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.

当每个消费者的实际选择集不可观察但可能受两个已知集（即最大和最小可能选择集）的限制时，本文提出了一种估计多项选择模型的新方法。选择集的边界与从效用最大化派生的单调性属性相结合，意味着对观察到的选择概率的不等式限制系统，可用于识别和估计模型。一个关键的见解是，在没有消费者选择集的确切信息的情况下，可以实现随机效用模型的识别，这概括了标准多项选择模型的识别结果。