Should central banks care about inequality? To address this question, we extend a standard model of time inconsistency in monetary policy to allow for heterogeneity. As in the standard analysis, lack of policy commitment leads to a bias towards socially excessive inflation. But the novel result is that, in the presence of heterogeneity, the bias can be offset by assigning the central bank a mandate under which agents with higher nominal wealth are given a higher relative weight than under the social welfare function. In other words, society should choose a central banker that is less egalitarian than itself, a result reminiscent of Rogoff’s “conservative central banker”. Our analysis underscores that including a concern for redistribution in the central bank’s mandate can enhance policy credibility, but the details can be unexpected and should reflect the role of the mandate in overcoming policy distortions.