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School Entry Educational Attainment and

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Niveau: Supérieur, Doctorat, Bac+8
School Entry, Educational Attainment and Quarter of Birth: A Cautionary Tale of LATE Rashmi Baruayand Kevin Langz August 2011 Abstract Partly in response to increased testing and accountability, states and dis- tricts have been raising the minimum school entry age, but existing studies show mixed results regarding the e?ects of entry age. These studies may be severely biased because they violate the monotonicity assumption needed for LATE. We propose an instrument not subject to this bias and show no e?ect on the educational attainment of children born in the fourth quarter of mov- ing from a December 31 to an earlier cuto?. We then estimate a model that reconciles the di?erent IV estimates including ours. We ?nd that one standard instrument is badly biased but that the other diverges from ours because it estimates a di?erent LATE. We also ?nd that an early entry age cuto? that is applied loosely (as in the 1950s) raises educational attainment but one that is strictly enforced lowers it. We are grateful to Josh Angrist, Garry Barrett, Sandy Black, Jim Heckman, Caroline Hoxby, Claudia Olivetti, Daniele Paserman and participants in seminars at the Australian National Uni- veristy, Boston University, University of Chicago, MIT, UC Irvine, NYU, Pomona College, Singapore Management University, Tilburg University, the Tinbergen Institute, the University of Wollongong, SOLE and Econometric Society for helpful comments and suggestions.

  • school entry

  • studies ?nd

  • educational attainment

  • mum age

  • ?nding no

  • reduces human capital

  • no child

  • age


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SchoolEntry,EducationalAttainmentandQuarterofBirth:ACautionaryTaleofLATERashmiBaruaandKevinLangAugust2011AbstractPartlyinresponsetoincreasedtestingandaccountability,statesanddis-trictshavebeenraisingtheminimumschoolentryage,butexistingstudiesshowmixedresultsregardingtheeffectsofentryage.ThesestudiesmaybeseverelybiasedbecausetheyviolatethemonotonicityassumptionneededforLATE.Weproposeaninstrumentnotsubjecttothisbiasandshownoeffectontheeducationalattainmentofchildrenborninthefourthquarterofmov-ingfromaDecember31toanearliercutoff.WethenestimateamodelthatreconcilesthedifferentIVestimatesincludingours.WefindthatonestandardinstrumentisbadlybiasedbutthattheotherdivergesfromoursbecauseitestimatesadifferentLATE.Wealsofindthatanearlyentryagecutoffthatisappliedloosely(asinthe1950s)raiseseducationalattainmentbutonethatisstrictlyenforcedlowersit.WearegratefultoJoshAngrist,GarryBarrett,SandyBlack,JimHeckman,CarolineHoxby,ClaudiaOlivetti,DanielePasermanandparticipantsinseminarsattheAustralianNationalUni-veristy,BostonUniversity,UniversityofChicago,MIT,UCIrvine,NYU,PomonaCollege,SingaporeManagementUniversity,TilburgUniversity,theTinbergenInstitute,theUniversityofWollongong,SOLEandEconometricSocietyforhelpfulcommentsandsuggestions.Theusualcaveatapplies.BaruaacknowledgesfundingunderNSF-AERAgrantREC-0634035.LangacknowledgesfundingfromNICHDundergrantnumberR03HD056056-01andNSFundergrantnumberSEC-0339149.Theopinionsexpressedherearethoseoftheauthorsandnotnecessarilythoseofthefundingagen-.seicrashmibarua@smu.edu.sg,SchoolofEconomics,SingaporeManagementUniversitylang@bu.edu,DepartmentofEconomics,BostonUniversityandNBER1
1IntroductionOverthelastfourdecadesmanystatesandschooldistrictshaveincreasedthemini-mumageatwhichchildrenmayenterkindergarten.Inthe1960schildrenfrequentlyenteredkindergartenwhentheywereconsiderablylessthanfiveyearsold(orfirstgradewhentheywerelessthansixyearsold).Thiswasformallypermittedinmanystateswhereas,inotherstates,itwasrelativelyeasytogetaroundtherules.Today,thirty-eightstateshavecutoffdatesrequiringchildrenenteringkindergartentobefiveyearsoldbeforeOctober16oftheyearinwhichtheyenterkindergarten,andsomeoftheremainingstateshavedistrictsthatapplyastricterstandard.Whetherdelayedentryimprovesorworsenseducationoutcomesiscontroversial.Manyrecentstudiesinbotheducationandeconomicshavebeendevotedtoobtain-ingconsistentestimatesoftheeffectsofschoolentryageonshortrunandlongrunoutcomes.AngristandKrueger(1992)addressthepotentialendogeneityofentryagebyusingquarterofbirthasaninstrumentforentryage.They(AngristandKrueger,1991)showthathistoricallyindividualsborninthefirstquarterstartedschoollaterthanthoseborninthefourthquarter,completedlesseducationandearnedlessthanthosebornintherestoftheyear.1Criticsofthisapproacharguethatquarterofbirthmaybedirectlyrelatedtostudentoutcomesorparentalsocioeconomicstatus.2BucklesandHungerman(2008)provideevidencethatchildrenbornatdifferenttimesintheyearareconceivedbywomenwithdifferentsocioeconomiccharacteristics.Toaddressthisissue,severalresearchershaveexploitedthevariationinstatelawsgov-erningentryage(or,the“legalentryage”)toidentifyitseffectontestscores,wages,educationalattainmentandotheroutcomes.3However,sinceentryagedependsonbothstatelawanddateofbirth,thepotentialendogeneityofdateofbirthremainsproblematicforthisapproach.Theaimofthispaperisthreefold.First,weaddresscertainunder-appreciatedissuesintheinstrumentalvariableliterature.ImbensandAngrist(1994),AngristandImbens(1995)andAngrist,ImbensandRubin(1996)showthatwithheterogeneoustreatmenteffects,undercertainconditions,IVidentifiestheLocalAverageTreatment1SeealsoMayerandKnutson,1999andCahanandCohen,1989.2Bound,JaegerandBaker,1995;BoundandJaeger,2000.3AllenandBarnsley,1993;BedardandDhuey,2006,2008;CascioandLewis,2006;Datar,2005;DobkinandFerreira,2010;ElderandLubotsky,2009;FertigandKluve,2005;FredrikssonandOckert,2006;PuhaniandWeber,2007.2
Effect(LATE).Onecondition,termed“monotonicity,”generallytreatedasanunim-portantregularitycondition,requiresthatwhiletheinstrumentmayhavenoeffectonsomeindividuals,allofthosewhoareaffectedshouldbeaffectedunidirectionally.Wearguethatbothstandardinstruments,quarterofbirthandlegalentryage,maypro-videinconsistentestimatesofLATEbecausetheyviolatemonotonicity.4Therefore,weproposeaninstrumentthatsatisfiesmonotonicityandgivesconsistentestimatesoftheLATEofschoolentryageoneducationalattainment.Ourtwo-sampletwo-stageleastsquares(TS2SLS)results,consistentwithAngristandKrueger,showalargenegativeeffectofschoolentryageoneducationalattainmentwhentheIVisquarterofbirth.Usingthe“legalentryage”instrumentyieldsasmallerbutstillsubstantialadverseeffectthoughitfallsshortofstatisticalsignificanceatconventionallevels.Fi-nally,whenweusetheconsistentestimatorthatmeetsthemonotonicityrequirement,theeffectofschoolentryageoneducationalattainmentisveryclosetozero.ComparingthedifferentIVestimatesdoesnottelluswhethertheydivergebecausethetraditionalestimatorsareinconsistentorbecausetheyaremeasuringdifferentLATEs.AsecondaimofthispaperistoaddressthisissueandtoreconcilethedifferentIVestimatesincludingours.Toachievethis,wedevelopasimplemodelofschoolentryandeducationalattainmentanduseindirectinferencetoestimatetheparametersofthemodel.WethensimulateourmodeltocomparetheIVestimateswiththeirrespectiveLATEs.“Quarterofbirth”provestoberobusttothefailureofmonotonicitybutlegalentryagedoesnot.Third,weareinterestedinthebroaderquestionoftheoptimalageatwhichtostartschooland,inparticular,optimalpolicyregardingschoolentryage.Legislation,suchastheNoChildLeftBehind(NCLB)actof2001,hasputgreatpressureonschoolstoimprovestudentperformanceontests.Somestateshaverespondedbyraisingtheschoolentryage(DemingandDynarski,2008;Stipek,2006).Giventhehistoricalnatureofourdata,theinstrumentalvariablesapproachcapturestheeffectofdelayingschoolentryasitwaspracticedinthe1950s.Butschoolentryagelawsarenowenforcedmuchmorestrictly.Thus,weconductapolicyexperimentusingsimulateddatatostudytheeffectofhavingstrictentryagerules(thecurrentpractice)onaverageeducationalattainment.Weshowthattheentryagethatmaximizesachild’seventualeducationalattainmentvariesconsiderablyfromaboutage4.5yearstowell4Aswediscussinsomedetaillater,dependingonthesizeofthebandaroundthediscontinuity,similarconcernsmayariseforanalysesbasedonregressiondiscontinuity.3