Estimation of DSGE models with the effective lower bound

We propose a new approach for the efficient and robust Bayesian estimation of medium- and large-scale DSGE models with occasionally binding constraints. At its core lies the Ensemble Kalman filter, a novel nonlinear recursive filter, which allows for fast likelihood approximations even for models with large state spaces. We combine the filter with a computationally efficient solution method for piece-wise linear models a state-of-the-art MCMC sampler. Using artificial data, we demonstrate that our approach accurately captures the true parameters of models with a lower bound on nominal interest rates, even with very long lower bound episodes. We use the approach to analyze the US business cycle dynamics until the Covid-19 pandemic, with a focus on the long lower bound episode after the Global Financial Crisis.