Discrete Choice and Rational Inattention: A General Equivalence Result
33 Pages Posted: 23 Dec 2016 Last revised: 15 May 2019
Date Written: May 9, 2019
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, the choice probabilities in the rational inattention (RI) model take the multinomial logit form. We show that RI choice probabilities may take the form of any additive random utility discrete choice model (ARUM) when the information cost belongs to a class of generalized entropies defined in this paper. The prior information of the rationally inattentive agent is summarized in a constant vector of utilities in the corresponding ARUM. Conversely, any combination of ARUM and prior information can be rationalized by an RI model. Nevertheless, there are key behavioral differences between the two paradigms: the generalized rational inattention models developed here permit options to be complements as the prior information changes; such behavior is explicitly ruled out in discrete choice models as well as in the RI-logit model. We illustrate our results utilizing the nested logit, an empirically relevant discrete choice model.
Keywords: rational inattention; discrete choice models; random utility; complements; convex analysis; generalized entropy
JEL Classification: D03; C25; D81; E03
Suggested Citation: Suggested Citation