  We provide sufficient conditions for semi-nonparametric point identification
of a mixture model of decision making under risk, when agents make choices in
multiple lines of insurance coverage (contexts) by purchasing a bundle. As a
first departure from the related literature, the model allows for two
preference types. In the first one, agents behave according to standard
expected utility theory with CARA Bernoulli utility function, with an
agent-specific coefficient of absolute risk aversion whose distribution is left
completely unspecified. In the other, agents behave according to the dual
theory of choice under risk(Yaari, 1987) combined with a one-parameter family
distortion function, where the parameter is agent-specific and is drawn from a
distribution that is left completely unspecified. Within each preference type,
the model allows for unobserved heterogeneity in consideration sets, where the
latter form at the bundle level -- a second departure from the related
literature. Our point identification result rests on observing sufficient
variation in covariates across contexts, without requiring any independent
variation across alternatives within a single context. We estimate the model on
data on households' deductible choices in two lines of property insurance, and
use the results to assess the welfare implications of a hypothetical market
intervention where the two lines of insurance are combined into a single one.
We study the role of limited consideration in mediating the welfare effects of
such intervention.
