What Drives Demand for State-Run Lotteries? Evidence and Welfare Implications

We use natural experiments embedded in state-run lotteries and a new nationally representative survey to provide reduced-form and structural estimates of risk preferences and behavioral biases in lottery demand. We find that sales respond more to the expected value of the jackpot than to price, but are unresponsive to variation in the second prize—a pattern that implies probability weighting but is inconsistent with standard parameterizations. In the survey, we find that lottery spending decreases modestly with income and is strongly associated with measures of innumeracy, poor statistical reasoning, and other proxies for behavioral bias. These bias proxies decline with income and statistically account for 43 percent of lottery purchases, suggesting that at least some of lottery demand is due to behavioral bias, not just anticipatory utility or entertainment value. We use these empirical moments to estimate a model of socially optimal lottery design. In the model, current multi-state lottery designs increase welfare but may harm heavy spenders.