Estimating Demand Parameters with Choice Set Misspecification

Abstract:

We describe methods to estimate demand parameters in the presence of choice set misspecification due to unobserved individual choice sets. We show that a consumer’s probability of making a choice from her true choice set can be written as the probability she makes the same choice from a universal choice set less a bias term capturing the probability that she would choose any of the elements in her true choice set. This bias term is ignored in the vast majority of applications of differentiated product demand estimation, which estimate preferences based on a universal choice set. We show how to estimate models that account for this bias under Logit demand using both (1) a variation of the Fixed Effect Logit approach due to Chamberlain (1980) and (2) observed individual-specific purchase histories. We illustrate these ideas using household-level scanner data exploiting variation in choice sets based on heterogeneous product offerings across stores and the introduction of a new product variety in the market for ketchup in the UK. Our results show that accounting for choice set misspecification is critical for accurately estimating own- and cross-price elasticities of demand.