Efficient Allocations in Dynamic Private Information Economies with Persistent Shocks: A First-Order Approach

TLDR: In this article, a first-order approach is proposed to find efficient allocations in a dynamic private information economy with a continuum of idiosyncratic shocks that are persistent, where the social planner decreases the informational rent of the agent today at the cost of providing higher insurance in the future.

Abstract: This article studies efficient allocations in a dynamic private information economy with a continuum of idiosyncratic shocks that are persistent. I develop a first-order approach for this environment and show that the problem has a simple recursive structure that relies on only a small number of state variables, making the problem tractable. I find sufficient conditions that guarantee that the first-order approach is valid. To illustrate the first-order approach I numerically compute the efficient allocations in a Mirrleesean economy with productivity shocks that follow a random walk and verify the validity of the first-order approach. I show that persistent shocks create a new trade-off where the social planner decreases the informational rent of the agent today at the cost of providing higher insurance in the future. Copyright 2013, Oxford University Press.