how decentralizing school finance may narrow … · joonho lee and bruce fuller june 2017 how...

UNIVERSITYOFCALIFORNIA,BERKELEYInstituteofHumanDevelopmentWorkingPaperJoonHoLeeandBruceFullerJune2017

HOW DECENTRALIZING SCHOOL FINANCE MAY NARROW ACHIEVEMENT GAPS – UnevenProgressinCaliforniaafter$41Billion

DecentralizingFinance,OrganizationalChangeandAchievement–2

Summary

Severalgovernorshavemovedtodistributeschooldollarsbasedonpupilweights,recognizingthatdisadvantagedstudentsrequirefreshresourcestoreachstateproficiencybars.Thispolicystrategy,afterwinningbroadsupportinCalifornia,balancesadequatedollarsforallstudentswiththeadditionalcostofhoistingchildrenheldbackbyfamilypovertyorlimitedEnglish.California’srenditionofweighted-pupilfunding,approvedin2013,providesconcentrationgrantstodistrictsinwhichatleast55percentofenrollmentconsistsofdisadvantagedchildren.Localdistrictsenjoydiscretionoverwhetherthenewfundsgeneratedbythesechildren–equaling$41billiontodatewhensupplementalgrantsareincluded–gotoschoolsthatservethem.WefindthatschoolsindistrictsreceivingconcentrationgrantsduringtheinitialtwoyearsofLocalControlFundingdidengageinorganizationalchangethatparallelsgainsinpupilachievement,comparedwithschoolsinalmostidenticaldistrictsnotreceivingconcentrationgrants.ThesebenefitswerelargelyexperiencedbyLatinostudentsandnotbyothergroupsatsignificantlevels.Weexploitaregression-discontinuitydesign,capturingthislargenaturalexperimentandallowingforstrongercausalinferences.

SpecialthankstoSophieFanelli,MaryLouFulton,andPeterRiverawhohavegenerouslysupportedourworkthroughtheCaliforniaCommunityFoundation,CaliforniaEndowment,andtheStuartFoundation.GregDuncan,BettyMalen,LarryPicus,andJesseRothsteinofferedwonderfullyhelpfulcommentsonearlierdrafts.RyanAndersonandEdgarCabralansweredmanyquestionabouttheinnerworkingsofthefundingformula.SophiaRabe-Hesketh,ourgenerouscolleagueatBerkeley,contributedtothisanalysis.EarlierpiecesofthispaperwerepresentedinBerkeley,Sacramento,andSanAntonioattheAmericanEducationalResearchAssociation.ThanksgotoDavidPlankandPolicyAnalysisforCaliforniaEducationforfacilitatingdiscussionswithpolicythinkers.

HowDecentralizingSchoolFinanceMayNarrowAchievementGaps–UnevenProgressinCaliforniaafter$41Billion


HowDecentralizingSchoolFinanceMayNarrowAchievementGaps–UnevenProgressinCaliforniaafter$41Billion

Statepolicymakershaveturnedtoweightedpupilformulae,goingbackfourdecades,toadvancesufficientandequitablefundingforpublicschools.Manystateshadmovedawayfromrelianceonpropertytaxtofinanceschoolsbythe1980sinthewakeofCalifornia’sSerranodecisionandsimilarcases.Thislitigationhadrevealedgrossdisparitiesinperpupilspendingamongdistricts.Toequalizestatesupportbetweenrichandpoordistricts,ortobetterservespecificgroups,moststatescentralizedfunding,thenregulatedabevyof“categoricalaid”programsfromtheirstatecapital.Thisreformagendadramaticallynarroweddisparitiesinperpupilspendingamonglocaldistricts,whethertheyenjoyedampletaxbasesornot(Wirt&Kirst,1972;Odden&Picus,2014).

Butasgovernorsandlegislaturesputinplaceaggressiveschoolaccountabilityregimes

throughthe1990s–expectingallstudentstoreachrigorousproficiencystandards–thedifferentialcostofliftinglow-achievingstudentscameintofocus.Severedeclinesinschoolspending,especiallyinthewakeoftheGreatRecession,alsopromptedtheadditionalquestionofwhetherlocalschoolswereadequatelyfunded,andthenwhetherallstudentsenjoyedawell-resourcedopportunitytolearn

Weighted-pupilfunding(WPF)hasgainedappealamongavarietyofpolicyactivists,under

whichstudentsfromdisadvantagedbackgroundsareassignedalargerweightinthestatefundingformula.Thisresultsinadditionaldollarsfordistricts(notnecessarilyschools)thatservehigherconcentrationsoftheseyoungsters.Basegrantstodistricts,whereallpupilsareweightedequally,alongwithsupplementalgrantsweightedforpoorstudents,servetobalancethetandempolicyaimsofadequacyandequity(Augenblick,Myers,&Anderson,1997;Leppert&Routh,1980).SeveralstateshadcreatedWPFfinancestructuresbythe1990s,includingFlorida,Oklahoma,andTexas(King,1983;Berne&Stiefel,1979).

Long-termdatasuggestthatpro-equityfinancereformsoverallhavecontributedtogainsin

studentachievement,evenliftingtheperformanceofpoorchildren(Jackson,Johnson,&Persico,2015;Lafortune,Rothstein,&Schanzenbach,2016).Theefficiencywithwhichequityreformshaveraisedachievementornarroweddisparitiesremainsakeyquestion(Hanushek&Woessmann,2017).NordoweunderstandwhetherWPFstrategies–bankingondecentralizedgovernance–leadtoorganizationalchangesinsideschoolsthatstrengthenpupilengagementandlearning.AdvocatesoftenremainsatisfiedwiththeredistributiveeffectsofWPFreforms,whethertheyalterschoolsinwaysthatelevatelearning,ornot.

WefocusononeelementofCalifornia’srenditionofWPFreform,whatGov.JerryBrown

cametocalltheLocalControlFunding(LCF)Formula.Approvedinthesummerof2013,itrecasthowlocaldistrictsweretobefunded,kicking-injusttwomonthslater.Stateaidtiedtoweightedpupils–thosefrompoorornon-Englishspeakingfamilies,andthoseinfostercare–grewby$41billionduringtheinitialfouryearsofimplementation(California,2016).Thispaper


estimatestheextenttowhichoneportionofthefundingapparatus–about$3.3billioninannualconcentrationsgrants–areassociatedwithschool-levelchangesthatmayshapestudentlearning,alongwithactualdifferencesinpupiltestscores,comparedwithalmostidenticaldistrictsthatdidnotenjoythisextrafunding.

UndertheCaliforniareform,thestateawardsconcentrationgrantstolocaldistrictswhen

morethan55%oftheirenrollmentsconsistofpupilsintheweightedcategories(poor,Englishlearners,orkidsinfostercare).Weexploitthisdiscretecutpointtoestimatechangesinschoolorganizationsand,inturn,pupilachievementlevelsindistrictsjustabovethe55%thresholdandthosejustbelowbutotherwisealmostidenticalintheirpupilcomposition,whichcouldconfoundthediscreteinfluenceofreceivingthisextrafunding.Notethattheadditionalfundingbecomessubstantialonlyasadistrict’senrollmentreflectsmanymoredisadvantagedstudentsabovethe55%line.

Inshort,wefindthatdistrictsreceivingconcentrationgrants,duringtheinitialtwoyearsof

LCFimplementationassignedsignificantlyfewerinstructionalperiodstoteachersandprovidedmoreadvancedcoursesatthehighschoollevel,comparedwithdistrictsjustbelowthecutoffforreceivingthesegrants.Thosewinningtheextrafundingdidnotmovetowardsmallerclassesonaverage.Studentperformanceofpupils,grades3-8,alsorangedhigherwhenattendingschoolsindistrictsthatreceivedconcentrationgrants.ThesebenefitswereexperiencedbyLatinostudents,butnotbyothergroupsatstatisticallysignificantlevels.Futureworkwillformallyassesstheextenttowhichtheseandotherschool-levelorganizationalchangesmediateobservedgainsinachievement.

AHazyTheoryofOrganizationalChange

WhytheRiseofWeighted-PupilFunding?

AffectionforWPFstrategiesstemsfromtheconfluenceofthreepolicydevelopments.First,there’stherecognitionbypolicymakersthat–aftersettingdemandinglearningstandardsorproficiencybars–itwillcostmoretoliftmanypoorchildrenoverthesehurdles.Childrenmaybedisadvantagedbyfamilypoverty,language,orunstablehomessituations.Growingupinneighborhoodswithconcentratedpovertymayconstrainthecapacityofchildrentoengageandgrowwithinclassrooms(Bryk,Sebring,Kerbow,Allensworth,&Easton,2010).“Becausenotallstudentscometoschoolwiththesameindividual,family,orneighborhoodadvantages,someneedmoreresourcesthanotherstomeetagivenachievementstandard,”asarguedbyinitialdesignersofCalifornia’sLCFreform(Bersin,Kirst,&Liu,2008:5).

Second,theaccretionofcentrallyregulatedcategoricalaidfellintodisfavorbythelate

1990s.Californiaofficials,forinstance,monitoredover65separatefundingstreams,mostrequiringbureaucraticoversightatstateanddistrictlevels.Onesurveyofschoolprincipalsdetailedthesubstantialtimespentsimplycompletingbudgetsandforms,tryingtokeeppacewithdisparateregulationstiedtomultiplefundingstreams(Fuller,Loeb,Arshan,Chen,&Yi,2007).InCalifornia,Gov.Schwarzeneggerpushedthroughlegislationin2009toconsolidate


manyofthestate’scategoricalprograms,amovewelcomedbylocalschoolboardsandunionleaders(placingmoredollarsonthebargainingtable),whileworryingequityadvocateswhofeareddiminishedaccountabilityoverhowtargetedfundswouldbespentlocally(Fuller,Marsh,Stetcher,&Timar,2011).Theoriginalargumentforstate-runcategoricalaidwasthatdollarsforpoorchildrenmightotherwisegotoschoolssituatedinpoliticallystrongercommunities.

Theconsolidationofcategoricalaidintoblockgrantsmirrorsathirdpolicyshiftthat’s

gainedmomentumoverthepasthalf-century:delegatinggreaterauthoritytoschoolprincipalsoverbudgetandpersonnel.Risingdistrustofeducationbureaucracies,alongwithfaithinschool-levelcontrol,hadalreadybeenexploitedbycharterschooladvocates,includingearlyadvocatesofneighborhoodcontrol,largelyonthepoliticalLeft(Finn,Manno,&Wright,2016;Fuller,2015).TwoCaliforniadistricts,OaklandandSanFrancisco,hademployedweighted-pupilformulaetomoreprogressivelydistributedollarstoschools–onefacetofdecentralizedfiscalcontrolouttoprincipals.Resultsintermsofalteringschoolstaffingorquality,however,provedmixed(Chambers,Shambaugh,Levin,Muraki,&Poland,2008).

Still,thedecentralizingofschoolfinanceandbudgetdecision-makingdowntoschool

districtsfeelsconsonantwiththeshifttowardschool-sitemanagement.Atthesametime,designersofCalifornia’sWPFreformappliedstudentweightsonlytoallocationsfromSacramentoouttothestate’snearlyonethousanddistricts.NothinginGov.Brown’sinitiative–beyondhisrhetoricandthereform’spro-equityspirit–requiresdistrictstoallocatenewdollarstoschoolsthatservehigherconcentrationsofdisadvantagedstudents.Legalactionshavebeenfiledinthreemajorurbandistricts,claimingthatnewdollarshavebeendivertedfromtheintendedstudents.

WhenDoesDecentralizedFinanceTouchSchools?

WPFfinancingunfoldshighabovetheinnerworkingsofschools.Thisfundingstructuredoesofferasimplewayofgrantingresourcestodistrict-levelleaders,theactorsthatgaindiscretionunderCalifornia’sLCFinitiative,notnecessarilyprincipalsorschool-levelleaders.OnesageactivistpunctuatesthispivotalfacetofCalifornia’sreform,askingwhetheritoperatesasadumptruckorabackpack.Thatis,doesthestatedriveuptoaschooldistrictofficeanddumpnewdollarsontotheloadingdock,noquestionsasked,ordidpolicymakersbelievetheywerestrappingfundsontothebacksofdisadvantagedstudents,withdollarsflowingtotheirparticularschools?1

NothinginCalifornialaworregulationsunderLCFrequiresthebackpack.Schoolboardsdo

notneedtotakeintoaccountpupilweightswhendistributingdollarsamongschoolswithintheirdistrict.Somefeelethicallyobligedtodoso,butthat’snottheletterofthelaw.Indeed,between-schooldistributionsshapedbyweightingpupilshaveyieldedmixedresults.Hawaii’sstatewidereformdidresultinlargerallocationstoschoolsthatservedgreatersharesofdisadvantagedstudents(Levinetal.,2013).ButanambitiousWPFexperimentinPrinceGeorge’sCounty,Maryland,unearthedonlyslightredistributionbasedonstudentattributesafterthedistrictmovedtoboostper-pupilspendingamongschools.Thedistrict“unlocked”


onlycertainschool-levelpoststhatotherwiseremainedcentrallycontrolled.Overallprogresstowardequalizingspendingperpupilwasslight(Malen,Dayhoff,Egan,&Croninger,2015).

HawleyMilesandRosa(2006)similarlyfoundthatthedevilliesinparticulardetails,after

studyingWPFprogramsinCincinnatiandHouston:theshareofdistrictbudgetstowhichpupilweightsareapplied,fine-grainelementsoftheformula,andprior,ofteninstitutionalized,waysofdistributingteachingpostsandfungibledollars.Between-schoolallocationsinNewYorkCityunderformermayorMichaelJ.Bloombergdidbecomeweightedtowarddisadvantagedstudents,butonlywhenfederalTitleIandothernon-staterevenueswereincluded.Stateandcitydollarswerenotprogressivelyallocatedandmoreexperiencedteachersweredisproportionatelyassigned(orseniorityruleseasedmigration)toschoolsservingfewerpoorstudents(Rubenstein,Schwartz,Stiefel,&Amor,2007).

California’sLCFlegislationdoesrequirethateachlocaldistrictestablishabaselinelevelof

supportin“supplementalservices”provideddisadvantagedpupil(thatis,priortopassageofLCF).Then,districtsreceivingso-calledsupplementalorconcentrationgrantsmustincreasespendingonweightedstudentsinproportiontotheamountofnewdollarsgeneratedbythesepupils(theproportionalityrequirement;California,2013).Somedistrictsrespondedbyover-estimatingwhattheyhadearlierspentonweightedpupils,byasmuch$450millionperyearinthecaseoftheLosAngelesUnifiedSchoolDistrict(LAUSD),laterchallengedbythestateDepartmentofEducation.Thisallowsthedistricttoallocatefewernewdollarsforservicesthatbenefittheweightedstudentsthanthelevelrequirediftheyhadaccuratelyreportedtheirpre-LCFbaselinelevelofsupport(UnitedWay,2017).

Wealsoarriveatthetheoreticalvagariesofdecentralizedfinancing,namelythelackof

specificityinhowdistrictflexibility,blendedwithextrafundingforcertainstudents,willalterschoolorganizations.UnderWPFregimes,stateofficialsoftenreasserttheirfaithinlocalschoolboards,thecapacityofdistrictleaderstocraftanddiscerneffectiveschoolpractices.ButintheCaliforniacase,thesedistrictofficialsarenotrequiredtomovenewfundingtoschoolsthatservedisadvantagedstudents.Noristhereanyrequirementthatdistrictsreporthardevidenceonwhatschool-levelchangesarepredictiveofachievementgains.(Tobefair,state-runcategorical-aidprogramsoftenmetthefirstcriterionyetfellmiserablyshortonthesecond.)

ThemaldistributionofCalifornia’slargeinfusionofnewfunding–oratleasterratic

channelingofpupil-weighteddollarstotheirschools–maystemfromcollateralfiscalpressuretobackstopemployeebenefitsandpensionliabilities,fixedfacilitycosts,andongoingpressurefrommiddle-classandaffluentparentswithindistrictstoprotecttheirschools.ResearchinsideLAUSDalsorevealsalackofanalyticcapacityinsidethisparticularheadquarterstodeterminewhichschoolsbenefitfromnewstatefunding,areticencetoevenaskthequestion(Partnership,2017;UnitedWay,2017).Whatevertheunderlyingforces,thelackofprogressivedistributionoffundingouttoschoolsservingthekidsthatgeneratethenewmoniesmanifestsoneweaklinkintheWPFtheoryofaction.Ifdistrictsfailtoprogressivelytargetdollarsonhigh-needsschools,howcanweightedfundingnudgeorganizationalchangesinsideschoolsthatareproximaltoteachingandlearning?


TheCaliforniaCase

Thestate’sLCFreformsweptasidescoresofcategoricalaidprogramsinthesummerof

2013,retainingaboutsevenmajorprograms.Italsoreplacedearlierlocalrevenuelimits(putinplacebyProposition13in1978)withanelegantlysimpleWPFprogram.Gov.Brown’slegislationsetforththreefundingtiers.Thebasegrantprovidesequaldollarsperpupil,varyingbygradelevels,inamountssetatabout$6,900perK-6student,$7,200formiddleschoolpupils,and$8,300foreachhighschoolstudent,adjustedforinflationeachyear(California,2013).Supplementalgrantsprovidedistrictsanadditional20%foreachstudentfromalow-incomefamily,designatedEnglishlearners,andthoseinfostercare.Concentrationgrantsfurtherboostper-pupildistributionsbyanamountequalto50%ofthebasegrant,kicking-inforthefirsttargetedstudentafterthedistrictreaches55%ofitstotalenrollmentfallingintooneoftheweightedcategories.2

Atthesametime,districtsonlyreceivethe50%additiontotheirbasegrantforeach

studentenrolledoverthe55%leveloftargetedstudentsinthedistrict.So,adistrictthathypotheticallyenrollsjust10studentsinoneoftheweightedcategoriesabove55%ofallweightedstudentswouldreceiveverylittleadditionalfunding.Thusouranalysisfocusesonwhatanalystscallthe“intent-to-treat”–thatis,alldistrictsoverthe55%cutpointreceivesomelevelofadditionalfunding,nomatterhowlargeorsmalltheiraugmentation.Futureworkwillcomparethepresentresultswiththeestimatedeffectofactualdollaraugmentationstiedtoreceiptofconcentrationgrants.

RisingSchoolSpending,withTargetingonPoorChildren

TheLCFreformwentintoeffectsoonafterbeingsignedbytheGov.Brownforthe2013-14schoolyear.“Wearebringinggovernmentclosertothepeople,totheclassroomwhererealdecisionsaremade,anddirectingthemoneywheretheneedandthechallengeisgreatest,”hesaid(Brown,2013).California’sresurgingeconomyandtheconstitutionallyrequiredallocationforK-12educationwasalreadyspurringnewspendingonpublicschools.California’sset-asideforschoolsequaled$63.6billionby2016-17,about88%flowingtolocaldistrictsthroughtheLCFmechanism,theremaining12%viasurvivingcategoricalprograms(California,2016).

Overallspendingreboundedtojustabovepre-recessionlevelsby2016-17afteradjusting

forinflation,reaching$10,657perpupil(Figure1,California,2016).ThislevelstillplacesCaliforniainthebottomthirdofallstatesnationwide.ThebulkofLCFfundingistiedtothenon-weightedbasegrant,equaling$45.3billioninthesameyear,comparedwith$5.7and$3.3billioninsupplementalandconcentrationgrants,respectively.Still,districtswithlargesharesofdisadvantagedpupilsalreadyenjoythebiggestgainsinstatesupport;thiswillcontinueinto2018-19whenLCFwilllikelybefullyimplemented.Districtswithenrollmentsthatincludemorethan25%weightedstudentswillseeper-pupilspendingrise5%oversixyears,comparedwithaboutaone-thirdgaininspendingfordistrictsinwhich80%ofallstudentsfallintoatleastoneofthedisadvantagedcategories(EdSource,2016).


Figure1.Post-recessionrecoveryinperpupilspending,Californiaschools

TheLCFinitiativeintendstowidencivicparticipationinlocalbudgetdiscussions,aprocessresultinginathree-yearLocalControlAccountabilityPlan(LCAP).Districtleadersmustconsultavarietyofstakeholdersanddeviseablueprintthatspecifiesspendingpatternsthataimtoadvancethestate’seightprioritiesandimproveservicesfordisadvantagedstudents(Wolf&Sands,2016).3Districtsdonothavetoreportonthebetween-schooldistributionofdollars.

DoesLocalControlFundingImproveSchools?

StudiesofLCFimplementationhavereliedmostlyoninterviewswithdistrictofficialsorschoolprincipals.TheGovernor’sOfficeandstateBoardofEducationhaveshownlittleinterestinsupportingrigorousevaluationoftheirmassiveexperiment(Baker,2013).4SincetheinceptionofLCF,twoteamshaveconductedqualitativeresearchinsidedistrictofficestolearnaboutimplementation.Theyfindthatdistrictleadersdoexercisefiscaldiscretionbywideningcivicparticipationinbudgetdiscussions,andavarietyofneweffortsareoftenmountedtobetterengagedisadvantagedstudents(Fuller&Tobben,2014).Districtofficialsexpressconfusionoverwhether,andifsohow,toallocatesupplementalandconcentrationgrants,includinghowtoimprovepedagogyorsupportsforweightedstudents(Wolf&Sands,2016).SomedistrictleadersreportseeingtheLCAP’snudgeforparticipatorybudgetasacomplianceexercise,notonethatspursinventivethinkingorseriousassessmentofwhat’sworkinginsideschoolstoliftachievement.

Concernhasspread,fouryearsintoLCFimplementation,overwhetherdollarsgenerated

throughsupplementalandconcentrationgrantsarebeingdirectedtoschoolsthatservelargerconcentrationsofweightedstudents.Onelargedistrict,FresnoUnified,soughttousesupplementalandconcentrationgrantdollarstohelpfundteachersalaryincreases,evena


gunshottrackingprogrampushedbythecitypolicedepartment.ThisdiversionofLCFfundswasdiscouragedbythestateschoolschieffollowingalegalcomplaintfiledbytheACLU(Fensterwald,2015).Thislocalboardreverseditsearlierdecision.Thestate’schiefeducatorhasalsoruledthatLAUSDoverestimatedhowmuchitspentonweightedstudentspriortothegovernor’sreform,allowingthedistricttounderspecifybyabout$245millioninwhatit’slegallyrequiredtospendannuallyforservicesaimedatdisadvantagedpupils(Kholi,2016).

ResearchQuestionsandAnalyticStrategy

Overall,littleisknownabouttheextenttowhichtheLCFreformaltersthesocial

organizationofschools,especiallyinwaysthatelevatestudentlearningovertime.Figure2advancesasimplecausalsequencebywhichtargetedaid–ifallocatedtoschoolsthatservedisadvantagedstudents–mightspurorganizationalchange.Weassumethatdistrictsvaryintheextenttowhichtheyprogressivelydistributenewdollarstoschoolsthathostgreatersharesoflow-achievingpupils(detailedforLAUSDinUnitedWay,2017).Racialorclassinterestsinsidedistricts,orthelackoftechnicalcapacity,mayacttopreserveinstitutionalizedwaysinwhichteachersanddollarsareallocatedamongschools(Fuller,Marsh,Stetcher,&Timar,2011;HawleyMiles&Rosa,2006;Shipps,2006).

Figure2.Causallogicforhowtargetedfundingmayaffectschoolorganizations,mediatingachievementeffects

Whendistrictleadersdoallocatenewdollarstoschoolswithgreatersharesofweightedpupils,learninggainscanonlyresultiforganizationalchangeorgainsinteacherqualityresultfromthesefreshallocations.Suchorganizationalchangesmustbeproximaltostudentengagementorlearning.GiventhedataavailableinCalifornia,wecanassesswhetherdistrictsreceivingadditionalfundingtendtoreduceaverageclasssize,enrollmorehighschoolpupilsinrigorouscourses,orimproveworkingconditionsbyassigningteacherstofewerinstructionalperiodseachday.What’skeyisthatsuchchangesinthesocialorganizationofschoolingorthequalitiesofteachersmustpresumablybeobservedbeforeachievementgainscanbeexpected.

Wefocusonwhetherorganizationalshiftsorachievementdifferencescanbeobservedin

whendistrictssurpassthe55%thresholdintermsofdisadvantagedpupilenrollments.Wecomparethesewinnersofconcentrationgrantstodistricts,almostidenticalintermsofpupildemographics,butfallingshortofthe55%cutoff.Thisnaturalexperimentallowsforaregression-discontinuitydesign(RDD)inwhichconfoundingfactorsamongdistrictsareheld

Newschoolfundingfordistrictsservinglow-achievingpupils

èSchool-levelstaffingororganizationalchanges(proximaltostudentlearning)

ì

Gainsinpupillearning

(Unobserved)confoundingfactors–familybackgroundandneighborhoods

è


constant.Theonlyfactorthat’schangingindiscretefashionisthe“intent-to-be-treated,”thereceiptofconcentrationgrants.

ThiscaptureshowLCFpolicyreflectsatreatmentinbinaryfashion,beloworabovethe55%

cutpoint.Theactualtreatmentismorecontinuousinthatdistrictsreceivetheadditionfundingforeachpupilenrolledabovethe55%compositionoftargetedstudents(seeAppendix).Ourintent-to-treatapproachyieldsinsightintothenetimpactofallofpossiblechangespotentiallyinducedbyassigningdistrictstothetreatmentgroup.Futureworkandotherresearcherswillexaminethatdiscreteeffectofrisingperpupilspendingabovethe55%cutpoint.

Thestatisticalanalysisspecificallyinformstheseempiricalquestionsfortheconcentration-

grantportionofCalifornia’sLocalControlFunding–RQ1.Howdoschooldistrictscomparedescriptivelywhenfallingoneithersideofthe55%threshold,triggeringconcentrationgrants,basedontheirshareofstudentswhoaredisadvantagedandweighted?5RQ2.Doschoolsdisplayorganizationaldifferencesthatareproximaltostudentlearningwhensituatedindistrictsreceivingconcentrationgrants,comparedwithschoolsinotherwiseidenticaldistrictsthatdonotreceiveconcentrationgrants?WefocusonorganizationalfeaturesthatallschoolsmustreporttothestateDepartmentofEducation,including(a)thenumberofnewlyhiredteachers,(b)countofclassassignmentsforteachers,and(c)thepercentageofhighschoolcoursesmeetingA-Gcollege-entryrequirementsinCalifornia.RQ3.Dostudentsdisplaystrongerachievementonstandardizedtestswhensituatedindistrictsreceivingconcentrationgrants,comparedwithpeersinotherwisesimilardistrictsthatdidnotreceiveconcentrationgrants?Welookatbothendsofthetest-scoredistribution,includingtheshareofstudents,enrolledingrades3-8,fallingbelowstandardfortheirgradelevel,andthoseexceedingthestandard,inmathematicsandEnglishlanguagearts.

Wealsoidentifywhichgroupsofstudentsbenefitmostfromtheinfusionofconcentrationgrants,andwhetherdifferinggainsmayreflectanarrowingofachievementgaps,definedalonglinesofraceorethnicity.Ideally,concentrationgrantsnarrowlearningdisparitiesbetweendisadvantagedandbetter-offchildrenstatewideandamonggroupswithindistricts.


Methods

DataToinformthesequestionswedrawdatafromthreemainsources:the2013-14LCF“fundingsnapshots,”2014-15LCF“stateprioritiessnapshots”,and2014-15staffassignmentandcourse-takingdatasubmittedbydistrictstotheCaliforniaDepartmentofEducation(CDE).Thesedatareportsarenewlyrequiredunderthe2013financelegislation,offeringawealthoffundingandschool-performanceinformation,postedathttp://www.cde.ca.gov/ds.Wemergedthesedatatoprovidecompleteaccountsfor949districtsstatewide,allowingustotestfororganizationalandachievementeffectsobservedamongdistrictthatreceivedconcentrationgrants.

LCFfundingsnapshotdata.ThisincludesLCFfundingallocations,alongwithcountsofdifferingtypesofweightedstudentsfromwhichfundinglevelsarederivedforthe2013-14fiscalyear.Thesedataspecifythepercentageofunduplicatedcountsofweightedstudentsforeachdistrict,thoseclassifiedbydistrictsasEnglishlearners,comingfrompoorfamilies,andthoseinfostercare.

Ourassignment-to-treatmentvariable–thepercentageofadistrict’senrollmentconsisting

ofunduplicatedweightedpupils(UPP)–iscalculatedbydividingeachdistrict’sweightedpupilcountbytotaldistrictenrollment.TheUPPisusedindeterminingeligibilityforaconcentrationgrant,whenexceeding55%,thencalculatingtheconcentrationgrantlevel.Thismakesforaclearassignmentvariableforourregressiondiscontinuitydesign.Figure3showsthedistributionofUPPsharesamongallCaliforniaschooldistrictsinthreerecentyears.

LCFFstateprioritiessnapshotdata.Currentlawrequiresdistrictstoannuallyupdatetheir

LCAP,whichmustincludedataon26elements,includingmeasuresofstudentachievement,studentengagement,andschoolclimate.TheCDEthencompilestheLCAPdatacomingfromdistricts,generatingtheso-calledstateprioritiessnapshotdata.Wedrawmeasuresofstudentachievementforeachdistrictfromthegeneral2014-15CDEfile,utilizingstandardizedtestsadministeredtostudentsinspring,2015.

Thesestudentoutcomes,aggregatedtothedistrictlevel,include(a)thepercentofstudents

whopassedanAdvancedPlacement(AP)Examwithascoreof3orhigher,(b)thepercentofstudents,grades3to8,whoscoredStandardExceededinthestate’sSmarterBalancedexamsinmathematicsandEnglish-languagearts(ELA),and(c)thepercentofthirdtoeighth-gradepupilswhoscoredStandardNotMet.

AlthoughthetestresultsforELAandmathematicsarecategorizedbyfourlevelsof

performance(StandardNotMet,StandardNearlyMet,StandardMet,andStandardExceeded),wefocusonthehighestandthelowestachievementranks,testinghowconcentrationgrantsmayberelatedtopupilperformanceatthelowandhighends,lendinginsightintochangeinachievementdisparities.Giventhatspring2015wasthefirstyearofSmarterBalanced


assessments,wegaugepossibleachievementeffectstwoschoolyearsaftertheinitialconcentrationgrantswereawardedtoeligibledistricts.

Figure3.Thedistributionofdistricts’unduplicatedpercentageofweightedstudentsstatewide

Staffassignmentandcoursedata.Tomeasureorganizationalchangewithinschools(aggregatedtothedistrict),weexploitdataonstaffingandcourse-takingcompiledbyCDE.Thesedatasetincludeeachcoursetakenbyhighschoolstudents,includingcoursesmeetingcollegeadmissionrequirementsoftheUniversityofCalifornia,knownastheA-to-Gcoursesequence,alongwithinformationoncompletionofAPcourses.StudentscompletingA-GorAPcoursesaregenerallyviewedastravelingamorerigorouscurriculumpath.

Theschoolstaffingandcourse-takingdataallowedustogeneratemeasuresof

organizationalfeaturesthatmayfosterhigherachievement.Thesemeasuresinclude(a)thenumberofnewlyhiredfirstyearteachersinthedistrict,(b)theaveragenumberofclassperiodsassignedtoteachers,onedimensionofworkingconditions,and(c)thepercentofcoursesmeetingA-Grequirements.ThestaffassignmentandcoursedatawerecollectedinOctober2014,whichfellbetweenthedistributionofLCFfunding(August2013)andtheadministrationofstateachievementtests(April2015).Table1showsdescriptivestatisticsfortheassignmentvariableandtheoutcomevariablesdiscussedabove.

Quasi-ExperimentalAnalysis–RegressionDiscontinuityDesign

WeemployanRDDanalysis,definedbyImbensandLemieux(2008),toestimatethemagnitudewithwhichconcentrationgrantsmayshapeschool-levelorganizationalchangeorpupilachievementwhenaggregatedtothedistrictlevel.Ourstrategytakesadvantageofthefactthatreceiptofaconcentrationgrantistriggeredwhendistrictenrollmentismadeupof


55%weightedstudents,plusone.Figure4showshowconcentrationgrantsarrivewhentheunduplicatedpupilpercentage(UPP)exceeds55%,thenvarieswidelybasedontheunduplicatedcountofweightedstudents.

Table1.Descriptivestatisticsforassignmentandoutcomevariablesusedinregressiondiscontinuitydesign

Variable N Mean SD Min Max

Assignment variable

Unduplicated pupil percentage 949 0.60 0.25 0.01 1.00

Outcome variables 1. Social-organizational features of high schools

The number of newly hired first-year teachers in the district 414 11.7 24.76 0 414

The average number of class periods assigned to teacher 414 5.5 1.32 2.67 14.97

The percent of classes meeting A to G requirements 414 57.3 15.32 0.00 86.71

Outcome variables 2. Student achievement

The percent of students who passed an Advanced Placement (AP) Exam with a score of 3 or higher 400 57.4 19.11 0 100

The percent of 3-8 grade students who have scored “Standard Exceeded” in SBA ELA test 859 13.9 11.77 0 62

The percent of 3-8 grade students who have scored “Standard Not Met” in SBA ELA test 859 32.1 16.15 0 100

The percent of 3-8 grade students who have scored “Standard Exceeded” in SBA Math test 859 13.6 12.73 0 71

The percent of 3-8 grade students who have scored “Standard Not Met” in SBA Math test 859 34.8 16.81 0 100

Thepolicy’sstrictcutoffallowsustoutilizetheso-called“sharp”regressiondiscontinuitydesign.InsharpRDD,theprobabilityofreceivingthetreatmentequals1aboveagiventhresholdand0below,thatis! " = 1 % > %∗ = 1and! " = 1 % < %∗ = 0.Inoursettingtheassignmentvariable%isthepercentageofUPPandthethreshold%∗is55%.Thetreatment"iswhethertoreceivetheconcentrationgrants.

Weassumethatthetreatment-assignmentmechanismisdeterminedonlybythe

observable%,sothatthediscontinuityapproximatesarandomizedexperimentaroundthethreshold%∗.Schooldistrictsoneithersideofthethresholdandclosetoitareexpectedtobeverysimilar.Therefore,adifferenceinoutcomevariablescanbeattributedtothetreatment.

Theestimatorofaveragetreatmenteffect(ATE)is:

*"+ = + , % ∈ %∗, %∗ + 0 − + , % ∈ %∗, %∗ − 0 ,

where,isanoutcomevariable.SincethisATEisonlyidentifiedwhen0isaverysmallvalue(i.e.,for0 → 0),theATEisquantifiedinthedifferencebetweenregressionlinesrightatthe


cutoffvalue%∗.Inotherwords,weestimatethejumpintheregressionlinerelatingtheunduplicatedpupilpercentagetooutcomevariablesrightattheUPPcutoffof55%atwhichthetreatmentassignmentswitches.ThisATEisinterpretedasanintent-to-treat(ITT)effectofassigningdistrictstothetreatmentgroup,thosereceivingconcentrationgrants.

Figure4.ThedistributionofCaliforniaschooldistricts’concentrationgrants,stemmingfrompercentageofunduplicatedweightedstudents

Estimationandbandwidthselection.Wefitthefollowingmodeltoestimatethetreatment

effectofdistrictreceiptofconcentrationgrants:

,3 = 4 %35 + 6"3 + 73

Inthismodel,,3 isthevalueofanoutcomeforthe8thschooldistrict,andtheassignmentvariable%35 istheunduplicatedpupilpercentageinthe8thdistrict,re-centeredsothatithasavalueofzeroatthecutoffof55%(%35 = %3 − %∗).Since"3 indicateswhetherthe8thdistrictreceivedaconcentrationgrant(1=receivedconcentrationgrant,0=otherwise),itsassociatedregressionparameter6representsthetreatmenteffectoftheconcentrationgrantsontheoutcome,estimatedattheunduplicatedpupilpercentageof55%.

4 %35 isagenericrepresentationofthefunctionalformofthehypothesizedrelationshipbetweentheoutcomeandthecenteredassignmentvariable%35.6Wechoosetousenonparametriclocallinearregressionforthe4 %35 ,whichprimarilyconsidersdatapointslocatedcloselyaroundthe55%cutoff.TheweightedlocallinearregressionmodelwiththeEpanechnikovkernelfunctionisfittedoneithersideofthecutoff,imposinghigherweightstoschooldistrictswhichareclosertothecutoff.Todeterminetheweightsofthelocallinearregressionatthecutoff,weusetheImbens–Kalyanaraman(Imbens&Kalyanaraman,2009)bandwidthselectionalgorithm(IKhereafter).TheIKalgorithmconsidersthesamplesizeaswellasthevariationandfunctionalformoftheoutcomevariablenearthediscontinuityingeneratinganidealbandwidthwhichminimizesthemeansquareerror.


Figure5showstheestimatedkernelweightsforlocallinearregressionusingIKbandwidth

selectionwhentheoutcomeisthepercentof3-8gradestudentswhohavescoredStandardNotMetinthestateELAtest.SincetheestimatedIKbandwidthis7.98,datapointsoutsidetherangeof55 ± 7.98areexcluded,givingzeroweightstothosepoints.Fordatapointsreceivingnon-zerokernelweights,weseethatkernelweightsforthedistrictsclosertothe55%cutoffareestimatedhigher.

Wealsochecktherobustnessofourfindingsbyusingdifferentbandwidthselection

algorithmdevelopedbyCalonico,Cattaneo,andTitiunik(2015).Theirbandwidthselectionalgorithmattemptstocorrectforbiasduetoundersmoothing,whichmightemergebecausethefunctionalformoftheregressionlinesatthecutoffisnotwellapproximated.Inthefindingsection,wecalltheirestimatorasabias-correctedRDDestimator.Wealsopresentrobustestimateswhichcorrectstandarderrorsduetouncertaintyinthebiascorrection.SeeColonic,Cattaneo,andTitiunik(2015)formoredetail.

Figure5.TheestimatedkernelweightsforlocallinearregressionusingImbens–Kalyanaramanbandwidthselectionwhentheoutcomeisthepercentof3-8gradestudentswhohavescored“StandardNotMet”onELAtest.

Checkingassumptions.Identificationoftreatmenteffectsreliesontheassumptionthatthetreatment-assignmentmechanismbehavedasassumed.Forexample,theremaybeconcernsthatschooldistrictswithslightlylowerUPPscouldmanipulatetheirrecordstoreceiveconcentrationgrants.Inthatcase,thedistributionoftheassignmentvariablecouldbediscontinuousatthecutoff,withsurprisinglymanydistrictsjustbarelyeligibleforreceivingconcentrationgrantsandsurprisinglyfewfailingtoeligibility.Thesediscontinuitiesorbumpsinthedensityofassignmentvariablecanbevisuallyinspectedorformallytestedwithahypothesistest.WeperformtheMcCrarytest(McCrary,2008)toassesspotentialdiscontinuitiesatthecutoffoftheassignmentvariable(UPP).Figure6showstheresultsfromtheMcCrarytest,suggestingnosignificantdiscontinuityofdensityaroundthe55%cutoff.


Figure6.TheMcCrarytestforcheckingdiscontinuitiesaroundthecutoffoftheassignmentvariable

AnotherassumptioncheckistoreplacetheactualoutcomeintheRDDanalysiswithnon-outcomecovariates,particularlythosecollectedpriortotreatmentimplementation.Ifwewouldobserveatreatmenteffectonapre-treatmentcovariate,doubtwouldbecastonthevalidityoftheRDDanalysis.Adesiredresultisthatnoeffectatthecutoffisfoundinanyofthepretreatmentcovariates.Wechosetwosetsofvariables—averagedailyattendanceineachgradespanandenrollmentbyethnicityandELstatus.Thesevariablescanclearlyberegardedaspre-treatmentcovariates,becausetheyaremeasuredandreportedbeforedistributingconcentrationgrants.

Findings

Wefirstdescribehowdistrictscomparewhenfallingoneithersideofthe55%cutpoint.

Table2presentsestimateddifferencesinthepre-treatmentcovariatesbetweentreatmentandcontrolgroups.Notethatpre-treatmentcovariatesweretransformedbytheirnaturallogarithmtomitigateagainsttheextremelyheavyrighttailsofthedistributionsofenrollmentvariables.Thefirstcolumngivesrawdifferences,whicharemeandifferencesbetweenalldistrictslocatedontheright-handsideofthecutoffandalldistrictsontheleft-handside.Itshowsthatdistrictsintreatmentgrouphavesignificantlymorekindergarten,elementary,middle,andhighschoolstudentsonaveragethandistrictsinthecontrolgroup,whilenodifferenceswerefoundin4-6gradestudents.ThedifferenceinsizebecomesstatisticallyinsignificantwhenwerestrictoursampletoobservationswithintheIKbandwidth.

ThesecondsetofestimatesusesImbensandKalyanaraman(2009)’sbandwidthselectionalgorithm,providingrawmeandifferencefordistrictswithinselectedrangeandweightedlocalconditionalmeandifferencewithintherange.ThelatterindicatesRDDestimates.Asshown,noneoftheRDDestimatesisstatisticallysignificant.Thissuggeststhatdistrictsfallingoneither


sideofthe55%thresholdforreceivingconcentrationgrantsdonotdiffersignificantlybasedontheirstudentenrollmentforeachschoollevelorgradespan.Table2.Estimateddifferencesbetweentreatmentandcontrolgroupsin(log-transformed)pre-treatmentcovariates

Variable

Descriptive statistics Raw difference Imbens & Kalyanaraman (2009)’s

bandwidth selection algorithm

Mean (Std.Dev)

Total N

Mean diff.

Band width

Band range (non-zero weights)

N within band

Mean diff.

RDD Estimate (Std.Err)

Average Daily Attendance (ADA) in each grade span (log transformed)

Total ADA 7.15 (2.00) 949 0.02

(0.13) 5.18 [49.90, 60.10] 122 0.11 (0.34)

0.87 (0.68)

ADA K-3 5.63 (2.50) 949 0.30*

(0.17) 5.15 [49.87, 60.06] 122 -0.51 (0.44)

0.61 (0.79)

ADA 4-6 5.33 (2.49) 949 0.23

(0.17) 4.91 [50.20, 59.90] 120 -0.46 (0.44)

0.91 (0.90)

ADA 7-8 4.69 (2.65) 949 0.39**

(0.18) 4.81 [50.20, 59.60] 118 -0.35 (0.46)

0.51 (0.94)

ADA 9-12 5.63 (2.50) 949 0.30*

(0.17) 5.15 [49.87, 60.06] 122 -0.51 (0.44)

0.61 (0.79)

Enrollment by student subgroups (log transformed)

Total enrollment

7.18 (2.02) 937 0.02

(0.13) 5.23 [49.90, 60.20] 123 0.11 (0.34)

0.81 (0.67)

English learner 5.50 (2.26) 866 1.28***

(0.15) 5.91 [49.10, 60.90] 128 0.33 (0.42)

0.74 (0.73)

Latino/Hispanic 6.17 (2.33) 925 0.89***

(0.15) 5.66 [49.40, 60.60] 133 0.09 (0.38)

0.84 (0.71)

Black 3.63 (2.29) 767 0.10

(0.16) 6.00 [49.10, 60.90] 119 0.29 (0.42)

1.02 (0.84)

Note. ***p≤.01, **.01<p≤.05, *.05<p≤.10DistrictsinthetreatmentgrouptendtohavemoreLatinostudentsandEnglishLearners,

butthesedifferencesnolongerpersist,becominginsignificant,whenthesampleisrestrictedtodistrictswithintheIKbandandwhenwegivemoreweighttodistrictsclosertothe55%cutoff.Thus,wecanconcludethat,atleastonobservedpre-treatmentstudentcomposition,theconditionalexpectationsaresmoothatthediscontinuity.Thisboostsourconfidenceinthevalidityofanyestimatedtreatmenteffects.

Table3displaysasampleof10unifiedorhighschooldistrictslocatedclosetothe55%

cutoff.TheyvaryintermsofenrollmentsizeandtheshareofstudentsdesignatedasEnglishlearners.Yetotherwise,pupilcompositionslookquitesimilaracrosstheseillustrativedistricts.Notealsothattheamountofconcentrationgrantsreceivedvariesgreatly,whichlikelyconditionsthemagnitudeofpossibleeffects.Ouranalyticmethodtestsonlyforwhetherreceiptofaconcentrationgrant,nottheamount,ispredictiveoforganizationalchangeorachievementdifferences.


Table3.Tenschooldistrictsaroundthe55%threshold

District Enrollment %EL %Latino %Black UPP Concentration Grant (CG)

Per-pupil

CG

Per-pupil Total

Funding San Rafael City High 2,365 16.6 53.3 2.3 48.0 0 0 8,355

Hanford Joint Union High 3,845 8.6 61.2 5.8 53.3 0 0 9,262

Escalon Unified 2,695 20.5 47.7 0.4 53.7 0 0 8,855

Santa Barbara Unified 14,291 30.6 60.4 0.9 54.1 0 0 8,394

Imperial Unified 3,898 23.1 80.9 1.5 54.9 0 0 8,278

East Side Union High 23,685 14.8 46.5 2.9 55.2 196,879 15 9,640

Tracy Joint Unified 15,761 25.8 49.9 6.4 55.5 323,896 37 8,704

Elk Grove Unified 62,196 17.3 25.9 14.1 56.0 2,218,799 64 8,350

Grossmont Union High 17,580 12.8 34.1 5.9 56.2 845,789 86 9,522

Chaffey Joint Union High 24,598 10.1 63.5 8.1 57.7 2,828,169 199 9,614

EffectsonSocial-OrganizationalFeaturesofHighSchoolsTable4summarizesestimateddifferencesinoutcomevariablesbetweentreatmentandcontrolgroups,districtsfallingaboveorbelowthe55%cutoff,respectively.Thefirstsetofoutcomevariablespertaintosocial-organizationalfeaturesofhighschools,asreportedby412districtswithcompletedata.Rawdifferencesbetweenalltreatmentandcontroldistrictsarenotable.Weseealmostnodifferenceinthecountofnewteachershiredbetweendistrictsfallingbelowversusabovethe55%cutoff(1.4teachers).However,districtsabovethecutoffassigntheirhighschoolteachersaboutone-thirdmoreclassperiodseachday,onaverage,comparedwithdistrictfallingbelowthe55%marker.Theformerdistrictsofferalmost9%fewercoursesmeetingA-Gcriteriathanthelatterdistricts.

Butresultsarequitedifferentwhenestimatingthediscreteeffectofreceivingconcentrationgrantsafterpruningdistrictsfarfromthe55%cutoff.TheIKregression-discontinuityestimatesshowthatweighteddistrictsabovecutoffwereabletohire10additionalteachersbeyondtheaverageforweighteddistrictsfallingbelowthe55%cutoff.Thedistrictsreceivingconcentrationgrantsassignedteachersonefewerclassperiodseachdayonaverage,andofferedagreatershareofcoursesthatmetA-Grequirements(about10%higher),comparedwithweighteddistrictsnotreceivingconcentrationgrants.

Figure7vividlyillustratesthebumpexperiencedbydistrictswithhighschoolsthat

benefitedfromconcentrationgrants.Eachdotonthispairofplotsrepresentsaschooldistrict,placedinrelationtoitsUPPandtheoutcomeofinterest:newteachershiredorclassperiods


Table4.Estimateddifferencesbetweentreatmentandcontrolgroupsfororganizationalfeaturesofschoolsandstudentachievement

Variable

Raw difference IK algorithm CCT algorithm

Total N

Mean diff.

(Std.err.)

Band widt

h

Band range (non-zero weights)

N within band

Mean diff.

within IK band (Std.err)

IK RDD

Estimate (Std.err.)

Bias-corrected

RDD Estimate (Std.err.)

Robust RDD

Estimate (Std.err.)

Outcome variables 1. Social-organizational features of high schools

The number of newly hired first-year teachers in the district 412 1.36

(2.12) 11.58 [43.90, 66.50] 122 2.21 (3.04)

9.87** (3.96)

13.62*** (4.43)

13.62** (5.39)

The average number of class periods assigned to teacher 412 0.30**

(0.12) 5.31 [50.20, 60.20] 56 -0.44 (0.30)

-1.12 (0.73)

-1.12** (0.50)

-1.12* (0.58)

The percent of classes meeting A to G requirements 412 -8.75***

(1.42) 10.24 [45.10, 64.70] 109 -1.39 (2.92)

10.31* (5.26)

12.34** (5.26)

12.34** (6.16)

Outcome variables 2. Student achievement The percent of students who passed an Advanced Placement (AP) Exam with a score of 3 or higher

400 -18.29*** (1.73) 9.36 [45.80, 64.40] 98 -3.01

(3.18) 17.21***

(6.08) 22.46***

(7.08) 22.46***

(8.14)

The percent of 3-8 grade students who have scored “Standard Exceeded” in SBA ELA test

859 -14.98*** (0.76) 7.61 [47.40, 62.60] 157 -1.30

(1.00) 3.61** (1.51)

3.31** (1.35)

3.31** (1.54)

The percent of 3-8 grade students who have scored “Standard Not Met” in SBA ELA test

859 20.26*** (0.86) 7.98 [47.20, 62.90] 160 1.33

(1.53) -6.11***

(1.99) -5.34***

(1.89) -5.34** (2.17)

The percent of 3-8 grade students who have scored “Standard Exceeded” in SBA Math test

859 -16.05*** (0.83) 8.04 [47.20, 63.00] 161 -2.13*

(1.13) 3.01* (1.75)

2.67* (1.50)

2.67 (1.74)

The percent of 3-8 grade students who have scored “Standard Not Met” in SBA Math test

859 21.94*** (0.88) 8.96 [46.20, 63.80] 175 1.71

(1.59) -4.49** (2.21)

-4.61** (2.03)

-4.61** (2.34)

Note. ***p≤.01, **.01<p≤.05, *.05<p≤.10; IK=Imbens&Kalyanaraman(2009),CCT=Calonico,Cattaneo,andTitiunik(2015)bandwidthselectionalgorithm.

assignedtoteachers(leftandright-handpanels).Thedarklinestracetheestimatedassociationbetweenthetwovariables(aregressionline).Thelightgraylinesrepresenttheconfidenceintervalwithwhichtheregressionestimatesarecalculated.Thesharpbreaksatthe55%cutoffillustratesthejumpinnewteachershired(leftpanel)andfewerclassperiodassigned(rightpanel)indicatetheeffectsofconcentrationgrantsondistricts’organizationalbehaviors.

EffectsonStudentAchievementTable4alsoshowsdifferencesinstudentachievementlevelsfordistrictaboveorbelowthe55%cutoff.WeobtainedCalifornia’sstandardizedtestscoresinmathandELAforstudentsenrolledingrades3-8,withn=859districtsreportingcompletedata.Inaddition,wereportontheperformanceofsecondaryschoolpupilsonAPexams,scoring3orhigher,withn=412districtsoperatinghighschoolsandprovidingcompletedata.Weagaindisplayrawdifferencesbetweenthetwosetsofdistrict,thenestimatedifferencesbetweenweighteddistrictslayingwiththebandwidtharoundthe55%cutoff.

Let’sfirstlookatachievementdifferencesinELAamongpupils,grades3-8.Weseethatover20%(20.3)morestudentsfailtomeettheproficiencystandard(“StandardNotMet”)indistrictsabovethe55%cutoff,comparedwithpeersattendingschoolsindistrictsbelow.Thisisnotsurprisinggiventhattheformergroupofstudentsismorelikelytocomepoorornon-Englishspeakinghomes.Thiscanbeclearlyseenintheupper-rightpanelofFigure8.TheupwardlyslopingregressionlineindicatesthatthepercentageofstudentsfailingtomeetproficiencyclimbsrapidlyasUPPsharesrise.

Butnotethedropintheregressionlinesatthe55%cutoff:detectinganinterruptioninthe

expectedassociationbetweenpupilbackgroundandachievement.BackonTable2weseethattheshareofpupilsfailingtomeettheELAstandardwasabout6%(6.1)lesswhencomparedwithweighteddistrictsbelowthe55%cutoff.Similarly,theshareofstudentsmeetingtheELAstandardwasabout4%(3.6)higherindistrictsabovethecutoffandthusreceivingconcentrationgrants(seenintheupper-leftpanel,Figure8).TheseresultsforELAareconsequentialandstatisticallysignificant.

Differencesbetweendistrictsbelowandabovethe55%arelessremarkablewhenitcomes

tomath.Thelower-leftpanelinFigure8showstheshareofpupilsmeetingthemathstandard,grades3-8,plottedagainstUPPenrollmentshares.Asexpected,thepercentageofstudentsexceedingthemathstandardfallsasUPPsharesrise.Butnearthe55%cutoffweseeajumpupintheestimatedpercentageofstudentsclearingthemathproficiencybar.Thisadvantageequals3%.Butthedifferenceisonlymarginallysignificant(atp<.10)andnotsignificantforoneofthetestsinmeandifferences(Table4).Ontheotherhand,the4.5%fewerstudentswhofailtomeetthemathstandardisstatisticallysignificant.Overall,mathachievementeffectsstemmingfromconcentrationgrantsarelessconsistentthantheencouragingeffectsonpupils’ELAperformanceindistrictsabovethe55%cutoff.


Number of first-year teachers

Percent of courses meeting A-G requirements

Figure7.Positiveorganizationaloutcomesfordistrictsclosetothe55%cutoff.Linesrepresentlocallinear

regressionsusinganEpanechnikovkernelandIKbandwidth.Dotsrepresentschooldistricts.

Finally,weseethattheshareofhighschoolersscoringa3orhigheronAPexamswasconsiderablegreaterfortheaverageweighteddistrictabovethe55%cutoff.Thepercentageofpupilsscoring3orhigherequaled17%percent(17.2)greaterthantheaverageweighteddistrictabovetheline,comparedwiththeaveragedistrictbelow.Thisdifferenceishighlysignificantandconsequentialinpragmaticterms.

Wealsotestedforheterogeneoustreatmenteffectsbyestimatingseparatemodelsfor

specificracialorethnicgroups.Table5showsthatmostsignificanteffects,stemmingfromreceiptofconcentrationgrants,arefeltbyLatinostudentsandnotbyothergroups.ThisistrueforthepercentofhighschoolstudentspassingAPcourseswithascoreof3orhigher,aswellastestscoreresultsforpupilsingrades3through8.

Thisspecificityofstudentachievementeffectsmaynotbesurprising,giventhatdistrictswithmorethan55%UPParedominatedbyLatinopupils.Ontheotherhand,thelackofeffectsforBlackstudentsisworrisome.ThelackofpositiveeffectsonWhitestudents–adistinctminorityindistrictswinningconcentrationgrants–doessuggestthatthetreatmentoverallmaynarrowachievementgapsbetweenLatinoandWhitestudents.Moreworkisrequiredtounderstandhowgap-closingworksamongschoolswithindistricts.


ELA Test Scores – Standard Exceeded ELA Test Scores – Standard Not Met

Math Test Scores – Standard Exceeded Math Test Scores – Standard Not Met

Figure8.EachCaliforniadistrictplacedinrelationtopercentageofstudentsmeetingornotmeetingproficiency

standardandUPP.LinesrepresentlocallinearregressionsusinganEpanechnikovkernelandIKbandwidth.

DiscussionandPolicyImplications

California’swageronrestoringbudgetauthoritytolocalboards–thenawardingmanywith$41billioninprogressivelydistributedfundinginrecentyears–offersahugeexperimentindecentralizedpublicfinance.TheLocalControlFundinginitiativestemmedfromgrowingfrustrationwithdivergentstreamsofcategoricalaid,fragmentedprogramsthatwerecentrallydesignedandtightlyregulated.Collateralfaithinsite-basedmanagement,freeingprincipalstoselecttheirownstaff,managetheirbudgets,andperhapsfocusoninstructionalgains,alsoshiftedthepolicydiscourseinCaliforniaoverthepastgeneration.


Table5.Heterogeneouseffectsofconcentrationgrantsonstudentachievementbyethnicitysubgroups

Variable Estimate Combined White Latino Black

The percent of students who passed an Advanced Placement (AP) Exam

with a score of 3 or higher

N (Bandwidth)

400 (9.36)

380 (10.80)

388 (8.92)

241 (9.59)

IK RDD Estimate (Std.err.)

17.21*** (6.08)

6.04 (3.77)

20.13*** (7.72)

11.37 (16.97)

The percent of 3-8 grade students who have scored “Standard Exceeded” in SBA ELA test

N (Bandwidth)

859 (7.61)

690 (8.75)

681 (6.47)

293 (8.68)


3.61** (1.51)

1.10 (1.84)

2.14** (1.01)

2.19 (2.52)

The percent of 3-8 grade students who have scored “Standard Not

Met” in SBA ELA test

N (Bandwidth)

859 (7.98)

690 (8.27)

681 (8.77)

293 (10.33)


-6.11*** (1.99)

-2.92 (2.21)

-3.67* (2.20)

-4.31 (4.28)

The percent of 3-8 grade students who have scored “Standard

Exceeded” in SBA Math test

N (Bandwidth)

859 (8.04)

690 (8.77)

680 (6.59)

293 (7.24)


3.01* (1.75)

0.52 (2.20)

0.14 (1.17)

-1.89 (2.90)

The percent of 3-8 grade students who have scored “Standard Not

Met” in SBA Math test

N (Bandwidth)

859 (8.96)

690 (8.90)

680 (8.60)

293 (10.45)


-4.49** (2.21)

-2.79 (2.62)

-3.81** (1.90)

-3.50 (6.91)

Note. ***p≤.01, **.01<p≤.05, *.05<p≤.10; IK=Imbens&Kalyanaraman(2009)bandwidthselectionalgorithm.

TheGoldenStatedevisedahybridfinancestructure:devolvingbudgetauthoritywithina

frameworkofeightstatepolicygoals,progressivelydistributingdollarsamongdistricts,andmandatingaseeminglydemocraticprocessfordevisingbudgetslocally.Manyadvocatesarguethattwopiecesaremissing:holdingdistrictsaccountableforwhethertheychanneldollarstothekidsthatgeneratenewrevenuethroughsupplementalandconcentrationgrants;andanexplicitstrategytoevaluatetheschool-leveleffectsofthismassivepublicinvestment.PositiveOrganizationalandAchievementEffects

Wedofindencouragingresultsfromtheconcentration-grantelementoftheLCFreform.Districtswithmorethan55%oftheirenrollmentsintheweighted-pupilcategories–thuswinningconcentrationgrantsfromSacramento–aremorelikelytoengageinorganizational


changesthatmaymediatelearninggains.Additionalanalysiswilltelluswhetherimprovedworkingconditionsforteachers(e.g.,byteachingfewerclassperiods)oramorerigorouscurriculum(offeringahighershareofA-Gcourses)helpstoexplaintheachievementgainsthatwedetected.Thepresentanalysisatleastestablishesthatconcentrationgrantsofferedfreshresourcesthatpromptedorganizationalchangeattheschoollevel.

Followingalongthishypothesizedcausalpathway,weestimatedhigherachievementinELA

forstudentsenrolledindistrictsthatreceivedconcentrationgrants.Weseegainsatboththelowandhighendsofpupilperformance.Thatis,theshareofstudents,grades3-8,whofailedtomeetthestate’sproficiencystandardeasedamongdistrictsabovethe55%cutpoint.Andthesharethatdidmeetstandardrangedhigher,comparedwith(weighted)districtsfallingbelow55%,failingtowinconcentrationgrants.TheseachievementbenefitswerefeltbyLatinostudents.Pupilsinotherethnicgroupsdidnotshowcommensurategainsintestscores.

LimitationsandPersistingQuestions

OuranalysisislimitedtothefirsttwoyearsofLCFimplementation.Theinitiativeisabouttoenteritsfifthyearofimplementation.Asdatabecomeavailable,wecantestforwhethertheseorganizationalandpupil-achievementgainspersistovertime.Wehopetoidentifyadditionalorganizationalfeaturesofschools–includingassignmentofnewteachers–whichmayhelptoexplainchangesinpupilachievement.Wecanfurtherdisaggregatehowstudentsubgroupsmaydifferentiallybenefitfrominfusionsofconcentrationgrants.

ThefactthatgainswerefeltbyLatinostudentsisencouraging,suggestingthatachievement

gapsarenarrowingvis-à-visWhitepeers.Moreworkisrequired,however,tounderstandwhetherconcentrationgrantsorparallelelementsofLCFareclosingdisparitiesamongstudentgroupswithindistricts,andthroughwhatorganizationalchanges.OurinabilitytodetectgainsforBlackstudentsisworrisome.

Staffingdatacanbefurtherexploitedtobetterunderstandpossibleeffectsonthekindsof

teachingorstudentsupportpositionsaddedtoschoolpayrolls,alongwithrelatedorganization-levelchange.OurworkinLosAngelesrevealsthatnewLCFfundinghasledtoshrinkingsharesofdollarsgoingforteachingpostsinhighschools,asdollarsgoforcounselors,assistantprincipals,andpupilsupportstaff(UnitedWay,2017).

Theeffectsweestimatestemsolelyfromtheconcentration-grantportionofLCF,which

equaled$3.3billionstatewidein2016-17,oraboutone-sixthofthegovernor’sprogram.Wecouldestimatehowsupplementalgrantscontributetotheseeffects–perhapsinteractingwithlevelsofconcentrationgrants–althoughsuchestimatescouldbecontaminatedbyconfoundersproxiedbythelevelofsupplementalgrants.Inaddition,perpupilspendingtiedtoconcentrationgrantsisnotasdiscontinuousaswhethergrantsaregivenornot(discussedaboveandseetheAppendix).Furtheranalysisisrequiredtolearnhowspendinggainsshapeschool-levelorganizationalchangeandachievement.


Thispaperoffersonemethodforunderstandingoneelementofthismassiveexperimentin

progressivepublicfinance.Weemphasizehoworganizationalchangeorshiftsinteacherqualitieslogicallyprecedesgainsinstudentengagementandlearning.Simplyassociatingnewfundingwithpupiloutcomesdoeslittletobuildtheoryoverhowdecentralizingfinancemaysetinmotionpracticesonthegroundthatalterschoolsandpupilmotivation,ornot.Nordogoodintentionsorhigh-soundingrhetoricabouthelpingpoorchildrensuffice.Whenthepoliticalstarsdoaligntoprogressivelyfundschools,wemustrigorouslydigintowhetherthesewell-meaninginitiativestrulyadvancefairnessand,ifso,throughwhatpracticesinsideschools?

Appendix

Thedollarincreaseperpupilreceivedbydistrictsthatreceiveconcentrationgrants,seenbelowfor2013-14,isnotasdiscontinuousatthe55%cutpointrelativetotheoverallintent-to-treatdiscontinuity.Futureworkmightuse“kinkedregression”techniquestoassociatespendingchangeswithorganizationalpracticesanddifferencesinstudentachievement.

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Endnotes

1ThanksgotoBillLuciaoftheEdVoiceorganizationinSacramentoforthisvividanalogy.2Thestatecountsweightedstudentsjustonce,so-called“unduplicatedpupils”,whentheyfallintomorethanonecategoryofdisadvantage.3Thestate’scentrallyarticulatedgoalsofferamixofintentions,whichemphasizeimplementationofCommonCoreStateStandards;improvingparentparticipation,schoolclimate,andbasicservices;widening“courseaccess”anddeepeningstudentengagement,alongwithraisingstudentachievementand“otherstudentoutcomes”(California,2013).4Themedium-termassessmentofGov.Schwarzenegger’sconsolidationofcategoricalaidprogramsdidfindawarmreceptionfromdistrictofficials,manyreportingthattheywelcomedthenewfiscaldiscretion.Atthesametime,districtsdisplayedlimitedcapacityoverallinassessingschool-levelchangeorachievementeffectsstemmingfromneworrecastprogramsaimedatliftingstudents(Fuller,Marsh,Stetcher,&Timar,2011).5Thatis,thepercentageofadistrict’senrollmentthatincludesstudentsfromlow-incomefamilies,Englishlearners,orthoseinfostercare.6Weincludedadditionalcovariatessuchasthenaturallogoftotalenrollmentandthetypeofschooldistrict(unified,elementary,orhighschool)inthemodelspecification.Thisisnotnecessaryfortreatment-effectidentification.Still,itcanbeusefulinimprovingprecision.Theresultswithorwithoutincludingcovariatesdidnotdiffersignificantly.

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