Identification in discrete choice models with imperfect information

Abstract

In this paper we study identification and inference of preference parameters in a single-agent, static, discrete choice model where the decision maker may face attentional limits precluding her to exhaustively process information about the payoffs of the available alternatives. By leveraging on the notion of one-player Bayesian Correlated Equilibrium in Bergemann and Morris (2016), we provide a tractable characterisation of the sharp identified set and discuss inference under minimal assumptions on the amount of information processed by the decision maker and under no assumptions on the rule with which the decision maker resolves ties. Simulations reveal that the obtained bounds on the preference parameters can be tight in several settings of empirical interest.

Estimating Dynamic Games with Unknown Information Structure

“…Theorem 2 says that, if the researcher knows that the data are generated by a Markov perfect equilibrium but does not know the underlying information structure, the researcher can proceed by treating the data as if they were generated from a Markov correlated equilibrium. Similar results have been obtained by Gualdani and Sinha (2020), Magnolfi andRoncoroni (2022), andSyrgkanis, Tamer, andZiani (2021) in static environments to leverage the informational robustness and computational tractability of Bayes correlated equilibrium.…”

“…One may understand this assumption as discretizing the space of latent variables for estimation to be feasible. The discretization of state space for feasible estimation is also used in Gualdani and Sinha (2020), Magnolfi andRoncoroni (2022), andSyrgkanis, Tamer, andZiani (2021).…”

“…We illustrate the performance of our approach via numerical examples. This paper contributes to the burgeoning literature that develop econometric tools that are robust to misspecification of information structures (Pakes, Porter, Ho, and Ishii (2015), Gualdani and Sinha (2020), Syrgkanis, Tamer, and Ziani (2021), Magnolfi and Roncoroni (2022), Koh (2022)). While Doval and Ely (2020) and Makris and Renou (2021) extend Bayes correlated equilibrium to extensive form games and multi-stage games respectively, this paper limits attention to a class of dynamic games that has served as workhorse models for empirical analysis and exploit the special structure of the model (namely that that the unobserved latent variables are independent over time) to reduce computational burden.…”

Stable Outcomes and Information in Games: An Empirical Framework

“…An early work in this spirit is Grieco (2014) who considers a parametric class of information structures that nest standard assumptions. Our work is most closely related to recent papers that use Bayes correlated equilibrium as a basis for informationally robust econometric analysis: Magnolfi and Roncoroni (2022) applies Bayes correlated equilibrium to static entry games (which are also considered in this paper), Syrgkanis, Tamer, and Ziani (2021) to auctions, and Gualdani and Sinha (2020) to static, single-agent models. 5 We contribute to the literature on the econometrics of moment inequality models by proposing a simple approach to constructing confidence sets based on the idea of Horowitz and Lee (2021).…”

“…They assume that the underlying data generating process is described by Bayes Nash equilibria, whereas we rely on rational expectations equilibria. Also see Gualdani and Sinha (2020) for the single-agent case.…”