  Recent advances in computing power and the potential to make more realistic
assumptions due to increased flexibility have led to the increased prevalence
of simulation models in economics. While models of this class, and particularly
agent-based models, are able to replicate a number of empirically-observed
stylised facts not easily recovered by more traditional alternatives, such
models remain notoriously difficult to estimate due to their lack of tractable
likelihood functions. While the estimation literature continues to grow,
existing attempts have approached the problem primarily from a frequentist
perspective, with the Bayesian estimation literature remaining comparatively
less developed. For this reason, we introduce a Bayesian estimation protocol
that makes use of deep neural networks to construct an approximation to the
likelihood, which we then benchmark against a prominent alternative from the
existing literature. Overall, we find that our proposed methodology
consistently results in more accurate estimates in a variety of settings,
including the estimation of financial heterogeneous agent models and the
identification of changes in dynamics occurring in models incorporating
structural breaks.
