A Time Series Analysis of U.k. Lottery Sales: Long and Short Run Price Elasticities

The widespread popularity of lotteries in general and the introduction of the U.K. National Lottery in November 1994 has generated concern over the potential addictiveness of gambling and numbers games in particular. Indeed, the Director General of the Of®ce of the National Lottery (who regulates the U.K. game that is operated by a private sector franchisee) is directed by the Secretary of State not to license games that encourage `excessive participation'. Despite this concern there has been no economics research into the extent to which lottery participation is subject to addiction. Most modern lottery games are variations of the pari-mutuel `lotto' design: players buy a ticket where they have chosen m numbers from n; when the draw takes place m numbered balls are selected randomly from n; prizes are shares of a proportion of the stakes and the remaining portion of the stakes (the take-out) is used to administer the game, pay the ticket outlets, and cover tax liabilities and other charges; and prizes are awarded to ticket holders that match different numbers of the balls drawn (usually there is a large jackpot prize pool for those few that match all m, and smaller prize pools are shared by those who match mÿ 1, mÿ 2 etc.). The distinctive feature of such games is that there may be no m-ball matches in a given draw in which case the jackpot is `rolled-over' to the following draw. Rollovers give rise to variations in the expected value (de®ned as the price of a ticket minus the expected winnings) of tickets between regular draws (where the jackpot from the previous draw has not rolled over) and rollover draws. This generates systematic variation in the level of sales across draws because a rollover induces an exogenous change in price that causes a movement along the demand curve. The excess of revenue over prize payouts, which is approximately 50 percent of sales, is divided between the operator (5%, on average), the distributor (5%), sales tax (12%), and `good causes' (28%, on average) OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 61, 4 (1999) 0305-9049