Do choice sets matter?

This paper considers at the preference information contained in choice set membership. As would be expected, our empirical analyses show that knowing the choice set from which a brand was selected significantly improves the fit of discrete choice models. More surprisingly is the consistent result that a model that assumes rectangular choice probabilities over choice set members fits significantly better than a mulitnomial logit model estimated on choice data alone. These results demonstrate that choice set membership contains considerable preference information. Furthermore, they lead us to question the emphasis in the discrete choice modeling literature on the process of selecting a brand out of a choice set rather than on the process of forming that set