Discrete Choice and Rational Inattention: A General Equivalence Result

33 Pages Posted: 23 Dec 2016 Last revised: 15 May 2019

See all articles by Mogens Fosgerau

Mogens Fosgerau

University of Copenhagen

Emerson Melo

Indiana University Bloomington

André de Palma

Ecole Normale Superieure de Cachan (ENS)

Matthew Shum

California Institute of Technology

Date Written: May 9, 2019

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, 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

Fosgerau, Mogens and Melo, Emerson and Palma, André de and Shum, Matthew, Discrete Choice and Rational Inattention: A General Equivalence Result (May 9, 2019). Available at SSRN: https://ssrn.com/abstract=2889048 or http://dx.doi.org/10.2139/ssrn.2889048

Mogens Fosgerau

University of Copenhagen ( email )

University of Copenhagen, Building 26
Øster Farimagsgade 5
Copenhagen K., DK-1353
Denmark

Emerson Melo (Contact Author)

Indiana University Bloomington ( email )

100 South Indiana Ave.
Bloomington, IN 47405
United States

André de Palma

Ecole Normale Superieure de Cachan (ENS) ( email )

61 avenue du président Wilson
Cachan, Paris 94235
France

Matthew Shum

California Institute of Technology ( email )

Pasadena, CA 91125
United States

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