Would a free banking system stabilize NGDP growth?

Since the 2008 financial crisis, a number of economists have suggested that central banks should follow an NGDP-targeting rule. Other researchers have argued that a free and unregulated banking system stabilizes NGDP growth as an unintended consequence. We explore this argument in a simple model of a free banking system. We find that a free banking system does indeed stabilize NGDP growth in response to aggregate demand shocks. However, we find that in response to aggregate supply shocks it stabilizes the inflation rate. An implication of this is that, unlike an NGDP-targeting central bank, a free banking system would not allow for disinflation or even deflation in response to a positive aggregate supply shock.