Date of this version


Document Type

Working Paper


lottery, gambling, price elasticity, policy evaluation


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 elasticity of demand for the evening Pick 3 and Pick 4 games are both approximately -0.5. During the promotions, the loss in margin outweighs the gain in sales because of this inelastic demand. However, Green Ball promotions increase state profits by about $14.5 million because of the increase in sales of Pick 3/Pick 4 games and instant games after the promotion ends, and because of the complementarity of Pick 3 with Pick 4 and instant games during the promotion. Red Ball promotions reduce state profits by an estimated $2.6 million because increased evening Pick 4 sales after the promotion ends are not sufficient to offset the losses during the promotion, and the Pick 4 promotion has a net negative effect on other lottery games. (JEL D12, H71, L83, L98)