Heterogeneous demand responses to discrete price changes: an application to the purchase of lottery tickets

During the survey period of any household expenditure survey price variations may occur. Such variation can be used to identify heterogeneous demand responses to price changes. This is feasible because expenditure surveys usually contain a large number of observations. The principal difficulty for estimation arises because of the sampling process which generates the data. An estimable model of individual purchase is presented and is estimated in the case of the demand for lottery tickets. This model allows identification of heterogeneous responses to changes in the rollover state (i.e. whether last week's jackpot has been added to the current jackpot). The distribution of heterogeneous responses, in the form of a bivariate mixing distribution, is shown to be identified from the available data. The EM algorithm is used to estimate the parameters of the mixing distribution. The estimates imply that there is substantial heterogeneity in the population both in the normal expenditure levels and in the reaction to a jackpot rolled over.