We study monetary policy under dierent central bank constitutions when the labor-market insiders set the nominal wage so that the outsiders are involuntarily unemployed. If the insiders are in the ma jority, the representative insider will be the median voter. We show that an independent central bank, if controlled by the median voter, does not produce a systematic in ation bias, albeit equilibrium employment is too low from a social welfare point of view. A dependent central bank, in contrast, is forced by the government to collect seigniorage and to take the government's re-election prospects into account. The predictions of our theory are consistent with the evidence that central bank independence decreases average inflation and inflation variability, but does not affect employment variability.