nber -The Impact of Public School Choice - Evidence from Los Angeles'Zones of Choice-此为英文文档

NBERWORKINGPAPERSERIES

THEIMPACTOFPUBLICSCHOOLCHOICE:EVIDENCEFROMLOSANGELES'ZONESOFCHOICE

ChristopherCampos

CaitlinKearns

WorkingPaper31553

/papers/w31553

NATIONALBUREAUOFECONOMICRESEARCH

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Cambridge,MA02138

August2023

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TheImpactofPublicSchoolChoice:EvidencefromLosAngeles'ZonesofChoiceChristopherCamposandCaitlinKearns

NBERWorkingPaperNo.31553

August2023

JELNo.I20,I21,I24

ABSTRACT

Doesaschooldistrictthatexpandsschoolchoiceprovidebetteroutcomesforstudentsthananeighborhood-basedassignmentsystem?ThispaperstudiestheZonesofChoice(ZOC)program,aschoolchoiceinitiativeoftheLosAngelesUnifiedSchoolDistrict(LAUSD)thatcreatedsmallhighschoolmarketsinsomeneighborhoodsbutleftattendance-zoneboundariesinplacethroughouttherestofthedistrict.Westudymarket-levelimpactsofchoiceonstudentachievementandcollegeenrollmentusingadifferences-in-differencesdesign.StudentoutcomesinZOCmarketsincreasedmarkedly,narrowingachievementandcollegeenrollmentgapsbetweenZOCneighborhoodsandtherestofthedistrict.TheeffectsofZOCarelargerforschoolsexposedtomorecompetition,supportingthenotionthatcompetitionisakeychannel.Demandestimatessuggestfamiliesplacesubstantialweightonschools'academicquality,providingschoolswithcompetition-inducedincentivestoimprovetheireffectiveness.Theevidencedemonstratesthatpublicschoolchoiceprogramshavethepotentialtoimproveschoolqualityandreduceneighborhood-baseddisparitiesineducationalopportunity.

ChristopherCampos

BoothSchoolofBusiness

UniversityofChicago

5807SouthWoodlawnAvenue

Chicago,IL60637

andNBER

Christopher.Campos@

CaitlinKearns

ckearns@

Adataappendixisavailableat/data-appendix/w31553

1

IIntroduction

Inrecentyears,centralizedschoolchoicesystemshavebecomeincreasinglypopularforallocating

K-12studentstoschools,ashiftawayfromtraditionalneighborhood-basedassignment(Ab-dulkadiroğluandSönmez2003;Neilson2021).Thisalternativeapproachtoeducationmarketsexpandsstudents’accesstoeffectiveschools,introducespotentialimprovementsinallocativeefficiency,andundercertainconditions,competitioncanleadtoimprovementsinthequalityofeducation(ChubbandMoe1990;Friedman1955;Hoxby2000,2003).Largeschooldistricts,suchasthoseinNewYorkCity,Denver,andNewOrleanshaveadoptedsuchsystems(Abdulka-diroğlu,AgarwalandPathak2017;HarrisandLarsen2015;PathakandSönmez2008,2013).

However,existingresearchisunclearonhowstudentoutcomescompareunderthetwomarket

structures.Doesapublicschooldistrictthatexpandsschoolchoiceprovidebetteroutcomesforstudentsthananeighborhood-basedassignmentsystem?Whatmarket-leveleffectsdosystemsofpublicschoolchoiceproduce,ifany?

ThispapertacklestheseimportantquestionsbystudyingtheZonesofChoice(ZOC)pro-gram,aninitiativeoftheLosAngelesUnifiedSchoolDistrict(LAUSD).Theprogram’sdesign

providesanaturalexperimentwhereroughly30–40percentofthedistrictoperatesunderschool

choicesystemsmirroringexpansionsinotherdistricts,whiletheremainingneighborhoodsop-erateunderthestatusquoofneighborhoodassignment.Inparticular,theprogramcreatessmalllocalhighschoolmarketsofvaryingsizeinsomeneighborhoodsbutleavestraditionalattendancezoneboundariesinplacethroughouttherestofthedistrict.ZOCstudentsareeligibletoattendanyschoolwithintheirneighborhood-basedzone,evenifitisnottheclosestone,andacentralizedmechanismisusedtorationaccesstooversubscribedschools.Thedesignofthisprogramprovidesanovelsettingtostudymarket-leveleffectsofchoiceasopposedtoindividualeffectsofchoicethatarecommoninliterature(Abdulkadiroğluetal.2011;Abdulka-diroğlu,PathakandWalters2018;Cullen,JacobandLevitt2006).Thefocusonmarket-leveleffects,whichapproximategeneralequilibrium-likeeffectsfromareduced-formperspective,fillsagapintheliteratureandprovidesamorecompleteoverviewoftheunderlyingchannelsandmechanismsoftheshort-andmedium-runeffectsofchoiceandcompetition.

Weorienttheempiricalanalysisaroundastylizedmodelofschoolchoiceandcompetitioninwhichfamilieschooseaschoolbasedonitsproximity,itsquality,andtheiridiosyncratictastes.Onthesupplyside,weassumeschoolprincipalsarerewardedforlargermarketsharesbutmustexertefforttoimproveschoolquality.WethenmodelZOCasanexpansionofhouseholds’choiceset,simultaneouslyintroducingstrategicconsiderationsbetweenschoolsintheirqualitydetermination.Themodelgivesrisetoasimplestatisticthatcaptureshouseholds’

expectedwelfaregainfromthechoicesetexpansion:“optionvaluegain”(OVG).Thechanging

distributionofOVGsacrossstudentsinresponsetocompetitiongovernsschools’incentivestoincreasequalityandthusservesasausefulempiricalstatistictostudytheroleofcompetitiveeffects.ThetheoreticalframeworkpredictsthattheintroductionofZOCwillimproveschoolqualityandtheimprovementwillbeconcentratedamongschoolsexposedtomorecompetition

asmeasuredbyOVG.

Wetestthesepredictionsusingadifference-in-differencesdesignthatcompareschangesin

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outcomesbetweenZOCandnon-ZOCstudents.ToisolatetheimpactofZOConschoolquality,wedecomposetreatmenteffectsintoeffectsonstudent-schoolmatchqualityandeffectsonschools’valueadded,interpretingthelatterasameasureofschoolquality.Estimatesofquantiletreatmenteffectsonschoolqualitythenallowustoassesswhetherthelowest-performingschoolsimprovemore.Wethenpivottothedemandsideandusestudents’rank-orderedpreference

liststoestimatepreferencesandcalculateOVGempirically.LookingattheheterogeneityoftreatmenteffectswithrespecttoOVGallowsustostudyhowthecausalimpactsofZOCvarywiththeextentofcompetition.Last,studyingpreferencesforschoolqualityallowusto

reconcileZOCsupply-sideeffectswiththeincentivesschoolsfacedascapturedthroughthechoicesfamiliesmake.

WefindlargepositiveeffectsofZOConstudentachievementandfour-yearcollegeenroll-ment.Event-studyestimatesrevealthatbythesixthyearoftheprogram,ZOCstudents’

Englishandlanguagearts(ELA)examperformanceimprovedby0.16σrelativetocomparablenon-ZOCstudents.ZOCalsoraisedfour-yearcollegeenrollmentbyroughly5percentagepoints,a25percentincreasefromthebaselineZOCstudentmean,aneffectmostlyexplainedbyin-

creasesinenrollmentatCaliforniaStateUniversity(CSU)campuses.Bothoftheseeffectsleadtovastreductionsinbetween-neighborhoodinequalityineducationaloutcomes.Adecomposi-tionoftheachievementimpactsrevealsthatimprovementsinschoolqualitymostlyexplaintheeffects,leadingtoasubstantialreductioninneighborhood-basedachievementgaps.Next,wefindthatimprovementsinschoolqualityareconcentratedamongthelowest-performingschools,afindingconsistentwiththetheoreticalframework.Furthersupportingthecompetitiveeffectshypothesis,wefindthattheeffectsoftheprogramarelargerforschoolsandstudentswith

higherOVGs.Thesefindingssuggeststhatthecompetition-inducedincentivesgeneratedbyZOCareakeymechanismforitseffectsonschoolperformance.

Oursubsequentanalysispivotstostudyingthedemandside.Estimatesofpreferences

derivedfromrank-orderedpreferencelistsareconsistentwiththeZOCeffects.Wefindthatparents’reportedpreferencesplaceahigherweightonschooleffectivenesscomparedtootherschoolcharacteristics,includingaschool’sstudentbody.Thisfindingsupportsthenotionthatparents’choicesprovideschoolstheincentivestoimprovestudentlearning.Thisfindingcontrastswithotherstudies’findings(e.g.,Abdulkadiroğluetal.2020andRothstein2006)andwithevidencethatlower-incomefamiliesarelesssensitivetoschoolquality(Burgessetal.2015;Hastings,KaneandStaiger2005).Wehypothesizethatthehomogeneityoffamilieswithrespecttoethnicityandsocioeconomicstatusreducestothescopetosortintoschoolsbasedoneasilyobservablepeerattributes.Thisnaturallyleadstoasettingwherefamiliesmaysystematicallychooseschoolsbasedonotherschoolattributesmorelikelytocorrelatewithschoolquality.RecentevidencefromCampos(2023)findsthatfamilies’beliefsaboutschoolqualityarenottoofarofffromthetruth,alleviatingconcernsthatfamiliesmayimperfectlyperceiveschoolquality.

Weaddressavarietyofconcernsrelatedtoourempiricalapproach.Wefindthatalterna-

tivesourcesofcompetitionfromcharterandmagnetschoolsdonotdifferentiallyaffectZOCneighborhoods,alleviatingconcernsthatourresultsaredrivenbythesealternativeschoolingmodels.Wealsofindthatthecompositionofstudentsdidnotdifferentiallychangeafterthe

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programexpansion.Last,weconductanintent-to-treat-likeanalysisandfindqualitativelysimilarresults.

Toprobeatadditionalmechanisms,wefindseveralpiecesofevidencesuggestingthatchangesinschoolingpracticesplayedarole.Themostrelevantrelatestoanuptickinsus-pensions,suggestingthatZOCschoolspivotedtowardaschoolingpracticestronglycorrelatedwiththeno-excusesapproachtourbaneducation,alsoshowntoelevatetheoutcomesofBlack

andLatinochildreninothersettings(Angrist,PathakandWalters2013;DobbieandFryerJr2011;Fryer2014).1Weconcludebydemonstratingthatintermediateoutcomesarealsoaf-fected;namelythatstudentsimprovedtheircollegepreparedness,ascapturedbychangesin

courseportfolioandimprovedSATscores,conditionalontakingtheSAT.Overall,weaddtothegrowingbodyofevidencesuggestingthattheno-excuses-likepractices—thatis,disciplinarypractices—elevatesstudentoutcomesinurbansettings,butwealsoshowthatstudentsinthissettingwerepositiveabouttheresultingchanges.

WearguethatcertainfeaturesofZOCmayexplainwhyourfindingscontrastwiththose

ofmanypreviousstudies.ZOCallowsforrelativelypersonalizedinteractionsbetweenZOCadministratorsandparents,makingiteasierforparentstoacquireinformation(Page,CastlemanandMeyer2020).Inparticular,administrator-ledinformationsessionsprovideparentswithapotentiallyrichopportunitytolearnaboutdifferencesinschoolquality.Moreover,because

choiceiswithinzonesratherthandistrictwide,ZOCparentsfacemanageablechoicesets,

whichmayhelpthemavoidthechoiceoverloadissuespresentinotherschoolchoicesettings(Beuermannetal.2023;Corcoranetal.2018).Thesefeaturescombinetocreateasettinginwhichacquiringadequateinformationaboutschoolsismorelikely.Last,asZOCneighborhoodsarehighlysegregated,theoptionsavailabletofamiliesdifferedminimallyintermsofstudentbodycomposition,potentiallynudgingparentstoselectschoolsintermsofothercharacteristicsmorecorrelatedwithschooleffectiveness.

Thispapercontributestoseveralstrandsofresearch.Mostclosely,itcontributestothe

literaturestudyingthesupply-sideeffectsofschoolchoicepoliciesorreforms.Onestrandoftheliteraturereliesoncross-districtorcross-municipalitycomparisonstoestimatetheeffectsofchoice(Hoxby2000,2003;HsiehandUrquiola2006;Rothstein2007)andreachesmixedconclusions.Otherpapershavefocusedonchoiceoptions,suchasCatholic,voucher,orcharterschools,thatdirectlycompetewithnearbyschooldistrictsforstudents(Card,DooleyandPayne2010;Dee1998;Neal1997).Ourpaperfocusesonwithin-districtpublicschoolcompetitionand,asaconsequence,isoneofthefirstpiecesofevidencedemonstratingthattheincreasinglypopulardistrict-widechoicereformscanmeaningfullyimprovestudentoutcomesandreduceeducationalinequality.Inaddition,weprovidecompellingevidencethatcompetitioninthepublicsectorisakeymechanismexplainingtheimprovementsinstudentoutcomes.

Anothersetofpapersfocusontheindividualeffectsofschoolchoice(Abdulkadiroğluetal.2011;Abdulkadiroğlu,PathakandWalters2018;Cullen,JacobandLevitt2006;Demingetal.2014;MuralidharanandSundararaman2015).Ourpapergoesbeyondthatandfocusesonmarket-leveleffectswhichrelatetobenefitsaccruedtoallstudentsinthemarket,asopposedto

1Wefindcomplementaryevidencethattrackingpracticesandclassroomassignmentpolicieschanged,alludingtofurtherchangesinschoolingpracticesnotnecessarilyassociatedwiththeno-excusesapproach.

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justparticipants.Thenaturalexperimentweleverageallowsustoestimatehowtwootherwiseseeminglysimilartrendingmarketsevolvebothintheshort-andmedium-run.Therefore,thispaperisrelevanttothegrowingnumberofdistrictsandmunicipalitiesaroundtheworldintroducingchoicethroughcentralizedassignmentsystems(Neilson2021)andhighlightsthepotentialofthesesystemstogeneratesustainedimprovementsinstudentoutcomesrelativetotraditionalneighborhood-basedassignment.

Last,thispaperdemonstratesthatanimportantneighborhoodattribute—schoolquality—ismalleableandthuscontributestotheliteraturestudyingtheimpactsofneighborhoods(Bergmanetal.2019;ChettyandHendren2018;Chetty,HendrenandKatz2016;Chyn2018;Kling,LiebmanandKatz2007).Althoughrecentevidencedemonstratesthatmovingtohigher-opportunityneighborhoodstendstoproducepositivelong-runoutcomes,itremainsanopenquestionwhatfactorsmediatetheseeffects(ChynandKatz2021).Acommonhypothesispointstodifferencesinschoolquality.Forexample,Laliberté(2021)findsthatvariationin

schoolqualityacrossneighborhoodsexplainsroughly50–70percentoftheeffectsofneighbor-hoodsinMontreal,Canada.Ourpapershowsthatapotentialkeydeterminantofneighbor-hoodqualityismalleableandschool-orneighborhood-specificpoliciesareameansofreducing

neighborhood-baseddisparitiesinoutcomes(FryerandKatz2013).

Therestofthispaperisorganizedasfollows.SectionIIoutlinesthefeaturesoftheprogramandourdatasources.SectionIIIoutlinestheconceptualframeworkforthesubsequentanalysis,andSectionIVdiscussesthedata.SectionVreportsevidenceonhowtheprogramaffectedstudentachievementandcollegeenrollment.SectionVIestimatesdemandandstudiestheroleofcompetition,andSectionVIIpresentsevidenceonadditionalmechanismsanddiscussesinstitutionalfeaturesthatmayhavecontributedtotheresults.SectionVIIIconcludes.

IIInstitutionalDetails

II.ATheChoiceLandscapeinLosAngelesandaBriefHistoryofZOC

ZOCisaninitiativeofLAUSD,thesecond-largestschooldistrictintheUnitedStates.ItisasignificantexpansionofchoiceforhighschoolsinLosAngeles,buttherewasanexistingandrapidlychangingchoicelandscapethatprecededtheprogram.BeforeZOC,familiesinLos

Angeleshadtheoptiontoenrollincharterschools,applytomagnetprogramswithinLAUSD,andoptforintra-districttransfers,providedcapacity.TheZOCexpansionispartlyaresponsetotheevolvingchoicelandscapeandtheenrollmenttrendsthatprecededit.

Ashasbeencommoninseverallargeurbanschooldistrictsaroundthecountry,LAUSDcontinuestoexperienceenrollmentdecline,potentiallyamplifiedbychartergrowth(seeOnlineAppendixFiguresA.1andA.2).ThecharterlandscapewasrapidlyevolvinginthedecadebeforetheZOCexpansion.Thenumberofcharterhighschools,asreportedintheCommonCoreData,increasedfrom65in2002to306in2012.CharterhighschoolsresidinginZOC

neighborhoodsrepresented38percentofthecharterschoolgrowthoverthatdecade.Families’out-of-districtoptionsincreasedyearly,andasaconsequence,LAUSDhighschoolenrollment

startedadownwardtrendin2008.

Magnetprogramsaremoreprevalentthanintra-districttransfers,sowediscussthisoptionin

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detail.MagnetprogramtrendsinthedecadeprecedingtheZOCexpansionweremorestagnant

comparedtochartergrowth.Therewere38magnetprogramsavailabletohighschoolstudentsuntil2010,withthecreationof4newonesbetween2010and2012.Magnetenrollmentwasflat,representingroughly8–9percentofallLAUSDhighschoolenrollmentduringthistimeperiod.Evenastheseprogramshaveexpandedacrossthedistrict,2018wastheyearwiththelargestmarketshareof12.8percent.Insummary,whilefamilieshavemanyoptions,relativelyfewfamiliesoptforthemagnethighschoolsector.

ZOCemergedfromtheBelmontZoneofChoice,locatedinthePicoUnionareaofdown-

townLosAngeles.Thiscommunity-basedprogramcombinedseveralaspectsofthevariousongoingreforms.Apressingconcernamongcommunityadvocateswastheovercrowdingoftheirneighborhoodschools.TheschoolconstructionprogramstudiedinLafortune,RothsteinandSchanzenbach(2018)addressedtheovercrowdingbycreatinglargehighschoolcomplexesthathousedmultiplepilotschoolsandsmalllearningcommunities.2Communityorganizers

helpeddeveloptheBelmontZoneofChoicebycreatinganinformalenrollmentandassignmentsystemforeligibleresidents.FamiliesresidingwithintheBelmontZoneofChoicewereeligibletoapplytothevariousschoolslocatedwithinthezone.TheBelmontpilotstartedin2007andcontinuedinformallyforfiveyears.

Thecontinuingexodusofstudentsfromthedistrictandincreasingcommunitypressureforaccesstobetterschoolspartlyledtheschoolboardtoconsiderremovingattendancezonebound-aries(seeResolutiontoExamineIncreasingChoiceandRemovingBoundariesfromNeighbor-

hoodSchools)anddevisingotherwaysofexpandingschoolchoice(seeResolutiononExpandingEnrollmentandEqualAccessthroughLAUSDChoice)inearly2012.Theschoolboard’staskforcerecognizedthecommunity’spositiveresponsetotheBelmontpilotandbeganreplicatingthemodelinothersuitableneighborhoods.ByJuly2012,aZOCofficewasestablishedalongwith16zones.FigureIshowsthatin2010,theprogrammostlycovereddisadvantagedstudents. IncontrasttotheBelmontZoneofChoice,thenewzoneswereorganizedandadministeredbyacentraldistrictofficeandusedformalassignmentandenrollmentmechanisms.Theyalsohadambitiousgoals:accesstomoreeffectiveschools,improvementinstudent-schoolmatchquality,andincreasedparentalinvolvement.Eachofthesepointswasexplicitlymentionedin

theschoolboardminutesandmotivatedtheexpansionofZOC.

II.BProgramFeaturesandIncentives

ZOCexpandsstudents’highschooloptionsbycombiningcatchmentareasintochoicezonesand,insomecases,pullingschoolswithundefinedassignmentareasintozones.Thiseffectivelyexpandsfamilies’choicesetstoincludeseveralnearbyoptions.Theprogramexpansionwestudyincludesothernotablechangesaswell.

TheprogramiscentrallyrunbyateamofadministratorswhofocusonlyonaspectsofZOCthatrunonayearlycycle.Themosttime-extensiveperiodoftheyearistheapplicationcycleinwhichparentsofeighth-gradestudentssubmitzone-specificapplicationscontainingrank-

2LAUSDdefinespilotschoolsasanetworkofpublicschoolsthathaveautonomyoverbudget,staffing,gov-ernance,curriculumandassessment,andtheschoolcalendar.Tiestothelaborunionremainandisakeydistinctionbetweennon-LAUSDcharterschoolsandLAUSDpilotschools.

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orderedpreferencelists.Admissionintoanyparticularschoolisnotguaranteed,althoughsomepriorityisgivenbasedonproximity,incumbency,andsiblingstatus.

Theneighborhood-basedprogramdesignallowshighschoolstoknowwheretheirpooloffuturestudentsisenrolled.Schoolanddistrictadministratorstakeadvantageofthisfeaturebycoordinatingvariousparentalinformationalsessionshostedbyeitherfeedermiddleschoolsorcandidatehighschools.Concurrently,someclustersofschoolsorganizecommunityeventsoutsideofschoolhourstopitchtheirschoolstopotentialstudents.Theseeventscontinueforroughlysixweeksuntilrank-orderedpreferenceapplicationsaredueinmid-November.

Althoughschoolsdifferintheamountofefforttheydevotetorecruitment,theydonothavetheleveragetogiveprioritytoparticularstudentsassomeschoolscaninotherschoolchoicesettings.

Theprogramexpansionalsoformalizesassignmentpracticesacrossallzones.Theschooldistrictusesparents’rank-orderedpreferenceliststodetermineassignmentsusingacentralizedalgorithm,analogoustoaBoston—orimmediateacceptance—mechanism.Schoolsthatareoversubscribedfillseatsusingrandomlyassignedlotterynumbersandschool-specificpriorities.

BecauseLAUSDusesanimmediateacceptancemechanism,parentshavestrategicincentivesandmaychoosetomisreporttheirpreferencestoguaranteeadmissionintoschoolstheymightnotpreferthemost.

Strategicincentivesnotwithstanding,manyparentslistnon-neighborhoodschoolsastheirmostpreferredoptions.FigureIIshowsthatroughly65–70percentofapplicantslistaschoolthatisnottheirneighborhoodschoolastheirmostpreferredoption.Prioritiesandcapacityconstraintsprecludeallapplicantsfromenrollingintheirmostpreferredschool,soapproxi-

mately30percentofapplicantsenrollinaschoolthatisnottheirneighborhoodschool.The30percentafterthepolicyexpansionisanoticeableincreasefrom7percenttheyearbefore.

Importantly,althoughcapacityconstraintsarebindingatsomeschoolswithineachzone,the

concurrentdistrict-wideenrollmentdeclineprovidesasettinginwhichschoolscanabsorbaddi-tionalstudents.Thedecliningenrollmentmeansthatmostschools,includinginitiallypopularschools,arenotoperatingatcapacity,makingthethreatofcompetitionmoresignificant.

PublicschoolsinLosAngeleshaveseveralreasonstocareaboutlosingstudentstocom-petitorsintheirzone.AlthoughLAUSDdoesnotemployastudent-centeredfundingmodelinwhichschoolbudgetsareexactlyproportionaltostudentenrollment,rigidschedulesdetermineresourceandstaffallocation.Adropinenrollmentcouldmeanschoolshavetoreducetheirteaching,counseling,nursing,oradministrativestaff.Anecdotalevidencesuggestsprincipalscareaboutthispossibility,providingthemwithincentivestocareabouttheirschools’zonemarketshare.

Another,admittedlymorespeculative,reasonisprincipals’careerconcerns.Anextensive

literaturehasdocumentedthepotentialofcareerconcernstodynamicallyinduceincentivesforpublicsectorworkers(Dewatripont,JewittandTirole1999).InLAUSD,roughly10percent

ofprincipalsbetween2008and2018tookadministrativepositionsatthedistrictheadquarters,

whichcanbeseenasglitteringprizes(Bertrandetal.2020).Viewedthroughthislens,ZOCintroducesatournament-likestructure,inthesenseofLazearandRosen(1981),inwhichprincipalshaveincentivestooutperformotherprincipals.

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Thenextsectionpresentsaconceptualframeworkthattakestheseincentivesasgiveninastylizedmodelofschoolchoiceandcompetition.Themodelimplicationsguidemostoftheempiricalexercisesthroughouttherestofthepaper.

IIIConceptualFramework

Webeginwithastylizedmodelofthestatusquothatconsistsofneighborhoodmonopolies

competingwithanoutsideoption,andthenweintroduceZOC,highlightinghowtheprogramalteredschoolincentives,anddiscussitspotentialbenefits.3Weusejtodenotebothschoolsandneighborhoods,indicatingthereisoneschoolperneighborhood.Letstudentsindexedbyiresideinneighborhoodj(i)∈{1,···,J},whichcontainsoneschoolalsoindexedbyj.Eachschooljoperatesasamonopolyinitsneighborhoodbutfacescompetitionfromanoutside

optionindexedby0.

Studentscanenrollineithertheirneighborhoodschoolj(i)ortheoutsideoption.Studenti’sutilityfromattendingschoolj∈{0,j(i)}is

Uij=U(αj,Xi,dij,εij)=Vij(αj,Xi,dij)+εij,

whereαjisschoolqualityasdefinedintheachievementmodelinOnlineAppendixC,dijisdistancetoschoolj,Xicapturesobservableheter