An Equilibrium Model of Rollover Lotteries

Abstract

We develop a novel model of rollover lottery ticket sales, assuming preferences over thrill and money won. Treating the monetary loss on tickets as an implicit price, lottery rules imply an inverse supply curve. Growing jackpots shift the inverse supply down, and help identify the falling demand curve arising from thrill heterogeneity. We nonparametrically estimate the demand for Powerball. Our model allows risk aversion or risk-loving preferences, but we show that even slight deviations from risk neutrality deviate from the data tremendously. This is a high stakes empirical test (based on 160 million gamblers) of Rabin’s (2000) calibration theorem that low stakes risk aversion yields implausible larger stakes implications. While ticket buyers are risk neutral, Powerball acts as a risk loving gambler for rollovers up to $540M, but should cap the jackpot at $920M. Aside from the excellent model fit, we check risk neutrality in two ways. First, we characterize how log ticket sales should convexly grow in the log jackpot at least up to $409M — which we verify in Powerball data. Next, lottery odds should scale linearly in the population — which we verify in a regression across forty state rollover lotteries.

JEL Classification: L10, L83, D81