Quantitativeeffectsofhighereducationexpansiononthereturns:EvidencefromtheUK

LeiXU

April2017

Abstract:

Thispaperstudiestheeffectofthe‘EducationReformAct1988’onthereturns

basedonQuarterLaborForceSurvey(QLFS)andUnderstandingSociety.After

examiningtheheterogeneousreturns,Iapplythedifference-in-difference(DID)

methodologytoexaminetheeffectoftheeducationreformonreturnsandthe

matchingDifference-in-Difference(MDID)methodologytoaccountfortheability

biassincethosenewlyrecruiteduniversitygraduatesafterthereformmightbe

differentfromthepreviousgraduates.Newlyrecruitedgraduatesconsistof

“freshstudents”whojustgraduatefromA-levelorotherschoolsandworkers

withseveralyearsofworkingexperiencescalledthe“maturestudents”.1 The

MDIDresultsshowthattheincreasinguniversitygraduatesreducethereturnsin

generalandthemagnitudeofthedecreaseisincreasingalongwiththeexpansion.

However,thematurestudentshavemorestablereturnscomparedtofresh

students.

JELClassification:I23,I26

Keywords:educationexpansion,maturestudent,Matching

Difference-in-Difference,psacalc

LeiXu

EconomicStudies,UniversityofDundee

E-mail:lxxu@dundee.ac.uk

1 Maturestudentsaredefinedasthestudentswhohaveworkingexperiences.Theworkingexperiencesiscalculatedbysubtractingtheageoffull-timeeducationwiththeagewhenobtainhighestqualification.Ontheotherhand,freshstudentsareindividualswhodon’thaveanyworkingexperiencesbeforewenttouniversity.

1.Introductionandliteraturereview

1.1.Introduction

Afterthe‘EducationReformAct1988’enactedin1988,increasinglygraduates

leavefull-timeeducationwithadegree.Thenumbersofuniversitygraduate

increasedfrom15%formenand13%forwomento30%and35%respectively

(WalkerandZhu,2008).Notonlythenumbersofgraduateincreasedduetothe

reform,butalsotheaveragelevelofeducationincreasedfollowedbythereform.

However,theincreasedaverageeducationisnotsolelyduetothereform.Itwas

increasingrapidlyinrecentdecades.ThepeoplewhoholdA-levelsincreased

significantlyandontheotherhandthenumbersofindividualwhoholdGCSEsas

thehighestqualificationfell.AlthoughduetotheendeavoroftheBritish

governmenttothevocationaleducationsuchasNationalVocational

Qualification(NVQ),thenumbersofvocationalstudentsincreasedslightly

duringthatperiod.

Thereformalsomadeuniversitiesrelaxtherecruitingrequirementsforstudents.

Thenewlyrecruitedgraduatesareregardedaslesscapablecomparedtothe

previousgraduatesasaresultoftheeducationreform,leadingtoambiguous

results.Theliteratureminimizestheabilitybiasbynarrowingdownthescopein

whichonlyincludesindividualswithatleastoneortwoA-levels(Blundelletal,

2000;WalkerandZhu,2008).WalkerandZhu(2008)examinehowthe

educationexpansionaffectstheuniversitywagepremium.Interestingly,they

don'tfindstrongnegativeeffectsonreturnsofnewgraduatesandevenmarginal

positiveeffectforwomen.23 AfterthatDevereuxandFan(2011)arguethat

becauseoftheincreasingindividualswithA-levelsqualification,theresultsmay

alsobebiased.TheyapplyTwo-StageLeaseSquared(2SLS)toexaminethewage

premiumofadegreebasedonQLFSandarguethattheincreasededucationhas

6%wagepremiumbothformenandwomen.However,thereareamountof

maturestudentswhopursuedegreeafterthereform.Their2SLSresultsmay

alsoleadtomisunderstandingduetothisheterogeneity.Iftheincreasingmature

studentsbecomeuniversitygraduatesduetothereform,theirresultswouldbe2 Theypointoutthattheresultsmightbebiasedbypersonalinnateability.Theyalsoexaminetheheterogeneitybasedonquantileregression.3 OneimportantpointforDIDanalysisistoselectthecomparablecontrolgroup.Theresultsmaybecompletelydifferentwiththedifferentcontrolgroups.

biasedonthebasisofindividualswhoatleastholdtwoA-levels.Theydon’t

checkhowrelaxedrequirementsaffecttheopportunityofattendinguniversity

mostlyduetothelimitofdata.WalkerandZhu(2011)arguethatthereturns

varyalotbysubjectsandtheriseoftuitionfeeshadrelativelylowereffectson

overallreturnforastudentintheUK.LindleyandMcintosh(2015)firstly

examinetheincomeinequalityamonggraduates.Theyapplythevariance

analysisandarguethatthewideningvarianceofthetestscoreisbecauseofthe

differentialacceptingrulesamonguniversities.Theyarguethatthelargeincome

inequalityamonggraduatesmostlycomesfromthedifferenceswithinasubject

ratherthanbetweensubjects.Italsoshowsthattherelationbetweenrelaxed

universityrequirementruleandlargewagedifferences.Theliteratureimplies

thereexistsstrongheterogeneitiesamongthereturnsofuniversitygraduates.

Duetothefactthatthereformmayleadtomorestudentswithdistinctive

educationalbackgroundintouniversities,theresultsmightbevery

heterogeneous.Therelaxedrequirementsinuniversitiesmaynotonlyopen

doorsforthefreshstudentsbutalsoindividualswhohaveasimilarlevelof

educationandseveralyearsofworkingexperiences,namelythematurestudents.

Commonlybelievedthatindividualswithlowerlevelofeducationtendtohave

lowerinnateability.However,BirchandMiller(2007)findthatstudentswho

liketodeferuniversitiesarefoundwithhigherschoolingmarkscomparedto

thosewhostartuniversityrightawayfromhighschools.Theirresultsmayimply

thisquestionmightbemorecomplexthanweexpected.Duetothelimitofthe

data,previousstudiesarelackofexaminingthisheterogeneity.Iprovide

evidenceoftheheterogeneityofeffectsinducedbythereform.

Currentliteraturearguesthattheeducationreformdon’thavelargelynegative

effectsonthereturnstonewlyrecruitedgraduates.Surprisinglytheeffectsof

educationreformonmaturestudentshavenotbeenexamined.Individualswith

workingexperiencestendtobeolderandmorematurecomparedtoother

youngerstudents.Theymayarrangetheirlearningplanandalsothecareerplan

afterstudybetter.Moreimportantly,theymaychoosethemostsuitablelearning

plancombiningwiththeirexistinghumancapitalandthefutureplan.Onthe

otherhand,theytendtohavemoreyearsofworkingexperiences,buttheyhave

feweryearsoffundamentaleducation.Tomyknowledge,Idon’tfindanypapers

inwhichfocusonthedeterminantsofthedecisionofre-education,theeffectof

re-educationortheeffectof‘EducationReformAct1988’onmaturestudents.

NotonlythoseA-levelsgraduateswillcomplywiththisreform,butalsosome

maturestudentswhoarewillingtoobtainmoreeducationwillalsocomplythis

reform.Thisgroupofpeoplecouldbeveryheterogeneousandthereforeneeda

veryinformativedataset.Butanalyzingtheeffectofre-educationonthisgroupis

ofbothpoliticalandpersonalinterest.

1.2.Mywork

Thispapermainlyfocusesonexaminingthequantitativeeffectoftheincreasing

universitygraduatesonreturnsandcorrectingtheabilitybias.Moreover,I

illustrateanotherimplicitachievementoftheeducationexpansion.Thatisto

provideopportunitiesnotonlyforthefreshstudentsbutalsoforthemature

studentswhomaybenefitmorefrombecominguniversitygraduatesoutofclear

purposes.Icontributetotheliteratureinthreeways.

First,the2SLSandstatisticalresultsshowthatthereturnsarerather

heterogeneous.Individualswithlowerprobabilitiesofattendingtheuniversities

maybenefitthemostamongthosenewlyrecruitedgraduates.However,they

maycomefromspecificreasons,namelytheunobservablefactors.FromFigure2,

itisclearthatthereturntouniversityisnegativelycorrelatedwiththe

propensityscoreoftheattendinguniversities.FromFigure3,thetrendsarevery

clearthatindividualswithlowerprobabilitiesofattendinguniversityhave

higherworkingexperiencesandlowereducation,holdinglowernumbersof

A-levelsandGCSE.Tosumup,therearethreetypesofnewuniversitygraduates.

Theyarematurestudents,A-levelfreshstudentsandhighereducationfresh

studentsrespectively.4 Duetotheheterogeneousbackgroundamongnew

universityentrantsandcomplexmeasurementerrorproblemssuchthat

individualsmayreportasauniversitystudentsincetheiroriginalschoolwas

promotedintoauniversity.Theinstrumentstoestimatethepropensityscores

4 Fromtheresults,mostnewlyrecruiteduniversitygraduatesarewithlessthan24continuousyearsofeducation,seeFigure1.

arebirthcohortsandtheinstrumentsareconsideredtobeexogenousandmeet

theexclusionrestriction(DevereuxandFan,2011).Moreover,thesubjectsare

includedascontrolvariablesinthereducedformtocontrolfortheunderlying

heterogeneity.Duetothefactthatdifferentsubjectshavedifferentrequirements,

itmayleadtothebiasintotheresultsifitisnotcontrolled(Lindleyand

Mcintosh,2015;WalkerandZhu,2011).

Second,IapplythesimpleDifference-in-Difference(DID)toestimatetheeffectof

anincreaseinthesupplyofuniversitygraduatesonthereturnsdirectly(Walker

andZhu,2008).Theyalsohighlightthepotentialbiasfrompersonalability.Here

IapplyMatchingDifference-in-Difference(MDID)tocorrectforthebias.The

propensityscoreistheprobabilityofattendinguniversity.5 Iapplytwodifferent

methodstoperformthematchingstrategy.Oneisthepopularpropensityscore

matching.AnotheriscalledCoarsenedExactMatchingwhichitisbecoming

popularinrecentyears.Comparedtothepreviousliterature,Idon’tfocuson

individualswhoatleasthaveoneA-levelduetothefactthatincreasingmature

studentsobtaindegreebornafter1976.Itwillbringunnecessarybiasintothe

resultsifdroppingindividualswhodon’thaveA-levels.Thematchingstrategy

willbalancethecharacteristicsbetweentreatmentgroupandcontrolgroup

beforeandafterthereform.Itcorrectstheabilitybiasandestimatesthe

quantitativeeffectofincreasinggraduatesonthereturns.AsImentionedabove,

duetothelimitofthedata,Ican’tcapturethechangeinthescoresofA-level.

Sincethedatadoesn’tincludeinformationregardingtheexactnumbersof

A-levelandthescoreofA-levels,thechangesinthecompositionofA-levelsare

ambiguoustoidentifynewgraduateswhoenterintouniversitywithoutwork

experiences.Inordertoaccountfortheheterogeneouseffectinmybesteffort,I

dividedsampleintotwodifferentperiods,pre-expansionandpost-expansion

basedontheirbirthcohorts(DevereuxandFan,2011).6

Third,Inoticethatthereisacompositionalchangeamonggraduates.Itis

expectedthatthedegreeofrelaxationofrequirementschangedovertime.The5 Thepropensityscoreisestimatedby“Probit”model,basedonyearofbirth,numbersofA-level,numbersofGCSE,industry,sex,yearsofsurvey,quarterofsurveyeducation,squaredofeducation,experiences,squaredofexperiences,tenure,marriage,jobtraining,disable,andLondon.6 Individualsbornbetween1970and1975belongtopre-expansion.Individualsbornafter1975belongtopost-expansion.

proportionofthematurestudentsamongthoseuniversitygraduatesincreased

significantlyafter1976.Thecompositionalchangemaybringuncertain

heterogeneitiesintotheresults.Aftercorrectingtheabilitybiasinthe

post-expansionperiod,theresultsshowthatthereisastrongpenaltyforthose

newmatureandfreshgraduates.Therearearound46%universitygraduates

whoobtainthehighestqualificationafterfinishedthecontinuouseducation.

FromtheDIDresults,bothfreshstudentsandmaturestudentsdon’thave

significantpenaltyinthepre-expansionperiodinwhichthereareincreasing

supplyofuniversitygraduateswhodon’thaveworkingexperiencesbefore.The

MDIDresultscorrecttheinnateabilitybiasandestimatethequantitativeeffect

onreturnsformaturestudents,leadingtoapenaltytothematurestudents.

Interestingly,duringthepost-expansionperiod,theDIDresultsshowthatfresh

studentshavebeenmoreaffectedbytheincreasingsupplyofmaturestudents.

Aftercorrectingtheabilitybias,bothresultsbecomemorenegative.Here,the

MDIDresultsforthematurestudentsmaycorrectthechangesinthe

characteristicsinwhichiscapturedbyage,yearsofeducationandnumbersof

A-levels.TheMDIDresultsforthefreshstudentsaredifferentfromtheDID

resultsinpost-expansionperiodbecausethereareincreasingindividualswho

havemoreyearsofeducation.7

1.3.SourceofVariationofDIDmatching

Theproblemamongthecurrentliteratureisthatfewliteratureshedlighton

howthecharacteristicschangedamongnewlyrecruiteduniversitygraduates.In

anotherword,thebiascomesfromthechangeintheinnatepersonalability,

leadingtoanon-identicaltreatmentgroupasaresultofthereform.Thesimple

DIDresultscombinequalitativeeffectwithquantitativeeffect.

ThenumbersoftheA-levelcan’tfullycapturethechangeofacceptingrulesfor

freshstudents.Butthecompositionalchangemaycapturethechangeinrelative

probabilitiesofattendinguniversitiesformaturestudents.Thematurestudents7 FromFigure3,wecanseethattheyearsofeducationincreasecontinuouslyalongwiththepropensityscore.IndividualswiththehighestpropensityscoremightbestudentswithhigheryearsofeducationthanA-levelgraduates,butobtainthedegreeduetothereform.

wouldbecapturedintheMDIDresultsduetothecompositionalchangeof

numbersofA-level,yearsofcontinuouseducationoryearsofworking

experience.Forthefreshstudents,althoughwecan’tobservethescoreof

A-levels,InoticethatthereisalittledecreaseinnumbersofA-levels.Thatmay

comefromvocationalstudentswhohavesimilaryearsofeducationwiththe

freshstudents.ThosevariationsmayalsobecapturedinMDIDresults.Thatmay

explainwhythereisadifferencebetweenDIDandMDIDresultsfornon-mature

studentsinpost-expansionduration.

1.4.Potentialbiasesandfuturework

ThefirstoneisthechangesinscoresofA-levels.ThisismainlyforA-levelfresh

students.Thesecondcouldbethetypesofuniversity.Universitiescouldbevery

heterogeneousandthetypesofqualification.Itisexpectedthatsomemature

studentswilltakeapart-timedegreethatcan’tbecapturedinmydataandalso

thequalityofinstitutions(WalkerandZhu,2011).Thethirdisthatthereisalack

ofinformationregardingtotheeducationalbackgroundofmaturestudents.In

thecurrentdata,onlytheircontinuousyearsofeducation,numbersofA-level

andnumbersofGCSEareavailabletome.ButIamalackoftheinformationin

termsoftheirhighesteducationbeforeobtainingadegree.Thiscouldleadto

ambiguousresults.Lastly,duetothefactthattheparentalbackgroundhasa

massiveimpactonhighereducationattainment,Idon’thavethatinformationas

well(Chowdryetal,2010).Dearden(1999)arguethattheOLSresultcanbe30%

upwardbiasedduetoomittedvariablesofpersonalabilityorbackground.For

thematurestudents,thenewlyrecruiteduniversitygraduatesmightbedifferent

fromthosewhodon’tparticipateinuniversitieswithoutthecontroloffamily

background.

Regardlessoftheabovepotentialbiases,thereareseveralinterestingextensions

canbedone.Thematurestudentsarebothpoliticallyandpersonallyinteresting

toexplore.Inthisstudy,IpresenttheheterogeneousreturnscomparedtoFresh

students.However,duetothelimitofdata,Icouldn’texaminetheeffectsof

characteristicsofdeterminingtopursueadegree,whichpresumptivelyitwill

leadselectionbiaswhenexaminesthereturnsamongmaturestudents.Itneedsa

veryinformativedatasetinwhichincludesacomprehensivebackgroundorthe

historyofthematurestudents.Afterdeterminingwhytheydecidetopursuea

degreeandwhatistheoutcomeofthat,morepoliciescouldbemadeinorderto

differentiatethemarketandtoprovidemoreefficientcoursesforthemature

students.

2.Data

2.1.Datadescription

Themaindataisdrawnfromthe2002to2013QuarterLaborForceSurvey.The

agerangeofthesampleisfrom33to43years-oldandbirthcohortsarefrom

1965-1979sinceobservationsareonlymatchedinthisageband,shownin

Figure1A.Thisfeaturehasanadvantagethatitcanallowustoexaminethefull

potentialreturnwhentheyareinthemiddleoftheircareer(Blundelletal,2000).

AnotherpartofthedataisdrawnfromUnderstandingSocietywaveAtowaveE.

Theagerangeisfrom40to45years-oldandthebirthcohortsarefrom

1965-1975.TheparentaloccupationisavailableinUnderstandingSociety.It

couldbeusedtocapturethebackgroundofthosenewlyrecruiteduniversity

graduates.

<Figure1AHere>

ThenumbersofindividualswhoholdwithA-levelsareshowninFigure2A.The

categoricalvariableinLFSindicatesifindividualholdsone,morethantwoor

noneA-levels.8 Soherethey-axisshowstheambiguousnumberofA-levels

whichindividualholdsgivendifferentbirthcohorts.Itclearlyshowsthatthe

totalnumberofindividualsholdingA-levelhaslargelyincreasedafter

individualsbornafter1970.Itsuggeststhatthehighereducationexpansionhas

pushedthestudentstogetmoreA-levels.

<Figure2AHere>

8 “NUMAL”inLFSdenotesifindividualholdone,twoandabovetwoornoneA-level.

Figure3AshowsthatthenumbersofA-levelamonggraduatesgivenbirth

cohorts.ItshowsthattheproportionofA-levelamongthegraduatesgradually

decreasedovertime,indicatingthatthereisahugechangeofthecompositionof

graduates.ThepersonalinnateabilitymightbeabigbiasbasedonsimpleDID.

<Figure3AHere>

Previousliteratureneglectsthecompositionalchangeamonguniversity

graduates.Itturnsouttobeaveryimportantchangealongwiththehigher

educationexpansion.Withtheprocessofthereform,morematurestudents

becomeuniversitygraduates,especiallybornafter1975.Inmysample,the

proportionofthematurestudentsishigherthanthefreshstudentsafter1978.

Thatmaypotentiallyexplainwhythereisrobustheterogeneousreturnsamong

thegraduatesandwhythereturnsinthe1976-1979aresignificantlylower

comparedtotheperiodbetween1970and1975.Figure1hasshownthistrend.

After1970,thenumbersofuniversitygraduateoffreshstudentsincreased.

However,maturestudentstendtobeconstantduringthatperiodandit

increasedsignificantlyafter1975.

<Figure1Here>

Figure2showstheindividual’sagewhencompletedthefull-timeeducationof

thematurestudentswithadegree.Itsuggeststhatthepreviouseducationofthe

maturestudents.Therearearound41%universitygraduateswhobelongtothe

maturestudents.Amongthemtherearesufficientamountofthemature

studentswithatleast20yearsofcontinuouseducationbeforebecoming

universitygraduates.Mostofthematurestudentswhoobtainthedegreehave

lessthan22continuousyearsofeducation.

<Figure2Here>

2.2.Measurementerror

First,itisaself-reporteddata.Peoplemayreporttheir“university”statusgiven

thecurrentclassification,buttheiryearsofeducationarestilltheoldone,

leadingtoaloweryearsofeducationbutwithadegree.Second,itisapart-time

degree.Ittakesmoretimecomparedtoafull-timedegreeinwhichcan’tbe

controlledinthisstudy.Moreover,Idifferentiatethematurestudentsandthe

freshstudentsbasedontheirself-reportedcontinuousyearsofeducationand

agewhencompletedthehighestqualification.Iftheageofobtainingthehighest

qualificationistwoyearslargerthantheageoffinishingfull-timeeducation,

thenindividualisconsideredasthematurestudent.

3.Difference-in-DifferenceMatching

Duetothefactthatuniversitieshaverelaxedtheentryrequirements,the

universitygraduatesbeforeandafterthereformmayhavedifferentpersonal

innateability.ThesimpleDIDmaybebiasedifthedataarelackofinformation

regardingone’sinnateability.MDIDisapromisingmethodtotacklewiththis

problem,althoughitalsodependsonthedatainwhichitincludesvariable

describingthechangeinone’sentrylevel,suchasscoresornumbersofA-level.

Inmydataset,itonlyincludesnumberofA-level,sointuitivelyitcanonly

captureindividualswithseveralworkingexperiencessincetheytendtohold

fewerA-levelsorevennone.ThemethodwasfirstlydevelopedbyHeckmanetal

(1997,1998).

Therearemainlythreetypesofbiases.Oneistheselectiononthe

un-observables.Anotheroneisthefailureofacommonsupportconditionand

lastoneisafailuretoweighttreatmentandcomparisongroupcomparablyfor

whichtheyarguethatitisunlikelyhappenedinmatchingstrategy(Heckmanet

al1997).Thefirstandthesecondbiaswillbecorrectedbymatchingmethod.

However,thecommonsupportmaybringadditionalbiasiftreatmenteffectis

heterogeneousamongtreatedgroup(Blundelletal,2005).

Inthispaper,theuniversitygraduatesaretreatedindividuals,denotedas 𝐷! = 1.

Othersremaininthecontrolgroup,denotedas 𝐷! = 0. 𝑌!" denotestheoutcome

ofindividualiintimet,beforethereform. 𝑌!!! denotestheoutcomeof

individualiintime 𝑡!,afterthereform.

𝐴𝑇𝐸 = 𝐸 𝑌! 𝑋!,𝑈!)− 𝐸(𝑌!|𝑋!,𝑈!)

𝐵 = 𝐸 𝑈! − 𝐸(𝑈!)

Andthebiaswillbecomezerowhentreatmentassignmentisindependent

conditionalonX.

𝑌!,𝑌! ⊥ 𝐷 | 𝑋

Thatmeans 𝐸 𝑌! 𝑋!,𝐷 = 0) = 𝐸(𝑌!|𝑋!,𝐷 = 1)

Giventheassumptionof“StrongIgnorability”proposedbyRosenbaumand

Robin(1985),0<P(D=1|X)<1.Togetherwiththeformertwoequations,that

impliesbelow,

𝑌!,𝑌! ⊥ 𝐷 | 𝑃(𝑋)

𝐸 𝑌! 𝑃(𝑋),𝐷 = 0) = 𝐸(𝑌!|𝑃(𝑋),𝐷 = 1)

EssentiallyXcanbedecomposedinto(T,Z).Tisvariablesremainedinreduced

formandZistheexogenousvariablesinthefirststage.

𝑌! = 𝑓! 𝑇 + 𝑈!, 𝑌! = 𝑓! 𝑇 + 𝑈!

DuetothefactthatZiscompletelyexogenous,itleadsto 𝑈! ⊥ 𝐷 | 𝑍.Withsame

spiritwith“StrongIgnorability”,itleadsto 𝑌!,𝑌! ⊥ 𝐷 | 𝑃(𝑍).Then,

𝐸 𝑈! 𝑃(𝑍),𝐷 = 0) = 𝐸(𝑈!|𝑃(𝑍),𝐷 = 1)

Matchingisstilla“selection-on-observables”method,underthelanguageof

HeckmanandRobb(1985).Commonsupportproblemcanbeeliminatedif

matchingisperformedovercommonsupport.TheConditionalIndependence

Assumption(CIA)doesn’tholdwhentheunobservablesaffecttheoutcomeeven

underthecontrolofpropensityscore.MDIDrelaxestheCIAfromsingle

observationtopair-wise.Inthissetting,weonlyneedtheCIAholdsinthefirst

differenceequation.

𝐸 𝑌!! − 𝑌!!! 𝑋!,𝐷 = 0) = 𝐸(𝑌!! − 𝑌!!!|𝑋!,𝐷 = 1)

Underindexsufficiencytheequationbecomes

𝐸 𝑌!! − 𝑌!!! 𝑃(𝑍),𝐷 = 0)− 𝐸(𝑌!! − 𝑌!!!|𝑃(𝑍),𝐷 = 1)

Theresultsnormallyvarywithdifferentmatchingscheme.Differentweights

havebeenproposed.

𝐴𝑇𝑇 =1𝑁 [𝑄!! − 𝑊!!,!!(𝑖, 𝑗)𝑄!!

!∈!!]

!∈!!

Innearestneighborsmatching, 𝑄!! = 𝑌!! ,𝑄!! = 𝑌!! ,definedamatchedsampleas

𝐶 𝑋! =∥ 𝑋! ,𝑋! ∥< 𝜀, 𝑊!!,!! 𝑖, 𝑗 = 1 formatchedobservations,othersare

zero.

Inkernelmatching,theweightsare𝑊!!,!! 𝑖, 𝑗 = !!"!!"!∈!!.

AregressionadjustedmatchinghasbeencomplementedintoDIDbyHeckmanet

al(1997).Inthissetting, 𝑄!! = 𝑌!!" − 𝑌!"!! ,𝑄!! = 𝑌!! − 𝑌!!!!

𝑊!!,!! 𝑖, 𝑗 =𝐺!"𝐺!"!∈!!

AconditionalDIDmatchingestimatorisbeenproposedaswell,

𝑄!! = [ 𝑌!!" − 𝑋!"𝛽!! − 𝑌!"!! − 𝑋!!!𝛽!! ]=[( 𝑌!!" − 𝑌!"!!)-( 𝑋!!! − 𝑋!") 𝛽!!]

𝑄!! = [ 𝑌!!" − 𝑋!"𝛽!! − 𝑌!"!! − 𝑋!!!𝛽!! ]=[( 𝑌!!" − 𝑌!"!!)-( 𝑋!!! − 𝑋!") 𝛽!!]

Thesettingisperfectlysuitableforsolvingtheproblemofchangesin

characteristicsoftreatmentgroupbeforeandaftertimet.

ChenandJin(2012)suggestthattheheterogeneitywithinagroupallowusto

controlfortheunobservableattributesbasedonanassumptionthatindividual’s

unobservableattributeshavethesamedistributionwithobservableattributes.9

HallaandZweimueller(2013)suggestcombiningDIDandmatchingmay

effectivelyeliminatedbiasescausedbyunobservableattributesinthepresence

9 UnlikeHeckmanetal(1997)andHeckmanetal(1998)inwhichtheyuselongitudinaldata,herethey

useallhouseholdswithineachcountywithunequalprobabilitytoparticipatetheprogramtoaccountfortheunobservableheterogeneityattributes.

oflongitudinaldata.

4.Results

4.1.Heterogeneityamonguniversitygraduates

Figure3showsthechangesinthereturnsbetweenuniversitygraduatesand

non-universitygraduatesgiventhepropensityscoreofattendinguniversity.

FromFigure3,itisclearshowsthatindividual’sreturnisnegativelycorrelated

withpropensityscore.Obviouslythehighlysignificantdifferencesareduetothe

factthattheuniversitygraduatesandthenon-universitygraduatesarerather

differentbasedonthepropensityscore.10

<Figure3Here>

Inordertohavetheintuitionoftheheterogeneity,Ishowthepersonal

characteristicsonthebasisofthepropensityscoreofattendinguniversities.

Figure4showsthatindividualswithlowestlevelofattendinguniversityhave

substantiallylowernumbersofA-levels,numberofGCSEsandyearofeducation.

Maturestudentshavealoweruniversityattendancerate,alongwithmore

workingexperiencesandfeweryearsofeducation.

<Figure4Here>

Table1showsthesimplebreakdownbytypeofstudentanduniversity

graduates.Fortheuniversitygraduates,theaverageeducationofthemature

studentincreasescomparedtothefreshstudents.Presumably,thenewmature

studentswouldcomefromGCSE,A-levelgraduates,andHNCorequivalent

qualifications.ButthemeannumbersofA-levelforthematurestudentswho

haveadegreedoesn’tchange.Itsuggeststhatthosenewmatureuniversity

graduatesmaycomesfromindividualswhosehaveahigherfull-timevocational

education.Moreover,forthematurestudentswhodon’thaveadegree,the

10 Isuspectthatthelowestpropensityscoresconsistofindividualswhohavelowerlevelsofeducation.ThemiddlepartofthefigureconsistsofA-levelgraduates.Therightpartwiththehighestpropensityscoresmaycomefromindividualwithpostgraduatesandhigherlevelsofvocationaleducation,suchasNVQ,HNDetc.Thatimpliesthereshouldbemanychannelsforwhichareneededtobecontrolled.

averageeducationdoesn’tchange.Itsuggeststhattherearemorestudentswho

havemoreyearsofeducationwenttouniversitiesasaresultsofthereform.Not

onlytheaverageyearsofeducation,butalsothenumbersofuniversitygraduate

increaseforbothtypesofthestudents.11

<Table1Here>

<Figure4A>

Table2showsthe2SLSresultsforfreshstudentsandmaturestudents

separatelyonthebasisoftheperiodsofattendinguniversities.Theresults

suggestthatmaturestudentsmaybenefitaround20%afterbecominguniversity

graduatescomparedtofreshstudents.TheresultsaresimilarwithDevereuxand

Fan(2011)inwhichtheyrunthesufficientrobustnesschecks.Myresultsare

quitesimilartotheirs,onlydifferentiatedbymaturestudentsandfreshstudents.

Theresultssuggestthatthematurestudentsandthefreshstudentshave

differentreturnsofhavingadegree.

<Table2Here>

4.2DIDandMDID

Inordertotestifythesourceofbias,Isplitthesampleintotwogroups,one

withoutexperiences(freshstudents)andonewithworkingexperiences(mature

students).Thoseindividualscouldbeverydiverse.Unlikefreshstudentswhogo

touniversitywhentheyfinishA-levels,thisgroupofpeoplemayhavevery

differenteducationalbackgroundandworkingexperiences.LFSisnotvery

informativeregardingtothisperspective.ItonlyincludesnumberofA-levels

withoutthegradesofthoseA-levelsinwhichcan’tallowmecapturethe

compositionalchangebeforeandafterthereformfornormalgraduates.Butit

cancapturewhoseindividualswhogotouniversitywithlowernumberof

A-levelsorevenwithoutA-levels.Andtheresultsshowthatallofthebiascomes

11 Figure4Aalsoshowsthattheproportionalchangeformaturestudentswhoobtainadegreeasaresultofthereform.Itshowsthedistributionofcontinuousyearsofeducationofmaturestudentswhowenttouniversities.

fromthisgroupofpeople.Parentaloccupationsareusedtocapturethe

compositionalchangeinUnderstandingSociety,aswellastheyearsof

education.

Table3presentstheDIDandMDIDresultsforthefreshstudentsandthemature

studentsrespectivelyonthebasisofdifferenteducationexpansionperiods.PSM

andCEMareusedtobalancethecompositionalchangeamongthenew

universitygraduates.TheDIDresultsdon’tshowsignificantpenaltiestothe

returnstonewuniversitygraduates.FortheMDIDresults,theresultsshow

variouspatterns.Visually,thepenaltiesconcentrateonfreshstudentsinthe

post-expansionperiod.TheresultsareconsistentingeneralbetweenLFSand

UnderstandingSociety,exceptformaturestudentsinPSMmatching.Thereis

penaltytomaturestudentsbothinthepre-expansionperiodandthe

post-expansionperiodinPSMmatching.However,theCEMmatchingdoesn’t

findthepenalties.Theresultssuggestthatoversupplygraduatesmaydecrease

thereturnsofmaturestudentssincethesupplyofmaturestudentsdoesn’t

changesignificantcomparedtofreshstudents.Moreover,Inoticethatthe

returnsoffreshstudentshavebeenlargelydecreasedinpost-expansionperiod,

butthereturnsofmaturestudentsholdconstantinDIDresults.Thatmay

suggestthatmaturestudentsmaybenefitmoreafterbecominguniversity

graduates.Aftercorrectingabilitybias,thenegativeeffectofoversupplying

maturestudentsonreturnsissmallerformaturestudentscomparedtofresh

students.

<Table3Here>

Figure5showsthebalanceinfatheroccupationinUnderstandingSociety.This

figureisusedtotestifythiscondition 𝐸 𝑌!! − 𝑌!!! 𝑃(𝑍),𝐷 = 0)− 𝐸(𝑌!! −

𝑌!!!|𝑃(𝑍),𝐷 = 1).Visually,CEMdoesabetterworkcomparedtoPSM.Eachbar

presentsthedifferenceintheproportionoftheuniversitygraduatesandthe

non-universitygraduatesunderthefather’soccupationsbeforeandafterthe

reform.Bluebarsrepresentproportionalchangesintheproportionofuniversity

graduatesgiventhefather’soccupations.Orangebarsrepresenttheproportional

changesafterweightedbySEM.Graybarsrepresenttheproportionalchanges

afterweightedbyPSM.Figure6showsthebalanceinnumberofA-levels.Figure

7showsthebalanceineducationformaturestudents.Clearly,CEMdoesabetter

workinthesenseofbalancing.

<Figure5-7Here>

4.3.Sensitivitytest

Inordertoshowtherobustnessoftheresults,Iperformthesensitivityteston

thebasisoftherelativenewtechnic.Oster(2016)proposedanewsensitivity

testinwhichshearguesthatR-squaredshouldtakeintoconsiderationsincethe

coefficientwouldnotchangemassivelywhenuninformativecontrolisincluded,

aswellastheR-squared.Sheproposedamethodtoderivearangebetweena

truetreatmenteffectandacontrolledtreatmenteffectandtakeR-squaredinto

considerationcomparedtotheAltonji,ElderandTaber(2005).

Table4showsthesensitivityoftheCEM-DIDresultsinLFS.InTable4,the

matchingvariablesincreasewiththeorderofthecolumn.Thevariablesareall

pre-treatmentvariableswhicharethevariablesofindividualsbeforewentto

universities.IalsoperformtheOster(2016)’ssensitivitytestforthesignificant

resultsinTable3inordertoshowtherobustnessoftheresults.Themaximum

ofR-squaredisassumedtobe1,twicetheR-squared_tildaand1.25timesthe

R-squared_tilda.TheR-squared_tildaistheR-squaredofafullycontrolled

regression.Ineachweightedregression,thecontrolvariablesarethesame.Only

theweightingvariablesaredifferent.TheLFSCEM-DIDresultsshowthestrong

robustnesstotheresults.Therangesofthetruetreatmenteffectalmostalllayin

thetwostandarddeviations.

Table5showsthesensitivitytestoftheCEM-DIDresultsinUnderstanding

Society.Theresultsdon’thaveanysignificantresultsonthebasisofmultiple

setsofmatchingvariables.AlthoughInoticethatthereisasignificantpositive

effectinthethirdcolumn,buttherangeofthetreatmenteffectvarymassively

evenwhenthemaximumR-squaredisveryclosetotheR-squared_tilda.

<Table4and5>

5.Conclusions

Althoughtheeffectofthehighereducationexpansiononreturnshasbeen

largelyexamined.Theresultsarestillambiguoustosomeextentduetothe

measurementerrorandthecompositionalchanges.Inthisstudy,IapplyMDID

toexaminetheheterogeneousreturnstotheuniversitygraduatesandhighlight

thedifferencesinreturnsbetweenthefreshstudentsandthematurestudents.

TheDIDresultsareconsistentwiththepreviousstudiesthatthereareno

significantpenaltiestothenewlyrecruiteduniversitygraduates.However,the

MDIDresultscorrectthebiasduetothefactthatnewgraduatesmayhavelower

innateability.Itshowssignificantpenaltiesforboththefreshstudentsandthe

maturestudents.Theresultswillvarybythematchingstrategies.ForPSM-DID,

therearepenaltiesforthematurestudentsforboththepre-expansionandthe

post-expansionperiods.However,theCEM-DIDdoesn’texaminethepenalties

forthematurestudents.Bothmatchingstrategiesexamineastrongpenaltyfor

thefreshstudentsinthepost-expansionperiod.Thatmightbeduetothefact

thattherearemorestudentswithworsebackgroundsbecominguniversity

graduatesinthepost-expansionperiod.

Giventheresults,thereareenoughreasonstobelievethatitmaybenotthebest

ideatopushmorefreshgraduatesintouniversities.Gettingtheminto

employmentishardandpushingthemintoeducationiseasy,butindividuals

whohave“worse”backgroundandarenotpreparedtobecomeuniversity

graduatesneedtimeandexperiencestothinkthereasonforgoingintoa

university.

References:

Altonji,JosephG.,ToddE.Elder,andChristopherR.Table.2005.Selectionon

ObservedandUnobservedVariables:AssessingtheEffectivenessofCatholic

Schools.JournalofPoliticalEconomy,Vol.113,No.1,pp.151-184.

Birch,ElisaRose.,andPaulW.Miller.2007.TheCharacteristicsof‘Gap-Year’

StudentsandTheirTertiaryAcademicOutcomes.TheEconomicRecord:Vol.83,

No.262.

Blundell,Richard.,LorraineDearden,AlissaGoodman,andHowardReed.2000.

TheReturnstoHigherEducationinBritain:EvidencefromaBritishCohort.The

EconomicJournal:Vol.110,No.461,pp.F82-F99.

Blundell,Richard.,LorraineDearden,andBarbaraSianesi.2005.Evaluatingthe

effectofeducationonearnings:models,methodsandresultsfromtheNational

ChildDevelopmentSurvey.JournalofRoyalStatisticsSocietyA:168,part3,pp.

473-512

Chen,yuyu.,andJinGingerZhe.2012.Doeshealthinsurancecoverageleadto

betterhealthandeducationaloutcomes?EvidencefromruralChina.Journalof

HealthEconomics:31,1-14.

Chowdry,Haroon.,ClaireCrawford,LorraineDearden,AlissaGoodman,and

AnnaVignoles.2010.WideningParticipationinHigherEducation:Analysisusing

LinkedAdministrativeData.IFSWorkingPaper:W10/04.

Dearden,Lorraine.1999.Theeffectsoffamiliesandabilityonmen’seducation

andearningsinBritain.LabourEconomics:6,551-567.

Devereux,PaulJ.,andWenFan.2011.EarningsreturnstotheBritisheducation

expansion.EconomicsofEducationReview:30,1153-1166.

Halla,Martin.,andMartinaZweimueller.2013.Theeffectofhealthonearnings:

Quasi-expenrimentalevidencefromcommutingaccidents.LabourEconomics:24,

23-38.

Heckman,JamesJ.,andRichardRobb.1985.ALTERNATIVEMETHODSFOR

EVALUATINGTHEIMPACTOFINTERVANTIONS.JournalofEconometrics:

239-267.

Heckman,JamesJ.,HidehikoIchimura,andPetraE.Todd.1997.Matchingasan

EconometricEvaluationEstimator:EvidencefromEvaluatingaJobTraining

Programme.TheReviewofEconomicStudies:Vol.64,No.4,pp.605-654.

Heckman,James.,HidehikoIchimura,JeffreySmith.,andPetraTodd.1998.

CharacterizingSelectionBiasUsingExperimentalData.Econometrica:Vol.66,No.

5,pp.1017-1098

Heckman,JamesJ.,andEdwardVytlacil.2005.STRUCTURALEQUATIONS,

TREATMENTEFFECTS,ANDECONOMETRICREFORMEVALUATION.

Econometrica:Vol.73,No.3,669-738.

Lindley,Joanne.,andStevenMcIntosh.2015.Growthinwithingraduatewage

inequality:Theroleofsubjects,cognitiveskilldispersionandoccupational

concentration.LabourEconomics:37,101-111.

Oster,EmilyF.Forthcoming.UnobservableSelectionandCoefficientStability:

TheoryandValidation.

Walker,Ian.,andYuZhu.2008.TheUniversityWagePremiumandthe

ExpansionofHigherEducationintheUK.ScandinavianJournalofEconomics:

110(4),695-709.

Walker,Ian.,andYuZhu.2011.Differencesbydegree:Evidenceofthenet

financialratesofreturntoundergraduatestudyforEnglandandWales.

EconomicsofEducationReview:30,1177-1186.

Figuresandresults:

Figure1.Changeincompositionofdegreegivenbirthcohorts

Notes:Y-axisrepresentstheproportionofgraduatesamongallqualificationsonthe

basisofbirthcohorts.Thesampleincludesallobservations.

Sources:LFS

00.020.040.060.080.10.120.140.160.18

1964 1966 1968 1970 1972 1974 1976 1978 1980

Compositionofcollegegraduates

undergraduate-freshstudents undergraduate-maturestudents

postgraduate-freshstudents postgraduate-maturestudents

Figure2.Ageswhencompletedfull-timeeducationofmaturestudentsamong

universitygraduates.

Notes:Fractionofcontinuousyearsofeducationamongmatureuniversitygraduates.

Sources:LFS

Figure3.Wagedifferencebetweenuniversitygraduatesandnon-university

graduates

Notes:Sampleperiodsincludesbirthcohortfrom1965to1979.Thewagedifferences

arecalculatedbysubtractingthereallogofwagebetweenuniversitygraduatesand

non-universitygraduatesonthebasisofpropensityscores.

Sources:LFS

0.0

5.1

.15

.2.2

5

Frac

tion

10 15 20 25 30 35Age when completed full time education

-0.15-0.1-0.05

00.050.10.150.20.25

0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

wagedifference

Figure4.Characteristicsgivenpropensityscoreofdegree

Notes:X-axisispropensityscoreofattendinguniversity.Herethepropensityscores

havebeencutintobands.Ifsquaredofyearsofeducationisincluded,thentherateof

degreewouldbelineargiventhepropensityscore.

Sources:LFS

0.5

11.

52

mea

n of

NU

MA

L

.1- .2- .3- .4- .5- .6- .7- .8-

010

2030

40

mea

n of

age

.1- .2- .3- .4- .5- .6- .7- .8-

0.2

.4.6

mea

n of

deg

ree

.1- .2- .3- .4- .5- .6- .7- .8-

01

23

mea

n of

rlnw

age

.1- .2- .3- .4- .5- .6- .7- .8-

05

1015

20

mea

n of

exp

.1- .2- .3- .4- .5- .6- .7- .8-

0.5

11.

52

mea

n of

gcs

e

.1- .2- .3- .4- .5- .6- .7- .8-

010

2030

mea

n of

edu

.1- .2- .3- .4- .5- .6- .7- .8-

0.1

.2.3

.4.5

mea

n of

mot

i

.1- .2- .3- .4- .5- .6- .7- .8-

Figure5.Balanceoffatheroccupation

Notes:PSMisweightedunderthename“_weights_rcs”.CEMisweightedunderthe

name“cem_weights”.∆Y1representsthedifferencesinthenumbersoftheuniversity

graduatesbeforeandafterthereform.∆Y0representsthenon-universitygraduates.

Thebluebarsidentifytherelativelyproportionalchangebetweenuniversitygraduates

andnon-universitygraduates.Theorangebarsrepresentthesituationafterre-weighted

bySEM.ThegreybarsareafterPSMweighted.VisuallytheSEMworksbetterthanPSM.

Sources:UnderstandingSociety

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1 2 3 4 5 6 7 8 9

Fatheroccupationbalance(UnderstandingSociety)

∆Y1-∆Y0 ∆Y1-∆Y0(SEMweighted) ∆Y1-∆Y0(PSMweighted)

Figure6.BalanceinNumberofA-levels(LFS)

Notes:Thisfigureissimilartothepreviousfigure.Itdescribesthebalanceinnumberof

A-levels. “1”,”2”,and”3”representnone,one,andtwoandabovetwoA-levels

respectively.

Sources:LFS

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

01 2 3

BalanceinNumberofA-levels(LFS)

∆Y1-∆Y0 ∆Y1-∆Y0(SEMweighted) ∆Y1-∆Y0(PSMweighted)

Figure7.Balanceineducationformaturestudents

Notes:Abovefiguredescribesthebalanceintheyearsofeducationformaturestudents

sincethereareratherdifferentresultsbetweenSEMweightedandPSMweighted.

Visually,thePSMhasmassivefailureincapturingtherelativelyproportionalchangein

theyearsofeducationcausedbytheeducationreformcomparedtotheSEM.

Sources:LFS

-8-7-6-5-4-3-2-10123

15 16 17 18 19 20 21 22 23 24 25

Balanceineducationformaturestudents

∆Y1-∆Y0(CEMweighted) ∆Y1-∆Y0(PSMweighted)

Table1.Statisticsummary

Undergraduate Beforereform(Born<1970) Afterreform(Born>=1970)

Freshstudents Maturestudents Freshstudents Maturestudents

Numberof

observations

2386 1626 4428 3306

Education 22.02 18.49 22.14 20.16

Experience 20.36 21.53 16.40 18.72

No.A-level 1.54 0.898 1.46 0.895

No.GCSE 0.898 0.844 0.881 0.728

Non-Undergraduate

Numberof

observations

15974 12620 15126 15875

Education 17.68 17.34 18.55 17.70

Experience 20.94 21.67 17.19 19.13

No.A-level 0.370 0.376 0.476 0.386

No.GCSE 0.715 0.619 0.731 0.638

Notes:Theabovepanelsummarizesindividual’scharacteristicsamonguniversity

graduatesandbelowpanelsummarizesindividual’scharacteristicsamong

non-universitygraduates.“No.A-level”and”No.GCSE”arecategoricalvariableswhich

indicateroughnumbersofA-levelorGCSE.

Sources:LFS

Table2.2SLSresults

Freshstudents Maturestudents

2SLS

1965-1975

è Male 0.051*** 0.060***

è Female 0.063*** 0.059***

1965-1969and1976-1979

è Male 0.056*** 0.062***

è Female 0.066*** 0.061***

Notes:The2SLSresultsaresimilarresultswithDevereuxandFan(2011).Ionly

separatelyruntheregressionbasedonsampleperiodsandtypesofstudents.

Sources:LFS

Table3.DIDandMDIDbetweenindividualswithorwithoutworking

experiencesforundergraduates

LFS UnderstandingSociety

Freshstudents Maturestudents Freshstudents Maturestudents

DID

Pre-expansion -0.013 -0.020 -0.081 0.000

Post-expansion -0.056* -0.008

MDID(PSM)

Pre-expansion 0.002 -0.051*** -0.165*** -0.017

Post-expansion -0.111*** -0.074***

MDID(CEM)

Pre-expansion -0.028 -0.011 -0.098 0.003

Post-expansion -0.065*** -0.038

Notes: Given the result of female without working experiences, theremight be other

factors which bias the results. The results only include male. In LFS, the control

variablesarenumbersofA-level,numbersofGCSE,yearsofeducation,experience,year

oftenure,havejobtraining,disability,marriage,workinLondon,full-timejob,quarter,

year,industryandsubjectinuniversity.InUnderstandingSociety,thecontrolvariables

areage,yearsofeducation,marriage,fatheroccupation,yearandindustry.

ForPSM,theweightsarestoredinthevariableunderthename“_weights_rcs”.ForCEM,

it is stored in “cem_weights”. InLFS,birthcohortsandnumbersofA-levelareused to

capture thecompositionalchangeamonguniversitygraduates.Yearsofeducationand

experiences are also used to capture the mature students reacted to the education

reform. In Understanding Society, birth cohorts and father’s occupations are used to

capturethecompositionalchange.

Sources:LFSandUnderstandingSociety

Table4.SensitivitytestforLFS

Estimates (1) (2) (3)

Birthcohorts + + +

A-levels + +

GCSEs +

CEM

Post-expansion(Fresh) -0.073** -0.065** -0.065***

Rsquared 0.344 0.306 0.289

N 9361 10008 9249

PSACALC(Rmax=1) [-0.115,-0.073] [-0.092,-0.063] [0.065,0.070]

PSACALC(Rmax=2*Rsquared) [-0.091,-0.073] [-0.075,-0.063] [-0.065,-0.018]

PSACALC(Rmax=1.25*R

squared)

[-0.077,-0.073] [-0.067,-0.063] [-0.065,-0.054]

Post-expansion(Mature) -0.031 -0.038 -0.021

Rsquared 0.336 0.344 0.28

N 8677 8030 7998

PSACALC(Rmax=1) [-0.031,0.035] [-0.037,0.129] [-0.022,0.157]

PSACALC(Rmax=2*Rsquared) [-0.031,0.139] [-0.037,0.039] [-0.022,0.043]

PSACALC(Rmax=1.25*R

squared)

[-0.031,0.007] [-0.037,-0.020] [-0.022,-0.006]

Notes:Solelyforthemale.Thereisatrade-offbetweenbiasandefficiencyforCEMsince

the strata could be enormouswith increasing variables. PSMmay not encounter this

problem. For CEM, theweights are estimatedwith different covariates. Birth cohorts,

A-levels, GCSEs, education, marriage, and disable are pre-treatment variables. I use

“psacalc”commend toperformto test therobustnessof thesensitivity test. “Rmax” in

thePSACALCtestis1whichistheRsquared.“mcontrol”includesallvariableappearsin

theregression.

Sources:LFS

Table5.SensitivitytestforUnderstandingSociety

Estimates (1) (2) (3)

Birthcohorts + + +

Fatheroccupation + +

Motheroccupation +

CEM

Pre-expansion(Fresh) -0.087 -0.098 -0.061

Rsquared 0.306 0.309 0.307

N 4729 4397 3222

PSACALC(Rmax=1) [-0.087,5.76] [-0.097,5.68] [-26.6,-0.061]

PSACALC(Rmax=2*Rsquared) [-0.087,3.79] [-0.097,3.76] [-26.0,-0.061]

PSACALC(Rmax=1.25*Rsquared) [-0.087,1.85] [-0.097,1.83] [-25.6,-0.061]

Pre-expansion(Mature) 0.002 0.003 0.078**

Rsquared 0.250 0.226 0.230

N 7344 7587 6305

PSACALC(Rmax=1) [-2.78,0.002] [0.003,2.84] [0.078,1.88]

PSACALC(Rmax=2*Rsquared) [-1.60,0.002] [0.003,1.53] [0.078,0.494]

PSACALC(Rmax=1.25*Rsquared) [-0.80,0.002] [0.003,0.766] [0.078,0.171]

Notes:Allresultsarebasedontheobservationsafterdroppingthemissingobservations

of father’s occupation. The sample decreases around 30% after dropping themissing

mother’s occupation observations. Including the missing observations doesn’t make

significantchangetotheresultsonlymakingthevariancelarger.Isuspectthatthereis

serious multicollinearity among parental information. So it is better to only include

father’soccupationtocapturethecompositionalchange.

Sources:UnderstandingSociety

Appendix:

Figure1A.Proportionofagebandbeforeandafterthereform

Notes:Proportionof observationsborn indifferent years, dividedbybornbefore and

after1970.

Sources:LFS

Figure2A.NumberofA-levelsgivenbirthcohorts

Notes:Meanof“NUMAL”whichiscategoricalnumbersofA-levelinLFS.

Sources:LFS

0.0

2.0

4.0

6.0

8.1

Frac

tion

20 30 40 50Age of respondent

birth before 1970 birth after 1970

0.2

.4.6

.8

mea

n of

NU

MAL

1965 1970 1975 1979

Figure3A.NumberofA-levelsamonggraduatesgivenbirthcohorts

Notes:Meanof“NUMAL”amonggraduates

Sources:LFS

Table4A.Proportionalchangeformaturestudentsobtainingdegreebeforeand

afterthereform

Notes:Relativeproportionalchangecomparedtobeforethereformformaturestudents

onthebasisofyearsoffull-timeeducation.Y-axisisnumberoftheproportionalchange

comparedtobeforethereform

Sources:LFS

0.5

11.

5

mea

n of

NU

MAL

1965 1970 1975 1979

0

2

4

6

8

10

12

16 17 18 19 20 21 22 23 24 25 26

Maturestudents