Fast Simulation-Based Bayesian Estimation of Heterogeneous and Representative Agent Models using Normalizing Flow Neural Networks

TL;DR

This paper introduces a deep learning Bayesian estimation method using normalizing flows that efficiently estimates complex macroeconomic models with many latent states without requiring likelihood functions or filtering.

Contribution

It presents a novel simulation-based Bayesian approach leveraging normalizing flow neural networks for estimating large-scale macroeconomic models with intractable likelihoods.

Findings

Successfully estimates a 10-parameter HANK model with 810 latent variables.

Estimates an 11-parameter model with value function iteration, infeasible for traditional methods.

Achieves higher quality and faster posteriors compared to Metropolis-Hastings.

Abstract

This paper proposes a simulation-based deep learning Bayesian procedure for the estimation of macroeconomic models. This approach is able to derive posteriors even when the likelihood function is not tractable. Because the likelihood is not needed for Bayesian estimation, filtering is also not needed. This allows Bayesian estimation of HANK models with upwards of 800 latent states as well as estimation of representative agent models that are solved with methods that don't yield a likelihood--for example, projection and value function iteration approaches. I demonstrate the validity of the approach by estimating a 10 parameter HANK model solved via the Reiter method that generates 812 covariates per time step, where 810 are latent variables, showing this can handle a large latent space without model reduction. I also estimate the algorithm with an 11-parameter model solved via value function iteration, which cannot be estimated with Metropolis-Hastings or even conventional maximum likelihood estimators. In addition, I show the posteriors estimated on Smets-Wouters 2007 are higher quality and faster using simulation-based inference compared to Metropolis-Hastings. This approach helps address the computational expense of Metropolis-Hastings and allows solution methods which don't yield a tractable likelihood to be estimated.