Demand for Marijuana, Alcohol and Tobacco: Participation, Frequency and Cross-Equation Correlations

Transcription

1 Demand for Marijuana, Alcohol and Tobacco: Participation, Frequency and Cross-Equation Correlations Xueyan Zhao Mark N. Harris Department of Econometrics and Business Statistics Monash University Australia July 2003 Abstract This paper considers recreation consumption of marijuana, alcohol and tobacco, using the most recent micro-unit data from the National Drug Strategy Household Surveys in Australia. Previous studies have focused on solely the binary choices of participation of particular drugs in isolation. We extend this research in two directions. Firstly, we consider not only participation, but also the frequency of consumption. The results indicate that some factors may have different effects on the two decisions of participation and frequency. Secondly, we allow for the fact that these decisions across different types of drugs are very likely to be inter-related. JEL Classification: C3, D1, I1 Keywords: Drug consumption, discrete data, multivariate probit, sequential outcomes, ordered models, multivariate ordered probit We wish to thank Ben Machado and Jennine Boughton of ABCI and Steve Whennan from ABS for supplying the data, Ken Clements for helpful discussion, and Alastair Boast, Shiguang Ma and Glenn Bunker for research assistance. Financial support from the ARC (large grant # A ) is also kindly acknowledged. 1

2 1 Introduction and Background Consumptions of marijuana, alcohol and tobacco have long been identified as associated with a range of adverse health, both physical and psychological, and social effects (see, for example, Cleeland 1989, Model 1993). Significant amounts of public funds are being spent by many governments on dealing with the consequences and on educational programs aimed at reducing participation and consumption, particularly in the cases of alcohol and tobacco. Much debate has surrounded the use of governments coercive power in influencing drug consumption through public policies such taxation and legislation (see, for example, Dave and Kaestner 2002, Glied 2002). For instance, some have imposed regulations restricting or banning tobacco advertising. Marijuana consumption is slightly different. While still an illicit drug in Australia, the consumption of marijuana among a significant proportion of Australians has persevered, and the price of marijuana has declined by almost 40% over the last decade (Clements 2002). The trend towards hydroponic cultivation has prevailed in recent years which has significantly increased the productivity and product quality. Recent surveys indicate that some 34% of the population in Australia aged fourteen and over have used marijuana, and 14% have reported regular use of at least once a year (see Section 2). According to an estimate by Clements and Daryal (1999), the expenditure on marijuana in Australia is almost twice of that on wine. During 2000/01, Australian law enforcement seized almost ten thousand kilograms of marijuana, almost twice of the seizure in the previous year (ABCI 2002). 2

3 Commonly considered a soft drug, marijuana and its related drug policies have continued to be the centre of debate in western societies. The issue is a complex one with health, social, political, as well as economic dimensions. One aspect of the discussion concerns whether legal sanction is the best approach to reduce the use of the drug, or whether marijuana market should be regulated just as the markets for alcohol and tobacco. Indeed, while the current marijuana market price is way below the production costs, the price premium has been taken by the underground dealers. Substantial tax revenue for the government would be generated if it were regulated. No doubt, there are many policy issues regarding the taxation of the drug and the potential economic implications to other related drug industries (Clements and Zhao 2003). Economic analysis will contribute to the discussion. Separately, there is an exhaustive literature on the consumption of tobacco, alcohol and, to a lesser extent, marijuana. However, few empirical studies acknowledge the potential intrinsic crosscommodity correlation when a consumer makes decisions regarding the consumption of all three drugs. According to recent survey data from Australia (see Table 2, Section 2), while the probability of an individual participating in marijuana consumption is estimated as 14%, 34% of the tobacco smokers and 17% of the alcohol consumers use marijuana. This suggests that these three drugs are likely to be closely related commodities. Thus, studies that consider the consumption of only one of these goods in isolation could lose important cross-commodity correlations and result in erroneous conclusions. Indeed, there has been empirical evidence that alcohol and tobacco are complementary goods. One would also expect mar- 3

4 ijuana consumption to be closely related to both that of alcohol and tobacco, though, apriori, directions of the relationships are not immediately obvious. Using aggregated consumption data in Australia, Clements and Daryal (1999) show that marijuana is a likely substitute for each of the three alcoholic drinks of beer, wine and spirits. Cameron and Williams (2001) show with unit-record data that participations in tobacco, alcohol and marijuana are closely related, with marijuana being substitute for alcohol and complement to cigarette, and alcohol and cigarette being complements. However, while the responsiveness of participation in one drug with respect to changes in other drug prices are examined in an individual s decision, the correlation across decisions of different drugs for the same individual is often ignored. This paper reports an investigation into the most recent data from the Australian National Drug Strategy Household Surveys (NDSHS 2001) regarding the household consumption of marijuana, alcohol and tobacco. While there have been many studies on tobacco and alcohol consumption in Australia (for example, Bardsley and Olekalns 1999), studies on marijuana demand in Australia are limited. This is due to the illicit nature of marijuana consumption. Unlike legal commodities such as tobacco and alcohol, very limited data are available for marijuana market. Traditional demand analysis of the economic relationship among different drugs encounters difficulty due to the absence of published quantity and price data for marijuana. The only available source of information of a large scale on marijuana usage among the Australian population is the NDSHS surveys. Clements and Daryal (1999) has used the consumption frequency data from NDSHS to estimate the sizes of the marijuana 4

5 markets between 1988 and Using the estimated data of aggregated quantity for marijuana consumption and the published aggregated data for beer, wine and spirits, they have also estimated a demand system for marijuana, alcohol and tobacco. Cameron and Williams (2001) is the only known study that has used the unitrecord data from the Australian survey. They used data from the four surveys between 1988 and 1995 to estimate a binary choice model explaining the participations of the three drugs, with each drug equation estimated independently. The current paper will extend the existing studies in this area in several ways. First, we consider the participations of the three drugs jointly by estimating a multivariate probit model (MVP), recognising the correlations between the decisions of participation of the three drugs for the same individual and how these decisions relate to changes in drug prices, drug policies in the state of residency, and other social, economic and demographic characteristics for the individuals. Second, we extend the focus from the participation of the drugs to the frequencies/levels of consumption. A multivariate ordered probit model (MVOP) is developed and estimated for the Australian data to study the relationship between an individual s frequencies/levels of consumption of the three drugs and a set of explanatory variables, recognising the correlations across equations in an individual s decisions. Third, we consider the sequential nature of an individual s decisions of whether to use a drug and how often/much to use it by estimating the sequential models. It is reasonable to speculate that the two decisions, of participation and level of consumption, may be related to different explanatory factors. For example, a non-smoker of marijuana may not choose to become a 5

6 smoker because of a decrease in marijuana price while it is still illegal, but a monthly smoker maybe more likely to change to a weekly or daily smoker in response to a price decrease. Finally, our study extends the existing studies by using the three most recent NDSHS surveys of 1995, 1998 and Marijuana price data for individual states and territory are obtained fromtheaustralian Bureauof Criminal Intelligence (ABCI 2002) and the Australian Crime Commission (ACC 2003), which are based on information from police undercover purchases. Given the study is somewhat data driven, the paper will proceed with a description of the data and some descriptive discussion in Section 2. The suite of econometric models and results are presented in Section3. Inparticular, themultivariate probit (MVP) model for participation analysis is described and results discussed in Section 3.1. The multivariate ordered probit (MVOP) model analysing the frequencies/levels of consumption is presented, and results discussed in Section 3.2. The sequential models for the two decisions of participation and level of consumption are estimated next in Section 3.3. Implications of results and limitation are discussed in the final section. 2 The Data There have been seven surveys since 1985 conducted through the Australian National Drug Strategy Household Survey (NDSHS 2001). The surveys collect information from individuals aged 14 and over on drug awareness, attitudes and behavior. The questions involve alcohol, tobacco, marijuana, heroin, cocaine, and other prescription 6

7 or illegal drugs. The first survey in 1985 only has around 2,500 respondents, whereas in the 2001 survey over 26,000 individuals are involved. The questions are also becoming more comprehensive in later surveys. Various measures have been put in place in the surveys to ensure confidentiality and to reduce under reporting. In this paper, data from the three most recent surveys of 1995, 1998 and 2001 are used which involve over 40,000 individuals. The information about an individual s consumption of each drug is collected through questions such as Have you ever used marijuana (or cannabis) and How often do you now smoke cigarettes, pipes or other tobacco products. Although questions are not designed exactly the same in the three surveys involved in this study, a discrete choice variable Y h (h = M,A and T ) is compiled (see Appendix) for each drug from various questions in each survey that represents the frequency/level of an individual s participation in consumption. The number of individuals in different frequency/level categories for each of the three surveys and for the three surveys combined, together with the associated proportions are given in Table 1 for each of the three drugs. As indicated in the first line of the marijuana section in Table 1, the proportions of the surveyed samples who smoke marijuana at least once a year are 14.1% for 1995, 19.3% for 1998, and 12.7% for While the proportion of regular marijuana users are highest in 1998 among the three surveys, overall there has been a relatively stable proportion of around 15% since the 1985 survey (see, for example, NDSHS 2001). Data for tobacco consumption in Table 1 show that the percentage of cigarette smokers has reduced from 27.6% in 1995 to 22.0% in 2001 (first line in the tobacco section). 7

8 Table 1: Summary Of Consumption Frequencies a Combined N % N % N % N % Tobacco Frequency Non-smoker Less than daily Daily, less than 20/day Daily, more than 20/day Total Alcohol Frequency Non-drinker Less than weekly days a week > 4 days a week Total Marijuana Frequency Non-smoker Once or twice a year Every few months Once a month Once a week or more Everyday Total a Based on data from NDSHS (1995;1998; and 2001). Missing observations for each drug are excluded in calculations. The proportion of daily smokers has reduced even more significantly, from 24.2% to 18.3% which is a reduction of over 24%. Note that the real price for tobacco has increased by over 40% during the same period between 1995 and 2001 (see ABS 2003a, ABS 2003b). It would be interesting to know how the tobacco price increase and the educational champaigns against smoking cigarettes have contributed to the observed decrease in tobacco participation. Finally, turning to the summary of the individuals frequencies of alcohol consumption, the percentage of alcohol drinkers has increased slightly: from 80.1% in 1995 to 82.7% in 1998 and 83.0% in Again, this modest increase corresponds with a more significant increase in the percentages of more regular drinkers; the proportion of people who drink more than 4 days a week has changed from 16.7% in 1995 to 23.7% in The real alcohol price during this period has in fact increased 8

9 moderately (see ABS 2003a, ABS 2003b). While the increase in the proportion of more regular drinkers may also be related to income increase and changes in other recreational drug markets as later examined in this paper, the change in the perceived health benefit of daily consumption of red wine of small amount may also be a contributing factor. There is evidence at the aggregated level that there has been an increase in wine consumption in Australia and a shift to red and premium wine (see Wittwer and Anderson 2002, Zhao, Anderson, and Wittwer 2003). Table 2 presents joint summary information on individuals participation across all three drugs, based on the combined sample of the 1995, 1998 and 2001 surveys. It is interesting to compare these participation figures to those given in Cameron and Williams (2001) based on the four surveys between 1988 and While the average marijuana participation rate has hardly changed from the level of 14% over the two periods, the participation rate for tobacco has decreased from 31.7% during to 23.7% during , which represents an over 25% reduction in participation. Participation in alcohol consumption has shown a slight increase from 81.1% to 82.9% during the two periods. Note in Table 2 that 7.7% of the population take all three drugs, and 14.7% of the population take none of them. These percentages are 8.7% and 15.6% in comparison for the period before 1995 from the Cameron and Williams (2001) study. Some estimated unconditional and conditional probabilities for participation are calculated from Table 2 and presented in Table 3 to highlight the correlation across an individual s participation across the three drugs. For example, while 23.7% of the general population 9

10 Table 2: Summary of Participation in Tobacco, Alcohol and Marijuanas a Percent Joint T A M participating in: Probability (marginal) (marginal) (marginal) T only A only M only T and A only T and M only A and M only T and A and M None 14.7 Total a Measured as percentages of total respondents based on samples from NDSHS (1995;1998; and 2001) involving over 40,000 individuals. Missing observations are excluded in calculations. Table 3: Conditional and Unconditional Participation Probabilities a P (.) P (. YBI M =1) P (. YBI A =1) P (. YBI T =1) Marijuana Alcohol Tobacco a Calculated from Table 2 are estimated as tobacco smokers, the probabilities of an individual being a tobacco user within the alcohol drinking population and the marijuana smoking population are higher at 25.9% and 56.3% respectively. Similarly, figures in Table 3 show that the chance of an individual participating in marijuana or alcohol consumption is much higher than that for the general population if we know he/she is taking one of the other drugs. The surveys also collect social, economic and demographic information for each respondent. In this paper, age, gender, marriage status, state of residence (and the associated legal status of marijuana consumption), work status, level of education, whether a person resides in a capital city, whether speaks mainly English at home, whether has dependent children, whether of Aboriginal and Torres 10

11 Island origin, and real personal income have been considered as explanatory factors that may be related to the participation and the frequency of an individual s drug consumption. The marijuana prices are obtained frominformation providedby the Australian Bureau of Criminal Intelligence (ABCI 2002) and the Australian Crime Commission (ACC 2003). These data were collected quarterly from each police service and are based on information supplied by covert police units and police informants. They include detailed reports of prices of marijuana in the forms of leaf, head, hydroponic, skunk, mature plant, hash/resin, or oil and purchased in various quantities. Clements (2002) summarized the data into four annual price series from 1990 to 1999: prices for head or leaf, and purchased in grams or ounce. According to data from ND- SHS (2001), these are the most popular form of purchases. In this paper, these four prices are updated to 2001 and are then weighted averaged into a single price for each year and each state, according to the proportions of the respondents forms of purchases. Consumer price indexes for tobacco and alcoholic drinks for individual states are obtained from the Australian Bureau of Statistics (ABS 2003b). Consumer price index by states for all groups, which are used to deflate income and prices, are also obtained from ABS (ABS 2003a). Annual average prices are obtained by averaging the quarterly prices. All variables in the paper are definedintheap- pendix. Summary statistics for all variables are given in Table 4. 11

12 Table 4: Summary Statistics a Variable Mean Std.Dev. Minimum Maximum Cases Dependent Variables Y T Y A Y M YBI T YBI A YBI M Y 1 T Y 1 A Y 1 M Explanatory Variables LNAGE MALE MARRIED NSW VIC QLD SA TAS ACT NT WA DECRIM WORK STUD UNEMP OTH CAPITAL ATSI ENGLISHS DEGREE DIPLOMA YR SCHOOL NOQUALS DEPCHILD LNPT LNPA LNPM LNINC a Calculated from the combined sample of 1995, 1998 and 2001 (NDSHS 2001) 12

13 3 The Econometric Models and Results 3.1 A Multivariate Probit Model (MVP) for Participation Analyses A useful starting point is to define the underlying latent propensities (Yh ) for consumption of each of these three goods. These underlying propensities are related to the individual s observed characteristics and related variables in the drug markets (X h ), and other unobserved characteristics (ε h ), with unknown weights (β h ) for the former. Assuming a linear relationship, the population regression function is Y h = X 0 hβ h + ε h, (h = M,A and T ) (1) with h = M, A and T, corresponding to marijuana, alcohol, and tobacco, respectively. In its simplest form, equation (1) translates itself into a binary Probit, or participation, equation under the following mapping from the latent variable to its observed realisation: ( 0 if Yh YBI h = 0 1 if Yh > 0 (h = M, A and T ) (2) Assume ε h (h = M,A and T ) are distributed as trivariate normal with mean vector of zero and covariance matrix Σ with diagonal elements equal to 1 and off diagonal elements equal to the correlation coefficients between each pair of the three drugs; that is, (ε M, ε A, ε T ) 0 MVN (0, Σ), where 1 ρ MA ρ MT Σ = ρ MA 1 ρ AT ρ MT ρ AT 1 (3) 13

14 Note we have assumed Var(ε h ) 1(h = M,A and T ), asthe size of the variance for the disturbance term cannot be identified foreachprobitequation(greene2003). Thismodelistermeda Multivariate Probit Model (MVP). Indeed,suchaformulationformedthebasisoftheCameron and Williams (2001) study. However, they have assumed that ε h (h = M,A and T ) independently follow univariate normal distributions, with ρ hk =0(h, k = M, A and T ; h 6= k). Given the potential complementarity or substitutability among these goods, and that the individuals in the sample are the same across equations, it is highly likely that the error terms of these equations are correlated. The more general specification given in Equation (3) allows for the correlation of disturbances for the same individual across decisions about different drugs, which embody unobserved characteristics. The multivariate probit model is estimated via maximum likelihood method. As the probabilities that enter the likelihood are functions of high dimensional multivariate normal distributions, they are simulated using the GHK algorithm (see, for example, Greene 2003). Before applying the model to our large set of drug data, we conduct an experiment on a simulated dataset, to examine how recognising the cross equation correlations would impact on the estimation results. A sample of 2,000 individuals are generated from three probit equations that are correlated with predetermined correlations coefficients. These are used to estimate the three probit equations independently first as three univariate probit (UVP) models and then jointly as correlated trivariate probit (MVP) models. The assumed model, together with the estimated coefficients, t-statistics, and the percentage errors of the estimates for both specifications 14

15 Table 5: Summary Statistics UVP MVP Explanators true coeff. t-value % Bias coeff. t-value % Bias constant x constant x constant x ρ 1, ρ 1, ρ 2, are given in Table 5. While there is on average a 4.1% error for the estimates for the six coefficients of the three probit equations when the correlations across equations are ignored, the average error reduces by almost half to a 2.7% when the correlations are recognised. While the UVP assumes zero correlation across the error terms of the three equations, the MVP yields rather good estimates for the underlying correlation coefficients, with point estimates of 0.90, 0.21 and 0.56 for the true values of 0.9, 0.1 and 0.5. All estimates are statistically highly significant, with the MVP estimates having slightly higher t-values. The MVP model is then estimated using the combined data from the 1995, 1998 and 2000 surveys, involving up to 40,000 unit-record observations. Results from the MVP model, together with the estimates from a univariate specification are summarised in Table 6. Comparing the two sets of results, although they look rather close, the estimated marginal effects, for example, for all coefficients show average differences of 8%, 11% and 16% for tobacco, alcohol and marijuana equations respectively. As suggested in the Monte Carlo 15

16 study in Table 5, these could represent significant reduction of estimation errors, almost reducing half of the estimation bias in the simulated example. Also note that the estimated correlation coefficients, with point estimates of 0.20, 0.50 and 0.36 among the error terms of the three drug equations, are highly significant for all three cases (t-value >14). This indicates, as expected, a strong correlation among the decisions of an individual with regard to the participations in the three drugs. Another note before we discuss the results is regarding the marginal effects. There are many marginal effects that can be calculated for the MVP model, depending on which ones are of interests. For example, we can evaluate marginal effects to the joint probabilities such as P (YBI M =1,YBI A =0,YBI T =1), or to the conditional probabilities such as P (YBI M =1 YBI T =0,YBI A =1), or to the unconditional (or marginal) probabilities such as P (YBI M =1) and P (YBI T =1). Without special interests to any particular joint or conditional probabilities, we have reported the marginal effects to the marginal probabilities in Table 6. In other words, the marginal effects for the MVP model reported in Table 6 relate to the effects on the participation probabilities for each drug in response to unit changes of individual explanatory variables, assuming no prior information as to whether the person participates in the consumptions of the other two drugs. For each continuous explanatory variable, the marginal effect relates to an absolute change in the probability of participation in a particular drug in response to one unit increase in the explanatory variable, while for each dummy variable it represents the change in probability of participation when the dummy variable changes from 0 to 1, all evaluated at the means of all ex- 16

17 Table 6: Indepedent (UVP) and Correlated (MVP) Probit Results UVP MVP Tobacco Coefficients t-value ME Coefficients t-value ME Constant LNAGE MALE MARRIED DECRIM WORK STUD UNEMP CAPITAL ATSI ENGLISHS SCHOOL DEGREE DIPLOMA YR DEPCHILD LNPA LNPM LNPT LNINC Alcohol Constant LNAGE MALE MARRIED DECRIM WORK STUD UNEMP CAPITAL ATSI ENGLISHS SCHOOL DEGREE DIPLOMA YR DEPCHILD LNPA LNPM LNPT LNINC Marijuana Constant LNAGE MALE MARRIED DECRIM WORK STUD UNEMP CAPITAL ATSI ENGLISHS SCHOOL DEGREE DIPLOMA YR DEPCHILD LNPA LNPM LNPT LNINC ρ AT ρ MT ρ MA

18 planatory variables. Note however that we have scaled all of the continuous explanatory variables (see details in the Appendix) to aid convergence of the calculation, and as a consequence care is needed in interpreting the implications of these marginal effects. So what do the results tell us about the impacts of various demographic, social and economic factors on the participation probabilities, concentrating on the MVP results? We will look at the price and income effects first, bearing in mind that the price and income variables are scaled down in the estimation as the logarithms of real prices or real income then divided by 10. The marginal effects in the marijuana equation show that marijuana participation negatively responds to own price and tobacco price changes with high statistical significance (p-value<0.01); participation probability for marijuana decreases by 0.69% for a 10% increase in marijuana price and decreases by 0.48% for a 10% increase in tobacco price, indicating a complementary relationship between the two drugs. This result is hardly surprising given that many participants roll the two together to smoke. For a total population of 15 million aged 14 and above, these marginal effects translate into reductions of 104,000 and 72,000 thousand marijuana participants respectively for the 10% price increases. The coefficient for the alcohol price is not statistically significant at the 5% significance level, though with a p-value of 0.41 a substitution relationship is indicated with an estimated increase of 0.52% in the marijuana participation probability for a 10% increase in alcohol price. The income coefficient indicates a negative effect with high statistical significance, implying a reduction of 0.12% participation probability for a 10% increase in personal income. Turning to the tobacco and alcohol equations, both participation 18

19 probabilities are shown to be income responsive with very high statistical significance, though having opposite directions. For a 10% increase in income, there is a 0.42% lower chance for participation in tobacco but a 0.44% higher probability for engaging in alcohol consumption. This is consistent with the general perception that smoking has a negative income effect but drinking has a positive income effect. The tobacco participation is shown own price responsive statistically, with a estimated reduction of 1.34% probability for a 10% increase in tobacco price. This is an equivalent of 13 less smokers for every 1,000 people. Tobacco participation is not statistically significant to changes in the other two drug prices, though at a 37% significance level, marijuana is shown a complement in participation. Interestingly, the alcohol participation is shown not to be responsive to own price changes. As discussed in the data section, while the participation rate has increased over the recent years, the overall alcohol price has also increased. Recent research and publicity promoting the positive health effect of frequent wine drinking may have contributed to this result. The aggregation of the three rather different alcoholic types would have also complicated the results, as different trends have been observed regarding the prices and consumptions of beer, wine and spirit. However, the aggregated alcohol participation has shown negative responsiveness to marijuana price changes at 5% significance level. In order to compare our results to the previous studies (especially those in the Cameron and Williams (2001) study) we have converted the marginal effects to the price and income elasticities in Table 7. These figures indicate the percentage changes in the participation probabilities in response to one percent change in price or 19

20 income. Comparing these elasticities, estimated with nearly 40,000 observations from the survey data between 1995 and 2001, to those from Cameron and Williams (2001) (Table 7) which used nearly 10,000 observations between 1988 and 1995, there are some similarities and differences. While our results do not show significant own price response in the alcohol participation due to the possible reasons discussed above, both studies have found significant own price responsiveness in the participation of marijuana and tobacco. While the tobacco own price elasticities are of similar magnitudes of versus -0.56, our marijuana participation elasticity of is much smaller than that of in the Cameron and Williams (2001) study. With regard to the cross-price effects, while both have found some evidence in marijuana and tobacco being complements in participation, our results show some evidence of marijuana being complement for alcohol (with cross price elasticity of -0.04) whereas Cameron and Williams (2001) found evidence of alcohol being substitute for marijuana (with cross price elasticity of 2.9). Note the asymmetry in the cross-price effects in both studies where no cross equation restrictions are imposed. Lacking of observations in the actual quantities of consumption in this kind of micro unit data, it is difficult to impose conventional economic regularity conditions. No significant cross price relationships are found between tobacco and alcohol participation, while Cameron and Williams (2001) have found evidence of complementarities between the participation of the two drugs. In fact, at the 15% significance level, our results for the alcohol equation seem to show a substitution relationship between alcohol and tobacco. The difference in our results, apart from the difference in the data used, may also be partly due to the 20

21 Table 7: Price and Income Elasticities for Participation a,b YBI M YBI A YBI T ZH CW ZH CW ZH CW PM PA PT INC a Indicates significance at 5% and at 15% b ZH denotes current study, CW Cameron and Williams (2001) fact that we have included the income variable in the study. While no income elasticities are estimated in the Cameron and Williams (2001) study, our results indicate significant income effects for all three drugs, with marijuana and tobacco participation being negatively income responsive and alcohol participation being positively related to income level. Turning to the impact of marijuana decriminalization, the decriminalization dummy variable is not statistically significant at 5% level but is significant at 20% level in all three equations. In particular, other factors being equal, the data seem to suggest lower participation probabilities for marijuana and tobacco but higher particiption probability for alcohol for the three decriminalised states. In comparison, using earlier data and capturing the initial effect of decriminalization in South Australia which is the only state included in their decriminalization variable, Cameron and Williams (2001) find a significant higher participation probability for marijuana for SA residents. Our results seem to suggest that after nearly ten years of changes in the criminalization status in the states of South Australia, Northern Territory and Canberra, the initial effect of this jurisdictional difference hasdieddownovertheyears,andpeople in these states are now even less likely to participate in marijuana 21

22 consumption. The participation probabilities are also shown to be related to many individual characteristics. Males have 5.2%, 3.5% and 3.1% higher probabilities to participate in marijuana, tobacco and alcohol consumption respectively. Married or partnered individuals have 6.8%, 6.7% and 1.0% lower probabilities to be a marijuana user, a tobacco smoker and alcohol drinker respectively. Given our specification of age as a continuous variable, overall being older reduces the chance of participating in all three drugs. In terms of an individual s main occupation, relative to the group of retired and home makers, working and unemployed people have high probabilities and students have lower probabilities to participate in all three drugs; for example, unemployed people have 8.8% high chance to use marijuana and 12.4% high chance to smoke tobacco than retirees and home makers, other factors being equal. People in the capital cities are more likely to use marijuana, with a 1.7% higher probability, but there is no statistical difference in the tobacco and alcohol participation between country and city folks. People who use English as the main language at home have significantly higher chance of using all three drugs, with 7.8%, 6.9% and 20.0% higher probabilities than the English speakers for participation in marijuana, tobacco and alcohol respectively. No evidence is found in the participation rate between people from Aboriginal and Torres Strait Island background for any of the three drugs. After controlling the marriage status and other factors in the model, having dependent children or not does not seem to make a difference in the participation of marijuana, but at 10% significance level, it seems to increase the probability of smoking cigarette by 1.9% and decrease the 22

23 chance of drinking alcohol by 0.8%. Finally, turning to the effects of education, in comparison to people with less than Year-12 education, all other groups have significantly lower chances of smoking tobacco, with people of Year-12, diploma and degree qualifications and people still at school having 4.9%, 2.8%, 12.6% and 17.8% lower participation probabilities. Education also have significant impacts on alcohol participation, but seem to have opposite effect on that of tobacco; more educated people seem to have higher chance of participating in alcohol consumption than people with lower than Year-12 qualification, though the good news is that children who are aged14andabovebutwhoarestillstudyingatschoolhavea16.9% lower probability of drinking. In comparison with the lowest educated groups, qualification seems to have a less significant and less straightforward impact on marijuana participation; while children still at school have a 8.6% lower probability and diploma or trade certificate holders have a 1.5% higher probability, the Year-12 graduates and the tertiary degree holders have no significant difference in the participation of marijuana. 3.2 A Multivariate Ordered Probit Model (MVOP) for Consumption Analysis Astheprobitmodelinequation(2)isonlyconcernedwiththeparticipation of a drug, no distinction is made between, for example, those individuals who drink once a year, and those who consume multiples of the recommended daily intake of alcohol. That is, in attempting to answer the question are alcohol, tobacco and marijuana compliments or substitutes?, withtheprobitspecification, no information can be revealed as to how an individual changes 23

24 from less frequent consumption to more frequent consumption due to price changes. In this section, a multivariate ordered probit model is specified to jointly study the changes in consumption frequencies of the three drugs. Relaxing the assumption dictating that frequent and infrequent users be treated in exactly the same manner, whilst retaining the underlying latent propensities of equation (1), leads to the following mapping of the latent to the observed variable: 0 if Yh 0 1 if 0 <Yh µ h1 Y h = 2 if µ h1 <Yh µ h2 (h = M,A,and T ).. J h if µ h,jh 1 <Yh, (4) where the µ s are cut-off points, or boundary parameters, and Y h =0, 1,...,J h are ordered outcomes, which in our example represent the frequency of consumption for drug h, withy h =0for non-participation and Y h =1,...,J h forlessfrequenttomorefrequent participation with ascending order. Details for the coding of frequencies of Y h (h = M,A,and T ) are given in the Appendix. Under the assumption that the ε h (h = M,A and T ) independently follow standard normal distributions and the correlation matrix Σ is an identity, three standard Ordered Probit Models result. Dropping the subscript for ease of notation, the associated proba- 24

25 bilities (Maddala 1983) are Pr (Y h =0 X hi )=Φ( X 0 hi β) Pr (Y h =1 X hi )=Φ(µ 1 X 0 hi β) Φ ( X0 hi β) P i = Pr (Y h =2 X hi )=Φ(µ 2 X 0 hi β) Φ (µ 1 X 0 hi β). Pr (Y = J h X hi )=1 Φ µ Jh 1 X 0 hi β, (5) where Φ(.) is the cumulative distribution function of univariate standard normal distribution. We label this model univariate ordered probit (UVOP). However, just as in the participation equations, the three equations given in (1) and (4) are concerned with the consumption frequencies of related products by the same individuals. Therefore a more general specification is a multivariate ordered probit (MVOP) that allows for non-zero correlations across the error terms of different equations, with a correlation matrix Σ given in (3). Unfortunately, this more general specification significantly enhances the complexities of estimation. Suppose the trivariate normal cdf is denoted Φ 3 (w 1,w 2,w 3, Σ) =Pr W 1 <w 1,W 2 <w 2,W 3 <w 3 (W 1,W 2,W 3 ) 0 MVN (0, Σ) ª. (6) To construct the log-likelihood function, we need the probabilities of all combinations of three dimensional outcomes Pr (i, j, k) = Pr (Y M = i, Y A = j, Y T = k)(i =0,...,J M ; j =0,..., J A ; k =0,..., J T ). 25

26 Consider a few examples of such probabilities: Pr(0, 0, 0) = Pr (YM 0,YA 0,YT 0) (7) = Pr(ε M X 0 Mβ M, ε A X 0 Aβ A, ε T X 0 T β T ) = Φ 3 ( X 0 Mβ M, X 0 Aβ A, X 0 T β T ), Pr (0, 0, 1) = Pr (YM 0,YA 0, 0 <YT µ T 1 ) (8) = Pr(ε M X 0 Mβ M, ε A X 0 Aβ A, X 0 T β T < ε T µ T 1 X 0 T β T ) = Φ 3 ( X 0 Mβ M, X 0 Aβ A,µ T 1 X 0 T β T ) Pr (0, 0, 0), Pr (0, 0,J T ) = Pr Y M 0,Y A 0,µ T,JT 1 <Y T < + (9) = Pr ε M X 0 Mβ M, ε A X 0 Aβ A,µ T,JT 1 X 0 T β T < ε T + and = Φ 3 ( X 0 Mβ M, X 0 Aβ A, + ) Pr (0, 0, 0) Pr (0, 0, 1)... Pr (0, 0,J T 1), Pr (3, 2, 1) = Pr (µ M2 <YM µ M3,µ A1 <YA µ A2, 0 <YT µ (10) T 1 ) = Pr(µ M2 X 0 M β M < ε M µ M3 X 0 M β M, µ A1 X 0 A β A < ε A µ A2 X 0 A β A, X 0 T β T < ε T µ T 1 X 0 T β T ) = Φ 3 (µ M3 X 0 Mβ M,µ A2 X 0 Aβ A,µ T 1 X 0 T β T ) 3X 2X 1X Pr (i, j, k) i=0 j=0 k=0 (i,j,k)6=(3,2,1) 26

27 In general, if we denote µ h, 1 =, µ h,0 =0and µ h,jh =+ (h = M,A,T), Pr (l, m, n) = Pr µ M,l 1 <YM µ M,l,µ A,m 1 <YA µ A,m,µ T,n 1 <YT µ T,n = Φ 3 µm,l X 0 Mβ M,µ A,m X 0 Aβ A,µ T,n X 0 T β T lx mx nx Pr (i, j, k), (11) i=0 j=0 k=0 (i,j,k)6=(l,m,n) l = 0,..., J M ; m =0,..., J A ; n =0,...,J T. The multivariate probit model is estimated via maximum likelihood method, using CML maximizer in Gauss. The MVOP model is first estimated using a set of generated artificial data, with and without the cross equation correlation. The estimated coefficients and boundary parameters from the MVOP model using the consumption frequency data from the unitrecord surveys are presented in Tables 8 to 10, together with the results from a univariate specification where the three equations are estimated independently. 3.3 Sequential Models A possible drawback of all of the preceding models is that no distinction is made between the decision of participation, and then, conditional on participation, the decision of how much/often to participate in the consumption. With all of these drugs, there is a clear and distinct two-stage process at work, and the two decisions could well be related to different explanatory factors. The first stage is the 27

28 Table 8: Univariate Ordered Probit Results: Marijuana Marginal Effects, Y h = Coefficients t-value Constant LNAGE MALE MARRIED DECRIM WORK STUD UNEMP CAPITAL ATSI ENGLISHS DEGREE DIPLOMA YR SCHOOL DEPCHILD LNPT LNPA LNPM LNINC µ µ µ µ

29 Table 9: Univariate Ordered Probit Results: Alcohol Marginal Effects, Y h = Coefficients t-value Constant LNAGE MALE MARRIED DECRIM WORK STUD UNEMP CAPITAL ATSI ENGLISHS DEGREE DIPLOMA YR SCHOOL DEPCHILD LNPT LNPA LNPM LNINC µ µ

30 Table 10: Univariate Ordered Probit Results: Tobacco Marginal Effects, Yh= Coefficients t-value Constant LNAGE MALE MARRIED DECRIM WORK STUD UNEMP CAPITAL ATSI ENGLISHS DEGREE DIPLOMA YR SCHOOL DEPCHILD LNPT LNPA LNPM LNINC µ µ

31 participation decision. For non-participants, zero levels of consumption will always be recorded. Participation of these goods are more likely to be driven by individual social and demographic factors, or the decriminalization status in the state of residence in the case of illegal drugs. Conditional on participation, there is (arguably) a separate, although not necessarily independent, equation driving the level/frequency of consumption. The drivers of this second-stage equation, are more likely to be standard demand schedule factors, such as price and income. Thus, not only is there strong apriori justification for having different sets of drivers in each of the two equations,butalsoitdoesnotappearwarrantedtoenforcethatthe samevariables havethesameeffect in both decisions. For example, one might expect income to have a negative effect in the participation decisions of drugs, as it is a reflection of social class/standing, whereas in the amount/frequency equation, its effect is likely to be positive for standard microeconomic demand reasons. The first decision of participation can be modelled by a probit model given by equations (1) and (2). For those who have decided to participate, the conditional probabilities for the discrete choices of frequency/level of consumption is given by an ordered probit model driven by a different underlying latent process that relates to a set of explanatory variables that are not necessarily the same as those for the probit equation. The joint probabilities are given by the multiplication of probabilities from the two models. Recognising the fact that the disturbances in the two equations for the participants are likely to be correlated, a more general specification is to allow them to follow a bivariate normal distribution with a correlation coefficient ρ h. 31

32 Results for the sequential model for each of the three drugs, with the estimated coefficients for both the probit and ordered probit latent equations and the marginal effects on the probability of participation and the conditional probability for each consumption level, are given in Tables 11 to 13. Using the same set of explanatory variables for both probit and ordered probit equations, any differences in the effects of each explanatory variable on the two decisions are discussed below. All threshold parameters in the ordered probit equations for all three drugs are highly significant, indicating the discrete choices are indeed ordered as expected. So, what are the more important factors in the participation decision and what plays a more important role in the decision of how much to consume? Does each explanatory variable have a similar impact on the two decisions? Do the answers to the question of substitute or complement differ for participation and level of consumption? The signs for the significant price and income coefficients (at 5% significant level) for both the participation equation and the level of consumption equation are listed in Table 14, indicating whether the relationship between each pair of drugs is complementary or substitute. Looking at the price and income effects first in Tables 11 to 13 and 14, we can see some interesting differences in the impacts on the consumption levels and the impacts on participation. Starting with marijuana participation and consumption, while alcohol price is not significant in either decisions and there are significant and negative effects for income and tobacco price for both equations (indicating tobacco being complements for both participation and level of consumption for marijuana), the own price effects for marijuana are significant and have opposite signs in the 32