THE UNIT ROOT PROPERTY WHEN MARKETS ARE SEQUENTIALLY INCOMPLETE

We consider pure exchange, one good OLG economies under stationary Markov uncertainty. It is known that when markets are sequentially complete, a stationary equilibrium at which the agents common matrix of intertemporal rates of substitution has a Perron root which is less than or equal to one is conditionally Pareto optimal (CPO). We assume that there exists a long-lived dividend paying asset and show that if dividends are strictly positive then the relation between the unit root condition and optimality holds even if markets are not sequentially complete. However, every equilibrium allocation is shown to be constrained CPO under the additional requirement that assets be freely disposable, which seems reasonable when dividends are positive and whose importance was pointed out by Santos and Woodford (1997) in their work on bubbles; this fact undermines the relation between the unit root property and optimality. The relation is less clear when dividends and asset prices are allowed to be negative in some states.