An Equilibrium Model of Rollover Lotteries

37 Pages Posted: 15 Apr 2024 Last revised: 3 Dec 2024

See all articles by Giovanni Compiani

Giovanni Compiani

University of Chicago Booth School of Business

Lorenzo Magnolfi

University of Wisconsin-Madison

Lones Smith

University of Wisconsin at Madison - Department of Economics

Date Written: March 19, 2024

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

Suggested Citation

Compiani, Giovanni and Magnolfi, Lorenzo and Smith, Lones, An Equilibrium Model of Rollover Lotteries (March 19, 2024). Available at SSRN: https://ssrn.com/abstract=4765155 or http://dx.doi.org/10.2139/ssrn.4765155

Giovanni Compiani

University of Chicago Booth School of Business ( email )

Chicago, IL
United States

Lorenzo Magnolfi (Contact Author)

University of Wisconsin-Madison ( email )

1180 Observatory Drive
Madison, WI Wisconsin 53706
United States
6082628789 (Phone)

HOME PAGE: http://lorenzomagnolfi.com

Lones Smith

University of Wisconsin at Madison - Department of Economics ( email )

1180 Observatory Drive
Madison, WI 53706-1393
United States
608-263-3871 (Phone)
608-262-2033 (Fax)

HOME PAGE: http://www.lonessmith.com

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