Why does the Fed have difficulty controlling the money supply?

The Fed can control precisely the monetary base, which consists of money held by commercial banks in their reserve accounts, and notes and coins circulating in the economy. The monetary base is multiplied up to become the money supply by the decisions of individuals to hold money in checking accounts.  How large this multiplier effect is depends on the ratio of deposits to currency  holdings (that is the ratio of the fraction of money people hold in their bank accounts to the fraction they hoild as cash). Because this ratio varies over time, the Fed cannot directly control the money supply. A good example of the difficulties faced by the Fed comes from the banking pankings of the Great Depression. Bank closures reduced the deposit-currency ratio as individuals held (a lot) mnore of their money as cash. This caused a sharp decline in the money supply even though the monetary base was rising.