Maturity and school outcomes in an inflexible system: Evidence from Catalonia

Calsamiglia, Ca e ina; Lo iglio, Annalisa A icle Ma u i y and school ou comes in an in lexible sys em: E idence om Ca alonia SERIEs - Jou nal o he Spanish Economic Associa ion P o ided in Coope a ion wi h: Spanish Economic Associa ion Sugges ed Ci a ion: Calsamiglia, Ca e ina; Lo iglio, Annalisa (2020) : Ma u i y and school ou comes in an in lexible sys em: E idence om Ca alonia, SERIEs - Jou nal o he Spanish Economic Associa ion, ISSN 1869-4195, Sp inge , Heidelbe g, Vol. 11, Iss. 1, pp. 1-49, h ps://doi.o g/10.1007/s13209-019-0196-6 This Ve sion is a ailable a : h ps://hdl.handle.ne /10419/286509 S anda d-Nu zungsbedingungen: Die Dokumen e au EconS o dü en zu eigenen wissenscha lichen Zwecken und zum P i a geb auch gespeiche und kopie we den. Sie dü en die Dokumen e nich ü ö en liche ode komme zielle Zwecke e iel äl igen, ö en lich auss ellen, ö en lich zugänglich machen, e eiben ode ande wei ig nu zen. So e n die Ve asse die Dokumen e un e Open-Con en -Lizenzen (insbesonde e CC-Lizenzen) zu Ve ügung ges ell haben soll en, gel en abweichend on diesen Nu zungsbedingungen die in de do genann en Lizenz gewäh en Nu zungs ech e. Te ms o use: Documen s in EconS o may be sa ed and copied o you pe sonal and schola ly pu poses. You a e no o copy documen s o public o comme cial pu poses, o exhibi he documen s publicly, o make hem publicly a ailable on he in e ne , o o dis ibu e o o he wise use he documen s in public. I he documen s ha e been made a ailable unde an Open Con en Licence (especially C ea i e Commons Licences), you may exe cise u he usage igh s as speci ied in he indica ed licence. h ps://c ea i ecommons.o g/licenses/by/4.0/ SERIEs (2020) 11:1–49 h ps://doi.o g/10.1007/s13209-019-0196-6 ORIGINAL ARTICLE Ma u i y and school ou comes in an in lexible sys em: e idence om Ca alonia Ca e ina Calsamiglia1·Annalisa Lo iglio2 Recei ed: 5 Oc obe 2016 / Accep ed: 22 June 2019 / Published online: 8 July 2019 © The Au ho (s) 2019 Abs ac The exis ence o a igid cu o da e which de e mines when child en s a p ima y school c ea es a la ge he e ogenei y in s uden s’ le el o ma u i y wi hin he class- oom. We use ich adminis a i e da a o he uni e se o public schools in Ca alonia o show ha : (1) ela i ely younge child en do signi ican ly wo se bo h in es s adminis- e ed a he school le el and a he egional le el, and hey expe ience g ea e e en ion. (2) These e ec s a e homogeneous ac oss SES and signi ican ac oss he whole dis i- bu ion o pe o mance. (3) Younge child en in ou da a exhibi highe d opou a es and choose he academic ack in seconda y school less o en. (4) Younge child en a e mo e equen ly diagnosed wi h lea ning diso de s. Keywo ds Human capi al ·En y age ·School cu o da e JEL Classi ica ion I21 ·I28 ·H75 We a e g a e ul o he s a a he Depa amen d’Ensenyamen and IDESCAT, and in pa icula o Xa ie Co ominas and Miquel Delgado, o hei help in p ocessing he da a. We a e also g a e ul o Manuel A ellano, Joan Llull, Alejand a Ramos and o pa icipan s o semina s in CEMFI and UAB o hei use ul commen s on he pape . All e o s a e ou s. Ca e ina Calsamiglia acknowledges inancial suppo by he Spanish Plan Nacional I+D+I (ECO2014-53051-P), he Gene ali a de Ca alunya (SGR2014-505) and he Se e o Ochoa p og am (SEV-2015-0563) and om he ERC S a ing G an 638893. Annalisa Lo iglio acknowledges inancial suppo o La Caixa Founda ion (La Caixa-Se e o Ochoa In e na ional Doc o al Fellowship). BAnnalisa Lo iglio [email p o ec ed] Ca e ina Calsamiglia [email p o ec ed] 1ICREA and IPEG, Ca e Ramon T ias Fa gas, 25-27 08005 Ba celona, Spain 2Uni e si a Au ònoma de Ba celona and Ba celona GSE, Ba celona, Spain 123 2SERIEs (2020) 11:1–49 1 In oduc ion The ac ha a unique school cu o da e de e mines when a child begins p ima y educa ion induces la ge he e ogenei y in he age a which child en en e school. Olde child en will be subs an ially mo e ma u e han hei younge pee s, which may lead hem o ini ially pe o m be e . Fo ins ance, in Spain he school en y cu o da e is Janua y 1, and child en s a p ima y educa ion in Sep embe o he calenda yea in which hey u n 6 yea s old. The e o e, child en bo n in Janua y a e abou 20% olde han hei pee s bo n in Decembe . In his pape , we use de ailed adminis a i e da a o he Spanish egion o Ca alonia o p o ide e idence ha age a en ollmen in p ima y educa ion a ec s s uden s’ ou comes h oughou hei educa ion. Wo k by Heckman and co-au ho s shows ha ea ly child de elopmen is comple- men a y o la e lea ning—see Cunha e al. (2006) o a e iew. Beda d and Dhuey (2006) use in e na ional da a o show ha hese ini ial ma u i y di e ences ha e long- las ing e ec s on s uden pe o mance. Se e al pape s look a he e ec s wi hin a coun y: F ed iksson and Öcke (2014) o Sweden, Puhani and Webe (2007) o Ge many, Schneeweis and Zweimülle (2014) o Aus ia, Black e al. (2011) o No - way, C aw o d e al. (2010) o England, McEwan and Shapi o (2008) o Chile, Ponzo and Scoppa (2014) o I aly, and Elde and Lubo sky (2009) o he USA. Thein e na ionale idenceag ees ha ela i elyolde s uden s pe o m signi ican ly be e du ing p ima y educa ion. The magni ude o he e ec and he consequences o la e ou comes seem o a y ac oss coun ies. Fo ins ance, Black e al. (2011)show ha in No way he school s a ing age ba ely a ec s he esul s in a cogni i e es a age 18 and does no ma e o hei p ime-age ea nings. Con e sely, s udies o coun ies wi h ea ly acking such as Ge many (Puhani and Webe 2007) and I aly (Ponzo and Scoppa 2014) show ha di e ence in pe o mance is pe sis en and a ec s s uden s’ alloca ion o academic o oca ional educa ion, which in u ns will a ec hei labo ma ke ou comes. This sugges s ha he longe un e ec o age a en ollmen depends upon he educa ional sys em in place. The case o Spain, mo e speci ically o Ca alonia, deems pa icula ly in e es ing o se e al easons. Fi s , child en a e no allowed o pos pone o an icipa e en ance o p ima y school, ensu ing a clean iden i ica ion. Second, g ade epe i ion is common, especially du ing ad anced g ades o compulso y educa ion. I is impo an o explo e how age a en y and g ade epe i ion in e ac . In ac , on he one hand, g ade epe i ion migh o se he e ec o age a en y i i gi es mo e ime o less ma u e s uden s o mas e ing he ma e ial. On he o he hand, he empi ical li e a u e p o ides mixed e idence o i s e ec i eness in imp o ing s uden pe o mance (F uehwi h e al. 2016) and sugges s ha when e en ion akes place in ad anced g ades, he p obabili y o d opou subs an ially inc eases (Jacob and Le g en 2009). The e o e, e en ion may widen he gap be ween younge and olde s uden s a he han closing i . Thi d, he e is no acking un il he end o lowe seconda y educa ion ( en h g ade). In o he coun ies, he e ec o age a en y on pe o mance o on he choice o d opping-ou om school may be con ounded wi h he di e en quali y o he educa ion o e ed by di e en acks, especially i s uden s’ ma u i y a ec s hei selec ion in o acks. Fou h, a e comple ing lowe seconda y educa ion, s uden s can choose whe he o acqui e u he educa ion, o ei he academic o oca ional ype. Only he o me gi es di ec access o 123 SERIEs (2020) 11:1–49 3 Uni e si y; he e o e, i age a en y a ec s s uden s’ choice o en olling in academic uppe seconda y educa ion, i is e y likely ha i will a ec hei u u e educa ional and labo ma ke ou comes. Whilesomep e iousc oss-coun ys udiesincludeSpainamong hecoun iesunde analysis, hey can only analyze he e ec o ma u i y on s anda dized assessmen s adminis e ed o a subsample o s uden s who a e in educa ion a a gi en poin in ime.1In his pape , we use adminis a i e da a o he uni e se o public schools in Ca alonia o child enen olleding ades om 1 o12in heacademicyea s2009/2010– 2013/2014. We s udy he e ec o age a en ollmen on se e al ou comes o e ime, including pe o mance, e en ion, educa ional choices o whe he o comple e lowe seconda y educa ion and whe he o unde ake uppe seconda y educa ion, and diag- nosis o lea ning disabili ies.2 We ind ha ela i ely younge child en a e e ained mo e o en and pe o m wo se bo h in es s adminis e ed a he school le el and a he egional le el. Pa icula ly s a k a e he esul s on e en ion: while a small ac ion o s uden s a e e ained a he beginning o p ima y educa ion (abou 3% du ing he i s wo g ades), hose bo n a he end o he yea a e wo imes mo e likely o be e ained han he a e age child. A age 14, hey a e almos 11 pe cen age poin s mo e likely o be in a lowe school g ade han hei pee s bo n a he beginning o he yea . The nega i e e ec o being younge on pe o mance is dec easing as child en ge olde , al hough signi ican h oughou . In pa icula , he gap be ween younge and olde child en is almos 0.6 s anda d de ia ions when hey a e in second g ade and s ill 0.2 s anda d de ia ions in middle school. The e ec is signi ican and sizeable o all pe o mance le els, as con i med by quan ile eg essions. G ade epe i ion does no close he gap be ween younge and olde s uden s. Con a y o wha o he s ha e ound o o he coun ies, younge child en in Ca - alonia d op ou om educa ion mo e o en.3A child bo n a he end o Decembe is 2 p.p. mo e likely o lea e lowe seconda y educa ion wi hou ob aining a diploma han a simila child bo n a he beginning o Janua y. Mo eo e , younge s uden s a e less likely o en oll in academic uppe seconda y educa ion. Abou 50% o s uden s 1No iceable examples a e he seminal wo k by Beda d and Dhuey (2006), whe e Spain is among he coun ies used o measu e ma u i y e ec on pe o mance in TIMSS es in eigh g ade, and Sp ie sma (2010), which uses esul s om a wa e o PISA es s. Howe e , he use o PISA es s o Spain can be p oblema ic in he cu en se ing, because hey a e adminis e ed in he sp ing o a gi en yea o s uden s who u n 16 ha yea . 16 yea s old is also he manda o y age o schooling in Spain, meaning ha om hen on s uden s can lea e educa ion. The e o e, es ake s bo n in Janua y ha e al eady passed he manda o y age o schooling, while es ake s bo n in Decembe did no : he o me g oup may no pe ec ly ep esen he o al popula ion o child en bo n in Janua y. See, o ins ance, PISA 2012 Technical Repo , OECD, 2014. 2To he bes o ou knowledge, no p e ious wo k ocuses on Spain o one o i s egions. De eloped a he same ime o his s udy, Be niell and Es ada (2017) use se e al wa es o PISA es s o documen ha Spanish child en bo n in Decembe a e mo e likely o ha e lowe sco e and ha e epea ed a g ade han child en bo n in Janua y. They also use in o ma ion om he Spanish popula ion census o show ha adul s who we e younge a school en y ha e less schooling. We compa e some o ou indings wi h hei s in Sec . 7. 3E.g., Cook and Kang (2016) o USA In Ca alonia, child en ge a deg ee a he end o en h g ade. As we discuss la e in he ex , incen i es o s ay in school and ob ain he deg ee may be somehow s onge han in o he coun ies, whe e a deg ee is awa ded only a he end o he wel h g ade. 123 4SERIEs (2020) 11:1–49 o e all en oll in he academic ack, bu he p obabili y o choosing i is 5 p.p lowe o he younges . Finally, younge child ena e mo e equen lydiagnosedwi h lea ning disabili ieso a en ion-de ici diso de s (e.g., ADD, ADHCD). The p obabili y o being diagnosed o a child bo n a he end o he yea is 50% highe han o an o he wise-iden ical child bo n a he beginning o he yea . In he li e a u e, he e is also e idence ha he gap in achie emen due o he age a en ollmen may be la ge o child en coming om amilies wi h high socioeconomics (SES). In pa icula , Elde and Lubo sky (2009) show ha in he USA, he impac o ma u i y is la ge o high SES han o low SES. They a gue ha p eschool expe ience changes wi h SES and hence he impac o spending one mo e yea a home o in p eschool is pa icula ly bene i ing o child en coming om high SES. On he o he hand, high SES could also help ill he gap du ing school yea s, by p o iding suppo and addi ional aining o he ela i ely younge who a e acing g ea e challenges. We ind ha in Ca alonia he e ec o ma u i y on pe o mance is qui e homogeneous by SES. This may be because he e p e-p ima y educa ion is gua an eed and ee, and 97% o child en a end p eschool. This means ha in he ex a yea be o e p ima y educa ion olde child en om all amily backg ound spend a la ge ac ion o hei ime in a ela i ely simila en i onmen . Hence, he e may be less he e ogenei y due o he expe ience acqui ed in ha addi ional yea . The es o his pape is o ganized as ollows. Sec ion 2desc ibes he Ca alan educa ional sys em and en ollmen ules. Sec ion 3desc ibes he da a and discusses desc ip i e s a is ics. Sec ion 4ou lines he empi ical s a egy. Sec ion 5p esen s he main esul s. Sec ion 6discusses obus ness checks. Sec ion 7discusses he e ogenei y analyses. Finally, Sec . 8concludes. 2 Ca alan educa ional sys em and en ollmen ules P ima y educa ion (Educació p ima ia, co esponding o ISCED le el 10) is he i s s age o compulso y educa ion in Ca alonia; no mally, a child begins p ima y school in Sep embe o he calenda yea in which he o she u ns 6 yea s old. In o he wo ds, he cu o da e is Janua y 1. Fo ins ance, bo h a child bo n on Janua y 1, 2003 and a child bo n on Decembe 31, 2003 s a p ima y school in Sep embe 2009, while someone bo n on Janua y 1, 2004 s a s 1 yea la e , in Sep embe 2010. This en ollmen ule is qui e sha p, and excep ions a e ex emely a e. Un il 2008, hey equi ed he app o al o he egional minis y o educa ion.4A e o m o compulso y educa ion app o ed in Sep embe 2008 in oduced a sligh ly mo e lexible ansi ion om p eschool o p ima y school. The gene al ule is he same, bu excep ions a e managed by he school, oge he wi h he amily ins ead o he depa men o Educa ion.5Howe e , as shown in he nex sec ion, also in mo e ecen yea s he o e whelming majo i y o 4Dec ee 94/1992, issued on Ap il, 28 (in Dia i O icial de la Gene ali a de Ca alunya (DOCG), núm. 1593-13/05/1992). 5Dec e 181/2008, issued on Sep embe , 9 (in DOGC núm. 5216-16/9/2008), and O de EDU/484/2009, issued on No embe 2, (in DOGC núm. 5505-13/11/2009). 123 SERIEs (2020) 11:1–49 5 child en comply wi h he ule: mo e han 99% o hem en oll in p ima y school a 6 yea s old. Be o e p ima y educa ion, child en can a end p eschool (Educació in an il) o 3yea s ( om Sep embe o he yea in which hey u n 3). A endance is no com- pulso y, bu in p ac ice almos all amilies en oll hei child en.6No mally, p ima y educa ion akes 6 yea s, ollowed by 4 yea s o lowe seconda y educa ion (Edu- cació seconda ia obliga ò ia, co esponding o ISCED le el 24). S uden s a e legally equi ed o s ay in school un il hey u n 16 o un il hey g adua e. A e success ully comple ing lowe seconda y educa ion, s uden s can en oll in uppe seconda y educa- ion o wo mo e yea s. Uppe seconda y educa ion is ei he academic (Ba xille a , co esponding o ISCED le el 34) o oca ional (G au Mi jà, co esponding o ISCED le el 35). Only s uden s who comple e academic uppe seconda y educa ion can aim a en olling in a 4-yea bachelo deg ee in a Uni e si y. The a es o comple ion o seconda y educa ion and en ollmen in u he educa ion a e low in Ca alonia (and mo e in gene al in Spain), in compa ison wi h o he Eu opean coun ies. Acco ding o Eu os a in yea s 2011–2013, abou 25% o he popula ion aged 18 o 24 in Ca alonia a ained a mos lowe seconda y educa ion and ha e no been in ol ed in u he educa ion o aining.7 S uden s whose pe o mance is no su icien can be e ained and spend one mo e yea in he same g ade. By law, child en can be e ained a mos once du ing p i- ma y educa ion and a mos wice du ing lowe seconda y educa ion.8Excep ions a e allowed only o child en wi h special educa ional needs and a e ex emely a e in p ac ice.9Howe e , as shown in Sec . 3.2, e en ion is ela i ely in equen du ing p ima y educa ion and mo e common du ing lowe seconda y educa ion. 3 Da a Ou analysis ocuses on s uden s en olled in public schools in Ca alonia om school yea 2009/2010 o school yea 2013/2014. P ima y educa ion and lowe seconda y educa ion is ypically p o ided by di e en schools. We call “p ima y schools” he p o ide s o he o me and “middle schools” he p o ide s o he la e . Each yea mo e han 50.000 child en en oll o he i s ime in he i s g ade o a public p ima y 6In ou da a, abou 97% o child en en olled o he i s ime in p ima y school in 2012 o 2013 we e en olled in p eschool he yea be o e. Some o he emaining 3% may ha e been en olled in a semip i a e o p i a e school. (Only en ollmen da a o public p eschools a e a ailable o us.) 7S a is ics “Ea ly lea e s om educa ion and aining by sex and NUTS 2 egions” (eda _l se_16) a ailable on ec.eu opa.eu/eu os a . 8Fo p ima y educa ion: Dec e 142/2007, issued on June, 26 (in DOGC núm. 4915-26/6/2007). Fo seconda y educa ion: Dec e 143/2007, issued on June, 26 (in DOGC núm. 4915-26/6/2007). 9Ou da a con i m ha e en ion ules a e en o ced. Fo ins ance, among child en bo n in 2003 (who no mally en e p ima y educa ion in 2009 and a e in g ade 5 by yea 2013), only 30 (0.05%) we e e ained wice du ing he i s wo cycles o p ima y educa ion. Among hose bo n in 2001 (who ypically comple e he second and he hi d cycle o p ima y school be o e 2013), only 27 (0.04%) we e e ained wice in he ime pe iod spanned by ou sample. Simila ly o middle school, only 13 child en bo n in 1997 and 22 child en bo n in 1996 we e e ained h ee imes om 2009 o 2013. 123 6SERIEs (2020) 11:1–49 school o he egion. They a e abou 65% o he o al numbe o s uden s who en e p ima y educa ion in ha yea .10 3.1 Da a sou ces and sample selec ion We exploi da a om di e en sou ces ha p o ide us wi h de ailed in o ma ion on en ollmen , school p og ession, academic ou comes and socio-demog aphic cha ac- e is ics o Ca alan s uden s. The Ins i u Ca alà d’Es adis ica (IDESCAT) anonymized he da a sou ces and p o ided us wi h s uden iden i ie s o me ge hem. The Depa amen d’Ensenyamen ( egional minis y o educa ion in Ca alonia) p o ided en ollmen eco ds o he schools in he egion, om p eschool o high school. The IT in as uc u e ha suppo s he au oma ic collec ion o da a has been p og essi ely in oduced since he school yea 2009/2010. By yea 2010/2011, almos all schools ha e al eady adop ed i , while we ha e da a o abou 60% o hem in 2009/2010.11 Fo all s uden s in he public sys em, we obse e he school and he class in which she is en olled, he day o bi h, he gende , he na ionali y, and whe he she has special educa ional needs. Mo eo e , da a include e alua ions ha he s uden s ecei e a he end o g ades 2, 4, and 6 (p ima y educa ion), and a he end o each g ade om 7 o 10 (seconda y educa ion), o each subjec ha hey ha e unde aken. These e alua ions a e assigned by eache s aking in o accoun he p og ession o he child and he pe o mance in se e al es s adminis e ed du ing he cycle. Fo s uden s en olled in g ade 10, i.e., he las g ade o middle school, we can obse e whe he hey g adua ed a he end o he yea .12 Da a also include some en ollmen in o ma ion and da e o bi h o s uden s a ending a p i a e school, bu nei he o he demog aphics no hei e alua ions. The e o e, his pape ocuses on s uden s en olled in public schools. “Appendix B” eplica es some o he analyses o s uden s en olled in p i a e schools. The Consell d’A aluació de Ca alunya (public agency in cha ge o e alua ing he educa ional sys em) p o ided us wi h he esul s o s anda dized es s aken by all he s uden s in he egion a ending he las yea o p ima y school (g ade 6) and he las yea o middle school (g ade 10). Such es s a e adminis e ed du ing sp ing since 2009/2010 o p ima y school and since 2011/2013 o middle school. They assess basic compe ences in Ma hs, Ca alan, Spanish and English and ha e a pu ely s a is ical pu pose: hey do no a ec he s uden s’ inal e alua ions o p og ess o he nex g ades. We will e e o he esul s in hese examina ions, whose g ading is blind, as ex e nal e alua ions, in con as o he inal e alua ions gi en by he school, ha we will call in e nal e alua ions. Finally, we collec in o ma ion on he s uden ’s amily backg ound, mo e speci - ically on pa en al educa ion om he Census (2002) and local egis e da a (Pad ó). When he in o ma ion could be e ie ed om bo h sou ces, we impu ed he highes 10 Mo e han 30% o he s uden s a end semip i a e schools (Conce adas), which a e un p i a ely and unded ia bo h public and p i a e sou ces. The emaining s uden s a end a ully p i a e school. Fo simplici y in his pape , we will de ine as “p i a e” all schools ha a e no ully public. 11 Some schools ini ially epo da a only o hei lowe g ades, co e ing he en i e pool o s uden s only a e 2 o 3 yea s. The e o e, he sample used o s udy he ou comes in he lowe g ades is sligh ly la ge . 12 We could no e ie e some o all he e alua ions o abou 2% o he s uden s, who a e excluded om he analysis in which e alua ions a e used as ou comes. 123 SERIEs (2020) 11:1–49 7 le el o educa ion, p esumably he mos up- o-da e in o ma ion. We could no e ie e in o ma ion abou hei pa en s o 4.5% o child en, and hose s uden s a e excluded om he analyses. 3.2 Va iables used and desc ip i e s a is ics 3.2.1 School and s uden cha ac e is ics Table 1desc ibes he public educa ion sys em in Ca alonia in he academic yea 2013/2014, he las in ou sample. The e a e 1556 p ima y schools and 538 mid- dle schools. On a e age, p ima y schools ha e 1.6 classes pe g ades, while middle schools ha e 3.3 classes pe g ade.13 Abou hal o he s uden s a e emale, 14.3% o s uden s in p ima y educa ion do no ha e Spanish ci izenship (17.5% in lowe seconda y educa ion).14 We de ine h ee ca ego ies o pa en al educa ion: low, a e age, and high. Pa en s’ educa ion is low i bo h pa en s ha e comple ed a mos lowe seconda y educa ion. I is high i one pa en has e ia y educa ion and he o he has a leas comple ed uppe seconda y educa ion. I is a e age in he o he cases.15 Abou 36.4% o s uden s in p ima y educa ion ha e low educa ed pa en s, while 27.2% ha e highly educa ed pa en s. Figu es a e 41.8% and 22.0%, espec i ely, o lowe seconda y educa ion. 5.5% o p ima y school s uden s a e “behind”; namely, hey a e a ending a lowe g ade han wha no mally expec ed o s uden s o hei age. The sha e is 8.7% among s uden s who a end g ade 6 ( he las g ade o p ima y school), while i ises o 16.2% in g ade 7 ( he i s g ade o middle school). O e all 22.6% o s uden s in lowe seconda y educa ion a e behind. This sugges s a sha p inc ease in g ade epe i ion in middle school. 3.2% o s uden s ha e special educa ional needs.16 This assignmen is qui e pe sis- en : bo h in p ima y and seconda y educa ion, abou 97% o s uden s who a e labeled as special needs in a gi en yea ha e he same label he ollowing pe iod. 3.2.2 E alua ions The main measu e o pe o mance used in he analysis is he a e age o he e alua ions in he ou co e subjec s ha all s uden s unde ake h oughou compulso y educa ion: Ma hema ics, Ca alan, Spanish, and English. In lowe seconda y educa ion, e alua- ions a e assigned using a 0–10 scale, while in p ima y e alua ions he ma ks “Fail,” “Pass,” “Good,” “Ve y good,” “Excellen ” a e used. We con e hem in o nume ic al- 13 S a is ics o s uden s a e simila in he p e ious yea s. Howe e , as poin ed ou in Sec . 3.1, no all he schools joined he da a collec ion a he same ime. In 2009/2010, only 717 p ima y schools appea in he sample (496 middle schools) and hei numbe sha ply inc eases o 1440 in 2010/2011. 14 Fo simplici y, om now on we will e e o s uden s whose na ionali y is no he Spanish one as “immig an .” Howe e , some o hem may be second-gene a ion immig an s; i.e., hey may be bo n in Spain bu no quali y o ci izenship (e.g., i hei pa en s jus a i ed in Spain). 15 The classi ica ion is made using only he le el o in o ma ion o one pa en when in o ma ion o he o he pa en is missing. 16 Special needs assigna ion is egula ed by Llei O gànica d’Educació LOE 2/2006 (a icles 71 and 72). 123 8SERIEs (2020) 11:1–49 Table 1 Public schools in Ca alonia Pa en s’ educa ion Female (%) Immig an (%) Behind (%) Special needs (%) Schools Low (%) A g (%) High (%) NClasses P ima y S. 36.4 36.5 27.2 48.4 14.3 5.5 3.2 1556 1.6 Middle S. 41.8 36.2 22.0 48.6 17.5 22.6 3.2 538 3.3 S a is ics compu ed o s uden s en olled in a public p ima y o middle school in Ca alonia in he academic yea 2013/2014 123 SERIEs (2020) 11:1–49 15 Table 4 Tes s o balance o p ede e mined co a ia es (1) (2) (3) Female 0.000 −0.000 −0.001 (0.010) (0.014) (0.003) Immig an 0.003 −0.001 0.012 (0.007) ( 0.011) (0.002)** Pa en s’ edu low −0.006 0.003 0.019 (0.010) (0.015) (0.003)** Pa en s’ edu a g 0.015 −0.014 0.001 (0.010) (0.015) (0.003) Pa en s’ edu high −0.002 −0.003 −0.016 (0.009) (0.012) (0.003)** **p<0.01. Tes s a e pe o med using he sample o s uden s bo n om July 2002 o June 2005. Fo e e y line o he able, each en y epo s he es ima ed di e ence o he co a ia e o s uden s bo n be o e and a e he cu o da e (Janua y 1). The s anda d e o o he es ima e is epo ed in pa en hesis. Columns (1) and (3) pe o m a es o di e ence in mean; he sample o (1) includes only s uden s bo n in he i s 15 days o Janua y and in he las 15 days o Decembe , while all s uden s a e included in (3). Column (2) uses all he s uden s in he sample and pe o ms a local nonpa ame ic RDD speci ica ion ollowing Calonico e al. (2014). (We allow he algo i hm o selec he op imal bandwid h.) algo i hm, p o iding u he isual e idence ha he e is no discon inui y a ound he cu o da e. Nex , we p o ide e idence ha he p ede e mined co a ia es (gende , immig an s a us, pa en al educa ion) a e con inuous a ound he cu o da e. Fi s , we es whe he he mean alues a e signi ican ly di e en o s uden s bo n a ound he cu o da e (mo e speci ically in he las 15 days o Decembe and in he i s 15 days o Janua y). As shown in column (1) o Table 4, we canno ejec he null hypo hesis ha he e is no di e ence o any o he a iables unde analysis. Second, we use s uden s bo n h oughou he yea o es whe he any o he co a ia es is discon inuous a ound he cu o da e. Mo e speci ically, o each p ede e mined co a ia e xi, we implemen a eg ession discon inui y design using he ollowing equa ion: xi=ζDi+θ (di)+κDi (xi)+ci+i,(5) whe e Diis a dummy ha akes alue 1 i he s uden is bo n be ween Janua y 1 and June 30, (di)is a polynomial unc ion o he day o bi h, and ciis he coho ixed e ec . We es ima e (5) using he nonpa ame ic app oach wi h a iangula ke nel and a second o de polynomial o he unning a iable, ollowing he implemen a ion p oposed in Calonico e al. (2014).21 The pa ame e ζcap u es di e ence in xibe o e and a e he cu o . We epo es ima e o ζand s anda d e o s in column (2) o 21 Using a linea o highe o de polynomial p oduces compa able esul s. 123 16 SERIEs (2020) 11:1–49 Table 4. None o he co a ia es exhibi s a s a is ically signi ican di e ence a ound he cu o . A u he conce n ha may a ise is ha some pa en s may ake in accoun he day o bi h o hei child when choosing be ween public and p i a e schools. Fo ins ance, hey may hink ha a p i a e school would sui be e he needs o a child bo n in Decembe . This ype o pa en s would be o e ep esen ed in Janua y and unde ep esen ed in Decembe in ou sample o child en in public schools. We use en ollmen da a o es whe he he p obabili y o being en olled in a public p ima y school is di e en be o e and a e he cu o da e. Bo h he simple di e ence in mean and he RDD app oach canno ejec he null hypo hesis ha he e is no di e ence. We canno ejec null hypo heses also when he sample o he es s is es ic ed o s uden s wi h a gi en pa en al educa ion.22 4.2.2 Bi h seasonali y and pa en al backg ound Resul s discussed so a suppo he hypo hesis ha child en bo n a ound he cu o da e a e no di e en a he beginning o hei li e. Howe e , he dis ibu ion o bi hs h oughou he yea may di e by pa en al backg ound. In column (3) o Table 4,we es whe he he mean alues o he co a ia es a e di e en o child en bo n om July o Decembe and hose bo n om Janua y o June. We ind ha he la e a e 1.6 pe cen age poin s mo e likely o ha e highly educa ed pa en s and 1.2 pe cen age poin s mo e likely o be na i e Spanish. Equa ions (1) and (2) a e linea in age a en y A. I s uden s bo n in he i s hal o he yea a e mo e likely o ha e good educa ional ou comes because o hei pa en al backg ound, he es ima ed coe icien s o age a en y Ain Eqs. (1) and (2) may be upwa d biased. Figu e 4shows sugges i e e idence ha his should no be a conce n. Fo he le panel o he igu e, we eg ess a dummy o highly educa ed pa en s on a ec o o dummies o he mon h o bi h, con olling o gende , immig a ion s a us, and coho . The g aph plo s he es ima ed coe icien s wi h hei con idence in e al, showing ha child en bo n in Ma ch, Ap il, and May a e mo e likely o ha e highly educa ed pa en s. The opposi e is ue o hose bo n in Augus , while he e is no signi ican di e ence o he o he mon hs. I di e ences in educa ional ou comes be ween olde and younge s uden s a e due o unobse ed cha ac e is ics which a e co ela ed wi h hei pa en al backg ound, we would expec o see a simila pa e n when we eg ess hei GPA on he dummies o he mon h o bi h. Con e sely, as shown in he igh panel o he igu e, he GPA is dec easing in he mon h o bi h in a e y linea way. The analyses in Sec . 5 ely on he assump ion ha Ahas a linea e ec on e al- ua ions (Eq. 1) and on he la en a iables o he bina y ou comes s udied wi h he p obi model (Eq. 2). In Sec . 6, we discuss wo al e na i e app oaches o suppo ou inding. 22 We use 8-yea -old s uden s o pe o m he es s o make su e ha we a e aking in accoun all child en, also he ew child en who delayed he en ance. The p alues o es s as he one in columns (1) and (2) o Table 4a e 0.3 and 0.6, espec i ely. Fo child en o highly educa ed pa en s, hey a e 0.61 and 0.44, espec i ely. 123 SERIEs (2020) 11:1–49 17 −.04 −.02 0 .02 .04 Es ima ed coe icien 1 2 3 4 5 6 7 8 9 10 11 12 Mon h o bi h Pa en s’ educa ion high 0.2 .4 .6 Es ima ed coe icien 1 2 3 4 5 6 7 8 9 10 11 12 Mon h o bi h GPA g ade 2 Fig. 4 Co ela ion o mon h o bi h wi h pa en s’ educa ion and s uden ’s pe o mance. We eg ess a dummy o highly educa ed pa en s (le igu e) o he GPA in g ade 2 ( igh igu e) on a ec o o dummies o he mon h o bi h, con olling o gende , immig an s a us and coho . The igu es plo he es ima ed coe icien s wi h hei con idence in e al Fi s , we eplica e all he analysis using mo e lexible speci ica ions. Mo e speci i- cally, we use dummies o he mon h o bi h, o dummies o he week o bi h. Second, we eplica e he analyses using only s uden s bo n a he beginning o Janua y and a he end o Decembe , who ha e simila obse able cha ac e is ics as shown in Table 4. We compa e he es ima ed coe icien s o an indica o o being bo n in Janua y wi h he es ima ed coe icien s om ou baseline speci ica ions. I he es ima ed e ec s a e spu iously cap u ing unobse ed di e ences be ween child en bo n in di e en pe iods o he yea , we would ind much smalle e ec s when using he subsample o s uden s bo n a ound he cu o da e. I is impo an o ema k ha in his obus ness check we a e compa ing ou comes o s uden s bo n in Janua y o a gi en calenda yea wi h s uden s bo n in Decembe o he same yea . We do no implemen a eg ession discon inui y design, because i would equi e o compa e s uden s bo n in Decembe o a gi en calenda yea wi h s uden s bo n in Janua y o he ollowing calenda yea . Howe e , hose s uden s belong o di e en coho s: hey begin hei educa ion 1 yea apa , and hey ha e di e en eache s, si di e en examina ions, and a e po en ially exposed o di e en educa ional e o ms. These di e ences may bias he es ima ion in unp edic able ways. 5 Main esul s 5.1 Re en ion We s a ou analysis by s udying he e ec o age a en ollmen on p obabili y o being e ained du ing compulso y educa ion. Resul s a e shown in Table 5. Each column shows esul s o a p obi speci ica ion ha ollows Eq. (2). We exploi wo ypes o dependen a iables. Fi s , we use dummy a iables ha ake alue 1 i he s uden has 123 18 SERIEs (2020) 11:1–49 Table 5 G ade epe i ion du ing compulso y educa ion Repea Behind a G ade 1 o 2 G ade 7 o 8 Age 8 Age 12 Age 14 Age a en y −0.637 −0.163 −0.698 −0.597 −0.382 (0.023)** (0.020)** (0.019)** (0.017)** (0.012)** [−0.043] [−0.038] [−0.059] [−0.088] [−0.109] <0.002><0.005><0.002><0.004><0.003> Female −0.123 −0.308 −0.139 −0.143 −0.283 (0.013)** (0.013)** (0.011)** (0.009)** (0.008)** [−0.008] [−0.072] [−0.012] [−0.021] [−0.081] <0.001><0.003><0.001><0.002><0.002> Immig an 0.327 0.226 0.444 0.672 0.523 (0.020)** (0.019)** (0.017)** (0.027)** (0.015)** [0.022] [0.053] [0.037] [0.099] [0.149] <0.001><0.004><0.002><0.006><0.004> Pa en s’ edu a g −0.365 −0.350 −0.328 −0.336 −0.397 (0.016)** (0.015)** (0.014)** (0.018)** (0.011)** [−0.024] [−0.081] [−0.028] [−0.050] [−0.113] <0.001><0.004><0.001><0.003><0.003> Pa en s’ edu high −0.704 −0.854 −0.596 −0.661 −0.899 (0.023)** (0.023)** (0.020)** (0.029)** (0.018)** [−0.047] [−0.199] [−0.050] [−0.098] [−0.256] <0.002><0.006><0.002><0.006><0.005> N163,910 72,079 205,242 188,075 178,871 **p<0.01. Coho FE included. S anda d e o s in i s and second columns (“Repea ...”) a e clus e ed by school. S anda d e o s in he o he h ee columns (“Behind a ...”) a e obus . A e age ma ginal e ec s and hei s anda d e o s a e epo ed in squa ed and angled b acke s, espec i ely been e ained in any o he i s wo g ades o p ima y educa ion ( i s column) and in any o he i s wo g ades o lowe seconda y educa ion (second column). S udying he p obabili y o e en ion in he ollowing g ades would be less in o ma i e, because, as explained in Sec . 2, s uden s can be e ained a mos once du ing p ima y educa ion and a mos wice du ing lowe seconda y educa ion. We exploi only coho s o which we can obse e bo h s uden s who a e behind and s uden s ha a e p og essing a he egula pace up o he second g ade o p ima y o lowe seconda y educa ion. The e o e, he sample o he analysis in he i s column consis s o s uden s bo n om 2002 o 2005, and he sample o he second column consis s o s uden s bo n om 1997 o 1998. Second, we assess he o e all e ec o ma u i y on he p obabili y o being en olled in a lowe g ade han he expec ed one gi en he yea o bi h. Mo e speci ically, we use dummies ha akes alue 1 i he s uden is behind a 8 yea s old (i.e., she is no ye in g ade 3), i he s uden is behind a 12 (i.e., she did no s a seconda y educa ion ye ), and i she is behind a 14 (i.e., she is no ye in g ade 9). Resul s a e shown in 123 SERIEs (2020) 11:1–49 19 he las h ee columns o Table 5. The chosen dummies a e a close p oxy o he e en o ha ing expe ienced e en ion a leas once in he p e ious yea s, wi h he ca ea ha a s uden who s a ed p ima y school la e would be behind e en i she was ne e e ained du ing compulso y educa ion.23 In he analysis, we exploi all obse a ions belonging o s uden s o a gi en age in yea s 2009–2013. Fo ins ance, we use s uden s bo n om 2001 o 2005 o s udy he p obabili y o no ha ing eached g ade 3 a 8 yea s old.24 On a e age, being 1 yea younge inc eases p obabili y o e en ion du ing he i s wo g ades o p ima y school by 4.3 pe cen age poin s, a huge e ec gi en ha he a e age e en ion a e is abou 3%.25 Child en who we e younge when s a ing p ima y school a e also mo e likely o be e ained se e al yea s la e du ing lowe seconda y educa ion. The a e age ma ginal e ec o Aon he p obabili y o being e ained in he i s wo g ades o middle school is −3.8 pe cen age poin s (16.5% o s uden s a e e ained) The emaining columns o Table 5con i m ha younge s uden s a e signi ican ly less likely o p og ess egula ly h oughou compulso y educa ion. Mo e speci ically, he a e age ma ginal e ec o Aon he p obabili y o being behind a 8 yea s old is −5.9 p.p. ( 4.3% o s uden s a e behind). Simila ly, he a e age ma ginal e ec on he p obabili y o being behind a 12 (i.e., a ending p ima y school a he han middle school) is 8.8 p.p. (9.2% o s uden s a e behind), and he one on he p obabili y o being behind a 14 is 10.9 p.p. (24.8% o s uden s a e behind). Mos o hese sizeable e ec s should be a ibu ed o inc eased p obabili y o e en ion du ing compulso y educa ion o younge s uden s. In ac , as discussed in Sec . 3.2, o e all less han 0.9% o s uden s s a p ima y educa ion la e , and he sha e is a mos 2% in Decembe . 5.2 E alua ions We s udy he e ec o age a en ollmen on academic pe o mance, om second g ade (in p ima y educa ion) o en h g ade (in seconda y educa ion). Sec ion 5.2.1 desc ibes he subsamples used and he implemen a ion o he analysis, Sec . 5.2.2 discusses he esul s, and Sec . 5.2.3 es ima es quan ile eg essions o explo e he e ec o age a en y ac oss he dis ibu ion o pe o mance. 5.2.1 Sample selec ion Pe o mance is measu ed by in e nal e alua ions in p ima y educa ion (g ades 2, 4, and 6) and lowe seconda y educa ion (g ades 7 o 10) and ex e nal e alua ions a he end o each s age (g ades 6 and 10). Gi en he limi ed ime span o ou sample, we 23 Ideally, we would di ec ly measu e whe he hey ha e been e ained a any poin in ime du ing he p e ious yea s, bu we would need a longe panel o do so. 24 Resul s do no change i we es ic he sample in he hi d column o da a used in he i s column and he sample o he i h column o he da a used in he second column. 25 The age e ec is signi ican and sizeable, al hough smalle in size, also used as dependen a iable e en ion du ing second and hi d cycles o p ima y school. E en i child en bo n in he las mon hs o he yea a e o e ep esen ed among hose e ained in he i s cycle, i is s ill mo e likely o younge child en o be e ained h oughou p ima y school. 123 20 SERIEs (2020) 11:1–49 canno ollow he same pool o s uden s h oughou compulso y educa ion, bu we a he use di e en coho s o s uden s o es ima e he ma u i y e ec α o a gi en g ade .26 Whenanalyzing in e nal and ex e nale alua ions ing ade 10,a p oblemo selec ion a ises: child en aged 16 can d op ou o school wi hou comple ing lowe seconda y educa ion. Gi en he e en ion ules discussed in he p e ious sec ion, all child en conclude a leas g ade 8, bu hey may d op ou be o e concluding g ade 10 o e en g ade 9. This means ha he sample o s uden s o which we can obse e e alua ions in he wo las yea s o middle school is no ully ep esen a i e o he ini ial popula ion o child en. This selec ion issue is discussed ex ensi ely in Sec . 5.3, whe e we analyze he e ec o ma u i y on d opou . We include ou esul s o g ades 9 and 10 in he analysis discussed he ea e , in o de o p o ide some illus a i e e idence o he long-las ing e ec o ma u i y on pe o mance, bu we acknowledge ha we canno exclude ei he posi i e o nega i e biases due o selec ion. The subsample used o each eg ession includes only coho s o which we can obse e (a leas ) s uden s wi h a egula p og ession o 1 yea behind in p ima y educa ion and up o 2 yea s behind in seconda y educa ion. The e o e, we use ou coho s o s uden s o s udy pe o mance in p ima y educa ion and h ee coho s o lowe seconda y educa ion. Fo ins ance, when we s udy ou comes in second g ade o p ima y school, we use s uden s bo n om 2002 o 2005, while we do no include hose who we e bo n in 2001 (we would obse e only s uden s who a e one o mo e yea behind, bu no hose wi h a egula p og ession) o bo n in 2006 (we would obse e only s uden s in a egula p og ession, bu no hose e ained he yea be o e).27 This choice is aligned wi h he egula ion o en ollmen and p og ession in p ima y and seconda y school: s uden s can be e ained a mos once du ing he en i e cycle o p ima y school and a mos wice in seconda y school. The egion-wide es in g ade 10 was in oduced in he school yea 2011/2012; he e o e, we use only he coho o s uden s bo n in 1996 when ex e nal e alua ions in lowe seconda y educa ion a e used as dependen a iable. Mo eo e , when a s uden unde akes he same g ade wice, only he mos ecen e alua ion is included in he analysis. Conside , o ins ance, a s uden who a ended g ade2 in he yea 2010was e ainedand epea ed he same g ade in 2011, being inally p omo ed. The e alua ion ob ained in 2011 is included, while he o he is disca ded. This app oach ensu es ha we use he e alua ion ha he s uden ob ained when she is admi ed o he ollowing g ade.28 26 As a obus ness check, we es ic he es ima ion o s uden s ha we obse e in wo consecu i e le els; o ins ance, o hose bo n in 2003 o 2004, we ha e e alua ions bo h in g ade 2 and in g ade 4. We can hen pe o m he ele an eg essions only on his subsample and compa e he esul s wi h hose ob ained wi h he gene al speci ica ion. This simple obus ness check always con i ms he alidi y o ou app oach. Resul s a e a ailable upon eques s. 27 While o he oldes coho s, we can obse e also s uden s who a e mo e han 1 yea behind, his is no possible o 2005 coho s. Gi en ha he numbe o s uden s who a e wo o mo e yea behind o 1 yea in ad ance is negligible, we igno e his di e ence. Fu he educing he sample lea es he es ima es unchanged. 28 When he inal obse a ion coincides wi h s uden ’s las yea in he sample, we do no ha e di ec e idence ha he s uden was p omo ed; howe e , gi en he choice o he sample, he egula ion ensu es ha he s uden has o be p omo ed, excep o e y special cases. As a obus ness check (no shown), 123 SERIEs (2020) 11:1–49 21 Being e ained a ec s pe o mance bo h in he g ade epea ed wice and in he ollowing pe iods.In ac , e ained s uden s ha eanaddi ionalyea olea n hema e ial co e ed in a gi en g ade, and hey a e also 1 yea olde when hey e ake cou ses and examina ions.Fo ins ance, abou 85% o s uden s imp o e hei GPA when hey e ake a g ade in p ima y school. Mo eo e , s uden s who epea ed g ade a e olde when hey en oll in g ade +1 and, i e en ion is e ec i e, hey ha e a be e s ock o human capi al han o he wise iden ical pee s who did no epea g ade .Asshown in Sec . 5.1, younge s uden s a e mo e likely o be e ained, and hus, e en ion may con ibu e o closing he gap due o he day o bi h. In his case, α in Eq. (1) is smalle han wha would be ound in an ins i u ional se ing wi hou e en ion. Al hough such coe icien s cap u e a combina ion o he e ec o ma u i y on pe o mance and on p obabili y o being e ained, esul s a e s ill in o ma i e abou he o e all e ec o he age a en ollmen in p ima y school on he sequence o s uden s’ e alua ions in a sys em ha allows g ade epe i ion. P ecisely because ou p ima y in e es is o unde s and he longe e m conse- quenceso heini ialma u i y gap,in ou baselinespeci ica ionweuse he las a ailable ou come o e ained child en. Tha is, i a child has been e ained in six h g ade, we analyze he e alua ions he second ime she akes he examina ions in six h g ade. We also eplica e he analysis using e alua ions he i s ime s uden s ake he examina- ions. Compa ison o he esul s gi es us a sense o how much e en ion helps close he gap be ween olde and younge s uden s in a gi en g ade. 5.2.2 Resul s and al e na i e speci ica ions Each column o Table 6(panel A) con ains he es ima ed coe icien s o a eg ession o a measu e o pe o mance on age A, indi idual cha ac e is ics, and coho ixed e ec s, as in Eq. (1). Fo compa ison, panel B epo s esul s o a uni a ia e eg ession o each dependen a iable on A. Table 6p o ides compelling e idence ha ma u i y is a e y impo an de e minan o s uden s’ pe o mance a he beginning o hei school ca ee : ce e is pa ibus being bo n a he beginning o Janua y a he han a he end o Decembe inc eases he GPA by 0.57 s anda d de ia ions. This e ec is much la ge han bo h he gende gap and he na i e-immig an gap. I is jus sligh ly smalle han he e ec o ha ing pa en s wi h e ia y educa ion a he han wi h basic educa ion. The age e ec is highly pe sis en o e ime, al hough dec easing in magni ude: i is 0.41 s anda d de ia ions in g ade 4 and 0.33 s.d. in he las g ade o p ima y educa ion, while du ing lowe seconda y educa ion being 1 yea olde is s ill associa ed wi h abou 0.2 s anda d de ia ions inc ease in he GPA. Al hough he wo s pe o ming s uden s, who (as we showed) a e disp opo iona ely bo n in he las mon hs o he yea s, may ha e d opped ou be o e eaching he ou h g ade, age e ec is s ill signi ican a 1% le el in g ade 10. we pe o med he same se o analysis exploi ing one less coho and imposing he u he es ic ion ha s uden s a e included in he sample only i we can obse e hem in a highe g ade he ollowing yea . Resul s we e comple ely equi alen o hose discussed below. 123 22 SERIEs (2020) 11:1–49 Table 6 E alua ions in p ima y and lowe seconda y educa ion G ade 2 G ade 4 G ade 6 G ade 7 G ade 8 G ade 9 G ade 10 (in .) (ex .) (in .) (ex .) Panel A Age a en y 0.574 0.407 0.329 0.351 0.220 0.175 0.153 0.137 0.219 (0.008)** (0.008)** (0.009)** (0.009)** (0.010)** (0.010)** (0.010)** (0.011)** (0.021)** Female 0.170 0.218 0.293 0.134 0.339 0.338 0.339 0.324 0.071 (0.005)** (0.005)** (0.005)** (0.006)** (0.007)** (0.007)** (0.008)** (0.008)** (0.013)** Immig an −0.204 −0.222 −0.227 −0.414 −0.243 −0.225 −0.248 −0.305 −0.742 (0.011)** (0.011)** (0.011)** (0.014)** (0.014)** (0.014)** (0.013)** (0.013)** (0.025)** Pa en s’ edu a g 0.326 0.348 0.342 0.435 0.324 0.305 0.258 0.188 0.401 (0.006)** (0.007)** (0.007)** (0.010)** (0.008)** (0.009)** (0.009)** (0.008)** (0.016)** Pa en s’ edu high 0.621 0.670 0.679 0.837 0.681 0.661 0.591 0.492 0.854 (0.008)** (0.008)** (0.009)** (0.012)** (0.012)** (0.012)** (0.011)** (0.012)** (0.020)** R20.12 0.12 0.12 0.16 0.13 0.12 0.11 0.09 0.21 N160,438 148,472 136,281 117,752 106,707 102,960 96,170 86,025 24,465 Panel B Age a en y 0.583 0.412 0.334 0.350 0.220 0.170 0.154 0.144 0.226 (0.009)** (0.009)** (0.009)** (0.010)** (0.010)** (0.010)** (0.011)** (0.012)** (0.023)** **p<0.01. In panel A, coho FE a e included and s anda d e o s clus e ed by school. In panel B, s anda d e o s a e obus 123 SERIEs (2020) 11:1–49 23 Columns (ex .) con i m ha esul s a e no d i en by he pa icula e alua ion p o- cedu e used in schools. The es ima ed e ec is simila and i any hing sligh ly la ge using he es sco es ob ained by he s uden s in hei ex e nal e alua ions. A compa ison o he es ima ed coe icien s in panel A wi h hose in panel B sugges s ha he age e ec is o hogonal o socioeconomics. In ac , he es ima es a e almos unchanged when addi ional eg esso s a e in oduced. In a c oss-coun y analysis ha exploi s TIMSS and ECLS es sco es, Beda d and Dhuey (2006) ind ha he e ec o being bo n in Janua y a he han in Decembe anges om 0.12 o 0.35 s anda d de ia ions in g ade 4 and om 0.08 o 0.26 s anda d de ia ions in g ade 8. Ou esul s sugges ha he age a en y e ec o Ca alonia is among he highes in he wo ld. We eplica e he analysis in Table 6sepa a ely by subjec s, i.e., using as dependen a iable he es sco e in Ma hema ics, Spanish, Ca alan, o English. Resul s using he subjec s a he han hei GPA mimic he p e ious inding. Table 12 in Appendix C shows esul s o in e nal e alua ions in g ades 2, 6, and 7.29 We augmen he speci ica ion o each g ade wi h pee cha ac e is ics, including a e age age. We ocus on p ima y educa ion, because some middle schools may so child en ac oss classes based on hei pe o mance.30 Resul s a e shown in Table 13. Pee s’ a e age age, he sha e o highly educa ed pa en s, and he sha e o emales a ec nega i ely he in e nal e alua ions, while hey ha e a posi i e e ec s on ex e nal e alua ions in g ade 6.31 To he ex en ha olde s uden s, s uden s wi h high SES, and gi ls do be e in school, hese esul s a e cohe en wi h inding in Calsamiglia and Lo iglio (2018), who show ha being wi h be e pe o ming pee s ha ms nonblind e alua ions assigned by eache s. Mo e impo an ly, o he pu pose o his pape , coe icien s o own eg esso s a e i ually una ec ed by he in oduc ion o he new eg esso s, con i ming he obus ness o he baseline speci ica ion. Finally, we eplica e he analysis using e alua ions he i s ime s uden s ake he examina ions. Resul s, epo ed in Table 14, a e qui e simila o hose in Table 6. No su p isingly, he es ima ed  α a e sligh ly la ge in magni ude, bu he inc ease is always smalle han 4% o he baseline es ima e. Fo ins ance, he es ima ed age e ec in g ade 2 is 0.59 a he han 0.57 and in g ade 8 i is 0.23 a he han 0.22. The ac ha he e ec o ma u i y on school ou comes dec eases o e ime suppo s he hypo hesis ha younge child en c ea e a lowe s ock o human capi al in he ea lie s age o hei academic ca ee , bu la e on hey do no cumula e human capi al a a lowe a e o a gi en le el o human capi al om he p e ious pe iod. Howe e , he ini ial disad an age is so la ge ha he nega i e e ec s p opaga e o e ime and he gap is no closed a he end o lowe seconda y educa ion. 29 In he in e es o space, we do no epo esul s o o he g ades. They a e a ailable upon eques s. 30 See Calsamiglia and Lo iglio (2018) o a mo e de ailed discussion o child en’s alloca ion o classes in p ima y and middle schools in Ca alonia. We also eplica e he analysis using pee s a he school-yea le el, a he han a he class le el, o bo h p ima y and seconda y educa ion, inding e y simila esul s. 31 Coe icien s a e always signi ican bu he magni ude o he e ec s is ela i ely small compa ed wi h he e ec o own cha ac e is ics. In ac , a ia ion in pee s’ cha ac e is ics is ela i ely small wi hin school. Fo ins ance, an inc ease o 0.1 in pee s’ age a en y (which is much la ge han one s anda d de ia ion) would dec ease he GPA in second g ade by 0.05 s.d., abou one- hi d o he e ec o inc easing indi idual age by 3 mon hs (i.e., abou one s anda d de ia ion in expec ed age). 123 24 SERIEs (2020) 11:1–49 0.2 .4 .6 .8 E ec o age a en ollmen on GPA 2 3 4 5 6 7 8 9 10 G ade 25 pe cen ile 75 pe cen ile Quan ile eg ession Fig. 5 E ec o age a en ollmen on GPA o e ime. The g aph plo s he esul s o quan ile eg essions o GPA (in e nal e alua ions) on age a en ollmen a he 0.25 and 0.75 quan ile o e school g ades. Each blue do is he es ima ed ma ginal e ec o age a en ollmen Aa he 0.25 quan ile in a gi en g ade. Each ed diamond is he es ima ed ma ginal e ec o Aa he 0.75 quan ile. G ay ba s a e 95% con idence in e als (colo igu e online) Acon as ingexplana ionis ha he di ec e ec o ma u i y is s illla geinad anced g ades, bu he dec easing sequence o es ima ed coe icien s is due o he highe numbe o younge kids who epea ed a g ade, pa ially closing he gap. While we canno di ec ly es he wo al e na i e explana ions, he la e appea s unlikely o a numbe o easons. Fi s , we obse e a clea dec ease o  α also du ing p ima y school, when he e en ion a e is ela i ely low. Second, as jus discussed, he imp o emen in e alua ions due o e en ion in a gi en g ade ma e s li le o he es ima es. Thi d, a la gesha eo s uden spe o m well enough obebasicallyuna ec edby hepossibili y o e en ion. In he nex subsec ion, we pe o m quan ile analysis o in es iga e he age e ec a di e en poin s o he dis ibu ion o e alua ions. The same e olu ion o he age e ec o e ime is ound o all he quan iles. 5.2.3 Quan ile analysis We pe o m quan ile eg essions o s udy how he e ec o age a en ollmen changes along he dis ibu ion o e alua ions. We eg ess e alua ions om g ade 2 o g ade 10 on age a en ollmen Aand he o he co a ia es a a ious quan iles. Resul s a e shown in Table 15. Figu e 5plo s he es ima ed coe icien s o he e ec o age a en ollmen on in e nal e alua ions a he 25 pe cen ile and 75 pe cen ile. The e olu ion o he age e ec o e ime is ema kably simila o he lowe ail and he uppe ail o he e alua ions. As al eady obse ed o he linea eg ession model, he age e ec is e y la ge in g ade 2, and i slowly dec eases in he ollowing g ade, being s ill sizeable and signi ican a he end o lowe seconda y educa ion. This pa e n is simila a o he quan iles, as shown in Table 15. Fo each g ade and ype o e alua ions, he age e ec is sizeable and signi ican h oughou he en i e dis ibu ion. This is an impo an con i ma ion ha we should be conce ned abou he nega i e e ec o being younge a he ime o en ollmen o all child en, no only o hose who exhibi pa icula cha ac e is ics. 123 SERIEs (2020) 11:1–49 31 0.2 .4 .6 Es ima ed coe icien 1 6 11 16 21 26 31 36 41 46 51 Week o bi h GPA g ade 2 −.8 −.6 −.4 −.2 0 Es ima ed coe icien 1 6 11 16 21 26 31 36 41 46 51 Week o bi h Repea g ade 1 o 2 0.1 .2 .3 .4 Es ima ed coe icien 1 6 11 16 21 26 31 36 41 46 51 Week o bi h GPA g ade 6 −.1 0.1 .2 .3 Es ima ed coe icien 1 6 11 16 21 26 31 36 41 46 51 Week o bi h GPA g ade 7 −.4 −.2 0.2 Es ima ed coe icien 1 6 11 16 21 26 31 36 41 46 51 Week o bi h Behind a 14 −.4 −.2 0.2 Es ima ed coe icien 1 6 11 16 21 26 31 36 41 46 51 Week o bi h En oll Academic Fig. 7 Es ima ed e ec o week o bi h on educa ional ou comes. The igu es plo he es ima ed coe icien s o week o bi h dummies and hei con idence in e al. Week 52 is he baseline ca ego y 6.2 Analyses es ic ed o he subsample o s uden s bo n a ound he cu o We eplica e he analysis in Sec . 5using only s uden s bo n in he ini ial 15 days o Janua y and in he las 15 days o Decembe (16 o lap yea s). Fo ins ance, we eg ess Y i, he e alua ions in g ade , on a dummy oldiand he usual co a ia es: Y i=α oldoldi+Xiγ + i,(7) 123 32 SERIEs (2020) 11:1–49 whe e oldi akes alue 1 i he s uden is bo n in Janua y. α old is he expec ed di e ence in e alua ions in g ade Tbe ween s uden s bo n a he beginning and a he end o he yea . Resul s o he analyses on he much smalle sample o s uden s bo n a ound he cu o da e a e qui e aligned wi h he esul s discussed in Sec . 5.40 Mo e speci ically, he es ima ed e ec s on e alua ions a e qui e close o hose ound o he en i e sample. Fo ins ance, α2=0.574, while α2 old =0.531. The a e age ma ginal e ec s on he p obabili y o being e ained o being behind a e he same o sligh ly la ge in mag- ni ude. The ma ginal e ec s on he p obabili y o ecei ing a special needs diagnosis a e also e y simila o hose ound o he en i e sample (e.g., 1.5 pe cen age poin s in p ima y school). Es ima ed ma ginal e ec s on he p obabili ies o g adua ing and pu suing u he s udies a e close enough. The a e age ma ginal e ec on g adua ion is 3.5 pe cen age poin s (2 p.p. using he ull sample), while he a e age ma ginal e ec on en ollmen in academic uppe seconda y educa ion is 4.1 pe cen age poin s (5.6 p.p. o he ull sample). The es ima ed ma ginal e ec on en ollmen in oca ional educa ion is −1 pe cen age poin bu i is no signi ican (i is −3.3 p.p. in he ull sample). As explained in Sec . 5.3, hose analyses a e pe o med using only one coho o s uden s, hose bo n in 1995; he e o e, he sample size is ela i ely small. This may explain why he es ima es a e less p ecise han he ones discussed abo e. 7 He e ogenei y analysis We s udy whe he he e ec o age a en y is he e ogeneous ac oss subg oups o he popula ion. We augmen he speci ica ions es ima ed in Sec . 5wi h in e ac ion e ms be ween age a en y and pa en al educa ion, gende , immig an s a us. 7.1 Re en ion and e alua ions As shown in Table 18, he e ec o age on g ade epe i ion o on he e en o being behind does no exhibi signi ican di e ence by pa en s’ ype. Howe e , as epo ed in Table 9, he ma ginal e ec s o age a en y on e en ion p obabili y a e dec easing in pa en al educa ion. Fo ins ance, being 1 yea younge inc eases he p obabili y o being behind a age 14 o abou 13 pe cen age poin s o s uden s wi h low educa ed pa en s, while he inc eases o s uden s wi h highly educa ed pa en s a e only 6 pe cen age poin s. This is no su p ising, gi en he la ge e ec ha pa en al educa ion has on he ou come: in he p obi model, any change a ec s mo e hose whose la en a iable is close o 0, i.e., whose p obabili y is close o 50%. Fo ins ance, 34% o s uden s wi h low educa ed pa en s a e behind a 14 yea s old and hose sha es a e 18% and 8% o s uden s wi h a e age and highly educa ed pa en s, espec i ely. Columns (1) and (2) o Table 9con i m ha he es ima ed ma ginal e ec s a e almos iden ical 40 Table 17 shows he es ima ed coe icien s and ma ginal e ec s o a subse o ou comes: GPA (in e nal e alua ions) in g ades 2, 6, and 7, e en ion in he i s wo g ades o p ima y school, being behind a 14 yea s old, en ollmen in high school. Resul s o he emaining speci ica ions a e a ailable upon eques . 123 SERIEs (2020) 11:1–49 33 Table 9 Ma ginal e ec s o age a en y by pa en s’ educa ion Repea g ade 1 o 2 Behind a 14 G adua e En oll Academic (1) (2) (1) (2) (1) (2) (1) (2) Pa en s’ edu. low −0.066 −0.065 −0.134 −0.131 0.024 0.014 0.058 0.041 (0.003)** (0.004)** (0.004)** (0.006)** (0.010)* (0.012) (0.009)** (0.013)** Pa en s’ edu. a g −0.035 −0.038 −0.106 −0.113 0.020 0.044 0.061 0.096 (0.002)** (0.003)** (0.003)** (0.006)** (0.008)* (0.014)** (0.009)** (0.015)** Pa en s’ edu. high −0.017 −0.017 −0.064 −0.060 0.014 −0.003 0.048 0.024 (0.001)** (0.002)** (0.002)** (0.006)** (0.006)* (0.015) (0.007)** (0.019) All −0.043 −0.043 −0.109 −0.109 0.020 0.021 0.056 0.057 (0.002)** (0.002)** (0.003)** (0.003)** (0.008)* (0.008)* (0.009)** (0.008)** *p<0.05; **p<0.01. The able plo s he a e age ma ginal e ec s o age a en y when pa en s’ educa ion is se o be low, a e age, o high, and he o e all a e age ma ginal e ec s ( ow “All”). Columns (1) use he baseline speci ica ions es ima ed in Table 5( o dependen a iables “Repea g ade 1 o 2” and “Behind a 14”) and Table 7( o dependen a iables “G adua e” and “En oll Academic”). Columns (2) use he speci ica ions augmen ed wi h in e ac ion e ms in Table 18 ( o dependen a iables “Repea g ade 1 o 2” and “Behind a 14”) and Table 19 ( o dependen a iables “G adua e” and “En oll Academic”) 123 34 SERIEs (2020) 11:1–49 o he baseline model and he model wi h in e ac ions.41 In p ima y educa ion, he es ima ed age e ec on in e nal e alua ions is sligh ly la ge o s uden s whose pa en s ha e an a e age le el o educa ion. As shown in Table 18, he di e ence is signi ican in g ade 2 and 4, bu i is small in size (e.g., i is 0.05 s.d. in g ade 2, when he e ec o being 1 yea olde is 0.54 o s uden s wi h low educa ed pa en s). The e a e no di e ences be ween s uden s wi h low- and high-educa ed pa en s. Con e sely, in lowe seconda y educa ion, he age e ec is abou 0.07 s.d. la ge o s uden s wi h high educa ed pa en s, while i is no signi ican ly di e en o hose wi h a e age educa ion le el. On he o he hand, esul s using ex e nal e alua ions in g ade 6 show ha age a ec s sligh ly less he pe o mance o s uden s wi h highly educa ed pa en s.42 The age e ec is also simila o boys and gi ls. The e ec on e en ion is sligh ly smalle in size o emale s uden s du ing p ima y educa ion, while he e is no sig- ni ican di e ence in seconda y educa ion. The ma ginal e ec s a e smalle o gi ls, who on a e age a e less likely o expe ience e en ion. When e alua ions a e used as ou come, he es ima ed coe icien s o he in e ac ion e m a e posi i e bu small in size, and only signi ican in lowe seconda y educa ion. O e all, he di e ences in he age e ec on e en ion and e alua ions by pa en al educa ion o gende a e small, i any. The age a en y has la ge impac on educa- ional ou comes h oughou compulso y educa ion o bo h s uden s wi h high and low socioeconomic s a us (SES), and o bo h boys and gi ls. This inding con as s wi h Elde and Lubo sky (2009), who ind ha in USA he e ec is inc easing in child en’s SES.43 One possible explana ion comes om he di e ences in p eschool sys ems in Spain and USA. P eschool quali y is qui e he - e ogeneous in USA, and a subs an ial ac ion o child en do no a end p eschool egula ly. Pa en al con ibu ion is he e o e undamen al o de e mine he human cap- i al le el o he child a he beginning o o mal educa ion. Younge child en s a school ha ing spen less ime wi h hei pa en s, and ce e is pa ibus he gap is la ge among high SES, gi en ha hey ha e o egone mo e pa en al inpu s when s a ing school. Con e sely, in Spain almos e e y child is en olled in p eschool, o which he e is ee and uni e sal access s a ing in he yea in which he child u ns 3. E en i he gap ha we obse e in p ima y school may be e en la ge in p eschool, he quali y o he ime spen ou o school be o e age 6 depends less on hei SES.44 41 Ou ma ginal e ec s a e close enough o he es ima es in Be niell and Es ada (2017). They use Spanish da a om PISA es s and es ima e a linea p obabili y model o show ha , among low SES, s uden s who a e bo n in Decembe a e 12.7 p.p. mo e likely o expe ience e en ion du ing compulso y educa ion, while among high SES he gap dec eases o 4 p.p. Howe e , we hink ha his di e ence alone is no e idence o high SES in es ing mo e in hei child en i hey a e younge . In ac , as discussed, i can be obse ed also i high SES in es he same in child en bo n in Decembe and in child en bo n in Janua y, bu hey a e on a e age mo e likely o ha e high-pe o ming o sp ing. 42 The e a e no signi ican di e ences ac oss he h ee ca ego ies o pa en al educa ion when ex e nal e alua ions in g ade 10 a e used. Howe e , as explained in Sec . 5.2.1, s uden s sel -selec in o a ending he las g ade and he e o e in aking he es . This can be a pa icula ly ele an issue o he he e ogenei y analysis because s uden s wi h di e en pa en al backg ounds ha e di e en p opensi y o d op ou . We do no epo esul s o g ades 9 and 10 in he able. 43 Acco ding o hei esul s, he age e ec on es sco es is mo e han double o high SES han o low SES h oughou p ima y educa ion. 44 Younge child en om high SES may o egone mo e inpu s be o e he en ollmen in p eschool. Howe e , hose inpu s may ma e less o hei pe o mance in school. 123 SERIEs (2020) 11:1–49 35 As shown in Table 18, he age e ec on e alua ions is signi ican ly lowe o immi- g an s uden s. The gap is la ge in mo e ad anced g ades.45 A plausible explana ion o his esul is ha many non-Spanish s uden s a e ecen immig an s. They may ha e expe ienced a di e en educa ional sys em o he i s pa o hei educa ion, wi h di e en cu o da es o simply mo e lexibili y, and he e o e hey may be less a ec ed by ou measu e o ma u i y a en ollmen . Al hough his is a specula ion we canno di ec ly es , i is suppo ed by he e idence ha he di e ence widens in mo e ad anced g ades, whe e ecen immig an s ha e been exposed o ela i ely mo e educa ion ab oad han in Spain. 7.2 O he ou comes Table 19 eplica es he analysis in Sec s. 5.3 and 5.4, including he in e ac ion e ms in he speci ica ion. Resul s poin o a la ge e ec o age a en y on d opou and en ollmen in high school o s uden s in he middle ca ego y o pa en al educa ion. Con e sely, he e a e no signi ican di e ences be ween s uden s wi h low- and high- educa ed pa en s. Fo g adua ion, he es ima ed e ec on he la en a iable is almos double o s uden s whose pa en s ha e a e age le el o educa ion. Fo his ca ego y, he es ima ed ma ginal e ec on he p obabili y o g adua ion is 4.4 pe cen age poin s, while i is 2 p.p. using he baseline model (Table 9). The coe icien o he in e ac ion be ween age and he dummy o he middle ca ego y is also la ge and signi ican o he en ollmen in u he academic educa ion. The es ima ed ma ginal e ec is 9.6 pe cen age poin , while i is 6 pe cen age poin using he baseline speci ica ion. Simila ly, he e is a signi ican and sizable nega i e e ec on en ollmen in oca ional aining. Comple ing lowe seconda y educa ion and en olling in high school a e by a la ge ex en a choice o he s uden and his o he amily.46 Ou indings a e compa ible wi h he hypo hesis ha amily wi h a e age SES a e mo e esponsi e o he le el o skills o hei child en when aking educa ional decisions. Fo ins ance, his would be he case i high SES always push hei child en o acqui e mo e academic educa ion, e en i hey a e no pe o ming well in school, while low SES do no push hem enough, e en i hey ha e he po en ial o succeed. As discussed in he p e ious sec ion, age a en y a ec s simila ly pe o mance o gi ls and boys. Howe e , esul s in Table 19 sugges ha age ma e s much mo e o boys han o gi ls o g adua ion and en ollmen in academic uppe seconda y educa ion. In ac , we canno ejec he null hypo heses ha age a en y does no a ec emale g adua ion and en ollmen .47 One possible eason o his esul s is ha emales a e less esponsi e o hei le el o skills when choosing whe he o d op ou o o en oll in u he educa ion. 45 Wald es s ejec he null hypo heses ha he e ec is 0 o immig an s om g ade 2 o g ade 7. The null hypo hesis canno be ejec ed in g ade 8. 46 Condi ionaloncomple ion o lowe seconda yeduca ion,en ollmen inhigh schoolis eeand gua an eed o all applican s. 47 We es whe he he sum o he coe icien s o “Age” and “Age X emale” is 0. The p alues a e 0.71 o g adua ion and 0.14 o en ollmen in high school. 123 36 SERIEs (2020) 11:1–49 Resul s in he las wo columns o Table 19 con i m ha being younge inc eases he p obabili y o being diagnosed wi h lea ning disabili ies o all ypes o child en. A he beginning o p ima y school, he es ima ed age e ec is smalle o s uden s wi h highly educa ed pa en s and i is la ge o s uden s whose pa en s ha e a e age educa ional le el. Howe e , hey a e he same in mo e ad anced g ades. 8 Conclusions Schoolsa ound he wo lda e o ganizedby coho s; ha is, child en bo n in a gi enyea a e mixed in a class oom independen ly o hei ma u i y o abili y le el. This induces an ini ial he e ogenei y wi hin he class ha may a ec indi idual de elopmen in he long un. This pape exploi s an exogenous sou ce o he e ogenei y, i.e., he s uden day o bi h, o show ha an in lexible sys em ha allows o no pos poning o he en ance in p ima y school may lead o long-las ing consequences o he ma u i y e ec s. We use adminis a i e da a om he uni e se o public schools in Ca alonia o con i m he pe sis ence o he disad an age o younge child en o e ime. The e ec no only leads o wo se pe o mance o e ime, bu o hei choices as o whe he o con inue hei educa ion and wha ca ee o pu sue o be signi ican ly di e en . Al hough younge s uden s a e mo e likely o expe ience g ade epe i ion, his does no seem o con ibu e much o close he gap, while i migh nega i ely a ec hei p obabili y o pu suing u he educa ion, gi en ha hey lag behind hei pee s when hey u n 16.48 Mo eo e , age a en y nega i ely a ec s also child en ha a e doing well in school, meaning ha a high achie e bo n in Decembe would ha e pe o med e en be e i she we e bo n in Janua y. The ac ha he e ec is dec easing o e ime sugges s ha younge s uden s ini ially c ea e a lowe s ock o human capi al and his nega i ely a ec s hei human capi al accumula ion h oughou compulso y educa ion. The e o e, ea ly in e en ions a e likely o be he mos e ec i e. On he one hand, o e ing addi ional suppo o ex a school ime o less ma u e child en may help educe he ini ial he e ogenei y, allowing o a be e p og ession o e ime. On he o he hand, i appea s desi able o ha e a lexible sys em in which eadiness o school is assessed and school en ance can be pos poned i deemed app op ia e. Howe e , in e en ions ha inc ease lexibili y may ha e unin ended consequences i s uden s who pos pone he en ollmen a e allowed o d op ou a e spending less ime in educa ion. Thus, policymake s should also conside adjus ing he ules o manda- o y schooling o a oid hose unin ended in e ac ions be ween pos poned en ollmen and he d opping-ou decisions. In pa icula ,in Spain educa ioncould be made manda- o y un il s uden s comple e lowe seconda y educa ion. Al e na i ely, he cu en obliga ion o s aying in school un il a gi en age could be eplaced wi h he equi e- men o unde aking a leas a gi en numbe o yea s o basic educa ion. 48 Lo iglio (2019) inds ha in Ba celona epea ing a g ade imp o es s uden s’ cogni i e skills bu nega- i ely a ec s hei consump ion alue o schooling. The second e ec is p e alen , and he e o e, e ained s uden s a e less likely o comple e lowe seconda y educa ion and en oll in academic uppe seconda y educa ion. 123 SERIEs (2020) 11:1–49 37 Finally, i is undamen al o in ol e eache s and school adminis a o s and p o ide hem wi h mo e in o ma ion abou he p oblem. In pa icula , we ind ha younge child en a e mo e likely o be labeled as “special needs” s uden s. This sugges s ha i is impo an o aise he awa eness o he school pe sonnel, so ha hey ou inely ake in accoun hei age a en y when assessing child en du ing he ini ial g ades o p ima y educa ion. Compliance wi h e hical s anda ds Con lic o in e es The au ho s decla e ha hey ha e no con lic o in e es . E hical app o al This a icle does no con ain any s udies wi h human pa icipan s o animals pe o med by any o he au ho s. In o med consen Bo h au ho s o his pape ag ee wi h he submission o he pape o he Jou nal o he Spanish Economic Associa ion (SERIEs). The au ho s decla e no e hical issues o issues needing in o med consen . Open Access This a icle is dis ibu ed unde he e ms o he C ea i e Commons A ibu ion 4.0 In e na- ional License (h p://c ea i ecommons.o g/licenses/by/4.0/), which pe mi s un es ic ed use, dis ibu ion, and ep oduc ion in any medium, p o ided you gi e app op ia e c edi o he o iginal au ho (s) and he sou ce, p o ide a link o he C ea i e Commons license, and indica e i changes we e made. Appendix A: Two-s age leas squa e eg essions As explained in Sec . 5, we do no obse e he i s en ollmen in p ima y educa ion o mos o he s uden s in ou sample. The e o e, we in e he en ollmen yea om he da e o bi h. Howe e , a subse o s uden s ( hose bo n be ween 2003 and 2005) is obse ed bo h when hey begin p ima y school and when hey a e e alua ed a he end o hei second yea . We exploi his subse o child en o compa e wo-s age leas squa e es ima es wi h ou educed- o m app oach. Using he same no a ion o Sec . 5, and calling OAi he obse ed age a en ollmen o indi idual i, he app op ia e speci ica ion o e alua ions Yias linea unc ion o OAiand o he co a ia es Xiis: Yi=aOAi+Xib+ui,co (ui,OAi)= 0(A-1) OAi=γAi+Xiδ+ i,co ( i,Ai)=0,co (ui,Ai)=0(A-2) The wo-s age leas -squa es es ima ion es ima es i s γand  δin Eq. (A-2) and hen eplaces OAiin Eq. (A-1) wi h OAi=γAi+Xi δ. Gi en ha  Aiis unco ela ed wi h he e o (ui+ i), his makes possible a consis en es ima ion o a. The educed- o m app oach consis s in eplacing age in Eq. (A-1) wi h he RHS o Eq. (A-2): Yi=aγAi+Xi(b+aδ) +α i+ui(A-3) =αAi+Xiβ+i,co (i,Ai)=0(A-4) 123 38 SERIEs (2020) 11:1–49 Table 10 E alua ions and g ade epe i ion: ins umen al a iable app oach E alua ions Repea g ade 1 o 2 Fi s s age (RF) (2SLS) (RF) (2SLS) (2SLS) Age a en y (expec ed) 0.570 −0.040 0.988 (0.009)** (0.003)** (0.001)** Age a en y (obse ed) 0.577 −0.041 (0.010)** (0.003)** Female 0.161 0.163 −0.011 −0.011 −0.003 (0.006)** (0.006)** (0.001)** (0.001)** (0.000)** Immig an −0.162 −0.165 0.027 0.027 0.005 (0.013)** (0.013)** (0.003)** (0.003)** (0.001)** Pa en s’ edu a g 0.330 0.331 −0.028 −0.028 −0.002 (0.008)** (0.008)** (0.002)** (0.002)** (0.001)** Pa en s’ edu high 0.628 0.630 −0.039 −0.039 −0.004 (0.009)** (0.009)** (0.002)** (0.002)** (0.001)** N111,548 111,548 65,987 65,987 111,548 **p<0.01. In columns (2SLS), he obse ed en ollmen age OAiis ins umen ed wi h he expec ed age Ai α=aγcan be consis en ly es ima ed, bu in gene al i is di e en om ai γ= 1. In ou case, howe e , γis eally close o 1, because OAi=Ai o 99% o s uden s. The e o e, we can expec α o deli e a good app oxima ion o a, e en i sligh ly smalle . The in ui ion is con i med by esul s in Table 10. The i s wo columns o he able compa e es ima ed coe icien s o he eg ession o e alua ions in g ade 2 on age a en y and co a ia es. Column (RF) eplica es he i s column o Table 6using he subsample o s uden s bo n om 2003 o 2005. In column (2SLS), he obse ed age a en ollmen OAiis ins umen ed wi h he expec ed age Ai. The es ima ed e ec o age a en y is almos he same using he wo app oaches: i is 0.57 wi h he educed- o m es ima ion and 0.58 wi h he wo-s age using ins umen al a iable app oach. The hi d and ou h columns compa e esul s o g ade epe i ion in he i s wo g ades o p ima y educa ion, using he subsample o s uden s bo n in 2003 and 2004. Again, he es ima ed e ec is almos he same (−4 p.p. and −4.1 p.p., espec i ely). To conclude, we can ega d he es ima ions ob ained by educed o m as a lowe bound o he ue e ec . Appendix B: P i a e schools Some o he analyses discussed in Sec . 5can be eplica ed exploi ing also da a o s uden s en olled in p i a e schools. Resul s a e shown in Table 11. The eg essions in columns (1) a e pe o med using bo h s uden s en olled in public and p i a e schools, while hose in columns (2) a e es ic ed o s uden s in p i a e schools. 123 SERIEs (2020) 11:1–49 39 Table 11 E alua ions and g ade epe i ion: p i a e schools E alua ions g . 6 E alua ions g . 10 Behind a 14 En oll Academic (1) (2) (1) (2) (1) (2) (1) (2) Age a en y 0.339 0.329 0.174 0.114 −0.374 −0.394 0.153 0.142 (0.007)** (0.011)** (0.015)** (0.020)** (0.009)** (0.017)** (0.021)** (0.039)** [−0.099] [−0.085] [0.053] [0.043] <0.002><0.004><0.007><0.012> Public school −0.240 −0.352 0.184 −0.389 (0.013)** (0.019)** (0.006)** (0.024)** [0.049] [−0.134] <0.002><0.008> Pa en s’ edu a g 0.459 0.386 0.446 0.357 −0.450 −0.442 0.548 0.556 (0.008)** (0.015)** (0.014)** (0.021)** (0.006)** (0.011)** (0.015)** (0.030)** [−0.119] [−0.095] [0.189] [0.169] <0.002><0.002><0.005><0.009> Pa en s’ edu high 0.840 0.711 0.873 0.707 −0.963 −0.912 1.167 1.130 (0.011)** (0.019)** (0.018)** (0.024)** (0.008)** (0.012)** (0.021)** (0.037)** [−0.255] [−0.196] [0.402] [0.344] <0.002><0.003><0.006><0.010> N190,371 73,287 42,816 18,137 292,500 112,421 48,959 15,490 **p<0.01. In columns (1), bo h s uden s en olled in public and p i a e schools a e included in he analysis. In columns (2), only s uden s en olled in p i a e schools a e included 123 40 SERIEs (2020) 11:1–49 Being 1 yea olde inc eases ex e nal e alua ions in g ade 6 o s uden s en olled in p i a e schools by 0.33 s anda d de ia ions. The es ima ed coe icien is qui e simila o he one ound o public schools. In g ade 10, he e ec is signi ican and sizeable (0.11 s anda d de ia ions), bu somewha smalle han wha ound o public schools. Howe e , i is impo an o ecall ha only s uden s who do no d op ou unde ake e alua ions in g ade 10; he e o e, some selec ion bias may a ec he es ima e. The age a en y has a la ge e ec also on he p obabili y o being behind a 14 ( he a e age ma ginal e ec is −8.5 p.p.) and en olling in academic uppe seconda y educa ion ( he a e age ma ginal e ec is 4.3 p.p.). Those igu es a e compa able wi h he inding o public schools. I is no su p ising ha hey a e sligh ly smalle because, asshownincolumn (1),s uden sen olled inp i a eschoolsa e less likely obe e ained and mo e likely o unde ake academic educa ion. Appendix C: Addi ional ables See Tables12,13,14,15,16,17,18, and 19. 123 SERIEs (2020) 11:1–49 47 Table 18 Reg essions wi h in e ac ion e ms (I) Re en ion E alua ions Repea 1–2 Behind 14 2 4 6 6-ex . 7 8 Age a en y −0.671 −0.381 0.543 0.406 0.349 0.383 0.207 0.148 (0.043)** (0.021)** (0.017)** (0.017)** (0.017)** (0.022)** (0.019)** (0.019)** Age X pa en s’ edu a g −0.068 −0.034 0.053 0.056 0.022 −0.012 −0.004 0.023 (0.051) (0.026) (0.019)** (0.019)** (0.019) (0.025) (0.023) (0.022) Age X pa en s’ edu high 0.007 0.019 0.027 −0.023 −0.004 −0.052 0.068 0.076 (0.078) (0.038) (0.020) (0.022) (0.023) (0.025)* (0.025)** (0.028)** Age X emale 0.085 0.018 0.028 0.015 0.009 0.013 0.044 0.051 (0.048)+ (0.024) (0.016)+ (0.016) (0.017) (0.020) (0.020)* (0.019)** Age X immig an 0.065 0.002 −0.075 −0.137 −0.165 −0.133 −0.122 −0.115 (0.057) (0.028) (0.025)** (0.023)** (0.023)** (0.030)** (0.026)** (0.025)** Pa en s’ edu a g −0.337 −0.380 0.300 0.321 0.331 0.441 0.326 0.294 (0.027)** (0.014)** (0.011)** (0.011)** (0.012)** (0.016)** (0.014)** (0.014)** Pa en s’ edu high −0.707 −0.907 0.608 0.682 0.681 0.863 0.647 0.623 (0.038)** (0.021)** (0.013)** (0.014)** (0.014)** (0.018)** (0.017)** (0.019)** Female −0.158 −0.291 0.156 0.211 0.288 0.128 0.317 0.313 (0.023)** (0.013)** (0.009)** (0.009)** (0.010)** (0.012)** (0.012)** (0.011)** Immig an 0.299 0.522 −0.167 −0.153 −0.145 −0.347 −0.182 −0.167 (0.031)** (0.016)** (0.017)** (0.015)** (0.016)** (0.021)** (0.019)** (0.018)** N163,910 178,871 160,438 148,472 136,281 117,752 106,707 102,960 +p<0.1; *p<0.05; **p<0.01 123 48 SERIEs (2020) 11:1–49 Table 19 Reg essions wi h in e ac ion e ms (II) G adua e En oll Special needs Academic Voca ional g 1–2 g 7–8 Age a en y 0.117 0.232 −0.039 −0.216 −0.230 (0.048)* (0.047)** (0.049) (0.042)** (0.043)** Age X pa en s’ edu a g 0.113 0.138 −0.146 −0.120 0.043 (0.058)+ (0.055)* (0.060)* (0.056)* (0.060) Age X pa en s’ edu high −0.055 −0.037 −0.092 0.136 0.111 (0.077) (0.074) (0.080) (0.066)* (0.089) Age X emale −0.134 −0.165 −0.074 −0.022 −0.037 (0.054)* (0.051)** (0.055) (0.050) (0.051) Age X immig an −0.074 −0.178 0.143 −0.100 0.012 (0.060) (0.066)** (0.063)* (0.070) (0.060) Pa en s’ edu a g 0.308 0.435 −0.085 −0.159 −0.381 (0.032)** (0.033)** (0.036)* (0.034)** (0.035)** Pa en s’ edu high 0.774 1.128 −0.501 −0.455 −0.641 (0.050)** (0.047)** (0.047)** (0.041)** (0.051)** Female 0.416 0.498 −0.211 −0.324 −0.271 (0.031)** (0.031)** (0.031)** (0.027)** (0.029)** Immig an −0.521 −0.466 −0.216 0.051 0.064 (0.038)** (0.039)** (0.038)** (0.041) (0.037)+ N33,624 33,624 33,624 149,142 115,204 +p<0.1; *p<0.05; **p<0.01 Re e ences Ang is JD, K uege AB (1991) Does compulso y school a endance a ec schooling and ea nings? 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