Efficiency and Distortions in a Production Economy with Heterogeneous Beliefs

In a production economy, in which agents have heterogeneous beliefs and a social planner has incomplete knowledge about which beliefs are correct, we introduce the concept of Incomplete Knowledge (IK) efficiency. IK-inefficient allocations can be improved upon without taking a stand on which belief, among a whole set of reasonable beliefs, is correct. We show that competitive equilibrium under heterogeneous beliefs is always IK-inefficient, and decompose this inefficiency into investment and speculative distortions. Overinvestment occurs in economies in which agents' elasticity of intertemporal substitution is high, whereas underinvestment arises when their elasticity is low. Using the IK concept to define mispricing, we show that equilibrium mispricing never arises intratermporally, but that intertemporal mispricing is generically present in economies with rich state spaces and heterogeneous beliefs. Finally, we argue that investment distortions may be easier to address by a social planner than speculative distortions in economies with idiosyncratic endowment shocks, and also show that transaction taxes may be welfare decreasing in such economies.