Endogenous Market Incompleteness Without Market Frictions

In this paper, we show that within the set of stochastic three-periodlived OLG economies with productive assets (such as land), markets are necessarily sequentially incomplete, and agents in the model do not share risk optimally. We start by characterizing perfect risk sharing and …nd that it requires a state-dependent consumption claims which depend only on the exogenous shock realizations. We show then that the recursive competitive equilibrium of any overlapping generations economy with weakly more than three generations is not strongly stationary. This then allows us to show directly that there are shortrun Pareto improvements possible in terms of risk-sharing and hence, that the recursive competitive equilibrium is not Pareto optimal. We then show that a …nancial reform which eliminates the equity asset and replaces it with zero net supply insurance contracts (Arrow securities) will implement to Pareto optimal stochastic steady-state known to exist in the model. Finally, we also show via numerical simulations that a system of government taxes and transfers can lead to a Pareto improvement over the competitive equilibrium in the model. Keywords: Stochastic overlapping generations, incomplete markets JEL Classi…cation numbers: D52, D61 We are grateful to Yves Balasko, Dave Cass, Michael Magill, Martine Quinzii, and Karl Shell for comments and suggestions. We are also indebted to two anonymous referees for invaluable help in the revisions of this paper.