Abstract
We estimate elasticities of demand for New Jersey’s Pick 3 and Pick 4 midday/evening numbers games by exploiting random price variation generated by episodic promotions for each game. These Pick 3 Green Ball and Pick 4 Red Ball promotions lower the price of a lottery ticket for an evening numbers game by increasing prize payments during the 28-day promotion periods. The own-price elasticities of demand for the evening Pick 3 and Pick 4 games are both approximately –0.5. During the promotions, the loss in profit margins outweighs the gain in sales because of this inelastic demand. However, the combined effects of lower evening Pick 3 profits and increased sales of complementary products boost lottery profits by $30,000 per day, or $840,000 during the 28 days of the Green Ball promotion, while the combined effects of lower evening Pick 4 profits and reduced sales of substitute products decrease lottery profits by $129,000 per day, or $3.61 million during the 28 days of the Red Ball promotion. If higher sales after the promotion are included, the total increase in profits potentially reaches $14.48 million under the Green Ball game, while the Red Ball promotion loses money for the lottery even considering its positive lagged effect.
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Notes
See Grote and Matheson [2011] for additional references on price elasticities of large jackpot lottery games.
For example, the Ohio Lottery has used a Red Ball promotion for its Pick 3 game that starts with six white balls and one Red Ball. In contrast to the New Jersey Lottery, the Ohio promotion is less generous to players as prizes are increased only 20 percent when the Red Ball is drawn. The Tennessee Lottery has used a Green Ball promotion for its Cash 3 game that starts with ten white balls and one Green Ball. Tennessee increases Cash 3 prizes 20 percent when its Pick 3 Green Ball is drawn. The Pennsylvania Lottery has run a “Shamrock Bonus Week” during the week including St. Patrick’s Day in which evening daily numbers games prizes are increased 10 percent if a Green Ball is drawn or 20 percent if a shamrock ball is drawn. Finally, the Illinois Lottery has operated Green Ball promotions for its Pick 3 game where two sets of winning numbers are drawn when a Green Ball is selected. These Illinois promotions start with nine white balls and one Green Ball.
Daily sales data are unavailable for the Mega Millions and Pick 6 lotto games, because sales for these games are recorded only twice per week to correspond with their twice-weekly drawings. The unavailability of daily data led to problems estimating the demand for these games with respect to the daily prices of Pick 3 and Pick 4. We also omit Jersey 5 because we could not explain more than about 30 percent of the variation in sales. See footnote 21 for more details.
Combs and Spry [2012] estimate the change in income elasticity after the introduction of a midday drawing for Pick 3 and Pick 4 numbers games in Ohio. They also give an estimate of the price elasticity of Pick 3 using data from episodic Red Ball promotions for the Pick 3 game. However, this is a crude estimate of the price elasticity of Pick 3 because their study combines data from a week’s worth of individual drawings and uses weekly sales rather than daily sales, and computes average weekly prices rather than daily prices. In addition, Ohio did not introduce a Pick 4 promotion so no Pick 4 own-price elasticity could be estimated in Ohio.
The New Jersey fiscal year runs from July 1 to June 30 of the following year.
Pick 3 and Pick 4 games are similar to the illegal numbers games that operated before the creation of the New Jersey Lottery in 1970, and have an enduring popularity, making up close to 30 percent of sales of New Jersey Lottery games.
Source: http://www.state.nj.us/lottery/index.shtml. The New Jersey Lottery pays out a higher percentage of money wagered on straight bets than on other bets. Terrell [1994] reports that for straight bets in the Pick 3 game, the New Jersey Lottery “places 52 percent of all money bet in the game into the payout pool to be split equally among all bettors choosing the correct number.”
When the numbers 5-8-7 were drawn the evening of November 12, 2001 after American Airlines Flight 587 crashed earlier that day, the winning 50 cent straight bet on the tragic numbers 5-8-7 paid only $16, the smallest payment in the history of the New Jersey Lottery Pick 3 game, because 27,829 straight bets were placed on that number. The previous time 5-8-7 were the winning numbers, the prize for a straight $0.50 bet was $290.50. When 7-7-7 was drawn on December 21, 1988, the winning prize for a straight $0.50 bet was only $63.50.
“The Federal Energy Policy Act of 1992, section 1942, requires the New Jersey Lottery to withhold a minimum 25 percent of all prize payments to any Lottery winner who has won more than $5,000 on any Lottery wager. At the end of the year, the winner will receive a W2-G form to properly credit the withholding as a tax payment on their federal income tax form. Winners who do not possess a social security number are subject to a 30 percent federal income tax deduction on any prize over $599.50. Under the provisions of P.L. 2009, c.69, as of January 1, 2009, the New Jersey Lottery is required to withhold 3 percent State taxes from all Lottery winnings over $10,000.” Source: http://www.state.nj.us/lottery/home.shtml.
During the Green Ball promotions, the New Jersey Lottery started with five or six white balls, depending on the year. The promotion is more generous when it begins with a smaller number of white balls, as this increases the odds of prize payments during the promotion period. The first Green Ball promotion in our sample ran from March 7, 2005 until March 29, 2005 with five white balls and one Green Ball. The rest of the Green Ball promotions were run with six white balls and one Green Ball from February 6, 2006 until March 5, 2006; February 19, 2007 until March 18, 2007; March 3, 2008 until March 30, 2008; and March 2, 2009 until March 29, 2009.
The Red Ball promotion was held October 30, 2006 until November 26, 2006; August 6, 2007 until September 2, 2007; and October 13, 2008 until November 9, 2008.
The New Jersey Lottery issues press releases related to its Green and Red Ball promotions so that consumers are aware of when they are running. Although the number of white balls left in the hopper is not reported in media outlets on a daily basis, colored ball drawings are reported. These media outlets include the New Jersey Lottery website, the New Jersey Network (local cable television), local news television on major networks/websites, and newspapers such as The Jersey Journal, The Trenton Times, and The Star-Ledger.
The New Jersey Lottery has a monopoly in the New Jersey market for lottery tickets. Therefore, there is no supply curve for this market.
It is important to note that since the New Jersey Lottery has decided to run Green Ball and Red Ball promotions only during the evening drawings, the expected value of a purchase of a $1.00 midday Pick 3 or Pick 4 lottery ticket remains $0.50 at all times.
The New Jersey Lottery only makes statewide sales data available; individual retailer and smaller geographical unit sales data are not publically available. Additional information about New Jersey Pick 3 and Pick 4 games and rules is available at the New Jersey Lottery Website: http://www.state.nj.us/lottery/index.shtml.
The AR(1) specification forces the estimated short- and long-run price elasticities to be equal, according to Cuddington and Dagher [2011, p. 11].
We examined the pattern of the average level of a game’s sales for each day after that game’s promotion had ended. We found that this average level of a game’s sales after the promotion was relatively high the first day after a promotion ended, and declined thereafter, for at least 75 days after the promotion ended. We used 75 days to define our lag period because the spillover effect persisted at least that long, and we wanted to make sure that the lag period ended before the next promotion. The minimum amount of time between promotions was 85 days.
New Jersey state holidays include New Year’s Day, Martin Luther King Day, Lincoln’s and Washington’s Birthdays, Good Friday, Memorial Day, Independence Day, Labor Day, Columbus Day, Election Day, Veterans’ Day, Thanksgiving, and Christmas Day. Lottery sales take place on all of these holidays except Christmas Day.
For more information, see http://climate.rutgers.edu/stateclim/.
The Mega Millions and Pick 6 Lotto sales and prizes are recorded only twice a week. After interpolating the twice-weekly data to obtain the missing days’ sales, our estimates of demand for these two games had extreme serial correlation and a high R-squared, as could be expected. Even so, there was no statistically significant effect of the Red and Green Ball promotions on sales of these large jackpot games. We also estimated the demand for Jersey 5, but very little of the variation in Jersey 5 sales was explained by the regression (whose adjusted R-squared was around 0.30). This may indicate missing independent variables for Jersey 5 sales, such as its jackpot size, for which we do not have data.
The augmented Dickey-Fuller unit root test was performed with the standard commands in EViews 6. We also conducted Phillips-Perron tests for a unit root in the level of the same series and also rejected the null hypothesis of a unit root.
While the coefficients on the continuous logarithmically transformed independent variables are easily interpreted from the table as elasticities, the coefficients for the dummy variables do not directly have a meaningful explanation. Tables with the estimated percentage changes in sales attributable to the non-holiday dummy variables that are statistically significant at the 95 percent confidence level and the percentage changes in sales attributable to each of the statistically significant holiday dummy variables at the same confidence level are available from the authors.
This compares with an own-price elasticity of Pick 3 games of −1.11 obtained from weekly (not daily) data in Combs and Spry [2012].
This compares with a cross-price elasticity of −0.51 of Pick 4 sales with respect to the average weekly price of Pick 3, using weekly (not daily) data [Combs and Spry 2012].
Tables reporting the estimated percentage changes in sales of these time series that can be attributed to dummy variables at the 95 percent confidence level can be obtained from the authors.
Because the New Jersey Lottery reports that it has a fixed budget of $1 million for annual advertising expenses, there is no additional advertising expense attributable to each promotion (e-mail correspondence from New Jersey Lottery, May 23, 2012).
One reviewer suggested adding dummy variables to our regression models to see if this large lag effect could be due to a misspecification. In response to this suggestion, we ran Models 1–6 with quarterly dummies and then again with monthly dummy variables. Although the gain in profit during the 75-day lag period was somewhat reduced, it was still remarkably large: $12.22 million for the quarterly dummy variable specification and $9.07 million for the monthly dummy variable specification. The regression results with the seasonal dummy variables are available by request from the authors.
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Acknowledgements
The authors wish to thank the editor and anonymous referees for several constructive suggestions. We also thank M.B. Crowley for his assistance.
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Combs, K., Elise Crowley, J. & Spry, J. The Effect of New Jersey Lottery Promotions on Consumer Demand and State Profits. Eastern Econ J 40, 326–348 (2014). https://doi.org/10.1057/eej.2013.39
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DOI: https://doi.org/10.1057/eej.2013.39