Appointing Rogoff's (1985) conservative central banker improves welfare if the economy is subject to large contractionary shocks and the policy rate occasionally falls to the zero lower bound (ZLB). In an economy with occasionally binding ZLB constraints, the anticipation of future ZLB episodes creates a trade-off between inflation and output stabilization. As a consequence, inflation systematically falls below target even when the policy rate is above zero. A conservative central banker mitigates this deflationary bias away from the ZLB, improving allocations both at and away from the ZLB through expectations.