nber-誰從較小的榮譽(yù)賽道中受益

NBERWORKINGPAPERSERIESWHOBENEFITSFROMASMALLERHONORSTRACK?ZacharySzlendakichardKMansfieldWorkingPaper31375http//papers/w31375NATIONALBUREAUOFECONOMICRESEARCHCambridgeMA8June3WethankScottImberman,TerraMcKinnish,BrianCadena,FranciscaAntman,AllisonAtteberry,TaylorJaworski,CoreyWoodruff,andBrachelChampionaswellasseminarparticipantsattheInstituteforDefenseAnalysesandCNAandtwoinsightfulbutanonymousrefereesforhelpfulcommentsanddiscussions.ThisresearchusesdatatheNorthCarolinaEducationResearchDataCenteratDukeUniversity.WeacknowledgetheNorthCarolinaDepartmentofPublicInstructionforcollectingandprovidingthisinformation.TheviewsexpressedhereinarethoseoftheauthorsanddonotnecessarilyreflecttheviewsoftheNationalBureauofEconomicResearch.NBERworkingpapersarecirculatedfordiscussionandcommentpurposes.Theyhavenotbeenpeer-reviewedorbeensubjecttothereviewbytheNBERBoardofDirectorsthataccompaniesofficialNBERpublications.?2023byZacharySzlendakandRichardK.Mansfield.Allrightsreserved.Shortsectionsoftext,nottoexceedtwoparagraphs,maybequotedwithoutexplicitpermissionprovidedthatfullcredit,including?notice,isgiventothesource.WhoBenefitsfromaSmallerHonorsTrack?ZacharySzlendakandRichardK.MansfieldNBERWorkingPaperNo.31375June3JELNoI,I21,I24STRACTMostU.S.highschoolcoursesseparateclassroomsintostandardandhonorstracks.Thispapercharacterizestheefficiencyanddistributionalimpactofchangingtheshareofstudentsenrollinginhonorsclassrooms.Usingasortingmodelwherestudentschoosetracksbycoursebutschoolsinfluencethesharechoosinghonors,weshowthatadministrators’optimalchoicesofhonorstracksizerequireknowledgeoftreatmenteffectfunctionscapturingtheimpactofalternativehonorsenrollmentsharesondifferentpartsofthestudentpredictedperformancedistribution.UsingadministrativedatafromNorthCarolinapublichighschools,weestimatethesetreatmenteffectfunctionsbypredictedperformancequintile.Acrossvariousspecifications,wefindthatsmallerhonorstracks(20%-30%ofstudents)yieldmoderateperformancegainsforthetopquintile(~.05-.07testscoreSDsrelativetonotracking)thatdeclinemonotonicallyacrossquintilestowardzeroforthebottomquintile.However,expandingthehonorssharebeyond30-35%generatesfurther(small)achievementincreasesonlyforthemiddlequintile,whilereducingtopquintilegainsandcausingsubstantialbottomquintilelosses.Sincemanycoursesfeaturehonorssharesabove35%ordonottrack,wepredictthatenrolling~25%ofstudentsinhonorsineachhighschoolcoursewouldimproveallquintiles’statewideperformance.ZacharySzlendakDepartmentofEconomicsUniversityofColoradoBoulderBoulder,CO80309zachary.szlendak@ichardKMansfieldEconomicsBuildingRoom206CUniversityofColorado-BoulderBoulder,CO80309andNBERrichard.mansfield@2lIntroductionofhhe3t1Thecoursesexc1udedeitherhavemu1tip1eadvancedtrackssuchashonorsandAdvancedP1acement,aregenera11ytakeninmidd1eschoo1,orareinfrequent1ytested.4to5ede6e7 f2ModelsummAry4Thereisa1iteratureontheimpactofattendingane1itemagnethighschoo1(see,e.g.,Abdu1kadirog1ueta1.(2014)orDobbieandFryerJr(2014)),butitsfndingsare1essre1evanttohighschoo1principa1sinschoo1sfeaturingtypica1distributionsofstudentpreparednesswhomustdecidehowtoregu1atetrackchoicesforcourseswithintheirschoo1s.82.lTheodminittrAtor,tProblemte5Whi1emostofthese1eversarenotobservab1eintheNorthCaro1inaadministrativedata,GPAboostsareanexception.Asimp1ebivariateregressionwithcourse,year,andschoo1fxedefectsprovidessuggestiveevidenceforourassumption:aonepointGPAboostthatmakesa"B,gradeinanhonorsc1assequiva1enttoan"A,inaregu1arc1assisassociatedwithahigh1ysignifcant12percentagepointincreaseinthesharechoosingthehonorstrack.Unfortunate1y,GPAboostsarenotreportedbyasufcientnumberofdistrictstobeusedtoforminstruments.9nNQfNfmax1θq(i)E[Yi(f)]≈maxWqθqNQfNfi=1q=1QQargmaxWqθqE[Yq(f)]=argmaxWqθqE[ΔYq(f)](2)fq=1fq=12.2TettscoreProductionAndTrAckChoicek6Thisaggregationapproachisana1ogoustothatusedbyCardandRothstein(2007)intheneighborhoodsortingcontext.noeret3DAtAaBAckgrounde7Natura11ythereareoccasiona1discrepanciesduetostudentschangingtrackduringtheacademicyearorstudentsmisreportingthetrackoftheirc1assroom.Insuchcasesweusetheschoo1-reportedtrackoftheirc1assroominourana1ysis,butourresu1tsarerobusttodroppingobservationsfeaturingdiscrepancies.etnok3.lottigningstudentttoPrepArednettQuintiletAndRettrictingthesAmpleofschoolteedt8Moreyearsareavai1ab1ebyrequestfromtheauthors.Nocourse-yearinoursamp1eexhibitsbunchingaroundtheupperor1ower1imitofthescorerange.9Wea1sodropschoo1-year-coursecombinationsfeaturingc1assroomsadheringtointernationa1bacca1aure-atestandardsforthesamereason.Thisprovestobeinconsequentia1,sincemostschoo1sthatofertheIBcurricu1umaretoohigh-achievingtosatisfyourothersamp1erestrictiondescribedbe1owthattheirdistributionsofstudentpredictedperformancep1ausib1ysatisfyAssumption1.10Weinvestigatesensitivitytothetreatmentofa11-honorscoursesinSection6.l pn11Specifca11y,weestimateYistj=English7istjβ1j+math7istjβ2j+English8istjβ3j+math8istjβ4j+_istj.Wethenassigncourse-specifcquinti1esbasedonthedistributionofPredictedScoreistj=English7istjβ?1j+math7istjβ?2j+English8istjβ?3j+math8istjβ?4j.Resu1tsarerobusttotheinc1usionofsciencetestscores;however,sciencescoresareon1yavai1ab1eforasma11numberofyears.3.2summArystAtittictgtfg12NorthCaro1inarankstowardthemidd1eofU.S.statesforeducationa1performance,suggestingthatourresu1tsshou1dbeexterna11yva1idformostschoo1sthroughouttheU.S.(U.S.News(2019)).ttattde4EmpiricAlopproAchc13Variousmeasuresofrankingonobservedabi1ity,inc1udingshorteror1ongerperformancehistoryona1ter-nativesetsoftests,a11showhigh1eve1sofsortingonunobservab1es.Ystjq=E[ΔYq(fstj)]+XstjqβX+ΓstjqβΓ+ωstjq. E[ΔYq(fstj)]=γfstj+γfj+γfjmnt14Threeofthe1argestsourcesofachievementchangesfroma1ternativehonorsenro11mentsharesarethesamewhenthefractionofstudentsinhonorsisequa1tozeroorone:peerefects,a11ocationofteachersamongtracks,andspecia1izedinstruction.ee15SeeAntonovicseta1.(2022)forevidencethatschoo1trackingpatternsrespondtochangesinstatewideaccountabi1itypo1icies.16Specifca11y,weassumeE[ωstjqfstj|Xstjq,Γstjq]=0,E[ωstjqftj|Xstjq,Γstjq]=0,andE[ωstjqfj|Xstjq,Γstjq]=0.ndtrnne17Forthesma11subsetofcontro1sfeaturinganontrivia1shareofmissingva1ues,werep1acetheseva1ueswithzerosandintroducecorrespondingmissingva1ueindicatorvariab1es.18Weuseatwo-yearratherthanaone-year1agtominimizeanyspi11oversamongstudentsfromadjacentcoursecohortswhomayberepeatingthecourseorwhoarepeersinothercourses.19Aweightingschemebasedonthenumberofstudentsratherthanwithin-schoo1-yearshareswou1dprioritizetheefcacyofadministrators'actionsat1argeschoo1soversma11erschoo1s.Giventhatweareinterestedinprovidinginputstoprincipa1sofa11schoo1types,wepreferweightingschoo1sratherthanstudentsequa11y.AspertherecommendationsofSo1oneta1.(2015),specifcationsareavai1ab1euponrequestwhichuseweightsproportiona1tothenumberofstudentsintheschoo1-year-coursequinti1ecombination.Pointestimatesandstandarderrorsaresimi1arforthediferentweightingschemes.5Retultt5.lQuintileTreAtmentEfecttnee20Wechosepointwiseconfdenceinterva1sratherthanconfdencebandsbecausewearegenera11ycomparingpredictedva1uesatparticu1arhonorssharesagainsttheabsenceoftracking,ratherthaneva1uatingjointhypothesesinvo1vingpredictedva1uesoveracontinuousrangeofhonorsfractions,suchaswhetherthereexistsanynonzerohonorsfractionthatmakesquinti1e2worseofthantheabsenceoftracking.21Theregressionsunder1yingthep1ottedtreatmentefectfunctionsa1soinc1udethe20%ofschoo1-year-coursesthatdonotfeatureanytracking.nteettetae40%ofthettudentbodyinthemandhurtbyhonortprogramtwithmorethan40%ofo22TheK1eibergen-PaapWa1dFstatisticassociatedwiththefrststageis109.2,farabovestandardcritica1va1uesfromStockandYogo(2002)forrejectinganu11hypothesisofweakinstruments.23TheK1eibergen-PaapWa1dFstatisticassociatedwiththefrststageforthec1assshareIVapproachis401.0.y5.2odminittrAtor,tProblemtreesDtand.007sDt.24Confdenceinterva1sfortheva1uesoftheadministrator'sobjectivefunctionateachhonorssharearea1sogeneratedusingthede1tamethod.25Confdenceinterva1sforthemaximizingshareandmaximumva1uearegeneratedusinganonparametericc1usterbootstrap,withschoo1sasc1usters.tetganr6RobuttnettCheckt E[ΔYq(fstj)]=1(q=q\)1(fstj=f\)λq\f\(5)q\f\tE[ΔYq(fstj)]=γfstj+γfj+γfj+γ1(fstj∈(0,1))E[ΔYq(fstj)]=γfstj+γfj+γfj+γfj26Recodingf=1asf=0and1eavingthecubicunrestrictedproducesnear1yidentica1resu1tsforhonorssharesbe1ow70%,butextreme1y1argestandarderrorsatveryhighhonorsshares.e27TheK1eibergen-PaapWa1dFstatisticassociatedwiththefrststageis3.95,sothatwecannotrejectthenu11hypothesisofinstrumentweaknessatstandardcritica1va1ues.28Somecorecourses,suchasEng1ish1andBio1ogy,aretakennear1yuniversa11y,whi1eothers,suchasChemistry,arenottakenbyasubstantia1shareofstudents.e29Addingthesesamecontro1stothebase1inespecifcation,wheretheextraschoo1-1eve1contro1sarenotmadeirre1evantbyschoo1fxedefects,doesnotmeaningfu11ychangethebase1inetreatmentefectfunctionseither.7ConclusionadrReferencetmichoodefectsAmericanEconomicReiewJ.D.AngristandV.Iavy.Usingmaimonides'ru1etoestimatetheefectofc1asssizeonscho1asticachieve-ment.TheQuarter1yjourna1ofeconomict,114(2):533-575,1999.AmericansecondaryEducation,pages26-42,2008.Po1icyana1ytitandManagement,pages623-645,1996.insecondaryschoo1s.EconomictofEducationRe"iew,19(1):1-15,2000.andta1entedprogramsonstudents.AmericanEconomicJourna1:EconomicPo1icy,6(3):30-62,2014.nEconomicRe"iew,106(10):2783-2816,2016.D.CardandJ.Rothstein.Racia1segregationandtheb1ack-whitetestscoregap.Journa1ofPub1icEco-nomict,91(11-12):2158-2184,2007.S.E.Carre11,B.I.Sacerdote,andJ.E.West.Fromnatura1variationtooptima1po1icy?theimportanceofendogenouspeergroupformation.Econometrica,81(3):855-882,2013.EconomicJourna1:EconomicPo1icy,12(1):127-66,2020.thenewyorkcityexamschoo1s.AmericanEconomicJourna1:A((1iedEconomict,6(3):58-75,2014.fromarandomizedevauationinkenyaAmericanEconomicRe"iew,101(5):1739-74,2011.nomictnaofUrbanEconomictURIhttps://.nxtimes.com/2y21/11/y4/us/california-math-curriculum-guidelines.html.S.A.Imberman,A.D.Kug1er,andB.I.Sacerdote.Katrina'schi1dren:Evidenceonthestructureofpeerefectsfromhurricaneevacuees.AmericanEconomicRe"iew,102(5):2048-82,2012.naJ.Mathews.Virginiaa11ieswith,thenbacksawayfrom,controversia1mathanti-trackingmovement.TheWathingtonPott,2021.URIhttps://.-ashingtonpost.com/local/education/fairfaw-countx-schools-math-classes-tracking/2y21/y4/29/197aa29c-a7a2-11eb-8d25-7b3ye74923eastorx.html.Inauiry,57(1):162-171,2019.doi:10.1111/ecin.12730.URIhttps://onlinelibrarx.-ilex.com/doi/abs/1y.1111/ecin.1273y.Z.Pei,J.-S.Pischke,andH.Schwandt.Poor1ymeasuredconfoundersaremoreusefu1onthe1eftthanontheright.Journa1ofButinett8Economicstatittict,37(2):205-216,2019.iveversusseectiveschooinginengandinwaesWhatdoweknow?WorkingPaper12176,Nationa1BureauofEconomicResearch,Apri12006.URIhttp://./papers/-12176.J.A.SmithandP.E.Todd.Reconci1ingcon日ictingevidenceontheperformanceofpropensity-scorematchingmethods.AmericanEconomicRe"iew,91(2):112-118,2001.nTAblesCourteNameNoon1yon1yHonort&Honort&APon1yAPHonort,AP,&0004183000100Chemittry43701000000Geometry2000PsCI000Phytict0008Notet:Eachcellprovidetthetotalnumberoftchool-yearcombinationtinxhichthecourteindicatedbytheroxtitleitoferedunderthetrackingregimefeaturedinthecolumntitlet.“PsCI刀denotetphyticaltcience.Thetampleoftchool-yeartitlimitedtothotexithatleatt30tetttcoret.Pane1A:ShareofStudentsEverTakingEachCourseA1gebra2Bio1ogyChemistryEng1ish1GeometryPSCIFina1Samp1e0.640.640.890.890.380.380.990.980.690.690.500.51Pane1B:GradeIeve1SharesByCourseinFina1Samp1eA1gebra2ChemistryEng1ish1GeometryPSCIShareingrade90.050.190.000.990.310.26Shareingrade100.420.670.270.010.570.24Shareingrade110.470.130.510.000.110.37Shareingrade120.060.010.220.000.010.13Notet:ThefrttroxofPanelAditplaytthethareofttudenttfromthecohortttcheduledtograduatebetxeen2005and20l0xhoevertookthecourtedetignatedbythecolumnlabel.Cohorttareattignedtoeachttudentbatedontheminimummodalgraduationyearimpliedbytheirtettyearandttudentgradeobtervationt.Thetecondroxlimittthetampletotchooltxithatypicaldittributionofttudentpreparednettquintilet(seesection3.l).Forbothtampletxelimittotchool-yeartxithatleatt30tetttcoreobtervationt.PanelBditplaytthedittributionofgradetinxhichthetecourtetxeretakenamongourfnaltampleofttudent-courteobtervationt.VarianceComponentVar(fstj)Var(fstj?Xstjβ?)etweenschoo40.3%33.6%11.7%17.4%48.0%49.0%Notet:Thetubtcriptts,t,andjdenotetchool,year,andcourte,retpectively.:Betxeenschool,capturetVar(fs)inColumnlandVar(fs?Xsβ?)inColumn2.:withinschool/AcrottYear,capturetVar(fst)?Var(fs)andVar(fst?Xstβ?)?Var(fs?Xsβ?),retpectively.:withinschool-Year/AcrottCourte,capturetVar(fstj)?Var(fst)andVar(fstj?Xstjβ?)?Var(fst?Xstβ?),retpectively.VARIABLEsNohonorttrackingmean(td)share∈(0,0.35)mean(td)share∈[0.35,1)mean(td)Cohorttizel45.4272.4302.l(l09.l)(l65.2)(269.9)Pupiltoteacherratiol263l405l36l(6.046)(4.679)(6.056)Averageclatttizel6.88l8.24l7.93(4.362)(3.877)(9.2l0)0.003090.002260.000957(0.036l)(0.0l54)(0.00906)Numberofttudenttattchool856.7l,079l,l4l(459.2)(433.2)(568.l)shareofttudenttthatareHitpanic0.04960.05l90.0568(0.05l6)(0.0478)(0.0522)0.2070.2250.254(0.l77)(0.l70)(0.l74)0.7090.6920.652(0.l97)(0.l89)(0.l92)0.0l600.0l450.0208(0.0244)(0.0206)(0.0223)7thgrademathtcoret0.3040.2760.497(0.54l)(0.449)(0.450)8thgrademathtcoret0.6230.5920.787(0.574)(0.442)(0.444)7thgradereadtcoret0.2650.2370.433(0.450)(0.37l)(0.4l5)8thgradereadtcoret0.5660.5370.725(0.440)(0.369)(0.403)AveragePraxittcore4l77434.9386.0(266.5)(247.8)(27l.8)0yeartexp02l80.2220.298(0.388)(0.390)(0.435)lyearexp0.02820.027l0.0286(0.l36)(0.ll4)(0.l27)2yeartexp0.03720.03320.0309(0.l63)(0.l29)(0.l28)5yeartexp0l0l0.09750.0770(0.258)(0.2l7)(0.204)llyeartexp0.l620.l680.l60(0.3l8)(0.277)(0.292)l2＋yeartexp0.4540.4530.406(0.440)(0.396)(0.4l0)WhoteparenttlackaHsdiploma/GED0.065l0.06030.0430(0.067l)(0.063l)(0.0594)WhoteparentthaveaHsdiploma02l30.2050l56(0.ll3)(0.l04)(0.ll4)Whoteparentthavetomecollege0.ll90.ll40.l06(0.0933)(0.0680)(0.0806)Whoteparenttattendedtradeorbutinetttchool0.02990.02860.026l(0.0403)(0.0243)(0.0232)Whoteparenttattendedcommunitycollege0.l960.l750.l54(0.l3l)(0.09l6)(0.l07)Whoteparentthavea4-yeardegree0.20l0.2l20.245(0.l2l)(0.ll5)(0.l39)Whoteparentthavegraduatedegreet0.08350.08400.l28(0.0877)(0.0734)(0.l20)Withgiftedttatut0.l040.l080.l34(0.l87)(0.l22)(0.l78)Withlearningditabilitiet0.03090.03640.0277(0.0382)(0.0564)(0.06l2)LimitedEnglithProfciency0.02770.02820.0337(0.0488)(0.0530)(0.0774)schoolcourte-yeart2,7677,5366,333Notet:Eachentryprovidetmeanvaluet(andttandarddeviationtinparenthetet)forthecontrolvariablelittedintheroxlabelamongalltchool-year-courteobtervationt.Thetampleherematchettheoneutedforourbatelinetpecifcation,xhichitlimitedtotchool-yeartxithatleatt30tetttcoreobtervationtandxhichfeaturetypicaldittributiontofttudentquality(seesection3.l).E[ΔYq(f)]atsevera1CandidateHonortEnro11mentFractiontfortheBate1ineandschoo1FEt(oLs).15LaggedIV.15C1attshareIV.15Notes:Predictedva1uesaregeneratedfromtheestimatesVforthespecifcationsnamedintherowpane1fortheva1uesofthehonorsenro11mentsharef1istedintherow1abe1s.95%confdenceinterva1scomputedusingeitherthede1tamethod(forpredictedva1uesatparticu1arenro11mentshares)aredisp1ayedinparentheses.Eachco1umnpresentsestimatesforadiferentquinti1eofthestatewidepredictedperformancedistributionamongstudents.:Base1ine(OIS)'referstothebase1inespecifcationthatpoo1sa11sourcesofvariationinthehonorsenro11mentshare.:Schoo1FE(OIS)'usesafu11setofschoo1fxedefectstoiso1atewithin-schoo1variation.:IaggedIV'usesthehonorsenro11mentsharefromtwoyearsprior(anditssquareandcube)asinstrumentsforitscontemporarycounterpartsinthechosenschoo1-year-course.:C1assShareIV'usesthehonorsc1assroomshare(anditssquareandcube)asinstrumentsforthestudent-weightedhonorsenro11mentshare(anditssquareandcube).Tab1e6:EttimatetoftheAchievement-MaximizingHonortshareandtheMaximumExpectedAchievementfortheQuinti1e-specifcTreatmentEfectFunctiontspecifcationshareinHonortArgmaxMaxschoo1FEt(oLs)ArgmaxMaxArgmaxMaxC1attshareIVArgmaxMaxNotes:Maximizingsharesandva1uesaregeneratedfromtheestimatesVforthespecifcationsnamedintherowpane1fortheva1uesofthehonorsenro11mentsharef1istedintherow1abe1s.95%confdenceinterva1scomputedusinganon-parametricbootstraparedisp1ayedinparentheses.Eachco1umnpresentsestimatesforadiferentquinti1eofthestatewidepredictedperformancedistributionamongstudents.:Base1ine(OIS)'referstothebase1inespecifcationthatpoo1sa11sourcesofvariationinthehonorsenro11mentshare.:Schoo1FE(OIS)'usesafu11setofschoo1fxedefectstoiso1atewithin-schoo1variation.:IaggedIV'usesthehonorsenro11mentsharefromtwoyearsprior(anditssquareandcube)asinstrumentsforitscontemporarycounterpartsinthechosenschoo1-year-course.:C1assShareIV'usesthehonorsc1assroomshare(anditssquareandcube)asinstrumentsforthestudent-weightedhonorsenro11mentshare(anditssquareandcube).Tab1e7:EttimatetoftheAchievement-MaximizingHonortshareandtheMaximumExpectedAchievementfortheCompentatoryWeightingandEqua1-Weighting ingBate1ine(oLs)Argmax0.2660.237Max0.0370.029 schoo1FEt(oLs)Argmax0.2620.213 Max0.0200.012 LaggedIVArgmax0.2550.230Max0.0620.053 C1attshareIVArgmax0.2420.172 Max0.0130.007 Notes:Maximizingsharesandva1uesaregeneratedfromtheestimatesVforthespecifcationsnamedintherowpane1fortheva1uesofthehonorsenro11mentsharef1istedintherow1abe1s.95%confdenceinterva1scomputedusinganon-parametricbootstraparedisp1ayedinparentheses.Co1umn1presentsmaximizingsharesandva1uesforaversionoftheadministrator'sprob1eminwhichequa1weightisgiventotheexpectedperformanceofeachquinti1eofthestatewidepredictedperformancedistribution.Co1umn2rep1acesequa1quinti1eweightingwithcompensatoryweight-inginwhichforscoresofquinti1es1-5areweighted,,,,,respective1y.SeeTab1e6fordescriptionsofthebase1ineanda1ternativespecifcations1istedinthepane1s.E[ΔYq(f)]atsevera1CandidateHonortEnro11mentFractiontforVarioutBinspecifcationUnconttrainedoLsIndicatoroLsNotes:Predictedva1uesaregeneratedfromtheestimatesVforthespecifcationsnamedintherowcategoryfortheva1uesofthehonorsenro11mentsharef1istedintherow1abe1s.95%confdenceinterva1scomputedusingthede1tamethodaredisp1ayedinparentheses.Eachco1umnpresentsestimatesforadiferentquinti1eofthestatewidepredictedperformancedistributionamongstudents.:BinSpecifcation'a1tersthebase1inespecifcationbyrep1acingthecubicfunctionwithseparateindicatorsforwhethertheshareofstudentsinhonorsfa11swithinmutua11yexc1usiveinterva1sof1ength0.2.:ConstrainedCubic'imposestherestrictionthatthetreatmentefectsfor0%and100%honorsenro11mentareequa1.:HonorsIndicator'a1tersthebase1inespecifcationbyinc1udingaseparateindicatorforanhonorsenro11mentshareof0.:Quartic'ftsaquarticratherthanacubicpo1ynomia1.E[ΔYq(f)]atsevera1CandidateHonortEnro11mentFractiontforVariouttPartspecifcationshareinhonortQuinti1e1otherCourteIV.15schoo1-YearFEt.15C1attshareIV/schoo1-CourteFEtAugmentedContro1t.15Rettrictedschoo1set.15Notes:Predictedva1uesaregeneratedfromtheestimatesVforthespecifcationsnamedintherowcategoryfortheva1uesofthehonorsenro11mentsharef1istedintherow1abe1s.95%confdenceinterva1scomputedusingthede1tamethodaredisp1ayedinparentheses.Eachco1umnpresentsestimatesforadiferentquinti1eofthestatewidepredictedperformancedistributionamongstudents.:OtherCourseIV'usesthecontemporaneoushonorsenro11mentshare(anditssquare)intheothertestedcoursesasinstrumentsfortheshareanditssquareinthechosencourse.:Schoo1-YearFEs'introducesafu11setoffxedefectsforschoo1-yearcombinations.:C1assShareIV/Schoo1-CourseFEs'introducesafu11setoffxedefectsforschoo1-coursecombinationsintotheC1assShareIVspecifcationfromTab1e8.:AugmentedContro1s'addsasetofadditiona1contro1scapturing1earningdisabi1itystatus,free/reducedprice1unche1igibi1ity,andteachereducationcategoryshares.:RestrictedSchoo1Set'restrictsthesamp1etoschoo1swhosedistributionsofpreparednessstrayfromtheuniformdistributionby1essthan1/3ofaquinti1eperstudentonaverage,ratherthanthe1/2thresho1dusedinthebase1inesamp1e.FiguresNotes:Eachfguredepictsthedistributionofthefractionofstudentswhoenro11inthehonorstrackforschoo1-year-coursesinwhichanhonorstrackexistsforthe1abe1edcourse.Thefguresre1yonthebase1inesamp1eofschoo1-course-yearobservations(SeeSection3.1fordetai1s).CourtewideHonortEnro11mentsharebyQuinti1eoftheschoo1-specifcPredictedNotes:Thefrstfvegraphsp1ottheshareofstudentsinthechosenquinti1eofpredictedperformancethatse1ectsthehonorstrackamongnarrowbinsofthecoursewidehonorsenro11mentshare.Quinti1esforthisfgurearebasedonschoo1-specifcratherthanstatewidepredictedperformancerankings.Eachbininc1udessharesin(binminimum,binmaximum].Thebottomrightce11p1otsthesupportofthedatausedfortheotherfvece11s,exc1udingschoo1-year-courseswhereeithernoneofthestudentsora11ofthestudentsareenro11edinhonors.Thefguresarebasedonthefna1samp1eofschoo1-course-year-quinti1eobservationsusedtoestimatethebase1inespecifcation.Notes:Eachgraphp1otsthemeanstandardizedtestscorebynarrowbinsoftheshareofthecourse'sstudentsenro11edinhonors(poo1edacrosssixsubjects)foradiferentquinti1eofaregressionindexofpredictedstudentperformancebasedongrade7and8testscores.Thebinforthe1owestshareofstudentsinhonorsinc1udesschoo1-year-courseswherenotrackingoccurs.Theremainingbinsconsiderhonorsenro11mentsharesintheinterva1(binminimum,binmaximum].ofPredictedstudentAchievement(E[ΔYq(f)]):Bate1ineandschoo1FixedEfecttNotes:Thefrstfvegraphsineachpane1p1otestimatesofthefunctionE[ΔYq(f)]thatmapscoursewidehonorsenro11mentfractionintoexpectedstandardizedtestperformancebyquinti1eofpredictedperformanceforthebase1ine(Pane1(a))