Estimation of Agent-Based Models Using Bayesian Deep Learning Approach of BayesFlow

This paper examines the possibility of applying the novel likelihood-free Bayesian inference called BayesFlow proposed by Radev et al. (2020) to 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 that implements a Normalizing Flow between parameters and standard Gaussian variables, with conditional on data from ABM simulation. This deep neural network-based method holds general applicability without any critical dependence on pre-selected design, and also attains high computational efficiency. BayesFlow certainly achieved superior accuracies to the benchmark method of KDE-MCMC of Grazzini et al. (2017) and also to 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 in a standard New Keynesian ABM (NK-ABM). Furthermore, the truly empirical estimation of NK-ABM with the real observation data of the US economy is carried out, in order to check robustness of the BayesFlow method against the data generated from unknow Data Generation Process. The result successfully showed the desirable pattern of posterior contraction along with the increase of observation periods, and clearly tighter posterior distributions than those constructed by KDE-MCMC. Over the validation experiments, BayesFlow did not involve any extensive search of the hyperparameters, and marked a considerably shorter computational time than the competing non-parametric MCMC methods. These features are desirable when scaling the method to practical-sized ABMs that typically have high dimensional parameters and observation variables