Revealed statistical consumer theory

Abstract

We provide a microfoundation to use aggregates (e.g. mean purchases) to evaluate consumer choice data. We study statistical consumer theory where an individual maximizes a preference over distributions of bundles when constrained by a statistic of the distribution (e.g. mean expenditure). We show statistical consumer theory is observationally equivalent to an individual whose preferences depend only on the statistic of the distribution. This means that despite working with distributions, the empirical content of the model only depends on a finite-dimensional statistic. This approach generalizes random quasilinear utility with random income and mean-variance preferences.

Random choice and market demand

“…Random choice models focus on choice probabilities directly. InMcCausland (2009), choice probabilities are restricted according to the IIA across budget sets leading to a Luce-type representation for regular utility functions (i.e., L-utility functions in McCausland's 2009 notation) Allen et al (2021). allowed for deliberate randomization in consumer theory ensuring that choices respect the budget set on average, but not for every realization (e.g., their figure1b).…”