Most monetary models make use of the quantity theory of money along with a Phillips curve. This implies a strong correlation between money growth and output in the short run (with little or no correlation between money and prices) and a strong long run correlation between money growth and inflation and inflation (with little or no correlation between money growth and output). The empirical evidence between money and inflation is very robust, but the long run money/output relationship is ambiguous at best. This paper attempts to explain this by looking at the impact of money growth on firm financing.
Stiver, John D., "Endogenous Financing and the Long Run Impact of Money Growth on Output and Prices" (2003). Economics Working Papers. 200336.