Discussion Paper No Young and Innocent. International Evidence on Age Effects Within Grades on School Victimization in Elementary School

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1 Dscusson Paper No Young and Innocent Internatonal Evdence on Age Effects Wthn Grades on School Vctmzaton n Elementary School Andrea M. Mühlenweg

2 Dscusson Paper No Young and Innocent Internatonal Evdence on Age Effects Wthn Grades on School Vctmzaton n Elementary School Andrea M. Mühlenweg Download ths ZEW Dscusson Paper from our ftp server: ftp://ftp.zew.de/pub/zew-docs/dp/dp09031.pdf De Dscusson Papers denen ener möglchst schnellen Verbretung von neueren Forschungsarbeten des ZEW. De Beträge legen n allenger Verantwortung der Autoren und stellen ncht notwendgerwese de Menung des ZEW dar. Dscusson Papers are ntended to make results of ZEW research promptly avalable to other economsts n order to encourage dscusson and suggestons for revsons. The authors are solely responsble for the contents whch do not necessarly represent the opnon of the ZEW.

3 Non Techncal Summary School entry age effects on (short-term) cogntve outcomes are well-documented n the economc lterature for many countres. These studes do not consder school entry age effects on the development of personalty or socal outcomes. However, the recent human captal lterature emphaszes the mult-dmensonalty of sklls. Cogntve as well as non-cogntve sklls are mportant determnants of labor market success. Ths s why the present study examnes age effects on socal outcome varables. Specfcally, avalable nternatonal school assessment data allow observaton whether younger chldren are more often vctms of school volence n elementary school. Precsely, the queston of nterest n ths study s whether chldren, as observed at one pont n tme, suffer from beng the youngest wthn grade. Harm s done for example f the youngest chldren are more often bulled or are more often vctms of any knd of school volence. Age effects are dentfed followng the nstrumental varables lterature based on natonal school entry age rules. Possble selecton nto complance wth offcal rules s taken nto account va the control functon approach as a robustness check. Based on the PIRLS data for 17 countres, ths paper demonstrates that younger chldren wthn grades (due to enterng school younger accordng to offcal school entry age regulatons) are harmed n terms of school vctmzaton. The sze of pont estmates of the age effect s mostly hgher for boys than for grls and for chldren wth an mmgrant background than for natve chldren. Addtonally, the study consders whether countres wth a hgh age effect on cogntve outcomes are also countres wth hgh age effects on socal outcomes. Along ths lne, I fnd that the socal effects of age wthn grade tend to be hgher n countres where there are also hgh age effects on the observed cogntve test scores. Less favorable socal outcomes seem to go hand n hand wth less favorable test performance.

4 Das Wchtgste n Kürze (German Summary) Mehrere aktuelle bldungsökonomsche Veröffentlchungen befassen sch mt den (kausalen) Auswrkungen des Enschulungsalters auf den weteren schulschen Erfolg und de kogntve Entwcklung. Dese Studen berückschtgen jedoch ncht, dass neben der kogntven Entwcklung de Persönlchketsentwcklung und sozale Ergebnsse relevant snd. De neuere Humankaptallteratur betont de Mehrdmensonaltät von Fähgketen: Kogntve we nchtkogntve Fähgketen snd wchtge Determnanten der Höhe des Humankaptals. Deshalb beleuchtet de vorlegende Stude Alterseffekte n Bezug auf sozale Ergebnsse. De Stude geht der Frage nach, ob Knder, de zu enem bestmmten Zetpunkt (n der verten Klasse) beobachtet werden, darunter leden, wenn se de jüngsten n der Klasse snd. Vorlegende Schülerlestungsdaten ermöglchen es nsbesondere zu analyseren, ob de jüngeren Schülernnen und Schüler häufger Opfer von Mobbng und Gewalt n der Schule werden. Auf der Grundlage von Daten für 17 Länder, de an der Grundschullesestude IGLU telgenommen haben, zegt sch folgendes: De (auf Grund der entsprechenden Enschulung nach offzellen Stchtagsregelungen) jüngeren Knder nnerhalb von Klassen haben ene sgnfkant höhere Wahrschenlchket, von Mobbng oder Gewalt n der Schule betroffen zu sen, als de älteren. Des glt nsbesondere für Jungen und für Schülernnen und Schüler mt Mgratonshntergrund. Betrachtet man de Effekte, de für de enzelnen Länder geschätzt werden, so zegt sch ene postve Korrelaton zwschen der Auswrkung des Alters auf de Lestungen n der Grundschullesestude und dem Alterseffekt auf de sozalen Ergebnsse. De Knder, de auf Grund hres Alters unter Mobbng/Gewalt leden, erzelen demnach (aus dem glechen Grund) tendenzell schlechtere Testergebnsse.

5 Young and Innocent Internatonal evdence on age effects wthn grades on school vctmzaton n elementary school Andrea M. Mühlenweg ZEW Centre for European Economc Research, Mannhem Correspondng address: ZEW Mannhem, P.O. Box , Mannhem, Germany Emal: muehlenweg@zew.de Phone: Fax: Abstract: Ths study examnes the mpact of chldren s age wthn grade on school vctmzaton n elementary school. Identfcaton of age effects reles on the nstrumental varables approach drawng on offcal school entry age rules based on chldren s month of brth. The emprcal analyss uses the PIRLS data for 17 countres where such school entry age rules are effectvely appled. Possble selecton nto complance wth offcal entry rules s taken nto account va a control functon approach. The study demonstrates that chldren are causally and sgnfcantly harmed by beng the youngest wthn grade. Sub-group analyss reveals that the sze of age effects on school vctmzaton tends to be hgher for boys than for grls as well as for chldren wth an mmgrant background compared to natves. The pont estmates suggest that the age effect on school vctmzaton s especally hgh n countres where there are also hgh effects on the cogntve outcome varable. JEL classfcaton: I21 Keywords: educaton, segregaton, school effects Acknowledgement: Fnancal support from the Wssenschaftsgemenschaft Gottfred Wlhelm Lebnz under the project Non-cogntve sklls: Acquston and Economc Consequences s gratefully acknowledged. I am grateful to Melane Arntz, Mchèle Belot, Holger Bonn, Katja Coneus, Clare Crawford, Stephan Dlugosz, Phlpp Esenhauer, Bernd Ftzenberger, James Heckman, Hendrk Jürges, Verena Nepel, Fredhelm Pfeffer, Pa Pnger, Patrck Puhan, Thomas Walter, Thomas Zwck and partcpants of the 2009 SOLE conference as well as semnar partcpants at the ZEW Mannhem and the Unversty of Freburg for valuable comments to earler versons of ths work. Thanks to Franz Georg Westermaer for double checkng school regulatons. All remanng errors are my own.

6 volence. 2 Based on data for a large set of countres, ths paper demonstrates that younger 1 Introducton Postve effects of age at school entry on (short-term) cogntve outcomes are welldocumented n the economc lterature for many countres (cf. for example Bedard and Dhuey, 2006; Casco and Lews, 2006; Puhan and Weber, 2006; Kawaguch, 2009; Mühlenweg and Puhan, 2010). None of these studes consders school entry age effects on the development of personalty or socal outcomes. However, the recent human captal lterature emphaszes the mult-dmensonalty of sklls (e.g. Cunha et al., 2006). Cogntve as well as non-cogntve sklls (ncludng socal sklls) are mportant determnants of labour market success. Ths s why the present study examnes age effects on socal outcome varables for pupls n a large set of countres. Specfcally, avalable nternatonal school assessment data allow observaton whether younger chldren are more often vctms of school volence n elementary school. 1 Age effects are dentfed followng the nstrumental varables lterature based on offcal school entry age rules (as ntroduced n Angrst and Krueger, 1992). Possble selecton nto complance wth offcal entry rules s taken nto account va a control functon approach as a robustness check (cf. Card, 2001). Precsely, what ths paper s nterested n s not the absolute effect of school entry age on chldren s performance (for example comparng the performance of chldren enterng at age 6 and those enterng at age 7). As noted recently for example n Angrst and Pschke (2009) ths effect may not be properly dentfed based on student data. The queston of nterest n ths study s whether chldren, as observed at one pont n tme, suffer from beng the youngest wthn grade. Harm s done for example f the youngest chldren are more often bulled or are more often vctms of any knd of school chldren wthn grades (due to enterng school younger accordng to offcal school entry age regulatons) are harmed n terms of school vctmzaton. The sze of pont estmates of the age effect s mostly hgher for boys than for grls and for chldren wth an mmgrant background than for natve chldren. Addtonally, the study consders whether countres wth 1 Among development psychologsts, there seems to be a consensus that non-cogntve sklls are predomnantly determned n early chldhood. Thus, the present applcaton s also an example of an examnaton whether an nsttutonal set-up (.e. school entry age regulaton) mght nfluence the formaton of personalty durng the schoolng years. 2 Besde possble non-cogntve effects related to such socal outcomes and ther nfluence on the development of personalty cogntve effects of age wthn grade mght also be crucal. For example n countres wth a system of secondary school trackng, students are typcally evaluated at one pont n tme and accordngly selected to dfferent secondary school tracks. Therefore, poorer cogntve performance of younger chldren wthn grade crucally affects those chldren s future educaton perspectves (cf. Mühlenweg and Puhan, 2010 for such evdence related to a school trackng system).

7 a hgh age effect on cogntve outcomes are also countres wth hgh age effects on socal outcomes. Along ths lne, I fnd that the socal effects of age wthn grade tend to be hgher n countres where there are also hgh age effects on the observed cogntve test scores. Less favorable socal outcomes seem to go hand n hand wth less favorable test performance. 3 The paper proceeds as follows: Secton 2 ntroduces the data base and s followed by Secton 3 on stylzed facts and a revew of the emprcal method to dentfy age of school entry effects. The accordng regresson results and robustness checks are dscussed n Secton 4. Secton 5 concludes. 2 Data The major data source used n ths paper s the Progress n Internatonal Readng Lteracy Study 2006 (PIRLS 2006). The orgnal PIRLS data base provdes data on chldren attendng elementary schools n 40 countres ncludng Canada wth fve separate samples for ts provnces. Sample sze vares by country: On average about 4,800 chldren are observed per country. Chldren wthn the observed grades are about ten years old, so that for most countres, data are collected n fourth grade of compulsory schoolng. In two countres, South Afrca and Luxembourg, the average students are somewhat older (about 11 years old). PIRLS ncludes nformaton from students, parents and school questonnares as well as chldren s results n the readng lteracy test. Test outcomes are standardzed to an nternatonal mean of 500 and a standard devaton of 100. For the purpose of the regresson analyss, I further standardze the test score by dvdng t by ts standard devaton n order to facltate the nterpretaton of the effect. The PIRLS data base provdes a set of socal outcome varables ndcatng whether pupls suffer from school vctmzaton. All these varables are reported by the chldren wthn the student background questonnare. Specfcally, the present study consders bnary varables ndcatng that wthn the last month n school somethng was stolen from the chld, whether the chld was bulled by another student, or whether she or he was njured by another student. I also use an aggregated bnary varable for school vctmzaton ndcatng whether any of these three events happened to the chld. For some chldren the socal outcome varables are not observed but the number of such mssng observatons s relatvely small (about 2 % for the aggregated varable n the estmaton sample). 3 It s not wthn the scope of ths paper to dsentangle nteractons of cogntve and non-cogntve development. Thus, I present evdence wth respect to the age effect on socal outcomes as well as the age effect on test scores. I do not dentfy or dscuss the channels of nteracton between these effects. 2

8 As concerns student background varables, I do not use data from the parents questonnares snce ths would notably reduce sample szes: Takng the average of all countres consdered n ths paper, parents response rate for basc nformaton amounts to 85 % but n some countres t s much lower (about 50 %). Therefore, restrctng the samples to chldren whose parents answered a questonnare would probably ntroduce selectvty. Informaton on students background s thus solely drawn from the students questonnares. However, there s also a crucal number of mssng observatons for some varables observed n the students questonnare. Consequently, only key varables (favorably wth a hgh response) rate are used. The frst key varable s gender whch s observed for 100 % of the chldren and verfed va PIRS admnstered nformaton. The second key varable s an ndcator for mmgrant background statng whether the chld or one of the chld s parents has been born abroad. Ths second varable s only avalable for 84 % of the chldren so that correspondng sub-group results have to be nterpreted wth a gran of salt. Furthermore, chldren s brth month and year of brth as well as the ntervew date (determnng chldren s age n the observed grade) are drawn from the admnstered nformaton. Actual age of school entry s deduced by subtractng tme n school from the observed age at tme of ntervew. Thus, possbltes of grade retenton are gnored. I assume that ths yeld the exact age of school entry for the vast majorty of chldren (frequences of grade retenton after frst grade and up to fourth grade should be small n most countres). Furthermore, grade retenton wll be addressed n a robustness check. Table 1 provdes means and standard errors of central outcomes and control varables for each country and based on the estmaton samples whch wll be used n Secton 4. Notably, there s sgnfcant varaton n the degree of school vctmzaton between dfferent countres: 81 % of chldren n South Afrca ndcate to suffer from some knd of school vctmzaton whle only 26 % of chldren n Poland report such problems. Average compulsory school entry age s between 5.2 and 7.3 years n the relevant countres. In countres where chldren enter when they are about fve years old (lke Scotland and England) chldren are accordngly observed n the ffth (nstead of the fourth) year of compulsory schoolng n PIRLS. In most countres, the average chld enters school at the age of sx. Besdes the student level data of PIRLS, the further analyss requres nformaton on natonal school entry regulatons. The prmary source for the natonal regulatons s the contextual data-base whch s drectly provded n PIRLS (PIRLS 2006 Currculum Questonnare). I further verfy and complement ths nformaton manly based on nformaton 3

9 from natonal mnstry of educaton homepages and the Eurydce data-base ( 4 Standard school entry age regulatons whch mply a cut-off month for school entry related to chldren s brth date are documented and verfed for 17 countres for the gven cohorts of chldren. 5 Table 2 provdes an overvew of the dfferent school entry regulatons wth respect to the dfferent cut-off dates n the 17 countres of nterest. 3 Stylzed Facts and Identfcaton Strategy A smple descrptve way to consder school age effects on school vctmzaton s presented n Fgure 1 based on the pooled data set ncludng all 17 countres. Ths fgure shows average test cores and socal outcomes by relatve age wthn grade (as deduced from the age structure n the observed school year). 6 There s a clear pattern that both the partcular young as well as the partcular old chldren wthn grade perform poorly n the PIRLS readng test and are most often subject to school volence. Ths evdence hnts to the endogenety of school entry age wth respect to the outcomes consdered: In countres where school entry regulatons are not strctly appled, for example chldren wth cogntve or behavoral problems may enter school later than prescrbed by the offcal regulaton and wll make up the group of extremely late entrants. In lght of parental dscreton and possble grade retenton, t s not surprsng that the relatvely old chldren acheve less favorable outcomes when observed n elementary school. It s also worth observng that there s a somewhat dfferent pattern related to the more regular aged school entrants wthn a one year age span around the average entrance age (85 % of chldren n the sample). Wthn ths sample, there seems to be a tendency that relatvely older students are less often subject to school volence (wth a nearly lnear trend). The patterns observed are very smlar for each gender and for chldren wth and wthout an mmgrant background. The correspondng means for all these sub-groups are 4 All nternet sources have been retreved n February and March Detaled nformaton on the sources s avalable upon request from the author. 5 I excluded countres where such school entry age regulatons exst but are obvously not appled. Ths s the case f eyeballng of school entry age by brth month demonstrates that the effectvely used cut-off month s not the cut-off month stated n the natonal school regulaton. As a formal crteron, I excluded all countres where regressng chldren s age n frst grade on the entry age accordng to the regulaton yelded coeffcents of less than 0.5 years for the sample of pupls born a month pror or after the cut-off month ( regresson dscontnuty sample ). I also excluded countres wth sgnfcant regonal varaton n school entry age regulatons (for example the U.S. as well as Germany at the year of observaton), snce regons cannot be dentfed n the data. More nformaton on ths for all 40 PIRLS countres s avalable upon request from the author. 6 Only the majorty of chldren who enter school at most a year earler and at least a year later than the average chld are ncluded. Ths crteron s met by 96 % of chldren. Older and younger chldren are not ncluded n Fgure 1 for practcal reasons (scalng of the x-axs). 4

10 summarzed n Table 3. Generally, grls test scores are somewhat hgher and the frequences of school vctmzaton are slghtly lower (except for the extreme age groups). For example 51 % of averaged aged grls and 55 % of the boys report to be subject to any knd of school volence. At the same tme, chldren wthout an mmgrant background score somewhat hgher and are less lkely to be vctms of school volence (agan except for the extreme age groups). As for these chldren, 50 % of average aged chldren wthout mmgrant background report not to experence school volence whle 59 % of average aged mmgrant chldren do so. The evdent endogenety of age wthn grades calls for an nstrumental varables strategy. Therefore, t s mportant to note that - besdes parental and teacher s dscreton - the age dstrbuton wthn grades s manly drven by natonal age of school entry regulatons. Such offcal entry age rules typcally mply a cut-off month for school entry so that assgned age at school entry depends on chldren s brth month. As shown n Table 2, n most countres the offcal rule s that chldren enter school n the calendar year when they turn sx. Ths mples that the cut-off date for school entry s December, 31 (the end of the calendar year). In Austra and Slovaka for example, the cut-off month s September: Chldren born before September, 1 are supposed to enter school n the year when they turn sx, whle chldren born between September and the end of December, enter n the year they turn seven. Assgned school entry accordng to the offcal regulatons s a vald nstrument for age wthn grades, assumng that month of brth s exogenous to educatonal and socal outcomes. However, as summarzed n Bound, Jaeger and Baker (1995), there mght be drect effects of season of brth on the chld s development. In order to elmnate such seasonal brth date effects on the outcome varables, I restrct the regresson samples to chldren born one month before and after the school entry age cut-off date (dscontnuty samples). 7 Usng Two-Stage-Least Squares (2SLS) estmaton wth brth month as an nstrument dentfes the age effect for the group of complers wth the offcal entry age rule n the sense of a local average treatment effect (LATE). Complance wth entry age rules s far from perfect n some countres. In order to deduce an mpact for the entre populaton of chldren, the crucal queston s how the LATE generalzes to an average treatment effect (ATE). In other words, the queston s how complers dffer from non-complers wth the entry age rule. For example Puhan and Weber (2007) present some evdence for a negatve correlaton of the 7 Concernng functonal form I manly use lnear probablty models. I also present a robustness check where probt IV estmatons are used for the school volence ndcators (estmated usng vprobt wth the margnal effects command n STATA 9.2). 5

11 degree of complance and the sze of the age effect on standardzed test scores. Ths suggests that complers are less affected by age effects than non-complers. In order to take possble selecton to the group of complers nto account (.e. complers are affected n a dfferent way than non-complers), n a frst (smple) robustness check I restrct the sample to countres wth strct enforcement of the school entry age regulatons. In ths case, practcally everyone s a compler. Ths also mples that countres wth consderable numbers of grade retenton are excluded. As a second robustness check, I use the control functon approach as suggested by Card (2001) followng Garen (1984). In prncple, I thus estmate the followng equatons n two steps: aˆ y = ˆ ε e ( b ) = b b a + b ( aˆ 2 ˆ ε e ( b )) + b 3 ( aˆ ˆ ε e ( b )) a where â s ndvdual s predcton of observed age at school entry (a ) from the frst stage regresson, e (b) s assgned age at school entry for ndvdual whch depends on brth month b and y s the outcome of nterest (test scores or socal outcomes). εˆ, b 1, b 2, and b 3 are regresson coeffcents of the frst and second step respectvely. Second step estmaton should accordngly yeld a consstent estmate of the age effect ( b 1 ). (1) (2), 4 Results In order to pn down the overall effect of age wthn grade on test scores and socal outcomes, Table 4 presents results from 2SLS estmaton based on the pooled sample ncludng all 17 countres. Snce absolute age at school entry dffers somewhat by country and I am not nterested n the absolute age effect but n relatve age wthn grade, estmaton s based on relatve age as the control varable. The frst panel of Table 4 demonstrates that 2 SLS yelds rather hgh and hghly sgnfcant frst stage coeffcents. Ths underpns confdence n the nstrument (assgned relatve age mpled by brth month) whch s far from beng a weak nstrument. Secondly, a hgher age wthn grade mples hgher test scores: Chldren who are about a year older (that s for most countres: chldren who entered school when aged about seven nstead of sx years) score about 0.3 test score standard devatons hgher compared to the younger chldren. Wth respect to school vctmzaton, older chldren are also less lkely to be vctms of school volence. The overall probablty to suffer from school volence s reduced by about nne percentage ponts for chldren beng a year older. Accordngly, the estmated age coeffcents are negatve for all socal outcome varables,.e. younger chldren 6

12 are sgnfcantly more lkely to get somethng stolen, to be bulled and to be hurt. Sub-group analyss presented n Table 4 shows that the absolute sze of pont estmates of the age effects s hgher for boys than for grls. For the socal outcomes varables, the absolute sze s addtonally hgher for chldren wth an mmgrant background than for natves. To refne the analyss, results are furthermore estmated separately for each country (cf. Fgure 2 and Table 5). Agan, ths yelds postve effects of age wthn grade on readng test scores. Postve pont estmates of the 2SLS regresson range from 0.01 test score standard devatons (South Afrca) to 0.49 standard devatons (Scotland). At the same tme, most of the pont estmates of the age effect on the probablty of school vctmzaton are negatve (wth the excepton of a zero effect for Slovaka). The negatve effects are hghest for Ontaro (-0.18), Scotland (-0.17) and England (-0.14). Even f these pont estmates are not always sgnfcant n the statstcal sense, Fgure 2 suggests that countres wth hgh postve age effects on cogntve outcomes also tend to be characterzed by hgh negatve effects on school volence. If the sample s reduced to countres where both the cogntve and the general school vctmzaton effect are sgnfcant at least on the ten percent level, the pattern clearly remans the same (not shown here). The sample of countres where all these effects are sgnfcant conssts of Scotland, England, Canada, Span, France and Tawan. The age effect on the readng score and the age effect on school vctmzaton are correlated wth a negatve Bravas-Pearson correlaton coeffcent n ths sample. The presented results from 2SLS regressons mght be drven by the selectvty of the group of complers. In order to check ths, n a frst step, the sample s reduced to countres wth a hgh rate of complance (frst stage coeffcents of 0.85 or more). Accordngly, the sample ncludes Ontaro (Canada), England, Iceland, Norway, Poland, Sngapore and Span. The results demonstrate that the estmated patterns are clearly robust to usng ths sample. Accordng to the lnear probablty regressons, the correlaton of the cogntve effect and the school vctmzaton effect amounts to n ths case. 8 In addton to ths check, Fgure 2 also ncludes results from control functon estmaton generalzng the estmated effect to an average treatment effect under ts functonal form assumptons. The results are robust compared to the 2SLS estmaton. As a further robustness check concernng functonal form, Fgure 2 also shows margnal effects from probt nstrumental varable (nstead of lnear probablty) regressons for the bnary outcome varable whch agan valdates the results. The sze of the estmated margnal effects s very close to the effects estmated va 2SLS. 8 If a somewhat less strct crteron, say complance correspondng to a frst stage effect of 0.8 s used, the sample remans larger and ncludes a dozen of countres. The correlaton of effects s n ths case. 7

13 It s beyond the scope of ths paper to explan dfferences n the age effects n dfferent countres n terms of nsttutonal and polcy characterstcs. There s too much heterogenety n educaton systems around the world and therefore t would be hard to pn down the relevant nsttutonal effects nteractng wth age effects. However, note that Fgure 2 mples that age effects n elementary school are hghest n countres wth so called à la carte ntegraton models (cf. the classfcaton by Duprez et al., 2008) lke Canada and the Unted Kngdom. A la carte ntegraton systems mply that prmary educaton s generally comprehensve - there s a core currculum common to all chldren - but groupng wthn elementary school classes may be based on the chld s ablty. 9 Compared to these countres, countres wth ndvdualzed teachng and ntegraton systems lke the northern European countres but also countres where chldren are prepared for beng educated n dfferent ablty tracks (lke n some central European countres) seem to deal better wth the age effects wthn grades. 5 Conclusons Based on pooled data for 17 countres, ths paper presents evdence that chldren s age wthn grade sgnfcantly affects standardzed readng test scores (as measured at one pont n tme) as well as socal outcomes. Older chldren wthn grades are less often vctms of school volence. It s also shown that there s a negatve correlaton of cogntve and socal effects. The presented results are robust to restrctng the sample to countres wth hgh complance and to alternatve estmaton strateges. Sub-group analyss reveals that the age effects tend to be hgher for boys than for grls. Analyss by mmgrant background has to be taken wth a gran of salt due to a reduced (possbly selectve) sample but suggests that the age effects on school vctmzaton are hgher for chldren wth an mmgrant background compared to natves. All n all, the paper demonstrates that age wthn grades matters for socal outcomes. Accordng to evdence from psychology (e.g. Cassdy, 2009) school vctmzaton s a crucal determnant for chldren s development of personalty. Thus, t s very lkely that beng the youngest n class (and thus sufferng from school vctmzaton) also affects the chldren s future non-cogntve outcomes. 9 There mght also be segregaton for example by school dstrcts n such systems. 8

14 References Angrst, J.D. and A.B. Krueger (1992), The Effect of Age at School Entry on Educatonal Attanment: An Applcaton of Instrumental Varables wth Moments from Two Samples, Journal of the Amercan Statstcal Assocaton 87: Angrst, J.D. and J.-St. Pschke (2009), Mostly harmless econometrcs, Prnceton Unversty Press, Prnceton. Bauer, Ph. and R. Rphahn (2009), Age at School Entry and Intergeneratonal Educatonal Moblty, Economcs Letters 103: Bedard, K. and E. Dhuey (2006), The Persstence of Early Chldhood Maturty: Internatonal Evdence of Long-Run Age Effects, The Quarterly Journal of Economcs 121: Bound, J., D.A. Jaeger and R.M. Baker (1995), Problems wth Instrumental Varables Estmaton When the Correlaton Between the Instruments and the Endogenous Explanatory Varables s Weak, Journal of the Amercan Statstcal Assocaton 90: Card, D. (2001), Estmatng the Return to Schoolng: Progress on some persstent econometrc problems, Econometrca 69: Casco, E.U. and E.G. Lews (2006), Schoolng and the Armed Forces Qualfyng Test: Evdence from School-Entry Laws, Journal of Human Resources 41 (2): Cassdy, T. (2009): Bullyng and vctmsaton n school chldren: the role of socal dentty, problem-solvng style, and famly and school context, Socal Psychology of Educaton 12: Cunha, F., J.J. Heckman, L. Lochner and D.V. Masterov (2006), Interpretng the evdence on lfe cycle skll formaton, n: E.A Hanushek and F. Welch, eds., Handbook of the economcs of educaton, Vol. 1. (North-Holland: Amsterdam): Duprez, V., X. Dumay and A. Vause (2008), How Do School Systems Manage Pupls Heterogenety?, Comparatve Educaton Revew 52: Garen, J. (1984), The Returns to Schoolng: A Selectvty Bas Approach wth a Contnuous Choce Varable, Econometrca 52: Kawaguch, D. (2009): Actual Age at School Entry, Educatonal Outcomes, and Earnngs, Journal of the Japanese and Internatonal Economes, forthcomng. Mühlenweg, A.M. and P.A. Puhan (2010), The Evoluton of the School Entry Age Effect n a School Trackng System, Journal of Human Resources, forthcomng. 9

15 Puhan, P.A. and A.M. Weber (2007), Does the Early Brd Catch the Worm? Instrumental Varable Estmates of Early Educatonal Effects of Age of School Entry n Germany, Emprcal Economcs 32:

16 Tables Table 1: Means of outcome and control varables by country Country Test score Vctmzaton Thngs stolen Beng bulled Beng hurt Austra (1.93) Belgum (Flemsh) (1.93) Canada, Brtsh Columba (1.93) Canada, Nova Scota (1.93) Canada, Ontaro (1.93) Canada, Québec (1.93) England (1.93) France (1.93) Iceland (1.93) Italy (1.93) Luxembourg (1.93) Norway (1.93) Poland (1.93) Scotland (1.93) Sngapore (1.93) Slovaka (1.93) South Afrca (1.93) Span (1.93) Sweden (1.93) Tawan (1.93) Entry age Male Immgrant background (0.00) Note: Standard errors n parentheses. Number of observatons for test score sample s gven n the last column. Samples restrcted to students born one month pror to and after the school entry cut-off date as these samples are used for the regresson analyss. Source: PIRLS Own calculaton. Obs. (All) , ,

17 Table 2: Documented school entry age rules for PIRLS countres Country Cut-off date Age at School year cut-off startng date date Austra September 1 September (begnnng) Belgum (Flemsh) December 31 September (begnnng) Canada, Brtsh Columba December 31 September (begnnng) Canada, Nova Scota October 1 September (begnnng) Canada, Ontaro December 31 September (begnnng) Canada, Québec October 1 September (begnnng) England August 31 A September (begnnng) France December 31 September (begnnng) Iceland December 31 August (end) Italy December 31 September (begnnng / md) Luxembourg September 1 September (md) Norway December 31 August (md) Poland December 31 September (begnnng) Scotland August (md) August (md) Sngapore January 1 January (begnnng) Slovaka September 1 September (end) South Afrca December 31 January (begnnng) Span December 31 September (begnnng / md) Grade (year of observaton) Sweden December 31 August 7 B 4 (md) Tawan August (end) August (end) Note: A Several cut-off dates for frst grade entry n England; promoton polcy to followng grades effectvely yelds August, 31 cut-off. B Entrance s also possble by the age of sx n Sweden. Source: PIRLS The sample s restrcted to countres wth verfed rules and suffcent complance wth the rule. Own calculaton. 12

18 Table 3: Means of man outcome varables by relatve age for dfferent sub-groups Relatve age Test score Any type of school vctmzaton Male Female Immgrant Natves Male Female Immgrant Natves (10.40) (7.94) (16.88) (8.96) (10.07) (7.83) (19.58) (8.14) (7.42) (6.62) (11.01) (6.51) (6.48) (5.44) (9.00) (5.32) (3.64) (3.11) (5.28) (2.78) (1.76) (1.78) (2.65) (1.41) (1.47) (1.60) (2.37) (1.20) (1.33) (1.32) (1.91) (1.05) (1.56) (1.52) (2.24) (1.19) (1.55) (1.63) (2.60) (1.20) (1.42) (1.49) (2.19) (1.14) (1.54) (1.46) (2.41) (1.08) (1.42) (1.34) (1.88) (1.09) (1.64) (1.60) (2.52) (1.25) (2.12) (2.07) (3.54) (1.57) (3.11) (3.44) (4.45) (2.66) (6.21) (5.86) (6.63) (5.45) (5.19) (6.24) (6.64) (5.73) (6.94) (7.02) (7.76) (6.97) (5.56) (6.24) (8.52) (5.84) (8.10) (8.80) (11.38) (8.49) Obs. 46,997 46,925 18,343 61,578 45,937 45,984 18,237 61,238 Note: Standard errors n parentheses. Groups ranked by wthn country devaton from average age (measured n years). Source: PIRLS Pooled sample of 17 countres. Restrcted to age span +-1 year around average age wthn each country. Own calculaton. 13

19 Table 4: 2SLS estmates of relatve age on test scores and socal outcomes (all countres) Frst stage Second stage Sample Relatve age Test score Vctmzaton Thngs stolen Beng bulled Beng hurt (n years) (n s.d.) (probablty) (probablty) (probablty) (probablty) All Male Female Immgrants (0.10) Natves Obs. (all) 16,244 16,244 15,866 15,816 15,722 15,740 Note: Standard errors n parentheses. Relatve age defned as wthn country devaton from average age (measured n years). Source: PIRLS Pooled sample of 17 countres. Restrcted to age span +-1 year around average age wthn each country. Own calculaton. 14

20 Table 5: 2SLS estmates of age effects on test scores and socal outcomes by country Country /coeffcents (s.e.) Frst stage Test score (n s.d.) Vctmzaton (general) Thngs stolen Beng bulled Beng hurt Scotland (0.15) (0.08) (0.08) (0.08) England (0.08) Slovaka (0.12) 0.00 (0.09) Canada, Québec (0.08) Canada, Ontaro Span Canada, Brtsh Columba Iceland France Tawan Italy (0.09) Sweden Norway (0.08) Poland (0.09) Canada, Nova Scota (0.08) Belgum (Flemsh) Luxembourg Austra (0.10) Sngapore * 0.01 South Afrca (0.13) Note: Countres ordered by sze of age effect on readng test scores. Source: PIRLS Own calculaton. 15

21 Fgures Fgure 1: Means of outcome varables by relatve age (pooled sample of all countres) score relatve frequeny relatve age mean test score frequency of school vctmzaton frequency "thngs stolen" frequency "bulled" frequency "hurt" 0.2 Note: Relatve age ndcates wthn country devaton from average age (measured n years). Table 3 ncludes detaled means for sub-groups. Source: PIRLS Pooled sample of 17 countres. Restrcted to age span +-1 year around average age wthn each country. Own calculaton. 16

22 Fgure 2: Robustness of IV and control functon estmates of age effects by country South Afrca Sngapore Austra Luxembourg Belgum (Flemsh) Canada, Nova Scota Poland Norway Sweden Tawan Italy France Iceland Canada, Brtsh Columba Span Canada, Ontaro Canada, Québec Slovaka Scotland England age effect on test score (2SLS) age effect on test score (CF) age effect on probabalty of vctmzaton (2SLS) age effect on probabalty of vctmzaton (probt IV) age effect on probabalty of vctmzaton (CF) Note: Countres ordered by sze of age effect on readng test scores. Source: PIRLS Own calculaton.