The theory of an endogenous money supply is based on the idea that money is generated in an economy based on the needs of that economy. The banking systems then adapt the short term interest rates to ensure stability. An endogenous money supply allows the forces of supply and demand to determine to progression of the economy rather than external forces such as a banking system like the Federal Reserve.
I believe that the United States functions on an endogenous money supply for the most part. The Federal Reserve artificially manipulates the reserve as needed to stimulate economic growth or stability- at least that is the premise.