the university gender gap: the role of high school grades

TheUniversityGenderGap:TheRoleofHighSchoolGradesTorbenDrewesMESA2009‐4

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Toronto,Ontario,Canada‐May2009 www.mesa‐project.org

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TheUniversityGenderGap:TheRoleofHighSchoolGrades

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iiTheUniversityGenderGap:TheRoleofHighSchoolGrades

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Abstract

Giventhe differentdistributions ofhighschool grades formaleandfemalegraduates, the rationingofuniversity placesusingminimum admissions standards might potentially have pro‐ducedthegenderimbalanceobservedinCanadianuniversities.Whyhighschoolmarks havebeenlowerformalesthanfemalesthenbecomes aquestionofsomeinterest.The estimationofagrade production functionwasused inthispaper toexaminethe roleof different effort levels in generating gender differ‐encesinhighschoolgrades.Usingdata fromtheYouthInTran‐sitionSurvey(YITS),thepresentanalysis foundthatoverhalfofthe difference in mean grades between males and femalescould be accounted for by different levels of effort. Fewermales had aspirations for university education than femalesandthisfactmightaccountforthelowerlevelsofeffortamongthem.However,itis alsotruethatmales werenotabletopro‐duce highschoolaverages (and, therefore, theentry require‐mentforuniversity)asefficientlyasfemales.

TorbenDrews is a Professor of Economicsat TrentUniversity.([email protected]).

Pleaseciteas:Drewes,Torben(2009).TheUniversityGenderGap:TheRoleofHighSchoolGrades.MESAPro‐ject Research Paper 2009‐4 . Toronto, ON: Canadian Educat ion Pro ject .(www.mesa‐project.org/research.php)


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TableofContents........................................................................................................Acknowledgements 5

....................................................................................................................Introduction 6

.....................................................................................................................Background 7

............................................................................................................LiteratureReview 9

......................................................................................DataandDescriptiveStatistics 10

....................................................................................TheGradeProductionFunction 12

..........................................................................................................TheModel 12

............................................................................................EffortandCausality 13

............................................................................................................Estimates 15

.....................................................................................DecompositionAnalysis 16

...................................................................................Mathvs.ReadingGrades 17

.....................................................................................................................Conclusion 18

....................................................................................................................References 20

.........................................................................................................TablesandFigures 22

.......................................................................................................................Appendix 28

AcknowledgementsThis researchwas financedbytheCanada MillenniumScholar‐shipFoundation throughtheMESA project. Iwish to thankRossFinnie for his advice andStephenChilds forhis excellentresearchassistance. Helpful comments werereceivedfromFe‐lice Martinello, Lorne Carmichael, David Johnson and otherparticipants intheMESA sessions inVancouver andMontreal,as well asthe MESA researchcommittee. Any errors are thesoleresponsibilityoftheauthor.


IntroductionIn a single generation, women have

movedfromminority representationinCan‐ada’s universities to a significant majority,accountingfor58percentoffull‐timeunder‐graduate enrolment in 2006 (AUCC, 2007).This phenomenon is not uniquetoCanada.Women now form a majority of universitystudentsin19outof22OECDcountries.Thedramaticevolutionofgenderpatterns inuni‐versity enrolment is a fascinatingsocial andeconomic phenomenon, but its causes andconsequencesare,as yet,notentirelyunder‐stood.

Mostoftheresearchonthecausesofthechanging gender gap has focussed ondemand‐side explanations, trying to under‐standwhymales arenowless likely thanfe‐males towant tocontinue ontoauniversityeducation. Possibleexplanations rangefromsociological perspectives on the failure ofschoolstoinstil in males a desirefor educa‐tion tomoreorthodox economic paradigmssuggestingthatmales facelower ratesofre‐turn. Thispaper takes as itspointofdepar‐turethequestionofwhymales are nowlesslikelytobeabletopursuea universityeduca‐tion. University spaces arerationedon thebasis of high school averages, a practicewhich, although gender neutral on the sur‐face,mayplaya roleinthegendergap,giventhat males have lower high school gradesthanfemales.1 Indeed,as will beshownbe‐low, even if there were equal applicationrates, the current gender difference in par‐ticipationrates couldtheoretically be gener‐atedbyuniversityadmissionstandards.

Before concluding that low high schoolgrades arewhatis preventingmales frombe‐ingadmittedtouniversities,however,itmustberecognizedthat thesegradesare endoge‐nously determinedbystudents. Forall ofitsapplications and importance in understand‐ing the outcomes of education, thehumancapital perspective has only infrequentlybeenappliedtothe process ofeducation it‐self. Yet it seemsonly reasonablethat highschool grades reflect optimizing choices onthepartofstudents,representingabalancingof the costs of producing higher averagesagainst thebenefits of doing so. Formanystudents, the primary benefit of havinghigher gradesis that they enableentry intopostsecondaryeducation(PSE).AnAmericansurvey sought to determine themotivationforeffortamonghighschool studentsbyask‐ing the question: “When youwork reallyhard in school, which of the following rea‐sonsarethemost important for you?”. 79percent of the 36,000 high school respon‐dentsreported“I needthegrades togetintocollege”(Bishop,1999,2).Lowerhighschoolgrades amongmales may therefore not bethecauseoftheir lower university participa‐tionrates;instead,theirlowergrades maybetheresultofdecisions madeby themnot toattend university and, consequently, not toexpend the effort required tomeet admis‐sionsstandards.

This paper doesnot unravel the thornyeconometric issue of simultaneity betweenhighschool performanceanduniversity par‐ticipation.Its contributionis rathertoexploittherichYouthinTransitionSurvey(YITS)dataonhighschool behaviour andgradestoex‐

1TheUniversityGenderGap:TheRoleofHighSchoolGrades

1Thisis,ofcourse, trueonlyforindividualsseekingdirectentryintouniversitiesfromhighschools. A smallminorityofuniversity stu‐dentsareadmittedasmaturestudents.

plore the process by which high schoolgrades areproduced.Inparticular,this paperestimates the relationship between gradesandeffort levels todetermine theextent towhichthelowerhighschool performanceofmales canbeattributedtolowereffortlevelson their part. If all of their lower perform‐ancecanbeattributedtotheir lowereffort,then theobservedgender gap in universityattendance may be the result of males’choices not toparticipate, forwhateverrea‐son. However,ifless thanall ofthis gapcanbeattributedtoeffortlevels,thenitmightbeconcluded that males and females differ inthe efficiency withwhich they canproducetheentrance requirements, andtherequire‐ments themselvescouldbedeemeda culpritin the production of the observed genderimbalance.

BackgroundIflowerhighschoolgrades amongmales

playany roleintheuniversity gendergap,itmust be truethat rationing on the basis ofthosegradesoccurs.Someindirectevidenceinsupport of this case exists. For example,Coelli (2005) founda significantnegative re‐lationshipbetweencohortsizeanduniversityattendance and interpreted this finding asevidence oftherationingofuniversityplaces.Fortin(2005)concurred, arguingthattuitionlevels aretoolowtoclear themarket inthefaceoflargeincreases inthedemandforuni‐versity education, leaving the short side ofthe market to determine enrolment. Theshortsideis thesupply sideanduniversitiesuserationing onthe basisofgradestoallo‐categovernmentfunding‐determinedspaces.

Direct evidence of rationing is muchhardercome by,asitrequiresinformationonindividuals who applied to universities butweredeniedadmission. However, theappli‐cationprocess in Ontario produces aset ofdata that candirectly showtheexistenceofrationing in that province. All high schoolgraduates seeking admission to any of theprovince’suniversitiesmust apply throughacentralized application centre (Ontario Uni‐versities Application Centre). Applicantssupply somepersonal informationandmakeunlimited choices of universities and pro‐grams towhichtheywishtoapply.2 Thehighschools attended by the applying studentssupply informationon their grades in theirfinalyear. Universitiestowhichthestudentappliedprovideinformationonwhetherindi‐vidualswere offeredadmissiontotheirpro‐gram of choice and whether or not theyeventuallyregisteredattheuniversity.Figure1(below)illustratesthenumbers ofsuccess‐ful and unsuccessful applicants by highschoolgradeaverage.

Notall 2005applicants toOntariouniver‐sities wereofferedadmission,with6.5per‐centofapplicantsnotreceivinganofferfromany institution. Since different universitiesand programs have different admissions re‐quirements,there is nocleardemarcationofa single cut‐offgradein Figure1. Neverthe‐less, itis clear thatrationingdoes take placelargely onthebasis ofhighschool averages.Since the application process is costly interms oftimeandmoney,andsincestudentshave fairly good information onminimumentrancerequirements,OUAC applicants areself‐selected in the sense that high school

MESA‐MeasuringtheEffectivenessofStudentAid2

2 A fixedfeepermits 3choiceswitheachadditionalchoice addingtothe cost. The greatmajorityofapplicantsmake nomorethan3choices.

graduateswithlowgrades maynot incur thecost if there is no reasonable hope of suc‐cess. Withlowergrades,males areless likelyto apply (and appear in the data), even ifthey have aspirations for higher educationsimilar tofemales. Therefore,onecouldnotsimply compare the gender distribution ofapplicants tothatofsuccessful applicantstodetermine the impact of rationing on thegendergap.

The YITS data does not contain unsuc‐cessfulapplicationsfor admission touniver‐sity but does containhighschool gradesforall individuals,whetherornot theywereap‐plicants. Table1 reports thedistributionofhighschoolgradesbygender.

To illustrate how rationing by gradesmight produce the observed gender gap,suppose that all malesandfemaleswanted

togo touniversity but a minimumgradeof70%foradmissionhadbeenestablished.Foreach100males and100females,howmanywouldgetin? Therewouldbe 74males and86 females admitted,withthe resultingpro‐portionoffemales in universitybeing54per‐cent. If the cut‐offgrade were set at 80%,theproportionof females wouldbe60per‐cent. Hypothetically, then, theuse of highschool gradestorationplaces inuniversitieswould have the potential to generate thegendergapactuallyobserved.3

The YITS data then show that genderblind rationing on thebasisof high school averages would theoretically be capable ofproducing the observed gender gap in uni‐versity participation even if males were aslikely toapplyas females.But it isalsotheo‐reticallypossiblethatthegradedistributionsoutlinedaboveweretheresultof gradetar‐

getingbymales,manyof whom had no in‐tention of pursuing auniversity educationand who thereforehavenoreasontoex‐erttheeffortrequiredto obtain the mini‐mum a dm i s s i o n scut‐offs.4 Infact, thereality is likely tobe acombination of thesetwo explanations, thepossibility of whichpresumably explainsFrenette andZeman’s


3Changesinthe gendercompositionare anothermatter. Americanevidencesuggeststhatgirlshaveheldanadvantage inhighschoolgradesrelativetoboys overaconsiderableperiodoftime(seeCho(2007)andGoldinetal. (2006)). Canadianevidenceonhighschoolgradesovertime isnotavailable,butifthesamepatternholdstrueforCanada,wewouldhavetoappealtoanincrease inthedegreeofrationingtoproducethechangeingendercompositionwehaveobserved.

4SeeAllgood(2001)foramodelofgradetargets.

(2007) attributing both grades andpersonalcharacteristics as underlying reasons for thegender gap. Indeed, their results indicatethatslightlymore than30percentofthe gapwas caused by differences in high schoolgrades,althoughtherewasnocorrectionfortheendogeneityofgrades.

The question then becomes why maleshavelower grades thanfemales and,specifi‐cally, what role effort plays in theprocess.An educationproduction function approachwasdeemednecessarytoaddressthisissue.

LiteratureReviewSeveralauthors have takenintoaccount

theactiveroleplayedby learners inproduc‐ingoutcomes andhavesoughttomodeltheireffort levelsina choice‐theoreticframework.Forexample,Cho(2007)treatedhighschoolaverages as an outcome that could be in‐creased throughgreater effort,withthe op‐timal levelofeffort chosen tobalance mar‐ginal benefits and costs, where the benefitproducedbymoreeffortwas a higher prob‐ability of admission to PSE and subsequentenjoymentofhigherincome.This model wasused toexaminehowincreases inwomen’shighschool performancehavecontributedtothe changing gender composition ofAmeri‐canuniversity students. Improvedperform‐ancewas foundtoexplainmorethanhalfofthechange in theuniversity enrolmentgen‐der gapover thepast thirty years. Theim‐provement inwomen’s highschoolachieve‐ment was attributed partly to exogenouschanges inhowhighschools preparewomenfor university and partly to increasedeffort

levels inducedby the greater benefits pro‐ducedby the availabilityofexpandedlabourmarketopportunitiesforwomen.

Bishop (2006) argued that most of theeducation production function literaturetreats students as “goodsinprocess” ratherthanactiveparticipantsinthe productionofacademic achievement. He provided evi‐dence that student effort accounted for animportant shareof the varianceacrossindi‐viduals in achievement but, unfortunately,did not investigate gender differences. Amorecompletemodel of student effortwasprovidedinthreeequations: a learningfunc‐tion, arewardsfor learning function, and acost of student effort function. A Cobb‐Douglas specificationofthe learningfunctionwasusedtoderive theoretical results, suchas the optimal effortlevel,butthemodel wasnotimplementedempirically.

Numerousstudies havefoundthatindica‐tors of student effort, such as hours spentstudyingor onhomeworkassignments, havesignificant effects on learning.5 Althoughmultivariatemethodshavebeenusedtocon‐trol for prior achievement and family back‐ground, effort indicators havetypically beenregarded as exogenously determined. Thefairly large bodyofliterature ontherelation‐ship between academic performance andworking while inschool is moredirectly re‐lated to the research in this paper, as theconnection between working and perform‐anceis derivedfromchoices of timealloca‐tionwithina fixedtimebudget. The findingson the impact of working on academicachievement (and, by extension, the impact


5See,forexample,Betts(1996).

oftimeavailable for studies)have tendedtobeambiguous.6

Stinebrickner and Stinebrickner (2004,2007) haveproduced the researchmost di‐rectly related to the estimates to follow inthis paper. Inbothpapers referencedabove,theirobjectivehasbeentoestimate therela‐tionshipbetweeneducational outcomesandstudents’ study timeand effort. Althoughtheendogeneityofeffortwasacknowledged,theauthors contendedthatthecausal effectof studying could be identified by using auniquefeatureofthe institution‐specificdataavailable tothem. At theparticular institu‐tion they studied, the assignment of room‐mates wasmaderandomly andthe data al‐lowed for the observationof certain room‐matecharacteristics. Specifically, someindi‐viduals found themselves housed withroommateswho brought video games withthem,whileothers didnot. Theresultingex‐ogenous variationinthequantityandqualityof studying inducedby thepresence or ab‐sence of such distractions allowed theauthors toconclude thatstudyefforts hadasubstantial causal role to play in the gradeproduction function. Furthermore, the IVestimates weremuch larger than OLS esti‐mates. Thesedifferencesmight have arisenfrom unobserved, permanent ability differ‐encesor throughwhat theauthors calleda“dynamicselection”effect,wherebystudentsreceiving an unexpectedly low grade mighthavereactedby changingtheir effort levels.Thelattereffectwas foundtobethe underly‐ingcauseofthedifferencebetweenOLSandIVestimates.

DataandDescriptiveStatisticsThedata weredrawnfrom theYouth in

TransitionSurvey (YITS),alongitudinal surveydesigned to provide information about theeducation, trainingandworkexperiencesoftwotargetpopulations: acohortofindividu‐als whowere18to20years oldonDecember31, 1999(Cohort B)andacohortwhowere15 years oldon that date(Cohort A). Theanalysis presented here made use of datafrom Cohort A. The YITS has now gonethrough4 cycles, the first oneconducted in2000onalmost30,000 students andthe lat‐estfollow‐uptakingplace in2006whenCo‐hort A respondents were 22 years of age.Since almost all respondents were finishedhighschool bythetimeofthelastcycle,onlythefirstthreecycles wereusedinthis paper.In the first cycle, YITS obtainedinformationfrom students, parents andschool adminis‐trators toproducearichset of informationonstudentbehaviours andaspirations,familybackground, school resources available, andsoon. Inaddition, CohortAparticipatedintheOECD’s Programmefor InternationalStu‐dent Assessment (PISA) evaluations, writingstandard tests in the areas of reading,mathematicsandscienceskills.

YITSrespondentswereaskedtheiroverallgrade average intheirlastyearofhighschoolin all cycles, with the results reported bygrade category (as in Table 1). This self‐reportedmeasure served asthedependentvariable.Threemeasures ofeffortwereusedin the estimates of the grade productionfunction. First,YITSrespondentswereaskedtoreportthe numberofhoursperweekthey


6SeeOettinger(1999)foracarefulanalysisthattakesintoaccountchoice‐basedendogeneity.

spentstudyingoutsideofclass.7 Second,theYITScollectedinformationonthenumber oftimestheindividual skippedclasses. Finally,respondents were askedtoreporthowoftenthestatementthat“theydidas little workaspossible, wanting to just get by” applied totheir approachtotheir studies. Other vari‐ables includedinthegradeproductionfunc‐tion were derived from information on pa‐rental financial resources, education andsupport, aswell as school resources. TheYITSgathered this informationdirectly fromparentsandschoolofficials, but only in thefirstcycleofthesurvey.

Tables 2 through 5 provide a statisticalpreview of differences in grades and effortlevels betweenmales and females in theirfinalyearofhighschool. Toget somepre‐liminary sense ofwhethereffortlevels mighthavebeendrivenby theneedtosatisfy uni‐versity entrance requirements, the descrip‐tivestatisticswere alsobrokendownbyaspi‐rations for a university education. Clearly,simultaneity was a problem here (and onethat has been left unresolved), since effortmighthavebeenmotivatedbyaspirations forhighereducationbutthoseaspirations might,inturn, havebeenaffectedby thestudent’sassessmentofhisorherability,as measuredbyhighschoolgrades. Onlymeasures ofuni‐versity aspirations reported in the first YITScyclewere used in this analysis in order toavoid, as muchas possible, the kindof dy‐namic endogeneity resulting from revisionsto aspirations that might have occurred asindividuals underwent periodic assessments

oftheirabilities as theymovedthroughhighschool.

Table 2repeats theinformationinTable1andadds a comparisonofgradedistributionsfor only those students with stated aspira‐tionsfor at least a university degree.8 Theproportionwithgrades ofatleast80percentwere significantly higher when only thosewith university aspirations wereconsidered,risingfrom32.2 percent to43.9 percent formales andfrom46.5percentto56.0percentfor females. Again, whether higher gradesamong thosewith aspirationsfor universitywere the result of high school students’working harder in the knowledge that theywouldneedtomeetadmissions standardsor,rather, their higher gradeswere influencingthoseaspirations is aquestionnotsettledinthis paper. Itis interestingtonote,however,thatthegendergapinthe proportionof“A”studentsfell from14.3 percentagepoints inthepopulationas a wholeto12.1percentagepoints among those with university aspira‐tions. If hopes for a university educationdrive efforts to earn grades in high school,this last finding might be seenas evidencethatdifferencesinsucheffortsmatter.

Tables 3 through 5 show tabulations ofthethreemeasures ofeffortinthe YITSdatausedin the estimatesof theeducationpro‐ductionfunction. Table 3 shows themostdirect measure of effort by tabulating thenumber of hours of study outside theclass‐room. Only 16 percent of males reportedspending less than one hour studying per


7Individualswere askedtoreportthisinformationforthelastyearofhighschool,soeffortlevelsweretiedtothehighschoolaverage inthesameyear.

8Inthesampleusedtoestimate thegradeproductionfunction,56.5percentofmalesand66.9percentoffemaleshaduniversityaspira‐tions.

week compared to six percent of females.Using the mid‐points of the categories and17.5hours for the topopen‐endedcategory,theaveragenumberofhoursspentstudyingwas 4.7 for males and 6.4 for females.Amongthosewithuniversity aspirations, thenumber of hours spent studyingwentup to5.5and7.1hours,respectively.

Timespenton studies outside theclass‐room is onemeasureof effort. So, too, istime spent inside the classroomwhich, ap‐parently, is a choicevariable for many highschool students. Over 21 percent ofmalesreported skipping classes at least once aweek,as comparedto15percentoffemales.Those with university aspirations weresomewhat less likely to skip class this fre‐quently,butthepractice was clearly notun‐commonamongbothgenders.

Table 5 revealssignificant gender differ‐ences in respondents’ self‐assessment oftheir effort. While almost 60 percent ofmales stated that they had worked at lessthanfullcapacityatsomepoint,only40per‐cent of females reported behaving in thisway.

By all threemeasures of or proxies foreffortexertedinhighschool,females workedharder and longer thanmales. Hadmalesworkedas hardasfemales,wouldtheyhavebeenable togeneratesimilargrades orwerethere gender differences in the efficiencywithwhichgradeswere produced?Toexam‐

inethis question, the next sectionestimatesagradeproductionfunction.

TheGradeProductionFunctionTheModel

Thegeneral formofthe gradeproductionfunctionis

G=g(F,S,E,ε)Where:Gisthemeasuredfinalyearschoolgradeaverage,

Fisavectoroffamilyinputs,bothcur‐rentandpast,

Sisavectorofschoolinputs,Eisavectorofcurrentstudenteffort,εisameasureoftheindividual’sex‐ogenouslydeterminedinnateaca‐demicability.

As Hanushek(1986)has pointedout, theeducationproductionfunctionliteraturede‐rivesits conceptualbasis from thestandardproduction function literature but withouttheemphasis onfunctionalform. This paperfollows thepracticeofmostauthors whousea linearized empirical specification whichmightbe regardedasareducedformor localapproximation:9

where Xi is a vector of non‐effort vari‐ables.

The specific explanatory variables usedare listedinthetableofsamplemeans,Table6.10 Interms offamily inputs,themodel in‐


9Although,seeFiglio(1999)foradiscussionoffunctionalforminthis context. Anotherspecificationissuethatneedstobepointedoutisthecapacityofstudentstochoosetheir coursesofstudy. Malesandfemalesmaywellmake selectionsthat reflecttheircomparativeadvantages. Thus, inthe language ofproductionfunctions,the twogenders may be producing differentoutputs. I amgrateful toananonymousreviewerforpointingthisout. Unfortunately, theYITSdata didnotpermitthe estimationofgradeproductionfunctionsforindividualcoursesorsetsofcourses.

10SamplemeansfortheeffortvariableshavealreadybeenreportedandarenotrepeatedinTable6.

cludedmeasuresoftheparents’ capacity toprovidesupport for theeducational process,measuresofindirectparental influence,andmeasuresofparentalactivity. Capacitywasmeasuredusingcombinedparental incomein1999 as reportedincycleoneofthesurvey.All sourcesof income were accounted for,includinggovernmenttransfers. Theeduca‐tional attainmentofparentsorguardians wasincluded to capture, separate from financialcapacity, the indirect influence of parentaleducation in terms of expectations, under‐standingofthePSEsector,etc.While incomeandeducationmighthavecapturedtheenvi‐ronment inwhich therespondents grewup,they didnotmeasureproactiveinvolvementandencouragement onthepart of parents.Toproxyforactivesupportoftheirchildren’seducation, theestimates use thePISA vari‐able onthe frequencywithwhichthemotheror the father worked with the student onschool work (ranging from never toseveraltimesa week). Notethat,beinga PISAvari‐able,this measureappliedatthe timeofcy‐cle one andwas not contemporaneous withhighschoolaverages inthe final yearofhighschool.

School resources available to supportstudent learning and grade achievementwere captured in three variables from thePISAschoolsurvey.Anindexofthequalityofschool infrastructurewas basedonprincipals’reports concerning building conditions andinstructionalspace. Theindex rangedfrom‐1.12 to 3.38, with higher values implyingbetterconditions.Similarly,theavailabilityofeducational resources (including computers,library resources, scienceequipment and soon) was captured by an index that rangedfrom ‐1.9 to 3.22. Teaching support was

measuredbythestudent‐teachingstaffratio:thenumberofstudents inthe schooldividedby the numberoffull‐timeequivalentteach‐ers. Again,thesemeasures havebeenmadeavailableonlyforcycleone.

Provincial dummieswereusedtopickupany differences in theway in whichgradingoccurred,as well as any provincial variationsin resources not captured in the school re‐sourcevariables.

As discussed above, the student’s owneffort was measured using three proxies:hours of study per week; incidenceof skip‐ping classes; and the degree to which theyagreed that they didaslittle workas possi‐ble.

Mostofthevariables measuredin Table6shouldhaveproducedmeansthat werenotsignificantly different formales andfemales,sincegenderplayednoroleintheirdetermi‐nation. There were, therefore, only twocomparisonsofinterest. First,males andfe‐males received about the same amount ofhelpwith their schoolwork from their par‐ents,sothereappearedtobenogenderdif‐ference in theinvestment of timemadebyparents.Second,the meanfamilyincome forwomenwas lowerthanitwas formen,whichmayhavebeenaccountedforbythemargin‐ally lower levels of educational attainmentamongtheparentsoffemales. Whythis oc‐curredisnotclear.

EffortandCausalityThere is a strong possibility that effort

levels, whichareendogenous values chosenby students, are correlated with academicability which, inturn, is likely tobeadeter‐


minant of high school grades. Without ameasureof this ability, itwouldwindup intheerror termandOLSestimatesoftheef‐fects of included effort variables on gradeswouldbebiased,aproblemakintothe stan‐dard ability bias issue inestimating theef‐fectsofeducationonearnings. Ifmoreablestudents devoted greater effort to earninggrades, perhaps because learning activitieswere moreenjoyable for them, an upwardbias in the estimated effort effect in thisanalysis could be expected, as the highergrades ofstudentsexertinggreater levelsofeffort couldbeattributedentirely tothatef‐fort(insteadof,atleastpartly,totheirhigherabilitylevels).

As StinebricknerandStinebrickner(2004)pointed out, however, the bias story is un‐likely to be that simple when the humancapitalmodel ofthe learningactivityis takenseriously. Highschoolaveragesmay notbetheultimategoal ofstudents’optimizingcal‐culations. Instead,theirdecisionsaboutef‐fortmaybebasedontheprobabilityofentryintopostsecondary educationandthe higherincomeresultingfromthatentry.Itis plausi‐bletosuppose,as theseauthors pointedout,that highability studentswithgradetargetsin mind exert less effort than those withlower abilityas they aimonly toachievetheminimumgradesrequiredforadmissionintoPSE. Incomparisonsofthe grades ofhighereffort/lower ability students to those oflower effort/higher ability students, esti‐mates of the effect of effort appear to be

downwardbiased.

Unlike thedata usedbyStinebricknerandStinebrickner (2007), there was no naturalexperimentinthe YITSthatproducedexoge‐nous changes ineffort. Neitherwere theresuitable instruments available for the stan‐dardIVstrategyappliedinthecontextofen‐dogenousregressors.11 Onemighthopethat,sincethe ultimateuseof the gradeproduc‐tion function inthis analysiswas tomakeacomparison between genders, differencingthe functions might alsodifference out anybiases. This wouldhave occurredonlyunderverylimitingassumptions,however.Supposethetruemodelsformalesandfemaleswere:

Without ameasureofability, theinitial esti‐mationwouldbe:

followedby

with δj representing the slope coefficientfroma regressionofabilityoneffortforgen‐der j.The estimateddifferenceinthecontri‐butionofefforttogrades wouldbe unbiasedonly if the last term equalled zero, whichwouldbeunlikely.

The YITS data contained the results ofstandardized PISA scores, measured at age


11 DavidJohnsonsuggestedtheuse ofdistance toapostsecondaryeducationasapossible instrument,notingFrenette’s(2002)findingthatdistancematters indecisionsregardingpost‐secondaryeducationattendance. With lower incentives toattend, studentsliving far‐therawaymightexert lowereffort levelsforreasonsunrelatedtoacademicability. Unfortunately, thepostalcodedata requiredtocon‐structarelatedinstrumentwerenotavailable.

Introducinga laggedmeasureofperformanceapproximatesthevalueadded,oraugmentations,tolearningspecificationsusedby someauthorswhenestimatingeducationproductionrelationships.See,forexample,EhrenbergandBrewer(1994).

15, andthese scoreshadsomepotential toact as proxies for ability. Unquestionably,PISAtestscoreswereindeedcorrelatedwithinnate ability, but they were also likely tohave been correlated with effort. Note,however, that PISAperformancewouldhavebeen influencedby effort levelsin thepast,whilethe effortvariables usedinthegradesproduction equation weremeasured in thelast year ofhighschool. If the correlationbetweenpastandcurrent effort levels wereless thanperfect, using PISA reading scoresas a plug‐in solution to the omitted abilityvariable problemwouldhave not eliminatedthebiascompletely butmighthavereducedit.

EstimatesIn the spirit of descriptive statistics, the

present analysis first estimated the gradeproductionfunctionwithoutthePISAreadingscore proxy for ability, without claiming ameasureof causality. The productionfunc‐tionswerethenre‐estimatedafter includingthe PISA reading score as the only feasibleapproach to resolving the omitted abilityvariable problem.Theresults arereportedinTable7.

Notethat theYITS reported gradeaver‐agesinthefinal yearofhighschoolas acate‐gorical variable; these categories are pre‐sentedin Tables1 and2. Since thediffer‐ences in the categories were meaningful,employinga categoricalmethodlike orderedlogit wouldnot havebeenappropriate. In‐stead, studentswereassignednumericalval‐ues equal to the mid‐points of the gradecategoryandthegrade productionfunctions

wereestimatedby OLSappliedtoeachgen‐derseparately.

All three effort measures were stronglycorrelatedwiththelevelofhighschoolaver‐ageintheregressions thatexcludedthePISAscoreabilitycontrol.12 Additional time spentstudyinghadsignificantandlarge coefficientswhich tended tobe smaller for males thanfor females, except for thehighestcategory.Compared to thosewho claimed to alwayshave worked hard, those who sometimes,oftenoralwaysdidas littleworkas wasnec‐essary togetbyearnedlowergrades. Therewerenocleardifferencesbetween thegen‐ders in the behaviour of these coefficients.The estimated impacts of skipping classeswerenegativeandsimilar for malesand fe‐males. Aninterestingoutcomefromthere‐gressionresults isthatthecoefficients ofthethreedifferent effortmeasures weresimilarforthetwogenders.

Comparedtostudents whose motherhadcompletednomorethanahighschool edu‐cation, sons and daughters of college‐educated mothers achieved higher gradesandthosewithuniversity‐educatedmothersearnedevenhigher averages. Theeffect ofmothers’ education levels was similar formales and females. A similar patternwasseen in the impacts of fathers’ income, al‐thoughthe estimatedcoefficientontheindi‐cator for fathers’ college educationwas in‐significant. Having controlled for parentaleducation, theeffect of incomewasstatisti‐cally significant only for females and wassmall inmagnitude. As discussedabove,thefrequency with which parents helped their


12Again,noclaimforcausalitycanbemadesinceeffortlevelsareendogenous.

childrenwiththeir school workwas usedtocaptureparental involvement. As it turnedout,highschool performancewasnegativelyrelatedtoparentalhelpwithschool workex‐cept for females, where fathers’ help wasfoundtohave nosignificant impact. The ob‐vious interpretation wouldbe that parents intercededwhen their childrenwere havingdifficultywithschool.

None of the three measures of schoolqualityappear tohavehadaneffectonhighschool performance. This observationis notentirely inconsistent with other findings inthe literature on school quality, but mightalsobe attributableinthis casetothe inclu‐sionofprovincial controls. Ifprovincial fund‐ingschemes were uniform,inthatschoolre‐sources varied by province but not withinprovinces,therewouldbelittleindependentvariationinthequalitymeasures. Turningtothe estimates on these provincial controls,compared to Ontario, high school averagesforbothmales andfemaleswere significantlylower inNewfoundlandandLabrador,aswellas in Alberta, especially for females in the latter province. Relative high school per‐formance was higherinPrinceEdwardIsland.It was alsohigher for femalesonly inNovaScotiaandformalesonlyinQuebec.

Turning to the model with PISA scoresserving as proxies for ability, the impact ongrades ofspendingtimestudyingdiminishedfor males and became statistically insignifi‐cant for females. Thisfinding is consistentwith the simpler ability bias story discussedabove, where the data showed that effortandabilitywere positivelycorrelated,leadingto an upward bias in the estimated causal effectofeffortwhencontrols forabilitywere

not included. The deleterious effects ofshirking work and skipping classes, on theother hand, remained largely unaffected bytheinclusionofthePISAreadingscore.

ThePISA scores themselves werehighlysignificant determinantsofhighschool aver‐ages. Onestandarddeviationincrease inthePISAreadingscorewas estimatedtoadd3.6percentage points tothat averageformalesand3.8percentagepointsfor females. Theywerealsoclearlycorrelatedwithmeasures offamilybackgroundandsupport,reducingtheestimated impact of parental education, in‐comeandassistance. Provincial differences,however, appeared to be morepronouncedwiththeinclusionofthePISAscores.

DecompositionAnalysisWiththeaboveestimatescalculated, the

questionoftheextent towhich thegendergapinhighschool grades couldbeattributedtodifferencesineffortlevels was addressed.A standard Blinder‐Oaxaca decompositionwasusedtoanswerthis questionbyestimat‐ingtheproportionof thegrade gapattribut‐able to different distributions of the effortvariables. Normally, thechoiceofreferencegrouptouse ina decompositionis somewhatarbitrary; however, therationale involved inthe present analysis was to assume thatmales exerted the same levels of effort asfemalesandthentodetermine howmuchoftheoverall gendergapremained. Therefore,thedecompositionusedwasasfollows:

The first component on the right handside represents the portionofthegendergapinmeanhighschoolaveragesaccountedforby differencesin themeansof theexplana‐tory variables. Essentially, the effort vari‐


ables (as well as theremaining explanatoryvariables) were reset for males to those offemales and observationswere made as tohowthegrades ofmaleschanged. Thesec‐ond component captures differences in theefficiencywithwhichmales andfemalescon‐vertedinputsintothe gradeproductionfunc‐tion intohighschool averages. Table8 re‐ports the decomposition, isolating the pro‐portionofthefirstcomponentattributabletodifferencesineffortlevels.14

ConsideringfirstthespecificationwithoutthePISAscoreproxyforability,differencesineffort levels accountedfor slightly over onehalfofthe threepercentagepointgapinfinalhighschoolgradesandmore thanthe entireportionofthegap“explained”bydifferencesintheexplanatoryvariables.Theexplanatoryvariables not related to effort levels, whentakentogether,actually worked infavour ofmales,althoughonlymarginally so. Accord‐ing to this specification, then, if males hadworkedashardasfemales inhighschool, itcouldbe assumedthatthe gendergapinav‐erageswouldhavebeencutinhalf. Itwouldnot havebeen eliminated completely, how‐ever,as femalesappearedtohave beenabletoconvertinputs intotheproductionofhighschoolaveragesmoreeffectivelythanmales.

Introducing the PISA reading scoresasaproxy for ability reducedthe contributionofthe effort variables to the gender gap, butonlymarginally(toapproximately44percentof thegap). ThePISAscore, inthisapplica‐tion, was considered part of the “endow‐

ment” ofan individual and, not surprisingly,the total contributionof endowment differ‐encestoaveragegradedifferencesincreasedto almost 80 percent of theoverall genderdifference. Viewedinthis light, the reason‐ableness ofusingthe PISAscores as a controlfor pure ability differences could be calledintoquestion. Onthe other hand, thecon‐tinued finding of gender differences in theability toconvert inputsintogradeaveragesstrengthens the conclusionthatfemaleswerebetter able to earn the high school gradesrequiredforentry intopostsecondary educa‐tion.

Mathvs.ReadingGrades15

Giventhat theprimarygoalofthispaperwasto investigate the ability of highschoolstudents to pass minimum entry require‐ments for universities, its focus so far hasbeenonfinal highschoolaverages. Inordertodelvedeeperintotheexaminationofgen‐der differences, the differences in gradessortedby subject wereanalysed. TheYITSasked students about the last mathematics,language,andsciencecourses theyhadtakeninhighschool and,formathematics andlan‐guagecourses, their final grades wereavail‐able inthe data.Table9repeats thedecom‐position procedure used for overall highschool averages to see if the difficultiesamongmalesweregeneralor specific tothekindofsubjectmatterstudied.16 Thespecifi‐cations usedfor theindividual coursegradesresultsdidnotincludePISAscores.


14Inkeepingwiththejargonofthisliterature,theexplanatoryvariablesaretermed“endowments”. CompleteresultsarereportedintheAppendix.

15IamgratefultoFeliceMartinelloforsuggestingseparateestimatesforlanguageandmathematicsgrades.

16Theregressionresultswerenotreportedhere.Theyareavailablefromtheauthoruponrequest.

Clearly, subjectmatters. Almost nogen‐der difference was observed in the gradesobtained inmathematics courses, but thereappearedtobe a very substantial advantagefor females in language courses. Interest‐ingly, lowereffort inhighschool producedasimilar grade pointpenaltyformalesinbothmathematics andlanguagecourses.17 How‐ever,males appearedtobemoreefficientattranslating effort into mathematics grades,with their mathematics grade productionfunction lying higher at themeanof femaleendowments,andthis partiallyoffsetthelossofgradesthroughlowereffort.Inthecaseoflanguagecourses,however,theeffectoftheirlower effort was compounded by a lowerability to convert their efforts into goodgrades. A male who was observationallyequivalenttothe averagefemaleinthesam‐plewaspredictedtoearnalanguagecoursegradethatwasmorethan3.5percentlower.

Cautionshouldbeexercisedininterpret‐ing thesedisaggregated results,however, aseffort levels in the YITS data were not re‐portedby course, so itwouldbeimpossibleto determine or differentiate betweenhowmuch effort was put into mathematicscourses and how much into languagecourses. The twogendersmayhave haddif‐ferentcomparativeadvantagesor “compara‐tiveinterests” leadingthemtoallocatetheireffort differently across these kinds ofcourses.18 If,forexample,males hadtakenaparticular interest in mathematics coursesand dedicated a disproportionately largeshare of their overall study time to thosecourses,effort levels in thosecourseswould

havebeenhigherthanthoseusedtoproducethedecompositioninTable 9. This would,inturn, have producedover‐estimates of theirefficiencyadvantage inconvertingeffort intomathematics grades. Withoutmeasures ofeffort disaggregatedby course, the directionofbiasescouldnotbedetermined.

ConclusionThegendergapinuniversityparticipation

is aremarkable sociological phenomenon.Totheextent that it reflects differential accessto universities, it is also an important eco‐nomic problemthat needs tobeaddressed.Undoubtedly, part of the explanation forlower participation rates by males lies in alowerdesire ontheirparttopursuea univer‐sity education,whetherbecausetheyexpecttoearn lower returns for participationthanwomendoor becausetheir “taste” foredu‐cationis somehowlower.Eveniftheirdesirefor further educationwere the same, how‐ever, entrance standards set by Canadianuniversities mightrepresenta greaterbarrierformales thanfor females, giventhelowerhigh school gradesachieved by the former.Beforecomingtothatconclusion,however,itis important to consider thepossibility thatthoselower grades themselvesrepresent anartefactofmalehighschoolstudents’ lowerdesire to attend university and the conse‐quentreducedeffortputintogeneratingthegradesrequiredforuniversityentry.

The YITS data show that males in thesampledid exert lower effort levels in highschool than females, but that this lower ef‐


17Theobservedsimilarityofmathematicsgradesbetweenthegenderswasconsistentwiththe findingsofnationalassessmentsthroughtheSchoolAchievementIndicatorsProgram.SeeLauzon(2001),p.4.

18IamindebtedtoLorneCarmichaelformakingthispoint.

fort (and other personal attributes affectinggrades)accountedforonly52percentofthegap in the observed gender difference inmeangrades. Theremainderofthegapwasattributable todifferences betweenthegen‐ders in their ability toproduce high schoolgrades. IntroducingPISAreadingtestscoresintotheestimatingequationsas controls forability differences increased the proportionof theraw differential “explained” by effortand endowments, but these scores werepoorproxies forpureabilityas theyalsocap‐turedpasthistoriesofinvestmentinproduc‐ingacademicachievement.

Hadmalesinthesampleworkedashardat producinghigh school grades as females,anygendergapinuniversity participationat‐tributabletorationingbyentrancestandardswould have been lessened but would nothavedisappeared. Therefore, itis importanttoconsider why thegendersdifferedin theefficiency with which they produced gradeoutcomes. A preliminary examination ofcoursegrades bysubjecttypeindicatedquiteclearly that thedifficulties formales lay notinmathematicsbutinlanguagecourses.

This paperraises a numberoftopics withpolicy implications. First,althoughtherehasbeen considerable interest in access issues,researchtodatehas beenalmostexclusivelyfocusedonwhy someindividuals have beenunabletoaffordhighereducationorhavenot

been interested incontinuingeducation be‐yondhighschool. Almost noconsiderationhas beengiventosupply constraints in themarket forhighereducation.19 Figure1sug‐gests the role that such constraints mightplay. Similarly,postsecondary educationpol‐icy makes much mention of under‐representedgroups in postsecondary educa‐tion,butthat listofgroupsrarely,ifever,in‐cludesmales. Yet,ifmaleparticipationratescould bebrought up to the levelof femalerates,there wouldbeasignificantincreaseineducational attainment in the Canadian la‐bour force. Admittedly, this paper does notquantify theextenttowhichtherationingofuniversity spaces bygradesaffectsmale par‐ticipation. However, by introducing thesetwodimensions of theprobleminto thede‐bate on university accessibility, this paperaimstomakeacontribution.

If the rationing of university spaces byhighschool grades is,infact,contributingtothegender gap, then remedial action is re‐quiredtoeliminate the relative disadvantageingrades facedby males. The research inthis papersuggeststhatsuchremedial actionwill require bothmeasures to increase theirmotivationandmeasures toincreasetheef‐ficiencywithwhichmales translatetheiref‐forts into grades, particularly in languagecourses.


19Finnie(2004)isanimportantexception.

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TablesandFiguresTable1.Highschoolgradedistributions

Grade Males Females

90%+ 5.8% 8.7%

80‐89% 26.4% 37.8%

70‐79% 41.8% 39.1%

60‐69% 21.4% 12.3%

55‐59% 3.1% 1.5%

50‐54% 0.9% 0.4%

<50% 0.6% 0.3%

Source:YITS,CohortA

Table2. Highschoolgradedistributions,bygenderanduniversityaspirationsAllRespondents WithUniversityAspirations

Grade Male Female Male Female

90%+ 5.8% 8.7% 8.6% 11.1%

80‐89% 26.4% 37.8% 35.3% 44.9%

70‐79% 41.8% 39.1% 39.8% 34.7%

60‐69% 21.4% 12.3% 13.7% 8.1%

55‐59% 3.1% 1.5% 1.9% 1.0%

50‐54% 0.9% 0.4% 0.5% 0.2%

<50% 0.6% 0.3% 0.3% 0.2%Source:YITS,CohortA

Table3. Weeklyhoursofstudy,bygenderanduniversityaspirations

All Respondents With University AspirationsHours Male Female Male Female

0 6.7% 1.9% 3.4% 0.6%< 1 9.3% 4.1% 7.3% 2.5%1-3 36.3% 27.9% 32.6% 23.2%4-7 29.7% 37.0% 32.8% 38.6%8-14 13.8% 20.7% 17.7% 24.9%15 + 4.3% 8.5% 6.2% 10.2%Source:YITS,CohortA


Table4.Incidenceofskippingclasses:bygenderanduniversityaspirations

All Respondents With University AspirationsNo. of Times Male Female Male Female

Never 31.4% 37.2% 34.7% 37.9%Less than once a month 19.3% 22.4% 19.4% 23.8%Once or twice a month 27.8% 25.6% 26.5% 25.5%Once a week 11.3% 9.1% 10.7% 8.0%More than once a week 10.2% 5.8% 8.8% 4.9%Source:YITS,CohortA

Table5.Workeffort,bygenderanduniversityaspirationsAll Respondents With University Aspirations

Response Male Female Male FemaleNever 39.7% 56.8% 42.6% 59.1%Rarely 23.2% 22.6% 24.4% 23.8%Sometimes 22.0% 13.1% 20.3% 11.6%Often 10.4% 5.3% 9.1% 3.8%Always 4.7% 2.2% 3.6% 1.8%Response tothequestion: “How oftenwasthe followingstatementtrue for you. ‘I didaslittlework as possible. I justwantedtogetby’?”Source:YITS,CohortA


Table6.Samplemeans

Variable Males Females

Mother’sEducation

HighSchoolorLess 0.523 0.539

SomePostsecondary:Incomplete 0.035 0.028

College 0.262 0.257

University 0.180 0.176

Father’sEducation

HighSchoolorLess 0.541 0.568


College 0.244 0.225

University 0.196 0.189

Parent’sCombinedIncome 71.441 68.001

FrequencyofMother’sHelp(1=never,5=severaltimes/wk) 2.520 2.667

FrequencyofFather’sHelp(“) 2.319 2.361

School’sPhysicalInfrastructureIndex(SCMATBUI) ‐0.358 ‐0.338

School’sEducationalResourcesIndex(SCMATEDU) ‐0.243 ‐0.236

StudentTeachingStaffRatio 17.00 16.99

Nfld 0.018 0.021

PEI 0.004 0.004

NS 0.033 0.034

NB 0.026 0.027

QUE 0.228 0.220

ONT 0.382 0.390

MAN 0.036 0.036

SASK 0.043 0.042

ALTA 0.102 0.101

BC 0.129 0.125

No.ofObservations 8131 8500

Source:YITS,CohortA


Table7. RegressionresultsMale Female

DependentVariableWithoutPISA

scoreWithPISAscore

WithoutPISAscore

WithPISAscore

HoursofstudyperWeek(ref.group:0hrs.)

Lessthan1hour 0.933 ‐0.050 2.027 0.680

1–3hours 1.827** 0.661 2.046 0.190

4–7hours 2.837** 1.223* 4.071* 1.268

8–14hours 4.635** 2.437*** 5.981** 2.678

15+hours 6.879** 4.854*** 5.875** 2.810

DidasLittleWorkasPossible(ref.group:never)

Rarely ‐1.208** ‐1.572*** ‐0.402 ‐0.771***

Sometimes ‐3.294** ‐3.332*** ‐2.732** ‐2.537***

Often ‐4.060** ‐4.130*** ‐4.426** ‐3.936***

Always ‐3.843** ‐3.937*** ‐6.520** ‐5.381***

IncidenceofSkippingClasses(ref.group:never)

LessthanOnceperMonth ‐1.329** ‐0.987*** ‐1.558** ‐1.591***

OnceorTwiceperMonth ‐2.749** ‐1.946*** ‐2.397** ‐2.272***

OnceperWeek ‐3.842** ‐3.114*** ‐3.465** ‐3.512***

MorethanonceperWeek ‐5.563** ‐4.508*** ‐5.045** ‐5.120***

PISAReadingScore 0.0358*** 0.0388***

Mother’sEducation(ref.group:HSorless)

SomePostsecondary:Incomplete ‐0.270 0.135 0.202 ‐0.091

College 1.221** 0.654** 1.393** 0.604**

University 3.045** 1.649*** 2.806** 1.401***

Father’sEducation(ref.group:HSorless)

SomePostsecondary:Incomplete ‐0.321 ‐0.773 0.289 ‐0.191

College 0.446 0.091 0.912** 0.342

University 3.013** 2.104*** 3.397** 2.251***

Parent’sCombinedIncome(,000’s) 0.003 ‐0.002 0.006* 0.000

FrequencyofMother’sHelp(1=never,5=severaltimes/wk)

‐0.395** ‐0.092 ‐0.488** ‐0.049

FrequencyofFather’sHelp(“) ‐0.342** ‐0.213 ‐0.120 ‐0.070

School’sPhysicalInfrastructureIndex(SCMATBUI) ‐0.155 ‐0.292 0.242 0.161

School’sEducationalResourcesIndex(SCMATEDU) ‐0.004 0.223 ‐0.060 0.014

StudentTeachingStaffRatio ‐0.074 ‐0.169*** 0.006 ‐0.067


Table7continued

Male Female

DependentVariableWithoutPISA

scoreWithPISAscore

WithoutPISAscore

WithPISAscore

Province(ref.group:Ontario)

NFLD ‐2.115** ‐1.380** ‐2.167** ‐2.048***

PEI 1.402* 2.080*** 1.284* 2.016***

NS 0.820 1.182*** 1.405** 1.445***

NB 0.823 1.884*** 0.598 1.191***

QUE 1.866** 1.478*** ‐0.128 ‐0.895**

MAN 0.021 ‐0.238 0.453 0.016

SASK 0.335 0.283 1.020* 0.634

ALTA ‐1.077* ‐1.737*** ‐3.996** ‐4.753***

BC 0.491 0.503 ‐0.834 ‐0.925**

Constant 77.82** 61.85*** 77.18** 59.82***

R2 0.204 0.317 0.223 0.341

No.ofObservations 8131 8118 8500 8493

MeanofDependentVariable 75.92 75.92 78.95 78.95

***significantatthe1%level;**significantatthe5%level;*significantatthe10%level.Source:YITS,CohortA

Table8.Decompositionofmeangradedifferences

WithoutPISAscore WithPISAscore

MeanPredictionforFemales 78.945 78.957

MeanPredictionforMales 75.922 75.930

RawDifference 3.023 3.027

DuetoDifferentEffortLevels 1.598 1.335

DuetoDifferencesinOtherEndowments ‐0.153 1.052

TotalDuetoEndowments 1.445 2.387

DuetoDifferencesinCoefficients(evaluatedatFemales’Means) 1.577 0.64

Source:YITS,CohortA


Table9.Decompositionofmeangradedifferencesinmathandlanguagecourses

Mathematics Language

MeanPredictionforFemales 74.995 79.592

MeanPredictionforMales 74.536 74.892

RawDifference 0.459 4.700

DuetoDifferentEffortLevels 1.132 1.235

DuetoDifferencesinOtherEndowments ‐0.128 ‐0.071

TotalDuetoEndowments 1.004 1.106

DuetoDifferencesinCoefficients(evaluatedatFemales’Means) ‐0.545 3.594

Source:YITS,CohortA


AppendixFullDecompositionResultsThefollowingtables showthe disaggregateddecompositionresults. Somecaremustbe exercisedininterpretingthedisaggregationofthe overall differences duetocoefficients onindividual factors thathavenonatural zeropoint.20Changes inthescaleofanyindividual factorwouldchangetheallocationoftheunexplaineddifference(i.e., thatduetocoefficients)tothatfactor. Thus, theseemingly largecontributionofthestudent‐staffteachingratio(relativetoother factors)inthe right‐mostcolumnre‐flectsthemagnitudeofitsscale.


20ThispointwasmadebyJann(2008,8‐9).

Table10.Decompositionresults:specificationwithoutabilitycontrol

DependentVariable DuetoEndowments DuetoCoefficients

HoursofstudyperWeek(ref.group:0hrs.)Lessthan1hour ‐0.047 0.042

1–3hours ‐0.164 0.061

4–7hours 0.215 0.463

8–14hours 0.317 0.281

15+hours 0.283 ‐0.085

DidasLittleWorkasPossible(ref.group:never)Rarely 0.005 0.186

Sometimes 0.295 0.073

Often 0.220 ‐0.018

Always 0.095 ‐0.058

IncidenceofSkippingClasses(ref.group:never)LessthanOnceperMonth ‐0.040 ‐0.052

OnceorTwiceperMonth 0.052 0.090

OnceperWeek ‐0.104 0.034

MorethanonceperWeek 0.263 0.028



College ‐0.006 0.044

University ‐0.012 ‐0.042

Father’sEducation(ref.group:HSorless)


College ‐0.009 0.066

University ‐0.022 0.072

Parent’sCombinedIncome(,000’s) ‐0.010 0.199

FrequencyofMother’sHelp(1=never,5=severaltimes/wk) ‐0.058 ‐0.142

FrequencyofFather’sHelp(“) ‐0.015 0.534

School’sPhysicalInfrastructureIndex(SCMATBUI) ‐0.003 ‐0.134

School’sEducationalResourcesIndex(SCMATEDU) 0.000 0.014

StudentTeachingStaffRatio 0.001 1.351

Province(ref.group:Ontario)

NF ‐0.008 ‐0.001

PEI 0.000 0.000

NS 0.000 0.020

NB 0.001 ‐0.006

PQ ‐0.014 ‐0.439

MB 0.000 0.015

SK 0.000 0.028

AB 0.001 ‐0.293

BC ‐0.002 ‐0.166

Constant ‐0.637

Total 1.445 1.557


Table11.Decompositionresults:specificationwithabilitycontrol

DependentVariable DuetoEndowments DuetoCoefficients

HoursofstudyperWeek(ref.group:0hrs.)Lessthan1hour 0.003 0.1021–3hours ‐0.059 ‐0.2144–7hours 0.093 0.0108–14hours 0.166 0.01815+hours 0.200 ‐0.006

DidasLittleWorkasPossible(ref.group:never)Rarely 0.006 0.191Sometimes 0.299 0.245Often 0.225 0.031Always 0.095 ‐0.102

IncidenceofSkippingClasses(ref.group:never)LessthanOnceperMonth ‐0.031 ‐0.099OnceorTwiceperMonth 0.038 ‐0.096OnceperWeek 0.084 ‐0.057MorethanonceperWeek 0.216 ‐0.091



College ‐0.003 ‐0.013University ‐0.007 ‐0.046Father’sEducation(ref.group:HSorless)SomePostsecondary:Incomplete 0.001 0.012College ‐0.002 0.066University ‐0.015 0.030Parent’sCombinedIncome(,000’s) ‐0.006 0.152

FrequencyofMother’sHelp(1=never,5=severaltimes/wk) ‐0.014 0.104

FrequencyofFather’sHelp(“) ‐0.009 0.325School’sPhysicalInfrastructureIndex(SCMATBUI) ‐0.006 ‐0.172School’sEducationalResourcesIndex(SCMATEDU) 0.001 0.052StudentTeachingStaffRatio 0.001 1.731Province(ref.group:Ontario)NF ‐0.005 ‐0.010PEI 0.000 0.000NS 0.001 0.009NB 0.003 ‐0.017PQ ‐0.011 ‐0.558MB 0.000 0.009SK 0.000 0.016AB 0.002 ‐0.311BC ‐0.002 0.190PISAreadingscore 1.109 1.466

Constant ‐2.071Total 1.445 0.064


the university gender gap: the role of high school grades

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