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1 SPORTS GAMBLING AS CONSUMPT ION: AN ECONOMETRIC ANALY SI S OF DEMAND FOR SPOR TS LOTTER Y By LUNHUA MAO A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2013
2 2013 Lunhua Mao
3 To my family and friends for their unwavering support and encouragement over the years
4 ACKNOWLEDGMENTS I would never have been able to finish my dissertation without the guidance of my committee members, help from friends, and support from my family and wife. I would like to express my deepest gratitude to my mentor, Dr. James Zhang, for his excellent guid ance, caring, patience and support during the past four years, and for investing much time, effort and interest in this research project. I wou ld also like to thank Dr. Dan Co nnaughton for his willingness to chair my committee after Dr. Zhang moved to the University of Georgia, for his advice, encouragement, and support over the years. I am fortunate to have these two advisors in my life and am truly indebted for their guidance. I would like to give special thanks to Dr. Steven Shugan, who was more than ge nerous with his expertise and precious time I benefited tremendously from his inspiring writings, lectures and comments. I am also grateful to my other committee members, Dr. Stephen Holland Dr. J. O. Spengler and Dr. Beth Cianfrone, for providing numer ous hours of advice and critiques I would like to thank Dr. Hai Li at the Shanghai University of Sport for providing me some valuable research materials. I would like to thank my friends and fellow doctoral students at UF for their support, feedback, and friendship. Finally, I thank my parents, my sisters, and my wife for their love and continuing support.
5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 8 LIST OF FIGURES ................................ ................................ ................................ .......... 9 LIST OF ABBREVIATIONS ................................ ................................ ........................... 10 ABSTRACT ................................ ................................ ................................ ................... 11 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 13 Significance of Sports Gambling Industry ................................ ............................... 13 Need for Empirical Demand Research ................................ ................................ .... 15 Statement of Problem ................................ ................................ ............................. 18 Purpose of the Study ................................ ................................ .............................. 22 Significance of the Study ................................ ................................ ........................ 22 Delimitations of the Study ................................ ................................ ....................... 23 Definition of Terms ................................ ................................ ................................ .. 24 2 REVIEW OF LITERATURE ................................ ................................ .................... 26 Gambling, Lottery, and Sport ................................ ................................ .................. 26 Gambling ................................ ................................ ................................ .......... 26 Lottery ................................ ................................ ................................ .............. 28 Sports Gambling ................................ ................................ ............................... 32 Lottery Gambling in China ................................ ................................ ...................... 36 Theory of Demand and Utility of Lottery Gambling ................................ ................. 40 Expected Utility Theory and its Generalizations ................................ ............... 41 Indivisibility in Expenditure Hypothesis ................................ ............................. 43 Consumption Utility Hypotheses ................................ ................................ ....... 47 Determinants of Lottery Demand ................................ ................................ ............ 51 Product Attributes and Demand ................................ ................................ ....... 51 Effective price ................................ ................................ ............................ 51 Jackpot size ................................ ................................ ............................... 55 Estimation problems ................................ ................................ .................. 58 Game attractiveness ................................ ................................ .................. 61 Consumer Characteristics and Demand ................................ ........................... 61 Income ................................ ................................ ................................ ....... 61 Age ................................ ................................ ................................ ............ 65 Education ................................ ................................ ................................ ... 66
6 Gender ................................ ................................ ................................ ....... 68 Religion ................................ ................................ ................................ ...... 68 Ethnicity ................................ ................................ ................................ ..... 69 Marketing Variables and Demand ................................ ................................ .... 70 Border competition ................................ ................................ ..................... 70 Product substitution ................................ ................................ ................... 72 Venue accessibility ................................ ................................ .................... 74 Social responsibility marketing ................................ ................................ ... 75 Summary ................................ ................................ ................................ .......... 76 3 METHOD ................................ ................................ ................................ ................ 78 Background about Shengfu game ................................ ................................ .......... 78 Econometric Framework ................................ ................................ ......................... 81 Decision Calculus ................................ ................................ ............................. 81 Prize Pool ................................ ................................ ................................ ......... 82 Risk of Prize Shar ing ................................ ................................ ........................ 83 Expected Prizes ................................ ................................ ............................... 85 Relationships between Expected Value and its Determinants .......................... 85 Empirical Models ................................ ................................ ................................ .... 86 Time Series Analysis ................................ ................................ ........................ 86 Derivation of e ffective p rice ................................ ................................ ........ 87 Derivation of p rediction d ifficulty c oefficient ................................ ............... 87 Derivation of ticket composition variables ................................ .................. 88 Marketing and game feature dummies ................................ ....................... 90 Panel Data Analysis ................................ ................................ ......................... 90 Population and p opulation c ompositions ................................ .................... 90 Derivation of the income v ariable ................................ ............................... 91 Derivation of the sport v ariable ................................ ................................ .. 91 Venue a ccessibility ................................ ................................ .................... 92 Method of e stimation ................................ ................................ .................. 92 4 RESULT S ................................ ................................ ................................ ............. 103 Results of Time Series Analysis ................................ ................................ ........... 103 Stationarity, Autocorrelation, and Dynamic Specification ............................... 105 Ordinal Least Squares Results ................................ ................................ ....... 107 Instrumental Variables Results ................................ ................................ ....... 110 Using CAP as Instrument ................................ ................................ ............... 111 Results of Panel Data Analysis ................................ ................................ ............. 113 Pooled Models ................................ ................................ ................................ 113 Fixed Effects Models ................................ ................................ ...................... 114 Two Way Random Effects Models ................................ ................................ 115 Instrumental Variables Results ................................ ................................ ....... 116 5 DISCUSSION ................................ ................................ ................................ ....... 131
7 Theoretical Contributions ................................ ................................ ...................... 1 32 Sp orts Lottery as Consumption ................................ ................................ ...... 132 Rationality in Sports Gambling ................................ ................................ ....... 134 Impact of Social Demographics ................................ ................................ ...... 135 Impact of Marketing and Structural Changes of the Game ............................. 136 Consumer Learning or Consumer Attrition ................................ ..................... 139 Dynamic Nature of Sports Gambling Behavior ................................ ............... 139 Managerial I mplications ................................ ................................ ........................ 140 Limitations and Future Directions ................................ ................................ ......... 142 Conclusion ................................ ................................ ................................ ............ 143 APPENDIX : SUPPORTING INFORMATION FOR CHAPTER 3 ................................ 147 LIST OF REFERENCES ................................ ................................ ............................. 148 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 160
8 LIST OF TABLES Table page 2 1 A comparison of CWLDMC and CSLAC lottery products in China ..................... 77 3 1 Historical changes of the Shengfu game design ................................ ................. 97 3 2 Description of variables included in time series analyses ................................ ... 98 3 3 Coding the combination of the matches ................................ ........................... 100 3 4 Description of variables included in panel data analyses ................................ 101 3 5 Descriptive statistics and factor solution for deriving SPORT variable ............. 102 4 1 Descriptive statistics for time series data ................................ .......................... 118 4 2 Results of time series regressions ................................ ................................ .... 124 4 3 Descriptive statistics for the panel data analysis ................................ .............. 128 4 4 Results of panel data regressions ................................ ................................ .... 129 5 1 Prediction difficulty coefficients by ticket compositions ................................ ..... 145 5 2 Sales comparison between two simultaneous draws ................................ ....... 146
9 LIST OF FIGURES Figure page 3 1 Relationships among sales, expected value, and market level skill coefficient .. 95 3 2 Time series line of sales of Shengfu game over 2001 2012 ............................... 96 3 3 Distribution of Prediction Difficulty Coefficient as measured by log(RATIO2) ..... 99 4 1 Historical change of market level skill coefficients ( 1, 2 ) ................................ 119 4 2 Impact of rollover on demand ................................ ................................ ........... 120 4 3 Impact of ticket composition and rollover on demand: Using four most popular leagues as an example ................................ ................................ ........ 121 4 4 ACF PACF of sales and residuals of its AR(2) model ................................ ...... 122 4 5 ACF PACF of log(Sales) and residuals of its AR(4) Model ............................... 123 4 6 Within and between variations in panel data ................................ .................... 126 4 7 Separate simple regressions of 30 provinces: sales on effective price ............. 127
10 LIST OF ABBREVIATIONS C SLAC China Sports Lottery Administration Center C WLDMC China Welfare Lottery Distribution & Management Center G BGC Global Betting and Gaming Consultants G GY Global Gambling Yield, gross bets minus winnings payments N GISC National Gambling Impact Study Commission P ASPA Professi onal and A mateur Sports Protection Act of 1992 U KNL United Kingdom National Lottery
11 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy SPORTS GAMBLING AS CONSUMPT ION: AN ECONOMETRIC ANALY SIS OF DEMAND FOR SP ORTS LOTTER Y By Lunhua Mao August 2013 Chair: Daniel P. Connaughton Major: Health and Human Performance Despite that sports lottery gambling has become a prevalent economic and recreational activity, it remains a n under researched area in sports management literature. an econometric model of demand for sport s lottery gambling was constructed and e xamined in this study The model assumes an experiential utility associated with sports lottery gambling, and proposes that rational consumers are mainly motivated by three clusters of variables: product attributes, cons umer demographics, and market ing variables. The model is empirically examined by using a set of draw to draw sales data (from 2001 to August 2012) of the Shengfu game the most representative sport s lottery in China. Through time series and panel data analyses, this study has the followin g major findings: (a) s ports lottery has consumption value for players for which t icket composition has considerable impact on the demand. Draws composed of popular leagues and tournaments are often associated with higher demand ; whereas draws composed o f small er leagues often sell less ; (b) c onsumers are sensitive to the implicit cost of a buying l ottery ticket (i.e., effective price) where the estimated effective price
12 elasticity is around 1 ; (c) a t least in the context of Chinese sports betting marke t, the province with higher income level had hi gher demand for sports lottery contradicting the regressivity property of traditional lottery games The estimated income elasticity is around 0.4 ; (d ) consistent the research findings of previous studies population segments with higher financial and social burdens tends to buy more lottery tickets ; (e) m arketing variables and structural arrangements of the game were found have significant impact on consumer demand of sports lottery tickets; ( f ) consumers s howed signs of learning from betting experience and increasing the odds of winning as evidenced by an ever increasing median probability of winning the first and second prizes ; and (g) population, education level, sport development, and venue accessibility were found not significantly related to the demand of sports lottery
13 CHAPTER 1 INTRODUCTION Significance of Sports Gambling Industry The To purchase a ticket in a lottery, indeed, is to buy a kind of fiction in which oneself is the hero. Chance, New Statesman and Nation, June 6, 1931. Both gambling and sports are ancient and ubiquitous. People flock to casinos, horse tracks, and betting shops P eople play and spectate sports in droves. The magnitude of dollars involved in gambling is staggering 2.6 trillion U.S. dollars were spent in 2007 worldwide ( Morss, 2012 ) The f orms of legal gambling are various, including lotteries, bingo, casino and sport s gambling. Most Americans have participated in some form of gambling whether it involves purchasing a lottery ticket, playing fruit machine placing a bet at the track, or making a bet with friends in an office pool ( Welte, Barnes, Wieczorek, Tidwell, & Parker, 2002 ) As staggering is people s passion about sports ; f or instance, the top four professional leagues in North America, National Football League (NFL), National Basketball Association (NBA), National Hockey League (NHL) and Major League Baseball (MLB), collectively bring in about 24 billion U.S. dollars in revenue during a typical year, which is just the tip of the iceberg. The estimated sport business scale in the United States alone is worth between 400 to 435 billion U.S. dollars ( Plunkett Research, 2012 ) What tie s gambling and sports together is that people like betting o n the outcome of sporting events. Apart from forerunners in ancient Rome and Greece, organized and sanctioned sports betting date s back to the late 18 th century when modern bookmaking and pari mutuel systems came into being ( Munting, 1996 ) Today, the proliferation of
14 modern technology in the sport arena has further contributed to the growth of gambling participation ( Claussen & Miller, 2001 ) Although r epresenting only 2.6% of the legalized gambling market, sport s gambling has become the fastest growing gambling segment, with an annual growth rate of 14.7% in the past five years ( AAP News, 2012 ) For instance, in the United States where bookmaking is only legal in Ne vada and certain forms of sports lotteries in Oregon, Delaware, and Montana sport s gambling represents 9.86% of the sports industry ( Zhang & Cianfrone, 2011 ) In 2011, 2.88 billion U.S. dollars w ere legally waged in Nevada s sports books, representing less than 1 % of all sports betting in U.S. Approximately $ 93 9 million was wagered on the Super Bowl in the 2 according to the Nevada Gaming Control Board, and the event earned a net income of $ 5 1 million for the Nevada sports books ( American Gaming Association, 2012 ) During the 20 10 20 11 fisca l year, the British gambling industry generated a gross yield of £5. 5 billion where the sports betting sector had the largest market share within the sports industry, ac counting for 53% of all gambling transactions ( Gambling Commision, 2012 ) Regardless of its relatively short appearance in the world gambling and sport business milieu, China has achieved rapid developments in both industries. The average annual growth rate of the sport industry has been about 20% or higher in recent years I n 2008, the sports industry realized a total transaction value of $22.87 billion ac counting for 0.52% of GDP ( Li et al., 2012 ) The last two decade s also witnessed a gradual open up of China s gam bling market. Yet, the only legal form of gambling in China remains national lotteries, which are administered by two national agencies : Chin a Welfare Lottery Distribution and Management Center (
15 CWLDMC) and China Sports Lottery Administration Center ( CSLAC) Since the inception of the first national lottery in 1987, the lottery gambling market has been growing rapidly in the past 25 years. T he entire market reached to 221. 6 billion yuan (about 35.1 billion U.S. dollars) in 2011, re presenting a 33.3% annual growth The sales of CWLDMC lottery reached 127.8 billion yuan making a net revenue of 39 billion yuan ; and the sales of CSLAC lottery reached 93.8 billion yuan making a net revenue of 25.3 billion yuan (Ministry of Finance, 2012 ) Almost all mainstream lottery schemes, including lotto, numbers game, instant games, and high frequency lotteries are now administered by both centers, however the sports l otter y are only available from the CSLAC. Sports lotter y provide s a niche market for the CSLAC. In 2011, the sales of the sports lotter y climbed to about 21.8 billion yuan representing 2 3 % of the CSLAC lotter y market and 10 Ministry of Finance 2012). counterparts can be found in other countries, such as the Sports Select in Canada, La Quiniela in Spain, Football Pool in UK, and the Delaware sports lottery in the U.S. Need for Empirica l Demand Research The burgeoning of the gambling and lottery industry is puzzl ing Gambling is a zero sum game. Gambling market in general can not simultaneously yield profits for both sides of gambling participants (Sauer, 1998). L ottery market is even wor se. With a higher take out ratio compar ed to other forms of gambling and an extremely low probability of wining, the average expected return on one dollar lottery ticket is between 40 and 60 cents (Thaler & Ziemba, 1988). Lottery ticket s are evidently a ty pe of
16 goal is to maximize their expectation of return. Yet, people continue to buy lotteries, in droves anyway, violating the standard economic assumption of rationality and risk aversion in human behavior (McCaffery, 1994; Quiggin, 1991). Furthermore, the coexistence of gambling and insurance purchase constitutes a paradoxical phenomenon that has attracted much scholarly interest Scholars working in the separate discipli nes of psychology, economics, sociology, and among others have explored the phenomenon. This has led to two broad categories of explanation: rational vs. irrational. The stream of rationality of playing lottery has focused on the consumption value of lotte ry play ( Conlisk, 1993 ; Forrest, Simmons, & Chesters, 2002 ) lottery play as motivated by indivisibility in expenditures ( McCaff ery, 1994 ; Ng, 1965 ) and lottery play as a means to gain something for nothing ( Nyman, Welte, & Dowd, 2008 ) The stream of irrationality has largely drawn on the Prospect Theory ( Kahneman & Tversky, 1979 ) and cognitive theories of gambling ( Rogers, 1998 ) maintaining that lottery play is out of ignorance or cognitive error of the player s. Nevertheless, empirical investigations of the demand for lottery products in the economics literature explicitly or implicitly adopt a paradigm based on the expected utility theory. They have examined the demand for lottery products empirically from either of two perspectives: a source of public revenue or a consumer commodity ( Clotfelter & Cook, 1990 ) Since public lotteries were introduced as a way to increase governments budgetary income, and the takeout of lottery revenues can be regarded as an implicit tax levied on the players, a line of research examines the economic and social implications The main empirical questions arising from this perspective are the estimation of income elasticity of demand (i.e., whether this lottery tax is progressive,
17 neutral or regressive) to assess the impact of lottery tax on the relative distribution of income among the population ( Clotfelter, 1979 ; Garrett & Coughlin, 2009 ; Ghent & Grant, 2010 ; Spiro, 1974 ) and the estimation of own price elasticity of demand to assess whether the price or takeout rate is optimal to maximize revenue ( DeBoer, 1986 ; Forrest, Gulley, & Simmons, 2000 ; Gulley & Scott, 1993 ) The main empirical questions arising from the later perspective are whether consumer demand for lottery games responds to true expected returns, as maximizing behavior predicts, or whether consumers seem to be misinformed about the risks and returns of l ottery game, and what factors to be included in the estimable demand functions. These works may be divided into those who used product attribute variables such as effective price, jackpot and prize structure ( Forrest et al., 2002 ; Garca & Rodrgue z, 2007 ; Scoggins, 1995 ) those who used consumer characteristic variables such as income, gender, age, education, religion, and ethnicity ( Felsher, Derevensky, & Gupta, 2003 ; Herring & Bledsoe, 1994 ; Walker, Courneya, & Deng, 2006 ) and those who used marketing va riables such as venue accessibility ( Hing & Haw, 2009 ) cross border competition and product substitution ( Forrest, Gulley, & Simmons, 2004 ; Garrett & Marsh, 2002 ) and social responsibility marketing ( Li, Zhang, Mao, & Min, 2011 ) The purpose of demand analys is is to explain the process by which a consumer makes choices to maximize the utility he or she can derive from selecting the best possible combination of commodities within the budget constraint ( Clarkson, 1963 ) Traditional demand analysis starts with an underlying utility function. Whereas utility preferences and rationalizes that demand behavior ( Varian, 19 92 ) The theory of
18 demand evolves with the debates centering the fundamental assumption of rationality in human behavior, and has been gradually given much behavioral interpretation ( Becker, 1962 ; Domencich, McFadden, & Charles River Associates. 1975 ; Zhang, Lam, & Connaughton, 2003a ; Zhang, Lam, Williamson, Braunstein, & Ellis, 2003c ) Market demand is regarded as consumer expectations towards the main attributes of the core product ( Zhang et al., 2006 ; Zhang, Lam, & Connaughton, 2003b ) Demand analysis in terms of product features, consumer characteristics, and market ing environment is essential to develop a product that can deliver values to the consumers; demand analysis in terms of consumer characteristics is fundamental to segment consumers; demand analysis in terms of market ing variables can facilitate the formulation of marketing plans and forecast of sales ( Kotler & Keller, 2009 ) In lottery gambling literature, the insights from demand studies thus far have been consequential. The extant evidence suggests that lottery participation rates and levels of lottery pu rchases are strongly influenced by the effective price and the jackpot. Furthermore, the results from previous studies indicate that the heaviest lottery players are poor, young, and uneducated single men who live in urban areas and belong to specific mino rity (African American and Hispanic) and/or religious (Catholic) groups. Statement of Problem T here is apparent paucity in research on sports lottery gambling. Conceptual and empirical investigation of this topic has been limited to a very small number of studies, for example, Forrest and Simmons (2003) made a case of the symbiotic relationship between gambling and sport; Smith (1992) documented the development of sports lottery in Canada; Claussen and Miller (2001) made a conceptual arguments about the dri ving forces of sports gambling in the U.S.; and Garca and Rodrguez (2007) and
19 Garca, Prez, and Rodrguez (2008) tested the demand for football pools in Spain. There is thus far a wide gap between theory and practice with regard to sports lottery. S port s lotter y comes into being as a compromise between traditional lottery games and sports betting. Arguably a form of lottery, sports lottery differs from traditional games in several critical aspects. The f irst difference is in the non randomness of the dra wing. All traditional lotteries that share the characteristic of random selection of winners without any intellectual factor, such as skill and knowledge, associated with picking a winning ticket ( Mikesell & Zorn, 1987 ) In contrast sports lottery has no well defined objective probability of winning. I nformation and knowledge players have about the sport team s such as competition records, competence of the coach, and performance of the players may influence one s winning probability. It has been shown that the probability of winning a grand prize by correctly forecasting the completion results of all matches in the parlay is much higher than the probability if the competition results were complete ly random ( Garca & Rodrguez, 2007 ) It is exactly because of its non randomness in determining a winner, the Football Pool in the UK is not regarded as a component of its national lottery system ( Munting, 1996 ) The s econd d ifference is in knowledge based reasoning and over confidence. Relating to the nature of sports gambling, players tend to rely more on their ba ckground knowledge of the sport than evaluation of risk dimensions (e.g., probability of winning and pay out rate ) in their lottery ticket purchasing decision ( Ranyard & Charlton, 2006 ) Moreover, sports fans often consider themselves as expert s Du e to simplistic nature of various s port competition forms along with their familiarity and interest of sports, sport gamblers often feel they hav e superior expertise and intelligence in beating the prediction odds. This
20 over confidence would likely carry o ver to their lottery purchase decision, and may also induce stronger wishful thinking than what has been found in traditional lottery games. Th e th ird difference is related to the experiential utility in sports gambling. Sporting events are emotionally cha rged and the final result of a game means much to a real sports fan. For a loyal fan, sports gambling may be used as a way to express their allegiance with the ir teams or hedge the potential disappointment and sadness in case of lose ( Koning & van Velzen, 2009 ) Therefore, sports lottery consumption shares some commonality with spectator sports consumption. S ome fan attributes that influence spectator sports demand such as the quality of teams, were shown to have a positive and significant effect on the volume of bookmaker betting in the U S ( Paul & Weinbach, 2010 ) as well as the demand for sports lottery in Spain ( Garca, Prez, & Rodrguez, 2008 ) Finally, the sports lottery market may be inherently heterogeneous. Besides sports fans, there are also fan s of sports gambling and profess ional sports betters, who ha ve much less passion attached to any individual teams and cares more about the monetary gain ( Delaney, 2007 ) This inherent heterogeneity in different customer segments may lead to different demand function for sports lottery. Much of the knowledge gained from lotteries has been conducted on lott ery games in the U.S. and in the U.K There have been no studies that provide any empirical analysis on lottery games in China. Hsee and Weber (1999) found that Chinese people were significant ly more risk seeking than Americans in investment decisions Thi s risk preference likely carries over to Chinese lottery gambling decisions. Moreover, t he Friedman Savage (1948) utility function, elaborated upon expected utility theory, argues that utility in a specific segment of wealth is increasing. The ambition of
21 social improvement and dream of moving up into a higher class is a key motivation behind lottery gamblers This dream can arise from socio economic inequalities and lottery gambling wa s found to be more frequent and intense in countries with more acute social inequalities ( Kaizeler & Faustino, 2008a ) China is one of these countries with the GINI index estimated at around 0.47 in 2005 ( Wang, 2010 ) A Gini coefficient around 0.5 means the inequality problem is extremely severe The increasing ly widening gap between the rich and the poor in China calls for a critical look at its lottery demand and its implications for China s social and economic reforms. Furthermore, China has a very unique lottery market st ructure. Unlike the U.S. and Europe China has a national lottery market that is highly regulated by the national government. Meanwhile, the lottery market is facing a vigorously dynamic marketing environment with duopoly of CWLD M C and CSLAC, and possible cannibalization of dozens of other types of lotteries. As the market follower, the CSLAC has developed competing lottery products for almost all products currently sold by the CWLDMC. All main types of lotteries, including lotto, numbers, and instant tickets, are available at both the CWLDMC and the CSLAC retailing outlets and terminals. Furthermore, the lottery market is also subject to the threat of cross border gambling and illegal gambling. The mainland of China is surrounded by many gambling ventu res, including casinos in Macau, Malaysia, Vietnam, Laos, Cambodia, and North Korea. Wealthy Chinese gamblers flock to these venues on national holidays and weekends. Gambling also takes place in card and mahjong rooms on street corners and underground cas inos in the cities, through unofficial lotteries in the countryside, and on hundreds of websites catering to I nternet gamblers. The money wagered on illegal gambling was estimated at
22 least 10 times of legal wagers on national lotteries The uniqueness of t his market offers the potential of greater insight about lottery gambling for which o ne could not obtain from previous studies that were based on European or American markets. Purpose of the Study The overarching purpose of this study wa s to examin e the market demand for sports lotter y in China. The current research ha d two main foci : (a) to develop an econometric model to estimate the market demand for s ports lotter y and (b) to identify and examine the relative impact of three classes of determinants, including product attributes, consumer demographics, and marketing variables. To accomplish these goals, th is study focus ed on the demand for the Shengfu lottery game, a soccer betting lottery establis hed in October 2001 and the most popular sports betting game in China. A set of nation wide aggregate sales data for each draw of the Shengfu game from draw 2001001 (October 2001) to 2012 110 (August 2012) and a set of p rovincial level sales data for each draw of the Shengfu game from draw 2011001 to 2012110 w ere be obtained and analyzed through both time series and panel regression modeling. Significance of the Study The current study represents an initial effort to explore the demand for sports lottery gambling in China, a fast paced develop ing country with enormous demand and a more sophisticated gambling market with dozens of national lottery products. The research findings from this study have contributed to fill a void in the sport management literature by first developing an econometric mod el for the demand for sport s lottery, and then testing the model based on a unique set of draw to draw data. Gaining an in depth understanding of the demand for sports lottery would help lottery consumers make more informed and rational decision choices, f acilitate the governing bodies to
23 make more sensible decisions regarding the sanctioning of gambling products, and enable sports lottery agencies to allocate their resources toward optimizing their product portfolio. Furthermore, knowledge of sports lotter y may also make a humble contribution to the growing gambling literature in general This study is timely, when several countries and U.S. states, including India and New Jersey, are considering legaliz ing sports lottery. The findings of this study certain ly can lend some evidence for legislators to consider. Delimitations of the Study As the focus of this study was on the aggregate market demand for one type of sports lottery, namely the Shengfu game in mainland China, this study had the following delimi tations. First, this study focuse d on aggregate demand and ha d recourse to the theories of rational expectations to model the utility of sports lottery gambling. The units for data analyses were 30 provinces in China. This study did not intend to model the consumer demand on an individual level. A model of individual demand for sports lottery would call for a different theoretical framework, require micro data, and perhaps involve a different set of explanatory variables. Second, this study only consider ed the Shengfu game not other types of sports lottery The game is the oldest and most representative lottery of its kind in China, and resembles many important characteristics of other sports betting products available in other countries, such as Sport Select, La Quiniela and Delaware Sport s Lottery. The e mpirical findings of this study may be revealing to other games of similar characteristics, but may not be directly applicable to other games with different characteristics. Third, this study focuse d market. The findings of this study ma y be unique to the context due to the different development political, economic, and social factors of China.
24 Definition of Terms B ETTING P OOL A type of betting system in which players pay a fixed entry fee into a pool to make a selection on some outcomes, and the pool is shared by winners between those who have made the correct selection. B OOKMAKING A type of betting system in which bookmakers post odds and charge a commission for placing a bet on the outcome of sporting events, political contest s, and other competitions. In this system, bettors are promised a fixed payoff according to the odds posted at the time of making their bets (Chung & Hwang, 2010). CSLAC L OTTERY K t refers to any type of lottery administ ered by the China Sports Lottery Administration Center including both sports lottery and traditional lottery CWLDMC L OTTERY K i t refers to any type of lottery administered by the China Welfare Lottery Distribution & M anagement Center. CWLDMC does not have a sports lottery. D RAW A lso drawing, an occurrence of the process of deciding the winning numbers. E FFECTIVE P RICE The cost of buying a probability distribution of prizes that has expected value of one dollar (Clotf elter & Cook, 1987). Effective price of a unit price lottery ticket can be measured by the difference between its face value and the expected value of the prize, which tends to converges to the takeout rate with sufficiently long periods of time (Gulley & Scott, 1993). An alternative expression of effective price is the inverse of the expected value of the prize ( Garrett & Sobel, 2004 ) G AMBLING Various types of wagering activities involving material gains (losses), with consciousness of risk and hope of gain, on the outcome of an event whose result may be determined by chance or accident or have an unexpected result by calculation (Encyclopdia Britannica, 2012). It involves consideration, chance, and rewards (Rychlak, 1992). J ACKPOT The highest prize in a lottery game. Jackpots are paid either in annuity payments or in one lump sum. L OTTERY Traditionally, a lottery is a game of chance rather than a game of skill whereby winners are chosen by some random selection process. The most popular forms are Lotto, numbers games, and instant games. It may also refer to a game of skill, such as sports lottery. L OTTO A type of lottery game involving a selection of number combinations to be purchased by lottery players. Lotto games offer players the possibility of winning very large sums of money.
25 P ARI MUTUEL BETTING A type of betting system in which the payout from a specific outcome is inversely related to the aggregate amount wagered on that outcome relative to the aggregate amount bet across all outcomes (Chung & Hwang, 2010). P ARLAY A single bet that involves two or more individual wagers and is dependent on all of those wagers winning together P RIZE P OOL The total amount of money that is available to be divided among the winners in a lottery game or drawing. R OLLOVER The rolling over of an unallocated prize pool from previous draws to successive draw in a lottery syst em. S PORTS L OTTERY A form of lottery involves bets on the results of preselected sport s events. Sports lotteries are popular lottery games in much of the world, Football P ools In North America, sports lotteries are available in Canada and the state of Delaware. S PORTS B OOK An establishment that accepts wagers on sporting events. W AGER A wager is to have risked money, or something of value, on the outcome of an event.
26 CHAPTER 2 REVIEW OF LITERATURE Despite of the prevalence of sports lottery gambling in modern society, there is a paucity of research specifically addressing the issues related to the consumer demand for this type of gambling pr oduct. Instead, various streams of research in gambling, lottery, and sports betting proffer a broad foundation to analyze the economic principles underlying the sports lottery industry. This chapter begins with a brief survey of the concept and characteri stics of gambling and lottery, and the germination of sports lottery, followed by an overview of sports lottery operations in China. Next, I reviewed the theory of demand and the utility of lottery gambling, focusing on the Expected Utility Theory and its derivatives. Then, I present a review of the econometric models of market demand for gambling products with an aim to identify influential factors of sports lottery demand to be empirically tested in this study. Gambling, Lottery and Sport Gambling Gambling is an ancient and ubiquitous recreational activity worldwide and peculiarly difficult to define. It has a wide variety of incarnations, ranging from such informal pastime as matching fingers and rolling pebbles, to such institutionalized chance ga mes as lotteries, horsing racing, sports betting, and casino games ( Bloch, 1951 ) In some casual writings it may broadly refer to any area of risk or chance where some material gain (loss) is involved, including stock market speculation, and investments on some financial derivatives. All gambling seems to dwells on the chance factor of success for its participants, but differs from market speculation in that gambling itself does not determine or influence the outcome of the event ( Munting, 1996 )
27 Theoretically, the amount of betting will not make a horse run more or less slowly; the volume of gambling will not affect the performance of the sports teams on field, or the probability o f winning a prize over the slot machines. By contrast, in the case of speculative market, the aggregate effect of demand on a particular share is to determine the price. A consensual and narrower understanding of gambling will include various types of wage ring activities involving material gains (losses), with consciousness of risk and hope of gain, on the outcome of an event whose result may be determined by chance or accident or have an unexpected result by reason of the better s miscalculation ( Encyclopdia Britanni ca, 2012b ) Rychlak (1992 ) succinctly concluded that all gambling relates to three elements: consideration, chance, and rewards. Ga m bling has huge consumer demand and is indeed a big industry in the world. Bloch (1951 ) argued that human beings in modern society are motivated to gamble in an attempt of escaping from the routine and boredom characteristic of modern industrial life. It is a type of entertainment, likening to movies, spectator sports, or other plays. From labor supply market perspective, Nyman et al. (2008 ) suggested that people escape from daily work for gambling because the gain from gambling is additional income for which the gamblers do not need to work. The Global Betting and Gaming Consultants ( GBGC, 2007 ) estimated that the Global Gambling Yield (GGY), defined as gross bets minus winnings payments, was 337.1 billion U.S. dollars in 2007, with casino being the primary vehicle for gambling and representi ng 32% of market shares. North America (120.1 billion U.S. dollars) and Europe (102.5 billion U.S. dollars ) generated the most gambling revenue with Asia and the Middle East (75.6 billion U.S. dollars) in
28 third place. The United States, with 94.9 billion U .S. dollars revenue, is the leading country in worldwide gambling market. The major types of gambling in the United States now includes casinos (traditional, tribal, and riverboat), pari mutuels (horse, greyhounds, jai alai), state run lotteries, bookmakin g (sports, horse), card rooms, charity bingo and other charity games ( Pavalko, 2000 ; Welte et al., 2002 ) The global betting totals however are even larger as bettors do not expect to lose all they bet. Using GGYs as if the institutional take out it is estimated that the global bets in 2007 were 2.6 trillion U.S. dollars ( Morss, 2012 ) Lottery Lottery is a major player in contemporary global gambling milieu. Its contribution to the GGY reached 98.3 billion U.S. dollars in 2007, second only to casino ( GBGC, 2007 ) The w orldwide sales of lotteries are estimated to amount to 224.3 billion U.S. dollars in 2007 ( LaFleur's 2008 World Lottery Almanac, cited in Ariyabuddhiphongs, 2011 ) and 240.1 billion U.S. dollars in 2009 ( LaFleur's 2010 World Lottery Almanac, cited in Scientific Games, 2012a ) Lottery is also one of the faste st growing sectors in gambling, growing by 78% in the 1999 2007 period ( GBGC, 2007 ) Lotteries are games of chance, to which the over 100 countries and 200 jurisdictions have recourse for raising general re venues or earmarked purposes ( Ariyabuddhiphongs, 2011 ) In history, it is known that British kings sanctioned lotteries to fund London s water supply, Westminster Bridge, and the British Museum ( Munting, 1996 ) Throughout early American history, lotteries helped to build cities, including the Jamestown settlement, and establish universities by financing buildings on the campus of Harv ard and Yale ( Clotfelter & Cook, 1990 ) During the American Revolutionary War, lotteries were even authorized by the Continental Congress to help offset the high cost of the war ( Scientific
29 Games, 2012b ) Regardless of its historical significance, lotterie s of all kinds were gradually discarded in the nineteenth century as nations developed what are now standard methods of finance and taxation. In the United States, lotteries had been prohibited since 1895 after the outset of the Louisiana lottery scandal ( NGISC, 1999 ) The modern lottery was not introduced to the public policy sphere until 1964, when New Hampshire became the first state to employ lotteries to raising revenue. The lottery ex peditiously diffused across the country. New York adopted a lottery in 1966, New Jersey in 1970, and ten more states in 1975 ( NGISC, 1999 ) Today there are lotteries in 41 states plus the District of Columbia. In the United Kingdom, the UK National Lottery was introduced in 1994 which has soon grown into one of the largest lotteries in the world ( Forrest et al., 2000 ) Lotteries are sold in various forms, the most popular being the lotto, the numbers games (e.g., Pick 3, Pick 5), and instant games (e.g., scratch cards). The prize structure of a game can be organized in a format of fixed payout or pari mutuel. For example, the inaugural UK National Lottery was a standard pari mutu el 6/49 lotto game ( Forrest et al., 2000 ) The buyers select 6 two digit numbers from 01 49. The jackpot pool is to be shared by all those selecting the six winning numbers. There are also smaller fixed payout prizes for partially correctness (e.g., 5 numbers in the 6/49 game). If no one selects the full set of winning numbers, a rollover is declared and the jackpot prize money is added to the jackpot pool for the following draw. There are also variants in terms of prize structure. In the case of Chinese Sports Super Lotto, a 5/35 plus 2/12 game, both the grand and second prizes adopt a pari mutuel format, and there is maximum payout for the grand prize (i.e., 5 million yuan ) ( China Sports Lottery
30 Administration Center, 2012 ) Traditional numbers game is similar to a raffle. The players buy a fixed face value ticket on which the numbers have already printed, and the winning number to be declared in a later time. Today this old fashioned game is virtually extinct, having been replaced by modern numbers game which apparently requires players active selection of a certain digit nu mber ( Clotfelter & Cook, 1990 ) Those who pick the winning number will be typically awarded a fixed amount of prize (e.g., 1,000 yuan and 10,000 yuan for Chinese Pick 3 and Pick 5 game respectively). In instant games, the players scratch the surface of the tickets to reveal the award information. The games have become more complex and have greater intrinsic play value nowadays. Instant games can be analogous to slot machines in casino ( Ariyabuddhiphongs, 2011 ) For example, the Mas sachusetts scratch cards, with varying cash and non cash prizes, were priced at different rates: $1, $2, $5, $10, and $20. Prizes vary from card to card but the minimum win is 1 U.S. dollar and the maximum winnable amount on a card is 10 million U.S. dolla rs. More interesting, some organizations become affiliated with the issue of scratch cards, notable the NBA and MLB. These special cards often offer extra prizes such as a season ticket for life ( ScratchCards.org, 2012 ) In 2011, the China Sports Lottery Administration Center launched a series of NBA theme scratch cards with official authorization of the National Basketball Association. These scratch cards sold out soon after they hit the market. In addition to these three major types of lotteries, many lottery administrations have launched game variants or new games, including high frequency lotte ry, new media lottery, and sports (betting) lottery.
31 Lotteries share common characteristics of all gambling as they involve consideration, chance, and rewards. The consideration component is the fee for a lottery ticket, the chance component is the rando mly selected winning numbers, and the rewards component is the lottery prize ( Scientific Games, 2012a ) Meanwhile, lotteries have three distinctive features in comparison with other gambling forms. The first is the monopoly power of the nation or state. Lotteries provid ed by the private sectors are outlawed. In the United States, each state has granted itself a monopoly over lottery gambling within its boundaries ( NGISC, 1999 ) In the United Kingdom, the operation of the lottery was exclusively franchised to the private consortium, Camelot group plc ( Forrest et al., 2004 ) One ostensible motivation for state monopolies has been the desire to keep lotteries free of corruption, fraud and criminal influence ( NGISC, 1999 ; Zelenak, 2000 ) More subtly however, is that the monopoly power allows the governments to maximize their revenues by producing monopoly profit. Zelenak (2000 ) found that 19 out 38 American lottery jurisdictions were very explicit abo ut their intent to maximize revenues from their lottery monopolies. Forrest et al. (2000 ) also found evidence to support that Camelot, combined with government oversight, was maximizing their revenue with respect to the UKNL lotto g ame. Hyman (2010 ) put it this way: otteries are profit making enterprises that most states run like any business, with heavy a dvert ing and innovation in products to generate sales Economies of scale may provide another rationale for a lottery monopoly. It is long established abnormal phenomenon in gambling literature that betters prefer larger jackpot with lower winning probability than smaller jackpot with higher winning probability a phenomenon known as longshot bias ( Garrett & Sobel, 1999 ; Golec & Tamarkin, 1998 ) A monopol ized
32 lottery market makes it easier to offer big jackpots. That s exactly why states have voluntarily participated in such multiple sate games as Tri State, Lotto America, Powerball and Mega Millions ( Clotfelter & Cook, 1990 ; Cook & Clotfelter, 1993 ) A second feature of lottery relates to its low pay out ratio, or the proportion of the total amount of money returned to the players to the total sales revenue. Clotfelter and Cook (1990 ) estimated that the pay out ratio of lottery is approxim ately 50%, much lower than that offered by other gambling forms such as bingo (74%), horseracing (81%), and slot machines (89%). Based on the figures of GGY and total sales revealed by GBGC and LaFleur s 20 08 World Lottery Almanac respectively, one may est imate that the pay out ratio in 2007 was approximately (1 $98.3 billion / $224.3 billion) = 0.56. Considering the costs and taxes occurred to the gambling institutions, 0.50 would be a good estimation. The third feature of lottery is its extremely low prob ability of winning, as a consequence of monopolized operation, high take out ratio, and consumers preference for big jackpot. Take the 6/49 game as an example, it only carries a one in 14 million probability of winning grand prize. If it is 6/53 game, the n the chance of buying the winning combination shrinks to approximately 1 in 23 million. Because the size of jackpot is subject to sales of current draw and rollovers from previous draws, the games have to be designed in such a way that the winning probabi lity is extremely low and rollovers will appear at a certain pace, not too frequent and not too infrequent, thus to maximize revenue ( Walker & Young, 2001 ) Sports Gambling There has been a long history of the symbiotic relationship between sports and gambling, to the extent that som etimes they are indistinguishable. Some sports also owe their very existence to the sales of their complementary good, betting, including
33 horse racing and jai alai in the United States ( Forrest & Simmons, 2003 ) Horse racing by itself was not a viable spectator sport in the United States. By enacting bans on bookmaking at the track, some states were able to effectively close down horse racing completely in the first quarter of 19th century ( Forrest & Simmons, 2003 ) Then durin g the interwar period, the introduction of pari mutuel betting had directly led to the revival of horse racing ( Muntin g, 1996 ) Jai alai, a speedy sport involving a ball bounced off a walled space is another non viable spectator sport but remains popular in Florida, where the game is used as a medium for legalized pari mutuel gambling. Forrest and Simmons (2003 ) suggested that the existence of a betting market for a sport can stimulate the public interest and attention to the sport, which may well translate into the profitability of particular professional sports regardless that the sports clubs may not land direct income from betting. Although representing only 2.6% of legalized gambling market, sports betting has become the fastest growing gambling segment according to industry research group IBISWorld s report, with an annual growth rate of sports gambling is 14.7% in t he past five years ( AAP News, 2012 ) Because of the unpredictability of competition results, sporting event has alwa ys been an attractive medium for betting. In fact, the origins of three major types of betting systems, bookmaking (fixed odds betting), pari mutuel betting (totalisator), a nd betting pool (sports lottery) were closely related to sports ( Munting, 1996 ) Bookmaking is a gambling system in which bookmakers post odds and charge a commission for placing a bet on the outcome of sporting events, political contests, and other competitions In this type of market, bettors are promised a fixed payoff according to the odds posted at the time of mak ing their bets ( Chung & Hwang, 2010 ) This profession is known from
34 the time of ancient R o me, when betting on the outcome of gladiator ial matches or chariot races was prevalent ( Encyclopdia Britannica, 2012a ) and develops rapidly in the United Kingdom in 19th century for horse racing wagering ( Munting, 1996 ) In countries where bookmaking is legalized, bookmakers may open chains of betting shops; and with the arrival of internet, many bookmakers begin to offer internet g ambling outlets as well as such derivatives as betting exchanges ( Koning & van Velzen, 2009 ) Bookmaking remains the major form of gambling in the Great Britain, whereas it is outlawed in all states but Nevada in the United States. Notable bookmakers include William Hill plc, Ladbrokes plc, and Gala Coral. Pari mutuel, a betting system invented in 1867 in French, differs from fixed odds betting in that the final payout is not determined until the pool is closed. T he payout from a specific outcome is inversely related to the aggregate amount wagered on that outcome relative to the aggregate amount bet across all outcomes ( Chung & Hwang, 2010 ) That means the payoff odds are calculated by sharing the pool among all winning bets. In this system, there are no bookmakers, the bettors are essentially betting against each other. In the United Kingdoms Australia, and New Zealand, this system is also known as the Tote after the totalisator, a machine invented to calculates and display bets already made. Pari mutuel betting is relative insignificant in Great Britain. In the United States, pari mutuel betti ng on horseracing, hound racing, and jai alai is legalized by the federal law, Professional and Amateur Sports Protection Act of 1992 (PASPA). Pari mutuel gambling often takes place at off track facilities, where players may bet on the events without actua lly attending the event in person.
35 Betting pool, a concept introduced in 1923 by Littlewoods Pools based on soccer matches ( Munting, 1996 ) can be regarded a variant of pari mutuel betting influenced by lotteries. In this system, players pay a fixed price into a pool, and then make a selection on some outcome, usually related to sport. The pool is evenly divided betwee n those who have made the correct selection. Differing from the original pari mutuel system, there are no odds involved; each winner s payoff depends simply on the aggregate amount of betting and the number of winners. Sports lottery in most countries typi cally employ s this adapted pari mutuel system, including La Quiniela in Spain, and Shengfu Game in China. Today in England, sports lotter y is more commonly referred to as football pool The nascence of sports lottery exemplifies the symbiosis of sports and gambling, and the increasingly blurring line between lottery and sports betting. In the United States, betting on the NCAA basketball games is very popular, which gives r ise to the March Madness and a plethora of office pool, a derivative of betting pool ( Kaplan & Garstka, 2001 ) The goal in these pools is to predict the winners of as many games as possible, or more sophisticatedly the point spread ( Bialik, 2011 ) An office pool typically charges an entry fee for players to take part in the game. T h e entry fees contribute t o a prize that is awarded to the winners of the pool in some pre specified manner. It is estimated that the total amount of money wagered in each year s March Madness can rival that on the Super Bowl ( Kaplan & Garstka, 2001 ) However, because of its moral concerns and potential threat to the integrity of the sports, betting on s ports is a very controversial issue involving tremendous contentions between the proponents and opponents. Legal sports betting exist in many countries and region, notably most European countries, Australia, Canada, and Las Vegas,
36 typically high regulated. In the United States, bookmakers are only legal in Nevada and certain forms of sports lotter y in Oregon, Delaware, and Montana in accordance with the Professional and Amateur Sports Protection Act of 1992 ( Moorman, 2010 ) I llegal bookmaking with respect to NFL, MLB, and NBA, however, is prevalent in most parts of the country ( Munting, 1996 ) Organizations of sports also oppose to being associated with gambling as it may lead to a disregarded status of their sports ( Smith, 1992 ) Their concerns are not unwarranted T h ere are notorious cases that gambling led to match fixing and other corruptions in soccer ongoing in over 25 countries, including Chinese Supper League and Italian Soccer Leagu e ( Forrest, 2012 ) In the United States, the National Intercollegiate Athletic Association s (NCAA) official policy prohibits any form of legal or illegal betting on their sports. I n 2009, the National Football League (NFL), a llying with NBA, NHL, MLB, and the NCAA sued De laware for its legalization of offering a new type of sport s lottery that allows players bet on the result of single NFL game ( Moorman, 2010 ) Lottery Gambling in China Gambling is pervasiv e in Chinese society, and can be traced back to the first documented Xia dynasty (2000 1500 B.C.) around 4000 years ago ( Lam, 2005 ) Higher prevalence rates of recreational and problem gambling have been reported in Chinese population among all the populations studied ( Tang, Wu, & Tang, 2007 ; Wong & So, 2003 ) which can be supported by findings in behavior research. Hsee and Weber (1999 ) have compared Chinese and American approaches to financial risk. In a series of experiments, they found that both nationals predicted that the American would be more risk seeking, yet Chinese were significantly more risk seeking than the Americans in the domain of investment. They suggest that traditionally large Chinese family
37 network afford people confidence that they can receive fi nancial help if a risk does not succeed, c onsequently, they are less risk averse than those in an individualistic society s uch as the USA. Although gambling in China is virtually a national pastime, gambling had been outlawed since the founding of the People s Republic of China in that it violates the moral system of socialism and serves a seedbed for criminal activities. Acco rding to the purpose of profit, gathers people to engage in gambling, runs a gambling house or makes gambling his profession shall be sentenced to fixed term imprisonment of not more than three years, criminal detention or public surveillance and shall also be fined. If the circumstances are serious, he shall be sentenced to not less than three years but not more than ten years in prison, and shall be imposed upon to a fine However, as the term gambling is not defined in the law, which left leeway for the governments to sneakily introduce various gambling devices under the framework of national lotteries It seems that the Chinese governments toleration of national lott eries and other forms of gambling activities is strikingly different. Whereas buying private lotteries was illegal, buying national lotteries is deemed as contributing to the good causes and thus is never mentioned as gambling in any officially released do cuments, regardless that indulgence in lottery gambling is becoming a serious social issue ( Li et al., 2012 ; Li et al., 2011 ; Phillips, Liu, & Zhang, 1999 ) Since the establishment of the China Welfare Lottery Committee for Raising Fund ( ) in 1987, which changed to China Welfare Lottery Distribution and Management Center in 1994, and the inception of the f irst lottery ticket,
38 t he lottery gambling market has been rising remarkably in the last 25 years. I n 1994, the second lottery distribution agency, the China Sports Lottery Administration Center (CSLAC), was officially founded The entire market grew in tot al sales from 17 million yuan (about 2.7 million U.S. dollars) to 221.4 billion yuan (about 35.1 billion U.S. dollars). Specifically, Scratch card rose from a low of $138 million in 2005 to a high of $2.95 billion in 2008, an increase of more than 20 times over a period of 4 years. Lotto realized a steady increase from $5 billion in 2004 to $11.8 billion in 2008, among which dual color ball and super lotto were pillars of welfare lottery and sports lottery, respectively ( Li et al., 2012 ) The total sales of welfare lotteries the lotteries issued by the CWLDMC, reached 127.8 billion yuan representing 57.7% of the market, and the sales of sports lotteries the lotteries issued by CSLAC, reached 93.8 billion yuan representing 42.3% of the market ( CSLAC, 2012 ; CWLDC, 2012 ) 1 A lmost all mainstream lottery schemes including lotto, numbers game, instant games, and high frequency lotteries are now administered by both centers, whereas the sports lotter y is only avail able from the CSLAC. Table 2 1 compares current CWLDC and CS LAC lotter y products available in China and their market share in 2011. The CWLDC lotter y ranging from the highest to lowest in terms of total sales in 2011, include s : Duo Balls ( 6/33 plus 1/16 lotto ), 3D (numbers game) guaguale ( 1 The lottery products managed by the CWLDMC are known as welfare lotter and those by the CSLAC as sports lottery in China. However, it should be noted that the CSLAC lottery products include both actual sports lottery games which is the focus of this dissertation and the traditional non sports lottery games. They are referred to as China because they are managed by sports administrations and the revenues are earmarked for sports related courses. To distinguish these two different meanings of sports lottery, CSLAC lottery is used in this dissertation when it comes to all types of lot tery products managed by the CSLAC. Accordingly, CWLDMC lottery is
39 instant game) zhongfu video lottery terminal), Happy 7 ( 7/30 lotto), and kailecai ( numbers game) The CSLAC lotter y ranging from the highest to lowest in terms of total sales in 2011 include s instant game), 5/ 22 high fre quency game ( 22 5, lotto, high frequency), Super Lotto ( 5/35 plus 2/12 lotto), soccer betting ( sports betting) Pick 3 ( shengfu sports betting) Pick 5 ( numbers game), 7 star ( numbers game), shengfu select 9 sports betting ), basketball betting ( sports betting ), 5/22 L otto (22 5) goals of 4 matches ( sports betting ), Super Lotto Luck Prize ( lotto), and 6 matches double result ( 6 sports betting ). In addition, there are many types of province run lottery variants approved by either centers. Sports lotter y essentially a betting pool, provide s a niche market for the CSLAC. In 2011, the sales of the sports lotter y summed to about 19 billion yuan rep resenting 20% of CSLAC lotter y market and ( CSLAC, 2012 ) Public lotteries, as a revenue source for the governments, are essentially implicit taxes ( Clotfelt er & Cook, 1987 1990 ; DeBoer, 1986 ) The institution of lotteries is often based on the notion that an unhealthy but not necessarily evil course can be allowed with regulation if it can be used to raise funds for good course s ( McGowan, 1994 ) In China the CWLDMC lottery is to raise funds for social welfares courses, including orphanages, nursing homes, medical care, education, legal assistance, and etc. ( Ministry of Finance, 2008 ) The allocation of the funds to each cause is not earmarked but on a need base. CSLAC lotter y is to raise funds for sports development.
40 Specifically, 60% of the revenue is earmarked for the implementation of National Fitness Plan and the rest 40% is complementary financial source for Olympic Glorious Program ( General Administration of Sport of China, 1998 ) According to this interim regulation, the revenue may be used for promoting sports for all programs, building sports infrastructures for mass participation, hosting mega sporting events, and sports development in the regions under poverty line. For most types of lotteries, 50% of total sales is allocated to prizes, 35% to government revenue, and 15% to administration cost. Sports lotter y is exceptional: up to 69% of total sales is allowed to allocate to prizes, and only 18% to government revenue. Overall, th e rapid growth of gambling opportunities in China is unforeseen by both gambling administrators and consumers. Chinese gambling market is facing a vigorous ly dynamic marketing environment with duopoly of the CWLDMC and CSLAC, and possible cannibalization of dozens of types of lotteries. Theory of Demand and Utility of Lottery Gambling Microeconomic theory of demand is a theory about the behavior of consumer in the market place. Its purpose is to explain the process by which consumer makes choices to maximize the utility he or she can derive from selecting the best possible combination of commodities within the budget constraint ( Clarkson, 1963 ) Traditional demand analysis starts with an underlying utili ty function. Whereas utility itself involves no psychological interpretation, it is supposed to describe consumer s preferences and rationalizes that demand behavior ( Varian, 1992 ) The theory of demand evolves with the debates centering the fundamental assumption of rationality in human behavior, and has been gradually given much behavioral interpretation ( Becker, 1962 ; Domencich et al., 1975 ; Zhang et al., 2003a ; Zhang et al., 2003c ) Adhering to the tradition of
41 economic analysis the discussion of demand for lottery gambling starts a discussion on the utility a l ottery product has to offer. W hy do people buy lottery tickets? A nd why do people simultaneously seek and avoid risks, as demonstrated in the paradoxical coexistence of gambling and insurance purchase behaviors? These have puzzled economists, sociologists, psychologists and other scholars for decades, and lead to the germination of various modifications of the modern expected utility theory. Expected Utility Theory and its Generalizations The expected utility theory (EUT), originally introduced by Bernoul li in 1738 and axiomatized by Von Neumann and Morgenstern (1944), has been the underpinning of modern economic analysis of choice under risk and uncertainty EUT holds that people take action to maximize the sum of the probability weighted utilities of th e different outcomes by comparing their expected utility values. In the context of lottery play, it of the expected utility values of a sure thing of spending 2 dollars for buying a ticket and that of 1 in millions probability of winning the grand prize. EUT predicts that the former should always be greater than the later in that EUT takes status quo utility level into consideration and presumes a diminishing marginal ut ility of wealth, i.e., a continuously concave utility function. That means additional units of wealth are worth subjectively less than prior ones. And the disutility of losing one dollar is higher than the utility of gaining an extra dollar, which is known as loss aversion in the literature. Under the intuitively plausible assumption of loss aversion, people will not be even willing to take a fair bet, not to say such unfair ones as lottery. Simply put, people should not play lotteries under the normative f ramework of expected utility.
42 The puzzle of lottery play motivated an important modification to the original EUT insurancing against losses, in which they pay in order not t o take risks, and purchasing lottery tickets, in which they pay to take risks, they suggested a utility curve that has two inflection points. Differing from the utility curve in EUT, the Friedman Savage utility curve has a convex segment, reflecting increa sing marginal utility and risk seeking, in the between of an otherwise concave utility curve. The lower and upper concave segments represent two qualitatively different socioeconomic levels, and the convex segment corresponds to the transition between the two levels. It can be predicted from the curve that there exists a region where the lottery ticket has greater expected utility than the certain loss of the cost of the ticket, because of the positively accelerated total utility curves. Likewise, there is a region where the expected disutility of certain loss of insurance premium is less than that of the serious loss against which he is insuring. The concave segment at higher levels of wealth limits the gains from gambling. The advantage of Friedman Savage utility curve lies in its ability of accommodating the empirical phenomenon of coexistence of gambling and insurance buying. It also predicts that the extremely poor and wealthy are not willing to gamble, which may or may n ot be true. Empirical studies indeed often show that lotteries are more prevalent in the lower income classes than higher income classes, but we have very limited knowledge about the extremely poor. There is another critical pitfall in this approach. As th e middle segment is inherently unstable, the middle income individuals are predicted to gamble their way into either the rich, or more likely, the poor (McCaffery, 1994; Sauer, 1998). More importantly, the utility function predicts that
43 behavior will be se nsitive to changes in initial wealth, whereas the observed gambling behavior does not appear to change radically in response to changes in their initial wealth (Quiggin, 1991). Other refinements of expected utility curve, such as Markowitz (1952), avoided this pitfall by allowing multiple dents in their utility curve. Markowitz (1952) modified the Friedman Savage theory by assuming that utility is a function of change in wealth (i.e., gains and losses) rather than level of wealth. Another enduring problem i s that the curve only fits with observed behavior without proposing efficient functions consistent with lottery play ultimately do little more than to tell us wh at we already know Indivisibility in Expenditure Hypothesis Indivisibility in expenditure offers an alternative explanation of rational consumption of lottery. Whereas the kinks in the Friedman Savage utility curve are inher ent in the nature of utility, Ng (1965) was able to derive a utility curve with a convex kink caused by the existence of indivisibilities. The idea is that as consumption expenditures are not indefinitely divisible, some items must be purchased in discrete units. For example, a consumer may choose between one or two cars, but it does he little good to have, say, half a car or one and one third cars. The introduction of indivisibility of expenditure will give rise to increasing marginal utility because the c onsumption of an indivisible good will lead to a reduction of consuming other goods s insufficient to pay for an indivisible good, such as university education, and would do it if he won a lottery prize, then he may buy lottery ticket even if it is less than fair.
44 ence of accessibility of financing market. Ng argued that rental market may reduce the impact of indivisibility but cannot effectively eliminate it. A further question is to what extent the mortgage market or other borrowing instruments will influence the indivisibility of consumption. McCaffery (1994) pointed out another flaw is that some apparent indivisible goods can be implicitly divisible. For example, one can buy a lesser quality car, or a smaller house, instead of a luxury sporty car, or a four bedr oom house with swimming pool. Therefore, the indivisibility theory is often combined with a theory of capital market imperfection. Flemming (1969) was able to explain lottery play by assuming differences between buying and selling prices of consumer durabl e goods. Thus borrowing and lending in perfect capital markets removes the demand for gambles. In contrary, Bailey, Olson, and Wonnacott (1980) and Hartley and Farrell (2002) showed that when the rates of interest and time preference are equal, agents seek to gamble unless income falls in a finite set of values. When they differ, there is a range of incomes where gambles are desired. Different borrowing and lending rates can account for persistent gambling provided the rates span the rate of time preference This offers an adequate explanation of gambling in developed countries with well developed credit markets where a large proportion buy lottery tickets. Based on previous research, McCaffery (1994) advanced the theory and told a more compelling story of the links between lottery play and indivisibility in consumption. McCaffery (1994) concluded that true indivisibility comes from two distinctive sources: (a) a lack of financial instruments, such as leasing or borrowing arrangements, for certain goods; and
45 consumer, a luxury sporty car is unsubstitutable and he cannot obtain it through financing arrangement. Then indivisibility should come to play and influence his risk seeking behavior. In such all or nothing situations, people are motivated to buy lottery, regardless its unfairness. As purchases that are rather easily financed by the rich become indivisible to the poor, the idea fits the empirical phenomenon that lower income groups play lower jackpot games, and upper income groups play for high jackpots. McCaffery (1994) further suggested that desire for leisure, indivisible in nature for most people, along with impediments to savings, plays a consequential role in This (2008) gambling behavior model Leisure, a good that cannot be obtained in relatively small quantities, or through financing arrangements is a fixed cost of work ( McCaffery, 1994 ) The ind ivisibility nature of leisure, as the Ng s (1965) theory suggests, will derive a locally non concave utility function for people. Dobbs (1988 ) actually showed the derivation of this kind of utility curve based on the assumption of the institutional rigidness of working hours, say, people can only choose e ither working or not working. This assumption is rather plausible at least in the context of the US labor market, where hiring household help, or choosing retire earlier, are not particularly vibrant ( McCaffery, 1994 ) Dobbs (1988) analysis conclu ded that people are willing to participate in small stake large prize lotteries in order to get enough money to free them from the need to work, and choose an alternative life style the life of leisure. This labor supply perspective apparently fits the pos itive correlation between lottery play and the drudgery of work, with unskilled,
46 clerical, and professional workers playing in decreasing order ( Clotfelter & Cook, 1989b ) There is more than the mere utility gained from the winnings in lottery playing. Rather, it is additional utility costs that are saved by not having to work to earn the income that plays a significant role in one s ex ante ga mbling decisions, a basic motivation termed as something for nothing by Nyman et al. (2008 ) .Their theory suggests that the utility of gambling can be evaluated in two different ways: (a) mere utility gained from the winnings, and (b) utility gained from the winnings plus t he utility cost savings of not working for it, and one s working experience (i.e., labor market orientation) influences one s perception about the gambling utility. The different perceptions about the utility of gambling in turn induce different gambling d ecisions: to not take part in in the case of (a) or to take part in in the case of (b). Furthermore, when one indeed takes part in the gambling, then the amount and frequency of gambling are at least partially determined by the extent of difficulty to earn additional income. This labor market based theory was empirically tested based on the data from 1999 2000 Survey of Gambling in the United States. Nyman et al. (2008 ) used a logistic regression and ordinary least squares regression to test the hypotheses derived from their theory. They found that the odds of those who with working experiences, no matter full time, part time or not now working (but having working experience), were 2.39 to 2.72 times larger than the odds for those who never worked. In terms of amount and frequ ency of gambling, they found recreational gambling was more prevalent among those who engaged in service occupations, were non white, and lived in a census block group with higher percentage of unemployment.
47 e relationship between the amount of lottery tickets purchased across the United States and the distribution of government transfer payments also lend evidence to the interplay between consumption indivisibility and limited accessibility of credit market. Using weekly lottery sales data, they demonstrated an increase in lottery activity during weeks in which transfer payments are distributed. They also found that spending increases during check week are relatively more concentrated in games with lower jackp ots, indicating differences in preferences for the transfer recipient group (i.e., low income group) from the population at large. The Pick 3 and Pick 4 games are found to exhibit significant increases in sales during check week, while Pick 5 and Pick 6 ga mes do not. They suggested that the choice of lottery games is at least partially influenced by wealth and accessibility to theory. Consumption Utility Hypotheses Whereas the previous accounts primarily rely on the derivation of local non concavity in the utility function without assuming any utility in gambling itself, the principal alternative explanation of gambling is that it offers direct consumption value (Bru ce & Johnson, 1995; Conlisk, 1993; Forrest et al., 2002; Johnson, O'Brien, & Shin, tricky concept. When I go to a casino, I go not alone for the dollar prizes but also for the pleasures of gaming for the soft lights and the sweet music. In such cases the X's casino gaming, the experiential utility of lottery play is much subtle and thus cont roversial. A typical lotto or number game involves no more than picking some
48 numbers or number combinations, but players can be enjoying the sense of pseudo control by having recourse to the dream books, lucky numbers, or astrology. A scratch card requires no more than scratching off the surface of the card, but players can be enjoying the thrill and excitement of discovering the numbers. A stand alone VLT device can offer similar experience as slot machines in casino, only with lower pay out rate. Sports l otter y may require some knowledge and considerations of the teams, which may fun of predicting. Furthermore, all types of lottery seem to offer players an opportunity o f day dreaming if life after they win the prize. If these nonmonetary activities associated with lottery gambling offers direct utility for consumers, then they certainly could be included in the calculations of expected value. Therefore, it is easy to rat ionalize the purchase of a lottery ticket by saying that for a dollar purchase, the customer is paying 50 cents for a fantasy (Thaler & Ziemba, 1988). Johnson et al. (1999) documented an apparently abnormal phenomenon in the horse racing betting market in the UK: more than 18% of bets were placed by gamblers who choose to pay 10% gambling tax on the return of a successful bet instead of on the wager when they have the freedom to choose either act. It can be shown that the former act is strictly dominated b y the later act. They claimed that this phenomenon can be explained by a component of psychological utility which represents the consumption value of gambling. They modeled this consumption utility as a function of the amount of wagering. Likewise, Forrest et al. (2002) suggested that the traditional effective prize based models, such as Forrest, Gulley, and Simmons (2000) and Scoggins (1995), cannot efficiently capture the variations in demand for lottery. By contrast, Forrest et al.
49 (2002) proposed a key role for consumption benefit in the demand for the UK National Lottery. They argued that the impact of the maximum possible prize (i.e., jackpot) on the demand was evident for consumption utility of gambling. Using data from the U.K. National Lottery, they found that jackpot size exerted an influence over and above that of variations in effective price. The lottery play as consumption argument is particularly tenable with regard to sports wagering and sports lotter y Indirect evidence comes from Paul and W einbach (2010) and Garca, Prez, and Rodrguez (2008). Through an analysis of the betting volumes of the National Basketball Association (NBA) and National Hockey League (NHL) obtained and aggregated across three on line sportsbooks for the 2008 09 season Paul and Weinbach (2010) found that betting behavior is much like fan behavior as key fan attributes, such as the quality of teams and the availability of television coverage, were shown to have a positive and significant effect on betting volume. They r esort to the consumption hypotheses to explain the pattern in their data. Garca et al. (2008) examined the impact of having a professional football team in the Spanish First or Second Division in a certain province on the amount of sales of football pools in Spain (La Quiniela). They estimated a demand equation using a panel data set at the provincial level for the years 1985 2005. Their results showed that ha v ing a club in the top divisions has a significant effect on sales of La Quiniela. Despite that J ohnson et al. (1999) and Forrest et al. (2002) explicitly advocated the consumption utility of gambling, their treatments were somewhat curious. Neither did they specify the nature of the consumption utility, nor the determinants of the utility. They were rather loose in reasoning the links between experiential utility and the
50 amount of wagering or the size of jackpot. Conlisk (1993) offered a different and more elegant treatment of experiential utility of gambling, by allowing the money values and probabil ities in any risky prospect have direct value beyond that included in the expression for expected utility. Conlisk contended that there is a tiny utility residing in the characteristics of gambling. He observed the following characteristics of gambling in comparison with insurance: gambling typically involves games with relatively simple rules; the probability of winning is typically straightforward or easily to conceive; although gambling involves anticipation and other time effects, but nonetheless the re solution of uncertainty is rather quick and often in entertaining ways; and gambling is typically not associated with disastrous consequences. These characteristics of gambling may stimulate a feeling of excitement or suspense for the players, which is tra nsferable to an experiential utility. Without assuming any utility in other nonmonetary acts associated with gambling and by adding an arbitrarily small utility function of gambling to an otherwise standard expected utility function, Conlisk derived a Smal l Gamble Theorem and a Lottery Theorem, which specifies the boundary conditions that an individual will accept a gamble. Breuer, Hauten, and Kreuz (2009) lend additional appar ently offer nonmonetary utility for betters because some individuals have utilized sports betting to hedge the disappointment of an unsuccessful outcome of an event they are emotionally attached to. However, they did not find the nonmonetary utility compon
51 Determinants of Lottery Demand The expected utility theory and its modifications have motivated most empi rical investigations of the demand for lottery gambling. The main empirical questions are whether consumer demand for lottery games responds to true expected returns, as EUT predicts, and what factors to be included in the estimable demand functions. These works lead to two most prominent econometric models in lottery literature: effective price model ( Forrest et al., 2000 ; Gulley & Scott, 1993 ) and jackpot pool model ( Cook & Clotfelter, 1993 ; Forrest et al., 2002 ; Garrett & Sobel, 1999 ) Besides product attributes variables, namely effective price and jackpot size consumer characteristics variab les such as income, gender, age, education, religion, and ethnicity ( Felsher et al., 2003 ; Herring & Bledsoe, 1994 ; Walker et al., 2006 ) and used market ing variables such as venue accessibility ( Hing & Haw, 2009 ) cross border competition and product substit ution ( Forrest et al., 2004 ; Garrett & Marsh, 2002 ) and social responsibility marketing ( Li et al., 2011 ) were also included to model the demand for lottery products. Finally, drawing upon the consumption utility experience hypothesis, a third product attributes variable that m ay be unique to sports lottery is the attractiveness of the matches included in the parlay Product Attributes and Demand Effective p rice There are two different prices in the market for lottery games. The n ominal price of a lottery ticket usually fixed at a very small value, say, $1 in US, or two yuan in China, is what the players actually pay for a chance of winning a prize. The actual price of a ticket, however, is different. It is known as effective price in literature, and can be defined as the cos t of buying a probability distribution of prizes that has expected value
52 of one dollar ( Clotfelter & Cook, 1987, p. 534 ) Effective price of a unit price lottery ticket can be measured by the difference between its face value and the expected value of the prize, which tends to c onverges to the takeout rate with sufficiently long periods of time ( Gulley & Scott, 1993 ) An alternative specification of effective price is the inverse of the expected value ( Garrett & Sobel, 2004 ) S ome earlier empirical analyses of lottery sales included the takeout rate as a proxy explanatory variable for effective price, but found no significant relationship between effective price and sales ( Mikesell, 1987 ; Vasche, 1985 ; Vrooman, 1976 ) It is likely due to lack of variability in th e takeout rate. For example, in the United States, states typically do not vary this rate over time nor does it vary much across states. When the variation in the takeout rate is rather limited researchers can hardly detect a significant relationship. DeBoer (1986 ) however, is an exception. Using panel data for seven state lotteries from 1974 to 1983 and controlling for per capita disposable income, the number of years the lottery has operated, and the percentage of the population residing in urban areas, the researcher found a significant relationship between the takeout rate and sales. The price elasticity of demand was estimated at 1.19, meaning a 1 percent cut in the takeout rate increased sales by nearly 1.2 percent. DeBoer (1986 ) further showed that if the payout rate is 50 percent and marginal administrative costs 3 cents per dollar of additional sales combined with an average sates commission of 5 percent, net revenues for the state are maximized if the elasticity is 1.19. Although the effective price has to average at the takeout rate over the whole period of the lottery business, variation from this is permitted in any given draw. Indeed, the rules of roll over and pari mutuel betting along with a carefully designed prize
53 structure induce substantial changes in price between draws ( Gulley & Scott, 1993 ) We observe that the draw to draw sales of lottery tickets sometimes fluctuated dramatically. This can hardly be explained by nonprice variables, such as income or demographic charac teristics, which do not vary much in short run. Gulley and Scott (1993 ) suggested that the expected value of holding a ticket is a function of the prize structure, the amount of the previous jackpots rolled over into the current jackpot, and the number of tickets purchased in the current drawing, and formally defined it as: EV = | p |*| JACKPOT |*| SHARE | + EV s where EV is the expected value of a $1 lotto ticket, p is the pr obability of winning the jackpot, JACKPOT is the value of jackpot, and SHARE is the expected portion of the jackpot a winner will keep, and EV s is the expected value of smaller prizes. EV s is usually fixed in the UK Lottery and the United States state lott eries However, it can be modeled differently in cases where lotteries have a different prize structure. Cook and Clotfelter (1993 ) and Gulley and Scott (19 93 ) showed that the probability of winning a grand prize can be appropriately approximated by the Poisson distribution. Subsequently, P = 1 EV = 1 ((1/Q)(R+(1 t )Q)(1 e Q p )+EV s where P stands for the effective price of a $1 lotto ticket, Q is the number of tickets sold in the draw, t is the take out rate, and p is the probability of any ticket winning the jackpot. This has been a classic specification in modeling price elastici ty of lottery demand, and adopted by several subsequent researchers, notably Scott and Gulley (1995 ) and Garrett and Sobel (2004 ) for the US state lotteries, Walker (1998 ) Farrell and Walker (1999 ) Farrell, Morgenroth, and Walker (1999 ) and Forrest et al. (2000 ) for the UK Lottery.
54 However, there is one critical estimation problem in empirical investigation. The effective price variable is necessarily endogenous as it is influenced by sales. As sales increase, the number combinatio ns covered by players will increase, making it less l ikely that the grand prize will remain unwon. Hence, expected value to ticket holders improves and effective price falls when sales increase. But the sales cannot be exactly known ex ante Assuming that players form their rational expectations of the effec tive price using all the available information, researchers may remedy this endogeneity problem by running a two stage estimation procedure. In the first stage, the effective price is estimated using information that was likely available to players at the time of purchase, such as sales in previous draws, trends in sales, prior rollover amounts, or public sales forecasting. In the second stage, the predicted effective price is then include d as a regressor in the demand equation. Gulley and Scott (1993 ) obtained expected effective price by regressing actual effective price on the amount of roll over from previous drawing, the predicted jackpot and a time trend. Using data related to various periods over 1984 to 1991 and the number of drawings observed for individual game varied between 120 and 569, they found that the price elasticities vary across different games. I n the cases of Kentu c ky Lotto and Ohio Super Lotto the mea sured elasticity was 1.15 and 1.20 respectively, which was consistent with profit maximization; however, in the cases of MassMillions and Megabucks, the measured elasticity was 1.92 and 0.19 respectively, which was significantly deviated from 1 .19. In a similar token, Forrest et al. (2000 ) used the size of rollover and its square as instrumental variables in their two stage procedure. They estimated the steady state
55 long run elasticity of demand for the UK National Lottery was 1.03 which is not significantly different from revenue maximization Modeling demand in terms of the effective price describes the effect of the implicit cost (i.e., the effective price) on the amount of tickets players choose to purchase. It is consisten t with the logic of the expected utility theory and rests on t he assumption that players form rational expectation of effective price and use this information in the process of purchase decision. The importance of this model lies with its regulatory implications to maximize sales implies an approximate price elasticity of 1. However, the effective price model relates sales only to the total prize payouts, but not to the structure of p rizes, which effectively limits the applications of this model in real world lottery operations. Forrest et al. (2002) cited an anecdote in the history of the UKNL that evidently violates the prediction of the effective model. In September 1998, an introdu ction of extra prize money to the second tier prize pool (i.e., a reduction in effective price) surprisingly reduced the sales of the lottery. Jackpot s ize A number of studies have explored the effect of characteristics of prize structure on the demand, especially the size of jackpot. Motivated by Conlisk s (1993) tiny utility in gambling and the idea of buying a lottery ticket is buying a dream ( Clotfelter & Cook, 1989b ) Forrest et al. (2002 ) raised the hypotheses that the variati on in sales of lottery ticket may be driven primarily not by the effective price but by the prospective size of jackpot pool. S imilar ideas actually could be found in Cook and Clotfelter (1993 ) and Garrett and Sobel (1999 ) They argued that lottery playe rs may be simply motivated by the enjoyment of the dream of spending the largest prize that could be won from holding the ticket, rather than the expectation of winning the prize. The jackpot pool was defined
56 as the largest amount that anyone could win as a single winner. model, in which they include jackpot as a major predictor for lotto demand. Based on a dataset of 169 consecutive lotto draw (1993) estimated the jackpot elasticity of demand was 0.347, implying that a $1000 increase in the expected jackpot increased sales by $347 dollars. For the same reason as the effective price that the total sale s cannot be determined until the close the drawing, the jackpot pool is necessarily endogenous. The players, however, may be able to form an expectation of the jackpot size using the information available at the time of purchase. This assumption might be m ore plausible than that in the effective price model according to the cognitive decision theory. Players likely attend to only a few key discrete values such as the amount of the large prize rather than statistics such as expected value in their decision t o buy lottery ticket ( Shapira & Venezia, 1992 ) Both Cook and Clotfelter (1993) and Forrest et al. (2002) used the amount of rollover from previous drawings as an instrument for the jackpot size in their two stage least square procedure. The jackpot pool model has the same structure as the effective price model. Based on 137 drawings of UKNL data, Forrest et al. s (200 2) estimated the elasticity of demand with respect to expected jackpot were 0.162 and 0.195 for the Wednesday and Saturday draws, respectively. I n comparison with effective price model, they found that the jack pool model explains a greater proportion of v ariance (88% and 90% vs. 83% and 72% for W ednesday and Saturday draws, respectively).
57 Modeling demand in terms of the jackpot describes the halo effect of the grand prize on the amount of tickets players choose to purchase. It is consistent with the lotte ry play as consumption experience account and rests on t he assumption that larger jackpot represents greater utility for players. It is also consistent with an information account proposed by Shugan and Mitra (2009 ) that under adverse environments favorable outcomes convey more information than unfavorable outcomes. In this case, the maximum data (jackpot) may contain more information than the average data (effective price). The importance of this model lies with its implications for lottery design. F or example, by increasing the difficulty of the game, say, switching from 6/49 to 6/53 while preserving the total prize money can effectively increase the possibility of rollover, hence a greater jackpot. If the jackpot pool model holds, the increased jackpot should bolster additional sales. Cook and Clotfelter (1993 ) showed that the lure of a larger jackpot brought new money into the lottery. The increased sales did not come at the cost of sales of other l ottery games However, the jackpot pool model, relating sales only to the grand prize payouts, cannot effectively explain the lottery demand in a situation where prize cap is enforced. For example, the Chinese lottery administrations voluntarily set a 5 mi llion yuan prize cap for a single stake. Whereas the jackpot pool can be hundreds of million yuan the expected jackpot for a 2 yuan single stake ticket will be at most 5 million yuan However, players can increase their chances of winning more than 5 mill ion yuan by buying more tickets. The traditional jackpot pool model fails to account the prize cap. Furthermore, this model fails to predict the optimal difficulty level of the game. The jackpot pool model suggests that more difficult game is always prefer able than those easier game.
58 Estimation p roblems Forrest et al. (2002 ) used the Cox statistic for testing the effective price model and jackpot pool model as these two models were non nested Results revealed that neither model contains a correct set of regressors. Forrest et al. (2002 ) suggested that both effective price and jackpot pool were important determinants of demand of lottery, and should be included in the demand model. But a test of this model was empirically not feasible in their study as rollover was used as instrumental va riable for both effective price and jackpot pool. This problem was evident in Cook and Clotfelter (1993 ) who did include both the expected value and jackpot size in their model. Their findings were peculiar: sales were positively related to the jackpot, but negatively related to expected value. They suggested that the results were due to high multicollinearity. Garca and Rodrguez (2007 ) in their estimation of the demand for the Spanish football pools u sing data corresponding to the fixtures (football matches) from the 1972 73 to the 2002 03 seasons, also included both effective price and jackpot in their equation. Although they claimed that this approach was appropriate f ollowing Kelejian (1971 ) Again their results were peculiar: sales of Spanish football pool was positively related to the jackpot, but also positively related to the effective price. Beenstock and Haitovsky s ( 2001 ) investigation of lottomania phenomenon in Israel was an exceptio n. T h e Israel lottery administration, Mifal Hapayis has a minimum jackpot policy for its lotto game. The lower bound for the first prize, to be announced a week in advance of the following drawing, is based on the lotto managers assessment of ticket sale s. T h e first prize will be greater than the announcement under the circumstances that sales exceed expectation; otherwise, Mifal Hapyis absorbed the loss and pay the promised jackpot. Because the Mifal Hapyis does not use a simple projection rule based on rollover data
59 alone, the promised jackpot was shown sufficiently independent of rollover data. This enables the separate identification of the effective price and jackpot size induced by rollover. The logline ar model relating sales to promised jackpot and price based on 594 lotto drawings in Israel from 1985 to 1996 revealed a jackpot elasticity of 0.415 and price elasticity of 0.663. Prize s tructure Another line of research examined the relationship betwe en the skewness of the prize distribution and lottery demand. It has been an established abnormality in horse racing, known as long shot bias, that betters prefer low probability, high variance bets (long shots) than high probability, low variance bets ( fa vorites ) ( Thaler & Ziemba, 1988 ) Golec and Tamarkin s ( 1998 ) explanation was succinct : bettors love s kewness not risk, at the horse track The enjoyment of the high skewness offered long shots was the key motivation for horse track betters. Golec and Tamarkin used the third moment about the mean of return to model this skewness Garrett and Sobel s ( 1999 ) examination of the skewness of the prize distribution on lottery demand was simply an application of Golec and Tamarkin (1998) Gar rett and Sobel estimated the model (X g ) = (X G ) P G /P g = 0 + 1 X g + 2 X g 2 + 3 X g 3 based on data of 216 on line lottery games offered in the U.S. during 1995. This equation implies that (X g ), the expected utility of winning first prize of any lottery game g equals to (X G ), the expected utility of winning first prize of the lottery game G which offers highest jackpot among all games, multiply by the ratio of the probability of winning X G (P G ) and the probability of winning X g (P g ). Similar to the jackpot pool model, Golec and Tamarkin s model explicitly assumed that players were motivated by the top prize jackpots. The coefficient 1
60 the mean of returns, whereas risk aversion is determined by the size of 2 : 2 > 0 suggests risk loving, 2 < 0 suggests risk aversion, and 2 = 0 suggests risk neutrality. A 3 A positive 3 would imply a favorable preference for skewness, whereas a negative 3 would reflect a dislike for skewness. The empirical results supported their original prediction: 1 >0, 3 >0 and 2 <0 suggesting that the mean return along with the skewness of prize structure have an impact on demand. A complementary line of research examined the relationship betw een other aspects of prize structure and lottery demand. Shapira and Venezia (1992 ) investigated the ro les of size and frequency of prizes play in determining the demand of lottery. Their first study was conducted based on the Israeli Lotto system for a period of 60 months from 1986 to 1988 The weekly sales data were regressed on two explanatory variables: the promised minimal first prize, a proxy variable for the amount of the first prize, and the number of winning tickets from the previous winning tickets from the previous week, a proxy variable for the probability of winning. The regression results revea led that both variables were significant determinants of lottery demand. Their second study was run in an experimental type setting. S ubjects rank ordered their preferences among various hypothetical lotteries that differ in price, probability of winning, and frequency of winning but with a fixed pay out rate of 50% The results of the experiments indicate d that larger jackpots were preferred to larger secondary prizes, and more frequent secondary prizes are preferred to lower ticket prices. Overall, the size of the first prize as well as the number of small prizes had the effect on the demand for lotteries in Israel
61 Game a ttractiveness Unlike other lottery games, attractiveness of the sporting events is likely a nother product feature influencing deman d for sports lottery. Game attractiveness has been established as the most important determinant in market demand for spectator sports in sports management literature ( Zhang, Pease, Hui, & Michaud, 1995 ; Zhang et al., 2003a ; Zhang et al., 2001 ) In accordance with the lottery play as con sumption argument the attractiveness of the sporting events seems also play an important role in influencing decision to buy a ticket. Through an analysis of the betting volumes of the National Basketball Association (NBA) and National Hockey Lea gue (NHL) obtained and aggregated across three on line sportsbooks for the 2008 09 season, Paul and Weinbach (2010) showed that betting behavior is much like fan behavior as key fan attributes, such as the quality of teams and the availability of televisio n coverage, were shown to have a positive and significant effect on betting volume. They resort to the consumption hypotheses to explain the pattern in their data. Garca et al. (2008) examined the impact of having a professional football team in the Spani sh First or Second Division in a certain province on the amount of sales of football pools in Spain (La Quiniela). They estimated a demand equation using a panel data set at the provincial level for the years 1985 2005. Their results showed that haying a c lub in the top divisions has a significant effect on sales of La Quiniela. Consumer Characteristics and Demand Income There is evidence that the demand for lottery is likely to depend on the socio demographic structure of the population. Previous studie s have sought to explore the impact of socio demographic factors on lottery demand, particularly income. The
62 estimated effects of income on lottery demand in previous studies have been mixed, but the collective evidence suggests that lottery expenditures do not systematically depend on income, and the lottery tax generally is regressive but with substantial differences in the degree of regressivity across different lottery games The regressivity of tax mean s that the percentage of total tax burden consist ently exceeds the corresponding percentage of total income all the way through the income scale. In literature, there are two ways to demonstrates this regressivity: a computation of the Suits Index of tax incidence ( Suits, 1977b ) or an estimation of income elasticity through regression analysis. A direct measure of tax regressivity develop ed by Suits (1977b ) was frequently adopted to evaluate the regressivity of tax incidence of lotteries. Calculation of this index is analogous to calculating the Gini coefficient It is defined as S=1 (L/K) where L is the area under a Lorenz type curve and K is the area under the diagonal The value of Suits index of regressivity ranged from 1 of the extremely regressivity to +1 of the extremely progressivity with the former value reflecting extreme regressivity and the latter value extreme progressivity. A value of 0 indicates a proportional tax. Suits (1977a ) found that state lotteries rated 0.31 on the regressivity index and illegal numbers games 0.44, more regressive than horses at the track ( 0.17) and off track betting parlors ( 0.07). Adopting Suits measure, Clotfelter (1979) estimated the regressivity index value of the daily and weekly numbers games in Maryland at 0.41 and 0.24 respectively showing that the daily numbers game was more regressive than the weekly game. Also, Clotfelter and Cook (1987 ) found both Maryland's three digit ( 0.42) and four digit numbers games ( 0.48) were more regressive than the state's lotto
63 g ame ( 0.36) More recent application of this measure includes Price and Novak (1999 ) who found the Suits index values of lottery games in Texas ranged from 0.18 to 0.48, and Combs, Jaebeom, and Spry ( 2008 ) who advocated a bootstrap method to make statistical inference on the Suits index and compared eight games in Minnesota with Suits index values ranging from 0.13 to 0.34. Income elasticity measures the responsiveness of the demand to a one per cent change in one s income. It can be readily obtained by regressing the natural logarithm transformation of sales to the natural logarithm transformation of income, controlling other variables. A coefficient of log income below one demonstrates regressiv ity I f the coefficient is one the tax is proportional and if greater than one it is progressive. Based on a survey of the Pennsylvanian Lottery winners, Spiro (1974 ) found an income elasticity of 0.22 However, the conclusion was merely suggestive as the survey itself was marred by a relatively small sample size (271) and an unusually low rate of usable responses (22%). Likewise, Brinner and Clotfelter (1975 ) showed an inverse relationship between family hold income and the percentage of their incomes on public lotteries. More recent studies that demonstrate regressivity include Clotfelter and Cook (1987 ) Price and Novak (1999), Ghent & Grant ( 2010 ) for various states in the US Farrell and Walker (1999 ) for the U.K. National Lottery and Garca et al. (2008 ) for the Spanish Football Pool Despite that these studies differ in empirical approach and in the use of aggregate or survey data, this regressive pattern persi sts. However, Mikesell (1989) question ed the conventional wisdom about the regressive character of the lottery. He show ed that estimated income elasticities for instant games and on line games in Illinois are not statistically different from one. Scott
64 and Garen (1994) found income have a positive, but declining effect on the probability that an individual plays the lottery. Interestingly, once they control for the probability that an individual plays the lottery, income has no significant effect on lott ery expenditures. Rubenstein and Scafidi (2002) found similar results using individual level data from Georgia. Ghent and Grant (2010 ) examine d the distributional impact of three types of lottery games oper ated by the South Carolina Education Lottery (SCEL). They found substantial differences in the degree of regressivity across three types of games. By estimating the determinants of lottery sales using variables that capture the distribution of income rathe r than simply its level, they concluded that lotteries may not be as regressive as suggested by the earlier literature. Miyazaki, Hansen, and Sprott (1998 ) lend additional evidence that lottery regressivity levels were not constant over time and may become less regressive as they progress through their individual life cycles and as new marketing efforts such as anonymous methods o f play -become more prevalent. Similarly, Garrett and Coughlin (2009 ) estimate d annual income elasticities of demand for lottery tickets using county level panel data for three states and find that the income elasticity of de mand for lottery tickets has changed over time. This is due to changes in a state's lottery game portfolio and the growth in consumer income more so than competition from alternative gambling opportunities. Oster (2004 ) found evidence based a dataset on Powerball lotto sales that large stakes game is significantly less regressive at higher jackpot sizes. Out o f sample extrapolation of this result suggest ed the lottery becomes progressive at a jackpot around $806 million. At country level, Kaizeler and Faustino (2008b ) found an inverted U relationship between lottery sales and per capita GDP. Using lottery sales data in 2004 for 80 countries, lottery sales increase together
65 with increases in GDP up to a point where a country has reached a level at which the GDP is high enough and lottery sales become an inferior good and as a result, start to decrease. Age Although t he ability to maximize expected value improved with age there was an inverted U shaped developmental pattern for risk seeking ( Burnett, Bault, Coricelli, & Blakemore, 2010 ) suggesting there may be an inverted U relationship between age and lottery expenditures. Clotfe lter and Cook (1989a ) found individuals aged 25 64 are more likely to play the lottery than those who are younger (18 24) and who are older (65 and above). Also, Scott and Garen (1 994 ) detected an inverted U relationship between age and lottery participation in the United Stage. However, this trend was no longer detected in the 1999 2000 survey ( Welte et al., 2002 ) Lottery participation by four age groups (18 30, 31 40, 41 50, and 51 60) did not differ much from each other (68, 70, 69, and 66% respect ively) with mean amounts of individual lottery expenditure per year varied at $234, $382, $321, and $336 respectively P articipation by the 61 + age group was the lowest at 55% but their mean amount of individual lottery involvement was the highest at $424 ( Welte et al., 2002 ) Jackson (1994 ) in his study of the Massachusetts state lottery lend some in sights for this transition. He found i n 1983 the proportion of the population age 65 or older was inversely related to per capita lottery sales B y 1990, this relationship had been reversed. T he 65 or older age group had become a significant factor in raising per capita sales during the period from 1983 to 1990. Price and Novak (1999) f ou nd that median age is inversely related to sales of Lotto and Pick 3 tickets, but positively related to the sales of instant games. Ghent a nd Grant (2010 ) in their study of North Carolina Education Lottery found t he proportion of the county population
66 age 65 or older was significantly and positively related to the sales of instant lottery tickets, but ha d no effect on the sales of fixed nu mber or Lotto games Additionally, a survey of adult Chinese lottery gambling behavior revealed a strict decreasing relationship between 5 age groups (21 to 30, 31 to 40, 41 to 50, 51 to 60, and 61+) and lottery gambling, with the 21 to 30 age group repres enting highest 29.5% and 61+ age group representing lowest 5.6% market shares ( Li et al., 2012 ) A trend was consistent with that of general gambling behavior as reported by Mok and Hraba (1991 ) As adolescents were not allowed to purchase lottery tickets in China, this may have prevented the observation of an inverted U relationship between age and lottery expenditures. Education The level of education is an important determinant of one s earning function. It has been confirmed by h undreds of studies that better educated individuals earn higher wages than th eir less educated counterparts ( Card, 1999 ) W ith understanding that lottery participation is generally negatively associated with income level, it is also likely to be true with educat ion. Additionally, there is some evidence to support the notion that certain courses received from formal education may improve one s rationality, thus better educated individuals may fall less to those cognitive misconceptions frequently identified in gam bling. For example, Schoemaker (1979 ) found a statistics course might help students make more consistent and less risky gamb ling decisions Fong, Krantz, and Nisbett (1986 ) found that statistical training sometimes transfers to real world decision making. Nisbett, Fong, Lehman, and Cheng (1987 ) conducted several tests on the effects of different kinds of training on logical skills. T hey found that logical skills (as measured by their tests) did improve as a result of two years of graduate courses in law,
67 medicine, or psychology. Although never demonstrated empirically in the lottery gambling literature, it is rather plausible that education has an additional impact on lottery expenditure beyond its effect through income. Indeed, researchers in lottery gambling typically found a decreasing relationship with general education. Brown, Kaldenberg, and Browne (1992 ) disaggregated the socio economic effects of education, occupational status and income to conclude that it was the poorer households who spent the greatest percentage of their household budgets on the state lottery. Education, the single best predictor of lottery play, was a significant and negative correlate. Scott and Garen (1994) and Rubenstein and Scafidi (2002 ) f oun d an inverse relationship between education and the probability of lottery play. In their analysis of the Tennessee Education Lottery, Giacopassi, Nichols, and Stitt (2006 ) report a negative relationship lotte ry sales. Ghent and Grant (2007 ) confirm ed the role of education in determining lottery sales by fi nding that total sales depend positively on t he pro portion without a high school diploma in South Carolina. Price and No vak (2000) reported degree wa s positively associated with Lotto sales, but negatively associate d with scratch off instant games. Similarly Ghent and Grant (2010 ) found the percentage of a county s residents with a bachelor s degree and percentage of a county s residents without a hig h school diploma were positively associated with Lotto sales, but negatively associated with fixed number and instant games. However, all the coefficients were not significant.
68 Gender Men are found more likely to be less risk averse, in addition to being more susceptible to over confidence ( Barber & Odean, 2001 ) which may inte nsify gambling behavior in men According to a national random digit dial telephone survey of U.S. adults conducted in 1999 2000 men gambled in lottery slightly more than did women (68 vs. 64%), but the amount gambled was significantly higher for men ($36 2) than for women ($295 ) ( Welte et al., 2002 ) The pattern of gambling participation has changed significantly comparing with the previous two national surveys conducted in 1975 ( Kallick Kaufmann, 1979 ) and 1998 ( Gerstein et al., 1999 ) The pattern of participation also differs in different culture and society, being influenced by the availability and social acceptance of different types of gambling for both males and females For example, w omen in Australia were reported h a ving a higher preference for bingo, lotto, and lotteries than men ( Hing & Breen, 2001 ) Whereas women were reported gambl ing in lottery more than men by a small margin in Thailand(52.6% vs. 47.4%) ( Ariyabuddhiphongs, 2006 ) men had a much higher share in China s lottery market (77.3%) ( Li et al., 2012 ) Religion R eligiosity is an important construct in understanding individual s gambling behavior. Roberts, Arth, and Bush (1959 ) ascertain that gambling as games of chance, is associated with religious beliefs and is exercised in relationships with the supernatural. On the other hand, religion is a proxy for moral opposition. The perception of gambling as an immoral activity based on the greediness and overindulgence in humanity is the reason some religions forbid or strongly o ppose it ( Cotton, 1996 ) Diaz (2000 ) found that the religion and the religious practices of Las Vegas residents did
69 affect their gambling patterns, including the frequency of gambling and amount of money spend on gambling. Also, Lam (2006 ) found that gambling participation acro ss four types of games, namely casino games, track betting, lottery, and bingo, was significantly associated with one s frequency of religious participation. Scott and Garen (1994 ) found Neo fundamentalist Protestants are less likely, and Roman Catholics are more likely to participate in lottery gambling. Other r eligious affiliations had no discernible effect on whether or not an individual buy lottery tickets. Ghent and Grant (2007 ) found that religious affiliation has a significant effect on the vote to establish a lottery, but has not on lottery sales once a lottery has been established. At country level, Kaizeler and Faustino (2008a ) found a positive relation between Christians and lottery sales. The increase of 1% in a country s Christian followers leads to an increase in per capita lottery sales of $ 40.20 But t his variable was not significant for the model. Ethnicity Another feature studied by various researchers is the link between race, ethnicity and gambling behavior. Risk perception s and risk taking behaviors were found to be culture sensitive ( Weber & Hsee, 1998 ; Weber, Hsee, & Sokolowska, 1998 ) People from different cultural background thus may have different gambling propensity In the United States, s e veral studies revealed that the black play the lottery more than whites do (Clotfelter and Cook, 1987; Borg and Mason, 1988; Rubenstein and Scafidi, 2002; Ghent and Grant, 2007). Gerstein et al. (1999 ) in their national in their 1998 national survey found that the black respondents spend nearly twice as much on lottery tickets as do white and Hispanic respondents. The average reported expenditure among blacks is $200 per year, $476 among those who played the lottery last year. Black men have the highest average expenditures. Giacopassi, Nichols, and Stitt (2006) find no
70 effect of race on total lottery sales in Tennessee, but when sales a re sorted by game type, they fi nd that African Americans play significantly more online games than their white counterparts Additionally Clotfelter and Cook (1989), and Price and Novak (1999) defend t hat Hispanics are more likely to gamble than other ethnicities. Kaizeler and Faustino (2008a ) in their cross country study did find African countries spend, on average, 51 U SD more per capita than other countries. But they did not find a significant positive relationship between the Latin countries and lottery sales O n average, Latin countries spend 6.68 USD more per capita than other countries. Several studies have also mad e reference to the prevalence of lottery gambling among Chinese residents in mainland China ( Li et al., 2012 ) Canada (Chinese Family Services of Greater Montreal, 1997), Hong Kong (Chen et al, 1993) and Taiwan (Hwu et al, 1989; Yeh et al, 1995). Higher p revalence rates of recreational and problem gambling have been reported in Chinese population among all the populations studied. Market ing Variables and Demand Border c ompetition Researchers have shown that a lottery product is likely to subject to the competition from the bordering state, other gambling opportunities, and other types of lottery. Cross border shopping of consumer products exists in many places in Europe and North A merica due to differences in tax rates, prices, and geographical convenience (minimal transportation costs) across states or countries ( Asplund, Friberg, & Wilan der, 2007 ; Ferris, 2000 ) In the United States, there is substantial evidence showing that this cross border shopping for lottery products indeed exists. Alm, McKee, and Skidmore (1993 ) and Caudill, Ford, Mixon, and Peng (1995 ) defended that the
71 inauguration of a lottery in neighboring states, thus a concern for the potential lottery revenue loss to neighboring states, was a primary motiva tion for some American states to adopt a lottery scheme. Mikesell and Zorn (1987 ) showed that the absence of competing lotteries in neighboring states has a significant p ositive effect on per capita sales. Besides the apparent advantages of neighboring with non lottery states, bordering with lottery states is inevitable a disadvantage. Each state offers lottery games that are unique to the state thus lotteries differ considerably across states in terms of prize payouts, odds of winning, jackpot size, or effective price. P layers living in border area actually take advantage of these pr oduct differentials and engage in cross border lottery patronage Garrett and Marsh (2002 ) was the pioneer in detecting this spatial correlation pattern in lottery demand by examining lottery revenues in Kansas, which is surrounded by Nebraska, Oklahoma Colorado, and Missouri. T h ey provided evidence that cross border lottery shopping had a significant net negative impact on state lottery revenues in Kansas and the amount of cross border shopping depends on the size of the retail sector in the relevant border county. Tosun and Skidmore (2004 ) confirmed this negative impact of border competition in their study of the demand for West Virginia lottery. Data related to lottery sales for all 55 counties in West Virginia over the period 1987 2000. They focus ed on the effects of the introduction of new neighboring state lottery games on West Virginia lottery revenue gen erating capabilities. Their findings indicate that border state competition wa s an important determinant of lottery sales. Furthermore, Brown and Rork (2005 ) showed that the take out rate of lottery is subject to interstate competition. Using data from 1967 to 2000, they provided evidence that the payout rate of state lotteries responds positively to the payout rates of
72 neighboring states. Moreover, their estim ates of competition become even stronger upon controlling for the issue of self selection that occurs with adopting a lottery Product s ubstitution Virtually al l lottery administrations offer a variety of games to suit the tastes of players in an attempt to maximize revenue to the government It is a natural concern that different games may cannibaliz e each other. A major competitive threat of introducing a new g ame consists of two factors that influence demand: the newly introduced game substitutes or complements the existing games. Economic theory predicts that complementary goods will facilitate sales for each other, whereas close substitutes can potentially in tensify internal rivalry and reduce profitability. Clotfelter and Cook ( 1989 ) believed that the standard lottery games were not substitutes for one another. T he sales of scratch card tickets was not affected by the introduction of lotto games Purfield and Waldron (1999 ) tested the substitutability (complementarity ) between the pari mutuel lotto game and the fixed odd betting on the Lotto draw in the Republic of Ireland, and found the two games tend to be complementary to each other. Forrest et al. (2004 ) however, f ound evidence of some substitution among the variety of games offered by the United Kingdom National Lottery : the lo tto and scratch card games were partial ly substitut able, whereas Thunderball appear ed independent of the other two games ; the Wednesday and Saturday drawings of the lotto game were substitutes but the introduction of a new game Big Draw 2000 contributed to net sales. Grote and Matheson (2006 ) consider ed the potential substitution relationship between two lotto games offered simultaneously in Colorado. One is the Powerball, a larger multi state lotto game run in coordination with other states, and the other Colorado Lotto, a smaller individual state run lottery The y concluded that while the two products
73 do tend to be complements to one another, overall the individually run state lottery games experience a reduction in sales from the presence of the multi state game. Several researchers also explored the demand impacts of competition between state lotteries and other forms of gambling opportunities, such as pari mutuel racing and ca sino gambling. Gulley and Scott (1989 ) explored the substitute relationship between lotteries and thoroughbred horseracing based on relevant data covered a time period of 1976 to 1980. They reported an estimated coefficient of 0.18 for real lottery revenue per capita, which means that an additional dollar bet per capita on the state lottery leads similar substitution effect was found in California from 1986 to 1989 by Vasche (1990 ) who estimated a coefficient of 0.26. Empirical research on the issue of commercial casino and lottery competition is explored by Elliott and Navin (2002 ) They found that during the period 1989 1995, expenditures on riverboat gambling had a negative impact on state lottery demand. They estimated that a dollar increase in riverboat gambling was met by an 83 cent decline in net lottery revenue. However, as l ow revenue lottery states are more likely to legalize casinos, this can partly explain the negative relationship between casinos and lotteries By correcting potential sample selection bias Fink (2003 ) extended Elliott 0.56. Walker and Jackson (2008 ) analyzed the competitive pattern of the four major gambling industries in the United States, including casinos, greyhound racing, horse racing, and lotteries during a period of 1985 2000. T he ir results indicated that casinos and lotteries cannibalize each other, whereas both dog racing and horse racing help lottery sales. In contrast, in the
74 UK setting, Forrest, Gu lley, and Simmons (2010 ) found some evidence that bettors do substitute away from horse race, soccer and numbers betting when the effective price of lottery tickets is unusually low induced by a rollover or other special draw. Borg, Mason, and Shapiro (1991 ) examined a series of lottery expenditure models at the household level and had different insights about the interrelationship between lottery and other gambling activities Their results showe d that lottery expenditures did not come at the expense of other household or gambling expenditures, but at the expen se of charitable contributions. Kearney (2005) confirmed that spending on lottery tickets is financed completely by a reduction in non gambling expenditures, which implies that other forms of gambling are not harmed by a lottery. Paton, Siegel, and Williams (2003 ) reported that the substitution effect between the UK National Lottery and sports be tting was not significant. They contended that the introduction of the National Lottery may actually have led to a climate in which gambling as a whole became more socially acceptable. Over all, t he literature suggests that t he relationships among differ ent lotteries or gambling industries are complicated. A n industry (lottery) can either harms another industry (lottery) or does not affect it or different gambling industries (lotteries) help each other. Venue a ccessibility Venue d istribution plays a fu ndamental role in marketing gambling products. Several studies have examined the relationship between gambling venue accessibility and the demand for gambling products. Shiller (2000 ) contended geographical whereabouts may induce gambling, when considering the greater availability of gambling facilities in urban areas that provid es more opportunities to buy tickets. The availability of gambling opportunities, particularly with regard to facility
75 density and venue proximity to home, work or other convenient locations was found to be associated with demand for gambling products and the prevalence of program gamblers ( Hing & Haw, 2009 ; Welte, Wieczorek, Barnes, Tidwell, & Hoffman, 2004 ) Sleight, Smith, and Walker (2002 ) reported a case about how Camelot managed to optimize its outlets to increase venue accessibility for it s customers. The effects of venue accessibility on lottery demand, however, has not yet empirically documented in the literature. S ocial responsibility m arketing Governments establish lotteries, aiming at channeling people s innate gambling impulse to m ore constructive courses. Nevertheless, lottery is a product of potential addictiveness. It can induce some social problems and lead to unnecessary social costs. For th is reason, lottery issuance and administration institutions need to limit the pervasive effects of adverse consequences associated with lottery gambling. The impact of social responsibility on the lottery demand has limited to Li et al. (2011 ) who investigated the interrelationship in the context of China s sports lottery market. T hey found that government social responsibilities primarily lie in two dimensions: regulation responsibility and product development responsibility. T he first dimension represents the administrative process with heightened social responsibility. The second dimension represents the inherent nature and fairness of a lottery product. Based on a survey data obtained through stratified multi stage sampling process, their results indicated that g overnment regulation responsibility was positively associated with c of gambling expenditure and frequency of lottery purchasing. Meanwhile, product development responsibility was negatively associated with frequency of lottery purchasing and time spends on lottery related activities. They concluded that wh ereas
76 an improvement in social responsibility associated with lottery products would reduce purchasing frequency, a n improvement in social responsibility associated with regulations would eventually increase consumption level in terms of absolute expenditu re Summary In summary all three classes of variables reviewed above are important determinants for the demand of sports lottery. However, several variables are excluded from the current investigation, because they are either of less relevance or of less significance in the context of China. Religion is excluded because the Chinese government only permitted very limited freedom of religious belief, which subject to legal and regulatory restrictions and a predominant Chinese population apparently had no rel igious belief ( Potter, 2003 ) Gende r is excluded because there is minimal variance among different provinces in terms of gender composition in their populations. Ethnicity is excluded because over 91.5% of Chinese population is Han according to the Sixth National Population Census of China. Cross border competition is not a consideration because China has a national lottery market and players are unlikely do cross border shopping on purpose. Finally, social responsibility marketing has to be excluded because there is no objective metric avai lable for current analysis.
77 Table 2 1 A c omparison of CWLDMC and CSLAC l otter y products in China (Unit: 10,000 yuan ) CWLDMC Lotter y CSLAC Lotter y Product Sales Market Share (%) Product Sales Market Share (%) Instant Game guaguale 20,044 9.2 dingguagua 19,962 910 Lotto & Numbers Game s Duo Balls 48,746 22.3 Super Lotto 13,848 6.3 Super Lotto Luck 208 0.1 Happy 7 1,547 0.7 7 Star 7 2,831 1.3 kailecai 568 0.3 5/22 Lotto 22 5 724 0.3 3D 3D 21,521 9.8 Pick 3 3 8,298 Pick 5 5 3,155 1.4 High Frequency 19,731 Video Lottery Terminal Zhongfu online 17,014 7.8 Sports Betting Football Betting 10,554 4.8 Shengfu 3,788 1.7 Shengfu Select 9 9 2,490 1.1 Basketball Betting 1,842 0.8 Goals of 4 Matches 4 211 0.1 6 Match Double Result 6 60 0.03 Local Game s 18,357 8.4 3,224 1.5 Total Sales 127,797 58.4 90,924 41.6 Data source: The data of sales of CWLDMC lotter y are based on the final release of CWLDMC 2011 report, and those of CSLAC lotter y are based on a preliminary release of CSLAC 2011 report. The CSLAC data are not final
78 CHAPTER 3 METHOD Background about Shengfu game The current in vestigation focus ed on the Shengfu game (Win Tie Lose Game ). The g ame is the very first sports lottery in the China, and remains as the most representative form and a major player in China s lottery market A pproved by the Ministry of Finance in December 2000 the game was in troduced in October, 2001 in only 12 pilot provinces (municipalities). The game then gradually expanded to other provinces and became available in all 31 provinces by Sept ember 2002 Since its origination the game has undergone some minor changes with respect to the rules of play and prize structures. For the first 3 seasons, each drawing was composed of 13 football (soccer) matches, selected from prominent European league s, for players to bet on. Since August 2004 14 football matches are selected from a wider range of football competitions (See Appendix I for a sample ticket) These include but are not limited to the British Premier League, German Bundes l iga, Italian Seri e s A, Spanish Primere League, the UEFA Champions League and the Asian Cup The Chinese domestic football leagues are not allowed to be used in sports l ottery betting. The Shengfu game ticket has been sold at the fixed face value of 2 yuan Figure 3 2 plot s sales over time since the inauguration of the game in October 2001 to August 2012, a total of 9 45 draws. The game took off rapidly in its introduction phase. T h e sales reached a maximum of over 316 million yuan in draw 2003009 (March, 2003), and the second highest sale of 296 million yuan was found in draw 200214 (April 2002). Only after a few seasons of irrational prosperity, however, the sales of Shengfu game plunged in 2004 when a new football betting lottery, Goals Betting ( ), was
79 introduced to the market. There is a clear negative trend in the period of 2003 to 2005. Since 2006, the game entered into a more stable phase, yet still with significant draw to draw variation. During this period of time, the average sales was about 26 million yuan per draw (Figure 3 2). In the 20 10 0 19 draw (Ma rch 20 10 ), the sales hit the lowest point: 2. 39 million yuan In the 2007016 draw (March 2007), the sales had the highest sales of 86 million yuan Unlike the Lotto game which is usually draw n on a fixed wee kday the sports lottery depends on the schedule of the sports events The CSLAC attempted to schedule the Shengfu game on a regular time interval. For the first a few seasons, with a few exceptions, the game was a weekly draw and the winning announcements were made on Mondays. The tickets would be available to purchase for one to two weeks in advance of the kickoff of the first match in the parlay This regular drawing practice seems to have be en abandoned gradually since 2008. As of sales period, it has been significantly shortened since 2005 as more draws were introduced during these seasons. As of the 2012 season, each week usually has more than one draw of the game which could be announced in any given day. The number of draws has increased from 31 in 2002 to 141 in 2011. The Shengfu game is a pari mutuel game where prizes represent a share of sales revenue. Currently, only two prizes are awarded for each drawing. To win the first prize, pla yers have to correctly choose all of the 14 matches listed in the parlay Those correctly predicting 13 of the 14 results win a second prize. If there are no winners of the first and/ or second prize, this money roll s over to the jackpot pool of the next d rawing. The rollover is not allocated to the second prize. T he sports lotter y enjoy s a
80 more favorable pay out rate: 35% of the sales is taken by the governments and 1% goes to an adjustment fund. The Shengfu game is of no exception : up to 6 5 % of sales is r eturned to players. Yet, there is a prize cap policy for most sports lotter y Lottery players can only win a maximum of 5 million yuan for each winning ticket. Players may win more than 5 million yuan if they hold multiple winning tickets. In history of the Shengfu game first prize often reaches this prize cap when the winners are very few. In the case of prize cap, the unallocated prize money will also roll over to the next drawing. T h erefore, in the Shengfu game the rollover can come from two sources either there is no winner in the previous drawing(s) or there is a prize cap in the previous drawing(s). Beside the grand prize, smaller prizes are also subject to this prize cap. Through out the history of the Shengfu game the second prize reached this pr ize cap only twice in draws 2005016 and 2008057 respectively Shengfu game players have the possibility of choosing the final result of each of the 14 match es from among three alternative results: home team win (3), tie (1), an d away team win (0). For ea ch 14 match ticket there are 4,782, 969 (i.e., 314) combinations of the numbers. When there is an ex ante probability of holding a winning ticket and the results are selected randomly, then the winning probabilities for first and second prizes are 1/3 14 a nd 14 1/ 3 13 2/3 respectively Therefore, it can be expect ed that for every 4,782, 969 tickets sold, on average there are likely one first prize winner and 28 second prize winners. This assumption, however, is rather implausible. U nlike lotto games where the winning combinations are random numbers and there exists a theoretical ex ante probability of having a winning ticket, the results of sports competition are not randomly chosen and the ex ante probability of winning is not
81 known Furthermore, the issue of conscious selection, the process by which lottery players choose numbers non randomly, is probably more prominent in sports lotter y (Farrell, Hartley, Lanot, & Walker, 2000; Garca & Rodrguez, 2007). Players use their knowledge and available information about the teams to predict the results of competitions, and some results are easier to predict. Even when encountering difficult matches, players can effectively increase their chance of winning by buying more combinations. Howev er, this strategy becomes more costly when the results of more matches in the parlay are subjectively difficult to predict. For example, the player needs to buy up to 243 tickets to completely eliminate the uncertainty from 5 matches. Empirically the prob ability of winning a prize in Shengfu game is usually higher than the probability calculated based on random selection. The discrepancies are nontrivial. Over the whole period, the median of the ratio between the actual number and the calculated number for first and second prize winners are is 4 77 and 5. 33 respectively. In some extreme cases, the actual probability of winning can be thousands times of that based on calculated probability. Take the drawing No.12051 as an example, there were 4,174 first priz e winners when the c alculated number was only 1.46. However, the mean ratio between the actual number of first prize winners and that of second prize winners is 28.7, remarkably close to the theoretical ratio of 28. Econometric Framework Decision Calculus Following Conlisk (1993 ) and Beenstock and Haitovsky (2001 ) and considering the uniqueness of sports lottery as previously mentioned, w e assume the individual s preference function will be an expected utility function modified to allow a consumption
82 utility associated with sports betting. For K heterogeneous potential sport s lottery game players, this preference value function, denoted as U k can be expressed by U k = U (G i i P; Z k ) + V (J, S, A ), k=1 K, i=1, N, ( 3 1) where U () is an archetypal utility function, which is assumed to pass through the origin, to be increasing, and to display risk aversion; G i denotes th e monetary rewards if the individual wins the i th prize i is the probability of winning the i th prize by purchasing a single ticket (i = 2 in current context), P is the price of a ticket ( P = 2 yuan in current context), Z k is a vector of socio economic c ontrols including income, age, and other is the consumption utility of sports gambling, which is transformed from the excitement, suspense and fantasy associated with sports betting. Based on the literature, we assume it is a function of the jackpot size (J) prize structure (S) and the attractiveness of the matches (A). The coefficient is a positive parameter used to scale the utility of sports gambling. G i and P are the same for all players As the objective probabilities of winning prizes do not exist i can be interpreted as subjective probability players rationally hold toward winning a prize In accordance with the subjective expected utility theory ( Savage, 1954 ) the utility function from playing Shengfu lottery can be expressed by E( U k )= 1 U (W k +G 1 P T k ) + 2 U (W k +G 2 P T k ) + (1 1 2 ) U (W k P T k )+ J S, A ) ( 3 2) where W k denotes the initial level of wealth, and T k denotes the number of tickets bought by the individual. The individual will only participate in the game only if E( U k ) is greater than 0, in which case T k otherwise T k =0. Prize Pool The prize pool, J, is the possible pool for all prizes. It can be expressed as
83 J = S + R ( 3 3) where is pay off rate; R is the unallocated prize money rol led over from previous drawings ; S is the total revenue at the current drawing. S is the product of unit price demand N and price of a ticket P i.e., S= P N The prize pool devoted to the first prize, J 1 is defined as J 1 = 1 S +R ( 3 4 ) where 1 is the proportion allocated to first prize Therefore, the first prize is G 1 = J 1 / W 1 ( 3 5) where W 1 is the number of win ning tickets of first prize Depending on the design of the game, the equations for smaller prizes can also be specified. For simplicity of presentation, we assume this particular game has two prizes and the rollover is not allocated t o the second prize, t he second prize can be defined as J 2 = 2 S ( 3 6 ) where 2 is the proportion allocated to second Therefore, the second prize is G 2 = J 2 / W 2 ( 3 7) where W 2 is the number of winners of second prize. Risk of Prize Sharing I n any pari mutuel games, the player faces the risk that the prize pool may be shared with other winners. A r ational player, before deciding whether or not to buy a ticket or how many tickets to buy, has to consider the possibility of prize sharing. Cook and Clotfelter (1993) and Gulley and Scott (1993) show that the expected numbers of winners can be approximate by the Poisson distribution if the selection of winning
84 combinations is random. Assuming each player buys one ticket and there are N players, the pr obability that there will be x winners is (3 8 ) From the perspective of player k choices made by others are probabilistic. Therefore, as Cook and Clotfelter (1993) argued the random play assumption is not critical here. Skill Coefficient Problem lies with the objective probability p is not known ex ante in sports lotter y It can only be estimated ex post One approach to handle this problem is using the random probability as the base probability to be adjusted by a market level skill t E xpertise plays a role in sports gambling and individual players differ in their betting expertise. The skill coefficient t captures only an averaged expertise level in the market at time t. The subscript t captures the fact that consumers may learn and improve their betting skills with time. A simple measure of t is the median of the ratios between the actual number of winners and the calculated numbers of winners for draws prior to t Therefore, at draw t the skill c oefficient can be expressed by the following equation: t = Median (N a 1 /N 0 1 N a2 /N 02 a ( t 2 ) /N 0 (t 2 ) N a ( t 1) /N 0 ( t 1) ) ( 3 9) Where N a1 N a2 a(t 2 ) N a ( t 1) are the actual number of winners from draw 1 to draw t 1 ; N 01 N 02 0(t 2 ) N 0 ( t 1) are the calculated number of winners from draw 1 to draw t 1
85 Expected Prizes To avoid the problem of distinguishing between individuals and tickets, it is assumed that each player buys only one ticket. Then, f r om Eq. 3 5 and Eq. 3 9 for player k the expected first prize of buying one ticket will be: ( 3 10 ) The expected second prize of buying one ticket will be: ( 3 11 ) Therefore, the expected value of winning any prize of holding one ticket will be: = ( 3 12 ) And the effective price of holding one ticket will be simply: ( 3 1 3 ) or alternatively, ( 3 14 ) The advantage of E q 3 1 4 over E q 3 1 3 is that the former generates non negative values of EP, which allows for natural logarithm transformation without losing information. In contrast, Eq. 3 1 3 will generate negat ive value and zero value of EP. Relationships between E xpected Value and its Determinants From Eq. 3 12 the relationships between expected value and its determinants can be examined. Without rollover, it can be proved that the expected value converge s to the pay out rate quickly with the increasing of sales because the partial derivative of E(G) with regard to N when R=0 is strictly positive. The relationship between N and
86 E(G) is more complex when there is a rollover The sales has a positive margina l effect on expected value only if the sales is rather small. It is unlikely in reality because players will expect an increased return and buy more tickets, which in turn increase the probability of prize sharing. Further, the improved betting skills will increase the expected value. Figure 3 1 shows the relationship between the expected value, sales, and market level skill coefficient. Empirical Models To examine the demand for sports lotter y two studies were conducted. The first study, using a time ser ies data, aim ed to investigate the impact of product attributes on the demand for the Shengfu game The second study, using a panel data, aim ed to jointly investigate the impact of demographic, marketing variables, and product attributes on the demand for Shengfu game Time Series Analysis The first model we considered is an ordinary regression model using time series data y t x t t where y t is aggregate nationwide sales of Shengfu lottery at draw t and x t includes variables capturing game characteristics and structural changes of the game. Data of aggregate nationwide sales of Shengfu lottery since the inception of the game in 2001 to August 2012 (total 945 draws) are obtained from the prize announcements publicized by the CSLAC. Additionally, prize announcements include information about the date of the prize announcement, total sales, number of first prize winners, amount of first prize, numbers of smaller prizes winners and amount of them, unallocated pr ize money to be rolled over to next draws, and the matches included in the draw.
87 Derivation of e ffective p rice Table 3 4 summarizes the variables included in the time series analyses. PP for all prizes can be calculated based on Eq. 3 3. The EP of each draw can be calculated based on Eq. 3 1 4 and Eq. 3 1 2 For Eq. 3 1 2 P has been fixed at 2, R is readily available from the prize announcements, and N is simply sales divided by 2. Over the years, 1 and 2 were changed a couple of times (Table 3 3) Further, during 2003 2005 seasons, there were three prizes instead of two prizes. In the history of Shengfu game there were occasional jackpot promotions, in which the lottery administration added a certain amount of additional money to the first priz e pool, or set up a temporary special prize. Eq 3 1 2 allows this type of modification. Regarding p p 1 can be expressed as 1t / 3 13 in the case of 13 matche 1t / 3 1 4 in the case of 14 matche s per draw ; p 2 can be expressed as 2 t / 3 1 3 in the ca se of 13 matche s per draw and 2 t / 3 1 4 in the case of 14 matche s per draw. When there was a third prize, p 3 can be expressed as 312 3 t /3 1 3 in the ca se of 13 matche s per draw and 364 3 t /3 1 4 in the case of 14 matche s per draw. t can be calculated based on E q 3 9. Table 3 3 also summarizes the historical changes of p. Derivation of p rediction d ifficulty c oefficient Whereas EP subsumed the market level skill factor through its configuration, overlooked the draw specific difficult y factor. The difficulty level associated with correctly predicting 14 matche s varies draw by draw, which may ha ve an impact on consumer purchasing behavior. Specifically, a moderately easy game will sell more because players have greater probability to wi n a prize. However, when the game became extremely easy, consumers may lose their interests in predicting those results. Therefore, in addition to EP, adding a variable capturing this draw specific difficulty
88 factor may increase the explanation power of the demand equation. A prediction difficulty/easiness coefficient ( P D C ) 2 ). PDC actually 2 ) the easier the game is. 2 1 is bec ause there were few undefined data points. Because through the history of the game, there were only three draws when 2 is undefined). Furthermore PD C can be approximated by a normal distribution (Figure 3 3 ). Additional ly to examine a potential quadratic effect of PDC, the square of PDC is also included in the regression analyses. Derivation of ticket composition v ariables Furthermore, attractiveness of th e football matches is an important determinant of patron interest of the Shengfu lottery. The attractiveness of the matches is measured by the information of ticket combination. Because Shengfu game involved over 4 0 different l eagues or football tournaments and there are even more different combinations of these leagues it is inefficient to dummy code all these different combinations and include them in regression analyses An alternative approach is to classify those leagues into several manageable categories. In order to classify these leagues, 2 0 football fan s and experts in a sport university in China were interviewed. They were asked to evaluate popularity of 35 football leagues among Chinese fans as well as the general perception of predictability of the competition results They were explicitly instructed not to evaluate any of those listed leagues if they were not comfortable to do so Four measures were obtained through this process: mean score of popularity, number of experts who evaluate on popularity dimension, mean score of predictability, and number of experts who evaluate on predictability dimension. These four measures were subsequently used in a principal
89 factor analysis. One factor was extracted with an eigen value of 3.13, explaining 97% of variances in these four variables. Based on the factor s cores of the extracted variable, these leagues were classified into three groups (Table 3 5). Leagues with factor scores greater than 1 were classified as Group 1, leagues with factor scores between 0 and 1 were classified as Group 2, and leagues with fact or scores below 0 were classified as Group 3. English Premier League, German Bundesliga 1, Italian Series A, and Spanish La Liga have been four major leagues for sports betting in China More than half of all draws are composed of matche s selected from the se four leagues Particularly one third of all draws are involved the combination of English Premier League and German Bundesliga 1 (EPL&GB), and the combination of Italian Series A and Spanish La Liga (ISA&SLL). Two dummy variables EPL&GB and ISA&SLL wer e generated to represent these two combinations. A third dummy variable MAJOR4 was generated to represent any other combinations of these four leagues. Furthermore, dummy variable 1TIER was generated to represent combinations of matche s from the following most popular leagues: FIFA World Cup, European Championship, and UEFA Champions League. Dummy variable 2TIER represents the combinations of matche s from the following less popular leagues: Ligue 1, and AFC Champions League AFC Cup, FIF A Women World Cup, Copa America, Olympic Men Soccer, European National Teams Qualifying Games, Championship, FA Cup, and Asian National Teams Qualifying Games. Dummy variable 3TIER represents the combinations of matche s from the least popular leagues. Fina lly, a dummy variable OTHER which serves as the baseline was generated, which represent the rest combinations that were not accounted by previous dummy variables.
90 Additionally because sometimes matche s are selected from one league, and other times they ar e selected from multiple leagues. Variable NUM captures the number of different leagues a given draw involves. Marketing and game feature d ummies To control for the historical changes of the game structure, dummy variable D3P equals 1 when there was a thir d prize, and 0 otherwise; dummy variable D14M equals 1 when the draw was composed of 14 matche s, and 0 otherwise; dummy variable D2D equals 1 when there were two draws declared on the same day, and 0 otherwise; dummy variable DPRO equals 1 when there was a jackpot promotion, and 0 otherwise. Panel Data Analysis T o further investigate the demand for sports lottery, a panel data containing sales of 211 draws of 30 provinces in 2011 and 2012 will be obtained from the official website of the CSLAC (www.lottery .org.cn). The response variable in the panel regression models is the sales of province i at draw t. The explanatory variables include product attributes variables and province characteristics variables (Table 3 4 ). All product attributes variables includ ed in previous time series analysis but D2D, D14M and D3P were also included in the panel data analysis. The province characteristics variables include population of a province in 2010 (POP), total dependence rate (TDR), proportion of population with comp leted higher education (HER) and proportion of population who are illiterate (ILR), sport development (SPORT), income (INCOME), and venue accessibility as measured by number of sports lottery outlets (NTER). Population and population c ompositions T he monthly sales data is obtained from the Yearbook of the Chinese Lotteries 2011. And the PCSALES is derived by dividing SALES by the population in 2010 (POP).
91 The population and population composition variables, including POP, AGE0 14, AGE15 64, AGE65+, HER and ILR, will be obtained from the Sixth National Population Census of the People's Republic of China which was conducted in 2010 Because the sum of AGE0 14, AGE15 64, and AGE65+ is necessarily 100%, the value of one variable is predetermined by the other two. Only, AGE15 64 and AGE65+ are included in the regression because age group. Further, to increase the degree of freedom of th e model, an alternative variable TDR is also considered in the model. TDR is the total dependence rate, which is calculated by the following equation. TDR = (AGE0 14 + AGE65+)/AGE15 64 Derivation of the income v ariable The National Bureau of Statistics of China does not provide the information about household income, but the Per Capita Annual Income of Urban Households (PCIUH) and Per Capita Income of Rural Households (PCIRH) are reported by the Sixth National Population Census of the People's Republic of C hina Further, the proportions of rural and urban residents in the population are reported by the China Population and Employment Statistics Yearbook 2011 Therefore, INCOME is the per capita income of urban household and per capita income of rural househo ld weighted by the proportion of urban and rural residents in the population. It is derived by the following equation: INCOME = PCIUH %(Urban Population ) + PCIRH %(Rural Population ) Derivation of the sport v ariable The s ports d evelopment level is measured by the medals each province won at the 2009 China National Games (MED CNG ) Olympic Games (MED O G ) and other prominent international sports competitions (MED other ) and the number of professional football clubs in a province in 2010 (PRO). The variable SPORT is the factor score
92 obtained through a factor analysis of MED CNG MED O G MED other and PRO. Table 3 2 reports the results of the factor analysis. Venue a ccessi bility The main marketing factor included in the model is venue accessibility. This will be measured by the number of sports lottery terminals available in each province (NTER). NTER is obtained from the Yearbook of the Chinese Lotteries 2011. Method of e stimation For panel data, dependent variables and regressors can potentially vary over both time (i.e., within variation) and individuals (i.e., between variation). The benefits of using panel data include increased precision in estimation by using more in formation and increasing degrees of freedom, allowing for unobserved heterogeneity, discriminat ing economic models, and provid ing micro foundations for aggregate data analysis ( Hsiao, 2003 ) However, panel data methods are also more complicated, which often require adjusting standard errors of panel data estimators because each additional time period of da ta is not independent of previous periods Additionally, there may be correlation across individuals, such as country panels, or state panels where spatial autocorrelation is very common ( Brown & Rork, 2005 ; Rabe Hesketh & Skrondal, 2012 ) There are two major characteristics associated with t his data set, which in turn determine the estimation strategy to be employed. First, T (i.e., 211) is large relative to N (i.e., 30). It is not possible to obtain st andard errors that control for serial correlation in the error without explicitly stating a model for serial correlation (e.g., OLS using cluster robust standard errors, or population averaged estimator (also known as Pooled FGLS estimator)). A model for s erial correlation in the error, such as ARMA model for the errors, thus needs to be specified. On the other hand, given N is fixed, it is often
93 possible to relax the assumption of independence across individuals ( Cameron & Trivedi, 2005 2010 ) Yet, it i s possible to obtain standard errors that allow autocorrelated errors of general form by applying the method of Driscoll and Kraay (1998 ) Second, given the existence of time invariant regressors (i.e., zero within variation), they cannot be identified by estimators using only within variations (e.g., OLS on the mean difference data, or Fixed Effects Estimator). A possible approach is using Hausman Taylor ( 1981 ) estimator, which estimates coefficient of time invariant regressors by two stage least squares, using those elements of time averaged time variant regressors that are uncorrelated with individual speci fic part of the error term as instruments for time invariant regressors ( Hsiao, 2003 ) However, estimat es of model specification. Arellano and Bond ( 1991 ) proposed an IV approach using first difference that provides unbiased and consistent estimation for dynamic mo dels, but the time invariant regressors will be removed by first differencing. An alternative strategy often adopted in empirical research is to use random effects models, if stronger assumptions can be made. The crucial distinction between fixed and rando m effects is not in the nature of the effect, but whether to make inference with respect to the population characteristics or only with respect to the effects that are in the sample ( Hsiao, 2003 ) Finally, if the individual provinces are considered as a sample from a population of sports lottery jurisdictions, and the draws are a sample from a population of all draws, then it would make sense to associate random effects with both these factors. Unlike most application of mixed effects models (also known as hierarchical linear models), the covariance structure in this study is nonested, because individual is
94 not nested in time and time is not nested in individual. The random intercept for provinces is shared cross all draws for a given province i whereas the random intercept for draws is shared by all provinces in a given draw t This type of completely cross ed effects model can be estimated by the xtmixed procedure in STATA, following suggestions of Rabe Hesketh and Skrondal (2012, p. 476 )
95 Figur e 3 1. Relationships among sales, expected value, and market level skill coefficient
96 Figure 3 2. Time s eries line of s ales of Shengfu game o ver 2001 2012
97 Table 3 1 Historical changes of the Shengfu game design Time Period Draws 1 2 3 p 1 P 2 P 3 10/30/2001 06/20/2003 a 61 (2001001 200301) 0.5 0.5 0.5 1t / 3 13 2 t / 3 1 3 08/03/2003 09/04/2004 50 (2003022 2004028) 0.5 0.48 0.42 0.1 1t / 3 13 2 t / 3 1 3 312 3t /3 13 09/20/2004 08/29/2005 b 43 (2004029 2005029) 0.5 0.48 0.42 0.1 1t / 3 1 4 2 t / 3 1 4 364 3t /3 14 09/12/2005 b 2005030 0.65 0.7 0.3 1t / 3 1 4 2 t / 3 1 4 Note: (a) During this period, there were 14 draws had a 10 million yuan jackpot promotion by adding a temporary third prize to the game. The EP for those draws was adjusted accordingly. (b) During this period, there were 16 draws had a jackpot promotion by adding additional prize money ranging from 3 million to 10 million yuan to the first prize pool. The EP for those draws was adjusted accordingly.
98 Table 3 2 Description of variables included in time series analyses Variable Definition Response Variables SALES A ggregate nationwide sales of Shengfu lottery at draw t. Explanatory Variables EP E xpected effective price, it is the inverse of expected value. PP E xpected possible prize pool. PDC Prediction Difficulty Coefficient. PDCSQ Square of PDC. EPL&GB Matche s selected from English Premier League & German Bundes Liga. ISA&SLL Matche s selected from Italian Series A League & Spanish La Liga. MAJOR 4 Matche s selected from the four major leagues, and the combinations are other than EPL&GB and ISA&SLL 1TIER Matche s selected from most popular leagues 2TIER Matche s selected from less popular leagues 3TIER Matche s selected from least popular leagues. D2D A dummy variable that represents simultaneously declare two draws on the same day. DPRO A dummy variable that represents jackpot promotion. D3P A dummy variable that represents a third prize. D14M A dummy variable that represents 14 matche s. NUM Number of different leagues in a given draw.
99 Figure 3 3 Distribution of Prediction Difficulty Coefficient as measured by log(RATIO2)
100 Table 3 3 Coding the combination of the matche s Leagues Popularity Grouping FIFA World Cup (International) 1.41 1 P rimera Division (Spain) 1.38 1 Premier League (England) 1.35 1 Euro pean Championship 1.33 1 Bundesliga 1 (Germany) 1.25 1 Serie A (Italy) 1.22 1 UEFA Champions League (Europe) 1.04 1 Ligue 1 (France) 0.96 2 AFC Champions League (Asia) 0.9 2 AFC Cup (Asia) 0.85 2 FIFA Women World Cup (International) 0.82 2 Copa America (America) 0.78 2 Olympic Men Soccer (International) 0.66 2 Qualifying (Europe) 0.28 2 Championship (England) 0.24 2 FA Cup (England) 0.11 2 Qualifying(Asia) 0.05 2 Friend ship (International) 0.18 3 Super Cup (Germany) 0.2 3 Serie A (Brazil) 0.32 3 UEFA Cup (Europe, Changed to Europa) 0.42 3 Qualifying (South America) 0.44 3 DFB Pokal (Germany) 0.68 3 Bundesliga 2 (Germany) 0.72 3 J1 League (Japan) 0.77 3 Qualifying (Africa) 0.83 3 Community Shield (England) 0.89 3 Series B (Italy) 1.05 3 Eliteserien (Norway) 1.19 3 Segunda Division (Spain) 1.33 3 CONCACAF Champions League (N/C America) 1.36 3 Allsvenskan (Sweden) 1.37 3 J2 League (Japan) 1.39 3 Eerste Divisie (Netherlands) 1.4 3 Veikkausliiga (Finland) 1.4 3
101 Table 3 4 Description of variables included in panel data analyses Variable Definition Response Variables EP E xpected effective price, it is the inverse of expected value. PDC Prediction Difficulty Coefficient. PDCSQ Square of PDC. EPL&GB Matche s selected from English Premier League & German Bundes Liga. ISA&SLL Matche s selected from Italian Series A League & Spanish La Liga. MAJOR 4 Matche s selected from the four major leagues, and the combinations are other than EPL&GB and ISA&SLL 1TIER Matche s selected from most p opular leagues 2TIER Matche s selected from less popular leagues 3TIER Matche s selected from least popular leagues. D2D A dummy variable that represents simultaneously declare two draws on the same day. NUM Number of different leagues in a given draw. Province Characteristics Variables POP Total population of each province in 2010 LPOP Natural logarithm transformation of POP TDR Total Dependence Rate. HER Proportion of population with completed higher education. ILR Proportion of population who are illiterate. SPORT A derived variable measuring sport development. INCOME A derived variable measuring average income level in the province. LINCOME Natural logarithm transformation of INCOME. NTER T he number of sports lottery outlets in each province. L NTER Natural logarithm transformation of NTER Intermediate Variables AGE0 14 Proportion of age group (0 14) in the population. AGE15 64 Proportion of age group (15 64) in the population. AGE65+ Proportion of age group (15 64) in the population. PCIUH Per Capita Annual Income of Urban Households in 2010. PCIRH Per Capita Income of Rural Households in 2010. MED CNG M edals each province won at the 2009 China National Games. MED OG M edals each province won at all Olympic Games. MED other M edals each province won at all other prominent events. PRO Number of professional football clubs in a province in 2010.
102 Table 3 5 Descriptive statistics and factor solution for deriving SPORT variable Construct and Items M SD MIN MAX MED CNG 45.32 43.3 9 2 153 0.99 MED OG 9.19 9.81 0 33 0.95 MED other 36.13 34.81 2 136 0.96 PRO 1.03 1.30 0 5 0.77 Eigen V alue 3.42 Variance E xplained 94.4%
103 CHAPTER 4 RESULTS Results of Time Series Analysis Preliminary Analysis Figure 3 2 show s the historical sales of Shengfu lottery from 2001 to August 2012 for all 945 draws. Table 4 1 further summarizes the overall descriptive statistics for all 945 draws as well as those by the phase. The average sales of the lottery for the three phases, namely introduction, recession, and equilibrium were 207.5 million, 113.5 million, and 27.3 million yuan The variances of sales judg ed by the values of standard deviation bec a me significantly narrower with time. The average first prizes were 1.75 million, 1.15 million, and 1.20 million. And the average second prizes were 90590, 116325, and 117263 yuan The cost for buying the probability distribution of winning 1 yuan was 0.48 yuan in the first phase, and increased to 0.53 yuan in the second phase, and then decreased to 0.27 yuan in the third phase More interesting were the statistics of the market le vel skill coefficients. The skill coefficient of winning a first prize 1 ) as measured by the median ratio between actual number of first prize winners and theoretical number grew from .66 to 2.96 and then to 5.31. A similar trend was also found with sk ill coefficient of winning a second prize Figure 4 1 shows the historical change of th e market level skill coefficients It is possible to explore some of the relationships between the demand for Shengfu lottery and its primary determinants through preliminary analysis. For example, rollover is often regarded as the driving force for both effective price and jackpot pool. By plotting sales against rollover, we can see a clear positive relationship between sales and rollover. The left column of Figure 4 2 shows this positive correlation and almost all
104 points are within the 95% confidence interval of the predicted values. A more interes ting question, however, is how much of the sales can be attributable to rollover ? By differencing the current sales and the sales of the previous draw, we obtain ed sales difference. The right column of Figure 4 2 plots the sales difference against rollover, and it tells a completely different story. Sales difference was barely related to rollover, a finding that goes again st the findings of previous studies. A positive impact is more evident when the rollover is sufficiently large, but we have too scarce data points to conclude this A comparison of these two plots suggests that this strong positive correlation between sale s and rollover may be an artifact of serial autocorrelation. As rollover is determined in preceding draw, a higher rollover is often the result of higher sales in the preceding draw. Due to serial autocorrelation (i.e., the current sales are highly associ ated with preceding sales), therefore, we observe d a positive correlation between sales and rollover. We also explore d the impact of different leagues on sales. English Premier League, German Bundesliga 1, Italian Series A, and Spanish La Liga have been four major leagues for sports betting. In our sample, one third of the draws involved the combination of English Premier League and German Bundesliga 1 (EPL&GB), and the combination of Italian Series A and Spanish La Liga (ISA&SLL). We use d EPL&GB and ISA&SLL to illustrate the impact of leagues. Overall, lottery draws involving EPL&GB matche s sell better than those involvin g ISA&SLL matche s. As leagues represent the consumption value of the game, this suggests that sports lottery has consumption value for players. Furthermore, after controlling consumption value variable, the positive effect of rollover on sales is now evide nt. Overall, draws with rollover sell better than those
105 without rollover. The claimed spurious zero correlation between rollover and sales difference is likely due to the failure of considering the league information. This preliminary analysis suggests tha t autocorrelation, consumption value of the game, and rollover need to be considered to reach a valid conclusion. Figure 4 3 shows these preliminary results. Stationarity, Autocorrelation and Dynamic Specification Prior to any formal analysis involving time series, it is necessary to investigate the stationarity properties of the variables. A stationary series (i.e., mean reverting) fluctuates around a constant long run mean, which implies the series has a finite variance which does not depend on time. O n the other hand, if a series is non stationary (i.e., ever changing), it has no tendency to return to a long run deterministic path and the variances of the series are time dependent. In a marketing setting, a non stationary series implies an evolving mar ket, where the sales wander freely in one direct ion or another, or has a seasonal pattern ( Hanssens, Parsons, & Schultz, 2001 ) The tests of sta tionarity, known as unit root tests, check whether the autoregressive polynomial (1 ) has a root on the unit circle. The Augmented Dickey Fuller (ADF) test is used to assess the stationarity of sales, which readily rejected the null hypothesis of existen ce of a unit root at 1% critical value level ((Z(t)= 5.7, 1% critical value= 3.43, MacKinnon approximate p value for Z(t) =.0000) The result of ADF test suggests that the Shengfu lottery market has been stationary since its initial inception in 2001. There is no obvious trend of growth or declining due to exogenous shocks, such as effective marketing, population growth, introduction of competitive products, or fatigue ( Hanssens et al., 2001 )
106 After confirming the stationarity of the market, the behavior of the time series is ( 1976 ) three step modeling procedure, which consists of identification, estimation, and diagnostic checking. First, a candidate AR I MA process is selected by inspe cting the autocorrelation function (ACF) and partial autocorrelation function (PACF) of the original series. The ACF at lag k is simply the correlation of two data points that are k periods apart. The PACF at lag k is a similar correlation, but it holds co nstant all k 1 observations between two data points. The ACF plot of Figure 4 4 autocorrelation. Further, the PACF plot shows two obvious spikes in the series, which param eters and saving the residuals. If the model is adequate, the residuals will be whitened (i.e., the residuals are white noise) and the ACF PACF should be flat without any spikes. However, the ACF PACF of the residuals still show significant spikes, and bot h Bartlett test (B=1.65, p=0.0086) and Portmanteau test (Q=143.19, p=.0000) for white noise suggest residuals are significant deviates from white noise, thus the original AR(2) model is not appropriate. Even by increasing the number of lags to 3 and 4 did not completely whiten the residuals (Bartlett test failed to reject the null of white noise, but the Portmanteau test did in both cases). Box and Jenkins ( 1976 ) also suggested taking the logarithm of a heteroscedastic step modeling proc edure was repeated on the natural logarithm transformed sales data. The PACF plot show ed four spikes in the transformed series, which suggest ed an AR(4) process (Figure 4 5 ). A further inspection of the ACF PACF of the residuals show ed no
107 significant spike s. Both Bartlett test and Portmanteau test for white noise this time reject the null of white noise, suggesting the AR(4) model is appropriate. There are essentially two ways of dealing with serial correlation: one approach is to include a lagged dependent variable in the set of independent variables; and the other is to estimate a model via serial correlation errors ( Beck & Katz, 1996 ) Because over time persistence in the data constitutes substantive information, an d can have theoretical explanation ( e.g., Farrell et al., 1999 ) the first approach is more preferable in this study. Therefore, in the following regression analysis, the natural logarithm transformed sales data would be used as response variable, and fou r lags would be included in the right side of equation. Ordinal Least Squares Results Previous studies suggest expected jackpot size and expected effective price are two underlying drivers for lottery demand. The hybrid model including both effective pric e and jackpot size is considered first ( Column 1 of Table 4 2 ) As expected, the jackpot size ha d a significant positive impact on the demand. But surprisingly, t he coefficient of effective price was also positive which means people buy more tickets when the price is higher. This result is inconsistent with microeconomic theory and previous studies in the fie ld (e. g., Clotfelter & Cook, 1990 ; Forrest et al., 2000 ; Garrett & Sobel, 2004 ) Including ticket composition and prediction difficulty variables (Column 2), and marketing variables (Column 3) in the regression reveal ed that the positive sign of effective price persists. Furthermore, the coefficient on the prediction difficulty was negative, which means people buy more tickets when the games are more difficult to predict wh en other variables are held constant. The coeffi cient on promotion was negative, suggesting jackpot promotion was associated with a decrease in sales holding
108 other variables constant. Across all three regressions, after controlling jackpot size the magnitude of four lags of sales became rather small co mpar ed with the results of previous time series analysis. These lend us little confidence in the hybrid model. A further examination of the zero order correlation matrix among sales and jackpot size revealed that the simple bivariate correlation was 0.9 1 .T his is not surprising because the jackpot pool was directly calculated based on sales. The y would have be en perfectly correlated if there were no prize cap policy The only deviation from perfect correlation is induced by the prize cap policy. Cook and Clotfelter (1993 ) reported a similar result when they tried to includ e expected value and jackpot size in a regression to estimate the demand for a state lottery in the U.S. Without a valid instrumental variable or proxy variable, it is impossi ble to estimate the expected jackpot pool model. Furthermore, in the current context where a prize cap is imposed, it is speculated jackpot size will not matter as much as in traditional lotto games. Therefore, we subscribe to the effective price model. Co lumn 4 of Table 4 2 show s the baseline effective price model (M1) which only include four lags of sales and effective price. Column 5 extends the model by including ticket composition and prediction difficulty variables (M2). Column 6 further extends the model by including marketing variables (M3). All three models fit the data reasonably well with 70.8% to 81.8% variances explained. Further, a Breusch Godfrey LM Test for a utocorrelation suggests that M2 suffer from an autocorrelation problem, whereas M1 and M3 do not. A Breusch Pagan test for heteroskedasticity suggest s all three models have heteroskedastic residuals, and thus heteroskedasticity robust standard error are us ed and reported in Table 4 2
109 After dropping the jackpot size variable in the regression model, across all three regressions the coefficient of effective price had a negative sign as microeconomic theory predicted. The OLS estimated elasticity around 0.5 6 in the final regression, suggesting one percent decrease in price is associated with 0.56 percent increase in sales. Across all three regressions, the four lags of sales were significantly related to the current sales. The ticket composition ha d a signif icant impact on sales. According to the results developed by Halv orsen and Palmquist (1980 ) and Kennedy (1981 ) an estimate of the percentage impa ct of a dummy variable in a log transformed model is given by g=100(exp(b v(b)/2) 1), where b is estimated coefficient on a dummy variable and V(b) is the estimated variance of b. Compar ed to a mixture of all kinds leagues, draws composed of EPL&GB were as sociated with 100*(exp(0.484 0.04*0.04/2) 1) percent change in sales, approximately 62.12% increase in sales. Likewise, draws composed of ISA&SLL, prominent cup games ( 1TIER ), other major league combinations (MAJOR 4 ) were associated with 15.64%, 9.25%, and 62.01% change in sales, respectively. Whereas EPL&GB, ISA&SLL, MAJOR 4 and 1TIER were all positively associated with sales, 2TIER and 3TIER were negatively associated with sales. Draws composed of minor leagues and middle leagues were associated with approximately 27.85% and 19.81% decrease, respectively. Prediction difficulty coefficient was also significantly related with sales, but with a relative small coefficient ( 0.0159 ) It means that a one unit change in prediction difficulty coefficient is approximately associated with 1.59% (i.e., e 0.0159 1) change in sales. The quadratic term of prediction difficulty coefficient is not significant at 5% confidence level.
110 Draws that were declared on the same day sell significantly less. The i mpact of simultaneity wa s associated with 14.99% decrease in sales. Draws with jackpot promotion s old about 24.29% more. Changing a two prize structure to a three prize structure wa s associated with 15.22% increase in sales. Compar ed to draws when only 13 matche s were included, draws consist ing of 14 matche s s old 41.16% less. The number of different leagues included in a draw ( NUM ) was found negatively associated with sales. Adding one more l eague to the ticket was associated with 4.18% decrease in sales (i .e., e 0.04 1). Instrumental Variables Results As discussed, the effective price is necessarily endogenous in the regression model due to simultaneity Furthermore, as the expected jackpot pool was left out of the cu rrent model, the OLS model may thus als o suffer omitted variable issue. The conventional instrumental variable approach was therefore chosen to correct the endogeneity bias of OLS. Following previous studies ( Forrest et al., 2000 ; Garca & Rodrguez, 2007 ) the amount of rollover was used to instrument effective price Column 7 of Table 4 2 reports the second stage results of instrumental variable s estimation The model overall fits the data well, with 81.48% variance in sales explained by this set of explanatory variables. The general specification test of serial correlation proposed by Cumby and Huizinga after instrumental variables estimation fa iled to reject the null of nonautocorrelation at the 5% confidence level. All coefficient estimates from i nstrumental variables approach were in the same direction as OLS, and the magnitude of most coefficient estimate s remain ed close, with the exception o f effective price. The demand for s ports lottery wa s more elastic than the OLS suggested. The coefficient estimate of effective price from instrumental variable approach was about 1/2 larger
111 than that obtained from OLS, suggesting OLS estimation bias towards zero in this case. The point estimate of elasticity with regard to effective price was 0.78, and the corrected standard error 0.075. In terms of the first stage, the centered R 2 was 0.83 and the F statistic was 162.30. The coefficient estimate of the instrument was significant at .01 confidence level. These suggest that the first stage is adequately strong, and rollover is relevant. It can be a good instrument for effective price. Howeve r, t he validity of an instrument also relies on a second condition: instrument exogeneity. It is a strong assumption that rollover has no partial effects on sales and is strictly exogenous to the equation. Beenstock and Haitovsky (2001 ) have show n the lottomania phenomenon driven by multiple rollovers. They showed a direct effect of rollover on consumption. Instrument exogeneity condition also means that the instruments should not correlate with the disturbances. Assuming jackpot pool is indeed a driving factor, omitting expected jackpot pool in the equation means expected jackpot pool is in the disturbances. Therefore, as rollover is determinant of jackpot pool, they are correlated. Thus the exogeneity assumption can be violated under this alternative theoretical framework Never theless, the instruments may hold if we are willing to assume rationality in lottery consumption behavior. Consumers are not spontaneous, not impulsive, but rational. Under this assumption, after partialing out effective price, jackpot pool should not impa ct sales. And we have more credibility by using rollover as an instrument in the estimation. Using CAP as Instrument Because prize cap is imposed on the game, it causes exogenous variation in the expected prize. A further investigation of the occurrence of cap reveals that it can hardly be predicted by using the information of previous sales level, ticket composition,
112 pr ediction difficulty, and marketing variables. The success rate of a logit regression relating occurrence of cap to all the explanatory variables included in previous studies is 0/53, which means the occurrence of CAP is quite random and unpredictable. This lends our confidence to the exogeneity of CAP. As CAP is potentially a weaker instrument for effective price, limited information maximum likelihood (LIML) method, which is more robust to the presence of weak IV, was used ( Baum, Schaffer, & Stillman, 2007 ) To assess the strength of the first stage regression, a variety of test statistics were used. The centered R 2 was 0.36, and F statistic was 46.36. The coefficient estimate of CAP is significant at .01 confidence level. Because we have one instrument for one endogenous variable, the model is just identified. Further, t he Cragg Donald Wald F statistic is large (28.25). By comparing it to th e 10% maximal LIML size (16.38) of Stock Yogo weak ID test critical values for K1=1 and L1=1, the null hypothesis of weak identification can be rejected. The robust Kleibergen Paap Wald rk F statistic (18.42) also reject ed the null of we a k identification, suggesting that the first stage was strong. These lend great confidence to the results of the model. Column 8 of Table 4 2 reports the results of second stage of the model. Not surprisingly, the magnitude of coefficient estimate of effective price is eve n larger, with elasticity around 1.01. This means that a one percent increase in price will lead to one percent decrease in sales. A trade off of this model, however, is a larger standard error (0.39). Furthermore, coefficient estimates of all the rest va riables are very close to previous analysis.
113 Results of Panel Data Analysis Because dependent variables and regressors can potentially vary over both time (i.e., within variation) and individuals (i.e., between variation), cross sectional analysis and pure time series analysis usually suffer from the estimation bias arising from heterogeneity or selection I n our sample, the individuals are provinces in C h ina except Tibet. W e can observe substantial within and between variations of sales of S hengfu lot tery (Figure 4 6 ). W hereas the dependent variables and its four lags necessarily vary over both time and individuals, the included regressor s can be time invariant or individual invariant. For example, the effective price of any given draw wa s the same for every individual (i.e., individual invariant) but the income level was considered stable over the period from 2010 to 2011 of any given individual (i.e., time invariant). Table 4 3 presents the descriptive statistics of dependent variables and included re gressors Further, simply regressing sales on effective prices reveals substantial variability in co efficient estimates (Figure 4 7 ). Panel data methods, therefore, are desirable. Pooled Models F or completeness, a natural starting point is a class of pool ed models, which specify the same regression model for all individuals in all draws. The first pooled model (PM1) is a static regression model using OLS with cluster robust standard error. The second model (PM2) is pooled OLS with standard errors assuming general serial correlation in the error to four lags and correlation over states ( i.e., Driscoll Kraay (1998) standard errors; Hoechl e, 2007 ) The third model (PM3) is a dynamic model by including four lags of dependent variable in the right side and estimated by the Pooled Feasible Generalized Least Squares estimator (PFGLS). In principle, PFGLS is the best estimator for pooled mode l s ( Cameron & Trivedi, 2010, p. 268 ) Column 1 3 of Table 4
114 8 report the results of these three models. Coefficient estimates of PM1 and PM2 are the same. The differences lie with their standard errors. The standard errors of time variant variables of PM2 are about 4 times larger than those obtained by PM1, and those of time invariant variables of PM2 are ab out 4 times smaller than those obtained by PM1. However, as mentioned both models suffer from an autocorrelation problem. A Wooldridge test for autocorrelation in panel data ( Drukker, 2003 ; Wooldridge, 2002 ) readily rejects null of no first order autoco rrelation (F(1,29)=5.9, p=0.02). There are noticeable changes in the coefficient estimates of PM3. Particularly, after controlling the lags of sales in the model, the magnitude of those time invariant variables decreased drastically. For example, the point estimate of income elasticity decreased from 2.03 in PM1 and PM2 to 0.11 in PM3. Fixed Effects Models The second class of models is fixed effects models, which explicitly consider the individual specific effects. The first FE model (FE1) is static mode l fitted with Least Squares Dummy Variables (LSDV) approach of including a set of dummy variables, here for each province. The second model (FE2) is a dynamic version of FE1. To examine the coefficients of time invariant variables, the fourth model (FE3) is estimated ( 1991 ) approach to account for dynamic specification. Column 4 7 of Table 4 8 report the results of these four models. As discu ssed, the FE1, FE2, and FE4 were un able to identify time invariant regressors. The coefficient estimates of those time variant variables of FE1 are same as those of PM1. The coefficient estimates of FE3 are same as those of PM1. The coefficient estimates o f FE2 and FE4 are generally consistent. The key insight is that the intra class correlation (IC) of FE1 is 0.876,
115 suggesting that 87.6% variances of sales are due to differences across provinces. The IC of FE2 is 0.699, suggesting that even after controlli ng historical sales level (i.e., four lags of sales), 69.9% variances are still attributable to regional differences. FE3 does not account for dynamics but includes time invariant variables. The IC of FE3 dropped to 0.774, meaning about 10.2% (i.e., 0.876 0.774) variances are explained by those time invariant variables. The key insight from FE4 is that including four lags of sales in the model is likely appropriate. Arellano Bond test for zero autocorrelation in first differenced errors reject the null of no autocorrelations at order 1 (z= 2.41, p=.016) but not at higher orders (z=.11, p=.91 at order 2; z= .67, p=.50 at order 3). Therefore, we can conclude that after including four lags, there is no serial correlation in the error as desired. Two Way Random Effects Model The third class of models is a dynamic two way random effects model (RE1) using MLE via EM algorithm ( Baltagi, 2005 ; Rabe Hesketh & Skrondal, 2012 ; Rubin & Szatrowski, 1982 ) Column 8 of Table 4 8 reports the results of the model. The coefficient estimates of RE1 are generally consistent with previous studies: (a) The estimated elasticity with regard to effective price is about 1.0; (b) Ticket combination variables have significant impact on the demand. Specifically, major league matches sell more and minor league matches sell less; (c) Prediction difficulty coefficient is marginally significant at 10% confidence level, and the magnitude is rat her small (0.04); (d) Simultaneous selling two draws at a time reduce sales by about 21.4% (i.e., exp( 0.237 0.088*0.088/2) 1 percent) averagely for each draw; (e) Diversifying the draw by including matches from one more league has a small negative impact on sales, reducing sales by about 5.4% (i.e., exp( 0.055) 1); (f) Population was not found a
116 significant predictor of sales after controlling all the other variables; (g) Dependence rate is significantly related to sales, one percent increase in TDR is as sociated with about 2.1% increase in sales; (h) The demand elasticity with regard to income is about 0.39, quite different from previous models. In a cross sectional setting using aggregate monthly sales, we found the income elasticity was a positive 1.59. The estimates of PM1, PM2 and FE3 were about a positive 2.03, which did not include lags in their models; (g) HER, ILR, SPORT, and NTER were found not significant related to sales. The estimated residual standard deviation between provinces wa s 0.15, and the estimated residual standard deviation between draws wa s 0.3 3 The remaining residual standard deviation, not due to additive effects of provinces and draws, wa s estimated as 0.20. The residual intra h class correlation ( IC C) for provinces wa s estimated as and the residual IC C for draws wa s estimated as Hence, there is a high correlation over draws within provinces and a small correlation over provinces within draws. I nstrumental Variables Results The fourth class of model us ed instrumental variables approach because expected price is endogenous in the model. FE3 and FE4 are IV models, which use lags of the endogenous regressor (i.e., EP) as instruments. As discussed previously, rollover and the dummy variable of prize cap (CAP) are used as instruments for endogenous variables respectively in two one way random effect models (RE2 and
117 RE3). Column 9 10 of Table 4 8 report the results of estimates. RE2 using rollover as an instrument reports an elasticity of 1.19 ( SE =.029), and RE 3 using CAP as an instrument reports an elasticity of 0.94 ( SE =.13). Both results are not very different from p revious analysis, which lend confidence to the results.
118 Table 4 1. Descriptive s tatistics for time series data Mean SD Min 25% Me dian 75% Max Overall SALES (million yuan ) 45.82 53.29 2. 39 20.36 27.36 40.82 316.43 First Prize (thousand yuan ) 1259.12 2073.89 0.00 38.26 388.76 1611.21 38800.00 Second Prize (thousand yuan ) 115.78 433.33 0.00 2.92 11.08 49.22 5000.00 Expected Value 1.38 0.38 0.89 1.28 1.28 1.28 4.63 Effective Pric e (1/EV) 1.53 0.31 0.43 1.56 1.56 1.57 2.24 Total Jackpot 29.02 30.70 0.00 10.70 17.60 34.10 223.00 STAGE 1 SALES (million yuan ) 207.55 62.97 21.21 186.17 220.54 253.02 316.43 First Prize (thousand yuan ) 1752.13 1900.97 0.00 110.51 1175.12 2913.33 5000.00 Second Prize (thousand yuan ) 90.59 164.49 0.28 4.79 36.16 106.79 998.28 Expected Value 1.04 0.09 0.98 0.98 0.98 1.07 1.34 Effective Pric e (1/EV) 1.94 0.15 1.50 1.86 2.04 2.04 2.04 Total Jackpot 111.47 39.35 10.20 102.00 124.00 132.00 223.00 STAGE 2 SALES (million yuan ) 49.27 46.18 2.22 22.66 29.83 56.20 256.19 First Prize (thousand yuan ) 1420.00 2495.62 0.00 48.81 449.73 1917.27 38800.00 Second Prize (thousand yuan ) 121.70 480.24 0.00 2.62 11.28 48.77 5000.00 Expected Value 1.36 0.41 0.89 1.26 1.28 1.28 4.63 Effective Pric e (1/EV) 1.57 0.33 0.43 1.56 1.56 1.59 2.24 Total Jackpot 31.06 26.71 0.00 13.90 20.90 39.60 178.00 STAGE 3 SALES (million yuan ) 24.84 11.40 2.39 15.95 24.75 31.29 76.72 First Prize ( yuan ) 1046.81 1547.51 0.00 23.72 331.48 1341.17 5000.00 Second Prize ( yuan ) 112.68 404.17 0.00 2.90 9.87 43.17 4774.88 Expected Value 1.44 0.35 0.93 1.28 1.28 1.29 3.52 Effective Pric e (1/EV) 1.44 0.24 0.57 1.55 1.56 1.56 2.15 Total Jackpot 18.05 15.60 0.00 8.29 15.40 21.40 109.00
119 Figure 4 1 Historical c hange of market level skill coefficients ( 1 2 )
120 Figure 4 2 Impact of rollover on demand
121 Figure 4 3 Impact of ticket composition and rollover on demand: Using f our most popular leagues as an e xample
122 Figure 4 4 ACF PACF of sales and residuals of its AR(2) m odel
123 Figure 4 5 ACF PACF of log(Sales) and r esiduals of its AR(4) Model
124 Table 4 2 Results of time series regressions (1) (2) (3) (4) (5) (6) (7) (8) OLS OLS OLS OLS OLS OLS 2SLS LI M L L.lsales 0.131** 0.0857** 0.0800** 0.240** 0.254** 0.204** 0.205** 0.206** (0.0261) (0.0187) (0.0177) (0.0407) (0.0346) (0.0308) (0.0309) (0.0315) L2.lsales 0.159** 0.0693** 0.0615** 0.327** 0.260** 0.196** 0.200** 0.203** (0.0237) (0.0167) (0.0169) (0.0371) (0.0326) (0.0318) (0.0318) (0.0335) L3.lsales 0.141** 0.0808** 0.0650** 0.262** 0.201** 0.128** 0.131** 0.134** (0.0280) (0.0196) (0.0193) (0.0428) (0.0371) (0.0342) (0.0334) (0.0344) L4.lsales 0.0449* 0.0369** 0.0252 0.149** 0.128** 0.0781** 0.0837** 0.0895** (0.0258) (0.0187) (0.0183) (0.0447) (0.0367) (0.0334) (0.0326) (0.0345) Log(EP) 0.162** 0.277** 0.196** 0.377** 0.425** 0.564** 0.780** 1.009** (0.0698) (0.0570) (0.0615) (0.0865) (0.0786) (0.0835) (0.0745) (0.390) Log(TJ) 0.475** 0.613** 0.590** (0.0205) (0.0209) (0.0211) EPL&GB 0.132** 0.168** 0.379** 0.484** 0.490** 0.497** (0.0246) (0.0251) (0.0417) (0.0406) (0.0404) (0.0427) ISA&SLL 0.00977 0.0230 0.0380 0.146** 0.148** 0.149** (0.0251) (0.0252) (0.0425) (0.0419) (0.0416) (0.0428) MAJOR 4 0.147** 0.162** 0.420** 0.484** 0.500** 0.516** (0.0274) (0.0279) (0.0488) (0.0458) (0.0452) (0.0552) 1TIER 0.0437 0.0347 0.132** 0.0899* 0.0972* 0.105* (0.0286) (0.0308) (0.0508) (0.0535) (0.0536) (0.0563) 2TIER 0.0887* 0.0979* 0.187* 0.216** 0.205** 0.194** (0.0491) (0.0511) (0.103) (0.0966) (0.0911) (0.0891) 3TIER 0.0916** 0.111** 0.306** 0.325** 0.319** 0.312** (0.0351) (0.0348) (0.0607) (0.0570) (0.0555) (0.0587) PDC 0.134** 0.126** 0.00646 0.0159** 0.0155** 0.0150** (0.00688) (0.00694) (0.00733) (0.00694) (0.00694) (0.00717) PDCSQ 0.0161** 0.0156** 0.000885 0.000555 0.000919 0.00130 (0.00123) (0.00122) (0.00168) (0.00160) (0.00158) (0.00172)
125 Table 4 2. Continued (1) (2) (3) (4) (5) (6) (7) (8) OLS OLS OLS OLS OLS OLS 2SLS LIML D2D 0.0578** 0.162** 0.161** 0.160** (0.0226) (0.0399) (0.0397) (0.0404) D PRO 0.0911** 0.220** 0.197** 0.173** (0.0412) (0.0672) (0.0713) (0.0880) D3P 0.0812** 0.143** 0.197** 0.254** (0.0287) (0.0544) (0.0560) (0.110) D14M 0.163** 0.562** 0.582** 0.604** (0.0376) (0.0785) (0.0808) (0.0870) NUM 0.00498 0.0425** 0.0439** 0.0454** (0.0106) (0.0180) (0.0178) (0.0182) Constant 0.393** 0.707** 1.086** 0.223** 0.543** 1.959** 2.008** 2.060** (0.0409) (0.0436) (0.102) (0.0624) (0.0725) (0.209) (0.212) (0.226) N 938 938 938 941 938 938 938 938 F 1278.1 713.5 574.8 673.7 309.6 287.4 270.8 247.1 R 2 0.862 0.929 0.932 0.708 0.786 0.818 0.815 0.806 BIC 435.6 130.1 138.8 1130.0 892.4 776.1 790.6 835.8 Note: (a) Heteroskedasticity robust standard errors in parentheses (b) p<0.10, ** p<0.05
126 Figure 4 6. Within and between variations in panel data
127 Figure 4 7. Separate simple regressions of 30 provinces: sales on effective price
128 Table 4 3 Descriptive s tatistics for the panel data analysis Variables C ategory M ean SD M in M ax N L og( sales ) overall 6. 10 1.23 1.64 9.7 3 6330 between 1.1 2 3.2 7 8.09 30 within 0.56 2.9 2 8.92 211 Time variant Individual invariant Variables EP within 0.34 0.20 0.56 0.50 211 EPL&GB within 0.14 0.34 0 1 211 ISA&SLL within 0.08 0.27 0 1 211 1TIER within 0.08 0.27 0 1 211 MAJOR4 within 0.25 0.43 0 1 211 2TIER within 0.06 0.23 0 1 211 3TIER within 0.18 0.39 0 1 211 PDC within 1.72 2.04 3.80 7.27 211 PDCSQ within 7.14 9.03 0 52.80 211 D2D within 0.09 0.29 0 1 211 NUM within 3.00 1.09 1 5 211 Time invariant Individual variant Variables Log(POP) between 3.48 0.87 1.10 4.65 30 TDR between 34.46 6.91 20.95 51.04 30 HER between 9.79 5.24 5.29 31.50 30 ILR between 4.24 2.26 1.70 10.23 30 SPORT between 0.02 0.99 1.01 2.10 30 Log(INCOME) between 9.26 0.43 8.59 10.41 30 L og(NTER) between 7.91 0.87 5.37 9.39 30
129 Table 4 4 Results of panel data regressions Pooled Models Fixed Effects Models Random Effects Models PM1 PM2 PM3 FE1 FE2 FE3 FE4 RE1 RE2 RE3 L.lsales 0.37** 0.20** 0.13 0.37** 0.29** 0.30** (0.01) (0.01) (0.16) (0.01) (0.01) (0.01) L2.lsales 0.19** 0.06** 0.00 0.18** 0.16** 0.16** (0.01) (0.01) (0.19) (0.01) (0.01) (0.01) L3.lsales 0.20** 0.11** 0.05 0.13** 0.23** 0.24** (0.01) (0.01) (0.08) (0.01) (0.01) (0.01) L4.lsales 0.18** 0.11** 0.07 0.12** 0.22** 0.22** (0.01) (0.01) (0.08) (0.01) (0.01) (0.01) log(EP) 1.07** 1.07** 0.94** 1.07** 1.09** 1.07** 1.09** 1.09** 1.23** 0.95** (0.05) (0.14) (0.10) (0.03) (0.02) (0.03) (0.32) (0.12) (0.03) (0.13) EPL&GB 0.46** 0.46** 0.34** 0.46** 0.44** 0.46** 0.46** 0.44** 0.39** 0.38** (0.01) (0.06) (0.06) (0.02) (0.02) (0.02) (0.16) (0.07) (0.02) (0.02) ISA&SLL 0.30** 0.30** 0.04 0.30** 0.17** 0.30** 0.21** 0.10 0.07** 0.07** (0.01) (0.06) (0.06) (0.02) (0.02) (0.02) (0.09) (0.08) (0.02) (0.02) MAJOR4 0.34** 0.34** 0.16** 0.34** 0.30** 0.34** 0.32 0.27** 0.25** 0.25** (0.02) (0.07) (0.06) (0.02) (0.02) (0.02) (0.20) (0.08) (0.02) (0.02) 1 TIER 0.36** 0.36** 0.21* 0.36** 0.28** 0.36** 0.32 0.21 0.22** 0.20** (0.02) (0.14) (0.11) (0.03) (0.03) (0.03) (0.40) (0.13) (0.03) (0.03) 2 TIER 0.15** 0.15 0.24** 0.15** 0.21** 0.15** 0.18 0.25** 0.26** 0.26** (0.02) (0.10) (0.09) (0.02) (0.02) (0.02) (0.52) (0.11) (0.02) (0.02) 3 TIER 0.72** 0.72** 0.50** 0.72** 0.68** 0.72** 0.68** 0.66** 0.66** 0.64** (0.03) (0.09) (0.07) (0.02) (0.02) (0.02) (0.15) (0.08) (0.02) (0.02) PDC 0.03** 0.03* 0.02* 0.03** 0.03** 0.03** 0.03** 0.03* 0.03** 0.03** (0.00) (0.02) (0.01) (0.00) (0.00) (0.00) (0.01) (0.02) (0.00) (0.00) PDCSQ 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) D2D 0.24** 0.24** 0.17** 0.24** 0.24** 0.24** 0.21 0.24** 0.25** 0.25** (0.01) (0.08) (0.07) (0.02) (0.02) (0.02) (0.64) (0.08) (0.02) (0.02)
130 Table 4 4. Continued Pooled Models Fixed Effects Models Random Effects Models PM1 PM2 PM3 FE1 FE2 FE3 FE4 RE1 RE2 RE3 NUM 0.07** 0.07** 0.05** 0.07** 0.08** 0.07** 0.07 0.08** 0.08** 0.09** (0.00) (0.03) (0.02) (0.01) (0.01) (0.01) (0.09) (0.03) (0.01) (0.01) log(POP) 0.22 0.22** 0.01** 0.22 0.04 0.02 0.02 (0.39) (0.01) (0.01) (0.45) (0.09) (0.02) (0.02) TDR 0.11** 0.11** 0.01** 0.11** 0.02** 0.01** 0.01** (0.04) (0.00) (0.00) (0.04) (0.01) (0.00) (0.00) HER 0.02 0.02** 0.00 0.02 0.00 0.00 0.00 (0.04) (0.00) (0.00) (0.05) (0.01) (0.00) (0.00) ILR 0.00 0.00 0.00 0.00 0.00 0.00 0.00 (0.08) (0.00) (0.00) (0.08) (0.02) (0.00) (0.00) SPORT 0.03 0.03** 0.00 0.03 0.01 0.00 0.00 (0.22) (0.01) (0.00) (0.27) (0.05) (0.01) (0.01) log(INCOME) 2.03** 2.03** 0.11** 2.03** 0.39** 0.19** 0.19** (0.94) (0.03) (0.02) (0.97) (0.19) (0.04) (0.04) log(NTER) 0.32 0.32** 0.01** 0.32 0.06 0.03* 0.03* (0.32) (0.02) (0.01) (0.45) (0.09) (0.02) (0.02) Constant 19.56** 19.56** 0.65** 6.55** 3.70** 19.56** 4.99* 3.31* 1.22** 1.31** (9.56) (0.36) (0.20) (0.02) (0.08) (9.18) (2.59) (1.78) (0.35) (0.35) Note s : (a) PM1 OLS with cluster robust standard error; PM2 Pooled OLS with serial correlation in the error and correlation over provinces (i.e., Driscoll Kraay standard errors): PM3 Pooled Feasible Generalized Least Squares including 4 lags of log(sales)(PFGLS); FE1 Least Squares Dummy Variables (static); FE2 Least Squares Dummy Variables (including 4 lags); FE3 Hausman Taylor meth od; FE4 Arellano Bond method; RE1 Two way Random effects models; RE2 One way random effect model using rollover as instrument; RE3 One way random effect model using prize cap as instrument ( b ) Heteroskedasticity robust standard errors in parentheses ( c ) p<0.10, ** p<0.05
131 CHAPTER 7 DISCUSSION Despite that sports lottery gambling has become a prevalent economic and recreational activity, it remains a n under researched area in sports management literature. Having recourse to Expected Utility Theory and its generalizations, an econometric model of demand for sport s lottery gambling was constructed. The model assumes an experiential utility associated with lottery gambling, and proposes that rational consumers are mainly motivated by three clus ters of variables: product attributes, consumer demographics, and marketing variables. The model is empirically examined by using a set of draw to draw sales data of the Shengfu game the most representative sport s lottery in China. Through time series and panel data analyses, this study has the following major findings: (a) s ports gambling has consumption value, as evidenced by that the ticket composition has considerable impact on the demand ; (b) c onsumers are sensitive to the implicit cost of a buying lo ttery ticket (i.e., effective price) where t he estimated price elasticity is around 1 ; (c) a t least in the context of Chinese sports betting market, the province with higher income level had hi gher demand for sports lottery contradicting the regressivi ty property of traditional lottery games The estimated income elasticity is around 0.4 ; (d) c onsistent with the research findings of previous studies population segments with higher financial and social burdens tends to buy more lottery tickets ; ( e ) m ark eting variables and structural arrangements of the game were found have significant impact on consumer demand of sports lottery tickets; ( f ) consumers showed signs of learn ing from betting experience and increasing the odds of winning as evidenced by an ever increasing median probability of winning first and second prizes ; and ( g ) p opulation, education level, sport
132 development level, and venue accessibility were found not significantly related to the demand of sports lottery tickets Theoretical Contrib utions Sports L ottery as C onsumption Through time series and panel data regressions, this study revealed that the ticket composition has considerable impact on the demand. As mentioned, six dummy variables ( i.e., EPL&GB, ISA&SLL, MAJOR4, 1TIER, 2TIER, and 3TIER ) were included in the models. Comparing with the baseline, a mixture of different levels of leagues and tournaments, EPL&GB, ISA&SLL, MAJOR4, and 1TIER had significant positive impact on the demand, whereas 2TIER and 3TIER had significant negative i mpact on the demand. The magnitude of impact is non trivial. Since the inception of the Shengfu game the draws consist ing of EPL&GB were associated with about 60% more sales; whereas the draws consist ing of 3TIER were associated with about 30% less sales. The finding of this study is consistent with Garca and Rodrguez (2007 ) who found that in Spanish La Quiniela game, draws with the absence of First Division matches were associated wit h a 53% reduction in sales. They suggested that the finding justifies why asking to increase this percentage. But, they did not further explain why this phenomenon would occur from a theoretic al perspective. If sports lotter y is merely gambling, the consumption values of spectatorship of a given match should not have direct systematic impact on the demand for its gambling product. After all, according to existing lottery gambli ng theories, it is the probability of winning, size of jackpot pool (amount of prizes), prize structure, and the potential dilution of the prizes that affect the expected value of a lottery product ( Cook &
133 Clotfelter, 1993 ; Garrett & Sobel, 2004 ; Shapira & Venezia, 1992 ) Ticket composition is indeed systematically associated with the objective probability of winning as measured by predic tion difficulty coefficients. A MANOVA analysis revealed that there were significant differences with RAT1 and RAT2 among different ticket composition groups (Table 5 1). Comparing with the ba seline, the probabilities of winning any prize when draws are composed of EPL&GB, ISA&SLL, MAJOR4, and 3 TIER are lower. In contrast, the probability of winning any prize when draws are composed of 1 TIER and 2 TIER are higher. This also justifies the inclusi on of PDC. Although the objective probability of winning and accordingly the potential dilution of the prizes indeed depend on the composition of the matches t he traditional theory predicts no additional impact of ticket composition on the demand after controlling the indirect routes. This study suggests that sports lottery gambling may be considered as a con sumption practice. As such, players may derive additional utility from gambling on different matches There are, however, two theoretical accounts First, the market is resides inside of gambling itself as Conlisk (1993 ) proposed. For instance, betting on certain leagues or tournaments can generate more excitement or thrill, which can in turn translate into greater gambling utility, then gamblers may increase their consumption on those draws because they gain more utility. W hy then is betting on EPL&GB more exciting than betting on ISA&SLL? Do these two combinations differ on some aspects of their gambling properties, such as confidence of prediction, knowledge, prize pool, and ob jective winning probability? For instance if consumers can foresee larger prize pool is often associated with EPL&GB, or those draws are easier to predict, then they may buy
134 more tickets in those draws. This flies in the face of the fact that both the win ning probabilities and size of prizes appear to be very close. Given that all four leagues have a prominent presence in China for a long time and there is extensive media coverage about all these four leagues i t is unlikely that these two combinations dif fer significantly in terms of their gambling properties. Second, the additional demand may arise from an additional segment of players who view sports betting as a derivative of spectator sports and consume sports betting. Can the additional demand associ ated with EPL&GB be that they collectively have a larger fan base in China? Draws composed of EPL&GB attract additional sports fan s to the betting market. For professional gamblers, they gamble anyway. However, sports fans may only gamble on their favorite leagues. Then the additional demand actually arises from sports fans consuming sports. Given that ticket composition does have direct systematic impact on the demand, we subscribe to the second explanation. The market is composed of at least two heterogen eous segments: one is gamblers and the other is sports consumers. Sports consumers take part in sports betting as consuming a derivative product of spectator sports. Rationality in S ports G ambling Besides the consumption value of sports betting, players also exhibit some rationality in sports betting as they are rather sensitive to the implicit cost of buying a lottery ticket. The estimated effective price elasticity is around 1 by using time serie s and panel data analysis, which implies that 1% increase in effective price will lead to 1% decrease in sales. Although several studies have estimated effective price elasticities of different lottery products in the United States, United Kingdom, and Spa in, the results are not directly comparable because this study adopts a different specification of
1 35 effective price and the lottery products differ in nature. Because effective price essentially converges to the take out rate when the sales are large, resea rchers often interpret effective price elasticity as if the elasticity of sales with regard to take out rate and conclude a 1 elasticity implies profit maximization. However, because effective price is not only a function of take out rate but also a funct ion of prediction difficulty coefficient, it is not appropriate to interpret it as actual price but merely an indication of a lottery ticket. Additionally, the prediction difficulty coefficient is positivel y related to sales, indicating that draws that are perceived as easier are associated with larger sales. Furthermore, the quadratic term of prediction easiness coefficient is not found significantly related to sales, suggesting that the increasing relation ship between prediction easiness and sales is monotonic. In a similar token, the number of leagues included in a draw is negatively related to sales, indicating that having more leagues in a draw is associated with smaller sales. This is b ecause h aving mor e leagues in a draw potentially increase s the difficulty of betting as players may need to allocate more time to follow the matches or require broader knowledge about soccer betting. Although an easy game increases the probability of prize sharing, it simu ltaneously increases the prize pool. With sufficient ly large sales, the effective price approximates the take out rate. Considering sports gambling as a consumption practice, the rationality of buying sports lotter ies can be justified. Furthermore, the mon otonically increasing relationship between demand and prediction easiness further supports this notion. Impact of S ocial D emographics Through panel data regressions, this study revealed that some social demographics have significant impact o n the demand for sports lotter y First, in the
136 context of the Chinese sports betting market, the provinces with higher income level s had a higher demand for sports lotter y contradicting the regressivity property of traditional lottery games found in many studies ( Clotfelter, 1979 ; Combs et al., 2008 ; Miyazaki et al., 1998 ; Price & Novak, 1999 ; Suits, 1977a ) Although the estimations of income elasticity from the static and dynamic models differ drastically in terms of its magnitude, the sign remains positive. The income elasticity of Shengfu lotteries is estimated around 2 in the static models, suggesting the demand is highly income elastic and can even be viewed as a C hinese consumers. In the dynamic models, however, the in come elasticity of Shengfu lottery is estimated around 0.4. This suggests that given the initial state of demand, the players are less responsive with regards to the change of income levels. Second, the population composition wa s found to be related to th e demand for sports lottery. Using TDR as a measure of financial and social burdens, this study found that TDR is positively related to demand, which is c onsistent with previous research that us ed transfer payment as a measure of financial and social burde ns ( Weinbach & Paul, 2008 ) Within the context of China, intergene rational support family based care has been at the core of Chinese famil ies A majority of the elderly live with one of their children and rel y on their support. With the skyrocketing of real estate prices and living costs in China, many families encounter high financial and social burdens Lottery has long been regarded as the only vehicle for them to buy hope The finding i n this study seems to be reflective on this soci al reality. Impact of M arketing and S tructural C hanges of the G ame Over the years, the sports lottery administration has modified the structure of the Shengfu game in several aspects, accompan ied with infrequent jackpot promotion al
137 activities or simultaneo usly declaring two draws on the same day. For instance, during August 2003 to August 2004, there were three prizes instead of the current two prizes; before September 2004, there were 13 matches included in a draw instead of 14 matches The current study s howed that since the adoption of 14 games, the demand for the Shengfu game has decreased. However, this significant negative relationship is not necessarily causal. It can be coincident al simply due to the life cycle of the game. Nevertheless, changing th e game structure has a potential impact on demand for the following possible reasons. First, increasing the number of matches in a draw means matches This study has shown the popular leagues can a ttract more players to buy lottery ticket s Therefore, choosing only top teams will maximize consumer surplus and revenue. However, compar ed to 13 matches having 14 matches in a draw results in a greater probability of picking less popular matches Becaus e, less popular matches have negat ive impact on sales, the adoption of 14 matches therefore, has a potential negative impact on demand. Second, for consumers, predicting 14 matches is apparently more difficult. If the finding that people like easy game holds, then the adoption of 14 matches has a second negative impact on demand. Jackpot promotion is positively associated with sales, which is rather intuitive. And this positive rela tionship is unlikely coincident al as the jackpot promotion was done in an irregular fashion. Draws that had a jackpot promotion had a higher pay off compar ed to those without a promotion. As demonstrated that players are indeed sensitive to price, jackpot promotion can effectively increase sales. This marketing
138 strategy c oul d be especially useful when administrators can foresee a decrease for certain draws that are composed of unpopular matches Having three prizes is positively associated with sales. Alth ough this significant positive relationship is not necessarily causal, prize structure has the potential to impact demand. By having a third prize, players have a greater probability of winning a prize. From gambling as learned practice perspective, winnin behavior and thus stimulates the demand. It is common phenomenon in gambling that when a player w ins a small prize, they wish to win a larger one more earnestly because winning a prize was no longer merely a dream. It bec ame a reality instead. Simultaneously selling two draws in the same period of time will apparent ly reduce the sales of each draw. But collectively, simultaneously selling two draws can be more profitable for the sports lottery administrators. Although two draws were sold simultaneously and the prize would be declared on the same day, the two draws had an order. For instance, if draw 2012001 and 2012002 were declared same day, the prize pool of 2012001 is composed of a possible rollover from its previous dr aw(s). This information is known to players who buy 2012001. However, because the prize pool of 2012002 also depends on 2012001, players who buy 2012002 actually face more uncertainty about the prize pool. Comparing draws with uncertainty to draws with rol lover information revealed that the former sells significantly less (Table 5 2 ) This suggests that players do not like uncertainty in the prize pool, which is consistent with the uncertainty aversion (i.e., ambiguity aversion) in decision theory. Ambiguit y aversion phenomenon found in this study also suggests the players hold rational attitude towards the probability of future outcomes, both unfavorable and favorable.
139 Consumer L earning or C onsumer A ttrition Desp ite the fact that lottery administrat ion has made the Shengfu game more difficult by increasing the number of the matches to 14, there is an ever increasing trend of median probability of winning prizes. This suggests that overall the players are doing a better job in predicting the results of socce r games. There is the possibility that the skills of players do es improve as a result of more experience and more information which is now accessible online. However, this phenomenon can also be explained by consumer attrition. It is possible that the ma rket lost the players who never won or had less skill in betting, and only those more sophisticated players are left in the market thus increasing the median chance of winning. Or, it can be the result of both consumer learning and consumer attrition. Dynamic N ature of S ports G ambling B ehavior It has been suggested that t he consumption of lottery products is dynamic in nature due to myopic addiction ( Farrell et al., 1999 ) inertia ( Beenstock & Haitovsky, 2001 ) or social learning ( Rogers, 1998 ) Despite different behavioral assumptions made under these three theoretical accounts, they are not mutually exclusive and have the same prediction that consumption in the previous period(s) has a positive and s ignificant effect on consumption in the current period. This study used a dynamic model with four lagged dependent variable s to explain the demand for sports lottery. A four lag period is about 2 to 4 weeks. Whereas this study does not preclude the plausi bility of addiction, inertia or learning, an alternative mechanism is suggested. It is conjectured that information contained in the previous draws has an impact on the betting behavior for the current draw. Forecasting
140 the expected return of a draw often involves predicting the odds of winning, the prize pool, and the possibility of prize sharing, and correct forecasting is not an easy task for players. It is plausible that the players will consider the results of previous draws in making their betting dec ision. Because of recent publicity about the prize pool and the odds of winning may be more salient in their minds, they may use this information to guide their forecasting. Additionally, although matches were selected from vario us leagues and differ draw by draw, many matches have a natural progression in a season. Typically, a regular season is followed by a play off. As a consequence, the demand for sports lottery shows a dynamic pattern. Managerial I mplications Despite the the oretical im plications of player s betting behavior and demand for sports lottery, this study also proffers some managerial implications for sports lottery administrators. First, the consumption value of sports lottery games need s to be better appreciated. The notion that nonmonetary activities associated with sports lottery gaming has consumption value has considerable implications in terms of designing lotter y products and delivering value to its consumers. For instance, if simply dreaming of winning a grand prize ca n generate utility, then players would probably prefer a week long dream rather than a shorter one. If talking about betting on a team can enhance their identification with a team, then they would probably prefer a larger audience. Or if bragging about win ning can show off their expertise in their own circles, then making prizes more accessible would probably boost the morale of players. In a nutshell, under the theory of consumption, players should be treated and managed as consumers; and their behavior ne ed s to be understood in order to develop value added programs for them.
141 Second, players are rational in terms of their responsiveness to the cost of the game. The empirical results suggests that the administrators have already done a fairly good job in max imizing profits. The panel regression analysis also suggested there were significant differences among the 30 provinces. The effective price elasticity ranged from 0.7 to 1.8. Currently, m arketing activities, such as jackpot promotion, are often conducte d on the national level with very limited customizations to the local markets. It is advisable that marketing strategies to be developed to meet local needs. For instance, in a marketplace where players are more sensitive to the effective prices, additiona l jackpot promotions may be conducted to bring down the effective price of the game in that market; in a marketplace where players are less sensitive to the effective prices, the take out rate actually may be increased in order to be more profitable. In or der to keep the whole market unified, a higher take out rate can be unanimously levied, but with differentiated jackpot promotion s taking place in regional level s Third, time series analysis revealed that the market for Shengfu game was not evolving. Most lotteries suffer from 'fatigue' O nce the initial excitement of the launch wears off, and revenues tend to stagnate or even decline (Creigh Tyte & Farrell 2003). The good news for Shengfu game was that fatigue did not appear to set in or the administr ators s uccessfully overc a me the market fatigue through product innovation. The bad news, however, was that the game never truly took off. Furthermore, empirical data suggest s a positive effect of jackpot promotion on demand. Unfortunately, this effective marketing tool is seldom exercised by the administrators. Further, this study suggested that structural features, such as number of matches include in a game and
142 the number of prizes, were associated with dem and. Lottery administrators may experiment with different game features in order to design a better product for players. Limitations and Future Directions Although this dissertation has provided valuable insight into under standing betting behavior and the determinants for sports lotter y there are some limitations that should be considered for future research. This first limitation is related to the fact that this study only focused on one sports lotter y product namely the Shengfu game in the context of China. Despite its theoretical contribution to the gambling and sports management literature, the generalizability of some findings from this study might be limited. Therefore, the theory of sports gambling as consumption p ractice should be tested repeatedly with empirical data obtained from other types of sports lottery products both in China and other markets for future studies. Second, this study used macro level (i.e., provincial level) data to examine the arrogate mark et demand. Although it identif ied several major factors influencing the demand for sports lottery in China, it did not thoroughly tak e individual preference and decision making into consideration. Some findings are merely suggestive f or instance, the posi tive relationship between prediction easiness and demand, and the positive elasticity of income. For future research, individual level data would be more desirable as they contain richer information to examine the demand function in a more refined fashion. A third limitation relates to the data source. The data were obtained through public records or officially released government documents. However, some of the data released were rather coarse and might also be inaccurate as China has been notoriously know n for its suspect statistics. Finally, not all determinants would be included in the empirical regression model, due to either limited variability in the data
143 (e.g., gender and ethnicity) or unavailability of the data (e.g., religion and cross border shopp ing behavior). The current research has identified several interesting avenues for future research. These include, but are not limited to, investigation of the following questions: How to measure consumption value of sports gambling? What are the interrela tionships between sports betting and sports spectatorship? How do players make decisions and how do they improve their betting skills? What are the implications of consumer learning on sports lottery administration? How do players respond to marketing acti vities, such as jackpot promotion, outlet expansion, and lottery advertising? Furthermore, there are many other types of sports betting products, such as office pool s and parlay betting, that warrants future scholarly efforts. Conclusion This study exami ned the demand for sports lottery based on the assumption that players are rational and sports gambling has consumption value. Our raw data suggests that there is quite a considerable consumption value of sports gambling and that this is essentially induced by the different matches include d in the game. The effective price elasticity is identified through changes in the expected value of holding a ticket, variations in whi ch are driven by rollovers and consumer learning. This study found that the implied elasticity is estimated around 1, suggesting the realization of revenue maximization for regulators. Although it is not conclusive, there is evidence to suggest that sport s lottery is progressive, i.e., that the rich tend to buy more sports lottery than the poor. Consistent with the notion that buying lottery is to buy hope, this study found a positive relationship between demand and financial burden as measured by the Tota l
144 Dependence Rate and demand. Jackpot promotion and structural arrangements of the game were found have significant impact on the demand.
145 Table 5 1 P rediction difficulty coefficients by ticket compositions F requency P ercentage RAT1 RAT2 EPL&GB 173 18.31 1.96 1.5 0 ISA&SLL 182 19.26 2.03 1.45 MAJOR4 204 21.59 1.42 1.31 1TIER 73 7.72 2.83 2.81 2TIER 52 5.5 0 2.9 2.13 3TIER 105 11.11 2.21 1.23 Baseline 156 16.51 2.41 1.82 Note: RAT1 = log(observed number of first prize winners / theoretical number based on null model); RAT2 = log(observed number of second prize winners / theoretical number based on null model)
146 Table 5 2 Sales comparison between two simultaneous draws Group n Mean SD T df p Draw_1 72 39.36 21.55 5.30 104.8 <.001 Draw_2 73 24.30 10.91 Note: df is Satterthwaite's degrees of freedom which takes into account that the variances are assumed to be unequal. It is a more conservative approach than using the traditional degrees of freedom.
147 APPENDIX SUPP ORTING INFORMATION FOR CHAPTER 3 China CSLAC Lotter y Shengfu Game Sample Ticket (14 Matches) UK Football Pool Jackpot 12 Sample Ticket (12 Matches) Note: 1. Shengfu Game is very similar to Jackpot 12. One apparent difference is the former is composed of 14 matches instead of 12 matches. 2. In Shengfu Team Wins. 3. Wins.
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160 BIOGRAPHICAL SKETCH completed his Doctor of Philosophy degree in health and human performance (concentration: sport management) from the University of Florida in August 2013. He is a recipient of the University of Florida Alumn i Graduate Fellowship. Prior to coming to the Gator Nation, Mao worked for the international affairs office at Shanghai University of Sport China. Mao has been actively participating in research projects within and outside of the college, including the 2 1 st Century Community Learning Centers project funded by the Florida Department of Education, the gambling problem and corporate social responsibility project funded by the National Foundation of Philosophy and Social Science of China, and the sports spons orship and branding effects project funded by the Shanghai Sports Bureau of China. He has published his research in Sport, Business, and Mana gement ; Journal of Gambling Studies ; Journal of Customer Behaviour ; Journal of Applied Marketing Theory ; and Intern ational Journal of Sports Management and Marketing Mao was a representative of P. R. China at the IOC 7 th International Session for Educators and Officials. He has presented his research findings at the North American Society for Sport Management Sports M arketing Association Association of Marketing Theory and Practice and other conferences. He has also served as an ad hoc reviewer for several academic journals and conferences, including Sports Management Review ; International Journal of Sport Marketing & Sponsorship ; Measurement in Physical Education and Exercise Science ; Journal of Sports Communication ; and Sport, Business, and Mana gement