Dealing with ZLB in DSGE models An application to the Japanese economy

In this paper we propose an estimation strategy for DSGE models with occasionaly binding constraints, such as models with a zero lower bound for the nominal interest rate (ZLB). The usual likelihood approach is based on a first order approximation of the model around its deterministic steady state. This is not possible when we deal with a model with occasionally binding constraints, because the model is non differentiable everywhere and because, putting this first problem aside, the agents in the approximated model do not anticipate that the economy may hit the zero lower bound in the future. A medium scaled DSGE model with ZLB is estimated by the Simulated Method of Moments, using the Extended Path approach to simulate artificial time series for the observed variables. The Extended Path approach to simulation of stochastic forward{looking models, takes into account the full nonlinearities of the deterministic part of the model, but ignores the Jensen inequality. The extended path method is well suited for models including the zero lower bound because (contrary to the perturbation method) it does not rely on a strong smoothness assumption and so can handle problems with non differentiabilities. This approach proves to be feasible in practice.