Working Paper: NBER ID: w24138
Authors: Timo Boppart; Per Krusell; Kurt Mitman
Abstract: We propose a new method for computing equilibria in heterogeneous-agent models with aggregate uncertainty. The idea relies on an assumption that linearization offers a good approximation; we share this assumption with existing linearization methods. However, unlike those methods, the approach here does not rely on direct derivation of first-order Taylor terms. It also does not use recursive methods, whereby aggregates and prices would be expressed as linear functions of the state, usually a very high-dimensional object (such as the wealth distribution). Rather, we rely merely on solving nonlinearly for a deterministic transition path: we study the equilibrium response to a single, small "MIT shock'' carefully. We then regard this impulse response path as a numerical derivative in sequence space and hence provide our linearized solution directly using this path. The method can easily be extended to the case of many shocks and computation time rises linearly in the number of shocks. We also propose a set of checks on whether linearization is a good approximation. We assert that our method is the simplest and most transparent linearization technique among currently known methods. The key numerical tool required to implement it is value-function iteration, using a very limited set of state variables.
Keywords: Heterogeneous-Agent Models; Aggregate Shocks; Fiscal Policy; Linearization Techniques
JEL Codes: C68; E1
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| linearization method (C51) | accurate computation of equilibria (C62) |
| deterministic transition path (C69) | analysis of fiscal policies (H30) |
| linearization method (C51) | straightforward analysis of countercyclical budget deficits (E62) |
| linearization method (C51) | captures first-order effects of aggregate shocks (E19) |
| linearization method (C51) | does not eliminate important mechanisms in heterogeneous-agent economy (E19) |
| linearization method (C51) | accurate predictions in various settings (C53) |