Wage inequality and returns to schooling in Europe: a semi-parametric approach using EU-SILC data

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1 MPRA Munch Personal RePEc Archve Wage nequalty and returns to schoolng n Europe: a sem-parametrc approach usng EU-SILC data Marco Bagett and Sergo Sccchtano Unversty La Sapenza Rome, Mnstry of Economc Development, Italy 28. November 2009 Onlne at MPRA Paper No , posted 8. December :20 UTC

2 Wage nequalty and Returns to Schoolng n Europe: a Sem Parametrc Approach Usng EU SILC Data Marco Bagett a and Sergo Sccchtano a,b * a Mnstry for Economc Development, Department for the Development and the Economc Coheson, va Scla 162, 00187, Rome, Italy. b Unversty "La Sapenza", Faculty of Economcs, Department of Publc Economcs, Va del Castro Laurenzano 9, 00161, Rome, Italy. Abstract In ths paper we apply a sem parametrc approach (quantle regresson QR) to the last 2007 wave of the EU SILC data set, n order to explore the connecton between educaton and wage nequalty n 8 European countres. We fnd that wages ncrease wth educaton and ths holds true across the whole dstrbuton. Furthermore, ths effect s generally more mportant at the hghest quantles of the dstrbuton than at the lowest, mplyng that schoolng ncreases wage dsperson. Ths evdence s found to be rather robust as showed through tests of lnear hypothess. We also corroborate the dea that, although OLS coeffcents estmates are substantally n lne wth the QR s, the former technque really msleads relevant nformaton about cross countres heterogenety n the mpact of educaton on wthn group nequalty at dfferent ponts of the wage dstrbuton. Hence ths paper confrms that a sem parametrc QR approach s more nterestng, as well as more approprate, because t measures the wage effect of educaton at dfferent quantles, thus descrbng relevant cross countres changes or bounces not only n the locaton, but also n the shape of the dstrbuton. Keywords: Returns to educaton; Wage nequalty; Quantle regresson; Europe JEL Classfcaton: C14, I21, J31. * Correspondng author. E mal: sergo.sccchtano@unroma1.t, Tel: , fax

3 1. Introducton 1 There s a wde consensus that schoolng has a relevant mpact on wage nequalty across countres. In partcular returns to educaton tend to be ncreasng over the wage dstrbuton: ths evdence s nterpreted as a drect effect of educaton on wthn groups nequalty. As a matter of fact, some emprcal analyss have explored the gan effects of schoolng over the entre wage dstrbuton, by usng not only dfferent specfcatons of the mnceran equaton, but several econometrc procedures as well. In partcular, snce the semnal paper by Koenker and Basset (1978), quantle regresson (QR) was adopted by many authors. It has been exploted both n surveys concernng sngle countres and n comparatve studes. As to the former strand of emprcal lterature, Buchnsky (1994) for the US, Budría and Moro Egdo (2008) for Span, Machado and Mata (1997, 2005) Hartog et al. (2001), Martns (2004) and Andn (2007, 2008) for Portugal, Goslng et al. (2000) for UK, McGunness et al. (2009) for Ireland, are only some examples. As to the latter strand, just a few papers have explored comparable crosscountres dfferences. Ths n depth examnaton has been constraned by the use of older homogenzed data sets, but has been also due to the greater avalablty of dvergng data sets, as argued by Budra and Perera (2005). Wth regard to the former pont Barros, Preto Rodríguez and Vera (2008) have examned the connectons between educaton and wage across 14 European countres by usng the European Communty Household Panel data set. Wth regard to the latter, on the one hand, Budra and Perera (2005) have evaluated how the mpact of educaton on wage nequalty has evolved over tme n 9 European countres, coverng a perod rangng from 26 years n the case of 1 We would lke to thank Marco Marn for valuable suggestons and comments. The vews expressed n ths artcle are those of the authors and, n partcular, do not necessarly reflect those of the Mnstry of Economc Development. The usual dsclamer apples. 2

4 Sweden ( ) to 7 years n the case of Portugal ( ) and by dstngushng for educatonal qualfcaton. On the other hand, Martns and Perera (2004, MP henceforth), usng cross sectonal data sets whch refer to dfferent years, rangng from 1991 n the case of Sweden to 1996 n the case of Netherlands, have shown that n 16 European countres hgher educaton s assocated wth hgher wage dsperson. Both these papers were completed under a framework of research projects 2 where each country team analyzed ther own country dfferent data set. However, they assure that these data sources were as smlar and thus comparable as possble (MP, 2004 p.356). In ths paper we apply a smlar approach to 8 European countres, usng the European Unon Statstcs on Income and Lvng Condtons nqury (EU SILC), the new European homogenzed panel survey, wdely consdered an attractve source of nformaton, as t adopts the same communty questonnare, thus obvously makng comparsons across natons easer. More specfcally, our prmary purpose s to explore the potental for EU SILC data to shed some lght on the relatonshp between wage nequalty and returns to schoolng n Europe. In partcular, a couple of questons are relevant here: 1) to what extent can educaton be called to explan the behavour of ncome nequalty across European countres? 2) Is a sem parametrc approach.e. QR more approprate than the standard Ordnary Least Squared (OLS) n order to clear up ths ssue? As outlned above, we try to answer these questons through the use of the last 2007 wave of the EU SILC data set, avalable snce march 2009 and whch has succeeded the European Communty Household Panel (ECHP) snce The 2 The projects are the Educaton and Wage Inequalty n Europe (EDWIN) for Budra and Perera (2005) and the Publc Fundng and Prvate Returns to Educaton (PuRE) for MP. 3 EU SILC was launched gradually between 2003 and 2005 n all EU Member States and has become the source of data for the analyss of ncome dstrbuton and socal ncluson at EU level. More precsely, EU SILC was frst brought out n 2003 on the bass of a gentlemen s agreement n sx Member States (Belgum, Denmark, Greece, Ireland, Luxembourg and Austra) as well as n Norway. In 2004, under Regulaton N 1177/2003 of the EP and the European Councl, EU SILC 3

5 EU SILC data set frstly provdes two advantages wth respect to the ECHP, namely: a) an update of ndcators, and b) a larger cover of European countres. Secondly, t keeps the man advantage that ECHP had on other data sets: attanng comparablty by explotng common gudelnes, defntons and procedures. Thus, through EU SILC, one s able to evaluate possble smlartes between a much hgher number of European countres whose educatonal systems and labour market nsttutons are qute dfferent. To address these ssues we apply the QR sem parametrc approach whch seems more nterestng, as well as more sutable, for t allows us to get a more precse pcture of the dynamcs of the dependent varable at dfferent ponts of the dstrbuton, rather than at the condtonal mean. We also compare QR wth OLS, n order to provde a cross countres comparable vew. The paper demonstrates that there s a hgh cross country heterogenety n returns to educaton at dfferent ponts of the wage dstrbuton, whch OLS modellng of condtonal average of a dependent varable completely fals to account for. Ths emprcal paper s organzed as follows. The next secton descrbes the data. Secton 3 llustrates our econometrc specfcaton. Secton 4 reports the results of the returns to educaton across European countres, both n terms of OLS and QR as well as a robustness check. In the Secton 5 we show the robustness check, whle the fnal secton presents our man conclusons. 2. Data selecton was mplemented n 12 EU 15 countres (Germany, Netherlands and the Unted Kngdom delayed the launch for one year) as well as n Estona, Iceland and Norway. In 2005, EU SILC was operatng n all EU 25 countres, plus Iceland and Norway, all wth avalable cross sectonal data. Bulgara, Turkey and Romana launched EU SILC n 2006, and Swtzerland followed sut n Also Former Yugoslav Republc of Macedona and Croata are evaluatng ts start. 4

6 Data are collected from the 2007 European Unon Statstcs on Income and Lvng Condtons (EU SILC) wave for 6 out of our 8 countres 4, the only ones havng avalable data for our nterest varables. EU SILC s the new homogenzed panel survey that has replaced ECHP, and actually covers EU 25 (old and new) member states. Smlarly to ECHP, EU SILC s an attractve source of nformaton because t adopts the same communty questonnare used by the natonal data collecton unts n each ncluded country, whch obvously makes comparsons across natons easer. Furthermore, EU SILC actually covers a larger and ncreasng number of European countres wth respect to the ECHP. We have focused our analyss on the personal fle of EU SILC 5. In the 2007 wave 387,170 ndvduals from EU 25 countres were ntervewed. 184,879 of them were males, 202,287 females. The two countres for whch we extract data from the 2005 wave have ntervews for 22,355 ndvduals, 10,793 of whch are men. We chose to concentrate the survey on males aged between 25 and 65 workng fulltme: women were dsregarded on account of potental selectvty bases 6. Younger males were dropped because they are stll n the almost exclusvely educatonal perod of ther lfe,.e. they are very lkely enrolled n a secondary or tertary course and at the same tme do not perform any work actvty. People who had mssng or NA data on the educatonal varable were also dropped. Our dependent varable s the hourly (logarthmc) gross wage, avalable for 24,118 fulltme workng males aged between 25 and 65 for the 6 countres of the 2007 wave and 3,621 Belgan and Greek men of the 2005 wave. Thus our analyss focuses on 27,739 ndvduals altogether. 4 For Greece and Belgum we used the 2005 wave. The tme msmatch s not supposed to greatly weaken nternatonal comparsons as we deal wth structural varables,.e. values changng slowly between years. 5 A household data fle s also avalable together wth two more regster fle for household and ndvduals as well. 6 See Buchnsky (1998) to have an nsght on methods developed to deal wth selectvty bases. 5

7 EU SILC does have data for the hghest educatonal attanment from whch we have bult up our frst ndependent varable (schoolng years) followng the usual framework,.e. by makng use of the hghest ISCED level of educaton attaned by a male worker, and for each level assgnng the legal mnmum number of years typcally requred to acheve t 7. Our second and thrd regressors are respectvely the number of years spent n pad work and ts squared: the former s regarded as beng a proxy for ndvdual experence whle the latter takes account of possble non lneartes. The summary statstcs of these varables are shown n table 1, whle n the appendx the fgures concernng the lnk between ISCED levels and monthly gross ncome for all of our 8 countres are reported educ. [Table 1 here] 3. Econometrc specfcaton: OLS versus quantle regresson The frst equaton has the followng smple form: 2 ln w = α + β edu + γ exp+ δ exp + ε (1) The equaton (1) s solved through a classc OLS method, based on the mean of the condtonal dstrbuton of the dependent varable. As s well known, t mplctly assumes that the mpact of the regressors along that condtonal dstrbuton are rrelevant. Ths fact s referred to as a pure locaton shft. In other words, the x s are unable to cause a scale effect or any other consequence on the dstrbutonal shape. But as covarates may nfluence the condtonal dstrbuton 7 Those who reached only an ISCED 1 grade have been gven 5 years of schoolng; 8 years of school have been assgned to those wth an ISCED 2 grade; 13 years to those wth an ISCED 3; 14 to people who attaned an ISCED 4 grade and 18 years to those who reached an ISCED 5. 6

8 of the response n many other ways, we are wllng to estmate the whole dstrbuton of the condtonal quantles of the dependent varable, and to be able to study the nfluence of the regressors on ts shape, We do ths performng a quantle regresson (QR), whch has the followng functonal form (Koenker & Basset, 1978): Quant θ + :ln w x β θ ln w 2 ( α + β edu + γ exp + δ exp ) + 2 ( ) ( ) 1 θ ln w αθ + βθ edu + γ θ exp + δθ exp :ln w xβ θ θ θ θ (2) The equaton (2) s normally wrtten as: mn k β R ρ θ 2 ( ln w α β edu γ exp δ exp ) θ θ θ θ (3) where ( z ) θz ρ θ = f 0 z or ρ θ ( z ) ( θ 1)z = f z<0. Ths problem s solved usng lnear programmng methods. Standard errors for the vector of coeffcents are obtanable by usng a bootstrap procedure descrbed n Buchnsky (1998). The quantle regresson has other advantages whch can be summarzed as the followng (Buchnsky, 1998): ) t provdes robust estmates of the coeffcent vector,.e. estmates nsenstve to outlers of the dependent varable; ) when error terms are not normally dstrbuted, estmators provded by the quantle regresson can be more effcent than OLS estmators; ) f dfferent estmates for several quantles are observed, the nfluence change of the covarates on the y varable along the whole condtonal dstrbuton can be easly understood. 4. Results 7

9 In table 2 we show OLS returns as well as condtonal returns at 19 representatve quantles: 0.05, 0.10, 0.15, 0.20, 0.25, 0.30, 0.35, 0.40, 0.45, 0.50, 0.55, 0.60, 0.65, 0.70, 0.75, 0.80, 0.85, 0.90 and 0.95, whch are denoted θ5, θ10, θ15, θ20 θ25, θ30, θ35, θ40, θ45, θ50, θ55, θ60, θ65, θ70, θ75, θ80, θ85, θ90 and θ95 henceforth. [Table 2 here] Both OLS and QR estmated coeffcents are postve and sgnfcant at the 1% level n every country. Dfferences between percentles of the wage dstrbuton computed for 6 dfferent extremes taken by twos (θ95 θ5, θ90 θ10 and θ75 θ25) are also reported. In fg. 1 we rank countres by ther OLS estmates and compare each country both n terms of OLS coeffcents and of dfferences between percentles at the levels of the wage dstrbuton specfed above. In terms of OLS returns of educaton, Portugal n lne wth prevous studes shows the hghest coeffcent (8%), whle Austra, Poland, Ireland, Belgum and Span exhbt values respectvely equal to 6.7%, 6.3%, 5.5%, 4.9% and 4.6%. At the bottom of the wage dstrbuton Greece dsplays the lowest value (3.5%), whle Italy shows a slghtly hgher coeffcent (4.3%). [Fgure 1 here] In terms of dfferences between percentles computed at the 6 consdered extremes, t seems useful to us to remnd and make clear that, n every country, they are decreasng wth the dstance between percentles: n other words, n all of the countres nspected θ95 θ5 (θ75 θ25) s hgher (lower) than θ90 θ10. Smlarly to MP whch found that Portugal was top ranked both n terms of OLS and dfference between the nnth and the frst decle, our estmates show that the country havng the greatest OLS coeffcent and the largest spreads between 8

10 percentles, for all of the 3 comparsons, s stll Portugal ( for θ95 θ5, for θ90 θ10 and for θ75 θ25). The same stuaton occurs for Greece at the bottom of the dstrbuton, whch s also the only country wth no dfference between the 75 th and 25 th quantles (2.1% for θ95 θ5, 1.3% for θ90 θ10 and 0.0% for θ75 θ25). Austra has a partcular evdence: n fact, t dsplays a hgh OLS returns on educaton but qute low dfferences between the percentles of the wage dstrbuton. Poland shows both relatvely hgh return on educaton and hgh nter quantles dfferences, whle n Italy a low OLS coeffcent s assocated to a relatvely hgh nequalty between dfferent percentles of the wage dstrbuton. It should be also noted that coeffcents obtaned by QR estmates resemble those obtaned by OLS. That s also confrmed when the correlaton matrx between OLS estmates and the 3 dfferences of the QR estmated coeffcents at the chosen percentles s computed (see tab. 3). Of course the smallest nter quantle dfference (θ75 θ25) s more correlated wth ts nearest neghbour dfference (θ90 θ10). When the OLS estmates are consdered, evdence s found that the larger the dfference between quantles and ther assocated estmates the stronger the correlaton wth OLS: 0,533 for θ75 θ25, 0,697 for θ90 θ10 and 0,783 for θ95 θ5. [Table 3 here] Nevertheless, OLS technque really msleads relevant nformaton about cross countes dfferences n the mpact of educaton on wthn group nequalty at dfferent ponts of the wage dstrbuton. Ths arses from the fg 2 a c whch compares the OLS results wth the QR estmates at dfferent ponts of the wage dstrbuton. There s a clear evdence that wages ncrease wth educaton and ths s true across the whole dstrbuton. Furthermore, ths effect s generally more mportant at the hghest quantles of the dstrbuton than at the lowest, mplyng that schoolng ncreases wage dsperson. Also Greece, whch was found the only excepton by MP, follows the same pattern. It can be further noted that n MP the 9

11 data for Austra, Greece and Italy were based on net wages, whch troubles a full comparson wth the remanng countres (MP, p. 365). [Fgure 2 a c here] Despte ths common pattern across countres, fg. 2a c puts also on dfferent paths across countres from the bottom to the top of the dstrbuton. As to Portugal, t can be noted an ncreasng dstance from Span when passng from the lowest to the hghest percentles. Ths gap decreases n the last 4 quantles. Indeed n Portugal hghest returns to educaton are obtaned at the 80 th percentle (9.2%), and after that they slghtly decrease. On the other hand Span shows a more bounceless (and weaker) growth. Belgum follows a path smlar to that of Span, wth a small decrease from the 5 th to the 10 th quantle. Fg 2 b makes clear that Poland has a changng path over the wage dstrbuton: returns to educaton of Polsh adult male workers trace a curve whch s concave n the lower half of t and then convex, wth a couple of jumps (around 1%) from the 5 th to the 10 th quantle and from the 90 th to the 95 th. Ireland dsplays a smlar but somewhat flatter path, wth the same jumps at the two extremes of the wage dstrbuton. In Austra, returns to schoolng of adult full tme workng men are on the contrary decreasng n the frst 4 quantles of the dstrbuton and after that almost always ncreasng. In fg 2 c a flat path all around the OLS returns to schoolng s found for Greece: smlarly to Poland and Ireland, on the left half QR estmates lay on a concave curve, whle on the rght half they lay on a convex one, but unlke them they are much more lower: ndeed, Greece shows the lowest return to schoolng, at the frst quantle (2.3%). As for Italy, after a decreasng n returns from the frst to the second percentle, the values are almost always ncreasng. It s also evdent a convex path snce the 50 th quantle. 10

12 5. Robustness check Further, n addton to MP and smlarly to Budrìa and Perera (2005) who appled an F test to the dfferences between quantles n terms of educaton levels, n table 4 we test whether gaps between quantle coeffcents estmated n our QR are statstcally sgnfcant. [Table 4 here] The test has been carred out wth respect to the three spreads consdered n the paper (θ95 θ5=0, θ90 θ10=0 and θ75 θ25=0) and to all quantles. More specfcally, p values are obtaned through a bootstrapped varance covarance matrx that ncludes between quantles blocks. The results ndcate that the frst lnear hypothess (θ95 θ5=0) s found to be sgnfcant at all levels of confdence for almost each of the 8 countres. Only Austra dsplays a weaker dfference, as the assocated p value s not sgnfcant at the 1% confdence level. As to the second lnear hypothess (θ90 θ10=0), overall sgnfcance s found. As expected, sgnfcance decreases when the thrd lnear hypothess (θ75 θ25=0) s analysed: n partcular t s detected not sgnfcant at the 1% confdence level for Ireland and Poland, whle t s not sgnfcant for any confdence level n Greece. Ths result s absolutely straghtforward f one observes the precse equalty between the θ75 and θ25 estmated coeffcents of returns to educaton for greek full tme workng males (3.4% at both percentles). Fnally, the jont equalty of coeffcents at all quantles s rejected as well. 6. Conclusons 11

13 In ths paper we have appled a QR technque to the last 2007 wave of the EU SILC data set, n order to explore the connecton between educaton and wage nequalty n 8 European countres. Our comparatve study gves a contrbuton to the lttle comparable evdence for Europe (Budra and Perera 2005, p.1). We found that wages ncrease wth educaton and ths s true across the whole dstrbuton. Furthermore, ths effect s generally more mportant at the hghest quantles of the dstrbuton than at the lowest, mplyng that schoolng ncreases wage dsperson. Ths evdence s found to be rather robust as showed through tests of lnear hypothess carred out on 3 partcular dfferences between estmated quantle coeffcents of the returns to educaton, as well as through a jont test of equvalence for all of the estmated quantle coeffcents. We have so corroborated the dea that, although coeffcents obtaned by OLS estmates are substantally n lne wth the those acheved through QR, OLS technque really msleads relevant nformaton about cross countres dfferences n the mpact of educaton on wthn group nequalty at dfferent ponts of the wage dstrbuton. Hence we confrm that a sem parametrc QR approach s more nterestng, as well as more approprate, because t measures the wage effect of educaton at dfferent quantles, thus descrbng relevant cross countres changes or bounces not only n the locaton, but also n the shape of the dstrbuton. 12

14 References Andn, C., 2007, Returns to Educaton and Wage Equatons: a Dynamc Approach. Appled Economcs Letters, 2007, vol. 14, pp Andn, C., 2009, Wthn Groups Wage Inequalty and Schoolng: Further Evdence for Portugal. Appled Economcs, forthcomng. Barros, C., Preto Rodríguez, J., and J. C. Vera, 2008, What a Quantle Approach can tell us about Returns on Educaton n Europe. Educaton Economcs, Educaton Economcs, Taylor and Francs Journals, vol. 16(4), pages Buchnsky M., 1994, Changes n the U.S. wage structure : applcaton of quantle regresson. Econometrca, 63. Buchnsky M., 1998, Recent Advances n Quantle Regresson Models: A Practcal Gudelne for Emprcal Research. Journal of Human Resources, vol. 33(1), pp Budra, S and P. S. Perera, 2005, Educatonal Qualfcatons and Wage Inequalty: Evdence for Europe," IZA Dscusson Papers 1763, Insttute for the Study of Labor (IZA) Budría, S. and A. I. Moro Egdo, 2008, Educaton, educatonal msmatch, and wage nequalty: Evdence for Span. Economcs of Educaton Revew, Elsever, vol. 27(3), pages , June Goslng, A. & Machn, S. and C. Meghr, 2000, The Changng Dstrbuton of Male Wages n the U.K. Revew of Economc Studes, Blackwell Publshng, vol. 67(4), pages , October. Hartog, J., 2000, Over educaton and earnngs: where are we, where should we go? Economcs of Educaton Revew 19, Koenker, R. and G. Bassett, Regresson quantles. Econometrca 46, Machado, J. A. F. and J. Mata, 2001,Earnng functons n Portugal : Evdence from quantle regressons. Emprcal Economcs, Sprnger, vol. 26(1), pages

15 Machado, J. A. F. and J. Mata, 2005, Counterfactual decomposton of changes n wage dstrbutons usng quantle regresson, Journal of Appled Econometrcs, John Wley & Sons, Ltd., vol. 20(4), pages Martns P., 2004, Industry Wage Dsperson: Evdence from the Wage Dstrbutonʹ. Economcs Letters, 83(2), , Martns P. T. and P.S. Perera, 2004, Does Educaton Reduce Wage Inequalty? Quantle Regresson Evdence from 16 Countres. Labour Economcs, 11(3), , McGunness, S., McGnnty, F. and P. J. O Connell, 2009, Changng Returns to Educaton Durng a Boom? The Case of Ireland, n Labour 23 (Specal Issue), pp

16 Tables and fgures Tab. 1. Summary statstcs Country Year Varable Obs Mean Austra 2007 Belgum 2005 Greece 2005 Ireland 2007 Italy 2007 Poland 2007 Portugal 2007 Span 2007 Std. Dev. Std. Err. [95% Conf. Interval] Log hourly wage edu exp Log hourly wage edu exp Log hourly wage edu exp Log hourly wage edu exp Log hourly wage edu exp Log hourly wage edu exp Log hourly wage edu exp Log hourly wage edu exp

17 Tab. 2. Condtonal returns to schoolng OLS and QR. Quantle Austra Belgum Span Greece Irland Italy Poland Portugal θ= θ= θ= θ= θ= θ= θ= θ= θ= θ= θ= θ= θ= θ= θ= θ= θ= θ= θ= OLS θ95 θ θ90 θ θ75 θ Obs Note. Data for Austra, Span, Irland, Italy, Poland and Portugal are from cross sectonal UDB SILC 2007 verson 1 of March 2009; Belgum and Greece from EU SILC All coeffcent sgnfcants at p<0.001, t statstcs n talcs. 16

18 8% Fg 1: Returns to schoolng: OLS and dfference between percentles 7% 6% Returns 5% 4% 3% 2% 1% 0% Portugal Austra Poland Ireland Belgum Span Italy Greece Countres θ95-θ5 θ90-θ10 θ75-θ25 OLS Tab 3. Correlaton between OLS and nter quantle dfferences θ95 θ5 1 θ95 θ5 θ90 θ10 θ75 θ25 OLS θ90 θ θ75 θ OLS

19 Fg 2 a-c: Returns to schoolng 10% 9% 8% Returns 7% 6% 5% 4% 3% 2% OLS Percentles Span Portugal Belgum 10% 9% 8% Returns 7% 6% 5% 4% 3% 2% OLS Percentles Austra Ireland Poland 10% 9% 8% Returns 7% 6% 5% 4% 3% 2% OLS Greece Percentles Italy 18

20 Table 4: Null Inter quantle dfferences and jont equalty: hypothess testng by country Countres θ95 θ5=0 θ90 θ10=0 θ75 θ25=0 All quantles equal Austra Belgum Span Greece Irland Italy Poland Portugal F( 1, 2752) = 6.34 F( 1, 2752) = F( 1, 2752) = F( 9, 2752) = Prob > F = Prob > F = Prob > F = Prob > F = F( 1, 1740) = F( 1, 1740) = F( 1, 1740) = F( 9, 1740) = 6.86 Prob > F = Prob > F = Prob > F = Prob > F = F( 1, 5346) = F( 1, 5346) = F( 1, 5346) = F( 9, 5346) = Prob > F = Prob > F = Prob > F = Prob > F = F( 1, 1863) = F( 1, 1863) = F( 1, 1863) = 0.08 F( 9, 1863) = Prob > F = Prob > F = Prob > F = Prob > F = F( 1, 1518) = F( 1, 1518) = F( 1, 1518) = 6.08 F( 9, 1518) = Prob > F = Prob > F = Prob > F = Prob > F = F( 1, 7320) = F( 1, 7320) = F( 1, 7320) = F( 9, 7320) = Prob > F = Prob > F = Prob > F = Prob > F = F( 1, 5232) = F( 1, 5232) = F( 1, 5232) = 6.52 F( 9, 5232) = Prob > F = Prob > F = Prob > F = Prob > F = F( 1, 1698) = F( 1, 1698) = F( 1, 1698) = F( 9, 1698) = Prob > F = Prob > F = Prob > F = Prob > F =

21 Appendx Austra 2007 Full tme male workers: age Percent Monthly gross ncome n euros graphs by educaton level attaned Belgum 2005 Full tme male workers: age Percent Monthly gross ncome n euros graphs by educaton level attaned 20

22 Greece 2005 Full tme male workers: age Percent Monthly gross ncome n euros graphs by educaton level attaned Span 2007 Full tme male workers: age Percent Monthly gross ncome n euros graphs by educaton level attaned

23 Ireland 2007 Full tme male workers: age Percent Monthly gross ncome n euros graphs by educaton level attaned Italy 2007 Full tme male workers: age Percent Monthly gross ncome n euros graphs by educaton level attaned 22

24 Poland 2007 Full tme male workers: age Percent Monthly gross ncome n euros graphs by educaton level attaned Portugal 2007 Full tme male workers: age Percent Monthly gross ncome n euros graphs by educaton level attaned