NBER WORKING PAPER SERIES

SCHOOL FINANCE REFORM AND THE DISTRIBUTION OF STUDENT ACHIEVEMENT

Julien LafortuneJesse Rothstein

Diane Whitmore Schanzenbach

Working Paper 22011http://www.nber.org/papers/w22011

NATIONAL BUREAU OF ECONOMIC RESEARCH1050 Massachusetts Avenue

Cambridge, MA 02138February 2016

This research was supported by funding from the Spencer Foundation and the Washington Centerfor Equitable Growth. We are grateful to Apurba Chakraborty, Elora Ditton, and Patrick Lapid forexcellent research assistance. We thank Julie Cullen, Tom Downes, Kirabo Jackson, Rucker Johnson,Richard Rothstein, Max Schanzenbach, and conference and seminar participants at APPAM, AEFP,Bocconi, Brookings, Chicago, Erasmus, Wisconsin (IRP), LSE, New York University, Northwestern,Princeton, RAND, Teachers’ College, Texas A&M, Warwick, and the 2015 Stavanger-Bergen-Berkeleyworkshop for helpful comments and discussions. The views expressed herein are those of the authorsand do not necessarily reflect the views of the National Bureau of Economic Research.

NBER working papers are circulated for discussion and comment purposes. They have not been peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies officialNBER publications.

© 2016 by Julien Lafortune, Jesse Rothstein, and Diane Whitmore Schanzenbach. All rights reserved.Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission providedthat full credit, including © notice, is given to the source.

School Finance Reform and the Distribution of Student Achievement Julien Lafortune, Jesse Rothstein, and Diane Whitmore Schanzenbach NBER Working Paper No. 22011February 2016, Revised July 2016JEL No. H73,H75,I22

ABSTRACT

We study the impact of post-1990 school finance reforms, during the so-called “adequacy” era, on absolute and relative spending and achievement in low-income school districts. Using an event study research design that exploits the apparent randomness of reform timing, we show that reforms lead to sharp, immediate, and sustained increases in spending in low-income school districts. Using representative samples from the National Assessment of Educational Progress, we find that reforms cause increases in the achievement of students in these districts, phasing in gradually over the years following the reform. The implied effect of school resources on educational achievement is large.

Julien LafortuneDepartment of EconomicsUniversity of California, Berkeley530 Evans Hall #3880Berkeley, CA 94720julien@econ.berkeley.edu

Jesse RothsteinGoldman School of Public Policyand Department of EconomicsUniversity of California, Berkeley2607 Hearst AvenueBerkeley, CA 94720-7320and NBERrothstein@berkeley.edu

Diane Whitmore SchanzenbachSchool of Education and Social PolicyNorthwestern UniversityAnnenberg Hall, Room 2052120 Campus DriveEvanston, IL 60208and the Brookings Institutionand also NBERdws@northwestern.edu

2

Economistshavelongbeenskepticalofresource-basededucationpolicies,basedin

partonobservationalstudiesshowingsmallorzeroeffectsofadditionalfunding(see,e.g.,

Colemanetal.1966,Hanushek1986,Hanushek2006).2Hanushek,forexample,writes:

“Simplyprovidingmorefundingoradifferentdistributionoffundingisunlikelytoimprove

studentachievement(eventhoughitmayaffectthetaxburdensofschoolfinancingacross

thecitizensofastate)”(1997,p.153).Accordingly,recentpolicydiscussionshavefocused

onwaystoimprovetheproductivityofexistinginputsratherthanonchangesinschool

resourcelevels.

Nevertheless,stateshavecontinuedtoimplementaggressiveresource-based

policies,aimedinpartatreducingachievementgaps.Between1990and2011,averagereal

spendingperpupilinK-12schoolsrosebynearly40percent.Thisincreasewas

concentratedinlow-incomeschooldistricts.Figure1showstheevolutionofaverage

revenuesperpupil,in2013dollars,inthelowest-incomeschooldistricts(definedasthe

bottomfifthofeachstate’sdistrict-levelmeanhouseholdincomedistribution)andthe

highest-incomedistricts(thetopfifth),from1990to2012.3Overthisperiod,realper-pupil

revenuesrosebyroughly30%inthehighest-incomedistricts,andbyoverhalfinthe

lowest-incomedistricts.Thus,whilelow-incomedistrictscollectedabout20%lessthan

high-incomedistrictsin1990,theyhavebeeninroughparitysincearound2001.

Muchofthischangecameviareformstostateeducationfundingformulas.Figure2

showsrevenuesoflow-incomedistrictsrelativetohigh-incomedistricts,eachdefinedasin

2Therearealsoobservational(CardandKrueger1992a)andexperimental(Krueger1999;Dynarski,Hyman

&Schanzenbach2013)studiespointingtopositiveschoolresourceeffects.Thereisnoconsensusabouthow

toreconcilethese(see,e.g.,Burtless1996;Hanushek2003;Krueger2003).3HawaiiandtheDistrictofColumbiaareexcluded.Statemeansweightdistrictsbylogenrollment,thenare

averagedwithoutweightsinFigure1.Numbersinthetextweightstatesbyenrollmentforcomparabilitywith

nationalaggregates.WediscussdatasourcesanddefinitionsinSectionIII.

3

Figure1,separatelyforthe26statesthathaveimplementedschoolfinancereforms—

typicallybutnotalwaysundercourtorder—since1990andfor23statesthathavenot.

Growthinlow-incomedistricts’relativerevenueshasbeenmorethantwiceasrapidinthe

formerstatesthaninthelatter.

Theimplicationsofschoolfinancereforms(SFRs)forschoolfundinghavebeen

muchstudied(see,e.g.,HanushekandLindseth,2009;CardandPayne,2002;Murray,

Evans,andSchwab,1998;LaddandFiske2015).Theexistingresearchfocusesonso-called

“equity”reformsinthe1970sand1980s,whichaimedtoreduceresourcedisparities

acrossdistricts.Butmostreformssince1990havebeen“adequacy”reformsthataimto

achievesufficientfundinginlow-incomedistricts,regardlessoftheimplicationsforequity.

Adequacyreformshavebeenmorenumerousthantheearlierequityreforms,buthave

beenmuchlessstudied.

SFRsarearguablythemostsubstantialnationalpolicyeffortaimedatpromoting

equalityofeducationalopportunitysincetheturnawayfromschooldesegregationinthe

1980s.Butthereislittleevidenceabouttheireffectsonstudentachievement.What

evidencethereisderivesfromnon-representativedataonstudentswhotooktheSAT

collegeentranceexam(CardandPayne2002);fromlong-runoutcomesmeasuredinthe

relativelysmallPanelStudyofIncomeDynamicssample(Jackson,Johnson,andPersico

2016);orfromcasestudiesofindividualreforms(Clark2003;Hyman2013;Guryan

2001).4Thesestudiesprimarilyexaminepre-1990,equity-basedSFRs,andgenerallyfind

positiveeffectsonstudentoutcomes.Butfundinglevelsweremuchhigherby1990than

4CascioandReber(2013)andCascio,Gordon,andReber(2013)examinetheintroductionoffederalTitleI

fundingtolow-incomeschoolsviathe1965ElementaryandSecondaryEducationAct.

4

earlier,andthemostsevereinequitiesinschoolresourceshadbeenaddressed.Thus,there

mayhavebeenlessscopeformorerecent,adequacy-basedSFRstobenefitstudents.

Theliteratureregardingwhether“moneymatters”ineducation(CardandKrueger

1992a;Hanushek1986,2003,2006;Burtless1996)iscontentiousanddoesnotofferclear

guidance.Statefundingformulasarethemainpolicytoolavailabletoaddressinequitiesin

academicoutcomes,sofundingshiftsderivingfromchangesintheseformulasarethemost

policy-relevantvariationinschoolresources.Theverylimitedevidenceontheimpactsof

earlySFRs,andthenear-totallackofevidenceregardingmorerecentreforms,representsa

majorshortcomingintheliterature.

Weprovidethefirstevidencefromnationallyrepresentativedataregardingthe

impactofSFRsonstudentachievement.Weexploitlittle-useddatafromtheNational

AssessmentofEducationalProgress(NAEP),alsoknownas“theNation’sReportCard.”

NAEPhasadministeredtestsinmathandreadingtostate-representativesamplesof

100,000-200,000studentsinthefourthandeighthgradeseverytwotofouryearssince

1990.Importantly,thetestshavebeenuniformacrossthecountryandovertime,

facilitatingcomparisons.5

WeusetheNAEPdatatoconstructastate-by-yearpanelofrelativeachievementin

low-incomeschooldistricts,covering1990to2011.Conveniently,thebeginningofour

NAEPpanelcoincideswiththeonsetoftheadequacyeraofschoolfinance,whichdatesto

the1990KentuckyEducationReformAct(KERA).Figure3showstheNAEPscoregap(in

standarddeviationunits)betweenlow-andhigh-incomedistrictsovertime,usingthe

5Severalstudies(e.g.,DeeandJacob2011,LevineandSchanzenbach2009)exploitstatemeanscores.

Microdataareavailableunderrestricted-usedatalicensesfromtheNationalCenterforEducationStatistics

(NCES).WearegratefultoBruceKaplan,KatePashley,andFatihUnlufortheirassistanceinlocatingthe

crosswalkfromtheolderNAEPdatatoschoolsanddistricts.

5

samedefinitionsasinFigures1and2.Itshowsthatthetestscoregaphasnarrowedin

statesthatimplementedreformsbuthasbeenstableinstatesthatdidnot.

Figures2and3canbeseenaslong-differenceestimatesoftheeffectsofSFRs,and

indicatethatSFRsledtoincreasesinfundingandtestscoresinlow-incomeschooldistricts.

Butthesepatternscouldbedrivenbyothertrendsthatdifferbetweenstatesthatdidand

didnotimplementreforms.Totestthis,weuseaneventstudyframework,taking

advantageofplausiblyrandomvariationinthelocationandtimingofpost-1990SFRs.We

findnosignofsystematicchangesineitherfundingortestscoresintheperiodleadingup

toareform,supportingourassumptionthatreformtimingisexogenous.Following

reforms,wedocumentsharpincreasesinstaterevenues,withlargerincreasesinlow-

incomedistrictsandsmallerbutstillpositiveincreasesinhigh-incomedistricts.6These

changesoccurquicklyafterreformevents,persistformanyyears,andarenotoffsetby

reductionsinlocalrevenues.Absoluteandrelativefundinginlow-incomedistrictsrisesby

approximately$1,200and$700perpupilperyear,respectively.

Notsurprisingly,wefindnoimmediateeffectofreformsonachievement.Butwedo

findclearchangesinachievementtrendsfollowingevents.Thesecumulateovertime:Ten

yearsafterareform,relativeachievementofstudentsinlow-incomedistrictshasrisenby

roughly0.1standarddeviation,approximatelyone-fifthofthebaselinegapbetweenhigh-

andlow-incomedistricts.Theimpliedimpactisbetween0.12and0.24standarddeviations

per$1,000perpupilinannualspending.Thisisatleasttwicetheimpactperdollarthatis

6Anecdotally,legislatorsfacingcourtorderstoincreasefundingtolow-incomedistrictsoftenrespondby

increasingoverallfunding,asawayofdisguisingtheresultingredistribution.Reformsareassociatedwith

sharpincreasesintotalstateeducationexpendituresandtaxcollections.

6

impliedbytheTennesseeProjectSTARclasssizeexperiment.7Givenexistingestimatesof

therelationshipbetweentestscoresandstudents’subsequentearnings,ourresultsimply

thatthebenefitsofmarginalincreasesinschoolresourcesinlow-income,poorlyresourced

schooldistricts,intermsofstudents’increasedeventualearnings,exceedthecosts.

Ourpapermakesthreeprimarycontributions.First,wepresentthefirst

comprehensiveevidenceregardingthefiscalimpactsofpost-1990,adequacySFRs.8We

showthatthesereformsleadtoincreasedprogressivityofstateaidandtotalschool

finance,withlittleifanyoftheadditionalstatefundingdissipatedthroughreducedlocal

effortandwithnosignofreactionsthatreduceoverallfunding.

Second,wepresentthefirstnationalevidenceregardingtheeffectofanyfinance

reformsontheachievementofarepresentativesampleofstudents.Ourestimatesimply

thatadditionalfundingdistributedthroughcourt-mandatedchangesinfinanceformulasis

highlyproductiveinlow-incomeschooldistricts.

Finally,wepresentthefirstanalysisoftheimpactoffinancereformsonoverall

educationalequity.Wefindnodiscernableeffectofreformsoneitherthegapin

achievementbetweenhigh-andlow-incomestudentsortheminority-whitegap.Thisisnot

becausefundingisunproductive.Rather,low-incomeandminoritystudentsarenotvery

highlyconcentratedinschooldistrictswithlowmeanincomes,soarenotcloselytargeted

bydistrict-basedfinancereforms.Thus,whileouranalysissuggeststhatfinancereforms

canbequiteeffectiveatreducingbetween-districtinequities,otherpolicytoolsaimedat

7STARraisedcostsbyabout30%inK-3,andraisedtestscoresby0.17SDs(KruegerandWhitmore2001).

CurrentspendingperpupilinTennesseeisaround$9,000,socomparableproportionalclasssizereductions

wouldcostaround$2,700perpupilperyear.Theimpliedeffectisthusaround0.06SDsper$1,000perpupil.

ThiscomparisonimplicitlyassumesthatmaintainingthesmallerSTARclasssizesbeyond3rdgradewould

yieldnoadditionalgrowthintestscores.8Sims(2011a)andCorcoranandEvans(2015)contrastfiscalimpactsofequityandadequacyreforms.But

theirsamplesendin2002,andthusreflectonlythebeginningoftheadequacyera.

7

within-districtresourceandachievementgapswillbeneededtoaddressoverallequity

concerns.

I. Schoolfinancereforms9

Historically,Americanpublicschoolswerelocallymanagedandfinancedprimarily

vialocalpropertytaxes.Asschooldistrictsvarywidelyinboththeirtaxbasesandtheir

voters’willingnesstotaxthemselvestofundschools,thismeantthatschoolresources

variedsubstantiallyacrossdistricts.

Inthe1960s,agroupoflegalscholarsarguedthatlocalschoolfinanceviolates

federalandstateconstitutionalprovisionsthatguaranteeequalaccesstopublicservices

(see,e.g.,Wise1967;Horowitz1966;Kirp1968;andCoons,Clune,andSugarman1970).

Advocatesbroughtandwonsuitsinmanystatesdemandingmoreequitableschoolfinance

systems;inotherstates,legislaturesactedwithoutcourtdecisions(oftentostaveoff

potentialrulings).10

Theresultingfinanceregimesofteninvolvedsubstantialincreasesinstatetransfers

todistrictsthatdependedeitheronlocalfiscalcapacity(“powerequalization”)orrealized

localrevenues(“matching”or“variable”grants).Anextensive“fiscalfederalism”literature

examinestheeffectsofthesereformsonthedistributionofschoolfunding(see,e.g.,

HanushekandLindseth,2009;CorcoranandEvans,2015;CardandPayne,2002;Murray,

Evans,andSchwab,1998).Aparticularfocusiswhetherformulasthatraisethemarginal

9OurdiscussionheredrawsheavilyonKoskiandHahnel(2015).10AnearlyU.S.SupremeCourtdecision,SanAntonioIndependentSchoolDistrictv.Rodriguez(411US1,1973)heldthateducationisnotafundamentalrightundertheU.S.Constitution.Subsequentsuitsfocusedonstate

constitutions,whichoftenarticulateresponsibilityforasystemofpubliceducation.

8

localcostofadditionalschoolspendingaffectvoters’choicesaboutthelocalspendinglevel

(e.g.,Hoxby2001).

Asecondwaveoffinancereforms—thefocusofthispaper—iscommonlydatedtoa

1989KentuckySupremeCourtruling.Here,theCourtfoundthatthestateconstitution,

whichasinmanyotherstatesdictatesan“efficientsystem”ofpublicschools,requiresthat

“[e]achchild,everychild,…mustbeprovidedwithanequalopportunitytohavean

adequateeducation”(Rosev.CouncilforBetterEducation11;emphasisinoriginal).The

rulingemphasizedthatequalfundingwasnotsufficient,andarticulatedastandardcloser

toequalityofoutcomesforstudentsinlow-incomedistricts(“sufficientlevelsofacademic

orvocationalskillstoenablepublicschoolstudentstocompetefavorablywiththeir

counterpartsinsurroundingstates,inacademicsorinthejobmarket”).TheKentucky

legislaturerespondedwiththeKentuckyEducationReformActof1990(KERA),which

revampedthestate’seducationalfinance,governance,andcurriculum.Clark(2003)and

FlanaganandMurray(2004)findKERAsubstantiallyincreasedspendinginlow-income

districts.

Since1990,courtsinmanyotherstateshavefoundadequacyrequirementsintheir

ownconstitutions.Inmanycasesreformshaveaimedathigherspendinginlow-income

thaninhigh-incomedistricts,tocompensatefortheout-of-schooldisadvantagesthatlow-

incomestudentsface.12

Reformadvocateshaveconsciouslyimitatedthelegalcampaignforschool

desegregationinthe1950s-1980s,andlikethatmovementhaveoperated

11790SW2d186.Rosewasnotthefirstadequacyruling,butearlierrulingsattractedlessattention.12Asmallindustryhasdevelopedtocalculatethespendinglevelneededtosatisfyanadequacystandard.See,

e.g.,DownesandSteifel(2015)andDuncombe,Nguyen-Hoang,andYinger(2015).

9

opportunistically,takingadvantageofvariationinlegalprecedentandtheavailabilityof

sympatheticjudgestoadvanceanationaleffort.Courtsindifferentstateshaveinterpreted

seeminglysimilarstateconstitutionallanguagequitedifferently,eitherimposingorruling

outadequacyrequirements.13Thereislittlereasontothinkthatthecasesarebroughtin

responsetopoliticalorotherdevelopmentsthatwouldhaveindependentlyaffected

achievementgapsinastate.Moreover,thevagariesofthejudicialprocess—casesare

typicallyappealedupwardthroughseverallevelsofreview—anddecisionsinsomestates

toimplementlegislativereformstosettleongoingcasesorforestallfearedcourtrulings

generateadditionalquasi-randomvariationintiming.Ouranalyticstrategy,developed

below,ispremisedontheassumptionthatreformtimingisuncorrelatedwithother

determinantsoftrendsin(relative)spendingandachievementinlow-incomedistricts.We

presentevidenceinsupportofthisassumptioninSectionsIVandV.

WehaveattemptedtoidentifyallmajorSFRsbetween1990and2011.Webegan

withlistsofcourt-orderedreformscompiledbyJacksonetal.(2016)andCorcoranand

Evans(2015).Wesupplementedthesewithourownresearchintocasehistories,and

updatedthemthrough2011.WealsotabulatedmajorlegislativeSFRs.Insomeimportant

cases(e.g.,Colorado,California),legislaturesreformedfinancesystemswithoutpriorcourt

decisions,oftentoforestalladversejudgmentsinthreatenedorongoinglawsuits.Our

primaryanalysesincludethese,thoughwealsopresentresultsthatfocusexclusivelyon

courtorders.

13Forexample,theIllinoisSupremeCourthasfoundthatschoolfinancerulesarenotjusticiablebythecourts

andmustbeaddressedinsteadbythelegislature(672N.E.2d1178).Therelevantclauseinthestate’s

constitution(“anefficientsystemofhigh-qualitypubliceducationalinstitutionsandservices”)issimilarto

thatinOhio(“athoroughandefficientsystemofcommonschoolsthroughouttheState”),wherethecourts

haveintervened.

10

AppendixTableA1presentsacompletelistofoureventsandcomparesittothose

usedinotherstudies.Weidentifyatotalof64schoolfinancereformeventsin26states

between1990and2011.1439(61%)involvecourtorders;theremainderarelegislative

actionswithoutamajorcourtorderinthesameyear.

Figure4showsthedistributionofeventsovertime,withlegislativeSFRsindicated

bydarkerbars.Therehavebeensubstantiallymorecourt-orderedSFRsduringthe

adequacyerathanintheprior,morestudiedequityera.15Figure5showsthegeographic

distribution.Stateswitheventsarequitegeographicallydiverse,thoughreformsarerarein

theDeepSouthandupperMidwest.

18stateshadmultipleeventsinourperiod.Theseweregenerallycloselyspaced:

60%werethreeorfeweryearsapart.Inthesecases,wesuspectthatonlyonegenerateda

majorchangeinthestate’sfinancerulesandthatotherswereproceduralsteps(e.g.,court

ordersthatweredisregardedorlegislationchangesthatwerelaterfoundinadequate).Our

analyticalstrategyisbuiltwiththisideainmind,thoughourresultsarenotsensitiveto

howmultipleeventsaretreated.

Aswithearlierequityreforms,statesunderadequacyordershavevariedinthe

financesystemsthattheyhaveadopted.Despitethisheterogeneity,therearetwo

importantreasonstoexpectthatadequacyreformshaddifferentimpactsontheleveland

distributionofschoolfundingthandidearlierequityreforms.First,equityreformsoften

focusedondistricts’propertytaxbases,whereadequacyreformsfocusedonstudent

disadvantage;thetwomaynotbestronglycorrelated(Fischel1989).Second,whereastate

14Ourpanelexcludesthe1989RosedecisionbutincludesKERA,thelegislature’sresponsein1990.15Jacksonetal.(2016)code15court-orderedSFRsfrom1971through1989,and48sincethen.Wecodeafewcasesdifferentlythanhaveearlierauthors.ThesearediscussedintheAppendix.

11

mightrespondtoanequityorderby“levelingdown”tostingybutequalfunding,thiswould

notsatisfyanadequacymandate.Statesseeminsteadtohaveincreasedfundingtoall

districtstomeetadequacyrequirementswhilestillallowinghigher-incomedistrictsto

differentiatethemselves.

Overall,then,weexpectthatadequacyreformscausedhigherspending,ingeneral

andparticularlyinlow-incomedistricts,thandidequityreforms,butperhapsalsoyielded

smallerreductionsinthebetween-districtdispersion(BakerandGreen,2015;Downesand

Stiefel,2015).Weconfirmthesepredictionsbelow.

II. Analyticapproach

Theprimarychallengeinestimatingthecausaleffectofschoolfundingisthatitmay

becorrelatedwithotherfactorsthataffectrealizedschoolfinanceorstudentoutcomes.An

importantconcernisthatstatesthataremoreaggressiveintargetingfundingtolow-

incomeschooldistrictsmayalsodifferinotherways—theymayhavebetterdeveloped

socialwelfaresystems,moreequitablehousingpricedistributions,ordifferentapproaches

toregulatingschoolquality(Hanushek,Rivkin,andTaylor1996a,b).

Toaddressthis,weleveragevariationinthetimingofreformeventsinanevent-

studyframework.Ourstrategyisbasedontheideathatstateswithouteventsina

particularyearformausefulcounterfactualforstatesthatdohaveeventsinthatyear,after

accountingforfixeddifferencesbetweenthestatesandforcommontimeeffects.Thekey

assumptionisthattheexacttimingofeventsisasgoodasrandom.Wethinkthisis

plausible,giventheidiosyncrasiesofjudicialprocessesdiscussedabove.Anattractive

12

featureofourapproachisthatitbuildsinplaceboteststhatshouldidentifylikely

violationsofthisassumption.

Oursimplesteventstudyspecificationmodelseventsaspermanent,immediate

shiftsinoutcomesrelativetootherstates:

(1) !"# = %" + '# + 1 ) > )"∗ ,-./0 + 1"# .

Here,!"#representssomesummaryofthedistributionoffundingorachievementinstates

inyeart.Wediscussourparticularmeasuresbelow.%"and'#representstateandyear

effects,respectively.)"∗isthedateonwhichstates’seventoccurred.(Fornow,weassume

thateachstatejustoneevent;thistermissettozeroforstatesthatdonothaveevents.)

Thecoefficientestimate,-./0representsthechangeintheoutcomefollowingtheevent.

SFRsmaynotaffect!"#immediately,butmaydevelopmoregradually.Thisis

particularlytrueforstudentachievementoutcomes,astheachievementofastudentin

yeartlikelydependsinpartonthequalityoftheschoolingshereceivedinprioryears.In

addition,ifeventtimingisnon-random,stateswitheventsmaydivergefromstateswithout

eventsevenbeforethedateoftheevent.Toaccommodatetheseideas,weaddtwotrend

termsto(1):

(2) !"# = %" + '# + 1 ) > )"∗ ,-./0 + 1 ) > )"∗ ) − )"∗ ,034"567 + ) − )"∗ ,#8579 + 1"# .

,034"567capturesdelayedeventeffectsandrepresentstheannualchangeinoutcomesin

statesafter)"∗,relativetothesamestatepriortotheevent.,#8579 ,whichisidentifiedfrom

changesinsrelativetootherstatesinyearspriorto)"∗,representsafalsificationtest:

,#8579 ≠ 0wouldindicatethateventtimingismeaningfullynon-random.

Wealsoestimatenon-parametricmodelsthatdonotconstrainthephase-inand

priortrendeffectstobelinear:

13

(3) !"# = %" + '# + 1 ) = )"∗ + <=>?@8A=>BC ,8 + 1"# .

Here,�rrepresentstheeffectofaneventinyear)"∗onoutcomesryearslater(or

previously,forr<0).Theseeffectsaremeasuredrelativetoyearr=0,whichisexcluded.We

censorratkmin=-5,so�-5representsaverageoutcomesfiveormoreyearspriortoan

event,relativetothoseintheeventyear.

Comparisonsoftheparametricandnon-parametricestimatesindicatethatthe

simplespecification(2)doesagoodjobofcapturingdynamicsinfinancesandstudent

achievementsurroundingevents,thoughthepost-event“jump”issometimesspreadout

overafewyearsfollowingtheevent.The{β-k,…,β-1}pre-eventtermsin(3)arethe

equivalentofthepre-eventtrendcoefficient,#8579 in(2).Inonlyoneofthespecifications

thatweestimateiseither,#8579 orthesetofnonparametricpre-eventcoefficients

significantlydifferentfromzero,andinthiscaseitappearstobeanidiosyncraticblipina

singleβ-rcoefficient(seeFigure12,below).Thissupportsouridentifyingassumption.

Whenweexaminefinanceoutcomes,allofthepost-eventeffectappearstobenearly

immediate,sowefocusonthesimplerspecification(1).Bycontrast,inourstudent

achievementanalysis,the“jump”isneverdistinguishablefromzero,andalloftheeffect

thatweestimateoperatesthroughthe,034"567coefficient.Wethusemphasize

specificationsthatallowforaphase-ineffectbutnopost-eventjump.Ineachcase,these

simplespecificationsfitthenon-parametricresultsquitewell.

Difference-in-differencesandtriple-differences

Theeventstudymethodologyoutlinedaboveisaformofdifference-in-differences

(DD),identifyingtheeffectofeventsfromdeviationsinthetrendin“treated”statesrelative

14

tostatesthathavenotyethadevents.Theidentifyingassumptionisthatwithoutfinance

reforms,outcomeswouldhavemovedinparallelintreatedanduntreatedstates.Hanushek

etal.(1996a,b)arecriticalofthisassumptionwithregardtotheimpactsofschoolspending

instate-by-yearpanels.Theyarguetheparalleltrendassumptionisunlikelytohold,

biasingDDestimates.

Accordingly,whilewepresentbelowDDestimateswithmeanspendingormean

testscoresinastateastheoutcome,webelievethatmorecredibleestimatesoftheeffectof

fundingreformscanbeobtainedfromtriple-difference(DDD)modelsthatcomparethe

impactsofSFReventsonhigh-andlow-incomedistrictsinastate.Weimplementthese

usingtheDDmethodologyabovebyusingasthedependentvariable!"#ameasureofthe

achievementoflow-incomedistrictsinastaterelativetothatinhigher-incomedistricts.

Withthistypeofdependentvariable,theeventstudystrategyisrobusttoarbitrarystate-

by-yearshockstospendingorachievement,solongastheyhavesimilareffectsondistricts

atdifferentincomelevels.Theidentifyingassumptionisthattherelativeoutcomesoflow-

incomedistrictswouldhavefollowedparalleltrendsacrossstatesintheabsenceofSFRs.

Weconsidertwomeasuresofrelativespendingorachievementinlow-income

districts.First,weusethegapbetweendistrictsinthetopandbottomquintilesofthestate

incomedistribution,asinFigures2and3.Thesequintilegapscanbenoisy,inpartbecause

theydiscardinformationonthemiddle60%ofdistricts.Wethusemphasizeasecond

measure,theslopeofdistrict-leveloutcomeswithrespecttologaverageincomeacrossall

districtsinthestate.16Amorenegativeslopecorrespondstohigherrelativeoutcomesin

16Specifically,weregressdistrict-levelspendingperpupilormeanachievementonlogmeanincome,

controllingforlogenrollment.Theregressionisestimatedseparatelyforeachstateandyear,andin

15

low-incomedistricts.AppendixFigureA2showsthatthelong-differenceanalysisfrom

Figures2and3isrobusttousingourslopemeasuresinplaceofquintilegaps,andyields

evenstrongerresults.

Toillustrate,Figure6showsthescatterplotofperpupilstatetransferstodistricts

againstlogmeandistrictincome(measuredin1990)foreachdistrictinOhio,firstin1990

andthenin2011.Asthefigureshows,statetransfersrosedramaticallyoverthisperiod,

particularlyinthelower-incomedistricts.Weoverlaytwofittedseriesontopofthis:One

showsmeantransfersacrossalldistrictsineachincomequintile,andtheothershowsthe

slopeasdescribedabove.Inthiscase,thelog-linearspecificationfitsthequintilemeans

fairlywell.Acrossstates,theslopeiscorrelated-0.73withthefirst-quintile/fifth-quintile

gap.

WeshowbelowthatSFRsleadtohigherabsoluterevenuesinalldistrictsinastate

andtohigherrelativerevenuesinlow-incomedistricts,asseenforOhioinFigure6.Eachof

thesecouldaffecttherelativeachievementofstudentsinlow-incomedistricts.First,if

moneymatters,thentheincreaseinrelativespendingshouldraiselow-incomedistricts’

achievement.Second,themarginaleffectofextrafundsmaybehigherinlow-income

districts,perhapsduetodecliningmarginalproductivityofadditionalresources.Ifso,even

anacross-the-boardspendingincreasewouldraisetheirrelativeachievement.Giventhese

twochannels,andtimingissuesthatwillbecomeclearbelow,wearecautiousinconverting

ourestimatedeffectsonachievementintoestimatesofoutputperdollar,asitisnotclear

whatistheappropriatedenominatorforourDDDtreatmenteffects.

achievementmodelsforeachsubjectandgrade.Thedistrictlogincomecoefficientsareusedas!"#forsubsequentanalysesatthestate-year-(subject-grade)level.SeetheAppendixforfurtherdetail.

16

Eventstudieswithmultipleevents

Asnotedabove,manystateshadmultipleevents(courtordersorlegislation)over

ourperiod.Unfortunately,thereisnoacceptedstrategyforconductingeventstudieswith

multipleeventsperunit.

Ohioillustratesboththechallengeandourproposedsolution.ThestateSupreme

CourtruledfourtimesontheDeRolphv.Statecase,in1997,2000,2001,and2002.The

1997rulingdeclaredthestate’sfinancesystemunconstitutionalonadequacygrounds,and

specificallyrejectedthestate’srelianceonlocalpropertytaxes.TheCourtordereda

“completesystematicoverhaul”oftheschoolfundingsystem.In2000,theCourt

determinedthatthelegislaturehadfailedtoactandthatfundinglevelsremained

inadequate.Thesameyear,thelegislaturerevisedthesystem,andasubsequentrulingin

2001determinedthatthenewsystem,withafewminorchanges,satisfiedconstitutional

requirements.Thisdecisionwasreversedin2002,bythesameCourt(albeitwitha

differentmakeupofjudges),andthelegislatureorderedtomakefurtherchanges.Toour

knowledge,thelegislaturedidnothingtocomplywiththis.

OurreformdatabaseincludesOhioeventsin1997,2000,and2002.Basedonthe

abovecasehistory,wemightexpectonlythe2000eventtobeassociatedwithmajor

changesinschoolfinanceinOhio.Butthedatatelladifferentstory.Figure7showsthe

timeseriesofourtwomeasuresoftheprogressivityofstateaidinOhio:Thedifferencein

averagestatetransfersperpupilbetweenthelowest-incomeandhighest-incomefifthsof

Ohioschooldistricts(black)andtheslopeofstatetransferswithrespecttologincome,

multipliedby-1forcomparability(gray).Verticallinesindicatethereformevents.The

figureshowsthatstatetransferswereprogressivein1990andslowlybecamemoresoin

17

thefirstfewyearsofourdata.Around1998,thetrendbecamenotablysteeper,andby

2002averagestateaidperpupilwas$4,851higherinlow-incomethaninhigh-income

districts.Ifanything,relativefundinghasdeclinedsince2002.Thispatternappears

consistentwithagradualreactiontotheinitial1997ruling.Thereislessvisualevidenceof

the2000event,whichdidnotinterrupttheprevioustrend,whilethe2002rulingseemsto

coincidewithanendtotheincreasesinprogressivity.

BasedonthepatternsinOhioandelsewhere,weadoptedtwoanalyticaldecisions

forourprimaryestimates.First,wechooseasingleeventineachstate.Ourideahereisthat

whenstateshavemultipleevents,theyoftenrepresentjockeyingbetweenthelegislature

andthecourtswithonlyminorchangesinschoolfinanceuntilthelegislaturefinallyenacts

amajorreform,andthencontinuedjockeyingafterwardasadvocatescontinuetopushfor

smalleradditionalchanges.

Second,wedonotrelyonreviewsofcasehistoriestoidentifytheconsequential

events,astherhetoricincourtordersandpreamblestobillsisoften(asinOhio)

misleadingaboutthemagnitudeofthechangebeingmade.Rather,weusethestateaid

datatoidentifyaregimechangeintheprogressivityofastate’sfinancesystem,relyingon

methodsfortheidentificationofchangepointsintimeseriesdata(e.g.,Bai1997;seealso

Card,Mas,andRothstein2008).

Specifically,let!"#beourslopemeasureoftheprogressivityofstateaid.Foreach

stateandeachpotentialeventdate)"∗,weestimateatimeseriesregressionusingasthe

onlyexplanatoryvariableanindicatorforobservationsafterthatdate:

(4) !"# = D + 1 ) > )"∗ ' + 1"# .

18

Weselectthedatethatyieldsthelargesttstatisticfor'–or,equivalently,thesmallest

meansquarederror–forthistimeseriesregression.17Wetreattheselecteddateasthe

singleeventinstates.Bai(1997)showsthatthismethodissuper-consistent(withfaster

than Econvergence)forthelocationofastructuralbreakinatimeseries,permitting

inferenceregardingthemagnitudeofthebreaktotreatitslocationasknown.

Wepresentestimatesfromtwoadditionalapproachestomultipleevents.One

includesallevents,withoutjudgmentabouttheirrelativeimportance.Wecreateaseparate

copyofthetimeseriesforthestateforeachevent,usingadifferentvalueof)"∗foreach

copy.Wethenstackthecopies,replacingthestateeffectsinequations(1)-(3)withstate-

by-eventeffects.18InMonteCarlosimulations,thismethodworkswelltoidentifythe

averageeffectofeventsbothwheneacheventhasthesameeffectandwhenonlyoneevent

inastatehasanon-zeroeffect.

Ourfinalapproachfollowsthepriorliteraturebyfocusingontheinitialcourtorder

ineachstate.Pastauthorshavearguedthatthetimingofinitialcourtordersiseffectively

randombutthatlegislativeeventsandsubsequentcourtordersmaynotbe.Thedrawback

tothisapproachisthattherecanbelonglagsbetweentheinitialcourtorderandthe

implementationofareform.Itisthusbettersuitedtosimplemodelslike(1)thatarenot

sensitivetomis-timingthestructuralbreak—mostpastworkusingthisapproachhas

focusedonsuchmodels—thantomoreflexiblemodelslikeournon-parametric

specification(3).

17Werestrictattentiontot*forwhichtheestimated'hastheexpectedsign.18Resultsareunchangedwhendataarereweightedtooffsettheoverrepresentationofstateswithmultiple

events.

19

Inappropriatespecifications,resultsarequiterobustacrossallthreemethods.

Accordingly,wedonotviewmultipleeventsasamajorissueinpractice.

III. Data

Ouranalysisdrawsondatafromseveralsources.Webeginwithourdatabaseof

stateSFRevents,discussedabove.Wemergethistodistrict-levelschoolfinancedata,from

theNationalCenterforEducationStatistics’(NCES)annualcensusofschooldistricts(the

CommonCoreofData,orCCD,districtfinancefiles,alsoknownasthe“F-33”survey)and

theCensusofGovernments;meanhouseholdincomebydistrictfromthe1990Census;and

NAEPachievement.

TheCCDdistrictfinancedatareportenrollment,revenuesandexpenditures

annuallyforeachlocaleducationagency(LEA).19Weconvertalldollarfiguresto2013

dollarsperpupil,andexcludeverysmalldistrictsandthosewithhighlyvolatileenrollment

orimplausibleper-pupilfunding.Detailsareintheappendix.

OurstudentoutcomemeasurescomefromtheNationalAssessmentofEducational

Progress(NAEP).Weuserestricted-usemicrodatafromthe“StateNAEP,”designedto

producestate-representativesamples.StateNAEPbeganin1990,with42states

participating.Ithasbeenadministeredroughlyeverytwoyearssince.Since2003,allstates

haveparticipatedin4thand8thgradeassessmentsinmathandreadingineveryodd-

numberedyear.20Table1showstheschedule.Testsareadministeredtoaround100,000

students(moreinlateryears)ineachsubject-grade-year.Theseconsistofrepresentative

samplesofabout2,500studentsperstate,spreadacrossabout100schools.

19Censusdataareavailablein1989-90and1991-92,andannuallysince1994-95.Weusesamplesfromthe

CensusBureau’sAnnualSurveyofGovernmentFinancesfor1992-93and1993-94.20TheNAEPalsotests12thgraders,butsamplesaresmaller,andothersubjects.

20

TheNAEPusesaconsistentscoringscaleacrossyearsforeachsubjectandgrade.

Westandardizescorestohavemeanzeroandstandarddeviationoneinthefirstyearthat

thetestwasgivenforthegradeandsubject,butallowboththemeanandvarianceto

evolveafterward.Wethenaggregatetothedistrict-year-grade-subjectlevelandmergeto

theCCDandSDDB.21

Table2apresentsdistrict-levelsummarystatistics,poolingdatafrom1990-2011.

Table2bpresentssummarystatisticsforthestate-yearpanel.

IV. Financereformsandschoolfinance

WebeginourempiricalanalysisbydocumentingtheimplicationsofSFReventsfor

schoolfinance.WeusetheapproachdiscussedinSectionIItoidentifyasingleSFReventin

eachstate,selectingamongcandidateeventstheonethatbestexplainsthetimeseriesof

thestateaid–logdistrictincomeslopeinthestate.

Figure8,panelAgraphseventstudyresultsforaveragestatetransfersperpupilin

thestate,poolingalldistricts.Wepresentanumberofplotsofthisbasicform.Thesolid

linepresentsestimatesofthenon-parametriceventstudyspecification(3),whiledotted

linesshowpointwise95%confidenceintervals.Thedashedlineshowstheparametric

specification(2).

Pointestimatesindicatethataveragestatetransferstodistrictsriseintheyears

leadinguptoanevent,thoughthiscouldbejustsamplingerror–thep-valueforequality

acrossallyearspriortotheeventsis0.31.Bycontrast,inthefouryearsfollowingtheevent

averagestatetransfersrisebyroughly$1,000.Theydeclinesomewhatinsubsequent

21Thepre-2000NAEPdatadonotusethesamedistrictcodesastheCCD.Wecrosswalkusingalinkfile

producedforNCESbyWestat(andobtainedfromtheEducationalTestingService),usingdistrictnamesto

checkandsupplementthecrosswalk.

21

years,buteven15yearsafterthefocaleventremainapproximately$500abovewhat

wouldhavebeenexpectedwithouttheevent.Thedifferencesfromtheeventyearare

significantbothcollectively(p<0.001)andindividuallyforrelativeyears1-10.The

parametricspecificationfitsthenonparametricresultswell.PanelBofFigure8repeatsthe

exercise,thistimeusingtotalper-pupilrevenues(inclusiveoflocalrevenuesandfederal

transfers)asthedependentvariable.Thepatternisquitesimilarhere,withlittleindication

thatincreasesinstaterevenuesareoffsetbyreductionsinlocaleffortonaverage.

Columns1and3ofTable3presentcoefficientsfromoursimplestone-parameter

eventstudyspecification(1),firstforstaterevenuesandthenfortotalrevenues.Eventsare

associatedwithincreasesinstateaidof$912perpupil,andwithslightlysmallerincreases

($829perpupil)intotalrevenues.Columns2and4presentthethree-parameter

specification(2).Post-eventeffectsarequitesimilartothoseseenintheone-parameter

models;whilepointestimatesindicatethattheytrenddownoversubsequentyears,these

arenotdistinguishablefromzero.Incolumn2,theupwardtrendprecedingeventsthatwas

visibleinFigure8aissmallandinsignificant,supportingourassumptionthateventtiming

israndom.

Theseresultspreviewageneralpatternweseethroughoutourfinanceanalyses.

Nonparametricmodelsshowalargejumpoverthefirstthreetofouryearsfollowingthe

event,withrelativelysmalltrendsbeforeandafter.Pre-eventtrendsareneverstatistically

significant,andwhilewecangenerallyrejectzeroeffectofeventsonallpost-event

outcomes,wecannever(inthethree-parametermodel)rejectasinglejumpfollowingthe

eventthatpersistsunchangedthereafter.Accordingly,wefocusontheone-parameter

modelforsubsequentfinanceanalyses.

22

Inadditionalanalysesofstatebudgets,(AppendixTableA2)wehavefoundno

indicationthatgrowthineducationalspendingfollowingeventscrowdsoutstatespending

onotherprograms;rather,SFRsareassociatedwithincreasesinstatetaxcollectionslarge

enoughtofullyfundtheincreaseinstatetransferstodistricts.

WeturnnexttoexaminingtheimpactofSFRsonthedistributionoffundingacross

schooldistricts.Figure9presentseventstudyanalyses,similartothoseinFigure8,for

averagestateaidandtotalrevenuesperpupilindistrictsinthetopandbottomquintilesof

thestateincomedistribution.Thereisagainsomeindicationofpre-eventupwardtrendsin

staterevenues,butagainwecannotrejectthenullhypothesisofzeropre-eventdifferences.

Bothlow-andhigh-incomedistrictsseeincreasesinstateandtotalrevenuesfollowingthe

event,buttheincreasesarelargerinlow-incomedistricts:Roughly$1,300bythe4thpost-

eventyear,vs.lessthanhalfthat(andnotrobustlysignificant)inhigh-incomedistricts.

Thoughout-yearestimatesarenoisy,impactsappeartopersistthroughtheendofour

sample.Patternsfortotalrevenuesareverysimilartothoseforstaterevenues,andshow

littlesignthatstaterevenueincreasesareoffsetbyreductionsinlocalrevenues.

PanelsBandCofTable3presenttheparametricestimatesforthelowest-and

highest-incomedistricts.Averagestatefundingis$1,225higheraftereventsinfirstquintile

districtsand$527(notsignificant)higherinfifthquintiledistricts;ineachcase,total

revenuechangesareofsimilarmagnitude,andthemoreflexiblespecificationyieldssimilar

results.

Figure10showsestimatesofimpactsontheprogressivityoftotalrevenues,usingin

thetoppanelthedifferenceinfundingbetweenbottom-andtop-quintiledistrictsandin

thelowerpaneltheslopeoffundingwithrespecttologdistrictincome.Parametricmodels

23

fortheseoutcomesareshowninColumn4ofTable4.Usingeachmeasure,weseesharp

increasesinrelativestatefundingforlow-incomedistrictsfollowingeventsthatare

sustained(thoughnotalwayspreciselyestimated)formanyyears.Innocaseisthereany

signofapre-eventtrendthatwouldsuggestaviolationofourrandomtimingassumption.

NoristhereanysigninTable4thatincreasedprogressivityofstateaidisoffsetbylocal

revenues.22

Anaturalquestionishowtheadditionalfundsarespent.Table5presentsevent-

studycoefficientsfromourone-parametermodelforper-pupilrevenuesandspendingin

variouscategories.ThereisnoapparentimpactofSFRsonlocalorfederalrevenues.We

seesubstantialimpactsofSFRsonaverageinstructionalspending,bothoverallandinQ1

districts(columns2and3).Wealsoseeeffectsonteachersperpupil,suggestingthat

districtsuseadditionalfundstoreduceclasssize,thoughwefindnosignofimpactson

teacherpay.23Wealsoseelargeincreasesinnon-instructionalexpenditures,particularly

capitaloutlays.

Columns4and5showresultsforrelativespendinginlow-incomedistricts.Littleof

theincreaseinrelativefundinggoestoinstructionalexpenditures,whileroughlyhalfgoes

tocapitalspending.Thecapitalspendingeffectisnotsurprising;manylawsuitsspecifically

concerndreadfulconditionsinlow-incomeschools,andSFRremediesoftencreatedfunds

tosupportrenovationofschoolsinpoorshape.24

22WhenweestimatespecificationssimilartoCardandPayne’s(2002)closelyrelatedanalysisofearlierSFRs

(AppendixTableA3),estimatedSFReffectsareslightlylargerbutimprecise,andwellwithintheearlier

confidenceintervals.WhereCardandPaynefindthattotalrevenuesrisebyabout$0.50perextra$1instate

aid,ourestimatesindicatemuchmorestickinessfortherecentreforms.23Usingadifferentresearchdesign,Sims(2011b)findseffectsofSFRsonteacherpay.24NeilsonandZimmerman(2014)findthatschoolreconstructioncausesincreasesinstudentachievement.

Cellinietal.(2010)andMartorell,Stange,andMcFarlin(2015)failtofindsignificanteffects,buteachstudyis

under-poweredtodetecteffectsofplausiblemagnitude.

24

V. Financereformsanddistrict-levelstudentachievement

Wecannowturntoourmainanalysis,examiningtheeffectofSFRsonstudent

achievement.Theaboveresultsestablishthatreformeventsareassociatedwithsharp,

immediateincreasesintheprogressivityofschoolfinance,withabsoluteandrelative

increasesinrevenuesinlow-incomeschooldistricts.Ifadditionalfundingisproductive,we

mightexpecttoseeimpactsonstudentoutcomes.

Wherethe!"#schoolfinancemeasuresformedastate-by-yearpanel,fortestscores

wehavetwoadditionaldimensions:Gradeandsubject.Wereplacetheyearfixedeffects

('#)in(1)-(3)withsubject-grade-yeareffects.Thesecaptureanydifferencesintests

betweenadministrations,aswellaschangesinstudentperformancebygradeand/or

subjectthatarecommonacrossstates.Toavoidconfoundingfromstate-levelshocks,we

focusonDDDspecificationsthatusetheachievementgapbetweenlow-andhigh-income

districtsasthedependentvariable.

Sharp,permanentchangesinfunding,ifusedproductively,shouldincreasetheflow

ofeducationalservices.Achievementiscumulative,sotheseservicesareunlikelytohave

immediateimpactsontestscores,butshouldraisescoresgraduallyasstudentsare

exposedforlonger.Effectsshouldgrowatleastuntilstudentshavebeenexposedtothe

newfundinglevelsfortheirentirecareers.Theymayevencontinuetogrowbeyondthis

point.Forexample,considerastatethatrespondstoacourtorderbycreatinganew

permanentfacilitytofundseveralschoolrenovationandconstructionprojectseachyear.

Initially,onlyafewstudentsbenefit,butovertimegrowingsharesofstudentsareexposed

tofundedprojects.Insofarasbetterfacilitiespromotestudentlearning,achievement

effectswouldcontinuetogrowuntilseveralyearsafterthelastprojectiscomplete,

25

potentiallydecadesaftertheinitialpolicychange.Wethusemphasizethephase-in

coefficientfromequation(2)astheprimarymeasureofSFReffectsontestscores.

Figure11presentsourevent-studyanalysisoftheslopeofachievementwith

respecttodistrictincome.Asbefore,wepresentnon-parametricresults(equation3)asa

solidlineandestimatesofourthree-parametermodel(equation2)asadashedline.There

isnoindicationofadifferentialtrendinreformstatespriortoevents.Followingevents,the

non-parametricseriesdoesnotreactimmediately,butbeginstrendingnoticeably

downwardstartinginaboutthefifthpost-eventyear.Thedownwardtrendcontinues

throughtheendofoursample.25

Table6presentsparametricestimates.WebegininColumn1withourthree-

parametermodel,asshowninFigure11.Again,theestimatedpre-eventtrendisessentially

zeroandthepost-eventjumpisalsosmall,butthepost-eventchangeintrendislargeand

statisticallysignificant.Column2presentsaspecificationthatdiscardstheothertwo

coefficients.Resultsarequitesimilar.Theestimatedchangeintheslopeis-0.010peryear.

Thisimpliesthateachyearafteranevent,adistrictwithlogmeanincomeoneunit(about

twothirds)belowthestateaverageseesitsscoresriserelativetothestateaverageby

0.010standarddeviations,accumulatingto0.10SDsovertenyears.Thisisquantitatively

meaningful–onaverageinoursampletheslopeoftestscoreswithrespecttologincomeis

0.96soSFRsreducethisgradientbyapproximatelyone-tenthwithintenyears.

Asdiscussedabove,thepatternofgraduallygrowingeffectsinFigure11is

consistentwithaviewofachievementasastockreflectingaccumulatedpastinputflows.

Thepatterndeviatesfromexpectationsinonerespect,however:Thereisnoindicationthat

25ThesawtoothpatternattheendofthesamplelikelyreflectsthebiannualNAEPtestingschedule.

26

thephase-inoftheeffectslowsfiveornineyearsaftertheevent,whenthe4thand8th

graders,respectively,willhaveattendedschoolsolelyinthepost-eventperiod.26Thismay

reflecttheuseofsomeadditionalfundsfordurableinvestments,asdiscussedabove.Wedo

nothaveenoughprecision,however,toruleoutaflatteningoftheeffectattheexpected

time.

Figure12presentsestimatedtestscoreimpactsforthelowest-andhighest-income

districts.Theeffectsontheincomegradientaredrivenbydramaticincreasesintestscores

inthelowest-incomedistricts.27Inhigher-incomedistricts,thereislittlesignofa

systematicpost-eventchange.ParametricestimatesareshowninColumns3and4ofTable

6;Column5showsthattheimpactofeventsonthetestscoregapbetweenbottom-and

top-quintiledistrictsis0.008SDsperyear.Thisgrowswhentrendtermsareincluded

(column6).Thegapinmeanlogincomesbetweenthetopandbottomquintilesaverages

0.65,sothequintilepointestimateisabitlargerthanwhatweobtainforourincomeslope

measureincolumns1-2.Ourearlierfinanceanalysesalsoindicatedlargereffectsfor

quintilegapsthanforslopes.

AppendixFigureA3presentsestimatesofthephase-incoefficientforallfive

quintiles.Onlythefirstquintileeffectislargeordistinguishablefromzero.Theratiooftest

scoreeffectstospendingeffectsislargeratthebottomoftheincomedistribution,

consistentwiththeideathatfundingismoreproductiveinlow-incomedistricts,butequal

ratioscannotberuledout.

26Wehaveestimatedseparatenon-parametricmodelsfor4thand8thgradescores.Bothsetsofeffectsgrow

roughlylinearlythroughtheendofourpanels.SeeAppendixFigureA4.27Forthelowest-incomedistricts(Figure12A),wecanrejectthenullhypothesisofzeropre-eventeffects.

Thisisdrivenbywhatappeartobeablipintestscorestwoyearspriortoevents.Asimilarblipisapparent

forhigh-incomedistrictsinPanelB.Thereisnosignofsystematicpre-eventtrends.

27

Table7presentsestimatesseparatelybygradeandsubject.Wecannotrejectthe

nullhypothesisofequaleffectsacrosseachdimension.

Robustness

Table8presentsestimatesofourkeyspecificationsfromourtwoalternative

approachestoeventmultiplicity.Column1repeatstheestimatesfromourpreferred

approachfromTables4and6.InColumn2,weincludeallidentifiedevents,creating

separatepanelsforeach;inColumn3,wefocusonlyonthefirstcourtorderineachstate.

Resultsaresimilartothosefromourmainspecifications,thoughtheinitialcourtorder

approachyieldslessprecise,insignificantestimatesoffinanceeffects.

Onepotentialexplanationfortheachievementimpactsthatweidentifyisthatthey

reflectchangesinpopulationstratificationratherthanchangesineducationalproduction.

SFRsthatflattenthegradientofschoolfundingwithrespecttodistrictincomeandthat

reducethelocalshareofschoolfinancereducethevalueoflivinginahigh-incomedistrict,

andmayleadsomehigh-incomefamiliestorelocatetopreviouslylow-incomedistricts.

Thiscouldleadtorisingachievementinthesedistrictswithnochangeinschool

effectiveness.

Weassessthispossibilityinthreeways.First,wehavetestedwhetherbetween-

districtincomegapsnarrowintheyearsfollowingSFRs.Wehavefoundnoevidencefor

this–districtlogincomesin2011arehighlycorrelatedwiththosein1990,andthereisno

signthatgapsnarrowinstatesthathadreformsvs.thosethatdidn’t.Second,wehave

conductedeventstudyanalyses,paralleltothosefortestscores,fordistrictincomeorthe

districtnon-whiteorfree-orreduced-priceluncheligibleshare(AppendixTableA5).In

onlyonespecification–forthebetween-quintilegapinthefreelunchshare–dowefind

28

evidencethatthedemographiccompositionof(initially)low-incomedistrictschanges

followingSFRs.Thisresultisnotrobust,andissmallrelativetothetestscoreimpactsthat

weestimate.

Third,wedecomposetestscoresintotwocomponents,andestimateseparateSFR

effectsoneach.Specifically,weestimateanindividual-levelregressionoftestscoreson

studentdemographiccharacteristics,poolingNAEPdataacrossyearsforeachgrade-

subjectpairandincludingyearfixedeffects.Wethenconstructseparateachievement-log

districtincomegradientsfromthefittedvalues(excludingthefixedeffects)forthis

regression,representingstudentcharacteristicsthatwouldbeaffectedbySFRsonly

throughchangesinsorting,andfromtheresiduals.Table9presentsresultsofourevent

studyanalysesofthesegradients.Wepresenttwodecompositions:Thefirstpaneluses

onlyraceandgender,whichareconsistentlyavailableineachNAEPwave,alongwith

schoolmeansofthese.Thenextusesadditionalcovariates,parentaleducationandfree

lunchstatus,thatarelessconsistentlyavailable,includingindicatorsforyearsinwhich

eachisunavailable.Thefirstsetofvariablesexplains22%ofthevarianceinstudenttest

scores(netofthesubject-grade-yeareffects),whilethesecondsetexplains28%.

Wefindnoevidencethatreformsaffectthedemographiccomponentofourtest

scoreprogressivitymeasures.Pointestimatesarelessthanhalfthesizeofouroveralltest

scoreimpacts,andareneversignificantlydifferentfromzero.Bycontrast,estimatedeffects

ontheresidualcomponentoftestscoresaresignificantandabouttwo-thirdsthesizeofthe

overallimpacts.Thus,whilewecannotruleoutsmalleffectsofSFRsonstudentsorting,the

robustnessofeffectsontheresidualcomponentsupportsourinterpretationthatour

resultsprimarilyreflectchangesineducationalproductioninlow-incomeschooldistricts.

29

Asafinalrobustnessexercise,wehavetestedwhethertheSFReffecton

achievementissensitivetoincludingcontrolsforthepresenceofaschoolaccountability

policyinastate,orwhethertheSFReffectvarieswithschoolaccountability.Wefound

evidenceforneither.

VI. Financereformsandstatewideachievementgaps

Thefinaltopicthatweinvestigateiswhetherfinancereformsclosedoveralltest

scoregapsbetweenhigh-andlow-achieving,minorityandwhite,orlow-incomeandnon-

low-incomestudentsinastate.Theseareperhapsbettermeasuresthanourslopesand

quintilegapsoftheoveralleffectivenessofastate’seducationalsystematdelivering

equitable,adequateservicestodisadvantagedstudents(KruegerandWhitmore2002;Card

andKrueger1992b).However,becausemostinequalityiswithindistricts,changesinthe

distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedtomeaningfully

closethesegaps.

Table10presentsestimatesofeffectsonmeantestscoresacrossdifferent

subgroupsofinterest.ThefirstpanelshowsaDDestimateoftheeffectonmean(pooled)

testscores.Thepointestimate(notinsignificant)impliesasmallerimpactperdollarthan

doourbetween-districtcontrasts,thoughwecannotruleoutcomparableeffectsizes.In

anyevent,ourresearchdesignismorecredibleforoutcomedisparitiesthanforthelevelof

outcomes,asthelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesin

astatethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek,Rivkin,and

Taylor1996a,b).Forexample,ifSFRsfollownegativeshockstomeanstudentachievement,

30

thiseffectwouldbedownward-biased.Anotherinterpretationisthatthemarginal

productivityofrevenuesisinfacthigherinlow-incomedistricts.

Thesecondpanelshowsimpactsonthestandarddeviationorinterquartilerangeof

achievementwithinstates,whilethethirdandfourthpanelspresentresultsbyraceand

income,respectively.Thereisnodiscernibleeffectonachievementgapsbyraceorincome

orontheoveralldispersionoftestscores.Pointestimatesareallroughlyafullorderof

magnitudesmallerthantheearlierestimatesfordistrict-levelprogressivityofmeanscores.

AppendixTablesA6andA7resolvethediscrepancy.Whilenon-white,low-income,

andlow-scoringstudentsaremorelikelythantheirwhite,higher-income,andhigher-

scoringpeerstoattendschoolinlow-incomeschooldistricts,thedifferencesarenotvery

large.Roughlyone-quarterofnon-whiteandlow-scoringstudents,andone-thirdoflow-

incomestudents,liveinfirst-quintiledistricts,whileabout10%ofeachliveinfifth-quintile

districts.ThisleaveslittleroomforSFRstosubstantiallyaffecttherelativeresourcesto

whichthetypicalminority,lowincome,orlowscoringstudentisexposed.

Toassessthismorecarefully,weassignedeachstudentthemeanrevenuesfor

his/herdistrictandestimatedeventstudymodelsfortheblack-white,income,ortestscore

gapintheseimputedrevenues.Results,inAppendixTableA7,indicatethatfinanceevents

raiserelativeper-pupilrevenuesintheaverageblackstudent’sschooldistrictbyonly$195

(S.E.164),intheaveragelow-incomestudent’sdistrictby$23(S.E.195),intheaverage

low-scoringstudent’sdistrictby193(S.E.101).Eveniffundingwasmuchmoreproductive

thantheaverageeffectimpliedbyouranalysis,thefundingchangesseenherewouldstill

notbeenoughtoyieldeffectsonblackorlow-incomestudents’averagetestscoreslarge

enoughtodetectwithourresearchdesign.Thus,whilereformsaimedatlow-income

31

districtsappeartohavebeensuccessfulatraisingresourcesandoutcomesinthese

districts,weconcludethatwithin-districtchangeswouldbenecessarytohavedramatic

impactsontheaveragelow-income,minority,orlow-scoringstudent.

VII. Discussion

Afterdesegregation,schoolfinancereformisperhapsthemostimportanteducation

policychangeintheUnitedStatesinthelasthalfcentury.Butwhiletheeffectsoftheearly

reformsonschoolfinancehavebeenwellstudied,thereislittleevidenceaboutthefinance

effectsofmorerecent“adequacy”reformsorabouttheeffectsofanyofthesereformson

studentachievement.Ourstudypresentsnewevidenceoneachofthesequestions.

Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacyera

markedlyincreasedtheprogressivityofschoolspending.Theydidnotaccomplishthisby

"levelingdown"schoolfunding,butratherbyincreasingspendingacrosstheboard,with

largerincreasesinlow-incomedistricts.Usingnationallyrepresentativedataonstudent

achievement,wefindthatthisspendingwasproductive:Reformsincreasedtheabsolute

andrelativeachievementofstudentsinlow-incomedistricts.Ourestimatesthus

complementthoseofJacksonetal.(2016),whoexaminethelong-runimpactsofearlier

schoolfinancereformsandfindsubstantialpositiveimpactsonavarietyoflong-run

outcomes.

Thedifferenttimepatternsofimpactsonresourcesandonstudentoutcomes,

combinedwiththecumulativenatureofthelatter,preventsasimpleinstrumental

variablesinterpretationofthereduced-formcoefficientsintermsoftheachievementeffect

perdollarspent–itisnotclearwhichyears’revenuesarerelevanttotheaccumulated

32

achievementofstudentstestedryearsafteranevent.Toassessthemagnitudeofthe

impactsweestimate,wefocusonestimatedeffectsonstudentachievementtenyearsafter

anevent.Becauseeffectsonschoolresourcesarestableintheyearsfollowingevents,these

canbeinterpretedastheimpactofachangeinresourcesforeveryyearofastudent’s

career(through8thgrade).Nevertheless,thefocusonther=10estimateisarbitrary.We

wouldobtainlargerestimatesoftheachievementeffectperdollarifweusedimpactsmore

thantenyearsafterevents,orsmallereffectswithashorterwindow.

Ourpreferredestimates,basedonthegradientofstudentachievementwithrespect

todistrictincome,indicatethatanSFRraisesachievementinadistrictwithlogaverage

incomeonepointbelowthestatemean,relativetoadistrictatthemean,by0.1standard

deviationsaftertenyears.Ourfinanceestimatesindicatethatthisdistrictsawanincrease

inrelativestateaidof$622perpupilforeachofthosetenyears,andanincreaseintotal

revenuesof$424perpupil.

$424perpupilinspendingeachyearfromkindergartenthroughgrade8,

discountedtothestudent’skindergartenyearusinga3%rate,correspondstoapresent

discountedcostof$3,400.Chettyetal.(2011)estimatethata0.1standarddeviation

increaseinkindergartentestscorestranslatesintoincreasedearningsinadulthoodwith

presentvalueof$5,350perpupil.Thisimpliesabenefit-costratioof1.5,evenwhenonly

earningsimpactsarecountedasbenefits.28

Thisratioisnotwhollyrobust.Ourquintileanalysisshowslargerrevenueeffects,

implyingabenefit-costratiobelowone,whileJacksonetal.’s(2016)studyoftheeffectsof

28Theearningseffectsofincreasesin8thgradetestscoresarelikelylargerthanthoseofincreasesin

Kindergartenscores,sousingestimatesofthelatterbiasesourbenefitcalculationdownward.Wedonot

countthecostofincreasedspendingingrades9-12,aswehavenowaytocaptureitsbenefits.

33

earlierfinancereformsonstudents’adultoutcomesimpliesmuchlargerbenefitsperdollar

thandoesourcalculation.Thus,althoughthesesortsofcalculationsarequiteimprecise,

theevidenceappearstoindicatethatthespendingenabledbyfinancereformswascost-

effective,evenwithoutaccountingforbeneficialdistributionaleffects.

Itisimportanttonotethatourresearchdesignispoorlysuitedtoidentifyingthe

optimalallocationofschoolresourcesacrossexpenditurecategories,ortotestingwhether

actualallocationsareclosetooptimal.Itallowsusonlytosaythattheaveragefinance

reform—whichweinterprettoinvolveroughlyunconstrainedincreasesinresources,

thoughinsomecasestheadditionalfundswereearmarkedforparticularprogramsortied

tootherreforms—ledtoaproductive(thoughperhapsnotmaximallyproductive)useof

thefunds.29

Ourresultsthusshowthatmoneycananddoesmatterineducation,and

complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom

Jacksonetal.(2016).Schoolfinancereformsareblunttools,andsomecritics(Hanushek,

2006;Hoxby,2001)havearguedthattheywillbeoffsetbychangesindistrictorvoter

choicesovertaxratesorthatfundswillbespentsoinefficientlyastobewasted.Our

resultsdonotsupporttheseclaims.Courtsandlegislaturescanevidentlyforce

improvementsinschoolqualityforstudentsinlow-incomedistricts.

Butthereisanimportantcaveattothisconclusion.AswediscussinSectionVI,the

averagelow-incomestudentdoesnotliveinaparticularlylow-incomedistrict,soisnot

welltargetedbyatransferofresourcestothelatter.Thus,wefindthatfinancereforms

29Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmore

efficiently(Hanushek2006).Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinance

reformeventsandthestate’saccountabilitypolicy,butfoundnoevidenceforthis.

34

reducedachievementgapsbetweenhigh-andlow-incomeschooldistrictsbutdidnothave

detectableeffectsonresourceorachievementgapsbetweenhigh-andlow-income(or

whiteandblack)students.Attackingthesegapsviaschoolfinancepolicieswouldrequire

changingtheallocationofresourceswithinschooldistricts,somethingthatwasnot

attemptedbythereformsthatwestudy.

References

Bai,J.(1997).Estimationofachangepointinmultipleregressionmodels.ReviewofEconomicsandStatistics,79(4),551-563.

Baker,B.D.,&Green,P.C.(2015).Conceptionsofequityandadequacyinschoolfinance.In

H.F.LaddandM.E.Goertz,eds.,HandbookofResearchinEducationFinanceandPolicy,2ndedition.NewYork,NY:Routledge.

Burtless,G.(1996).DoesMoneyMatter?TheEffectofSchoolResourcesonStudentAchievementandAdultSuccess.Washington,D.C.:BrookingsInstitutionPress.

Card,D.,&Krueger,A.B.(1992a).Doesschoolqualitymatter?Returnstoeducationandthe

characteristicsofpublicschoolsintheUnitedStates.JournalofPoliticalEconomy,100(1),1–40.

Card,D.,&Krueger,A.B.(1992b).Schoolqualityandblack-whiterelativeearnings:Adirect

assessment.QuarterlyJournalofEconomics,107(1),151-200.Card,D.;Mas,A.,&Rothstein,J.(2008).Tippingandthedynamicsofsegregation.Quarterly

JournalofEconomics,123(1),177–218.Card,D.,&Payne,A.A.(2002).Schoolfinancereform,thedistributionofschoolspending,

andthedistributionofstudenttestscores.JournalofPublicEconomics,83(1),49-82.Cascio,E.U.,Gordon,N.,&Reber,S.(2013).Localresponsestofederalgrants:evidence

fromtheintroductionoftitleIintheSouth.AmericanEconomicJournal:EconomicPolicy,5(3),126-159.

Cascio,E.U.,&Reber,S.(2013).Thepovertygapinschoolspendingfollowingthe

introductionofTitleI.AmericanEconomicReview,103(3),423-427.Cellini,S.,Ferreira,F.,&Rothstein,J.(2010).Thevalueofschoolfacilityinvestments:

Evidencefromadynamicregressiondiscontinuitydesign.QuarterlyJournalofEconomics125(1),215-261.

Chetty,R.,Friedman,J.N.,Hilger,N.,Saez,E.,Schanzenbach,D.W.,&YaganD.(2011).How

doesyourKindergartenclassroomaffectyourearnings?EvidencefromProject

STAR.QuarterlyJournalofEconomics,126(4),1593-1660.Clark,M.A.(2003).Educationreform,redistribution,andstudentachievement:Evidence

fromtheKentuckyEducationReformAct.Unpublishedworkingpaper,Mathematica

PolicyResearch,Princeton,NJ.

Coleman,J.S.,Campbell,E.Q.,Hobson,C.J.,McPartland,J.,Mood,A.M.,Weinfeld,F.D.,&

York,R.(1966).EqualityofEducationalOpportunity.Washington,DC,1066-5684.

35

Coons,J.E.,Clune,W.H.,&Sugarman,S.(1970).PrivateWealthandPublicEducation.Cambridge,MA:BelknapPress.

Corcoran,S.P.,&Evans,W.N.(2015).Equity,adequacy,andtheevolvingstaterolein

educationfinance.InH.F.LaddandM.E.Goertz,eds.,HandbookofResearchinEducationFinanceandPolicy,2ndedition.NewYork:Routledge.

Dee,T.S.,&Jacob,B.(2011).TheimpactofNoChildLeftBehindonstudentachievement.

JournalofPolicyAnalysisandManagement,30(3),418-446.Downes,T.,Stiefel,L.(2015).Measuringequityandadequacyinschoolfinance.InH.F.

Ladd&M.E.Goertz,eds.,HandbookofResearchinEducationFinanceandPolicy,2ndedition.NewYork,NY:Routledge.

Duncombe,W.D.,Nguyen-Hoang,P.,&J.Yinger(2015).Measurementofcostdifferentials.

InH.F.Ladd,&M.E.Goertz,eds.,HandbookofResearchinEducationFinanceandPolicy,2ndedition.NewYork,NY:Routledge.

Dynarski,S.,Hyman,J.,&Schanzenbach,D.W.(2013).Experimentalevidenceontheeffect

ofchildhoodinvestmentsonpostsecondaryattainmentanddegreecompletion.

JournalofPolicyAnalysisandManagement,32(4),692-717.Fischel,W.A.(1989).DidSerranocauseProposition13?NationalTaxJournal42(4):465-

73.

Flanagan,A.E.,andMurray,S.E.(2004).ADecadeofReform:TheImpactofSchoolReform

inKentucky.InJ.Yinger,ed.,HelpingChildrenLeftBehind:StateAidandthePursuitofEducationalEquity(pp.165-213).Cambridge,MA:MITPress.

Guryan,J.(2001).Doesmoneymatter?Regression-discontinuityestimatesfromeducationfinancereforminMassachusetts.NationalBureauofEconomicResearchWorkingPaperNo.8269.

Hanushek,E.A.(1986).Theeconomicsofschooling:Productionandefficiencyinpublic

schools.JournalofEconomicLiterature,24(3),1141-1177.Hanushek,E.A.(1997).Assessingtheeffectsofschoolresourcesonstudentperformance:

Anupdate.EducationalEvaluationandPolicyAnalysis,19(2),141-164.Hanushek,E.A.(2003).Thefailureofinput-basedschoolingpolicies.TheEconomicJournal,

113,F64-F98.

Hanushek,E.A.(2006).Schoolresources.InE.A.HanushekandF.Welch,eds.,HandbookoftheEconomicsofEducation,vol.2.Elsevier.

Hanushek,E.A.&Lindseth,A.A.(2009).Schoolhouses,CourthousesandStatehouses:SolvingtheFunding-AchievementPuzzleinAmerica’sPublicSchools.Princeton:PrincetonUniversityPress.

Hanushek,E.A.,Rivkin,S.G.,&Taylor,L.L.(1996a).Aggregationandtheestimatedeffects

ofschoolresources.TheReviewofEconomicsandStatistics78(4),611-627.Hanushek,E.A.,Rivkin,S.G.,&Taylor,L.L.(1996b).Theidentificationofschoolresource

effects.EducationEconomics,4(2),105-125.Horowitz,H.(1966).Unseparatebutunequal:TheemergingFourteenthAmendmentissue

inpublicschooleducation.UCLALawReview,13,1147-1172.Hoxby,C.M.(2001).Allschoolfinanceequalizationsarenotcreatedequal.TheQuarterly

JournalofEconomics,116(4),1189-1231.Hyman,J.(2013).Doesmoneymatterinthelongrun?Effectsofschoolspendingon

educationalattainment.Unpublishedmanuscript.

36

Jackson,C.K.,Johnson,R.C.,&Persico,C.(2016).Theeffectsofschoolspendingon

educationalandeconomicoutcomes:Evidencefromschoolfinancereforms.

QuarterlyJournalofEconomics131(1),157-218.Kirp,D.L.(1968).Thepoor,theschools,andequalprotection.HarvardEducationalReview

38,635-668.

Koski,W.S.,&Hahnel,J.(2015).Thepast,presentandfutureofeducationalfinancereform

litigation.InH.F.LaddandM.E.Goertz,eds.,HandbookofResearchinEducationFinanceandPolicy,2ndedition.NewYork:Routledge.

Krueger,A.B.(1999).Experimentalestimatesofeducationproductionfunctions.TheQuarterlyJournalofEconomics,114(2),497-532.

Krueger,A.B.(2003).Economicconsiderationsandclasssize.TheEconomicJournal113,F34-F63.

Krueger,A.B.,&Whitmore,D.M.(2002).Wouldsmallerclasseshelpclosetheblack-white

achievementgap?InJ.E.ChubbandT.Loveless,eds.,BridgingtheAchievementGap.Washington:BrookingsInstitutionPress.

Ladd,H.F.,&Goertz,M.E.(Eds.).(2015).HandbookofResearchinEducationFinanceandPolicy,2ndEdition.NewYork,NY:Routledge.

Levine,P.B.,&Schanzenbach,D.(2009).Theimpactofchildren’spublichealthinsurance

expansionsoneducationaloutcomes.ForumforHealthEconomics&Policy,12(1),1-26.

Martorell,P.,Stange,K.M.,&McFarlin,I.(2015).Investinginschools:Capitalspending,

facilityconditions,andstudentachievement.NBERWorkingPaper21515,

September.

Murray,S.E.,Evans,W.N.,&Schwab,R.M.(1998).Education-financereformandthe

distributionofeducationresources.AmericanEconomicReview,88(4),789-812.Nielson,C.,&Zimmerman,S.(2014).Theeffectofschoolconstructionontestscores,school

enrollment,andhomeprices.JournalofPublicEconomics120.Sims,D.P.(2011a).Liftingallboats?Financelitigation,educationresources,andstudent

needsinthepost-Roseera.EducationFinanceandPolicy,6(4),455-485.Sims,D.P.(2011b).Suingforyoursupper?Resourceallocation,teachercompensationand

financelawsuits.EconomicsofEducationReview,30(5),1034-1044.Wise,A.(1967).RichSchools,PoorSchools:ThePromiseofEqualEducationalOpportunity.

Chicago,IL:UniversityofChicagoPress.

Figures

Figure 1: Mean revenues per pupil for highest and lowest income school districts, 1990-2012

80

00

10

00

01

20

00

14

00

0Q

1,

Q5

Me

an

To

tal R

eve

nu

es

1990 1995 2000 2005 2010Year

Q1 Mean Q5 Mean

Notes: Highest (lowest) income districts are those in the top (bottom) 20% of their states’ district-leveldistributions of mean household income in 1990, and are labeled as ”Q5” and ”Q1”, respectively. Seeappendix for details of quintile classifications. Revenues are expressed in real 2013 dollars. Districts areaveraged within states, weighing by log district enrollment; states are then averaged without weights. Hawaiiand the District of Columbia are excluded.

37

Figure 2: Gap in revenues per pupil between lowest and highest income districts, by state finance reformstatus, 1990-2012

−1

00

0−

50

00

50

01

00

0Q

1−

Q5

Me

an

To

tal R

eve

nu

es

1990 1995 2000 2005 2010Year

No Reform States Finance Reform States

Notes: See notes to Figure 1. Finance reform states are those with school finance reforms between 1990 and2011, as listed in Appendix Table A1. Lines show unweighted best linear fit to time series.

38

Figure 3: Gap in average test scores between lowest and highest income districts, by state finance reformstatus, 1990-2011

−.7

−.6

−.5

−.4

Q1

−Q

5 M

ea

n S

co

re

1990 1995 2000 2005 2010Year

No Reform States Finance Reform States

Notes: Lowest (Q1) and highest (Q5) income districts are defined as in Figure 1. NAEP observations indistricts in each quintile are averaged, using NAEP sampling weights and separately for each grade andsubject tested, and the Q1-Q5 di↵erence is computed for each state. State-grade-subject Q1-Q5 di↵erencesare averaged separately for each group of states, weighting by the harmonic mean of the sum of the studentweights in Q1 and Q5 districts. Lines show best linear fit to the time series.

39

Figure 4: Timing of school finance events

02

46

8E

ve

nts

pe

r ye

ar

1990 2000 2010Year

Statute

Court

Notes: Each entry represents a state with a school finance reform event (a major court ruling and/orsubstantial statutory change) in a particular year. States may have multiple events. When states havemultiple events in the same year, they are counted only once, as a court event if any of the events were courtrulings and as a statute otherwise. Events are listed in Appendix Table A1.

40

Figure 5: Geographic distribution of post-1989 school finance events

No Event

Post-1990 Reform Event

Notes: Map indicates states that had school finance reform events, as listed in Appendix Table A1, between1990 and 2011.

41

Figure 6: State revenues per pupil vs. district income, Ohio, 1990 and 2012

05000

10000

15000

20000

9.5 10 10.5 11 11.5 12

1990

05000

10000

15000

20000

9.5 10 10.5 11 11.5 12

2012

Sta

te a

id p

er

pupil

(2013$)

ln(district avg. HH income, 1990)

Notes: Each circle represents one district; size is proportional to average district enrollment over 1990-2012.Solid lines represent a regression of state revenue per pupil (2013$) on log 1990 district mean householdincome, controlling for enrollment and district type (see footnote 16). Dashed lines represent means amongdistricts in each quintile of the district mean income distribution.

42

Figure 7: Progressivity of state revenue distributions, Ohio, 1990-2012

10

00

20

00

30

00

40

00

50

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

Q1−Q5 difference

−1*(Log income gradients)

Notes: Dark line represents the di↵erence in mean state revenue per pupil (2013$) between the lowest (Q1)and highest (Q5) income districts in Ohio. Districts are classified based on 1990 mean household incomeand are weighted by log enrollment; see notes to Figure 1 for details. Lighter line represents regressions ofstate revenue per pupil on log mean income, controlling for enrollment and district type (see footnote 16); inthis figure, coe�cients are multiplied by -1 to facilitate comparisons. Solid vertical lines represent plainti↵victories in the Ohio Supreme Court in De Rolph v State I, II, and IV in 1997, 2000, and 2002.

43

Figure 8: Event study estimates of e↵ects of school finance reforms on mean state and total revenues

−2000

−1000

01000

2000

Change in m

ean s

tate

revenues

−5 0 5 10 15 20Years Since Event

Non−Parametric Estimate Parametric Estimate

(a) State revenue

−2000

−1000

01000

2000

Change in m

ean tota

l re

venues

−5 0 5 10 15 20Years Since Event

Non−Parametric Estimate Parametric Estimate

(b) Total revenue

Notes: Figure displays coe�cients from event study regressions, where the dependent variable is mean state(panel A) and total (panel B) revenues per pupil (2013$) across all districts in a state. Dashed lines showthe three-parameter parametric model (equation 2). Solid lines show the non-parametric model (equation3), with the event year (indicated as 0) as the excluded category; dotted lines represent 95% confidenceintervals. Estimates for the parametric models are reported in Table 3, Panel A, Columns 2 and 4. p valuesfor omnibus hypothesis tests of zero pre- and post-event e↵ects in the non-parametric model are 0.31 and<0.001, respectively, in Panel A, and 0.15 and <0.001 in Panel B. In the parametric model, the p-value forthe hypothesis that the pre-event trend is zero is 0.18 in Panel A and 0.79 in Panel B; for the test that thepost-event jump and change in trend is zero it is 0.11 and 0.01, respectively.

44

Figure 9: Event study estimates of e↵ects of school finance reforms on mean revenues in lowest and highestincome districts

−2000

02000

4000

Change in Q

1 m

ean s

tate

revenues

−5 0 5 10 15 20Years Since Event

Non−Parametric Estimate Parametric Estimate

(a) State revenue, Q1−

2000

02000

4000

Change in Q

1 m

ean tota

l re

venues

−5 0 5 10 15 20Years Since Event

Non−Parametric Estimate Parametric Estimate

(b) Total revenue, Q1

−2000

02000

4000

Change in Q

5 m

ean s

tate

revenues

−5 0 5 10 15 20Years Since Event

Non−Parametric Estimate Parametric Estimate

(c) State revenue, Q5

−2000

02000

4000

Change in Q

5 m

ean tota

l re

venues

−5 0 5 10 15 20Years Since Event

Non−Parametric Estimate Parametric Estimate

(d) Total revenue, Q5

Notes: Figure displays coe�cients from event study regressions. Dependent variables are mean state revenuesin the lowest income quintile of districts (panel A), mean total revenues in these districts (panel B), andmean state and total revenues in the highest income quintile of districts (panels C and D, respectively), allmeasured in 2013 dollars per pupil. Dashed lines show the three-parameter parametric model (equation 2).Solid lines shows the non-parametric model (equation 3), with the event year (indicated as 0) as the excludedcategory; dotted lines represent 95% confidence intervals. Estimates for the parametric models are reportedin Table 3, Panels B and C, Columns 2 and 4. p values for omnibus hypothesis tests of zero pre-event e↵ectsin the non-parametric model in Panels A-D are 0.53, 0.40, 0.41, and 0.74, respectively; p-values for zeropost-event e↵ects are <0.001 in all panels. In the parametric model, the p-values for the hypothesis thatthe pre-event trend is zero are 0.24, 0.68, 0.21, and 0.78; for the test that the post-event jump and changein trend is zero they are 0.01, <0.001, 0.30, and 0.22.

45

Figure 10: Event study estimates of e↵ects of school finance reforms on progressivity of district revenues

−2000

−1000

01000

2000

Change in Q

1−

Q5 m

ean tota

l re

venues

−5 0 5 10 15 20Years Since Event

Non−Parametric Estimate Parametric Estimate

(a) Q1-Q5 mean

−2000

−1000

01000

2000

Change in tota

l re

venue s

lope

−5 0 5 10 15 20Years Since Event

Non−Parametric Estimate Parametric Estimate

(b) Total revenue slope

Notes: Figure displays coe�cients from event study regressions. Dependent variables are the di↵erence inmean total revenues per pupil (in 2013$) between districts in the bottom and top quintile by mean familyincome in the state (panel A), and the slope of total per-pupil revenues (in 2013$) with respect to logmean family income, controlling for log enrollment and district type (panel B). Dashed lines show the three-parameter parametric model (equation 2). Solid lines shows the non-parametric model (equation 3), withthe event year (indicated as 0) as the excluded category; dotted lines represent 95% confidence intervals.Estimates for the parametric models are reported in Table 4, Panels A and B, Columns 2 and 4. p-valuesfor omnibus hypothesis tests of zero pre-event e↵ects in the non-parametric model are 0.86 in Panel A and0.96 in Panel B; p-values for zero post-event e↵ects are <0.001 in each panel. In the parametric model, thep-value for the hypothesis that the pre-event trend is zero is 0.72 in Panel A and 0.58 in Panel B; for thetest that the post-event jump and change in trend is zero it is 0.01 and 0.11, respectively.

46

Figure 11: Event study estimates of e↵ects of school finance reforms on progressivity of test scores

−.3

−.2

−.1

0.1

Ch

an

ge

in

te

st

sco

re s

lop

e

−5 0 5 10 15 20Years Since Event

Non−Parametric Estimate Parametric Estimate

Notes: Figure displays coe�cients from event study regressions. Dependent variable is the slope of meantest scores with respect to log mean family income, controlling for log enrollment. Dashed lines show thethree-parameter parametric model (equation 2). Solid lines shows the non-parametric model (equation 3),with the event year (indicated as 0) as the excluded category; dotted lines represent 95% confidence intervals.Both event study regressions include state and subject-grade-year fixed e↵ects. Estimates for the parametricmodels are reported in Table 6, Column 1. p-values for the hypothesis that pre-event e↵ects are zero are 0.43in the non-parametric model and 0.80 in the parametric model; for zero post-event e↵ects, they are <0.001and 0.02, respectively.

47

Figure 12: Event study estimates of e↵ects of school finance reforms on mean test scores in highest andlowest income school districts

−.1

0.1

.2.3

Change in Q

1 M

ean T

est S

core

s

−5 0 5 10 15 20Years Since Event

Non−Parametric Estimate Parametric Estimate

(a) Q1 mean test scores

−.1

0.1

.2.3

Change in Q

5 M

ean T

est S

core

s

−5 0 5 10 15 20Years Since Event

Non−Parametric Estimate Parametric Estimate

(b) Q5 mean test scores

Notes: Figure displays coe�cients from event study regressions. Dependent variables are mean test scores forstudents at districts in the bottom quintile (panel A) or top quintile (panel B) of the state’s distribution of1990 district mean household incomes. Dashed lines show the three-parameter parametric model (equation2). Solid lines shows the non-parametric model (equation 3), with the event year (indicated as 0) as theexcluded category; dotted lines represent 95% confidence intervals. Both event study regressions includestate and subject-grade-year fixed e↵ects. p-values for omnibus hypothesis tests of zero pre-event e↵ects inthe non-parametric model are 0.01 in Panel A and 0.02 in Panel B; p-values for zero post-event e↵ects are<0.001 in each panel. In the parametric model, the p-value for the hypothesis that the pre-event trend iszero is 0.86 in Panel A and 0.15 in Panel B; for the test that the post-event jump and change in trend iszero it is 0.01 and 0.25, respectively.

48

Tables

Table 1: NAEP Testing Years

Year Subjects and grades covered Number of Number ofMath G4 Math G8 Reading G4 Reading G8 States Students

1990 X 38 97,9001992 X X X 42 321,1201994 X 41 104,8901996 X X 45 228,9801998 X X 41 206,8102000 X X 42 201,1102002 X X 51 270,2302003 X X X X 51 691,3602005 X X X X 51 674,4202007 X X X X 51 711,3602009 X X X X 51 775,0602011 X X X X 51 749,250

Notes: In final column, students are cumulated across all tested subjects and grades, and rounded to thenearest 10.

49

Table 2: Summary statistics

(a) District-year panel

Overall Mean by subgroup

N Mean SD Q1 Q5

Enrollment 229,386 67,523 181,811 13,537 31,403

Log(mean income, 1990) 223,334 10.53 .2935 10.21 10.9

Total revenue p.p. 229,386 11,087 3,489 10,809 11,871

State 229,386 5,135 2,291 6,371 4,003

Local 229,386 5,094 3,273 3,258 7,349

Federal 229,386 858.2 641.4 1,180 518.4

Expenditures p.p. 229,386 11,264 3,685 10,837 12,116

Instructional 229,386 5,845 1,953 5,659 6,167

Non-instructional 229,386 5,419 2,221 5,178 5,949

NAEP scores 49,867 .2559 .4578 .02925 .5884

(b) State-year panel

N Q1 Q5 Q1-Q5 di↵erence Gradient

Mean SD Mean SD Mean SD Mean SD

Log(mean income, 1990) 49 10.2 .135 10.8 .234 -.645 .167

Total revenue p.p. 1,078 11,527 3,905 11,844 3,351 -329 2,158 539 3,574

State 1,078 6,552 2,822 4,347 2,006 2,196 2,244 -3,086 3,470

Local 1,078 3,658 1,600 6,893 3,477 -3,231 2,624 5,190 3,313

Federal 1,078 1,317 1,082 604 482 706 722 -1,565 1,532

Mean NAEP score 532 .0374 .316 .513 .304 -.475 .326 .955 .337

Notes: Panel (a) reports summary statistics at the district by year level, weighted by district enrollmentfor the financial variables and by the sum of the student weights for the mean NAEP score. Panel (b) showssummary statistics for the unweighted state-year panel.

50

Table 3: Event study estimates of e↵ects of school finance reforms on mean revenues per pupil, by districtincome

State Revenue Total Revenue

1p 3p 1p 3p

Mean:

Post Event 912⇤⇤ 672⇤⇤ 829⇤⇤⇤ 839⇤⇤⇤

(359) (320) (302) (269)Trend 68 9

(50) (32)Post Event * Yrs Elapsed -61 -17

(60) (52)

Observations 1,078 1,078 1,078 1,078

Q1 Mean:

Post Event 1,225⇤⇤⇤ 954⇤⇤⇤ 1,233⇤⇤⇤ 1,164⇤⇤⇤

(343) (302) (370) (287)Trend 60 16

(50) (39)Post Event * Yrs Elapsed -40 -11

(70) (70)

Observations 1,078 1,078 1,078 1,078

Q5 Mean:

Post Event 527 351 544⇤⇤ 471⇤

(378) (325) (277) (277)Trend 72 9

(56) (32)Post Event * Yrs Elapsed -84 2

(61) (41)

Observations 1,076 1,076 1,076 1,076

Notes: Table reports estimates of the parametric event study models, equations (1) (columns 1 and3) and (2) (columns 2 and 4). Dependent variables are mean state revenues per pupil (columns 1-2) andmean total revenues per pupil (columns 3-4), weighting districts by their log enrollment; each is computedseparately for each state and year. In panel A, means are computed over all districts in each state; in panelsB and C, they are computed over the bottom and top, respectively, quintiles of the states’ district 1990mean household income distributions. Event study regressions include state and year fixed e↵ects, and areunweighted. Standard errors clustered at the state level.

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Table 4: Event study estimates of e↵ects of school finance reforms on progressivity of school finance

State Revenue Total Revenue

1p 3p 1p 3p

Q1-Q5 Mean:

Post Event 711⇤⇤ 606⇤⇤⇤ 701⇤⇤ 696⇤⇤⇤

(316) (231) (309) (243)Trend -10 9

(25) (24)Post Event * Yrs Elapsed 42 -14

(36) (44)

Observations 1,076 1,076 1,076 1,076

Slopes:

Post Event -622⇤⇤⇤ -522⇤⇤ -424 -469⇤⇤

(223) (209) (304) (233)Trend -11 -25

(25) (45)Post Event * Yrs Elapsed -5 53

(21) (61)

Observations 1,078 1,078 1,078 1,078

Notes: Table reports estimates of the parametric event study models, equations (1) (columns 1 and3) and (2) (columns 2 and 4). In Panel A, dependent variable is the gap in state (columns 1-2) or total(columns 3-4) revenues per pupil between districts in the bottom and top quintiles of the states’ district 1990mean household income distributions. In Panel B, dependent variable is the coe�cient from a district-levelregression of the relevant per-pupil revenue measure on the log of the district’s 1990 mean household income,controlling for district log enrollment and district type (elementary / secondary / unified) and weighting bythe district’s average log enrollment over time. Event study regressions include state and year fixed e↵ects.Event study regressions are unweighted in Panel A, and is weighted by the inverse squared standard errorof the dependent variable in Panel B. Standard errors clustered at the state level.

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Table 5: Event study estimates of e↵ects of school finance reforms on components of district finance

Mean of depvar Mean Q1 Mean Q1-Q5 Mean Slope

Revenue E↵ects:

Total revenue 11,593 829⇤⇤⇤ 1,233⇤⇤⇤ 701⇤⇤ -424(302) (370) (309) (304)

State revenue 5,449 912⇤⇤ 1,225⇤⇤⇤ 711⇤⇤ -622⇤⇤⇤

(359) (343) (316) (223)Local revenue 5,238 -146 -126 -126 90

(307) (233) (235) (339)Federal revenue 907 63 134 116 34

(83) (143) (116) (33)

Expenditure E↵ects:

Total expenditures 11,595 907⇤⇤⇤ 1,377⇤⇤⇤ 753⇤⇤ -449(290) (367) (309) (309)

Current instructional exp. 6,000 443⇤⇤⇤ 604⇤⇤⇤ 243⇤ -161(134) (155) (127) (208)

Teacher salaries + benefits 5,533 339⇤⇤ 449⇤⇤⇤ 143 -103(153) (169) (117) (189)

Mean teacher salary 63,425 -286 -245 272 -259(1,024) (1,107) (947) (1,122)

Pupil teacher ratio 15.40 -0.62⇤⇤⇤ -0.67⇤⇤⇤ 0.00 0.23(0.19) (0.19) (0.20) (0.17)

Non-instructional exp 5,595 464⇤⇤ 773⇤⇤⇤ 511⇤⇤ -232(186) (257) (235) (176)

Student support 3,426 221⇤⇤ 299⇤⇤ 100 -81(102) (119) (83) (88)

Total capital outlays 1,076 272⇤⇤ 486⇤⇤⇤ 369⇤⇤ -87(114) (177) (181) (78)

Other current exp. 431.0 7.9 9.2 -2.5 -2.9(12.4) (14.5) (13.3) (12.1)

Notes: Each entry in columns 2-5 represents the coe�cient from a separate event study regression, usingthe one-parameter specification in equation (1). Dependent variables are constructed from district-levelfinance summaries indicated by row headings and expressed in per-pupil terms; means across districts arereported in column 1. Specifications correspond to columns 1 and 2 of Table 3, panels A (column 2) and B(column 3), and Table 4, panels A (column 4) and B (column 5). See notes to Tables 3 and 4.

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Table 6: Event study estimates of e↵ects of school finance reforms on student achievement

Slopes Q1 Q5 Q1-Q5

(1) (2) (3) (4) (5) (6)

Post Event * Yrs Elapsed -0.011⇤⇤ -0.010⇤⇤⇤ 0.007⇤⇤ -0.001 0.008⇤⇤ 0.013⇤⇤

(0.004) (0.003) (0.003) (0.003) (0.004) (0.006)

Trend 0.001 -0.006(0.003) (0.005)

Post Event 0.001 0.011(0.023) (0.024)

Observations 1498 1498 1509 1506 1504 1504p, total event e↵ect=0 0.02 0.01 0.02 0.69 0.04 0.07State FEs X X X X X XSub-gr-yr FEs X X X X X X

Notes: Each column represents a separate event study regression, using specification (2) and, in columns2-5, constraining �jump = �trend = 0. Dependent variable in columns 1-2 is the slope of test scores with re-spect to log mean 1990 income in the district, using NAEP weights and controlling for log district enrollment.In columns 3-4, dependent variable is the weighted mean score in districts in the bottom or top quintile,respectively, of the state district-level income distribution. In columns 5-6, dependent variable is the di↵er-ence between the bottom and top quintiles. All are computed separately for each state-year-subject-gradecell with available data. All event study specifications include state and subject-grade-year fixed e↵ects, andare weighted by the inverse squared standard error of the dependent variable. p-values for total event e↵ectin columns 1 and 6 test the hypothesis that the �jump and �phasein coe�cients are both zero; in columns2-5, the p-value is for the hypothesis that �phasein = 0, with �jump constrained to zero.

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Table 7: Event study estimates of e↵ects of school finance reforms on student achievement by subject andgrade

Test Score Slope Q1-Q5 Mean

Pooled -0.010⇤⇤⇤ 0.008⇤⇤

(0.003) (0.004)

By Subject :

Math -0.012⇤⇤⇤ 0.007⇤

(0.003) (0.004)Reading -0.006 0.009⇤⇤

(0.005) (0.004)

Di↵erence -0.006 -0.002p-value 0.09 0.46

By Grade:

G4 -0.010⇤⇤ 0.009⇤

(0.005) (0.005)G8 -0.010⇤⇤ 0.007⇤⇤

(0.004) (0.004)

Di↵erence 0.000 0.001p-value 0.93 0.72

Notes: First row repeats specifications from Table 6, columns 2 and 5. See notes to that table for details.Subsequent models restrict the event study sample to slope and quintile gaps computed in specific subjectsor grades. Di↵erence entries report the di↵erence in coe�cients between math and reading or grade 4 andgrade 8 specifications, with p-values for the hypothesis that the event study coe�cient is equal in the twosubsamples.

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Table 8: Sensitivity of event study estimates to the treatment of states with multiple events

Selected Events All events (stacked) Initial court events

Panel A: Gradients

State revenue p.p. -622⇤⇤⇤ -479⇤⇤⇤ -432⇤

(223) (160) (222)Total revenue p.p. -424 -197 -399

(304) (269) (292)NAEP scores -0.010⇤⇤⇤ -0.009⇤⇤⇤ -0.009⇤⇤⇤

(0.003) (0.003) (0.003)

Panel B: Q1-Q5 di↵erences

State revenue p.p. 711⇤⇤ 463⇤⇤ 516(316) (191) (354)

Total revenue p.p. 701⇤⇤ 448⇤⇤ 584(309) (195) (398)

NAEP scores 0.008⇤⇤ 0.011⇤⇤⇤ 0.008⇤⇤

(0.004) (0.004) (0.004)

Notes: Column 1 repeats estimates of the one-parameter parametric event study models from Table 4,columns 1 and 3, and Table 6, columns 2 and 5. See notes to those tables for details. In column 2, eachpotential event in each state is included, with a separate copy of the state’s finance or test score panelfor each event. Event study specification is modified to include state-by-event (-by-grade-by-subject) fixede↵ects; standard errors are clustered at the state level. Column 3 returns to the single-event specification,but uses the first post-1990 court order in each state as its event; states without judicial events are treatedas not having finance reforms.

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Table 9: Impacts of student sorting on student achievement results

Q1-Q5 di↵erence Slope

Baseline Estimates 0.008⇤⇤ -0.010⇤⇤⇤

(0.004) (0.003)

Decomposition 1: Common covariates

Predicted score 0.003 -0.003(0.004) (0.004)

Residual score 0.005⇤⇤ -0.007⇤⇤

(0.002) (0.003)

Decomposition 2: Richer covariates

Predicted score 0.004 -0.004(0.004) (0.003)

Residual score 0.004⇤ -0.006⇤⇤⇤

(0.002) (0.002)

Notes: First row repeats estimates from Table 6, columns 2 and 5. In subsequent rows, dependentvariables are modified. We estimate student-level regressions of NAEP scores on student demographiccharacteristics, with year fixed e↵ects, then compute predicted and residual test scores. We compute separateslopes with respect to district income and quintile gaps for the predicted and residual test scores, andestimate separate event study regressions for each. In decomposition 1, student demographic characteristicsare race/ethnicity and gender, along with school means (in the NAEP sample) of each. Decomposition 2adds indicators for students whose parent is a college graduate and for free or reduced-price lunch receipt,along with indicators for NAEP samples where these variables are unavailable and school means of each.

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Table 10: Event study estimates for mean NAEP scores by subgroup

Post Event * Yrs Elapsed

Overall mean 0.004 (0.003)

Spread of distribution:

Std Dev. -0.000 (0.001)25th percentile 0.004 (0.003)75th percentile 0.003 (0.002)P75 - P25 -0.001 (0.002)

By race:

Black 0.001 (0.003)White 0.004⇤ (0.003)White - black 0.002 (0.002)

By free lunch status :

Free lunch 0.001 (0.003)No free lunch 0.004 (0.003)No free lunch - free lunch gap -0.000 (0.002)

Notes: Table reports event study specifications, using equation (3) with �jump and �phasein constrained tozero. Dependent variables are the indicated summaries of the state-level student achievement distribution:The mean score; the standard deviation of scores; the 25th and 75th percentile scores; the interquartilerange; mean scores for black and white students, respectively; the white-black mean score gap; mean scoresfor free/reduced-price lunch and non-free/reduced-price lunch students; and the gap between these.

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APPENDICES

AppendixA.Eventdatabase

AppendixTableA1listsalloftheeventsinourdatabase,coveringtheperiodfrom1990forward.Asnotedinthetext,weincludebothcourtordersandmajorlegislativereforms.ColumnsofthetableindicatehowourlistcompareswiththoseofJackson,Johnson,andPersico(2016)andCorcoranandEvans(2015).AppendixD,below,discussesindeptheachcasewhereourlistdiffersfromthatofJackson,Johnson,andPersico(2016).

AppendixB.Detailsofsamplesandempiricalspecifications

TheprimarysourcesforouroutcomemeasuresaretheCommonCoreofDataLocalEducationAgency(LEA)financesurvey(alsoknownastheF-33),forfinanceoutcomes,andtheNAEP,fortestscores.Eachismatchedtodistrictmeanhouseholdincomefromthe1990SchoolDistrictDataBook(SDDB),atabulationofDecennialCensusdataatthedistrictlevel.Meanincomespertaintoallhouseholdsinthedistrict,withandwithoutchildrenandwithoutregardtopublicschoolattendance.Ouranalysisreliesoncollapsingthedistrict-andstudent-levelmeasurestosummariesatthestate-by-yearlevel.Weusethreetypesofsummaries:Meansfordistrictsineachquintileoffamilyincome,thedifferenceinbetweenthefirstandfifthquintilemeans,andslopeswithrespecttologdistrictincome.Ourmethodsdifferslightlyamongthese;wedescribethemhere.

Sampledefinitions

AllofoursamplesexcludeHawaiiandtheDistrictofColumbia,eachofwhichhasonlyoneschooldistrict.Ourfinanceanalysesexcludedistrict-yearobservationswithenrollmentoffewerthan100students.Thisremoves8%ofdistrict-yearobservations,withonly0.1%oftotalenrollment.Wemaketwoadditionalexclusionsaimedatreducingvolatilityintheper-pupilfundingmeasures.Bothtotalfundingandenrollmentcanvarydramaticallyfromyeartoyearinadistrict,particularlyinsmalldistricts,creatingenormousswingsinper-pupilrevenues.Weviewthisvariabilityaslikelytoreflectmeasurementerror;itisparticularlyproblematicwhenitderivesfromlargeproportionalswingsinenrollmentwithmorestablefunding.

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Webeginbycomputingeachdistrict’saverageenrollmentoveroursample,aswellasitsaveragegrowthrateoveroursampleperiod.Weexcludefromoursampleanydistrict-yearobservationwithenrollment(a)morethandoublethedistrict’saverageenrollment;(b)morethan15%aboveorbelowtheprioryearorthesubsequentyear’senrollment;or(c)morethan10%aboveorbelowthedistrict’sconstant-growth-ratetrend.Inaddition,foranydistrictforwhichmorethanone-thirdofannualobservationsareexcludedunderthesecriteria,weexcludeallremainingobservationsaswell.Exclusion(a)inparticularlikelyleadsustoexcludedistrictsservingnewlydevelopedareas,butwearenotconfidentthat1990incomesarereliablemeasuresofpopulationresourcesinthesedistrictsinanycase.Together,theseexclusionscapture18%ofdistrict-yearobservations,with8%ofenrollment.Toaddressvolatilityinthenumeratorofourrevenueandexpendituremeasures,weexcludeaswelldistrict-yearobservationswithper-pupilrevenues(respectively,expenditures)greaterthan500%orlessthan20%oftheunweightedstate-by-yearmean.Only0.02%ofdistrict-yearobservationsareexcludedbytheserules.Whenanalyzingmeanteachersalariesandpupil-teacherratios,eachofwhichissomewhatnoisilymeasured,weexcludethetopandbottom2%ofdistricts(unweighted)ineachstate-yearcell.Finally,ourNAEPanalysesexcludestudentsincharterschools.Formanypurposes,itisusefultohaveaweightforeachdistrictthatdoesnotvaryovertime.Weusethegeometricmeanofthedistrict’senrollmentinallavailableyearsforthis.

Definitionofincomequintiles

Thebasisforourincomequintilecalculationsisthefinancesample,asdefinedabove.Districts’quintileassignmentsaretreatedasfixedovertime.Toconstructourincomequintilecutoffs,wesortdistrictsinastatebytheir1990meanfamilyincomeandcomputethe20th,40th,60th,and80thpercentileofthestatedistributionof1990meanfamilyincome.Thesepercentilesarebasedonthedistrictsinourfinancesamplein1994(thefirstyearinwhichcompleteCCDdataareavailable),weightedbyourstableenrollmentcount.Districtsspanningthequintilecutoffsareassignedwithpartialweightstoeachoftherelevantquintiles.QuintilemeansQuintilemeansofourfinancemeasuresarecomputedasweightedaveragesoverthedistrictsineachquintile,weightingeachdistrictbyitsaveragelogenrollmentandincludingonlydistrictsthatmeetthecriteriaoutlinedabove.Thespecificdistrictsincludedcanvaryslightlyovertimeduetodifferencesintheavailabilityofthedependentvariable.

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OurNAEPquintilemeansaresimilarbutweightdistrictsbythesumoftheNAEPstudentweightsinthedistrict.Onlydistrictsmeetingthefinancesamplerestrictionsfortherelevantyearareincluded.

Incomeslopes

Toconstructstate-by-yearslopesofrevenueswithrespecttodistrictincome,weestimateaseparateregressionforeachstateandeachyear.Explanatoryvariablesarethelogmeanincomeofthedistrict,basedonthe1990data,thedistrict’slogenrollmentinthatyear,andindicatorsforwhetherthedistrictisanelementaryorasecondarydistrict(unifieddistrictsaretheexcludedcategory).Theseregressionsareweightedbyourstablelogenrollmentmeasureandsamplesaredefinedasabove.Thecoefficientonthelogmeandistrictincomeisextracted,alongwithitsstandarderror.NAEPscore-incomeslopesarecomputedsimilarly,usingNAEPdataaggregatedtothedistrict-year-subject-gradelevel.Separateregressionsareestimatedforeachstate-year-subject-gradecombination.Thedistrict-levelregressionisweightedbythesumofNAEPstudentweightsinthedistrict,anddoesnotincludedistricttypecontrols.StandarderrorsaccountfortheNAEPplausiblevaluesmethodology,asdiscussedbelow.

Eventstudyregressions

Oncequintilemeans,between-quintilegaps,andincomeslopesareconstructedatthestate-yearlevel,weestimateevent-studyregressionsasdescribedinthemaintext.Forfinanceoutcomes,wherewehaveacensusofschooldistricts,theeventstudyregressionsusingquintilemeansasdependentvariablesareunweighted.Fortestscoreoutcomes,ourquintilemeaneventstudyregressionsareweightedbythesumoftheNAEPstudentweightswithinthegrade-subject-quintile-yearcell.Whenweexaminequintilegapsinscores,weweightbytheharmonicmeanofthetwoquintileweights.Alleventstudieswithincomeslopesasthedependentvariableareweightedbytheinversesamplingvarianceofthestate-yearslope.

NAEPplausiblevalues

NAEPdoesnotreportasingletestscoreforeachstudent,butratherreportsfiveplausiblevalues,randomdrawsfromthestudent’sposteriordistribution.Weaveragethesefiveplausiblevaluesbeforecomputingquintilemeansorincomeslopes.Ourestimatedstandarderrorsfortheincomeslopesaccountforthe

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contributionofthesamplingfromtheposteriordistribution,followingNAEPguidance.JacobandRothstein(2016)pointoutthattheuseofNAEPplausiblevaluesasdependentvariablesmaycreatebiases,asthemeasurementerrorinPVsisnotclassical.Thebiasdependsonthedegreetowhichthe“conditioningvariables”intheNAEPmodelcanpredicttherelevantexplanatoryvariablesintheresearchregression,butlikelytakestheformofattenuatedtreatmenteffects.JacobandRothstein(2016)discussmethodsforobtainingunbiasedestimatesfromasingleNAEP.WearenotawareofmethodsforavoidingbiasinanalysesthatpoolacrossmanyNAEPsamples.Wehaveverifiedthatcross-sectionalregressionsofNAEPPVsonmeasuresofdistrictfinance,bothacrossandwithinstates,areminimallybiasedrelativetounbiasedMMLestimates,andthereforeconcludethattheuseofPVsisunlikelytomeaningfullybiasourresults.

AppendixC.Robustnessandadditionalanalyses

Appendixfiguresandtablespresentnumerousadditionalresults.FigureA1tabulatesourfinanceandNAEPsamplesbyeventtime,thenumberofyearsrelativetothedateoftheevent.IntheNAEPdata,wehavelargesamplesforeventyearsupto10,butbeyondthatsamplesizesdiminish.FigureA2showsthetimeseriesoftotalrevenueslopesandtestscoreslopes,eachwithrespecttologdistrictincome,separatelyforreformandnon-reformstates.Bothrevenueandtestscoreslopesdeclineinreformstates,relativetonon-reformstates,between1990and2011.FigureA3plotsoureventstudyestimatesofimpactsontotalrevenuesandmeantestscoresineachofthefivequintiles,alongwith95%confidenceintervals.FigureA4presentseventstudyestimates,analogoustoFigure11,separatelyfor4thand8thgradescores.Thereisnoindicationofmeaningfuldifferencesbetweenthese.FigureA5showstheeventstudyforthebetween-quintilegapinmeantestscores.TableA1listsalloftheeventsinourfinancereformdatabase,alongwiththoseintheJackson,Johnson,Persico(2016)andCorcoranandEvans(2015)databases.ThisisdiscussedingreaterdetailinAppendixD.TableA2presentsaneventstudyanalysisforstate-levelbudgets,onbothper-capitaandper-pupilbases.Ourone-parameterspecification(equation1)isused.Eventsareassociatedwithsharpincreasesinbothtotalrevenuesandtotalexpenditures.Expenditureincreasesareconcentratedintheeducationandintergovernmentaltransfercategories;thereisnosignificanteffectonotherexpenditures.Theimpacts

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ontotalper-pupilrevenuesandexpendituresarelargerthaninourdistrict-levelanalyses.Thismayindicatethatsomeofthenewstateexpendituresinvolvere-labelingexistingfundsratherthanallocatingnewfundstoeducation.Anotherpotentialexplanationisthatsomereformsmayhaveledtostatespendingonpre-Keducationthatdoesnotshowupondistrictbalancesheets.TableA3presentsCardandPayne’s(2002)analysisoftheeffectofSFRsontheslopeofdistrictrevenueswithrespecttodistrictincome.CardandPayneusetheincomelevel,indollars,ratherthanlogincomeastheexplanatoryvariableinthisslopecalculation.Theycomputeasinglelong-differenceofthisslopeforeachstate,from1977to1992,andregressitonindicatorsforplaintiffanddefensevictoriesincourtcases.Weconstructasimilarslopewithrespecttoincomelevels,andasimilar1990-2012longdifference.Columns2and5reportregressionsofthisonanindicatorforapost-1990event.Columns3and6reportestimatesofourone-parametereventstudymodel.OurestimatesoftheimpactsofcourtrulingsaresomewhatlargerthaninCardandPayne(2002),butwecannotruleoutequaleffects.TableA4presentsasimilarcomparisontoCorcoranandEvans’(2015)analysisoftheimpactofSFRsonunivariatemeasuresofdistrictfinancesineachstate.Columns1-3aredrawnfromCorcoranandEvans.Column1reportscoefficientsofaregressionoftheindicatedfinancesummaryonanindicatorforapriorcourtruling,usingCorcoranandEvans’1972-2002panel.Thisregressioncontrolsforstatedemographiccharacteristicsandstateandyeareffects.Columns2and3reportrulingmaineffects(column2)andtheeffectofanadequacyruling(column3)fromspecificationsthatincludebothtogether.Columns4-5reportestimatesusingour1990-2012panel,withoutdemographiccontrols,wherewetimeeventsasinourmainanalysis(column4)ortothefirstcourtrulinginastate(column5).Notethatthecoefficientsincolumns4-5arecomparabletothesumofthoseincolumns2and3,ortothoseincolumn1withoutadjustment.Estimatesforper-pupilrevenuesaresimilar.Weobtainsmallerimpactsonlogmeanper-pupilexpendituresandonthecoefficientofvariationofper-pupilexpenditures.TableA5reportseventstudyestimateswherethedependentvariableistheslopeofvariousdemographiccharacteristicsofadistrict’sstudentswithrespecttodistrictlogincome(panelA)orthebetween-quintilegapinmeandemographiccharacteristics(panelB).Logmeanincomeismeasuredin1990,2000,and2011.(Theslopeoflogmeanincomein1990withrespecttoadistricts1990logmeanincomeisbyconstruction1ineverystate,butthisslopecanvaryinsubsequentyears.)Minorityandfreelunchsharesaremeasuredineveryyear,thoughfreelunchdataismissingforsomestatesandyears.TableA6reportstheshareofstudentsofvariouscharacteristicswhoareindistrictsineachquintile.Rowssumto1.

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TableA7reportseventstudyregressionswherethedependentvariableisthedifferenceintherevenuesofthedistrictattendedbytheaverageblack(orfreelunch,orlowscoring)studentandtherevenuesofthedistrictattendedbytheaveragewhite(ornon-free-lunch,orhighscoring)student.

AppendixD.Reconciliationofschoolfinancereformtabulations

Theliteratureonschoolfinancereformshasbeenplaguedbyalackofauthoritativetabulationsofcourt-orderedreforms,withsubstantialdiscrepanciesbetweenthetabulationsusedbydifferentauthors.Ourtabulation,too,differsfromallpreviouslistings.Inanefforttoprovideclaritytotheliteraturegoingforward,inthisappendixwediscusseverycasebetween1990and2011whereourtabulationofcourt-orderedschoolfinancereformsdiffersfromthatofJackson,Johnson,andPersico(2016;hereafterJJP).Manyofthesediscrepanciesreflectjudgmentcalls.Wehaveestimatedourmainresultswithanumberofvariantsoftheeventsample,andingeneralhavefoundlittlesensitivityoftheresults;weneverthelesspresentthebasisforourpreferredtabulationforcompleteness.Thestatesandyearsforwhichthetwotabulationsdisagreeare:

- Alabama,1993- Arizona,2007- Connecticut,1995&2010- Idaho,1993&1998- Maryland,1996&2005- Michigan,1997- Montana,1993&2008- NewHampshire,2006- NewJersey,1991,1998&2000- NewMexico,1998&1999- Oregon,2009- SouthCarolina,2005- Texas,2004- Washington,1991,2007&2010

Thisincludesonlycasesinscopeforbothlistsbutcodeddifferently.Thisinparticularmeansthatwedonotdiscussourtabulationoflegislativeschoolfinancereforms,astheseareoutofJJP’sscope.Foreachstate,wediscussonlytheeventswherethetwotabulationsdisagree;seeAppendixTableA1forafulllistingofeventsineachstate.Alabama1

1Casehistoriesfromhttp://schoolfunding.info/2012/01/school-funding-cases-in-alabama/;http://www.encyclopediaofalabama.org/article/h-2045.

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1993:JJPcourtorder;Lafortune-Rothstein-Schanzenbach(LRS)noeventIn1993’sAlabamaCoalitionforEquity(ACE)v.Hunt,thepublicschoolfundingsystemwasfoundinequitable,onbothadequacyandequitygrounds,byalowercourt,andaremedyorderwasissued.Theremedynegotiatedamongthepartiesandorderedbythecourt,inACEv.Folsom,includedequitableandadequatefunding,andinadditionalsocoveredperformance-basededucation,professionaldevelopment,earlychildhoodprograms,andinclusivespecialeducation—alltobefullyfundedwithinsixyears.Noeducationalreformpackagemadeitthroughthelegislaturebeforethe1994electionseason,andeducationreformbecameanimportantissueinthegubernatorialcampaign,withincumbentgovernorFolsompromisingreformandcompliancewiththeremedyorderandhisopponent(andeventualwinner)Forrest“Fob”Jamesvowingtofightwhathedescribedasausurpationofexecutiveandlegislativepowers.Uponappeal,theAlabamaSupremeCourtdecidedin1997thatwhileschoolswereinadequatelyfunded,itwoulddeclinetoissuearemedyorder,leavingthefundingsystemunchanged.Becausethelowercourtwasoverturnedandnoschoolfinancelegislationwaspassed,wedonotcodethiseventasaschoolfinancereform.Arizona22007:JJPcourtorder;LRSnoeventFloresv.Arizonawasfirstdecidedin1992underFederallaw,intheUnitedStatesDistrictCourtfortheDistrictofArizona.TheplaintiffsclaimedthatthestatefailedtoadequatelyfundprogramsforEnglishlanguagelearners(ELLs).In2000,thedistrictcourtfoundthatthestate'smethodandleveloffundingELLprogramswas"arbitraryandcapricious"andorderedthatthelevelofstatefundingforELLprogramsbeararationalrelationshiptothecostofthoseprograms.Thepartiesreachedanagreementin2002,andthecourtorderedacosting-outstudy.Thestate'srepeatedfailuretocomplyledtoaDecember2005orderanddailyfinesthatmountedto$21millionbeforethestateenactedadditionalfundinginearlyMarch2006.InAugust2006,theNinthCircuitCourtofAppeals,inFloresv.Rzeslawski,vacatedthe2005districtcourtjudgmentandremandedthecasesothedistrictcourtcouldholdnewhearingstodeterminewhethercircumstanceshadchangedandrequiredmodificationofthe2000courtorder.InMarch2007JudgeRanerCollinsoftheU.S.DistrictCourtfortheDistrictofArizonaruledthatArizonawasinviolationoftheEqualEducationalOpportunitiesAct(EEOA)byunder-fundingprogramsdirectedtowardsEnglishlearners,invalidatingHB2064,thefundingformulapassedbytheArizonalegislatureinresponsetothecourt'searlierdecision.JudgeCollinsorderedthestatetocomplywiththeorderbytheendofthe2007legislativesession,butwhenthelegislature

2Casehistoryfromhttp://www.clearinghouse.net/detail.php?id=11194;http://www.schoolfunding.info/states/az/lit_az.php3.

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failedtodosothejudgeissuedacontemptorder.TheNinthCircuitCourtofAppealsupheldtherulingin2008.InSeptember2008,thedefendantspetitionedtheU.S.SupremeCourttoreviewthe9thU.S.CircuitCourtofAppeals'holding.In2009’sHornev.Flores,129S.Ct.2579decision,theSupremeCourtreversedanddirectedtheDistrictCourttoexamineseveralspecificfactors,includingwhethernon-compliancewasstatewide.OnMarch28,2013,theplaintiff'sstatewideclaimsweredismissed,requiringdistrict-by-districtanalysisinstead.ThedismissalwasupheldbytheCourtofAppealsinJune2015.Becausethe2007rulingwasaFederaldistrictcourtorderthatthestatenevercompliedwithandwassubsequentlyoverturnedbytheSupremeCourt,wedonotcodethiseventasaschoolfinancereform.Connecticut31995:JJPcourtorder;LRSnoevent2010:JJPcourtorder;LRSnoeventIn1996,theStateSupremeCourtruledinSheffv.O’Neill(codedbyJJPas1995)thattheseparationofsuburbanandHartfordstudentsviolatedthesegregationclauseintheConnecticutConstitution,andorderedtheStateLegislaturetotakenecessarymeasurestointegrateschoolsandtoprovideequaleducationalopportunitytoallchildren.Thisresultedinaplanbythe1997StateLegislaturegearedatpromotingvoluntaryschooldesegregationandmagnetschools.Thoughplaintiffsmadeadequacy-basedarguments,therulingandsubsequentlegislationfocusedondesegregationandnotschoolfunding.In2010,theSupremeCourtruledinCoalitionforJusticeinEducationFunding,Inc.v.Rellthatthestate’sconstitutionguaranteedallstudentsanadequateeducation.Itdidnotorderchangesinschoolfinance,however,butrathersentthecasebacktoatrialcourttodeterminewhethertheappropriatestandardhadbeenmet.Asof2013,thecasewasstillpending.Wethereforedonotcodeitasaschoolfinancereformorder.Idaho43Casehistorydrawnfromhttps://www.jud.ct.gov/external/news/sheff.htm;http://connecticuthistory.org/sheff-v-oneill-settlements-target-educational-segregation-in-hartford/#sthash.6QnsSrbm.dpuf;https://scholar.google.com/scholar_case?case=10572221569547466633&q=Sheff+v+o+neill+199&hl=en&as_sdt=400006;http://schoolfunding.info/2012/01/school-funding-cases-in-connecticut-2/.4Casehistoryfromhttp://www.educationjustice.org/states/idaho.html;https://nces.ed.gov/edfin/pdf/lawsuits/ISEEO_v_idaho.pdf.

ix

1993:JJPnoevent;LRScourtorder1998:JJPcourtorder;LRSnoeventInthe1993rulingonIdahoSchoolsforEqualEducationalOpportunityv.Evans(ISEEO)(850P.2d724),theIdahoSupremeCourtfoundthatthestateconstitutionrequiredadequate(butnotequitable)schoolspending.In1994,thelegislaturepassedSenateBill1560whichrevisedthestatefundingformulainregardtoteachersalaries,allocatingmorethan$90milliontopublicschoolsfundthischange.Wecodethe1993decisionasacourt-orderedschoolfinancereform.Afterthelegislativechanges,thetrialcourtdeclaredthelawsuitmoot,butthisdecisionwasoverturnedbythestateSupremeCourt,whichconcludedthatwhethera"thorougheducation"wasbeingprovidedtostudentswasstillinquestion.In1997,thetrialcourtagaindismissedtheplaintiffs'claim.ThestateSupremeCourtreversedinpartin1998,inISEEOv.State(976P.2d913),remandingthefacilitiesandcapitalfundingportionofthecase.Thecourtheldthat"theLegislaturehasthedutytoprovideameansforschooldistrictstofundfacilitiesthatofferasafeenvironmentconducivetolearning."In2000and2001,thelegislaturepassedminorfacilitiesmeasuresthathelpproperty-poordistricts,butplaintiffsarguedthesemeasureswereinsufficient.Wedonotcodethisasanindependentschoolfinancereform,dueinparttoitslimitedscope.Maryland51996:JJPnoevent;LRScourtorder2005:JJPcourtorder;LRSnoeventTheACLUandBaltimoreCityallegedthatBaltimore’sstudentswerenotreceivinganadequateeducation.Ina1996summaryjudgmentdecisionintheconsolidatedBradfordv.MarylandStateBoardofEducationcase,thetrialcourtagreed,thoughthecauseoftheinadequacieswasindispute.ThepartiesenteredintoasettlementthatprovidedanincreaseinstatefundingfortheBaltimoreCityPublicSchoolsforthenextfiveyears.Duringthisperiod,the“Thornton”CommissiononEducationFinance,Equity,andExcellencewasestablishedtoaddressstatewideadequacyinfunding.Wecodethe1996courtorderasaschoolfinancereform,inpartbecauseBaltimoreissuchalargedistrict.In2004,theBaltimoreschoolshadanaccumulatedbudgetdeficitof$58million.Inresponsetoanewstatelawrequirement,itcutitsbudgetdrastically,andplannedatwo-yearpaydownofthedeficit.TheACLUreturnedtocourtinBradford,tryingtorestorefundingtoBaltimoreschoolsandstopcutstoacademicprogramsimpactingstudents.TheCircuitCourtruledthatthebudgetcutshadresultedinreducededucationalopportunitytostudentsandthat$30millionto$45millioninfundsshouldberestored,preferablywithadditionalrevenuefromthecityandstate.The5Casehistorydrawnfromhttp://www.schoolfunding.info/states/md/lit_md.php3;http://www.aclu-md.org/uploaded_files/0000/0173/bradford_summary.pdf.

x

Stateappealed,arguingthateducationfundinglevelsareoutsidecourtjurisdiction.In2005,MarylandʼshighestcourtruledagainsttheStateʼsattempttostrikethelowercourtorder,butdidnotoverturnthestatelawforthedeficitpaydown.Asaresult,theadditionalfundingawardedundertheThorntoncommissionwouldproceed,butsincenoadditionalfundswereorderedatthistimewedonotcodethisasaseparatecourtorderedschoolfinancereform.Michigan61997:JJPcourtorder;LRSnoeventDurantv.StateofMichigan(“DurantI”),wasfiledin1980anddecidedin1997.Themajorissuewasstatefundingforspecialeducationmandates.InitsrulingonDurantI,theMichiganSupremeCourtunanimouslyheldthatstategovernmenthadnotproperlyfinancedthreestate-imposedmandates:specialeducation,specialeducationtransportationandaschoollunchprogram.Thecourtsplitawardedmonetarydamagestolocalschooldistrictstorepaypastcostsofmandates.Duetothelimitednatureofthelawsuit,wedonotcodethisasaschoolfinancereform.Montana71993:JJPcourtorder;LRSlegislativeeventbutnocourtorder2008:JJPcourtorder;LRSnoeventMontana’sSupremeCourtruledinHelenaElementarySchoolDistrictNo.1v.Statein1989thatthestate’sschoolfinancesystemwasunconstitutional.Thisisoutsidethescopeofoursample.Thelegislaturerespondedin1989,thenoverhauledtheformulaagainin1993viaHouseBill667.Earlierthatyear,theMontanaRuralEducationAssociationv.Statecasewastriedbutnotdecided.Followingthelegislativeaction,butstillin1993,thestate’sFirstJudicialDistrictCourtforLewisandClarkCountyruledthatthecasewasmootduetothenewlaw.Itpermittedtheplaintiffstoarguethatthenewlawremainedunconstitutional,buttoourknowledgethecaseendedthen.JJPcodethisasacourtorder;wecodeHouseBill667asalegislativeaction,butdonotcodethecaseasacourtorder.In2005,inColumbiaFallsElem.Sch.Dist.6v.State,thetrialcourtfoundthatthestatewasnotprovidinga“quality”educationasmandatedbytheconstitution,and6Casehistoryfromhttps://www.mackinac.org/8568.7Casehistoryfromhttp://www.mqec.org/school-funding-history/;http://schoolfunding.info/2011/12/school-funding-cases-in-montana/;https://static1.squarespace.com/static/53ab63e1e4b0cb2b67560152/t/55ef5b40e4b064e46223df9f/1441749824419/CF-Decision-II.pdf;http://static1.squarespace.com/static/53ab63e1e4b0cb2b67560152/t/55ef3dcbe4b0adc4e323efbc/1441742283987/Rural_Ed_Assoc-v-State_District_Order_re_Mootness_Issue_1993.pdf;http://leg.mt.gov/content/committees/interim/2005_2006/edu_local_gov/minutes/02242006exhibits/ELG02242006_ex5.pdf.

xi

inparticularithadviolatedtheprovisionofthestateconstitutionrequiringthestatetocommittopreservetheculturalheritageofAmericanIndians.JJPandLRSeachcodethisasacourt-orderedschoolfinancereform.Asubsequent2007legislativereform(whichwecodeasalegislativeevent)madesubstantialchangestotheschoolfinancesysteminlightofthisruling.Suitwasfiledin2008seekingsupplementalmonetaryrelieftohelpdistrictsavoidfundingshortfallsin2009.InDecember2008,thedistrictcourtdeclinedtoawardanysupplementalrelief,sowedonotcode2008asacourt-orderedschoolfinancereform.NewHampshire82006:JJPcourtorder;LRSnoevent

InSeptember2006inLondonderrySchoolDistrictv.StatetheNewHampshireSupremeCourtorderedthestatetodefinea“constitutionallyadequateeducation”byJune2007.Afterrecountingthefailuretoestablishthisdefinitioninseveralpreviouscases(bothJJPandLRScodecourtordersin1993,1997,and1999),thecourtconcludedthatitiswillingtodefertothelegislatureonemoretime,andthat“intheabsenceofaction…,ajudicialremedyisnotonlyappropriate,butessential”inordertovindicatetheconstitutionalrightsofNewHampshire’sstudents.

Inthe2006decision,theCourtorderedtheStatetodefinea“constitutionallyadequateeducation”bytheendofthe2007legislativesession,butdeferredtothelegislatureforappropriateaction.Wecodethe2008legislativeactionbutnotthe2006courtorder.NewJersey91991:JJPcourtorder;LRSnoevent1998:JJPnoevent;LRScourtorder2000:JJPnoevent;LRScourtorderNewJersey’sschoolfinancelitigationhistoryisextremelycomplex,withadecades-longexchangebetweenthelegislatureandthecourts.Therehavebeenmany,manyrulingsintheAbbottv.Burkecaseinparticular.ThecourtruledinAbbottIIin1990(countedbybothJJPandLRS)thatstatefundingstatutesfailedtoensureadequate8Casehistoryfromhttps://www.nhbar.org/publications/display-journal-issue.asp?id=365. 9Casehistoriesdrawnfromhttp://www.schoolfunding.info/resource_center/legal_docs/New%20Jersey/Abbott%20Decisions/Abbott-SupremeCourt_May1997.PDF;http://www.schoolfunding.info/resource_center/legal_docs/New%20Jersey/Abbott%20Decisions/Abbott-SupremeCourt-May-1998.PDF;http://www.schoolfunding.info/resource_center/legal_docs/New%20Jersey/Abbott%20Decisions/Abbott-SupremeCourt-Feb-2002.PDF.

xii

fundinginthelow-wealth“Abbottdistricts”,andnotedthatstudentsinthesedistrictsneedprogramsandservicesbeyondthoseprovidedtostudentsinwealthierdistricts.Inresponse,thelegislaturepassedtheQualityofEducationActof1990(QEA;LRScodethisasalegislativeevent).In1991,theplaintiffsappliedtothecourttodeclaretheQEAunconstitutional.Thecourtdeclinedtohearthemotionatthattime.JJPcodethisasacourtorder,butwedonot.ThecourtdidfindtheQEAunconstitutionalinthe1994AbbottIIIruling;bothJJPandLRScountthisevent.In1998’sAbbottVruling,thecourtrequiredthestatetoincreasefundingtoensureparityinper-pupilexpendituresbetweentheAbbottdistrictsandtheaverageofthestate's110successfulsuburbanschooldistricts,anddirectedthestatetoconductastudytodeterminetheneedsofAbbottstudentsandtheprogramsnecessarytomeetthoseneeds.BasedontheState’sstudy,thecourtorderedadditionalremedialmeasuresfortheAbbottchildren,includingpreschoolforallthree-andfour-yearolds,adequateschoolfacilities,and“supplemental”programs.Wecodethisasaschoolfinancereform,thoughJJPdonot.AfterplaintiffsbroughtanothermotionallegingthestatedidnotcomplywiththeAbbottVruling,thecourtprovided(inthe2000AbbottVIruling)moredetailonthepreschoolrequirements,includingsubstantiveeducationalstandards,certifiedstaff,andamaximumstudent/teacherratioof15:1.Wecodethisasaschoolfinancereform;again,JJPdonot.NewMexico101998:JJPcourtorder;LRSnoevent1999:JJPnoevent;LRScourtorderIn1998,anumberofdistrictsbroughtacapitalfunding/facilitiessuit,ZuniSchoolDistrictv.State,CV-98-14-II(Dist.Ct.,McKinleyCountyOct.14,1999),claimingthatthefundingsystemforcapitalitemswasunconstitutional.Thetrialcourtgrantedpartialsummaryjudgmentinfavorofplaintiffsandorderedthestateto"establishandimplementauniformfundingsystemforcapitalimprovements...andforcorrectingexistingpastinequities."Thecasewasfiledin1998butdecidedin1999.JJPcodeitasa1998event,butwecodeitasa1999eventbasedonthedecisiondate.Oregon112009:JJPcourtorder;LRSnoevent10Casehistoryfromhttp://www.schoolfunding.info/states/nm/lit_nm.php3;https://nces.ed.gov/edfin/pdf/lawsuits/Zuni_v_%20nm.pdf;http://ielp.rutgers.edu/resources/New_Mexico.11Casehistoryfromhttp://www.educationjustice.org/states/oregon.html.

xiii

InJanuary2009,theOregonSupremeCourtfoundinPendletonSchoolDistrict16Rv.Statethatthelegislaturehad,inviolationofa2000constitutionalamendment,failedtofundtheOregonpublicschoolsystematalevelsufficienttomeetthequalityeducationgoalsestablishedbylaw.However,itconcludedthatthestateconstitutiondidnotgivethecourtauthoritytoissueaninjunctionrequiringthestatetoprovidesufficientfundingtoreachthosegoals.Becausethecourtruledthatthelawwasnotjudiciallyenforceable,andnosubsequentlegislativeactionsweretaken,wedonotcodethiseventasaschoolfinancereform.SouthCarolina122005:JJPcourtorder;LRSnoeventIn1999,inAbbevilleCountySch.Dist.v.State,theSouthCarolinaSupremeCourtheldthatplaintiffshadavalidclaimunderthestateconstitution'seducationclause,interpretedtheclausetomeanthatthelegislaturemustprovidechildrenwitha“minimallyadequateeducation,”andremandedthecasefortrial.Thelowercourtruledin2005thatthestate’sfailedtomeetitsconstitutionalrequirementbyinadequatelyprovidingearlyeducationprograms,butruledagainstplaintiffclaimsrequestingreliefregardingschoolbuildingsandqualityteaching.Becausethecourtdidnotordersubstantialschoolfinancereform,wedonotcodea2005event.BothplaintiffsanddefendantsappealedtotheSouthCarolinaSupremeCourt,whichheardoralargumentin2008andagainin2012.In2014,thestatesupremecourtheldthestate’sschoolfundingunconstitutional,declaringthat"SouthCarolina'seducationfundingschemeisafracturedformuladenyingstudents...theconstitutionallyrequiredopportunity."Thecourtexplainedthattheresourcesprovidedfailedtoproducesufficienteducationalopportunities.Thecourtexplicitlyrefrainedfrommandatinghowthestateshouldremedythesystem,butorderedthepartiestoworktogethertopresentanewfundingsystemtothecourt“withinareasonabletime.”The2014courtordermeetsourdefinitionofacourt-orderedschoolfinancereform,butisoutsideofoursampleperiodsoisnotincludedinourtabulation(orinJJP’s).Texas132004:JJPcourtorder;LRSnoevent.AtrialcourtfoundinWestOrange-CoveConsolidatedISDv.Nelson(2004)thattheTexasschoolfinancesystemfailedtoprovide“anadequate,suitableandefficienteducationsystem”asrequiredbythestateconstitution,andadditionallyfoundthestatepropertytaxtobeunconstitutional.12Casehistoryfromhttp://www.educationjustice.org/states/southcarolina.html.13Casehistoryfromhttp://caselaw.findlaw.com/tx-supreme-court/1153227.html;http://www.schoolfunding.info/states/tx/McCown.pdf.

xiv

In2005,thestateSupremeCourtruledinNeeleyv.WestOrange-CoveIndep.Sch.Dist.thatthestatepropertytaxwasunconstitutional,butheldthatdespitefundinginequitiesthestate’seducationfinancesystemdidnotviolatetheconstitutionaladequacy,efficiency,andsuitabilityrequirements.Thecourtwrotethattheschoolfinancesystemdisplayeddeficienciesthatcouldintimerenderitunconstitutionalundertheeducationarticle.Becausethesupremecourtdidnotorderreform’s,wedonotincludethiscase.Washington141991:JJPcourtorder;LRSnoevent2007:JJPcourtorder;LRSnoevent2010:JJPnoevent;LRScourtorderSeattleSchoolDistrictv.State,alsoknownasSeattleII,wasa1983trialcourtrulingfollowinguponthe1978SeattleIdecisionthatpromptedanoverhauloftheschoolfinancesystemandtheintroductionoftheBasicEducationAct.SeattleIIexpandedthedefinitionof“basiceducation”inthestatetoincludespecialeducation,andbilingualandremedialprograms.Thestatedidnotappeal,andthelegislatureamendedtheschoolfinancesystemtoincludefundingfortheseprograms.JJPdatethiscaseto1991.Toourknowledge,itoccurredin1983,sodoesnotfallintooursampleperiod.InFederalWaySch.Dist.v.State,filedin2006,plaintiffsallegedthatthestatefundingsystemfailedtoamplyfundeducationinallschooldistrictsandwasunconstitutional.In2007,JudgeMichaelHeaveyheldinfavorofplaintiffs,findingthattheState’smethodofprovidingsalaryfundingwasunconstitutional.ThestateSupremeCourt,however,issuedanarrowerrulingin2009thata“uniformsystem”ofeducationgovernseducationalcontent,teachercertification,instructionalhourrequirementsandtheassessmentsystem,butdoesnotrequireuniformfundingofstaffsalaries.Thecourtdidnotruleonwhethertheplaintiffshad“ample”fundsunderthestateconstitution.Becausethe2009SupremeCourtrulingdidnotinvolvefinances,wedonotcodethisasanevent.McClearyv.State,filedin2007,arguedthatalthoughthestatehaddevelopedstandardsforaconstitutional“basiceducation,”itwasnotfullyfundingthateducation.In2010,theSuperiorCourtheldthatthestatefundingsystemwasunconstitutionalbecauseitneitherdeterminedthecostofnorprovidedtheresourcesneededforabasiceducationforallchildreninthestate.Thecourtorderedthestatetofundaconstitutionallyadequateeducation,usingstableand14Casehistorydrawnfromhttps://www.courts.wa.gov/opinions/pdf/843627.opn.pdf;http://digitalcommons.law.seattleu.edu/cgi/viewcontent.cgi?article=2290&context=sulr;https://www.courts.wa.gov/opinions/pdf/843627.opn.pdf;http://www.schoolfunding.info/states/wa/lit_wa.php3.

xv

dependablestatesources.Inresponse,thelegislatureenactedlegislativereforms,andinearly2012theWashingtonSupremeCourtaffirmedtheSuperiorCourtruling.Wecodethe2010event,asthelegislatureactedonitwithoutwaitingforittobeupheldbytheSupremeCourt.

References

Corcoran,S.P.,&Evans,W.N.(2015).Equity,adequacy,andtheevolvingstateroleineducationfinance.InH.F.LaddandM.E.Goertz,eds.,HandbookofResearchinEducationFinanceandPolicy,2ndedition.NewYork:Routledge.

Jackson,C.K.,Johnson,R.C.,&Persico,C.(2016).Theeffectsofschoolspendingoneducationalandeconomicoutcomes:Evidencefromschoolfinancereforms.QuarterlyJournalofEconomics131(1),157-218.

Jacob,B.&Rothstein,J.(2016).Themeasurementofstudentabilityinmodernassessmentsystems.JournalofEconomicPerspectives,forthcoming.

Appendix Figures

Figure A1: Event time balance

01

02

03

0#

of

Sta

tes

−5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) Finance (# of states)

01

02

03

04

0#

of

St−

Gr−

Su

b C

ells

−5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) NAEP (# of state-grade-subject cells)

Notes: Figure shows the number of state-year (panel A) or state-subject-grade-year (panel B) observationsused in our event study samples, for each year relative to the focal event.

xvi

Figure A2: Slopes of revenues per pupil with respect to log district mean income, by state finance reformstatus, 1990-2012

0500

1000

1500

2000

Tota

l R

evenue S

lope

1990 1995 2000 2005 2010Year

No Reform States Finance Reform States

(a) Total revenue slopes

.8.8

5.9

.95

11.0

5T

est score

slo

pes

1990 1995 2000 2005 2010Year

No Reform States Finance Reform States

(b) NAEP slopes

Notes: See notes to Figures 2 and 3. This figure repeats those, but uses the slopes of revenues (panel A) ortest scores (panel B) with respect to log district mean income in place of the between-quintile gaps.

xvii

Figure A3: Event study estimates for total revenues and test scores by district income group

0500

1000

1500

2000

Revenue e

ffects

1 2 3 4 5District Income Quintile

Finance Beta: Tot Rev

(a) Total revenue

−.1

−.0

50

.05

.110−

year

NA

EP

effects

1 2 3 4 5District Income Quintile

NAEP Beta

(b) NAEP

Notes: Figure shows event study estimates from one-parameter parametric models for mean revenues andmean test scores in each quintile. Estimates for quintiles 1 and 5 are shown in Table 3, panels B and C,column 3, and Table 6, columns 3 and 4. 95% confidence intervals shown by dotted lines.

xviii

Figure A4: Event study estimates of NAEP e↵ects, by grade

−.6

−.5

−.4

−.3

−.2

−.1

0.1

.2C

hange in test score

slo

pe

−5 0 5 10 15 20Years Since Event

Non−Parametric Estimate Parametric Estimate

(a) Grade 4

−.6

−.5

−.4

−.3

−.2

−.1

0.1

.2C

hange in test score

slo

pe

−5 0 5 10 15 20Years Since Event

Non−Parametric Estimate Parametric Estimate

(b) Grade 8

Notes: Figure shows event study estimates for NAEP scores, separately for 4th and 8th grade. Eachspecification includes state and subject-year fixed e↵ects. p-values for omnibus hypothesis tests of zeropre-event e↵ects in the non-parametric model are 0.05 in Panel A and 0.24 in Panel B; p-values for zeropost-event e↵ects are <0.001 in each panel. In the parametric model, the p-value for the hypothesis thatthe pre-event trend is zero is 0.97 in Panel A and 0.69 in Panel B; for the test that the post-event jump andchange in trend is zero it is 0.23 and 0.005, respectively.

xix

Figure A5: Event study estimates of school finance reform e↵ects on the di↵erence in mean test scoresbetween lowest and highest income school districts.

−.1

0.1

.2.3

Ch

an

ge

in

Q1

−Q

5 M

ea

n T

est

Sco

res

−5 0 5 10 15 20Years Since Event

Non−Parametric Estimate Parametric Estimate

Notes: Figure shows event study estimates for the gap in mean test scores between the bottom (Q1) and top(Q5) quintiles of the state’s distribution of district mean household income. p-value for the hypothesis thatpre-event e↵ects are zero is 0.64 in the non-parametric model and 0.23 in the parametric model; p-values forzero post-event e↵ects are <0.001 and 0.07, respectively.

xx

Appendix Tables

AppendixTableA1CompleteEventList,1990-2011

State Year Event

Lafortune,Rothstein&Schanzenbach

(2016)

Jackson,Johnson&Persico(2016)

Corcoran&Evans(2015)

Alabama 1993 AlabamaCoalitionforEquity(ACE)v.Hunt;Harperv.Hunt

X

Alaska 1999 Kasayuliev.StateofAlaska Court XArizona 1994 Rooseveltv.Bishop Court X

1997 Hullv.Albrecht Court X1998 Hullv.Albrecht Court X2007 Floresv.Arizona X

Arkansas 1994 LakeViewv.Arkansas Court X1995 ApprovedEquitableSchoolFinance

Plan(Acts917,916,and1194)Bill n/a

2002 LakeViewv.Huckabee Court X X2005 LakeViewv.Huckabee Court X X2007 VariousactsresultingfromMaster's

ReportfindingsBill n/a

California 1998 LeroyF.GreeneSchoolFacilitiesActof1998

Bill n/a

2004 SenateBill6,SenateBill550,AssemblyBill1550,AssemblyBill2727,andAssemblyBill3001

Bill n/a

Colorado 2000 Bill181;VariousOtherActs Bill n/aConnecticut 1995 Sheffv.O’Neill X

2010 CoalitionforjusticeinEducationFunding,Inc.v.Rell

X n/a

Idaho 1993 IdahoSchoolsforEqualEducationalOpportunityv.Evans(ISEEO)

Court

1994 SenateBill1560 Bill n/a1998 IdahoSchoolsforEqualEducational

Opportunityv.State(ISEEOIII)X

2005 IdahoSchoolsforEqualEducationalOpportunityv.Evans(ISEEOV)

Court X

Indiana 2011 HB1001(Pl229) Bill n/a

(continued)

xxi

AppendixTableA1(continued)State Year Event LRS(2016) JJP(2016) CE(2015)Kansas 1992 TheSchoolDistrictFinanceand

QualityPerformanceActBill n/a

2005 Montoyv.State;Montoyv.Statefundingincreases

Both X X

Kentucky (1989) Rosev.CouncilforBetterEducation,Inc.

Court X X

1990 KentuckyEducationReformAct(HB940)

Bill n/a

Maryland 1996 Bradfordv.MarylandStateBoardofEducation

Court

2002 BridgetoExcellenceinPublicSchoolsAct(BTE)(SenateBill856)

Bill n/a

2005 Bradfordv.MarylandStateBoardofEducation

X (upheld)

Massachusets 1993 McDuffyv.SecretaryoftheExecutiveOfficeofEducation;MassachusettsEducationReformAct

Both X X

Michigan 1997 Durantv.StateofMichigan XMissouri 1993 CommitteeforEducationalEqualityv.

StateofMissouri;OutstandingSchoolsAct(S.B.380)

Both X

2005 SenateBill287 Bill n/aMontana 1993 HouseBill667 Bill X

2005 ColumbiaFallsElementarySchoolv.State

Court X X

2007 M.C.A.§20-9-309 Bill n/a2008 MontanaQualityEducationCoalition

v.MontanaX n/a

NewHampshire 1993 ClaremontNewHampshirev.Gregg Court X1997 ClaremontSchoolDistrictv.Governor Court X X1998 OpinionoftheJustices--School

Financing(ClaremontIII)X

1999 Claremontv.Governor(ClaremontIII);RSAchapter193-E

Both X X

2000 OpinionoftheJustices--SchoolFinancing(ClaremontVI)

X

2002 ClaremontSchoolDistrictv.Governor Court X X2006 LondonderrySchoolDistrictv.New

HampshireX

2008 SB539 Bill n/a

(continued)

xxii

AppendixTableA1(continued)State Year Event LRS(2016) JJP(2016) CE(2015)NewJersey 1990 TheQualityEducationAct;Abbotv.

BurkeBoth X X

1991 Abbottv.Burke X1994 Abbottv.Burke Court X X1996 ComprehensiveEducational

ImprovementandFinancingActof1996

Bill n/a

1997 SpecialMaster'sReport;Abbottv.Burke

Bill X

1998 Abbottv.Burke Court X2000 Abbottv.Burke Court2008 TheSchoolFundingReformActof

2008Bill n/a

NewMexico 1998 ZuniSchoolDistrictv.State X1999 ZuniSchoolDistrictv.State Court2001 DeficienciesCorrectionsProgram;

PublicSchoolCapitalOutlayActBill n/a

NewYork 2003 CampaignforFiscalEquity,Inc.v.State

Court X X

2006 CampaignforFiscalEquity,Inc.v.State

Court X

2007 EducationBudgetandReformAct Bill n/aNorthCarolina 1997 Leandrov.State Court X

2004 HokeCountyBoardofEducationv.State

Court X X

NorthDakota 2007 SB2200 Bill n/aOhio 1997 DeRolphv.Ohio Court X X

2000 DeRolphv.Ohio;Increasedschoolfunding(see93OhioSt.3d309)

Both X X

2001 DeRolphv.Ohio X2002 DeRolphv.Ohio Court X X

Oregon 2009 PendletonSchoolDistrict16Rv.State X n/aSouthCarolina 2005 AbbevilleCountySchoolDistrictv.

StateX

(continued)

xxiii

AppendixTableA1(continued)State Year Event LRS(2016) JJP(2016) CE(2015)Tennessee 1992 TheEducationImprovementAct Bill n/a

1993 TennesseeSmallSchoolSystemsv.McWherter

Court X X

1995 TennesseeSmallSchoolSystemsv.McWherter

Court X X

2002 TennesseeSmallSchoolSystemsv.McWherter

Court X X

Texas 1991 EdgewoodIndependentSchoolDistrictv.Kirby

Court X X

1992 Carrolton-FarmersBranchISDv.EdgewoodIndependentSchoolDistrict

Court X X

1993 SenateBill7 Bill n/a2004 WestOrange-CoveISDv.Nelson X2005 WestOrange-CoveConsolidatedISD

v.NeeleyX

Vermont 1997 Brighamv.State Court X X2003 RevisionstoAct68;H.480 Bill n/a

Washington 1991 SeattleII X2007 FederalWaySchoolDistrictv.State X2010 McClearyv.State Court n/a n/a

WestVirginia 1995 Tomblinv.Gainer Court XWyoming 1995 CampbellCountySchoolDistrictv.

StateCourt X X

1997 TheWyomingComprehensiveAssessmentSystem;TheEducationResourceBlockGrantModel

Bill n/a

2001 CampbellII;RecalibrationoftheMAPmodel

Bill X n/a

Notes:TablelistsalleventsincludedinanyoftheLafortune-Rothstein-Schanzenbach(2016);Jackson-Johnson-Persico(2016);orCorcoran-Evans(2015)eventlists,from1990onward.Xsindicateeventsthatappearintherelevanteventlist;n/aindicateseventsthatwereoutofscopefortherelevantlist,eitherbecausetheyweretoorecentorbecauseitincludedonlycourtcasesandnotlegislativeevents.InLafortuneetal.column,eventsareclassifiedas"court,""bill,"or"both";rowswithoutanentryarenotincludedinoureventdatabasebutareincludedinoneofthecomparisonsamples.Boldyearsindicatethesingleeventperstateselectedbyouralgorithm(seetext).AppendixDdiscussesdiscrepanciesbetweenLafortuneetal.andJacksonetal.lists.

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Table A2: Event studies for state budgets

Per capita Per pupil

Tax revenues :

Total revenues 433⇤⇤ 3,586⇤⇤

(187) (1,762)

Expenditures:

Total expenditures 415⇤⇤ 3,113⇤⇤

(162) (1,508)Education expenditures 137⇤⇤ 1,102⇤

(68) (605)Intergovernmental transfers 164⇤⇤ 1,264⇤⇤

(70) (581)General expenditures (less education, IG transfers) 83 537

(105) (707)

Notes: Table shows estimates from the one-parameter event study specification (equation (1)) for statebudgetary aggregates. State and year fixed e↵ects are included. Standard errors are clustered at the statelevel.

Table A3: Comparison to Card-Payne

State revenues (per capita) Total revenues (per capita)

1997-1992 1990-2012 (LRS) 1997-1992 1990-2012 (LRS)(CP) (CP)

Long di↵ Long di↵ Event study Long di↵ Long di↵ Event study

Court Ruling :Upheld -0.81 0.20

(0.67) (0.52)

Unconstitutional -1.89⇤⇤⇤ -1.10⇤⇤

(0.62) (0.48)Selected Events :Post Event -2.06 -2.25⇤⇤ -2.44 -1.61

(2.24) (0.89) (4.73) (2.38)

Notes: This table shows results using slopes from a regression of per capita state or total funding ondistrict mean household income (note: district mean income here is in levels, not logs). Columns 1 and 4 arefrom table 4 of Card and Payne (2002) and show the long di↵erence from 1977-1992 in the level-level slopecoe�cient. In columns 2 and 5, we replicate the Card and Payne specification using data from 1990 and2012. Columns 3 and 6 show estimated e↵ects from the one parameter event study specification (equation(1)) where level-level per capita slope coe�cients are the dependent variables.

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Table A4: Comparison to Corcoran-Evans

CE 2015 CE 2015 LRS 2016

Overturn Overturn Overturn* Selected FirstAdequacy Court

Per-pupil expenditure inequality :

Coe�cient of variation -0.029⇤⇤⇤ -0.044⇤⇤⇤ 0.028⇤⇤ 0.010 -0.001(0.010) (0.014) (0.014) (0.011) (0.008)

Per-pupil expenditures:

log(Mean) 0.092⇤⇤⇤ 0.056 0.068 0.056⇤⇤⇤ 0.044⇤⇤

(0.025) (0.037) (0.049) (0.021) (0.018)

Per-pupil revenues, by source:

Total revenues 701⇤⇤⇤ 478 416 829⇤⇤⇤ 759⇤⇤⇤

(256) (360) (445) (302) (264)State revenues 786⇤⇤⇤ 489⇤⇤ 556⇤⇤ 912⇤⇤ 998⇤⇤

(202) (199) (271) (359) (454)Local revenues -91 -31 -112 -146 -351

(266) (404) (452) (307) (372)

Notes: Columns 1-3 are from Table 19.3 of Corcoran and Evans (2015). In Columns 2 and 3, coe�cients ineach row come from a single regression, where column 2 represents the impact of a court ruling overturningthe existing school finance system and column 3 represents the additional impact of an adequacy rulingrelative to an equity ruling. Columns 4-5 repeat the analysis, using our sample and an approximation to theCorcoran and Evans specification.

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Table A5: Event study for log income, race, free lunch

(a) Income gradients

Log mean income Minority share Free lunch share

(1) (2) (3) (4) (5) (6)

Post Event * Yrs Elapsed -0.0010 0.0008 0.0022⇤ 0.0018 0.0062 0.0091(0.0029) (0.0040) (0.0013) (0.0015) (0.0064) (0.0071)

Trend -0.0026 0.0008 -0.0022(0.0042) (0.0008) (0.0030)

Post Event 0.0193 -0.0044 -0.0227(0.0368) (0.0051) (0.0291)

Observations 147 147 1045 1045 958 958p(post-event=post-event*trend=0) 0.72 0.87 0.09 0.49 0.34 0.39State FEs X X X X X XYr FEs X X X X X X

(b) Q1-Q5 di↵erence

Log mean income Minority share Free lunch share

(1) (2) (3) (4) (5) (6)

Post Event * Yrs Elapsed -0.0017 -0.0008 -0.0015 -0.0017 -0.0036⇤ -0.0052⇤⇤

(0.0029) (0.0035) (0.0017) (0.0020) (0.0019) (0.0024)

Trend -0.0004 0.0003 0.0018(0.0035) (0.0016) (0.0021)

Post Event -0.0073 -0.0005 -0.0048(0.0290) (0.0081) (0.0157)

Observations 145 145 1045 1045 962 962p(post-event=post-event*trend=0) 0.55 0.95 0.40 0.66 0.06 0.06State FEs X X X X X XYr FEs X X X X X X

Notes: Table presents event study specifications where the dependent variable is the slope of the indicateddemographic characteristic with respect to the district’s 1990 log mean household income (panel A) or thegap between the average for districts in the bottom and top quintiles of the 1990 income distribution (panelB). Minority share and free lunch share are available annually from the Common Core of Data (thoughmissing in some states and some years); log mean income is available from the Census in 1990 and 2000 andfrom the American Community Survey in 2007-11 (coded as 2011).

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Table A6: Stratification of race, FRL, & achievement, by quintile

Q1 Q2 Q3 Q4 Q5

Black 0.24 0.24 0.24 0.17 0.11

Black/Hispanic 0.25 0.23 0.24 0.18 0.11

White 0.20 0.20 0.18 0.20 0.22

Free/reduced-price lunch 0.32 0.23 0.20 0.15 0.10

25th pctl or below (NAEP) 0.27 0.21 0.22 0.17 0.13

75th pctl or above (NAEP) 0.14 0.15 0.17 0.22 0.32

Note: Table shows fraction of students of various groups in districts in various quintiles of the state’sdistrict income distribution. Each row sums to 1. Racial and free lunch shares are computed using CCDdistrict-level data for the year 1994. The distribution of high- and low-achieving students is based on the2003 NAEP data, which is the first year of comprehensive data for all grades and subjects.

Table A7: Event studies for district-mean resource gaps by race, FRL, & achievement

Black/White Free Lunch 25th/75th Pctl (NAEP)

St. Rev Tot. Rev St. Rev Tot. Rev St. Rev Tot. Rev

Post Event 197 195 2 23 143 193⇤

(160) (164) (185) (195) (141) (101)

Observations 1047 1047 938 938 1509 1509State FEs X X X X X XYr FEs X X X XSub-gr-yr FEs X X

Note: In columns 1 and 2, the dependent variable in event study specifications is the average per-pupilrevenue in the district attended by the average black student, less that in the district attended by theaverage white student in the same state. In columns 3 and 4, analogous revenue gaps are constructed forfree/reduced-price lunch and non-free/reduced-price lunch students. In columns 5 and 6, analogous revenuegaps are constructed for students scoring at or below the 25th percentile in the NAEP, and students scoringat or above the 75th percentile in the NAEP. The Post Event coe�cient shows the estimated event e↵ect fromparametric event study model without controlling for prior trends. State and year fixed e↵ects are includedin columns 1-4. State and grade-subject-year fixed e↵ects are included in columns 5 and 6. Standard errorsare clustered at the state level.

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