Modelling the Distribution of Returns to Higher Education: A Microsimulation Approach*

Transcription

1 Modelling he Disribuion of Reurns o Higher Educaion: A Microsimulaion Approach* Pierre Courioux Edhec Business School pierre.courioux@edhec.edu Séphane Gregoir Edhec Business School sephane.gregoir@edhec.edu Dede Houeo PSE-Paris School of Economics dkhoueo@homail.com Absrac Cos-sharing policy for higher educaion has been implemened in several counries wih various modaliies. We argue ha o assess heir appropriaeness and faciliae heir implemenaion i is necessary o develop saisical indicaors of he disribuion of reurns. When saring a higher educaion programme, he reurn on a paricular degree is uncerain and risk-adverse sudens or hose from a low-income family may be relucan o enrol. These saisical indicaors would herefore be naural inpus of cos-sharing policies inended o preserve he individual economic incenives o go o universiy and simulaneously providing an insurance role. We presen a dynamic microsimulaion model of individual lifeime educaional oupu on he French labour marke which uses economeric modelling of individual wages, labour marke ransiions, social securiy conribuions and benefis. I relies largely on labour force survey daa and moraliy ables. In he sandard inernal rae of reurn framework, he model is used o compue he disribuion of reurns o higher educaion for a given generaion. The resuls show ha he percenage of negaive reurns is relaively high and close o 7.5%. Keywords: Reurn o educaion; Higher educaion; Dynamic microsimulaion JEL classificaion: C6, J11, J24 *The esimaion of he microsimulaion model inroduced in his paper was carried ou wih hree ses of daa: he French Labour Force Survey for available online (hp:// he French Labour Force Survey , o which access was provided by he Queele Cenre (hp:// and he moraliy raes and heir forecass based on Vallin and Meslé (2001) and Rober-Bobée and Moneil (2005). Dede Houeo benefied from EDHEC Business School funding for his research work. The auhors wish o hank he anonymous referees for commens ha helped us o improve his aricle. 1

2 1. Inroducion In erms of public policies, invesing in educaion is one of he key issues for developed counries. The European Lisbon Sraegy and is educaional par, he socalled Educaion and Training 2010, emphasize he link beween he educaion sysem and social cohesion and esablish educaional arges such as numbers of early school leavers or an increase in he proporion of Maser of Science and Technology graduaes (Commission of he European Communiies, 2005). Mos of hese objecives have been mainained and complemened in he new guidelines issued in 2010 in EU 2020 (Commission of he European Communiies, 2010). More generally, a benchmarking process of he educaion organizaion and oucomes in developed counries is in progress (OECD, 2008). I relies on a se of naional indicaors such as he mean reurn o higher educaion. In his aricle, we illusrae how a microsimulaion approach o educaion oucomes can enhance he issue by means of relaively sraighforward modelling. We presen a dynamic microsimulaion model of educaional oupu for France based mainly on Labour Force Survey daa and moraliy ables for a presenaion of he French educaion sysem see for insance Givord and Goux (2007). We show how i could complemen he OECD (2003, 2008) indicaor of he mean reurn o higher educaion by producing an indicaor of higher educaion valuaion risk. For every counry, he OECD indicaor shows ha reurns o higher educaion are largely above he ineres rae; his is generally inerpreed as an argumen in favour of developing a cos-sharing policy. For counries where higher educaion coss are largely subsidized, his leads o he recommendaion of an increase in he suden conribuion o he raining coss wihou aking ino accoun he possibly large variabiliy of hese reurns. In his conex, our modelling sraegy focuses on he risks associaed o hese reurns which should also be aken ino accoun in he design of cos-sharing schemes o promoe a sound higher educaion policy. The paper is organized as follows: in Secion 2, we inroduce and discuss he higher educaion inernal rae of reurn framework for he individuals of a given generaion; in Secion 3, we deail he microsimulaion modelling; in Secion 4, we presen and discuss he resuls for our indicaor of higher educaion valuaion risk; Secion 5 concludes. 2

3 2. A disribuion perspecive on higher educaion reurns According o he classical approach of educaion economics, educaion can be considered as an inpu of human capial ha impacs on earnings over he course of a lifeime. The gains of such an invesmen are usually assessed by compuing he individual inernal rae of reurn of one addiional year of educaion. Since he seminal work of Mincer (1974), measuring he inernal rae of reurn o educaion has become a key dimension of he analysis of educaion choices see also Heckman e al., (2006). More recenly, he inroducion of uncerainy in he dynamic modelling of educaion choices pu he sress on analysing he disribuion of reurns. For insance in he model of Buchinsky and Leslie (2010) he schooling choice is deermined by inegraing over uncerain fuure oucomes, including wages which depend on he individual level of educaion and experience: hey assume ha he agen has access o esimaes of pas wage disribuions from which hey forecas fuure disribuions in order o make heir educaion choice. As heir model is parially esimaed and parially calibraed, hey can es he impac of he level of unobserved heerogeneiy on he individual oucomes. They show ha he inroducion of unobserved heerogeneiy can play a major role in one s educaional choices and consequenly in wage oucomes. Our research explores he idea ha a subsanial par of his heerogeneiy sems from he educaion sysem and ha his heerogeneiy is linked o he heerogeneiy of he educaion services he sudens benefied. As repored by Alonji e al. (2012), here are few works assessing why individuals choose differen ypes of educaion and he career consequences of hese choices. In his perspecive, our research aims a illusraing how he heerogeneiy of educaion services in erms of subsidies and coss may impac he disribuion of inernal raes of reurn o higher educaion. From an empirical poin of view, such a perspecive is demanding, as i requires o work on some long panel daa for insance as in Guvenen (2009) wih variables including diploma obained and rajecories on he labour marke. Such daases are rarely available. In France, he DEPP (Naional deparmen of educaion evaluaion) panel daa is available for some recen generaions he individuals who compleed a secondary educaion in 1996 and This panel only allows for a modelling of 3

4 he firs years of a career. This is he reason why we use a microsimulaion modelling o produce under some conservaive assumpions long panel daa for a given cohor wih such variables. Based on his cohor, we compue a disribuion of inernal rae of reurns o higher educaion ha is discussed in secion 4. The simulaion of he cohor analyzed is obained by combining esimaion and calibraion see secion 3 for a more deailed presenaion of he modelling sraegy. In his view based on pas observaions, we analyse he disribuion of ex ane reurns in a framework of choices wih uncerainy on he reurns. Four assumpions are necessary o inerpre our resuls as ex ane disribuion. 1) There is uncerainy for he realizaion of fuure wages offered o he individual from a known fuure wage career disribuion; his disribuion is condiional on he diploma obained bu could also be analysed by gender or he wo-digi secors of economic aciviy of a career. 2) The suden is no aware of his/her own alen/preferences o sudy and work. 3) The educaion decision does no concern a marginal schooling year bu raher an educaion rack which leads o a diploma. 4) The individual decision of pursuing higher educaion is aken a he age when he suden could legally ener he labour force. This decision is irreversible. As explained earlier he assumpion 1 has become a key feaure o analyze educaion choices Bushinsky and Leslie (2010). The assumpion 3 is no commonly used in educaion economics: his is parly due o he difficuly of esimaing srucural dynamic model of educaion choice bu his is a promising research agenda in educaion economics see Alonji e al. (2012) for a discussion. Moreover, his assumpion is more in line wih he insiuional feaures of he French educaion sysem han he schooling year approach used in numerous sudies for a presenaion of he French higher educaion sysem see for insance Courioux (2010) and could lead o more clear-cu policy recommendaion concerning he differen segmens of he educaion sysem. The assumpion 4 is clearly a simplificaion of a more complex decision-making process which is by naure sequenial and leads o parial irreversibiliy for some decisions concerning he invesmen in human capial see Alonji e al. (2012) for a discussion. In his view, he resuls presened in he aricle correspond o an exreme case: he irreversibiliy 4

5 of educaion choices is oal and occurs a he enrance of he eriary educaion sysem. In a dynamic modelling of choices, he resuls we presen also corresponds o he disribuion of ex ane reurns for he firs sequence of individual choice for educaion i.e. when s/he could ener he labour force and has a whole uncerainy on his/her eriary educaion success poenials. In furher researches he impac of hese assumpions on our resuls should be more specifically analyzed. An ineresing complemen will be o compue a disribuion of reurns for every year of schooling choice, condiional on he diploma already obained. Such a developmen needs daa on he individual educaional rajecories which are no used in he analysis we propose here. However, a his sage i is noeworhy ha he assumpion 2, 3 and 4 are also implicily made in he consrucion of OECD (2008) indicaors of reurns o higher educaion. However, he OECD s mehodology does no ake ino accoun he uncerainy linked o he realizaion of fuure wages condiional o he diploma obained. In his view, he resuls we propose for France are innovaive and complemen he previously available OECD benchmark. To produce a large se of individual hisories for a given cohor, we use microsimulaion echniques. The microsimulaion approach has been used o analyse various issues in economics, noably welfare reforms (Arnz e al., 2008), corporae ax sysem (Creedy and Gemmel, 2009) or o complee compuable general equilibrium models see for insance Magnani and Mercenier (2009), Mabugu and Chiiga (2009). From an educaion economics perspecive, microsimulaion modelling has o ackle wo ses of problems. On he one hand, i has o capure he dynamics of individual rajecories in a given socio-fiscal regime. Such problems are radiionally addressed by dynamic microsimulaion echniques see for insance Harding (1993), Nelissen (1998) van Sonsbeek (2010), van Sonsbeek and Ablas (2012). On he oher hand, i has o ake ino accoun as precisely as possible educaional heerogeneiy in erms of schooling years and diploma ypes as well as heir economic counerpar on he labour marke in erms of employmen rajecories, direc wages, unemploymen benefis and reiremen pensions. Working wih a simulaed cohor, we can compue he disribuion of inernal rae of reurns o eriary educaed individuals. Following he human capial approach iniiaed by Becker (1962), he inernal rae of reurn is obained by equaing he presen value of he sream of income when one invess in human capial o is 5

6 presen value when one does no. If X is he sream of income when an agen pursues higher educaion and herefore eners he job marke laer and Y is he sream of income when s/he does no pursue higher educaion and hus eners he job marke, he inernal rae of reurn of his individual (r) solves he following equaion: T = 0 Y X ( 1+ r) = (1) where is a ime period index and T is he oal number of period unis lived by he individual. We look for a represenaive measure of reurns o higher educaion consecuive o he uncerainy of fuure wages offered o he individual. We have o decompose he sream of incomes of people in boh siuaions. If we firs consider he labour marke oupus relaed o higher educaion Y can be decomposed ino five componens as follows: Y = W + U + R T F (2) where W is he individual ne wage a period, U he unemploymen benefi, R he reiremen pension, T he individual income ax and F he fees. For a given poin in ime, some of he elemens which compose he labour marke oupus may be equal o zero. For insance, he fees (F ) are posiive during he eriary educaion period and equal o zero aferwards. If he individual is employed during period, he unemploymen benefi (U ) is equal o zero. If he individual is no reired during period, he reiremen pension (R ) is equal o zero. When one considers he course of a lifeime, he componens of Y are no independen: he level of pension and of unemploymen benefi are linked o he pas wage rajecories. In our modelling we analyze hese links wih he ax benefi componen of our microsimulaion model see secion 3.2. We work on he assumpion ha he counerfacual sream of income obained when no pursuing eriary educaion can be esimaed by he average earnings by age for he individuals who did no obain a higher educaion degree. 1 This assumpion is consisen wih he educaion choice framework we presened above. Their earnings are hus defined as follows: 1 We decided no o reain a gender-specific counerfacual, in order o produce a se of reurn indicaors which were no biased by he fac ha he individual behaviour vis-à-vis he labour marke could be deermined by a join decision wihin he household. 6

7 X N ( W, i + U, i + R, i T, i F, i ) = i= 1 N (3) where N is he number of individuals wihou a eriary diploma wihin he given generaion, and X is he average ne income for a given generaion a he age corresponding o he period for he individuals wihou eriary diploma, weighed by he probabiliy of being employed a his age. The individual sream of income of individuals who have invesed in higher educaion herefore consiues a way of assessing he disribuion of reurns o higher educaion associaed wih a paricular degree. However, a given diploma can iself be relaed o paricular ses of characerisics in erms of skills and social posiion which are no capured in he reference counerfacual sream of incomes when no degree has been compleed. This unobserved heerogeneiy may have an impac on he ex pos rae of reurn o higher educaion i.e. he realizaion of individual wage career. In he framework inroduced above, his compuaion is consisen wih he assumpion ha he suden s knowledge abou his/her alens is weak. I does no ake ino accoun he influence of he signal associaed o a degree ha may reduce he correlaion beween he professional alens and academic skills. Consisenly wih our non-sequenial analyical framework of higher educaion choice, here is a large variey of opporuniy coss for higher educaion raining ha he compuaion resuling from equaion (3) does no ake ino accoun. Indeed, some sudens follow a eriary curriculum for only wo years and hen ener he labour marke a a subsanial wage premium, whereas ohers choose o follow a longer curriculum and herefore face higher opporuniy coss: hey have already aained a cerain level in eriary educaion which is associaed wih higher wages bu hey prefer o pospone heir enry ino he labour force. Moreover, some individuals who already have a degree pursue heir sudies o obain a higher level degree, bu may fail heir exam; hey hen ener he labour force a a greaer age wih higher opporuniy coss han he average for individuals wih he same degree level. To capure his variey in higher educaion invesmen ha have an impac on he level of reurns, we compue a paricular version of X during he educaion period of he lifeime for each level of eriary educaion (e) already aained by each person. Here, e sands for he degree level and can be ordered i corresponds o a pariion of higher educaion degrees presened in Appendix, Table A1 (classificaion 2). 7

8 = if L (4.1) X e, W0, + U 0, + R0, T0, X e, MAX{ X 0,, X1,,..., X e, } = if L > (4.2) where L is he period uni a which he individual in our simulaed cohor eners he labour force. In his framework, wo individuals wih he same diploma enering he labour force a differen ages (L) suppor differen opporuniy coss. The one who eners he labour force he laer suppors he addiional X corresponding o he delay period. Moreover, he opporuniy cos esimaion is specific for he period of sudy (equaion 4.2). This means ha for a given diploma, he opporuniy coss are increasing wih age (): hey ake ino accoun he experience premium on wages of hose who ener early he labour force and he educaion premium of hose who have go heir degree and are on he labour marke whaever heir posiion a his given age. For insance, he opporuniy cos of a five-year degree enering very laely he labour force is esimaed by he income level of he five-year degrees already in he labour force under he condiion ha he average income of ha class of educaion level is he highes for his age i.e. a he very end of his/her sudies period. In his framework, a negaive individual inernal rae of reurn o educaion remains possible for educaed people: i means ha he individual gains associaed wih his/her highes degree are no sufficien o cover he losses associaed wih he raining years so ha he presen value of his/her sream of income remains less han ha of he average career of hose who do no complee a eriary diploma. 3. A dynamic microsimulaion model for France Our modelling simulaes age effec condiionally o diploma obained. The specificaion of our microsimulaion model is consrained by daa available. We have a our disposal he French Labour Force Survey (FLFS) for he period However, he daa collecion mehod was changed in One of hese changes concerns he educaion variable: his variable is now more deailed. We wan o use as far as possible he FLFS o capure he effec of diploma a a level disaggregaed as much as possible. In his view, FLFS is used o define he deerminan of wages condiionally on he diploma obained. I is also used o idenify he relaive probabiliy of ransiion on he labour marke condiionally on he diploma obained. This leads us o focus on he simulaion of a generaion mainly on 8

9 he labour force during he s period in order o have smaller cohor effec bias in our simulaion. We choose o focus on he generaion born in However, he s period is oo shor o capure dae effecs such as he impac of business cycle on employmen, experiences and wages a a disaggregaed diploma level. Our modelling sraegy aims a conrolling he business cycle effec on individual rajecories by esimaing a chronogram of siuaion on he labour marke condiionally o curren unemploymen rae. This chronogram is esimaed on he FLFS In he microsimulaion, he chronogram is used o calibrae he desiny of a whole generaion, whereas he wage modelling and he ransiion on he labour marke modelling are used o simulae condiional on heir degree individual rajecories under his generaional consrain. This means ha we assume ha we can forecas he chronogram of a generaion based on he observed former generaion. Doing so, we poenially miss some cohor effecs mainly effecive a he end of he career, linked for insance o he raise of reiremen age in France. Addiional simulaions have confirmed ha he consequences of disregarding hese cohor effecs are small. 2 The dynamic microsimulaion model used o simulae he careers of a generaion has a specificaion ha can be decomposed ino hree basic operaions: (1) a simulaion of he individual ransiions on he labour marke, (2) a simulaion of individual earnings, and (3) a simulaion of moraliy raes over he course of a lifeime. A each level, we explicily ake ino accoun he heerogeneiy deriving from he ype of eriary diploma obained Modelling ransiions on he labour marke over he lifecycle In order o esimae he disribuion of reurns o higher educaion, we are ineresed in modelling he ransiions on he labour marke for a given generaion over is lifeime. Because of he characerisics of he French socio-fiscal regime noably he exisence of specific careers for public employees (foncionnaires) which are eniled for insance o paricular righs concerning reiremen pensions we have o model he ransiions beween five saes: (1) inaciviy, (2) self-employmen, (3) public employmen, (4) oher privae employmen, (5) unemploymen, bu wan o keep he 2 We esed he effec of an exension of high employmen years and a consecuive delay on reiremen ages. I has a small impac on our resuls, mainly because he inernal rae of reurn is principally impaced by he years a he beginning of he life cycle. 9

10 random simulaion of hese ransiions under conrol by imposing an overall consrain on he implici disribuion of a generaion over he differen saes ha is consisen wih he observed labour force paricipaion rae. To model he individual ransiions on he labour marke over he lifecycle, we assume ha P i,, he probabiliy for an individual i o be in a given sae a he period, is a funcion of some invarian individual characerisics gender and diploma of he macroeconomic condiions noably he level of unemploymen and he pas rajecory of he individual. This can be illusraed by he following equaion where m i is he gender of he individual i, e i he educaion characerisics, and U he curren unemploymen rae: P i, ( i i i, i,( 1) i,( 2) i,( ) = f m, e, a, U, P, P,..., P ) (5) Our modelling sraegy consiss of wo seps: we firs esimae general aggregaed paerns of he posiions on he labour marke for a generaion across he ageing process. The dependen variables are he labour force paricipaion rae, he unemploymen rae and he self-employmen rae a a given age and ime period; we hen esimae individual differenials in ransiion probabiliy for individuals in he ligh of heir educaion and heir pas rajecories. The simulaion of ransiion consiss of a random draw based on an individual probabiliy differenial which is aligned wih he age-specific aggregaed rae of he firs sep 3. In his very firs sep, we posi a model o capure he mean paern of aciviy over he lifecycle for a given generaion. The mean paern of he hree aggregaed raes (P) a he period for a given generaion is supposed o be a funcion of gender (m), age of he generaion during he curren period (a ) and he curren siuaion of he labour marke capured by he curren unemploymen rae (U ): P = f m, a, U ) (6) ( We herefore assume ha his age-specific paern a a given poin of ime corresponds o he combinaion of he raes associaed wih five labour marke posiions: (1) labour force paricipaion rae, (2) unemploymen rae, (3) selfemploymen rae, (4) public employmen rae, and (5) oher privae employmen rae. We model he various aggregaed raes associaed wih (1), (2), (3) and for he sake of simpliciy assume ha he public employmen rae (4) is no age-specific and 3 For a recen survey and discussion of alignmen mehods, see La and O Donoghue (2011). 10

11 corresponds o he one observed during he period in France (i.e. 20% of employmen). The indicaor (5) is hen compued as he remainder. The specificaion of he indicaor modelling equaion corresponds o he use of a polynomial approximaion in he age variable ( - g). Technically he following model is esimaed separaely for men and for women o accoun for heir specific aciviy paerns during he life course: log( 1 P g, P g, x ) = α + β( g) + χ( g) + δ ( g) + ϕ( g) φ( g) + U + D + ε (7) where P g, is he indicaor associaed wih generaion g a he period ha can ake hree values: respecively he rae of labour force paricipaion, he unemploymen rae, and he self-employmen rae and U he curren unemploymen rae, whereas D g is a generaion dummy. The model is esimaed from he segmens of generaion paerns compuable from he FLFS For insance, he generaion born in 1950 is observed from age 18 o 55; he generaion born in 1951 is observed from age 17 o 54, ec. The differen orders of he polynomial approximaion are esed. The final esimaion only reains he orders ha are significan. The resuls of his final esimaion are reproduced in Table 1. g Table 1 Esimaes of he age-specific aciviy paern modelling esimaes men women men women men women α * * 3.53 * 3.25 * * * β 1.75 * 2.74 * * * 0.28 * 0.31 * χ * * 0.01 * 0.01 * * * δ * * * * * * φ * * LFP U SE U * * 0.26 * * 0.55 ns 1.30 ns R-square Source: French Labour Force Survey (Insee, 1999); auhors calculaions. Noe: Taking 1970 as a reference, his model is esimaed wih dummies for each generaion which are no reproduced here. LFP: Labour force paricipaion, U: unemploymen, SE: self-employmen. (*) significan a 1%, (ns), non-significan. Knowing he aggregaed age-specific levels of aciviy paern of a given generaion for he curren macroeconomic condiions we can urn o he modelling of he differenial in he probabiliy of ransiion across lifeime for he individuals of a given 11

12 generaion. As noed above, we assume ha his differenial can be characerized by he educaion level and he pas individual labour marke hisory. Several approaches can be used o model he ransiions beween he five saes inroduced above. For insance, a mulinomial logi model could be considered. Adoping a pracical perspecive, we follow he approach ha has been used wih success in anoher French microsimulaion model (Desinie) developed by Insee see Insee (1999), Blanche and Le Minez (2009). This approach moreover faciliaes he alignmen process during he simulaion. We esimae a se of sequenial binomial logi models wih he FLFS raher han a mulinomial logi model. They correspond o he sequence of binary decomposiions of he labour marke posiions. We firs model he probabiliy condiional on he pas labour marke posiion and he educaion level; second, P (l i, = 1) of being in he labour force a he period denoed by l i, =1, P (o i, = 1 l i, = 1) where o i, is a dummy variable equal o one when he individual is selfemployed a he period ; hird, P (q i, = 1 l i, = 1 and o i, = 0) where q i, is a dummy variable equal o one when s/he is employed in he public secor a he period ; and fourh, P (r i, = 1 l i, = 1 and o i, = 0 and q i, = 0) where r i, is a dummy variable equal o one when s/he is employed in he privae secor a he period. The equaions esimaed are of he following form: Z. i, = α. Pi,( 1) + β. Ci,( 1) + δ ei (8) where Z i, is a laen variable corresponding o he four condiional probabiliies previously specified, P i,(-1) is a variable saing he saus vis-à-vis he labour marke he previous year, and C i,(-1) is a marix of cumulaive indicaors of he pas individual rajecories, namely years of experience he difference beween curren age and age when enering he labour force used as a proxy variable, he ime spen ou of he labour force, a dummy for long-erm unemploymen, and e i as he educaion level a diploma variable broken down ino 20 iems which are deailed in he Appendix (Table A1, specificaion 1). The esimaes are given in Table 2. 12

13 Table 2 The deerminans of he individual posiion on he labour marke (logi) (A) (B) (C) (D) α inacive ( -1) unemploymen (- 1) self-employmen ( -1) public employmen ( -1) oher privae employmen ( -1) β experience (in years) experience (square) ime ou of he labour force (in years) long-erm unemploymen ref * * * * * * * * ref * * * * ref * * * * ref * * * * * * * * ** * δ no diploma (e a ) ref. ref. ref. ref. CAP/BEP (e b ) * * * * bac (general) (e c ) * * * * bac (profesionnal) (e d ) * * * * bac (echnical) (e e ) * * * * capacié en droi (e f ) * ** * * DEUG (universiy wo-year degrees) (e g ) * * * * DUT/DEUST (universiy wo-year degrees) (e h ) * * * * BTS (wo-year degrees) (e i ) * * ns * oher higher echnician (wo-year degrees) (e j ) * * * * paramedical (wo-year degrees) (e k ) * * * * licence (universiy hree-year degrees) (e l ) * * * * oher hree-year degrees (e m ) * * * * maîrise ( universiy four-year degrees) (e n ) * * * * DEA (universiy five-years degrees) (e o ) * * * * DESS (universiy five-year degrees) (e p ) * * * * business schools (five-year degrees) (e q ) * * * * engineering schools (five-year degrees) (e r ) * * * * Ph.D (medical degree excluded) (e s ) * * * * Ph.D (medical degree) (e ) * * * * Sommers'D percenage concordan percenage discordan percenage ied Source: French Labour Force Survey (Insee, 1999); auhors calculaions. Noe: The modelled probabiliies are P (l i, = 1) for A, P (o i, = 1 l i, = 1) for B, (q i, = 1 l i, = 1 and o i, = 0) for C, P (r i, = 1 l i, = 1 and o i, = 0 and q i, = 0) for D. To esimae hese coefficiens, we conrolled for gender, number of children for women, he presence of children aged up o hree (equaions A, B, C and D), several age dummies for age 55 and more, age 60 and more, age 65 and more (equaion A); hey are no reproduced here. The simulaion of consisen individual ransiions over a lifeime replicaes he same paern for each period uni. I proceeds as follows. Firs, he individual probabiliy of ransiion o he posiion of labour force paricipaion is calculaed. This probabiliy is included in he ]0;1[ segmen. Then, a random number is drawn from a uniform 13

14 probabiliy law on he uni segmen and muliplied by he individual probabiliy. The individuals are ordered according o his value and he individual saus acive versus inacive is deermined by an alignmen wih he age-specific arge associaed wih he corresponding age. This simulaion procedure is consisen wih our modelling sraegy: i akes explicily ino accoun he probabiliy differenial beween individuals wih differen characerisics. However a given individual has an ex pos probabiliy of having been seleced in line wih his/her esimaed probabiliy. The procedure is repeaed for self-employmen, employmen in he public secor and employmen in he privae secor. The individuals in unemploymen are hose who have no ye been allocaed a he end of he process Modelling earnings The modelling of earning uses a wo-sep mehod. Firs, he earnings semming direcly from employmen are modelled. Second, based on a ax and benefi model corresponding o he curren French socio-fiscal regime he indirec earnings semming from he labour marke unemploymen benefi and reiremen pension are compued from he individual rajecories. The ne earnings are compued during his second sage: based on he gross earnings, he income ax is calculaed. In line wih our analyical framework, our modelling sraegy aims a disinguishing he deerminans of wages by diploma bu we do no ry o model he dynamic choice of a curriculum. We work condiionally on a level of educaion aainmen. In his view, his is no possible o use he FLFS We esimae separaely Mincer s earnings equaion by educaion level and consider he following sandard specificaion: log( 2 w e, s, i ) α e. ei + βe. xe, i + δ e. xe, i + ηe, s. s + µ e. fe, i + ε e, i = (8) where w e,s,i is he monhly wage as available in he FLFS of individual i, wih diploma e, working in he indusrial secor s he differen educaion and indusrial secor iems are lised in Appendix Tables A1 and A2, and where x is he number of years of experience and f a dummy saing if he individual is a civil servan (foncionnaire) or no. The sum of he indusrial secor effecs is consrained o be equal o zero. Moreover, in order o capure he specificiy of women s careers he experience parameer (β) is decomposed ino wo elemens: a mean slope (β 1 ) and a woman-specific slope (β 2 )). 14

15 β. x β + β e 1 2 e, i =. xe i x e,. e e, i (8.1) Because of he small number of observaions for some diplomas, we have o pool some of hem when esimaing he equaions. The pooling of some diplomas means our esimae could be affeced by some endogeneiy bias ha one could limi by considering pools of similar levels of educaion aainmen. We consequenly use a paricular approach o decide which diplomas have o be pooled. The pooling is based on he proximiy of diplomas regarding heir siuaion in he labour marke. In order o idenify his proximiy we use a clusering mehod based on facor analysis whose resuls are available on reques. When he resuls of he facor analysis are no conclusive, he pooling is based on he proximiy of diplomas in erms of educaion level. Finally, eigh earning equaions are esimaed wih six equaions concerning higher educaion diplomas. The resuls of he esimaes are given in Table 3. In he case of pooled esimaions, we idenify he specific effec of a given diploma in he se of pooled diplomas by a dummy wih respec o a reference. In Table 3, he coefficien associaed wih he reference diploma is α 1 and he se of coefficiens of he specific dummies associaed wih he oher diplomas are denoed by α 2 crossed wih he diploma label. The exac number of years of experience in employmen is no available in he FLFS. As menioned earlier, however, he difference beween curren age and age of enry o he labour force is used as a proxy. Neverheless, o esimae he impac of his variable measured wih errors on he wage level, we use an insrumenal variable mehod (IV) on he Mincer equaions. Our insrumens are: he youh (under 25) unemploymen rae, he year of enry o he labour force and a variable describing he family siuaion differeniaed by gender number of children (1) up o 18 monhs, (2) beween 18 monhs and hree years, (3) beween hree and six years, (4) beween six and 18 years, and (5) a dummy variable for lone parens. To analyse he explanaory power of hese insrumens, we run an OLS regression of he number of years of experience for each sex. We consider ha hey are adaped when he coefficien of deerminaion is above 0.35 (R² 0.35). The las line of Table 3 saes he mehod finally reained for each of he esimaions. For he final esimaion, we discard he indusrial secor variables (η) wih non-significan esimaes. 15

16 Table 3 Esimaion of wage equaions by diploma (monhly wage log in 2005) e a, e b e d e c, e e, e f, e g e h e i, e j, e k e l, e m, e n e o, e p, e q, e s, (A) (B) (C) (D) (E) (F) (G) (H) α * 6.96 * 6.99 * 7.07 * 7.07 * 7.19 * 7.36 * 7.52 * α 2 no diploma (e a ) * CAP/BEP (e b ) ref. bac (general) (e c ) ref. bac (echnical) (e e ) * capacié en droi (e f ) * DEUG (universiy wo-year degrees) (e g ) 0.11 * BTS (wo-year degrees) (e i ) ref. oher higher echnician (wo-year degrees) (e j ) ref. paramedical (wo-year degrees) (e k ) 0.17 * licence (universiy hree-year degrees) (e l ) 0.00 * oher hree-year degrees (e m ) 0.11 * maîrise ( universiy four-year degrees) (e n ) ref. DEA (universiy five-years degrees) (e o ) ref. DESS (universiy five-year degrees) (e p ) ref. business schools (five-year degrees) (e q ) 0.12 * Ph.D (medical degree excluded) (e s ) 0.08 * Ph.D (medical degree) (e ) 0.25 * β * * * * * * * * β * * * * * * * * δ * * * * * * * * η manufacure and consrucion (s a ) 0.05 * 0.06 * 0.06 * 0.07 * 0.08 * 0.07 * 0.19 * 0.07 * energy (s b ) 0.20 * 0.22 * 0.17 * 0.10 * 0.09 * 0.28 * 0.23 * 0.18 * finance (s c ) 0.19 * 0.13 * 0.10 * 0.09 * 0.11 * 0.12 * 0.09 * services for firms (s d ) * 0.01 * 0.07 * 0.02 * 0.04 * 0.08 * 0.07 * services for consumers (s e ) * * * * * * * * adminisraion (s f ) * * * * * * * * oher secors (s g ) * * * * * 0.08 * µ 0.26 * 0.12 * 0.19 * 0.07 * 0.10 * 0.23 * 0.08 * 0.06 * e r R² Esimaion mehod IV simple IV simple simple IV simple simple Source: French Labour Force Survey (Insee, 1999); auhors calculaion. Noe: (*) for 1% level of significance. (A) no diploma and CAP/BEP, (B) bac (professional), (C) bac (general and echnical), capacié en droi and DEUG, (D) DUT/DEUST, (E) oher wo-year degrees (F) hree- and four-year degrees, (G) five-year and more degrees (engineering school excluded), (H) engineering school. The individual residuals corresponding o he esimaes (ε i ) are socked and used during he simulaion. A he saring sep of he microsimulaion, each individual is randomly assigned an observed residual depending on his/her diploma. During he dynamic simulaion process, he residual is kep unil he individual leaves employmen. When s/he finds a new job, a new residual is hen randomly assigned. Unforunaely, daa on self-employmen earnings are no always available in he FLFS or are poorly measured. In he simulaion we decided o impue wages as a 16

17 proxy of self-employmen earnings bu, being aware of he limiaions of such an assumpion, we limi he use of he simulaion for his caegory. The microsimulaion akes ino accoun he main feaures of he French socio-fiscal regime: unemploymen benefi, pensions and income ax. According o social legislaion, he calculaion of workers righs o unemploymen benefis and pensions is linked o gross wages, which are no available in he FLFS. In line wih he curren level of social conribuion raes, we proxy he gross wages as a fixed share (120%) of ne wages. The unemploymen benefi is compued in line wih he curren legislaion: he Allocaion d aide au reour à l emploi (ARE). The enilemen and he amoun of ha benefi are legally linked o pas wages and employmen duraion. The hree main componens of he pension sysem are simulaed. The basic pension is obained by applying he official formula for he 25 bes years resuling from he simulaion as well as he complemenary pensions. Middle ranking and senior execuives (cadres) benefi from a specific scheme. Following he common collecive labour agreemen, we assume ha hose wih a five-year higher educaion degree or more are cadres. The complemenary pensions are based on payroll axes acually paid hroughou a person's career and we use he curren raes. The civil servans regime is also simulaed. I applies o hose who have worked for more han 41 years in he public secor; heir pension is hen a fixed share of heir final salary. The French income ax is no based on individuals bu on a paricular definiion of a household. Theoreically, he ax depends on he number of persons including children wihin he household. In our simulaion, we assume ha all he individuals are single. This is a simplifying assumpion ha will limi he inerpreaion of our resuls bu, in his firs sep, we do no wan o ake ino accoun he peculiar influence ha he French fiscal sysem may have on household formaion. Furher research will be devoed o his analysis because of he possible impac of endogamy relaed o he educaion level in our measure. This means ha he aggregae revenues of income ax are overesimaed inasmuch as hey do no ake ino accoun he ax cu (dépense fiscale) for family condiions. 17

18 3.3. Modelling moraliy The exisence of a posiive correlaion beween educaion and life expecancy is well documened and confirmed for France see for insance Mackenbach e al. (2008) and Menvielle e al. (2007). The pure impac of educaion on life expecancy is, however, difficul o disenangle from he influence of income and healh pracice ha are correlaed wih educaion. When one conrols for he effec of hese variables he impac of educaion ends o decrease bu remains significan. 4 Keeping accoun of hese resuls, our modelling sraegy consiss of inroducing a weigh a he differen ages of an individual corresponding o he survival funcion of heir educaion level. The survival funcions are differeniaed by sex and educaion. Our modelling sraegy does no ake ino accoun he fac ha he apparen educaion/moraliy link may resul of some selecion in eriary schooling of he healhier individuals whose oher characerisics induce beer healh. We consider ha no aking ino accoun his unobserved heerogeneiy in our modelling is an accepable simplificaion given our analyical framework i.e. under he assumpion of uncerainy of he individual on his/her own alen/preferences for sudies. 5 In France, moraliy ables by educaion level are no available. Vallin and Meslé (2001) and Rober-Bobée and Moneil (2005), however, give some cross-secion moraliy ables by socio-economic saus. To esimae he moraliy ables by diploma for he individual of a given generaion, we proceed in wo seps. Firs, we esimae cross-secion moraliy ables by diploma for he period. Second, we design a mehod o exrapolae hese ables. Survival funcions by level of educaion To model moraliy differenials, we firs compue a moraliy able by diploma. We use moraliy ables by age, gender and socio-economic saus currenly available for France and he French Labour Force Survey (FLFS) for his compuaion. Rober-Bobée and Moneil (2005) provided moraliy raes for he period. We apply he moraliy raes by age, gender and socio-economic saus for his period o 4 See for insance Schniker (2004), Culer and Lleras-Muney (2006). 5 The modelling does neiher ake ino accoun he fac ha for a given diploma differen pas rajecories may impac he moraliy age for insance differen he level of income. Insofar as he magniude of his effec is difficul o esimae for economericians, we consider as an accepable assumpion ha his effec does no impac he ex ane disribuion of reurns o higher educaion condiioning educaion choices. 18

19 he individuals in he FLFS We hen compue he average moraliy rae by level of educaion and age in he FLFS sample. The sample is oo small o allow for a robus esimaion of highly disaggregaed ables by level of educaion so we aggregae some diplomas. In he aggregaion process, we choose o mainain as much as possible a differeniaion by educaion ype. For insance, we differeniae high school degrees according o heir ype general versus specialized and we differeniae he higher educaion diplomas according o heir specificiy school sysem versus universiy. Finally, we reain eleven diploma classes he aggregaed classes are presened in Appendix Table A1, specificaion 3. The daa on moraliy raes by socio-economic saus and he FLFS daase used do no correspond o he same ime period. The moraliy ables cover he period, bu hey are applied o he FLFS sample. A compuaion based on he FLFS sample is possible, bu he available diploma variable in hese surveys is no disaggregaed enough for our analysis. This mismach in he periods could bias he moraliy raes if he relaive proporion of various socio-economic groups in he populaion changed beween and To assess his issue, we analyse he repariion of he populaion ino he various socio-economic groups beween 1999 and 2003, he las years of he wo periods we consider he ables are available on reques. We find ha his repariion has no changed significanly. The second sep is o model and esimae moraliy raes by age and diploma. We posi he following equaion for men and women separaely: M log 1 M a, e a, e M a = α e + βe.log + γ e. a + δe. a 1 M a 2 (9) where: α e = α 1 + α 2,e (9.1) β e = β 1 + β 2,e (9.2) γ e = γ 1 + γ 2,e (9.3) δ e = δ 1 + δ 2,e (9.4) and M a sands for he moraliy rae a age a, and e for he level of educaion. The ineracion erms reflec he fac ha he impac of he level of educaion on moraliy no only affecs he inercep of he moraliy curves he coefficien α, i.e. a difference in value for each age bu also he slope he coefficien β, i.e. a difference in he rae of moraliy as age increases. This specificaion is inspired by 19

20 Insee (1999), bu we add ineracions wih age and age squared o reflec he fac ha he impac of he level of educaion on moraliy decreases owards he end of life. This specificaion is jusified by Rober-Bobée and Cado's (2007) resuls: hey show ha alhough moraliy differenials persis in old age, heir magniude decreases. We esimae equaion (9) using on he one hand he moraliy ables by level of diploma ha we compued, and on he oher hand he moraliy ables by age and sex provided by Vallin and Meslé (2001). The resuls of our regression are repored in Table 4. This modelling allows for he compuaion of survival funcions. 20

21 Table 4 Regression of moraliy by age on moraliy by level of educaion variable men women α * * β * * γ * * δ ns * α 2 CAP/BEP (e b ) * * bac (general) (e c ) * * bac (ohers) (e D ) ns * wo-year degrees (paramedical degree excluded) (e G ) * * paramedical (wo-year degrees) (e k ) * * hree-year degrees (e L ) * * four-year degrees (e n ) * * universiy five-years degrees (e O ) * ns business and engineering schools (five-year degrees) (e Q ) * * Ph.D (e S ) * * β 2 CAP/BEP (e b ) *** * bac (general) (e c ) ns * bac (ohers) (e D ) * ** wo-year degrees (paramedical degree excluded) (e G ) * * paramedical (wo-year degrees) (e k ) ** * hree-year degrees (e L ) * * four-year degrees (e n ) * * universiy five-years degrees (e O ) * * business and engineering schools (five-year degrees) (e Q ) ** * Ph.D (e S ) * * γ 2 CAP/BEP (e b ) * * bac (general) (e c ) * * bac (ohers) (e D ) * * wo-year degrees (paramedical degree excluded) (e G ) ns * paramedical (wo-year degrees) (e k ) * ns hree-year degrees (e L ) * * four-year degrees (e n ) * * universiy five-years degrees (e O ) * * business and engineering schools (five-year degrees) (e Q ) * * Ph.D (e S ) * * δ 2 CAP/BEP (e b ) ns * bac (general) (e c ) * * bac (ohers) (e D ) * * wo-year degrees (paramedical degree excluded) (e G ) * * paramedical (wo-year degrees) (e k ) * * hree-year degrees (e L ) * * four-year degrees (e n ) ** * universiy five-years degrees (e O ) * * business and engineering schools (five-year degrees) (e Q ) * * Ph.D (e S ) * * R² Source: FLFS (Insee), Vallin and Meslé (2001), Rober-Bobée and Moneil (2005); auhors calculaions. Noe: The caegory of reference for he educaion variable is No Diploma ; (*) for 1%, (**) for 5% level of significance, (***) for 10% level of significance, (ns) for no significance. 21

22 Exrapolaing survival funcions The previous sub-secion showed how we esimae moraliy differenial by diploma a a given poin of ime. In his subsecion, we explain our exrapolaion mehodology of moraliy rae for a given generaion which by definiion covers several poins in ime. To illusrae his issue, if one considers he 1970s' generaion, one needs he differenial in moraliy rae in 2000, when he individuals are hiry; for his, we can reasonably use he esimaions previously presened which are for he period bu he moraliy rae differenial is also needed for each forhcoming year of he period during which an individual born in 1970 is sill alive. Moraliy raes have been decreasing in France for he pas wo and a half cenuries (Pison, 2005) and in order o model he average yearly decrease in moraliy rae we need he moraliy raes for wo poins in ime. Unforunaely he only available moraliy rae forecass are only hose by age and gender for 2049 see Vallin and Meslé (2001). We make he assumpion ha he relaive evoluion of moraliy raes over ime is he same regardless of he level of educaion. We hus apply he average yearly decrease in moraliy by age and gender o he moraliy raes by educaion level. This simple hypohesis is conservaive and may no be consisen wih pas observaions (Menvielle e al., 2007). Research works in his area are no numerous and owing o lack of informaion we selec his assumpion. I is also consisen wih our approach since, in he esimaion of wages in he microsimulaion model, we do no include a change in he wage differenial by level/ype of diploma. Similarly we do no model any oher changes over ime ha could explain he evoluion of he moraliy differenial, such as differeniaed changes in access o healh care by educaion level, for example. This exrapolaion assumes ha he logarihm of moraliy rae decreases linearly as ime goes on. This assumpion seems reasonable given he fac ha he evoluion of moraliy raes in France has so far been linear (Vallin and Meslé, 2001). To exrapolae he moraliy rae differenial hroughou he years, we use he midpoin of he available moraliy raes in and hose compued in 2049 and proceed by linear inerpolaion, as follows. M a, e exp a, ( n) = log( M (1995)) + ( n 1995) e log ( M (2049)) log( M (1995) ) a 54 a (10) 22

23 where M a,e (n) is he moraliy rae by age and level of educaion for year n. In he microsimulaion exercise, he ageing process is capured by a reducion of he weigh associaed wih each individual: each individual rajecory is simulaed from age 16 o age 100 and he specific weigh of each individual is correced by a facor equal o he moraliy rae a each age depending on he associaed educaion level. A picure of he survival funcion obained by gender and level of educaion is presened in Appendix Figure A4. As expeced, hose wih he highes levels of educaion have higher survival raes. However, hese differences remain relaively small. Moreover, consisen wih he lieraure, moraliy differenials are smaller for women. 4. Resuls We now urn o he presenaion of he resuls of he disribuion of inernal rae of reurns o eriary educaion for he generaion born in 1970 obained by microsimulaion. We ake he characerisics gender, diploma and age of enry o he labour force of he individuals born beween 1968 and 1972 as a represenaive disribuion of he characerisics of ha generaion. On he basis of he FLFS we can disinguish 457 weighed classes. For insance, women wih a business school degree enering he labour force a 25 consiue one of hese classes. From hese 457 weighed classes we creae 34,782 arificial observaions for which we relae randomly an indusrial secor based on he empirical disribuion by gender and diploma for he individuals under 30 in he FLFS daase. Then we simulae heir life course as explained in secion 3. We hen compue on his simulaed daabase an inernal rae of reurns for each individual wih a eriary diploma as explained in secion 2 and herefore obain a disribuion of hese reurns by diploma. Firs of all, i is ineresing o compare our resuls wih hose obained by OECD (2003, 2008). According o OECD, he mean rae of reurn o higher educaion in is 12.2% for men and 11.7% for women; for 2004 he mean rae of reurn is 8.4% for men and 7.4% for women. When we apply OECD s mehodology on our simulaed panel (only one generaion), we obain a mean rae of reurn of 12.6%. 23