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This paper proposes a simulation-based deep learning Bayesian procedure forthe estimation of macroeconomic models. This approach is able to deriveposteriors even when the likelihood function is not tractable. Because thelikelihood is not needed for Bayesian estimation, filtering is also not needed.This allows Bayesian estimation of HANK models with upwards of 800 latentstates as well as estimation of representative agent models that are solvedwith methods that don't yield a likelihood--for example, projection and valuefunction iteration approaches. I demonstrate the validity of the approach byestimating a 10 parameter HANK model solved via the Reiter method thatgenerates 812 covariates per time step, where 810 are latent variables, showingthis can handle a large latent space without model reduction. I also estimatethe algorithm with an 11-parameter model solved via value function iteration,which cannot be estimated with Metropolis-Hastings or even conventional maximumlikelihood estimators. In addition, I show the posteriors estimated onSmets-Wouters 2007 are higher quality and faster using simulation-basedinference compared to Metropolis-Hastings. This approach helps address thecomputational expense of Metropolis-Hastings and allows solution methods whichdon't yield a tractable likelihood to be estimated.

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