Identifying Preferences under Risk from Discrete Choices

When studying consumption choices, economists have often relied on the abstraction of a representative agent. Such an agent can indeed be shown to exist and to replicate the aggregate consumers' demand under standard, but not necessarily convincing assumptions (Kirman (1992)). There was also ajustifiable reluctance to introducing heterogeneous preferences, as such a step may seem ad hoc when trying to explain different consumption behaviors. The rise of empirical studies based on micro data has opened new perspectives. The micro-economic importance of uninsurable risks is now recognized, and threatens the foundations of the representative agent hypothesis often used in macroeconomics. The continuing controversies surrounding the question of individual attitudes towards risk has motivated many empirical studies and observations; most of them conclude to a bewildering diversity of individual preferences. This paper proposes to check the conditions under which heterogeneous individual attitudes toward risk can be non-parametrically identified from discrete data on choices under risk. Our main result establishes that given data that is usually available (essentially market shares of the different options, plus the realizations of the final outcomes of agents), the analyst can recover the whole distribution of individual preferences if this can be indexed by a one-dimensional parameter, provided that a fairly weak single-crossing condition holds. We then discuss several applications of our general methodology.