2025-02-09-国际清算银行-用神经网络估计非线性异构代理模型（英）_80页_1mb

Summary of "Estimating Nonlinear Heterogeneous Agent Models with Neural Networks"

Core Content

This paper introduces a novel method using neural networks (NNs) to solve and estimate nonlinear heterogeneous agent models, particularly focusing on HANK models (Heterogeneous Agent New Keynesian models) with aggregate uncertainty and zero lower bound (ZLB) constraints. The method leverages recent advances in machine learning to overcome computational challenges in estimating complex economic models with nonlinear dynamics and agent heterogeneity.

Main Points

1. Motivation

• Traditional methods for solving and estimating heterogeneous agent models often rely on linear approximations, which limit the ability to capture nonlinear interactions and aggregate uncertainty.
• These nonlinearities are essential for understanding recent macroeconomic phenomena, such as ZLB periods, recessions, and inflation surges.
• The paper proposes a neural network-based approach that allows for global estimation and nonlinear solution of such models.

2. Methodology Overview

• The method involves two main neural networks:
  • One to approximate policy functions (both aggregate and individual).
  • Another to approximate the likelihood function using a neural network particle filter.
• The parameters are treated as pseudo-state variables, allowing the model to be solved once and then evaluated at any parameter combination.
• This approach enables efficient estimation by reducing the need for repeated model solutions during the optimization process.

3. Computational Advantages

• Scalability: NNs can handle high-dimensional problems, making them suitable for models with a large number of state variables and parameters.
• Speed: The use of pre-trained NNs for policy functions and steady-state solutions allows for fast simulation and likelihood evaluation.
• Accuracy: The NN particle filter improves the accuracy of likelihood evaluations by smoothing out the inaccuracies of standard Monte Carlo (MC) filters.

4. Model Structure

• The model includes idiosyncratic shocks and aggregate shocks.
• It features nonlinearities such as individual borrowing limits and the ZLB constraint.
• The steady-state equilibrium is approximated using an auxiliary neural network, reducing computational intensity.

5. Implementation Steps

• Step 1: Generate quasi-random parameter draws (training sample).
• Step 2: Use standard particle filters to evaluate the likelihood at each draw, leveraging pre-trained policy function approximations.
• Step 3: Train a neural network particle filter to predict the likelihood based on the training sample.
• Step 4: Use validation samples to assess overfitting and determine when to stop training.
• Step 5: Apply Bayesian estimation techniques using the approximated likelihood and standard simulators like the Random-Walk Metropolis-Hastings (RWMH) algorithm.

6. Empirical Application

• The method is applied to a nonlinear HANK model using U.S. data.
• The model captures aggregate uncertainty and heterogeneity in agents' behavior.
• The estimated model closely matches key data moments, including output volatility and inflation dynamics.
• The ZLB constraint is identified as a key driver of aggregate output volatility, as idiosyncratic income risk leads to higher savings and lower interest rates, increasing the probability of hitting the ZLB.

Key Findings

• Idiosyncratic income risk plays a significant role in explaining macroeconomic volatility.
• The ZLB constraint exacerbates this volatility by limiting the central bank's ability to stabilize the economy.
• The proposed method successfully recovers true parameter values in simulated data.
• The method is more flexible than existing techniques, allowing for estimation of a broader set of parameters.
• The approach supports Bayesian estimation and real-time forecasting by reusing pre-trained models and updating them with new data.

Conclusion

The paper presents a comprehensive framework for estimating nonlinear heterogeneous agent models using neural networks. It addresses the computational bottlenecks associated with global solution and estimation, and demonstrates its effectiveness through simulated and empirical applications. The method is particularly well-suited for models with aggregate uncertainty and nonlinear constraints, offering greater flexibility and accuracy in economic modeling and policy analysis.