Revealed Statistical Consumer Theory

Abstract

We investigate a model of deterministic stochastic choice for the standard consumer problem. We introduce the framework of statistical consumer theory where the individual maximizes their utility with respect to a distribution of bundles that is constrained by a statistic (e.g. mean expenditure). We show that this behavior is observationally equivalent to an individual whose preferences depend only on the statistic of the distribution. Statistical consumer theory neither nests nor is nested in the random utility approach. We provide a formal statistical test of the model accounting for sampling variability and demonstrate it in an illustrative example using data on capuchin monkeys. * We thank Keith Chen for providing access to the data.

Correlated Choice

“…For other explanations of stochastic choice, see Machina (1985), Manzini and Mariotti (2014), Cerreia-Vioglio et al (2019), andAllen et al (2021).…”

Making sense of monkey business: Re-examining tests of animal rationality

“…Also, it suggests the subject may have distributional considerations in mind when making choices. See Allen et al (2021) for a theoretical study of these models.…”

“…The literature following Kagel et al (1975) has often implicitly treated the data as a distribution of choices and looked at rationality criteria on average choices. Thus, this effectively evaluates average choice rationality (Allen et al, 2021). However, when one has a distribution of choices it is also sensible to model choices generated by random utility maximization following McFadden and Richter (1990).…”

“…First, we describe the standard method to elicit choices from nonhuman animals. After this, we define the dataset collected in these experiments and describe how to check whether the data is consistent with standard deterministic utility maximization (Afriat, 1967;Diewert, 1973;Varian, 1982), average choice rationality (Allen et al, 2021), and random utility maximization (McFadden and Richter, 1990;McFadden, 2005;Hoderlein and Stoye, 2015;Kitamura and Stoye, 2018). While average choice rationality has been examined in the literature, until this paper there was no statistical test.…”

“…For example,Swait and Marley (2013),Fudenberg et al (2015),Freer and Martinelli (2016),Cerreia- Vioglio et al (2019), andAllen et al (2021) characterize different models where individuals express preferences over distributions. Similarly, there is evidence on human subjects inSopher and Narramore (2000),Agranov and Ortoleva (2017),,Ortoleva (2020), andFeldman andRehbeck (2020) that also suggests individuals may prefer a distribution of choices.…”