We have all heard of the German, Hungarian, and other hyperinflations studied by Cagan (1956) and subsequently by many others. The price level explodes upward in his model, as it did in practice. As long as the Reichsbank, or other central banks, allowed the money stock to accelerate, the price level accelerated. Indeed, this is the point of Cagan's model, and its success in explaining hyperinflations is evidence that there was not a bubble in these cases.
What's in a bubble?
The first lesson