Aggregation, Determinacy, and Informational Efficiency for a Class of Economies with Asymmetric Information

In this paper we identify and analyze a class of economies with asymmetric information that we call quasi-complete. Quasi-complete economies have many of the properties commonly associated with complete markets, but unlike the latter they may support equilibria that do not perfectly aggregate agents' private information. Special cases include a class of economies with traded endowments and linear risk tolerance, Grossman's (1976) exponential-normal model, the setting of the no-trade theorem of Milgrom and Stokey (1982), and an economy with no aggregate endowment risk. For quasi-complete economies we determine equilibrium trades, we show that the set of fully informative equilibria is a singleton, and we give necessary and sufficient conditions for the existence of partially informative equilibria. Besides unifying some familiar settings, the following new results are proved: (a) The same restrictions that deliver Gorman aggregation under symmetric information, are sufficient for Gorman aggregation under asymmetric information, even under partially revealing prices. (b) The traditional assumptions of quadratic utilities and endowment spanning that result in the CAPM under symmetric information deliver a conditional CAPM under asymmetric information, prices that need not be fully informative, and no distributional assumptions. (c) The linear equilibrium in Grossman's (1976) model is the only equilibrium (linear or not), while minor changes in the normality assumptions result in indeterminacy and partially informative equilibria. (d) If there is no aggregate endowment risk, agents with common priors will always sell the risky part of their endowment, no matter what private information they receive.