A Model of Multi-Pass Search: Price Search Across Stores and Time

In retail settings with price promotions, consumers often search across stores and time. However, the search literature typically only models one pass search across stores, ignoring revisits to stores; the choice literature using scanner data has modeled search across time but not search across stores in the same model. We develop a multi-pass search model that jointly endogenizes search in both dimensions; our model nests a finite horizon model of search across stores within an infinite horizon model of inter-temporal search. We apply our model to milk purchases at grocery stores; hence the model also accounts for repeat purchases across time, inventory holding by households, and grocery basket effects. We note that the special case without these additional features can be used to study one-time purchases with repeat store visits as in the case of durable goods and online shopping. We formulate the empirical model as a mathematical program with equilibrium constraints (MPEC) and estimate it, allowing for latent class heterogeneity using an iterative E-M algorithm. In contrast to extant research, we find that omitting the temporal dimension underestimates price elasticity. We attribute this difference to the relative frequency of household stockouts and purchase frequency in the milk category. Interestingly, increasing the promotional frequency (while reducing its depth to maintain the mean and variance of prices across all stores) can increase loyalty to the household’s preferred store.