10 e11–e19 e1 e2 e3–e5 e6–e10 e11–e12 e13–e19

−0.21 −0.18 −0.36 −0.13 −0.05 −0.31 −0.38 −0.48 −0.39 −0.30

(0.03) (0.05) (0.06) (0.07) (0.03) (0.03) (0.04) (0.05) (0.10) (0.11)

e2 e3–e19

−0.30 −0.13

(0.01) (0.02)

e1 e2 e3–e5 e6–e10 e11–e12 e13–e19

−0.17 −0.37 −0.35 −0.45 −0.16 −0.13

(0.01) (0.01) (0.03) (0.03) (0.06) (0.05)

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Table A3 (continued) Reference individual's diploma

Men older

Men younger

Women younger

Partner's diploma

Partner's diploma

Partner's diploma

e3–e5

e1–e2 e3–e5 e6–e17 e18–e19

−0.04 −0.10 −0.12 −0.35

(0.02) (0.02) (0.02) (0.12)

e2 e3–e5 e6–e10 e11–e12 e13–e19

−0.14 −0.53 −0.42 −0.28 −0.45

(0.05) (0.05) (0.06) (0.10) (0.09)

e6–e10

e1–e2 e3–e5 e6–e10 e11–e12 e13–e17 e18–e19

−0.13 −0.11 −0.27 −0.22 −0.14 −0.44

(0.02) (0.03) (0.02) (0.04) (0.04) (0.11)

e1–e2 e3–e5 e6–e10 e11–e12 e13–e19

−0.10 −0.30 −0.65 −0.45 −0.34

(0.05) (0.06) (0.05) (0.09) (0.08)

e11–e12

e1 e2–e10; e13–e17 e11–e12 e18–e19

0.09 −0.07 −0.14 −0.43

(0.05) (0.03) (0.04) (0.11)

e1–e5 e6–e10 e11–e12 e13–e19

−0.20 −0.43 −0.61 −0.49

(0.07) (0.10) (0.10) (0.10)

e13

e1–e5 e6–e12; e14–e19 e13

0.13 −0.08 −0.26

(0.04) (0.04) (0.06)

e1–e12 e13 e14–e19

−0.24 −0.61 −0.62

(0.07) (0.14) (0.17)

e14–e17

e1–e5 e6–e10 e11–e12 e13 e14–e17 e18–e19

−0.06 −0.19 −0.28 −0.25 −0.31 −0.41

(0.03) (0.03) (0.05) (0.05) (0.04) (0.08)

e1–e5 e6–e10 e11–e12 e13 e14–e17 e18–e19

−0.19 −0.49 −0.52 −0.43 −0.85 −0.76

(0.06) (0.08) (0.10) (0.11) (0.08) (0.16)

e18–e19

e1–e5 e6–e17 e18–e19

0.10 −0.09 −0.25

(0.05) (0.03) (0.05)

e1–e12 e13 e14–e17 e18–e19

−0.19 −1.02 −0.67 −0.89

(0.08) (0.24) (0.19) (0.14)

e1 e2 e3–e5 e6–e10 e11–e12 e13–e19 e1 e2 e3–e5 e6–e10 e11–e12 e13 e14–e17 e18–e19 e1–e2 e3–e5 e6–e10 e11–e12 e13 e14–e17 e18–e19 e1–e2 e3–e5 e6–e10 e11–e12 e13 e14–e17 e18–e19 e1 e2 e3–e5 e6–e10 e11–e12 e13 e14–e17 e18–e19 e1–e5 e6–e10 e11–e12 e13 e14–e17 e18–e19

−0.16 −0.33 −0.38 −0.43 −0.15 −0.14 −0.20 −0.35 −0.50 −0.57 −0.26 −0.36 −0.40 −0.15 −0.12 −0.38 −0.59 −0.41 −0.42 −0.50 −0.19 −0.17 −0.26 −0.55 −0.45 −0.53 −0.50 −0.40 −0.21 −0.16 −0.43 −0.41 −0.45 −0.36 −0.65 −0.23 −0.20 −0.64 −0.58 −0.24 −0.61 −0.37

(0.02) (0.02) (0.02) (0.03) (0.05) (0.03) (0.02) (0.02) (0.03) (0.02) (0.04) (0.06) (0.03) (0.05) (0.03) (0.05) (0.04) (0.04) (0.07) (0.04) (0.08) (0.04) (0.06) (0.05) (0.07) (0.06) (0.05) (0.09) (0.07) (0.07) (0.07) (0.05) (0.07) (0.07) (0.04) (0.08) (0.08) (0.11) (0.11) (0.13) (0.08) (0.05)

Source: French Labour Force Survey 2003–2010 (Insee); authors' calculations. Note: All estimates are significant at the 1% level; standard errors are in parentheses.

A.2. Some characteristics of the birth cohort 1970

Fig. A1. Proportion of individuals living in a couple, by age. Source: FLFS 1969–2010; authors' calculations. Note: Simulation for the 1970 birth cohort. We assume an unemployment rate of 8% throughout the period.

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Table A4 Share of matching by diploma for the cohort born in 1970 (men). Reference individual/partner diploma

e1

e2

e3

e4

e5

e6

e7

e8

e9

e10

e11

e12

e13

e14

e15

e16

e17

e18

e19

e1 e2 e3 e4 e5 e6

0.414 0.256 0.137 0.197 0.142 0.414

0.263 0.373 0.141 0.233 0.213 0.263

0.075 0.070 0.226 0.103 0.091 0.075

0.033 0.042 0.026 0.076 0.033 0.033

0.051 0.070 0.056 0.073 0.145 0.051

0.010 0.012 0.025 0.014 0.018 0.010

0.008 0.013 0.020 0.019 0.025 0.008

0.053 0.071 0.104 0.123 0.126 0.053

0.003 0.003 0.006 0.005 0.006 0.003

0.028 0.035 0.049 0.057 0.059 0.028

0.023 0.022 0.070 0.048 0.057 0.023

0.005 0.004 0.016 0.006 0.009 0.005

0.016 0.015 0.060 0.029 0.038 0.016

0.003 0.002 0.012 0.004 0.005 0.003

0.008 0.006 0.025 0.007 0.018 0.008

0.001 0.001 0.007 0.001 0.002 0.001

0.002 0.002 0.004 0.002 0.004 0.002

0.001 0.001 0.005 0.000 0.002 0.001

0.003 0.001 0.011 0.003 0.007 0.003

e7 e8 e9

e10 e11

e12 e13 e14 e15

e16

e17

e18 e19

No diploma CAP/BEP Bac (general) Bac (profesional) Bac (technical) DEUG (two-year university degrees) DUT/DEUST (two-year University degrees) BTS (two-years degree) Other higher technical diploma (two-year degrees) Paramedical diploma (two-years degrees) Bachelor's degree (three-year university degrees) Other three-years degrees Maîtrise (four-year university degrees) DEA (five-year general university degrees) DESS (five-year profesional university degrees) Business Schools or grande école (five-year degrees) Engineering Schools or grande école (five-year degrees) PhD (medical degree excluded) PhD (medical degree)

0.063 0.092 0.150 0.024 0.042 0.115 0.022 0.112 0.008 0.064 0.111 0.021 0.099 0.021 0.038 0.004 0.001 0.006 0.010 0.077 0.109 0.102 0.030 0.068 0.032 0.100 0.148 0.008 0.078 0.094 0.020 0.064 0.007 0.031 0.012 0.009 0.004 0.009 0.103 0.153 0.106 0.037 0.077 0.024 0.026 0.192 0.007 0.064 0.071 0.014 0.062 0.011 0.028 0.005 0.010 0.003 0.009

0.088 0.157 0.104 0.014 0.045 0.023 0.009 0.157 0.030 0.082 0.075 0.030 0.063 0.021 0.031 0.020 0.011 0.012 0.028 0.067 0.102 0.064 0.009 0.040 0.021 0.027 0.080 0.005 0.380 0.060 0.011 0.059 0.008 0.031 0.005 0.003 0.001 0.028

0.056 0.067 0.101 0.021 0.045 0.035 0.022 0.080 0.005 0.071 0.246 0.022 0.112 0.019 0.053 0.008 0.011 0.009 0.015 0.047 0.056 0.079 0.012 0.027 0.020 0.025 0.125 0.020 0.054 0.089 0.139 0.107 0.039 0.076 0.020 0.019 0.020 0.026 0.042 0.048 0.088 0.015 0.041 0.025 0.022 0.084 0.004 0.060 0.146 0.027 0.228 0.029 0.083 0.011 0.013 0.016 0.019 0.033 0.029 0.062 0.002 0.021 0.024 0.029 0.068 0.007 0.059 0.126 0.041 0.173 0.125 0.117 0.011 0.025 0.026 0.025

0.037 0.046 0.069 0.009 0.025 0.018 0.031 0.097 0.011 0.066 0.094 0.046 0.120 0.042 0.188 0.031 0.017 0.023 0.031

0.037 0.041 0.069 0.007 0.017 0.013 0.034 0.115 0.012 0.058 0.066 0.055 0.102 0.041 0.098 0.180 0.016 0.011 0.029

0.042 0.052 0.078 0.011 0.028 0.019 0.022 0.116 0.008 0.071 0.096 0.036 0.103 0.032 0.077 0.031 0.129 0.022 0.026 0.015 0.018 0.038 0.008 0.021 0.020 0.018 0.068 0.005 0.057 0.090 0.037 0.151 0.085 0.115 0.030 0.041 0.150 0.033

Source: French Labour Force Survey 2003–2010 (Insee); authors' calculations. Note: Men living in a couple, 1970 birth cohort.

Table A5 Share of matching by diploma for the cohort born in 1970 (women). Reference individual/partner diploma

e1

e2

e3

e4

e5

e6

e7

e8

e9

e10

e11

e12

e13

e14

e15

e16

e17

e18

e19

e1 e2 e3 e4 e5 e6

0.488 0.289 0.225 0.294 0.229 0.488

0.357 0.506 0.258 0.372 0.362 0.357

0.037 0.036 0.157 0.049 0.056 0.037

0.024 0.034 0.038 0.078 0.044 0.024

0.022 0.034 0.038 0.035 0.089 0.022

0.003 0.004 0.018 0.007 0.007 0.003

0.008 0.012 0.029 0.021 0.028 0.008

0.031 0.048 0.087 0.082 0.096 0.031

0.002 0.004 0.007 0.002 0.004 0.002

0.003 0.004 0.007 0.003 0.006 0.003

0.006 0.007 0.028 0.017 0.018 0.006

0.003 0.003 0.013 0.005 0.007 0.003

0.005 0.005 0.027 0.012 0.018 0.005

0.001 0.001 0.006 0.000 0.003 0.001

0.003 0.004 0.015 0.005 0.008 0.003

0.001 0.001 0.006 0.002 0.002 0.001

0.006 0.007 0.029 0.011 0.016 0.006

0.001 0.001 0.004 0.002 0.003 0.001

0.001 0.001 0.008 0.003 0.003 0.001

e7 e8 e9

e10 e11

e12 e13 e14 e15

e16

No diploma CAP/BEP Bac (general) Bac (profesional) Bac (technical) DEUG (two-year university degrees) DUT/DEUST (two-year University degrees) BTS (two-years degree) Other higher technical diploma (two-year degrees) Paramedical diploma (two-years degrees) Bachelor's degree (three-year university degrees) Other three-years degrees Maîtrise (four-year university degrees) DEA (five-year general university degrees) DESS (five-year profesional university degrees) Business Schools or

0.160 0.231 0.091 0.030 0.040 0.072 0.047 0.106 0.008 0.012 0.051 0.018 0.039 0.011 0.021 0.006 0.037 0.010 0.010 0.119 0.224 0.069 0.042 0.053 0.013 0.143 0.113 0.003 0.015 0.030 0.021 0.034 0.013 0.034 0.016 0.042 0.009 0.008 0.168 0.249 0.073 0.050 0.053 0.013 0.042 0.165 0.010 0.009 0.023 0.021 0.026 0.006 0.021 0.011 0.045 0.007 0.007

0.153 0.210 0.080 0.033 0.046 0.017 0.042 0.102 0.036 0.010 0.027 0.063 0.024 0.013 0.042 0.021 0.057 0.010 0.016 0.151 0.237 0.062 0.041 0.046 0.014 0.041 0.101 0.010 0.079 0.036 0.017 0.034 0.010 0.026 0.010 0.048 0.010 0.029

0.125 0.137 0.086 0.031 0.041 0.023 0.047 0.104 0.009 0.012 0.121 0.027 0.080 0.020 0.035 0.011 0.063 0.015 0.014 0.100 0.095 0.073 0.018 0.025 0.017 0.040 0.081 0.013 0.008 0.042 0.161 0.056 0.025 0.068 0.035 0.092 0.025 0.026 0.097 0.110 0.083 0.025 0.033 0.023 0.037 0.108 0.008 0.013 0.062 0.036 0.140 0.031 0.052 0.019 0.077 0.030 0.016 0.075 0.077 0.075 0.017 0.020 0.022 0.018 0.083 0.012 0.008 0.046 0.058 0.078 0.099 0.081 0.034 0.108 0.073 0.018

0.094 0.072 0.063 0.011 0.026 0.016 0.031 0.087 0.007 0.012 0.055 0.046 0.091 0.037 0.145 0.035 0.110 0.039 0.022

P. Courtioux, V. Lignon / Economic Modelling 57 (2016) 221–237

237

Table A5 (continued) Reference individual/partner diploma

e17

e18 e19

grande école (five-year degrees) Engineering Schools or grande école (five-year degrees) PhD (medical degree excluded) PhD (medical degree)

e1

e2

e3

e4

e5

e6

e7

e8

e9

e10

e11

e12

e13

e14

e15

e16

e17

e18

e19

0.049 0.051 0.063 0.003 0.014 0.006 0.048 0.056 0.018 0.007 0.031 0.046 0.047 0.013 0.091 0.236 0.164 0.039 0.016

0.052 0.058 0.027 0.007 0.017 0.001 0.025 0.083 0.007 0.003 0.030 0.031 0.039 0.022 0.036 0.015 0.496 0.039 0.014 0.065 0.046 0.057 0.000 0.018 0.011 0.020 0.042 0.013 0.003 0.041 0.055 0.081 0.038 0.085 0.017 0.134 0.233 0.040

Source: French Labour Force Survey 2003–2010 (Insee); authors' calculations. Note: Women living in a couple, 1970 birth cohort.

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