Borrowers pay depositors, it will alway be so

Scott Sumner trying to figure out what accounts for the Fed balance sheet.

There is a sense in which the size of the balance sheet can be viewed as demand determined, especially if the Fed is targeting inflation at 2%. But that's only true if the Fed doesn't pay interest on reserves. Without interest on reserves (IOR), the Fed's balance sheet would be about 7% of GDP, slightly above the demand for currency.

The IOER comes from the IOEL, interest on excessive loans match interest on excessive deposits, within the 5% NGDP variance we need. 

Look at the law, Scott, the law determines the algebra.   Net the interest rate flows, the Fed rarely carries losses or gains forward, hence on net; the Fed carries no risk, it is all placed on Treasury, the sole borrower on the sheet.  On net, the Fed pays its salaries and rent, not much more.

If the Fed did not pay IOER, there would be an automatic reduction in lending rates to Congress, which is completely unrelated to general inflation. Since the Fed is limited to borrowing only from Treasury, the Fed is always off equilibrium, it is always chasing an equilibrium point off to the side of NGDP because the Fed never measures excess borrowings of the member bank, hence the Fed is working with half a brain.