Decriminalization

Decriminalization - '9? (om-qmmnozro—L . Jars-r:-...

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Unformatted text preview: '9? (om-qmmnozro—L . Jars-r:- nan‘nmmmmmmmmmmm 5|mmimm—Lorom-srmmno:mdomg38$§$%gga$33ai§afiija mmmmmmmaa U1 54 _ H591 seal 59 i it: 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, two-part, 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 short-term 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 Era-les’ drags gritty casts (ti/film? gimme/y 9’5 f semen/3M Major zine). whirl e rm as-tmir‘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 law-abiding 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, amid-03' 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’J-HIM Ct. gear awarding geles andJRand Corporation 1, and Divisfim “C 99 trio 7 V so 61 62 as 64 as as 67 as as 70 71 72 73 74 75 75 7? re 79 so at 82 as 84 as as 87 as as so 9: s2 93 94 95 96 9'7 93 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 115 117 118 to fire same issue n" has ricer: {Miran-led QDOJ‘JQU'I-p-LDN—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 two-part model as its nested alternatives, called the binary probit, bivaiiate probit, and two-part 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(M|a) + (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 6 1 62 63 64 65 66 57 68 69 70 71 72 73 7'4 .75 76 77 78 79 80 5'1 82 83 a4 35 36 87 88 as so 9‘! 92 93 94 95 96 Q7 98 99 ion ' 101 102 103 104 105 106 107 108 109 110 111 1i2 113 114 115 116 117 118 ates M . O mm-qmmewM-A ...L_L_A._.._n_n._s_n...u.4 (coo-atonmhwm—‘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‘: dual-7301+ 80, (2-2) 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 reduced-form 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 two-part 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 ennui-nation the effect -. of decriminalization with M given by (2.7) and LUICOITB-s lated with (2.5). Wild 1) If 011,;31,oeo, fig, and density functions of 121 13-114 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 (2-3) and the average treatment effect of the treated (ATET) by [@0361 ifirx) — (Mao + £301)if(xld= lldx (2-9) 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 62 c 63 64 * 55 as 67 as so 70 71 72 73 74 75 re 4;": 7? ix- ra - 79 80 81 % 82 83 84 85 86 57 88 89 90 91 92 93 95 96 97 as 99 10b 101 102 103 104 105 106 107 105 109 110 111 112 113 114 115 116 117 11s CDCOKlmtJ'lvth-l mmmmmmmmmmhAh-ni: ##A-hwmm (.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 . limited-information 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 state-specific effects) are also used to predict residential choice as well as to provide exclusion restric— tions needed to identify-the 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 drop-and—collect questionnaire, 21 facevto-face personal inter- view, and a computer-assisted 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). State-level 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 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 7’6 79 so 81 82 as 34 85 as a? as as so 91 92 93 94 95 96 97 as 99 ' 1'00 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 CDCDNlmtJ'Ith-l 2s 29 so 31 32 33 34 35 as 37 38 39 40 ,4.1, 42 43 44 45 4s 47 48 4s 50 51 52 53 54 55 56 57 58 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 own-price 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 own-price 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 marijuana-smokers 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 effect-63' 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. 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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 @TiiyEiJJ-dilp(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 51 62 63 65 as 67 ea 69 7o 71 72 73 74 75 76 77 7.8 i 79 so 81 82 83 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 wmwmmhmma wmimimmmmmmm m—nommwmmnmfifigfiaiaiaiafifla A as 34 35 35 37 35 39 40 41 42 43 44 45 45 47 4a 49 50 51 52 53 54 55 55 57 55 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 0.05-0.45 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 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 .78 79 80 81 82 as 54 as as 07 as as 50 91 92 93 94 95 95 97 as 99 100 101 102 103 104 105 106 107 105 109 110 111 112 113 114 115 11s 1?? 11s EDOJ‘JO'JOl-hmM-J- bahmwmmmmwwmmm m—socomxlmm-c-wm—nomEBBEEBQBBEE-iQLEaiafija figdficfi 45-b- (0C0 50 51 52 53 55 55 57 58 59 Damrongplasit, Hsiao, and 21130: Decriminalization and Marijuana Smoking Prevalence multaneously, provided that the model’s assumptions are con— sistent with the data-generating 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, two-part model, sample selection model, and dummy variable model as special cases. The data-generating 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(ui|x;-) = 0, whereas under the alternative, H1 :E(u,-|x,-) 75 0. Testing E (uiIJCj) = 0 is equivalent to testing E {Mr-E (Minor (160} = 0- (6-1) 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[HE-k(_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] (6-2) 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 finite-sample 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 agar-3° = Pr(y,- = 1|d; = 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: 62 53 54 as 65 67 as 59 “Th 70 71 72 73 74 75 76 77 73 79 so _ 81 32 83 at; 85 as 87 as 89 90 91 92 93 94 95 96 97 93 99 71623077: 101 102 103 104 105 106 10? 108 109 110 111 112 113 114 115 116 117 118 coca-simm-Awmd mmmmmmmmmmeahaeaanae ' ,wmmmwm ’ mmummsmmflommammsumuoomumms‘d‘dflBBEfiRaEBBBlBe‘a-tn‘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 two-sided test by comparing Jn with the 1%, 5%, and 10% critical values from the bootstrap empirical dis— tribution. The two-sided 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; (6-9). then the model has the form of a generalized two-part 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 chi-square 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% (two-tailed test). 50 61 62 63 E4 65 66 67 68 69 70 71 72 73 74 75 76 .. 73...... 79 80 B1 82 83 B4 85 86 87 88 89 90 91 92 Q3 94 95 96 97 95 99 100 101 102 103 104 105 106 107 103 109 110 11 1 112 113 114 115 116 117 118 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 their helpful comments. [Received November 2006. Revised January 2009. ] REFERENCES ABCI (2002), “Australia Illicit Drug Report," discussion paper, Australia Bu- reau of Criminal Intelligence. ABS (2003a), “Consumer Price Index 14th Series: By Region, All Groups," Cat. No. 640101b, Australia Bureau of Statistics. (2003b), “Australian National Accounts: State Accounts,” Cat. No. 5220.0, Australia Bureau of Statistics. . .ACC..(2003), l‘Australialllicit Dmg_Rep,ort,’.’ Report 2001402, Ausu% Commission. Amemiya, T. 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(1993), “Decriminalization of Marijuana and the Demand for Alcohol, Marijuana, and Cocaine,” The Social Science Journal, 30, 385—399. “filliams, J. (2004), “The Effects of Price and Policy on Marijuana Use: What Can Be Learned From the Australian Experience?” Health Economics, 13, 123—137. Zhao, X., and Harris, M. (2004), “Demand for Marijuana, Alcohol and To- bacco: Participation, Levels of Consumption, and Cross—Equation Correla— tions,” Economic Record, 80 (251}, 394410. ' pm. NM, ,4] We when,ng and HM reference on pair; a, Am 9345;. For lino stowage/e filffiaéafi “Well im reference are [my/z 5/. line or. Please. insert an addi'iimflal relevance. l‘leorej‘f; (Roar), Australian governmcnf Swill??? 'efi'fimn‘ffi, aux/inn No.27 “PPM? fictieiin éeri'ee/ “Taming i’olfii dlfioflol and PW} Wolfe, Pliny: Mel beoffifls é—__.l so 61 E2 53 64 65 66 6? 68 69 70 71 72 73 74 75 7B 77 7a . 79 I. 80 a1 32 83 84 as 85 87 as 89 go . 91 92 93 94 95 95 97 98 .99 as 101 102 103 104 105 106 107 108 109 110 1 1 1 112 113 114 115 116 117 118 mummhmma fi 12 13 14 15 16 17 18 19“ 20 21 22 23 24 25 26 27 28 29 30 31 32 33 35 as 37 as 39 4:) 4i 42 43 44 45 4s 47. 4a 49 50 51 52 53 54 55 55 57 58 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! 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