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Factors influencing the adoption of state lotteriesO. HOMER EREKSON , GLENN PLATT , CHRISTOPHER WHISTLER & ANDREA L. ZIEGERTPublished online: 04 Oct 2010.

To cite this article: O. HOMER EREKSON , GLENN PLATT , CHRISTOPHER WHISTLER & ANDREA L. ZIEGERT (1999) Factorsinfluencing the adoption of state lotteries, Applied Economics, 31:7, 875-884, DOI: 10.1080/000368499323832

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Applied Economics, 1999, 31, 875–884

Factors in¯ uencing the adoption ofstate lotteries

O. HOMER EREKSON, GLENN PLATT* ,CHRISTOPHER WHISTLER ³ and ANDREA L. ZIEGERT §

Miami University, Oxford, Ohio 45056, USA, ³ Ohio Legislative Budget O� ce, Columbus,Ohio 43286, USA and §Denison University, Granville, Ohio 43023, USA

This paper explores the factors in¯ uencing the adoption of state lotteries in the UnitedStates. The conceptual framework utilizes a common utility framework in whicha representative legislator maximizes utility derived from the current and expected® scal position of a state, subject to a political constraint. The empirical results supportthe theoretical hypotheses, including the ® nding that changes in the ® scal health of thestate, the predicted pro® t potential of a lottery, and the political climate of the state alla� ect the likelihood that a lottery is adopted. By introducing a sound conceptualframework, using better data than used in previous studies, utilizing an appropriateestimation technique, and obtaining strong results, this study advances our know-ledge of why states adopt lotteries.

I. INTRODUCTION

The adoption of state-operated lotteries as revenue gene-rating entities is not a recent phenomenon. It is welldocumented that lotteries in the United States date back asfar as 1612, when the Virginia Company of London conduc-ted a lottery authorized by the British Crown (Filer et al.,1988). Lotteries became very popular in southern statesafter the Civil War as a means to aid the recovery ofwar-damaged states. The federal government, because ofmoral objections to legalized gambling and fear of corrup-tion, forced the closure of these state operations in 1895 bymaking the distribution of tickets through the mail illegal(Martin and Yandle, 1990).

With the aid of newly introduced mainframe computersand more urbanized populations (not requiring the postalservice for the distribution of tickets), lotteries again wereintroduced as an alternative source of state revenue. Popu-larity of this form of legalized gambling has steadily in-creased since New Hampshire’s adoption in 1964. Of the 33operating lotteries in 1990 (32 states and the District ofColumbia), 20 were adopted since 1980.

Along with the recent surge of adoption has come in-creased interest in the factors that have led to the decision toadopt or not adopt. The question is often asked, why is

a form of gambling, often thought to be morally objection-able, a state-run operation that promotes its good likea private enterprise?’ It is the purpose of this paper toaddress this question. While this study is not the ® rst of itskind, it extends the current literature in signi® cant ways.Most of the prominent lottery studies to date introducevariables in an ad hoc fashion with only loose underpinningsto a conceptual model. This paper provides a conceptualframework before turning to the e� ects of individual vari-ables. Moreover, we have used somewhat better data thanearlier studies and utilized appropriate estimation tech-niques and structural analysis.

II . CONCEPTUAL FRAMEWORK:MOTIVATIONS FOR ADOPTION

Two theoretical frameworks motivating lottery adoptionare commonly used in the current literature. The legislator-support maximization model was ® rst introduced into thelottery adoption literature by Filer et al. (1988). Martin andYandle (1990) were the ® rst to explain lottery adoption asa duopoly transfer mechanism. These two frameworks areexplored next.

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1 Caudill et al. (1995) also consider Martin and Yandle’s (1990) duopoly transfer mechanism approach.2 The constraint conforms to the Stigler–Peltzman framework discussed above.

The legislator-support maximization approach viewslottery adoption as an attempt by legislators to maximizetheir own success. For this reason, the legislator-supportmodel of lottery adoption is based primarily on theStigler–Peltzman framework of voter support maximizationby the legislators. In short, legislators recognize that in-creased programme spending to enhance the welfare ofconstituents will increase their political support. This in-crease, however, must be at the expense of the loss ofsupport due to the increased tax burden placed upon theconstituents. In an attempt to maximize support, alternativerevenue raising mechanisms, such as a lottery, are con-sidered so that the direct tax burden on constituents will notbe increased.

The duopoly transfer mechanism approach perceivesstate adoption of lotteries as an attempt to directly competewith both legal and illegal gambling operations in order toobtain revenue that states miss by not being able to taxillegal operations.1 Because gambling is often tied to organ-ized crime, Martin and Yandle (1990) hypothesize that pre-venting corruption in gambling activities is di� cult becausepeople are seldom willing to act as plainti� s against organ-ized crime. Policing of illegal gambling is therefore carriedout within the criminal sector. Upon the entrance of a statelottery, lower cost policing of legitimate lottery operators iscarried out by the state. Martin and Yandle (1990) suggestthat this does not give the state lottery a monopoly, butrather they argue that the state ® rm (lottery) achieves a kindof duopoly equilibrium with the illegal lottery operators’.

In this paper, we use a common utility framework inwhich the utility function of a representative legislator ismaximized subject to a constraint. The model is based onthe representative legislator, the legislator who votes at themedian level in the state, because it is the vote of thislegislator that represents’ the action of the majority. Theutility a legislator receives from the adoption decision isbased on the legislator’s ability to improve the state’s ® scalwell-being. His utility maximizing decision, however, is con-strained by his desire to satisfy his constituents, and, in turn,to be reelected. In short, the legislator will only attempt toimprove ® scal well-being to the point that voter support iscompromised.2 If the utility gained by adoption is greaterthan that which is lost, the legislator will vote to adopta lottery.

Utility gained is more likely to exceed utility lost (i.e.,adoption will occur) if current ® scal well-being is low andpotential is high. If a state’s current ® scal position is stressed(low well-being), the state is in greater need of revenue andwill likely turn to the lottery as an additional source ofrevenue. Furthermore, if the potential of lottery revenue ishigh in a state, the legislator will be more likely to adopt

when increased revenue is needed. Current ® scal well-beingdepends upon the extent to which revenue meets the budget(termed ® scal health’ by Berry and Berry, 1990) and the taxbase. The marginal utility gained from lottery adoptiondecreases as ® scal health’ increases when ® scal health ispositive. This is because states do not attempt to maximize® scal health but rather attempt to keep it from becomingnegative. As ® scal health becomes negative, the marginalutility gained from adoption increases as ® scal health be-comes more negative because of the increasing ® scal stress.In short, low ® scal health is hypothesized to lead toadoption, and high ® scal health is expected to lead tonon-adoption.

A structural change in the tax base relative to aggregatemovements in the US will a� ect state revenues and decreasethe likelihood of lottery adoption. As noted by Caudill et al.(1995), lottery adoption appears to have occurred by region,beginning in the Northeast, moving to the West, then backto the Midwest, and now to the South. Using a tax baseargument, one possible explanation for the regional move-ment in adoption is that lotteries chase’ decreases in the taxbase resulting from signi® cant declines in a state’s manufac-turing sector relative to the decline in the US manufacturingsector as a whole. Thus, the relative decrease in tax base ishypothesized to increase the probability of adoption.

The utility a representative legislator derives from theadoption decision also depends upon the revenue potentialof a lottery. If a state has a large tourism industry, thepotential is high for the state to raise revenue by sellingtickets to residents of other states (i.e., tax export). Thus,legislators are more likely to adopt a lottery because thereexists an opportunity to raise revenue without burdeningresidents of their own state. To defend themselves againsttax exporting e� orts of other states, states will tend to adoptlotteries as a greater percentage of their neighbouring statesadopt lotteries. Another indicator of lottery revenue poten-tial is income per capita. Although it is well-documentedthat the poor spend a higher percentage of their income onlottery tickets than middle-to-high income individuals, thelatter group spends a larger nominal amount (Mikesell andZorn, 1986). Therefore, as income per capita increases, it ishypothesized that the revenue potential of a lottery alsoincreases. Thus, as income per capita increases, the prob-ability of adoption increases as well.

As mentioned above, the representative legislator iscognizant of voter preferences about the lottery. As thepercentage of the state’s population morally opposedto a state-run lottery increases, the probability of lotteryadoption is expected to decrease because the votes ofthose who are `morally outraged’ by a lottery will belost. This idea is proxied by a measure of religious a� liation

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3 Twelve of the 32 states with lotteries in 1990 earmarked lottery pro® ts for education.4 Mixon et al. (1997) argue that lottery adoption is more likely to occur in older states where rent-seeking groups are more organized andcan more e� ectively engage in collective action.5 The probability that the state adopted before time t (i.e. spell length T < t) is the integral under the pdf from negative in® nity until timet in continuous time.6 Berry and Berry (1990) use a standard normal distribution while Alm et al. (1993) and Caudill et al. (1995) use a logistic distribution.

which will be discussed in more detail in the nextsection.

Lottery adoption is often tied to promises to increase thesupport for elementary and secondary education.3 If educa-tion expenditure per pupil is too low, legislators will turntowards lotteries to raise the additional revenue. But, aseducation expenditure in states without lotteries increases,less voter support will be given for a lottery. Therefore,a negative sign is expected.

Finally, lottery adoption appears to be increasing overtime. This could be because the presence of lotteries in otherstates re¯ ects changing perceptions towards gambling.Thus, a bandwagon ’ e� ect may be occurring; such an e� ectwould override the spurious negative duration dependenceoften found in duration models, as discussed below.4

III. ECONOMETRIC TECHNIQUE

Three econometric techniques have been applied to lotteryadoption studies: cross-sectional binary choice and Tobitmodels and duration models (survival analysis). Due to thenature of the data, we believe that duration analysis is thebest econometric approach since it allows for both explana-tory variables as well as probabilities of adoption to changeover time.

Often referred to as hazard models, duration techniquesincorporate the time until a state adopts a lottery. Nat-urally, states which adopt early give more informationabout reasons for adopting, and states which adopt laterprovide more information to the likelihood function aboutwhy states do not adopt. As a result, the concept of timing ismodelled. Duration analysis discards observations on statesafter the year of adoption because this study is not con-cerned with why states keep lotteries, since no state has shutdown a lottery.

The probability density function (pdf ) in a hazard modelcan be expressed as:

f(t) = Pr[T = t] (1)

which can be interpreted as the unconditional probability oflottery adoption at time t. The cumulative density functionis the probability that the state adopted before time t (i.e.,spell length T < t):

F(t) = Pr[T < t] (2)

which is the sum of the pdfs, f(s), from s = 0 to t - 1 in thediscrete case.5 We say that the survivor ’ function, S(t), is the

probability that the spell of non-adoption lasts beyondperiod t. Mathematically, this can be expressed as 1 - F(t).More formally,

S(t) = Pr[T > t] (3)

The hazard function, l (t) is interpreted to be the condi-tional probability of a state adopting in period t given that itdid not adopt before period t:

l (t) = Pr[T = t | T > t] = f(t)/S(t) (4)

The hazard function may be increasing (positive durationdependence), decreasing (negative duration dependence), orremaining constant (spurious duration dependence) overtime. Negative duration dependence is often found in dura-tion studies. In the context of lottery adoption, this could beattributed to states with a predisposition to adopting doingso early, leaving only those which are initially predisposedto non-adoption in the data set. Positive duration depend-ence was found by Alm et al. (1993). This suggests thata bandwagon ’ e� ect of adoption by states with a lowerpredisposition to lottery adoption outweighs a decline inadoption attributed to states with a predisposition to non-adoption remaining in the study.

The likelihood function of lottery adoption can thus beexpressed as:

L = Õyit= 1

{l (XitB)} Õyit= 0

{1 - l (XitB)} (5)

where the ® rst product represents the product of the condi-tional probabilities of states adopting lotteries in periodt given that they have not already adopted. The secondproduct represents the conditional probability that a statewill not adopt a lottery in period t given that they have notadopted in an earlier period (Kiefer, 1988).

The duration model is estimated using a limited infor-mation maximum likelihood SAS procedure, using aNewton–Raphson iteration process. Under the above speci-® cation, the data can be organized so that observations areread into the log-likelihood function by state. For example,data on Ohio is read in through 1974, with 1964–73 obser-vations included in the product on the right and 1974 dataincluded in the product on the left. After 1974, Ohio dropsout of the model because it is no longer at risk of adoption.Both standard normal and logistic distributions have beenused with similar success in lottery adoption studies.6 Thisstudy uses the logistic distribution.

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7 Filer et al. (1988), Davis et al. (1992), and Caudill et al. (1995) examine the impact of tourism on lottery adoption, focusing on the impact ofthe hotel and lodging industry.8 Per capita income has appeared in Berry and Berry (1990), Martin and Yandle (1990), Davis et al. (1992), Alm et al. (1993), and Caudill etal. (1995). Percentage of families with incomes below the poverty line has been used in both Filer et al. (1988) and Davis et al. (1992).9 Clotfelter and Cook (1989, p. 16). Proponents of lotteries, on the other hand, often cite evidence that lottery participation rates are higherfor high income individuals (Mikesell and Zorn, 1986, p. 315).

IV. EMPIRICAL MODEL

The dependent variable in this model is ADOPT , equal toone for the year of adoption, zero otherwise. In specifyingthe independent variables, we have followed the conceptualframework described above. In this framework, we attem-pted to specify variables that would capture the variousmotivations related to lottery adoption stemming from® scal well-being, revenue potential, and political factors.

Of immediate concern to legislators is the ® scal well-being of the state. To the extent that the state faces ® scalpressures with respect to meeting its budgetary obligations,legislators are prone to explore alternative revenue sourcesand may be more likely to support the adoption of a lottery.We use two speci® cations to capture these concerns. First,® scal health (FISCAL ) is de® ned as general revenue minusgeneral expenditures divided by general expenditures, fol-lowing the study by Berry and Berry (1990). The ® scalhealth variable is lagged one period (year) in accordancewith the hypothesis that lottery adoption is a lagged re-sponse to ® scal position. General revenue is restricted tostate revenue from its own sources. Although Berry andBerry (1990) ® nd weak support for this speci® cation (likelydue to omitted variables bias), this appears to be a goodmeasure of the extent to which state revenue meets thebudget.

The second important set of variables involve changes inthe tax base. Alm et al. (1993) hypothesize that a change ina state’s tax base will have a signi® cant e� ect on lotteryadoption. They state that if a state is experiencing a reces-sion, policymakers may ® nd it di� cult to increase revenuesfrom conventional forms of taxation and may be moreinclined to introduce new revenue sources’. This, theybelieve, will lead to an increased probability of lotteryadoption. As a measure of the change in the tax base, theyuse the percentage change in real state income and ® ndempirical support for a negative relationship between themovement in tax base and adoption.

In this study, we take a quite di� erent approach to exam-ining the e� ects of changes in the tax base. Rather thanfocusing on overall state income, we believe it is more usefulto examine changes within industries.7 First, we examine theimpact of changes in manufacturing earnings per capita(MANUPC), service earnings per capita (SERV PC), andgovernment services earnings per capita (GOV T PC). Asdescribed later, we also examine changes in tourism employ-ment per capita (T OURPC). In each case, the hypothesis isthat increases in the earnings of a particular industry will

increase the tax base and make supplemental revenuesources less critical, thus reducing the likelihood of lotteryadoption.

Although this approach is consistent with various studiesfocusing on regional economic e� ects, we believe a some-what altered approach is more desirable. One might arguethat legislators care most about the most prominent indus-tries in their state in considering the tax base. Where manu-facturing or services would be important in one state, theywould not be in others. Therefore, we have created threevariables that capture the percentage change in earningsin the three largest industries within a particular state(IMAXCHG, IMAX2CHG, IMAX3CHG). Our hypothesisis that as the percentage change in earnings in a state’s mostprominent industries increases, the tax base increases, andthus the desirability of lottery adoption is lessened. Thisapproach allows for state speci ® c variation in componentsof the tax base.

The second major focus of this study is on the potential® scal well-being of a state if a lottery is adopted. Variablesassociated with a state’s potential lottery pro® ts, the abilityof a state to tax export, and a state’s attempts to defend itselffrom tax exporting have all been considered in lottery ad-option literature. Although variables associated with the percapita well-being of the state, such as per capita income andper cent poor, have been primarily used in current literatureas a means of measuring constituent views towards gamb-ling, it appears that a more logical placement for sucha variable is as a measure of ® scal potential.8 The prevailinghypothesis in the current literature surrounding per capitaincome and per cent of the state’s population that is poor isthat the higher the per capita income in the state (the lowerthe poor population), the more likely is the adoption ofa lottery. While the studies all hypothesize a positive rela-tionship between per capita income and adoption anda negative relationship between per cent poor and adoption,they cite di� erent reasons. Although lotteries are voluntary,they are often viewed as regressive taxes because low incomeindividuals spend a higher percentage of their incomes onlottery tickets than individuals with higher incomes.9

Authors such as Filer et al. (1988) believe that legislatorswill not approve lotteries when they feel that agreater tax burden will fall on the poor population. In aStigler–Peltzman framework, more votes will be lost witha large low income (high per cent poor) population thanwould be gained. Martin and Yandle (1990), however,recognize the possibility that lotteries may be voted downbecause the poor vote against the opportunity to lose what

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little money they have. They go on to say, however, that themain reason higher incomes lead to lottery adoption is thatlotteries are a mechanism for higher income voters to redis-tribute income in their favour’.

Because a larger nominal amount is spent on lotterytickets by higher income individuals than lower incomeindividuals, it appears that income per capita would servea more clear purpose in a lottery adoption study if it wereconceived as a� ecting lottery revenue potential. It followsthat the higher the per capita income in the state(INCOMEPC), the greater the revenue potential of a lot-tery, and thus the higher the probability of adoption. Thisalternative hypothesis seems more realistic, and it avoids thecomplex arguments of voter desires discussed above.

Some studies hypothesize that the level of tourism ina state will a� ect both the occurrence and timing of ad-option. The greater the number of out-of-state tourists ina given state, the greater the potential of ticket sales tonon-residents. This would allow the lottery tax’ to be ex-ported’ to residents of other states, which will raise thesupport of the constituents in the given state without losingsupport through higher taxes. Because it is illegal to selllottery tickets across state lines, the authors believe that thegreater the number of tourists in a state, the more likely andsooner the state will adopt a lottery. Alternatively, if oneviews the primary impact of increases in tourism as increas-ing the tax base of the state, then increases in tourism wouldresult in decreases in the need for supplemental revenue anddecrease the likelihood of lottery adoption. Thus, the ex-pected sign of T OURPC is ambiguous.

Since states can potentially use lotteries to export taxes toother states, it has been hypothesized that the higher the percent of a state’s border contiguous with states with lotteries,the more likely and earlier the state will adopt a lottery asa defence mechanism to protect against other states export-ing taxes into their own state. The results have been highlysigni ® cant and positive in every case (Berry and Berry, 1990;Davis et al., 1992; Alm et al., 1993; Caudill et al., 1995). Thus,we hypothesize that an increase in the percentage of con-tiguous states with lotteries (BORDER), the greater thelikelihood of lottery adoption.

A state’s decision to adopt a lottery is based not only on® scal factors but is in¯ uenced by political considerations aswell. The tax burden on constituents, constituent viewstoward gambling, and the political features of a state haveall been hypothesized to a� ect the lottery adoption decision.

Constituent views towards gambling have become in-creasingly popular in adoption literature. Both religiousa� liation and measures of the level of existing gambling ineach state have been modelled to proxy for prior beliefsabout gambling. Per cent Southern Baptist, per cent funda-mentalist Christian, and per cent Catholic have been used inlottery adoption models with a di� erent hypothesis placedon the latter than on the ® rst two. The existing studieshypothesize that the higher the per cent of Southern

Baptists and fundamentalist Christians in the state, thegreater the opposition towards gambling (the lower theprobability of adoption) (Berry and Berry, 1990; Martin andYandle, 1990; Caudill et al., 1995). Alternatively, Alm et al.(1993) argue that Catholics are often times more open tolegal gambling, such as bingo, and would tend to supportthe introduction of a lottery. Moreover, other more liberalChristian denominations such as the United MethodistChurch have opposed lotteries other than strictly on thegrounds of basic moral opposition. For instance, they mightargue that the existence of lotteries would unduly encouragecompulsive gambling or that citizens may view lottery rev-enues as replacement for government revenues and reducesupport for education or other government services. Wehypothesize that increases in the percentage of a state popu-lation that is Protestant (PROT ), lagged one period, willresult in decreased lottery adoption.

As mentioned earlier, lotteries are often promoted tocitizens as providing incremental support for education.Many argue that lottery revenues are fungible (see, forexample, Borg et al., 1991). That is, increases in lotteryrevenues supplant general fund revenues that would havebeen allocated otherwise. Although these concerns aboutfungibility are likely quite valid, the political reality is thatlotteries have been sold’ to the public by promising in-creases in the quality of education. Thus, in states whereeducation expenditures per pupil (EDUPP), lagged one pe-riod, are lower, one might expect to see increases in theprobability of lottery adoption.

Finally, Alm et al. (1993) and Caudill et al. (1995) ® nd anincreasing trend of lottery adoption. The ® rst study uses thetotal number of lotteries which have been adopted, and thesecond uses a time variable. Alm et al. (1993) suggests thatone reason for an increasing trend is that as more states areobserved to successfully operate lotteries, the perceived risksof unsuccessful lottery introduction decrease’. Additionalreasons are political in nature. One suggests that politicianshave to guard against constituents perceiving other states ashaving `more’ than they have in their own states. Also, Almet al. (1993) contend that as the lottery industry becomeslarger, its lobby becomes more powerful. As the lobbygrows, the authors hypothesize that the probability of ad-option increases. Thus, we include a trend variable(T REND) to capture these e� ects, which also will be cap-tured to a degree by the BORDER variable. In addition,T REND tests for duration dependence – speci ® cally,whether or not a bandwagon e� ect is present. Instead ofusing actual years in the model (to guard against in¯ atedintercepts), 1962 through 1990 are assigned values of 1 to 29.

V. EMPIRICAL RESULTS

Determining what date to use as the start of the studyis a di� cult question associated with the hazard model

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1 0 Data for 1961 have been used for variables which are lagged. Observations for states which have adopted lotteries are only includedthrough the year they adopt, resulting in a smaller data set.

Table 1. V ariable means

ADOPT – Year of adoption NON-ADOPT – 1990

Mean Std. Dev. Mean Std. Dev.

FISCAL 0.0018 0.0613 0.0422 0.0459IMAXCHG 0.0164 0.0417 0.0171 0.0354IMAX2CHG 0.0321 0.0537 0.0225 0.0224IMAX3CHG 0.0215 0.0393 0.0204 0.0241MANUPC 22.1319 8.4278 14.3604 6.6452SERV PC 16.7068 4.3593 20.3949 9.3385GOV T PC 14.2658 3.3503 16.3701 2.5173T OURPC 0.0049 0.0026 0.0120 0.0260INCOMEPC 114.2589 13.8400 111.1212 10.6893PROT 25.2030 12.6184 50.4625 15.7799BORDER 0.4477 0.3392 0.3788 0.3194EDUPP 22.6384 7.9947 30.3263 5.5600Sample size 32 18

approach to lottery adoption. Since New Hampshire wasthe ® rst state to adopt (1964) in the recent wave of lotteryadoption (the previous wave ended when they were madeillegal in the late nineteenth century), three duration studiesbegan with 1964 in accordance with the idea that otherstates began considering lotteries as an alternative form ofrevenue after observing New Hampshire’s adoption. In con-trast, the panel data set utilized in this study consists ofobservations from 1962 to 1990 for ® fty states, resulting in1392 observations at the start of each estimation.1 0

Table 1 contains calculated means for the independentvariables of states with and without lotteries. Means forstates with lotteries have been calculated using cross-sectional observations in their corresponding year of ad-option. Fiscal variables are expressed in real terms, with thebase of the consumer price index set to 1982-84. For stateswithout lotteries, means are cross-sectional averages in 1990.While these results must be viewed with caution, since thestandard deviation for some of the variables are large relativeto the means and because the data are from two periods(1990 and 1990 prior), the results are suggestive relative tothe hypotheses associated with current ® scal well-being,potential ® scal well-being, and political constraints. Forexample, the adoption mean of FISCAL , 0.0018, is lowerthan the non-adoption mean, 0.0422. This supports thehypothesis that worse current ® scal well-being leads tolottery adoption because lottery states have low ® scal healthwhen they adopt relative to the ® scal health of states whichhave not adopted in 1990 (though the standard deviationsare quite large in this instance). Means for the prominentindustry changes are very similar, although the mean forIMAXCHG for adoption states is slightly lower than that

for non-adoption states. This supports the hypothesis thatlotteries are more likely to be adopted when the tax base isrelatively low. However, of more interest is the variablepattern for MANUPC, SERV PC, and GOV T PC. Formanufacturing, mean earnings in adoption states are higher,while for the other two industries mean earnings are lower.Some argue that lottery have followed declines in manufac-turing. We believe that lotteries follow declines in themost prominent industries. Looking at the e� ect of earningschanges in any one industry may lead to false conclusionsabout the tax base and the resultant impact on lotteryadoption.

The hypothesis that the probability of lottery adoption ishigher when there is a higher potential for lottery pro® t alsoreceives support from means comparisons. BORDER is0.4477 for lottery states in their adoption years compared to0.3788 for non-lottery states in 1990. This supports thehypothesis that when a state has a high percentage ofcontiguous states with lotteries, it is more likely to adopt alottery to defend itself from the tax exporting e� orts of otherstates, or just to join the bandwagon’. Moreover, per capitaincome is higher for adopting states, again con® rming theimportance of potential revenue as a determining factor.

The hypotheses associated with the political constraintalso receive support from a means comparison. The mean ofPROT is lower for lottery states in their adoption year(25.2030) than for non-lottery states in 1990 (50.4625) , sug-gesting that states with low moral or other social oppositionare more likely to adopt lotteries. Finally, the mean ofEDUPP is higher for non-lottery states in 1990 (30.3263)than for lottery states in their adoption years (22.6384). Thislends support to the hypothesis that the probability of

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Table 2. L ogistic hazard results

1 2 3 4 5 6 7

CONST - 0.0234 - 0.0231 - 0.0227 - 0.0081 - 0.0099 - 0.0101 - 0.0110( - 3.21) ( - 3.16) ( - 3.05) ( - 3.65) ( - 3.39) ( - 3.20) ( - 3.14)

FISCAL (T - 1) - 0.0290 - 0.0290 - 0.0286 - 0.0104 - 0.0124 - 0.0143 - 0.0157( - 2.35) ( - 2.37) ( - 2.33) ( - 2.86) ( - 2.59) ( - 2.61) ( - 2.55)

IMAXCHG - 0.0171 - 0.0164 - 0.0163 - 0.0051( - 1.60) ( - 1.56) ( - 1.50) ( - 0.87)

IMAX2CHG - 0.0071 - 0.0066( - 0.62) ( - 0.55)

IMAX3CHG - 0.0050( - 0.80)

MANUPC - 0.0000 0.0033( - 0.02) (1.38)

SERV PC - 0.0002( - 2.74)

GOV T PC - 0.0000( - 0.95)

T OURPC - 0.0939 - 0.1268 - 0.1512( - 1.63) ( - 1.60) ( - 1.57)

INCOMEPC 0.0001 0.0001 0.0001 0.0001 0.0000 0.0001 0.0001(1.87) (1.93) (1.95) (2.54) (0.96) (1.86) (1.77)

PROT (T - 1) - 0.0003 - 0.0003 - 0.0003 - 0.0001 - 0.0002 - 0.0002 - 0.0002( - 3.35) ( - 3.28) ( - 3.31) ( - 4.55) ( - 4.54) ( - 4.51) ( - 4.49)

BORDER 0.0095 0.0092 0.0092 0.0021 0.0029 0.0038 0.0043(4.13) (4.08) (4.04) (2.88) (3.25) (3.91) (3.97)

EDUPP(T - 1) - 0.0004 - 0.0004 - 0.0004 - 0.0001 - 0.0001 - 0.0002 - 0.0002( - 2.83) ( - 2.77) ( - 2.78) ( - 2.07) ( - 2.23) ( - 2.62) ( - 2.55)

T REND 0.0008 0.0007 0.0007 0.0003 0.0005 0.0005 0.0005(3.75) (3.64) (3.60) (4.33) (4.18) (4.75) (4.77)

Scale factor 0.0038 0.0037 0.0038 0.0010 0.0013 0.0016 0.0018f(3 avg*B)

Log-likelihood - 101.92 - 101.73 - 101.50 - 92.70 - 92.43 - 93.03 - 93.38

Joint test 87.71 88.08 88.54 106.14 106.68 105.48 104.78

Sample size 1136 1136 1136 1136 1136 1136 1136

Note: Dependent variable is ADOPT .

lottery adoption decreases as the expenditure on educationincreases.

VI . HAZARD RESULTS

The results of seven logistic hazard estimations are reportedin Table 2. Marginal probability e� ects are given along withtheir corresponding t-values (in parentheses). Summarystatistics, including log-likelihood statistics and a joint testof all independent variables except the constant equal tozero, are also reported. The calculated joint test statisticsshow that each model is signi® cant at the 99% level. The

scale factor, the probability density function evaluated atthe average values of the independent variables, is alsoreported. The reported marginal probability e� ects are cal-culated by multiplying the estimated coe� cients by the scalefactor. Using marginal probability e� ects rather than theestimated coe� cients allows comparisons to be made be-tween models.

Model 1 is the base model in this study, with Models2 through 7 having only slight variations. With the excep-tion of the industry change variable discussed below, all ofthe variables in Model 1 are signi® cant at the 5% level andhave their hypothesized signs. In this model, FISCAL hasits hypothesized negative marginal probability e� ect of

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1 1 The reported marginal probability e� ect of - 0.0234 on FISCAL is the product of the estimated coe� cient, - 7.6413 (not reported),multiplied by the reported scale factor, 0.0038. All other marginal probability e� ects are calculated in the same manner.1 2 To test for the existence of multicollinearity, we used the regression diagnostic technique suggested by Belsley et al. (1980). This techniqueinvolves identifying degraded regression coe� cient estimates by performing a singular-value decomposition of the data matrix ofindependent variables, identifying near dependencies in the data, using auxiliary regressions to display the relations among theindependent variables. In this case, IMAXCHG was signi ® cantly related to the pivot variable (INCOMEPC). Since the absolute value ofthe t-statistic for IMAXCHG was greater than 1, one can conclude that multicollinearity did result in signi® cant degrading of thecoe� cient and that IMAXCHG was a signi ® cant determinant of lottery adoption. The results are available upon request.1 3 The restricted log-likelihood statistic is calculated by multiplying the number of adoption observations (32) by the log of the ratio ofthe number of adoption observations to the total number of observations (ln 32/1136). This product is then added to the product of thenumber of non-adoption observations (1104) multiplied by the log of the ratio of the number of non-adoption observations to the totalnumber of observations (ln 1104/1136).

- 0.0234, suggesting that as the ratio of general revenuerelative minus general expenditures to general expendituresincreases by 0.01 (® scal health improves), states have less® scal stress and less need to adopt a lottery as an additionalrevenue source – decreasing the probability of adoption by0.0002.1 1 But as ® scal health falls by 0.01, ceteris paribus, theprobability of lottery adoption increases by 0.0002. Al-though the coe� cient on IMAXCHG is not quite signi® -cant at the 5% level, given the likely collinearity with othervariables, the standard error is likely in¯ ated with a result-ing degraded t-statistic.1 2 The results from the percentagechange in earnings for the maximum industry in a state areinteresting. The marginal probability e� ect of - 0.0171 onIMAXCHG suggests that as the change in the earnings fora state’s prominent industry declines by one percentagepoint, the probability of lottery adoption increases by0.0171. This result is consistent with the hypothesis thata structural change in the tax base in a state has an e� ect ona state’s lottery adoption decision.

The variables associated with the potential ® scal successof a lottery included in Model 1 are BORDER andINCOMEPC. The positive sign on BORDER is consistentwith the hypothesis that as the percentage of contiguousstates with lotteries increases, a state will likely adopt itsown lottery to defend itself from the tax exporting e� orts ofits neighbouring states. and/or join the bandwagon’. Theprobability of lottery adoption will also increase asINCOMEPC increases because a greater potential forrevenues from ticket sales exists when income per capita ishigh, since middle to high income individuals spend alarger nominal amount on lottery tickets than low incomeindividuals.

The variables representing political constraints in thebase model are PROT , EDUPP, and T REND. The negativecoe� cient on PROT supports the hypothesis that increas-ing moral or social opposition to lotteries (as represented bya larger percentage of Protestants) leads to a decreasingprobability of adoption because legislators do not want tolose the support of a large portion of the population. Speci® -cally, as the percentage of Protestants in a state increases byone percentage point, the probability of lottery adoption inperiod T will decrease by 0.0003. As education expense perpupil falls, the probability of lottery adoption increases,

according to the negative sign on the EDUPP coe� cient.This supports the notion that as education expense fallsbelow some optimal value, legislators may pro® tably turn tolotteries as an alternative source of revenue. As per pupileducation expense increases, however, constituents are lesslikely to support a lottery to raise additional revenue.T REND receives its hypothesized positive sign, which leadsto the conclusion that a bandwagon ’ e� ect dominates thespurious negative duration dependence often found in dura-tion studies. In the context of lottery adoption, spuriousnegative duration dependence would result if states predis-posed to adopting lotteries adopt early, leaving only thosestates not predisposed to adoption in the study.

From a policy standpoint, changes in the levels of theindependent variables can a� ect the probability of lotteryadoption. For example, the marginal probability e� ect of- 0.0004 on EDUPP suggests that a US$10 increase ineducation expenditure per pupil from the previous periodwill decrease the probability of lottery adoption in periodT by 0.004. Thus, legislators opposing lottery adoption canattempt to decrease the probability of the representativelegislator voting for the adoption of a lottery by increasingeducation expenditure per pupil. In order to increase anexpenditure, however, additional funding is generally re-quired. Therefore, legislators attempting to in¯ uence theprobability of adoption must also consider how the sourceof the expenditure increase a� ects the probability of lotteryadoption. In Model 1, an increase in education expenditurethrough an increase in general expenditure, ceteris paribus,will decrease the FISCAL ratio and increase the probabilityof adoption.

The joint test value reported is a test that all of thecoe� cients in the model except the constant are jointlyequal to zero. The statistic is calculated using the formula:

Z = 2*[lnL U - lnL R]

= 2* [( - 101.92)

- {32 * ln(32/1136)+ 1136 * ln(1104/1136)}] = 87.71

where ln L U is the unrestricted log-likelihood statistic forModel 1 and ln L R is the restricted log-likelihood statistic.The former is the reported log-likelihood statistic, and thelatter restricts all coe� cients except the constant to zero.1 3

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1 4 To test for the e� ect of aggregate changes in the concentration of various industries within a state, a Her® ndahl–Hirschman Index wastested in lieu of the industry variables. However, variations in industry concentration did not have a signi ® cant e� ect on lottery adoption.

The joint test statistic has a chi-square distribution withk - 1 degrees of freedom, where k is the number of variablesin X. In Model 1, the joint test statistic of 87.71 exceeds thecorresponding critical chi-squared value of 2.17 (5% signi® -cance, eight degrees of freedom). Thus, we reject the hypo-thesis that all of the coe� cients in the model except theconstant are equal to zero.

In Models 2 and 3, respectively, we test whether lotteryadoption is signi® cantly related to percentage changes in theearnings of the second and third most largest industries ina state. In neither case are the variables close to beingsigni ® cant.1 4 Model 4 replaces the maximum industriesvariables with per capita earnings variables for manufactur-ing, service, and government. Only the services measure issigni ® cant. We believe that this leads credence to the ap-proach we suggest above, focusing on the e� ect on the taxbase of the largest industries, and the resulting e� ect onlottery adoption. Examining the impact on lottery adoptionby following variations in one industry are likely to obscurethe very e� ect that is being sought.

Models 5 through 7 introduce T OURPC into the hazardmodel with di� erent combinations of industry variables.Although not quite signi® cant at the 5% level, increases inT OURPC lead to decreased likelihood of lottery adoption.This is interesting in several ways. First, the argument thatincreasing tourism leads to increased tax exporting su� -cient to make lottery adoption more likely to occur is notsupported. Rather T OURPC seems to be another proxy forchanges in the tax base, where increases in the tax basemake the need for alternate revenue sources, including lot-teries, less critical. Moreover, the change in T OURPC hasa relatively big impact on lottery adoption in comparison toSERV PC (a much more aggregated SIC category). Thismay argue for further disaggregation below the level ofmanufacturing, service, and government used in this study.

VII. SUMMARY OF RESULTS

Taken as a whole, the conceptual framework of lotteryadoption as a utility maximization decision of the represen-tative legislator receives strong empirical support in thisstudy. Results are signi® cant for current and potential ® scalwell-being variables as well as for those associated with thepolitical constraint.

FISCAL is signi ® cant at the conventional levels in all ofthe models. This seems to give strong support to the hypo-thesis that representative legislators vote to adopt lotterieswhen current ® scal stress is high. The hypothesis that thelottery adoption decision is a� ected by structural changes in

the tax base of a state is supported by the performance of theIMAXCHG and SERV PC variables. Both BORDER andINCOMEPC are signi ® cant and positive supporting theidea that legislators will vote for their states to adoptlotteries when the revenue potential of a lottery is high. Thenegative sign on T OURPC suggests that while the taxexporting possibilities of a large tourism industry mighttheoretically in¯ uence adoption, they are statistically over-shadowed by the current ® scal well-being associated witha large tourism industry. Finally, the notion that alegislator ’s utility maximization decision is subject to a pol-itical constraint is also well supported in this study. Theproxy for moral and social outrage to lotteries, PROT ,provides strong empirical support in each model. Thissuggests that as opposition to lotteries increases, legislatorsare less likely to adopt because they fear losing voter sup-port. The concept of an optimal value for an expenditureseems to also be supported econometrically. EDUPP hasa negative sign, which suggests that when education expen-diture falls below its optimal value, legislators will turn tolottery adoption as an additional revenue source. Finally,the strong positive sign on T REND in each model suggeststhat there is a bandwagon ’ e� ect in lottery adoption.

Variables such as lagged ® scal health and the relativechange in the tax base suggest that as the current ® scalwell-being of the state falls, there is a higher probability thatthe representative legislator will vote to adopt a lottery. Thehypothesis that as the pro® t potential of a lottery increasesin a given state, the representative legislator will be morelikely to vote to adopt a lottery is supported by the perfor-mance of both the border and income per capita variables.Furthermore, the notion of political in¯ uence on the repre-sentative legislator’s voting decision also is strongly sup-ported by the moral and social opposition variables, theoptimal expenditure variable (lagged education expenditureper pupil), and the trend variable.

By introducing a sound conceptual framework, usingbetter data than used in previous studies, utilizing an appro-priate estimation technique, and obtaining strong results,this study advances our knowledge of why states adoptlotteries.

ACKNOWLEDGMENTS

An earlier version of this paper was presented at theMidwest Economic Association meetings in March, 1997.Helpful comments were received from participants atthose meetings, as well as an anonymous reviewer of thisjournal.

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