Controlling a Distribution of Heterogeneous Agents
44 Pages Posted: 22 Nov 2015
Date Written: November 20, 2015
This paper analyzes the problem of a benevolent planner wishing to control a population of heterogeneous agents subject to idiosyncratic shocks. This is equivalent to a deterministic control problem in which the state variable is the cross-sectional distribution. We show how, in continuous time, this problem can be broken down into a dynamic programming equation plus the law of motion of the distribution, and we introduce a new numerical algorithm to solve it. As an application, we analyze the constrained-efficient allocation of an Aiyagari economy with a fat-tailed wealth distribution. We find that the constrained-efficient allocation features more wealth inequality than the competitive equilibrium.
Keywords: Kolmogorov forward equation, wealth distribution, social welfare function, mean field control
JEL Classification: C6, D3, D5, E2
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