Modelling demand for lotto using a novel method of correcting for endogeneity

Modelling lottery sales as a function of the mean, standard deviation and skewness of the probability distribution of returns potentially gives insights into how the design of a game could be modified to maximise net revenue. But use of OLS is problematic because the level of sales itself affects values of the moments (and insufficient instruments are available for IV regression). We draw on the concept of a rational expectations equilibrium, developing a new regression model which corrects for endogeneity where the causal impact of the dependent variable on the right-hand side variables is deterministic. We apply the model to data on lotto sales from Spain. Using the Spanish data, we show that results provide more reliable guidance to lottery agencies because accounting for endogeneity leads to significantly different results from OLS and these results have superior performance in out-of-sample forecasting of sales. More generally, results prove consistent with the Friedman-Savage explanation of why people buy lottery tickets and with evidence from racetrack data that 'bettors love skewness'.