Research / BFI Working PaperMar 19, 2024

An Equilibrium Model of Rollover Lotteries

Giovanni Compiani, Lorenzo Magnolfi, Lones Smith

In a rollover lottery, buyers pick their own numbers, and a jackpot not won adds to the next draw. We develop an equilibrium model of this lottery, since it is a major source of government revenue. Buyers differ in their lottery enjoyment levels, and the market-clearing price is the expected monetary loss on a lottery ticket — namely, ticket face value less expected winnings. The supply curve captures the relation between tickets sold and expected loss implied by the rules of the game. We use this equilibrium model in two empirical applications. First, we test the model’s predictions on the optimal relationship between odds and population size using data from many countries, and across U.S. states. Second, we propose a structural empirical implementation of the model and nonpara-metrically estimate demand for U.S. national rollover lotteries by exploiting the randomness inherent in the rollover mechanism. We find that the model predicts well out of sample and show how to use it to inform lottery design.

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