This paper shows that if unemployment (or some other real variable) fo
llows a dynamic autoregressive process, the government can still achie
ve its precommitment outcome in monetary policy, by offering the centr
al banker a linear inflation contract, where the penalty for increment
al inflation depends positively on lagged unemployment. This note ther
efore offers an extension of recent results of Walsh to the case of pe
rsistence in real economic variables such as output or unemployment.