Efficient Allocations under Ambiguous Model Uncertainty

We investigate consequences of ambiguity on efficient allocations in an exchange economy. Ambiguity is embodied in the model uncertainty perceived by the consumers: they are unsure what would be the appropriate probability measure to apply to evaluate consumption and keep in consideration a set P of alternative probabilistic laws. Consumers are heterogeneously ambiguity averse with smooth ambiguity preferences and P is point identified, and the aggregate risk is ambiguous. Our analysis addresses, in particular, the full range of set-ups where under expected utility the efficient consumption sharing rule is a linear function of the aggregate endowment. We identify the systematic differences ambiguity aversion introduces to efficient sharing rules in these environments. We also characterize the representative consumer and use it to find implications of heterogeneity in ambiguity aversion for the pricing kernel. The pricing kernel is shown to be qualitatively different under heterogeneity and has the empirically compelling implication that the Sharpe ratio is counter-cyclical. More generally, we show that ambiguity aversion increases the elasticity of the pricing kernel, thereby increasing the Hansen-Jagannathan bound