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

2026-06-04

AI Summary

This study addresses the bias in parameter estimation commonly arising in discrete choice models due to unobserved consideration sets. The authors propose a practical approach that constructs individual-specific consideration sets based on historical choices, enabling consistent estimation within a Logit framework without relying on exhaustive universal set evaluations or subjective self-reports. Theoretically, the paper provides the first rigorous proof that, under homogeneous choice probability assumptions, such consideration sets satisfy sufficient conditions for consistent estimation, while also offering a refined interpretation of the alternative sampling theorem. Methodologically, the approach is validated through Monte Carlo simulations, synthetic Logit-generated data, and large-scale passive behavioral datasets—such as smart card and mobile phone records. Empirical results demonstrate that the proposed method yields consistent and robust parameter estimates under specified conditions, thereby opening a new avenue for applied research in discrete choice modeling.

Abstract

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. 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. The article concludes by discussing the practical implications of this result and potential extensions to other modeling frameworks and assumptions.

Problem

• consideration set
• choice modeling
• logit model
• consistent estimation
• historical choices

Innovation

• consideration set
• logit model
• consistent estimation
• historical choices
• uniform conditioning