alcohol cannabis substitution

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ContentslistsavailableatSciVerseScienceDirect

Journal

of

Health

Economics

jou rn a l h o m e pa g e:w w w . e l s e v i e r . c o m / l o c a t e / e c o n b a s e

The

effect

of

alcohol

availability

on

marijuana

use:

Evidence

from

the

minimum

legal

drinking

age

Benjamin

Crost

a,∗

,

Santiago

Guerrero

b

aDepartmentofEconomics,UniversityofColoradoDenver,Denver,CO80127,UnitedStates bBankofMexico,DireccionGeneraldeInvestigaciónEconómica,Mexico

a

r

t

i

c

l

e

i

n

f

o

Articlehistory:

Received16June2011 Receivedinrevisedform 12December2011 Accepted16December2011 Available online 13 January 2012

JELclassification:

I18

Keywords:

Alcohol Marijuana Druguse

Minimumlegaldrinkingage Regressiondiscontinuity

a

b

s

t

r

a

c

t

Thispaperexploitsthediscontinuitycreatedbytheminimumlegaldrinkingageof21yearstoestimate

thecausaleffectofincreasedalcoholavailabilityonmarijuanause.Wefindthatconsumptionof

mar-ijuanadecreasessharplyatage21,whileconsumptionofalcoholincreases,suggestingthatmarijuana

andalcoholaresubstitutes.Wefurtherfindthatthesubstitutioneffectbetweenalcoholandmarijuana

isstrongerforwomenthanformen.Ourresultssuggestthatpoliciesdesignedtolimitalcoholusehave

theunintendedconsequenceofincreasingmarijuanause.

© 2012 Elsevier B.V. All rights reserved.

1. Introduction

Economictheorysuggeststhatwhenthecostofconsuminga goodincreases,peoplewillconsumemoreofitssubstitutesandless ofitscomplements.Inthecaseofalcohol,thesubstitutesarelikely toincludeotherintoxicatingsubstances.Theminimumlegal drink-ingage(MLDA),whichrestrictsaccesstoalcoholforthoseunder21, isthereforelikelytoaffecttheconsumptionofotherdrugsamong thatagegroup,asitsharplydecreasesthecostofconsumingalcohol forindividualsjustovertheMLDA.Whenassessingthecostsand benefitsofpoliciesthataimtoreducealcoholconsumption–like theMLDAoralcoholtaxes–weneedtotakepossiblesubstitution behaviorintoaccount.

Forexample,proponentsoftheMLDAatage21arguethat alco-holconsumptioninchildrenandadolescentscancauselongterm and,sometimes,irreversibledamagestothebrain(AMA,2008). In particular,adolescentswhodrinkaremore likelytodevelop smallerhippocampi,apartofthebrainthatcontrolslearningand memory,andaremorelikelytoshowalterationsintheirprefrontal cortex(AMA,2008).Alcoholconsumptionhasalsobeenshownto

Correspondingauthor.Tel.:+13033152036. E-mailaddress:ben.crost@gmail.com(B.Crost).

inducesuicidesandcaraccidents(CarpenterandDobkin,2009). However,ifrestrictingaccesstoalcoholcausespeopletoswitchto substitutes,suchasmarijuanaorotherillegaldrugs,thebenefitsof reducedalcoholconsumptionneedtobeweighedagainstthecost ofincreasedconsumptionofalcohol’ssubstitutes.Thepotential alcoholsubstituteweanalyzeinthispaperismarijuana, a sub-stancemadeofamixtureofflowers,seedsandleavesofthehemp plant.ThehempplantcontainstetrahydrocannabinolorTHC,a psy-choactivechemicalthatproducesmostoftheintoxicatingeffects. ConsumptionofTHChasbeenassociatedwithcognitivedeficits andchangesinbrainmorphologyandpsychiatricdisorders(Wilson

etal.,2000;Popeetal.,2003;HallandDegenhardt,2009).Inthis

paperwestudytheeffectsofanincreaseintheavailabilityof alco-holontheconsumptionofmarijuana.

Mostpreviousstudiesofsubstitutionbetweenalcoholand mar-ijuana(e.g.DiNardoandLemieux,2001;ChaloupkaandLaixuthai,

1997;Pacula,1998;Williamsetal.,2004;SafferandChaloupka,

1999;Farrellyetal.,1999)arebasedoncross-sectional(usually

between-state)variationinthepricesofalcohol andmarijuana, theMLDA,alcoholtaxes,orlawsthatpartiallydecriminalize mar-ijuana.Aproblemfortheseapproachesisthatstate-levelpricesof alcoholandmarijuanaandthepoliciesgoverningtheir consump-tionarelikelytobecorrelatedwithunobservedcharacteristicsof thepopulationlivinginthosestates, makingit difficulttoinfer

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causalityfromcross-sectionalcomparisons(CarpenterandDobkin,

2009).

We address the problem of causal identification that has plagued previous research through a regression discontinuity design.Thisapproachexploitsthesharplydiscontinuousnature oftheminimumlegaldrinkingage,thefactthatapersoncannot legallypurchasealcoholupuntilthedaybeforeher21stbirthday, butcandosofromher21stbirthdayonwards.Bycomparing sub-stanceuseinindividualsjustbelowandjustabovetheageof21,1 wecanthereforeisolatethecausaleffectoftheMLDAonalcohol andmarijuanaconsumption.Theidentifyingassumptionisthat, apartfromtheabilitytolegallypurchasealcohol,individualsjust aboveandjustbelowtheageof21aresimilarinall character-isticsthatdeterminesubstanceuse.Theregressiondiscontinuity approachallowsustoestimatetheextentofsubstitutionbetween alcoholandmarijuanaandidentifythecausaleffectofchangesin theMLDAonindividualscloseto21yearsofage.

Ourresultsshowthatalcoholandmarijuanaaresubstitutes.At age21,weobserveasharpincreaseinalcoholconsumptionbut adecreaseinmarijuanaconsumption.Thissuggeststhatpolicies thatrestrictaccesstoalcoholcauseanincreaseinmarijuana con-sumption.OurestimatessuggestthattheMLDAatage21decreases theprobabilityofhavingconsumedalcoholinthepast30daysby 16%andincreasestheprobabilityofhavingconsumedmarijuana by10%.Resultsfrominstrumentalvariablessuggestanelasticityof substitutionofapproximately0.7fortheprobabilityofuseand0.4 forthefrequencyofuse(definedasthenumberofdaysinwhich asubstancewasconsumed).Wefurtherfindthatthesubstitution effectissubstantiallystrongerforwomenthanformen.Ourresults suggestthatbyrestrictingtheageatwhichpeoplecanlegally pur-chasealcohol,theMLDAcausesanincreaseintheconsumptionof illicitdrugs,especiallybyyoungwomen.

ThenextsectionreviewstheexistingliteratureontheMLDAand marijuanause.Section3describestheempiricalstrategyinmore detail.Section4presentsthedataandresults,Section5showsthe robustnessofourestimatesandSection6concludes.

2. Literaturereview

Mostofthepreviousliteratureonsubstitutionbetween mari-juanaandalcoholexploitsbetween-statevariationintheminimum legaldrinkingage(MLDA)andmarijuanadecriminalization dur-ingthe1970sand1980s.DiNardoandLemieux(2001)estimate astructuralmodelofalcoholandmarijuanaconsumptiontotest theeffectofincreasesintheMLDA.Theyanalyzestate-level per-centagesofhighschoolseniorsthat reportedhavingconsumed alcohol/marijuanafromtheMonitoringtheFutureSurveys(MFS) duringtheperiod1980–1989.Theirfindthatalcoholandmarijuana aresubstitutesandthatincreasesintheMLDAleadtoadecreasein alcoholconsumptionandanincreaseinmarijuanaconsumption. Inasimilarstudy,ChaloupkaandLaixuthai(1997)findthatyouths livinginstateswheremarijuanawasdecriminalizedreporthaving consumedlessalcohol,providing someevidenceofsubstitution betweenmarijuanaandalcoholconsumption.

Otherstudieseitherfindnoevidenceofsubstitutionorevidence of complementarity.Using data fromtheNationalLongitudinal Survey of Youth (NLSY),Thies and Register(1993) do not find statisticallysignificantevidencethatstate-levelmarijuana decrim-inalizationaffectsconsumptionofalcoholormarijuana.Alsousing datafromtheNLSY,Pacula(1998)findsthatstateregulationsthat reducetheconsumptionofalcohol,suchasstatebeertaxesand

1Forreasonsofconfidentiality,thedatausedforourempiricalanalysisis

aggre-gatedtothemonth-of-agelevel.

increasesintheMLDA,arenegativelycorrelatedwithmarijuana consumption.Focusingoncollegestudents,Williamsetal.(2004) analyzealcoholandmarijuanaconsumptionreportedinthe Har-vardSchoolofPublicHealthCollegeAlcoholStudy.Theyfindthat campusregulationsbanningtheconsumptionofalcohol,andto a lesser extentstate policiesthat restrictalcohol consumption, arenegativelycorrelatedwithmarijuanause.Usingdatafromthe NationalHouseholdSurveysonDrugAbuse(NHSDA),Safferand

Chaloupka(1999)findthat,controllingforthepriceofmarijuana,

county-levelalcoholprices arenegativelycorrelated with mari-juanaconsumption.AlsousingdatafromtheNHSDA,Farrellyetal.

(1999)findthatincreasesinstate-levelbeerpricesarenegatively

correlatedwithmarijuanaconsumptionforyouthsaged12–20,but notforyoungadultsaged21–30.

In summary, the literature onsubstitution betweenalcohol andmarijuanafindscontradictingresults. DiNardoandLemieux

(2001)andChaloupkaandLaixuthai(1997)interprettheirfindings

asreflecting substitutionbetweenalcoholandmarijuana, while

Pacula(1998),Williamsetal.(2004),SafferandChaloupka(1999)

andFarrellyetal.(1999)interprettheirfindingsasreflecting

com-plementarity.Onepossiblereasonforthesemixedresultsisthat differentstudiesusedifferentsurveysandtimeperiods,which pre-ventscomparability.Anotherreason,perhapsmoreimportant,is thatmanyofthepreviousstudiesarebasedonstate-level(orinthe

caseofWilliams,2004,campus-level)variationsinpricesofalcohol

andmarijuana andpoliciesgoverningtheirconsumption.While this approachcanestablishcorrelationsbetweensubstanceuse, pricesandpolicies,thecorrelationsdonotnecessarilyreflectcausal effects,sincestate-levelpricesandpoliciesgoverningalcoholand marijuanaarelikelytobecorrelatedwithunobservedpopulation characteristics thatdeterminealcohol andmarijuana

consump-tion (Carpenterand Dobkin, 2009).In this paper,weovercome

thisproblembyexploitingthediscontinuousnatureoftheMLDA, whichcreatesanabruptchangeinindividuals’abilitytolegally pur-chasealcoholatage21.Theempiricalapproach,knownasa regres-siondiscontinuitydesign,isdescribedindetailinthenextsection.

3. Empiricalstrategy

This paper uses a regression discontinuity design (RDD) to identifytheeffectofthelegalminimumdrinkingageonalcohol and marijuanause. TheRDDapproachexploitsthesharply dis-continuous natureof theminimum legaldrinkingage, thefact that a person cannot legallypurchase alcohol upuntil theday beforeher 21stbirthday,but cando sofromher21stbirthday onwards.Individuals thereforeswitch fromthecontrol regime, inwhichtheyarelegallyprohibitedfrombuyingalcohol,tothe treatmentregime,inwhichtheyareallowedtodoso,fromone daytothenext.Wecan thereforeestimatethecausaleffectof theminimumlegal drinkingagebycomparingindividuals who havejustturned21andindividualswhoareabouttoturn21.Our identifyingassumption is that,apart fromtheability tolegally purchasealcohol,individualsjustbelowandjustabovetheageof 21aresimilarinallcharacteristicsthatdeterminesubstanceuse, sothatdifferencesbetweenthetwogroupscanonlybeexplained bytheeffectoftheminimumdrinkingage.

Ourestimatesarebasedonthestandardregression discontinu-ityestimatordescribedbyImbensandLemieux(2008):

RD=lim

x↑21[Yi|Xi=x]−xlim↓21[Yi|Xi=x]

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40

50

60

70

Used in last 30 days (%)

18 19 20 21 22 23 24

Age

Mean Linear fit

Probability of Alcohol Use by Age

12

14

16

18

20

22

Used in last 30 days (%)

18 19 20 21 22 23 24

Age

Mean Linear fit

Probability of Marijuana Use by Age

2

3

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# days used in last 30 days

18 19 20 21 22 23 24

Age

Mean Linear fit

Frequency of Alcohol Use by Age

1.5

2

2.5

3

3.5

# days used in last 30 days

18 19 20 21 22 23 24

Age

Mean Linear fit

Frequency of Marijuana Use by Age

Fig.1.Alcoholandmarijuanausearoundage21.Scatterpointsdenoteaveragesbymonthofage.Linesarelinearfits,estimatedseparatelyonbothsidesofage21. Datasource:NSDUH2002–2007.

age.WefollowCarpenterandDobkin(2009)andestimatethelimits bylocallinearregressiononbothsidesoftheageof21.Inpractice, thisisequivalenttoestimatingakernel-weightedregressionofthe followingmodel(ImbensandLemieux,2008):

Yi=ˇ0+Xiˇ1+Xi∗Diˇ2+DiRD+εi (1)

Asbefore, YiandXidenoteindividuali’ssubstanceuseandage, respectively.Diisanindicatorthattakesthevalue1ifindividual iis21yearsoldorolder.TheestimatedcoefficientRDyieldsthe (local)reducedformeffectoftheminimumlegaldrinkingageon

alcoholandmarijuanause.Thiscanbeinterpretedasthecausal effectofa marginal increase (ordecrease)oftheMLDA onthe alcohol/marijuanauseofindividualswhoareexactly21yearsold.

3.1. Instrumentalvariablesestimatesofthesubstitutionbetween alcoholandmarijuana

Inordertoestimatetheextentofsubstitutionbetweenalcohol andmarijuana,weemployaninstrumentalvariablesapproachthat treatsalcoholastheendogenousvariable,whichisinstrumented

Table1

EffectoftheMLDAonalcoholandmarijuanause:regressiondiscontinuityestimates.

Usedinlast30days(%) #ofdaysusedinlast30days

Alcohol Marijuana Alcohol Marijuana

Over21(RD) 9.83 −2.01 1.30 −0.31

(0.79)*** (0.54)*** (0.10)*** (0.11)***

Age 5.23 0.83 0.55 0.23

(0.44)*** (0.30)*** (0.06)*** (0.06)***

Age×Over21 −6.25 −2.15 −0.73 −0.47

(0.62)** (0.42)*** (0.08)*** (0.09)***

Constant 60.0 20.3 4.34 2.97

(0.56)*** (0.38)*** (0.07)*** (0.08)***

Numberofobservations 68 68 68 68

Datasource:NSDUH2002–2007.

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Table2

EffectoftheMLDAonalcoholandmarijuanause:men.

Usedinlast30days(%) #ofdaysusedinlast30days

Alcohol Marijuana Alcohol Marijuana

Over21(RD) 10.76 −1.47 1.48 −0.31

(1.11)*** (0.92) (0.15)*** (0.19)*

Age 6.11 1.39 0.78 0.35

(0.62)*** (0.51)*** (0.08)*** (0.10)***

Age×Over21 −7.04 −3.45 −0.87 −0.73

(0.87)*** (0.72)*** (0.11)*** (0.15)***

Constant 64.5 25.2 5.43 4.01

(0.79)*** (0.65)*** (0.10)*** (0.13)***

Numberofobservations 68 68 68 68

Datasource:NSDUH2002–2007,subsampleofmalerespondents.

Eachobservationistheaverageofsubstanceuseoveramonth-of-agecell.Allestimatesarefromlocallinearregressionsusingatriangularkernelwithbandwidthof3years, centeredatage21.Standarderrorsinparenthesis.*,**and***denotestatisticalsignificanceatthe10%,5%and1%levels.

Table3

EffectoftheMLDAonalcoholandmarijuanause:women.

Usedinlast30days(%) #ofdaysusedinlast30days

Alcohol Marijuana Alcohol Marijuana

Over21(RD) 8.85 −2.62 1.08 −0.29

(1.06)*** (0.68)*** (0.12)*** (0.10)*

Age 4.50 0.45 0.37 0.15

(0.59)*** (0.38) (0.06)*** (0.06)**

Age×Over21 −5.65 −1.02 −0.61 −0.27

(0.83)*** (0.53)* (0.09)*** (0.08)***

Constant 55.9 15.5 3.30 1.92

(0.75)*** (0.48)*** (0.08)*** (0.07)***

Numberofobservations 68 68 68 68

Datasource:NSDUH2002–2007,subsampleoffemalerespondents.

Eachobservationistheaverageofsubstanceuseoveramonth-of-agecell.Allestimatesarefromlocallinearregressionsusingatriangularkernelwithbandwidthof3years, centeredatage21.Standarderrorsinparenthesis.*,**and***denotestatisticalsignificanceatthe10%,5%and1%levels.

byanindicatorforbeingolderthan21years,andmarijuanaasthe outcomeofinterest.Asbefore,wecontrolforlineartimetrends aboveandbelowtheageof21.Thisapproachestimatestheratio ofthechangesinmarijuanaandalcoholuseacrossthethreshold atage21:ˇIV=m/a.

Thisestimate can beinterpreted as the rateof substitution

betweenalcoholandmarijuanathatisinducedbytheMLDA(or

theelasticityofsubstitution, ifalogarithmic functionalformis

chosen).However,whenextrapolatingfromthisestimatetothe

substitutioninducedbyotherpoliciesthatlimittheuseofalcohol, itshouldbekeptinmindthattheIVapproachonlyestimatesthe localaveragetreatmenteffectforthesub-populationofcompliers, thoseindividualswhoareexactly21yearsoldandwho(atleast partly)complywiththeMLDA,sothattheirconsumptionof alco-holincreasesdiscontinuouslyattheageof21.Thustheexternal validityoftheestimatedsubstitutioneffectshouldbehighestfor policiesthataffectthealcoholuseofindividualswhoarecloseto 21yearsofageandlikelytocomplywithregulationsliketheMLDA.

4. Dataandresults

Data onalcohol and marijuana use was obtained from the

NationalSurveyofDrugUseandHealth(NSDUH),whichis

admin-istered annuallyby theU.S. Department of Health and Human

Services’SubstanceAbuseandMentalHealthServices

Administra-tion(SAMHSA)andconductedbytheResearchTriangleInstitute.

TheNSDUHprovidesestimatesofalcoholandillicitsubstanceuse

amongpersonsaged12andolderatthenationalandstate-level

usingarandomlyselectedsampleofapproximately70,000people.

The period of observation for our analysis is 2002–2007.

The NSDUHuses two measuresof substance use, whether the

respondenthasusedthesubstancewithinthepast30daysand

thenumberofdaysonwhichtherespondenthasusedit.For alco-holconsumption,thequestionthesurveyasksis“Thinkspecifically aboutthepast30days,from[30daysbeforetheinterviewdate],

uptoandincludingtoday.Duringthepast30days,onhowmany

daysdidyoudrinkoneormoredrinksofanalcoholicbeverage?” Formarijuanause,thequestionitasksis“Thinkspecificallyabout thepast30days,from[30daysbeforetheinterviewdate]upto andincludingtoday.Whatisyourbestestimateofthenumberof daysyouusedmarijuanaorhashishduringthepast30days?”.Since respondents’preciseageisnotavailableintheNSDUH’spublic-use files,weobtaineddataontheaveragesofthesubstanceuse

mea-suresbymonthofagefromSAMHSA.Weobtainedtheseaverages

forthewholesampleandseparatelyformenandwomen.To

main-tainconfidentialityofthedata,SAMHSAonlyprovideduswiththe

averageresponsebymonthofagebutcouldnotprovideuswith

thenumberofindividualresponsesthatwereusedtocalculatethe average.Forourbaselineregressionsweuseabandwidthof3years aroundage21,sothatweusedataonindividualsbetweentheages of18and24.Forthisage-groupthereare71month-of-agecells, leadingto71observations.Toavoidmeasuringtheeffectofthe (anticipated)birthdaycelebrationitself,wedroptheobservations forthemonthofthe21stbirthdayaswellastheprecedingand fol-lowingmonth.2Weuseatriangularkerneltoestimatelocallinear regressionsoneachsideofage21.

2TheNSDUHusesarecallperiodof30days,sothattheobservationinthemonth

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Table4

Rateofsubstitutionbetweenalcoholandmarijuana:instrumentalvariablesestimates.

UsedMJinlast30days(%) #ofdaysusedMJinlast30days

All Men Women All Men Women

Alcoholuse −0.20 −0.14 −0.30 −0.23 −0.21 −0.27

(0.06)*** (0.09) (0.09)*** (0.09)** (0.13) (0.10)***

Age 1.90 2.22 1.78 0.36 0.52 0.25

(0.59)*** (0.95)** (0.78)** (0.10)*** (0.18)*** (0.09)***

Age×Over21 −3.43 −4.41 −2.69 −0.64 −0.91 −0.43

(0.61)** (0.96)*** (0.83)*** (0.11)*** (0.19)*** (0.11)***

Constant 32.6 34.0 32.0 3.98 5.16 2.81

(4.0)*** (6.15)*** (5.58)*** (0.46)*** (0.80)*** (0.39)***

Numberofobservations 68 68 68 68 68 68

Datasource:NSDUH2002–2007.

Eachobservationistheaverageofsubstanceuseoveramonth-of-agecell.EstimatesaretheresultsofInstrumentalVariablesregressionsinwhichalcoholuseisinstrumented byanindicatorforagegreaterthan21years.Allestimatesarefromlocallinearregressionsusingatriangularkernelwithbandwidthof3years,centeredatage21.*,**and ***denotestatisticalsignificanceatthe10%,5%and1%levels.

Table5

Elasticityofsubstitutionbetweenalcoholandmarijuana:instrumentalvariablesestimates.

Log.MJuseinlast30days(%) Log.#ofdaysusedMJinlast30days

All Men Women All Men Women

Log.ofalcoholuse −0.69 −0.39 −1.23 −0.41 −0.34 −0.52

(0.23)*** (0.29) (0.42)*** (0.19)** (0.25) (0.25)**

Age 0.11 0.10 0.14 0.14 0.16 0.15

(0.04)*** (0.05)** (0.06)** (0.05)*** (0.07)** (0.06)**

Age×Over21 −0.20 −0.21 −0.22 −0.27 −0.28 −0.28

(0.04)** (0.05)*** (0.07)*** (0.05)*** (0.07)*** (0.07)***

Constant 5.83 4.84 7.67 1.69 1.96 1.27

(0.96)*** (1.22)*** (1.72)*** (0.30)*** (0.46)*** (0.33)***

Numberofobservations 68 68 68 68 68 68

Datasource:NSDUH2002–2007.

Eachobservationistheaverageofsubstanceuseoveramonth-of-agecell.EstimatesaretheresultsofInstrumentalVariablesregressionsinwhichthelogarithmalcoholuse isinstrumentedbyanindicatorforagegreaterthan21years.Allestimatesarefromlocallinearregressionsusingatriangularkernelwithbandwidthof3years,centeredat age21.Standarderrorsinparenthesis.*,**and***denotestatisticalsignificanceatthe10%,5%and1%levels.

Fig.1displaysaveragealcoholandmarijuanausebetweenthe ages of18 and24. Theindividual observationsareaverages by monthofage;thefittedlinesareestimatedbylinearregressionsof substanceuseonageonbothsidesofage21.Thetoppanelsshow thatalcoholconsumptionincreasesdrasticallyatage21.The prob-abilityofhavingconsumedalcoholinthelast30daysincreases byabout10percentagepointsfromabaselinejustunder60%.A similarresulthaspreviouslybeenfoundbyCarpenterandDobkin

(2009)andisconsistentwiththehypothesisthatthecostof

con-sumingalcoholdecreasessignificantlyatage21.Thefrequencyof alcoholconsumptionincreasesaswell,from4to5.5daysdrinking outoftheprevious30days.

Formarijuana,theeffectgoesintheoppositedirection,though its size is smaller.At age 21, the probability of marijuana use decreasesbyabout2percentagepointsfromabaselineofabout 20%.Thefrequencyofmarijuanausedecreasesbyabout0.3days outofa30-dayperiod,fromabaselineofabout2.3days.

Table1presentsquantitativeestimatesfromthelocallinear

regressionapproachdescribedintheprevioussection.Theresults reportedinthetableareforlocallinearregressionswitha triangu-larkernelandabandwidthof3years.Eachobservationisthemean ofalcohol/marijuanaconsumptioninthemonthofage.Robustness testsfordifferentbandwidthsarereportedinSection5.The regres-sionresultsreinforcethevisualimpressiongainedfromthegraphs. Thereisastrongincreaseinconsumptionofalcohol(both probabil-ityandfrequencyofuse)atage21,whileconsumptionofmarijuana decreases.Thechangesarestatisticallysignificantandtheirsizes aresimilartothechangesvisibleonthegraphs.

Theresultsindicatethatalcoholandmarijuanaaresubstitutes, atboththeextensiveandtheintensivemargin.Thedecreasein

theprobabilityofmarijuanauseatage21suggeststhatsome indi-vidualswhousemarijuanabeforetheageof21stopusingit(or atleastuseit lessregularly) oncetheyturn21 andareableto legallyconsumealcohol.Inabsoluteterms,thesubstitutioneffect ontheprobabilityofmarijuanauseisnotverylarge–a9.8 percent-agepointincreaseintheprobabilityofalcoholconsumptionleads toa2percentagepointdecreaseinmarijuanause.However,the 9.8percentagepointincreaseinalcoholconsumptionconstitutesa 16%increasefromtheestimatedbaselineconsumptionof60%just belowage21,andthe2percentagepointdecreaseinmarijuana useconstitutesa10%decreasefrombaselineuse.

Theestimateddecreaseinthefrequencyofmarijuanauseis0.3 dayspermonthwhichconstitutesa10%declinefromthebaseline of3daysatage21.Sincethedeclineinthefrequencyofmarijuana useisofsimilarsize(inpercentageterms)asthedeclineinthe probabilityofuse,itisunlikelythattheestimateddropinthe fre-quencyofuseissolelydrivenbytheextensivemargin,sincepeople whostopusingmarijuanaaltogetherprobablyuseditwithlower frequencythantheaverageusertobeginwith.Iftheentiredecline camefromthese‘lighter’users,wewouldthereforeexpectthat thedeclineintheaveragefrequencywouldbelower(intermsof percentage)thanthedeclineintheprobabilityofuse.Hence,our estimatessuggestthatthedeclineinmarijuanauseatage21occurs onboththeextensiveandintensivemargins.

4.1. Resultsbygender

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40

50

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70

80

Used in last 30 days (%)

18 19 20 21 22 23 24

Age Mean Linear fit Probability of Alcohol Use by Age: Men

15

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25

30

Used in last 30 days (%)

18 19 20 21 22 23 24

Age Mean Linear fit Probability of Marijuana Use by Age: Men

2

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6

8

# days used in last 30 days

18 19 20 21 22 23 24

Age Mean Linear fit Frequency of Alcohol Use by Age: Men

2

3

4

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# days used in last 30 days

18 19 20 21 22 23 24

Age Mean Linear fit Frequency of Marijuana Use by Age: Men

Fig.2. Placebotests:RDestimatesbylocationofRDthreshold.TheverticalaxisplotsRDestimatesofthechangeinmarijuanauseacrosstheage-thresholdspecifiedonthe horizontalaxis.FordetailsontheRDestimation,seethedescriptioninTable1.

Datasource:NSDUH2002–2007.

usearoundage21formenandwomen,respectively.Tables2and3 showthecorrespondingRDestimates.Theresultsshowthatmen havehigherbaselinelevelsofuseofbothalcoholandmarijuanabut thattheeffectoftheMLDAonmarijuanauseislargerforwomen. Formentheprobabilityofmarijuanausedecreasesby1.5 percent-agepointsatage21,whichcorrespondstoa6%decreasecompared tothebaselineprobabilityof25%.Forwomen,theprobabilityof marijuanausedecreasesby2.6percentagepointsatage21,which correspondstoa17%decreasecomparedtothebaselineprobability of15%.TheeffectoftheMLDAonthefrequencyofmarijuanauseis alsostrongerforwomen.Womenjustabovetheageof21use mar-ijuanaon0.29days/monthlessthanwomenjustbelowtheageof 21.Comparedtobaselineuse,thiseffectsrepresenta15%decrease inthefrequencyofmarijuanause.Formen,theMLDAinducesa decreaseof0.3days/month,whichrepresentsa7.5%decreasein thefrequencyofmarijuanause.

4.2. IVestimatesofsubstitutionbetweenalcoholandmarijuana

Thissectiondiscussestheestimatesofthesubstitutionbetween alcoholandmarijuanathataregeneratedbytheinstrumental vari-ablesapproachdescribedinSection3.1.Table4presentsratesof substitutionthatareestimatedbya linearspecification.For the entirepopulation,weestimatethataonepercentagepointincrease intheprobabilityofusingalcoholleadstoastatisticallysignificant

0.2percentage pointreductionintheprobabilityofusing mari-juana.Similarly,aone-dayincreaseinthefrequencyofalcoholuse leadstoa0.23dayreductioninthefrequencyofmarijuanause. While theestimatedratesofsubstitutionmayappearsmall,the resultsofthelogarithmicspecificationsinTable5showthat,dueto thesmallerbaselineuseofmarijuana,thecorrespondingelasticities arefairlylarge.Fortheentirepopulation,weestimatestatistically significantelasticitiesofsubstitutionof0.7fortheprobabilityand 0.4forthefrequencyofmarijuanause.

Inaddition,theresultsinTables4and5suggestthatthe sub-stitutionbetweenalcoholandmarijuanaislargerforwomenthan formen.Forwomen,theestimatedratesofsubstitutionare0.3 fortheprobabilityofuseand0.27forthefrequencyofuse,while theestimatedelasticitiesare1.2fortheprobabilityand0.5forthe frequency.Formen,theestimatesaresubstantiallysmaller– espe-ciallyfortheelasticitiesofsubstitution,whichareestimatedat0.4 fortheprobabilityand0.34forthefrequencyofuse–andnot statis-ticallysignificant.Overall,theseresultssuggestthatpoliciesthat limitaccesstoalcoholarelikelytoleadtoasubstantiallylarger increaseinthemarijuanaconsumptionofwomenthanofmen.

4.3. Canunder-reportingofsubstanceuseexplaintheresults?

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40

50

60

70

Used in last 30 days (%)

18 19 20 21 22 23 24

Age

Mean Linear fit Probability of Alcohol Use by Age: Women

8

10

12

14

16

18

Used in last 30 days (%)

18 19 20 21 22 23 24

Age

Mean Linear fit Probability of Marijuana Use by Age: Women

2

2.5

3

3.5

4

4.5

# days used in last 30 days

18 19 20 21 22 23 24

Age

Mean Linear fit Frequency of Alcohol Use by Age: Women

1

1.5

2

2.5

# days used in last 30 days

18 19 20 21 22 23 24

Age

Mean Linear fit Frequency of Marijuana Use by Age: Women

Fig.3.Robustnessofresultstochoiceofbandwidth.Inthetop4panels,theverticalaxisplotsRDestimatesoftheeffectoftheMLDAonmarijuanause.Inthebottom4 panels,theverticalaxisplotsIVestimatesoftherate/elasticityofsubstitutionbetweenmarijuanaandalcoholuse.Thebandwidthisspecifiedonthehorizontalaxis.Intervals are95%confidenceintervals.FordetailsontheRDestimation,seethedescriptioninTable1.

Datasource:NSDUH2002–2007.

However,fortheregressiondiscontinuity(RD)estimates, under-reportingisonlyaconcernifindividualsjustundertheageof21 aremore(orless)likelytounder-reportsubstanceusethan individ-ualsjustabovetheageof21.Thisislikelytobethecaseforalcohol use,sincedrinkingisillegalundertheageof21andindividuals maybeunwillingtoadmitillegalbehavior.Theself-reporteddata arethereforelikelytounderestimatethealcoholuseofindividuals under21,whichleadstoanupwardbiasintheRDestimatesof theeffectoftheminimumdrinkingageonalcoholuse.3However, under-reportingisunlikelytoaffectourestimatesoftheeffectof theMLDAonmarijuanause.Sincemarijuanauseisillegalatall ages,thereisnoreasontoexpectthatindividualsjustunderthe ageof21wouldunder-reportmarijuanausemoreorlessstrongly thanindividuals justabovetheageof21.Thechanges in mari-juanauseatage21arethereforelikelytobedrivenbychangesin alcoholavailabilityandnotbychangesinmisreporting.Itshould, however,bekeptinmindthatourestimatesofthesubstitution

3Itis,however,unlikelythattheeffectoftheMLDAonalcoholuseisentirelyan

artifactofthesurveymethodology.CarpenterandDobkin(2009)findalargespike inmortality,particularlyfromcaraccidents,attheageof21,whichsuggeststhat thereisarealincreaseinalcoholuseatthatage.

betweenalcoholandmarijuanaarelikelytobebiaseddownward, sincetheeffectoftheMLDAonalcoholuse,whichentersinthe denominator,ismostlikelybiasedupward.

5. Robustnesstests

5.1. Placebotestsforlocationofthediscontinuity

Inordertomakesurethatourestimateddeclineinmarijuana useisdrivenbythechangeinalcoholaccessibilityatage21andnot thanmerelyduetoatimetrendthatfollowsaninvertedu-shape, weconductplacebotestsforthelocationofthediscontinuity.For thesetests,weestimatethesameregressionasinTable1,butvary thelocationofthethreshold.Iftherereallyisadiscontinuityatage 21theestimatedchangeinsubstanceuseshouldbelargestifthe regression’sthresholdislocatedcloseto21years.

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−5

0

5

10

15

Estimated Change Across Threshold

20 20.5 21 21.5 22

Location of Threshold Probability of Alcohol Use

−.5

0

.5

1

1.5

Estimated Change Across Threshold

20 20.5 21 21.5 22

Location of Threshold (Age) Frequency of Alcohol Use

−2

−1

0

1

2

Estimated Change Across Threshold

20 20.5 21 21.5 22

Location of Threshold Probability of Marijuana Use

−.4

−.2

0

.2

.4

Estimated Change Across Threshold

20 20.5 21 21.5 22

Location of Threshold (Age) Frequency of Marijuana Use

Fig.4. Alcoholandmarijuanausearoundage21:men.Scatterpointsdenoteaveragesbymonthofage.Linesarelinearfits,estimatedseparatelyonbothsidesofage21. Datasource:NSDUH2002–2007,subsampleofmalerespondents.

inthesample.Anotherexplanationisthatalcoholuseissteeply upwardslopingbelowtheageof21anddownwardslopingabove it.Therefore,movingthethresholdtotheleftleadstoabig reduc-tionintheestimatedalcoholuserightbelowthethresholdand onlyasmall(ifany)reductionoftheestimateduserightabovethe threshold.Eitherway,thebottompanelsofthefigureshowthat forbothprobabilityandfrequencyofmarijuanause,theestimated decreaseinuseislargestifthethresholdislocatedatexactly21 years.Whiletheresultsforalcoholusesuggestthatthisplacebotest isnotalwayscompletelyprecise,itdoesincreaseourconfidence thattheestimatesreportedabovearedrivenbythediscontinuous changeinalcoholaccessibilityatage21ratherthanbyatimetrend ofmarijuanausethatfollowsaninvertedu-shape.

5.2. Robustnesstestsforchoiceofbandwidth

Acrucialparameterforlocallinearregressionsliketheones reportedaboveisthechoiceofbandwidth.Bychoosinga band-widththatistoosmallwereducetheeffectivesamplesizeand obtainestimatesoflowprecision.Bychoosingabandwidththat istoolargeweincreasetheriskofmis-specificationifthe rela-tionship betweenage and substance useis non-linear. Though some authors have suggested rules-of thumb for bandwidth choice (e.g. Fan and Gijbels, 1996), no rule-of-thumb guaran-teesanoptimalchoiceofbandwidth.ImbensandLemieux(2008)

thereforesuggestrobustnesstestsfordifferentchoicesof band-width.

TheresultsofthesetestsarereportedinFig.3.Forthetests,we graduallydecreasethebandwidthuntilwereachhalfofthe ini-tialbandwidthof3years.Thepointestimatesand95%confidence intervals areplotted ontheverticalaxesof thegraphs,against thebandwidthonthehorizontalaxes.Iftheestimatesbasedon largerbandwidthssufferfromspecificationbiasduetoanon-linear relationshipbetweenageandsubstanceuse,wewouldexpectthe pointestimatestochangesubstantiallyasthebandwidthbecomes smaller,sincethelinearfunctionalformbetterapproximatesthe truerelationshipoversmallerintervals.Ifthereisnospecification bias,wewouldexpectthepointestimatestohavesmall fluctua-tionsandhenceberobusttothechoiceofbandwidth.Sincethe estimatesforsmallerbandwidthsarebasedonsmallereffective samples,wenaturallyexpecttheconfidenceintervalstoincrease asthebandwidthbecomessmaller.

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−2

0

2

4

6

8

10

12

14

Estimated change at age 21 (% points) 3 2.5 2 1.5 Bandwidth (triangular kernel)

Point Estimate 95% C.I.

Alcohol (probability of use)

−.5

0

.5

1

1.5

2

Estimated change at age 21 (days/month) 3 Bandwidth (triangular kernel)2.5 2 1.5

Point Estimate 95% C.I.

Alcohol (frequency of use)

−4

−3

−2

−1

0

1

Estimated change at age 21 (% points) 3 2.5 2 1.5 Bandwidth (triangular kernel)

Point Estimate 95% C.I.

Marijuana (probability of use)

−.8

−.6

−.4

−.2

0

Estimated change at age 21 (% days/month)

1.5 2

2.5 3

Bandwidth (triangular kernel)

Point Estimate 95% C.I.

Marijuana (frequency of use)

−.5

−.4

−.3

−.2

−.1

0

IV Estimate

1.5 2

2.5 3

Bandwidth (triangular kernel)

Point Estimate 95% C.I.

Probability of Use

Substitution Between Marijuana and Alcohol

−.6

−.4

−.2

0

IV Estimate

1.5 2

2.5 3

Bandwidth (triangular kernel)

Point Estimate 95% C.I.

Frequency of Use

Substitution Between Marijuana and Alcohol

−1.5

−1

−.5

0

IV Estimate

1.5 2

2.5 3

Bandwidth (triangular kernel)

Point Estimate 95% C.I.

Probability of Use

Elasticity of Substitution Between Marijuana and Alcohol

−1

−.8

−.6

−.4

−.2

0

IV Estimate

1.5 2

2.5 3

Bandwidth (triangular kernel)

Point Estimate 95% C.I.

Frequency of Use

Elasticity of Substitution Between Marijuana and Alcohol

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6. Conclusions

Byexploitingthesharpdecreaseintheeffectivecostofalcohol consumptioninducedbytheminimumlegaldrinkingage(MLDA) atage21,thispaperestimatesthecausaleffectoflegalaccessto alcoholonmarijuanaconsumption.Ouridentifyingassumptionis that,apartfromtheabilitytolegallypurchasealcohol,individuals justaboveandjustbelowtheageof21aresimilarinall characteris-ticsthatdeterminesubstanceuse.Comparedtopreviousresearch (e.g.DiNardoandLemieux,2001;ChaloupkaandLaixuthai,1997;

Pacula,1998;Williamsetal.,2004;SafferandChaloupka,1999;

Farrellyetal.,1999),thisapproachhastheadvantageofnothaving

torely oncross-sectional(oftenstate-level)variation inalcohol andmarijuanapricesandrelatedpolicies,whicharelikelytobe correlatedwithunobservedcharacteristicsofthepopulation.This allowsustocleanlyidentifythecausaleffectoftheMLDAinaway thatisnotafflictedbyomittedvariablebias.

Ourresultsshowthatlegalaccesstoalcoholcausesa signifi-cantdecreaseinmarijuanauseamongyoungadultsclosetothe ageof21.Thepointestimatessuggestthatmarginallylowering theMLDAwoulddecreasetheprobabilityofmarijuana consump-tionintheaffectedagegroupbyabout10%.Thesubstitutioneffect issubstantiallylargerforwomenthanformen.Ourresults sug-gestthatmarijuanaandalcoholaresubstitutes,sothatadecrease inthe‘full’priceofalcohol(includingthecostofaccess)leadsto adecreaseinmarijuanause.Themainimplicationofourstudyis thatpolicies,suchastheMLDA,thatareaimedatrestrictingalcohol consumptionamongyoungadultsarelikelytohavetheunintended consequenceofincreasingtheuseofillegaldrugssuchas mari-juana.Whenassessingthenetbenefitsofalcohol-relatedpolicies thesesubstitutioneffectsneedtobetakenintoaccountinorder toassessthetrade-offbetweenthepositive healtheffects from reducedalcoholconsumptionandthenegativeeffectsofincreased useofothersubstances.

References

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Carpenter,C.,Dobkin,C.,2009.Theeffectofalcoholconsumptiononmortality: regressiondiscontinuityevidencefromtheminimumdrinkingage.American EconomicJournal:AppliedEconomics1(1),162–182.

Chaloupka, F.J., Laixuthai, A., 1997. Do youths substitute alcohol and mar-ijuana? Some econometric evidence. Eastern Economics Journal 23 (3), 253–276.

DiNardo,J.,Lemieux,T.,2001.Alcohol,marijuana,andAmericanyouth:the unin-tendedconsequencesofgovernmentregulation.JournalofHealthEconomics 20(6),991–1010.

Fan,J.,Gijbels,I.,1996.LocalPolynomialModelinganditsApplications.Chapman andHall,London.

Farrelly, M.C., Bray,J.W., Zarkin,G.A.,Wendling,B.W., Pacula,R.L.,1999. The effectsofpricesandpoliciesonthedemandformarijuana:evidencefrom theNationalHouseholdSurveysonDrugAbuse.NBERWorkingPaperSeries, 6940.

Hall,W.,Degenhardt,L.,2009.Adversehealtheffectsofnon-medicalcannabisuse. Lancet374(9698),1383–1391.

Imbens,G.W.,Lemieux,T.,2008.Regressiondiscontinuitydesigns:aguideto prac-tice.JournalofEconometrics142(2),615–635.

Pacula,R.L.,1998.Doesincreasingthebeertaxreducemarijuanaconsumption. JournalofHealthEconomics17(5),557–586.

Pope,H.G.,Gruber,A.J.,Hudson,J.I.,Cohane,G.,Huestis,M.A.,Yurgelun-Todd,D., 2003.Early-onsetcannabisuseandcognitivedeficits:whatisthenatureofthe association?DrugandAlcoholDependence69(3).

Saffer,H.,Chaloupka,F.J.,1999.Demographicdifferentialsinthedemandforalcohol andillicitdrugs.NBERWorkingPaperSeries,6432.

Thies,C.F.,Register,C.A.,1993.Decriminalizationofmarijuanaandthedemand for alcohol, marijuana, and cocaine. The Social Science Journal 30 (4), 385–399.

Williams,J.,Pacula,R.L.,Chaloupka,F.J.,2004.Alcoholandmarijuanauseamong collegestudents:economiccomplementsorsubstitutes?HealthEconomics13 (9),825–843.

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