Discrete Choice and Rational Inattention: a General Equivalence Result

TL;DR

This paper proves a broad equivalence between discrete choice models and rational inattention models, showing that various entropy-based information costs lead to observationally equivalent choice probabilities, including popular models like probit and nested logit.

Contribution

It generalizes the equivalence beyond Shannon entropy to a class of generalized entropy functions, linking rational inattention to a wide range of discrete choice models.

Findings

Rational inattention models with generalized entropy are equivalent to additive random utility models.

Includes models like probit and nested logit within the equivalence framework.

Provides a unified interpretation of bounded rationality in discrete choice.

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.