The last term is included to avoid unrealistically large quarterly movements in the “optimal” federal funds rate path. 18  This illustration takes the anticipated scale of asset purchases as fixed. The effect of these purchases, given that the modal expectation in the primary dealer survey was for $ billion of purchases, is implicitly already incorporated into the baseline forecast.
In principle, we could use the FRB/US model to perform a joint optimization exercise in which the optimal paths of asset purchases and the federal funds rate are simultaneously determined, but the results from such an exercise would be highly sensitive to assumptions about possible costs of asset purchases that are not well defined, such as the potential for market disruption.