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Crawford's et al. (2021) article on estimation of discrete choice models withunobserved or latent consideration sets, presents a unified framework toaddress the problem in practice by using "sufficient sets", defined as acombination of past observed choices. The proposed approach is sustained in are-interpretation of a consistency result by McFadden (1978) for the problem ofsampling of alternatives, but the usage of that result in Crawford et al.(2021) is imprecise in an important matter. It is stated that consistency wouldbe attained if any subset of the true consideration set is used for estimation,but McFadden (1978) shows that, in general, one needs to do a samplingcorrection that depends on the protocol used to draw the choice set. This notederives the sampling correction that is required when the choice set forestimation is built from past choices. Then, it formalizes the conditions underwhich such correction would fulfill the uniform condition property and cantherefore be ignored when building practical estimators, such as the onesanalyzed by Crawford et al. (2021).

A Note on "A survey of preference estimation with unobserved choice set heterogeneity" by Gregory S. Crawford, Rachel Griffith, and Alessandro Iaria