Solving non-linear dynamic models (more) efficiently: application to a simple monetary policy model

There has been an increased acceptance of non-linear linkages being the major driver of the most pronounced phases of business and financial cycles. However, modelling these non-linear phenomena has been a challenge, since existing solutions methods are either efficient but not able to accurately capture non-linear dynamics (e.g. linear methods), or accurate but quite resource-intensive (e.g. stacked system or stochastic Extended Path). This paper proposes two new solution approaches that try to be accurate enough and less costly. Moreover, one of those methods lets us do Kalman filtering on non-linear models in a non-linear way, which is also important for this kind of models, in general, to be more policy-relevant. Impulse responses, simulations and Kalman filtering exercises show the advantages of those new approaches when applied to a simple, but strongly non-linear, monetary policy model.