Solving Heterogeneous Agent Models with the Master Equation / Adrien Bilal.

Format:

Book

Author/Creator:

Bilal, Adrien.

Contributor:

National Bureau of Economic Research.

Series:

Working Paper Series (National Bureau of Economic Research) no. w31103.

NBER working paper series no. w31103

Language:

English

Physical Description:

1 online resource: illustrations (black and white);

Place of Publication:

Cambridge, Mass. National Bureau of Economic Research 2023.

Summary:

This paper proposes an analytic representation of perturbations in 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 economy: 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 simplifications. 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 six main advantages: (i) finite dimension; (ii) closed-form mapping to steady-state objects; (iii) applicability when many distributional moments or prices enter individuals' decision such as dynamic trade, urban or job ladder settings; (iv) block-recursivity bypassing further fixed points; (v) mapping to analytic sequence-space derivatives; (vi) fast implementation using standard numerical methods. I develop the Second-order Approximation to the Master Equation (SAME) and show that it shares these properties, making the approach 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.

Notes:

Print version record

April 2023.