Keynesians do believe in an indirect link between the money supply and real GDP. They believe that expansionary monetary policy increases the supply of loanable funds available through the banking system, causing interest rates to fall. With lower interest rates, aggregate expenditures on investment and interest-sensitive consumption goods usually increase, causing real GDP to rise. Hence, monetary policy can affect real GDP indirectly.
Keynesians, however, remain skeptical about the effectiveness of monetary policy. They point out that expansionary monetary policies that increase the reserves of the banking system need not lead to a multiple expansion of the money supply because banks can simply refuse to lend out their excess reserves. Keynesians tend to place less emphasis on the effectiveness of monetary policy and more emphasis on the effectiveness of fiscal policy, which they regard as having a more direct effect on real GDP.
Adherents of monetarism, called monetarists, argue that the demand for money is stable and is not very sensitive to changes in the rate of interest. Hence, expansionary monetary policies only serve to create a surplus of money that households will quickly spend, thereby increasing aggregate demand. Unlike classical economists, monetarists acknowledge that the economy may not always be operating at the full employment level of real GDP. Thus, in the short-run, monetarists argue that expansionary monetary policies may increase the level of real GDP by increasing aggregate demand. However, in the long-run, when the economy is operating at the full employment level, monetarists argue that the classical quantity theory remains a good approximation of the link between the supply of money, the price level, and the real GDP—that is, in the long-run, expansionary monetary policies only lead to inflation and do not affect the level of real GDP.
Monetarists believe that persistent inflation (or deflation) is purely monetary phenomena brought about by persistent expansionary (or contractionary) monetary policies. They believe that the Fed should conduct monetary policy so as to keep the growth rate of the money supply fixed at a rate that is equal to the real growth rate of the economy over time. Thus, monetarists believe that monetary policy should serve to accommodate increases in real GDP without causing either inflation or deflation