> adding credit to its member banks' deposits.

The Fed does not just add credits. It buys Treasuries on the open market in exchange for reserves. It is a balance sheet portfolio shift that leaves the assets of the private sector unchanged.

Now the question is, why would this operation "help extend credit". Banks would rather have the treasuries.

Indeed the only thing that affects private credit expansion is interest rates. Lower interest rates is what encourages private credit expansion and higher rates inhibit it. That is all that matters -- not monetary aggregates, but interest rates.

So why does the Fed do open market operations in which reserves are exchanged for treasuries? Three reasons, but they boil down to basic plumbing to keep the financial sector going. It's like adding oil to your car:

1. To satisfy financial sector demand for reserves, as we have an antiquated system in which banks need to lend reserves to each other as opposed to a more modern zero-reserve system (corridor). Many factors determine the financial sector demand for reserves, but whatever that demand happens to be, the Fed must meet it or there will be a liquidity crisis and banks will go bust. Thus there isn't much choice, if banks need a hundred million more of reserves, then that's what the Fed gives them. OTOH, if the Fed gives them too many reserves, then as banks will want to lend excess reserves in the overnight market, the overnight interest rate will fall to zero, as banks in aggregate are as unable to rid themselves of excess reserves. It's like a game of hot potato, if in aggregate the financial system needs 1 billion in reserves, but the Fed adds 1.1 billion, there will always be a bank with an extra hundred million. Wanting to earn interest on that hundred million, it will loan it to another bank, which will loan it to another bank, etc until the overnight rate is 0%. So even a little excess of reserves and the rate falls to zero. Even a little insufficiency of reserves and some bank can't make its payments. Clearly this is a fragile system. This unnecessary complexity is why our system is antiquated and other central banks moved to a corridor system that requires no reserves at all. Reserves are just the oil that greases the engine and prevents it from seizing, they are not the gasoline that causes it to run faster. The gasoline is the interest rate.

2. To satisfy private sector demand for paper money. When individuals withdraw paper money, the banks need to purchase that paper money with reserves, which means that reserves need to be added. When individuals deposit money in a bank, those bills are shredded and converted into reserves. Thus banks swap reserves for currency in response to private sector currency demand. As that process of adding/subtracting reserves requires buying/selling treasures, it is also a swap of treasuries for cash. Once again, we see why the reserves are unnecessary intermediate steps and why other nations moved to corridor systems to get rid of these inter-bank overnight lending markets.

3. In the last round of QE, the Fed purchased a lot of reserves in an attempt to drive down long dated yields as overnight yields were already at zero. Thus banks now find themselves with excess reserves. We have seen in 1 that this means the overnight rate was zero, but now the Fed wants to raise the rate without unwinding all these positions. Thus to support a positive interest rate, we now pay interest on reserves, converting reserves into an effective treasury bill. As the reserves pay a positive interest, banks will not try to get rid of them for zero interest and so the overnight rate will be positive even if there are excess reserves. That truly makes the operation of swapping bills for reserves a NULL OP because now you are swapping two interest bearing assets for each other.

None of this promotes or inhibits bank lending, it is just technical stuff to keep the plumbing working correctly in the inter-bank market. That's all reserves do. They are not a harbinger of hyperinflation. They are motor oil for our antiquated financial system. Economists did think that driving down long term yields via 3 would encourage lending, even though the amount that yields changed was miniscule and subject to a lot of debate, as longer term interest rates are the expected time path of short term rates, which are determined from the overnight rate, so you never know whether a long term rate falling is due to technical factors or to changes in the expected future overnight rates. Thus the ability of QE to drive down long term rates remains subject to interpretive ambiguities.