Our framework aims ex ante for inflation to average 2 percent over time, but it does not make a (time-inconsistent) commitment to achieve ex post inflation outcomes that average 2 percent under any and all circumstances. The same is true for the TPLT studies I cited earlier.
In these studies, the only way in which average inflation enters the policy rule is through the timing of liftoff itself. Yet in stochastic simulations of the FRB/US model under TPLT with a one-year memory that reverts to flexible inflation targeting after liftoff, inflation does average very close to 2 percent (see the table).