ESSAYSONLABORMARKETANDEDUCATION By SoobinKim ADISSERTATION Submittedto MichiganStateUniversity inpartialoftherequirements forthedegreeof EconomicsŒDoctorofPhilosophy 2015 ABSTRACT ESSAYSONLABORMARKETANDEDUCATION By SoobinKim TheessayfiIntergenerationalMobilityinKoreaflinvestigatesintergenerationalearnings mobilityinKoreaforsonsbornbetween1958and1973andcomparesKorea'smobilitytothat ofothernations.ItusesdatafromtheKoreaLaborandIncomePanelStudyandtheHousehold IncomeandExpenditureSurveyconductedbytheKoreanNationalStatisticsBureau.Sincenosin- gleKoreandatasetincludesinformationonbothsons'andtheirfathers'adultearnings,thisstudy followsthetwo-sampleapproachpreviouslyappliedinKoreabyUeda(2013),whoseestimated intergenerationalearningselasticityis0.22,andextendstheanalysisbyusingfathers'earnings frommoreapproximalcohort.Theestimateofaround0.4issimilartoestimatesforsomealready- developedcountriesandsmallerthantypicalestimatesforrecently-developingcountries. ThesecondessayfiCollegeEnrollmentovertheBusinessCycle:TheRoleofSupplyCon- straintsflstudiestheimpactofsupplyconstraintsoncyclicalityinenrollment.Manystudieson cyclicalityofhighereducationexaminetherelationshipbetweencyclicalvariationinlabormarket conditions,andchangesinenrollment.Changesinenrollmentarecausedbychangesonboththe demandsideandthesupplyside.However,muchofthepreviousliteratureimplicitlyassumed elasticsupplyofenrollment.Thisstudyinstitutionswithsupplyconstraintsandinvesti- gateshowthoseconstraintshaveaffectedinstitutionsdecisionsonenrollment,andhowsucheffects varyacrossinstitutions.Ithat,intheshortrun,institutionsaredifferentincapacitytoabsorb additionalstudents,sothatrecessionshaveheterogeneouseffectsonenrollmentsizeandonfresh- manachievement.Duringrecessions,somecapacityconstrainedinstitutionsincreaseenrollment lessthanproportionatelytotheincreaseinthenumberofapplicationsand,asaresult,increase theiradmissionsselectivity.Otherinstitutionsrespondtoincreaseindemandbyacceptingmore students,resultinginadropinnew-studentachievement. Finally,thethirdessayfiRacialDifferencesinCourse-takingandAchievementGapflinvesti- gatestheblack-whitedifferencesincourse-takingandachievementinhighschool.Despitethe overallincreaseincourse-takingintensityinthelasttwodecades,theachievementgapbetween blackandwhitehigh-schoolstudentshaspersisted.Usingnationally-representativedata,thisstudy examinesracialdifferencesinthecourse-takingpatternanditsassociationwiththeachievement gap.Initialresultsshowaracially-differentcourse-takingpatterninmathematicscourses,inthat whitestudentsaremorelikelytobeenrolledinadvancedcoursesthanblackstudentsare,inall high-schoolyears,andthatthedifferencebeginsoccurringinthemathematicscourse,and increasesovertheyears.Moreover,theblack-whitetest-scoregapinGrade12differsbycourse levelandbyschoolyearofmathematicscoursetaken. ACKNOWLEDGMENTS Bythemomentofmydissertation,momentarilyawayfrompilesofpapers,Ilook backthesixandahalfyearatMichiganStateUniversityandrealizehowfortunateIamtohave endlesssupportandguidance.IwouldliketobeginbyexpressingmysinceregratitudetoScott Imberman,fortheincredibleeffortthroughouttheprocessofthedissertation.Ialsowouldliketo thankStevenHaider,ChristianAhlin,BarbaraSchneider,andGarySolonforgenerouslysharing theirintuitionandinsights,forpatientlyhelpingmedevelopresearchideasandrevisedrafts,and forbeingnexttomeandtalkingwithmeaboutmypersonalandacademicconcerns.Iamprivileged tohavethem,whohelpedmegrowasaresearcherandateacher,andamlookingforwardournext journey.Ialsowouldliketothankmyfellowgraduatestudentsinthedepartmentofeconomics andinthecollegeofeducationforhelpfulconversationsandsharingideas.Iowemanythanksto MargaretLynchandLoriJeanNicholsfortheirkindsupporthelpingmecompletingthedegree. Last,Iwishtothankmyfamily.,Ithankmyparents,KyungryangKimandChanghee Won,forhavingbeliefinmeandsupportthroughoutmylife,andtomybrother,WonbinKim, forhelpingmepersuademydream.Mostimportantly,mysincerestgratitudegoestomywife, HyeYoungJang,forherunconditionalloveandsupportandfortheandtomychildren, Jihong,Jian,andJiel,formylifewithjoyandforenablingmetodreamthefuturetogether. iv TABLEOFCONTENTS LISTOFTABLES ....................................... vii LISTOFFIGURES ...................................... ix CHAPTER1IntergenerationalMobilityinKorea ................... 1 1.1Introduction......................................1 1.2LiteratureReviewandMethod............................3 1.3Data..........................................7 1.4EmpiricalResults...................................10 1.4.1TheRoleofHIES...............................11 1.4.2InternationalComparison...........................13 1.5Remarks........................................14 APPENDICES.......................................15 APPENDIXAFIGUREFORCHAPTER1.....................16 APPENDIXBTABLESFORCHAPTER1.....................18 APPENDIXCADDITIONSFORCHAPTER1...................26 REFERENCES.......................................29 CHAPTER2CollegeEnrollmentovertheBusinessCycle: TheRoleofSupplyConstraints ...................... 33 2.1Introduction......................................33 2.2ConceptualFramework................................36 2.3Data..........................................39 2.3.1IPEDS.....................................39 2.3.2Variables...................................39 2.3.2.1Enrollment.............................39 2.3.2.2CapacityConstraints........................40 2.3.2.3StudentAchievement........................42 2.3.2.4FinanceandFaculty........................43 2.3.2.5UnemploymentRate........................44 2.4Responsestolabormarketshockinthehighereducationmarket..........46 2.4.1Budget.....................................47 2.4.2Enrollment..................................48 2.4.3StudentAchievement.............................50 2.4.4Faculty....................................52 2.4.5SizeofSupplyConstraints..........................53 2.4.6Prestige....................................54 2.4.7OtherMeasures................................55 2.5Conclusion......................................57 APPENDICES.......................................59 APPENDIXAFIGURESFORCHAPTER2....................60 APPENDIXBTABLESFORCHAPTER2.....................64 v APPENDIXCSUPPLEMENTALFIGURESFORCHAPTER2..........73 APPENDIXDSUPPLEMENTALTABLESFORCHAPTER2..........81 REFERENCES.......................................85 CHAPTER3RacialDifferencesinCourse-takingandAchievementGap ...... 88 3.1Introduction......................................88 3.2BackgroundandLiterature..............................90 3.3Data..........................................92 3.4Empiricalresults...................................97 3.4.1RacialGapinCourseIntensity........................97 3.4.2RacialGapinCourse-Taking........................98 3.4.3RacialGapinTimingofHighest-LevelofMath...............100 3.4.4AchievementGap..............................102 3.5Discussion.......................................104 APPENDICES.......................................106 APPENDIXAFIGUREFORCHAPTER3.....................107 APPENDIXBTABLESFORCHAPTER3.....................109 APPENDIXCADDITIONSFORCHAPTER3...................121 APPENDIXDSUPPLEMENTALTABLESFORCHAPTER3..........125 REFERENCES.......................................135 vi LISTOFTABLES Table1.B1Father-SonAgeDifference..........................19 Table1.B2DescriptiveStatistics..............................20 Table1.B3ChoiceofFather'sEarningsPredictors....................21 Table1.B4FirstStepRegression.............................22 Table1.B5IntergenerationalEarningsElasticity.....................23 Table1.B6SensitivityofIntergenerationalEarningsElasticity..............24 Table1.B7ComparableIntergenerationalEarningsElasticitywithTwo-SampleEsti- mation.....................................25 Table2.B1NumberofObservationswithDormitoryPolicy...............65 Table2.B2DescriptiveStatistics(2004-2011).......................66 Table2.B3RegressionofLogEnrollmentonLocalUnemploymentRate........67 Table2.B4RegressionofStudentAchievementonLocalUnemploymentMeasures(4- yearInstitutions,2004-2011).........................68 Table2.B5RegressionofFacultyonWeightedLocalUnemploymentMeasures(4-year Institutions,2004-2011)............................69 Table2.B6ChangesinEnrollmentandStudentAchievementwithCapacitySize(4- yearInstitution)................................70 Table2.B7ChangesinEnrollmentandStudentAchievementwithPrestige(4-yearIn- stitution)....................................71 Table2.B8RegressionofVariousMeasuresonWeightedLocalUnemploymentMea- sures(4-yearInstitutions)...........................72 Table2.D1RegressionofLogEnrollmentonWeightedLocalUnemploymentMeasures (4-yearInstitutions)..............................82 Table2.D2RegressionofStudentAchievementonLocalUnemploymentMeasures(4- yearInstitutions,2001-2011).........................83 vii Table2.D3ChangesinEnrollmentandStudentAchievementwithPrestigeandCapac- ityConstraints(4-yearInstitution).......................84 Table3.B1SummaryStatisticsbyRace..........................110 Table3.B2MostCommonCourseSequence.......................111 Table3.B3EstimatedBlack-WhiteGapinNumberofCredits..............112 Table3.B4EstimatedBlack-WhiteGapinNumberofCreditswithDropout.......113 Table3.B5EstimatedBlack-WhiteGapinCourse-TakingbyLevel...........114 Table3.B6EstimatedBlack-WhiteGapinCoursebyGrade...............115 Table3.B7EstimatedBlack-WhiteGapinCoursebyGrade...............116 Table3.B8SensitivityAnalysisofCourse-TakingGap..................117 Table3.B9EstimatedBlack-WhiteGapinTimingofHighest-Level...........118 Table3.B10EstimatedBlack-WhiteGapinTimingofHighest-LevelinGrade12....119 Table3.B11EstimatedBlack-WhiteGapinGrade12Test................120 Table3.D1HighestLevelofMathbyRaceandGrade..................126 Table3.D2MostCommonCourses............................127 Table3.D3SummaryStatisticsIncludingDropoutbyRace................128 Table3.D4EstimatedBlack-WhiteGapinTimingofHighest-LevelinGrade11....129 Table3.D5EstimatedBlack-WhiteMathScoreGapinGrade10.............130 Table3.D6EstimatedBlack-WhiteMathScoreGapinGrade12.............131 Table3.D7SensitivityAnalysisofMathAchievementGap................132 Table3.D8EstimatedBlack-WhiteMathScoreGapbyRaceinGrade10........133 Table3.D9EstimatedBlack-WhiteMathScoreGapbyRaceinGrade12........134 viii LISTOFFIGURES Figure1.A1AverageAgeDifferencebetweenFathersandSons..............17 Figure2.A1ChangesinShareofTotalEnrollment.....................61 Figure2.A2Application,Admission,andEnrollment]...................62 Figure2.A3StudentAchievementofFTFYbyInstitutionTypes.............63 Figure2.C1AcceptanceandYieldRatebyInstitutionTypes...............74 Figure2.C2FTEAppropriationandNon-TuitionSharebyInstitutionTypes.......75 Figure2.C3TuitionandNetPricebyInstitutionTypes..................76 Figure2.C4EnrollmentByResidencein4-yearInstitutions................77 Figure2.C5StudentAchievementofFTFYbyInstitutionTypes.............78 Figure2.C6FacultyEmploymentbyInstitutionTypes...................79 Figure2.C7EnrollmentandStudentAchievementbyDormitoryCapacity........80 Figure3.A1ProgressinMathLevel............................108 ix CHAPTER1 IntergenerationalMobilityinKorea 1.1 Introduction Intergenerationalmobilityreferstothepersistencebetweenparents'andchildren'soutcomes.If parents'earningsdonotimpactmuchontheiroffspring'searnings,thedegreeofintergenerational earningsmobilityishigh,anditcouldbethatrelativeeconomicdisadvantagesintheearlyyears willpersisttoalowerextentinadulthood.Thatis,intergenerationalearningsmobilityexploresthe characteristicsofinequalityineconomicopportunityaswell.Forasurveyofrelevantliterature, seeSolon(1999)andBlackandDevereux(2011). KoreaexperiencedrapidandextensiveeconomicgrowthinthepasthalfcenturywhenrealGDP percapitaincreasedAtthesametime,inequalityinlaborearningssteadilydecreased fromthe1970stothe1990s.Becauseofthesetrends,anaturalquestioniswhethereconomic developmentwithaconsistentdropininequalitywasaccompaniedbyanoverallincreaseinincome thelevelofallmarketparticipants,orwassharedbyparties. Becauseofalackoflongitudinaldataspanningtwogenerations,onlyalimitednumberof studiesonintergenerationalearningsmobilityinKoreahavebeendone.RecentstudiesinKo- reabyKim(2009)andChoiandHong(2011)employedco-residingfather-sonpairsintheinitial roundofpaneldata.However,asnotedbySolon(2002),thissamplemaydisplayadifferentin- tergenerationalassociationthanwouldamorerepresentativesample. 1 Moreover,asinmostother 1 Infact,theyfurtherrestrictedthesampletothosesonswhomovedouttoformanewhousehold.Thissample selectionapproachhasapotentialriskofendogenoussampleselection;non-coresidencesonsduringcertainbirthyears areoutofthesampleandthewaytheymovedoutisendogenous.Moreover,iftheaverageson'sageinthesampleis olderthantheaverageormedianhome-livingson'sage,thenthesampleover-representssonswholefthomeatlate ages.FrancesconiandNicoletti(2006)intheUKfoundadownwardbiasofupto25%inintergenerationalelasticity whenthesampleisrestrictedtoco-residencefather-sonpairs. 1 empiricalstudies,theyestimatedintergenerationalearningselasticitiesusingshort-runproxiesfor permanentearnings,whichmaygeneratedownwardbiasesinestimates. 2 Animportantexcep- tionavoidingthisdifisUeda(2013)whoutilizedatwo-samplemethodtoimputefathers' permanentearningsandshowedrelativelylowerestimatedintergenerationalearningsmobilityin Korea. ThisstudyestimatesintergenerationalearningsmobilityinKoreafollowingthemethodpre- sentedinUeda(2013)andextendsempiricalanalysisintwodimensions.First,Iuseanadditional nationalrepresentativesampletobetterapproximatethecohortofactualfatherssothatfathers' missingpermanentearningsaremoreaccuratelyimputed,andcarefullychooseagerangesfor eachgenerationtominimizelife-cyclebias. 3 Second,Icomparemyresultstocomparableresults ofothercountries,BjörklundandJäntti(1997)inSwedenandintheU.S.;FortinandLefebvre (1998)inCanada;NicolettiandErmish(2008)intheUK;Leigh(2007)inAustralia;Piraino (2007)andMocetti(2007)inItaly;Lefrancetal.(2011)inJapan;NúñezandMiranda(2011)in Chile;Lefranc(2011)inFrance;Gongetal.(2012)inChina;UedaandSun(2012)inTaiwan;and Cervini-Plá(2013)inSpain. Theremainderofthisstudyisorganizedasfollows:Section2presentsthebasicmodelto estimateintergenerationalearningspersistence,andreviewspreviousempiricalmethodsforesti- mation.Section3presentsthedatasource,variables,anddataselectionprocesstogeneratethe sampleforanalysis.Section4showsestimationresultswithcomparisonstootherinterna- tionalcountries'results.Section5concludeswithremarks. 2 SeeSolon(1992)fordetails. 3 Earningsvarywithobservedageandalife-cyclepatternexistsinthecorrelationbetweencurrentobservedand lifetimeearnings,knownaslife-cyclebias.Studiesshowedestimatestobesensitivetonotonlythefather'sobserved agebutalsototheson'sage.If,forinstance,theson'searningsareobservedintheearlystageofhiscareer,itcauses adownwardeffectontheestimate.Theoreticalandempiricalanalysesoflife-cyclebiasarewelldocumentedinthe U.S.byHaiderandSolon(2006);inSwedenbyBöhlmarkandLindquist(2006);andinGermanybyBrenner(2010). Theevidencefromthesestudiesshowsthatincomemeasuresintheagerangebetweentheearly-30sandthemid-40s shouldbeleastaffectedbylife-cyclebiaswhendependentvariablesareproxied.Thereisnostudyoflife-cyclebias foranyAsiancountriesnorforgeneratedregressors;yetIadoptedtheirresultsandwithinreasonthembased onKoreanlabormarketfeatures. 2 1.2 LiteratureReviewandMethod Inthissection,IprovideskeletalderivationofintergenerationalmobilitydevelopedinSolon(1992) andBjörklundandJäntti(1997).Thebasicempiricalapproachinintergenerationalmobilityliter- atureistoestimateearningselasticity,whichistoestimate r 1 inthefollowingequation. y i = r 0 + r 1 x i + e i (1.1) where y i isthelogofthepermanentcomponentoftheson'searningsinfamily i , x i isthelogof thepermanentcomponentofthefather'searningsinfamily i ,and e i isarandomdisturbanceun- correlatedwith x i .If y i and x i areobserveddirectlyfromarandomsample,onecanestimate r 1 in equation(1.1)byapplyingleastsquaresregression.Heretheparameter r 1 istheintergenerational earningselasticityand(1- r 1 )canbeinterpretedasameasureofintergenerationalmobility.There- fore,bycomparing ‹ r 1 ofeachcountry,comparisonsofintergenerationalmobilityacrosscountries arepossible;thehigher ‹ r 1 is,thelessmobilethesocietyis. 4 However,inmoststudies,availablemeasuresoftheearningsvariablearecurrentearningsin repeatedcrosssectionsamples,orinlongitudinalsamples,andinpracticeresearchershaveused short-runproxiesof y it forlong-runeconomicstatusvariablesof y i intime t , y it = l t y i + h ( Age it )+ n it (1.2) where l t istheassociationbetweencurrentandlifetimeearningsattime t ,whichisallowedto varyoverthelife-cycle;and n it ,themeasurementerrorin y it asaproxyfor y i ,isassumedtobe uncorrelatedwith y i and e i . h ( Age it ) isanarbitraryfunctionofason'sageattime t suchasa polynomialinage. 4 Analternativewaytomeasuretheextentofintergenerationalearningsmobilityistoestimateintergenerational correlation, k . k =( s 0 = s 1 ) r 1 where s 1 isthestandarddeviationofason'slogearningsand s 0 isthesamevariableforhisfather.Byconstruction, k isequalto r 1 onlyifthestandarddeviationsoflogearningsarethesameforbothgenerations. 3 Ifonehasanappropriatemeasureofafather'slong-runearningsbutisforcedtousecurrent earningsasaproxyfortheson'slong-runearnings,pluggingequation(1.1)intoequation(1.2) yields y it = l t r 0 + l t r 1 x i + h ( Age it )+ h it (1.3) where h it isequalto l t e i + n it .HaiderandSolon(2006)showedthattheprobabilitylimitofthe leastsquaresestimatorofthecoefof x i isequalto l t r 1 ,andsuggestedtheagerangesbe usedforbothfatherandsonattheirmid-careers,whichmoreaccuratelywouldrepresentlifetime earnings. 5 Anotherestimationproblemexistswhenasingledatasetcontainingearningsinformationfor pairsoffathersandsonsinalong-timeseriesisunavailable.BjörklundandJäntti(1997)proposed atwosamplemethodtoimputefathers'missingearningsfromanauxiliarysampleofafather's generationonthebasisofason'sreportonafather,suchaseducation,industry,andoccupation. 6 Let z i denoteasetoffathers'socio-demographicvariablessuchaseducationandoccupationand assumethatthepermanentcomponentoffathers'earningsisgeneratedbythefollowingrelation- ship: x i = z i f + x i (1.4) where z i isorthogonalto x i bylinearprojection.Fromequation(1.4)fathers'long-runeconomic statusvariablesaregenerated,‹ x i = z i ‹ f ,withagecontrolsinthepotentialfathers'sample. 7 Rewriteequation(1.1)as y i = r 0 + r 1 ‹ x i + e i + r 1 ( x i ‹ x i ) andplugintoequation(1.2)gives y it = l t r 0 + l t r 1 ‹ x i + h ( Age it )+ w it (1.5) 5 Inaclassicalerrors-in-variablesmodelwhen l t = 1,theOLSestimateof l t r 1 isunbiasedeveninthepresence ofthemeasurementerrorinthedependentvariable.However,HaiderandSolon(2006)showedthat l t variesovera life-cycle,whichneedsnotequaltoone,andtheestimatorisbiasedbyafactorof l t .AlsoseeSolon(1992)forthe attenuationbiaswhenthereisaclassicalmeasurementerrorinbothson'sandfather'searnings. 6 Iimputefathers'missingearningsduetodataavailabilitybuttheissueofmeasurementerrorbyusingcurrent earningsforlong-runearningsisincidental. 7 Thistwo-sampleapproachissometimesincorrectlylabeledasTS2SLS.Howeveritisnotbecausenotallexoge- noussecond-stageregressorsincludingtheson'sagevariablesareincludedintheintheequation(1.4). 4 where w it isequalto l t e i + n it + l t r 1 ( x i ‹ x i ) .UnderregularityconditionsdescribedintheAp- pendix,theprobabilitylimitoftheleastsquaresestimatorofthecoefof x i isequalto plim n ! ¥ ‹ r 1 = l t r 1 Var ( x i )+ Cov ( x i ; n it ) Var ( x i ) (1.6) whichreducesto l t r 1 if Cov ( x i ; n it )= 0.(TheproofcanbereviewedintheAppendix.)However, theconsistencystilldependson l t evenwiththegeneratedregressoranditcallsforresearcher cautioninchoosingtheappropriateagerangeasHaiderandSolon(2006)proposed. 8 Finally,ordinaryleastsquaresregressionisappliedtoequation(1.5)toestimate r 1 . 9 Generally,moststudieswiththismethodologyhavetwodatasets:Theprovidessons' economicstatusvariableswithsons'recollectedinformationoffathers'education,industryand occupationalcharacteristicsattheson'sparticularageduringchildhood.Thosevariablesareused togeneratefathers'missingeconomicstatusvariables.Theseconddatasetcontainspotentialfa- thers'economicstatusvariableswithsocio-demographiccharacteristics.Thissupplementarysam- pleisusedtopredictfathers'economicstatusvariableslikeearnings,basedonfathers'socio- demographiccharacteristicswhensonswereataageasreportedinthedataset.Then r 1 canbeestimatedfromequation(1.5)withpredictedfathers'earnings,‹ x i ,inlieuoffathers' permanentearnings, x i . Similartomanyothercountries,Koreadoesnothaveasuflongintergenerationalpanel 8 NybomandStuhler(2011)providedanexamplewhenonesuspectsthatlifetimeearningscorrelatewithinfamily, i.e., Cov ( x it ; n it ) 6 = 0 : Ifmeasurementerrorsinearningsgrowthratesoffathersandsonsarecorrelated,afather's lifetimeearningscorrelatewithcareeroutcomesandthereforethesameshapeofearningtrajectoriesashischildren. 9 Notethat r 1 inequation(1.3)willnotbeequalto r 1 inequation(1.5)ascompositeerrorsdifferexceptfor x i = ‹ x i . Onefeasibleexpectationofthemagnitudeof r 1 isthat r 1 inequation(1.5)wouldbelargerthaninequation(1.3) ifthereisapositivecorrelationbetweenfathers'socio-demographicvariablesandsons'economicstatusvariable; BjörklundandJäntti(1997)andUeda(2013)useditasanupperboundonthetrueestimates.Exceptforfathers' education,itisnotclearhowotherfathers'industryoroccupationvariablescanaffectsons'earnings.Moreover,the directionofbiasisevenmorequestionablewhenlife-cyclebiascomesintoconsideration.Thusinthisstudy,Idonot interpret ‹ r 1 inequation(1.5)asanupperboundof ‹ r 1 inequation(1.3).Hereafterthevalueof r 1 isdenotedas r 1 in equation(1.5).Piraino(2007)testedorthogonalityconditionsforhissetofpredictorsandthatatleastsome offathers'characteristicsarecorrelatedwiththeregressionerrorterm.Thegeneralapproachbypractitionersisto choosepredictorssuchthatthe R 2 ofthestepregressioninequation(1.4)isashighaspossible.Researchercaution isrequiredtochoosetheappropriatestandarderrorsofgeneratedregressors.MurphyandTopel(1985)andPagan (1984)showedthatstandardtwo-stepproceduresnotaccountingforgeneratedregressorproblemsunambiguously underestimatestandarderrorsoftheconsistentsecond-stepestimators;andthatcorrectedstandarderrorsarelarger thanaretheiruncorrectedcounterparts,insomecasesbyafactoroftwoormore. 5 datasetwhereexplicitinformationoffather-sonpairs'economicstatusvariablesareobserved. 10 SeveralstudiesinKoreaweredonebyemployingtheKoreanLaborandIncomePanelStudy (KLIPS),whichisonlyavailablefrom1998to2008.Kim(2009)andChoiandHong(2011)em- ployedKLIPSdataandestimated r 1 inKorea.Theyfocusedonfather-sonpairswhoco-resided in1998,andrestrictedsonswhoinsubsequentyearsmovedintoanon-memberhousehold(for instance,throughmarrying).Thishomogeneoussampleofco-residentfather-sonpairsisanen- dogenouslyselectedsampleandwoulddemonstrateanintergenerationaltransmissionofearnings differentfrominthepopulation.Theyaveragedavailableearningstoovercomeattenuationbias becausecurrentearningsareproxiedforpermanentearnings.However,includingyoungersons- around30-andolderfathers-inthelate50s-tendstolowerestimatesduetolife-cyclebias.For monthlyearnings,coefare0.141(0.042)and0.349(0.096)whenthefather'seducationis instrumentedforthefather'searnings. Ueda(2013)alsousedKLIPStoestimateintergenerationalmobilityinKoreaandemployeda two-samplemethodtoimputeactualfathers'permanentearningsusingsons'recollectionsoftheir fathers'educationallevelsandoccupationswhentheywere14.Amongworkingmenwithpositive wagesaged25-54forfathersand30-39forsons,Uedarestrictedthesons'sampleto2006and pooledannualearningsforthepotentialfathers'sampleobservedovertheperiod2003-2006.The coefis0.223(0.072)butUedaimputedatoo-recentearningsfunctioninsteadofchoosing thefathers'sampleinactualcalendartime. 10 Anotherwaytoestimate r 1 ,takingintoaccountthemissingfathers'permanentearningsproblem,couldbeby adoptingthepropensityscoreweightingestimation.ButNicolettiandErmisch(2008)arguedthatit'susefulnessis sensitivetodataavailabilityoffather'searnings. 6 1.3 Data KLIPScontainssons'earningsandtheirrecollectionsoffatherswhentheywere14andisthe Koreanlongitudinalsurveyonthelabormarketandincomeactivitiesofhouseholdsandindividu- als,collectedfrom1998to2008.Duringthewavein1998,arepresentativesampleof5,000 householdsandtheirmembers(15andover),coveringmorethan13,000individuals,wasinter- viewedusingthesamplingframefromthecensusandtheybecametheoriginalpanelofhouseholds andhouseholdmembers. 11 Inaddition,HouseholdIncomeandExpenditureSurvey(HIES)isrepeatedcrosssectionsurvey datathataretheonlypubliclyavailableatanindividuallevelwitheconomicstatusvariablessuch aslaborearnings,familyincomeinformationofeachhousehold,andsocio-demographiccharac- teristics.Surveydataareavailablesince1982;however,educationinformationwasaddedtothe surveysince1985.HIES,asinKLIPS,usedthesamplingframeofthecensus,whichsupportsthe argumentthatbothdatasetsarerepresentativesamplesoftheKoreanlabormarket. Monthlylaborearningsarerecordedpre-taxinHIESandnetoftaxesinKLIPS.However,pre- taxlaborearningsinKLIPScanbecalculatedbecausetaxonlaborearningsisalsoavailablein KLIPSfrom2004.OnedatalimitationisthatKLIPSrecordstheincomeofself-employedworkers byafter-taxvaluewhereasHIESdoesnotprovideincomeinformationforself-employedworkers. Thisrendersithardertoestimateaccuratemobilitywhenself-employedfathersareincluded.In thisstudy,laborearningsarethemainfocus,becausetheyenableinternationalcomparisonof intergenerationalmobility,asmostpreviousstudiesusedearnings;more,earningsmobilitybetter measuresmobilitybasedanindividual'smeritthandoothereconomicstatusvariables. 12 Since 11 Sincethe2ndwavein1999,householdandindividualsamplearemaintainedbyfollow-uprules,whichistypical inhouseholdpanelsurveys.Individualswhocometoformbloodandeconomictiestooriginalpanelmembersare addedtotheoriginalsample.Forexample,ifapanelmembermarriesandformsanindependenthouseholdwith his/herspouse,thelatterbecomesa`newrespondent'totheoriginalpanelandthecoupleisfollowedandinterviewed thereafter.Ontheotherhand,ifforinstanceoneofthepanelmembersmovesintoanon-memberhousehold,via marriageforinstance,he/sheisalsofollowedandhis/herspouse'shouseholdmembersareinterviewed.Inthisway, thesizeofthesamplemembersgrowsandexpandsinwaves.Whenapanelmembermovesoutoftheoriginal household,forinstanceviadivorce,heorsheisalsotrackedaslongasheorsheliveswithhisorherchildren. 12 SeeBjörklundandJäntti(2009)formorediscussionondifferentincomemeasuresandtheirfeatures. 7 HIESdoesnotofferanyincomeinformationforself-employedworkers,sonswhosefatherswere self-employedduringtheirchildhoodareexcluded. 13 KLIPSandHIEShaverecordededucation,occupation,andindustryindifferentcategories. EspeciallyoccupationandindustryvariablesarerecordedwiththreedigitsinKLIPS,butinone digitandtwodigitsinHIES,respectively.Sincethecategoriesusedforindustryandoccupation inKLIPSarethanthoseusedinHIES,thosevariablesarematchedaccordingtotheHIES schedule.Afterrecodingcategoriestohaveahomogeneousacrosssamples,seven differentlevelsofeducation,nineindustrygroups,andsevenoccupationalgroupsareavailableto predictfathers'missingearnings.Thenumberofpredictorsforfathers'missingearningsaswell asthenumberofgroupsofeachvariablearerelativelyricherthaninpreviousstudiesinother countries. 14 IntheanalysisIusetwowavesofKLIPSforsons'sampleandbothKLIPSandHIESfor potentialfathers'sample.WhenreplicatingUeda'sempiricalresults,IuseKLIPSin2003for sons'sampleandKLIPSin2006forpotentialfathers'sample.Sincetheagegapbetweensonsin KLIPSin2003andpotentialfathersinKLIPSin2006isthree,tousemoreapproximalcohorts ofactualfathers,Iretrievesons'samplefromKLIPSin2008andpotentialfathers'samplefrom HIESin1985. 15 Preferredagerangeforbothgenerationsisbetween35and50aserrors-in-variablesbiasin sons'earningsstayssmall,followingHaiderandSolon(2006),giventhatKoreanmaleworkers generallyenterthelabormarketabout3-5yearslaterthanintheU.S.duetomandatorymilitary serviceobligations. 16 13 Noteself-employedsonsareincludedwhensonswithself-employedfathersareexcluded.IfIexcludeself- employedsons,Ilose50%ofthesample,however,theestimatesaresimilar. 14 Forinstance,BjörklundandJäntti(1997)usedfathers'educationandoccupation;NicolettiandErmisch(2008) usedoccupationalprestigeandeducation;andLefranc(2011)usededucation. 15 Thesetwosamplesare23yearsapartthusenablesmatchingoffather'sgenerationmorecloselytoactualfathers thandoesusing2003forpotentialfathers'sample.Usingtheaverageagedifferencebetweenfathersandsonsfrom thenationalcensus,potentialfathers'agerangein1985issetto35-50whenthesonswere14,whichcoversaround 95%ofthefather-sonpairs.Table1demonstratesagedifferencesbetweenfathersandsonsanditisclearthatstatistics forKLIPS2005andNationalCensus2005arecloselysimilar;thiscanbeveasilyinFigure1.Thisevidence theuseofKLIPS2008asarepresentativesampleandrestrictionofsamplesbasedontheageinformation fromKLIPS2008. 16 Infact,forsons35-50in2008,theirpossiblefatherswere34-68in1985;thiscovers95%offathersbasedon 8 BothKLIPSin2008andHIESin1985arerestrictedtoworkingmenagebetween35and50 withpositivewages,whichleaves1700observationsinKLIPSand1780inHIES. 17 Especiallyin HIES,thefathers'samplewasfurtherrestrictedtothosewithapositivenumberofchildrenaged 6-19in1985.Fathersorsonswholivedinforeigncountrieswhentheirsonswere14areexcluded. Furthermore,employedsonswhosefatherswereself-employedalsoareexcluded.Narrowingthe sampletothosewithalleducation,industry,andoccupationvariablesrecorded,thenumberof observationdropsto675inKLIPSand1,577inHIES. 18 Descriptivestatisticsofvariablesused forthemainsampleandthesupplementalsamplearesummarizedinTable ?? . agedifferenceinformationfromcensusdatain2005.IfImatchtheagerangeof35-50forfathersin1985,Ilose20% ofthesample;however,theestimatesaresimilar.Moreinformationisprovidedinthenextsection. 17 Betweenhouseholdheadandnon-headsons,differencesexistinearningsandeducationalattainment.Butex- cludingnon-headsandrestrictingonlytoheadscouldbeanendogenousselection.Moreover,thereisnoformal requirementtoanswerasaheadbutitiswhorepresentsthehousehold.ThusIincludedallmaleworkersandpre- sentedtheresultsforbothsamples.Inaddition,nationalunemploymentrateinKoreaisaround5%inlate1980sand around3.5%in2000s,indicatingthattheexcludingunemployedpopulationisnottroublesome. 18 Totalsampleagebetween35and50inKLIPSis3700and1897aremale;1700workershavepositivewages; 1016workershaveself-employedfatherswhentheywere14,whichleaves684workers.Allhavefathers'education information.Thesamplesizedecreasesbysixformissingfathers'industryinformationandbyanotherthreefor missingoccupationinformation,thussamplesizeis675.HIEShas1787maleworkersagedbetween35and50 and1780havepositiveearnings.Thesamplesizedropsby223whenrestrictedtoworkerswithchildrenagedbetween 6and19.Allhaveinformationoneducation,industry,andoccupation. 9 1.4 EmpiricalResults ToextendtheempiricalresultsfromUeda(2013),theanalysisstartsbyfollowinghis strategyofapplyingthetwostepmethodtoasingledataset,KLIPS,andextendstheanalysisby introducingHIESforpotentialfathers'sample.Ueda(2013)averagedannualearningsbetween 2003and2006forpotentialfathersandretrievedsons'earningsfrom2006,andrestrictedagesfor sonsto30-39andforfathersto25-54.ToprovideresultssimilartoUeda,Iretrievesons'earnings fromKLIPSin2006andpotentialfathers'annualearningsfrom2003,andrestrictthesameage rangesforsonsandfathers.Toimplementthetwo-samplemethod,inthestepinequation (1.4),fathers'logearningsin2003areregressedonage,agesquared,industry,occupation,and educationvariablesfollowedbysampleselectionrulesdescribedintheprevioussection.Then, asinequation(1.5),sons'logearningsin2006fromKLIPSareregressedongeneratedfathers' permanentearnings,ageandagesquaredofsons. 19 Standarderrorsareestimatedbythebootstrap methodfollowingBjörklundandJäntti(1997). 20 Table1.B5summarizesresultsandtheestimate replicatingUeda'sapproachis0.205withabootstrappedstandarderrorof0.050,whichissimilar toUeda'sbaselineestimateof0.223.Uedausededucationandoccupationtopredictfathers' missingearningsandwhenIusethosetwovariablesaspredictors,theestimateis0.244(0.054). Whenthelaterroundin2008isusedforsons'sample,theestimateis0.310(0.049). Restrictingtothepreferredagerangeof35-50forbothgenerations,theestimateinPanelD increasesto0.334(0.057),partlyduetoexcludingyoungfathers.Resultsareconsistentwith previousstudiesonlife-cyclebias;inclusionofyoungersonsorolderfatherslowersestimates. Thatis,thecorrelationbetweenafather'sage(son'sage)atmeasurementandthesizeof ‹ r 1 is 19 Notethatestimatesofagecontrolssuchasageandagesquaredoffathersarenotusedtogeneratefathers'missing earnings.ThisisbecauseIamnotpredictingearningsataparticularage,butaretryingtopredictfathers'long-run earnings,whichrequiresthestandardizationonages.Thusitisinappropriatetousere-age-adjustedfathers'earnings inthesecondstep. 20 First,IdrawabootstrapsampleoffathersfromKLIPS2003,fromwhichequation(1.4)isruntoestimate parameters.ThenIdrawanotherbootstrapsampleofsonsfromKLIPS2006,fromwhoserecollectionsdataisused togeneratefathers'earnings.Iestimate r 1 inequation(1.5)andsaveestimatesfor1000replications.Ifaresearcher ignoresthatfathers'earningsaregeneratedandusesabootstraponlyinthesecondstep,thenstandarderrorsare smallerthanourapproach,bootstrappingbothsteps,butstilllargerthanthosewithoutbootstrappinginOLS. 10 negative(positive).Theestimatesare0.144(0.083)forsonswithself-employedfathersand0.218 (0.061)forsonswithemployedfathers,whichfreesconcernthatself-employmentstatusoffathers mightaffecttheestimates. Thisapproach,however,implicitlyassumesthatpotentialfathers'characteristicsin2003are closetothoseforactualfathers,andusesinformationfromtheyounger-fathergeneration.In otherwords,iftheaverageagegapbetweenfathersandsonsis30,thenfathers'actualagesin 2003,whosesonsareaged30-39in2008,are55-64insteadof25-54.Moreover,occupation, industry,andeducationdistributionin2003,usedforpotentialfathers'characteristics,aremore similartothoseforsonsin2008thantothoseforactualfathers.Thusresultsofthisapproachare vulnerableifonesupposeschangesoccurredinthewagestructureinrecentdecades.To retrievepotentialfathers'informationfrommoreapproximalcohortofactualfathers,IuseHIES andgeneratepseudofathers'earningsbasedonsons'recollectionsonfathers'industry,seven categoriesofoccupation,andeducation. 1.4.1 TheRoleofHIES EstimatesinPanelsBandCinTable1.B5presentthesensitivityofsons'samplebetweenKLIPS 2006and2008,suggestingthatdetailedmatchingofpotentialfatherswithactualfatherscouldbe important.Byretrievingpotentialfathers'informationfromHIESin1985,thefather-sonagegap becomesmorerealisticandthedistributionofearningspredictorsincludingeducation,occupa- tion,andindustry,becomesclosertothoseofactualfathersrememberedbysonsthantothoseof potentialfathersinKLIPS2003. Agerangesforbothgenerationsarerestrictedto35-50asitbestthefeatureofthe Koreanlabormarketthatmandatorymilitaryservicegenerallydelaysmenfromjoiningit.More- over,thepreferredagerangebetterrepresentsmid-careerearnings,andthiswiththree earningspredictorsforfathersandagerangesforfathersandsonsbetween35and50isservedas thebaselinemodel. 21 Byexcludingyoungersonsintheirlater20sandearly30sandolderfathers 21 Keyfather'searningspredictorsarechosentomaximize R 2 ofthestageregressionandtheresultsaresum- marizedinTable3.Theadjusted R 2 inthestage,0.393,isrelativelylargerthanotherstudiesinTable1.B7; 11 above50,theestimateincreasesto0.386(0.059). 22 Table1.B6urtherreportsregressionresultswithseveraldifferentsampleSome concernmightarisethattheoccupationdistributionofpotentialfathersandrealfathersareimper- fectlymatched.Althoughrequiredinformationfromthestepisthesampleaverageofearnings ineachpredictorcategory,inPanelAtheoccupationcategoriesaremergedandreorganizedtogen- eratesimilardistributions.However,thenumberofcategoriesdoesnotchangeestimates cantly.Infact,estimateslieintherange0.401to0.407whenthenumberofoccupationcategories ischangedfrom6to4,whichindicatesthattheestimatesarerobusttooccupation Thusdifferentoccupationcategorydistributionhasnegligibleimpactonestimates. Theagerangeof35-50ischosentohave l t closeto1sothatmeasurementerroriscloseto classicalerrors-in-variables.Manystudiesusingcurrentearningstoproxyforpermanentearnings averagedearningsoveryearstodealwiththemeasurementerrorfollowingSolon(1992).Estimates ofintergenerationalearningselasticitybecomelargerasfathers'earningsareaveragedovermore years.SincepotentialfathersaretakenfromHIESin1985andHIESisrepeatedcrosssectiondata, whichmakesithardertocalculatemissingfathers'averageearnings,sons'earningsareaveraged overyears.ResultsinPanelBshowthattheestimatesincreaseasearningsareaveragedovermore years. Inthebasemodel,allthreeearningspredictorsareused.Ifonechangesthecombinationof earningspredictorsandusesasubsetofpredictors,samplesizeincreasesbyonlynine,whichfrees theconcernofhavingasmallersamplesizeinexchangeforhavingmorepredictors.However, estimateschangefrom0.35to0.59,implyingthatresearchersshouldpayattentionwhenthey chooseappropriatepredictorsandespeciallywhentheycomparewithothercountries'estimation Piraino(2007)with0.322,Mocetti(2007)with0.301,NicolettiandErmisch(2008)with0.289,andUeda(2013)with 0.23.PreferredstepregressionresultsaresummarizedinTable1.B4withagerangeof35-50forbothgenerations usingallthreeearningspredictors. 22 IfImatchtheagerangeof34-68forpotentialfathersin1985covering95%ofthefather-sonpairs,theestimate is0.397,verysimilartotheestimateinthebaselinemodel.Thushereafter,agerangeoffathersin1985isedat 35-50insteadof34-68.Whenself-employedsonsexcluded,thesamplesizedecreasesto502,andtheestimateis 0.409(0.064).Furtheranalysisshowsthattheestimateisrobusttothetreatmentontheself-employmentworkers.In addition,forhouseholdheads,thesamplesizeis572and ‹ r 1 is0.351(0.062).Headsearnapproximately15%to30% morethannon-headmembersandthismightresultinarelativelylowerestimate. 12 results.ResultsaresummarizedinPanelC. Whentheindustryvariableisdropped, ‹ r 1 is0.392(0.065).Mostothercountries'studieson intergenerationalelasticitywithtwo-sampleestimation,documentedinTable1.B7,didnotuse anindustryvariabletopredictfathers'earnings.However,itisnotclearinwhichdirectionthe estimatewouldmoveifanindustryvariableisincluded. 23 1.4.2 InternationalComparison Insummary,theestimateofintergenerationalelasticityisaround0.4,similartoalready-developed countriesandrelativelylowerthanrecently-developedordevelopingcountries.Arelativelyhigher extentofintergenerationalmobilityisshowninKorea,evenhigherthanotherdevelopingcountries (e.g.,0.69inBraziland0.52inChile). 24 Somestudies,forinstancePiraino(2007)inItaly,investigatedthechannelsinthetransmission ofeconomicstatusandfoundparentaleducation'scontributiontotheintergenerationalmobility. InKorea,parent-childschoolingcorrelationamong20-69sonsin2008isonly0.333, 25 oneof thelowestvaluesaccordingtoHertzetal.(2008). 26 SomecountriesinTable1.B7,forexample BrazilandChile,showanegativerelationshipbetweenintergenerationalschoolinginheritance andintergenerationalearningsmobility.Morethoroughexaminationontherelationshipbetween educationinheritanceandintergenerationalmobilityinKoreaisleftforfutureresearch. 23 IfIexcludetheagriculturesectorinindustryandinoccupationcategories,whichmostlyconsidersthesample residinginurbanareas,theestimateis0.337,thelowestamongallmodels.Asaresult,areasonableclaimisthat intergenerationalmobilityishigherinurbanareasthanthatinruralareas,accountingforjobopportunitiesinthose areas. 24 KeycomparablecountriesinTable1.B7havedifferentagerangesforfathersandsons,anddifferentsetsof fathers'earningspredictors.Sinceeachcountryhasadifferenteducation-,industry-,andoccupationstructureand history,anddifferentworkerquality,preciseinternationalcomparisonismorechallengedandnoformalstatisticaltest existsforcomparison.Constructingaintervalforestimatesforcomparisonisapossibleoption.However, thosefactsasideforsimplicity,whenImatchagerangesandsetsofpredictorswithcorrespondingcountriesinTable 1.B7,exceptforChilewherefathers'age-rangeinformationisunavailable,therelativemobilityinKoreastaystable. 25 Approximately90%ofsonsareeducatedbeyondhighschool,whereasasmanyasapproximately80%oftheir fathershaveeducationlessthanhighschool. 26 Hertzetal.(2008)documentedinternationalcomparisonofeducationalinheritanceforsons20-69.Someno- ticeablecountriesinTable1.B7areBrazil(0.59),Chile(0.6),China(rural,0.2),Italy(0.54),Sweden(0.4),UK(0.31), andU.S.(0.46). 13 1.5 Remarks ThisstudyexaminesintergenerationalearningsmobilityinKoreawiththetwo-sampleestimation methodtogeneratefather'smissingpermanentearningsbycombiningapaneldataset,whichin- cludesson'searningsandrecollectioninformationonfather'ssocio-demographiccharacteristics, andacrosssectiondataset,whichcontainsearningsandsocio-demographicinformationofpoten- tialfathers. Thisstudyshowsthatthemeasurementerrorinsons'currentearningsasaproxyforpermanent earningsisasourceofinconsistencyevenwhenfathers'earningsaregenerated.Thustheworking father-sonsampleisrestrictedtoage35-50tobeleastaffectedbylife-cyclebias,andtheelastic- ityisaround0.4.Estimatedintergenerationalearningselasticityissimilartoestimatesforsome already-developedcountriesandsmallerthantypicalestimatesforrecently-developingcountries. PreviousstudiesonKoreanintergenerationalearningsmobilitytendtohavelowerestimates than0.4.Someincludedyoungersonsandolderfathersinthesample,andthosefactorscontributed tolowerestimates.Moreover,focusingonahomogeneoussampleofco-residingfather-sonpairs mayresultinlowerestimates.Ueda(2013)alsoemployedtwo-sampleestimation;however,less attentionwaspaidtodetailedmatching,asaninaccurateperiodofobservationforpotentialfa- thers'samplewasusedforimputation. 27 Thusthisstudycontributestomore-accuteestimationof mobility,withtworepresentativesamplesaimingtomatchpairscorrectlybychoosingtheright agerangeforbothgenerations,whichbetterrepresentspermanentearnings. Perhapsoneofthemostimportantremainingissuestodealwithisthelife-cyclebiasinKorea. MaleworkersinKoreagenerallyhavetoserveinthearmyfromtheirlateteens,whichonaverage delayslabormarketparticipationtimingbythreetoveyearscomparedtotheU.S.Sincedata accessislimitedinKoreatoanalyzetheframeworkasinHaiderandSolon(2006),alternative approachestostudyinglife-cyclebiasinKoreaarerequiredinfuture. 27 RealGDPpercapitainKoreaincreasedmorethanthreetimesbetween1985and2003,implyingthatpotential fathers'cohortin1985,whoaremoreproximaltoactualfathers,aredifferentfromthecohortsin2003. 14 APPENDICES 15 APPENDIXA FIGUREFORCHAPTER1 16 Figure1.A1AverageAgeDifferencebetweenFathersandSons Notes: Averageagedifferenceintheoriginalsamplesisintheleft.Averageagedifferencewhenthedifference betweenKLIPS2005andCensus2005iscorrectedisintheright. 17 APPENDIXB TABLESFORCHAPTER1 18 Table1.B1Father-SonAgeDifference Census2005KLIPS2005KLIPS2006KLIPS2008 Observation139,8322,6542,6552,564 AverageAgeDifference30.5429.7929.7429.79 StandardDeviation4.254.254.224.21 AgeRangefor90%ofObservation24-3923-3723-3723-37 AgeRangefor95%ofObservation22-4122-3922-3922-39 19 Table1.B2DescriptiveStatistics ActualFathersPotentialFathersSons DescribedbySonsinHIES MeanAge4141 Education None6.91.70.2 Elementary26.115.41.8 Middle20.823.74.1 High29.234.830.6 CommunityCollege(2Years)2.02.418.2 University(4Years)13.720.434.3 GraduateSchool1.41.710.8 Occupation Professional,Technical,Managerial12.78.136.5 High-RankGovernmentOf,Entrepreneur2.60.72.6 AdministrativeWorker16.724.919.2 OfWorker5.27.73.7 ServiceWorker3.25.33.5 ProductionWorker37.451.133.3 Agriculture,Fishing,Forestry22.32.21.2 Industry Agriculture,Fishing,Forestry12.12.00.6 Mining2.41.50.0 Manufacturing18.230.328.6 Utilities0.21.11.4 Construction19.618.012.6 WholesaleandRetailTrade10.38.811.6 Communication,Transportation8.912.37.7 Banking,BusinessService5.04.117.8 PublicAdministration,Education23.422.019.8 Notes: Ageoffather-sonsampleisrestrictedto35-50. 20 Table1.B3ChoiceofFather'sEarningsPredictors CaseEarningsPredictorsF R 2 Adj R 2 RootMSE 1Industry24.610.1370.1320.499 2Occupation80.220.2930.2890.451 3Education99.150.3390.3350.436 4Ind&Occ47.260.3290.3220.441 5Occ&Edu66.640.3770.3710.424 6Ind&Edu56.260.3690.3620.427 7Ind&Occ&Edu46.770.4020.3930.417 Notes: Ageoffather-sonsampleisrestrictedto35-50. 21 Table1.B4FirstStepRegression DependentVariable:LogFather'sEarnings CoefStd.Err Education NoneOmittedDummy Elementary0.21640.1032 Middle0.31990.0999 High0.45780.1006 CommunityCollege(2Years)0.73880.1230 University(4Years)0.77120.1043 GraduateSchool0.79100.1313 Occupation Professional,Technical,Managerial0.07350.1301 AdministrativeandGovernmentOf,Entrepreneur0.03150.1923 ClericalWorker0.11720.1247 SalesWorker0.39160.1272 ServiceWorker0.39920.1415 ProductionWorker0.31190.1243 Agriculture,Fishing,ForestryOmittedDummy Industry Agriculture,Fishing,ForestryOmittedDummy Mining0.25360.1711 Manufacturing0.40530.1452 Utilities0.43920.1933 Construction0.17010.1486 WholesaleandRetailTrade0.33480.1503 Communication,Transportation0.37030.1478 Banking,Insurance,BusinessService0.39560.1547 Community,Social,andPersonalServices0.38850.1445 Notes: Ageoffather-sonsampleisrestrictedto35-50. 22 Table1.B5IntergenerationalEarningsElasticity Sons'AgeFathers'AgeSampleSize ‹ r 1 Std.Err PanelA:OriginalfromUeda 30-3925-548090.223***0.072 PanelB:ReplicationofUedaUsingKLIPS2006 30-3925-5411420.205***0.050 PanelC:ReplicationofUedaUsingKLIPS2008 30-3925-5410830.310***0.049 PanelD:RoleofAge 35-5025-5419110.307***0.054 35-5035-5016660.334***0.057 PanelE:EmployedFathers 35-5035-506750.218***0.061 PanelF:Self-EmployedFathers 35-5035-509910.144*0.083 PanelG:PotentialFathersfromHIES 35-5035-506750.386***0.059 Notes: Sons'informationisretrievedfromKLIPS2006forPanelA-B, andfromKLIPS2008forPanelC-G.Potentialfathers'informationis retrievedfromKLIPS2003forPanelA-FandfromHIES1985for PanelG.Bootstrappedstandarderrorsareinparentheses. atthe1%levatthe5%level. atthe10%level. 23 Table1.B6SensitivityofIntergenerationalEarningsElasticity SampleSize ‹ r 1 Std.Err Baseline6750.386***0.059 PanelA:RoleofOccupationCategory OccupationCategory 66750.401***0.062 56750.407***0.061 46750.405***0.061 PanelB:RoleofAveragingforBalancedSample Period 2007-20084830.426***0.058 2006-20084590.445***0.057 2005-20084100.471***0.060 PanelC:PredictorCombination Predictor Industry6780.585***0.105 Occupation6750.398***0.074 Education6840.354***0.076 Ind&Occ6750.411***0.063 Occ&Edu6750.392***0.065 Ind&Edu6780.394***0.065 Ind&Occ&Edu6750.386***0.059 Notes: Baselinemodelusesindustry,occupation,andeducation aspredictors,andageoffather-sonsampleisrestrictedto35-50. Sevengroupsofoccupationcategoryareusedandstandarderrors arebootstrapped. atthe1%levatthe5%level. atthe10%level. 24 Table1.B7ComparableIntergenerationalEarningsElasticitywithTwo-SampleEstimation CountryAuthors ‹ r 1 Std.ErrAge f Age s EarningsPredictors AustraliaLeigh(2007)0.410.13725-5425-54Occ BrazilDunn(2007)0.690.01430-5025-34Edu CanadaFortinandLefebvre(1998)0.220.05140-5017-59Occ ChileNúñezandMiranda(2011)0.52N.A.N.A.23-65Edu,Occ ChinaGong(2012)0.630.11748-7430-42Edu,Occ,Ind FranceLefranc(2011)0.500.02825-6028-50Edu ItalyPiraino(2007)0.440.05330-5027-49Edu,Occ,Ind ItalyMocetti(2007)0.490.06930-5030-50Edu,Occ,Ind,Region JapanLefrancetal.(2011)0.340.04230-5930-50Edu,Occ,Ind SpainCervini-Plá(2013)0.400.04237-5730-50Edu,Occ SwedenBjörklundandJäntti(1997)0.280.0944330-39Edu,Occ TaiwanUedaandSun(2012)0.210.06030-5930-49Edu,Occ UKNicolettiandErmisch(2008)0.290.06131-5530-45Edu,Occ USBjörklund&Jäntti(1997)0.420.121N.A.28-36Edu,Occ Notes: Leigh(2007)usedpredictedhourlywagefora40-yearoldandtheestimatesinthetableshow resultswiththe1987sample.Whenthe2004sampleisused,theestimateis0.18withstandard errorsof0.043.Fortin&Lefebvre(1998)assumed25-35yeardifferencebetweenfatherandson. BjörklundandJäntti(1997)usedthemeanageof43. 25 APPENDIXC ADDITIONSFORCHAPTER1 26 IderivetheconsistencyofOLSestimator ‹ r inequation(2.7),wheredependentvariablehasa measurementerrorduetousingtheproxyandindependentvariableisgeneratedfromanauxiliary regression. y it = r 1 ‹ x i + w it (2.7) where w it isequalto l t e i + n it + l t r 0 + h ( Age it )+( l t 1 ) r 1 ‹ x i + l t r 1 ( x i ‹ x i ) . Writeequation(1)as y = x r + u (2.8) where x = f ( x 1 ; q ) , x 1 isavectorofvariablesfromthestepthatdeterminestheunobservables, f ( ) ,whichisa1 K vectoroffunctionsdeterminedbytheunknownvector q ,whichis Q 1. Assumethat E ( u j x 1 )= 0anderrorsareindependentacrossobservations.Furtherassumethat ‹ q is a p N -consistentestimatorof q .Nowlet ‹ r betheOLSestimatorfromtheequation y i = ‹ x i r + error i (2.9) where‹ x i = f x 1 i ; ‹ q and error i = u i +( x i ‹ x i ) r ,theordinaryleastsquaresestimatoris ‹ r = N å i = 1 ‹ x 0 i ‹ x i ! 1 N å i = 1 ‹ x 0 i y i ! (2.10) Write y i = ‹ x i r +( x i ‹ x i ) r + u i ,where x i = f ( x 1 i ; q ) ,thenpluggingthisinandmultiplyingthrough by p N gives p N ( ‹ r l t r )= N 1 N å i = 1 ‹ x 0 i ‹ x i ! 1 ( N 1 = 2 N å i = 1 ‹ x 0 i [( x i ‹ x i ) l t r + x i ] ) (2.11) where x i = l t e i + n it + l t r 0 + h ( Age it ) . 27 UnderregularityconditionstatedinTheorem1inMurphyandTopel(1985)orTheorem12.3 inWooldridge(2010), 28 ameanvalueexpansionof ‹ q gives N 1 = 2 N å i = 1 ‹ x 0 i x i = N 1 = 2 N å i = 1 x 0 i x i + " N 1 N å i = 1 Ñ q f ( x 1 ; q ) 0 x i # p N ( ‹ q q )+ o p ( 1 ) (2.12) Because E Ñ q f ( x 1 ; q ) 0 x i = 0,itfollowsthat N 1 å N i = 1 Ñ q f ( x 1 ; q ) 0 x i = o p ( 1 ) ,andsince p N ( ‹ q q )= O p ( 1 ) , N 1 = 2 N å i = 1 ‹ x 0 i x i = N 1 = 2 N å i = 1 x 0 i x i + o p ( 1 ) (2.13) Usingsimilarreasoning,bymeanvalueexpansion N 1 = 2 N å i = 1 ‹ x 0 i ( x i ‹ x i ) l t r = " N 1 N å i = 1 ( r x i ) 0 Ñ q f ( x 1 ; q ) # p N ( ‹ q q )+ o p ( 1 ) (2.14) Nowassumethat p N ( ‹ q q )= N 1 = 2 N å i = 1 r i ( q )+ o p ( 1 ) (2.15) whereIassume E [ r i ( q )]= 0,whichevenholdsformostestimatorsinnonlinearmodels. 29 IfIassumethat Cov ( x i ; h ( Age it ))= 0,then plim n ! ¥ ‹ r = l t r Var ( x i )+ Cov ( x i ; n it ) Var ( x i ) (2.16) whichreducesto l t r if Cov ( x i ; n it )= 0.Forconsistency,replacing x i with‹ x i inanOLSestimation causesnoproblemasinWooldridge(2010). 28 (a) D 0 plim n ! ¥ N 1 å N i = 1 ‹ x 0 i ‹ x i = E ( x 0 x ) ,(b) f ( ) istwicecontinuouslydifferentiablein q foreach x 1 withthesamplesecondmomentsof ¶ f = ¶q uniformlyboundedinthesenseof plim n ! ¥ N 1 å N i = 1 ‹ x 0 i ‹ x i N 1 å N i = 1 Ñ q f ( x 1 ; q ) x i = D 1 ,where Ñ q f ( x 1 ; q ) isthe K Q Jacobianof f ( x 1 ; q ) 0 , and(c) ‹ q isaconsistentestimatorof q . 29 SeeChapter6and12inWooldridge(2010)fordetails. 28 REFERENCES 29 REFERENCES Björklund,AndersandJäntti,Markus. 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MITPress. 32 CHAPTER2 CollegeEnrollmentovertheBusinessCycle: TheRoleofSupplyConstraints 2.1 Introduction Manystudiesoneffectsofrecessiononhighereducationhaveinvestigatedtherelationshipbe- tweencollegeenrollmentandlabor-marketconditions,mainlymeasuredbytheunemployment rate,andhavefoundclearcountercyclicality;ManskiandWise(1983)foundaweakrelationship betweenfour-yearcollegeapplicationsandthelocalunemploymentrate,BettsandMcFarland (1995)foundthatpubliccommunitycollegeenrollmentsriseandfallinphasewiththeupsand downsofunemployment 1 andBarrandTurner(2013)claimedthattheGreatRecessionhaspro- ducedunambiguousincreasesincollegeenrollment. Muchattentionhasbeenpaidtochangesinenrollmentdemandwheneconomicconditions changes,usuallyanalyzingtherelationshipwithindividualleveldata.Someclaimedthattheop- portunitycostofgoingtocollegedecreasesduringarecessionbuttheliquidityconstraintsalso simultaneouslybecomessevere,andthislimitstheenrollmentincrease(Christian,2004;Loven- heim,2011).Inthislineofresearchtheimplicitassumptionisthatinstitutionshaveadequate xibilitytoadjusttochangesindemand,andthatsupply-sidedifdidnotarise(Bound andTurner,2007;BarrandTurner,2012). Somerecentstudiesacknowledgethatinthehigher-educationmarket,thesupply-sideislikely tobeaffectedbylocaleconomicconditionsandthatenrollmentcanbecomeinelasticifsupply isinelasticdespitedemandcyclicality.Ifaninstitutionfacesareductioninnon-tuitionrevenue 1 SomenotableresearchonthetheoryofcyclicalityonhighereducationincludesSakellarisandSpilimbergo (2000),DellasandKoubi(2003),andDellasandSakellaris(2003). 33 includingstate/federalappropriationsduringarecession,ithasfewerresourcestospendonin- struction;inturn,thisdecreaseseducationquality.Further,ifaninstitutionhasanenrollment capacitylimit,itcannotaccommodateallincreasesindemandand,intheshortrun,hasonlya limitedquantityresponse.Forinstance,Lovenheim(2011)andBarrandTurner(2013)conjec- turedthatsupplyelasticitymightdependonresidentialprograms,subsidiesperstudent,andan institution'sprestige.However,nonehavetestedthehypothesis. 2 Motivatedbytheirconjectures, thisstudycollecteddatatoidentifyinstitutionswithsupplycapacityconstraintsintheshortrun, andshowedthatduringrecessionsthoseinstitutionsexperiencedlimitedadjustmentinthequantity dimension;supplywasinelastic. Manypreviousstudiesonhigher-educationcyclicalityfocusedonadjustmentofthequantity dimensionandanalyzedhowenrollmentsizerespondedtoeconomicSimultaneously, thosestudiespaidscantattentiontowhathappensintheaspectofnewstudentachievement,im- plicitlyassumingthatincomingstudentachievement,and/orthatofproducedhumancapital,are homogenous. 3 However,qualityofhumanresourceproducedinhighereducationisaffectedby recessionsanditrelatestocapacityconstraints. Topresentamorecompleteaccountingofcyclicalmovementofcollegeenrollment,thisstudy introducesasimpleconceptualmodelandderivesimplicationsoftheroleofcapacityconstraints oncyclicalresponses.Previousstudiesoncyclicalityinhighereducationpaidlessattentionto supplysideandmighthavepartiallyunderstoodactuality.Amongothers,aninstitution'spolicy toprovidehousingfornewfreshmencapturescapacityconstraintsonthesupply-side,andduring recessionsproducesdifferentpredictedadjustmentsinenrollmentdecisions.Themodelimplies thatinstitutionsrequiredtoprovideon-campushousingcouldhavebeensupplyelastic.Duringan economicdownturn,theseinstitutionsbecomemoreselective,andcyclicalvariationsindemand 2 Lovenheim(2011)statedsupplyattop-rankedpublicandprivateschoolsisinelastic,andBarrandTurner(2013) arguedthatresearchuniversitiesandliberalartscollegesaremostlikelytobesupplyinelastic,andthatsupplyiselastic forcommunitycolleges,open-accesspublic4-yearinstitutions,andforinstitutions. 3 Christian(2004)usedcollege-agecohortsizeasasourceofchangeindemandforhighereducationandshowed thatstateuniversities1980-1995tightenedtheiradmissionpolicy,representedbyadeclineinacceptancerate,and experiencedadropineducationquality,measuredbyexpenditureperstudent,inresponsetotheincreaseindemand forhighereducation. 34 donotturnintofull-realizationinenrollment.Ontheotherhand,quantityexpansionintheshort runoccursatinstitutionswithoutcapacityconstraints,i.e.,thosenotrequiredtoprovidehousing forstudentssuchascommunitycollegesandcommuteruniversities. Thisstudypresentscompellingevidencethatinfactthecapacityconstraintsonthesupply- sideisbinding,andthatenrollmentincreaseisdisproportionateacrossinstitutions,dependingon theconstraints.Inrecessions,thoseinstitutionswithlimitedquantityadjustmentrespondedbya smallerincrementinenrollment,elevatingadmissionstandards,andacceptingstudentsofhigher achievement,whereasotherinstitutionswithouttheconstrainttendedtoincreaseenrollmentsize, thusresultinginadeclineinnewfreshmanachievement. Thisanalysisbeginswithanintroductionofasimpleconceptualframeworkthatillustratesan institution'smaximizationproblemwithdifferentsupplyconstraints,andderivesimplicationsof choicesandresultsduringrecession.Section3presentsdatasource,variables,anddataselection processtogeneratethesampleforanalysis.Section4describeschangesinrevenueresources andestimationresultsoftherelationshipbetweenenrollmentaswellasnewstudentachievement, andvariationsinlabormarketcondition.Section5istheconclusion. 35 2.2 ConceptualFramework Considerasimpleworldwithtwotypesofinstitutions.Eachinstitutionactsasoneutilitymaxi- mizingagentprovidingsupplytothehighereducationmarketviadecisionsonenrollmentsubject totheirownresourcesandhasenrollmentpolicyonhowmanyandwhomtoaccept. 45 The numberofenrolledstudents, n ,servesasasourceofrevenueandcosttoeachinstitutionatthe sametime. 6 TypeAhasnocapacityconstraintsinsupplyintheshortrun,inthesensetheyare xibleinacceptingstudentsifdemandincreases.Thussupplyofthoseinstitutionsiselasticand demand-driven.TypeAincludes4-yearprivatecommutingcolleges,localpubliccolleges,and communitycolleges,wheremoststudentslikelylivenearcampusand/orcommutefromhome.On theotherhand,TypeBfacescapacityconstraintsintheshortrunandhaslimitedadjustmentin enrollmentwhentheredemandincreases.Ifenrollmentexceedscapacity,theseinstitutionsneed toconsiderbuildingnewhousingorarrangingextracontractswithotherfacilities.Thesehaverel- ativelyinelasticsupplysuchaselite4-yearprivateandpubliccolleges,andaregenerallyoccupied bytalentedstudents.Forexample,theseinstitutionsrequirenewfreshmentoresideinon-campus housing-i.e.,residencehallsand/oroff-campusfacilitiesthathavecontractswithinstitutions-and intheshortrunhavecapacityconstraints.Theseinstitutionsplacemoreemphasisonmaintaining arelatively-highqualityofenrolledstudents. Institution i 'sdecision-maker'sutilityfunction, U ( ) ,isincreasinginandthestudent quality. 7 p ,isasthedifferencebetweenrevenuereceivedandcostpaid.Revenue, 4 Iusetheindividualinstitutionastheagentthatsetsenrollment,studentquality,andadmissionpolicy.Some previousstudies,especiallyforpublicinstitutions,modeledstatesasaunitofanalysis.(Lowry,2001;Boundand Turner,2007) 5 Institutionspickthenumberof admitted studentsandemployalltheirresourcesinpredictingthenumberof enrolled students.Thatis,enrollmentisafunctionoftheacceptancerate,whichistheproportionofnewapplicants accepted,tuition,studentquality,outsidewagesstudentscanearnwhentheychoosetowork,andyieldrate-i.e.,the proportionofadmittedstudentswhoenroll.Forsimplicity,ignorethepossibilityofinterdependencebetweentuition, studentquality,outsidewage,acceptancerate,andyieldrate.Alsoignoreanyimmigration-constraintsinpermission forinternationalstudentstoworkexceptoncampusorinoff-campusworkdirectly-relatedtotheirmajors,andassume onemarketwagethatcollegeapplicantscanearn. 6 Institutionschoosethenumberofadmissionsandhavesufexperienceinpredictingactualenrollment. Ifenrollmentisassumedtobeaknownfunctionthatbehavedwellforalongtime,itisreasonabletopick n with uncertaintybutuncertaintyisnotimportantinthiscontext. 7 Mainfocusofthisstudyisonthechoicesofthenumberofundergraduatefreshmeneventhoughempiricalresults, 36 R ,isthesumoftuitionchargedtoenrolledstudents, p n ,andnon-tuitionrevenue, S ,including governmentsubsidyplusendowmentpayouts. 8 Aschool'scostdependsonthenumberofstudents enrolledandtheexpenditureoneducationalquality.Assumethatallschools,privateandpublic, havethesimplecostfunction c ( n ) . 9 Studentquality, Q ,decreasesifenrollmentsizeincreases,all elseequal. 1011 Duringaneconomicdownturn,asinDellasandKoubi(2003),theopportunitycostofeduca- tionisprocyclicalandoutsidewagedecreases.Thus,intheabsenceofsevereliquidityconstraints, educationalpursuitsoughttobecountercyclical,whichincreasesthetotalnumberofnewappli- cants.Atthesametime,institutionsreceivelessnon-tuitionrevenue,whichincludesfederaland stateappropriations,andendowmentearnings.Thus,arecessionismodeledasadeclinein S . Withsubstantialdecreaseinappropriationandfunding,institutionscanincreasetuitionrevenueby increasingenrollmentsizeifpricesareassumedstableintheshortrun. Duringeconomicrecession,institutionshaveheterogeneousresponsesinenrollmentquantity. Schoolswithoutcapacityconstraintincreasetheenrollmentsizewhereasinstitutionswithlimited capacitytendtohaveeithernochangesinenrollmentorasmallerincrementinenrollment.TypeA collegeswhereon-campushousingisnotnecessaryforfreshmenshowcountercyclicalresponses: theyincreaseenrollmentsizeduringrecession.Theycanexpandenrollmentsize( ¶ n ¶ S j A < 0)and offsetthedecreaseinoutsidefundingbymaintainingasimilaracceptancerate,whichinturnin- forinstanceDeGrootetal.(1991)andKoshalandKoshal(2000),employedvarioustypesofcostfunctiontocapture synergies,oreconomiesofscope,associatedwiththejointproductionoftwoormoreproductssuchasundergraduate andgraduateeducation,andresearch. 8 Note p inpublicinstitutionsincludesgovernmentper-studentorper-creditsubsidy.Forsimplicity, p represents tuitionnetofgovernmentsubsidyifany.Aslongastuitionsubsidydecreasesduringrecessions,thedistinctiondoes notaffectthemodel. 9 c ( ) includesexpenditureperenrolledstudentpluscustodialcostsincludingfacultyandstaffsalaries,andother costsassociatedwithprovidingphysicalspacetoenrolledstudents,namelyclassroombuildings,residencehalls, libraries,gatheringspaces,administrativepremises,etc.. 10 Forexample, Q = ¯ Q a n ,where ¯ Q capturesapplicantqualityifonlyonestudentisenrolledand a represents howqualityissensitivetothenumberofstudents,orbyhowmuchaveragequalitydropswithadditionalstudents. 11 ACobb-Douglasofutilityfunctionthatplacesweight1 a onstudentquality Q is U = p a Q 1 a ; a > 0 As a increases,aninstitutionplacesmoreimportanceonwhilethatofstudentqualitydecreases.Bothtypes ofinstitutionshavethesameformofutilityfunctionforsimplicity;however,theymayhavedifferentweightson arguments.Forexample,TypeAcollegesmayputmoreweightondimensionwhileTypeBcollegesmayvalue studentqualitymore,whichimplies a A > a B . 37 creasestuitionrevenue( ¶p ¶ S 5 0atleastwithoneequality).Duringarecession,marginalof $1ismorevaluablewiththedropin S andstudentqualitybecomeslessvaluableasthequality ofapplicantsincreases,whichprovidesenoughincentivesfortheseinstitutionstoincreaseenroll- ment.Ontheotherhand,TypeBcolleges,whichhavesupplyconstraintsintheshort-run,needto buildadditionaldormitoriesorcontractwithotherhousingfacilitiesiftheydecidetoaccommodate theincreaseindemandbyacceptingstudentnumbershigherthanexistingmaximal.Theyinthe shortrunchoosenottohavemuchresponseinthequantitydimension;theyadmitasimilarnumber ofstudentsoraslightlymoreiftheyhavesoftconstraintswhentheyhaveacutinoutsidefunding ( j ¶ n ¶ S j A > j ¶ n ¶ S j B , ¶ n ¶ S j B 5 0). Differingimpactsonstudentqualityresultfromdifferingresponsesinquantitytoanincrease indemand.TheeffectoftheincreaseinenrollmentsizeonstudentqualityisclearforTypeBin- stitutions:theyelevateadmissionstandardsandacceptstudentsofhigherquality.Withanincrease innumberandqualityofapplicantsduringarecession,TypeBcollegeswithsupplyconstraints choosetomaintainenrollmentsizearoundthecapacityintheshort-run,andelevateadmission standardsandadmitstudentswithbetterquality( ¶ Q ¶ S j B < 0 ) .Ifthequalityofapplicantincreases, theseinstitutionsbecomemoreselectiveand,fromamongtheadditionalapplicants,choosemore talentedstudents,whichimprovesoverallquality.Ontheotherhand,collegeswithoutcapacity constraintacceptmorestudentsandexperienceadecreaseinoverallqualityofnewstudents.With theincreaseindemand,somebetterstudentsresultbutthemajorityofmarginalstudentscome fromthelowertailofthequalitydistribution.Oncetheyacceptmorelower-qualitystudentsthan better-,overallqualitydeclines( ¶ Q ¶ S j A > 0 ) : Sincethemarginalutilityofrevenuedecreasesand thatofstudentqualityincreasesasenrollmentincreases,thoseinstitutionschoosenotto nitelyincreaseenrollment. 12 12 Anotherinterestingapproachwouldbebymatchinginstitutionswithnewstudents.Thenthesigndependsonthe prestigeoftheschool( ¶ Q ¶ n S 0).Fortop-rankedschools,thequalityofmarginalstudentsduetotherecessiontends tobeloweronaveragethanthatoftheiroriginalstudents.Thusiftheyadmitmorestudents,studentqualitywould decrease( ¶ Q ¶ n < 0 ) .Iftheschoolisless-selectiveandacceptsonlybetter-qualitystudents,whowouldhaveenrolledin higher-tierschoolbutcouldnotduetotheincreaseinadmissionstandards,thenstudentqualitycanincrease ( ¶ Q ¶ n > 0 ) . Ontheotherhand,iftheyacceptsomemarginalstudentswhowouldhaveworkedandwhogenerallyarelesstalented, itmightdecreasestudentquality( ¶ Q ¶ n < 0 ) ;asimilarresultisexpectedforleast-competitivecolleges.Iflasttwotypes 38 2.3 Data 2.3.1 IPEDS Thisstudyinvestigateshowaninstitutionoptimizesitsresourcesinresponsetochangesinde- mand.Institutionalenrollment,prices,faculty,studentachievement,anddataaredrawn fromtheIntegratedPostsecondaryEducationDataSystem(IPEDS)since1986,anannualsurvey bytheU.S.DepartmentofEducation'sNationalCenterforEducationStatistics(NCES).IPEDS providesaggregateinformationbyinstitutionsparticipatinginTitleIVfederalaidpro- grams.Thedatasetisusedtoexploretherelationshipbetweeninstitutions'decisionsonenrollment andchangesinlabormarketconditionsduringrecessions,andissuitableforin-detailobservations oftypesofinstitutionalresponses.Thenumberofinstitutionsvariesfrom7,066to14,104be- tween1986and2011.ThedatasetissmallerbecauseIexcludedclosedinstitutions,military institutions,tribalcolleges,collegesnotinthecontiguousUnitedStates, 13 andextremelysmall institutionsreportingfewerthan200undergraduates. 2.3.2 Variables 2.3.2.1 Enrollment Giventheresearchinterest-namelyhowsupplyconstraints,i.e.,therequirementtoprovideon- campushousingtofreshmenaffectsdecisionsonenrollment-itisnaturaltouseenrollmentdatafor (FTFY)deundergraduateswhoapplied,wereadmitted, andenrolled(fulltime)forthemostrecentfallperiodavailable.Fallenrollmentdataisavailable from1986.OthermeasuressuchasFTFYenrollmentamonghighschoolgraduatesintheprevious 12months,andenrollmentbyage,residencestate,orrace,alsoareavailable. ofschoolsadmitmoreless-talentedstudentsthanbetterstudents,thentheoverallqualityofnewstudents woulddecreasewhentheenrollmentsizeincreases( ¶ Q ¶ n < 0 ) . 13 TheseareasincludeAlaska,AmericanSamoa,Guam,FederatedStatesofMicronesia,MarshallIslands,Northern MarianaIslands,Palau,PuertoRico,VirginIslands,andHawaii. 39 Figure2.A1plotsthechangesintheshareoftotalenrollmentbyinstitutiontypeandshowsthat theshareof2-yearinstitutionsand4-yearnon-eliteinstitutionsis procyclical whereastheshareof 4-yeareliteinstitutionsis countercyclical, implyingthattheoverallstudentachievementateach typeofinstituionsislikelytobechangedoverthebusinesscycle. 1415 2.3.2.2 CapacityConstraints Thevariabletoidentifycapacityconstraintsonthesupply-sideofhighereducationisconstructed inmultiplesteps.Thevariabletorepresenttheconstraintsistheon-campushousingrequirement- i.e.,dormitory,residencehall,orcollege-operatedor-afhousing-whichisequalto1(one) ifallFTFYdestudentsarerequiredtoresidetherein,or0(zero)ifnot.In- stitutionshaveexemptioncriteriaontheirresidentialpolicies,suchasnumberofcredits,proximity (commutingdistanceinactualmilesorcommutingminutes),age,maritalstatus,custodialcareof dependentchildren,dietarypeculiarities,andreligiousconstraints.Policiesaresubjecttochange, yeartoyear,dependingonspatial-,infrastructural-,andbudgetary-constraints. 16 InstitutionsrequiredtoprovideresidentialaccommodationsforFTFYstudentscannotalways changeenrollmenttocatertoincreaseindemand.Forexample,theycannotaddbuildingsand otherinfrastructureasrapidlyasenrollmenttrendsspike.Eveniftheydo,recessionorrecovery orevenboommayoccurormayendearlierthanexpected.IPEDSprovidesinformationwhether freshmenarerequiredtoliveinon-campushousingandisrecordedinInstitutionalCharacteristics from2004,whichislongenoughtocovertherecessionperiod.However,thevariableinthe governmentaldatasystemcontainsseriouserrors.Amongthe1,059institutionsmarkedashaving aon-campushousingresidencypolicyatleastoncesince2004,856changedtheanswer fromonetozeroor viceversa ,ormixed.Forexample,inIPEDS,MichiganStateUniversity 14 EliteinstitutionsincludeTop200National,Top120Public,Top65Private,andTop180LiberalArtsinstitutions, assembledfrom USNewsandWorldReport in2005andin2013 15 Manystudiesoncyclicalityconcludedthatlittlecyclicalityoccursat2-yearinstitutions,andweakcyclicality oralmostnoneat4-yearinstitutions.Somestudiesfurtherinvestigatedtherelationshipbasedonstudentattendance statusandclaimed procyclicality in2-yearfull-timeenrollmentand countercyclicality in2-yearpart-timeenrollment. 16 Onemightbeconcernedthatthepolicyadoptiontimingisdependentonlocallabormarketconditionsand changesindemand.However,aregressionofthetimingonlaggedstateunemploymentrate(includingtimeand institutionedeffects)yieldsanestimatedcoefclosetoandnotstatisticallydistinguishablefromzero. 40 answeredone,thusindicatingthatMichiganStateUniversity(MSU)requiresfreshmentostay indormitories,from2004to2009,andchangedtheanswertozerosince2010althoughMSU maintainedthepolicyduringthecorrespondingperiod. Sinceitisimpossibletodetectanyclearpatternoferrorbeingrecorded,those856institutions wereaskedindividuallybyphoneandemailwhethertheyhadfreshmendormitoryresidencyre- quirementpolicies. 17 Table2.B1comparesthenumberofinstitutionsundertheoriginalvariable fromIPEDSwiththatoftherevisedoneandtheresultsaresurprising:242institutionsmarkedas havingadormitoryresidencypolicyinIPEDSrespondedthattheyneverhavehadthepolicy,and afterdatacollectionthenumberofinstitutionsthatdidhaveitduring2004-2011changesfrom203 to724.Forcomparison,Carnegiecategorizesfour-yearinstitutionsintohighlyres- idential,primarilyresidential,andprimarilynonresidential.Fiftypercentofinstitutions asresidentialhavedormitoryresidencypoliciesandaround70%ofhighly-residential institutionsarefoundtohavethepolicy. Theediteddormitoryresidencypolicyvariablestilldoesnotproperlythesupplycon- straints.Notallinstitutionshavinglargeresidencehallsorahighproportionofout-of-statestu- dents(orforeignstudents)compelfreshmentostayinon-campushousing.UniversityofMichigan (UM),forexample,doesnothaveadormitoryresidencypolicy,butprovidesdormitoriesformore than10,000students;currently,approximately70%ofUMfreshmenresideinthose.Otherna- tionalschoolssuchasBostonCollege,UniversityofWisconsin,andCornellUniversityaremarked asnothavingtheresidencypoliciesalthoughingeneraltheyhavealargeshareofout-of-statestu- dentsmanyofwhomresideindormitories.Thustheconstraintvariableisrevisedconsidering dormitorycapacity,ratioofFTFYenrollmenttothecapacity,andshareofout-of-statefreshmen. 18 Moreover,ifaninstitutionisreportedtohavehadthepolicyformorethanhalftheobservedperiod, itisconsideredasacapacityconstrainedinstitution. 19 Thecapacityconstraintvariablecaptures 17 AsofSeptember152015,among856institutions,Icollecteddormitorypolicyinformationfrom773institutions. Therevisedlistofcollegeswiththepolicyisavailableuponrequest. 18 Thecapacityconstraintvariableisfurtherrestrictedtohavetheratiooffreshmentodormitorysizesmallerthan one,dormitorysizelargerthan3500,andtheratioofout-of-statestudentsgreaterthan0.45.Ifallofthoseconditions aretheconstraintvariableissettooneeventhoughfreshmenarenotrequiredtostayinon-campushousing. 19 Othervariableshelpidentifysupplyconstraintssuchasendowmentsizeorfacultysize.Forexample,duringthe 41 thedifferentresponsesinchangesoftotalenrollmentshareinFigure2.A1;80%of4-yearprivate elite-and62%of4-yearpublicelite-institutionsarecategorizedascapacityconstrained. Next,anadditionalconstraintmeasureisgeneratedretrospectivelyto1986.NotethatIPEDS startedtoquestionon-campusresidencypolicyfrom2004,thusariskexistsofmisclassifying constrainedinstitutionsbyextendingbackto1986.However,dataindicatestheriskisrelatively low.Between2004and2014,only92ofthe1,059institutionsadoptedtheresidencypolicy,which impliesthatinstitutionswiththepolicyaremorelikelytohavemaintainedtheirpolicy.Infact, among610institutionsreportedashavingthepolicy,morethan510havehaditsinceatleastprior to2004,andaround200collegesrespondedtheyhavehaditforatleast20years.Aninstitutionis ascapacity-constrainedin1986ifitwasmarkedasconstrainedeitherin2004orin2004- 2011.Finally,ifacollegeisreportedtoexperienceadramaticincreaseanddecreaseinenrollment, itisdropped. 20 2.3.2.3 StudentAchievement Studentqualityisimportantsincecollegesbothwantandneedtoenrollstudentstobeabletotake advantageofthekindsofcurricula,advising,andotherprogramoffered,andstudentqualityaf- fectsfutureenrollment.Manystudiesmeasurestocapturetheschoolqualitysuchasthenumber of(higher)degreeawarded,thevalueofresearchgrant,percentoffacultywithPhDdegree,and Barron'smeasurewhichareconsideredaslong-termqualitymeasuresthatcollegestrytomain- tain.Instead,thequalityoffreshmen,measuredbytheachievementscore,isusedtocapturethe changesinstudentqualityintheshort-term.AsinEppleandRomano(1998,2008),tomaintain thesimplicityandhighlighttheroleofpeergroups,thestudentqualityisdeterminedexclusively bythemeanabilityofitspeergroup.Iftheachievementoffreshmen,andthatofenrolledstudents GreatRecessionwhenstockmarketsdeclined,institutionsthatinvestedinriskassetslostlargeproportions oftheirendowmentandmighthavebecomemoresupplyconstrained.Endowmentearnings,however,stoppedbeing reportedtoIPEDSin1997forFinancialAccountingStandardsBoard(FASB)reportinginstitutionsandin2002for GovernmentalAccountingStandardsBoard(GASB)reportinginstitutions. 20 Thereare12schoolswhosemaximumenrollmentsizeismorethanvetimeaslargeastheminimumenrollment size.Someschoolswerereportedtohaveincreaseinfreshmenenrollmentmorethan80times2004-2011.Examples areSouthUniversity-Savannah97x,AshfordUniversity362x,andUniversityofPhoenix(online)100x. 42 arepositivelycorrelatedviapeer-effect,thenchoosingtalentedfreshmenwouldmeananincrease inoverallquality.Hereafterthestudentqualityintheshort-runreferstothefreshmenachievement score. StudentachievementismeasuredbyScholasticAptitudeTest(SAT)andAmericanCollege Testing(ACT)scores,primarilyconsideredtobepredictorsofstudents'performance,inreading (EnglishandcompositionforACT),math,andwritingbecausescorescanbecomparedbothacross collegesandovertime. 21 Testscoresarereportedatpercentiles25and75,from2001.One drawbackofthisachievementmeasureisthatSAT/ACTscoresareavailablefor75%of4-year public-,55%of4-yearnot-forprivate-,andmorethan98%ofnational-orTop120public-, orTop65private-colleges,butmostlyareunavailablefor4-yearforand2-yearinstitutions. 2.3.2.4 FinanceandFaculty Financevariables,includingaveragetuitionandfeesbystudent'sresidence,andnetprice,which istheso-called stickerprice andfeeslessaverageaidfromfederal,state,andinstitution, arecalculatedbymyself.Appropriationvariablesareaccessiblebylocal-,state-,andfederallevel, andothervariablessuchasrevenue,unrestrictedrevenue,andnettuitionrevenue,whichisthe differencebetweentuitionandinstitutionalgrantandaid,arecalculatedbyDeltaCostProject. 22 All pricevariablesareadjustedto2010pricelevelpertheconsumerpriceindex. Facultyvariablesincludeinformationofthenumberofcurrentfull-time/part-timefacultyand thenumberofnewly-hiredfaculty.Fornew-facultyvariables,detailedinformationisaccessible whethertheyaretenuredortenure-track,anddataareavailablefrom2001. 21 SmithandStange(2015),forexample,usedtheaveragePSATscoreofenrolledstudentsineachinstitutionto measuretheinstitutionalquality.However,inIPEDS,onlySAT/ACTscoresoffreshmenareavailable. 22 DeltaCostProjectprovidesalongitudinaldatabasederivedfromIPEDSenrollment,staff,completions andstudentaiddataforacademicyears1986-87through2009-10;however,somevariablesinenrollment,institutional characteristics,andstaffarenotthesameasinrawdatafromIPEDSDataCenter.Forthosemismatchedvariables, rawdataarepreferred. 43 2.3.2.5 UnemploymentRate VariablestomeasurethelabormarketconditionareunemploymentratefromtheBureauofLabor Statistics. 23 Whenitcomestothemeasureofunemploymentrate,itseemsnaturalforresearchers tochoosetheunemploymentrateofthestateinwhichtheinstitutionislocated,butitmightbe locallabormarketconditionsinotherstatesthataffectanapplicant'sdecisiononenrollment.For example,fromaninstitution'sperspective,ifoutsidefundingsuchasstateappropriationis tuatingalongwiththelabormarketconditionwithinastate,orifin-statestudentscomprisethe majorityofenrollment,itisappropriatetousetheunemploymentrateofthestateinwhichthe collegeislocated.Ontheotherhand,fromacollegeapplicant'sstance,thelocallabormarket conditionofwheretheapplicantnormallyresideshasmoreimpactontheenrollmentdecision; this,inturn,changesthedemandforhighereducation.Forinstance,highschoolstudentsfrom MichiganwouldconsidermoreaboutthelocaleconomyinMichiganthanthatinCaliforniaifthey aremakingcollege-goingdecisions. Thisissueisdealtwithbyconstructinganadditionalmeasureofthecolleunem- ploymentrateapplicantsface.Thisisaveragestateunemploymentrateamongacceptedstudents, weightedbytheirenrollmentsizebystate.Ifacollegeisatnationallevel,theweightedunemploy- mentvariousapplicants'localeconomyconditions.Forexample,duringtheeconomic downturninMichiganduetothedeclineoftheautomobileindustry,thedemandforUM,where morethan50%ofstudentsarefromotherstates,waslesslikelytobeaffectedbythelocallabor marketconditionthanwouldbethedemandforEasternMichiganUniversity,andismorelikelyto beaffectedbymarketconditionsinotherstates. Freshmenenrollmentbystatedataareavailablefrom1986foralmosteveryotheryear,butdata submissionwasmandatoryonlyin2004,2006,2008,and2010,wherearound85%ofinstitutions reportedtheenrollmentbystate,whereastheresponseratevariesfrom35to65%whenreporting 23 Othermeasuresincludemasslayoffstatisticsandaverageweeklyearnings.Masslayoffnumbersarefromestab- lishmentswithatleast50initialclaimsforunemploymentinsurance(UI)againstthemduringa5-weekperiod, however,overthepastdecade,onlyaboutone-thirdofthetotalunemployed,onaverage,receivedregularUI Moreover,therearevariationsintermsofUIacrossstatesandcomparabilityissueswithunemploymentrate.See http://www.bls.gov/cps/cps_htgm.htm#lausfordetails. 44 wasnotmandatory.Accordingly,weightedmeasurescoveradifferentnumberofinstitutionsyear byyearandthesamplesizeissmallerinestimationwhenweightedmeasuresareused.Soforeach school,averageweightbystateiscalculatedwithmandatoryreportingyears,andedweight isusedtogeneratetheinstitution-sunemploymentrate,whichcoversaround90%of4- yearpubliccollegesand65%of4-yearprivatecolleges.Whenaverageedweightiscalculated between1986and2011,coverageincreasesto92%for4-yearpublicand73%of4-yearprivate institutions. Table2.B2providesdescriptivestatisticsbyinstitutiontypes,between2004and2011andis bywhetheraninstitutioniscapacity-constrained,andbycontrol.Statisticsindicateinsti- tutionswithconstraintsaremostly4-yearcollegesandthatFTFYenrollmentsizeisabout40%- 80%largerforconstrainedcolleges.Moreover,thoseinstitutionshavea15-35%higherproportion ofout-of-statestudentsthandoinstitutionswithoutcapacityconstraints.Studentachievementas measuredbySATandACTscores,forcapacityconstrainedinstitutionsis6-10%higherbutthe costofattendanceforconstrainedinstitutionsasmeasuredby stickerprice isabout8%moreex- pensiveforpublic4-yearcollegesand40%moreforprivate4-yearcolleges.Anothernotable differenceisthedependencyonnon-tuitionrevenueincludingvariousappropriationsforcapacity constrainedpublicinstitutions. Last,dormitoryresidencypolicyinstitutionsaccountfor60%oflandgrantinstitutionsand 70%ofinstitutions. 45 2.4 Responsestolabormarketshockinthehighereducation market Giventhatthisstudy'sgoalistoexplorehowinstitutionsoptimizedtheirresourcesinresponseto theshockinthelabormarketalongwiththebusinesscycle,andhowconstraintsinthesupply-side affectedenrollmentdecisions,theanalysisstartswithperiodsfromyearspriortotheonsetofthe recentrecession,toyearspasttheendoftherecession,from2004to2011.Itmainlyhighlights thecircumstancesof4-yearpublicandprivateinstitutions,sincetheFTFYenrollmentfor2-year publicandprivateinstitutionswithcapacityconstraintshardlyexist,asdescribedinTable2.B2. 24 Asimplestatisticalmodelfordescribingcyclicalityinhighereducationis ln n it = a 1 + a 2 U t + e it (1.1) where n it isenrollmentatinstitution i inyear t , U t isunemploymentrate,and e it isarandomerror term.Iftheunemploymentrateproperlyrepresentsthelabormarketconditionorcyclicalvariation, then a 2 R 0asenrollmentiscountercyclical,noncyclical,orprocyclical. Equation(1.1)generallyisestimatedwithOLSincludingtime-anded-effects; however,thisapproachhaslimitationsinatleasttwoaspects.First,themodelisimprecisely inthatittreatedcapacityconstrainedandnon-capacityconstrainedinstitutionsinthe samemanner.Second,ifaresearcherusesnationalunemploymentrate,whichissameacrossall institutions,withedeffect,thenoneofyeardummyautomaticallywillberemoveddueto perfectmulticollinearity.Thus,inpractice,researchersusestatevariationtoanalyzecyclicality. Figure ?? showsthatthedemandforhighereducation,measuredbythenumberofapplica- tions,increasedduringtherecessionperiodacrossalltypes. 25 Itindicatesthatthereiscyclicality 24 Within4-yearprivateinstitutions,thereareforandnot-forinstitutions.Not-forinstitutions accountforaround80%ofnon-capacityconstrainedandover99%ofcapacityconstrainedinstitutions.Inother words,lessthan1%of4-yearprivateforinstitutionsiscapacityconstrained.HereafterImainlypresentresults fornot-forfor4-yearprivateinstitutions. 25 Regressionofthenumberofapplicationsonunemploymentrateandtuitionfeesyieldsastatistically positivecoefonunemploymentrateforalltypesofinstitutionsimplyingthatdemandiscountercyclical. 46 indemand, 26 whichimpliesthattheeffectofthedecreaseintheopportunitycostsofeducation outweighsthatoftheincreaseinliquidityconstraints.Duringrecessions,thedemandforhigher educationisrisingacrossalltypesofinstitutions;however,howitisservedtosupply,andthe extenttowhichinstitutionsareresponding,wouldvaryacrosstypesofinstitutions. Theempiricalanalysisbeginswithexploringtherelationshiplabormarketshockandinstitution revenue. 2.4.1 Budget Themostimportantsourcesoftotalrevenuearefromunrestrictedrevenues,whichisthesumof tuitionfromstudentsandappropriationlargelyfromstateandfederalgovernments.Table2.B2in- dicatesthattheshareofnon-tuitionrevenueincludingappropriationsisdifferentacrossinstitution types.Lowry(2001)reportedthatthemedianshareofallunrestrictedrevenuesfromthesesources was78%in1994Œ95.Figure2.C2displayssimilarFull-TimeEquivalent(FTE)appropriationand nontuitionrevenuepatternsacrossalltypesofinstitutionsanddifferencesareonlyintermsofthe level;publicinstitutionsaremoredependentonnontuitionrevenues.Figures2.C2furtherindicate thatthedeclineinappropriationandnon-tuitionsharehappenedtoeveryinstitutionduringthe GreatRecession,whichimpliesthatthoseinstitutionscouldtrytoincreasetuitiontorecoversome ofthelostrevenues. Figure2.C3showsthatallfour-yearinstitutionshavethesameincrease-trendintuitionbut thattheriseinout-of-statetuitionisrelativelysharperforcapacityconstrainedinstitutionsduring 2004-2010:17%forbothpublicandprivatecolleges.Fornon-capacityconstrainedinstitutions, theincrementissmaller:17%forpublicinstitutions,10%forprivate.While stickerprice orposted tuitionandfeehasbeenincreased,netprice,i.e.,thedifferencebetween stickerprice andfederal-, state-,andinstitution-aid,hasremainedrelativelystable.Thussomeinstitutionsfacing cutsinstate/federalappropriationwhilesimultaneouslyprovidingaidtostudents,have 26 YieldrateinFigure2.C1ismoderatelydecreasingoveryears,whichmightbeduetotheincreaseincompetition withotherinstitutionsandtodecreaseinapplicationfees,andisconsistentwiththeassumptioninthemodelthatan institutioncanaccuratelypredicttheyieldrate. 47 anotheroptiontomakeupthefallinappropriations:enrolladditionalstudents. 2.4.2 Enrollment Forinstitutions,oneofthenaturalresponsestorecessionsistoincreaseenrollmentbyeitherthe needorthedesiretoincreasetuitionrevenueasarguedbyDuffyandGoldberg(1998). 27 With largerenrollment,institutionscanincreaserevenue;however,notallinstitutionsarecapableof servingmorestudents;someschoolsrequiringtoprovidehousingtofreshmenhavetodealwiththe capacityconstraintsintheshort-run.Table2.B3summarizestheempiricalanalysisofestimation oftheelasticityofFTFYenrollment,asthenaturallogofFTFYenrollment,withrespect totheunemploymentrate,asthestateunemploymentrate.Stateunemploymentratein thesamecalendaryearisused,sincemarginalstudentsaffectedbylabor-marketconditionsare lesslikelytoapplytocollegeearlyinthepreviousyear.PanelAsummarizesestimationresults generallyusedinpreviousstudiesoncyclicalityinhighereducation.Previousresultsdidnot consideranyconstraintsinthesupplysideandestimatesintherowareconsistentwithprevious studies:countercyclicalityin2-yearinstitutionsandweakcyclicalityoralmostnonein4-year institutions.BycomparingPanelsBandC,however,itisobviousthatsupplyconstraintsplays aroleinenrollmentadjustmentwithrespecttochangesinthelabormarket;capacity constrainedinstitutionsexperiencedasmallerincreaseinenrollmentsize,althoughstatistically whichisconsistentwiththemodel'spredictiononsupplyconstrainedinstitutions. Ofinterestisthatpositivecoefforcapacityconstrainedinstitutions,albeitstatistically Ifsomeofthemincreasedenrollmentsizeduringrecession,itmightbethatthese collegeswerenotatcapacitylimitbeforerecessionandreachedcapacitylimitwithasmallex- pansion.Oritmightbetheyfacedrathersoft-constraintsinthesensethatinstitutionscanaccom- modatemorethanon-campushousinglimitsastheycanprovidehousingoff-campus,whichis 27 Itisassumedthattuition, p ,andper-studentresource, I ,werechosenbytheboardbeforeselectingthenumber ofstudents,andinstitutionstakethosevaluesasgiven.Somemayarguethatgivennon-tuitionrevenuereceived, I woulddecreasewhenenrollmentincreasesthusdecreaseseducationquality.If I changesasstudentnumberschange, institutionsneedtodecideonatleastthreedimensions(quantity,quality,expenditure),whichfurthercomplicatesthe analysis. 48 generallycostlierthanon-campushousing. 28 Certaininstitutions,wheremorefreshmenarrived thanon-campushousingcapacitycouldaccommodate,mighthavereservedextraspacewithoff- campusfacilitieswithwhomtheyhavecontractualagreements.Morediscussiononthesizeof supplyconstraintsandenrollmentareprovidedinSection4.5.Overall,resultsareconsistentwith theconjecturethatnon-capacityconstrainedinstitutionsexperiencedlargerincreasesinenrollment thandidconstrainedinstitutions. Table2.D1presentsOLSestimationresultsfocusingon4-yearinstitutionswithdifferentlocal unemploymentmeasuresbetween2004and2011sincethereareonly22public2-yearcollegesand veprivate2-yearinstitutionswithcapacityconstraints.4-yearprivateforinstitutionsare excludedbecauseonly25schoolsarecapacityconstrained. 29 PanelAisestimatedwithstateun- employmentrateweightedinallreportingyearsandresultsaresimilartothoseinTable2.B3inthe sensethatnon-capacityconstrainedcollegeshavelargerpositiveresponseinenrollmentwhenlocal labormarketconditionsworsen,albeit 30 PanelBisgeneratedbyexcludinginstitu- tionswithopenadmissionpoliciesthatacceptanyFTFYstudentswhoapplyandmeetminimum requirements.Thenumberofopen4-yearprivateadmissionpolicyinstitutionsincreasesfrom114 in1999to330in2011and7%of4-yearinstitutionswiththepolicyarecapacityconstrained. 31 Sincethemajorityofinstitutionswithopenadmissionpoliciesare4-yearprivateforinstitu- tionswithouttheconstraint,thedifferenceofcoefbetweenPanelsAandBisclosetozero exceptforthatforall4-year.Sincethefreshmenenrollmentsizeofforinstitutionsis1/6of publicinstitutionsandthatofnot-forprivateis1/4ofpublicinstitutions,equation(1.1)is estimatedwithweightsonfreshmenenrollment.ResultsinPanelsCandDshowthatcoef diminishacrossalltypesofinstitutions,andthatinstitutionswithoutopenadmissionpolicieshave 28 Institutionscanchangethemixtureofgradelevelinhousingfacilitiesandincreasefreshmencompositionwhile providinglessspacefor2nd,3rd,and/or4thyearstudents.Thisstatement,however,isnottestableduetodata unavailabilityinIPEDS. 29 Non-capacityconstrainedforinstitutionshavevetimeslargercoefwhilethesamplesizeisone thirdofnot-forinstitutions. 30 Whenestimatedfrom2004foronlymandatoryyearsforreportingenrollmentbystateorfrom1986forallyears, similarpatternsshow:capacityconstrainedinstitutionsexperienceddecreaseorsmallerincreaseinenrollment. 31 4-yearinstitutionswithopenadmissionpolicieshaveupto0.6timeslargerresponsetocyclicalvariationthando thosewithoutthepolicy;however,thedifferenceisnotstatistically 49 smallerresponse. 32 Anotherwaytorecoverthedeclineinappropriationisbyincreasingthenumberofout-of- statestudents.Figure2.C4plotsenrollmentbyresidencyin4-yearinstitutions,andshowsthatthe largestshareofenrollmentisfromin-statestudentsforpubliccollegeswhereasprivatecolleges havetheoppositecomposition.Publicinstitutionswithcapacityconstraintshavealargershareof out-of-stateenrollmentFTFYstudents(47%)thandothosewithouttheconstraint(41%),buthave notsteadilyincreasedtheshareofout-of-stateenrollmentduringrecession.Withlowerappropri- ation,institutionscouldrecoverthelossbyenrollingmoreofout-of-statestudentsandcapacity constrainedinstitutionsmighthavestrongerincentivetochangethemixofstudents;however,that mixremainedstableduringtherecession.Apossiblereasoncouldbethattheincreaseindemand ismostlyfromin-statestudentswhomightchoosein-stateinstitutionsasthemarginalcostof attendancegreater.Thataspectisleftforfutureresearch. 2.4.3 StudentAchievement Withthecountercyclicalityofdemandinhighereducation,numbersofapplicationsincreasedur- ingrecessions.However,giventhatintheshort-runcapacityised,institutionscanchoosean alternativedimensioninenrollment:raiseadmissionstandards,whichwillincreasenew-student achievement.Ifwebelievethattheproportionalincreaseindemandislowerformore-talented studentsandthattheyaremorepronetohavehighereducationandarelessaffectedbylocallabor- marketconditions,thenmostoftheincreaseindemandmightcomefromstudentsofaverage-or lowachievement. InIPEDS,around86%ofschoolsthatreportedSATscoresalsoreportedACTscoresatthe sametime.Thatis,ifbothmeasuresareusedtoestimatechangesinstudentachievementalong withthebusinesscycle,samplesizeincreasesbyapproximately10-15%comparedtowhenSAT measuresaloneareused.Andanalyzingdifferentmeasuresmightimproveourunderstanding ofstudentachievementdimension.ButACTscoresarewidelyreportedtoIPEDSsince2004, 32 Alternativelyonecanuserevisedon-campushousingpolicyvariableasaninstrumentfororiginalpolicyvariable inIPEDSbutitgivessimilarestimates. 50 fromapproximately700institutionsin2001toapproximately1000in2004,whichrendersSAT measuresmorefavorableforanalysiswhenthetimehorizonextendsbackto2001.Anotherfeature relatedtotestscoresisthatthenumberofinstitutionsreportingSATscoresvariesupto30% annually.Tocontrolforthecompositionofinstitutionsintheanalysis,thebalancedsampleis constructedtohavebothenrollmentandtestscores,whichleaves1042institutionswithSATscores 2004-2011and772institutions2001-2011.WhenACTscoresareanalyzed,thebalancedsample sizedecreasesfrom955to443. 33 Figure2.A3representsdifferentchangesinstudentachievementpatternacrossinstitution types,wherestudentachievementismeasuredbyaverageSATscoresoffreshmen.Fornon- capacityconstrainedinstitutions,thestudentachievementlevelofhigh-ability(SAT75thper- centile)orthatoflow-abilitystudents(SAT25thpercentile)issimilarbetweenpublicandprivate colleges.Changesinstudentachievementforthoseinstitutionsoccurredasexpectedinthemodel, andtheoverallachievementofnewstudentshasdecreasedduringtherecession;thepatternis mostexplicitforlow-achievementstudents(SAT25)inprivate4-yearinstitutions.Capacitycon- strainedprivateinstitutionshavehigherSATscoreonaverage,whichsupportstheclaimtheyare moreselective,andexhibitstheoppositepatternforchangesinstudentachievement:atrendof increasedachievementofstudentsduringtheeconomicdownturn.Figure2.C5displayschanges instudentachievementmeasuredbyACTscores,patternsbeingsimilartothosewithSATscores. Notethatthecompositionofinstitutionsdifferdependingonthestudentachievementmeasure.On average,SATandACTscoresarehigherforprivatecollegesexceptforSATscoresatpublicinsti- tutionsinthesecondtiercategorizedby USNewsandWorldReport ,whichindicatesthatstudent achievementmeasuredbyACTscoreshasmoreweightonlow-tierpubliccolleges. Amongvarioustest-scoremeasures,SATMathpercentile25andACTMathpercentile25 scoresareanalyzedsincei)thescorewasreportedbymostoftheinstitutions,andii)generallyitis inthelowertailofstudentachievementdistributionthatmarginalchangesoccur.Table2.B4sum- 33 Only2%of4-yearforhaveeitherSATorACT(math)whereas54%ofnot-forhavetestscores.And onlyoneinstitutionwithopenadmissionpolicyreportstestscore.Thusifstudentachievementchangesinresponseto unemployment,mostvariationcomesfromnot-for 51 marizesresultsoftheeffectoflocallabor-marketmeasuresontheachievementofnewstudents measuredbySATMathpercentile25andACTEnglishpercentile25,focusingonthebalanced panelof4-yearinstitutionsthathavebothenrollmentandtestscores2004-2011.Resultswithvari- ousunemploymentmeasuresindicatethatcapacityconstrainedinstitutionsexperiencedanincrease instudentachievement,albeitstatisticallywhereasstudentachievementdeclinedin mostnon-capacityconstrainedinstitutions.Table2.D2showsresultswhenthetimespanisex- tendedto2001,wherethenumberofinstitutionsinbalancedpaneldatadecreasedby30-55%. Thepatternofobservingincreaseinstudentachievementforcapacityconstrainedinstitutionsis similartothatinthe2004-2011sample. 3435 Changesinstudentachievementduringtherecessionaredeterminednotonlybysupplycon- straints,butalsobyinstitutionalprestige.Forexample,somestudentsatthemargin,whoare affectedbycyclicalvariationinthelabormarket,mightreceivemorerejectionsinrecessiondueto stricteradmissionstandardsandnowwouldneedtochoosealess-talentedschool.Inlower-tierin- stitutions,theeffectonstudentachievementisambiguous.Therearesomestudentswhowerenot acceptedfromcould-have-beenacceptedcollegeswithhighertier,somegoodstudentswhowould nothavegonetocollegesifmarketopportunityhadbeenbetter,andotherswhoareatthemargin withrelativelylowerstudentachievement.Sincepublicuniversitiesoftenseemlessselectivethan privatecounterparts,freshmanheterogeneityappliesneithertoselectivecollegesnortoprivate colleges,butmostlytopubliccolleges.Morediscussionontherelationshipbetweeninstitutional prestigeandchangesinenrollmentsizeandstudentachievementisofferedin4.6below. 2.4.4 Faculty Inresponsetothetransitoryincreaseindemand,onceinstitutionsdecidetoexpandenrollment, theyneedtohireextrafacultytoprovideasimilarqualityofeducationtonewstudents,atleastin 34 OfinterestisanincreaseinACTscoresevenfornon-capacityconstrainedinstitutions,althoughstatisticallynot distinguishablefromzero;however,byrestrictingtoabalancedpanel2001-2011,thecompositionchanged.Infact, thecompositionofinstitutionswithACTscoreschangedtowardhavingfewergood public institutionsandmoregood private institutions. 35 Forbalancedpanel,theanalysisoflogenrollmentonweightedstateunemploymentprovidessimilarpatternthat non-capacityconstrainedinstitutionshavelargerincrease. 52 termsofstudent-facultyratio.Sincehiringnewtenuredfacultycanbeconsideredasalong-term investment,institutionsmightadjustbyhiringfacultywithlowercostsuchasnon-tenure-track, ed-termfaculty,adjunctfaculty,orpart-timefaculty, 36 implyingthatthosefacultyareatthe marginofemployment. FigureA.6(a)showsthatinstitutionshireddifferenttypesoffacultyandhowtheyrespondedto cyclicalshocks.Duringtherecession,4-yearinstitutionswithouttheconstraint,whichexperienced anincreaseintheirenrollments,increasedfacultysizemostlyinpart-timepositions.Moreover,in FigureA.6(b),theseinstitutionshiredlessofnewnon-tenuredfaculty,implyingthatinshort-term thoseinstitutionsadjustedbyhiringfacultywithlowerorzeroedcost. 37 Table2.B5summarizes OLSestimationresultsoflogfacultysizeonstateunemploymentrateandthatmosttypes ofinstitutionshiredmorepart-timefacultyandfewerhigher-costfaculty,forexampletenuredor nottenurednewfaculty,bothforintenuretracknotintenuretrack. 2.4.5 SizeofSupplyConstraints Concernmightarisethattheenrollmentadjustmentincapacityconstrainedinstitutionswithlarger capacitywoulddifferfromthosewithsmallercapacity.Institutionswithsmallercapacitycanmore easilyincreaseenrollment,asthecostisrelativelylower.Contrarily,institutionswithlargerca- pacitycanincreaseenrollmentifon-campushousingisunder-utilized,orbyadditionalcontractual arrangementswithoff-campushousingthatmightbecostlier. 38 Capacityconstrainedinstitutions aregroupedbydormitorycapacitysize.Dormitorycapacityof700,1400,2600,and6500rep- resents25%,50%,75%,and99%ofobservation,respectively.Figure2.C7displaysenrollment andstudentachievementtrendsacrossdifferentcapacityandtheresponsesinFTFYenrollment differacrossdormitorycapacitysizes.Manysmall-sizeinstitutionsincreasedenrollmentandex- 36 Forlong-rungrowth,quality/costishigherwithtenuredfacultyandinstitutionswillbeabletospreadtheinvest- mentcostoveralongerperiod.Thenitwouldbereasonabletohirethem. 37 Incomparisonwith2-yearinstitutions,4-yearinstitutionshiremorefull-timethanpart-timefacultywhereas public2-yearinstitutionshiremorepart-timefaculty.Public2-yearinstitutionsespeciallyhiredmorenon-tenure facultynotontenuretrack,andnotmanyfull-time,whocanberelativelyreadilyemployedtemporarilyatlower wages. 38 MarginalcostforincreasingcapacityinstitutionsmightbeU-shapedwhichimpliesthatmarginalcostdecreases atandthenincreases,especiallywhenthereareeconomiesofscale. 53 periencedadropinstudentachievement,whereasmiddledormitory-size(2600 ˘ 6500)institutions relativelydecreasedenrollmentandraisedadmissionstandardsbylimitingacceptancetostudents whoseachievementseemedbetter. Table2.B6summarizesOLSestimationresultsofdifferentunemploymentmeasuresonenroll- mentsizeandstudentachievementofFTFYenrollment2004-2011among4-yearinstitutionsthat havebothenrollmentandSATMathscore,andindicatesthattheenrollmentadjustmentoccurred atadifferentrateamonginstitutionswithdormitories.Onaverage,institutionswithdormitorysize lessthan1400expandedclasssizeduringtheeconomicdownturn,althoughstatisticallynotdif- ferentfromzero,andexperiencedadropinstudentachievement.Ontheotherhand,collegeswith greaterdormitorysizebetween2600and6500decreasedenrollmentandrelativelyincreasedthe achievementoffreshmenmeasuredbySATMathpercentile25,albeitstatistically Resultsimplythatsmall-capacitycollegeshaverelativelylowercostofacceptingadditionalstu- dents,andsoftcapacityconstraints.Ontheotherhand,institutionswithlargesizeofdormitories increasedasmallersizeofenrollment,implyingthattheconstraintsarebindingrelativelyharder. 2.4.6 Prestige Atschoolsatnationallevel,localconditionswouldlessaffectdecisionsonenrollmentthanat lower-tierschools,becausemanyhigh-achievementstudentsarefromotherstatesandtheirwill- ingnessforgoingtocollegeisgenerallylessbylabor-marketconditions.Table2.B7 presentsdifferentquantityandstudentachievementadjustmentbyprestigestatus2004-2011.Pres- tigestatusisassembledfrom USNewsandWorldReport in2005andin2013,groupedintoTop 200National,Top120Public,Top65Private,andTop180LiberalArtsinstitutions. ResultsinPanelAshowthatmajorityofprestigiousschoolsreactedtorecessionbydecreasing enrollment,albeitstatisticallywhileless-prestigiousschoolsincreasedenrollment. ChangesinstudentachievementbyprestigetypearedescribedinPanelsB.Coefonun- employmentarenegativeforless-prestigiouscolleges,whichimpliesthattheoverallachievement ofnewstudentshasdeclinedatthoseschools.Ontheotherhand,eliteinstitutionshavepositive 54 coefindicatingthattheachievementofincomingstudentsincreasedduringrecession,albeit statistically,implyingthateliteschoolsbecamemoreprestigious.PanelsCandD presentresultswithweightedstateunemploymentrate,whichprovideasimilarpatternexceptfor SATMathfornationaltopprivateinstitutions;coefturnednegativebutarenotstatistically distinguishablefromzero. Table2.D3summarizeschangesinquantityofenrollmentandstudentachievementwhenboth prestigestatusandcapacityconstraintsaretakenintoaccount.Amongnon-capacityconstrained institutionsinPanelsAandC,heterogeneityexistswithrespecttoprestigestatus;lessprestigious collegesexperiencedmoreincreaseinquantityandrelativelymoredropinstudentachievement. Overall,capacityconstrainedinstitutionsinPanelsBandF,reactedtorecessionbysmallerincrease ormoredecreaseinquantity,andbylessdropdecreaseormoreincreaseinstudentachievement. Andtheeffectofcapacityconstraintsonenrollmentisconsistentamongprestigiouscolleges; capacityconstrainedprestigiousschoolstendtohavethelargestdecreaseinquantityandthelargest increaseinfrehmenachievement,althoughcoefarestatisticallynotdifferentfromzero. 2.4.7 OtherMeasures Table2.B8presentsOLSestimationresultsofvariousmeasuresonweightedlocallabormarket conditions.PanelAindicatesthat,duringrecession,full-timeenrollmentcompositionforwhite studentsincreasesacrossalltypesofinstitutionsexceptforconstrainedpublicinstitutions,albeit ,whichimpliesdiversityamongfreshmendecreased.theincreaseinthe shareofwhitestudentswasthelargestamongnon-capacityconstrainedforinstitutions. 39 ThechangesinshareoffederalgrantsduringrecessionaresummarizedinPanelB. Resultsshowthatalltypesofinstitutionsincreasedtheshareoffreshmenreceivingfederalgrants, andthatnon-capacityconstrainedinstitutionshavegreaterincreaseintheshare.Resultsfrom PanelsAandBimplythattheshareoflowerincomewhitestudentsincreasedinrecession.Finally 39 Excludingopen-admission-policyschoolsprovidessimilarresults.Whengroupedbynational,national-not- ranked,andnot-national,thelowesttier(not-national)hasthelargestincreaseinwhitesshare.Constrainedschools tendtohavesmallerincreaseinwhitesshareandonlynationalinstitutionsdecreasedwhitesshareduringrecession. 55 PanelCpresentsresultswhenanalysisisextendedbackto1986,andresultsaresimilartothosein Table2.D1. 56 2.5 Conclusion Withworseningeconomicconditions,institutionsexperiencedsimultaneouslyadeclineinoutside resourcesandanincreaseindemand.Institutionsmaximizingthecombinationofstudent qualityanddevisedanothermeanstocompensateforlostrevenue:acceptingmorestudents. Byfar,amajorityofstudiesimplicitlyassumedthatinstitutionsarecapableofenrollingmore students,especiallyduringrecessions,butonlyacknowledgedpossibleconstraintsonthesupply- side,andnotmuchattentionwaspaidtochangesinstudentquality. Thisstudypresentshowaninstitutionchoosesenrollmentquantityanditseffectonstudent achievement,andintroducesasimpleframeworkforinstitutions,fromwhichimplicationsare derivedontherelationshipbetweenenrollmentandstudentachievementwhenchangesoccurin labor-marketconditions.Thoseimplicationsaretestedbyusingdormitoryresidencyrequirement policyvariablesfromIPEDS,collectedandfurthertorepresentthesupplycapacitycon- straints.Resultsshowconsiderableheterogeneousresponsesbytypeofinstitutionsinenrollment, changesinstudentquality,andadjustmentinresources,whentheconstraintsaretakenintoac- count. Institutionswithoutthecapacityconstrainttendtohaveincreasedenrollmentcomparedtothose withtheconstraints. 40 Asaresult,institutionswiththeconstraintsacceptednewfreshmenwith higherachievement,whereasinstitutionswithoutconstraintfaceddecreaseinstudentachievement andadjustedresourcesbyhiringnewfacultyatlowercostsuchasnon-tenuredornotontenure- track.Amongcapacityconstrainedcolleges,responsestorecessionsdiffer,basedoncapacitysize andprestige. Anempiricalresultthatfreshmenachievementisdependentonthebusinesscyclehasanin- terestingimplicationforstudiesontheeffectofgraduatinginrecessions.Recentstudiesshowed initialadverselabor-marketconditionshavepersistenteffectonlaborearnings,whichrecovers overtime(BeaudryandDiNardo,1991;Hershbein,2012;Oreopoulosetal.,2012).Comparing 40 Notethatthechangesinenrollmentisnotenrielydrivenbythecapacityconstraintsastherearechangesin demandofhighereducationduringrecessionaswell. 57 wagesbycohortsacrossdifferentlabormarketconditionsimplicitlyassumesthatstudentsgradu- atingacrossbusinesscyclesarehomogeneous.Iflabormarketconditionsaffectnotonlyearnings afterjob-marketentry,butalsoqualityofhumancapitalproducedathighereducation,recession's effectonlong-termlabormarketoutcomesmightbeunderestimated.Similarly,returntoeducation overtimemightbedifferentforthosegraduatinginexpansionorincontraction. Aninferencefromtheresultsisthatifprestigiousinstitutionsfacecutsinoutsidefunding,in- stitutionswithsupplycapacityconstraintsmightbemuchmoreselectiveandincreasetheachieve- mentofnewstudents.Ifthatisthecase,theachievementgapwillwidenbetweenprestigious-and middle-rankedinstitutions.Anotherinterestingtopicwouldbeanexplorationofhowthematch betweencollegeprestigeandapplicantqualitywasalteredwhentakingsupplyconstraintsinto account. Somerecentstudieshavepointedouttheexpansionofnon-residentialprogramsandanincrease intheentryofforinstitutions.However,manyforinstitutionsarenotrequiredto provideon-campushousingtofreshmen,andreceivenegligibleappropriations. 41 Thusthosefor- institutionsarevirtuallynotcapacityconstrainedonthesupply-sideandmorepromptlycan expandenrollmenttomeetincreaseindemand. 41 Lessthan0.01%ofallforinstitutionshaveon-campusresidencyrequirementpoliciesandtheyreceived onaverageUS$285ofappropriationduring2004-2011. 58 APPENDICES 59 APPENDIXA FIGURESFORCHAPTER2 60 Figure2.A1ChangesinShareofTotalEnrollment Notes: LeftY-axisrepresentsshareandrightY-axisrepresentsunemploymentrate.. 61 Figure2.A2Application,Admission,andEnrollment] Notes: Dataarefromthisresearcher'scalculationusingIPEDSweightedbyFTFYenrollment size.LeftY-axisrepresentsapplicationandadmission,andrightY-axisrepresentsunemployment rate. 62 Figure2.A3StudentAchievementofFTFYbyInstitutionTypes Notes: SATdataarefromthisresearcher'scalculationusingIPEDSweightedbyFTFYenrollmentsize.LeftY-axis representsSATscoreandrightY-axisrepresentsunemploymentrate. 63 APPENDIXB TABLESFORCHAPTER2 64 Table2.B1NumberofObservationswithDormitoryPolicy RevisedDormitoryVariable 012345678Total 07,761000000007,761 1107254101152173 238023221155104 321121435068105 Original41820002236087 521120153280115 616120335388121 7210141123118151 800000000203203 Total8,00371412121619137248,820 Notes: Eachnumberindicatesthenumberofinstitutionwithoriginalandreviseddormitory policyforcorrespondingyears. Original referstoALLOCAMvariableinIPEDSand Revised referstonewdormitorypolicyvariableaftercollectinginformationfromeach individualinstitution. 65 Table2.B2DescriptiveStatistics(2004-2011) CapacityConstrainedNon-CapacityConstrained PublicPrivatePublicPrivate 4-year2-year4-year2-year4-year2-year4-year2-year FTFYEnrollment 1,9753645422341,365810304235 FTFYFTE 1,9603335392311,311671288228 UndergradFTE 9,6571,1452,3374797,4593,8041,525612 EnrollmentIn-State 53%53%34%38%59%63%51%60% Out-of-State 47%47%66%62%41%37%49%40% Application 5,093823,2126572,2804789873 Admission 3,220451,5554161,4643556453 DormitoryCapacity 3,7664561,5124801,825320746235 StudentSATVerbal25% 480437502389447404460405 SATVerbal75% 589563615499554514570524 SATMath25% 494449505393456397460401 SATMath75% 601591616506566509571511 AchievementACTEnglish75% 1916201318151915 ACTEnglish25% 2523271924212522 ACTMath75% 1917201518161815 ACTMath75% 2524261924202421 In-District 6,4413,22224,92320,5355,9882,46818,18313,874 TuitionIn-State 6,4423,37724,92320,5355,9962,94918,18413,874 Out-of-State 15,3587,33024,92320,57014,2886,41618,18513,875 Total 310171431124044409 RevenueUnrestricted 239151411318638449 NetTuition 9345677211319 Local 6800401600 AppropriationState 104780901610 Federal 7041707341 Total 8321063173763929616225 NewTenured 62514449 FacultyNewNotTenured 27414217654 NewNotonTrack 2139314662 Part-time/RA 8851343047216475 Obs 2422254553811,063890851 Notes: RevenueandappropriationvariablesaremeasuredinUS$1-M. 66 Table2.B3RegressionofLogEnrollmentonLocalUnemploymentRate AllInstitutions4-yearInstitutions2-yearInstitutions AllPublicPrivatePrivateNotAllPublicPrivate for PanelA:AllInstitutions Unemp0.021***0.015***0.015***0.016**0.014**0.022***0.038***0.018 (0.005)(0.006)(0.005)(0.008)(0.006)(0.009)(0.008)(0.016) Obs31,91616,1694,80411,3658,39315,7478,5667,181 PanelB:Non-CapacityConstrainedInstitutions Unemp0.025***0.022**0.017**0.025**0.024*0.023***0.038***0.019 (0.006)(0.009)(0.007)(0.013)(0.013)(0.009)(0.008)(0.016) Obs25,4169,8842,8727,0124,06415,5328,3907,142 PanelC:CapacityConstrainedInstitutions Unemp0.0030.0040.0060.0050.0050.0160.005-0.076 (0.005)(0.005)(0.006)(0.006)(0.006)(0.027)(0.028)(0.123) Obs6,5006,2851,9324,3534,32921517639 Notes: Eachincludesafullsetofedeffectsforindividualinstitutionsandyears, between2004and2011.Allstateunemploymentratesareweightedbyenrollmentsizebystate. Robuststandarderrorsclusteredattheinstitutionlevelareinparentheses. atthe1%level.atthe5%level.atthe10%level. 67 Table2.B4RegressionofStudentAchievementonLocalUnemploymentMeasures(4-yearInsti- tutions,2004-2011) Non-CapacityConstrainedCapacityConstrained AllPublicPrivateNotAllPublicPrivateNot forfor PanelA:StateUnemploymentRate(SATMath25th) Unemp-1.171*-1.569**-1.0670.2900.5390.174 (0.625)(0.705)(1.113)(0.578)(0.801)(0.718) Obs3,6531,6611,9604,3751,2593,110 PanelB:WeightedStateUnemploymentRate(SATMath25th) Unemp-1.778**-2.017**-1.7930.5120.6560.535 (0.728)(0.809)(1.549)(0.758)(0.908)(1.071) Obs3,4871,6201,8384,1841,2402,939 PanelC:StateUnemploymentRate(ACTMath25th) Unemp-0.042-0.010-0.0840.0090.0020.014 (0.040)(0.037)(0.078)(0.027)(0.042)(0.034) Obs2,3871,1281,2433,4971,2002,284 PanelD:WeightedStateUnemploymentRate(ACTMath25th) Unemp-0.047-0.010-0.1120.0060.0040.013 (0.046)(0.043)(0.101)(0.035)(0.050)(0.048) Obs2,2921,1031,1753,3421,1772,154 Notes: Eachincludesafullsetofedeffectsforindividualinstitutionsandyears between2004and2011.Robuststandarderrorsclusteredattheinstitutionlevelareinparentheses. atthe1%level.atthe5%level.atthe10%level. 68 Table2.B5RegressionofFacultyonWeightedLocalUnemploymentMeasures(4-yearInstitu- tions,2004-2011) Non-CapacityConstrainedCapacityConstrained AllPublicPrivateNotAllPublicPrivateNot forfor PanelA:FullTimeFaculty Unemp0.011-0.0020.0080.0030.0070.001 (0.007)(0.004)(0.009)(0.003)(0.004)(0.004) Obs7,2382,4872,9084,8491,6413,191 PanelB:PartTimeFaculty Unemp0.0160.043**-0.0130.0120.063**-0.011 (0.015)(0.022)(0.024)(0.014)(0.031)(0.015) Obs7,1562,4812,8674,7611,6123,132 PanelC:NewFaculty(Tenured) Unemp0.0300.0140.133-0.076*-0.062-0.112 (0.040)(0.041)(0.168)(0.044)(0.053)(0.076) Obs1,0198152001280749531 PanelD:NewFaculty(NotinTenureTrack) Unemp-0.026-0.059**-0.006-0.0080.009-0.022 (0.018)(0.024)(0.028)(0.019)(0.034)(0.022) Obs4,7742,0462,0883,9031,4142,476 PanelE:NewFaculty(NotTenured,TenureTrack) Unemp-0.050**-0.048*-0.031-0.001-0.011-0.008 (0.022)(0.026)(0.036)(0.021)(0.036)(0.025) Obs3,5522,1551,3933,8271,5182,308 Notes: Eachincludesafullsetofedeffectsforindividualinstitutionsandyears between2004and2011.Robuststandarderrorsclusteredattheinstitutionlevelarein parenthesesandfacultysizeisexpressedinlogvalue. atthe1%level.atthe5%level.atthe10%level. 69 Table2.B6ChangesinEnrollmentandStudentAchievementwithCapacitySize(4-yearInstitu- tion) EnrollmentStudentAchievement AllPublicPrivateNotAllPublicPrivateNot Sizeforfor PanelA:StateUnemploymentRate Size10.0030.011-0.002-2.083*-4.791**-1.869 (0.011)(0.018)(0.013)(1.166)(1.825)(1.341) Size20.0070.0040.008-0.227-1.8740.087 (0.007)(0.016)(0.007)(0.763)(1.584)(0.853) Size3-0.005-0.0110.0010.138-0.7380.631 (0.008)(0.017)(0.007)(0.662)(0.820)(0.944) Size4-0.003-0.003-0.0020.7660.8970.353 (0.007)(0.009)(0.009)(0.791)(0.895)(1.577) Size5-0.016-0.008-0.058-0.195-0.175-0.483 (0.010)(0.009)(0.050)(1.018)(1.133)(2.440) PanelB:WeightedStateUnemploymentRate Size10.0030.019-0.003-2.532*-6.457***-1.723 (0.013)(0.019)(0.015)(1.362)(2.083)(1.638) Size20.0100.0080.010-0.936-2.223-0.462 (0.010)(0.018)(0.012)(1.026)(1.697)(1.260) Size3-0.004-0.0140.014-0.18-0.7740.818 (0.013)(0.020)(0.015)(0.959)(0.961)(1.832) Size4-0.002-0.002-0.0051.655*1.1696.083*** (0.010)(0.011)(0.015)(0.978)(1.016)(2.294) Size5-0.023*-0.010-0.265-0.855-0.852-1.567 (0.014)(0.010)(0.156)(1.302)(1.354)(6.064) Notes: Dormitorysizesare1(<700),2(<1400),3(<2600),4(<6500),and5(>=6500). Eachincludesafullsetofedeffectsforindividualinstitutionsandyearsbetween 2004and2011.LogFTFYenrollmentandSATMath25thpercentilescoreareusedforenrollment andstudentachievementmeasure.Robuststandarderrorsareclusteredattheinstitutionlevel. atthe1%level.atthe5%level.atthe10%level. 70 Table2.B7ChangesinEnrollmentandStudentAchievementwithPrestige(4-yearInstitution) NotEliteInstitutionsEliteInstitutions NotPublicPrivateLiberalArtsNationalPublicPrivateLiberalArts NationalNotNotNot Top120Top65Top180Top120Top65Top180 PanelA:ChangesinEnrollment Unemp0.018***0.023***0.017**0.03-0.004-0.007-0.008-0.003 (0.006)(0.006)(0.008)(0.021)(0.005)(0.005)(0.007)(0.006) Obs14,0723,86810,8465851,6159365191,326 PanelB:ChangesinStudentAchievement(SATMath25th) Unemp-0.369-1.418**-0.101-0.7900.0050.3880.4201.599 (0.534)(0.672)(0.654)(2.878)(0.626)(0.759)(1.177)(1.066) Obs7,8442,5605,7934191,5308665121,189 PanelC:ChangesinEnrollment(WeightedStateUnemployment) Unemp0.025***0.027***0.025**0.052-0.006-0.01-0.01-0.008 (0.008)(0.006)(0.012)(0.032)(0.006)(0.007)(0.015)(0.011) Obs13,2383,74910,1035501,5809245061,248 PanelD:ChangesinStudentAchievement(SATMath25th,WeightedStateUnemployment) Unemp-0.88-1.623**-0.534-1.536-0.3710.374-1.1891.303 (0.663)(0.713)(0.945)(3.806)(0.833)(0.884)(2.195)(1.803) Obs7,4232,4865,4243941,4998545011,123 Notes: Eachincludesafullsetofedeffectsforindividualinstitutionsandyearsbetween2004 and2011.FTFYenrollmentandSATMath25thpercentilescoreareusedforenrollmentandstudentachievement measure.Robuststandarderrorsclusteredattheinstitutionlevelareinparentheses.Prestigevariablesis assembledbyUSNewsandWorldReport in2005andin2013. atthe1%level.atthe5%level.atthe10%level. 71 Table2.B8RegressionofVariousMeasuresonWeightedLocalUnemploymentMeasures(4-year Institutions) Non-CapacityConstrainedCapacityConstrained AllPublicPrivateNotAllPublicPrivateNot forfor PanelA:ChangesinWhiteShare Unemp0.007**0.0060.0040.006-0.0060.011 (0.003)(0.005)(0.007)(0.006)(0.008)(0.008) Obs9,2892,7743,7885,9901,8994,070 PanelB:ChangesinFederalGrantShare Unemp0.011*0.010***0.0040.007***0.007**0.007 (0.006)(0.003)(0.006)(0.003)(0.003)(0.004) Obs7,3091,8833,3305,2521,5363,697 PanelC:ChangesinEnrollmentQuantity(1986-2011) Unemp0.015***0.017**0.0070.0050.014-0.008 (0.006)(0.007)(0.008)(0.006)(0.010)(0.006) Obs25,5139,07312,63617,7885,19512,567 Notes: Eachincludesafullsetofedeffectsforindividualinstitutionsandyears, between2004and2011forPanelAandBandbetween1986and2001forPanelC. Allstateunemploymentratesareweightedbyenrollmentsizebystate. Robuststandarderrorsclusteredattheinstitutionlevelareinparentheses. atthe1%level.atthe5%level.atthe10%level. 72 APPENDIXC SUPPLEMENTALFIGURESFORCHAPTER2 73 Figure2.C1AcceptanceandYieldRatebyInstitutionTypes Notes: Dataarefromthisresearcher'scalculationusingIPEDSweightedbyFTFYenrollment size.LeftY-axisrepresentsacceptancerateandrightY-axisrepresentsunemploymentrate. 74 Figure2.C2FTEAppropriationandNon-TuitionSharebyInstitutionTypes Notes: Dataarefromthisresearcher'scalculationusingIPEDSweightedbyFTFYenrollmentsize.InPanelA,left Y-axisrepresentsFTEappropriationandrightY-axisrepresentsunemploymentrate.InPanelB,leftY-axisrepresents non-tuitionshareandrightY-axisrepresentsunemploymentrate. 75 Figure2.C3TuitionandNetPricebyInstitutionTypes Notes: Dataarefromthisresearcher'scalculationusingIPEDSweightedbyFTFYenrollmentsize.LeftY-axis representstuitionandrightY-axisrepresentsunemploymentrate. 76 Figure2.C4EnrollmentByResidencein4-yearInstitutions Notes: FTFYenrollmentdataarefromthisresearcher'scalculationusingIPEDSweightedbyFTFYenrollmentsize. InPanelA,leftY-axisrepresentsenrollmentandrightY-axisrepresentsunemploymentrate.InPanelB,leftY-axis representsshareandrightY-axisrepresentsunemploymentrate. 77 Figure2.C5StudentAchievementofFTFYbyInstitutionTypes Notes: ACTdataarefromthisresearcher'scalculationusingIPEDSweightedbyFTFYenrollmentsize.LeftY-axis representsACTscoreandrightY-axisrepresentsunemploymentrate. 78 Figure2.C6FacultyEmploymentbyInstitutionTypes Notes: Facultyenrollmentdataarefromthisresearcher'scalculationusingIPEDSweightedbyFTFYenrollmentsize. LeftY-axisrepresentsfacultysizeandrightY-axisrepresentsunemploymentrate. 79 Figure2.C7EnrollmentandStudentAchievementbyDormitoryCapacity Notes: FTEFTFYenrollmentandSATdataarefromthisresearcher'scalculationusingIPEDSweightedbyFTFY enrollmentsize.InPanelA,leftY-axisrepresentsenrollmentandrightY-axisrepresentsunemploymentrate.InPanel B,leftY-axisrepresentsSATscoreandrightY-axisrepresentsunemploymentrate. 80 APPENDIXD SUPPLEMENTALTABLESFORCHAPTER2 81 Table2.D1RegressionofLogEnrollmentonWeightedLocalUnemploymentMeasures(4-year Institutions) Non-CapacityConstrainedCapacityConstrained AllPublicPrivateNotAllPublicPrivateNot forfor PanelA:StateUnemploymentRate Unemp0.027**0.020***0.032*0.0060.0070.008 (0.011)(0.007)(0.019)(0.006)(0.008)(0.008) Obs9,2922,7743,7885,9901,8994,070 PanelB:StateUnemploymentRatewithoutOpenAdmission Unemp0.020*0.019**0.0350.0060.0080.007 (0.011)(0.009)(0.022)(0.006)(0.008)(0.008) Obs6,9612,2013,1905,7361,7953,929 PanelC:StateUnemploymentRateweightedbyEnrollmentSize Unemp0.018***0.015**0.023**0.0030.0010.01 (0.006)(0.007)(0.011)(0.006)(0.007)(0.007) Obs9,2922,7743,7885,9901,8994,070 PanelD:StateUnemploymentRateweightedbyEnrollmentwithoutOpenAdmission Unemp0.012*0.0090.0150.0020.0010.009 (0.007)(0.007)(0.012)(0.006)(0.007)(0.007) Obs6,9612,2013,1905,7361,7953,929 Notes: Eachincludesafullsetofedeffectsforindividualinstitutionsandyears, between2004and2011.Allstateunemploymentratesareweightedbyenrollmentsizebystate. Robuststandarderrorsclusteredattheinstitutionlevelareinparentheses. atthe1%level.atthe5%level.atthe10%level. 82 Table2.D2RegressionofStudentAchievementonLocalUnemploymentMeasures(4-yearInsti- tutions,2001-2011) Non-CapacityConstrainedCapacityConstrained AllPublicPrivateNotAllPublicPrivateNot forfor PanelA:StateUnemploymentRate(SATMath25th) Unemp-1.475**-1.714**-1.6990.252-0.3730.399 (0.698)(0.73)(1.315)(0.656)(1.011)(0.785) Obs4,0602,0851,9424,1641,1573,001 PanelB:WeightedStateUnemploymentRate(SATMath25th) Unemp-2.371***-2.336***-3.375*0.036-0.4580.476 (0.781)(0.827)(1.808)(0.933)(1.213)(1.307) Obs3,9412,0511,8594,0341,1472,882 PanelC:StateUnemploymentRate(ACTMath25th) Unemp0.004-0.0330.0570.018-0.0440.052 (0.041)(0.039)(0.081)(0.034)(0.053)(0.045) Obs1,8599548962,7121,0231,684 PanelD:WeightedStateUnemploymentRate(ACTMath25th) Unemp-0.021-0.0400.0200.003-0.0600.064 (0.046)(0.045)(0.105)(0.045)(0.061)(0.066) Obs1,8129378672,6361,0151,617 Notes: Eachincludesafullsetofedeffectsforindividualinstitutionsandyears between2001and2011.Robuststandarderrorsclusteredattheinstitutionlevelareinparentheses. atthe1%level.atthe5%level.atthe10%level. 83 Table2.D3ChangesinEnrollmentandStudentAchievementwithPrestigeandCapacityCon- straints(4-yearInstitution) NotEliteInstitutionsEliteInstitutions NotPublicPrivateLiberalArtsNationalPublicPrivateLiberalArts NationalNotNotNot Top120Top65Top180Top120Top65Top180 PanelA:ChangesinEnrollmentforNon-CapacityConstrainedInstitutions Unemp0.025**0.021***0.026**0.0340.001-0.002-0.0370.003 (0.010)(0.008)(0.013)(0.057)(0.010)(0.010)(0.037)(0.010) Obs9,0452,5556,94421746931768237 PanelB:ChangesinEnrollmentforCapacityConstrainedInstitutions Unemp0.0070.018*0.0060.027-0.007-0.013**-0.004-0.006 (0.005)(0.010)(0.006)(0.023)(0.005)(0.006)(0.007)(0.007) Obs5,0271,3133,9023681,1466194511,089 PanelC:ChangesinStudentAchievementforNon-CapacityConstrainedInstitutions(SATMath25th) Unemp-0.713-2.317***0.1780.670-0.918-0.477-1.5662.671 (0.814)(0.838)(1.183)(8.246)(1.172)(1.305)(2.157)(1.938) Obs3,8531,6462,54512043529064217 PanelD:ChangesinStudentAchievementforCapacityConstrainedInstitutions(SATMath25th) Unemp-0.2000.396-0.183-0.9130.5911.1210.3331.310 (0.747)(1.393)(0.819)(2.932)(0.766)(0.998)(1.284)(1.267) Obs3,9919143,2482991,095576448972 Notes: Eachincludesafullsetofedeffectsforindividualinstitutionsandyearsbetween2004 and2011.LogFTFYenrollmentandSATMath25thpercentilescoreareusedforenrollmentandstudentachievementmeasure. Robuststandarderrorsclusteredattheinstitutionlevelareinparentheses.Prestigevariablesisassembledby USNewsandWorldReport in2005andin2013. atthe1%level.atthe5%level.atthe10%level. 84 REFERENCES 85 REFERENCES Barr,AndewandTurner,SarahE. (2013).ExpandingEnrollmentsandContractingStateBud- gets:TheEffectoftheGreatRecessiononHigherEducation. AnnalsoftheAmericanAcademyof PoliticalandSocialScience, 650(1),168Œ193. Barr,AndewandTurner,SarahE. (2013).DownandEnrolled:AnExaminationoftheEnroll- mentResponsetoCyclicalTrendsandJobLoss. WorkingPaper. Beaudry,PaulandDiNardo,John. (1991).Theeffectofimplicitcontractsonthemovementof wagesoverthebusinesscycle:Evidencefrommicrodata. JournalofPoliticalEconomy, 665Œ668. Betts,J.R.andMcFarland,L.L.. (1995).SafePortinaStorm:TheImpactofLaborMarket ConditionsonCommunityCollegeEnrollments. JournalofHumanResources, 741Œ765. Bound,JohnandTurner,SarahE. (2007).titCohortcrowding:Howresourcesaffectcollegiate attainmentle. JournalofPublicEconomics, 91(5),877Œ899. 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AmericanEconomicReview, 33Œ62. DeGroot,HansandMcMahon,WalterWandVolkwein,JFredericks. (1991).Thecost structureofAmericanresearchuniversities. ReviewofEconomicsandStatistics, 424Œ431. Hershbein,BradJ. (2012).tiGraduatinghighschoolinarecession:work,education,andhome productiontle. BEJournalofEconomicAnalysis&Policy, 12(1). Koshal,RajindarKandKoshal,Manjulika. (2000).Doliberalartscollegesexhibiteconomies ofscaleandscope?. pEducationEconomics, 8(3),209Œ220. 86 Lovenheim,MichaelF. (2011).TheEffectofLiquidHousingWealthonCollegeEnrollment. JournalofLaborEconomics, 29(4),741Œ771. Lowry,RobertC. (2001).TheEffectsofStatePoliticalInterestsandCampusOutputsonPublic UniversityRevenues. EconomicsofEducationReview, 20(2),105Œ119. Manski,CharlesFandWise,DavidA. (1983).CollegechoiceinAmerica. HarvardUniversity Press. Oreopoulos,PhilipandvonWachter,TillandHeisz,Andrew. (2012).TheShort-andLong- TermCareerEffectsofGraduatinginaRecession. AmericanEconomicJournal:AppliedEco- nomics, 4(1),1Œ29. Sakellaris,PlutarchosandSpilimbergo,A.. (2000).Businesscyclesandinvestmentinhuman capital:internationalevidenceonhighereducation. Carnegie-RochesterConferenceSerieson PublicPolicy,Elsevier. 52,221Œ256. Smith,JonathanandStange,Kevin. (2015).ANewMeasureofCollegeQualitytoStudy theEffectsofCollegeSectorandPeersonDegreeAttainment. NationalBureauofEconomic Research. 87 CHAPTER3 RacialDifferencesinCourse-takingand AchievementGap 3.1 Introduction Overthepasttwodecades,high-schoolgraduateshavebeentakingmorecreditsinmathematics, andhaveshiftedfromtakinglower-levelmathcoursestotakingmore-advancedcourses(Adelman, 2006;Daltonetal.,2007).In2004blackandwhitestudentsonaverageearnedsimilartotalcredits inmath,3.7and3.6respectively,buttheracial/ethnicgapinenrollmentinadvancedmathematics coursespersisted;blackstudentsarelesslikelythanwhitestudentstobeenrolledinhigh-track mathcourses(Kelly,2009;Riegle-CrumbandGrodsky,2010). Despitetheincreaseincourse-takingintensityacrossgenderandrace,asubstantialblack-white achievementgapremains.FryerandLevitt(2004,2006)showedthattheblack-whitetest-score gapamongincomingkindergartnersisnegligibleaftercontrollingforcovariatesbutthegapwidens overthefour-yearsofelementaryschool.Theyestimatedthatthegapinrawmathscorewould beonestandarddeviationifblackstudentscontinuetolosegroundthroughGrade9. Amajorityofpreviousstudiesoncourse-takingusedthenumberofmathcredits,and/orthe highestlevelofmathachieved,asameasureofcourseintensity.Creditunitsprovideageneral overviewofstudentinvolvementinssubjectstoassesscourse-takingpatternsbutareun- suitabletogaugedepthoflearning.Ontheotherhand,thehighestlevelofmathcapturesone dimensionofthedepthbutdoesnotconsiderthefullhistoryofthecourse-takingpatternandits associationwithchangesinrigor-leveloveryears. Thisstudyexaminesonepossibleaspecttoexplaintheracialgapinachievement-racialdif- 88 ferencesincourse-taking-anddiffersfrompreviousstudiesinthatIconstructasequenceofmath coursescompletedbyahigh-schoolstudent,andmeasureracialdifferencesinrigorlevelaswell asinchangesinthelevelwithinthesequence.Ifwithinasequenceanyvariationcannotbeex- plainedbythehighestlevelorbythenumberofcreditsearned,thismeasurewouldimproveour understandingonracialdifferencesincourse-takinganditsrelationshipwiththeachievementgap. Theremainderofthispaperproceedsasfollows:Section2describesthebackgroundofmath course-takingandachievement,andreviewspreviousliterature.Section3describesandsumma- rizesthedataset.Section4presentsbasicresultsfortheblack-whitemathgapincourse-taking andinachievement,andSection5discussesfutureworks. 89 3.2 BackgroundandLiterature Course-takingreferstoenrollmentincoursessuchasalgebraorcalculusanditseffects onaspirationsandattachmenttoschoolthataccumulateovertheschooling,andwhichcontributes toastudent'seducationalattainment(Kelly,2009).Between1982and2004,onaverage, totalmathcreditsearnedbyhigh-schoolstudentsincreasedfrom2.7to3.6.Atthesametime, enrollmentinadvancedcoursesincreasedacrosscategoriesofgender,race,andsocioeconomic status(SES)butdisparitiesamongracialgroupsremained.Forexample,theshareofhighschool graduateswhocompletedpre-calculusorcalculusincreasedfrom10.7%in1982to33%in2004 but,in2004,theshareofwhiteswas37%whereasitwas19%forblacksand22%forHispanics (Daltonetal.,2007). 1 Whenmeasuringracialdifferencesinmathcourse-taking,thenumberofcreditsearnedandthe levelofmathtakenwouldgivedifferentanswersin2004;thetotalcreditsissimilar-3.7forblacks, 3.6forwhites-butcompletionrateinthehighestlevel,pre-calculusandcalculus,isalmosttwice aslargeforwhitestudents.Issueswiththosemeasuresarethatthetotalcreditsfailtocapturethe levelorcontentofthecourse,andthehighestlevelcompletedpaysnoattentiontovariationwithin coursesequence.Forexample,supposestudentAtookalgebraI,geometry,andalgebraII,and studentBtookpre-algebra,algebraI,geometry,andalgebraII.Thenintermsofthetotalcredits, studentBistakingamore-rigorousmathtrackbutbothhavethesamehighestmath.IfstudentC tookalgebraI,geometry,algebraII,andanotherbasiccourseoracoursefromaanothersubject suchasengineeringorthatmaybecountedasamathcreditinordertomeetstatewide graduationrequirements,thenbothmeasuresprovidethesameanswer,namelythatstudentBand studentCtookmathcourseswiththesameintensity. Previousstudiesonracialdifferenceincourse-takingshowedthatmuchofthevariationin course-takingisattributedtopriorachievementatthestartoftheyear.Forexample,lowertrack 1 Manystatesincreasedtheirrequirementsforhighschoolgraduation.Forexample,between1987and2004,the numberofstatesrequiringatleast2.5creditsinmathematicsgrewfrom12to26andin2004,17statesrequired coursesinmathtograduate.Theserequirementsappeartobeinhighschoolstudentcourse-taking (CouncilofChiefStateSchoolOf[CCSSO]2005). 90 placementamongblackstudentsareinpartduetolowerachievementscores(Lucas,1999;Kelly, 2009).Familybackgroundalsorelatestocourse-takingandincreasestheblack-whitecourse- takinggap,especiallyinadvancedmathcourses(Kelly,2004,Daltonetal.,2007).Otherkey explanationsincludeschoolqualitymeasuredbycompositionofraceordisadvantagedstudent, numberofcoursesoffered,andteacherquality. Ethnicdifferencesinacademicachievementhavebeenstudiedsincethe1960sandColeman etal.(1966)showedthatblack-whitescoregapincreasedwithstudentage.FryerandLevitt (2004)summarizedtheexplanationsforracialgapintestscores;differencesingeneticmake-up, differencesinfamilystructureandpoverty,differencesinschoolquality,racialbiasintestingor teachers'perceptions,anddifferenceinculture,socialization,orbehavior. 91 3.3 Data ThisstudyusestheEducationLongitudinalStudyof2002(ELS:02),anationally-representative sampleofover16,000studentswhowerehighschoolsophomoresinbaseyear2002,toexamine racialdifferencesincourse-takingandgapinachievement.Thefollow-upwasin2004,when moststudentswereseniors.Thesecondfollow-upwasin2006.Thisstudyrestrictsthesample tostudentswhohadcompletetranscriptinformation,andtoon-timehighschoolgraduates. 2 Data collectedfromstudentsincludedemographicandtranscriptdataforallcoursestaken,theirparents, andschooladministrators. Students'highschooltranscriptsarecollectedandcodedusingtheofSecondary SchoolCourse(CSSC)codes,updatedfromthe2000NationalAssessmentofEducationProgress high-schooltranscriptstudy.TheseweredevelopedbytheNationalCenterforEducationStatistics (NCES)andusedinpriortranscriptstudiessuchastheHighSchoolandBeyondof1980(HS&B) andtheNationalEducationLongitudinalStudyof1988(NELS).EachCSSCcoursecodecontains sixdigits.Thetwodigitsidentifythemainprogramarea;thesecondtwodigitsrepresenta subcategoryofcourseswithinthemainprogramarea;andthetwodigitsthe course.Forexample,regardingCSSCcode270405,thetwodigits(27)mathematics, themiddletwodigits(04)thepuremathematicssubcategory,andthetwodigits(05) thecoursealgebra2. UsingtheCSSCcodes,thisstudyconstructscourseintensityorrigorlevelbyemployingmath pipelinemeasures,introducedbyBurkamandLee(2003). 3 Pipelinemeasuresaredesignedto capturethehighestlevelofmathcompletedbut,forsimplicity,thisstudyassignstherigorlevel ofeachcoursetakenequivalenttothelevelofpipeline.Forinstance,algebra1andgeometryare 2 TheprocedureisdocumentedinDaltonetal.(2007).Thesampleofon-timegraduatesexcludesdropouts,who onaveragearelikelytotakelower-levelcourses,thusmightover-representrelatively-hightestscorers. 3 BurkamandLee(2003)dividedmathcoursesbylevel,intoeightcategories,movingfromleasttomostadvanced: (1)Nomathematics;(2)NonAcademic(e.g.,generalmathorconsumermath)mathematics;(3)LowAcademic(alge- bra1/plane,informalgeometry);(4)MiddleAcademic(algebra1,geometry/plane);(5)MiddleAcademic2(algebra 2);(6)Advanced1(algebra3/trigonometry/analyticgeometry);(7)Advanced2(pre-calculus);and(8)Advanced3 (calculus). 92 assignedwiththerigorlevelof3. Sincetheterminwhichthecoursewastakenvaries,quartertoyear-long,andthenumberof coursestakenperyearalsodiffersbystudents,onetoeightcourses,3122combinationsarisefrom 61mathcourses. 4 Thusthisstudyrestrictstomathcoursesthatareeitheryear-orsemester-long, whichaccountsfor80%ofthecourses,anddropsothertrimester-,quarter-long,andterm-unknown courses.Additionally,thisstudygeneratesmeasuresofrigorlevelforeachyearsuchasthehighest levelortheaveragelevelofmathpergrade. 5 Forexample,whenthehighestlevelofmathwithin agradeisused,astudentisassignedwithasequenceofmiddle-middle-middle2-advanced2if he/shetakesalgebra1infreshman,geometryinsophomore,algebra2injunioryear,andpre- calculusinsenioryear. Transcriptdatacover16,200studentswithmathcourses;13,900studentshavebothtran- scriptanddemographicinformation. 6 Among11,450on-timehighschoolgraduatestaking69,070 courses, 7 thisstudykeepscourseswithpositivecreditsearned,whichgives11,410studentswith 61,780mathcourses.Afterrestrictingtoyear-andsemester-longcourseswithpipelinemeasures available,andexcludingstudentswithoutpipelinemeasures,datainclude48,290courses takenby9350studentsfrom980highschools. SummarystatisticsforvariablesarepresentedinTable3.B1,withwhitereferringtonon- Hispanicwhites. 8 Theupperpaneloncreditpreviousresultsthattherearenoblack-white differencesinthenumberofmathcreditstaken,norinaveragecredittakenperyear.Sinceschools havedifferentunitmeasures,standardizedcreditsinCarnegieunitsareused . Thenextpanelon courseleveldescribesthatthehighestlevelofmathforwhitestudentsisclosetoadvanced1, 4 Sincemathcoursesareclearlysequencedandstudentsingeneraltakecoursesinorderdescribedbypipeline,the numberofmathcoursecombinationsismuchsmallerthanallpossiblecombinationsof61courses. 5 Asmanyas93%ofstudentstakeeitheroneortwomathcoursesperacademicyear,and6%takethreeorfour courses.Lessthan1%ofstudentstakeveormoremathcoursespergrade.Thiscomplicatesgeneratingamath sequenceandcomparisonacrossethnicgroups. 6 IncompliancewithNationalCenterforEducationStatisticsrestricteddata-licensingagreements,theunweighted samplesizeineachisroundedtothenearest10. 7 Reasonsfornotgraduatingon-timearedropout,transferred,GED,stillenrolled,withdrew,dismissed,health condition,incarcerated,andothers.Dropoutstudentsaccountsfor4%ofthesample. 8 Datainclude470studentswhoseracialstatusisasfiotherfl.Theseincludemixedrace,NativeAmerican, andAlaskaNativestudents.Suchstudentsareincludedinregressionsbutnotshowninthesummarystatisticstable. 93 whereasthatforblackstudentsisclosetomiddle2.Althoughthereisnoblack-whitedifferencein thelevelofyearmath,itseemsthegapisincreasingoveryearssothatthegapintheaverage levelis.35andthegapinthehighestlevelofmathis0.5.Thehighestlevelofmathisdivided intothreegroups,lowforlevels2and3,middleforlevels4and5,andadvancedforlevels6,7, and8.50%ofblacksendupwithmiddlelevel,whereas40%ofwhitesdo,butthepatterndiffers foradvancedlevel:54%ofwhitestudentsand65%ofAsianstudentsearnedthehighestlevel inadvancedcourses,whereas42%ofblackand39%ofHispanicstudentsmathcourses inadvancedlevel.Racialdifferencesincourse-takingpatterns,especiallyinadvancedlevelsof courses,mightexplainthegapinmathtestscores.DisparitiesintakingaremostapparentinAd- vancedPlacement(AP)courses,whichincludeAPcalculusandAPstatistics:11%forwhiteand 5%forblack. Approximately10%ofhigh-schoolgraduatesachievedthehighestlevelofmathintheirGrade 10,andmorethan50%ofstudentscompletedinGrade12.Ofinterestisthatthetimingofcom- pletingthehighestlevelofmathisdifferentbetweenblackandwhitestudents:38%ofblacks reachthehighestlevelinGrade11,while32%ofwhitesdo,andtherelationshipisoppositefor Grade12.SincetheproportionofmissingmathcourseinGrade12isnotdifferentbetweenwhite andblack,blacksmighttakelowerlevelofcourseinGrade12thaninGrade11. Course-takingpatternbygradeissummarizedinTable3.D1.Theblack-whitedifferencein thehighestlevelisincreasingoveryears,from0.1levelinGrade9to0.9levelinGrade12,and thesamepatternisobservedforaveragelevelofmathtaken.Blackstudentsaremorelikelyto takelow-levelcoursesinallhigh-schoolyears,whereastherelationshipisoppositeforenrollment inadvancedcourses.Formiddlelevelcourses,thepatternismixed.InGrades9and10,whites takemoremiddle-levelcoursesthantheirblackpeersdo,butblacksinGrade11and12takemore middle-levelcoursesthandotheirGrades9and10whitepeers. Insum,blacksandHispanicsareonaveragemorelikelytotakelower-levelcoursesthanwhites are.OnepossibleexplanationforwhitesandAsianstakinglesscreditsinlower-levelcourses,even inGrade9,isthattheyalreadytookthosecoursespriortoGrade9sothattheycantakeadvanced 94 coursessuchaspre-calculus,calculusorAPcoursesinhighschool. Freereducedlunch(FRL)schoolisacategoricalvariablerangingfromonetosevenandit indicatesthat,onaverage,blackstudentsareenrolledinschoolswithrelativelypoorerpeersthan whitesare. 9 Whitestudentsaremorelikelytoattendprivateschools.Parentaleducationiscoded oneifthehighesteducationlevelishigherthan4-yearcollege,andzerootherwise.Whitestudents comefromhighersocioeconomicstatusfamilies(parentsmorelikelytobecollege-educatedand wealthierthantheirblackcounterparts). ThekeyachievementvariableismathstandardizedtestscoresinGrades10and12.Among Grade10cohorts,whitesscoreonaverage2.1pointor0.21standarddeviationhigherthanmeanon themathexam,whereasblacksearn6.2pointor0.65standarddeviationlowerthanmeanonthat test,andtheblack-whiteachievementgapis8.3pointor0.86standarddeviation,whichiscloseto whatFryerandLevitt(2004)predicted.Unconditionalmathtestscoregapslightlydecreasesto8 pointor0.81standarddeviationamongGrade12cohorts. 10 Table3.D2describesthevemost-commoncoursestakeninhighschoolyears.Burkamand Lee(2003)showedthat14courseshave(unweighted)enrollmentabove5%ofthesample,using NationalEducationLongitudinalStudyof1988(NELS:88).Tenyearslater,itturnedoutthat18 courseshave(unweighted)enrollmentabove1%ofthesample,whichintotalcomprises90%of thesample,andonly4courseshaveenrollmentover5%inthesample.Noblack-whitediffer- enceexistsinthetopvecommoncourses,butcommoncoursesbylevelshowadifferentstory. Whitestakemoreadvancedcourses(19%)thandoblacks(9%),andblackstakemorelow-ornon- academiccourses(20%)thandowhites(7%);thisisconsistentwiththecourse-takingpatternin Table3.B1.Sincestudentsgenerallytakeupper-levelcoursesbyyear,fromlowtomiddle,orfrom middletoadvanced,themajorityofcoursesareconcentratedinmiddlelevel. Table3.B2presentsthevemostcommonsequences,orcourse-takingpatterns,basedonhigh- estlevelachievedineachyear.Among795sequences,thetopvecommonsequencescomprises 9 CategoriescorrespondingtoeachFRLratioare1for0-5%,2for6-10%,3for11-20%,4for21-30%,5for 31-50%,6for51-75%,and7for76-100%. 10 SummarystatisticsincludingdropoutsarepresentedinTable3.D3.Whitestudentsarelesslikelytodropandthe overallunconditionalblack-whitedifferencesenlarge. 95 lessthan30%,anditindicatesmorevarietyofsequencescomparedtoBurkamandLee(2003), whoshowedthatnearlytwo-thirdsofthestudentsareinonlyvepatterns. 11 Comparing thecommonsequencesbetweenblackandwhite,allstudentsstartinmiddlelevelcoursesinGrade 9butthedisparityincourselevelappearsinGrade10,inthatwhitestudentsstarttotakemiddle2 courses,andthosestudentstakefurtheradvancedcoursesintheir11thand12thgrade,endingup withadvanced3level.Atleast19%ofwhitestudentstakefouryearsofmathcoursesandreach advancedlevel,whereas12%ofblackstudentsfollowasimilarpattern.Figure3.A1indicates theprogressofhighest-levelmathachievedbygrade,andFigure ?? thatwhiteandblack studentstakeasimilarlevelofmathcoursesinGrade9,implyingthatpre-highschooldifferenceis notstrong.Rather,theblack-whitedifferenceinmathlevelhasdevelopedoveranumberofyears inhighschool. 11 Algebra1only(12.4%),algebra1andgeometryonly(9.2%),algebra1,geometry,andalgebra2only(20.8%), algebra1,geometry,algebra2,andanalysis/trigonometryonly(10.9%),andcalculusplusothercourses(9.9%). 96 3.4 Empiricalresults 3.4.1 RacialGapinCourseIntensity Theblack-whitegapincourse-takingamonghigh-schoolgraduates,andhowthegapevolvesover time,areestimatedbythefollowingmodel Y i = b 0 + b 1 Black i + b 2 Hispanic i + b 3 Asian i + b 4 OtherRace i + e i where Y i denotesforcourse-takingmeasureforstudent i .Sincenon-Hispanicwhitedummyis omitted, b 1 , b 2 , b 3 and b 4 capturesthemathcourse-takinggapbetweenwhiteandcorresponding race.Othercontrolsincludegender,familySESandincome,wherefamilyincome,whichis anordinalindicator,isrecodedbytakingthemidpointofeachincomecategory.Theanalysis startsbylookingatthedifferencesinthenumberofcredittakenbyeachgrade,andresultsare summarizedinTable3.B3.Consistentwithpreviousstudiesonintensitymeasures,thetotalcredits relatepositivelytofamilybackgroundandnoracialdifferencesareevidentwhenbetween-school variationisremovedthroughschooledeffects.Forcomparison,Asianstudentsaremostlikely totakemathcourses. AsinTable3.D3,thehigh-schooldropoutrateisdifferentbetweenblackandwhitestudents. Reasonsforleavinghighschoolvary,withwomenmorelikelytoleavebecauseofpersonalissues suchaspregnancyormarriageandmenmorelikelytoleavetogotowork;pooracademicper- formanceaccountsfor7%(Rumberger,1983).Ifdropoutstudentshavelowerperformancethan on-timegraduatingstudentshave,excludingdropoutswouldtakeoutthelefttailofperformance distribution,thusthecourse-takinggapmightbeunderestimated.Forsimplecomparison,dropout studentsareincludedinthesampleandtheirmathcreditsarerecordedaszeroaftertheyleavethe school.ResultsinTable3.B4includedropoutsandindicatethattheblack-whitedifferenceinthe numberofcreditstendstodropamong9thand10thgraders,andtoremainsimilaramong11thand 12thgraders.Consistentwithpreviousstudiesondropout,theimportanceofparentaleducation 97 andfamilyincometocourse-takingincreaseswhendropoutstudentsareincluded,anddropout studentstendtotakefewermathcourses. Asinpreviousstudies,nomeaningfuldifferencesexistsintotalmathcreditstaken,butthe qualityofthecoursetakenmightbedifferent.Table ?? summarizesordinaryleastsquaresesti- mationresultsofracialdifferencesincourse-takingmeasuredbyrigorlevel.Duringhigh-school years,thehighestlevelofmathforblackgraduatesis0.5levellowerthanwhitepeers.Whenthe averagelevelofmathcoursetakeniscalculated,blackstudentsonaveragetake0.2levellower coursesthanwhitestudentstake,whichinturnaccumulatesto2.4levelinfour-yearsofhigh school.Schooledeffectisincludedtoaccountforacross-schoolvariationsuchasschoolSES, racialcomposition,andteacherquality,andthemagnitudeoftheblack-whitegapincourse-taking increases,exceptfortotalrigor,implyingthatthegapincourse-takingisawithin-schoolphe- nomenon.Theblack-whitecourse-takingdifferenceoccursfromthelevelofmathcourse indicatingthatstudentsenterhighschoolwithdifferentlevelsofmathpreparation. Eachstatehasdifferentpolicyforcurriculumrequirementforgraduation,suchasthenumber ofminimummathcreditsandthelistofcoursestopass,andschooledeffectsmightnotexplain across-statedifferences.Whenstateedeffectsareincluded,theblack-whitegapis fromdifferencesbetweenblacksandwhitesattendingschoolinthesamestate,andthepattern issimilar,implyingthatthemajorityofvariationiswithin-school:thereisalmostnochangein coefforvel,totalrigor,andaveragerigorofmath.Butthecoefonthehighest- levelofmathincreases,whichisslightlysmallerthanthecoefwithschooledeffects. 12 Thenextstepistoanalyzeinwhatlevelofcourseandinwhichgradetheracialgapincourse-taking exists. 3.4.2 RacialGapinCourse-Taking Table3.B5showsthatblackstudentsaremorelikelytoenrollinlow-andmiddle-levelcourses thantheirwhitepeers,andlesslikelytotakecoursesbeyondmiddle2level,generallyconsidered 12 Hereafteronlyestimationresultswithschooleffectsarepresentedunlesscontrollingstateunobservablesprovides differentresults. 98 themaththresholdforcollegeadmission.Adelman(1999)showedthatstudentswhotakecourses beyondalgebra2scorehigheronentranceexaminationsandhavegreaterlikelihoodsofattending collegeingeneral(andmore-selectivecollegesanduniversitiesinparticular),aswellasgraduating fromcollege,thanstudentswhomeetbutdonotexceedthealgebra2threshold.Forexample, Riegle-Crumb&Grodsky(2010)dividedsamplesbasedonwhetherornotstudentscompleted anymathcoursebeyondalgebra2andconductseparateanalysesforeachgroup.Moreover,the black-whitegapintheenrollmentlevelismoreawithin-schoolthanawithin-statephenomenon forlow-levelcourses,buttherelationshipisoppositeformiddlelevelcourses.Interestingly,there isalmostnodifferencesintakingpre-calculcus(advanced2)orcalculus(advanced3)courses explainedbywithin-schoolorbetween-statevariation.Algebra1(middle)oralgebra2(middle 2),ontheotherhand,seemsmostlyaffectedbybetween-statevariationsuchasdifferentmath requirementsforgraduation. Table3.B7presentshowthedisparityinrigorlevelofcourse-takingevolvesovergrades.It isclearthattheblack-whitegapincreasesovertime.Averagerigorandthehighest-rigor-per- gradeprovidealmostthesameestimates,sincestudentsgenerallyaretakingyear-longcourse orsemester-longcourseswithsimilarintensitylevels. 13 Additionally,thepositiveassociation betweencourse-intensityandfamilybackgroundalsoincreasesoveryears. Table3.B8exploresestimatedracialdisparities,whichgrowsoverhigh-schoolyears,across course-intensity.Overall,whenbetween-schoolvariationisnotconsidered,noblack-whitegap incourse-takingappearsforlow-levelcoursetakers.Blackstudentsaremorelikelythanwhiteto takemid-levelcourses,andtherelationshipisoppositeforadvancedandAPcourses.Butmixed resultsappearforthepatternbygrade.Blackstudentsaremorelikelythanwhitestudentsto takelow-levelcoursesinGrade10.Formid-levelcourses,therelationshipismixed.Sinceblack studentsstarttheirGrade9withalowerlevelofmath,theyarelesslikelytotakemid-levelcourses suchasalgebra1,algebra2,andgeometry,inGrades9and10,andmorelikelytotakethose 13 SimilartoresultsinTable ?? ,thegaptendstobelargerwhenschooledeffectsareincludedthanwhenstate edeffectsareincluded,especiallyforGrades9and11,implyingthattheincreasingblack-whitegapinthelevelof courseismoreofawithin-schoolthanawithin-statevariation. 99 mid-levelcoursesthanwhitestudentsinGrades11and12.Foradvancedcourses,thereareno racialdifferencesfor9thgraders.ButaswhitesandAsiansaretakingmid-levelcoursesinGrade 9and10,ablack-whitegapinadvancedcourse-takingappearsinGrade10,andthegapincreases overyears.PanelDshowsthecourse-takingpatternforAPcoursessuchasAPCalculusandAP Statistics.OverallitshowsthatblackstudentsarelesslikelytotakeAPcoursesthanwhitestudents are.InGrade11,theblack-whitecourse-takingdifferenceisnegligibleas2%ofwhitesand1%of blacksaretakingAPcoursesintheirGrade11.NotablyAsiansaretakingmoreAP coursesinGrade11.InGrade12,blacksarelylesslikelytotakeAPcoursesthanare whites. 14 Includingschooledeffectsremovebetween-schoolvariations,andtendtoincreasethe magnitudeofblack-whitedifferencesinalllevelsofmathcourses.Particularly,blackgraduates attendingthesameschoolaremorelikelytotakelow-levelcoursesinallhighschoolyears. 3.4.3 RacialGapinTimingofHighest-LevelofMath Ingeneral,high-schoolstudentsapplyingforcollegesdosoattheendofGrade11andinearly Grade12,andsubmitthelistofmathcoursestaken,sohaveincentivetocompletethehighest- levelbytheendofGrade11.Atthesametime,ingeneral,national-level-orprestigiouscolleges requireacourse-takingplaninGrade12andstudentsapplyingforthosecollegesmighthavemore incentivestotakeadvancedcoursesinGrade12.Thusthetimingofhighestmathlevelachieved mightexplainthepersistentblack-whitegapincourse-takinginGrade12andinadvancedcourses. Tostudyracialdisparityinthetimingofhighest-levelobtained,thesampleisdividedbywhenthey takethehighest-level. Studentstakingthehighest-levelinGrade12areofthreepossibletypes:i)nomathcourse inGrade11andtakehighest-levelinGrade12;ii)lower-levelinGrade11andmoreadvanced levelinGrade12;iii)samelevelofmathinGrades11and12.Table3.B9showsthatwhitesare morelikelytoachievehighest-levelinGrade12albeittheestimateisstatistically 14 Parentseducationandfamilyincomearenegativelycorrelatedwithtakinglow-levelcourses.Formid-level coursetakers,studentsfrombetterfamilybackgroundaremorelikelytotakemid-levelcoursesin9thand10thgrade. Theoffamilybackgroundonadvancedcourse-takingisalsoincreasingoveryears. 100 Interestingly,blackswhotakehighest-levelofmathin12thgradearemorelikelythanwhitesto missmathcoursesinGrade11whereaswhitesaremorelikelytotakemoreadvancedcoursesin Grade12thaninGrade11. Similarly,studentswhotakethehighest-levelinGrade11aredividedintotwogroups:i)no mathcourseinGrade12;ii)lower-levelinGrade12.Consistentwithresultsfrom12thgraders, blacksaremorelikelytotakethehighest-levelinGrade11.,blackstudentsaremore likelythantheirwhitecounterpartstomissmathcoursesinGrade12,andmorelikelytotake lower-levelmathinGrade12. Onceschooledeffectsareincluded,allbutonecoefonblacksbecomestatistically indistinguishablefromzero,implyingthatthetimingoftakingthehighest-levelofmathmight relatetoschoolcharacteristics. 15 Thusthesampleisdividedbyschoolsector,public,private,and Catholic.ResultsarepresentedinTables3.B10and3.D4.Theformershownoracialdifferences inthetimingofachievingthehighest-levelofmathinGrade12inpublicandinprivateschool. ButblackstudentsinCatholicschoolsarelesslikelythantheirwhitepeerstotakemathcoursesin Grade11andadvancedcoursesinGrade12.Butonceacross-schoolvariationsarecontrolled,no racialdifferencesappearintakingthehighest-levelofmathinGrade12evenamongstudentsin Catholicschools;thisimpliesthepresenceofqualityvariationsacrossCatholicschools. 16 Similarly,inTable3.D4mostvariationinracialdifferenceinthetimingoftakingthehighest- levelofmathinGrade11occursamongstudentsinCatholichighschools.Blacksare16%less likelytotakethehighest-levelofmathinGrade11thanwhitecounterparts,wherethenational averageis5%,andare14%morelikelytomissmathcoursesinGrade12thantheirwhitepeers, whosenationalaverageis3%. 17 Inconclusion,black-whitedifferenceinthetimingofachievingthehighest-levelofmathis 15 IncludingstateedeffectsincreasesthelikelihoodforwhitestoachievethehighestlevelofmathinGrade12; generallythosestudentshavelowerlevelinGrade11andtakemoreadvancedcoursesinGrade12;thismightrelate todifferentacross-statepolicy. 16 Althoughstatisticallyamongprivateschools,between-statedifferencesexplainmostoftheblack- whitedifferenceinthelikelihoodoftakingthehighestlevelofmathinGrade12. 17 Whenacross-statevariationiscontrolled,thelikelihoodofblackstudentsachievingthehighestlevelofmathin theirGrade11tendstoincreaseforpublicandprivateschool,albeitstatistically 101 mostlyexplainedbybetween-schooldifferences,andnostatistically-andeconomically-mean- ingfuldifferenceswithinschoolareapparent.Thebetweenschooldifferencesinthetimingis largeamongCatholicschools,implyingthatschoolcharacteristicssuchasresources andteacherqualitymightaffectstudents'decisionsoncourse-takingpattern. 3.4.4 AchievementGap Table3.B11displayscoefentsonblack,Hispanic,andAsianracedummies,indicatingdiffer- encesrelativetowhite,andresultsareconsistentwithpreviousstudiesonachievementgap;the black-whitestandardizedmathscoregapof0.647inGrade12,1/8standarddeviation,ismostly explainedbypreviousstandardizedtestinGrade10. 18 Next,theachievementgapisestimatedby thelevelofmathcoursetakenineachgrade,whichismeasuringthegapamongstudentstakingthe samelevelofcourseinacertainperiod.Forexample,thecoefof-1.704inPanelAshows theblack-whitetestgapinGrade12amongstudentswhotookadvanced-levelcourseinGrade 11.Theblack-whitetest-scoregapforstudentswhoinGrade11tookmid-levelmathis-0.361, thusthistest-scoregapdiffersbycourselevel.Theblack-whitegapisrelativelylargerforstudents takingadvancedcourseinallgrades,about2xŒto6xlargerthantheaveragegap.Ofinterestisthat thetestscoregapisabout0.2standarddeviationamongstudentstakingthesameadvancedlevel inGrade11whenaveragerigorleveliscontrolled,whereasthegapissmallerthantheaveragegap among11thgraderstakingeithermid-orlow-levelmathcourses. Theblack-whitetest-scoregapforstudentswhoinGrade12tookmid-levelmathis-1.014, whereas(asweseeabove)thetest-scoregapforstudentswhoinGrade11alsotookmid-levelmath is-0.361,sothistest-scoregapdiffersbyschoolyearoftakingmid-levelmath.Blackstudents takingmid-levelcoursesinGrades9and10arelikelytohavetakenlow-levelcoursesinadvance andcanberegardedascollege-trackstudents.Thetestgapforthosestudentsisbut themagnitudeissmallerthan0.1standarddeviation.95%ofstudentsearnedcreditsinmidlevel coursesandsomepassedthecoursebyretakingorbytakingcreditrecovery,whichexplainsthe 18 GeneralresultsonachievementgapareprovidedinAppendixA. 102 negligibleachievementgapamongstudentstakingmidlevelcourses.Ontheotherhand,advanced levelcoursesarehardertopassbyretakingorbycreditrecovery. 19 Additionally,simpleanalysisshowsthat,aftercontrollingfortestscoreinGrade10,thecor- relationbetweenblack-whiteachievementgapinGrade12andcourse-taking,measuredeitherby theaverageintensityorbythehighestlevelofmath,isaround0.25andthataround10%ofthe variationinthetestgapisexplainedbythevariationincourse-taking.Consideringthefactthat achievementiscloselyrelatedtoeducationattainmentsuchashighschoolgraduationandcollege going,differentcourse-takingpatternsarelikelytohaverelationshipwithracialgapinattainment. Morerigorousresearchonthecasualpathisleftforfutureresearch. Last,theblack-whitetestgapinGrade12isabouttwiceaslargeamongstudentswhotakethe highestlevelofmathinGrade12thanthosecompletedinGrade11.InGrade12,onaverage, whitestakemoreofadvanced1level,whileblackstakemoreofmiddle2level.Thisdifferencein course-takingintensityseemscontributorytothetestgapinGrade12. 19 Whenstateedeffectsaresubstitutedforschooledeffects,thescoregapislargerforstudentstakingad- vancedcoursesintheirGrades10,11,and12,aswellasforthosetakingmid-levelcourses,implyingthatschool-level heterogeneityexistswithinthesamestate. 103 3.5 Discussion Thisstudyaimstoexploretherelationshipbetweenracialdifferencesinmathcourse-takingand achievementgap.UsingELS:02TranscriptStudydata,thisstudyconstructedmeasurestocapture course-takingpatternsandanalyzedtheracialdifferenceinmathcourse-takinginhighschool.For example,average-orhighest-levelofrigororintensityiscalculatedbygradeandbycourse-level fromamathsequencevariablethatastudenttookinhighschool.Moreover,thetimingofhighest- levelofmathachievedisusedtoidentifystudentstakingcourseswithrigorlevelcontinually increasing,whoareretakingthecourse,andotherswhoarechoosingtooptoutwhileonadvanced track. Racialdifferenceincourse-takingoccursnotonlyintermsofthehighestlevelofmathortotal numberofmathcreditstaken.Blackstudentsandwhitestudentsstarthighschoolwithdifferent mathlevelsandinfollowingyearstakedifferentmathlevel,wheretheblack-whitedifference inthelevelofmathisincreasingovertheschoolyears.Moreover,blackandwhitehigh-school graduatestendtoachievethehighest-levelofmathindifferentgrades,whichalsocontributesto thetest-scoregapinGrade12.Thusthesequencevariableisbettersuitedtounderstandracial differencesincourse-takingpatternsthatchangeoveryears. Between-schoolvariations,suchasschoolexpenditure,numberofcoursesoffered,andteacher quality,seemtoexplainracialdifferencesincourse-taking.Oncevariationsarecontrolled,the magnitudeofblack-whitedifferenceincourse-takinggenerallyincreases,implyingthatthegap isawithin-schoolphenomenon.Interestingly,substantialacross-schoolvariationsexistsamong Catholichighschools. Additionally,eachstate'spoliciesforhighschoolgraduationdiffer.Theseincludethenumber ofmathcredits,levelsofmathcoursetocomplete,andexitexams.In2013,atleast47stateshave statewiderequirementsonthenumberofcreditsforhighschoolgraduation(NationalCenterfor EducationStatistics,2014).Comparisonofempiricalresultscontrollingforschoolunobserved heterogeneity,andthosewithstateunobservedheterogeneity,showssomedegreeofbetween- 104 schoolvariationsamongstudentsattendingschoolinthesamestate. Thisstudywouldbeextendedbyusingtwoothersetsofnationally-representativedata,NELS:88 andHS&B:82,toexplorechangesincourse-takingpatternsandachievementgappatterns.Some hypothesestobetested:(1)WhitestudentsoutnumberblackstudentsinAPcourses;(2)Black studentsenrollmoreinremedialcoursesthanwhitesdo;(3)Blackstudentshavemoreretention; and(4)Blackstudentstakemorecredit-recoverycourses.Number1and3relatetoopportunity structure,and3islinkedtocoursepreparation.Byanalyzing2and4,thisstudycanexamine organizationalresponsestothe NoChildLeftBehind policy,whichmightkeepstudentsinhigh schooltograduatebutnotpracticallyhelptheirperformance. FryerandLevitt(2004)predictedthattheblack-whiteachievementgapinGrade9willbeone standarddeviationinrawscoreifblackstudentscontinuetolosegroundattherateexperienced inthetwoyearsofschool.The0.9standarddeviationdifferenceinGrade10mathscore isalittlesmallerthantheirpredictionbutthisimpliesthatblackstudentshavelostgroundsince kindergarten.Blackstudents'smallerresponseinmathtestscoretofamilySES,acomposite measureofparentaleducationandoccupation,inrelationtowhitepeers,seemstoexplainthelagin achievementbecausemanyblackstudentshavelowerfamilySES,thecumulativeimpactofwhich isnegativeonachievement.Thisassertion,however,hastobefurtheranalyzedbycontinuous trackingofstudentachievementovertheyears. 105 APPENDICES 106 APPENDIXA FIGUREFORCHAPTER3 107 Figure3.A1ProgressinMathLevel Notes: Course-takingdistributionbyraceinGrade9isintheupperleftandthatinGrade10isintheupperright. Course-takingdistributionbyraceinGrade11isinthelowerleftandthatinGrade12isinthelowerright. 108 APPENDIXB TABLESFORCHAPTER3 109 Table3.B1SummaryStatisticsbyRace VariableFullSampleWhiteBlackHispanicAsian Credit: TotalCredit3.3333.3923.2883.0623.462 Averageperyear0.7030.7230.7530.6360.625 CourseLevel: HighestLevelofMath5.7475.8385.3275.2926.407 Averageperyear4.5464.6084.2284.2595.012 LevelofFirstCourse3.8343.8663.7343.6854.011 HighestLevelofMath: LowLevel0.0490.0410.0650.0770.033 MiddleLevel0.4290.4050.5140.5380.314 AdvancedLevel0.5220.5540.4210.3850.653 AP0.1220.1160.0460.0700.329 TimingofAchievingHighestLevelofMath: 10thGrade0.1100.1150.0860.1120.091 11thGrade0.3250.3150.3810.3790.244 12thGrade0.5300.5390.4760.4660.643 MissingMathClassin: 9thGrade0.0900.0750.1200.1140.101 10thGrade0.0890.0710.1500.1360.066 11thGrade0.1450.1400.1580.1690.123 12thGrade0.3870.3810.4090.4480.307 OtherControls: Public0.7470.6930.8500.8010.886 Private0.0980.1260.0410.0380.060 Catholic0.1550.1810.1090.1610.054 FRLSchool2.0761.7163.2402.9121.804 ParentEducation0.4440.4790.3610.2810.545 FamilyIncome9.2759.8058.0368.3428.775 TestScore: 10thGrade52.09054.14445.89047.43353.416 12thGrade51.30252.93344.95346.90655.039 Notes: Theentriesaremeansofstudent-leveldataonwhoarenotmissingmathscores,race,andSES variable.Thehighestlevelofmathisdividedintothreegroups,Lowforlevels2and3,Middlefor levels4and5,andAdvancedforlevels6,7,and8.Freereducedlunch(FRL)schoolisacategorical variablerangingfromonetosevencorrespondingtoeachFRLratio(1for0-5%;2for6-10%; 3for11-20%;4for21-30%;5for31-50%;6for51-75%;and7for76-100%.) Parentaleducationiscodedoneifthehighesteducationlevelishigherthan4-yearcollegeandzero otherwise.Familyincomeisrecodedbytakingthemidpointofeachincomecategoryand logtransformed. 110 Table3.B2MostCommonCourseSequence 9thGrade10thGrade11thGrade12thGradePercent FullSample MiddleMiddleMiddle27.94 MiddleMiddleMiddle2Advanced16.43 MiddleMiddleMiddle2Advanced26.37 MiddleMiddle2Advanced2Advanced35.01 MiddleMiddle2.2 White MiddleMiddleMiddle2Advanced17.48 MiddleMiddleMiddle27.47 MiddleMiddleMiddle2Advanced26.74 MiddleMiddle2Advanced2Advanced35.24 MiddleMiddle2.35 Black MiddleMiddleMiddle210.08 MiddleMiddleMiddle2Advanced16.85 MiddleMiddleMiddle2Advanced25.64 MiddleMiddleAdvanced12.59 MiddleMiddle2.41 Hispanic MiddleMiddleMiddle29.97 MiddleMiddleMiddle2Advanced24.98 MiddleMiddleMiddle2Advanced14.49 MiddleMiddle2Advanced2Advanced33.35 MiddleMiddle2Advanced22.7 Asian MiddleMiddle2Advanced2Advanced39.78 MiddleMiddleMiddle2Advanced27.36 MiddleMiddleMiddle25.6 MiddleAdvanced1Advanced2Advanced32.42 Middle2Advanced2Advanced3Advanced32.42 Notes: Entriesaremeansofstudent-leveldataofwhoarenot missingmathscores,race,andSESvariable.Eachentryisthe highest-levelofmathineachgrade. 111 Table3.B3EstimatedBlack-WhiteGapinNumberofCredits Variables9th10th11th12thTotal PanelA:CreditandRacewithoutSchoolFixedEffect Black0.022*0.0060.023*0.054***-0.029 (0.011)(0.010)(0.010)(0.014)(0.034) Hispanic-0.031**-0.056***-0.021*-0.050***-0.248*** (0.010)(0.009)(0.010)(0.013)(0.032) Asian-0.010-0.0150.0150.0210.092* (0.012)(0.010)(0.011)(0.014)(0.036) Female-0.0060.0060.009-0.016*0.084*** (0.007)(0.006)(0.006)(0.008)(0.021) ParentEducation0.004-0.0010.0040.0160.190*** (0.007)(0.006)(0.007)(0.009)(0.022) FamilyIncome0.0010.0010.0020.0000.071*** (0.003)(0.003)(0.003)(0.004)(0.009) Adj. R 2 0.0020.0040.0020.0070.035 PanelB:CreditandRacewithSchoolFixedEffect Black-0.0030.0210.022-0.006-0.013 (0.018)(0.014)(0.015)(0.018)(0.042) Hispanic-0.020-0.0000.024-0.018-0.063 (0.015)(0.011)(0.013)(0.017)(0.038) Asian0.039*0.047**0.057***0.064**0.261*** (0.017)(0.015)(0.015)(0.021)(0.044) Female-0.0080.0100.003-0.0090.085*** (0.007)(0.006)(0.007)(0.010)(0.020) ParentEducation0.016*0.0090.017*0.026**0.140*** (0.008)(0.007)(0.008)(0.010)(0.022) FamilyIncome0.0040.0030.005-0.0020.047*** (0.003)(0.004)(0.003)(0.004)(0.010) Adj. R 2 0.2830.1810.1760.1830.340 Numberofobservations a 85108520800057309350 Notes: Dependentvariableisthenumberofcreditsinunweightedsample.Non-Hispanicwhites aretheomittedracecategory,soallracecoefaregapsrelativetowhites.Theunitof observationisastudent.Standarderrorsareinparentheses.Parentaleducationiscodedone ifthehighesteducationlevelishigherthan4-yearcollegeandzerootherwise.Familyincome isrecodedbytakingthemidpointofeachincomecategoryandlogtransformed. atthe1%level.atthe5%level.atthe10%level. a IncompliancewithNationalCenterforEducationStatisticsrestricteddata-licensing agreements,thenumberofcasesineachofthecellsofthistableandallsubsequenttables isroundedtothenearest10. 112 Table3.B4EstimatedBlack-WhiteGapinNumberofCreditswithDropout Variables9th10th11th12thTotal PanelA:CreditandRacewithoutSchoolFixedEffect Black0.009-0.0080.0200.045**-0.074* (0.012)(0.012)(0.011)(0.014)(0.034) Hispanic-0.048***-0.078***-0.036***-0.058***-0.293*** (0.012)(0.011)(0.011)(0.013)(0.032) Asian0.002-0.0070.0140.0180.094* (0.013)(0.012)(0.012)(0.014)(0.037) Female0.0010.015*0.011-0.016*0.103*** (0.008)(0.007)(0.007)(0.008)(0.021) ParentEducation0.031***0.028***0.0120.019*0.234*** (0.008)(0.007)(0.007)(0.009)(0.022) FamilyIncome0.013***0.011**0.007*0.0020.085*** (0.003)(0.003)(0.003)(0.004)(0.009) Adj. R 2 0.0090.0130.0050.0070.047 PanelB:CreditandRacewithSchoolFixedEffect Black-0.0010.0100.023-0.013-0.025 (0.020)(0.018)(0.016)(0.019)(0.044) Hispanic-0.039*-0.0280.001-0.021-0.099* (0.018)(0.015)(0.015)(0.018)(0.041) Asian0.042*0.043**0.051**0.064**0.263*** (0.018)(0.016)(0.016)(0.021)(0.043) Female-0.0010.019*0.005-0.0080.104*** (0.008)(0.008)(0.008)(0.010)(0.021) ParentEducation0.036***0.032***0.022**0.028**0.176*** (0.009)(0.008)(0.008)(0.010)(0.024) FamilyIncome0.014***0.010*0.009**0.0000.062*** (0.004)(0.004)(0.003)(0.004)(0.011) Adj. R 2 0.2080.1310.1660.1870.319 Numberofobservations88408830812057609790 Notes: Dependentvariableisthenumberofcreditsinunweightedsample.Non-Hispanicwhitesare theomittedracecategory,soallracecoefaregapsrelativetowhites.Theunitof observationisastudent.Standarderrorsareinparentheses.Parentaleducationiscodedone ifthehighesteducationlevelishigherthan4-yearcollegeandzerootherwise.Familyincomeis recodedbytakingthemidpointofeachincomecategoryandlogtransformed. atthe1%level.atthe5%level.atthe10%level. 113 Table3.B5EstimatedBlack-WhiteGapinCourse-TakingbyLevel VariablesLevel2Level3Level4Level5Level6Level7Level8 PanelA:Course-takingbyLevelwithoutSchoolFixedEffect Black0.019**0.026***0.008-0.007-0.005-0.024***-0.018*** (0.006)(0.007)(0.009)(0.006)(0.005)(0.004)(0.004) Hispanic0.0110.034***0.012-0.018***-0.026***-0.003-0.010** (0.006)(0.007)(0.008)(0.005)(0.005)(0.004)(0.004) Asian-0.027***-0.013-0.059***0.003-0.0100.036***0.070*** (0.007)(0.007)(0.009)(0.006)(0.005)(0.004)(0.004) Female-0.014***-0.009*-0.0050.010**0.006*0.007**0.004 (0.004)(0.004)(0.005)(0.003)(0.003)(0.003)(0.002) Parent-0.035***-0.047***-0.044***0.019***0.027***0.042***0.039*** Education(0.004)(0.005)(0.006)(0.004)(0.003)(0.003)(0.002) Family-0.017***-0.012***-0.006**0.008***0.008***0.009***0.009*** Income(0.002)(0.002)(0.002)(0.002)(0.001)(0.001)(0.001) Adj. R 2 0.0350.0300.0150.0110.0220.0600.092 PanelB:Course-takingbyLevelwithSchoolFixedEffect Black0.046***0.040***-0.009-0.014*-0.025***-0.018***-0.018*** (0.009)(0.010)(0.012)(0.007)(0.006)(0.005)(0.004) Hispanic0.037***0.032***-0.005-0.022***-0.014*-0.016**-0.011** (0.009)(0.009)(0.011)(0.006)(0.006)(0.006)(0.004) Asian-0.017*-0.016-0.058***-0.002-0.0010.031***0.063*** (0.008)(0.010)(0.013)(0.007)(0.006)(0.006)(0.007) Female-0.015***-0.012**-0.0010.014***0.007*0.007*0.001 (0.004)(0.004)(0.005)(0.004)(0.003)(0.003)(0.002) Parent-0.021***-0.028***-0.026***0.012**0.014***0.025***0.023*** Education(0.004)(0.005)(0.006)(0.004)(0.003)(0.003)(0.003) Family-0.011***-0.010***-0.0000.004*0.006***0.006***0.006*** Income(0.002)(0.002)(0.003)(0.002)(0.001)(0.001)(0.001) Adj. R 2 0.2130.3070.2480.2470.3950.2640.206 PanelC:Course-takingbyLevelwithStateFixedEffect Black0.023*0.030**0.019-0.015-0.015-0.024***-0.018*** (0.011)(0.009)(0.012)(0.009)(0.008)(0.005)(0.003) Hispanic0.024*0.031-0.002-0.020*-0.010-0.010-0.012*** (0.009)(0.016)(0.010)(0.008)(0.008)(0.006)(0.004) Asian-0.016-0.029*-0.075***0.0050.0070.037***0.072*** (0.009)(0.012)(0.014)(0.010)(0.006)(0.006)(0.007) Female-0.014**-0.009*-0.0040.012**0.0050.0070.004 (0.005)(0.004)(0.007)(0.004)(0.004)(0.003)(0.003) Parent-0.033***-0.048***-0.040***0.017***0.027***0.040***0.037*** Education(0.004)(0.006)(0.007)(0.004)(0.003)(0.005)(0.004) Family-0.017***-0.011***-0.006*0.007**0.008***0.009***0.009*** Income(0.004)(0.003)(0.003)(0.002)(0.002)(0.001)(0.001) Adj. R 2 0.0730.0940.0570.0500.0880.0880.101 Numberof9350935093509350935093509350 Observations Notes: Non-Hispanicwhitesaretheomittedracecategory,soallracecoefaregapsrelative towhites.Theunitofobservationisastudent.Standarderrorsareinparentheses.Parentaleducationis codedoneifthehighesteducationlevelishigherthan4-yearcollegeandzerootherwise.Familyincome isrecodedbytakingthemidpointofeachincomecategoryandlogtransformed.Level2(Non-Academic); Level3(Low);Level4(Middle);Level5(Middle2);Level6(Advanced1);Level7(Advanced2); Level8(Advanced3).atthe1%level.atthe5%level. atthe10%level. 114 Table3.B6EstimatedBlack-WhiteGapinCoursebyGrade Variables9th10th11th12th9th10th11th12th GradeGradeGradeGradeGradeGradeGradeGrade DependentAverageRigorbyGradeHighestRigorbyGrade Variable PanelA:RigorbyGradewithSchoolFixedEffect Black-0.187***-0.241***-0.365***-0.631***-0.185***-0.233***-0.332***-0.611*** (0.029)(0.039)(0.063)(0.105)(0.029)(0.040)(0.062)(0.106) Hispanic-0.109***-0.157***-0.271***-0.328***-0.101**-0.146***-0.248***-0.325*** (0.031)(0.038)(0.062)(0.097)(0.033)(0.039)(0.061)(0.098) Asian0.110**0.355***0.477***0.672***0.136***0.377***0.497***0.699*** (0.037)(0.054)(0.071)(0.108)(0.040)(0.054)(0.072)(0.107) Female0.0240.056**0.076*0.149**0.0210.058**0.075*0.136** (0.016)(0.019)(0.031)(0.049)(0.016)(0.020)(0.031)(0.050) Parent0.109***0.181***0.358***0.425***0.115***0.188***0.362***0.429*** Education(0.017)(0.021)(0.036)(0.054)(0.018)(0.021)(0.037)(0.055) Family0.056***0.053***0.111***0.153***0.055***0.052***0.111***0.148*** Income(0.008)(0.009)(0.015)(0.027)(0.008)(0.010)(0.015)(0.026) Adj. R 2 0.2530.2650.2540.2950.2530.2540.2360.274 PanelB:RigorbyGradewithStateFixedEffect Black-0.086**-0.210***-0.255**-0.679***-0.075*-0.204***-0.206**-0.631*** (0.031)(0.046)(0.078)(0.118)(0.030)(0.045)(0.074)(0.116) Hispanic-0.088*-0.117*-0.196**-0.459***-0.092*-0.120*-0.180**-0.448*** (0.041)(0.054)(0.059)(0.126)(0.045)(0.052)(0.055)(0.123) Asian0.189***0.388***0.532***0.667***0.205***0.415***0.565***0.683*** (0.036)(0.050)(0.078)(0.091)(0.030)(0.054)(0.079)(0.082) Female0.0320.047*0.090**0.137**0.0260.047*0.088**0.123** (0.017)(0.020)(0.030)(0.043)(0.017)(0.021)(0.031)(0.042) Parent0.170***0.288***0.533***0.668***0.172***0.287***0.526***0.655*** Education(0.021)(0.026)(0.034)(0.060)(0.021)(0.025)(0.034)(0.057) Family0.065***0.081***0.160***0.211***0.063***0.080***0.158***0.202*** Income(0.010)(0.013)(0.020)(0.026)(0.009)(0.014)(0.021)(0.026) Adj. R 2 0.0810.1130.1230.1460.0800.1100.1180.140 Numberof85108520800057308510852080005730 Observations Notes: Non-Hispanicwhitesaretheomittedracecategory,soallracecoefaregapsrelativetowhites. Theunitofobservationisastudent.Standarderrorsareinparentheses.Parentaleducationiscodedoneifthehighest educationlevelishigherthan4-yearcollegeandzerootherwise.Familyincomeisrecodedbytakingthemidpointof eachincomecategoryandlogtransformed.atthe1%level. atthe5%level.atthe10%level. 115 Table3.B7EstimatedBlack-WhiteGapinCoursebyGrade Variables9th10th11th12th9th10th11th12th GradeGradeGradeGradeGradeGradeGradeGrade DependentAverageRigorbyGradeHighestRigorbyGrade Variable RigorbyGradewithSchoolFixedEffect Black-0.187***-0.241***-0.365***-0.631***-0.185***-0.233***-0.332***-0.611*** (0.029)(0.039)(0.063)(0.105)(0.029)(0.040)(0.062)(0.106) Hispanic-0.109***-0.157***-0.271***-0.328***-0.101**-0.146***-0.248***-0.325*** (0.031)(0.038)(0.062)(0.097)(0.033)(0.039)(0.061)(0.098) Asian0.110**0.355***0.477***0.672***0.136***0.377***0.497***0.699*** (0.037)(0.054)(0.071)(0.108)(0.040)(0.054)(0.072)(0.107) Female0.0240.056**0.076*0.149**0.0210.058**0.075*0.136** (0.016)(0.019)(0.031)(0.049)(0.016)(0.020)(0.031)(0.050) Parent0.109***0.181***0.358***0.425***0.115***0.188***0.362***0.429*** Education(0.017)(0.021)(0.036)(0.054)(0.018)(0.021)(0.037)(0.055) Family0.056***0.053***0.111***0.153***0.055***0.052***0.111***0.148*** Income(0.008)(0.009)(0.015)(0.027)(0.008)(0.010)(0.015)(0.026) Adj. R 2 0.2530.2650.2540.2950.2530.2540.2360.274 Notes: Non-Hispanicwhitesaretheomittedracecategory,soallracecoefaregapsrelativetowhites. Theunitofobservationisastudent.Standarderrorsareinparentheses.Parentaleducationiscodedoneifthehighest educationlevelishigherthan4-yearcollegeandzerootherwise.Familyincomeisrecodedbytakingthemidpointof eachincomecategoryandlogtransformed.atthe1%level. atthe5%level.atthe10%level. 116 Table3.B8SensitivityAnalysisofCourse-TakingGap CoefonCoefonCoefon BlackforHispanicforAsianfor ByLevel Low0.042***0.038***-0.010 (0.012)(0.011)(0.010) Middle0.072***0.044*-0.107*** (0.020)(0.021)(0.023) Advanced-0.114***-0.082***0.117*** (0.020)(0.020)(0.023) AP-0.048***-0.033**0.175*** (0.011)(0.013)(0.021) PanelA:LowIntensity Lowin0.088***0.054**-0.024 9thGrade(0.017)(0.016)(0.016) Lowin0.060***0.038**-0.037* 10thGrade(0.015)(0.014)(0.015) Lowin0.028*0.023-0.025* 11thGrade(0.013)(0.012)(0.011) Lowin0.046***0.024*-0.016 12thGrade(0.013)(0.011)(0.011) PanelB:MidIntensity Midin-0.102***-0.068***0.002 9thGrade(0.021)(0.019)(0.020) Midin-0.063**-0.050**-0.045 10thGrade(0.020)(0.019)(0.025) Midin0.066**0.021-0.079** 11thGrade(0.022)(0.021)(0.026) Midin0.053**0.029-0.037* 12thGrade(0.016)(0.015)(0.016) PanelC:AdvancedIntensity Advancedin-0.014-0.0010.023* 9thGrade(0.007)(0.008)(0.010) Advancedin-0.026*-0.020*0.087*** 10thGrade(0.010)(0.010)(0.019) Advancedin-0.097***-0.064***0.126*** 11thGrade(0.018)(0.018)(0.022) Advancedin-0.082***-0.048**0.120*** 12thGrade(0.020)(0.018)(0.024) PanelD:APCourse APin-0.0050.0030.072*** 11thGrade(0.005)(0.006)(0.014) APin-0.045***-0.033**0.153*** 12thGrade(0.011)(0.013)(0.021) Notes: inthistablearevariationsonthosereportedinTable ?? . Onlytheracecoefarereported.Schooledeffectsareincluded. atthe1%level.atthe5%level. atthe10%level. 117 Table3.B9EstimatedBlack-WhiteGapinTimingofHighest-Level CoefonCoefonCoefon BlackforHispanicforAsianfor 11thGrade Total0.0100.007-0.076** (0.022)(0.020)(0.023) NoMath0.0030.004-0.045* in12thGrade(0.020)(0.020)(0.022) LowerLevel0.0070.003-0.031* in12thGrade(0.011)(0.009)(0.013) 12thGrade Total-0.005-0.0140.093*** (0.022)(0.020)(0.024) NoMath0.0100.005-0.021 in11thGrade(0.010)(0.009)(0.011) LowerLevel-0.021-0.0310.066* in11thGrade(0.021)(0.019)(0.026) SameLevel0.0070.0120.047** in11thGrade(0.013)(0.012)(0.016) Notes: inthistablearevariationsonthosereportedinTable ?? . Onlytheracecoefarereported.Schooledeffectsareincluded. atthe1%level.atthe5%level. atthe10%level. 118 Table3.B10EstimatedBlack-WhiteGapinTimingofHighest-LevelinGrade12 CoefonCoefonCoefon BlackforHispanicforAsianfor PublicSchool Total-0.000-0.0100.112*** (0.026)(0.023)(0.028) NoMath0.0140.005-0.022 in11thGrade(0.012)(0.010)(0.013) LowerLevel-0.025-0.0380.091** in11thGrade(0.023)(0.022)(0.028) SameLevel0.0100.0230.043** in11thGrade(0.014)(0.014)(0.016) PrivateSchool Total-0.043-0.011-0.090 (0.080)(0.098)(0.065) NoMath-0.024-0.015-0.008 in11thGrade(0.024)(0.032)(0.029) LowerLevel0.014-0.056-0.210* in11thGrade(0.076)(0.094)(0.091) SameLevel-0.0330.0600.127 in11thGrade(0.055)(0.044)(0.093) CatholicSchool Total0.004-0.0190.068 (0.051)(0.042)(0.053) NoMath-0.0040.010-0.008 in11thGrade(0.016)(0.018)(0.015) LowerLevel0.0140.0190.027 in11thGrade(0.055)(0.039)(0.077) SameLevel-0.006-0.048*0.050 in11thGrade(0.033)(0.023)(0.057) Notes: inthistablearevariationsonthosereportedinTable ?? . Onlytheracecoefarereported.Schooledeffectsareincluded. atthe1%level.atthe5%level. atthe10%level. 119 Table3.B11EstimatedBlack-WhiteGapinGrade12Test CoefonCoefonCoefon BlackforHispanicforAsianfor Total-0.647**-0.2670.898*** (0.226)(0.198)(0.266) PanelA:ByCourseLevel LowLevel 11thGrade0.509-1.005-0.398 (1.389)(1.026)(1.526) 12thGrade1.1791.9771.272 (1.190)(1.153)(1.859) MidLevel 11thGrade-0.3610.1060.234 (0.304)(0.283)(0.405) 12thGrade-1.014-0.3090.312 (0.945)(0.854)(1.197) AdvancedLevel 11thGrade-1.704**-0.4621.426** (0.615)(0.502)(0.516) 12thGrade-1.116**-0.0511.381*** (0.374)(0.348)(0.399) PanelB:TimingofHighest-LevelAchieved In12thGrade Total-0.916**-0.2951.205** (0.308)(0.296)(0.367) NoMath-1.431-2.2470.036 in11thGrade(1.980)(2.341)(5.178) LowerLevel-0.800*0.0051.143** in11thGrade(0.381)(0.339)(0.430) SameLevel-1.583-0.7511.62 in11thGrade(1.565)(1.350)(1.482) In11thGrade Total-0.408-0.170.470 (0.437)(0.397)(0.550) NoMath-0.371-0.350.446 in12thGrade(0.494)(0.456)(0.590) LowerLevel-0.3580.093-1.156 in12thGrade(1.530)(1.507)(2.617) Notes: DependentvariableisstandardizedmathtestscoreinGrade12. Controlsaregender,race,parentaleducation,familyincome,andstandardized mathtestscorein10thgrade.Onlytheracecoefarereported. Schooledeffectsareincluded. atthe1%level.atthe5%level. atthe10%level. 120 APPENDIXC ADDITIONSFORCHAPTER3 121 C.Black-WhiteAchievementGap Table3.D5summarizesordinaryleastsquaresestimationresultsofracialmathscoregapinGrade 10andunconditionalblack-whiteachievementgapis8.61pointor0.90standarddeviationand addinggenderinformationdoesnotchangethegapntly.WhenfamilySESandincome areincluded,theblack-whitegapdecreasesby30%andHispanic-whitegapdecreasesby44%,and onestandarddeviationincreaseinfamilySESimprovesmathscoreby0.34standarddeviation. 20 Studentsfromfamilies,whoregularlyreceivemagazineandhavebothcomputer,andmorethan 50booksathome.havearound0.5standarddeviationscorehighercomparedtothosewithout magazine,computer,andmorethan50booksathome.Tocapturebiasinteacher'sperceptionsor interactionwithstudents,teacherracedummyisincluded,whichisequaltoonewhenteacherand studenthavethesamerace.Studentstaughtbymathteacherswiththesameracehavestatistically- higherscorebuttheeffectisrelativelysmall:0.07standarddeviation. 21 Additionofa seriesofcovariatestotheregressiondecreasestheblack-whitegapby42%andtheHispanic-white gapby62%whereastheAsian-whitegapenlarges.Schooledeffectisincludedincolumn6 toaccountforacrossschoolvariationsuchasschoolSES,racialcomposition,andteacherquality, butchangesintheblack-whitegaparenotstatisticallydistinguishablefromzero. Table3.D6presentsestimationresultsfor12thgraderstoexplorewhethertheracialgapin mathachievementischangedinthelasttwoyearsofhighschool.Theblack-whitemathscore gapissimilarinGrade12until10thgrademathscoreisadded.Estimatesincolumn4how variationinlearningbetweenGrade10and12accountsforchangesinmathscores.Coefon blackdummydropsbymorethan90%andtheeffectisaround0.04standarddeviation,implying thatthemajorityofthemathachievementgapinGrade12isexplainedbyprevioustestscores. 22 FamilySESandincomestillcontributestotheachievementgapoverthelasttwoyearsbutthe 20 Estimatesdonotchangewhenacombinationofparentaleducationandoccupationdummiesare usedinplaceoffamilySES. 21 Notethat85%ofwhitestudentshavewhiteteacherswhereas13%ofblackshaveblackteachers.6%ofHispanic andAsianstudentshaveteachersofthesamerace,andtheestimatesincolumn5mightover-representwhitestudents. 22 When9thgradeGPAisincludedtoestimatethescoregapfor10thgraders,thecoefslightlychangesfrom -4.975(column5inTable3.D5)to-4.661. 122 effectsarenotmeaningfullylarge.Whenschooledeffectandothercovariatesareincluded,the black-whitegapandtheHispanic-whitegapbecomestatisticallynot Table3.D7displaysthesensitivityofestimatedmathachievementgaps.Eachrowisestimated separatelyandonlycoefandcorrespondingstandarderrorsforeachracedummyarere- ported.Baselineestimatesrefertothoseincolumn5inTables3.D5and3.D6.Estimatesare robusttosampleweightandalternativetestmeasures.Next,thesampleisdividedintoseveral subgroups-gender,familySESquintile,familycomposition,andschoolsector.Maleminority studentsseemedtoperformbetterrelativetowhitesthandofemalesanditismostapparentamong Hispanics.TherelationshipbetweenfamilySESandtestscoregapismixedacrossrace.The black-whitegapdoesnotseemtorelatewithfamilySES,whereastheAsian-white gaptendstoenlargeforthehighestSESsubgroup.Familycompositionseemsrelatedtoachieve- mentgap;studentslivingwithbothparentshavesmallerscoregapthanthoselivingwithasingle mother,andthedifferenceislargestamongHispanicstudents. 23 Blackandhispanicchildrenliving withasinglemotherhavethelargestscoregaprelativetowhites.Whendividedbyschoolsectors toaccountforthefactthatcourse-takingrequirementandoptionsvarybysectors,the achievementgapislargestamongpublicschoolsandsmallestamongprivateschools. Ifthereareheterogeneousresponsesinracialgapstocovariatesbyeachracialgroup,full- sampleanalysismightunderstateoroverstatetheachievementgap.Table3.D8summarizescoef cientestimatesthatreplicatecolumn5inTable3.D5estimatedseparatelybyeachracialsubgroup. ResponsivenesstogenderdoesnotseemtodifferbyracebutthatoffamilySEStellsdifferent story;onestandarddeviationimprovementinfamilySEShastheleastimpactontestscorein- creaseforblackstudents.Ontheotherhand,blackstudents'mathscoreismoreresponsivetoan increaseinfamilyincomethanwhitepeers'.Thusifonetriestoanalyzetheeffectoffamilyback- groundimprovement,baselineresultsarelikelytounderstateblack-whitetestgap.Interestingly blackstudentstaughtbyblackmathteachersonaveragehavelowertestscoresthantheirpeers 23 Amongwhites,64%livewithbothparents,whereas37%ofblackstudentsdo.Notably38%ofblackstudents and17%ofHispanicslivewithsinglemother. 123 taughtbywhite,Hispanic,orAsianmathteachers. 24 Table3.D9showsthesameanalysisfor12thgraders.Thecolumnisthereplicationof column5inTable3.D6.Blackstudentstheleastbyonestandarddeviationimprovement infamilySES,andtheeffectenduresforthelasttwo-yearsofhighschool.ThusiffamilySESis improvedbythesamerate,unconditionaltestscoregapbetweenblackandwhitestudentswouldbe largerinGrade12thaninGrade10.Resultsshowthatblackstudentstaughtbyblackmathteachers increasemathscoreby1pointbetweenGrade10and12,whichissomewhatdifferentfromresults inTable3.D8.Butthemechanismoftheeffectofteachers'raceonstudents'achievementsremain forfutureresearchuntilfurtherinformationonmathteachers(whattheyteachandwhenthey teach)becomeaccessible. 24 Sinceeachstudenthasoneentryformathteacher'srace,itisnotcertainwhentheteachertaughtwhichmath course. 124 APPENDIXD SUPPLEMENTALTABLESFORCHAPTER3 125 Table3.D1HighestLevelofMathbyRaceandGrade VariableFullSampleWhiteBlackHispanicAsian HighestLevelofMath: 9thGrade3.8453.8633.7503.7304.038 10thGrade4.2314.2513.9964.0624.644 11thGrade5.1675.2174.8474.8755.683 12thGrade6.0556.1855.3005.5076.748 AverageofLevelofMath: 9thGrade3.8143.8383.7123.6943.983 10thGrade4.1924.2133.9524.0274.584 11thGrade4.1924.2133.9524.0274.584 12thGrade5.1075.1694.7464.8125.604 HighestLevelofMath-Low: 9thGrade0.1880.1770.2290.2350.136 10thGrade0.1140.1020.1490.1500.070 11thGrade0.0700.0640.0820.0970.047 12thGrade0.0600.0530.0970.0780.040 HighestLevelofMath-Middle: 9thGrade0.6960.7240.6250.6300.711 10thGrade0.7330.7670.6740.6800.695 11thGrade0.5020.4950.5770.5290.415 12thGrade0.1330.1140.1870.1850.111 HighestLevelofMath-Advanced: 9thGrade0.0260.0240.0250.0200.052 10thGrade0.0640.0610.0270.0350.169 11thGrade0.2840.3010.1820.2040.414 12thGrade0.4190.4530.3070.2890.543 Notes: Entriesaremeansofstudent-leveldatawhoarenotmissingmathscores,race,andSES variable. 126 Table3.D2MostCommonCourses MostCommonCourseMostCommonLevel CourseTitleCourseLevelPercentCourseLevelPercent FullSample GeometryMiddle19.97Middle42.59 Algebra2Middle217.83Middle219.48 Algebra1Middle17.73Advanced19.52 Analysis,IntroductoryAdvanced28.44Low8.62 AlgebraandTrigonometryAdvanced13Advanced28.44 White GeometryMiddle20.37Middle42.7 Algebra2Middle218.43Middle219.99 Algebra1Middle17.5Advanced110.31 Analysis,IntroductoryAdvanced28.72Advanced28.72 AlgebraandTrigonometryAdvanced13.15Low7.69 Black GeometryMiddle21.28Middle44.78 Algebra1Middle19.67Middle218.81 Algebra2Middle217.34Low11.49 Analysis,IntroductoryAdvanced25.05Advanced19.26 AlgebraandTrigonometryAdvanced13.91Non8.48 Hispanic Algebra1Middle20.7Middle45.11 GeometryMiddle20.27Middle217.76 Algebra2Middle216.48Low12.45 Analysis,IntroductoryAdvanced27.48Advanced27.48 Pre-AlgebraLow3.92Non7.41 Asian Algebra2Middle217.03Middle36.72 GeometryMiddle16.27Middle219.45 Algebra1Middle13.33Advanced312.97 Analysis,IntroductoryAdvanced212.19Advanced211.99 APCalculusAdvanced36.55Advanced18.88 Notes: Entriesaremeansofstudent-leveldataofwhoarenotmissingmathscores,race, andSESvariable. 127 Table3.D3SummaryStatisticsIncludingDropoutbyRace VariableFullSampleWhiteBlackHispanicAsian Credit: TotalCredit3.2603.3413.1772.9493.408 Averageperyear0.7030.7230.7520.6330.627 CourseLevel: HighestLevelofMath5.6565.7675.2225.1776.343 Averageperyear4.4954.5674.1764.2024.978 LevelofFirstCourse3.8103.8443.7043.6714.002 HighestLevelofMath: LowLevel0.0630.0520.0860.0940.034 MiddleLevel0.4370.4110.5170.5470.330 AdvancedLevel0.5000.5370.3970.3590.635 AP0.1170.1120.0430.0650.319 TimingofAchievingtheHighestLevelofMath: 10thGrade0.1270.1270.1100.1380.102 11thGrade0.3190.3110.3670.3700.244 12thGrade0.5090.5230.4530.4360.626 MissingMathClassin: 9thGrade0.0970.0790.1300.1290.110 10thGrade0.0980.0770.1610.1480.075 11thGrade0.1700.1590.1960.2070.138 12thGrade0.4120.4000.4390.4830.324 OtherControls: Public0.7560.7000.8570.8150.885 Private0.0950.1240.0410.0360.063 Catholic0.1490.1760.1020.1500.052 FRLSchool2.1241.7483.2552.9701.867 ParentEducation0.4330.4700.3510.2680.539 FamilyIncome9.2069.7477.9838.2868.707 Dropout0.0440.0320.0620.0740.030 On-timeGraduation0.9560.9680.9380.9260.970 TestScore: 10thGrade51.71553.87545.45346.88653.245 12thGrade48.90651.12141.85243.19653.397 Notes: Entriesaremeansofstudent-leveldataonwhoarenotmissingmathscores,race,andSES variable.Thehighestlevelofmathisdividedintothreegroups,Lowforlevels2and3,Middlefor levels4and5,andAdvancedforlevels6,7,and8.Freereducedlunch(FRL)schoolisacategorical variablerangingfromonetosevencorrespondingtoeachFRLratio(1for0-5%;2for6-10%; 3for11-20%;4for21-30%;5for31-50%;6for51-75%;and7for76-100%.) Parentaleducationiscodedoneifthehighesteducationlevelishigherthan4-yearcollegeandzero otherwise.Familyincomeisrecodedbytakingthemidpointofeachincomecategoryand logtransformed. 128 Table3.D4EstimatedBlack-WhiteGapinTimingofHighest-LevelinGrade11 CoefCoefCoef onBlackforonHispanicforonAsianfor PublicSchool Total0.006-0.001-0.087** (0.025)(0.024)(0.027) NoMath-0.005-0.004-0.051* in12thGrade(0.023)(0.024)(0.026) LowerLevel0.0110.003-0.036* in12thGrade(0.013)(0.011)(0.014) PrivateSchool Total0.0080.0470.028 (0.078)(0.100)(0.067) NoMath0.032-0.0110.015 in12thGrade(0.061)(0.088)(0.060) LowerLevel-0.0230.0580.013 in12thGrade(0.042)(0.037)(0.050) CatholicSchool Total0.0190.030-0.087 (0.051)(0.036)(0.046) NoMath0.0280.041-0.069 in12thGrade(0.048)(0.041)(0.051) LowerLevel-0.009-0.011-0.017 in12thGrade(0.016)(0.019)(0.030) Notes: inthistablearevariationsonthosereportedinTable ?? . Onlytheracecoefarereported.Schooledeffectsareincluded. atthe1%level.atthe5%level. atthe10%level. 129 Table3.D5EstimatedBlack-WhiteMathScoreGapinGrade10 Variables(1)(2)(3)(4)(5)(6) Black-8.612***-8.560***-6.051***-5.390***-4.975***-4.873*** (0.289)(0.288)(0.275)(0.299)(0.353)(0.445) Hispanic-6.683***-6.662***-3.751***-2.988***-2.529***-2.183*** (0.273)(0.272)(0.261)(0.282)(0.349)(0.463) Asian0.706**0.707**2.080***2.413***2.874***1.897*** (0.309)(0.308)(0.288)(0.304)(0.368)(0.503) Female-1.412***-1.144***-1.412***-1.413***-1.485*** (0.178)(0.165)(0.172)(0.172)(0.189) SES2.965***2.696***2.698***2.133*** (0.118)(0.126)(0.126)(0.148) FamilyIncome0.363***0.262***0.262***0.202*** (0.051)(0.055)(0.055)(0.061) Magazine0.763***0.754***0.628** (0.221)(0.221)(0.270) Book1.695***1.688***1.440*** (0.261)(0.261)(0.278) Computer2.240***2.231***2.023*** (0.327)(0.327)(0.363) TeacherRace0.584**0.562 (0.263)(0.378) SchoolFENNNNNY R 2 0.1190.1240.2510.2500.2500.374 Numberofobservations102801028010280911091109110 Notes: Dependentvariableisstandardizedmathscoreinunweightedsample.Non-Hispanicwhitesarethe omittedracecategory,soallracecoefaregapsrelativetowhites.Theunitofobservationisa student.Standarderrorsareinparentheses.Magazineisequaltooneiffamilyregularlyreceivedmagazineand zerootherwise.Bookisequaltooneiffamilyhasmorethan50books.Computerisequaltooneiffamily hasacomputer.Teacherraceisequaltooneifteacherandstudenthavethesamerace. atthe1%level.atthe5%level.atthe10%level. 130 Table3.D6EstimatedBlack-WhiteMathScoreGapinGrade12 Variables(1)(2)(3)(4)(5)(6) Black-8.443***-8.381***-5.600***-0.351**-0.471**-0.256 (0.300)(0.299)(0.283)(0.156)(0.199)(0.274) Hispanic-6.416***-6.391***-3.181***0.0730.15-0.042 (0.284)(0.283)(0.269)(0.146)(0.196)(0.229) Asian1.623***1.625***3.151***1.346***1.360***1.198*** (0.322)(0.321)(0.297)(0.160)(0.206)(0.256) Female-1.691***-1.395***-0.403***-0.514***-0.547*** (0.185)(0.169)(0.091)(0.096)(0.104) SES3.226***0.653***0.583***0.368*** (0.122)(0.067)(0.072)(0.097) FamilyIncome0.423***0.108***0.107***0.067* (0.052)(0.028)(0.031)(0.037) PreviousTest0.868***0.860***0.850*** (0.005)(0.006)(0.009) Magazine0.0710.064 (0.123)(0.134) Book0.604***0.563*** (0.146)(0.164) Computer0.1680.246 (0.183)(0.197) TeacherRace-0.100-0.044 (0.147)(0.168) SchoolFENNNNYY R 2 0.1100.1170.2610.7860.7810.807 Numberofobservations1028010280102801028091109110 Notes: Dependentvariableisstandardizedmathscoreinunweightedsample.Non-Hispanicwhitesarethe omittedracecategory,soallracecoefaregapsrelativetowhites.Theunitofobservationisa student.Standarderrorsareinparentheses.Previoustestreferstomathstandardizedscorein10thgrade. Magazineisequaltooneiffamilyregularlyreceivedmagazineandzerootherwise.Bookisequaltoone iffamilyhasmorethan50books.Computerisequaltooneiffamilyhasacomputer.Teacherraceisequal tooneifteacherandstudenthavethesamerace. atthe1%level.atthe5%level.atthe10%level. 131 Table3.D7SensitivityAnalysisofMathAchievementGap CoefonBlackforCoefonHispanicforCoefonAsianfor 10th12th10th12th10th12th Baseline-4.975***-0.471**-2.529***0.152.874***1.360*** (0.353)-0.199(0.349)-0.196(0.368)-0.206 Weighted-5.109***-0.559***-2.546***0.0752.984***1.526*** (0.338)(0.188)(0.339)(0.186)(0.482)(0.265) Othertestscoremeasures: MathIRTestimatednumber-6.300***-0.576***-3.240***-0.1613.141***-0.049 rightfor2002scorers(0.425)(0.148)(0.420)-0.145(0.442)(0.153) ByGender: Males-4.565***-0.758**-1.521***-0.3633.417***0.920*** (0.553)(0.311)(0.533)(0.298)(0.554)(0.311) Females-5.389***-0.219-3.425***0.611**2.357***1.763*** (0.455)(0.259)(0.459)(0.259)(0.489)(0.275) BySESquintile: Top-5.198***-0.886*-2.202***-0.2653.451***0.196 (0.837)(0.475)(0.801)(0.452)(0.686)(0.389) Second-4.840***-1.023**-1.910**0.1192.843***1.505*** (0.739)(0.413)(0.745)(0.413)(0.745)(0.413) Third-5.495***0.182-2.942***-0.2642.259***2.178*** (0.670)(0.372)(0.695)(0.382)(0.817)(0.448) Bottom-4.859***-0.218-3.586***0.689*1.822**1.666*** (0.671)(0.385)(0.653)(0.372)(0.740)(0.420) ByFamilyComposition: LivewithbothParents-4.756***-0.452-1.638***0.2233.227***1.442*** (0.515)(0.291)(0.442)(0.248)(0.441)(0.248) LivewithOneGuardianand-4.477***-0.433-3.536***0.0360.4350.276 eitherwithFatherorMother(0.923)(0.488)(0.869)(0.458)(1.050)(0.550) LivewithSingleMother-5.371***-1.060**-3.968***-0.0623.253***1.590*** (0.710)(0.424)(0.859)(0.507)(1.048)(0.616) BySchoolSector: Public-4.981***-0.378*-2.579***0.1783.210***1.599*** (0.399)(0.223)(0.406)(0.225)(0.415)(0.231) Private-2.862*0.399-1.9850.2641.7211.361* (1.489)(0.939)(1.420)(0.894)(1.310)(0.825) Catholic-4.912***-1.164**-2.054**-0.1771.3450.166 (0.956)(0.517)(0.820)(0.441)(1.193)(0.640) Notes: inthistablearevariationsonthosereportedincolumn5inTableB.1andB.2.Onlytheracecoef arereported.atthe1%level.atthe5%level.atthe10%level. 132 Table3.D8EstimatedBlack-WhiteMathScoreGapbyRaceinGrade10 VariablesFull-sampleWhiteBlackHispanicAsian Black-4.975*** (0.353) Hispanic-2.529*** (0.349) Asian2.874*** (0.368) Female-1.413***-1.352***-1.123**-1.914***-1.463** (0.172)(0.210)(0.493)(0.525)(0.648) SES2.698***2.798***1.844***2.505***2.679*** (0.126)(0.162)(0.371)(0.349)(0.408) FamilyIncome0.262***0.218***0.474***0.348**0.224 (0.055)(0.074)(0.133)(0.143)(0.179) Magazine0.754***1.211***0.627-0.0170.028 (0.221)(0.297)(0.572)(0.573)(0.704) Book1.688***1.972***1.276**0.7272.503*** (0.261)(0.366)(0.598)(0.620)(0.889) Computer2.231***2.725***0.7752.726***5.245*** (0.327)(0.497)(0.633)(0.712)(1.633) TeacherRace0.584**1.231***-2.197***-0.210-2.314* (0.263)(0.295)(0.715)(1.096)(1.380) R 2 0.2500.1580.1680.1810.184 NumberofObservations911057809301090860 Notes: ThedependentvariableisstandardizedmathscoreinGrade10.Thecolumn replicatescolumn5inTable3.B3.Othercolumnsreportestimateswithinarace. atthe1%level.atthe5%level.atthe10%level. 133 Table3.D9EstimatedBlack-WhiteMathScoreGapbyRaceinGrade12 VariablesFull-sampleWhiteBlackHispanicAsian Black-0.471** (0.199) Hispanic0.150 (0.196) Asian1.360*** (0.206) Female-0.514***-0.638***-0.538*-0.128-0.162 (0.096)(0.118)(0.278)(0.291)(0.361) SES0.583***0.661***0.551***0.3060.437* (0.072)(0.093)(0.211)(0.197)(0.232) FamilyIncome0.107***0.089**0.132*0.220***0.100 (0.031)(0.042)(0.075)(0.079)(0.099) PreviousTest0.860***0.871***0.857***0.831***0.849*** (0.006)(0.007)(0.019)(0.017)(0.019) Magazine0.0710.356**-0.561*0.171(0.346) (0.123)(0.167)(0.322)(0.316)(0.391) Book0.604***0.686***0.5140.4141.061** (0.146)(0.206)(0.337)(0.342)(0.495) Computer0.168-0.1320.3180.3010.434 (0.183)(0.279)(0.356)(0.396)(0.912) TeacherRace-0.100-0.287*1.016**0.063-0.460 -0.147(0.166)(0.404)(0.605)(0.767) R 2 0.7810.7590.7560.7550.759 NumberofObservations911057809301090860 Notes: ThedependentvariableisstandardizedmathscoreinGrade12.Thecolumn replicatescolumn5inTableB.2.Othercolumnsreportestimateswithinarace. atthe1%level.atthe5%level.atthe10%level. 134 REFERENCES 135 REFERENCES Adelman,Clifford. 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