Estimating Non-Linear DSGEs with the Approximate Bayesian Computation: an application to the Zero Lower Bound

Non-linear model estimation is generally perceived as impractical and computationally burdensome. This perception limited the diffusion on non-linear models estimation. In this paper a simple set of techniques going under the name of Approximate Bayesian Computation (ABC) is proposed. ABC is a set of Bayesian techniques based on moments matching: moments are obtained simulating the model conditional on draws from the prior distribution. An accept-reject criterion is applied on the simulations and an approximate posterior distribution is obtained by the accepted draws. A series of techniques are presented (ABC-regression, ABC-MCMC, ABC-SMC). To assess their small sample performance, Montecarlo experiments are run on AR(1) processes and on a RBC model showing that ABC estimators outperform the Limited Information Method (Kim, 2002), a GMM-style estimator. In the remainder, the estimation of a new-keynesian model with a zero lower bound on the interest rate is performed. Non-gaussian moments are exploited in the estimation procedure.