  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.
