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.

We show that pooling countries across a panel dimension to macroeconomic data can improve by a statistically significant margin the generalization ability of structural, reduced form, and machine learning (ML) methods to produce state-of-the-art results. Using GDP forecasts evaluated on an out-of-sample test set, this procedure reduces root mean squared error by 12% across horizons and models for certain reducedform models and by 24% across horizons for dynamic structural general equilibrium models. Removing US data from the training set and forecasting out-of-sample country-wise, we show that reduced-form and structural models are more policy-invariant when trained on pooled data, and outperform a baseline that uses US data only. Given the comparative advantage of ML models in a data-rich regime, we demonstrate that our recurrent neural network model and automated ML approach outperform all tested baseline economic models. Robustness checks indicate that our outperformance is reproducible, numerically stable, and generalizable across models.

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