Characterizing efficiency in stochastic overlapping generations models

We introduce uncertainty about production in Diamond's OLG model. We compare any two feasible consumption-production allocations using stochastic ordering and define two types of efficient allocations (given initial capital stock). For stationary allocations it is shown that a necessary and sufficient condition for efficiency (type I) is that E[log r(ω)] is greater or equal to log(1 + n), where r(ω) generates the stationary interest factors corresponding to this allocation, n is the population growth rate. A complete characterization of type II efficient allocations is derived using the property of "cyclical monotonicity" between each generation's consumption allocation and the relevant interest rates.