Because we are choosing \gamma (a constant) to minimize our objective (here, the objective of the central bank), commitment or discretionary does not matter, right?
AFAIK, an OSR is always a commitment rule.
Like the central bank chooses \gamma at period 0 for all t, and commits to it? If I may ask, how would that be different from choosing \gamma sequentially for each t?
Or osr is always a commitment rule because even if the CB chooses \gamma sequentially, it does not change from period to period, right? Thanks!
Yes, it’s commitment because the central bank uses a rule with a fixed parameter and does not reoptimize. Say there is government debt, which is predetermined. The government may have a temptation in the first period to inflate it away and then implement a stable, low inflation rate. We prevent the central bank from doing that here, because it is committed to the same rule in all periods.