  Crawford's et al. (2021) article on estimation of discrete choice models with
unobserved or latent consideration sets, presents a unified framework to
address the problem in practice by using "sufficient sets", defined as a
combination of past observed choices. The proposed approach is sustained in a
re-interpretation of a consistency result by McFadden (1978) for the problem of
sampling of alternatives, but the usage of that result in Crawford et al.
(2021) is imprecise in an important matter. It is stated that consistency would
be 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 sampling
correction that depends on the protocol used to draw the choice set. This note
derives the sampling correction that is required when the choice set for
estimation is built from past choices. Then, it formalizes the conditions under
which such correction would fulfill the uniform condition property and can
therefore be ignored when building practical estimators, such as the ones
analyzed by Crawford et al. (2021).
