Inference under stability of risk preferences

Abstract

We leverage the assumption that preferences are stable across contexts to partially identify and conduct inference on the parameters of a structural model of risky choice. Working with data on households' deductible choices across three lines of insurance coverage and a model that nests expected utility theory plus a range of non-expected utility models, we perform a revealed preference analysis that yields household-specific bounds on the model parameters. We then impose stability and other structural assumptions to tighten the bounds, and we explore what we can learn about households' risk preferences from the intervals defined by the bounds. We further utilize the intervals to (i) classify households into preference types and (ii) recover the single parameterization of the model that best fits the data. Our approach does not entail making distributional assumptions about unobserved heterogeneity in preferences.

Heterogeneous Choice Sets and Preferences

“…Each household i (i) faces a menu of prices p i = (p ic c ∈ D), where p ic is the household-specific premium associated with deductible c and D is the feasible set of deductibles, (ii) has a probability μ i of experiencing a claim during the policy period, and (iii) has an array of observed characteristics t i . 16 Following the related literature (e.g., Cohen and Einav (2007), Sydnor (2010), Barseghyan, Prince, and Teitelbaum (2011), Barseghyan, Molinari, O'Donoghue, and Teitelbaum (2013), Barseghyan, Molinari, and Teitelbaum (2016)), 17 we make two simplifying assumptions about claims and their probabilities. Assumption 4.1(I) is motivated by the fact that claim rates are small, so the likelihood of two or more claims in the same policy period is very small.…”

Estimating Risk Preferences in the Field

“…With this approach, they can fully rationalize the behavior of roughly 30 percent of employees across all six contexts, which they take to be further evidence that there is a domain-general component of risk preferences (though they acknowledge that the size of the context-specific shifts "suggests that the implied levels of risk aversion exhibited may be very different across domains, or that other effects, such as framing or probability weighting, are particularly important in these contexts" (p. 2634)). Barseghyan, Molinari, and Teitelbaum (2016), discussed in section 5.2, demonstrate a close connection between rank correlation of choices and stability of risk preferences under a probability distortion model. They find that stability of risk preferences cannot be rejected for roughly five in six households whose choices are rationalizable by the model.…”

“…If in the data a dominated option is chosen with positive probability (something that often happens in practice), the researcher must either introduce some form of random trembles in choice or dismiss the subpopulation that chooses dominated options. For example, Barseghyan, Molinari, and Teitelbaum (2016), which we discuss in section 5.2, use a random-preference model where the curvature of the utility function is constrained to lie in a conservative range, and document that the model is incompatible with the choice of a dominated option made by 13 percent of households in their data. In contrast, a random-utility model predicts that all options in the choice set, even dominated options, should be made with positive probability.…”

Public Opinion Polarization by Individual Revenue from the Social Preference Theory

“…By this model, rational decisions could be made so as to reduce the impact of individual preference on evaluation accuracy. Barseghyan et al [31] studied the family risk preferences through expectation utility theory in 2016. All these studies mentioned above are of great significance to the field of public opinion, but they mainly focus on qualitative analysis and lack quantitative modeling and analysis process, leading to shortages of intuitiveness and validity of the characterization of complex and changeable public opinion evolution.…”