Bounding Demand Elasticities with Unobserved Choice Set Heterogeneity∗

[Preliminary and incomplete: please do not cite without authors’ consent] We describe methods to estimate demand parameters and bound elasticities in the presence of unobserved choice set heterogeneity. We show that an estimation bias arises whenever the econometrician mistakenly imputes to individuals supersets of their true but unobserved choice sets. We propose estimation methods that avoid this bias under logit demand using “sufficient sets,” instances in which consumers of the same type make at least two choices from “similar” unobserved choice sets. Examples of sufficient sets include observed individual-specific purchase histories and the collection of products purchased by a group of consumers going shopping to the same retailer in a given time period. We illustrate these ideas using household-level scanner data in the market for ketchup in the UK. Our results show that accounting for unobserved choice set heterogeneity is critical for accurately estimating preferences and bounding price elasticities of demand. ∗We would like to thank Clément de Chaisemartin, Xavier D’Haultfœuille, xx, xx, and seminar participants at xx, xx, and ECARES for helpful comments. Griffith gratefully acknowledges financial support from the European Research Council (ERC) under ERC-2009-AdG grant agreement number 249529, and the Economic and Social Research Council (ESRC) under the Centre for the Microeconomic Analysis of Public Policy (CPP), grant number RES-544-28-0001. Iaria gratefully acknowledges financial support from the research grant Labex Ecodec: Investissements d’Avenir (ANR11-IDEX-0003/Labex Ecodec/ANR-11-LABX-0047). †Dept. of Economics, University of Zürich and CEPR, [email protected] ‡University of Manchester and IFS, [email protected] §CREST (Paris) and IFS, [email protected]