Proposals for deploying monetary policy to fight climate change and reduce inequality rely on the use of the nation state’s monetary authority to allocate capital to different parts of the economy. Against those proposals stands the publicly stated commitments of central bankers to avoid ‘allocating credit’ by implementing ‘market-neutral’ policies. A review of the financial empirics of central banks’ market operations shows a historically consistent pattern of using monetary authority to allocate debt and equity capital to different sectors of the economy at critical moments. Legal frameworks impose no effective constraints on that state-guidance of investment and, when necessary, the law of central banking actively facilitates capital allocation in ways that allow policymakers to fight deflation, provide emergency fiscal support, and rescue crisis-stricken parts of the financial sector. Against those empirics, commitments to avoid capital allocation appear as communication strategies rather than descriptions of the reality of central bank operations. Given the position of central banks as statutory public agencies, this creates various types of constitutional problems, notably concerning the protection of liberal property rights from government interference. Understanding these legal, market, and political dynamics provides a principled basis to debate reform proposals regarding the constitutional status and institutional functions of central banks in market economies responding to climate change and destructive inequality.