Is Lottery Demand Driven by Effective Price? Evidence from the China Lottery Industry

There has been a long debate on whether the expected utility model can explain lottery purchase decision under uncertainty. The traditional strand of research, named the effective price approach, following the expected utility approach takes the expected loss of each ticket as the lottery price and uses this effective price to understand lottery demand. Another branch of literature, more from the prospect theory perspective, argues that lottery demand depends more on jackpot size, or small odds events, than expected values. It is hard to separately evaluate these two different approaches as they share common factors which are hard to cleanly differentiate. In this paper, we examine these two approaches by exploiting a unique lottery game setup in China. This lottery game is similar to the lotteries in other countries except that there is a cap policy on the grand prize, which limits the reward of each jackpot winner. We show that this seemingly complex cap-policy actually causes the whole lottery price to be almost fixed all of the time although the rollover money from the last draw significantly varies. This suggests that the effective price approach cannot explain the observed variation in lottery sales. We further conduct Monte Carlo simulations and provide evidence showing that the popular 2SLS method using rollover and its square as instruments in the effective price literature may give spurious estimation result. We also find that lottery sales are highly correlated to the rollover size.