A Stochastic Bubble Forest

We consider an economy with overlapping generations of relatively patient consumers who live for two periods. There is within-cohort heterogeneity in old-age endowments that depends on an aggregate state. That state is independent and identically distributed across generations. We assume consumers in their old age cannot be forced to give up any real resources. A stationary equilibrium in which state-contingent claims can be sold against the collateral of a single safe bubble security is efficient. The same allocation is also an equilibrium outcome in an economy with a sufficient number of stochastic bubble securities that can be traded subject to collateral constraints. When consumers cannot sell any securities short at all, the same efficient allocation can be implemented with a stochastic bubble forest: a continuum of Lucas trees that bear no fruit, with prices that evolve stochastically. Dynamic spanning is a potential rationale for the existence of distinct bubble assets.