Discrete Choice and Rational Inattention: A General Equivalence Result

Abstract

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

Identification of a class of index models: A topological approach

“…This generalizes the result by Matµ ejka and McKay (2015) that the multinomial logit model has a foundation as a rational inattention model. The Fosgerau et al (2018) result implies that our identi…cation result extends without e¤ort to a broad class of rational inattention models.…”

“…We here …rst demonstrate that additive random utility models (ARUM) belong to the class of models (1). Using existing results in the literature, this implies that our results also apply to a broad class of rational inattention discrete choice models (Fosgerau et al, 2018) and an even wider class of perturbed utility models.…”

“…Hofbauer and Sandholm (2002, Thm 2.1), and so injective which we will require to achieve identi…cation. Fosgerau et al (2018) show that any ARUM satisfying the conditions above is observationally equivalent to a rational inattention discrete choice model in which the prior is held constant. This generalizes the result by Matµ ejka and McKay (2015) that the multinomial logit model has a foundation as a rational inattention model.…”

Travel time variability and rational inattention

“…where p (a) then depend on p (a|t) still through (6) (Matějka and McKay, 2015;Fosgerau et al, 2017). This may be recognized as a logit model in which actions with p (a) = 0 are omitted (Matějka and McKay, 2015).…”

Rational Inattention and Sequential Information Sampling

“…The "signal" can thus be viewed as an instruction as to which action is advisable.19 This kind of cost function is instead called "uniformly posterior-separable" inCaplin et al (2017). The class of static cost functions that can be justified by Theorem 1 is also related to the class of "GERI" cost functions defined byFosgerau et al (2016).20 For a related foundation for this static cost function, in the special case in which there are only two possible states, seeMorris and Strack (2017).21 The continuous-time information sampling process that is required is simply the one in which the information-cost matrix function is given by equation(11).…”