Dynamics of Linear Forward-looking Structural Macroeconomic Models at the Zero Lower Bound: Do Solution Techniques Matter?

Yes, they do matter, sometimes a lot. In this paper, I compare various solution techniques that can be used to solve structural forward-looking macroeconomic models subject to the zero lower bound as the only non-linearity. I use stylized forward-looking models to compare the solution techniques based on impulse responses, on the implications of forward guidance, on the values of fiscal multipliers, and on solution accuracy. I disprove recent claims in the literature that various solution methods yield identical dynamics. The solutions are equivalent only if the zero lower bound constraint binds for no more than one period, otherwise the implied dynamics can be different. Moreover, I find that large effects of forward guidance and large fiscal multipliers at the zero lower bound are found especially when models are solved using 'shadow' shocks. On the other hand, the occasional-binding toolbox and solutions based on a non-linear deterministic solver imply small effects of forward guidance and fiscal multipliers that are not significantly larger at the zero lower bound than during normal times. Moreover, these two types of solutions seem to be the most accurate.