Estimating Multinomial Choice Models with Unobserved Choice Sets

Abstract This paper proposes a new approach to estimating multinomial choice models when each consumer’s actual choice set is unobservable but could be bounded by two known sets, i.e., the largest and smallest possible choice sets. The bounds on choice set, combined with a monotonicity property derived from utility maximization, imply a system of inequality restrictions on observed choice probabilities that could be used to identify and estimate the model. A key insight is that the identification of random utility model can be achieved without exact information on consumers’ choice sets, which generalizes the identification result of the standard multinomial choice model. The effectiveness of the proposed approach is demonstrated via a range of Monte Carlo experiments as well as an empirical application to consumer demand for potato chips using household scanner data.