As a followup to this post and this one, I think we finally have this sorted out. Some people were arguing that the Fed's lending to financial institutions during the financial crisis was subsidizing those financial institutions. But the bulk of lending was through the Term Auction Facility (TAF), and it appears that, if there was any subsidizing, that it had to occur through TAF. But, we have a record of all the loans made through TAF in the excel spreadsheet here. As you can see, the best deal that anyone was getting on a TAF loan was 0.20%, and all those loans occurred on January 2, 2009. Otherwise, the best deal was 0.25%, and no one could make a profit on that, given that the interest rate on reserves was 0.25% at the time, and the fed funds rate was lower than that, as were short T-bill rates.
So, was the Fed doing the appropriate thing? Maybe reading Lombard Street will help us? Fat chance. As Andolfatto can tell us, there's not a lot in Bagehot to go on. Bagehot tells us that the lender of last resort should "lend freely and at a penalty rate" during a crisis, which if anything seems like a contradiction. If you really want the banks to take the liquidity injection, you should not be penalizing them. Of course it makes sense that the Fed should not set up lending facilities which allow banks to simply make arbitrage profits, but that does not appear to have been happening during the financial crisis. Further, if the Fed was giving the posted collateral the correct haircuts, it was not taking on undue risk, and certainly the Fed does not seem to have come out on the short end of the stick on its lending. I have some too-big-to-fail moral hazard concerns, but that is about it.
The key question with these lending programs, as with any lender-of-last-resort lending, is why the central bank should not just buy the assets, instead of extending loans and taking the assets as collateral. I think the basic logic has to be that the central bank could buy the assets at their market price, but the market price is viewed as being inefficiently low. Instead, the central bank extends a loan for more than the market price of the collateral, and essentially takes the assets at a high price, temporarily. But, alternatively, the central bank could make an offer to buy quantity x of asset y at price p, and see how many offers come at that price. If total offers exceed x, then the central bank uses a lottery to choose.
Questions like this come up when we try to model how collateral is used in financial transactions. Indeed, I have never seen a satisfactory model of collateral. Basically, you have to explain why it is that someone who wants to borrow, and has an asset that they can use as collateral, does not just sell the asset. One can see how this works with mortgage lending, but in general it seems a difficult problem.