Sequential incompleteness and dynamic suboptimality in stochastic OLG economies with production

We study a stochastic overlapping generations model with production and three- period-lived agents. Agents trade bonds and risky capital. Unlike the two-period model, we show that a stationary equilibrium in which prices and allocations depend solely on the aggregate capital stock and the current shock does not exist. Hence, the recursive equilibrium becomes the relevant equilibrium concept. For the recursive formulation of the model, markets are sequentially incomplete and we show that there is room for Pareto improvements in terms of intergenerational risk sharing. Finally, we examine whether the introduction of capital income taxation improves the allocation of risk.