Dynamic Efficiency With Private Information

This paper studies the efficient allocation of capital and consumption in a production economy with many agents, private information, and aggregate risk. It extends the influential work of Andrew Atkeson and Robert E. Lucas Jr. (1992), who analyzed a related problem in an exchange economy. In a dynamic production setting, the planner faces a fundamental trade-off between providing some insurance against privately observed idiosyncratic risk and sustaining productive investment and economic growth. Using mean-field control techniques, we derive the infinite dimensional Hamilton–Jacobi–Bellman equation that characterizes constrained-efficient allocations. Under constant relative risk aversion preferences, the solution admits a simple characterization. We show that constrained-efficient allocations can be decentralized through a competitive market in which goods trade against a single safe asset supplied by fiscal or monetary authorities. Dynamic efficiency requires setting the growth rate of the safe asset to balance the demand of agents for insurance with the investment needed to maintain optimal growth.