Using the Sequence‐Space Jacobian to Solve and Estimate Heterogeneous‐Agent Models
提出一种高效方法，通过快速计算序列空间雅可比矩阵，求解和估计含总体冲击的离散时间一般均衡异质性主体模型，适用于新古典和新凯恩斯模型。
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.