Rachel Griffith (IFS)

“Estimating Demand Parameters with Choice Set Misspecication”

abstract

[Preliminary and incomplete: please do not cite without authors’ consent]
We describe methods to estimate demand parameters in the presence of choice set misspeci-cation due to unobserved individual choice sets. We show that a consumer’s probability ofmaking a choice from her true choice set can be written as the probability she makes the samechoice from a universal choice set less a bias term capturing the probability that she wouldchoose any of the elements in her true choice set. This bias term is ignored in the vast majorityof applications of dierentiated product demand estimation, which estimate preferences basedon a universal choice set. We show how to estimate models that account for this bias underLogit demand using both (1) a variation of the Fixed Eect Logit approach due to Chamberlain(1980) and (2) observed individual-specic purchase histories. We illustrate these ideas usinghousehold-level scanner data exploiting variation in choice sets based on heterogeneous productoerings across stores and the introduction of a new product variety in the market for ketchup inthe UK. Our results show that accounting for choice set misspecication is critical for accuratelyestimating own- and cross-price elasticities of demand.