Economic Modelling 38 (2014) 328–340

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Economic Modelling

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Modelling the distribution of returns on higher education: Amicrosimulation approach☆

Pierre Courtioux a,⁎, Stéphane Gregoir a, Dede Houeto b

a Edhec Business School, 16–18 rue du 4 septembre, 75002 Paris, Franceb PSE—Paris School of Economics, 48 boulevard Jourdan, 75014 Paris France

☆ The estimation of themicrosimulationmodel introducwith three sets of data: the French Labour Force Survey f(http://www.insee.fr); the French Labour Force Survey 1provided by the Quetelet Centre (http://www.centre.quetrates and their forecasts based on Vallin and Meslé (Monteil (2005). The microsimulation model is developVincent Lignon also contributed to the development of thefromEDHECBusiness School funding for this researchworanonymous referees for their comments that helped impr⁎ Corresponding author at: EDHEC Business School —

Septembre 75002 Paris, France. Tel.: +33 1 53 32 76 44;E-mail addresses: pierre.courtioux@edhec.edu (P. Cou

stephane.gregoir@edhec.edu (S. Gregoir), dkhoueto@hotm

0264-9993/$ – see front matter © 2014 Elsevier B.V. All rihttp://dx.doi.org/10.1016/j.econmod.2014.01.010

a b s t r a c t

a r t i c l e i n f o

Article history:Accepted 6 January 2014Available online 15 February 2014

JEL classification:C6J11J24

Keywords:Return to educationHigher educationDynamic microsimulation

Cost-sharing policies for higher education have been implemented in several countries in variousways.We arguethat to assess their appropriateness and facilitate their implementation it is necessary to develop statisticalindicators of the distribution of returns. When starting a higher education programme, the return on a particulardegree is uncertain, and risk-adverse students or those from low-income familiesmay be reluctant to enrol if thismeans taking out a loan. These statistical indicators would therefore be natural inputs of cost-sharing policiesintended to preserve the individual economic incentives to go to university and simultaneously provide aninsurance role. We present a dynamic microsimulation model of individual lifetime educational output in theFrench labour market which uses econometric modelling of individual wages, labour market transitions, socialsecurity contributions and benefits. It relies largely on labour force survey data and mortality tables. In thestandard internal rate of return framework, the model is used to compute the distribution of returns to highereducation, for a given generation. The results show that the percentage of negative returns is close to 3.5%.

© 2014 Elsevier B.V. All rights reserved.

1. Introduction

In terms of public policies, investing in education is a key issue fordeveloped countries. The European Lisbon Strategy and its educationalcomponent, the so-called ‘Education and Training 2010’, emphasises thelink between the education system and social cohesion, and it establisheseducational targets such as numbers of early school leavers or an increasein the proportion of Master of Science and Technology graduates(Commission of the European Communities, 2005). Most of these objec-tives have been maintained and complemented in the new guidelinesissued in 2010 in EU 2020 (Commission of the European Communities,2010). More generally, a benchmarking process of the organisation ofeducation and outcomes in developed countries is in progress (OECD,2008). It relies on a set of national indicators such as the mean returnon higher education. In this article, we illustrate how a microsimulationapproach to education outcomes can enhance the description of the

ed in this paper was carried outor 2003–2007, available online968–2002, to which access waselet.cnrs.fr/); and the mortality2001) and Robert-Bobée anded at EDHEC Business School,model. Dede Houeto benefited

k. The authorswish to thank theove this article.Paris Campus 16–18, rue du 4fax: +33 1 53 32 76 31.rtioux),ail.com (D. Houeto).

ghts reserved.

outcomes, and provide decision-makers and would-be students withrelevant information by means of relatively straightforward modelling.We present a dynamic microsimulation model of France's educationaloutput, based mainly on Labour Force Survey data and mortality tables(for a presentation of the French education system see for instanceGivord and Goux (2007)). Compiled statistics complement the OECD(2003, 2008) indicator of the mean return on higher education by pro-ducing indicators of higher education valuation risk. For every country,the OECD indicator shows that returns to higher education are largelyabove the interest rate. This is generally interpreted as an argument infavour of developing a cost-sharing policy. For countries where highereducation costs are largely subsidized, this leads to the recommendationof an increase in the student contribution to training costs,without takinginto account the possibly large variability of these returns. In this context,our modelling strategy provides a measure of the risks associated withthese returns, which should also be taken into account in the design ofcost-sharing schemes to promote a sound higher education policy.

The paper is organised as follows: in Section 2, we introduce and dis-cuss the internal rate of return framework in higher education for the in-dividuals of a given generation; in Section 3, we set out in detail themicrosimulation modelling; in Section 4, we present and discuss the re-sults for our indicator of higher education valuation risk; and Section 5concludes.

2. A distribution perspective on higher education returns

According to the classical approach of education economics, educa-tion can be considered as an input of human capital that impacts on

1 The classe préparatoire is a twoyear programme to prepare for entry into a grande écolefollowing national competitive exams. Education in the grandes écoles traditionally ends atMaster's level.

329P. Courtioux et al. / Economic Modelling 38 (2014) 328–340

earnings over the course of a lifetime. The gains of such an investmentare usually assessed by computing the individual internal rate of returnof one additional year of education. Since the seminal work of Mincer(1974), measuring the internal rate of return to education has becomea key dimension of the analysis of education choices (see alsoHeckman et al. (2006)). More recently, the introduction of uncertaintyin the dynamic modelling of education choices has put the stress onanalysing the distribution of returns, but few studies assess why indi-viduals choose different types of education, and the career conse-quences of these choices (Altonji et al. (2012)). For instance, inBuchinsky and Leslie (2010), the schooling choice is determined byintegrating over uncertain future outcomes, including wages which de-pend on the individual level of education and experience. They assumethat agents have access to estimates of past wage distributions fromwhich they forecast future distributions, in order to make their educa-tional choices. Their model is partially estimated and partially calibrat-ed. They show that the introduction of unobserved heterogeneity cansubstantially improve the description of educational choices and conse-quently of wage outcomes.

Our research explores the idea that part of this heterogeneity stemsfrom the education system linked to the heterogeneity of education ser-vices that students benefit from.We illustrate how this heterogeneity ofeducation services – in terms of subsidies and costs –may impact on thedistribution of internal rates of return on higher education.

From an empirical point of view, such a perspective is demanding, asit requires working on some long-term panel data (for instance as inGuvenen (2009)), with variables including diploma obtained and tra-jectories on the labour market. Such data sets are rarely available. InFrance, the DEPP (National Department of Education Evaluation)panel data is available for some recent generations: individuals whocompleted secondary education between1996 and 2001. However,this panel does not allow a career to be modelled. This is the reasonwhy we use microsimulation modelling to produce (under some con-servative assumptions) long-term panel data for a given cohort withsuch variables. Based on this cohort, we compute a distribution of inter-nal rates of return on higher education: see Section 4. The simulation ofthe cohort analysed is obtained by combining estimation and calibra-tion: see Section 3.

In this view based on past observations, we analyse the distribution ofex ante returns in a framework of choiceswith uncertainty about returns.Four assumptions are necessary to interpret our results as ex antedistribution.

1) There is uncertainty about future earnings an individual will obtainfrom a wage career distribution; this distribution is conditional onthe diploma obtained, but can also be analysed by gender or for thetwo-digit sectors of economic activity in which the career is situated.

2) 2.1) The student is not aware of his/her own talent/preferences forstudying and work. 2.2) However he/she thinks it is possible toobtain a higher education degree, even if he/she does not knowwhat level of degree will be obtained or does not have informationabout the relative quality of the higher education institution deliver-ing degrees.

3) The education decision does not concern a marginal year of school-ing, but an education track which leads to a diploma.

4) The individual decision of pursuing higher education is taken atthe age when the student could legally enter the labour force.This decision is irreversible.

As explained earlier, Assumption 1 has become a key feature of edu-cation choice analysis (Buchinsky and Leslie, 2010). Assumption 2.1 is asimplification of the information context an individual faces in makingdecisions about education. The knowledge the student has about his/her own talent may not be homogenous in a given cohort, and couldbe blurred by the institutional knowledge the student has of the variouspaths that lead to the same profession. Thismay depend on his/her fam-ily social background and associated social capital (see, for example,

Flacher and Harari-Kermadec (2013) for a review and discussion ofsocial capital). However, at this stage of our understanding of thisissue, incomplete information students have about their talents andinstitutions seems to be a reasonable assumption. Assumption 2.2, isanother simplification, as eventually there are numerous universitydrop-outs in France OECD (2010). In our analysis, relaxing this assump-tion would affect the computation of our distribution of returns (seeSection 4). University drop-outs cannot be identified in the data setwe have used. However, introducing them would negatively impacton the distribution of returns. This is because, while controlling for thelevel of the highest diploma obtained, the later entry into the labourforce by students who drop out raises their individual opportunitycosts (see below in this section for the calculation of individual rate ofreturn). We nevertheless stick to this assumption as it is consistentwith the organisation of France's very selective tertiary education sys-tem. (for a presentation of the French higher education system, seeCourtioux, 2012). From this point of view, it should be borne in mindthat the main uncertainty for a student who has been selected for aclasse préparatoire1 concerns the rank of the tertiary education institu-tion he/she is subsequently admitted to. In case a student fails to enteran elite school (grande école) he/she may still carry on studying at uni-versity, which is often seen as a less prestigious track. Assumption 3 isnot commonly used in education economics: this is partly due to the dif-ficulty of estimating structural dynamic models of education choices,but this is a promising area of research in education economics (seeAltonji et al. (2012) for a discussion). Moreover, this assumption ismore in line with the institutional features of the French education sys-tem, and leads to more clear-cut policy recommendations concerningthe different segments of the education system. Assumption 4 is clearlya simplification of amore complex decision-makingprocess, which is bynature sequential and leads to the partial irreversibility of some deci-sions concerning investment in human capital (see Altonji et al.(2012) for a discussion). From this point of view, the results presentedin this article correspond to a simplified case: the irreversibility ofeducation choices is total and occurs at entry into the tertiary educationsystem. The results we present also correspond to the distribution of exante returns for the first sequence of individual choices in education. Infurther research, the impact of these assumptions on our results shouldbe analysed more specifically. An interesting complement would be tocompute a distribution of returns for every year of schooling chosen,conditional on the diploma already obtained. Such a developmentneeds data on the individual educational trajectories which are notused in the analysis we propose here.

It is noteworthy that Assumptions 2, 3 and 4 are also implicitlymadein the construction of OECD (2008) indicators of returns on higher edu-cation. However, the OECD's methodology does not consider the uncer-tainty of future wages conditional on the diploma. In this view, theresults we obtain for France are innovative and complement the previ-ously available OECD benchmark.

Weusemicrosimulation techniques toproduce a large set of individ-ual histories for a given cohort. Themicrosimulation approach has beenused to analyse various issues in economics, notably welfare reforms(Arntz et al., 2008), corporate tax systems (Creedy and Gemmel,2009), or to complete computable general equilibrium models (see forinstance Magnani and Mercenier, 2009; Mabugu and Chitiga, 2009).From an education economics perspective, microsimulation modellinghas to tackle two sets of problems. On the one hand, it has to capturethe dynamics of individual trajectories in a given tax-benefit regime.Such problems are traditionally addressed by dynamic microsimulationtechniques (see for instance Harding, 1993; Li and O'Donoghue, 2013;Nelissen, 1998; van Sonsbeek, 2010; van Sonsbeek and Ablas, 2012).

330 P. Courtioux et al. / Economic Modelling 38 (2014) 328–340

On the other hand, it has to take into account as precisely as possible ed-ucational heterogeneity in terms of years of schooling and diplomatypes, as well as their economic counterparts in the labour market, interms of employment trajectories, direct wages, unemployment bene-fits and retirement pensions.

Working with a simulated cohort, we can compute the distributionof internal rate of returns for individuals who have passed through ter-tiary education. Following the human capital approach initiated byBecker (1962), the internal rate of return is obtained by equating thepresent value of the stream of income when a person invests inhuman capital to the present value when there is no investment. If Yis the stream of income when an agent pursues higher education andtherefore enters the job market later and X is the stream of incomewhen he/she does not pursue higher education and enters the jobmarket directly, then the internal rate of return of this individual (r)solves the following equation:

XMt¼0

Yt−Xt

1þ rð Þtþ1 ¼ 0 ð1Þ

where t is a time period index andM is the total number of period unitslived by the individual.

We look for a representative measure of returns to higher educationconsecutive to the uncertainty of future wages offered to the individual.We decompose the streamof incomes of people in both situations. Yt canbe decomposed into five components as follows:

Yt ¼ Wt þ Ut þ Rt−Tt−Ft ð2Þ

where Wt is the individual net wage at period t, Ut the unemploymentbenefit, Rt the retirement pension, Tt the individual income tax and Ftthe fees. For a given point in time, some of the elements which composethe labour market outputs may be equal to zero. For instance, the fees(Ft) are positive during the tertiary education period and equal to zeroafterwards.2 If the individual is employed during period t, theunemployment benefit (Ut) is equal to zero. If the individual is notretired during period t, the retirement pension (Rt) is equal to zero.When one considers the course of a lifetime, the components of Yt arenot independent: the level of pensions and of unemployment benefitsare linked to the past wage paths. In our model, we analyse these linkswith the tax benefit component of our microsimulation model (seeSection 3.2).

We work on the assumption that the counterfactual stream of in-come obtained when not pursuing tertiary education can be estimatedby the average earnings by age for the individuals who did not obtaina higher education degree.3 This assumption is consistent with the edu-cation choice framework we presented above. Their earnings are thusdefined as follows:

Xt ¼

XNi¼1

Wt;i þ Ut;i þ Rt;i−Tt;i−Ft;i� �

Nð3Þ

where N is the number of individuals without a tertiary diplomawithinthe given generation, and Xt is the average net income for a givengeneration at the age corresponding to the period t for the individualswithout tertiary diploma, weighted by the probability of beingemployed at this age. The individual stream of income of individualswho have invested in higher education therefore constitutes a way ofassessing the distribution of returns to higher education associated

2 In France, tuition fees are largely subsidised. Except for some specific courses, fees donot have a large impact on opportunity costs. As a simplification,we assume here that feesare equal to zero.

3 We decided not to retain a gender-specific counterfactual, in order to produce a set ofreturn indicators which were not biased by the fact that the individual behaviour vis-à-visthe labour market could be determined by a joint decision within the household.

with a particular degree. However, a given diploma can itself be relatedto particular sets of characteristics in terms of skills and social positionwhich are not captured in the reference counterfactual stream of in-comes when no degree has been completed. This unobserved heteroge-neity may have an impact on the ex post rate of return on highereducation (i.e. the realisation of an individual's wage career). In theframework introduced above, this computation is consistent with theassumption that the student's knowledge about his/her talents isweak. It does not take into account the influence of the signal associatedwith a degree thatmay reduce the correlation between professional tal-ents and academic skills.

Opportunity costs for higher education training varywith the curricu-lum followed by an individual, which is consistent with our non-sequential analytical framework of higher education choice. Eq. (3)does not explicitly take into account this feature. For instance, some stu-dents may follow a tertiary education curriculum for only two years andthen enter the labourmarket, whereas othersmay choose to followa lon-ger curriculum and therefore face higher opportunity costs. Moreover,some individuals may fail their exams; they then enter the labour forceolder with higher opportunity costs than the average for individualswith the same level of qualification. To capture this variety in higher ed-ucation investment that has an impact on the level of returns, we adaptthe computation of Xt during the education period of the lifetime toeach level of tertiary education (e) already attained by each person.Here, e stands for the degree level and can be ordered: it correspondsto the breakdown of higher education degrees presented in Appendix,Table A1 (classification 2).

Xe;t ¼ W0;t þ U0;t þ R0;t−T0;t if L≤t ð4:1Þ

Xe;t ¼ MAX X0;t ;X1;t ;…;Xe;t

n oif LNt ð4:2Þ

where L is the date atwhich the individual in our simulated cohort entersthe labour force. In this framework, two individuals with the same diplo-ma entering the labour force at different ages (L) face different opportu-nity costs. The one who enters the labour force later incurs an additionalcost due to the delay period. Opportunity cost estimation depends on thelevels of education that could have been attained by a person of the sameage (Eq. (4.2)). Thismeans that opportunity costs are increasingwith age(t): they take into account the experience premium on wages of thosewho enter the labour force early, and the education premium of thosewho have got their degree and are on the labour market – whatevertheir position – at the given age t.

In this framework, a negative individual internal rate of return on ed-ucation remainspossible for educatedpeople: itmeans that the individualgains associatedwith a person's highest degree are not sufficient to coverthe losses associated with the number of years training, so that the pres-ent value of the individual's stream of income remains less than that ofthe average career of those who do not complete a tertiary diploma.

3. A dynamic microsimulation model for France

Our modelling simulates the age effect conditionally on the highestdegree. The specification of our microsimulation model is constrainedby the data available. We have at our disposal the French Labour ForceSurvey (FLFS) for the period 1968–2007, but the definition of the educa-tion variable was changed in 2003 and is nowmore detailed. We choseto use the FLFS 2003–2007 to capture the effect of diploma at a moredisaggregated level. The FLFS 2003–2007 is then used to define the de-terminant of wages conditional to the highest degree obtained. It is alsoused to identify the relative probability of transition into the labourmarket conditional to the highest degree obtained. This leads us tofocus on the simulation of a generation which is well-represented inthe labour force during the years 2003–2007, in order to reduce thecohort effect bias in our simulation, i.e. the generation born in 1970.

331P. Courtioux et al. / Economic Modelling 38 (2014) 328–340

However, the 2003–2007 period is too short to capture time effects,such as the impact of the business cycle on employment, experiencesand wages at a disaggregated diploma level, an impact we want to con-trol for concerning individual trajectories. We thus estimate a chrono-gram of situations in the labour market, conditional to the currentunemployment rate with the FLFS 1968–2005. In the microsimulation,the chronogram is used to calibrate the aggregate trajectory of a wholegeneration, whereas the wagemodelling and the transition in the labourmarket modelling are used to simulate individual trajectories under thisgenerational constraint. This means that we assume that we can forecastthe chronogram of a present generation, based on the observed formergeneration. Doing so, we potentially miss some cohort effects, that aremainly effective at the end of the career, linked for instance to a rise inthe retirement age in France. Additional simulations have confirmedthat the consequences of disregarding these cohort effects are small.4

The dynamic microsimulation model used to simulate the careers ofa generation has a specification that can be decomposed into threeoperations: (1) a simulation of the individual transitions on the labourmarket, (2) a simulation of individual earnings, and (3) a simulationof mortality rates over the course of a lifetime. At each level, we explicitlytake into account the heterogeneity deriving from the type of tertiarydiploma obtained.

3.1. Modelling transitions in the labour market over the lifecycle

We first model the transitions in the labour market for a givengeneration over its lifetime. Because of the characteristics of the Frenchtax-benefits regime – notably the existence of specific careers for publicemployees (fonctionnaires) who are entitled for instance to particularrights concerning retirement pensions – we have to model the transi-tions between five states: (1) inactivity, (2) self-employment, (3) publicemployment, (4) other private employment, and (5) unemployment.But we want to control the random simulation of these transitions byimposing an overall constraint on the implicit distribution of a genera-tion over the different states that is consistent with the observed labourforce participation rate.

To model the individual transitions in the labour market over thelifecycle, we assume that Pi,t, the probability for an individual i beingin a given state at the t period, is a function of some invariant individualcharacteristics (gender and diploma), of themacroeconomic conditions(notably the level of unemployment), and the past trajectory of theindividual. This is formally summarised by the following equation:

Pi;t ¼ f mi; ei; ai;t ;Ut ; Pi; t−1ð Þ; Pi; t−2ð Þ;…; Pi; t−tð Þ� �

ð5Þ

wheremi is the gender of the individual i, ei the education character-istics, and Ut the current unemployment rate. The way the differentdeterminants are included in Pi,t are detailed in Eqs. (6), (7) and (8).

Our modelling strategy consists of two steps: we first estimategeneral aggregated patterns of the positions on the labour market fora generation, across the ageing process. The dependent variables arethe labour force participation rate, the unemployment rate and theself-employment rate at a given age and time period.We then estimateindividual differentials in the transition probability for individuals in thelight of their education and their past trajectories. The simulation oftransition consists of a random draw based on an individual probabilitydifferential which is alignedwith the age-specific aggregated rate of thefirst step.5

In this very first step, we posit a model to capture the mean patternof activity over the lifecycle for a given generation. The mean pattern of

4 We tested for the effect of an extension of high employment years and a consecutivedelay on retirement ages. It has a small impact on our results, mainly because the internalrate of return is principally impacted by the years at the beginning of the life cycle.

5 For a recent survey and discussion of alignment methods, see Li and O'Donoghue(2011).

the three aggregated rates (P) at the period t for a given generation issupposed to be a function of gender (m), age of the generation duringthe current period (at) and the current situation of the labour marketcaptured by the current unemployment rate (Ut):

Pt ¼ f m; at ;Utð Þ: ð6Þ

We therefore assume that this age-specific pattern at a given point intime corresponds to the combination of the rates associated with five la-bourmarket positions: (1) the labour force participation rate, (2) the un-employment rate, (3) the self-employment rate, (4) the publicemployment rate, and (5) the “other” private employment rate. Wemodel the various aggregated rates associated with (1), (2), (3) and forthe sake of simplicity assume that the public employment rate (4) isnot age-specific and corresponds to the one observed during the1968–2005period in France (i.e. 20%of employment). The rate associatedwith (5) is then computed as the remainder.

The specification of these equations corresponds to a polynomialapproximation in the age variable, which is different for men andwomen to account for their specific activity patterns during the lifecourse. It reads:

logPg;t

1−Pg;t

!¼ α þ β:aþ χ:a2 þ δ:a3 þ φ:a4 þ…þ ϕ:ax þ Ut þ Dg þ ε

ð7Þ

where Pg,t is the rate associated with a generation g, at the period t,which can take three values: respectively the rate of labour force partic-ipation, the unemployment rate, and the self-employment rate and Ut

the current unemployment rate, whereas Dg is a generation dummy.Themodel is estimated fromthe segments of generationpatterns comput-able from the FLFS 1968–2005. For instance, the generationborn in 1950 isobserved from age 18 to 55; the generation born in 1951 is observed fromage 17 to 54, etc. The different orders of the polynomial approximation aretested. Thefinal estimation only retains the orders that are significant. Theresults of this final estimation are reproduced in Table 1.

Knowing the aggregated age-specific levels of activity pattern of agiven generation for the current macroeconomic conditions, we canturn to the modelling of the differential in the probability of transitionacross lifetime for the individuals of a given generation. As noted above,we assume that this differential can be characterised by the educationlevel and an individual's past labour market history. Several approachescan be used to model the transitions between the five states introducedabove.We follow the approach that has been usedwith success in anoth-er French microsimulation model (Destinie) developed by INSEE (seeINSEE (1999), Blanchet and Le Minez (2009)). This approach moreoverfacilitates the alignment process during the simulation. We estimate aset of sequential binomial logit models with the FLFS 2003–2005, ratherthan amultinomial logitmodel. They correspond to the sequence of bina-ry decompositions of the labour market positions. We first model theprobability conditional on the past labourmarket position and the educa-tion level; second, P (li,t = 1) of being in the labour force at the period tdenoted by li,t = 1, P (oi,t = 1|li,t = 1), where oi,t is a dummy variableequal to 1 when the individual is self-employed at the period t; third, P(qi,t = 1|li,t = 1 and oi,t = 0) where qi,t is a dummy variable equal to 1when he/she is employed in the public sector at the period t; and fourth,P (ri,t =1|li,t =1 and oi,t =0 and qi,t = 0) where ri,t is a dummy variableequal to 1 when he/she is employed in the private sector at the t period.The equations estimated are of the following form:

Zi;t ¼ α þ β:Pi; t−1ð Þ þ χ:Ci; t−1ð Þ þ δ:ei ð8Þ

where Zi,t is a latent variable corresponding to the four conditionalprobabilities previously specified, Pi,(t − 1) is a variable giving the statusvis-à-vis the labour market in the previous year, and Ci,(t − 1) is a matrixof cumulative indicators of the past individual trajectories, namely years

Table 1Estimates of the age-specific activity pattern modelling.Source: French Labour Force Survey 1968–2005 (INSEE); authors' calculations.

Estimates LFP U SE

Men Women Men Women Men Women

a (Intercept) −21.25 * −27.11 * 3.53 * 3.25 * −6.47 * −7.12 *β (Age) 1.75 * 2.74 * −0.56 * −0.43 * 0.28 * 0.31 *X (Age2) −0.04* −0.10* 0.01 * 0.01 * −0.01 * −0.01 *δ (Age3) 0.00042 * 0.00153* −0.00010 * −0.00007 * 0.000006 * 0.000006 *φ (Age4) −0.000002 * −0.000001 *Ut (Current unemployment rate) −3.44 * −3.44 * 0.26 * −3.44 * 0.55 ns 1.30 ns

R-square 0.97 0.92 0.82 0.82 0.94 0.90

Note: Taking 1970 as a reference, this model is estimated with dummies for each generation which is not reproduced here. LFP: Labour force participation, U: unemployment, SE: self-employment. (*) significant at 1%, (ns), non-significant.

332 P. Courtioux et al. / Economic Modelling 38 (2014) 328–340

of experience (the difference between current age and agewhen enteringthe labour force used as a proxy variable), the time spent out of the labourforce, and ei as the education level (a diploma variable broken down into20 items which are detailed in the Appendix (Table A1, specification 1)).The estimates are given in Table 2.

The simulation of consistent individual transitions over a lifetimereplicates the same pattern for each period unit t. It proceeds as follows.First, the individual probability of transition to the position of labourforce participation is calculated. This probability is included in ]0;1[.Then, a random number is drawn from a uniform probability law onthe unit segment and multiplied by the individual probability. The

Table 2The determinants of an individual's position in the labour market (logit).Source: French Labour Force Survey 2003–2007 (INSEE); authors' calculations.

a (intercept)β (previous position)Inactive (t − 1)Unemployment (t − 1)Self-employment (t − 1)Public employment (t − 1)Other private employment (t − 1)

X (indicators of past trajectories)Experience (in years)Experience (square)Time out of the labour force (in years)

δ (education)No diploma (ea)CAP/BEP (eb)Bac (general) (ec)Bac (profesional) (ed)Bac (technical) (ee)Capacite en droit (ef)DEUG (two-year university degrees) (eg)DUT/DEUST (two-year university degrees) (eh)BTS (two-year degrees) (ei)Other higher technical diploma (two-year degrees) (ej)Paramedical (two-year degrees) (ek)Bachelor's degree (three-year university degree) (el)Other three-year degrees (em)Maitrise (four-year university degrees) (en)DEA (five-years university degrees) (eo)DESS (five-year university degrees) (ep)Business schools or grande ecole (five-year degrees) (eq)Engineering schools or grande ecole (five-year degrees) (er)PhD (medical degree excluded) (es)PhD (medical degree) (et)

Sommers'DPercentage concordantPercentage discordantPercentage tied

Note: Themodelled probabilities are P (li,t=1) for A, P (oi,t=1|li,t=1) for B, (qi,t=1|li,t=1andwe controlled for gender, number of children for women, the presence of children aged up to thage 65 and more (Equation A); they are not reproduced here.

individuals are ordered according to this value and an individual's status(active versus inactive) is determined by an alignment with the age-specific target associated with the corresponding age. This simulationprocedure is consistent with our modelling strategy: it takes explicitlyinto account the probability differential between individuals withdifferent characteristics. However, a given individual has an ex postprobability of having been selected in line with his/her estimated prob-ability. The procedure is repeated for self-employment, employment inthe public sector and employment in the private sector. The individualsin unemployment are those who have not yet been allocated at the endof the process.

(A) (B) (C) (D)

0.107 * 2.244 * 1.714 * 2.393 *

ref. −5.372 * −5.364 * −2.253 *2.446 * −6.391 * −6.450 * −1.922 *4.852 * ref. −5.861 * −2.328 *4.218 * −9.431 * ref. −3.510 *3.864 * −7.907 * −6.324 * ref.

−0.015 * 0.032 * 0.047 * 0.025 *0.0001 * −0.001 * −0.0003 *

−0.383 *

ref. ref. ref. ref.0.355 * 0.033 * 0.474 * 0.306 *0.333 * 0.375 * 0.502 * 0.345 *0.942 * 0.151 * −0.402 * 0.653 *0.633 * −0.161 * 0.639 * 0.540 *0.223 * −0.188 ** −0.892 * −0.437 *0.133 * 0.785 * 0.383 * 0.050 *0.718 * 0.235 * 0.176 * 0.734 *0.759 * 0.344 * −0.064 * 0.684 *0.469 * 0.765 * 0.034 ** 0.290 *0.674 * 2.286 * 3.345 * 0.972 *0.327 * 0.567 * 0.842 * 0.537 *0.814 * 0.963 * 0.089 * 0.310 *0.445 * 0.505 * 0.733 * 0.446 *0.725 * 0.245 * 0.954 * 0.046 *1.022 * 0.061 * 0.448 * 0.508 *0.943 * −0.916 * 0.618 *0.943 * 0.540 * 0.057 * 0.785 *0.979 * 0.124 * 1.028 * 0.212 *0.999 * 1.262 * 3.031 * 1.111 *0.957 0.952 0.906 0.69997.8 97.3 95.1 84.42.1 2.1 4.4 14.50.1 0.6 0.5 1.2

oi,t=0) for C, P (ri,t=1|li,t=1and oi,t=0and qi,t=0) for D. To estimate these coefficients,ree (Equations A, B, C and D), several age dummies for age 55 andmore, age 60 and more,

333P. Courtioux et al. / Economic Modelling 38 (2014) 328–340

3.2. Modelling earnings

Themodelling of earning uses a two-stepmethod. First, the earningsstemming directly from employment are modelled. Second, based on atax and benefit model corresponding to the current French tax-benefitregime, the indirect earnings stemming from the labour market –unemployment benefit and retirement pension – are computedfrom the individual trajectories. The net earnings are computed duringthis second stage: based on the gross earnings, income tax is calculated.

Complementing the dynamic microsimulation of individual labourmarket positions presented in Section 3.1 first requires a consistent es-timate of an individual'swage conditional onhis/her highest degree andpast trajectory on the labour market.

The usual strategy of wage modelling (Mincer) to identify educationpremium consists in estimating wage equation taking into account thepotential endogeneity of the regressors, mainly years of schooling thatmay be correlated to the unobserved error terms. Using the FLFS1968–2007 in a unified equation would require controlling for unob-served heterogeneity, as an individual's talents may be correlated withwages and unobservable, and introduces some selection equations foreach level of educational attainment.

As mentioned above, our modelling strategy differs from the usualone. First of all, the Mincer equation is not used to estimate the educa-tion premium directly, but rather to produce unbiased estimates ofthe impact of diplomaonwages: these estimates are then used as inputsin our simulation.6 Our modelling strategy consists in working at a verydetailed level of the diploma classification (which is possible with theFLFS 2003–2007), since it allows us for instance: i) to separate selectiveand non-selective tracks, for a given degree level; ii) to deal with homo-geneous sub-populations; and iii) to omit the usual independent vari-ables that characterise these sub-populations when working with thecomplete set of data. This means that we do not use a single Mincerequation to identify the education premiums associated with each di-ploma but a set of equations, with one equation per diploma. The setsof independent variables do not include variables associated with aca-demic achievement but with gender, socio-economic background andprofessional experience. These variables are assumed to beuncorrelatedwith the error terms that are interpreted as a signal of individual talentfor people having achieved a given level of academic excellence andhaving entered a matching job. This wage modelling strategy allowsus to differentiate wage careers based on the initial education. In partic-ular, in our modelling approach there is one experience coefficient perdiploma: the impact of experience on wages is specified conditionallyon the diploma obtained.

Moreover, it allows us to control for one source of changes for highereducation wage premiums over time: the composition of the graduatepopulation may have changed across the different types of diplomawhich could lead to a drift in the premium. By focusing on a relativelydisaggregated education variable, our modelling allows dynamic simu-lation of cohorts, controlling for this source of heterogeneity.

However, data stemming from the FLFS 2003–2007 leads to potentialproblems for estimating in-work experience premium. In these cross-section data sets we only have a proxy of in-work experience measuredby the difference between the current date of observation and the date ofentering the labour force. The measurement error of this proxy variablemay be correlated with the residual of the wage equation. In this view,our modelling strategy consists in treating this endogeneity problemwith instrumental variablemethod, in order to produce robust estimatesof the impact of in-work experience on wages. The underlying assump-tion of this modelling strategy is that the main sources of variation ofwages across ages (as measured in FLFS 2003–2007 at relatively disag-gregated levels of education) stems not from a pure generational effectbut rather from differences in exposure to different phases of the

6 As explained in Section 2, with our methodology, the higher education premium iscomputed after the simulation of the long-term panel data of our stylised cohort.

business cycle. Focusing our modelling on a relatively disaggregated ed-ucation variable allows us to take into account across-diploma differ-ences in the magnitude of the exposure to a depressed phase in thebusiness cycle.

We emphasise that we do not try to model the dynamic choice of acurriculum. We estimate separately Mincer's earnings equation bydiploma obtained during the initial education and consider the followingstandard specification:

log we;s;i

� �¼ αe:ei þ βe:xe;i þ δe:xe;i

2 þ ηe;s:sþ μe: f e;i þ εe;i ð9Þ

wherewe,s,i is the monthly wage (as given in the FLFS 2003–2007) of in-dividual i, with diploma e, working in the industrial sector s (the differenteducation and industrial sector items are listed in Appendix Tables A1and A2), and where x is the number of years of experience and f adummy stating if the individual is a civil servant (fonctionnaire) or not.The sum of the industrial sector effects is constrained to be equal tozero. Moreover, in order to capture the specificity of women's careersthe experience parameter (β) is decomposed into two elements: amean slope (β1) and a woman-specific slope (β2).

βe:xe;i ¼ β1e:xe;i þ β2

e:xe;i: ð9:1Þ

Because of the small number of observations for some diplomas, wehave to pool some of them when estimating the equations.

The pooling of some diplomas means our estimate could be affectedby some endogeneity bias that could be limited by considering pools ofsimilar levels of educational attainment. We consequently use a particu-lar approach to decide which diplomas have to be pooled. The pooling isbased on the proximity of diplomas regarding their situation in the labourmarket. In order to identify this proximity, we use a clustering methodbased on factor analysis whose results are available on request. Whenthe results of the factor analysis are not conclusive, the pooling is basedon the proximity of diplomas in terms of education level. Finally, eightearning equations are estimated with six equations concerning highereducation diplomas. The results of the estimates are given in Table 3. Inthe case of pooled estimations, we identify the specific effect of a givendiploma in the set of pooled diplomas by a dummy with respect to areference. In Table 3, the coefficient associatedwith the reference diplomais α1, and the set of coefficients of the specific dummies associated withthe other diplomas are denoted by α2 crossed with the diploma label.

The exact number of years of experience in employment is notavailable in the FLFS. As mentioned earlier, however, the differencebetween current age and age of entry into the labour force is usedas a proxy. Nevertheless, to estimate the impact of this variable mea-sured with errors on the wage level, we use an instrumental variablemethod (IV) on the Mincer equations. Our instruments are: youth(under 25), the unemployment rate; the year of entry into the labourforce and a variable describing the family situation differentiated bygender: number of children (1) up to 18 months, (2) between 18months and three years, (3) between three and six years, (4) betweensix and 18 years, and (5) a dummy variable for lone parents. To analysethe explanatory power of these instruments, we run an OLS regressionof the number of years of experience.We consider that they are adaptedwhen the coefficient of determination is above 0.35 (R2≥ 0.35). The lastline of Table 3 states the method finally retained for each of the estima-tions. For the final estimation, we discard the industrial sector variables(η) with non-significant estimates.

We interpret the individual residuals (εi) of the Mincer equation asthe result of a matching process between the worker and the firm. Inline with this interpretation, the residuals corresponding to the esti-mates are stocked and used during the simulation. In the first step ofthe microsimulation, each individual is randomly assigned an observedresidual depending on his/her diploma. During the dynamic simulationprocess, the residual is kept until the individual leaves employment.

7 See for instance Schnitter (2004), Cutler and Lleras-Muney (2006).

Table 3Estimation of wage equations by diploma (monthly wage log in €2005).Source: French Labour Force Survey 2003–2007 (INSEE); authors' calculation.

ea, eb (A) ed (B) ec, ee, ef, eg (C) eh (D) ei, ej, ek (E) el, em, en (F) eo, ep, eq, es, et (G) er (H)

α1(diploma intercept) 6.94 * 6.96 * 6.99* 7.07 * 7.07 * 7.19* 7.36* 7.52 *α2 (specific diploma dummies)No diploma (ea) −0.08 *CAP/BEP (eb) ref.Bac (general) (ec) ref.Bac (technical) (ee) −0.04 *Capacité en droit (ef) −0.16 *DEUG (two-year university degrees) (eg) 0.11 *BTS (two-year degrees) (ei) ref.Other higher technical diploma (two-year degrees) (ej) ref.Paramedical (two-year degrees) (ek) 0.17 *Bachelor's degree (three-year university degree) (el) 0.00 *Other three-year degrees (em) 0.11 *Maîtrise (four-year university degrees) (en) ref.DEA (five-years university degrees) (eo) ref.DESS (five-year university degrees) (ep) ref.Business schools or grande école (five-year degrees) (eq) 0.12 *PhD (medical degree excluded) (es) 0.08 *PhD (medical degree) (et) 0.25 *

β1 (experience) 0.021 * 0.036 * 0.026 * 0.043 * 0.034 * 0.043 * 0.053 * 0.047 *β2 (women experience, specific effect) −0.014 * −0.018 * −0.016 * −0.013 * −0.013 * −0.016 * −0.015 * −0.012 *δ (experience²) −0.0002 * −0.0005 * −0.0001 * −0.0005 * −0.0003 * −0.0005 * −0.0008 * −0.0007η (industrial sector)Manufacturing and construction (sa) 0.05* 0.06 * 0.06* 0.07 * 0.08* 0.07 * 0.19* 0.07 *Energy (sb) 0.20* 0.22 * 0.17 * 0.10 * 0.09* 0.28* 0.23* 0.18*Finance (sc) 0.19* 0.13* 0.10 * 0.09* 0.11 * 0.12 * 0.09 *Professional services (sd) −0.03 * 0.01 * 0.07 * 0.02 * 0.04* 0.08* 0.07 *Services for consumers (se) −0.23 * −0.11 * −0.26 * −0.27 * −0.19* −0.25 * −0.34 * −0.25 *Administration (sf) −0.17 * −0.13* −0.08 * −0.07 * −0.09 * −0.18* −0.15* −0.24 *Other sectors (sg) −0.002 * −0.04 * −0.03 * −0.07 * −0.13* 0.08 *

μ (civil servant) 0.26* 0.12 * 0.19* 0.07 * 0.10* 0.23 * 0.08* 0.06 *R2 0.37 0.40 0.42 0.53 0.41 0.45 0.47 0.54Estimation method IV Simple IV Simple Simple IV Simple Simple

Note: (*) for 1% level of significance. (A) no diploma and CAP/BEP, (B) bac (professional), (C) bac (general and technical), capacité en droit and DEUG, (D) DUT/DEUST, (E) other two-yeardegrees (F) three- and four-year degrees, (G) five-year and more degrees (engineering grande école excluded), (H) engineering grande école.

334 P. Courtioux et al. / Economic Modelling 38 (2014) 328–340

When he/shefinds a new job, a new residual is then randomly assigned.Unfortunately, data on self-employment earnings are not always avail-able in the FLFS, or are poorlymeasured. In the simulationwe decided toimpute wages as a proxy of self-employment earnings but, being awareof the limitations of such an assumption, we limit the use of the simula-tion for this category.

The microsimulation takes into account the main features of theFrench tax and benefits regime: unemployment benefit, pensions andincome tax. According to social legislation, the calculation of workers'rights to unemployment benefits and pensions is linked to grosswages, which are not available in the FLFS. We compute the grosswages on the basis of the simulated net wages, in accordance with thelegal rates of social security contributions.

Unemployment benefit is computed in line with the current legisla-tion: theAllocation d'aide au retour à l'emploi (ARE). The entitlement andthe amount of this benefit are legally linked to past wages and timespent in work. The three main components of the pension system aresimulated. The basic pension is obtained by applying the official formulafor the 25 best years resulting from the simulation, as well as the com-plementary pensions. Middle ranking and senior executives (cadres)benefit from a specific scheme. Following the common collective labouragreement, we assume that those with a five-year higher educationdegree or more are cadres. The complementary pensions are based onpayroll taxes actually paid throughout a person's career and we usethe current rates. The civil service regime is also simulated. It appliesto those who have worked for more than 41 years in the public sector;their pension is then a fixed share of their final salary.

French income tax is not based on individuals but on a particulardefinition of a household. Theoretically, the tax depends on the numberof persons – including children – within the household. In our simula-tion, we assume that all the individuals are single. This is a simplifying

assumption that will limit the interpretation of our results but, in thisfirst step, we do not want to take into account the peculiar influencethat the French tax system may have on household formation. Furtherresearch will be devoted to this analysis because of the possible impactof endogamy related to the level of education in our measure. Thismeans that the aggregate revenues of income tax are overestimated,inasmuch as they do not take into account tax breaks (dépense fiscale)for family circumstances.

3.3. Modelling mortality

The existence of a positive correlation between education and lifeexpectancy is well documented and confirmed for France (see for in-stance Mackenbach et al., 2008; Menvielle et al., 2007). The pure im-pact of education on life expectancy is, however, difficult todisentangle from the influence of income and health practices thatare correlated with education. When one controls for the effect ofthese variables, the impact of education tends to decrease but re-mains significant.7 Keeping account of these results, our modellingstrategy consists of introducing a weight at the different ages of anindividual corresponding to the survival function of his/her educationlevel. The survival functions are differentiated by sex and education.Our modelling strategy does not take into account the fact that theapparent education/mortality link may result of some selection in ter-tiary schooling of the healthier individuals whose other characteristicsinduce better health. We consider that not taking into account thisunobserved heterogeneity in our modelling is an acceptable simplifica-tion given our analytical framework: i.e. under the assumption of

Table 4Regression of mortality by age with mortality by level of education.Source: FLFS 2003–2005 (INSEE), Vallin and Meslé (2001), Robert-Bobée and Monteil (2005); authors' calculations.

Variable Men Women

a1 (intercept) 1.1832 * −1.221 *β1 (mortality) 1.0997 * 0.8383 *Y1 (age) −0.0116 * −0.0053 *δ1 (age square) 0.0000 ns 0.0002 *a2 (intercept specified by education)CAP/BEP (eb) −0.5125 * −0.3404 *Bac (general) (ec) 1.148 * −0.7679 *Bac (others) (eD) −0.4375 ns −0.3675 *Two-year degrees (paramedical degree excluded) (eG) −7.6262 * −1.267 *Paramedical (two-year degrees) (ek) 1.2109 * −0.5218 *Three-year degrees (eL) −1.4988 * −0.941 *Four-year degrees (en) 5.1688 * −1.3131 *Five-year university degrees (eO) −2.3255 * 0.0131 nsBusiness and engineering schools (five-year degrees) (eQ) −1.3314 * −2.4456 *PhD (eS) 7.1069 * −2.7472 *

β2 (mortality specified by education)CAP/BEP (eb) −0.0363 *** −0.0309 *Bac (general) (ec) 0.0558 ns −0.0799 *Bac (others) (eD) −0.153 * −0.0364 **Two-year degrees (paramedical degree excluded) (eG) −1.0102 * −0.0958 *Paramedical (two-year degrees) (ek) 0.071 ** −0.0267 *Three-year degrees (eL) −0.2511 * −0.0684 *Four-year degrees (en) 0.5859 * −0.106 *Five-year university degrees (eO) −0.3388 * 0.0704 *Business and engineering schools (five-year degrees) (eQ) −0.1213 ** −0.1822 *PhD (eS) 0.8084 * −0.2468 *

Y2 (age specified by education)CAP/BEP (eb) 0.005 * 0.0000 *Bac (general) (ec) −0.0368 * 0.0001 *Bac (others) (eD) −0.0347 * 0.0001 *Two-year degrees (paramedical degree excluded) (eD) 0.0075 ns 0.0001 *Paramedical (two-year degrees) (ek) −0.0435 * 0.0000 nsThree-year degrees (eL) −0.0249 * 0.0001 *Four-year degrees (en) −0.0555 * 0.0001 *Five-year university degrees (eO) −0.0197 * 0.0000 *Business and engineering schools (five-year degrees) (eQ) −0.0097 * 0.0000 *PhD (eS) −0.0791 * 0.0002 *

δ2 (age square specified by education)CAP/BEP (eb) 0.0000 ns −0.001 *Bac (general) (ec) 0.0003 * −0.0027 *Bac (others) (eD) 0.0004 * −0.0064 *Two-year degrees (paramedical degree excluded) (eG) 0.0007 * 0.0046 *Paramedical (two-year degrees) (ek) 0.0004 * 0.0002 *Three-year degrees (eL) 0.0004 * 0.0012 *Four-year degrees (en) 0.0001 ** 0.0022 *Five-year university degrees (eO) 0.0004 * 0.0036 *Business and engineering schools (five-year degrees) (eQ) 0.0002 * 0.0184 *PhD (eS) 0.0001 * 0.0096 *

R2 0.9978 0.9998

Note: The category of reference for the education variable is ‘No Diploma’; (*) for 1%, (**) for 5% level of significance, (***) for 10% level of significance, (ns) for no significance.

335P. Courtioux et al. / Economic Modelling 38 (2014) 328–340

uncertainty of the individual on his/her own talent/preferences forstudies.8

In France, mortality tables by education level are not available. VallinandMeslé (2001) and Robert-Bobée andMonteil (2005), however, givesome cross-section mortality tables by socio-economic status. Toestimate the mortality tables by diploma for the individual of a givengeneration, we proceed in two steps. First, we estimate cross-sectionmortality tables by diploma for the period 1991–1999. Second, wedesign a method to extrapolate these tables.

3.3.1. Survival functions by level of educationTomodel mortality differentials, we first compute a mortality table by

diploma. For this computationwe usemortality tables by age, gender and

8 The modelling also does not take into account the fact that for a given diploma differ-ent past trajectories may impact the mortality age: for instance differences in the level ofincome. Insofar as the magnitude of this effect is difficult to estimate for econometricians,we consider as an acceptable assumption that this effect does not impact the ex ante dis-tribution of returns to higher education conditioning education choices.

socio-economic status (currently available for France) and the French La-bour Force Survey (FLFS). Robert-Bobée and Monteil (2005) providedmortality rates for the 1991–1999 period. We apply the mortality ratesby age, gender and socio-economic status for this period, to the individualsin the FLFS 2003–2005. We then compute the average mortality rate bylevel of education and age in the FLFS sample. The sample is too smallto allow for a robust estimation of highly disaggregated tables by levelof education, sowe aggregate somediplomas. In the aggregation process,we choose to maintain a differentiation by education type as much aspossible. For example, we differentiate high school degrees accordingto their type (general versus specialized), andwe differentiate the highereducation diplomas according to their specificity (the Grande école sys-tem versus universities). Finally, we retain eleven diploma classes: theaggregated classes are presented in Appendix Table A1, Specification 3.

The data on mortality rates by socio-economic status and the FLFSdataset used do not correspond to the same time period. Themortality ta-bles cover the 1991–1999 period, but they are applied to the FLFS2003–2005 sample. A computation based on the FLFS 1991–1999 sampleis possible, but the available diploma variable in these surveys is not

336 P. Courtioux et al. / Economic Modelling 38 (2014) 328–340

disaggregated enough for our analysis. Thismismatch in theperiods couldbias the mortality rates if the relative proportion of various socio-economic groups in the population changed between 1991–1999 and2003–2005. To assess this issue, we analyse the distribution of the popu-lation into the various socio-economic groups between 1999 and 2003,the last years of the two periods we consider (the tables are availableon request). We find that this distribution has not changed significantly.The second step is tomodel andestimatemortality rates by age anddiplo-ma. We posit the following equation for men and women separately:

logMa;e

1−Ma;e

" #¼ ae þ βe: log

Ma

1−Ma

� �þ γe:aþ δe:a

2 ð10Þ

where:

αe ¼ α1 þ α2;e ð10:1Þ

βe ¼ β1 þ β2;e ð10:2Þ

γe ¼ γ1 þ γ2;e ð10:3Þ

δe ¼ δ1 þ δ2;e ð10:4Þ

andMa stands for themortality rate at age a, and e for the level of educa-tion. The interaction terms reflect the fact that the impact of the level ofeducation on mortality not only affects the intercept of the mortalitycurves (the coefficient α, i.e. a difference in value for each age), but alsothe slope (the coefficient β, i.e. a difference in the rate of mortality asage increases). This specification is inspired by INSEE (1999), but weadd interactions with age and age squared, to reflect the fact that the im-pact of the level of education on mortality decreases towards the end oflife. This specification is justified by Robert-Bobée and Cadot's (2007) re-sults: they show that although mortality differentials persist in old age,their magnitude decreases. We estimate Eq. (10) using on the one handthe mortality tables by level of diploma that we have computed, and onthe other hand the mortality tables by age and sex provided by Vallinand Meslé (2001). The results of our regression are reported in Table 4.This modelling allows for the computation of survival functions.

3.3.2. Extrapolating survival functionsThe previous sub-section showed how we estimate mortality differ-

entials by diploma, at a given point of time. In this subsection, we explainour extrapolation methodology of the mortality rate for a given genera-tion which, by definition, covers several points in time. To illustrate thisissue, if we consider the 1970s generation, then we need to obtain thedifferential in the mortality rate in 2000, when the individuals were 30years old. For this, we can reasonably use the estimations previously pre-sented (for the 2003–2004 period), but the mortality rate differential isalso needed for each forthcoming year of the period during which an in-dividual born in 1970 is still alive.

Mortality rates have been decreasing in France for the past 250 years(Pison, 2005), and in order to model the average yearly decrease in the

Table 5Returns on higher education.Source: authors' calculations.

Education

All graduatesDEUG (university two-year degrees) (U2)Other two-year degrees (S2)Bachelor's degree (university three-year degree) (U3)Other three-year degrees (S3)Maîtris (university four-year degrees) (U4)University five-years degrees (U5)Other five-year degrees (S5)PhD (Up)

Note: the specification of the tertiary diploma is detailed in Appendix Table A1 (Specification 4

mortality rate, we need data on the mortality rates for two points intime. Unfortunately the only available mortality rate forecasts arethose by age and gender for 2049 (see Vallin and Meslé (2001)). Wemake the assumption that the relative evolution of mortality ratesover time is the same regardless of the level of education. We thusapply the average yearly decrease in mortality by age and gender tothemortality rates by education level. This simple hypothesis is conser-vative and may not be consistent with past observations (Menvielleet al., 2007). Research in this area is not plentiful, and owing to a lackof information we select this assumption. This is also consistent withour approach since, in the estimation of wages in the microsimulationmodel, we do not include a change in the wage differential by level/type of diploma. Similarly we do not model any other changes overtime which could explain the evolution of the mortality differential,such as differentiated changes in access to health care by educationlevel, for example. This extrapolation assumes that the logarithm ofthe mortality rate decreases linearly as time goes on. This assumptionseems reasonable, given the fact that the evolution of mortality ratesin France has so far been linear (Vallin and Meslé, 2001).

To extrapolate themortality rate differential throughout the years,weuse themidpoint of the availablemortality rates in 1991–1999 and thosecomputed in 2049, and then proceed by linear interpolation, as follows.

Ma;e nð Þ ¼ exp log Ma;e 1995ð Þ� �

þ n−1995ð Þh i

� log Ma 2049ð Þð Þ− log Ma 1995ð Þð Þ54

ð11Þ

whereMa,e (n) is themortality rate by age and level of education for yearn. In themicrosimulation exercise, the ageing process is captured by a re-duction of the weight associated with each individual: each individualtrajectory is simulated from age 16 to age 100, and the specific weightof each individual is corrected by a factor equal to the mortality rate ateach age, depending on the associated education level. A picture of thesurvival function obtained by gender and level of education is presentedin Appendix Fig. A4. As expected, those with the highest levels of educa-tion have higher survival rates. However, these differences remain rela-tively small. Moreover, mortality differentials are smaller for women, asis consistent with the literature.

4. Results

We now turn to the presentation of the results of the distribution ofinternal rates of return on tertiary education for the generation born in1970 andwhichwas obtainedby thismicrosimulation.We take the char-acteristics – gender, diploma and age of entry into the labour force – ofthe individuals born between 1968 and 1972, as a representative distri-bution of the characteristics of this generation. On the basis of the FLFS2003–2007, we can distinguish 457 weighted classes. For instance,women with a business school (or grande école) degree entering the la-bour force at 25 constitute one of these classes. From these 457weightedclasses we create 34,782 artificial observations for which we relate

Median return Part of negative returns

13.6% 3.5%10.4% 9.4%16.0% 3.3%9.9% 5.5%

14.7% 2.9%11.4% 4.7%13.6% 1.8%16.4% 0.8%9.6% 2.0%

).

Den

sity

0.05

0.04

0.03

0.02

0.01

0.000 20 40

IRR60 80

Fig. 1.Density functions of returns to higher education (in percentage).Note: Irr stands forinternal rate of return; Irr values above 75% are excluded from the computation of theden-sity function.Source: authors' calculations.

Den

sity

0.05

men women

0.04

0.03

0.02

0.01

0.000 20 40 60 80 0 20 40 60 80

IRR

337P. Courtioux et al. / Economic Modelling 38 (2014) 328–340

randomly an industrial sector based on the empirical distribution by gen-der and diploma, for the individuals under 30 years old in the FLFS dataset. Then we simulate their life course as explained in Section 3. Wethen compute on this simulated database an internal rate of return foreach individual with a higher education diploma, as explained inSection 2, and hencewe obtain a distribution of these returns by diploma.

First of all, it is interesting to compare our results with those obtain-ed by the OECD (2003, 2008). According to the OECD, the mean rate ofreturn on higher education in 1999–2000 was 12.2% for men and 11.7%forwomen. For 2004, themean rate of returnwas 8.4% formen and 7.4%for women. When we apply the OECD's methodology to our simulatedpanel (only one generation), we obtain a mean rate of return of 13.7%.

Themain interest of ourmethodology, however, lies in the fact that itallows the distribution of returns to be analysed. First, themedian rate ofreturn is equal to 13.6%, which is very slightly below the mean (seeTable 5). As explained in Section 2, in a context of imperfect informationthe results presented here are interpreted as the ex ante distribution ofreturns to higher education: i.e. knowledge of the financial returns thestudent has when deciding whether or not to pursue a higher educationprogramme. The actual decisionmaydiffer between students, dependingon their risk aversion: even if the median rate is clearly higher than thecurrent growth rate of developed economies and seems to provide agood incentive to pursue tertiary education, it should be noted thatthere is a risk of low values of return. Our results show that the shareof educated people in our cohortwith negative returns is significant, run-ning on average at 3.5%. This figure can be interpreted as the risk of notbenefiting from tertiary education. It means that 3.5% of degrees have apresent value of associated net incomes that is lower than the averagepresent value of net incomes of those who have not completed a tertiarydiploma. These negative individual ratesmay be related to career choices,which are entirely or partially constrained by the institutional frameworkand labour market opportunities. These features result from the choicesmade by employers and employees, based on their respective sets of in-formation. From a student's perspective, they may be explained by im-perfect information about the hierarchy of returns across diplomatypes, related to salaries and unemployment exposure, or to personalknowledge of the ability to complete a tertiary diploma. Moreover,Fig. 1 shows that there is a great dispersion of internal rates of returnon higher education. It is noteworthy that the risk of having relativelylow returns is not symmetric with the risk of having high returns. Thelower returns are closer to the modal value than the higher returns.Moreover, there is a decrease in density across the zero value.

More generally, these results show that even with a high mean re-turn to tertiary education, there is a risk of discouraging risk-adversestudents from pursuing higher education. Given that there is some em-pirical evidence to show that risk-aversion is negatively correlatedwithsocial background,9 the recommendation of the OECD to increasestudents' contributions to financing their degrees should be analysedcarefully. The design of contribution schemes may have a varied impactover the distribution of ex ante financial returns on education. Studentsfrom modest social backgrounds who are sensitive to financial returnsbut are also risk-adverse may not enrol in tertiary education.

If we relax the Assumption 2.2. (see Section 2), and assume that in-dividual students have some personal knowledge about their talent forpursuing higher education, we could analyse more in depth the implicitincentive structure of such a distribution of returns. The level and dis-persion of returns are not homogeneous. They vary with the curriculumpursued. In France, the median return is highest for the five-year di-plomas obtained from very selective engineering and business schools,the so-called grandes écoles (S5). In contrast, the lowest return is associ-ated with two-year university degrees (U2), which have no professionaltraining. From this point of view, an individual knowing that he/she hasthe capacity to enter an elite school (whatever the actual ranking of the

9 See Flacher and Harari-Kermadec (2013) for a recent review of sociological and psy-chological biases that could be interpreted in this perspective.

elite school the student is finally admitted to) has substantially greaterfinancial incentives to pursue higher education. In contrast, if a studentknows that he/she can only go to university because of the need to havea job while studying (which in the French tertiary education system isincompatible with entering classes préparatoires for grandes écoles),then such a student will face lower financial incentives to pursue a ter-tiary education.

More generally, for the same education level, the diplomas obtainedin grandes écoles, which are selective, lead to a higher median rate of re-turn than do university degrees. When one considers a given system –

university versus grande école – themedian rate increaseswith the num-ber of schooling years, with two exceptions that can be explained by thespecificities of the French higher education system. First, the three-yearschool degree median rate is below the two-year school degree medianrate. This is mainly explained by the fact that it corresponds to differenttypes of diplomas. The three-year degrees aremarginal in the school sys-tem; they represent 1.6% of the generation born in 1970, whereas themore standard vocational shorter tertiary diploma – the so-called two-

Fig. 2.Density functions of returns to higher education (in percentage) by gender.Note: Irrstands for internal rate of return; Irr values above 75% are excluded from the computationof the density function.Source: authors' calculations.

Den

sity

0.081.U2 2.S2

3.U3 4.S3

5.U4 6.U5

7.S5 8.Up

0.06

0.04

0.02

0.00

0.08

0.06

0.04

0.02

0.00

Den

sity

0.08

0.06

0.04

0.02

0.00

0.08

0.06

0.04

0.02

0.000 20 40 60 80 0 20 40 60 80

IRR0 20 40 60 80 0 20 40 60 80

IRR

Fig. 3.Density functions of returns to higher education (in percentage), by diploma type formen.Note: 1-U2: DEUG (two-year university degrees); 2-S2: other two-year degrees; 3-U3: bachelor'sdegrees (three-year university degrees); 4-S3: other three-year degrees; 5-U4maîtrise (four-year university degree, equivalent to the first year of aMaster's degree); 6-U5: five-year university de-grees; 7-S5: other five-year degrees; 8-Up: PhDs. Irr stands for internal rate of return; Irr values above 75% are excluded from the computation of the density function.Source: authors' calculations.

10 Our modelling of individual trajectories is based on the identification of specific gen-der effects (see for instance Appendix, Fig. A3).11 Thedensity functions by diploma forwomen exhibit the same kind of shape that thoseformen, except thatmost of these functions exhibit this decrease indensity at the zero val-ue. This suggests that the male breadwinner model exists throughout tertiary education.

338 P. Courtioux et al. / Economic Modelling 38 (2014) 328–340

year degree BTS (brevet de technicien supérieur) – corresponds to8.8% of the generation. Second, a PhD (Up) exhibits a lower returnthan a university five-year degree (U5). To interpret these results,one has to keep in mind that in France grande école diplomas (engi-neering or business school) are more prestigious than universitydegrees, whatever their level. PhDs are overrepresented in thelow-wage sectors for tertiary educated employees, such as in publicadministration (see Table 3, where η estimates the impact of the dif-ferent sectors on wages). In the administration sector (sf) – whichcovers administration, education (higher education and research),health and social services – the share of university five-year degreesis relatively high (34%), reaching 54% for PhDs. Moreover, holders ofa PhD tend to enter the labour force very late. As a consequence,compared with five-year university degrees, the opportunity coststend to be higher for the marginal years of training (see Eqs. 4.1 and4.2). As an illustration, the mean age of entering the labour force for PhDdegrees (Up) is 28.3, whereas for the five-year degrees it is 25.3 for a uni-versity degree (U5) and 24.2 for engineering and business school or grandeécole diplomas (s5).

Our results suggest that the risk on the value of return to tertiaryeducation is not homogeneous. It differs across diploma classes. Therisk level is consistent with the diploma hierarchy, when one con-siders the part of negative rates of return: the lowest risk levelamounts to 0.8% for the five-year tertiary grande école degrees,whereas the highest level amounts to 9.4% for the two-year univer-sity degrees. The values taken by this indicator are in line with adecreasing dispersion of the returns with the number of yearsschooling, and with the selective processes used by institutions toselect their students. It also suggests that the financial risk is higherfor students with modest social backgrounds whomay not view eliteeducation in grandes écoles as part of their opportunity set.

The decreasing density around zero shown in Fig. 2 corresponds togender differences in employment patterns across the life cycle (seeAppendix Fig. A3). From this point of view, the probability of being outof employment and the impact it has on an individual's remaining career,captured by our modelling, explains this concentration of valuesbelow zero for women. This could be interpreted as a consequence

of the persistence of the male breadwinner model.10 The latter sug-gests that the value of pursuing tertiary education may be less directfor women, and partially linked to the marriage market, which ischaracterised by education endogamy (see for instanceVanderschelden, 2006). Our modelling does not allow this problemto be analysed specifically. Because of its specific gender effect, wefocus our comments about density functions by diploma on men,with the assumption that this is a good proxy of the direct value oftertiary education.11

Fig. 3, shows that the asymmetric shape is observed for the differentdiploma classes we pointed out previously (see Table 5). However, theshapes tend to be more symmetric for the highest levels of diploma:namely, the five-year university degrees (U5, box 6), the other five-yeardegrees (S5, box 7) and for PhDs (Up, box 8). This indicates that this longerkind of education produces amore predictable output, and should be pre-ferred by individuals who are risk-adverse, independently of the meanlevel of returns.

5. Conclusion

On the basis of a dynamicmicrosimulationmodel of the educationaloutputs for a given generation,we compute a distribution of the returnson tertiary education for France. In this context, ourmodelling producesindicators which complement the standard OECD indicator of meanreturns on tertiary education. The main complementary result consistsof measuring the risk of low returns in pursuing tertiary education. Pro-ducing such indicators at a country level could help to design andmon-itor cost-sharing policies which are recommended at the EuropeanUnion level, for the development of tertiary education.

339P. Courtioux et al. / Economic Modelling 38 (2014) 328–340

More specifically, theOECD indicator emphasises that because of thegap between the mean rate of return on tertiary education and the in-terest rate, which is verified for all countries, an increase in students' fi-nancial contributions is possible. Our results illustrate that in Francethere is a significant risk of low and negative returns for some higher ed-ucation degrees. This risk is not homogeneous and differs across diplo-ma types. It follows that an increase in students' financial contributionhas to be carefully designed to preserve incentives for pursuing tertiaryeducation: the policy design has to take into account the links betweenthe educational institutions and the labour market at a national leveland can be thought of as part of a broader reform of the higher educa-tion system. In this view, one way to implement such cost-sharingpolicy without a negative effect on financial incentives to pursue highereducation is to complement the increase of students' financial contr-butions with an income contingent loan scheme for students (see

Table A1Education: diploma items.

Diploma/variables Percentage of the 1970s' gener

No diploma 25.4%CAP/BEP 27.3%Bac (general) 6.8%Bac (profesional) 3.2%Bac (technical) 4.7%Capacite en droit 0.05%DEUG (two-year university degrees) 1.4%DUT/DEUST (two-year university degrees) 2.0%BTS (two-year degrees) 8.8%Other higher technical diploma (two-year degrees) 0.6%Paramedical (two-year degrees) 2.3%Bachelor's degree (three-year university degree) 3.8%Other three-year degrees 1.6%Maitrise (four-year university degrees) 4.3%DEA (five-years university degrees) 1.2%DESS (five-year university degrees) 2.2%Business schools or grande ecole (five-year degrees) 0.8%Engineering schools or grande ecole (five-year degrees) 1.9%PhD (medical degree excluded) 0.7%PhD (medical degree) 0.8%

Note: (*) we consider here that DUT/DEUST degrees are part of the school system, because the

Table A2Education: sector speciality items.

Diploma speciality

Manufacturing and construction sa

Energy sb

Finance sc

Professional services sd

Services for consumers se

Administration sf

Other sectors sg

Appendix A

Chapman (2006) for a review of loan schemes, and Courtioux (2012)for an analysis of the French case).

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ation Specification 1 Specification 2 Specification 3 Specification 4

ea eo ea –

eb eo eb –

ec eo ec –

ed eo eD

ee eo eD –

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0

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