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Unformatted text preview: '9? (omqmmnozro—L . Jarsr: nan‘nmmmmmmmmmmm
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the
HM tional Illicit Drugs Strategy since 1993‘; Decriminalization and Marijuana Smoking
Prevalence: Evidence From Australia Kannika DAMRONGPLASIT Department of Health Services, University of California, Los An ECWOWIICS; Nana/mg Technological University Chang Hser Department of Economics, University of Southern California, Department of Economics and Finance, City
University of Hong Kong, and WISE, Xiamen University (chsiao@usc.edu) Xueyan ZHAo Department of Econometrics and Business Statistics, and Centre for Health Economics, Monash University“ Australia This article uses the 2001 National Drug Strategy Household Survey to assess the impact of marijuana
decriminalization policy on marijuana smoking prevalence in Australia. Both parametric and nonparamet
ric methods are used. The parametric approach includes endogenous probit switching, twopart, sample
selection, and standard dummy variable models, while the nonparametric approach uses propensity score
stratiﬁcation matching. Speciﬁcation analyses are also conducted. A nonparametric kemel—bascd test is
constructed to select between parametric and nonparametric models, and the likelihood ratio testis used
to choose among parametric models. Our analyses favor the endogenous switching model where decrim— inalization increases the probability of smoking by 16.2%. KEY WORDS: Average treatment effect; Bootstrapping; Endogenous prohit switching; Parametric and
nonparametric speciﬁcation analysis; Prepensity score matching. 1. INTRODUCTION Illicit drug usage is widespread around the world, posing
signiﬁcant social and economic costs to the health care, jus—
tice, and social welfare systems in both1 eveloped and devel
oping countries. According to the July , 2001 issue of the
Economist, the global retail sale of illegal drugs is estimatedes?
US$150 billion a year, which is in the same league as world—
wide sale of tobacco and alcohol and about half the size of the
pharmaceutical industry; Signiﬁcant amounts of public funds
have been spent by governments worldwide to deal with the
consequences f bstance buse'andeucational programs;
for examl, the tts’ drugs policyoss 0“
ater US$35—$40 billion a year, while theLAustralian govern— ment has committed more than AUS$1 billn twd its N— r 7 r——i W V W , .WWiWu—m Amoiit d, marijuana is by far the most widely
used. It is commonly considered a “softer” drug compared with
“harder” drugs, such as cocaine, heroin, or amphetamines. The
prevalence of hydroponic cultivation in recent years has signif
icantly improved the productivity of covert production. While
there is more support for using marijuana for medical purposes
in treating patients with nausea, glaucoma, spasm, and pain,
much conthersy has surrounded the detrimental health ef~
fects of recreational use of marijuana. Some suggest that mari
j name use is linked to lung cancer, immune system deterioration,
harmful effects on blood circulation, and shortterm memory
loss. For heavy users, there is also the problem of drug depen
dency and the related withdrawal symptoms, such as anxiety
and loss of appetite. At the center of the controversy is whether legal sanctioning
is the best approach to reduce the use and the associated harm ‘ U n fired Erales’ drags gritty casts (ti/film? gimme/y 9’5 f
semen/3M Major zine). whirl e rm astmir‘m, .«avé’i’ﬂmé‘ﬂf Hirer} a?er en‘penda‘fwe
its $117174? £2 affirm for ill/LE year we zcbZ/ﬁ (Moan: inns)5 of the drug. The ongoing debate on marijuana decriminalization
concentrates on the potential beneﬁts and costs ofpol—
icy. A major supporting argument for decriminalization is that
a criminal charge is too severe a penalty relative to the crime
itself. A criminal record can have many negative consequences
on the subsequent life of an otherwise lawabiding person; for
example, an offender may lose out in future employment oppor—
tunities or face problems in international travel. Furthermore,
decrirninalization would allow the government to separate the
market of marijuana from the market of other, harder drugs,
thereby permitting the authorities to redirect their resources
used in law enforcement and criminal justice system from the
“softer” cannabis to “harder” drugs like cocaine, heroin, and
amphetamines. For instance, amid03' report by, Jeffrey Mitch,
“The Budgetary Implications of Marijuana Prohibition,” noted
that legalizing marijuana could reduce the cost of enforcement
in the United States by US$717 billion per year. Moreover, sup—
porters also argue that when marijuana is illegal, young mari
juana users are unnecessarily exposed to harder drug dealers,
making it easier for them to move on to consume harder drugs.
For those who argue against decriminalization, their ﬁrst claim
is that decriminalization inevitably lowers both the legal and
social costs associated with the use of marijuana, thus send—
ing a signal that it is acceptable to smoke marijuana, which
may encourage higher consumption of the drug. Another ar—
gument cited against decriminalization is the gateway theory;
that is, there is a growing concern that exposure to marijuana . © 2009 American Statistical Association
deumal of Business 8: Economic Statistics
Accepted for publication DOI: 10.1198/jbes.2009.06129 35$MJ é’JHIM Ct. gear awarding geles andJRand Corporation 1, and Divisﬁm “C 99 trio 7 V so
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has ricer: {Miranled QDOJ‘JQU'IpLDN—t 0‘1 (:1 U! U1 U1 Ln 01 01 U! 0‘1 4: 4’: 4: «L A J: 45 41 4 ~13 (J 03 DO (a m 0) 03 \5 0 l“ ‘ * —‘ "‘ ‘ —"
I C») CD 0 \J \J \3 U M —‘ " —‘ M 2 by youths may lead to their subsequent consumption of other,
harder drugs. Given the foregoing debates, empirical evidence
of the impact of marijuana decriminalization on marijuana us
age is crucial. In particular, if decriminalization has little or no
impact on smoking prevalence, then this is a strong argument
in favor of the policy. On the other hand, if there is evidence
that decriminalization signiﬁcantly stimulates more marijuana
smoking, then a liberal approach toward marijuana may not be
as beneﬁcial as is advocated by its supporters. Empirical results using various data sources from the United
States are mixed. Saffer and Chaloupka (1995, 1998), and Pac
ula, Chriqui, and King (2003) found the impact of decriminal—
ization on marijuana smoking prevalence to be positive and
signiﬁcant. In contrast, DiNardo and Lemieux (2001), Pacula
(1998), and Thies and Register (1993) reported insigniﬁcant ef—
fects of marijuana policy reform on individual smoking deci
sions. There have been three empirical studies of the Australian
experience. Cameron and Williams (2001) and Zhao and Har
ris (2004) both found ,a positive and significant marginal effect
of decriminalization on prevalence of about 2%, while Williams
(2004) found it to be signiﬁcant only for the subsample of males
age 25 years old and older. Typically, binary probit models have
been used in these studies, with the decriminalization dummy
variable treated as an exogenous explanatory variable. In this work, we used the 2001 Australian National Drug
Strategy Household Surveys (NDSHS) to study the‘impact of
marijuana decriminalization on marijuana usage. Australia con—
sists of six states and two territories. As of 2001, South Aus
tralia, Australia Capital Territory, and Northern Territory had
already decriminalized the possession and cultivation of small
quantities of marijuana for personal consumption. Under this regulation, while supplying and cultivating commercial quan _ tities of marijuana still attract severe criminal charges, an “on
the spot” ﬁne has replaced criminal charges for minor users.
An individual caught using or growing marijuana must pay a
ﬁne (usually AUS$150—$200) within a speciﬁed period, usually
within 60 days, to be eligible for the reduced penalty involving
no criminal record or imprisonment. If the person fails to pay
the ﬁne, however, a criminal proceeding may follow, possibly
leading to a jail sentence. The Australian policy of decriminal—
ization iscommonly known. as the Cannabis Expiation Notice
system (CEN). Finally, for those states that have not decrirn
inalized marijuana, criminal offenses for possessing, consum
ing, and cultivating the drug are retained. The present study aimed to assess the impact of decriminal—
ization on marijuana smoking prevalence. There are three major
differences between this study and earlier studies. First, existing
studies usually treat decriminalization as an exogenous dummy
variable when performing regression analysis. This is also the
case here, because our data are based on the 2001 survey. As of
2001, three states in Australia had already decriminalized mar
ijuana use: South Australia in 1987, Australia Capital Territory
in 1992, and Northern Territory in 1996. Thus, in analyzing this
set of data, we take a state’s decriminalization decision as pre
determined and focus on another source of joint dependence:
marijuana smoking behavior and residential choice. At the in
dividual level, the decision of living in a particular state may
not be random, and the decisions of where to live and whether
to smoke may be related. Individuals may not be randomly se—
lected to different states, and there may be selection bias arising Journal of Business 8: Economic Statistics, '2'??? 2009 from those living in the decriminalized states versus those in the
nondecriminalized states. In this article we attempt to address
the potential endogeneity of marijuana smoking and the indi~
vidual’s decision to reside in a decriminalized versus a nonde—
criminalized state by allowing an individual’s marijuana smok
ing behavior equation to be correlated with his or her residential
choice. Second, we provide a more ﬂexible marijuana smok—
ing behavior equation by allowing individuals to respond dif~
ferently when the legal and institutional arrangement changes.
Third, both parametric and nonparametric analyses are con
ducted, and their reliabilities are examined. Essentially, the advantages of the parametric approach are
the disadvantages of the nonparametric approach, and the ad—
vantages of the nonparametric approach are the disadvantages
of the parametric approach. The advantages of the parametric
approach are that it can simultaneously take into account selec—
tion on observables and unobservables (provided that the model
is correctly speciﬁed) and allows (efﬁcient) estimation of the ef—
fects of individual factors on the outcomes. The disadvantages
of the parametric approach are that both the conditional mean
functions of observable factors and the probability distributions
of the effects of unobservable factors must be speciﬁed. The
advantages of the nonparametric approach are that neither the
conditional mean functions of obsarvable factors nor the proba—
bility distributions of the effects of unobservable factors need to
be speciﬁed. The disadvantages (of propensity score matching)
are that it only takes into account selection on observables and
only estimates the treatment effects. We discuss the pros and
cons through our speciﬁcation analyses. The article is organized as follows. Section 2 presents an en—
dogenous probit switching model as the maintained hypothe—
sis and treat the traditional dummy variable approach, sample
selection model, and twopart model as its nested alternatives,
called the binary probit, bivaiiate probit, and twopart models,
respectively. Section 3 provides a description of our data. Sec~
tion 4 reports our estimation results and compares them with re—
sults in the literature. Section 5 presents alternative measures of
treatment effect from the propensity score stratiﬁcation match—
ing method. Section 6 presents specification analyses, and Sec
tion 7 concludes. 2. THE MODEL We assume that the utility for an individual’s residential
choice (d m 1 if residing in decriminalized state and 0 if not)
and marijuana consumption (M) is separable from the utility
of consuming other goods. Similar to Cameiro, Hansen, and
Heckman (2003), Keane and Wolpin (1997), and others, we
assume that an individual‘s utility function for marijuana con—
sumption and residential choice is statewdependent on the initial
endowment and institutional arrangement of the two residential
regimes. In particular, we let an individual’s utility function be
U(M, diet, 52*) = dU1(Ma) + (1 —d)U0(M]a) + h(d!a*), where
U1(v) and U0() are the utility functions of consuming mari
juana for an individual residing in a decriminalized state and a
nondecriminalized state, respectively; h() denotes the utility of
living in decriminalized state or nondecriminalized state; and a
and a* are sociodemographic, institutional, and idiosyncratic
components that affect M and (1, respectively. a and a"‘ may 60
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O mmqmmewMA ...L_L_A._.._n_n._s_n...u.4
(cooatonmhwm—‘o awmwmmm WOJDDI'O
ommwmma$m40w§ﬂgt§§$§£ #1
. mmmmmmmmmmh Damrongplasit, Hsiao, and Zhao: Decriminalization and Marijuana Smoking Prevalence contain overlapping elements. U1() and U0() are assumed to
be different, because the same amount of marijuana consump
tion may lead to different levels of utility in decrirninalized and
nondecriminalized states because of differing institutional se
tups; for example, the risk of smoking marijuana could be dif
ferent. Maximizing utility subject to budget constraint 1 yields
M1(p,1la) 2 O for an individual residing in a decriminalized
state and Mo(p,1la) 3 O for an individual residing in a nonde—
criminalized state, where p denotes price of marijuana. Substh
tuting M1() and Mg () into the utility function yields the condi
tional indirect utility V1(p, Ila, n*) for residing in a decriminal—
ized state and V0(p, Ila, a*) for residing in a nondecriminalized
state. Then d: 1 if d* = V1(p,1ln,a*) —— V009, Ila, 51*) > 0 and
d = 0 if (1* 5 0. Approximating M1() and M0() by if :Otr +151x+€1 (2'1)
and
323‘: dual7301+ 80, (22)
such that I
M106) :1»? ifyi‘ > 0 and
(2.3)
M105): 0 Hit 5 0,
and
M000 = y3 MS > 0 and (2.4)
Marx) = 0 ifyt s 0, where x denotes the observable factors of p, I, and a that affect
the demand for marijuana and a) and so denote the effects of unobservablej Equations (2.l)—(2.4) imply Prob(M; (x) 2 0) =
Probe? 6 01x) = fjéflwmneu 0'81 and_Prob(Mo(x) = 0) = Probozg g le) = fj‘mw 0X) f (80) dag. We approximate d* by 00
a reduced—form speciﬁcation, (2.5) such that d =_ 1 if d* > 0 and 0 otherwise, where z and 1) de—
note the additional observable factors in a* that are not in a and d*=1/1x+rzz+v, the effects of unobservable factors in both a and (1* that affect
' residential choiCe.‘ ' ' ' " ' ' " ” ‘ Our data are in the form (y, d), where y = 1 indicates that an
individual is a marijuana smoker and 0 otherwise, and d m 1 if
an individual resides in a decriminaiized state and 0 otherwise.
From (2.1)—(2.4), it follows that yr} ifdyT+(i—d)y3>0 and . (2.6)
y = 0 otherwise. Equations (2.l)—(2.6) lead to an endogenous switching model.
The model is in a limited information framework in which we
have a structural form specification for the demand for mari
juana for individuals residing in a decriminalized state and a
nondecriminalized' state and a reducedform speciﬁcation for
the residentiai choice. The identiﬁcation of the structural mar
ijuana use equation is achieved through the excluded vari«
ables, 2:, that are important in predicting the residential choice
(e.g., Hsiao 1983). Many of the conventional models have become special cases
of this model. For instance, we could have the following: 7 it in 3 ‘6 ii to an , ,0“, = p01,. yﬁ 0, known as a restricted Switching model,
where my and pm, denote the correlations between 81
and 1; and between 8.3 and 1), respectively. {by When ph, = pm, : O, the residential choice equation’s
error term is uncorrelated with the smoking equationﬁln
this case, model (2.1)7(2.6) is a generalization to the fre
quently used twopart model (Duan et at. 1983, 1984) or
the exogenous regime—switching model of Quandt (1972). (Q; When til 2 ,80 = ,6, and p1,, = pov # O, the model is anal
ogous to the sample selection model (Amemiya 1985) in which Mzct+ﬁx+6d+a ifur+l8x+dd+s>0 (a); and
(2.7)
M = 0 otherwise, where or = Oe'o and 5 = or; m org.
ti); When pm : p0,, = 0 and a1 = a}, modei/é.1)—(2.6) re—
duces to dummy variable approach to ennuination the effect
. of decriminalization with M given by (2.7) and LUICOITBs lated with (2.5). Wild 1) If 011,;31,oeo, ﬁg, and density functions of 121 13114 severe
known, then Prob(y = llx) is known for parametric analy
sis. We assume that (31,30, 1)) are jointly normally distrib
uted with mean 0 and covariance We“) 2 Wang) 2 Wm) = 1,
Govern. 801) = 1010, covtsn, v1) = 101:): and covtaor, v1) = pou
Therefore, wemay estimate the average treatment effect (ATE)
by [@0351 + 5136) f CPOXO + .50x)1f(x) 056 (23)
and the average treatment effect of the treated (ATET) by
[@0361 iﬁrx) — (Mao + £301)if(xld= lldx (29) or their restricted version, where @(a) denotes the integrated
standard normal from —00 to a. If the sampie is randomly
drawn, then the ATE or ATET may be approximated by 1 “ A .
a [we + ext) — cites + 50x11}, (2.10)
i=1 where the summation is over the complete sample or over those
residing in a decriminalized state. In what follows, we ﬁrst present parametric analysis, then
nonparametric analysis. We show that the results are sensitive
to model speciﬁcations and discuss which model is likely to
yield more accurate measurements of the effects of decriminal ization. 3. DESCRIPTION OF VARIABLES AND DATA 3.1 Selection of Explanatory Variables Marijuana is an addictive recreational drug, and studies on
recreational drugs have arisen from many disciplines, such
as psychology, medicine, epidemiology, sociology, and eco
nomics. Maximizing the state~dependent utility function leads
to demand for marijuana as a function of price, income, as
well as some standard socioeconomic and demographic vari
ables that capture heterogeneity in demand, such as age, sex, evalua'iii‘i} s1
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(.0030) ' 4 marital status, educational attainment, work status, and ethnic
background for the Australian indigenous population, as com
monly postulated in empirical studies (e.g., Becker and Murphy
1988; Pacula 1998; Williams 2004; Zhao and Harris 2004). The
impact of the legal risk of smoking via the decriminalization
policy is captured by allowing the responses to the conditional
variables to be different for the two types of states using the endogenous switching model described earlier.
For residential choice, the literature (Feridhanusetyawan and Kilkenny 1996; Kittiprapas and McCann 1999) suggests that
both personal and location characteristics are key determinants of an individual’s residential choice. Because we are taking a . limitedinformation approach, in addition to those variables den
termining marijuana smoking, additional variables, including
number of dependent children (which might inﬂuence residen
tial choice) and unemployment rate in each individual’s state
of residence (a proxy for statespeciﬁc effects) are also used to
predict residential choice as well as to provide exclusion restric— tions needed to identifythe marijuana use behavioral equations ‘ * (see, e.g., Hsiao 1983). _ 3.2 Data  The data used come from three different sources: the 200l
Australia National Drug Strategy Household Survey (NDSHS),
the Australia Bureau of Statistics (ABS), and the Australian ll
licit Drug Report. The NDSHS is a nationally representative
household survey of the noninstitutionalized civilian Australian
population age 14 and older. It provides information on individ
ual drug use, as well as many socioeconomic and demographic
variables. Three different survey methods were implemented:
a dropand—collect questionnaire, 21 facevtoface personal inter
view, and a computerassisted telephone interview. For more
sensitive questions (e.g., individual drug use), measures were m mau Journal of Business 8. Economic Statistics, 2??? 2009
put in lace to keep the information conﬁdential from the inter
viewer, to minimize potential underreporting of drug use. A to—
tal of 26,744 observations were available in the 2001 wave of
NDSHS. in addition, the 2001 NDSHS also provides informa
tion on explanatory variables, including household income (In
come), age (Age1419, Age2024, Age2529, Age3034, Age3539,
Age4069, Age70), sex (Male), marital status (Married, Divorce,
Widow, Never married), number of dependent children (# de
pchild), educational attainment (Degree), employment status
(Working stains), and ethnicity (Aboriginal). A dichotomous
variable (Decrim) is also deﬁned, indicating whether a person
resides in a decrirninalized state. After observations with miss
ing data were deleted, the resulting sample comprised 14,008
observations. Because South Australia, Australia Capital Terri
tory, and Northern Territory had already decriminalized mari
juana by 2001, observations from these three states were clas—
siﬁed as the treatment group. Table 1 deﬁnes all variables. The price of marijuana was obtained from the Australia Bu cﬁ‘ihé’ dandelion (ACC 2003); Four different pne‘é‘s by state
were available: price of head per ounce, price of head per gram,
price of leaf per ounce, and price of leaf pergram. These prices
were ﬁrst converted to the same unit, price per ounce. Then
for each state, a weighted average of the four prices was com«
puted using proportions of the respondents’ form of purchase
as weights. Each state’s weighted average price of marijuana
was deﬂated by the state‘s CPI, and a logarithmic function
was applied. The ﬁnal price of marijuana is denoted by PMAR.
A thorough discussion of Australia’s marijuana price has been
provided by Clements (2004). Statelevel CPIS and state~level
unemployment rates are drawn from the Australia Bureau of
Statistics (ABS 2003a, 200313), with the latter expressed as per—
centages. Table 1 provides summary statistics of dependent and
independent variables for all observations, treatment observa
tions, and control observations. Table 1. Summary statistics of dependent and independent variables (n = 14,008) All data Treatment Control
(n = 14,008) (it = 2968) (n = 11,040) Variable and deﬁnitionm Mean  SD Mean  SD7 7 . Mean~ . . SD.
y (1 if smoker, 0 if not) 0.157 0.364 0.181 0.385 0.151 0.358
Decrim (1 if in decriminalized state, 0 if not) 0.212 0.409 1 0 0 0
PMAR (log of real price of marijuana) 5.876 0.237 5.929 0.036 5.862 0.264
Income (log of real household annual income) 10.445 0.757 10.554 0.709 10.416 0.767
Age1419(1 if age is 14—19, 0 if not) 0.054 0.227 0.047 0.211 0.056 0.231
Age2024 (1 if age is 20—24, 0 if not) 0.077 0.267 0.075 0.263 0.078 0.268
Age2529 (1 if age is 25429, 0 if not) 0.100 0.300 0.l03 0.304 0.099 0.299
Age3034 (1 if age is 30—34, 0 if not) 0.122 0.327 0.121 0.326 0.122 0.327
Age3539 (1 if age is 35—39, 0 if not) 0.126 0.331 0.130 0.337 0.124 0.330
Age4069 (1 if age is 40—69, 0 if not) 0.455 0.498 0.466 0.499 0.452 0.498
Male (1 if male, 0 if female) 0.476 0.499 0.488 0.500 0.472 0.499
Married (1 if married, 0 if not) 0.619 0.486 0.621 0.485 0.618 0.486
Divorce (1 if divorced, 0 if not) 0.115 0.319 0.124 0.330 0.112 0.315
Widow (1 if widowed, 0 if not) 0.038 0.191 0.033 0.178 0.039 0.195
#depchild (# of dependent children under 14) 0.594 0.895 0.583 0.880 0.597 0.899
Degree { 1 if university degree, 0 if not) 0.260 0.438 0.292 0.455 0.251 0.434
Working status (1 if unemployed, 0 if not) 0.028 0.164 0.019 0.137 0.030 0.170
Aboriginal {1 if Aboriginal, 0 if not) 0.013 0.1 ll 0.017 0.127 0.012 0.107 6.986 1.375 6.331 1.386 7.162 1.318 State unemployment rate (rate in %) reau of Criminal Intelligence (ABCI 2002) and the Australian 60
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59 Damrongplasil, Hsiao, and Zhao: Decriminalization and Marijuana Smoking Prevalence 4. EMPIRICAL RESULTS We used the maximum likelihood method to derive our pa
rameter estimates. Because we do not simultaneously observe
y’i‘ and ya, the joint distribution of (81,80) or p10 is not iden
tiﬁed. Table 2 reports estimated coefﬁcients for the marijuana
use and the reduced—form residential choice equations and the
average treatment effects for all ﬁve models studied. Table 3
provides estimates of the marginal effects on marijuana partic—
ipation probability for a reference individual, a male age 14—
19 years with less than a university education, never married,
not unemployed, not of Aboriginal origin, residing in a nonde
criminalized state, having income equal to the mean of house—
hold income, and facing marijuana price equal to the mean
price. Our results Show that decriminalization has positive and gen
erally signiﬁcant impacts on marijuana smoking behavior, al
though the magnitude of these effects varies across different . models. TheATchdecriminalization for all models. is given a.t,.,... the bottom of Table 2 and the marginal effects of speciﬁc factors
for our reference individual are speciﬁed in Table 3. We ﬁrst
discuss each model’s estimated ATE. When using a simple bi
nary probit model not accounting for endogeneity of treatment
and ﬂexibility in behavior, the estimated ATE is 3.7%. This is
very similar to the values estimated by Cameron and Williams
(2001) and Zhao and Harris (2004). When accounting for en dogeneity of treatment as in model (iv), the ATE rises to 4%){e “Xowever, when allowing for behavioral differences between the
treatment and the control groups but ignoring endogenous treat
ment as in the two—part model, the ATE is 13.7%. Finally, in the
endogenous probit switching models (i) and (ii), the estimated
Allis are 16.2% and 18.3%, respectively. It is clear that the
two—part and the endogenous probit switching models provide
stronger support to the opponents of marijuana decriminaliza—
tion policy, because they yield substantially larger ATEs than
the binary probit and the bivariate probit models. For the impact of speciﬁc explanatory variables on mari—
juana use behavior, models (i), (ii), and (iii) yield similar re—
sults, while models (iv) and (v) generate comparable outcomes.
Consistent with an a priori conjecture that demand is nega»
tively associated ‘with the price of marijuana, the coefﬁcients
of PMAR are negative and signiﬁcant for all models, implying
a negative ownprice responsiveness. For a reference person, a
10% increase in the price of marijuana decreases the probabil
ity of using it by 1.27% according to our binary probit and the
bivariate probit models. When allowing for behavioral differ
ences between the treatment and control groups and/or taking
into account possible endogeneity, we ﬁnd a much larger nega
tive ownprice effect in the decriminalized states. In particular,
for a reference person, as marijuana price increases by 10%,
the probability of using the drug is estimated to fall by approxia
mater 21% in decriminalized states, but by only 1.18%—l.45%
in nondecriminalized states. The higher price responsiveness
in the decriminalized states is expected, because we would ex
pect price to play a much smaller role in the nondecriminaiized
states where the risk premium of being caught should have a
greater role than price in the smoking decision. If marijuana were a normal good, then we would expect the
coefﬁcient of household income to be positive and signiﬁcant. 5 But the coefﬁcient of household income is negative but insignif
icant for all models studied. This indicates an absence of in«
come effect. The literature reports mixed results on income.
For example, a fullusample estimation by Saffer and Chaloupka
(1998) found an insigniﬁcant effect of income on the probabib
ity of marijuana use, while Pacula (1998) and Thies and Regis—
ter (1993) both reported a signiﬁcant negative income effect.
As for other conditional variables that affect marijuana use
behavior, age is an important factor affecting marijuana smok
ing behavior. Cameron and Williams (2001) and Williams
(2004) both reported that the probability of participating in mar
ijuana peaks at age 20w24 years and then declines monoton—
ically thereafter. Our maximum likelihood coefﬁcients in Ta
ble 2 obtain this same ﬁnding for the treatment group of mod—
els (i), (ii) and (iii); however, for the other models [i.e., the
control group of models (i), (ii), and (iii), model (iv), and
model (v)], smoking prevalence peaks at age 25—29. Our results
indicate that young adults have the highest risk of becoming marijuanasmokers in decriminalized states, while adults have  the greatest exposure in nondecriminalized states. We ﬁnd a positive and signiﬁcant coefﬁcient on the gen—
der dummy variable across models, in agreement with previ
ous studies. Married individuals are less likely to use marijuana
than their never—married counterparts. Widowed individuals are
less likely to be marijuana smokers for all models and for both
the treatment and control groups. No difference in smoking be
havior was noted between divorced and single persons across
all models. Education attainment does not seem to play a role in the deci—
sion to consume marijuana when using models (iv) and (v). But
when allowing for behavioral differences due to policy changes,
as in model (iii), and possible endogeneity of treatment, as in
models (i) and (ii), the effects of education differ across the
treatment and control groups. For those who live in decriminal—
ized states, having a university degree substantially reduces the
likelihood of smoking marijuana. In contrast, for those living
in uondedriminalized states, marijuana smoking prevalence is
similar in those with and without tertiary education. In this study, Working status is assigned a value of 1 if the individualis unemployed and 0 otherwise. The coefﬁcient of K Working Status is found to be positive and signiﬁcant for bi
nary probit, bivariate probit, the control group of two—part, re
stricted, and unrestricted endogenous probit switching models.
The estimated marginal effect63' Table 3 suggests that a refer—
ence individual can have up to 12% greater chance of becoming
a marijuana smoker when unemployed. In contrast, there is no
evidence that being unemployed leads to higher prevalence of
the drug for the treatment group of models (i) and (iii). Finally, we turn to the ethnic variable. Being an Aborigi—
nal or Torres Strait Islander has a positive and signiﬁcant ef
fect on participation in marijuana use with models (iv) and (v),
but not with the treatment group of models (i), (ii), and (iii).
When allowing for joint dependence between marijuana smok—
ing and residential choice, in decriminalized states respondents
with this ethnic origin have more or less the same probability
of becoming marijuana smokers as do individuals from other ethnic backgrounds.
Table 2 presents the estimation results for the residential choice equation. As shown, household income, divorced status, 60
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Mamecamnocooodc:U13wro—nococo\Immg3$£8833§3§8§£3353333513:3 Damrongplasit, Hsiao, and Zhao: Decriminalization and Marijuana Smoking Prevalence working status, ethnic Aboriginal, and state unemployment rate
are important factors for predicting residential choice. These variables are either excluded or not signiﬁcant for the marijuana
behavior equations. 5. PROPENSITY SCORE
STRATIFICATION MATCHJNG When the marijuana smoking equations, y} and 31%, are un
speciﬁed, the ATE may still be identiﬁable and estimable un—
der the assumption that conditional on a set of confounding
variables, w, = {xi U zi}, (y’fi, ygi)_i_d, (ignorable treatment se
lection; see Rosenbaum and Rubin 1983; Heckman and Robb
1985). In this section we use the' propensity score method
of Rosenbaum and Rubin (1983) to correct for selection on
observables, with propensity score deﬁned as the conditional
probability of being assigned to treatment given the covariates.
In our context, this is simply the conditional probability of re
siding in decriminalized states given observable variables. Let
w, = {x, U zi}. We denote the propensity score, Pr(di : than),
by p(w,). Under the assumptions 0 <P(Wi) = Pr(di=1lwi) <1 and
(5.1)
@Tf: 373;)J—dilwi,
we have
@TiiyEiJJdilp(wi) (5.2)
and
WtidrlP(Wi) (5.3) Equation (5.3) establishes that conditioning on the propensity
score, the distribution of covariates w, must be the same across
the treatment and control groups. In other words, given the
propensity score, the assignment to treatment is random. We compute ATE under the assumption (5.1). Frequency .25
ptw) 9 Propensity score stratiﬁcation matching can be implemented
through the following steps: (a) estimating the propensity score
either parametrically or nonparametrically; (b) dividing the
propensity score into different intervals, such that for each in
terval there are both treated and untreated units; (c) within each
stratum, calculating the means differences of treatment and con—
trol outcomes; and ﬁnally (d) computing ATET and ATE by
simply taking the weighted average of these differences, with
the weight being the frequency of treated observations or the
frequency of both treated and untreated observations in each
interval (Becker and Ichino 2002, p. 7; Cameron and Trivedi
2005, Pp. 8754376), We follow Dehejia and Wahba (1999) and Becker and Ichino
(2002) in obtaining empirical estimations. First, because, as
shown by Horowitz (1993) and Newey, Powell, and Walker
(1990), there is little difference in predicting outcomes using
parametric or semiparametric methods, we estimate the propen
sity score by running a binary probit estimation given w,. This
step' provides us with the estimated propensity score; 13(wi),
which we can use to plot histograms for both the treatment
and the control groups. We draw the histograms shown in Fig—
ures 1 and 2 by focusing on a range of propensity score of 0.05—
045, because both the treated and control units are presented in
this region. Table 4 gives the values calculated for ATE, ATET,
and their associated standard errors. Four different ranges of
overlapping region (i.e., 0.05—0.45, 0075—0425, 0.05w0.4, and
01—035) and two different ways of partitioning the propen
sity scores (i.e., interval lengths 0.025 and 0.05) are consid«
ered in this study. In addition to our manual partition, we also
use STATA’s pscore command to divide propensity scores into
smaller stratums. The results given in Table 4 demonstrate that
ATE varies between 0.059 and 0.112, while ATET ﬂuctuates
between —0.069 and —0.021. Because both ATE and ATET
are highly sensitive to how the propensity score is stratiﬁed,
we check whether condition (5.3) is met by testing for any dif
ference in the ﬁrst moment between the treatment and control 275 Figure 1. Treatment group. Histograms of estimated propensity scores in the overlapping region. 60
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59 10 Frequency Journal of Business & Economic Statistics, '2’??? 2009 .25
MW) Figure 2. Control group. Histograms of estimated propensity scores in the overlapping region. groups for each interval. Regardless of how we or STATA parti
tion the propensity score, the Host and the t—squared test al—
ways rejects the null hypothesis of means’ equality between
the treatment and the control groups. This result suggests that
conditioning on the propensity score, the distribution of w, is
different between the treated and the control units, implying a
violation of the balancing condition. This violation could enough to perform reliable
nonparametric estimates, or because conditional independence
assumption does not hold. Thus our propensity scoreffnatching
estimates of the ATE and ATET could capture not only the treat—
ment effect, but also the impact of differences in observable and
unobservable covariates on smoking outcome. he, a, result 0‘} sample size 15 not large
6. SPECIFICATION ANALYSES Our numerical analyses using parametric and nonparamet
ric methods yield very different inferences regarding the im—
pact of decriminalization on marijuana smoking prevalence.
In this section we report speciﬁcation analyses to investigate
which model or method can more accurately capture the es«
sandals of our data. As discussed in the previous section, our
propensity scorei’matching analysis fails to satisfy the balanc—
ing condition implied by the conditional independence assump—
tion, possibly due to a violation of the conditional independence
assumption. In contrast, the parametric approach can take into
account of both selection on observables and unobservables si— Table 4. ATE and ATET using propensity score stratiﬁcation method Number of Number of
Range of estimated treatment control
propensity score observations observations ATE ATET
0.050.45 2810 10,301 0.092*** 411.032
Length of interval 0.025 (0.026) (0.053)
0.05—0.45 2810 10,301 0096*“ —0.069*
With STATA interval {0.025) (0.038)
0.0750425 2432 9,509 0074*“ ~0.056**
Length of interval 0.025 (0.018) (0.025)
0075—0425 2432 9,509 0086""H2 —0.056**
With STATA interval (0.020) {0.025)
005—04 2116 10.295 0.098*** —0.024*
Length of interval 0.05 (0.017) (0.014)
ODS—0.4 2116 10,295 0112*“ —0.026**
With STATA interval (0.026) (0.012)
0.1—0.35 1909 8,263 0.067’“M ~0.021i‘
Length of interval 0.05 (0.016) (0.015)
01:05 1909 8,263 0.059%” 40.02?
With STATA interval (0.020) (0.015)
NOTE: (1) *** signiﬁcant at 1%, (ii) "H‘ signiﬁcant at 5%, (iii) 4“ signiﬁcant at 10%, (iv) ? signiﬁcant at 10% oneatailed test, (v) standard errors are in the parentheses. 60
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59 Damrongplasit, Hsiao, and 21130: Decriminalization and Marijuana Smoking Prevalence multaneously, provided that the model’s assumptions are con—
sistent with the datagenerating process. If the parametric form
is misspeciﬁed, then inference based on parametric speciﬁca
tion can be misleading. For this reason, we ﬁrst conduct a non
parametric kernel consistent test of the null of unrestricted en—
dogenous probit switching model against the nonparametric alu
ternative that does not place a restriction on the functional form
or make any distributional assumptions. If the endogenous pro
bit switching model is not rejected, then we conduct likelihood
ratio tests to choose between the unrestricted endogenous pro
bit switching model and its nested binary probit model, sam
ple selection model, twoupart model, and restricted endogenous switching model. 6.1 Parametric versus Nonparametric Modeling
Irviatnrainggi Our main hypothesis for a parametric model is the unre
stricted endogenousprobit switching model that nests the re—
stricted endogenous switching model, twopart model, sample
selection model, and dummy variable model as special cases.
The datagenerating process couid possibly follow other alter
native speciﬁcations, however. To check the adequacy of our
unrestricted endogenous switching model in capturing the es
sential characteristics of the observed data, we test the null of
the unrestricted endogenous switching model against the depar
ture from the null in any direction. The basic idea of Bierens (1982), Hong and White (1995),
and others on testing a parametric null of y, = m(x,, [3) + it,
against the departure from the null in any direction is that un—
der the null H0 :E(uix;) = 0, whereas under the alternative, H1 :E(u,x,) 75 0. Testing E (uiIJCj) = 0 is equivalent to testing
E {MrE (Minor (160} = 0 (61) Because our x contains both continuous and discrete variables,
following Hsiao, Li, and Racine (2007) and Li and Racine (2007), we use 1”, 1", ql (xii—x93)
In=;;ui{;§:uj[HEk(_75_1_)] 1 he 5:1 J" >_< tot, xii, ml}
3:1
1” “M 41 (lea—xi)
=nZZm‘tLanih—Kli iﬁi jg: :1 f
x [Hlﬁegnn] (62)
5:1
as a sample analog of (6.1), where
51: = M — EO’ddr = l)
__ q) d1+l§ixt+ ﬁiutmﬁnvwﬁzu)
‘yi L _ A2 1/2
(1 pm)
if d, = 1 (6.3) 11 and
ﬁt ‘—“ 3’: * EO’tldi = 0)
_ (I) 5m +ﬁoxr — I301; (emu/(1 — chem»
—yi_ —1_A2 1,2
( pou)
if d, z 0, where xC and xd denote continuous and discrete variables, q and
r denote the dimensionSof continuous and discrete regressors,
k0) denotes the normal kernel function, and l() denotes the kernel function of the form “xii: Ar) = is otherwise I
when is an unordered discrete regressor and
xiii! A!) :1 and
V ' ' " '  r (6.5},
Ixtexil .
[(xii’xﬁ, As) 3 is " otherwme when x‘.1 is an ordered discrete regressor, where A; E [0,1]. .l Hsiao, Li, and Racine (2007) showed that under the null, 1,, x 11011 "apt/214% —> N(0, i), (6.6) . 2
, 2am}; , , q 1 (xi—x?)
Q=Wn2__q Ishs Js ) S=l 2‘ as r 2
x [Mantegna] . (6.7)
3:1 But under H0, J’ﬂ converges to the standard normal distribution
at the slow rate of 0p((h1   hq)1/2). To overcome this slow
convergence problem, we use the following bootstrapping pro—
cedure to approximate the ﬁnitesample distribution of (6.6): (i) From maximum likelihood estimates 31, do, 6:1, 6:9, j},
I611), '50” of the endogenous probit switching model
(2.1)—(2.6), compute ﬁgl‘é'my, a 1 ld; '=“1‘),’ an e:
1 agar3° = Pr(y, = 1d; = 0), ands?“ =1—fag0. (ii) Generate bootstrapping samples {ny xi}f‘=1, where y? is
the dependent variable from bootstrapping, x, denotes
the explanatory variables from the original data, It is
the number of observations (14,008 in our case), and y?
is drawn randomly from the binomial distribution with
p at,“ 1rd, = 1 andp=p30 ifd; = 0. (iii) Use the bootstrapping samples {3%, xi}?=[ from step (ii)
to estimate the endogenous probit switching model [i.e.,
model (2.1)—(2.6)] by the maximum likelihood method and obtain a new set ofﬁf, ,Bb, 65;), 51:5, )3'5, £33, and 1531, (iv) Use the maximum likelihood estimators ﬁg, [32%, 6:3,
33", ﬁg), and ﬁgv from step (iii) and the bootstrapping
samples {yfi xi}?=l from step (ii) to compute bootstrap
ping residuai it? and compute J5 using the ad hoc plug«
in bandwidth h, : (roamed/(2PM, where p is the
order of the kernel function, i denotes the dimension of so
a:
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102
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108
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,wmmmwm ’
mmummsmmﬂommammsumuoomumms‘d‘dﬂBBEﬁRaEBBBlBe‘atn‘aattauia " ‘p’ar‘ametricrnodels as nested hypotheses, it'f'o’l'lowsthat'(aj'if' L ' 12 continuous regressors, and as is the sample standard de«
viation for variable 5. We set a, = 0 for discrete regres—
sors. Repeat steps (ii)—(iv) 399 times and use the sorted test
statistics, {J%}f3, to construct a bootstrap empirical
distribution, which in turn is used to approximate the
null distribution of the test statistic J”. A
<
v We conduct a twosided test by comparing Jn with the 1%,
5%, and 10% critical values from the bootstrap empirical dis—
tribution. The twosided critical values are 2.71 at 1%, 1.995
at 5%, and 1.625 at 10%, and Jn = 1.282. In other words, it
does not appear that our endogenous probit switching model is
contradicted by the information contained in the data. 6.2 Likelihood Ratio Tests for Nested Alternatives Taking the unrestricted endogenous probit switching model
(2.1)w(2.6) as the maintained hypothesis and treating other 1116:9111 = 1001) ¢ 0: then the model becomes the restricted endogenous probit
switching model; (b) if 3*:9111 2 10012 2 0; (69). then the model has the form of a generalized twopart model;
(c) if H3” : a n so and (6.10) then the unrestricted endogenous switching model is reduced to
the sample selection model (Amemiya 1985); and (d) if :a = a toll) =P0u. (6.11) and 1011} 2 p01) = 0s 7 then the unrestricted endogenous switching model is reduced to the conventional dummy variable approach {model (2.7)]. To
conduct speciﬁcation tests for H*, H“, and 193*“, we
compute likelihood ratio statistics, LR1, LR2, LR3, and LR4,
respectively. Each is associated with different degrees of free dom.
_ [Table 5 presents the results of this speciﬁcation analysis. LR2 _ 7 and LR4 ﬁrmly reject the independence assumption between the errors of the marijuana smoking equation and the errors of
the residential choice equation, while LR; demonstrates that
the correlation of these error terms differ for the treatment and
control groups. LR3 and LR4 also indicate that individuals do
behave differently if marijuana smoking is decriminalized. In
other words, our speciﬁcation analysis appears to favor the un
restricted endogenous probit switching model; Journal of Business & Economic Statistics. '3??? 2009 7. CONCLUSION In this work, we have used the 2001 wave of the NDSHS
to empirically examine the impact of marijuana decriminaliza
tion on marijuana smoking prevalence in Australia. We used
both parametric and nonparametric approaches. The advantage
of the nonparametric approach is that it requires no functional
form or distributional assumptions; the disadvantage is that the
conditional independence assumption (i.e., ignorable treatment
assignment assumption) is a maintained hypothesis. Further
more, the impacts of other sociodemographic effects on mar
ijuana smoking are not estimated. The advantage of parametric
speciﬁcation is that the issues of selection of both observables
and unobservables can be taken into account, and the impact
of each variable on outcome can be assessed provided that the
parametric assumptions are not contradicted by information in
the data. The disadvantage is that both functional form and dis
tributional assumptions are imposed. If these assumptions are .. incorrect,» then the resulting inferences will be misleading. But our data analysis appears to indicate that the validity of the con—
ditional independence assumption for nonparametric matching
adjustment is contradicted by the information in the data. In
contrast, our parametric model does not appear to be contra—
dicted by the information in the data. In fact, the world is not
that benevolent. We could be asking too much of our data. As
noted by Griliches (1967, pp. 17—18), “we want them to test our theories, provide us with estimates of important parameters,
and disclose to us the exact form of the interrelationships be— tween the various variables.” When the information contained
in the data is limited, an integration of behavioral assumption
and parametric speciﬁcation may allow us to extract more use—
ful information from the data. . Conditional on a state’s decriminalization status, our speci—
ﬁcation analysis appears to favor the unrestricted endogenous
probit switching model that takes into account both selection
on observables and unobservables. This model suggests that
a decriminalization policy leads to greater marijuana smoking
participation. It indicates that on average, living in a decrimi—
nalized state signiﬁcantly increases the probability of smoking
marijuana, by 16.2%. This estimate is higher than the estimates
obtained from the dummy variable approach, the sample selecu
tion model, the two—part model, and previous studies. The dis—
crepancies could be due to the use of different data sets or to
differing model speciﬁcations, as demonstrated in the present
study. Our speciﬁcation analysis appears to favor the model that
allows both endogeneity of the decriminalization dummy and
ﬂexibility of different behavioral patterns due to changes in the
legal or institutional environment. Table 5. Likelihood ratio tests Model under null hypothesis Restricted switching Tworpart Bivariate probit Binary probit
Model under Unrestricted Unrestricted Unrestricted Unrestricted
alternative hypothesis switching switching switching switching
Degree of freedom of the chisquare dist 1 2 16 17
Likelihood ratio test statistics LRl : 5.3** LR2 : 8.49** LR3 = 80.964*** LR4 = 80.973*** NOTE: (1) “‘1‘ signiﬁcant at 1% (twmtailed test), {2) 3* signiﬁcant at 5% (twotailed test). 50
61
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76 .. 73...... 79
80
B1
82
83
B4
85
86
87
88
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Q3
94
95
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95
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118 mm«Immemm—L wmmmmmmmmmmmm '
mLoam—tommummom$gggaiaﬁﬁagjg 35
3? Damrongplasit, Hsiao, and Zhao: Decriminalization and Marijuana Smoking Prevalence ACKNOWLEDGMENTS The authors thank Ragui Assaad, Deborah Levison, and
Cristobal Ridao—Cano for the use of their maximum likelihood
computer program and Jeffrey Racine for the use of his R pro—
gram to conduct the speciﬁcation analysis. They also thank two
referees, an editor, and John Ham, Qi Li, Chiahui Lu, Jeffrey
Nugent, Michael Nichols, John Strauss, and Vai—Lam Mui for
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“PPM? ﬁctieiin éeri'ee/ “Taming i’olﬁi dlﬁoﬂol and PW} Wolfe, Pliny: Mel beofﬁﬂs é—__.l so
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59 META DATA IN THE PDF FILE Foilowing information will be included as pdf ﬁie Document Properties: Title Decriminalization and Marijuana Smoking Prevalence: Evidence From Australia Author Kannika Damrongplasit, Cheng Hsiao, Xueyan Zhao
Subject . Journal of Business \046 Economic Statistics, Vol.0, No.00, 2009, 1”}.4
Keywords: Average treatment effect, Bootstrapping, Endogenous probit switching. Parametric and nonparametric Propensity score matching,  u . specification analysis, THE LIST OF UR! ADRESSES Listed below are all uri addresses found in your paper. The nonactive uri addresses, if any, are indicated as ERROR. Please check and update the list
where necessary. The email addresses are not checked — they are listed just for your information. More information can be found in the support page: him://www.epubiications. orglims/supparr/Hriheipﬁtml. ewe mailto:chsiao@usc.edu [2:pp.1,1] Check skip 200 http://mm.amstat.org [2:pp.l,1} OK 302 http:Hpubs.amstat.org/1oi/jbes [2:pp.l,1] Found 200 .http: UdXdﬂi O_rg/ 1(1ll98/7j1293129997a 0.5.129“ [273994171117 9K . _ . CO'NIODU'IvhbJNiA 01 01 m m o1 01 m U1 01 m e A a. A A h '
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