Statistical Modeling of Consumers Participation in Gambling Markets and Frequency of Gambling

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1 Statistical Modeling of Consumers Participation in Gambling Markets and Frequency of Gambling Brad R. Humphreys University of Alberta Department of Economics Yang Seung Lee University of Alberta Department of Economics Brian P. Soebbing University of Alberta Faculty of Physical Education and Recreation May 21, 2009 Abstract Because many people do not gamble, survey data on consumers participation in gambling contains a large number of zeros. The presence of a large number of zeros in data presents a number of methodological problems for the statistical or econometric analysis of participation in gambling markets and gambling expenditure. The most common techniques for handling zeros in gambling participation data have been the Tobit estimator and the Heckman selectivity estimator. Tobit is a maximum likelihood approach that combines probit and truncated least squares estimators; the Heckman estimator is a two-stage approach that uses both probit and ordinary least squares estimators. Recent research indicates that hurdle models, including the full double hurdle model used by Jones (1989, 2000) and the Cragg (1971) model, are better suited to the study of participation in gambling markets and intensity of participation in gaming. Double hurdle models and Tobit models are consistent with zeros generated by corner solutions from consumer utility maximization models and abstention from gambling, while the Heckman model is consistent with zeros generated by truncation due to unobservable activity. Based on data from a survey of gambling participation in Alberta in 2008, we find evidence that the double hurdle model better describes observed gambling participation and frequency of play than the Tobit model. Introduction A significant body of literature analyzing consumers s participation in gambling activities using micro survey data exists. Beyond simple summary statistics and reduced from techniques like probit and logit models, the Tobit model and the Heckman sample selection model (sometimes called the heckit model) are the two most commonly used models in this literature. For example, in the literature on spending on lotteries Livernois (1989), Stranahan and Borg (1998), Sawkins and Dickie (2002), and Worthington, et al. (2007) estimate Tobit models of expenditure on lottery and Scott and Garen (1994) and Farrell and Walker (1999) estimate both Tobit and Heckman sample selectivity models of participation and expenditure on lotteries. In this paper, we argue that this Corresponding author. Address: 8-14 Tory, University of Alberta, Edmonton, Alberta T6G 2H4 Canada. phone: ; fax: ; brad.humphreys@ualberta.ca. Funding for this research provided by the Alberta Gaming Research Institute. 1

2 empirical approach is incorrect, and that a superior model of consumer participation in gambling activities, the double hurdle model, outperforms the alternatives. Since the Tobit model is nested in the double hurdle model, standard statistical tests tests can be used to determine which of the two are more appropriate for use in gambling data. We estimate both Tobit and double hurdle models using data from a recent gambling prevalence survey conducted in Alberta, and show that the Tobit model is rejected in favor of the double hurdle model. Understanding the determinants of participation in gambling has important policy consequences. Gambling is an important,a nd growing, source of revenues for governments. Because gambling is a voluntary activity, national and local governments around the world increasingly turn to gambling to generate additional revenues to augment general funds as well as to support specific activities like good causes and sport. While simple unconditional statistics like average rates of play and average levels of spending are useful, they often do not tell the entire story about participation in gambling markets because of the complex nature of consumers decisions to participate in gambling. The increasing reliance on gambling activities to raise revenues, coupled with the voluntary nature of participation, makes it especially important to understand the determinants of participation and intensity of play in gambling markets. In addition, the analysis of participation in gambling activities has a number of interesting features that are important for understanding consumer behavior. Unlike the purchase of food, clothing, shelter, transportation, and other necessities, gambling goods are not purchased by all consumers. The dominant feature of survey data on gambling participation is the presence of many zeros observations where the individual does not participate in that gambling activity for most or all of the gambling activities examined. The problem of zeros is present in many other settings, including the purchase of durable goods like automobiles and television sets. In general, zeros can be present in survey data for three different reasons: 1. the individual did not perform that activity during the period asked about in the survey (infrequency of purchase) 2. the individual would never perform that activity under any circumstances(abstention); 3. individual was interested in performing that activity but the current price or cost of the activity, given the individual s level of income and preferences, makes not performing that activity a utility maximizing choice (corner solutions). Gambling is one of a relatively small number of goods where the latter two possibilities are relatively likely explanations for observed zeros in survey data. Other examples include cigarette smoking and alcohol use. For that reason, the analysis of consumer participation in gambling can help economists to better understand consumer behavior. Infrequency of purchase may also be important for gambling activities like casino gambling or (legal) sports betting in the United States where relatively few locations exist that permit these activities. We focus on gambling activities with relatively easy access in the population of interest. The presence of zeros in gambling survey presents researchers with an interesting modeling problem because of the distributional characteristics of these variables; the presence of a sizable probability mass at zero presents problems for commonly used estimators like Ordinary Least Squares (OLS). This issue has led researchers to use alternative statistical techniques to overcome the distributional problems associated with the presence of zeros, including discrete dependent variable approaches and estimators that explicitly correct for censoring or truncation of the dependent variable. Gambling survey data contain both a large proportions of zeros and an interesting theoretical context that enables researchers to integrate statistical approaches to modeling with theoretical considerations that affect the underlying data generation process. 2

3 Modeling Zeros in Gambling Survey Data Consider a model of participation in gambling that describes the typical survey data on gambling. This model links observable characteristics of respondents in the sample, and other factors that affect the decision to gamble, to observed intensity of gambling. In this model, consumer decisions on gambling are decomposed into two separate but interrelated decisions: The decision to gamble and the decision on how much to gamble given that an individual has decided to gamble. Let yi be a latent variable describing the satisfaction that individual i derives from activity gambling. Although never observed, this variable is useful for understanding gambling behavior because when actual frequency of gambling by an individual, y i, is observed, then this expenditure is assumed to be equal to the satisfaction that the individual gets from this amount of gambling (y i = yi ). The demand function for gambling is y i = β X i + ε i where yi is a latent variable capturing utility generated from gambling activity, X i is a vector of explanatory variables containing characteristics of individual i and other factors, and ε i is an unobservable random variable that captures the effect of other factors on demand for gambling. yi can be thought of as a latent variable capturing utility generated from gambling activity, or notional demand for gambling, and y i as a variable capturing the observed intensity of gambling. Implicitly, this model assumes that individuals derive satisfaction from the act of gambling, and the more gambling that takes place, the greater the satisfaction. While researchers often use expenditure on gambling as a proxy for gambling activity, behavioral biases like loss aversion or mental accounting, as well as the tendency for gamblers to recall net spending in instances when they won, may weaken the relationship between expenditure on gambling and gambling activity. For now, we interpret y i as a measure of the amount of gambling that individual i undertakes in some period. In addition, consider an observability rule I i = α Z i + ν i that describes the decision of individual i to gamble. Ii is an unobservable indicator that determines participation in gambling for an individual. Z i is a vector of variables that affect the decision of individual i to gamble and ν i is a random variable that reflects all other factors that affect individual i s decision to participate in gambling. Both ν i and ν i are unobservable, and assumed to be independent and identically distributed random variables with a mean of zero and constant variance. If the decision to gamble and the decision to participate in gambling activities are simultaneously determined, and the unobservable error terms are correlated, then the process of deciding on participation in gambling and deciding on expenditure on gambling can be modeled by a likelihood function L DHD = 1 P (ν i > α Z i )P (ε i > β X i ν i > α Z i )f(y i ε i > β X i, ν i > α Z i ) (1 P (ν i > α Z i )P (ε i > β X i ν i > α Z i )) 0 (1) and the vectors of unknown parameters of this model can be estimated by evaluating this likelihood function numerically. This model is called a double hurdle model in the literature (Jones, 2000) and has been applied to a wide variety of economic decisions that can be decomposed into a participation 3

4 and expenditure decision, including cigarette smoking (Jones, 1989; Garcia & Labeaga, 1996), labor force participation and hours worked (Blundell, et al., 1987), and physical activity and exercise (Humphreys & Ruseski, 2007). Note that equation (1) can easily be manipulated to show that this likelihood function is composed of a standard probit model and a truncated regression model. The αs are the unknown parameters of the probit model and the βs are the unknown parameters of the truncated regression model. For the double hurdle model with dependent errors, the censoring mechanism, the process which generates the observed zeros, is y i = 1(I i = 1) max(y i, 0) where 1(Ii = 1) is an indicator function for the occurrence of the event Ii = 1. That is, positive expenditure is observed if there is both no abstention from gambling (Ii = 1) and if there is no corner solution, yi > 0. However, zero expenditure could still be observed in the sample in the case of a corner solution. The primary alternative to the double hurdle model found in the literature on the analysis of expenditure on gambling is the Tobit model. The Tobit model is nested in the double hurdle model, equation (1). The Tobit model represents the case where the first hurdle is irrelevant to consumer s decision about how much to spend on gambling, and the same factors determine whether or not a person decides to gamble and if so how much to gamble. From equation (1), simply set P (ν i > α Z i ) = 1, making the first hurdle irrelevant; this also means that P (ε i > β X i is no longer conditional on participation, and the likelihood function for the Tobit model is L T = 1 P (ε i > β X i )f(y i ε i > β X i ) 0 (1 P (ε i > β X i )). (2) where f( ) is the probability distribution function for a normal random variable. Again, the unknown parameters of this model can be estimated by evaluating the likelihood function numerically. For the Tobit model, the censoring mechanism, the process that generates the observed zeros, is y i = max(y i, 0) so observed non-zero expenditure is equal to notional demand, and in all instances where positive expenditure is not observed, yi is set equal to zero. Under the assumptions that generate the Tobit model, all observed zeros can be attributed to a corner solution, where the individual would gamble if the effective price of gambling were low enough, but at the existing effective price of gambling, the optimal choice is y i = 0. Note the effective price of gambling in this case can include the monetary cost of gambling, the cost of traveling to a location where the individuals preferred form of gambling is available, and any psychic costs of gambling. Under the assumptions that generate the Tobit model, the reason for any observed zero is unknown. Because the Tobit model is nested in the double hurdle model with dependent errors, it is possible to perform tests to determine if the data are consistent with the double hurdle model or the Tobit model. The Tobit model implicitly assumes that, if X i and Z i contain common variables, the signs of the estimated parameters on these variables are identical. Formally, the likelihood function for the Tobit model is the sum of the likelihood functions of the probit and truncated regression models that make up the double hurdle model, so a likelihood ratio test can be performed on the two models under the null hypothesis that the two likelihood functions are equal. 4

5 Finally, some empirical research on expenditure on lotto tickets has used Heckman selectivity models (sometimes called Heckit ) to estimate the relationship between observable characteristics of gamblers and expenditure (Garen & Scott, 1993; Farrell & Walker, 1999). The Heckman selectivity model is not nested in the double hurdle model specification. Instead, the Heckman selectivity model emerges from what Jones (1989) calls first hurdle dominance. Under first hurdle dominance, the decision to gamble or not to gamble is more important than the decision about how much to spend on gambling once an individual has decided to gamble. First hurdle dominance implies that none of the observed zeros represent corner solutions to the consumer s utility maximization problem; these zeros must be generated by some other mechanism. The likelihood function for the Heckman selectivity model is L H = 1 P (ν i > α Z i )f(y i ε i > β X i, ν i > α Z i ) 0 (1 P (ν i > α Z i )). (3) The process that generates the observed zeros in the context of the Heckman selectivity model is P (y i < 0 I i = 1) = 0 which clearly rules out corner solutions. Jones (2000) points out that the zeros in the Heckman selectivity model are generated by truncation, not censoring. This could be attributable to infrequency of participation in gambling by individuals in the sample. However, the survey data used here were generated by questions about spending on different gambling activities over the past year, and for a variety of gambling activities that people engage in frequently like the purchase of lotto tickets and gambling at bingo halls. The time period used in the survey question, and the nature of the gambling activities analyzed should ensure that the zeros in the sample are due to abstentions or corner solutions, and not dues to infrequent participation. Since the Heckman selectivity model is not nested in the double hurdle model, no formal test exists to determine which model fits the data better. Jones (2000) argues that researchers must use economic theory to determine which of these two options better describe the process that generates the data. We believe that the zeros in most gambling prevalence survey data represent either corner solutions to consumer s utility maximization problems, or abstentions from gambling that correspond to an absence of first hurdle dominance. The choice of modeling approaches comes down to the Tobit model or the double hurdle model. This choice, which is consistent with zeros generated by both abstentions from gambling (consumers who would not gamble under any conditions) and corner solutions to the consumer s utility maximization problem (consumers who would gamble of the effective price were low enough). In this case, the choice of modeling approach is empirically testable. Below, we conduct formal tests of the double hurdle model and the Tobit model using data from a recent gambling prevalence survey from Alberta. Analysis of Gambling Participation and Frequency Survey Description We use data from a random digit dial (RDD) telephone survey of gambling participation among residents of Alberta conducted in the Summer of Consumer Connect, a market research firm, carried out the actual survey work. Survey participants were asked questions about their attitudes toward gambling, participation in various gambling activities, expenditure on gambling over the past year, and other risky behaviors such as drug and alcohol use. The survey contained questions about participation and expenditure on specific types of gambling activities. We focus 5

6 on participation in six types of gambling activities: Large jackpot/long odds lottery, instant win lottery tickets, sports betting, bingo, video lottery terminal (VLT) gambling, and slot machines. Alberta has been a pioneer among Canadian provinces both in introducing new forms of gambling and in fashioning strict, but workable, regulatory controls (Wynne, Smith, & Volberg 1994, p. 2). A wide variety of gambling options exist in Alberta, and gambling has been a recreational and entertainment option for Albertans for years. In the fiscal year , gross sales from both liquor and gambling products in Alberta was 28,296,000,000 CAD according to the 2008 Alberta Gaming and Liquor Commission (AGLC) Annual Report. The report also contains data on the number of gaming types and venues available in the province. Alberta contained 42 licensed bingo facilities, 23 charitable casinos (4 of those casinos are First Nation operated), 3 Racinos, 2,342 lottery outlets, and 1,051 retailers and entertainment centers offering Video Lottery Terminals (VLT). Sports betting is available at all lottery outlets. These seven types of gambling are widely accessible to Albertans, reducing the likelihood that zeros in the data are generated from infrequency of play because of poor access to this type of gambling. The RDD survey had 3,001 participants and a response rate of percent, calculated using the method in Schonleau et al (2004). Table 1 presents the characteristics of the RDD survey sample. The average age for respondents was 48.8 years with the median age of the group at 48 years old with suggests symmetry in the age distribution of the sample. The group was composed of 58 percent females with a median income in the past year of 50,000 CAD. The middle section of Table 1 is the breakdown of the educational status reported by the participants. One notices that 41 percent of the participants have a high school education or less. The third section of Table 1 examines the marital status of the 3,001 participants. Almost 59 percent of the sample are legally married. Finally, the fourth section examines how many people aged 18 and older (including the participant) live in the household. The majority of the respondents (54.49 percent) said that two people live in the household over 18 years of age. Table 2 shows summary statistics for the some of the gambling related variables in the survey. The survey asked questions about participation in specific types of gambling, frequency of participation, and questions about the participant s net monthly spending on each type of gambling if the respondent indicated participation. The spending variable clearly asks the respondent to estimate net spending, including all gains and losses. Table 2 contains annual participation rates and the distribution of net monthly spending for the five types of gambling activities. Bear in mind that negative responses to the net monthly spending question imply losses and positive responses imply winnings. The final two columns report the average loss or gain for those who reported each. The market of lotto tickets has the highest participation rate with percent while bingo has the lowest participation rate with 5.36 percent of the sample participating. Scratch off lottery tickets and slot machines also show relatively higher participation rates. VLTs and sports betting have relatively low participation rates. Sports betting in Alberta takes place at lottery outlets, not at sports books located in casinos, so this low participation rate is not due to lack of access to betting opportunities. The province has 42 licensed bingo halls, so the low rate of participation in this activity may reflect lack of access for some residents. While we do not exploit data on net spending in this paper, the responses to the question about net spending on gambling types is informative. The small fraction of people reporting gains on lotto and scratch-off lottery tickets is consistent with the 47% take-out rate on lotto in Canada and the payout structure of scratch-off tickets. The average monthly net spending on slot machines and VLTs suggests that participants spend heavily on these activities. The large reported average monthly gain for sports betting is driven by a few observations. Only 21 participants reported positive average monthly net spending on sports betting, and three of them reported average monthly net spending of over $1,000 (one reported $15,000). 6

7 Table 1: Characteristics of RDD Population Survey Respondents Number/Value (%) Sample Size 3,001 Average Age 48.8 Median Age 48 Female 1, Median Income 50,000 Refused to answer income question Education Less than high school Completed high school Trades certificate College certificate University diploma Don t know Refused Marital Status Single Common Law Legally Married 1, Separated Divorced Widowed Refused to answer Number of Persons in Household , and above Table 3 summarizes the responses to the question In the past 12 months, how often have you purchased/played...? for each of the five types of gambling activities. In general, the reported frequencies of play indicate that gambling is a relatively infrequent activity for most Albertans. With the exception of lotto tickets, most of the reported frequencies of gambling fall into the ranges of 2-3 times per month to less than once a month and the non-participation rate is high for all gambling types except lotto. Again, given the relatively large supply of gambling opportunities in the province, we interpret non-participants the zeros in our sample as reflecting either abstentions from gambling or corner solutions to consumer s utility maximization problem. We used the data on reported frequency of purchase for each type of gambling to estimate the number of times in a year that each respondent reported taking part in that activity. Less than once a month was set to 6 times per year and the others were coded exactly as worded. The last line on Table 3 shows the average number of times per year that the participants in the sample reported engaging in each gambling activity. We interpret this variable, and not expenditure on gambling activities, as the appropriate proxy for participation in gambling activity in the context 7

8 Table 2: Participation and Monthly Net Spending Participation % Reporting Average Monthly ($) Gambling Activity Rate Loss Break Even Gain Loss Gain Lotto Tickets Scratch off lottery Slot Machines Video Lottery Sports Betting Bingo Table 3: Reported Frequency of Participation % Reporting by Game Reported Frequency of Play Lotto Scratch Off Slots Sports Bingo VLT Not at all Less than once a month Once a month times a month Once a week times a week or more times a week Average annual participation

9 Table 4: Characteristics of Participants Gambling Activity Age Income Male Employed Smoker Drinker W. Eur Lotto , Scratch off , Bingo Video Lottery , Sports Betting , Slot Machines , Entire Sample , of the latent variable model developed above. Again, reported expenditure on gambling may be influenced by loss aversion or other mental accounting biases; reported expenditure may also be influenced by the addition of winnings in instances when the gambler left the gambling venue ahead for the session. The assumption that the number of episodes of participation is a good proxy for gambling activity implicitly assumes that the participant gets about the same amount of satisfaction from each separate gambling event, be it the purchase of a lotto ticket or a trip to a bingo parlor. Table 4 compares the characteristics of participants in each type of gambling activity to the statistics for the entire sample. Interestingly, although gamblers tend to drink and smoke at higher rates than the general population, the percentage of gamblers who smoke and drink alcohol are different for each group of gambling participants. For example, 28 percent and 73 percent are smokers and drinkers for the entire sample. However, the fraction of smokers and drinkers in each of the subgroups differs significantly from the participation rate in the entire sample. The gender composition of participants in each type of gambling activity also shows some interesting patterns. Sports bettors and VLT players are predominantly male, and bingo players and scratch off card purchasers are predominantly female (the P-value on the t-test on participation of females and the general population for scratch-off tickets is 0.01). Empirical Approach As the likelihood functions show, the Tobit, and Double-Hurdle models are structured differently. The Tobit and double hurdle models rely on both a binary choice component and a linear regression component. The main difference between these two models is that Tobit is univariate while Doublehurdle is bivariate. It means that double hurdle model has two random processes while the Tobit has only one random process. Actually, the participation indicator is assumed to have another random process in Double-hurdle. Thus, Double-hurdle has two dependent variables, the participation indicator and frequency of gambling while Tobit has one dependent variable, the frequency of gambling. We estimate both Tobit and double hurdle models for each of the types of gambling activities described above. The continuous explanatory variables are age, age-squared, income, and education. The discrete explanatory variables are dummy variables for gender (male), marital status (married), employment status (employed), and ethnicity (Western European ancestry). By including agesquared, we can recognize if the relationship between age and participation is linear or non-linear. In particular, if age-squared has a positive sign then the frequency of participation in any gambling type would be a convex function of age. On the other hand, a negative sign on age-squared would 9

10 indicate that the frequency of participation is a concave function in age. The implication is that a gambler would have the minimum gambling activity in his or her life time under a convex case while a gambler would have the maximum gambling activity in his or her life time under a concave case. We also employ exclusion restrictions in order to identify the participation effect in the double hurdle model. While the literature on double hurdle models is silent on the need for exclusion restrictions, the double hurdle models estimated here would not converge to a local maximum without these exclusions. We use three variables, indicator variables for smoking and drinking and a variable that captures past gambling success, to identify the participation equation in the double hurdle model. The past gambling success variable is based on the survey question In the past 12 months, what do you recall as your largest gambling winnings on a single day? Clearly, this variable is randomly determined, and should not be correlated with the equation error terms in either the participation or frequency of play equations. We use the largest reported amount won in a single day on any type of gambling in the past year when the amount was greater than $100, expressed in thousands of dollars, to identify gambling participation; this variable is identified as Winnings on the tables below. 48% of the gamblers in the sample reported winning more than $100 on a single day in the past year. The mean of this variable was $4,127 and the standard deviation was 37,059. The largest value in the sample is $725,000. Note that this variable is not the largest amount won in a specific type of gambling activity. Respondents were asked to identify the type of types of gambling activities that generated these winnings, and the responses included lotto, casino table games, internet gambling, and high risk stocks, among others. This variable could take a positive value for both participants and nonparticipants in each type of gambling activity. Finally, we perform a likelihood ratio test on the Tobit model versus the double hurdle model. This test serves as the primary comparison between the two models. Recall from the discussion above that the Tobit model is nested in the double hurdle model, under the assumptions that the parameters on the participation and frequency of play equations are identical. Formally, if L( ˆβ, ˆσ 2 ) is the maximum value of the double hurdle log-likelihood function and L( β, σ 2 ) is the maximum value of the Tobit log-likelihood function, then asymptotically LR = 2[L( β, σ 2 ) L( ˆβ, ˆσ 2 )] χ 2 m (4) where m is the number of restrictions, in this case the number of unrestricted coefficients minus the number of restricted coefficients. The null hypothesis is that the log likelihood functions are identical, and the restrictions have no effect on the results. In our case, the null hypothesis is no difference between the double hurdle model and the Tobit model, which implies that the more parsimonious Tobit model fits the data better. Rejection of the null implies that the double hurdle model fits the data better. Results We estimate Tobit and double hurdle models for each of the six gambling activities. We also report the results of a probit model for participation in each of the gambling activities using the explanatory variables from the double hurdle participation equation for comparison. The tables also contain estimates of ρ, the coefficient of correlation between the error term in the participation equation and the frequency equation in the double hurdle model (ρ = corr(ε i, ν i )). Finally, the tables show the log-likelihood values and number of censored and total observations for each model. Table 5 shows the estimates for the three different models for purchase of lotto tickets. The second column contains the estimates and the p-values for the participation of double hurdle equation, 10

11 and the third column has the estimates and the P-values for the frequency of participation double hurdle equation. The final two columns contain estimates for the Tobit model and a simple probit model of participation in the market for lotto tickets. Again, lotto refers to low probability/high payoff on line lottery games like Mega Millions, Euro Millions, or PowerBall. In Alberta, this includes Lotto 6/49 and several similar games. Notice that both age and age squared are significant in all the models on Table 5. Participation and frequency of play vary systematically with age. Age squared is included to allow the participation and frequency of play to vary non-linearly with age. Notice the difference in the relationship between age and age squared and annual lotto ticket purchase in the double hurdle and Tobit models. The Tobit model indicates that the purchase of lotto tickets has an inverted-u shape; annual frequency of lotto ticket purchase at first increases with age, reaches a maximum (at about 55 years of age in this sample) and then declines. However, the double hurdle results indicate that only participation has this inverted-u shape. The estimated parameters on age and age squared in the frequency equation of the double hurdle model indicate that the average annual number of lotto tickets purchased, conditional on participation, declines steadily as age increases. This is a very different implied pattern of participation and purchase. The purchase of lotto tickets is unrelated to income. Males buy lotto tickets more frequently than females, and employed people buy fewer lotto tickets than unemployed people. Canadians of Western European descent buy lotto tickets less frequently than other ethnic groups. The frequency of lotto ticket purchase also declines with the level of education. In terms of the identifying variables that are included in the participation equation, only drinking is significantly associated with the decision to purchase lotto tickets. The estimate of ρ indicates negative correlation between the residual from the participation equation and the residual from the frequency of purchase equation. The likelihood ratio test rejects the Tobit model in favor of the double hurdle model for lotto ticket purchase. The data are consistent with a separate participation decision and frequency of purchase decision where the parameters on the explanatory variables in the two equations differ. This is consistent with the different relationships between age and participation discussed above. Table 6 contains the results for scratch off lottery tickets. In contrast to lotto tickets, there is little relationship between age and age squared an the decision to purchase scratch off lottery tickets or the frequency of purchase of these tickets. Gender, marital status, employment status and ethnicity all do not appear to influence the decision to purchase scratch off lottery tickets or the frequency of purchase. Education is related to the frequency of purchase of scratch off tickets, in that the higher the education of the individual, the lower the frequency of purchase. Income appears to affect only the decision to purchase scratch off tickets; lower income individuals are more likely to purchase these tickets. In terms of the identifying variables that are included in the participation equation, drinking, smoking, and large past gambling winnings are all associated with the decision to purchase scratch off lottery tickets. The estimate of ρ indicates negative correlation between the residual from the participation equation and the residual from the frequency of purchase equation. The likelihood ratio test strongly rejects the Tobit model in favor of the double hurdle model for scratch off lottery ticket purchase and frequency of purchase. Table 7 contains the results for bingo. According to the results, age does not seem to have any significant effect on frequency of attendance at bingo halls. Like scratch off lottery tickets, the gender dummy has a large negative estimate, -48 in the double hurdle frequency equation and -24 for Tobit. Males attend bingo halls much less frequently than females. Interestingly, the ethnicity indicator (Western European descent) has a positive estimate for participation (0.214) and the negative parameter estimate for frequency of play in both the double hurdle model and the Tobit model. The opposite signs indicate that consumers of western European descent have a larger probability of participation but attend less often than other ethnic groups, conditional on 11

12 Table 5: Maximum Likelihood Estimates - Lotto Participation Frequency Participation Variable Hurdle Hurdle Tobit Probit Age Age Income Male Married Employed W. European Education Drink Smoke Winnings Constant ρ Log likelihood Likelihood Ratio P-Value N Censored N

13 Table 6: Maximum Likelihood Estimates - Scratch-Off Tickets Participation Frequency Participation Variable Hurdle Hurdle Tobit Probit Age Age Income Male Married Employed W. European Education Drink Smoke Winnings Constant ρ Log likelihood Likelihood Ratio P-value N Censored N

14 participation. A possible explanation is that consumers of Western European descent have greater curiosity about bingo, but lose interests once they experience the game. None of the identifying variables are individually significant in the participation equation of the double hurdle model. The estimate of ρ indicates negative correlation between the residual from the participation equation and the residual from the frequency of purchase equation for bingo. The likelihood ratio test again rejects the Tobit model in favor of the double hurdle model for participation in bingo and frequency of attendance at bingo halls. Table 8 contains the results for sports betting. Recall, from Table 2, that betting on sports is not a particularly popular type of gambling in the survey. Only about 6 percent of the sample reported betting on sports in the previous year. The results on Table 8 for the Tobit model indicate that the frequency of sports betting declines with age, but the age and age squared are not significant in the double hurdle model. The relationship between sports betting and income is interesting. The Tobit model finds no relationship. The double hurdle results indicate that participation declines with income, although the P-value of is only marginally significant, while the frequencly of sports betting increases with the income of the participant. Among the indicator variables, it is also interesting that the double hurdle model indicates that frequency of play, but not participation, is higher among males; males are not more likely to bet on sports, but conditional on participation they bet on sports more frequently than females. The Tobit model results cannot detect the lack of a relationship between gender and participation. The other indicator variables are not statistically significant for sports betting. That lack of a relationship between education and sports betting is different from other types of gambling, where education has some effect on either participation or frequency. We used only the winnings variable to identify sports betting participation; the double hurdle model converged with only a single identifying restriction. The variable is not statistically significant in any of the models estimated. The estimate of ρ indicates weak negative correlation between the residual from the participation equation and the residual from the frequency of purchase equation for sports betting. The likelihood ratio test again rejects the Tobit model in favor of the double hurdle model for participation in sports betting and frequency of betting. Table 9 contains the results for slot machines. Albertans have access to slot machines at 23 casinos, and 3 racinos in the province. From Table 2, slots are a relatively popular form of gambling in Alberta with about 16% of the sample reporting playing slots at least once in the past year. Despite the perception that slots are favored by older people there is no evidence of any relationship between age and participation or frequency of play in the data. There is also no relationship between income and gambling on slot machines - the incidence of participation and frequency of play are constant across the income distribution. None of the demographic indicator variables are statistically significant. Neither the Tobit nor the double hurdle models identify many factors associated with slot machine play. The only significant explanatory variable is the level of education, where a clear distinction exists between the results for the two models. The Tobit model indicates that frequency of play decreases with the level of education. The double hurdle results indicate that participation increases (weakly) with level of education but frequency of play decreases. Conditional on participation, people with more education play slot machines much less regularly than people with less education. The pattern of play indicated by the two competing models differs significantly in the case of slot machines. Smoking, drinking, and past gambling winnings are all significant in the double hurdle participation equation. The estimate of ρ indicates negative correlation between the residual from the participation equation and the residual from the frequency of purchase equation for slot machines. The likelihood ratio test rejects the Tobit model in favor of the double hurdle model. Table 10 contains the results for VLTs. VLTs are widely available in bars, restaurants, and 14

15 Table 7: Maximum Likelihood Estimates - Bingo Participation Frequency Participation Variable Hurdle Hurdle Tobit Probit Age Age Income Male Married Employed W. European Education Drink Smoke Winnings Constant ρ Log likelihood Likelihood Ratio 101 P-value N Censored N

16 Table 8: Maximum Likelihood Estimates - Sports Betting Participation Frequency Participation Variable Hurdle Hurdle Tobit Probit Age Age Income Male Married Employed W. European Education Winnings Constant ρ Log likelihood Likelihood Ratio P-value N Censored N

17 Table 9: Maximum Likelihood Estimates - Slot Machines Participation Frequency Participation Variable Hurdle Hurdle Tobit Probit Age Age Income Male Married Employed W. European Education Drinks Smoke Winnings Constant ρ Log likelihood Likelihood Ratio 292 P-Value N Censored N

18 other entertainment venues in Alberta. However, the reported participation rates in the sample are low. Variation in age and income do not explain observed participation in VLT gambling or the reported frequency of play. Married people play VLTs less frequently than single people, but employment has no relationship to VLT play. Although the double hurdle model indicates no relationship between education and participation, both models indicate that the frequency of play declines with the level of education. Smoking, drinking, and past gambling winnings are used to identify participation in the double hurdle model, and all are significant. Interestingly, the past winning variable has a negative parameter; people reporting one incident of large gambling winning in the past year are less likely to play VLTs. The estimate of ρ is quite large, suggesting that the residuals from the participation and frequency of play equations in the double hurdle model are highly correlated - unobservable factors influencing participation in VLT gambling are negatively correlated with unobserved factors influencing the level of play. The likelihood ratio test does not reject the restrictions on the Tobit model, indicating that, for VLT gambling only, the Tobit model fits that data better than the double hurdle model. In summary, age, income, level of education, and the indicator have different effects on the frequency of play for each gambling type. First, age has a significant positive effect on lotto, and age-squared has a significant negative estimate. For other types of gambling, age does not have any correlation with frequency of play. Second, income has a significant and positive effect on the frequency of play for only VLTs. Third, more education significantly reduces the frequency of participation in most gambling types except for sports betting and bingo. One explanation for this result hypothesis could be that educated people are more able to assess the negative expected outcome of most gambling activities because of a better understanding of probability and risk. The dummy variables have diverse effects on the frequency of play for different types of gambling. The gender dummy (Male) has a positive and significant parameter for the following gambling activities: lotto, sports betting, and VLTs. Specifically, males participate much more frequently in sports betting, so we can infer that males strongly tend to spend more on sports betting than females. On the other hand, the male dummy has a negative and significant estimate for bingo. Thus, bingo is played more frequently by females. Lotto tickets, sports betting, VLTs, and bingo are the types of gambling most affected by gender. Marriage has an estimated negative and significant effect on frequency of play in sports betting and VLTs. This means that these gambling types are less preferred by married people. Although this result has been reported in other studies of gambling participation, the explanation in economic terms is unclear. The employment dummy shows a significant, positive sign for lotto and scratch offs. Thus, employed people tend to increase their frequency of play in these two types of gambling. The ethnicity indicator (Western European heritage) shows a a negative and significant estimate for most types of gambling except for sports betting and VLTs, and indicates that people of Western European descent do not prefer these gambling activities. The identifying variables have different estimated parameters and significance. Drinking has a significant and positive effect on lotto, scratch offs, and VLTs while smoking has a positive and significant effect on scratch offs, bingo, VLTs, and slot machines. Past gambling winnings have a significant effect on scratch offs, bingo, and VLTs. Specifically, higher winnings put the greatest impact on the probability of participating in scratch offs since it has the largest parameter estimate (21.57). 18

19 Table 10: Maximum Likelihood Estimates - Video Lottery Terminals Participation Frequency Participation Variable Hurdle Hurdle Tobit Probit Age Age Income Male Married Employed W. European Education Drink Smoke Winnings Constant ρ Log likelihood Likelihood Ratio P-value N Censored N

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