Jackpot Promotion Model for Taiwan Lotto

Transcription

1 Jackpot Promotion Model for Taiwan Lotto Chuan Lee, Chin-Tsai Lin * and Chien-Hua Lai Graduate School of Management, Ming Chuan University, Taipei 111, Taiwan, R.O.C. * Corresponding author. Tel: ; Fax: address: [email protected] (C. Lee). address: [email protected] (C.-T. Lin). address: [email protected] (C.-H. Lai) Abstract Lotto was inaugurated in January 2002, and immediately became a popular activity in Taiwan; as the big craze following its initial introduction has subsided, the growth of Lotto game sales has slowed. To maintain lottery sales momentum, operators have conducted numerous jackpot promotions; this study examines the effectiveness of various jackpot promotional strategies. The analytical results can provide a valuable reference for operators and governmental authorities regarding ways of increasing lottery earnings. The empirical findings of this investigation include the following: (1) the effective price elasticity of Lotto is 0.382, Taipei Fubon Bank can increase the revenue gained from Lotto by increasing the effective price. (2) operators can significantly increase lottery sales by declaring the jackpot an unconditional added fixed or variable bonus. I. Introduction 1

2 The Taiwan Lotto was inaugurated in January 2002, and immediately became the most popular form of gambling in Taiwan. Fink et al. (2004) found that overall tax revenues decline with increased lottery sales, but the earnings from the lottery still have contributed significantly to social welfare. Growth of lottery sales has subsided following the initial craze associated with the introduction of the lottery. Gramm (2005) found that larger pools increase the quality of the betting market; Forrest et al. (2000) and Lin and Lai (2006a) also found that if a special bonus is added to the jackpot will increase lottery sales. To maintain the momentum of lottery sales, the operators of Taiwan Lotto have performed numerous jackpot promotions. This investigation establishes different jackpot promotion strategies and defines the effective price of different models. This study also examines the effects of jackpot promotion to the sales of Taiwan Lotto. Both of these questions represent important issues for operators and government. II. Jackpot promotional tapes and the effective price This investigation divides jackpot promotion strategies into five types according the bonus prizes added to the jackpot and probability of such bonus prizes being added. Figure 1 illustrates different types of jackpot promotion. 2

3 Fixed bonus conditional Jackpot promotion Variable bonus Fixed bonus unconditional Variable bonus Minimum jackpot Figure 1 Types of jackpot promotion strategies This investigation calculated the effective price of tickets of different jackpot promotion strategies using the formula applied, by Gulley and Scot (1993) and Scoggins (1995), and the effective price then can be expressed as: P=1-((1/Q)(R+jQ)(1-e -Qp )+EV S ) (1) Where P is the effective price of a ticket;q is the number of tickets sold in that draw;r is the amount added to the prize fund by a rollover from the preceding draw; j is the proportion of the revenue from a draw that is allocated to the jackpot fund; p is the probability of any tickets winning the jackpot; and EV S is the expected value of smaller prize. In Taiwan, the price of Lotto ticket is NT$50, 56% of Lotto sales is returned to bettors in prizes. All three ball winners are paid the fixed prize of NT$200. The 3

4 remainder of prize money available is then distributed, as 35% (four balls), 15% (five balls), 12% (five balls plus the bonus ball) and 38% (for the jackpot). The effective price of Taiwan Lotto can be written as: P=50-((1/Q)(R+0.38*(0.56*50Q-200C)(1-e -Q/50*1/ )+EV S ) (2) Where C is the number of three matching ball winners The following describes five different jackpot promotion strategies and their effective price. Adding a fixed bonus to jackpot conditional Lottery operators declare that the jackpot is supplemented with a fixed bonus provided some condition is fulfilled. The effective price of this conditional bonus can be expressed as: P=50-((1/Q)(PA*A+R+0.56*50Q-200C) (1-e -Q/50*1/ )+EV S ) (3) Where PA is the probability of adding bonus to jackpot, A is the fixed bonus added to the jackpot. Adding a variable bonus to jackpot conditional The operators declare that the jackpot is supplemented with a specific percentage of total sales provided some condition is met. Taipei Fubon Bank declared that the jackpot would be supplement to the value of 16% of total sales 4

5 for draws and provided that the bonus ball has a higher value than of the six winning numbers. The effective price of adding variable bonus to jackpot on specific condition in Taiwan Lotto can be written as: P=50-((1/Q)(PA*AR*50Q+R+0.56*50Q-200C) (1-e -Q/50*1/ )+EV S ) (4) Where PA is the probability of adding bonus to jackpot, AR is a specific bonus rate added to jackpot. Adding a fixed bonus to jackpot unconditional The operators declare that the jackpot is supplemented with a specific bonus without any condition; government earnings from Lotto will be increase on condition that the net revenues from the jackpot promotion are larger than the value of the fixed bonus. Taipei Fubon Bank declared that the jackpot would be supplement by NT$ 1 billion for draws The effective price of add fixed bonus to jackpot can be expressed as P=50-((1/Q)(A+R+0.56*50Q-200C) (1-e -Q/50*1/ )+EV S ) (5) Where A is the fixed bonus added to jackpot. Adding a variable bonus to jackpot unconditional The operators declaring that the jackpot is added a specific percentage of total sales. Once the specific percentage that is added to jackpot from total sales is 5

6 less than take out rate, the government will gain the extra earnings form jackpot promotion. Taipei Fubon Bank declared that the jackpot is added 16% of total sales for draws The effective price of adding variable bonus to jackpot can be written as: P=50-((1/Q)(AR*50Q+R *50Q-200C) (1-e -Q/50*1/ )+EV S ) (6) Where AR is a specific bonus rate added to jackpot. Guaranteed minimum jackpot The operators declare that the jackpot is guaranteed and set it at a level higher than sales would normally generate. Taipei Fubon Bank declared that the jackpot was guaranteed to reach at least NT$ 1 billion for draws , and and at least NT$ 8.8 million for draws The effective price of guaranteeing the minimum jackpot is: P=50-((1/Q)(G-0.56*50Q)+0.56*50Q-200C) (1-e -Q/50*1/ )+EV S ) (7) Where G is the minimum prize of jackpot that be guaranteed. III. Regression Model This investigation estimated the following equations using the findings of Lin and Lai (2006b) as a basis to test the effective price elasticity of Taiwan Lotto and the effects of different jackpot promotions. 6

7 LQ= f (constant, EXPRICE, TREND, TREND 2, BIGLOTTO, NEWYEAR, 56DUM, 239DUM, 245DUM, PRO1, PRO2, PRO3, PRO4,) (6) As above, LQ is (log) number of tickets sold. EXPRICE is (log) effective price of Lotto. EXPRICE is included to calculate the effective price elasticity of Lotto. Most earlier studies (Gulley and Scott, 1993; Forrest et al., 2000a, Winfree et al., 2004, Wang et al., 2006) found that the effective price of lottery tickets is less than 0. TREND represents the Taiwan Lotto draw numbers in which numbers are allocated sequentially from 1 to 308. In the demand equation TREND is expected to reflect the tendency of lottery games. Caudill et al. (1995) and Eewkaon et al. (1999) find an increasing trend of lottery adoption, while TREND 2 is included to permit possible non-linearity. According to the experiences of the U.S. state and the U.K. lotteries, in which sales increase with lottery age at a certain point the lottery matures and sales begin to decline (Mikesell and Zorn, 1987; Gulley and Scott, 1993; Miers, 1996; Forrest et al., 2000a). Most previous studies (Mikesell and Zorn, 1987; Mason et al., 1997; Forrest et al., 2000b) found a substitute relationship between different lotteries; Misksell and Zorn (1987) proposed that new games need to be added to ensure continued successful sales of existing games To maintain the momentum of lottery sales, 7

8 Taipei Back inaugurated a new 6/49 numbers game (Big Lotto) in January BIGLOTTO is dummy for capturing the influence of Big Lotto on Lotto; Lin and Lai (2006b) found no significant substitutive or complementary relationships exist between single draws of Big Lotto and Lotto in Taiwan, so this study did not consider cross-price elasticity issues. NEWYEAR is a dummy to account for variations in bettor behavior during the Chinese New Year. Moreover, 56DUM, 239DUM and 245DUM are dummies to represent draw numbers 56, 239 and 245, the first draws to have double, triple and quadruple rollovers thus presenting bettors with a new situation to assess. This study used four dummies to test the effects of four different jackpot promotion strategies. PRO1 is a dummy captures the effect of adding a variable bonus to jackpot conditional, and is set equal to one for draws and 82-89; PRO2 is a dummy for capturing the effect of adding a fixed bonus to jackpot, and is set to one for draws 98-99; PRO3 is a dummy capturing the effect of adding a variable bonus to jackpot, and is set to one for draws ; PRO4 is a dummy for capturing the effect of declaring that the jackpot is guaranteed, and is set at a level higher than sales would normally generate, and is set equal to one for draws , , and

9 VI. Results Draws are adopted as the unit of analysis, and the analysis period runs from the establishment of Taiwan Lotto in January 2002 until December 2004, including all 308 draws during this period. Table 1 lists the regression results: Table1 OLS REGRESSION, DEPENDENT VARIABLE IS LOG LOTTO SALES Variable Coefficient CONSTANT ( )** EXPRICE (-9.888)** TREND (-3.419)** TREND2.000 (-2.641)** BIGLOTTO (-4.459)** NEWYEAR.211 (9.305)** 56DUM.545 (6.756)** 239DUM.122 (1.483) 245DUM.193 (2.326)* PRO1.003(.909) PRO2.071 (1.218)+ PRO3.246 (3.942)** PRO4.030 (1.681) R 2 (adj.) n 308 Note: Absolute value of t=statistics appear in parentheses. +Denotes significance at 10% ; *Denotes significance at 5%; **Denotes significance at 1%. In this equation, the regressors explain 88.8 percent of the variation in calculated sales of Taiwan Lotto. The sales equation is discussed in Section Four. First, the effective price elasticity of Taiwan Lotto is negative and significant, and the coefficient is , the increase in the effective price of Taiwan Lotto leads 9

10 to a reduction in sales, and the effective price elasticity of Taiwan Lotto is inelastic. Second, both the TREND and TREND 2 are considerably different from zero at the 5 percent level, the coefficient of TREND is negative, but the coefficient of TREND 2 is positive. The results on trend and its square indicate increasing public support for Taiwan Lotto following the initial period. The trend variable results may pick up the effects of the cyclical upswing in the Taiwanese economy (Forrest et al., 2000a). Third, the finding of a significantly negative coefficient on BIGLOTTO appears to indicate that the inauguration of Big Lotto has decreased the sales of Lotto in Taiwan. Moreover, the strength of the estimated coefficient of NEWYEAR allows us to confirm that sales of Taiwan Lotto are higher during the Chinese New Year than at other times. Regarding the effects of different jackpot promotion methods, this study finds the following: Incorporating the estimated coefficients of PRO1, PRO2, PRO3 and PRO4 into the Lotto sales equation can draw the implications of our finding for the effects of different jackpot promotion strategies. The finding of a significant, positive coefficient for PRO2 and PRO3 demonstrates that unconditionally adding both fixed and variable bonuses to jackpots significantly 10

11 increases the sales of Lotto, and adding a specific percentage of total sales to the jackpot has more significant effect in increasing public interest than adding a fixed bonus. The results of PRO1 and PRO4 are positive but not significant, apparently indicating that to the effects of adding a variable bonus to the jackpot and declaring the jackpot to be guaranteed and set at a level higher than sales would normally generate are not as significant as expected by operators. VII. Conclusions This investigation has demonstrated that negative relation exists between effective price and ticket sales for Lotto in Taiwan, a result that obeys the laws of supply and demand, furthermore, the effective price is inelastic; thus, a positive relation exists between effective price and total revenues. The Taipei Fubon Bank thus can increase the total revenues of Lotto through increasing the effective price. In Taiwan the National Lottery is franchised to Taipei Fubon Bank, and the government has an incentive to set the lottery rules so as to maximize net revenue. In fact the government selected a take-out rate of 43% for Taiwan Lotto, which is considerably less than in most other countries. This investigation estimated that the effective price elasticity during first three years of the Taiwan Lotto is significantly different from the value of minus one required to maximize net revenue. This investigation concludes that government has not successfully set the 11

12 framework for Lotto. Lotto has in inelastic effective price; thus the Taiwanese government can increase the effective price of Lotto by increasing the take-out rate to maximize net-revenue from Lotto. This investigation found that operators declaring the jackpot to be guaranteed and set at a level higher than sales generally failed to significantly increase the lottery sales, this finding differs from previous studies of lotteries in the U.K (Forrest et al., 2000a). Thus, the behaviors of Taiwanese lottery customers differs from that of those in the U.K Finally, operators declaring the jackpot to be supplemented by a fixed or variable bonus was found to considerably increase sales of Taiwan Lotto. Supplementing the jackpot with a specific percentage of total sales attracts more public interest than a fixed bonus. Additionally, provided the specific percentage that is added to the jackpot from total sales is less than take out rate, the government can use this technique to increase its earning from jackpot promotion. Considerable room always remains for improvement, and this study can be developed in several directions. First Viscusi prospect theory (Viscusi, 1995) can be applied to consider jackpot announcement effects. Another extension is analyzing the interaction effects of jackpot promotion between different lottery. Acknowledgment The authors would like to thank the Taipei Fubon Bank for supporting this 12

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