Heterogeneity, aggregation and long memory in lottery sales: some empirical evidence for Brazil

The paper investigates the prevalence of long memory for lottery sales, as previous literature suggests that aggregation of heterogeneous agents can potentially lead to a fractional differencing parameter consistent with highly persistent processes. Applications are considered for sales of 7 different lottery modalities in Brazil and also disaggregated at the level of federative units. The selected estimated models considered controls in terms of dummy variables for prize rollovers, special draws and weekends´ draws. The effects of rollovers and special draws on lottery sales are typically positive and non-negligible with an exception for the latter variable. The effect of draws that take place at weekends are mixed and not always positive. One observes long memory, for Brazil as a whole, only in the case of one modality. The evidence by federative units is mixed and indicates contrasts that suggest heterogeneities across regions and lottery modalities. At a more exploratory level, the evidence obtained with a stacked sample suggests relevant effects accruing from income inequality. on the probability of prevalence of highly persistent lottery sales, taking into account controls for regional heterogeneities. The initial evidence suggests that positional concerns may be relevant in the case of Brazil.