Embed Size (px)
Citation preview
Decriminalization Policy and Marijuana Smoking Prevalence:
a Look at the Literature
Kannika Damrongplasit Department of Health Services, University of California Los Angeles and Rand Corporation
Cheng Hsiao1
Department of Economics, University of Southern California, USA and Nanyang Technology University, Singapore
February 7, 2008
Abstract
This paper reviews the literature on the impact of marijuana decriminalization policy on
marijuana smoking prevalence. Due to mixed findings in the existing studies, we attempt to find
a common basis to explain the different results across papers. The main purpose is to provide a
coherent background as to what outcomes may be expected from certain type of data,
econometrics model, and explanatory variables. If possible, we also try to provide the
explanation as to why certain results are found.
JEL Classification: I12, I18
Keywords: Decriminalization, Marijuana Smoking Prevalence
* The authors would like to thank the editors and a referee for helpful comments. The first author also wishes to acknowledge the research support of Agency for Healthcare Research and Quality. 1 Corresponding author: Cheng Hsiao, Department of Economics, University of Southern California, Los Angeles, CA 90089, USA; Tel: +1-213-740-2103; Fax: +1-213-740-8543; Email: [email protected]
2
1. Introduction
This paper attempts to review the empirical literature on the casual relationship between
marijuana decriminalization policy and marijuana usage. Marijuana is the most widely used
illicit drug in developed countries. Governments across the world have spent huge amounts of
public funds to control its use. However, medical communities still have not reached a
consensus on the harmful effects of smoking marijuana.
Marijuana policy in general has two goals: to minimize health and safety hazards
associated with use, and to minimize the social costs and adverse individual consequences that
result from attempts to control use. The attainment of these two goals could be contradictory.
Vigorous enforcement of criminal sanctions against possession may reduce levels of use but it
also escalates the social costs and adverse individual consequences. Conversely, a reduction in
enforcement may reduce costs but contribute to an increase in consumption.
Decriminalization policy is usually known as a depenalization policy where an on the
spot fine has replaced criminal charge for personal usage. In the jurisdiction where
decriminalization policy is in effect, if a person gets caught of possessing small quantities of
marijuana for personal consumption, he/she can choose to pay a fine within a specified period of
time in order to get no criminal status from the offence and no jail sentence. If failing to pay the
fine, criminal proceeding may follow with a possibility of jail sentence. It must be noted that the
maximum amount of marijuana considered a minor offence and the corresponding fine do differ
across jurisdictions within a country and across countries2. There are two important exceptions
to this policy. First, this law is only applied to the demand for marijuana. The supply and
cultivation of commercial quantities of marijuana are still subject to severe criminal charge.
2 For example, Western Australia allows up to 30 grams of marijuana with the fine of AUS$100-150 while Australia Capital Territory only permits the maximum possession of 25 grams with AUS$100 penalty.
3
Second, decriminalization is not the same as legalization. Under this policy, it is still illegal to
possess small quantities of marijuana; however, the criminal offence is changed to that of a non-
criminal one. At present, Australia, Germany, Italy, Netherlands, Portugal, Spain and the United
States have already implemented some variants of this policy according to Pacula et al. (2004).
Marijuana decriminalization policy is one of the most intensely debated public policy
issues because there are both potential benefits and costs associated with it. For those in favor,
decriminalizing marijuana can help to reduce the resources used in the law enforcement and
criminal justice system. Although precise estimate of the monetary cost of enforcing marijuana
possession law is not available, we expect it to take a large portion of the overall drugs policy’s
cost. This is because marijuana is the most widely used illicit drug in developed countries.
Public funds being spent on drugs policy are quite substantial. For example, according to the
Economist magazine3, the United State’s drugs policy is estimated to cost at US$35 – US$40
billion while in Australia it is reckoned to be at about AUS$1 billion4. In addition to reducing
the high cost of enforcement, decriminalization policy also allows the authority to split the
market of marijuana, a softer drug, from the market of other harder drugs. This ultimately
permits the authority to direct more effort to eradicate drugs like cocaine, heroin, and
amphetamines instead of spending most time dealing with cannabis. At a personal level, the key
benefit of decriminalization is the elimination of the adverse effects that come with having a
criminal record. Criminal charge may be too severe a penalty for marijuana possession’s
offenders because it can have many negative consequences on ones’ lives. These negative
consequences are, for example, limited employment opportunity, problem with international
traveling, and family dispute resulting from marijuana arrest. For those against
3 See The Economist Survey: the case for legalizing drugs, July 28, 2001. 4 See Australian Department of Health and Ageing, National Illicit Drug Strategy, http://www.health.gov.au/internet/wcms/Publishing.nsf/Content/health-pubhlth-strateg-drugs-illicit-index.htm.
4
decriminalization, there could be two potential harms from decriminalization policy. First,
marijuana usage may be viewed as more acceptable behavior in the society because the legal and
social costs associated with it are now lower than before. This can lead to greater initiation of
marijuana use among current non-smokers and encourage more consumption among current
smokers. Another detrimental effect of decriminalization policy is the gateway theory, which
hypothesizes that the exposure to marijuana in the early years of life can be a gateway towards
the consumption of other harder drugs.
Because of the above debates, there are many empirical studies during the past two
decades assessing the impact of marijuana decriminalization policy on marijuana use. These
papers use various data sources both from the United States and Australia. In the US, the earliest
attempt known to us is Johnston, O’Malley and Bachman (1981), which uses 1975-1980
Monitoring the Future Survey (MTF) of high school seniors and looks at the mean difference of
marijuana smoking prevalence between the states that adopted decriminalization policy and the
states that did not. There is no regression analysis included in this paper. Although recently
published, DiNardo and Lemieux (2001)’s working paper version was available since 1992. It is
the next paper that employs MTF to analyze this issue by constructing a state-year panel data set
and estimating an econometrics model. The first paper to use individual-level data set in tackling
the problem is Thies and Register (1993), in which they utilize the National Longitudinal Survey
of Youth (NLSY) to find the impact of decriminalization. Subsequently, most papers shift
towards using individual-level data set in conducting their studies: Pacula (1998a, 1998b) use
NLSY; Saffer and Chaloupka (1995, 1998) employ National Household Survey on Drug Abuse
(NHSDA); Chaloupka, Grossman and Tauras (1999a) and Chaloupka et al. (1999b) utilize MTF;
Pacula, Chriqui and King (2003) analyzes National Educational Longitudinal Survey (NELS);
5
Williams et al. (2004b) makes use of Harvard School of Public Health College Alcohol Study
(CAS) in their work. In Australia, there have been four empirical studies, Cameron and
Williams (2001), Williams (2004a), Zhao and Harris (2004), and Damrongplasit, Hsiao and Zhao
(2007), all of which use National Drug Strategy Household Survey (NDSHS) to estimate the
impact of decriminalization policy.
So far, the empirical findings of these papers have been quite mixed. Some papers find
that decriminalization has little or no impact on usage, which lend strong support for the policy.
On the other hand, some papers find that decriminalization significantly encourages more
marijuana smoking, suggesting that liberal approach towards marijuana can have strong negative
consequence on use. Given a wide variety of results, this paper aims to review a number of
empirical studies of marijuana decriminalization policy and marijuana usage. However, since
some studies employ frequency of use data and some studies use binary data of whether one has
smoked marijuana or not in the past few months or years, we shall attempt to summarize the
empirical results in terms of marijuana smoking prevalence, namely, decision to use or not use
marijuana. This is because the frequency of use results can be converted to the binary outcomes
of using or not using marijuana (as shown in section 2). We look at fifteen different studies both
in the US and Australia. Our goal is to identify factors that can possibly explain these mixed
findings. We want to find out whether there are certain features of the papers that generate
positive and significant effect of decriminalization policy and whether there are other aspects of
the papers that make the result insignificant. We hope that such a review could provide the
background information needed for future empirical investigation and a better understanding of
the existing studies by policy makers.
6
To do so, we proceed in the next section, section 2, by categorizing papers according to
the type of econometrics model. Section 3 groups papers by the type of data set, and section 4
by the type of explanatory variables being omitted from the studies. For each of these sections,
we attempt to find a common basis to explain the different results across papers. Finally,
conclusion is given in section 5.
2. Type of Model
Table 1 provides a cross-tabulation of results in terms of econometric models and type of
data. There is one point worth noting, that is, when cross-section and repeated cross-section data
are used, papers with more sophisticated models than the simple dummy variable approach (i.e.
bivariate probit/logit, multivariate probit/logit, sample selection, two-part, endogenous
switching, joint consumption, and nonparametric models) tend to give positive and significant
impact of decriminalization policy on marijuana smoking prevalence. On the other hand, papers
that use panel data and/or dummy variable approach tend to give mixed results. In the next few
sub-sections, we attempt to give our explanation as to why papers with more sophisticated
models generate different trend of result than papers that use only the binary choice model. We
shall first set up a common basis then discuss the results in terms of different model estimates.
2.1 A Common Basis
Let yit*1 denote the marijuana smoking behavior for the ith individual at time t if marijuana
is decriminalized and yit*0 denote the marijuana smoking behavior if marijuana is not
decriminalized. Suppose, we can decompose the effects of marijuana smoking behavior into the
effects of observed factors, xit , and the effects of unobserved factors, then we may write
7
ε11
*1 )( ititit xgy += , (2.1)
and
ε 00
*0 )( ititit xgy += . (2.2)
If xit captures the essentials of marijuana smoking behavior, then we may assume
0)|()|( 01 == xExE itititit εε . Since practically all the studies assume (.)1g and (.)0g to be linear,
we can write (2.1) and (2.2) in the form
εβα 111
*1ititit xy ++= , (2.3)
and
εβα 000
*0ititit xy ++= . (2.4)
Then, the average treatment effect conditional on x is defined as
[ ]xyyExxATE |)()( *0*1 −=∆=
( ) ( )xββαα 0101 −+−= . (2.5)
The average treatment effect for a random individual is
[ ]yyEATE *0*1 −=∆=
( ) ( ) ( )xEββαα 0101 −+−= . (2.6)
In the case that changes in institutional arrangements do not affect an individual’s response to
changes in x , ββ 01 = , then
( )αα 01*0*1 −+= yy . (2.7)
Therefore, an individual’s smoking behavior is
εγβα +++= dxy 00* , (2.8)
8
where ( )ααγ 01 −= and d is the dummy status variable that takes the value 1 if marijuana is
decriminalized and 0 if not. Then
γ=∆== )(xATEATE . (2.9)
In other words, if ( )βαβα 0011 ,,, are known, ATE or )(xATE can be easily computed.
In many studies, we do not observe yit*1 or yit
*0 , but yit where 1=yit if an individual is a
marijuana smoker and 0 if not. To relate the dummy marijuana smoking outcomes with yit*1 or
yit*0 , we may assume that if marijuana is decriminalized, then
≤
>=
0. if 0,
0, if ,1*1
*1
y
yy
it
itit (2.10)
On the other hand, if marijuana is not decriminalized, then
≤
>=
0. if 0,
0, if ,1*0
*0
y
yy
it
itit (2.11)
We can then estimate the )(xATE by
),0|1(Prob),1|1(Prob)( xdyxdyxATE ==−===
( ) ( )
∫−∫=∞
+−
∞
+− xx
dfdf0011
0011 )( )(βαβα
εεεε . (2.12)
If )( 1εf and )( 0εf follow a normal distribution, (2.12) leads to the difference of the probit
model, ( ) )( 0011 xx βαβα +Φ−+Φ , where (.)Φ indicates the integrated standard normal. If
)( 1εf and )( 0εf are logistic, then (2.12) leads to the difference of the logit model,
e
e
e
ex
x
x
x
00
00
11
11
1 -
1 βα
βα
βα
βα
+
+
+
+
++. The ATE is simply the integration of (2.12) over the probability density
of x , )(xf
9
∫ ==−=== dxxfxdyxdyATE )( ),0|1(Prob),1|1(Prob . (2.13)
Some studies also compute the marginal effect of decriminalization, where the marginal effect is
evaluated at the mean of x , x_
,
),0|1(Prob - ),1|1(Prob effect Marginal__
xdyxdy ===== . (2.14)
In practically all studies, we do not simultaneously observe y *1 and y *0 , but only
ydydy ititititit*0*1* )1( −+= , (2.15)
where 1=d it if marijuana is decriminalized, and 0 if not. Therefore, we will consider the
differences in results from two perspectives: (i) the choice of x ; and (ii) the consistent
estimation of ( )βαβα 0011 ,,, from the observed ),( dy . To facilitate our discussion, we assume
)(εf is normally distributed. The results for other distribution of )(εf can be similarly
inferred. Furthermore, since the most commonly used approach in the literature is the dummy
variable approach, we shall use it as a benchmark for comparing different models.
2.2 Binary Probit Model vs Bivariate Probit Model (i.e. Joint Consumption Model) DiNardo and Lemieux (2001) and Williams et al. (2004b) use bivariate logit and bivariate
probit models to study a joint consumption between alcohol and marijuana, respectively. Zhao
and Harris (2004) analyzes the joint consumption of alcohol, marijuana and tobacco using a
multivariate probit model. We observe that the papers, which utilize the joint consumption
model, tend to give positive and significant impact of decriminalization policy unlike those using
the dummy variable approach (binary probit or logit) that are more inclined to give mixed
results. In this sub-section, we use algebraic expressions to explain this finding. We focus our
10
attention to the bivariate probit model. The explanation can then be generalized to the bivariate
logit and multivariate probit models.
A typical joint consumption model assumes that each individual i faces two decisions,
whether or not to use marijuana denoted by y i1 and whether or not to use other drug (i.e.
alcohol) denoted by y i2 . The two latent consumption equations are
εγβ iiii dxy 1*1
*1
*1 ++= , (2.16)
and
εγβ iiii dxy 2*2
*2
*2 ++= (2.17)
where
≤
>=
0 if ,0
0 if ,1*1
*1
1y
yy
i
ii ,
≤
>=
0 if ,0
0 if ,1*2
*2
2y
yy
i
ii , and
1
1 ,
0
0~
2
1
ρρ
εε
N . Maximum
likelihood method is used to derive the parameter estimates. Let ~
*1β ,
~*1γ ,
~*2β , and
~*2γ be the
coefficient estimates of the bivariate probit model. If indeed 0),|(),|( 21 == dxEdxE εε , then
both (2.8) and (2.16) is just the reduced form equation of y*1 from the simultaneous equation
model,
+
=
u
u
d
x
bb
bb
y
y
a
a
2
1
2221
1211
*2
*1
21
12
1
1, (2.18)
where we assume that there exist exclusion restrictions to identify each equation of (2.18) (e.g.
see Hsiao (1983)). Solving (2.18) yields the reduced form specification of (2.16) and (2.17)
where )(1
211211*1 bab
c−=β , )(
1221212
*1 bab
c−=γ , )(
1112121
*2 bab
c−=β , )(
1122122
*2 bab
c−=γ , and
aac 21121−= . Therefore, if both binary and bivariate models use the same set of explanatory
variables, and d is indeed exogenous, then the binary estimate of γ using (2.8) and the bivariate
11
estimate of γ *1 from the joint estimation of (2.16) and (2.17) should converge to the same value.
The difference between the two model estimates is just a matter of efficiency, not consistency.
On the other hand, if the binary and bivariate estimates are based on different sets of conditional
variables, say x and x* , then they could yield statistically significantly different results because
),|( dxE ε could be different from ),|( * dxE ε .
Our literature review supports this conjecture. DiNardo and Lemieux (2001) estimates
both binary and bivariate probit models by using exactly the same set of explanatory variables.
They find the impact of decriminalization policy on marijuana smoking prevalence to be
insignificant for both cases. Another example of similar results between the binary probit and
bivariate probit models is Pacula, Chriqui and King (2003) and Williams et al. (2004b). Because
these two papers include similar set of explanatory variables, Pacula, Chriqui and King (2003)
finds the marginal effect of decriminalization on smoking prevalence to be 1.8% for past month
use and 1.7% for past year use while Williams et al. (2004b) discovers the marginal effect of
1.32% and 1.51%, respectively. When different sets of explanatory variables are used in the
binary and bivariate probit models, the results usually turn out to be different. For example,
Williams et al. (2004b) estimates a bivariate probit model and uses a relatively complete set of
explanatory variables. When comparing it to Thies and Register (1993), Pacula (1998a),
Williams (2004a), and Saffer and Chaloupka (1995, 1998) that employ binary choice model and
use a subset of explanatory variables, this later set of papers tends to find the impact of
decriminalization policy that is insignificant or discovers a much larger effect of
decriminalization on smoking than Williams et al. (2004b).
Papers using binary probit model tends to give mixed results whereas papers employing
joint consumption model are more inclined to generate positive and significant effect of
12
decriminalization because typically more conditional variables, say other drugs’ prices, are used
for bivariate models than binary choice models. If these additional variables are significant, then
~*1γ ≠γ
^
. When this happens, these two models can lead to two very different ATEs or marginal
effects as )()(_~
*1
~*1
_~*1 xx βγβ Φ−+Φ ≠ )()(
_*
^^_*
^
xx βγβ Φ−+Φ .
2.3 Binary Probit Model vs Sample Selection Model
The binary or bivariate probit model can give consistent estimation of γ if (i) ββ 01 = ,
and (ii) 0),|( =dxE ε . Even (i) holds, (ii) could still be violated if (a) state decriminalization
decision is a function of marijuana smoking behavior of state residents, and (b) an individual
could make his residential choice depending on whether a state has decriminalized or not.
Studies using cross-section individual data presumably can ignore (a), but (b) may still be a
relevant consideration. Suppose an individual’s residential choice is given by the latent response
function,
υδ += zd * , (2.19)
and
≤>
=.0 if ,0
,0 if ,1*
*
d
dd (2.20)
Then
)|( 00* dEdxyE εγβα +++= . (2.21)
If ),( υε are jointly normally distributed with mean (0,0) and the following covariance matrix
1
1
ρρ
, then
13
) |( )1|( zEdE δυυρε −>==
) (
) (
z
z
δδφρ
Φ= (2.22)
and
))z (-(1
z) ( )0|(
δδφρε
Φ−==dE . (2.23)
When ),( **dy are not observed, but ),( dy are observed, this leads to a bivariate probit model in
terms of ),( dy . It should be noted that this bivariate probit model is different from the joint
consumption bivariate probit model discussed in the previous sub-section. Damrongplasit, Hsiao
and Zhao (2007) argues that at the individual level the decision to live in a particular jurisdiction
may not be random and the decisions of where to live and whether to smoke may be related,
which gives rise to selection bias. The sample selection model is able to capture what is called
the “selection effect” (i.e. (2.22) and (2.23)) that is completely ignored by the binary probit
approach. This selection effect is the main reason which explains why Damrongplasit, Hsiao and
Zhao (2007) finds different impacts of decriminalization policy on marijuana smoking
prevalence between the sample selection model and the binary probit model. The omitted
selection effect in the binary probit model makes γ^
≠ ~*γ .
2.4 Binary Probit Model vs Two-Part Model
Two-part model incorporates the fact that individuals may behave differently when living
in decriminalized versus non-decriminalized jurisdictions (i.e. ββ 01 ≠ ). In other words, people
in the treatment group may exhibit different marijuana smoking behavior from people in the
control group because different institutional arrangements lead to different optimum behavior.
14
However, the two-part model still treats d as exogenous. Since (2.3) and (2.4) are independent
of (2.19), they can be estimated independently from one another by using binary probit approach.
Let’s denote the coefficient estimates of the two-part model by ~
**1α ,
~**
1β , ~
**0α ,
~**
0β , and the
parameter estimates of the binary probit model (2.8) by ^
0α , ^
0β and γ^
. Then, the average
treatment effect (ATE) for the two-part model is
ATE = ∫ +Φ−+Φ dxxfxx )()]()([ 0011 βαβα
∑ +Φ−+Φ≈=
n
iii xx
n 1
~**
0
~**
0
~**
1
~**
1 )]()([1 βαβα , (2.24)
if samples are randomly drawn. The ATE for the binary probit model is
ATE = ∫ +Φ−++Φ dxxfxx )()]()([ 0000 βαγβα
∑ +Φ−++Φ≈=
n
iii xx
n 1
^
0
^
0
^^
0
^
0 )]()([1 βαγβα . (2.25)
It is clear that the two expressions of ATE are different, which explains why the results are
different for these two cases.
2.5 Binary Probit Model vs Endogenous Switching Model
Damrongplasit, Hsiao and Zhao (2007) introduces this model in order to take account of
both the potential endogeneity problem in decriminalization dummy variable and the possible
difference in marijuana smoking behavior between the treatment and the control groups. In other
words, the sample selection model and the two-part model can only take care of one problem at a
time whereas the endogenous switching model can fix both problems concurrently. The
structure of the model then consists of (2.3), (2.4), and (2.19), where
15
),,( 01 υεε iii are assumed jointly normally distributed with mean zeros and the following
covariance matrix
=1
1
1
),,cov(
01
010
110
01
ρρ
ρρ
ρρ
υεε
υυ
υ
υ
iii . (2.26)
This model can be estimated by using maximum likelihood method. Similar algebraic
expression as in section 2.3 can show that if ρ υ1 and ρ υ0 are different from zero, the two-part
model estimates of ),,,( 0011 βαβα are biased,
)(
)()0|( 111
**1
z
zxdyE
i
iiii δ
δφρβα υ Φ++=> , (2.27)
and
( ))(1
)()0|( 000
**0
z
zxdyE
i
iiii δ
δφρβα υ Φ−−+=≤ . (2.28)
The last terms of (2.27) and (2.28) are the selection effects. The endogenous switching model
takes into account these selection effect terms while the binary probit model ignores it.
Furthermore, the endogenous switching model also allows marijuana smoking behavior to be
different for the treatment and the control groups in a similar manner as the two-part model. The
expression of ATE for the endogenous switching model is the same as (2.24). However, if ρ υ1
and ρ υ0 are different from zero, the two-part model will yield biased estimates of
),,,( 0011 βαβα .
When 0: 010 == ρρ υυH holds, the endogenous switching model becomes the two-part
model. When ββ 01*0 : =H holds, the endogenous switching model becomes the sample
selection model. When 0: 01**
0 == ρρ υυH , ββ 01 = hold, the endogenous switching model
16
becomes the binary model. They are all nested hypotheses of the endogenous switching model
and can be empirically tested. Using the 2001 NDSHS survey data, Damrongplasit, Hsiao and
Zhao (2007) conducted likelihood ratio tests of H 0 , H *0 and H **
0 . They are all rejected at 5%
significance level.
2.6 Binary Probit Model (i.e. Parametric Analysis) vs Nonparametric Analysis
Damrongplasit, Hsiao and Zhao (2007) is the first paper to use nonparametric method to
analyze the impact of decriminalization policy on marijuana smoking prevalence. Specifically,
they employ propensity score stratification matching in estimating the impact. Propensity score
is defined as the conditional probability of being assigned into treatment given the covariates. In
this application, the propensity score is simply the conditional probability of living in
decriminalized states given observable variables. We can denote the propensity score
)|1Pr( xd ii = by )(xp i . The maintained assumptions of this approach are
1)(0 << xp i , (2.29)
and conditional on the set of confounding variables, xi , the distribution of y i*1 and y i
*0 are
independent of participation, d i ,
xdyy iiii |),( *0
*1 ⊥ . (2.30)
Equation (2.30) is often known as the conditional independence assumption or the ignorable
treatment assignment assumption, which states that once conditioning on xi the outcomes are
independent of treatment. From (2.29) and (2.30), Rosenbaum and Robin (1983) demonstrates
that
)(|),( *0
*1 xpdyy iiii ⊥ (2.31)
17
and
)(| xpdx iii ⊥ (2.32)
should follow naturally. Equation (2.32) establishes that conditioning on the propensity score,
the distribution of covariates xi must be the same across the treatment and the control groups. In
other words, given the propensity score, the treatment assignment is random. However, (2.32)
will not hold if there is selection on unobservables.
The propensity score, )(xp i , is a continuous variable. To implement propensity score
stratification matching, one has to divide the propensity score into different intervals and
assumes that for each interval there is a presence of both treatment and control units and the
distribution of xi between the treatment and control units are the same. Within each interval,
one can calculate the means difference of the treatment and the control outcomes, and finally
compute ATE by taking the weighted average of these differences across the intervals.
Using different ranges of overlapping region as well as different ways of partitioning the
propensity score, Damrongplasit, Hsiao and Zhao (2007) finds ATE to vary between 5.9% and
11.2%. When comparing this result to the binary probit model, it is clear that the propensity
score stratification matching method finds the impact of decriminalization on marijuana smoking
prevalence to be positive and significant while the binary probit model gives mixed findings.
That is, some of the papers that use the dummy variable approach find decriminalization policy
to have positive and significant impact on smoking whereas some other papers do not find any
significant impact.
The discrepancy of these two models’ results may be explained by their different
underlying assumptions. For the nonparametric model, neither functional form nor distributional
assumption needs to be made. However, the nonparametric analysis (particularly the propensity
18
score matching method) can only take account of selection on observables. The conditional
independence assumption (2.30) is assumed to hold. Furthermore, it can only estimate the
treatment effect and not the effects of individual factors on the outcome. The parametric
approach takes account the selection on unobservables as well as selection on observables, and
can estimate the impact of each variable on the outcome provided the effects of observables and
the effects of unobservables are correctly specified. The disadvantage is that the correct
specifications for both conditional mean function of observable factors and the probability
distribution of the effect of unobservable factors need a lot of prior information.
Damrongplasit, Hsiao and Zhao (2007) shows that their estimated ATE from the
propensity score matching method is highly sensitive to the way in which the propensity score is
stratified. They then check whether condition (2.32) is satisfied by testing whether there is any
difference in the mean of the covariates between the treatment and the control groups for each
propensity score’s interval. It turns out that no matter which way to classify the subintervals of
)(xp i condition (2.32) is violated. Once conditioning for the propensity score, the distribution
of xi is still found to be different between the treated and the control units. This violation casts
doubt on the validity of the conditional independence assumption (2.30), even though they
include a comprehensive set of explanatory variables, xi , that is commonly used in the existing
literature.
The sensitivity of nonparametric estimates to the way propensity score is computed, the
technical difficulty in implementing the procedure especially in dividing the propensity score
into intervals, and the differences between parametric and nonparametric analysis demonstrate
that the information contained in the data could be limited. They also demonstrate that we may
know too little about individual’s marijuana smoking behavior. By combining the knowledge
19
from many disciplines such as psychology, medicine, epidemiology, sociology, and economics, a
better understanding of why people smoke marijuana may be obtained. This may also lead to a
better specification of marijuana smoking equation that will allow us to extract more reliable
information from the data.
3. Type of Data
There are many ways that one can classify the existing studies by type of data set used.
In this section, we attempt three different ways of sorting. First, we group papers according to
the cross-section, repeated cross-section and panel nature of the data, and report it in Table 2. It
is clear that most papers use repeated cross-section data in conducting their analyses. There are
only three papers with panel data set and often this panel data is at the state-level. This is
because marijuana smoking is still an illegal activity. It is very difficult to track specific
individuals’ marijuana usage over time. Furthermore, respondents may have the incentive to
underreport their drugs’ consumption if they realize that their identities will be revealed to the
survey collectors through panel data collection. By closely examining Table 2, we observe that
the majority of the papers that use repeated cross-section data tend to give positive and
significant impact of marijuana decriminalization policy whereas papers that use cross-section
and panel data set tend to generate results that are evenly split between positively significant and
insignificant.
Second, we divide the papers according to the focus population of the data set. Some
data sets like MTF, NLSY, NELS, and CAS only include youths and young adults as their
samples. On the other hand, data sets like NHSDA and NDSHS comprise representative samples
of the overall population. Table 3 reports this type of sorting. When youth or young adult data
20
set is used for the analysis, the impact of decriminalization policy on the decision to use
marijuana is often found to be mixed. That is, some papers find positive and significant impact
while some other papers find insignificant effect. A clear trend of result is discovered when
samples of the overall population are used in the analysis. All papers under this category except
Williams (2004a) consistently find that decriminalization policy has positive and significant
effect on marijuana smoking prevalence.
Alternatively, we can categorize papers by using the timing of the data set. In general,
each of the fifteen papers that we review either uses data from the 1970s-1980s or the 1990s-
2000s. There are some exceptions to this rule: Cameron and Williams (2001) uses 1988, 1990,
1993 and 1995 NDSHS data; Williams (2004a) analyzes 1988, 1990, 1993, 1995 and 1998
NDSHS data; Saffer and Chaloupka (1995, 1998) employ 1988, 1990 and 1991 NHSDA data.
Since these four studies only include one year of the 1980s data, we classify them as the 1990s-
2000s category. Our goal here is to check whether the timing of the data set has any impact on
the result. Table 4 demonstrates our findings. When the data comes from the earlier periods (i.e.
the 1970s-1980s), we do not find any uniform trend for the effect of decriminalization policy on
marijuana smoking prevalence. When the data comes from the later periods (i.e. the 1990s-
2000s), some unified trend of result does exist. Particularly, we find that papers that employ data
set from the 1990s-2000s periods tend to give positive and significant impact of
decriminalization policy. These differences in results could be attributed to the fact that
behaviors have changed over time (i.e. ),,,( 0011 βαβα vary over time). However, it could also
happen even when behaviors have stayed constant over time (i.e. ),,,( 0011 βαβα are invariant
over time) if one or more x have a trend. If )()( xExE st > for t > s, then studies based on more
21
recent data tend to find more significant impact than studies using early period data as can be
seen from equation (2.6). The same goes with studies using repeated cross-section or panel data.
4. Type of Omitted Variable
In this section, we group papers according to the type of explanatory variables being
omitted. Specifically, we focus on three types of explanatory variables: (i) monetary price of
marijuana, (ii) other non-monetary price of marijuana apart from the decriminalization dummy
variable, and (iii) other drugs’ prices or proxies of other drugs’ prices. We do not pay attention
to the omission of the usual socioeconomic and demographic variables because most papers
already include them in their analyses.
Early literature in this area tends to exclude the monetary price of marijuana as one of the
explanatory variables because such information was frequently unavailable. Furthermore,
monetary price of marijuana is extremely difficult to quantify due to its illegal status. It usually
takes great undercover polices’ effort to get this price. Thus, early papers tend to use
decriminalization status as a way to partially control for the price of marijuana. Table 5 provides
a cross tabulation for categorizing papers by using two different criterions: inclusion/exclusion of
the monetary price of marijuana and type of data. There is one notable feature that we observe
from this table. Apart from the papers that use panel data, those that include monetary price of
marijuana as one of the regressors tend to find positive and significant impact of
decriminalization policy on marijuana smoking prevalence. This is true for all papers except
Williams (2004a) that discovers insignificant effect. On the other hand, studies that omit the
monetary price of marijuana are more inclined to give mixed results. That is, some papers
22
discover positive and significant impact while some other papers do not find any significant
impact.
The second type of explanatory variable considered in this paper is the non-monetary
price of possessing or using marijuana other than the decriminalization dummy variable. There
are other non-monetary price and legal dimensions to the marijuana law that some existing
studies include in their analysis. For example, the relative enforcement risk of dealing and using
marijuana (i.e. ratio of common crimes to number of officers), maximum/minimum jail time,
maximum/minimum fine, and conditional discharge provision. The main reason for including
these variables is the fact that there is variation in the enforcement level of the marijuana law
even across the decriminalized jurisdictions. Thus, including only the decriminalization dummy
variable may not entirely capture all aspects of the marijuana law and lead to misleading result.
Table 6 groups papers according to two criterions: inclusion/exclusion of at least one of the non-
monetary prices of marijuana and type of data. We spot the following notable feature. When the
data set has repeated cross-section or panel nature, the impact of decriminalization policy on
smoking prevalence is found to be positive and significant for papers that include at least one of
the non-monetary prices of marijuana. However, papers that exclude this type of variable tend to
give mixed findings. The discrepancy of these results may be explained by omitted variable bias
because oftentimes these variables are found to be statistically significant in the regression. For
example, Chaloupka, Grossman and Tauras (1999a) and Williams et al. (2004b) discover
significant effect of the fine for possession on the decision to smoke marijuana while Thies and
Register (1993) and Pacula (1998a, 1998b) find that stricter (more relaxed) enforcement level
decreases (increases) the probability of participating in the drug.
23
Finally, we sort papers according to whether or not they include other drugs’ prices or the
proxies of other drugs’ prices as the explanatory variables. Which drugs’ prices are included do
vary across papers. These variables may consist of price of alcohol, price of tobacco, state and
federal tax on beer, state and federal tax on cigarette, minimum drinking age, price of cocaine,
and price of heroin. The main reason for including these variables is to find the interrelationship
and to estimate the cross-price responsivenesses between marijuana and other drugs. Ultimately,
these papers try to conclude whether marijuana and other drugs are substitutes, complements or
independent from one another. Table 7 gives a cross tabulation for classifying papers according
to two criterions: inclusion/exclusion of at least one of the other drugs’ prices or proxies of the
other drugs’ prices and type of data. It is notable that papers that use repeated cross-section data
and include at least one of the other drugs’ prices or proxies of the other drugs’ prices tend to
find the impact of decriminalization policy that is positive and significant. On the other hand,
papers that exclude these variables are likely to give mixed results. These results appear to
corroborate our early analysis of single or joint consumption analysis (section 2.2).
Overall, it appears that there is greater tendency of discovering positive and significant
impact of decriminalization policy on smoking prevalence when these three types of explanatory
variables are used in the regression analysis. Next, we try to give our reconciliation as to why
this result may occur. We proceed by giving an algebraic expression for omitted variable bias
and how it applies to each omitted variable mentioned above.
Suppose the true marijuana smoking equation is
εηγα iiiii zdy +++=* . (4.1)
For ease of illustration, (4.1) has purged the effects of xi into the variable intercept α i . Suppose
the actual regression used is
24
υγα iiii dy ++=~~
* , (4.2)
in which it omits zi . In our case, zi may include (i) monetary price of marijuana, (ii) other non-
monetary price of marijuana apart from the decriminalization dummy variable, and (iii) other
drugs’ prices or the proxies of other drugs’ prices. The estimated coefficient
^~
γ , which is subject
to the omitted variable bias, can be expressed as
δηγγ^^^
^~
+= , (4.3)
where δ^
denotes )(
),(
dVar
zdCov. The first term on the right hand side of (4.3), γ
^
, is the effect of
decriminalization policy on marijuana smoking prevalence when there is no omitted variable
bias. The second term on the right hand side of (4.3), δη^^
, is the bias term. To determine the
direction of this bias, we need to look at the signs of η^
and δ^
. In what follows, we try to figure
out these signs for each of the omitted explanatory variable considered in this section.
4.1 Inclusion/Exclusion of the monetary price of marijuana
We start with omitted monetary price of marijuana (i.e. when zi represents the monetary
price of marijuana). From the top panel of Table 5, existing studies with monetary price of
marijuana often find the impact of decriminalization policy on smoking prevalence to be positive
and significant (i.e. γ^
> 0). For the bias term, the effect of marijuana price on smoking
prevalence is commonly found to be negative (i.e. η^
< 0), suggesting that there is a negative own
price responsiveness for marijuana. For δ^
, it may be commonly perceived that the jurisdictions
25
with decriminalization policy should be associated with lower monetary price of marijuana
because there is now lower legal and social costs associated with using it in these locations.
However, Damrongplasit, Hsiao and Zhao (2007) demonstrate in their summary statistics that the
mean price of marijuana is actually higher in the Australian decriminalized states than the non-
decriminalized states. One possible explanation for this finding is that decriminalization only
affects users with small quantities of marijuana possession, not for suppliers. Thus, the risk
and/or cost incurred on the suppliers do not change. This ultimately leads to no shift in the
supply curve and no lower price of marijuana. On the other hand, one can argue that the demand
curve has shifted upward due to lower risk, which in turn causes marijuana price to be higher in
decriminalized states. In sum, this argument suggests that δ^
> 0. When combining η^
< 0 and
δ^
> 0 together, the direction of the bias is determined to be negative (i.e. δη^^
< 0). In other
words, when there is omitted monetary price of marijuana, we find
{ {{ γδηγγ
^^^^^~
<+=+−+
. (4.4)
The effect of decriminalization policy on smoking prevalence is found to be lower than what it
would otherwise be if there is no omission of the monetary price of marijuana (i.e.
^~
γ < γ^
).
4.2 Inclusion/Exclusion of the non-monetary price of marijuana
Next, we turn to the omitted non-monetary price of marijuana: that is, when zi represents
the non-monetary price of marijuana. From the top portion of Table 6, papers using repeated
cross-section or panel data set with at least one of the non-monetary prices of marijuana tend to
find positive and significant impact of decriminalization policy (i.e. γ^
> 0). We attempt to
26
figure out the direction of the bias term in this situation. All the papers that incorporate non-
monetary price of marijuana in their analysis tend to find that stricter enforcement level such as
higher fine, longer jail sentence, and no conditional discharge usually decreases the likelihood of
using marijuana (i.e. η^
< 0). With regard to the sign of δ^
in (4.3), it is sometimes perceived that
decriminalized jurisdictions should be associated with more relaxed enforcement level than non-
decriminalized jurisdictions. However, that perception may not be entirely correct. As argued
by Pacula, Chriqui and King (2003), decriminalized US states do not necessary have lower
enforcement level compared to non-decriminalized US states. Pacula, Chriqui and King (2003)
has demonstrated in their paper that the mean of minimum fine is higher in decriminalized US
states and there is much smaller proportion of the US decriminalized states that allow conditional
discharge of marijuana possession for the first-time offender. The only factor that clearly
distinguishes these two types of states apart is that for decriminalized states possession of small
quantity of marijuana for personal consumption is not considered a criminal offence. This
policy’s differential is already captured by the decriminalization dummy variable. As a result, it
appears that the sign of δ^
is indeterminate depending on which enforcement variable and
jurisdiction is being considered in the study. The main implication of the ambiguous sign of δ^
is that we cannot exactly identify the direction of the omitted variable bias, hence cannot tell
from the algebra whether
^~
γ is greater than or smaller than γ^
.
4.3 Inclusion/Exclusion of other drugs’ prices or the proxies of other drugs’ prices
Finally, we consider the case where there is omitted price of other drugs or the proxies of
other drugs’ prices (i.e. zi represents price of other drugs or the proxies of other drugs’ prices).
27
From Table 7, papers using repeated cross-section data set and including at least one of the other
drugs’ prices or the proxies of other drugs’ prices tend to find the impact of decriminalization
policy on smoking prevalence that is positive and significant (i.e. γ^
> 0). If marijuana and other
drugs are substitutes, then we expect η^
to be greater than zero. As prices of other drugs
increase, it should generate more use of marijuana. If marijuana and other drugs are
complements, then η^
is expected to be less than zero. If there is no relationship among the
drugs, then η^
should be zero. The different studies have found that all three scenarios
mentioned above could happen. For example, marijuana and alcohol are found to be substitutes
in Cameron and Williams (2001), DiNardo and Lemieux (2001) and Pacula, Chriqui and King
(2003) for past year’s use; complements in Pacula (1998a, 1998b), Saffer and Chaloupka (1998),
and Williams et al. (2004b); independent in Zhao and Harris (2004), Thies and Register (1993)
and Pacula, Chriqui and King (2003) for past month’s use. With respect to marijuana and
cigarette, they are found to be complements by Cameron and Williams (2001) and Zhao and
Harris (2004) and to have no relationship by Pacula (1998a), Chaloupka et al. (1999b) and
Williams et al. (2004b). Thus, the sign of η^
is quite ambiguous. With regard to the second
component of the bias term, δ^
in (4.3), its sign is extremely difficult to determine. From our
knowledge, there is no previous study that attempts to find the relationship between
decriminalization and other drugs’ prices, making it hard for us to pinpoint the sign of δ^
. Thus,
in this case, the sign of δ^
is indeterminate. Combining both η^
and δ^
, we find
{ {{
?
^
?
^^^~
δηγγ +=+
. (4.5)
28
Because we cannot identify the direction of the bias in (4.5), we are unable to tell whether
^~
γ is
greater than or smaller than γ^
. Nevertheless, from our literature review in Table 7, it appears
that
^~
γ < γ^
.
5. Conclusion
Mixed findings of the impact of decriminalization policy on marijuana smoking
prevalence in the existing literature can be complicated for policy makers. It can lead to
uncertain policy making decision in term of what measures should be undertaken in order to
balance between minimizing health and safety hazards associated with marijuana use and
minimizing the social costs from attempting to control marijuana use. Given this problem, our
paper tries to identify any particular factor that can possibly explain these mixed results. To do
so, we group existing studies by type of data, type of model and type of explanatory variable
being omitted. We find that positive and significant impact of decriminalization policy on
marijuana smoking prevalence is often generated when the data set is of repeated cross-section
nature, covering overall population and/or from the 1990s-2000s time period; the econometrics
model is more sophisticated than the dummy variable approach; the monetary price of marijuana,
non-monetary price of marijuana, and/or prices of other drugs are included. We hope that our
summary can serve to establish a common basis for those interested in evaluating the impact of
decriminalization policy on marijuana use to better frame their analysis. We also hope that our
analysis would allow policy makers to evaluate and compare these results in a meaningful way to
formulate policies.
29
References
Cameron, L. and J. Williams (2001). Cannabis, alcohol and cigarettes: substitutes or complements? The Economic Record, 77, 19-34. Chaloupka, F., M. Grossman, and J. Tauras (1999a). The demand or cocaine and marijuana by youth. In The Economic Analysis of Substance Use and Abuse: An Integration of Econometric and Behavioral Economic Research, F Chaloupka, M Grossman, W. Bickel and H. Saffer (eds.), University of Chicago Press. Chaloupka, F., R. Pacula, M. Farrelly, L. Johnston, P. O’Malley, and J. Bray (1999b). Do higher cigarette prices encourage youth to use marijuana? NBER Working Paper No 6939. Damrongplasit, K., C. Hsiao, and X. Zhao (2007). Decriminalization and marijuana smoking prevalence: evidence from Australia. Working Paper. DiNardo, J. and T. Lemieux (2001). Alcohol, marijuana, and American youth: the unintended consequences of government regulation. Journal of Health Economics, 20, 991-1010. Hsiao, C. (1983). Identification. In Handbook of Econometrics, vol. I, Z. Griliches and M. Intriligator (eds.), Amsterdam: North-Holland. Johnston, L., P. O’Malley, and J. Bachman (1981). Marijuana decriminalization: the impact on youth 1975-1980. Monitoring the Future Occasional Paper 13. Pacula, R. (1998a). Does increasing the beer tax reduce marijuana consumption? Journal of Health Economics, 17, 557-585. Pacula, R. (1998b). Adolescent alcohol and marijuana consumption: is there really a gateway effect? NBER Working Paper No 6348. Pacula, R., J. Chriqui, and J. King (2003). Marijuana decriminalization: what does it mean in the United States? NBER Working Paper No 9690. Pacula, R., R. MacCoun, P. Reuter, J. Chriqui, B. Kilmer, K. Harris, L. Paoli, and C. Schaefer (2004). What does it mean to decriminalize marijuana? A cross-national empirical examination. JSP/Center for the Study of Law and Society Faculty Working Paper, University of California, Berkeley. Rosenbaum, P., D. Rubin (1983). The central role of the propensity score in observational studies for causal effects. Biometrika, 70, 41-55. Saffer, H. and F. Chaloupka (1995). The demand for illicit drugs. NBER Working Paper No 5238.
30
Saffer, H. and F. Chaloupka (1998). Demographic differential in the demand for alcohol and illicit drugs. NBER Working Paper No 6432. Thies, C. and C. Register (1993). Decriminalization of marijuana and the demand for alcohol, marijuana, and cocaine. The Social Science Journal, 30, 385-399. Williams, J. (2004a). The effects of price and policy on marijuana use: what can be learned from the Australian experience? Health Economics, 13, 123-137. William, J., R. Pacula, F. Chaloupka, and H. Wechsler (2004b). Alcohol and marijuana use among college students: economic complements or substitutes? Health Economics, 13, 825-843. Zhao, X. and M. Harris (2004). Demand for marijuana, alcohol and tobacco: participation, levels of consumption, and cross-equation correlations. Economic Record 80(251), 394-410.
31
Table 1: Cross tabulation between type of model and type of data
Type of data Type of model Cross-section Repeated cross-section Panel
No regressions Johnston, O'Malley and Bachman (1981), Insignificant
Johnston, O'Malley and Bachman (1981), Insignificant
Dummy variable approach
Damrongplasit, Hsiao and Zhao (2007), ATE = 3.7% and marginal effect = 6.7% Thies and Register (1993), Insignificant Pacula (1998a), Insignificant Pacula, Chriqui and King (2003), Marginal effect = 1.7% for past year use, and 1.8% for past month use
Cameron and Williams (2001), Marginal effect = 2% Williams (2004a) , Insignificant Saffer and Chaloupka (1995), Marginal effect = 6-7% for annual use and 4-5% for monthly use Saffer and Chaloupka (1998), Marginal effect = 4% for the full sample, 3% for white male non-Hispanic, 2% for Black, 19% for Asian, and 4% for Hispanic Chaloupka, Grossman and Tauras (1999a), Find insignificant effect for past month's participation equation and positive and significant effect for past year’s participation equation Chaloupka et al. (1999b), Marginal effect < 1%
DiNardo and Lemieux (2001), Insignificant Pacula (1998b), Marginal effect for unconditional demand = 0.254
Bivariate probit/logit
Williams et al. (2004b), Marginal effect = 1.32% for past month use, and 1.51% for past year use
DiNardo and Lemieux (2001), Insignificant
Multivariate probit/logit
Zhao and Harris (2004), Marginal effect ≈ 3%
32
Table 1: Cross tabulation between type of model and type of data (Continued)
Type of data Type of model Cross-section Repeated cross-section Panel
Sample selection model
Damrongplasit, Hsiao and Zhao (2007), ATE = 4% and marginal effect = 7.1%
Two-part model
Damrongplasit, Hsiao and Zhao (2007), ATE = 13.7%
Endogenous switching
model
Damrongplasit, Hsiao and Zhao (2007), ATE = 16.2%
Joint consumption
model
Zhao and Harris (2004), Marginal effect ≈ 3% Williams et al. (2004b), Marginal effect = 1.32% for past month use, and 1.51% for past year use
DiNardo and Lemieux (2001), Insignificant
Nonparametric model
Damrongplasit, Hsiao and Zhao (2007), ATE = 5.9-11.2%
Note: There are a few papers that study both the marijuana participation decision and the frequency of use decision. Williams (2004), Pacula (1998a), Chaloupka, Grossman and Tauras (1999a), and Chaloupka et al. (1999b) employ a two-step estimation where in the first step a binary probit or logit model is used to estimate the participation decision. Then, conditioning on using marijuana, an ordinary least square method or an ordered probit model is used to estimate the frequency of use in the second step. These two decisions are treated as independent from each other. Thies and Register (1993) and Pacula (1998b) also study both the use/no use and the frequency of use decisions by employing a Tobit model. Since the Tobit model can be estimated by Heckman two-stage estimation, we can view these two decisions as a two-step process. Our literature review focuses on the prevalence of marijuana use; thus, we categorize these papers’ econometric model as a binary choice model or a dummy variable approach.
33
Table 2: Categorizing papers by cross-section, repeated cross-section, and panel nature of the data
Impact of decriminalization policy on marijuana smoking prevalence Type of data Positive and significant effect Insignificant effect
Cross-section Damrongplasit, Hsiao and Zhao (2007), ATE = 3.7% and marginal effect = 6.7% Pacula, Chriqui and King (2003), Marginal effect = 1.7% for past year use, and 1.8% for past month use
Thies and Register (1993) Pacula (1998a)
Repeated Cross-section
Cameron and Williams (2001), Marginal effect = 2% Zhao and Harris (2004), Marginal effect ≈ 3% Saffer and Chaloupka (1995), Marginal effect = 6-7% for annual use and 4-5% for monthly use Saffer and Chaloupka (1998), Marginal effect = 4% for the full sample, 3% for white male non-Hispanic, 2% for Black, 19% for Asian, and 4% for Hispanic Chaloupka, Grossman and Tauras (1999a), Find positive and significant effect for past year's participation equation Chaloupka et al. (1999b), Marginal effect < 1% Williams et al. (2004b), Marginal effect = 1.32% for past month use, and 1.51% for past year use
Williams (2004a) Johnston, O'Malley and Bachman (1981) Chaloupka, Grossman and Tauras (1999a), Find insignificant effect for past month's participation equation
Panel Pacula (1998b), Marginal effect for unconditional demand = 0.254 Johnston, O'Malley and Bachman (1981) DiNardo and Lemieux (2001)
Note: Damrongplasit, Hsiao and Zhao (2007) employs many models in their study. However, since most papers use the binary choice model in their analyses, we only report the binary probit model’s result for Damrongplasit, Hsiao and Zhao (2007) to facilitate the comparison. This note is applied to all tables except Table 1.
34
Table 3: Categorizing papers by focus population of the data
Impact of decriminalization policy on marijuana smoking prevalence Type of data Positive and significant effect Insignificant effect
Youth or Young adult
Chaloupka, Grossman and Tauras (1999a), Find positive and significant effect for past year's participation equation Pacula (1998b), Marginal effect for unconditional demand = 0.254 Chaloupka et al. (1999b), Marginal effect < 1% Pacula, Chriqui and King (2003), Marginal effect = 1.7% for past year use, and 1.8% for past month use Williams et al. (2004b), Marginal effect = 1.32% for past month use, and 1.51% for past year use
Johnston, O'Malley and Bachman (1981) DiNardo and Lemieux (2001) Thies and Register (1993) Pacula (1998a) Chaloupka, Grossman and Tauras (1999a), Find insignificant effect for past month's participation equation
Overall population (all ages)
Cameron and Williams (2001), Marginal effect = 2% Zhao and Harris (2004), Marginal effect ≈ 3% Damrongplasit, Hsiao and Zhao (2007), ATE = 3.7% and marginal effect = 6.7% Saffer and Chaloupka (1995), Marginal effect = 6-7% for annual use and 4-5% for monthly use Saffer and Chaloupka (1998), Marginal effect = 4% for the full sample, 3% for white male non-Hispanic, 2% for Black, 19% for Asian, and 4% for Hispanic
Williams (2004a)
35
Table 4: Categorizing papers by timing of the data
Impact of decriminalization policy on marijuana smoking prevalence Type of data Positive and significant effect Insignificant effect
Data mostly covering the 1970s and
1980s
Chaloupka, Grossman and Tauras (1999a), Find positive and significant effect for past year's participation equation Pacula (1998b), Marginal effect for unconditional demand = 0.254
Johnston, O'Malley and Bachman (1981) DiNardo and Lemieux (2001) Thies and Register (1993) Pacula (1998a) Chaloupka, Grossman and Tauras (1999a), Find insignificant effect for past month's participation equation
Data mostly covering the 1990s and
2000s
Cameron and Williams (2001), Marginal effect = 2% Zhao and Harris (2004), Marginal effect ≈ 3% Damrongplasit, Hsiao and Zhao (2007), ATE = 3.7% and marginal effect = 6.7% Saffer and Chaloupka (1995), Marginal effect = 6-7% for annual use and 4-5% for monthly use Saffer and Chaloupka (1998), Marginal effect = 4% for the full sample, 3% for white male non-Hispanic, 2% for Black, 19% for Asian, and 4% for Hispanic Chaloupka et al. (1999b), Marginal effect < 1% Pacula, Chriqui and King (2003), Marginal effect = 1.7% for past year use, and 1.8% for past month use Williams et al. (2004b), Marginal effect = 1.32% for past month use, and 1.51% for past year use
Williams (2004a)
36
Table 5: Cross tabulation between inclusion/exclusion of monetary price of marijuana and type of data
Type of data Type of omitted variable
Cross-section Repeated cross-section Panel
Inclusion of monetary price of marijuana
Damrongplasit, Hsiao and Zhao (2007), ATE = 3.7% and marginal effect = 6.7% Pacula, Chriqui and King (2003), Marginal effect = 1.7% for past year use, and 1.8% for past month use
Cameron and Williams (2001), Marginal effect = 2% Williams (2004a) , Insignificant Zhao and Harris (2004), Marginal effect ≈ 3% Chaloupka, Grossman and Tauras (1999a), Find insignificant effect for past month's participation equation and positive and significant effect for past year’s participation equation Williams et al. (2004b), Marginal effect = 1.32% for past month use, and 1.51% for past year use
Exclusion of monetary price of marijuana
Thies and Register (1993), Insignificant Pacula (1998a), Insignificant
Johnston, O'Malley and Bachman (1981), Insignificant Saffer and Chaloupka (1995), Marginal effect = 6-7% for annual use and 4-5% for monthly use Saffer and Chaloupka (1998), Marginal effect = 4% for the full sample, 3% for white male non-Hispanic, 2% for Black, 19% for Asian, and 4% for Hispanic Chaloupka et al. (1999b), Marginal effect < 1%
Johnston, O'Malley and Bachman (1981), Insignificant DiNardo and Lemieux (2001), Insignificant Pacula (1998b), Marginal effect for unconditional demand = 0.254
37
Table 6: Cross tabulation between inclusion/exclusion of non-monetary price of marijuana and type of data
Type of data Type of omitted variable Cross-section Repeated cross-section Panel
Inclusion of non-monetary price of marijuana apart from
decriminalization dummy variable
Pacula, Chriqui and King (2003), Marginal effect = 1.7% for past year use, and 1.8% for past month use Thies and Register (1993), Insignificant Pacula (1998a), Insignificant
Chaloupka, Grossman and Tauras (1999a), Find insignificant effect for past month's participation equation and positive and significant effect for past year’s participation equation Williams et al. (2004b), Marginal effect = 1.32% for past month use, and 1.51% for past year use Chaloupka et al. (1999b), Marginal effect < 1%
Pacula (1998b), Marginal effect for unconditional demand = 0.254
Exclusion of non-monetary
price of marijuana apart
from decriminalization dummy variable
Damrongplasit, Hsiao and Zhao (2007), ATE = 3.7% and marginal effect = 6.7%
Cameron and Williams (2001), Marginal effect = 2% Williams (2004a) , Insignificant Zhao and Harris (2004), Marginal effect ≈ 3% Johnston, O'Malley and Bachman (1981), Insignificant Saffer and Chaloupka (1995), Marginal effect = 6-7% for annual use and 4-5% for monthly use Saffer and Chaloupka (1998), Marginal effect = 4% for the full sample, 3% for white male non-Hispanic, 2% for Black, 19% for Asian, and 4% for Hispanic
Johnston, O'Malley and Bachman (1981), Insignificant DiNardo and Lemieux (2001), Insignificant
38
Table 7: Cross tabulation between inclusion/exclusion of other drugs’ prices or the proxies of other drugs’ prices and type of data
Type of data Type of omitted variable Cross-section Repeated cross-section Panel
Inclusion of other drugs’ prices or the
proxies of other drugs’ prices
Thies and Register (1993), Insignificant Pacula (1998a), Insignificant Pacula, Chriqui and King (2003), Marginal effect = 1.7% for past year use, and 1.8% for past month use
Cameron and Williams (2001), Marginal effect = 2% Zhao and Harris (2004), Marginal effect ≈ 3% Saffer and Chaloupka (1998), Marginal effect = 4% for the full sample, 3% for white male non-Hispanic, 2% for Black, 19% for Asian, and 4% for Hispanic Chaloupka et al. (1999b), Marginal effect < 1% Williams et al. (2004b), Marginal effect = 1.32% for past month use, and 1.51% for past year use
DiNardo and Lemieux (2001), Insignificant Pacula (1998b), Marginal effect for unconditional demand = 0.254
Exclusion of other drugs’ prices or the
proxies of other drugs’ prices
Damrongplasit, Hsiao and Zhao (2007), ATE = 3.7% and marginal effect = 6.7%
Williams (2004a) , Insignificant Johnston, O'Malley and Bachman (1981), Insignificant Saffer and Chaloupka (1995), Marginal effect = 6-7% for annual use and 4-5% for monthly use Chaloupka, Grossman and Tauras (1999a), Find insignificant effect for past month's participation equation and positive and significant effect for past year’s participation equation
Johnston, O'Malley and Bachman (1981), Insignificant
