The Fed and GDP

GDP is equal to money times its turnover or velocity, which is called the "equation of exchange" as developed by Irving Fisher (Nominal GDP = MV).

M is comprised of the monetary base (currency plus reserves) times the money multiplier (m). V is the velocity of money.

According to Barron's definitions: 1. Monetary Base:

Sum of reserve accounts of financial institutions at Federal Reserve Banks, currency in circulation (currency held by the public and in the vaults of depository institutions). The major source of the adjusted monetary base is Federal Reserve Credit. The monetary base, as the ultimate source of the nation's Money Supply, is controllable, at least to some degree, by Federal Reserve Monetary Policy. The adjusted monetary base data is compiled weekly by the Federal Reserve Board and the Federal Reserve Bank of St. Louis, and is adjusted seasonally.

                                               2. The money multiplier:

Relationship between the Monetary Base and the Money Supply. The multiplier explains why the money supply as excess reserves are added to the banking system. When a bank makes a loan, it creates money, because part of the loan becomes a new deposit.
In practical terms, banks put money in circulation by extending credit. Assume that a bank makes a $100,000 loan and reserves 10% or $10,000 to meet its Reserve Requirement, depositing $90,000 in the borrower's bank. The borrower's bank sets aside a reserve of $9,000, leaving $81,000 available for another loan and another deposit. If carried to its logical extension, the original $100,000 loan would expand into more than $500,000 in deposits and $400,000 in new loans.

And V, velocity of money, equals how frequently the money supply is used.

Clearly the Fed and the Government can influence part of the supply but can not influence all of it, the multiplier or the velocity.

So why do they say they can influence GDP and, when they try, why does anyone pay attention?