  This paper establishes a general equivalence between discrete choice and
rational inattention models. Matejka and McKay (2015, AER) showed that when
information costs are modelled using the Shannon entropy function, the
resulting choice probabilities in the rational inattention model take the
multinomial logit form. By exploiting convex-analytic properties of the
discrete choice model, we show that when information costs are modelled using a
class of generalized entropy functions, the choice probabilities in any
rational inattention model are observationally equivalent to some additive
random utility discrete choice model and vice versa. Thus any additive random
utility model can be given an interpretation in terms of boundedly rational
behavior. This includes empirically relevant specifications such as the probit
and nested logit models.
