Ensemble MCMC sampling for robust Bayesian inference

This paper proposes a Differential-Independence Mixture Ensemble (DIME) sampler for the Bayesian estimation of macroeconomic models. It allows sampling from particularly challenging, high-dimensional black-box posterior distributions which may also be computationally expensive to evaluate. DIME is a "Swiss Army knife", combining the advantages of a broad class of gradient-free global multi-start optimizers with the properties of a Monte Carlo Markov chain. This includes (i) fast burn-in and convergence absent any prior numerical optimization or initial guesses, (ii) good performance for multimodal distributions, (iii) a large number of chains (the "ensemble") running in parallel, (iv) an endogenous proposal density generated from the state of the full ensemble, which (v) respects the bounds of the prior distribution. I show that the number of parallel chains scales well with the number of necessary ensemble iterations. DIME is used to estimate the medium-scale heterogeneous agent New Keynesian ("HANK") model with liquid and illiquid assets, thereby for the first time allowing to also include the households' preference parameters. The results mildly point towards a less accentuated role of household heterogeneity for the empirical macroeconomic dynamics.