We consider the optimality of various institutional arrangements for agencies that conduct macro-prudential regulation and monetary policy. When a central bank is in charge of price and financial stability, a new time inconsistency problem may arise. Ex-ante, the central bank chooses the socially optimal level of inflation. Ex-post, however, the central bank chooses inflation above the social optimum to reduce the real value of private debt. This inefficient outcome arises when macro-prudential policies cannot be adjusted as frequently as monetary. Importantly, this result arises even when the central bank is politically independent. We then consider the role of political pressures in the spirit of Barro and Gordon (1983). We show that if either the macro-prudential regulator or the central bank (or both) are not politically independent, separation of price and financial stability objectives does not deliver the social optimum.