Heterogeneous Choice Sets and Preferences

Abstract

We propose a robust method of discrete choice analysis when agents' choice sets are unobserved. Our core model assumes nothing about agents' choice sets apart from their minimum size. Importantly, it leaves unrestricted the dependence, conditional on observables, between choice sets and preferences. We first characterize the sharp identification region of the model's parameters by a finite set of conditional moment inequalities. We then apply our theoretical findings to learn about households' risk preferences and choice sets from data on their deductible choices in auto collision insurance. We find that the data can be explained by expected utility theory with low levels of risk aversion and heterogeneous non‐singleton choice sets, and that more than three in four households require limited choice sets to explain their deductible choices. We also provide simulation evidence on the computational tractability of our method in applications with larger feasible sets or higher‐dimensional unobserved heterogeneity.

Nonparametric Identification of Differentiated Products Demand Using Micro Data

“…However, for some questions-e.g., those involving information interventions or requiring identification of cardinal utilities-the interpretation becomes important. See Barseghyan, Coughlin, Molinari, and Teitelbaum (2021) for a recent contribution on this topic.…”

Finite Sample Inference in Incomplete Models

“…A game of perfect information with a pure strategy equilibrium concept, as in Jovanovic [1989] and Tamer [2003] is a prime example. Other examples include models of choice with limited attention, as in Barseghyan et al [2021], discrete choice with endogeneity, as in Chesher et al [2013],…”

“…Discrete choice with unobserved heterogeneity in consideration sets. We set out the structural model in Barseghyan et al [2021] in their notation, before translating it into our framework. Consider a finite set of alternatives D for a decision maker to choose from.…”

A Random Attention and Utility Model

“…De Los Santos et al (2012) on web browsing behavior of consumers when shopping online. Barseghyan et al (2021) on insurance purchases.…”

“…We differ from that work because we do not observe attributes (e.g., prices). Barseghyan et al (2021) obtain information about parametric distribution of preferences in a domain with attributes variation by introducing a support restriction on possible consideration sets. Our framework does not impose any parametric restrictions on the distribution of preferences and allows both shape and support restrictions on consideration probabilities.…”