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

Modelling lottery sales as a function of the mean, standard deviation andskewness of the probability distribution of returns potentially gives insights into how thedesign of a game could be modified to maximise net revenue. But use of OLS isproblematic because the level of sales itself affects values of the moments (andinsufficient instruments are available for IV regression). We draw on the concept of arational expectations equilibrium, developing a new regression model which corrects forendogeneity where the causal impact of the dependent variable on the right-hand sidevariables is deterministic. Results provide more reliable guidance to lottery agenciesbecause accounting for endogeneity leads to significantly different results from OLS andthese results have superior performance in out-of-sample forecasting of sales. Moregenerally, results prove consistent with the Friedman-Savage explanation of why peoplebuy lottery tickets and with evidence from racetrack data that ‘bettors love skewness’