State space

Quantum mechanics

Algorithm

Monetary policy

Biology

Statistics

Materials science

Applied mathematics

Aggregate (composite)

Computation

Jacobian matrix and determinant

Economics

New Keynesian economics

Computer science

Mathematical optimization

Genetics

Physics

Nonlinear system

Iterated function

Sequence (biology)

Mathematics

Monetary economics

Mathematical analysis

Composite material

Econometrica

We propose a general and highly efficient method for solving and estimating general equilibrium heterogeneous‐agent models with aggregate shocks in discrete time. Our approach relies on the rapid computation of sequence‐space Jacobians —the derivatives of perfect‐foresight equilibrium mappings between aggregate sequences around the steady state. Our main contribution is a fast algorithm for calculating Jacobians for a large class of heterogeneous‐agent problems. We combine this algorithm with a systematic approach to composing and inverting Jacobians to solve for general equilibrium impulse responses. We obtain a rapid procedure for likelihood‐based estimation and computation of nonlinear perfect‐foresight transitions. We apply our methods to three canonical heterogeneous‐agent models: a neoclassical model, a New Keynesian model with one asset, and a New Keynesian model with two assets.

Using the Sequence‐Space Jacobian to Solve and Estimate Heterogeneous‐Agent Models