Bayesian Estimation of Agent-Based Models

We consider Bayesian inference techniques for Agent-Based (AB) models, as an alternative to simulated minimum distance (SMD). We discuss the specificities of AB models with respect to models with exact aggregation results (as DSGE models), and how this impact estimation. Three computationally heavy steps are involved: (i) simulating the model, (ii) estimating the likelihood and (iii) sampling from the posterior distribution of the parameters. Computational complexity of AB models implies that efficient techniques have to be used with respect to points (ii) and (iii), possibly involving approximations. We first discuss non-parametric (kernel density) estimation of the likelihood, coupled with Markov chain Monte Carlo sampling schemes. We then turn to parametric approximations of the likelihood, which can be derived by observing the distribution of the simulation outcomes around the statistical equilibria, or by assuming a specific form for the distribution of external deviations in the data. Finally, we introduce Approximate Bayesian Computation techniques for likelihood-free estimation. These allow embedding SMD methods in a Bayesian framework, and are particularly suited when robust estimation is needed. These techniques are tested, for the sake of comparison, in the same price discovery model used by Grazzini and Richiardi (2015) to illustrate SMD techniques.