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Solving Heterogeneous Agent Models with the Master Equation

Adrien Bilal, Harvard University
Wednesday, October 26, 2022
4:00-5:30 PM
201 Lorch Hall Map
This paper proposes an analytic representation of heterogeneous agent economies with aggregate shocks. Treating the underlying distribution as an explicit state variable, a single value function defined on an infinite-dimensional state space provides a fully recursive representation of the econ- omy: the ‘Master Equation’ introduced in the mathematics mean field games literature. I show that analytic local perturbations of the Master Equation around steady-state deliver dramatic sim- plifications. The First-order Approximation to the Master Equation (FAME) reduces to a standard Bellman equation for the directional derivatives of the value function with respect to the distribution and aggregate shocks. The FAME has five main advantages: (i) finite dimension; (ii) closed-form mapping to steady-state objects; (iii) applicability when many distributional moments or prices en- ter individuals’ decision such as dynamic trade, urban or job ladder settings; (iv) block-recursivity bypassing further fixed points; (v) fast implementation using standard numerical methods. The Second-order Approximation to the Master Equation (SAME) shares these properties, making it amenable to settings such as asset pricing. I apply the method to two economies: an incomplete market model with unemployment and a wage ladder, and a discrete choice spatial model with migration.
Building: Lorch Hall
Event Type: Workshop / Seminar
Tags: Economics, seminar
Source: Happening @ Michigan from Department of Economics, Michael Beauregard Seminar in Macroeconomics, Department of Economics Seminars