Estimation of agent-based models using Bayesian deep learning approach of BayesFlow

This study examines the possibility of applying the novel likelihood-free Bayesian inference called BayesFlow proposed by Radev et al. (2020) for the estimation of agent-based models (ABMs). BayesFlow is a fully likelihood-free approach, which directly approximates a posterior rather than a likelihood function by learning an invertible probabilistic mapping between parameters and standard Gaussian variables, conditional on simulation data from the ABM to be estimated. BayesFlow certainly achieved superior accuracy to the benchmark method of Kernel Density Estimation-MCMC of Grazzini et al. (2017) and the more sophisticated method of Mixture Density Network-MCMC of Platt (2019), in the validation tests of recovering the ground-truth values of parameters from the simulated datasets of a standard New Keynesian ABM (NK-ABM). Furthermore, the truly empirical estimation of NK-ABM with the real data of the US economy successfully showed the desirable pattern of posterior contraction along with the increase in observation periods. This deep neural network-based method holds general applicability without any critical dependence on pre-selected design and high computational efficiency. These features are desirable when scaling the method to practical-sized ABMs, which typically have high-dimensional parameters and observation variables.