We derive the optimal monetary policy in a sticky price model when
private agents follow adaptive learning. We show that this slight departure
from rationality has important implications for policy design. The central
bank faces a new intertemporal trade-off, not present under rational expectations:
it is optimal to forego stabilizing the economy in the present in
order to facilitate private sector learning and thus ease the future intratemporal
inflation-output gap trade-offs. The policy recommendation is robust:
the welfare loss entailed by the optimal policy under learning if the private
sector actually has rational expectations is much smaller than if the central
bank mistakenly assumes rational expectations when in fact agents are
learning.