In this sense inequality is, and should remain, the domain of fiscal measures designed and implemented by democratically elected governments. This is especially true in a monetary union where fighting inequality may imply redistribution across countries. Monetary authorities lack the knowledge, the tools and most importantly the political legitimacy to act directly on the distribution of income and wealth.
This is not to deny that the actions of central banks can carry distributional implications, or that these may be inconsistent with the preferences of the public. In thinking about this issue, it may be helpful to draw an analogy with other realms in which public policy makers systematically take decisions that are welfare-improving but have undesirable distributional implications.