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

I study efficient allocations in a dynamic private information economy with a continuum of individual shocks that are persistent. I formulate the problem recursively and develop a first order approach to simplify it. The main advantage of the first order approach is that it allows for a substantial reduction of the state space of the dynamic program. This makes the problem tractable and permits quantitative implementation of the problem. I provide both qualitative and quantitative solutions for a taste shock economy where the shocks follow a random walk. I show that insurance against the shocks works very differently than in an otherwise identical economy with i.i.d. shocks. Both current and continuation utility are now positively correlated with the current shock and the social planner will optimally overinsure the agents, rather than underinsure. Also, for most of the population the intertemporal wedges are significantly larger than in an i.i.d. economy.