家長和學生時間在學年前后使用 Parental and Student Time Use Around the Academic Year

NBERWORKINGPAPERSERIES

PARENTALANDSTUDENTTIMEUSEAROUNDTHEACADEMICYEAR

BenjaminW.Cowan

ToddR.Jones

JeffreyM.Swigert

WorkingPaper31177

/papers/w31177

NATIONALBUREAUOFECONOMICRESEARCH

1050MassachusettsAvenue

Cambridge,MA02138

April2023

TheauthorswouldliketothankEzraKargerfortheschooldistrictcalendardata.TheywouldalsoliketothankXiaoxiaoBai,EunsikChang,KendallKennedy,andparticipantsatAEFPforusefulfeedback.TheviewsexpressedhereinarethoseoftheauthorsanddonotnecessarilyreflecttheviewsoftheNationalBureauofEconomicResearch.

NBERworkingpapersarecirculatedfordiscussionandcommentpurposes.Theyhavenotbeenpeer-reviewedorbeensubjecttothereviewbytheNBERBoardofDirectorsthataccompaniesofficialNBERpublications.

?2023byBenjaminW.Cowan,ToddR.Jones,andJeffreyM.Swigert.Allrightsreserved.Shortsectionsoftext,nottoexceedtwoparagraphs,maybequotedwithoutexplicitpermissionprovidedthatfullcredit,including?notice,isgiventothesource.

ParentalandStudentTimeUseAroundtheAcademicYear

BenjaminW.Cowan,ToddR.Jones,andJeffreyM.Swigert

NBERWorkingPaperNo.31177

April2023

JELNo.I12,I21,I31,J16

ABSTRACT

Wedemonstratehowmothers,fathers,and15–17-year-oldstudentsaltertheirschedulesaroundtheK-12academicyear.Usingregressiondiscontinuity(RDD)methods,combinedwithdatesonschoolyearstartandenddatesbylocality,wedocumentseveralnotableresults.First,mothersaresubstantiallymoreaffectedbytheschoolyearthanarefathers.Whenschoolisinsession,motherssleepless,spendmoretimecaringforfamilymembersanddrivingthemaround,andspendlesstimeoneating,freetimeandexercise.Fathersseechangesthataregenerallysimilarinsignbutsmallerinmagnitudecomparedtomothers.15–17-year-oldsnaturallyreducetimespentineducationalpursuitswhenschoolisout(adecreaseofabout5.5hoursperdayonweekdays),andmostofthattimeissubstitutedtowardfreetime(anadditional2+hoursperday)andsleep(1+hoursperday).OurresultsprovideaholisticpictureofhowfamiliesbuildtheirdaysaroundtheK-12schoolcalendarandhaveimplicationsforpoliciestargetedtowardwomen’sandteenagechildren’shealthandwell-being.

BenjaminW.CowanJeffreyM.Swigert

SchoolofEconomicSciencesSouthernUtahUniversity

WashingtonStateUniversityHealthEducationActionLab

103EHulbertHalljms858@

Pullman,WA99164

andNBER

ben.cowan@

ToddR.Jones

312DMcCoolHall

DepartmentofFinanceandEconomics

MississippiStateUniversity

MississippiState,MS39762

UnitedStates

trj234@

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1.Introduction

Howdoestheschoolcalendaraffectthetimeuseofparentsandchildren?Schooldatesareperfectlyforeseeable,andindividualshaveampleopportunitytoplanaroundthem.Evenso,whenschoolisout,behaviorsmightchangeinwaysthataffectthehealthandwell-beingoffamilieswithschool-agechildren.Inthispaper,weseektounderstandsuchchangesinbehaviorandfocusespeciallyondifferencesbetweenmothers,fathers,andolderteenagechildren.

IntheUnitedStates,roughly96%ofpublicK-12schoolshaveatraditionalsummerbreakofaround12weeks.1Researchintohowstudentandparentoutcomeschangewhenschoolisonsummerhiatusincludeslossesinacademicachievement(“summerlearningloss”;seeQuinnandPolikoff,2017);decreasesinmaternallaborsupply(PriceandWasserman,2022);andchangesinyouthmentalhealth,suicidality,andcriminalactivity(HansenandLang,2011;Hansen,Sabia,andSchaller,2022;JonesandKarger,2022).2Anothersetofstudieshasexaminedhowparentandstudenttimeusediffersovertraditionalsummerbreakmonthsrelativetootherpartsoftheyear(e.g.,HandwerkerandMason,2017;Gershenson,2013).3Toourknowledge,asidefromJonesandKarger(2022),noneofthesepreviousstudiesusevariation

1/programs/digest/d13/tables/dt13_234.12.asp.Amongtheschooldistrictsinourschoolcalendardata,theaverage(mean)breakis11.7weeks.The5thpercentileis9.9weeks,the25thpercentileis10.9weeks,the75thpercentileis12.6weeks,andthe95thpercentileis13.7weeks.

2Moregenerally,thereislong-standinginterestinhowschoolattendanceaffectsparents’andchildren’sbehaviors.Manypapersinthisliteraturefocusonpoliciesthataffecttheavailabilityofschoolinchildren’spre-Korkindergartenyears(see,forexample,studiesonmaternallaborsupplyinGelbach,2002;Cascio,2009;Fitzpatrick,2012;andstudiesonchildren’sacademicachievementandlong-runoutcomesinHeckmanetal.,2010;Bailey,Sun,andTimpe,2021).Anothersetofstudiesfocusonpoliciesthataffecthowmuchtimestudentsareinhighschool,suchasthoseonacademicachievement(Liu,Lee,andGershenson,2021)andshort-andlong-termcriminaloutcomes(e.g.,Anderson,2014andBacher-Hicks,Billings,andDeming,2019).Lastly,therearestudiesontheeffectsofthetimingofbreaksduringtheschoolyear(Graves,2013a,b)andthelengthoftheschoolweek(Ward,2019;DuchiniandVanEffenterre,2022)onmaternallaborsupply.

3Thereisalargeliteratureonchildsleeppatterns,someofwhichcompareschildsleepbetweentheschoolyearandthesummerbreak(see,forexample,Hansenetal.,2005;Crowleyetal.,2006;andStewart,2014).Hansenetal.(2005)comparesaveragesleepfor37highschoolstudentsinAugustandSeptemberacrosstheschoolstartdate.Itispossiblethatotherteenagesleepstudiesalsomakeuseofexactstartandenddates.

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stemmingfromexactschoolstartandenddatescombinedwithregressiondiscontinuity(RD)methodstoidentifychangesinoutcomes.

Inthispaper,weexploitinformationonschoolstartandenddatesaroundthesummerbreakfromacrosstheUnitedStatescombinedwithAmericanTimeUseSurvey(ATUS)data,whichcontain24-hourtimediarieswithexactdates,tomeasurehowbehaviorchangeswhenschoolstartsandends.Ourapproachallowsustoavoidconfoundingeffectsduetotheschoolyearwithotherfactorsthatchangeseasonallysuchasweather,daylight,andeconomicconditions(BarksyandMiron,1989;GeremewandGourio,2018;CoglianeseandPrice,2020).Wefurthercontributetotheliteratureonhowschoolbreaksaffectfamilies’schedulesbyexaminingacomprehensivesetof10time-usecategories—includingsleep,self-care,householdtasks,caringforothers,work,education,freetime,eating,physicalexercise,andtraveling—forparentsaswellasolderteenagestudents.45

Wefocusonhowchangesintimeallocationssurroundingthesummerschoolbreakaffectthehealthandwell-beingofindividuals.Forexample,mostteenagersreportgettinglessthanthenationallyrecommendedamountofsleeponschoolnights(BandyopadhyayandNinotchka,2019);andsleepdeprivationamongteenagershasbeenlinkedtopooreracademicperformanceandworsementalhealth(SetonandFitzgerald,2021).Lackofsufficientsleepisalsoaproblemforadults(Liuetal.,2016),asisinsufficientexercise—lessthanaquarterofU.S.adultsexerciseenoughtomeetfederalguidelines(BlackwellandClarke,2018).Finally,studiesshowthatmothersengageinmoreeducationalchildcaresuchashelpingwithhomework(e.g.,

415-year-oldsaretheyoungestparticipantsinATUS,sowecannotexaminethetimeuseofyoungerstudentsinouranalysis.Apreviousstudyofteenagers’timeuseexamineshowactivitiescorrelatewithfamilycharacteristics(suchasmother’semploymentandeducation)butdoesnotexaminehowsuchactivitiesvarywithschoolyeardates(Wight,Price,Bianchi,andHunt,2009).

5Wereferto15-17yearoldindividualsasstudents,thoughitispossiblethatnotallare.

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Ronning,2011)andhouseholdtasks(e.g.,Parker,Horowitz,andRohal,2015)thanfathersdo.Weaskwhetherthesummerschoolbreakaffectstimespentintheseandotheractivitiesthathaveimplicationsfortheoverallwell-beingofindividualsinthehousehold.

Inouranalysis,wefindthatmanybehaviorsexhibitsharpchangesacrossthestartorendoftheacademicyear.Onweekdayswhenschoolisin-session,mothersof6–17-year-oldchildrengiveup25-28minuteseachofsleepandfreetime.Theyspendanadditional35minutescaringforothersandwork19moreminutesperday.Theyalsospend4-7minuteslessperdayonbotheatingandphysicalexerciseactivities,whichisoffsetbya5-minuteincreaseintimespenttraveling(e.g.,driving).Ourresultsareinlinewithotherstudiesthatfindthatmothersworklesswhenschoolisout(Ward,2019;DuchiniandVanEffenterre,2022;PriceandWasserman,2022).Inaddition,however,wefindthatotheractivitiesthatarelikelyimportanttowomen’swell-being(e.g.,sleep,freetime,exercise)increaseduringthesummerschoolbreak.

Asaplacebotest,weexaminewomenwithnochildreninthehouseholdbetweenages3and17,whosetimeusepatternsshouldgenerallybeunaffectedbyschooldates.6Acrossthe10categoriesoftimeuse,wefindnostatisticallysignificanteffects—withtheexceptionofamarginallysignificanteffectoncaringforothers—withmostbeingsmallinmagnitude.

Wealsocomparetheexperienceoffathersofschool-agechildrenwiththatofmothers.Fathersaregenerallyaffectedbytheschoolyearinqualitativelysimilarwaystomothers:sleep,self-care,caringforothers,work,freetime,andexerciseallchangeinthesamedirectionastheydoformothers.However,withtheexceptionsofworktimeandself-care,alleffectsaresmallerinmagnitudethantheyareformothers,andeffectsonsleepandcaringforothersarestatisticallysignificantlylargerinmagnitudeformothers(atthe5%level).Inaddition,whenwedrilldeeper

6Becauseitisoursensethatpre-schoolsoftenfollowthesameacademiccalendarasK-12schoolsinthearea,weexcludethosewith3-5-year-oldsaswell.

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tolookspecificallyattotaltimespentactivelyengagedinactivitieswithchildren,theeffectoftheschoolyearisalmostthreetimesaslargeforwomenasitisformen.Overall,weconcludethatmothersaremoreelasticthanfathersintheirtimeusewithrespecttowhethertheirchildrenareinschool.

Wealsodistinguishbetweenmotherswhowereemployed2-5monthspriortotheirATUSinterview(i.e.,asofthetimeoftheirlastCPSinterview)andthosewhowerenotemployed.Previouslyemployedandnot-employedmothersbothseereductionsinsleepandfreetimeandincreasesincareforotherswhenschoolisin-session,butmagnitudesarelargerforthosewhowerenotemployed.Ontheotherhand,previouslyemployedmothersseeareductioninworkhoursduringsummerbreak,whilepreviouslynot-employedmothersseeanincrease.Thedecreaseinexercisetimeduringschoolisconcentratedamongpreviouslyemployedmothers.Wealsodivideoursampleofwomenbyhouseholdincomeandfindthatresultsarelargelysimilaracrosslow-andhigh-incomehouseholds,withanotableexceptionbeingthathigher-incomewomenaretheonlyonestoseeachangeinexercise.

Lastly,wefocusonolderteenage(15-17)childrensincetheyareoldenoughtobeinterviewedinATUS.Theseindividualsreportspendingmorethan5andahalffewerhoursineducationalactivitiesonweekdayswhenschoolisonsummerhiatus.7Thistimeisusedinavarietyofwayswhenschoolisout:notably,freetimeincreasesbyalittleover2hours,sleeptimeincreasesby1.4hours,worktimeandtimespentdoinghouseholdtaskseachincreaseby0.7hours,andphysicalexerciseincreasesby0.5hours.Thus,(older)studentsthemselvesaremoreaffectedbywhetherschoolisin-sessionthanparentswhenitcomestosleepandexercise.

7Forareferencepoint,thelengthoftheaverageAmericanschooldaywasabout6.6hoursin2008:

/surveys/sass/tables/sass0708_035_s1s.asp

.

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Weshowthatdespitesomewhatlatersummerbedtimes,teenagestudentsmorethancompensatewithlaterwaketimes,onaverage.Thisisconsistentwithresearchshowingthatchildrensleepmorewhenschoolstarttimesarepushedbackeventhoughtheycould(inprinciple)undothebenefitswithlaterbedtimes(Dunsteretal.,2018).Regardingexercise,justoverhalfofU.S.high-schoolstudentsattendphysicaleducationclassesinanaverageweek(andonly30%attenddaily),soeventhoughwedonotobservetimespentinP.E.classesduringtheschoolday(suchtimeiscountedastakingclasses),itisverylikelythatphysicalexerciserisesduringthesummerbreakmonthsfortheaverageyouth.8

Weviewouranalysisasafirststeptowardunderstandinghowhealthandwell-beingvaryaroundtheschoolcalendar.Thereisawell-knowngendergapinmentalhealthmeasuresincludingdepressionandanxiety(Churchilletal.,2020;Golin,2022),butlittleisknownabouthowthisgapvariesseasonallyor,moreparticularly,withwhetheranindividualhaschildreninschool.Ourresultssuggestthatwomenwithschool-agechildrenchangetheirbehaviormuchmoreduringtheschoolyearthansimilarlysituatedmen,withlargerlossesinsleep,freetime,andexerciseandincreasesintimespentcaringforanddrivingwithchildren.Someofthesefactorsmaycontributetorelativelypoorermentalhealthofmotherswhenschoolisinsession.9Becauseourdatacannotdirectlyaddressthispossibility,itisanimportanttopicforfutureresearch.

Regardingteenagers,wealsofindreasonswhytheirmentalhealthmaysufferduringtheschoolyearrelativetosummerbreak.Chiefamongtheseisourestimatethattheysleepoveranadditionalhourperdaywhenschoolisout.Thereisstrongseasonalityinteenagemental

8/healthyschools/physicalactivity/facts.htm.

9Asithappens,womenarefourtimesmorelikelytoexperienceSeasonalAffectiveDisorder(SAD)thanmenare:see/blog/seasonal-affective-disorder-spotlight#:~:text=According%20to%20the%20National%20Institute,often%20in%20women%20than%20men.

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healthcarevisitswithvisitsfallinginthesummer(Zhangetal.,2021),andpreviousstudieshavelinkedschoolbreakswithareductioninyouthsuicides(HansenandLang,2011;Hansen,Sabia,andSchaller,2022).Thoughmanyfactorschangewhenschoolisout(suchastheincidenceofbullying),ourresultssuggestthatthewayteensusetheirtimemaycontributetothesetrends.Ontheotherhand,wefindthatthemajorityoftheincreaseinsummerfreetimeisspentonvideogaming,television,andcomputeruse:intotal,theyincreasebynearlyanhourandahalfoverthesummer.Thehealthconsequencesoftheseactivitiesarenotwellunderstood:inthecaseofvideogames,forexample,recentstudyfindingsindicatecertainvideogamesmayhavetherapeuticpotentialforimprovingoutcomes(seeZayenietal.,2020,forareview);however,41%ofteenageboysand11%ofgirlsthemselvesreportthattheyspend“toomuchtime”playingvideo

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games.

2.Data

OurprimarydatasourceistheAmericanTimeUseSurvey(ATUS).WeuseMulti-YearMicrodataFiles,obtainedfromTheU.S.BureauofLaborStatistics(U.S.BureauofLaborStatistics,2021).TheATUSisa24-hourtimediary,wheretherespondentreportstheactivitiestheyweredoingbetween4:00amofthefirstdayand4:00amofthefollowingday.RespondentsarerandomlysampledfromindividualswhocompletedtheCurrentPopulationSurvey(CPS),andtheytaketheATUSbetweentwoandfivemonthsaftertheirfinalCPSinterview.WemakeuseofvariablesfromboththeATUSandthefinalCPSinterview.TheATUScontainsinformationonwheretherespondentlives(wheretheirhouseholdis).Thestateofresidenceisincludedforallrespondents.Countyand/orCBSAareonlyobservedforsomeindividuals.

10/fact-tank/2018/09/17/5-facts-about-americans-and-video-games/

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Ingeneral,werestrictthesampletousedatafrom2003-2019.11Whenwesplitbyhouseholdincome,weusedatafrom2010-2019becausetheincomevariableisoftenmissing(andnotimputed)inprioryears.12TheATUScontainsover400activitycodes.Wecollapsethesecodesintotenmaincategories:1)sleep;2)self-care;3)householdtasks;4)caringforothers;5)work;6)education;7)freetime;8)eating;9)exercise;and10)travel.Thesecategoriesaremutuallyexclusiveandexcludeasmallamountoftimewithcodingerrors,etc.SeetheDataAppendixtoseewhichactivitiesmakeupeachcategory.

Ouranalysisreliesonschoolstartdates.Weuseschoolcalendarinformationfrom,whichwasusedinJonesandKarger(2022).Thesedatacontainschoolcalendarinformation—schoolstartdate,summerstartdate,andvariousholidays—forover11,000USschooldistricts.Wefocusonschoolstartdateandsummerstartdateforthe2019-2020schoolyear,whichweusetoproxyforsuchdatesduringthe2010-2019schoolyearsaswediscussbelow.13TheearliestdateinthedataisApril24,andmorethan99%ofdistrictshaveasummerstartdateofMay11andafter.

Wefirstaddgeographicinformationtotheschoolcalendardata.WethenmergethesedatatotheATUSbasedonthelocationoftheATUSrespondent.Theonlyidentifiersfortheschoolcalendardataarestateandschooldistrict.WeusethesetomatchtoNCESschooldistrictdatathatcontainmoredetailedgeographicinformation(includingcountyandMCSA,whichweuse).Specifically,wefirstremoveanumberoftermssuchas“school,”“district,”and“public.”Wedothissothatthefuzzymatchingcanrelymoreonuniqueinformation.Thisresultsin76%

11Whileweusethe“2003-2020Multi-YearMicrodataFiles”versionofthisdata,wedonotconsider2020toavoidcomplicationsfromtheCovid-19pandemic.

12See/tus/atususersguide.pdf.

13Itappearsthatthe2020summerstartdatecorrespondstothescheduleddatebeforeCovid-19affectedschoolschedules.

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ofthe11,245schooldistrictswithaperfectmatchtoaschooldistrictintheNCESdata.Lessthan1%arenotmatchedatall.Amongthesematches,thereissomedegreeofmismatching,butthisdoesnotappeartobecommon.14Afterthematching,weaggregateto1)thecountylevel;2)theCBSAlevel;and3)thestatelevel.Witheachaggregation,wedetermineboththemostcommonlyoccurringschoolstartweekandsummerstartweek.Forinstance,perhapsacounty’smostcommonlyoccurringschoolstartweekisweek32,and90%ofdistrictsinthatcountystartedduringthisweek.Wedothisbecausewedonotobserveanindividual’sschooldistrictintheATUSdata,sowerelyontheaforementionedmethod.

Next,weaddtheschoolcalendarinformationtoeachobservationintheATUS.Ingeneral,itisbestifwecanusethedateswhichwereaggregatedtothecountylevelbecausecountiestendtobesmallerthanCBSAs(andthustheschoolcalendardatesarebettermeasured)andareneverlargerthanthestatetheyarein.Asmentionedabove,weonlyobservecountyforsomeindividualsintheATUS.Fortheseindividuals,weusethemost-commonlyoccurringschool(andsummer)startdateforthecounty(notaccountingforschooldistrictsize);15thesemakeup39%ofthedata(beforesamplerestrictions).WethenmatchtheCBSA-leveldatesforindividualsforwhomweobserveCBSAbutnotcounty;thesemakeup30%ofthedata.Forremainingindividuals,weusedatesaggregatedtothestatelevel;thesemakeup31%ofthedata.

Thereareseveralpotentialsourcesofmeasurementerrorcorrespondingtotheschoolcalendarinformation.First,theschoolcalendarinformationcorrespondstothe2019-2020schoolyear,butweusedatagoingbackto2003.Schooldistrictsmightchangetheirstartweekovertime.Second,tocalculateweekoftheyear,wecodeweek1asJanuary1-7,week2asJanuary

14Inrarecases,itdoesalsohappenthatasingledistrictmatchestomultipleNCESdistricts;inthesecases,wekeeponlyoneoftheNCESmatches.Italsohappens,afterremovingthetermsbeforematching,thatthereareduplicatedistricts.Forthese,werevertbacktothedistrict’soriginalname.

15Thisisassumingtheschooldistrictfilealsohasdataforthatcounty.

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8-14,andsoon;becauseyearsstartondifferentdaysoftheweek,agivenweekmeanssomethingslightlydifferentacrossyears.Third,becausewedonotobserveschooldistrictintheATUS(orhome-schoolstatus),wecannotmatchpreciselytotheschooldistricttherespondentlivesin,sowerelyonthemethoddescribedabove.Finally,whilewedoobservealargepercentageofschooldistricts,wedonotobservethemall.

Acrossallsamples,weexcludeholidaysandindividualsemployedinelementaryandsecondaryschools(asofthelastCPSinterview),sincetheirschedulesaremechanicallyaffectedbyschoolandsummerstartdates(PriceandWasserman,2022).16Thisyields197,191observations.Weconsidertwoagegroups:25-55yearolds(manyofwhomareparents)and15-17yearolds(manyofwhomarestudents).Afterrestrictingonage,thereare108,59125-55yearoldrespondentsand8,56115-17yearoldrespondents.Dependingonthesample,wealsolimitbasedononeormoreofthefollowingcriteria:byweekday/weekend;bygender;bywhetherthereisatleastoneownchildofschoolageinthehousehold;byfamilyincome(asofthelastCPSinterview);andbyemploymentstatus(asofthelastCPSinterview).Theserestrictionstendtogreatlyreducesamplesizes.

3.EmpiricalStrategy

Weusearegressiondiscontinuitydesign(RDD)toexploretheeffectsofbeinginschoolversusoutofschoolonourconstructedtimecategoriesforadultsand15-17yearolds.ThisstrategyfollowsBenson,Fitzpatrick,andBondurant(2022)andJonesandKarger(2022).Wepresentresultsbothinregressionformandgraphically.Fortheregressions,weestimatethefollowingequationaroundtheschoolstartdate:

16Wealsodroptheverysmallnumberofobservations(lessthan0.1%)thatarecodedasbeinginthesummercontrolgroupbutareactuallyintheverybeginningoftheschoolyearorintheveryendoftheschoolyear.Thiscanhappenifthesummerbreakisveryshort.

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yi=a+p?f(daysi)+y?1(daysi>cutOff)+Xip+ei,wit?|daysi|≤k(1)

where,forindividuali,yishoursspentinaparticulartimecategory(suchasexerciseorsleep);therunningvariabledaysisdaysrelativetotheWednesdayofthefirstweekofschool(whichisthecutOffdate);f(days)isalinearfunctionoftherunningvariable,whichweallowtovaryoneithersideofthecutoff;1(days>cutOff)isanindicatorforbeingoverthecutoff;andXisavectorofdayofweekfixedeffectsandcontrolvariables(metropolitanstatus,highestlevelofeducationattained,Hispanic,race,age,and,whereapplicable,sex).17Becauseschoolsstart(end)ondifferentdaysoftheweek,weestimateadonutholeregressioninthatwedonotconsiderthedaysoftheschoolstart(end)week.Weclusterthestandarderrorsatthelevelofgeographyweusedforschoolstartdate.18

Oneshortcomingofourpaperisoursamplesize,leadingustouseofabandwidthof9weeks(65-67days)toincreasestatisticalpower.Ifweweretouseanoptimalbandwidth,wewouldbeleftwithstandarderrorstoolargetodetecteffects.19However,forourbaselinetablewetestsensitivitytousingsmallerbandwidthsandgenerallyfindsimilarresultsuntilthebandwidthisreducedtoabout2-3weeks.

Werunequation1for1)thetimearoundtheendofsummer/startofschool.Wealsomodifyequation1for2)theendoftheschoolyear/startofsummer.Wefinallyrun3)astackedversionof1)and2),whichistheversionwefocuson.20Inorderforthecoefficientstohavesimilarinterpretationsacrosscutoffs,wecodethedaysvariablesuchthatnegativevalues

17Metropolitanstatus,education,Hispanic,andracearefromtheCPS,whileageandsexarefromtherosterfile.

18WecomparedthestandarderrorsforPanelAofTable3toalternativechoices.Thestandarderrorswecomputeareveryclosetothe“rdrobust”Statapackage(Calonicoetal.,2017)conventionalstandarderrors(withthe“vce(cluster)”optionanduniformkernel).Thestandarderrorsaresmallerthanthoseobtainedwiththedefaultrdrobust“vce(nn3)”option.

19Usingthe“rdbwselect”commandfromthe“rdrobust”packageinStata,coupledwiththe“mserd”optimalbandwidth,forthebaselinemotherweekdaysample,wewouldbeleftwithabandwidthbetween11and19days.

20Weincludethebeginningofschoolyear-specificandbeginningofsummer-specificresultsintheWebAppendix.

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correspondtosummerdaysandpositivevaluescorrespondtoschooldays.Fortheendofsummer/startofschoolcutoff,daysisnegativefortheendofthesummerandpositiveforthestartoftheschoolyear.Incontrast,fortheendoftheschoolyear/startofsummercutoff,daysispositivefortheendoftheschoolyearandnegativeforthestartofthesummer.Thus,apositivevalueofourcoefficientofinterest,y,correspondstoanincreaseintimeusageintheschoolyearrelativetothesummer.

InAppendixFigure1wepresentdensityplots(binnedattheweeklylevel)forourfourmainsamples.Statisticaltestsofmanipulationaroundtheschoolstart/enddatecutoffsdonotyieldevidencethatitisanissue,withp-valuesrangingfrom0.39to0.79.21

4.Results

4.1Effectsonspecificcategoriesrelatedtotimewithchildren

Wefirstconsideroutcomesthataredirectlyrelatedtotimespentwithchildrenformothersandfathersof6–17-year-oldhouseholdchi