Educational Expansion and its Heterogeneous Returns for Wage Workers

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1 Dscusson Paper No Educatonal Expanson and ts Heterogeneous Returns for Wage Workers Mchael Gebel and Fredhelm Pfeffer

2 Dscusson Paper No Educatonal Expanson and ts Heterogeneous Returns for Wage Workers Mchael Gebel and Fredhelm Pfeffer Download ths ZEW Dscusson Paper from our ftp server: ftp://ftp.zew.de/pub/zew-docs/dp/dp07010.pdf De Dscusson Papers denen ener möglchst schnellen Verbretung von neueren Forschungsarbeten des ZEW. De Beträge legen n allenger Verantwortung der Autoren und stellen ncht notwendgerwese de Menung des ZEW dar. Dscusson Papers are ntended to make results of ZEW research promptly avalable to other economsts n order to encourage dscusson and suggestons for revsons. The authors are solely responsble for the contents whch do not necessarly represent the opnon of the ZEW.

3 Non techncal summary Ths paper examnes the evoluton of returns to educaton n the West German labour market n the perod Graduates from the perod of educatonal expanson n the 1960s and 70s entered the labour market durng the perod of observaton. Wth a lag, ths educatonal expanson contrbuted to skll upgradng of the labour force. Our paper tres to contrbute emprcally to the queston, whether ths upgradng of schoolng devaluated ts monetary returns n the labour market n the longer run. Based on data from the German Soco-Economc Panel (GSOEP) we estmate returns to educaton over the past twenty years n West Germany dfferentated by soco-economc characterstcs to take nto account demographc factors and the rse n female labour market partcpaton. A major challenge for emprcal research on returns to educaton s that school choce nvolves complex decson processes. For nstance, students may select themselves nto secondary or post secondary educaton based on unobserved factors lke ablty, preferences, and parental household ncome. Students may choose to go to unversty because of ther hgh sklls and abltes. Students from a poor household may leave the educatonal system earler because of fnancal constrants. As a result presumably there wll be no sngle effect of an educatonal choce on wages but rather a whole dstrbuton of such effects,.e. returns vary across ndvduals. In order to tackle these ssues we apply two estmaton methods. On the one hand, Wooldrdge s (2004) approach uses a set of observable control varables. On the other hand, Garen s (1984) control functon approach requres an nstrumental varable that nfluences the educatonal decsons but not the wage outcome. For the populaton of workers from the GSOEP, we fnd that both approaches produce estmates of average returns to educaton that decrease untl the late 1990s and ncrease sgnfcantly afterwards. Accordng to the Wooldrdge approach, returns to one addtonal year of educaton fell from 6.5 percent n 1984 to 4.9 percent n From 1998 onwards, we fnd ncreasng returns to educaton reachng a new local maxmum of 6.4 percent n 2002 whch s just below the overall maxmum n Regardng the gender aspects, the average returns to educaton seem to have been larger for women durng the 1980s and early 1990s. However, the gap decreases over tme whch may be a consequence of ncreased partcpaton of women. Furthermore, we fnd that the so called baby boomer cohort (workers born between 1958 and 1965) has the lowest average return to educaton compared to the cohort before and the one thereafter (the former s charactersed by lower and the latter s charactersed by sharply decreasng cohort szes). However, accordng to our estmates the effect exsts only at young ages and dsappears when employees become older.

4 Educatonal Expanson and ts Heterogeneous Returns for Wage Workers Mchael Gebel* and Fredhelm Pfeffer** * Unversty of Mannhem, MZES ** Unversty of Mannhem, ZEW Mannhem Abstract: The paper examnes the evoluton of returns to educaton n the West German labour market over the last two decades. Durng ths perod, graduates from the perod of educatonal expanson n the sxtes and seventes entered the labour market and an upgradng of the skll structure took place. In order to tackle the ssues of endogenety of schoolng and ts heterogeneous returns we apply two estmaton methods: Wooldrdge s (2004) approach that reles on condtonal mean ndependence and Garen s (1984) control functon approach that requres an excluson restrcton. For the populaton of workers from the GSOEP, we fnd that both approaches produce estmates of average returns to educaton that decrease untl the late 1990s and ncrease sgnfcantly afterwards. In the observaton perod, the gender gap n returns to educaton seems to vansh. Furthermore, we fnd that the so called baby boomer cohort has the lowest average return to educaton n young ages. However, ths effect dsappears when they become older. Keywords: Educatonal expanson, correlated random coeffcent model, heterogeneous returns to educaton, condtonal mean ndependence. JEL-classfcaton: J21, J24, J31 Acknowledgements: Fredhelm Pfeffer acknowledges fnancal support from the German Scence Foundaton under grants PF 331/2 ( Mcroeconometrc Methods to Assess Heterogeneous Returns to Educaton ) and PF 331/3 ( Wages, Rent-Sharng and Collectve Wage Barganng ). For constructve dscussons we would lke to thank Andreas Ammermüller, Gunhld Berg, Mla Beyer, Kathrn Göggel, Wnfred Pohlmeer and Stephan Lothar Thompsen. All remanng errors are ours. Correspondng author: Fredhelm Pfeffer, Centre for European Economc Research, P.O. Box , D Mannhem. Tel.: , E-mal: [email protected]

5 1 Introducton In Germany, a major expanson of post secondary educaton occurred durng the 1960s and 70s. For nstance, n the year 2005, 40 percent of the Germans n the age group of 25 to 30 held an upper secondary degree, compared to 23 percent of the 50 to 55 years old (Mcrocensus data, Statstsches Bundesamt, 2006). Even though ths was a moderate expanson from an nternatonal perspectve (Müller and Wolbers, 2003), t shares common goals. Among others, the expanson was ssued to enhance ndvdual well-beng and equalty of educatonal opportunty. A number of studes ndcate that educatonal nequaltes by socal background have decreased n recent decades n Germany (Müller and Haun, 1994; Henz and Maas, 1995; Schmpl- Nemanns 2000) even though t seems as f the amount of educatonal nequalty was stll hgh (Dustmann 2004). Despte of an mpressve amount of emprcal research (see secton 2 below) the longer run labour market mpacts of educatonal expanson have not been studed systematcally so far. Ths s somewhat surprsng gven the ntensve dscusson of for nstance the negatve mpact of early trackng n the German educatonal system on the dstrbuton of educatonal outcomes (see Schuetz et al., 2005). Students of the perod of educatonal upgradng entered the labour market later on and sgnfcantly rased the qualfcaton structure of the workforce. For nstance, n our sample of workers from West Germany, extracted from the German Soco- Economc Panel (GSOEP), average years of schoolng ncreased from 11.2 years n 1984 to 12.3 years n Our paper tres to contrbute emprcally to the queston, whether the upgradng of schoolng devaluated ts monetary returns n the labour market n the longer run. We estmate heterogeneous returns to educaton over the past twenty years n West Germany dfferentated by soco-economc characterstcs to take nto account demographc factors and the rse n female labour market partcpaton. Economsts are nterested n the nfluence of educaton on varous soco-economc outcome varables, among them wages and unemployment rsk. To assess these returns to educaton, selectvty nto hgher educaton durng an expanson s of consderable nterest. The level of educaton s generally chosen n a complex choce process (Card, 1999). Factors such as preferences, ablty, fnancal constrants or dfferences n the qualty of schools are usually unobserved by the researcher. If ndvduals self-select nto educaton based on unobserved factors, ths creates an endogenety problem when estmatng returns to educaton snce the sample of ndvduals who make each schoolng choce wll not be random (Wlls and Rosen, 1979). Furthermore, when estmatng the standard Mnceran wage equaton t s usually assumed that the return to schoolng s homogenous,.e. constant across ndvduals, though observed and unobserved factors can lead to heterogenety n returns,.e. returns vary across ndvduals. Thus, t follows that there s no sngle ef- 1

6 fect of educaton but rather a whole dstrbuton of ndvdual effects (among others see Blundell et al., 2005; Heckman et al., 2006). A sgnfcant part of the recent German lterature s concerned wth varous data and methodologcal aspects of estmatng returns to educaton n the presence of selectvty and heterogenety (for recent surveys see Jochmann and Pohlmeer, 2004, Flossmann and Pohlmeer, 2006). Estmates for homogenous or constant returns to educaton for Germany reveal values between 5 and 14 percent, dependng on the nstruments used, whereas the average treatment effect of schoolng has been estmated to be 8.9 percent for West German males n 1998 (Maer et al., 2004). In ths paper we try to contrbute to the lterature on educatonal expanson and ts long run and heterogeneous returns. Our contrbuton s threefold. Frst, we nvestgate the evoluton of heterogeneous returns to educaton n the labour market n the twenty year perod from 1984 to The emprcal assessment s based on data from the German Soco-Economc Panel (GSOEP). Second, we take the endogenety and selectvty of school choce nto account. A correlated random coeffcent model s employed where the explanatory varable year of schoolng s measured as a contnuous treatment varable whch can be correlated wth unobserved heterogenety. Identfcaton s based on dfferent assumptons. On the one hand, followng Wooldrdge (2004) we dentfy the average return to educaton va condtonal mean ndependence assumptons. On the other hand, we mplement a control functon approach followng Garen (1984) whch uses excluson restrctons to control for selecton on unobservable heterogenety. Thrd, the returns to educaton n West Germany are dfferentated by demographc characterstcs to take nto account effects nduced by female labour force partcpaton and the rse of newborns untl the sxtes and ts declne afterwards. Our fndngs based on Wooldrdge s (2004) condtonal mean ndependence and Garen s (1984) control functon approach are that both approaches produce estmates of average returns to educaton that decrease untl the late 1990s and ncrease sgnfcantly afterwards. Usng Wooldrdge s approach, our results vary between 4.9 and 6.5 percent for the average partal effect of an addtonal year of schoolng, whch seems to be at the lower end of prevous fndngs (Flossmann and Pohlmeer, 2006). Regardng the gender aspects, the average returns to educaton seem to have been larger for women durng the 1980s and early 1990s. However, the gap decreases over tme whch may be a consequence of ncreased partcpaton of women. Furthermore, we fnd that the so called baby boomer cohort has the lowest average return to educaton compared to the cohort before and the one thereafter (the former s charactersed by lower and the latter by sharply decreasng cohort szes). Whle ths fndng s n lne wth the lterature on wages and cohort sze (Macunovch, 1999), accordng to our estmates, the effect exsts only at young ages and seems to dsappear when employees become older. 2

7 Ths paper s organzed as follows. Secton 2 dscusses factors that nfluence returns to educaton over tme. In Secton 3, we develop the dea of heterogeneous returns to educaton n a correlated random coeffcent model. We suggest dfferent mcroeconomc estmaton technques: conventonal approaches, Wooldrdge s (2004), and Garen s (1984) approach. Secton 4 descrbes the data set and varables used. Furthermore, frst descrptve results for the evoluton of educatonal attanment over tme are presented. In secton 5, we compare estmaton results dfferentated by estmaton technques, gender and cohorts over tme. Secton 6 concludes. 2. Educatonal Expanson, Wages and the Labour Market n West Germany Educatonal attanment started to ncrease n the 1960s n Germany leadng wth a lag to the upgradng of educatonal qualfcaton n the labour market. In a standard economc supply and demand labour market framework, a rsng supply of (hgh-) sklled workers may nduce, ceters parbus, a declne n the returns to educaton. A related concern s that educatonal expanson may have resulted n nsttutons dggng deeper nto the dstrbuton of student abltes so that weaker students mght have been admtted to hgher educaton, leadng to a decrease n the average productvty level of hgher educated workers (for nstance, Walker and Zhu 2005). Another concern s that teachng qualty mght have fallen because educatonal nsttutons were not able to provde the necessary qualty for the rsng quanttes of students. Ths could have resulted n decreasng returns as well. Besdes of educatonal expanson there are other factors that nfluenced demand and supply condtons on German labour markets over the last two decades. Some mportant factors have been, for nstance, brth cohort szes, wage determnaton processes, ncreasng female labour market partcpaton, and skll-based technologcal change. West Germany, as well as many other western countres, experenced a demographc change due to a baby boom that peaked durng the md-1960s and sharply decreasng cohort szes afterwards (see fgure A.1). Changes n the number of brths alter the supply of workers enterng the market about 20 years later,.e. n the perod that we observe n the GSOEP data. If larger brth cohorts enter the labour market and substtuton n producton s lmted between younger and older workers, ceters parbus, a downward pressure on returns to educaton for labour market entrants arses (Macunovch, 1999; Freeman, 1979). In addton, there was ferce wage competton for entrants due to unemployment rates as hgh as ten percent n Germany. Compared to entrants, ncumbent workers n Germany enjoy some protecton aganst wage competton due to, for nstance, strong unons and/or effcency wage consderatons (Franz and Pfeffer, 2006). Therefore, one mght expect decreasng returns to educaton for the baby boom cohorts and ncreasng returns to educaton for ndvduals born after 1964 when cohort 3

8 sze started to declne sharply. Because large cohorts are absorbed gradually by the labour market when experence ncreases, accordng to our expectaton, returns to educaton may have been lower manly for labour market entrants. However, as a result of skll upgradng and globalsaton the unon wage polces may have lost part of ts aggressveness. Startng around 1992/93 wage nequalty ncreased n Germany (Gernandt and Pfeffer, 2006b) combned wth rsng returns to educaton. The computer revoluton that started around 1970 changed the organsaton of labour away from routne manual tasks to non-routne analytcal and creatve tasks (Autor et al., 2006; Sptz-Oener, 2006). In ths process of acceleraton (Acemoglu, 2002), the demand for the hgh sklled created addtonal demand for hgh sklled workers, skll obsolescence ncreased for vocatonal sklls, but not for general ones n Germany (Ludwg and Pfeffer, 2006). These demand shfts towards analytcal sklls favoured presumably the hgh sklled and may be one addtonal reason for ncreasng returns to educaton. Another channel that nfluences labour market supply and demand condtons s female labour force partcpaton. In West Germany, the female partcpaton rate has been rsng durng the last decades, leadng to a catchng-up process to men and competton for college slots and labour market postons. Based on the decreasng gender-gap n educatonal attanment and labour market partcpaton, a convergence of gender-specfc returns to educaton can be expected. For nstance, Lauer and Stener (2001) report homogeneous returns to educaton around 8 percent for men and 10 percent for women n the perod from 1984 to 1997 based on the GSOEP. Ammermüller and Weber (2005) and Boockmann and Stener (2006) fnd that gender dfferences n returns to educaton seem to fade away. To sum up, we expect that supply sde factors lke educatonal expanson and ncreasng partcpaton of women lower the returns to educaton (n a ceters parbus sense) whereas supply sde factors lke decreasng cohort sze and demand sde factors lke skll-based technologcal change and workplace nnovatons ncrease the returns to educaton. In addton, the mpact of educatonal expanson on wages wll be formed by the process of wage determnaton, the regulaton of labour as well as the rate of unemployment and actve labour market polces. Over the twenty year perod of observaton, these factors have changed n West Germany and from a pror reasonng ts mpact on the returns to educaton seems to have been ambguous. Therefore, we would lke to nvestgate the evoluton of the returns to educaton after the perod of educatonal expanson n Germany dfferentated by gender and brth-cohort. Furthermore, we concentrate on methodologcal ssues of endogenety of schoolng and unobserved heterogenety n returns to educaton. 4

9 3. Statstcal Model and Identfcaton 3.1. The Correlated Random Coeffcent Model As a framework for the emprcal assessment of the returns to educaton we employ the correlated random coeffcent model (Heckman and Vytlacl, 2001): ln Y = a + b S + u wth a a X + ε a = and b = b X + εb (1), where the outcome varable ln Y s log wages and the explanatory varable S s years of schoolng of ndvdual. Ths equaton may result from optmal schoolng choce where educaton s determned by ndvdual s observed and unobserved margnal benefts and the costs of schoolng (see Card, 1999). The model has an ndvdual-specfc ntercept a and slope b that may depend on observable varables X and unobservable heterogenety ε a and ε b. The heterogenety components capture nfluences from gender, famly background, age, preferences, ablty, etc. such that a and b represent random coeffcents. In addton, we do not assume that b and S are ndependent, so that a and S as well as b and S can be correlated (Wooldrdge, 2004). For example, snce ndvduals wth hgher benefts from educaton are more lkely to partcpate longer n educaton, the returns to educaton b may n general be correlated wth S f varaton n unobserved (to the econometrcan) benefts mples postve self-selecton. In ths case, the schoolng varable s nfluenced by ts own coeffcent, yeldng an endogenety problem. We are nterested n estmatng the heterogeneous effects of S on ln Y represented by b n the structural model. In ths model, the return to educaton vares across ndvduals n both, observable heterogenety n returns X and unobserved ndvdualspecfc returns to schoolng ε b. Hence, there s no sngle parameter for the return to schoolng,.e. there s a dstrbuton of effects across ndvduals. The dstrbuton of the returns to educaton can be summarzed wth the average partal effect (APE) that measures the average return for an addtonal year of educaton n the expanson process for a randomly chosen ndvdual of the populaton: ( Y S ) = E( b ) = β E ln (2) β represents the average treatment effect for the case of a contnuous treatment varable (Flossmann and Pohlmeer, 2006; Wooldrgde 2004). The earnngs equaton (1) allows the consderng of the problem of homogeneous and heterogeneous returns to educaton n a common framework. If returns to educaton are homogenous, the outcome equaton can be re-wrtten as the classcal Mncer-type of earnngs functon (Blundell and Costa Das, 2000): 5

10 ln Y = a X + b S + ε + u (3) a where b s the common return to educaton. Tradtonally, unobserved heterogenety enters exclusvely the ntercept of the wage equaton but not the slope coeffcent. 1 One appealng feature of our model (1) s that varaton n unobserved heterogenety affects the slope as well,.e. unobserved heterogenety nfluences the wage effect of educaton Potental Ptfalls of Conventonal Approaches When estmatng (1) by OLS, there are three potental sources of a bas due to unobservable varables nducng a non-zero correlaton between schoolng and the error term n the outcome equaton (see Blundell et al., 2005; Heckman et al., 2006). Frst, f ndvduals wth hgh absolute earnngs capacty both acqure more educaton and earn hgher wages, schoolng SB B wll be postvely correlated wth ε a (Grlches, 1977). Ths ablty bas nduces an upward bas n the estmated average return. Second, there may be a measurement error n the schoolng varable SB B nducng a downward based n the case of classcal measurement error (Grlches, 1977). Thrd, there can be a return bas f ndvduals dffer n ther relatve earnngs capacty and act upon ther comparatve advantage when choosng ther level of educaton (Wlls and Rosen, 1979). The drecton of ths bas s less clear n the case when returns are heterogeneous (Blundell et al., 2005). If returns to educaton are by defnton homogeneous, return bas s absent. The majorty of the lterature on the return to schoolng uses nstrumental varables (IV) methods to handle the endogenety problems. To ths end, the nstrumental varable has to be correlated wth schoolng and should be uncorrelated wth unobserved ndvdual earnng capactes. For nstance, Lauer and Stener (2001) estmate homogeneous returns to educaton for Germany by IV-methods usng dfferent famly background varables as nstruments. The results depend on the nstruments used. The estmated returns to educaton vary between 6.6 and 14.8 percent. Jochmann and Pohlmeer (2004) use dfferent nstruments n the case of heterogeneous returns as for example the number of sblngs, secondary school densty or the unemployment rate at graduaton. Agan, the results vary to some degree wth the chosen nstruments. However, when schoolng s correlated wth unobserved ndvdual heterogenety n returns to educaton as assumed n the correlated random coeffcent model, standard IV methods may fal (Heckman and L, 2004). In ths case, one may redefne the parameter of nterest as the Local Average Treatment Effect (LATE) n the sense of 1 Note that there mght stll be endogenety problems, f the unobserved general ndvdual earnngs capacty ε a s correlated wth SBB 6

11 Angrst et al. (1996). For a bnary treatment varable, LATE estmates the average returns to schoolng for complers,.e. ndvduals who were nduced to change ther partcpaton status by a change n the nstrument. For example, Ichno and Wnter- Ebmer (1998) as well as Becker and Sebern-Thomas (2001) estmate LATE for Germany usng dfferent famly background varables as nstruments. Snce each nstrument mples ts own LATE and the group of complers cannot be dentfed wthout further assumptons, ths may be regarded as a drawback. However, LATE s especally nterestng when school reforms are used as nstruments snce LATE measures the returns to schoolng for those who changed ther level of schoolng because of the reform. Wth ths approach, Pschke and van Wachter (2006) fnd rather low margnal returns to educaton n Germany. In our emprcal analyss, we contrast two methods that do not suffer from bases lke standard OLS and IV technques because they try to capture both heterogenety and endogenety. They rely on dfferent dentfyng assumptons: Wooldrdge s (2004) condtonal mean ndependence (CMI) approach and Garen s (1984) control functon (CF) approach Wooldrdge s (2004) Condtonal Mean Independence (CMI) Approach The frst dentfcaton strategy consdered reles heavly on condtonal moment ndependence assumptons. Followng Wooldrdge (2004), we can dentfy APE wth the followng two assumptons as far as the lnear outcome equaton (1) holds: ( Y a, b, S, X ) = E( lny a, b, S ) = a b S ( S a, b, X ) E( S X ) and Var ( S a b, X ) = Var( S X ) E ln + (4) E =, (5) where the elements of X are sutable proxy varables for the observed and unobserved heterogenety,.e. the X should be good enough predctors of S. The frst assumpton postulates that the vector X s redundant gven S and (a, b ) n the structural condtonal expectaton (4). Ths dentfcaton assumpton obvously holds snce the control varables X enter the earnngs functon through a, b, and S only (Maer et al., 2004). The second assumpton s a redundancy condton of the form that both heterogenety terms a and b are redundant n the frst two condtonal moments of the schoolng varable S condtonal on a set of covarates X. Ths latter and strongest assumpton requres a dfferentated set of varables that control suffcently for observable and unobservable heterogenety. These condtonal moment ndependence (CMI) condtons are a weaker form of condtonal ndependence assumptons (CIA) (Wooldrdge, 2002: 607). Wooldrdge (2004: 23) shows that hs CMI approach can be nterpreted n the bnary treatment case as a weghtng matchng estmator. In contrast to methods that rely on excluson restrctons lke nstrumental varable approaches and control functons, 7

12 APE s dentfed wthout any excluson restrcton. Based on assumptons (4) and (5) Wooldrdge (2004) derves the followng estmator for APE: N ˆ 1 β = ( ) ( ) S E S X lny Var S X (6) N = 1 Because ln Y, S and X are observable, one needs to estmate E(S /X ) and Var(S /X ). The dffculty arses from consstently estmatng E(S /X ) and Var(S /X ). Snce S s nonnegatve, smple lnear models have shortcomngs. Therefore, we employ a generalzed lnear model (GLM) wth a Posson dstrbutonal assumpton for years of schoolng S : E γ X ( S X ) = e γ X and Var( S X ) σ e = 2 (7) Ths specfcaton guarantees postve estmates of both condtonal mean and varance. 2 2 A consstent estmator of σ s obtaned as the mean of squared Pearson resduals. Snce analytcal standard errors have not been developed so far, standard errors of APE are bootstrapped Garen s (1984) Control Functon (CF) Approach Garen (1984) proposed a possble alternatve soluton to the random coeffcent estmaton problem - called the control functon (CF) approach - that s smlar to the two-step procedure commonly used to correct for tradtonal selectvty bas (Heckman, 1978). Whle the standard IV approach does generally not dentfy APE n the heterogeneous returns context the CF approach does. The CF approach s mplemented by smultaneously modellng both the process of educatonal attanment and the process of generatng wages. Hence, an explct model of the schoolng selecton process whch relates the rule for assgnng ndvduals to treatment to the potental treatment outcomes s requred: S c X + dz + v = wth ( v Z, X ) = 0 E (8) where both X and Z nfluence the educatonal decson and v represents an usual error component, ncorporatng unobserved components whch determne the choce of educaton. Z s an excluson restrcton,.e. t should have no correlatons wth unobserved heterogenety n the wage equaton. The error terms v, ε a and ε b are 2 Contrary to the standard varance assumpton of equalty between the condtonal varance and the mean we specfy n (7) the weaker Posson GLM varance assumpton that allows the varance-mean rato to be any postve constant (Wooldrdge, 2002) 8

13 normally dstrbuted wth zero means, postve varances and are possbly correlated wth each other. 3 Followng Garen (1984) one can formulate an augmented wage equaton of the form: ln Y = a + ν S + w (9) βs + γ1ν + γ 2 where γ 1 ν and γ 2 ν S are the control functons wth γ1 = cov( ε a, ν ) var( ν ) and γ 2 = cov( ε b, ν ) var( ν ). Once these terms are ncluded n the outcome equaton (and mplctly subtracted from ts error term), the error term w has all the desrable propertes,.e. t s orthogonal to all of the regressors n the new equaton: E( w X, S, v ) = 0 (Heckman and Robb, 1985). Ths model can be estmated usng a generalzaton of the standard two-step approach. In the frst step an estmaton of the schoolng choce s used to construct the control functons that are ncluded as addtonal regressors n the augmented wage equaton n the second step. The estmated coeffcents of v and v S provde nformaton about the selecton on the unobserved absolute earnngs capacty term and about selecton on comparatve earnngs capacty, respectvely. If an ndvdual attans a hgher (lower) level of educaton than expected by our model the value of v s postve (negatve). For example, f the coeffcent γ 1 of the frst control functon s postve, ths mples that the unobserved factors that lead to educatonal overachevement (postve v ) have a postve mpact on earnngs. The sgn of the coeffcent γ 2 of the second control functon descrbes how ths effect changes for ncreasng levels of educaton. Followng the comparatve advantage hypothess (Wlls and Rosen, 1979), we would expect that γ 2 s postve,.e., those wth unexpectedly large amounts of schoolng (postve v ) tend to earn more than the others n hgher educaton (Garen, 1984). Based on ther hgher unobserved margnal returns they select nto hgher educaton accordng to ther comparatve advantage. 4. Data and Descrptve Analyss 4.1. Sample Selecton For the analyss, we use 21 waves of the German Soco-Economc Panel Study (GSOEP) that collects longtudnal representatve mcro-data on persons, households and famles on a yearly bass. GSOEP contans nformaton on varous socoeconomc factors lke educaton, employment and earnngs. In addton to annually collected nformaton, GSOEP retreves some retrospectve nformaton about fam- 3 Ths trvarate normalty assumpton can be weakened to the condton that condtonal expectatons of the unobserved earnng components ε a and ε b are lnear n the resdual of the selecton equaton (Blundell et al., 2005). 9

14 ly background, among others. We nclude new samples from 1998 and Due to mssng value problems on educatonal attanment and lack of comparablty, foregn-born ndvduals were excluded from the sample. Furthermore, for the purpose of comparablty, the analyss s restrcted to West German ctzens because of economc dfferences and dscrepances n the schoolng system between West and East Germany. Self-employed workers are excluded from the sample snce they are exposed to dfferent earnngs-generatng mechansms. The resultng sample s restrcted to full-tme dependent workers aged between 25 and 60, defned as ndvduals workng 30 hours or more per week. After elmnatng all unts wth mssng values n any of the varables consdered we obtan a fnal sample sze that ranges from 1,535 observatons n 1984 to 3,958 n The dependent varable s the natural logarthm of real earnngs per hour worked. The real gross hourly wage s obtaned by dvdng the monthly nomnal gross wage n the month precedng the date of the ntervew by the number of hours worked. Hence, the focus les exclusvely on the drect monetary returns to educaton. For the sake of comparablty wth economc studes on monetary returns to educaton, we measure school careers n years attended rather than educatonal degrees completed. Lnearty n the earnngs equaton mples that each year of schoolng yelds an dentcal return to educaton, rrespectve of the level of educaton. GSOEP contans nformaton on the hghest completed level and type of educaton for each ndvdual. The measure of years of schoolng s derved by attachng a standard number of years to the hghest educatonal level (cp. table A.1). However, t does not necessarly reflect the actual number of years attended snce a person may need less or more than standard tme to complete her educaton. 4 As standard control varables, gender and ndvdual s age (n lnear and quadratc terms) are ncluded. We use age varables nstead of potental labour market experence because the latter mght be endogenous wth respect to schoolng. To justfy the condtonal moment ndependence assumptons we make use of a set of famly background nformaton that s covered by recall questons and that s avalable for a suffcent number of persons n each wave consdered. Famly background characterstcs should proxy for the parental nfluence on educatonal attanment and later employment carrers. In detal, we dstngush between educatonal and occupatonal socal background. The measure for parents educaton follows the CASMIN educatonal classfcaton whch has the advantage to combne nformaton on the hghest school degree and the hghest vocatonal degree of the parents (Erkson and Goldthorpe, 1992). The CASMIN categores have been summarzed n fve categores for fathers and n a dummy-varable for mother s hgher educaton (cp. table A.1). Parents educaton 4 For an analyss of the ssue of over educaton n workers from dfferent educatonal degrees see Maer et al. (2004). 10

15 may ndcate ablty dfferences due to genetc endowments as well as the formaton of sklls n early chldhood to mprove educatonal performance, e.g. wth verbal tranng durng chldhood or practcal help wth school work (Erkson and Jonsson, 1996). Fnally, educaton may postvely nfluence parents taste and percepton of what s the best educatonal career for ther chldren (Dustmann, 2004). There are four categores of parents occupatonal poston (cp. table A.1). These categores should proxy for the economc crcumstances of the famly whch affect educatonal choce by nfluencng costs of schoolng. A further proxy for costs of schoolng s the dummy varable rural socalsaton that s smlar to other varables n the lterature measurng proxmty to college (see for nstance Card, 1995; Becker and Sebern-Thomas, 2001). To mplement the control functon approach we use the number of sblngs as an excluson restrcton and assume that t satsfes the two condtons for vald nstrumental varables (Wooldrdge, 2002). Frst, a number of authors (for nstance Becker and Tomes, 1976, Hanushek, 1992) hypothesze a postve correlaton between the number of sblngs and ndvdual educatonal attanment even after controllng for other famly background characterstcs. Parents try to optmally allocate fnancal and non-fnancal resources to ther chldren who compete for the attenton and resources of ther parents. Therefore, educatonal achevement and total famly sze mght be negatvely related under the constrant of lmted educatonal resources. Second, the nstrumental varable should be uncorrelated wth unobserved ndvdual s earnngs capactes,.e., the number of sblngs should not have an effect on ncome other than the ndrect effect transmtted over educatonal attanment. Because we control for a set of other famly background varables lke parents educaton, occupaton and the place of socalsaton we do not expect a non-neglgble, systematc and ndependent effect of the number of sblngs on earnngs. In the case of Wooldrdge s (2004) CMI approach the number of sblngs serves as a further control varable. To estmate the causal effect of educaton on ncome we do not control for varables that mght be a consequence of educaton lke actual famly status, economc sector, tenure, etc. Table A.1 gves an overvew of the varables and ts defntons. Table A.2 provdes summary statstcs for key ndvdual level varables n selected years Trends n educatonal attanment by sex and brth cohort Durng the past two decades the educatonal composton of the West German labour force has changed. Fgure 1 summarzes changes n the gender-specfc educatonal attanment of the West German labour force, aged 25 to 60 years, between 1984 and 11

16 2004 usng GSOEP. 5 PTAs ths fgure shows, the mean number of years of schoolng has steadly ncreased for both men and women whch ponts to an upward shft of the qualfcaton structure durng ths perod. For men (women), the ncrease was from 11.6 (10.8) years n 1984 to 12.4 (12.2) years n Women are catchng up constantly so that n recent years the female average educatonal attanment becomes smlar to the male educatonal attanment. A smlar analyss by brth cohorts reveals the same trends n educatonal attanment. Fgure 2 dsplays average years of schoolng for selected brth cohorts, as observed at roughly the same age of 31 to 38 years n dfferent years. For women, we observe a proportonal ncrease n years of schoolng as we move to younger brth cohorts. For example, the brth cohort of people born n has an average educatonal attanment of 11.1 years for women and 12 years for men. The gender gap n years of schoolng vanshes for the brth cohort of people born n ,5 Fgure 1: Average years of educaton by gender, (ndvduals aged 25-60) 12 years of educaton 11, , Men Women Source: SOEP ( ); own computatons. 5 All estmates n fgure 1 as well as n the followng fgure 2 are based on calculatons wth the weghts provded by GSOEP n order to reflect populaton totals. 12

17 Fgure 2: Average years of educaton by gender and brth cohorts, measured at roughly the same age of years. 13,5 13 years of educaton 12, , brth cohort Men Women Source: SOEP ( ); own computatons. Remark: Cohort s observed n 2004, cohort n 1996, and cohort n 1988 all at age Cohort s observed n 1984 at age reflectng only a small devaton n age from the other brth cohorts. 5. Estmaton Results 5.1. Comparson of Results from Dfferent Estmaton Technques Fgure 3 compares the evoluton of three dfferent estmates of ndvdual returns to educaton n West Germany durng the perod 1984 to 2004 (for detaled estmaton results and standard errors see table A.3). As a benchmark, fgure 3 contans results from an OLS regresson wth years of schoolng controllng for age n lnear and squared functonal form on log wage. Furthermore, the APE from the condtonal mean ndependence (CMI) approach and from the control functon (CF) approach are llustrated. Wth OLS we fnd a slght downward trend n the evoluton of returns to schoolng untl the late 1990s. The returns to one addtonal year of educaton fell from 7.3 percent n 1984 to 5.4 percent n From 1998 onwards, we fnd ncreasng returns to educaton reachng a new local maxmum of 6.7 percent n The estmates untl 1998 are n lne wth the fndngs of Franz (2006), Ammermüller and Weber (2005) or Lauer and Stener (2001). To the best of our knowledge, ncreasng returns to educaton startng around 1998 had not been documented so far. 13

18 Fgure 3: Average Partal Effect, : OLS, CMI, and CF compared 0,12 0,1 average return to educaton 0,08 0,06 0,04 0, Source: SOEP ( ); own computatons. APE (CF) OLS APE (CMI) Interestngly, the APE estmated under condtonal moment ndependence (CMI) follows a farly smlar evoluton pattern over tme. However, there are dfferences. Frst: the estmated APE s always lower than standard OLS, between 0.5 and 1 percentage ponts. Accordng to our nterpretaton ths dfference reflects the potental ablty bas from OLS estmates. Takng nto account the heterogenety of returns to educaton and controllng for famly background varables the CMI approach controls for postve ablty bas to a certan degree. Second: although OLS and APE estmates are comparable over tme, ther content vares. APE measures the average of the dstrbuton of heterogeneous returns, whereas OLS measures an ndvdually constant homogenous return to educaton. Compared to the lterature, our estmate of the APE seems to be rather low. Maer et al. (2004), for nstance report an estmated APE of 8.7 percent for the year 1999 for German male workers. The control functon (CF) approach has been mplemented n a two-stage estmaton procedure. The frst stage nvolves the educatonal attanment selecton equaton and can be used to test for the valdty of the nstrumental varables. Accordng to our fndngs the number of sblngs has a partally negatve nfluence on educatonal attanment, holdng constant other famly background characterstcs (cp. table A.4). Ths seems to be n lne wth the lterature mentoned above. A regresson that ncludes the number of sblngs n a smple OLS log-wage equaton together wth other famly background varables was nsgnfcant suggestng that the number of sblngs seems to be a reasonable excluson restrcton. The coeffcent of the control 14

19 functon for the selecton on unobserved absolute earnngs capacty s postve, although t decreases over tme (cp. table A.4) and s never sgnfcant. Ths s only weak evdence for a postve ablty bas. Probably, the nformaton regardng educatonal background of the famly proxes already well for the absolute earnngs capacty. The coeffcent of the control functon for the selecton on comparatve earnngs capacty s always negatve. Ths contradcts the comparatve advantage hypothess. In our sample we fnd that those wth unexpected hgh amounts of schoolng have lower margnal returns to educaton. Indvduals, who seem to rather not have gone to hgher educaton, but have anyway, have done worse. The effect s sgnfcant n the perod from 1984 to 1989 and from 2000 onwards. In these years, we fnd negatve selecton on unobservable returns, whch may confrm the zero returns to educaton fndngs from Pschke and van Wachter (2005). The evoluton pattern of the estmated APE under CF approach devates substantally from the CMI results. Frst, the yearly estmates derved from the CF approach are more volatle and less precse (the standard errors are hgher). Detaled tests show that the devatons are usually not sgnfcant durng the 1980s and the ntal fluctuatons (see fgure 3) mght be a consequence of lower numbers of observatons. Second, there s a stronger ncrease of the APE after 1998 compared to the CMI approach. In 2004, the APE s 12 percent, whch s n lne wth some recent IV studes for Germany, Flossmann and Pohlmeer (2006). From a methodologcal pont of vew the devatons reflect dfferences n the dentfcaton strateges. From a substantve pont of vew the dscrepancy durng the last years could be a hnt for rsng selecton on unobservables, whch the CF approach controls for (Taber, 2001). Ths concdes wth the sgnfcant effects for the second control functon from 2000 onwards. To summarze our fndngs so far: Independently of the method used, the returns to educaton (APE) were farly constant durng the 1980s and 1990s n (West) Germany. Despte of a contnung upgradng of educatonal qualfcaton they started to ncrease from 1998 onwards (see fgure 1). Ths surprsng fndng seems to be lne wth rsng wage nequalty n Germany that started around 1994 (see Gernandt and Pfeffer, 2006b) Gender and Cohort Effects The followng analyss dfferentates gender and brth cohorts n the returns to educaton snce t mght be helpful for understandng the recent ncrease n the APE. The comparson rests on the CMI approach because t produces lower standard errors than the CF approach. For women, we fnd a robust declne n returns to educaton untl the late 1990s: the average return to an addtonal year of educaton n the populaton of women from the GSOEP declned from 8.5 percent n 1984 to about 15

20 4.9 percent n 1996 (cp. fgure 4, for detals table A.5). Ths robust fndng can, at least n our nterpretaton, be best understood n terms of female educatonal expanson and rsng partcpaton, a tradtonal supply sde nterpretaton. Ths enhanced wage competton and pressure on the APE. However, snce 1999 the APE s ncreasng agan for women, as t s for men. 0,09 Fgure 4: Average Partal Effect by gender, : CMI approach 0,08 0,07 average return to educaton 0,06 0,05 0,04 0,03 0,02 0, Men Women Source: SOEP ( ); own computatons. Furthermore, fgure 4 ndcates that the gender gap n returns to educaton decreased over tme, whch s n lne wth fndngs from Ammermüller and Weber (2005), among others. Although women s returns to educaton are estmated as beng hgher n almost every year, the dfferences s nsgnfcant snce As a consequence of changes n the workplace organsatons durng the computer revoluton, the labour servces of women and men mght have become better to substtute (see for nstance Sptz-Oener, 2006) whch n turn mght be one reason for the equalty of returns to educaton. Another possble reason could result from collectve wage barganng n Germany. In a last step, the average returns to educaton are compared for four dfferent brth cohorts. 6 Each cohort s composed of eght years: people born between 1942 and 6 We dfferentate the cohorts based on relatve brth cohort szes and not relatve to labour market cohort szes because only the former are lkely to be exogenous. Indvduals change ther educatonal attanment and labour market entry wth respect to cohort sze (Macunovch, 1999; Berger, 1989). 16

21 1949, people born between 1950 and 1957, people born between 1958 and 1965 and those born between 1966 and The cohort boundares are geared to cohort szes (cp. fgure A.1): The oldest cohort has low brth rates due to the 2nd World War and the post-war perod. The second cohort s of relatvely constant sze, whereas the thrd cohort s the baby boom cohort wth strongly ncreasng cohort szes peakng n Fnally, the last cohort s characterzed by a sharply declnng cohort sze. However, n order to have cohorts wth a suffcent number of observatons, our estmatons are restrcted to brth cohorts that are older than 27 to 34 years, e.g. we estmate APE for cohorts born startng at the year Tme, cohort and lfe-cycle effects can not be easly dsentangled emprcally because t s mpossble to observe two dfferent brth cohorts at the same age and n the same year (Heckman and Robb, 1985). To emprcally assess cohort effects n average returns to educaton n Germany dfferent cohorts at the same age are compared at dfferent ponts n tmes n the same labour market. Both fgure 5 and 6 dsplay estmaton results for dfferent cohorts at a gven age (cp. tables A.6, A.7 and fgure A.2 for detals). We follow the development n the returns to educaton over a specfc phase of the workng lfe of a cohort for a perod of fve year. For example, all cohorts n fgure 5 are observed at age However, we do ths for the cohort n 1984, for the cohort n 1992 and for the cohort n Fgure 5 reveals that the baby-boomer cohort has the lowest average return to educaton compared to the cohort before ( ) and the one thereafter ( ) where the former and the latter are charactersed by lower and the latter even by sharply decreasng cohort szes. A large cohort sze seems to reduce the average return to educaton at young ages (27-38 years old). The hgher supply of labour market entrants ncreases wage pressure n ths group and decreases, ceters parbus, ther return to educaton whch seems to be lne wth recent fndngs of Boockmann and Stener (2006) and Stener and Lauer (2001). The dfferences n the APEs are not sgnfcant from a statstcal pont of vew. Surprsngly, the dfferences n the APE fully dsappear when the baby-boomer cohort s compared at older ages (35-46 years old) wth other cohorts at the same age (see Fgure 6). Ths mght reflect the fact that large cohort szes are absorbed by the labour market at later ages,.e. cohort effects exst only for the young when they enter the labour market. In general, the fndngs hnt at the exstence of brth cohort effects for the young labour force that dsappear when employees become older. Ths mght stem from wage rgdty for ncumbent workers and a hgher degree of wage flexblty for entrants to the labour market (see for nstance Gernandt and Pfeffer, 2006a). 17

22 Fgure 5: Average Partal Effect of returns to educaton by brth cohorts at same age 27-38: CMI Approach 0,06 0,05 average return to educaton 0,04 0,03 0,02 0, age Source: SOEP ( ); own computatons Fgure 6: Average Partal Effect of returns to educaton by brth cohorts at same age 35-46: CMI Approach 0,08 0,07 0,06 average return to educaton 0,05 0,04 0,03 0,02 0, age Source: SOEP ( ); own computatons

23 6. Conclusons In Germany, graduates from the perod of educatonal expanson n the sxtes entered the labour market durng the perod of observaton from 1984 to Wth a lag, ths educatonal expanson contrbuted to skll upgradng of the labour force. For example, n our sample from the GSOEP the average years of educaton ncreased by roughly one year n ths perod. In order to tackle the ssue of endogenety of school choce and ts heterogeneous returns we appled two estmaton methods: Wooldrdge s (2004) CMI approach and Garen s (1984) CF approach. The former method reles crucally on the condtonal moment ndependence assumpton whch requres suffcent observable control varables. The latter method employs dstrbutonal assumptons and needs an excluson restrcton such that t can control for selecton on unobservables. Our fndngs based on Wooldrdge s (2004) condtonal mean ndependence and Garen s (1984) control functon approach are that both approaches produce estmates of average returns to educaton that decrease untl the late 1990s and ncrease sgnfcantly afterwards. Durng the perod from 1984 to 2004 the estmated APE follows a roughly smlar evoluton pattern over tme although standard errors from Garen s approach are relatvely larger. Accordng to the Wooldrdge approach, returns to one addtonal year of educaton fell from 6.5 percent n 1984 to 4.9 percent n From 1998 onwards, we fnd ncreasng returns to educaton reachng a new local maxmum of 6.4 percent n 2002 whch s just below the overall maxmum n Durng the 1980s and early 1990s returns to educaton have been hgher for women than for men, but the gender gap n returns vanshed over tme. Accordng to our nterpretaton, decreasng returns to educaton for women are related to the strong female educatonal expanson and labour market partcpaton. Furthermore, we fnd that the so called baby boomer cohort (workers born between 1958 and 1965) has the lowest average return to educaton compared to the cohort before and the one thereafter (the former s charactersed by lower and the latter s charactersed by sharply decreasng cohort szes). Ths fndng s n lne wth the lterature on wages and cohort sze n general (Macunovch, 1999). However, accordng to our estmates the effect exsts only at young ages and dsappears when employees become older. For a more detaled analyss of cohort and age effects n the process of educatonal expanson longer tme perods and other data need to be taken nto account. In ths study educaton s measured as years of schoolng whch mght be problematc for a schoolng system whch s characterzed by early ablty trackng and general and vocatonal educatonal qualfcatons lke the German one. To apply mcroeconometrc methods to estmate the causal effect of dfferent educatonal degrees on labour market outcomes and on the ssue of over educaton should be a challenge for further research (e.g. Blundell et al., 2005, Maer et al., 2004). To ds- 19

24 entangle the dfferent nfluences on the evoluton of returns to educaton, crosscountry comparsons wth mult-level models are an nterestng approach (e.g. Gangl, 2003, Van der Velden and Wolbers, 2003). Furthermore, research s necessary to dg deeper nto potental ndrect outcomes of educatonal expanson, takng nto account the queston of labour market regulatons, employment and unemployment as well. References Acemoglu, D. (2002). Techncal Change, Inequalty, and the Labor Market. Journal of Economc Lterature 40(1), Ammermüller, A. and A. Weber (2005). Educatonal Attanment and Returns to Educaton n Germany. ZEW Dscusson Paper # Mannhem. Angrst, J., G. Imbens and D. Rubn (1996). Identfcaton and Causal Effects Usng Instrumental Varables. Journal of the Amercan Statstcal Assocaton 90: Autor, D., L. Katz and M. Kearney (2006). The Polarzaton of the U.S. Labor Market. Amercan Economc Revew Papers and Proceedngs 96(2): Becker, S. and F. Sebern-Thomas (2001). Returns to Educaton n Germany: A Varable Treatment Intensty Approach. IZA Dscusson Papers # Bonn. Becker, G. and N. Tomes (1976). Chld Endowments and the Quantty and Qualty of Chldren. Journal of Poltcal Economy 84: Berger, M. (1989). Demographc Cycles, Cohort Sze, and Earnngs Growth: A Reexamnaton of the Evdence. Journal of Poltcal Economy 93: Blundell, R. and M. Costas Das (2000). Evaluaton Methods for Non-Expermental Data. Fscal Studes 231(4): Blundell, R., L. Dearden and B. Sanes (2005). Evaluatng the mpact of educaton on earnngs: Models, methods and results from the NCDS. Journal of the Royal Statstcal Socety Seres A 168(3): Boockmann, B. and V. Stener (2006). Cohort Effects and the Returns to Educaton n West Germany. Appled Economcs 38: Card, D. (1995). Usng Geographc Varaton n College Proxmty to Estmate the Return to Schoolng. In L. Chrstofdes, E. Grant and R. Swdnsky (eds.), Aspects of Labour Market Behavour: Essays n Honour of John Vanderkamp. Toronto: Unversty of Toronto Press, Card, D. (1999). The Causal Effect of Educaton on Earnngs. In O. Ashenfelter and D. Card (eds.), Handbook of Labor Economcs 3. Amsterdam: North- Holland,

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28 Appendx Varable Name log wage educyears Descrpton Table A.1: Varable Defnton Log gross hourly wage Years of educaton: constructed wth standard tmes for hghest educatonal and vocatonal degree obtaned: no degree (7 years), lower secondary (9 years), ntermedate secondary (10 years), techncal secondary (12 years), hgher secondary (13 years), vocatonal tranng (+1.5 years), vocatonal school (+2 years), hgher techncal college (+3 years), unversty (+5 years) Demographcs age age2 female Age n years Age squared Dummy for sex (1= female; 0= male) Famly Background Aggregated CASMIN: Father s Educaton fcasmn1ab fcasmn1c fcasmn2ab fcasmn2c fcasmn3ab Reference category: Inadequately completed elementary educaton or (compulsory) elementary educaton Compulsory educaton plus vocatonal tranng Secondary ntermedate educaton, wth/wthout vocatonal tranng Full secondary educaton (Abtur), wth/wthout vocatonal tranng Unversty/ Unversty of appled scences Aggregated CASMIN: Mother s Educaton mcasmn1abc mcasmn2abc3ab Reference category: Inadequately completed elementary educaton or (compulsory) elementary educaton; compulsory educaton plus vocatonal tranng Secondary ntermedate educaton, wth/wthout vocatonal tranng Full secondary educaton (Abtur), wth/wthout vocatonal tranng Unversty/ Unversty of appled scences 24

29 Table A.1: Varable Defnton (contnued) Varable Name Descrpton Occupatonal Poston Father fbluecollar Dummy (1= father blue collar; 0 else) fwhtecollar Dummy (1= father whte collar; 0 else) fselfemployed Dummy (1= father self-employed; 0 else) fcvlcervant Dummy (1= father cvl cervant; 0 else) Place of Socalsaton socrural Dummy (1= rural socalsaton,.e. countrysde; 0= urban socalsaton,.e. cty, bg town, small town) Famly Composton numbersblngs Number of sblngs Source: SOEP ( ); own defntons. 25

30 Table A.2: Summary Statstcs Mean Std. dev. Mean Std. dev. Mean Std. dev. log wage educyears age age female fcasmn1ab fcasmn1c fcasmn2ab fcasmn2c fcasmn3ab mcasmn1abc mcasmn2abc3ab fbluecollar fwhtecollar fselfemployed fcvlcervant socrural numbersblngs N (number of observatons) 1,535 2,070 3,332 Source: SOEP ( ); own computatons. 26

31 Table A.3: Average Partal Effect, : OLS, CMI, and CF compared OLS OLS APE (CMI) APE (CMI) APE (CF) APE (CF) N coeff. s.e. coeff. s.e. coeff. s.e , , , , , , , , , , , , , , , , , , , , ,332 Source: SOEP ( ); own computatons. Remark: Standard errors of APE (CMI) and APE (CF) are bootstrapped each wth 500 repettons. 27

32 Table A.4: Control Functon Approach 1. Stage 2. Stage IV: Number of sblngs Selecton on unobserved absolute earnngs capacty ν and Selecton on unobserved comparatve earnngs capacty ν S coeff. s.e. coeff. γ 1 s.e. coeff. γ 2 s.e. N , , , , , , , , , , , , , , , , , , , , ,332 Source: SOEP ( ); own computatons. Remarks: 1. The frst stage ncludes addtonal regressors lke gender, age, rural socalsaton, educatonal and occupatonal background of the parents. 2. The second stage ncludes addtonal regressors lke years of educaton, gender, age, rural socalsaton, educatonal and occupatonal background of the parents. The IV number of sblngs s excluded. 3. Standard errors on the second stage are bootstrapped each wth 500 repettons. 28

33 Table A.5: Average Partal Effect by gender, : CMI approach Men Women APE (CMI) s.e. N APE (CMI) s.e. N , , , , , , , , , , , , , , , , , , , , , , , , , ,394 Source: SOEP ( ); own computatons. Remark: Standard errors of APE (CMI) are bootstrapped each wth 500 repettons. 29

34 Table A.6: Average Partal Effect by brth cohorts at same age 27-38: CMI approach Age Coeff. s.e. N Coeff. s.e. N Coeff. s.e. N Source: SOEP ( ); own computatons. Remark: Standard errors of APE (CMI) are bootstrapped each wth 500 repettons. Table A.7: Average Partal Effect by brth cohorts at same age 35-46: CMI approach Age Coeff. s.e. N Coeff. s.e. N Coeff. s.e. N Source: SOEP ( ); own computatons. Remark: Standard errors of APE (CMI) are bootstrapped each wth 500 repettons. 30

35 Fgure A.1: Brth Cohort Sze n West Germany Cohort Sze (number of brths) Source: Statstcal Offce Germany (2006) Remark: The boundares of brth cohort groups used n the analyss are marked by vertcal lnes. 31

36 Fgure A.2: Average Partal Effect by brth cohorts at same tme: CMI approach 0,09 0,08 0,07 average returns to educaton 0,06 0,05 0,04 0,03 0,02 0, year Source: SOEP ( ); own computatons. Remark 1: The dfferent startng ponts of the lnes are a result of dfferent cohort ages at a gven tme pont and sample sze problems. The lnes begn when the brth cohort s years old. Remark 2: Readng the graph horzontally, we can compare the returns to educaton for older (left) and younger (rght) brth cohorts at a gven age but at dfferent tme perods. Ths procedure produces fgures 5 and 6. 32