Mixture Models of Choice Under Risk

This paper is concerned with estimating preference functionals for choice under risk from the choice behaviour of individuals. We start from the observation that there is heterogeneity in behaviour between individuals and within individuals. By ‘heterogeneity between individuals’ we mean that people are different, not only in terms of which type of preference functional that they have, but also in terms of their parameters for these functionals. By ‘heterogeneity within individuals’ we mean that behaviour may be different even by the same individual for the same choice problem. Given the heterogeneity between individuals, the assumption of a ‘representative agent’ preference functional to represent the preference functional of all individuals may well lead to biased estimates. Given the heterogeneity within individuals, we should think carefully about the source of this heterogeneity and model it appropriately, for otherwise we get biased estimates. We propose solutions to both of these problems, concentrating particularly, but not exclusively, on using a Mixture Model to capture the heterogeneity of preference functionals across individuals.