If public finances get out of hand, the central bank can come under overwhelming pressure to jump to fiscal policy’s rescue and, in so doing, can undermine its primary objective of price stability. This lesson is not just derived from theoretical models, it has been evidenced time and time again in the past.
A particularly good example from history is the Latin monetary union comprising Italy, France, Belgium, Switzerland and Greece. Even before the treaty of union came into force, Italy’s debt exploded owing to the war with Austria.