Consistent estimation in Logit models using historical choices as practical consideration set

A key challenge in choice modeling lies in specifying the consideration set, the subset of alternatives that individuals actually evaluate when making choices, which is unobserved (latent) to the researcher. The classical homo economicus assumption posits that individuals assess the full universal set of alternatives, a behaviorally implausible premise. Practical options include directly asking individuals, which introduces behavioral biases; treating the consideration set as a latent construct, requiring full enumeration and strong identification assumptions; or relying on ad hoc heuristics that attempt to replicate how individuals form these sets or on non-parametric methods. Recently, some researchers have used historical choices as practical consideration set, an approach made increasingly feasible by the availability of passive data sources such as smartcards, mobile phone records, and scanner data. This article provides a formal demonstration of a sufficient condition, along with Monte Carlo evidence, showing that, under a Logit data-generating process with homogeneous choice probabilities across instances, defining a practical consideration set based on historical choices yields consistent parameter estimates when both the sample size and the number of historical choices tend to infinity. The demonstration is based on a reinterpretation of the sampling-of-alternatives theorem, viewing historical choices as draws from the true consideration set, and showing that under the stated assumptions, the uniform conditioning property holds asymptotically. The article concludes by discussing the practical implications of this result and potential extensions to other modeling frameworks and assumptions.