A Time Series Analysis of U.K. Lottery Sales: Long and Short Run Price Elasticities

This paper estimates the long‐ and short‐run elasticities for Lotto. It is particularly concerned with the dynamic response to price variations since, for some goods, this has sometimes been used to infer the presence of addiction. The price elasticity is identified through variation in the expected value of a Lotto ticket induced by rollovers whose high frequency results in surprisingly high variation in the expected value of holding a ticket. Unit root tests are applied to the series in order to identify their time series properties and to avoid a spurious regression problem. The series are found to be stationary. We apply instrumental variables to account for the endogeneity which arises due to correlation between the expected value and the dependent sales variable. The estimated long‐run elasticity exceeds the short‐run elasticity and this supports the hypothesis that there is an element of addictive behaviour in sales. The Lottery is regulated and the regulator’s objective is to maximize sales. Our estimated long‐run price elasticity of demand is inconsistent with revenue maximization and we find that greater revenue for the ‘good causes’ could be raised from the game if a smaller proportion of sales revenue were allocated to them.