A Flexible Class of Purchase Incidence Models

Purchase incidence models estimated on household scanner panel data typically assume the household's decision interval to be one week. However, it is well known in the econometrics literature that discrete-time models are highly sensitive to the assumed time interval of decision-making. In this study we investigate the consequences of endogenizing the household's decision interval, instead of restricting it to be one week. We characterize the household's random utility maximization problem, and therefore its purchase likelihood function, as a function of the household's decision interval. Such a flexible purchase incidence model is then used to explicitly estimate households' decision intervals in addition to their response to marketing activity and their baseline hazard functions. The proposed model of purchase incidence not only nests traditionally used choice models (such as the binary logit model) and hazard models (such as the discrete hazard model), but also allows for a gamut of more flexible parametric specifications. We estimate the proposed model across four category-level scanner panel datasets and find that the traditional assumption of restricting the household's decision interval to be one week may be too restrictive. We find that households are not only quite heterogeneous in their decision intervals but often have decision intervals longer than a week. From a managerial perspective, we show that estimated price elasticities are systematically understated if one does not allow for the effects of decision intervals. We demonstrate, using a fourth product category, that the results obtained from the category-level analyses generalize to the context of a full model of purchase incidence and brand choice.