Summary: The paper considers the role of econometrics in decision making under uncertainty. This leads to a focus on predictive distributions. The decision maker’s subjective distribution is only partly specified; it belongs to a set \({\mathcal S}\) of distributions. \({\mathcal S}\) can also be regarded as a set of plausible data-generating processes. Criteria are needed to evaluate procedures for constructing predictive distributions.
We use risk robustness and minimax regret risk relative to \({\mathcal S}\). To obtain procedures for constructing predictive distributions, we use Bayes procedures based on parametric models with approximate prior distributions. The priors are nested, with a first stage that incorporates qualitative information such as exchangeability, and a second stage that is quite diffuse. Special points in the parameter space, such as boundary points, can be accommodated with second-stage priors that have one or more mass points but are otherwise quite diffuse.
An application of these ideas is presented, motivated by an individual’s consumption decision. The problem is to construct a distribution for that individual’s future earnings, based on his earnings history and on a longitudinal data set that provides earnings histories for a sample of individuals.