WORKING PAPER SERIES CEEAplA WP No 04/005 Reurns o Schooling in a Dynamic Model Corrado Andini March 005 Universidade dos Açores Universidade da Madeira
Reurns o Schooling in a Dynamic Model Corrado Andini Research Fellow Universidade da Madeira (DGE) Working Paper nº 04/005 Março de 005
CEEAplA Working Paper nº 04/005 Março de 005 RESUMO/ABSTRACT Reurns o Schooling in a Dynamic Model The paper develops a dynamic approach o Mincer equaions I is shown ha a saic model is based on he resricive hypoheses ha he oal reurn o schooling is consan over he working life and independen of bargaining issues A dynamic approach allows o show ha he oal reurn o schooling of a new labor-marke enran posiively depends on his/her bargaining power as employee; he oal reurn increases a a decreasing rae in he firs par of he working life and depends of bargaining issues; aferwards i becomes roughly consan and independen of bargaining The main implicaion is ha a saic model may produce disored empirical resuls when using daa on young workers since unable o accoun for he paern of he oal reurn o schooling in he firs par of he working life I show he laer using daa from he US Naional Longiudinal Survey of Youh (1980-1987) and analyzing he impac of educaion on wihin-group wage inequaliy a la Marins and Pereira (004a) However, a saic model does no produce disored empirical resuls when using daa on relaively experienced workers I show he laer using Poruguese daa from he European Communiy Household Panel (1994-001) Keywords: Reurns o Educaion, Wage Inequaliy, Quanile Regressions JEL Classificaion: C9, J31, I1 Corrado Andini Universidade da Madeira Deparameno de Gesão e Economia Campus da Peneada 9000-390 Funchal Porugal
Reurns o Schooling in a Dynamic Model Firs version: December 4 h 004 This version: March 19 h 005 Corrado Andini* Universiy of Madeira Deparmen of Managemen and Economics Campus da Peneada 9000-390 Funchal Porugal andini@umap ABSTRACT The paper develops a dynamic approach o Mincer equaions I is shown ha a saic model is based on he resricive hypoheses ha he oal reurn o schooling is consan over he working life and independen of bargaining issues A dynamic approach allows o show ha he oal reurn o schooling of a new labor-marke enran posiively depends on his/her bargaining power as employee; he oal reurn increases a a decreasing rae in he firs par of he working life and depends of bargaining issues; aferwards i becomes roughly consan and independen of bargaining The main implicaion is ha a saic model may produce disored empirical resuls when using daa on young workers since unable o accoun for he paern of he oal reurn o schooling in he firs par of he working life I show he laer using daa from he US Naional Longiudinal Survey of Youh (1980-1987) and analyzing he impac of educaion on wihin-group wage inequaliy a la Marins and Pereira (004a) However, a saic model does no produce disored empirical resuls when using daa on relaively experienced workers I show he laer using Poruguese daa from he European Communiy Household Panel (1994-001) Keywords: Reurns o Educaion, Wage Inequaliy, Quanile Regressions JEL Classificaion: C9, J31, I1 * Financial suppor by he European Commission (EDWIN Projec, HPSE-CT-00-00108), he Universiy of Madeira and he Universiy of Salerno is graefully acknowledged This paper uses daa from he European Communiy Household Panel in he version of December 003 (he usual disclaimer applies) I sincerely hank Pedro Telhado Pereira, Saniago Budria and he paricipans a he 6 h Meeing of he EDWIN Projec for heir valuable commens (he usual disclaimer applies)
Conens 1 Inroducion Relaed lieraure 3 Theory behind a saic Mincer equaion 4 From a saic o a dynamic model 5 Empirical model 6 Esimaion resuls using daa on young workers 7 Esimaion resuls using daa on experienced workers 8 Implicaions of model specificaion and daa 9 Conclusions Appendix A Appendix B References Tables Figures 1
1 Inroducion The paper develops a dynamic approach o Mincer equaions I will argue ha a saic model is based on he resricive hypoheses ha he oal reurn o schooling is consan over he working life and independen of bargaining issues A dynamic approach allows o show ha he oal reurn o schooling of a new labor-marke enran posiively depends on his/her bargaining power as employee; he oal reurn increases a a decreasing rae in he firs par of he working life and depends of bargaining issues; aferwards i becomes roughly consan and independen of bargaining The main implicaion is ha a saic model may produce disored empirical resuls when using daa on young workers since unable o accoun for he paern of he oal reurn o schooling in he firs par of he working life I will show he laer using daa from he US Naional Longiudinal Survey of Youh (1980-1987) and analyzing he impac of educaion on wihin-group wage inequaliy a la Marins and Pereira (004a) However, a saic model does no produce disored empirical resuls when using daa on more experienced workers I will show he laer using Poruguese daa from he European Communiy Household Panel (1994-001) The reminder of he paper is as follows Secion briefly describes some common feaures of he lieraure using human-capial regressions Secion 3 describes he heory behind a saic Mincer equaion Secion 4 develops a heory for a dynamic Mincer equaion Secion 5 presens empirical models Secions 6 and 7 presen esimaion resuls Secion 8 deals wih implicaions of model specificaion and daa Secion 9 concludes he manuscrip Relaed lieraure Building on Mincer (1974), several sudies have esimaed he following wage equaion: (1) ln w = α + βs + δz + φz + ε where ln w represens he logarihm of hourly earnings, s is schooling years, z is labor marke experience and ε is an error erm Mos of exising sudies share hree common feaures: he esimaed models have a saic naure (ie hey do no allow for a leas one lagged value of he dependen variable as addiional regressor); he esimaed coefficien of educaion is dependen on number and ype of explanaory variables added o model (1) 1 (see Marins and Pereira, 004b); esimaion is generally based on ordinary leas squares, insrumenal variables, random effecs In his paper, I aemp o do a sep onwards wih respec o he curren sae of he ar The aim of his paper is o sudy reurns o schooling in a dynamic framework From an empirical poin of view, his mainly involves keeping he auoregressive naure of earnings ino accoun In doing so, I also deal wih he problem of choosing conrol-regressors by replacing he whole se of explanaory variables suiable o be added o model (1) wih one lagged value of earnings (his approach may be exended o more han one lag) Finally, building on Marins and Pereira (004a), I ake a quanile regression approach From a heoreical poin of view, he ransiion from a saic o a dynamic model involves re-hinking he heory behind he sandard Mincer equaion (1), allowing for bargaining issues o play a more imporan role 1 This is done in order o improve he explanaion of earnings and increase he reliabiliy of he esimaed coefficien of schooling
3 Theory behind a saic Mincer equaion The aim of his Secion is o presen he heoreical foundaions of he sandard saic Mincer equaion, following Heckman and Todd (003) In Secion 4, I will discuss he assumpions needed for he ransiion from a saic o a dynamic model Mincer (1974) argues ha observed earnings are a funcion of poenial earnings ne of human capial invesmen coss, and poenial earnings depend on invesmens in previous period If we denoe poenial earnings a ime as E, we can assume ha, in each period, an individual invess in human capial a share k of his/her poenial earnings wih a reurn of r Therefore we have ha: () E = E (1 r k ) + 1 + which, afer repeaed subsiuion, becomes: 1 (3) E = (1 + rjk j) E 0 j= 0 Taking logarihms, we ge he following expression: 1 (4) ln E = ln E 0 + ln(1 + rjk j) j= 0 If we define schooling as he number s of years spen in full-ime invesmen, ie = = k 1 (we assume ha schooling sars a he beginning of he life), we assume k 0 s 1 = ha he reurn o schooling is consan over ime, ie r 0 = = r s 1 = β, and we assume ha he reurn o pos-schooling invesmen is consan oo, ie r s = = r 1 = λ, hen we can wrie (4) in he following way: 1 (5) ln E = ln E 0 + sln(1 + β) + ln(1 + λk j), j= s which yields o: 1 (6) ln E ln E 0 + βs + λ k j j= s for small bea, lambda and key In order o build up a link beween poenial earnings and labor marke experience z, Mincer (1974) furher assumes ha pos-schooling invesmen linearly decreases over ime, ha is: z (7) k s + z = η 1 T 3
where z = s 0, T is he lengh of working life (independen of s) and η is beween 0 and 1 Therefore, we can re-arrange expression (6) and ge: (8) ln E ηλ T ηλ T ln E 0 ηλ + βs + ηλ + z z However, we are ineresed in poenial earnings ne of invesmen coss, which are given by: (9) ln E z ηλ η ηλ η 1 ln E0 ηλ η + βs + ηλ + + z z T T T T Finally, assuming ha observed earnings are equal o poenial earnings ne of invesmen coss, ie: z (10) ln w = ln E η 1 T, and using expression (9), we obain an expression ha is very closed o he sandard Mincer equaion: (11) or (1) ln w ln w ln E 0 ηλ η ηλ ηλ η + βs + ηλ + + z z T T T α + βs + δz + φz, where α 0 = ln E ηλ η, ηλ η δ = ηλ + + and T T ηλ φ = T Hence, afer insering an error erm, we ge he sandard model (1) To conclude his Secion, i is worh noicing ha he oal reurn o schooling in model (1) is given by he following expression: (13) ln w ln w s = + z β s s Expression (13) implicily assumes ha he oal reurn o schooling is consan over he working life since i is always equal o β for every value of labor-marke experience z from 0 o T In addiion, he oal reurn is clearly independen of bargaining issues, which are lef ouside of he classic consrucion of he saic Mincer equaion 4 From a saic o a dynamic model Several auhors have argued, in several ways, ha model (1) is oo parsimonious and ha here is a need of insering addiional regressors, in order o improve he explanaion of 4
earnings and ge a more reliable esimae of he coefficien of schooling Therefore, model (1) has been modified in he following way: (14) ln w = α + βs + δz + φz + τ1ω1 + τω + τ NωN + ε where variables ω are new explanaory variables, such as secors of aciviy, firm size, firm age, bargaining regimes, senioriy, and so on (see Marins and Pereira, 004b, p 56) However, he choice of he variables o be added o model (1) is quie conroversial and, more imporan, he esimaed coefficien of schooling seems o be dependen on researcher s choice of ω variables From an empirical poin of view, he ransiion from a saic o a dynamic model mainly involves recognizing ha earnings have auo-regressive naure and hen assuming ha ω 1, ω,, ωn (which should be used o improve he explanaion of ln w ) can be fully replaced by ln w 1 (our reasoning can be exended o more han one lag of earnings) However, here is also a more elegan way o go from a saic o a dynamic model I consiss of modifying Mincer s assumpion (10) such ha curren observed earnings are a weighed average of pas observed earnings and curren poenial earnings ne of invesmen coss Then equaion (10) becomes: z (15) ln w = ρ ln E η 1 + (1 ρ)ln w 1 T Expression (15) can be derived as he exac soluion of a Nash-bargaining maximizaion problem, once we assume ha: he employee maximizes earnings growh, namely U = ln w ln w 1, poenial earnings ne of invesmen coss are equal o acual produciviy, z he employer maximizes profis, namely V = ln E η 1 ln w T Under hese assumpions, we have he following sandard Nash-bargaining maximizaion problem : (16) max ln w ρln U + (1 ρ)ln V where ρ is he bargaining power of he employee beween 0 and 1, 1 ρ is he bargaining power of he employer, while (15) is he soluion of (16) as shown in Appendix A If we use expression (9) o replace ne poenial earnings in equaion (15), we ge: (17) ln w (1 ρ)ln w + ρ( α + βs + δz + φz ) or 1 I assume ha U and V are ne gains, ie he ouside opions are U = 0 and V = 0 5
(18) ln w (1 ρ)ln w 1 + ρα + ρβs + ρδz + ρφz I is worh noicing ha, if we se ρ = 1 (ie he employee has full bargaining power), hen expression (18) becomes (1) A paricular feaure of model (18) is he possibiliy o draw he paern of he oal reurn o schooling over he working life, if numerical expressions for β and ρ are available As assumed in Secion 3, an individual sops schooling a ime s 1 (ie afer s years, beginning from year 0), sars working a a ime s and receives an hourly wage equal o w Paricularly, a new labor-marke enran maximizes Us = ln w s ln w, where ln w is he logarihm of he minimum hourly wage 3, se by law Therefore, a ime s, expression (15) becomes: (19) ln w ρ( ln E η) + (1 ρ)ln w s = s This involves ha model (18), a ime s, can be wrien as follows: s (0) ln w s ρα + (1 ρ)ln w + ρβs + ρδ(0) + ρφ(0) and he reurn o schooling a ime s is given by: ln w s (1) ρβ s ln w under he reasonable assumpion ha = 0 s Expression (1) may be seen as he enry reurn o schooling, ie he reurn o schooling ha an individual receives when eners he labor-marke I is worh noicing ha i depends posiively on he bargaining power of he new enran as employee In addiion, (1) is lower han (13) excep in he paricular case of ρ = 1 A ime s + 1, we have he following: () ln w s + 1 ρα + (1 ρ)ln w s + ρβs + ρδ(1) + ρφ(1) and he oal reurn o schooling is given by: ln w + 1 ln w s (3) (1 ρ) + ρβ (1 ρ) ρβ + ρβ s s s A ime s +, we have he following: (4) ln w s + ρα + (1 ρ)ln w s+ 1 + ρβs + ρδ() + ρφ() and he oal reurn is given by: 3 The employer maximizes Vs ( ln Es η) ln w s = 6
(5) ln w s (1 ρ) ln w (1 ρ) s s+ s + 1 + ρβ [(1 ρ) ρβ + ρβ] + ρβ (1 ρ) ρβ + (1 ρ) ρβ + ρβ Therefore, a ime s + z, he oal reurn o schooling is given by: ln w + z ln w s+ z 1 (6) + ρβ z z 1 (1 ρ) (1 ρ) ρβ + (1 ρ) ρβ + + ρβ s s s We may call expression (6) as he dynamic oal reurn o schooling afer z years of labormarke experience I is worh noicing ha (6) gives he saic oal reurn (13) as a paricular case when he employee has full bargaining power ( ρ = 1) In general, he lef-hand side of expression (6) is z-dependen and (6) allows o draw he oal reurn o schooling over he enire working life, from 0 o T years of experience For a value of ρ 1, say ρ ~, we have he following: ln w ρβ ~ s+ z (7) lim β z s 1 (1 ρ ~ ) Therefore, under some general condiions, a dynamic model is able o provide a measure of he oal reurn o schooling which is comparable wih expression (13) We may call expression (7) as dynamic convergen oal reurn o schooling Expression (7) is prey imporan because i shows ha, if ρ 1, a rough equivalence beween a saic and a dynamic model only holds a very high values of z In oher words, if he employee does no have full bargaining power, a saic model does no produce an appropriae measure of he oal reurn o schooling a relaively low values of labor-marke experience Finally, he lower is he ρ ~ is, he slower is he process of adjusmen of he oal reurn from is enry value o is convergen value, he higher he z needed for a rough equivalence In general, as a simulaion in Figure 1 shows, he dynamic oal reurn o schooling may have a paern, in he firs par of he working life, which canno be approximaed by means of a consan line and a saic model, if used o measure he oal reurn of young workers, may produce a disored oupu A echnical explanaion is provided in Appendix B 5 Empirical model Based on expression (1) and on expression (18), I esimae he following wo empirical models: (8) ln w i = αθ + βθsi + δθzi + φθzi + εi (9) ln w i = γ θ + υθ ln w i 1 + πθsi + χθzi + ςθzi + εi where θ goes from 0 o 1 and represens he wage disribuion quanile As model (9) is linear in parameers, individual unobserved heerogeneiy is disregarded, and we focus on he case of iid innovaions in which condiioning variables play he classical role of shifing 7
he locaion of he condiional densiy of y [he auoregressive variable], bu hey have no effec on he condiional scale or shape (Koenker and Xiao, 004, p 3), hen we can apply he sandard quanile esimaion echniques due o Koenker and Basse (1978) Paricularly, model (9) can be wrien as a simple linear model: (30) ln w i x i ' ψ + εi Quan lnw = x ' ψ = θ wih θ( i i ) i θ and he lagged logarihm of earnings can be reaed as any sandard explanaory variable x An example of his approach is provided by Koenker (000) who applies he sandard quanile echniques o a firs-order auoregressive model for maximum daily emperaures in Melbourne (Ausralia) Anoher example is provided by Girma and Gorg (00) who presen a more sophisicaed quanile regression model where he auoregressive variable is oal facor produciviy Thus, he vecor of parameers ψ θ is esimaed as: (31) ψˆ θ = arg min ψ ϑθ (ln w x i ' ψ θ θ i i ) and ϑ θ (ε) is he usual check funcion defined as ϑ θ ( ε) = θε when ε is non-negaive or ϑ θ ( ε) = ( θ 1) ε when ε is negaive The same procedure applies o model (8) Our discussion will coninue as follows Firs, I will presen esimaion resuls based on model (9), focusing on π and υ for each decile As expression (1) suggess, I will refer o he esimaed π as enry reurn o schooling Insead, he esimaed υ measures he bargaining power of he employer in model (18) 4 If he rue heoreical model behind regression (9) looks like model (18), hen we should find ha he esimaed π is negaively correlaed wih he esimaed υ over he wage disribuion Aferwards, following Marins and Pereira (004a), I will presen decile esimaes of β in model (8), which are expeced o be higher han esimaes of π I will refer o he esimaed β as saic oal reurn o schooling In addiion, I will presen esimaes of he dynamic oal reurn o schooling as provided by expression (6), for each decile and over he working life Finally, I will compare he esimaed oal saic reurn o schooling β wih he esimaed dynamic convergen oal reurn o schooling as provided by expression (7) 6 Esimaion resuls using daa on young workers In my firs applicaion of model (8) and of model (9), I use daa from he US Naional Longiudinal Survey of Youh for he period of 1980-1987, as provided by Verbeek (000) The same daa-se is also used by Vella and Verbeek (1998) o sudy union premia The sample conains 4360 annual observaions on 545 young male workers I herefore assume, a la Marins and Pereira, absence of paricipaion issues ypically arisen for women Summary sample saisics for he seleced variables are repored in Table 1 Disregarding - for a momen - he quanile approach, model (9) can be esimaed by OLS Indeed, since we assume absence of individual unobserved heerogeneiy, he OLS esimaor is consisen We herefore presen, as a benchmark, several OLS esimaes In paricular, Table shows ha he enry reurn is almos a half of he saic oal reurn, which is x 4 The complemen o one of he esimaed υ clearly measures he bargaining power of he employee 8
consisen wih (13) and (1) on a heoreical basis 5 and wih he sylized fac (see Marins and Pereira, 004b) ha addiion of conrol-regressors (in our case, one lag of he logarihm of earnings) o model (8) deeply reduces he esimaed coefficien of educaion, specially when he conrol-regressor is an educaion-dependen covariae (like in our case) In addiion, Figure 3 plos he dynamic oal reurn over he working life, saring from he enry year I is increasing, a decreasing rae, during he firs par of he working life; aferwards, i becomes roughly consan This is a prey ineresing and new empirical resul, which can only be obained using a dynamic model Finally, he dynamic convergen oal reurn is almos equal o he saic oal reurn, because he average experience in he sample (651) is enough o suppor a saic model (he dynamic oal reurn in Figure 3 is roughly equal o is convergen value from roughly z = 6 onwards) Anoher ineresing poin, ha may be briefly discussed before presening he main empirical resuls of his paper, is abou he hypohesis of absence of individual unobserved heerogeneiy (a la Marins and Pereira) If we coninue disregarding he quanile approach and inroduce individual fixed effecs in model (9), han he OLS esimaor becomes inconsisen (based upward; see Nickell, 1981) Esimaing his new model would require implemenaion of he well-known GMM echniques by Arellano and Bond (1991) or by Blundell and Bond (1998), ha give consisen esimaes However, as he variable s (years of schooling) does no generally vary - for he same individual - over ime 6, hen he quoed GMM echniques, based on firs differences, will ineviably drop he variable of educaion ou of he model, ogeher wih individual unobserved heerogeneiy (which is he only required oucome) 7 Finally, i is worh noicing ha, in every model no explicily aking individual fixed effecs ino accoun, he presence of a lagged value of he dependen variable as addiional explanaory variable is likely o reduce he role of individual unobserved heerogeneiy (adding several lags of he dependen variable as regressors may make unobserved heerogeneiy becoming insignifican 8 ) Le us now come back o a quanile approach Figure plos, over he wage disribuion, he esimaed bargaining power of he employer and he enry reurn o schooling (see also Table ) The esimaed bargaining power of he employer increases ill o he forh decile and decreases ill o he ninh decile This paern can be explained by looking a heerogeneiy of jobs in erms of wage, job sabiliy, number of poenial job-applicans, and so on For insance, we may hink ha he forh decile involves he bes combinaion of hese elemens (which gives he highes bargaining power o he employer) while he ninh involves he wors combinaion A more ineresing finding is ha he esimaed bargaining power of he employer (employee) is negaively (posiively) correlaed 9 wih he esimaed enry reurn o schooling, which is consisen wih model (18) on a heoreical basis Our esing rejecs he hypohesis of a consan enry reurn o schooling over he wage disribuion and shows ha his reurn has a fla U-shape The reurns from he hird o he sevenh decile are roughly equal bu lower han hose esimaed for he second and he eighh decile, which are roughly equal and, in urn, lower han he roughly equal reurns for he firs and he ninh decile 5 I is worh sressing ha he esimae of he enry reurn provided by model (9) can be roughly obained as produc beween he bargaining power of he employee implicily esimaed by model (9) and he coefficien of schooling esimaed by model (8) This is consisen wih expression (1) 6 This is he case in our sample In general, inerviewed individuals are hose who work and sopped schooling; hence hey are likely o declare he same years of schooling from he firs o he las annual inerview 7 However, he quoed GMM echniques may be suiable for sudying reurns o educaion for working-sudens 8 See Arellano (003) for a esing procedure 9 We find r = 0781 wih p-value = 0013 9
Figure also plos he saic oal reurn and involves wo commens Firs, he esimaed saic oal reurn is higher han he enry reurn (see also Table ) Once again, as for he OLS esimaion, his is consisen wih our heoreical predicions and wih he sylized fac ha addiion of educaion-dependen covariaes (in our case, one lag of he logarihm of earnings) o model (8) deeply reduces he esimaed coefficien of educaion Second, he esimaed saic oal reurn is found o increase over he wage disribuion 10, which is consisen wih he main empirical resul by Marins and Pereira (004a) Finally, Figure plos he dynamic convergen oal reurn over he wage disribuion and involves wo furher commens Firs, i is clearly decreasing from he firs o he sevenh decile and a bi increasing from he sevenh o he ninh Second, i is higher han he saic oal reurn for lower-han-median wage groups while lower han he saic one for higherhan-median wage groups This raises he quesion of why he OLS esimaion gives as oucome ha he saic oal reurn is roughly equal o he dynamic convergen oal reurn, while he QR esimaion does no In our view, his is because he average experience in he sample is high enough o suppor a saic model, bu he average experience in several deciles is no high enough o do he same, and he saic model produces disored empirical resuls because a consan reurn is unable o accoun for some very big jumps (see he firs deciles in Figure 3) a low values of experience 7 Esimaion resuls using daa on experienced workers The European Communiy Household Panel (ECHP) is a very large daa-se conaining micro-daa for 15 counries of he European Union from 1994 o 001 We focus on Porugal To build up our sample, we sar exracing Poruguese daa (counry 1) on personal idenificaion numbers (pid), age (pd003), gender (pd004), monhly gross earnings (pi11mg), years of educaion (p03), weekly hours of work (pe005) We repea his operaion for each of he eigh waves of he ECHP and consruc a preliminary daa-se wih 91437 observaions Aferwards we drop individuals older han 65 or younger han 15 years, drop females, drop individuals sill a school and hose no providing informaion abou educaion, creae a variable for labor-marke experience (lme = pd003 p03 6), drop individuals wih negaive experience, drop individuals wih zero or missing earnings Finally, we obain an unbalanced panel wih 15049 observaions, which is described in Table 1 Figure 4 plos he esimaion resuls using echniques described in Secion 5 and confirms ha he enry reurn o schooling is lower han he saic oal reurn and posiively associaed wih he implicily esimaed bargaining power of he employee In addiion, we find ha he dynamic convergen reurn o schooling is consisen wih he saic oal reurn over he wage disribuion and when using ordinary leas squares Deailed esimaion resuls are provided in Table Figure 5 plos he dynamic oal reurn for several quaniles As a furher confirmaion, Figure 6 plos esimaion resuls when using a sub-sample of Poruguese workers beween he ages of 17 and 30, summarized in Table 1 Deailed esimaion resuls are provided in Table As expec, a saic model seems o give disored empirical resuls, even when using ordinary leas squares due o a very low average experience (481) Insead, when using a sub-sample of Poruguese workers beween he ages of 31 and 65 described in Table 1, a saic model seems o perform properly Table provides deailed esimaes 10 This is no sraighforward However our esing shows ha he ninh decile exhibis a significanly higher reurn han he firs decile 10
8 Implicaions of model specificaion and daa Summarizing my findings, I obain resuls ha are consisen wih hose of Marins and Pereira (004a) boh when esimaing a saic model a la Marins and Pereira and when esimaing a dynamic model wih daa on relaively experienced workers However, when esimaing a dynamic model wih daa on young workers, I ge a differen picure of he impac of educaion on wihin-group wage inequaliy Why? We will come back o his quesion afer briefly reviewing he main argumens used by Marins and Pereira (004a) in order o explain heir resul ha he reurn o schooling increases over he wage disribuion The main explanaions are hree: over-educaion, ineracion beween schooling and abiliy, and qualiy of schooling Over-educaion basically refers o people wih high schooling levels (in erms of years) who ake low-paid jobs If here are many over-educaed in he firs decile of he wage disribuion, hen he reurn o an addiional year of schooling will be very low If he number of over-educaed decreases over he wage disribuion (as he wage increases), hen he reurn o educaion is expeced o increase over he wage disribuion The same reasoning holds for abiliy or school qualiy If people abiliy or school qualiy increase over he wage disribuion, hen he reurn o an addiional year of schooling should follow he same paern These explanaions are appealing and provide a heoreical background o undersand he empirical resul ha he oal reurn o schooling increases over he wage disribuion in 15 of 16 counries examined by Marins and Pereira (004a), wih Greece as unique excepion due o he use of afer-ax earnings (ie he general resul is disored because of he influence of axaion) In my view, however, he general empirical resul ha he oal reurn o schooling increases over he wage disribuion is no robus o he use of daa on young workers A saic model, indeed, is based on wo resricive hypoheses: he oal reurn o schooling is consan of he working-life and independen of bargaining issues 11 However, a dynamic model shows ha he oal reurn o schooling is no consan over he working life I becomes consan once a cerain work-experience is maured, bu i is increasing in he firs par of he working life and, during his period, is evoluion depends on bargaining issues If a saic model is used o esimae he oal reurn o schooling for young workers, i may give a wrong picure because he phoography is relaed o a changing siuaion and he saic model is no able o accoun for i Finally, i is worh sressing ha he laer criique does no affec he validiy of empirical resuls by Marins and Pereira (004a), as hese auhors use of daa on relaively experienced workers (around 0 years) To conclude, we sugges carefulness when using a saic model o esimae he oal reurn o schooling wih daa on young workers 9 Conclusions The paper has developed a dynamic approach o Mincer equaions I have argued ha a saic model is based on he resricive hypoheses ha he oal reurn o schooling is consan over he working life and independen of bargaining issues A dynamic approach allows o show ha he oal reurn o schooling of a new labor-marke enran posiively depends on his/her bargaining power as employee; he oal reurn increases a a decreasing rae in he firs par of he working life and depends of bargaining issues; aferwards i becomes roughly consan and independen of bargaining The main implicaion is ha a saic model may produce disored empirical resuls when using daa on young workers since no able o accoun for he paern 11 The esimaion of a saic quanile Mincer equaion allowing for individual fixed effecs would be a furher ineresing exercise A recen aemp of inroducing individual fixed effecs ino a quanile regression framework is due o Koenker (004) 11
of he oal reurn o schooling in he firs par of he working life I have shown he laer using daa from he US Naional Longiudinal Survey of Youh (1980-1987) and analyzing he impac of educaion on wihin-group wage inequaliy a la Marins and Pereira (004a) However, a saic model does no produce disored empirical resuls when using daa on relaively experienced workers I have shown he laer using Poruguese daa from he European Communiy Household Panel (1994-001) 1
Appendix A This appendix solves problem (16), which is given by he following expression: (A1) max ln w ρln U + (1 ρ)ln V z where U = ln w ln w 1 and V = ln E η 1 ln w T I is worh noicing ha our objecive funcion comes from a sandard Cobb-Douglas We make a logarihmic ransformaion in order o make our life easier Once definiions of U and V are replaced in expression (A1), we ge: (A) max ln w ln ( ln w ln w ) (1 ) ln ln E 1 z ln w T ρ 1 + ρ η The maximizaion problem in (A) implies he following firs-order condiion: 1 1 (A3) ρ ( + 1) + (1 ρ) ( 1) = 0 ln w ln w 1 z ln E η 1 ln w T Afer adjusing (A3), we come up wih he following expression: (A4) ln w ρ ln w 1 = ln E 1 ρ η 1 z ln w T which, in urn, gives: z ρ 1 T (A5) ln E η 1 ln w = (1 ρ) ( ln w ln w ) Therefore, we obain he following equaion: z (A6) ρ ln E η 1 ρln w = (1 ρ)ln w (1 ρ)ln w 1 T which, afer furher manipulaion, becomes: 13
z (A7) ρ ln E η 1 ρln w = ln w ρln w (1 ρ)ln w 1 T or z (A8) ρ ln E η 1 = ln w (1 ρ)ln w 1 T Finally, we ge expression (15) in he main ex, ie: (A9) z ρ ln E η 1 + (1 ρ)ln w 1 = ln w T 14
Appendix B As shown in he main ex, expression (6) gives he dynamic oal reurn o schooling, ha is: (B1) ln w s + z ln w s+ z 1 + ρβ z z 1 (1 ρ) (1 ρ) ρβ + (1 ρ) ρβ + + (1 ρ) ρβ + ρβ s s or ln w s + z 1 z s z (B) ρβ[ 1+ (1 ρ) + + (1 ρ) + (1 ρ) ] ρβλ(z) Therefore, a general saic model is given by he following expression: (B3) ln w s+ z α + ρβλ(z)s + δz + φz Expression (B3) is equivalen o model (1) only if (B4) 1 Λ( z) ρ However, expression (B4) only holds as z ends o infiniy since: (B5) 1 lim Λ(z) z ρ In general, we may define a funcion ι (z) providing he difference beween Λ (z) and is convergen value ρ 1, ha is: 1 (B6) ι ( z) = Λ(z) ρ Then, using (B6), we may wrie expression (B3) as follows: (B7) ln w + α + βs + δz + φz ρβι(z) s s z Finally, expression (B7) allows o show ha boh OLS and QR esimaion of he empirical saic model (8) are more likely o produce biased empirical resuls a low z levels Indeed, we may noice ha he assumpions: (B8) Expec( z,s) 0 and ε + (OLS) s z = 15
(B9) Quan( z,s) 0 ε + (QR) s z = are more likely o be violaed a low z levels since ι(z) is more likely o be significanly differen from zero 16
References Arellano M (003) Panel Daa Economerics, Oxford, Oxford Universiy Press Arellano M, Bond SR (1991) Some Tess of Specificaion for Panel Daa: Mone Carlo Evidence and An Applicaion o Employmen Equaions, Review of Economic Sudies, 58, pp 77-97 Blundell RW, Bond SR (1998) Iniial Condiions and Momen Resricions in Dynamic Panel Daa Models, Journal of Economerics, 87, pp 115-143 Girma S, Görg H (00) Foreign Direc Invesmen, Spillovers and Absorpive Capaciy: Evidence from Quanile Regressions, GEP Working Papers, Universiy of Noingham, n 00/14 Heckman J, Todd P (003) Fify Years of Mincer Earnings Regressions, NBER Working Papers, Naional Bureau of Economic Research, n 973 Koenker R (000) Quanile Regression, in: Fienberg and Kadane (eds), Inernaional Encyclopedia of he Social Sciences, Amserdam, Norh-Holland Koenker R (004) Quanile Regression for Longiudinal Daa, Journal of Mulivariae Analysis, 91, pp 74-89 Koenker R, Basse G (1978) Regression Quaniles, Economerica, 46(1), pp 33-50 Koenker R, Xiao Z (004) Quanile Auoregression, unpublished manuscrip Marins PS, Pereira PT (004a) Does Educaion Reduce Wage Inequaliy? Quanile Regression Evidence from 16 Counries, Labour Economics, 11, pp 355-371 Marins PS, Pereira PT (004b) Reurns o Educaion and Wage Equaions, Applied Economics, 36, pp 55-531 Mincer J (1974) Schooling, Experience and Earnings, Cambridge, Naional Bureau of Economic Research Nickell S (1981) Biases in Dynamic Models wih Fixed Effecs, Economerica, 49(6), pp 1417-146 Vella F, Verbeek M (1998) Whose Wages Do Unions Raise? A Dynamic Model of Unionism and Wage Rae Deerminaion for Young Men, Journal of Applied Economerics, 13, pp 163-183 Verbeek M (000) A Guide o Modern Economerics, Chicheser, John Wiley & Sons 17
Table 1 Unied Saes: NLSY (1980-1987) Variable Obs Mean Sd Dev Min Max Logarihm of hourly wage 4360 164 053 357 405 Years of schooling 4360 1176 174 300 1600 Experience 4360 651 8 000 1800 Age 4360 48 77 1700 3000 Porugal: ECHP (1994-001) Variable Obs Mean Sd Dev Min Max Logarihm of hourly wage 13717 644 054 49 98 Years of schooling 1663 1559 569 900 5700 Experience 1663 1687 1186 000 4900 Age 1663 3847 115 1700 6500 Full sample: 17-65 Porugal: ECHP (1994-001) Variable Obs Mean Sd Dev Min Max Logarihm of hourly wage 4356 6 039 49 878 Years of schooling 4934 1447 66 900 400 Experience 4934 481 349 000 1400 Age 4934 59 310 1700 3000 Resriced sample: 17-30 Porugal: ECHP (1994-001) Variable Obs Mean Sd Dev Min Max Logarihm of hourly wage 9361 654 057 301 98 Years of schooling 1139 1608 65 900 5700 Experience 1139 13 108 000 4900 Age 1139 441 881 3100 6500 Resriced sample: 31-65 18
Disribuion decile Bargaining power of he employer Table Unied Saes: NLSY (1980-1987) Enry reurn Saic oal reurn Dynamic convergen oal reurn 01 07591 00404 00884 01677 0 08036 009 00954 01486 03 0801 000 00954 01 04 0831 0014 01004 0109 05 07911 0016 01036 01033 06 07660 0019 01066 00935 07 07017 004 01070 00750 08 0698 0036 01058 00880 09 04789 00511 0107 00980 OLS 05786 00447 0101 01061 Age 17-30 17-30 17-30 17-30 All esimaed coefficiens are significan a 1% level Disribuion quanile Bargaining power of he employer Porugal: ECHP (1994-001) Enry reurn Saic oal reurn Dynamic convergen oal reurn 005 0853 07166 0853 0004 00181 00030 0017 0044 00084 00137 00638 0003 015 09188 08571 0971 00011 00080 00011 00174 00575 00119 00135 00559 00151 05 09696 09177 09803 00008 00037 00006 0039 00617 00174 0063 00449 00305 035 0970 09165 09791 00009 00041 00007 00347 00664 0066 0030 00491 00335 045 09655 08914 0973 00013 00040 00011 0046 00654 00366 00376 00368 00410 055 09498 0871 09600 0003 00060 000 00556 00719 00500 00458 00465 00550 065 0934 08500 09443 00033 00077 0007 00671 00805 00617 00488 00513 00485 075 0915 08094 0965 00049 00098 00040 00787 0088 00746 00560 00514 00544 085 08800 07640 08993 00086 00147 00067 00893 00963 00848 00716 006 00665 095 08085 06449 08349 00171 0088 00134 00993 01008 00956 0089 00811 0081 OLS 08873 07567 09097 00047 00133 00036 00450 00763 00383 00419 00546 00399 Age 17-65 17-30 31-65 17-65 17-30 31-65 17-65 17-30 31-65 17-65 17-30 31-65 Significan a 5% level Significan a 10% level Non-significan Remaining esimaed coefficiens are significan a 1% level 19
Figure 1 Simulaion based on β = 0 10 and ρ = 0 0 0,1 0,10 Dynamic oal reurn 0,08 0,06 0,04 0,0 0,00 s s+4 s+8 s+1 s+16 s+0 s+4 s+8 s+3 s+36 s+40 Convergen Working life 0
Figure Unied Saes: NLSY (1980-1987) Age: 17-30 0,18 0,90 0,16 0,80 0,14 0,70 Reurn 0,1 0,10 0,08 0,06 0,60 0,50 0,40 0,30 Bargaining power 0,04 0,0 0,0 0,10 0,00 0,1 0, 0,3 0,4 0,5 0,6 0,7 0,8 0,9 Disribuion decile 0,00 Enry reurn Saic oal reurn Dynamic convergen oal reurn Bargaining power of he employer Bargaining power of he employee 1
Figure 3 Unied Saes: NLSY (1980-1987) Age: 17-30 0,1 0, 0,3 0,4 0,5 0,6 0,7 0,8 0,9 OLS 0,18 0,16 0,14 Dynamic oal reurn 0,1 0,10 0,08 0,06 0,04 0,0 0,00 s s+4 s+8 s+1 s+16 s+0 s+4 s+8 s+3 s+36 s+40 Convergen Working life
Figure 4 Porugal: ECHP (1994-001) Age: 17-65 0,1 1,00 0,90 0,10 0,80 Reurn 0,08 0,06 0,04 0,70 0,60 0,50 0,40 0,30 Bargaining power 0,0 0,0 0,10 0,00 0,05 0,15 0,5 0,35 0,45 0,55 0,65 0,75 0,85 0,95 Disribuion quanile Saic oal reurn Enry reurn Dynamic convergen oal reurn Bargaining power of he employer Bargaining power of he employee 0,00 3
Figure 5 Porugal: ECHP (1994-001) Age: 17-65 0,05 0,15 0,5 0,35 0,45 0,55 0,65 0,75 0,85 0,95 OLS 0,1 0,09 0,08 0,07 Dynamic oal reurn 0,06 0,05 0,04 0,03 0,0 0,01 0 s s+4 s+8 s+1 s+16 s+0 s+4 s+8 s+3 s+36 s+40 Convergen Working life 4
Figure 6 Porugal: ECHP (1994-001) Age: 17-30 0,1 1,00 0,90 0,10 0,80 Reurn 0,08 0,06 0,04 0,70 0,60 0,50 0,40 0,30 Bargaining power 0,0 0,0 0,10 0,00 0,05 0,15 0,5 0,35 0,45 0,55 0,65 0,75 0,85 0,95 Disribuion quanile 0,00 Enry reurn Saic oal reurn Dynamic convergen oal reurn Bargaining power of he employer Bargaining power of he employee Porugal: ECHP (1994-001) Age: 31-65 0,1 1,00 0,10 0,90 0,80 Reurn 0,08 0,06 0,04 0,70 0,60 0,50 0,40 0,30 Bargaining power 0,0 0,0 0,10 0,00 0,05 0,15 0,5 0,35 0,45 0,55 0,65 0,75 0,85 0,95 Disribuion quanile Saic oal reurn Enry reurn Dynamic convergen oal reurn Bargaining power of he employer Bargaining power of he employee 0,00 5