Which Factors Determine Academic Performance of Economics Freshers?. Some Spanish Evidence

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1 Whch Factors Determne Academc Performance of Economcs Freshers?. Some Spansh Evdence Juan J. Dolado* & Eduardo Morales** (*) Unversdad Carlos III & CEPR & IZA (**) Harvard Unversty Ths draft: October, 8 ABSTRACT Ths paper analyses the mpact of several factors potentally affectng academc performance of Economcs freshers (frst-course undergraduates) at Unversdad Carlos III de Madrd over the perod -5. Outcomes are the grades obtaned by these students n three core subjects whch dffer n ther requrements of math sklls. Controls nclude specalzaton track at hgh school, type of school, parental educaton background college attanment, grades obtaned at the unversty entry-exam, gender and natonalty. Our man fndng s that those students who completed a techncal track at hgh school tend to perform much better n subjects nvolvng math sklls than those who followed a socal scences track (supposedly talor-made for future economcs students) and that the latter do not perform sgnfcantly better n subjects where pror tranng n economcs helps. Moreover, students from publc schools preval n the lower and upper parts of the grades dstrbutons whle females tend to perform on average better than males. JEL Classfcaton: I1 and I9 Keywords: academc performance, pre-unversty determnants, selecton bases, quantle regressons. Correspondng author: Juan J. Dolado (dolado@eco.uc3m.es). We are ndebted to a Co-Edtor and two anonymous referees for many helpful suggestons whch greatly mproved the paper, and to Marsol Somolnos for provdng us wth the students admnstratve records at UC3M. We also thank Antono Cabrales, Lbertad González, Carmelo Nuñez, Tommaso Nanncn and partcpants at the 7 PEW conference (Madrd), EEA-ESEM (Budapest), SAE (Granada) and EEEPE workshop (Amsterdam) for nsghtful comments on prelmnary drafts of ths paper. The second author s currently a graduate student n the Economcs Ph. D. program at Harvard. Fnancal support from the European Commsson under the project The Economcs of Educaton and Educaton Polcy n Europe (MRTN-CT ), Consolder-Ingeno 1 (MEC), Excelecon (CM) (Dolado), and Consejería de Educacón de la Comundad de Madrd (Morales) s gratefully acknowledged. 1

2 G.M., an excellent student wth straght A s n the hgh-school track of socal scences, ncludng Maths, wshed to become an economst, lke hs father was. When he enrolled n an Economcs degree at the unversty, he faled mserably n the frst course of Maths Whch s the reason for ths falure?. One lkely explanaton s the nadequacy of the Maths taught n hgh school and those requred for such degree ths falure s not due to a poor performance of hgh-school teachers, but rather to the lack of nformaton about the level of Maths requred n Economcs. [Pedro Álvarez Martínez, La nfluenca del bachllerato en el fracaso en Economía EL PAÍS, 9/6/3] 1. Introducton It s often clamed that Economcs s the dscplne wth the hghest need for formalsm n theory-buldng among socal scences. Thus, undergraduate courses n Economcs requre a good background n basc mathematcs besdes pror tranng n ntroductory economcs and economc hstory. In ths paper we present some emprcal evdence about what sort of pror (pre-unversty) qualfcatons are related to good academc performance by frst-year undergraduates (hereafter labeled as freshers) enroled n an Economcs degree at one of the Spansh publc unverstes. In partcular, we are nterested n examnng whether factors correlated wth success n math-ntensve subjects dffer from those whch mprove performance n other economcs subjects wth less mathematcal content and where pror tranng s useful. To do so, we focus on the students performance n three core subjects ordered n decreasng level of math requrements: Mathematcs, Introductory Economcs and Economc Hstory (henceforth, Maths, Introecon and Econhst, respectvely). 1 More precsely, one of our man goals here s to analyze whether the socal scences track taken at hgh school - supposedly the one talor-made for future students of unversty-level economcs- helps to mprove performance n these subjects. As hghlghted n the newspaper quotaton at the epgraph of the paper, the ncreasng number of freshers who struggle at the early stages of ths degree, due to ther weak math tranng at hgh school, s rasng a growng concern among hgher-educaton pundts. Our evdence reles upon ndvdual-level data collected by us usng a sample of almost 4 freshers at Unversdad Carlos III de Madrd (UC3M) who took exams n the above-mentoned subjects between the /3 and 5/6 courses. The students n our sample were enroled at UC3M durng the frst semester of ther four-year BA degree (Lcencatura) n Economcs (LE) or 1 The syllabus n Maths conssts of lmts, dfferentaton and ntegrals. Introecon s a basc Mcroeconomcs course (consumer theory and theory of the frm) and Econhst deals wth the long-run development process n Western Europe. The choce of freshers s dctated by data avalablty. However, the fact that the wthdrawal rate s rather hgh (about 3%) durng the completon of a degree n the Spansh unversty system mples that the estmates obtaned for ths restrcted group of students are lkely to be less affected by selecton bases than the estmates for students n more advanced courses (due to the attrton of those who drop out after the frst course).

3 Busness Admnstraton (LADE). 3 Repeaters, ether drectly from these degrees or comng from alternatve ones (typcally from engneerng or medcne) are excluded from our sample n order to solate the treatment effects of varables lke the hgh school track or the type of hgh school. Informaton s avalable on the followng varables : type of hgh school (publc, prvate and charter 4 ) durng ther upper-secondary educaton (two years of Bachllerato at 16 and 17 years of age); specfc tranng receved durng ths perod (.e., the Bachllerato specalzaton track); and the grade obtaned grantng access to a unversty-level degree, whch s used as a proxy for unobserved sklls. Ths grade s a weghted average of: () the grade obtaned n a (natonwde) centralsed entry exam takng place at the unverstes (Selectvdad) just after students complete hgh-school at 18 years of age (wth a weght of 4%), and () an average of the hgh school grades obtaned durng the two courses of Bachllerato (wth a weght of 6%). These varables, n addton to gender, natonalty and some famly- background characterstcs, are the basc nputs we use to explan outcomes (grades awarded n the fnal examnaton of the three unversty-level subjects) usng an achevement producton-functon approach. At ths stage, t s worth stressng that an mportant shortcomng of our dataset s that we lack detaled nformaton related to parental background (ndeed, the only avalable proxy s an ndcator of whether any of the parents has a college degree). However, drawng upon prevous evdence on the exstence of a strong correlaton between type of school and (mssng) famly s soco-economc status (see Calero, 6), we clam that ths varable may be a good proxy for famly characterstcs. The reason s that qualty of educaton (student/teacher ratos, computer facltes, foregn languages, etc.) n nonpublc schools s generally consdered to be hgher than n most publc schools, n exchange for annual tuton fees of about 6 to 8 k. n prvate schools and around to 3 k. n charter schools. To the extent that famles where (at least one of the) parents have a college degree are wealther, they can afford to send ther chldren to prvate and charter schools. Indeed, the sample correlaton between our parental-background dummy varable and a dummy for nonpublc schools turns out to be very hgh (.89). Therefore, gven the dffcultes n dsentanglng separate effects for each of these two ndcators n our emprcal approach, we wll nterpret ther mpacts as ndstnctly stemmng from famly background. Grades n the Spansh educaton system are numercal, rangng from to 1, leadng to fve categorcal grades. Grades below 5 mply a Suspenso (Fal n the anglosaxon system), between 5 and 7 s an Aprobado (Thrd), between 7 and 9 s 3 Durng the frst year, freshers n LADE have the same subjects as those n LE. Thus, for brevty, we wll refer n the sequel to all of them as Economcs freshers. 4 A charter school (concertado) s a school subsdzed by the publc sector, typcally run by relgous orders. 3

4 a Notable (Lower Second), between 9 and 1 s a Sobresalente (Upper second) and 1 (or very close to that grade) s a Matrícula de Honor (Frst or Dstncton). The categorcal grades wll be used to descrbe the data n Secton where, to smplfy notaton, we wll denote them wth the labels SUS, AP, NOT, SOB and MH, respectvely. By contrast, the numercal grades (avalable from the archves of UC3M) are the ones whch wll be employed n mplementng the regressons dscussed n Secton 3. Our emprcal strategy reles upon two dfferent econometrc approaches. Frst, we run least-squares (OLS and IV) regressons to explan the outcomes (grades acheved n the three subjects at hand), analysng potental bases n each nstance. Secondly, we measure the mpact of the determnants on the dependent varable at dfferent ponts n ts condtonal dstrbuton, by means of quantle regressons (QR). In ths fashon, we wll be able to provde a sense of how the mpact of the explanatory varables may dffer throughout the grades dstrbuton. For example, one may fnd that a partcular covarate, whle seemngly mportant at the mean as a determnant of the outcome, may n fact have dfferent mpacts across students wth hgh or low grades. Our paper falls nto a large lterature that examnes the determnants of unversty students academc performance (see, e.g., Dearden et al., 1998, Smth and Naylor, 1, for the UK; Ede and Showalter, 1998, for the US; Marcenaro and Navarro, 7, for Span; and Hanushek, 1986, for a good overvew of the lterature). However, very few of these studes have focused on factors affectng performance n specfc subjects of a college degree, as we do here. To our knowledge, the only excepton s a recent lterature evaluatng the effect of remedal math nstructon on the perfomance n Prncples of Economcs n US and UK unverstes, respectvely (see, e.g., Pozo and Stull, 6 and Lagerlöf and Seltzer, 8). In ths sense, we expect that our fndngs here can shed some lght on the above-mentoned debate on the adequacy of the currently avalable system of hgh-school tracks n Span. The rest of the paper s structured as follows. Secton descrbes the dataset. In Secton 3, we present the alternatve econometrc approaches and dscuss potental bases. Secton 4 offers the man results. Secton 5 contans a dscusson about how representatve s the sample and checks for some potental selecton bases. Fnally, Secton 6 concludes.. Data and Descrptve Statstcs The data s made up of a questonnare dstrbuted among four cohorts of freshers enrolled n the blngual group of the BA degree (Lcencatura) n Economcs durng the academc years /3 to 5/6. 5 All these freshers 5 Beng a student n the blngual group means that, except for a few subjects (e.g. those related to Law), all teachng takes place n Englsh. Admsson to ths group s condtonal on passng an Englsh exam organzed by UC3M. Courses are organzed on a semester bass and 4

5 were taught Maths by the same nstructor (one of us) n classrooms wth a maxmum capacty of about 1 students per group. We solcted nformaton from them about the type of school (publc, charter and prvate) they attended durng hgh school (two years of Bachllerato at ages 16 and 17), the knd of tranng they receved durng ths perod (there are four types of Bachllerato tracks: techncal, natural scences & health, socal scences and humantes whch are chosen by students at age 15 just before startng ther frst hghschool year,.e., Prmero de Bachllerato) and the grades they obtaned both n the Selectvdad exam when they fnshed hgh school at age 18 and n the two Bachllerato courses at ages 16 and 17. To avod measurement errors, these last two peces of nformaton were cross-checked wth the UC3M admnstratve records. The response rate to the questonnare was 96.5%, yeldng a sample of 386 ndvduals (leavng repeaters asde, who represented 7.3% of the populaton). A bref descrpton of the relevant varables s provded n Table 1 where we present the condtonal dstrbuton of (categorcal) grades gven students characterstcs plus the uncondtonal frequences of the latter n the last column. For expostory purposes, we have grouped the fve categorcal grades nto three broader categores: S (SUS), AN (AP+NOT) and SM (SOB+MH). Overall, 49.% of the students are male whlst 89.3% are Spansh. By famly background, 7.3% had (at least) one of ther parents wth a college degree. 6 By type of school, 4% come from publc schools, 1% from charter schools and 37% from prvate schools. By type of Bachllerato track, 67% have done socal scences, 6% the techncal one and the remanng 7% dd natural scences & health (3%) and humantes (4%). It should be emphaszed that the hgh school tranng n mathematcs s more ntense n the techncal and natural scences & health Bachlleratos than n socal scences. These are the three tracks where students take two compulsory annual math courses, whereas t s only an optonal subject for those enroled n humantes. 7 Table summarzes the contents of the dfferent tracks n terms of compulsory and optonal subjects. [ Tables 1 and about here] Table 1 shows that male students are less successful than female students n passng these subjects (except n Introecon). Lkewse, those comng from publc schools wth socal scences or humantes Bachlleratos tend to do worse. Interestngly, however, students from publc schools (mostly wth a techncal track) do rather well n achevng the hghest category (SM=) n all the three subjects. Thus, students from these hgh schools seem to have a U-shaped there are ten subjects n the frst year (fve n each semester), wth exams takng place n February and June. 6 The ndcator varables Parent () and (1) denote no parent wth a unversty degree and at least one parent wth such a degree, respectvely. 7 We checked that all students n our sample comng from the humantes track had taken a math course as one of the optonal subjects n ths hgh-school track. 5

6 dstrbuton across grades. The lower tal contans those who chose socal scences or humantes tracks whlst n the upper tal there are those who dd more scentfc-orented tracks. Gven that 7% of hgh-school students n Span are enroled nto the publc educaton system, the latter fact could be explaned by the exstence of hgher competton among the best students n these hgh schools, partcularly among those completng a techncal track. Hence, comparng the best students n ths track (equvalent n all observable characterstcs but wth dfferent school backgrounds), t seems that the ones wth a publc school background are lkely to be drawn from a hgher pont n the underlyng ablty dstrbuton. As mentoned before, the condtonal dstrbutons of type of school and parental college background are remarkably smlar, whch wll render dffcult to dentfy ther separate effects on outcomes. It s also worth notcng that foregn students exhbt a slghtly hgher varablty n grades than natves. Fnally, the last row n Table 1 presents the correlatons between the numercal marks n each of the subjects and the marks n the Selectvdad exam. These correlatons range between.5 and.67, beng largest n the case of Maths. Fgure 1 depcts the (kernel) denstes of the (numercal) grades n the three subjects. The dstrbutons n Econhst and Introecon are unmodal wth the former beng the one more shfted to the rght (.e., hgher probablty of a pass grade). Conversely, the densty of Maths s bmodal and t s the one more shfted to the left (.e,. lower probablty of a pass grade). 8 To acheve comparablty across subjects n the estmaton of the mpacts of the dfferent pre-unversty determnants, we wll use the standarzed grades n the emprcal analyss. Hence, the estmated effects are measured n terms of the correspondng standard devatons (s.d. s). To convert these grades nto numercal ones, one should multply the former by the s.d s of the grades. [Fgure 1 about here] Fgure, n turn, dsplays the denstes of the Selectvdad and Bachllerato grades whch are smlar to a conventonal sklls dstrbuton. As expected, the latter tend to be unformly larger than the former llustratng the fact that students tend to do worse n centralzed exams than n those takng place at ther own schools (the grade gap between Bachllerato and Selectvdad s.51 wth a s.d. of.9). Snce t s sometmes argued that non-publc schools tend to nflate the Bachllerato grades of ther students more than publc schools, Fgure 3 depcts the respectve gaps for these two broader school types. We fnd some supportng evdence for ths clam n our sample: the grade gap n non-publc schools (.66, s.d=.6) s larger than n publc schools (.31, s.d=.18). Thus, 8 The moments (mean and s.d.) of the three dstrbutons are as follows: Maths (5.17,.5), Introecon (5.7, 1.57) and Econhst (6.48, 1.44) 6

7 beng less dstorted, the Selectvdad grades are the ones chosen as a more approprate proxy for unobserved ablty n the emprcal secton. 9 [Fgures and 3 about here] 3. Econometrc approaches 3.1 A bref overvew of the producton functon approach We rely upon an extensve lterature analyzng school outcomes n developng and developed countres usng a producton functon approach; cf. Hanushek (1986, 1995), Case and Deaton (1999), Bjorklund et al. (3), Todd and Wolpn (3) and Glewwe and Kremer (5). Accordngly, outcomes are explaned as a functon of several nputs n the followng manner: y = x δ + δ a + u (1) 1 y = x β + β a + u () where y and y 1 ( = 1,,..., n) represent some metrc of academc performance (grades) n two dfferent ponts n tme ( t =, 1) : before enterng unversty (e.g., grades n the Selectvdad exam, denoted by denoted by S y, or grades n Bachllerato, B y ) and at the unversty (.e., grades n each of the three dfferent subjects, y 1 ), respectvely; a t s unobserved ablty n each perod; x t s a vector of nputs contanng the ndvdual and famly background characterstcs dscussed above plus the hgh-school track; and u t are zeromean..d. dsturbances. Assumng that the regressors n (1) and () are uncorrelated wth the dsturbances, and that a 1 = a + v, where v s an error term, a standard soluton (see Hanushek, 1986) to control for unobserved ablty s to solve for for a n (1), so that y becomes a proxy for a 1. Ths mples that () can be rewrtten as: However, to the extent that y ς + w. (3) 1 = x 1 + x 1 ς + ς 3 y w u 1 ( β / δ ) u + β = v, errors-n-varables ( u s correlated wth y ) and other endogenety problems (potental correlaton of v wth some of the regressors) are bound to nvaldate the use of OLS as a consstent estmaton approach for the parameters n (3). For example, as wll become clear below, one of our nputs of nterest,.e., the hgh-school 9 Notce that some of the students have a Selectvdad grade below 5 (the pass grade) because, as mentoned earler, the centralzed exam grade only accounts for 4% of the overall mark. 7

8 track, s present n both (1) and () snce t s chosen before takng the Bachllerato/Selectvdad exams and t may not be random. For example, t s often argued that the best students are the ones who choose the techncal track n hgh school. Thus, f we fnd that ths track mproves academc performance n an Economcs degree, t does not follow necessarly that a randomly allocated hgh-school student to the techncal track would later on exhbt a better performance n such a degree. Ths would lead to potental bases. 1 In what follows, we brefly revew some of the procedures proposed n the lterature to crcumvent these shortcomngs. The frst one s based on the followng assumptons: () treatng ablty as a fxed effect,.e., a = a 1 = a, () assumng that x = x 1 = x, nsofar as the dates of the Selectvdad exam and the unversty exams are rather close n tme, and () Cov ( xt, u ) = Cov( xt, u 1) =, (t=,1). Further, under the addtonal assumpton of β = δ, subtractng (1) from () yelds: ( y y ) = x ( β 1 δ1) + ( u 1 u ). (4) 1 Note that (4) mmcs the well-known frst- dfferencng or wthn estmaton approach to control for fxed effects n panel data. Thus, under the prevous assumptons, one can obtan consstent estmates of the relatve gans n academc achevement before and after enterng unversty. Nonetheless, there are good reasons to suspect that β δ snce some of the nnate abltes to succeed n hgh school may be dfferent from those requred at unversty-level studes. In a such a case, estmaton of (4) wll not be not be a vald procedure. 3. Bases n estmatng average treatment effects by OLS There are, however, other ways of achevng consstency that do not requre the assumptons leadng to (4). They are often based on the use of nformaton on students academc achevements before beng subject to a partcular treatment (e.g. the choce of a partcular track or of a type of hgh-school). Bonhomme and Sauder (8) provde a nce llustraton of ths approach by usng pretreatment outcome varables as nstrumental varables (IVs) for post-treatment ones n order to obtan consstent estmates of the Average Treatment Effect (ATE) of the choce of type of school on later outcomes n the UK. Unfortunately, we lack ths type of nformaton because, besdes the Selectvdad exam, Spansh hgh-school students do not have any other centralzed examnaton, snce the abolton of the Reválda de Cuarto de Bachllerato. The latter was a centralzed examnaton taken when students were 14 years old, whch was abolshed n 1 We could, however, argue that, snce there are no repeaters n our sample, enrolng n an Economcs degree can be nterepreted to a large some extent as a random choce. The fact that there s an mportant fracton (33%) of freshers n our sample who dd not follow a socal scences Bachllerato (and that are not repeaters) probably reflects a hgh degree of uncertanty about what college degree they would subsequently enrol n. 8

9 1975. Thus, lackng any genune pre-treatment varables, our estmated ATE s lkely to be based. Nothwthstadng, under some (admttedly restrctve) alternatve assumptons to be lad out below, t can be shown that a slghtly dfferent IV approach to estmate (3) can yeld estmates of the ATEs whch are unambguously downward based. Note that ths s a rather helpful result snce gettng a lower bound means that, f our estmated ATE s quantatvely and statstcally relevant, then the true ATE wll be even more mportant. To llustrate the ntuton behnd ths approach, let us assume, for concreteness, that we are solely nterested n estmatng the ATE of choosng a gven hgh-school track at 16 years of age (treatment) whereas the reference category s choce of any other track (control). Let D be a dummy varable for those ndvduals who are treated, so that the coeffcent of D n () becomes the true ATE. 11 Then, choce of y as a proxy for unobserved ablty (for the S reasons dscussed n Secton 1), and denotng by c the remanng set of regressors n the vector x, wll lead to the followng equvalent expressons to (1) and (): 1 S S y = δ c + δ D + δ a + u, (5) , y = β c + β D + β a + u (6) where β 1 s the true ATE we are lookng for. Then, solvng for equaton: y 1 a n (5) and replacng t nto (6), yelds the followng β β β S β S = ( β δ ) c + ( β1 δ1) D + y + ( u 1 u ), (7) δ δ δ δ From (7), t becomes clear that the best we can acheve wth ths approach s a consstent estmate of the slope on D,.e., β1 ( β / δ ) δ1, whch dffers from the true ATE, β 1, unless δ1 =, a case that we dscarded before snce the choce of hgh-school track s prevous to the Selectvdad exam. However, ths based ATE can stll be useful to make statements about the true ATE f we mpose the followng reasonable assumpton. A.1: () sgn ( β 1 )=sgn ( δ 1 ), and () sgn ( β )=sgn ( δ ) >. 11 Notce that we are also assumng that the potental outcomes are a lnear functon of the dfferent covarates and the treatment effect s common across all ndvduals. 1 It s also assumed that c 1 = c = c, and that a 1 = a = a. 9

10 The dea behnd A.1.() s that f a partcular hgh-school track prepares students better/worse for future unversty-level exams, t also prepares them better/worse for the Selectvdad exam. Assumpton A..(), whch just ensures that ( β / δ ) >, s trval snce ablty s always thought to mprove performance n both exams. Ths means that, f we are able to fnd a consstent estmaton procedure for the parameters n (7), the estmated ATE of D under A.1 would yeld a downward based estmate (n absolute terms) of the true ATE. In other words, f the the estmated ATE s found to be postve, the true ATE would be even more postve whereas, f t s negatve, the true ATE wll be even more negatve. Such a lower bound wll be denoted n the sequel as LB (= β 1 ( β / δ ) δ ). Notce that, n prncple, OLS wll not yeld a consstent estmate of LB n (7). s Frst, due to the presence of u n the composed error term n (7) and the fact s S that, from (5), u s correlated wth y, we wll get an nconsstent (downward S based) estmate of the coeffcent on y due to errors- n- varables. Second, S the fact that, from (5), y and D are also correlated mples that the estmated coeffcent on D wll also be nconsstent. To be more precse about the sgn of the bas on LB, let us frst assume that S E ( Du ) = E( Du 1) = E( cu ) = E( cu 1) = E( y u 1) =. Next, after applyng by the projecton matrx M I c( cc ) 1 c = c to both sdes of (7), so that c s removed from ts RHS, let us denote the projected regressand n the (second- step) regresson as ~ y 1 ( ~ ~ y 1 = M c y 1, etc.), the matrx of regressors, ~ S ( D y ) as X ~, the composed error term as w ~, and the vectors of parameters and OLS estmators as b and b ) ols, respectvely. Usng the vector notaton, we can easly compute the sgn of the bas on LB by selectng the frst element (.e., the one pertanng to the coeffcent on D ) n the (x1) vector of probablty-lmts, gven ) ) ~ 1 by p lm( b b) E( ) E( ~ ~ ols = Χ Χ Χ w). Ths yelds: ~ ~ s ( ~ S Cov( D, y ) Var u ) p lm( LBols LB) = ( β / δ ) ~ ~ ξ, (8) det( E( Χ Χ)) whose sgn depends on the sgn of ~, ~ s Cov ( D y ) snce ( β / δ ) > from A.1.() ~ ~ and det E ( Χ Χ) >. Assumng as before that the regressors n (5) and (6) are uncorrelated ~ wth ther respectve error terms, equaton (5) mples that ~ S ~ ~ Cov D, y ) = δ Var( D) + δ Cov( D, ~ ). Snce the frst term s always postve and ( 1 a δ >, t becomes clear that the sgn of ξ wll depend on the sgn and sze of Cov ( D ~, a~ ). If t s negatve and suffcently large (.e., the least able students choose track D), ξ could be zero or negatve, n whch case LB ols (= β β / δ ) δ + ) remans a genune lower bound of the true ATE. By contrast, 1 ( 1 ξ 1

11 f t turns out to zero or postve (.e., f there s no relaton or f the most able students choose track D), the bas wll be unambguously postve, makng us no longer sure that LB ols s smaller than β 1. However, even n ths problematc case, a lower bound could be acheved f the szes of remang terms nvolved n the RHS of (8) lead to a suffcently small postve bas. The only way to check whether ξ s suffcently small would be to compare the OLS results wth those obtaned from an alternatve IV estmaton procedure that yelds consstent estmates of the parameters n (7). Ths ssue s dscussed next. 3.3 Instrumental varables To obtan consstent estmates of the parameters n (7), we adopt an IV approach based on usng students Bachllerato grades, denoted by y B, as an S nstrument for y. 13 Specfcally, as n (5) and (6), we assume that the equaton B determnng y s : B B y = c + γ 1 D + γ a + u Let us further make the addtonal assumpton. γ. (9) A: () The varables c, a and D are orthogonal to the error terms n (5), (6) and (9), and () the error terms n these equatons are uncorrelated among them. Then, projectng agan both sdes of (7) and (9) on c, and denotng the matrx ~ of projected IVs as ( ~, ~ B Z = D y ) and the vector of IV estmates as b ) IV, mply that ) ~ ~ 1 ~ p lm( biv b) = E( Z Χ) E( Z ~ w ). Thus, selectng the second element n such a (x1) vector yelds: ~ ~ ~ ( ~ B ~ ) ~ B Var( D) Cov y, (, ) (, ~ w Cov D y Cov D w ) plm( LBIV LB) = ~ ~ =, (1) det( E( Z Χ)) snce ~ B Cov( y, ~ w) = ~ ~ ~ Cov ( D, w ) = (from A.), whereas det E ( Z Χ ~ ). In other B S B words, f we accept A., then y wll be uncorrelated wth u, u and u 1, so that ths nstrument works n elmnatng the asymptotc bas n (8). Hence, as mentoned earler, a comparson of the OLS and IV estmates of (7) wll provde us wth some ndcaton of how serous the bas term (ξ ) s. How credble s A.?. In prncple, two crtcsms can be made aganst ths assumpton. Frst, t can be argued that, gven our lmted nformaton on students famly background (.e., parents college attanment and school type), omtted varables could lead to non-zero correlaton between regressors and dsturbances. Second, snce y s clearly not a pre-treatment covarate, there B 13 We are grateful to the Co-edtor and one of the referees for pontng out ths soluton to us. 11

12 can be a non-zero correlaton between the nstrument and u 1 (and hence wth w ), therefore nvaldatng the IV approach. Regardng the frst crtcsm, admttedly not much can be done about t wth our avalable dataset except to accept the strong assumpton that our two proxes capture almost perfectly parental background. As dscussed n Secton 1, we clam that ths s acceptable nsofar as parents educaton and choce of school are bound to be good proxes for parental nputs (socal status) n chldren s educaton. Moreover, teachng facltes are bound to be strongly related to type of school. Thus, our clam seems plausble. As for the second crtcsm, one could argue that the Bachllerato grades are also almost perfectly correlated wth students academc performance before they jon Bachllerato at age 16. In other words, our mplct assumpton s that someone performng well (badly) n earler stages of prmary and secondary educaton s bound to have a smlar performance n Bachllerato. By contrast, the novelty of takng the Selectvdad exam at a centralzed level (.e., n a dfferent envronment from the exams taken at hgh school) may yeld a somewhat dfferent performance, as llustrated n Fgure 3 by the worse grades obtaned by students n ths exam. In case the prevous arguments do not convnce the reader, we wll also report, for robustness, OLS regressons (to be nterpreted as partal correlatons) of unversty-subject grades on hgh- school track dummes and other exogenous regressors, therefore excludng the potentally endogenous posttreatment covarates-.e., y S and (possbly) type- of school - from the set of regressors. 3.4 Addtonal caveats An addtonal caveat to be consdered s the possblty that students enroled n the techncal or natural scences & health tracks may face toughter entryexams (except n those subjects whch are common across all tracks) than those dong socal scences or humantes. In such a case, ths may bas upwards ther ATEs snce hgh grades n hgher educaton wll be correlated wth lower entryexam grades. To check ths ssue, Fgures 4a and b dsplay the dstrbutons of Bachllerato and Selectvdad grades by hgh-school track, respectvely. We can observe that students n the techncal track do better than the rest n both exams. Snce there s no control for ablty n these dstrbutons, the most plausble nterpretatons of ths fact s that ether they have hgher ablty or that they are better prepared. Hence, the reader should be aware that all the results presented below are lkely to be subject to ths caveat that cannot be addressed snce we lack nformaton on the determnants of choce of tracks. By contrast, another type of selectvty bas wth respect to the overall populaton of freshers n 1

13 UC3M, stemmng from the fact that the freshers n our sample belong to a blngual group, for whch knowledge of Englsh s requred, can be addressed (see Secton 5 below). 4. Emprcal results [ Fgures 4a and 4b about here] The results obtaned wth the dfferent econometrc approaches are dscussed n ths secton. 4.1 Least-Squares: OLS and IV Tables 3a-3c show the results of estmatng (7) by OLS and IV n pooled regressons. The dependent varable s the standardzed (numercal) grade n each of the three subjects taken by fresher, whle the controls are: a gender dummy (female=1), a natonalty dummy (foregner=1), Selectvdad grades (numercal), two dummes for type of school (charter=1 and prvate schools=1), three dummes for hgh-school tracks (natural scences & health=1, techncal=1 and humantes=1), a dummy for parental background (unversty degree=1), and fnally three dummes for cohorts. Thus, the reference group corresponds to Spansh male students from publc schools wth a hgh school track n socal scences, whose parents lack a college degrees, and who took the (February) exams n the /3 course. [ Tables 3a to 3c about here] Before dscussng the results, t s worth hghlghtng that, as mentoned n Secton, we found hgh multcollnearty n all specfcatons between the controls capturng type of school and parental background. 14 In all nstances, the estmated coeffcents on the correspondng dummes were not sgnfcant but, when one of these controls was skpped from the regresson, the estmated coeffcent of the one left n showed up hghly sgnfcant. Snce the dummes for school type had hgher sgnfcance level on ther own than the ones for parental college attantment, for sake of brevty we wll only report n the sequel the specfcatons ncludng the former control. Hence, an approprate nterpretaton for the estmated ATEs of type of school s that they are capturng, n addton to ther own genune effect, other famly background effects that we cannot separately dentfy. Further, to confrm that the Selectvdad exam grades are n fact a post-treatment varable wth respect to the choce of hgh-school track, we also ran a regresson (not reported here) of those grades on the remanng set of controls n (7), yeldng smlar qualtattve results to those obtaned when the subject grades are used as the dependent varables. As dscussed n Secton 3, ths mples that endogenety could be a potental problem. For ths reason, we wll start by reportng results from 14 As mentoned n Secton 1, the correlaton coeffcent between the parental background dummy and a sngle dummy for non-publc schools s

14 smple regressons of subject grades on the ndvdual characterstcs, excludng the (potentally endogenous) Selectvdad grades and the dummes for school type. These should be nterpreted as partal correlatons that could be very nformatve f we are unable to properly address the endogenety bases. Columns (1) n each of the three Tables present the partal correlatons excludng both the Selectvdad grades and the school type dummes. Columns () offer the results from estmatng specfcaton (7) wth all nputs. In columns (3), the lnear specfcaton s augmented wth nteracton terms between the Selectvdad grades and type of track to check whether the dffculty of ths exam dffers across tracks. Fnally, the last set of columns dsplays the IV estmates where the Bachllerato grade s used as an nstrument for the Selectvdad grade. In all cases, robust standard errors are reported n parentheses. The most mportant fndng s that the IV estmates of (7) are very smlar to the OLS ones. Ths s not surprsng, gven that the computed (partal) covarance terms n the RHS of (8), ˆ s Cov ( D, yˆ ), are farly small (.11,.4 and -.5 for the the techncal, natural scences & health, and humantes tracks, respectvely). Moreover, the correlaton between the Selectvdad and Bachllerato grades s very hgh (.96). To the extent that our assumpton that the Bachllerato grades are a good proxy for academc performance before Bachllerato s a plausble one, ths means that the Selectvdad grades are also capturng a sgnfcant fracton of the students sklls at the pre-treatment stage, mplyng that the OLS bas, ξ, s bound to be small. Therefore, ths result yelds favourable support to usng OLS n estmatng (7) to obtan a lower bound for the true ATE. Ths seems to be further confrmed by the results obtaned from the partal-correlaton regressons n columns (1) whch are are qualtatvely smlar to the OLS and IV results. 15 Fnally, the nteracton terms do not seem to matter. In all nstances, havng followed a techncal track seems to lead to a better performance n Maths and Introecon (and not sgnfcatvely worse n Econhst) than havng completed a socal scences track (reference category). By contrast, students wth a humantes background tend to do unformly worse. Interestngly, female students tend to perform better n Maths than male students whereas there are no statstcally sgnfcant dfferences between domestc and foregn students. 15 As regards the ATE of Bachllerato track, we fnd larger (n absolute value) estmates for the techncal (postve) and the humantes (negatve) tracks n columns (1) than n columns (), ndcatng that these varables are the ones whch are more correlated wth the omtted covarates (Selectvdad grades and type of school). Lkewse, the estmated coeffcents on the female gender dummy seem to be larger n columns (1) than n columns () for Maths and Econhst. 14

15 Gven the smlarty between the OLS and IV results, we wll focus next on hghlghtng the man results n column () of each subject. The largest effects are found for the Selectvdad grade and the techncal track dummy. For example, an extra pont n the unversty entry-exam leads to about.6 extra s.d. s (1.54,.95 and.83 ponts, respectvely) relatve to the reference group n each subject. Lkewse, havng completed the techncal track leads to.68 extra s.d. s (1.7 ponts) n Maths and.45 s.d. s (.7 ponts) n Introecon, wthout any sgnfcant gan n Econhst, whereas.5 extra s.d. s (1.5 ponts) n Maths are acheved by those who followed the natural scences & health track. By contrast, the humantes track has a penalty of almost.6 s.d s (1.5 ponts) n that subject. Regardng the effect of type of school (subject to the key nterpretatonal caveat mentoned earler), havng attended a non-publc school (or comng from a hgher-educated famly) s related to be a better grade on average. For example, comng from a prvate school leads to.3 and.5 extra s.d s. n Maths (.73 ponts) and Introecon (.38 ponts), respectvely, relatve to comng from a publc school. As regards gender, female students get.14 s.d. s (.38 ponts) more than ther male classmates n Maths, wthout sgnfcant dfferences n the remanng subjects. Lastly, wth the excepton of the 4/5 course, the cohort dummes are sgnfcantly negatve. Despte the short sample perod, ths gves some support to the extended opnon among several pundts that tranng n hgh schools has been deteroratng over tme due to expandng partcpaton n secondary educaton. Notwthstandng, ths effect mght be contamnated by the presence of dfferent nstructors n two of the three subjects. Fnally, for completeness, we report n Table 4 the OLS results obtaned from the wthn specfcaton n (4). The estmates are of course quanttatvely dfferent from those n colums () of Tables 3a-3c snce we are mpossng the restrcton ( β / δ ) = 1. Therefore, they should be nterpreted as the net effects of the vector of covarates x on the gap between the subject and Selectvdad grades. Yet, the prevous qualtatve fndngs reman smlar n ths restrcted specfcaton. [ Table 4 about here] 4. Quantle Regressons The fact dscussed earler that we may not have well-behaved dstrbutons n the outcome and n some of the other varables mples that least-squares coeffcents may yeld partal nformaton. Accordngly, n lne wth a growng lterature on the applcaton of ths technque to achevement producton functons, we use quantle regressons (QR). 16 Followng the well-known methodology frst proposed n Koenker and Bassett (1978), the model of QR n 16 Illustratons of the use of QRs n the lterature on schoolng outcomes can be found, e.g., n Ede and Showalter (1998), Levn (1), and Marcenaro and Navarro (7). Gven the smlarty of the OLS and IV estmates, the appled QRs are solely based on OLS. 15

16 ths setup can be descrbed as follows. Usng numercal grades, let (y 1, g ) be a random sample, where g =(D, y, c ) and Q θ (y 1 g ) s the condtonal θ th S quantle of the dstrbuton of y 1 gven g. Then, under the assumpton of a lnear specfcaton as n (3), the model can be defned as y 1 = g β θ + u θ1, Q θ (y 1 g ) = g β θ (11) where the dstrbuton of the error term u θ, F uθ ( ), s left unspecfed, just assumng that u θ1 satsfes Q θ (u θ g ) =. The estmated vector of QR coeffcents, θ, s nterpreted as the margnal change n the condtonal quantle θ due to a margnal change n the correspondng element of the vector of coeffcents on g, and can be obtaned usng the optmzaton technques descrbed n Koenker and Bassett (198). β In order to facltate the comparson of results across subjects, we choose dfferent quantles for each subject so that the percentles become smlar n terms of both numercal and categorcal grades. These are: θ=.5 (grade:.8, SUS),.75 (7. NOT) and.95 (9.5, SOB) for Maths; θ=.1 (3.8, SUS),.8 (7, NOT) and.98 (1, MH) for Introecon; and, fnally, θ=.1 (4.5, SUS),.7 (7., NOT) and.98 (9.3, SOB) for Econhst. Tables 5a-5c report the estmated coeffcents at the relevant quantles (together wth the regresson at the medan,.e., at θ=.5) usng the specfcaton n the columss () of Tables 3a-3c. For convenence, we reproduce the OLS estmates n the frst column (average) n order to compare the coeffcents at the mean as opposed to the coeffcents at the chosen quantles of the condtonal dstrbuton of (numercal) grades. 17 [Tables 5a to 5c about here] The QR results offer valuable addtonal nformaton to the one dscussed above. 18 The key result n Maths s that the mpact of prvate and charter schools (n the range of. to.4 extra s.d. s or.5 to 1 ponts relatve to publc schools) s much weaker at the top quantle, n lne wth the prevalence of students comng from publc schools at the hgher part of the grade dstrbuton. A smlar effect s observed for the Selectvdad grades (the most sgnfcant varable, together wth the techncal track), whose effect decreases throughout the dstrbuton. The opposte effect holds for the humantes track. As regards the other subjects, the results are smlar, wth the only excepton that completon of more scence-based tracks does not seem to help n Econhst. The 17 For the sake of brevty, we do not report the estmated coeffcents on the cohort dummes. However, the pattern of negatve coeffcents for the 3/4 and 5/6 cohorts remans the same across quantles. 18 An F test on the jont equalty of all the coeffcents across the chosen quantles yelds p- values very close to zero, therefore rejectng the null. 16

17 natural scences & health track even has a negatve effect at the top quantle. 19 Fnally, foregn students seem to perform better than natve students at the hgher quantles. 5. Other selecton bases Whle the bases dscussed n Secton 3 affect the nternal valdty of our results, our sample of students has two characterstcs that could lead to (favourable) sample selecton bases and affect therefore the external valdty of our conclusons. The frst one s that UC3M s consdered to be one of the Spansh unverstes wth the hghest reputaton n Economcs. That, n prncple, could lead to attractng better students than other unverstes wth a lower rankng n ths feld. Unfortunately, we do not have any control group n order to test for ths selecton bas. However, there s ample evdence that the moblty of students across regons s very low and the entry-exam grade requested by UC3M to get admsson n the Economcs degree s a low pass (5.), despte beng somewhat larger n LADE (6.). These acceptance grades are smlar to those requested by most unverstes. Thus, we conjecture that bases are bound to be mnor n ths respect. The second potental selecton bas stems from the fact that students n our sample belong to a group s taught n Englsh. Gven that Span s one of the European countres wth the lowest share of the populaton speakng foregn languages (44%), t could be the case that the freshers n ths group are not representatve of the populaton of freshers takng lectures n Spansh, whch s an ample majorty. An ndcaton that ths bas could be present s that the proporton of students comng from publc schools n the blngual group (4%) s sgnfcantly lower than the correspondng share n the total populaton of students completng hgher-secondary educaton (66%). In order to check whether our students n the sample are somewhat dfferent from those enroled n non-blngual groups, we have used another dataset regardng two groups (taught n Spansh) of freshers n Economcs at UC3M durng -6. The aggregate sample sze for these control groups s 57 students. Informaton on these freshers was agan obtaned from the unversty archves and relates to gender, natonalty, grades at the Selectvdad exam and on whether students completed hgh school n the regon of Madrd (CM) or n other Spansh regons. Unfortunately, we lack the remanng ndvdual 19 These results reman qualtatvely smlar when a multnomal logt setup s used to explan the probabltes of fallng nto each of the categorcal grades, as we dd n a prevous verson of ths paper (see Dolado and Morales, 7). Accordng to the rankngs publshed n the newspaper EL MUNDO (CAMPUS magazne) snce 7, UC3M s one of the two best unverstes n Span to complete lcencaturas n Economcs or LADE, together wth UPF. 17

18 nformaton whch was used before n analyzng the determnants of outcomes for the blngual group. To control for ths sort of sample selecton bas we estmate a partcpaton equaton n the blngual group as the frst step n the conventonal two-stage Heckman approach for selecton correcton. We use the pooled sample of all students (both from the Spansh and blngual groups) whch ncludes 958 students (=57+386). Gven the scarce nformaton avalable, we use the resdence n CM (whch s also avalable for the students n the blngual group, but has not been used as a covarate n the prevous sectons) as the dentfyng varable. The nsght for ths choce s as follows: f the blngual group s a (favourably) selected group from the populaton of students enrolled n Economcs degrees at UC3M, then t s lkely that a larger share of students from other Spansh regons wll enrol n ths group, gven that there are very few unverstes n Span offerng blngual courses. 1 [ Table 6 about here] The frst column n Table 6 presents the results from a frst-stage probt model where the dependent varable equals 1 f a student belongs to the blngual group and otherwse. The covarates are gender, natonalty, a dummy varable on resdence (CM=1), (numercal) grade at the Selectvdad exam and the cohort dummes (not reported). Results pont out that beng a foregner and lvng outsde CM ncrease the probablty of belongng to the blngual group whlst the other covarates do not have sgnfcant effects. Thus, our dentfyng strategy seems to work approprately. The next three columns n Table 6 report the results the OLS estmaton of the lnear model n columns () of Tables 3a-3c but ths tme augmented wth the nverse Mlls rato (lambda) from the partcpaton equaton. Ths last term turns out to be always nsgnfcant and, despte some mnor quanttatve changes n the estmated coeffcents, none of the qualtatve results stressed above change wth the selecton correcton. Hence, although we cannot completely dscard selecton bases wth respect to the overall populaton of Spansh freshers n Economcs, our results seem to provde vald nference n the context of UC3M undergraduates and, possbly, n relaton to the overall populaton of smlar students completng an Economcs degree n other unverstes n Madrd. 6. Conclusons Our man fndng n ths paper s that, condtonal on our proxy for sklls and all the nterpretatonal caveats dscussed above, the most mportant covarate related to academc success n Maths (for Economsts) courses durng the frst year of an Economcs degree s to have prevously followed a techncal track n the last two years of Bachllerato. Interestngly, we also fnd that havng 1 The fractons of students lvng outsde the regon of Madrd are 18.3% and 1.% n the blngual and Spansh groups, respectvely. The averages of the entry-exam grades are 6.8 and 6. respectvely, though a test for equal means does not reject the null wth a p-value of

19 completed a socal scence track, nstead of a techncal track, does not sgnfcantly mprove performance n other two subjects wth less (Introecon) o very lttle (Econhst) mathematcal content but whch requre more pror economcs tranng. Gven that the socal scences track was desgned by the Spansh educaton authortes to provde the approprate tranng for hgh school students wllng to become economsts, t s farly strkng that a background n, e.g., mathematcs, physcs or chemstry leads to a better academc performance. Another nterestng fndng s that, among the best students, there s a majorty of those comng from publc schools. One possble explanaton for ths fndng s that publc schools seem to exert hgher competton among the best students than non-publc schools. Ths prevous hgher exposure to competton may help them to adapt better to the compettve envronment of publc unverstes. Fnally, on average, females tend to do better than males. As stressed throughout the paper, some of these fndngs have to be taken wth cauton when drawng educaton-polcy mplcatons, snce we have not been able to address the ssue of non-random selecton, partcularly n the choce of Bachllerato tracks. Moreover, one further qualfcaton s that our outcomes are very short-term (grades at the end of the frst semester of freshers) rather than longer-term ndcators lke fnal grades or term of completon. Notwthstandng, one possble prelmnary lesson to be drawn s that, as suggested n the quotaton at the epgraph of the paper, hgh-school students n the socal scences track, ntendng to later enrol n an Economcs degree, do not seem to get enough math tranng and therefore struggle n the more mathematcally ntensve subjects. Ths may explan the hgh dropout rate (close to 3%) at the early stages of ths degree. A possble soluton to ths problem could be to adopt the math courses n the techncal track as compulsory subjects for those wllng to enrol n Economcs wthn the socal sences track. Alternatvely, extensve remedal math courses could be offered, as UC3M and other Spansh unverstes currently do. Whether these remedal courses are effectve n helpng less techncally able students s n our future research agenda. References 1. Bjorklund, A. Edn, P-A., Fredrksson, P. and Kruger, A. (3), "Educaton, Equalty and Effcency: An Evaluaton of Swedsh School Reforms" SNS, Stockholm, Sweden.. Bonhomme, S. and U. Sauder (7), Accountng for Unobservables n Comparng Selectve and Comprehensve Schoolng, CEMFI (mmeo). 3. Calero, J. (6) Desgualdades tras la Educacón Oblgatora: Nuevas Evdencas, DT 3/6. Fundacón Alternatvas, Madrd. 19

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