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When the Fed buys securities from banks, it pays the banks by putting the funds into checking accounts that banks have at the Fed. These checking account balances are reserves for banks. Banks are required to hold only a fraction of reserves against the checking account balances they issue to their customers. If banks sell $3 trillion of securities to the Fed, they can issue $30 trillion more in checking account balances of their customers (which they do by extending more loans to their customers). The Fed is worried about the inflationary potential of excess reserves of banks that it created by purchasing the securities from banks. By selling the securities back to banks, the banks’ reserves will be diminished and the inflationary potential reduced.
Moreover, roughly half of the Fed’s build-up in its balance sheet was the purchase of U.S. Treasuries and the other half was the purchase of mortgage backed securities. Currently, the Fed is holding $2.2 trillion in U.S. Treasuries and $1.6 trillion in MBS. The Fed can find willing buyers for either of these. For Treasuries, the market is deep and wide. For MBS, the Fed can sell if it offers at a low enough price. Banks will be willing to take MBS for steep discounts. Of course, doing this will not shrink the excess reserves of banks as much as selling Treasuries.
Finally, the Fed is raising its target federal funds rate. The problem here for the Fed is that the Fed pays banks interest on bank reserves. So, the more it raises rates the more its payments to banks rise. The Fed has adopted this policy of paying interest on bank reserves to control the extent to which banks create credit by lending into customer checking accounts and thereby, reducing their excess reserves.