Getting a monetary stimulus to work
Models and Agents hints at the Fed increasing the interest rate it pays on banks' excess reserves. Is that a good idea? Given that banks seem to be building up those reserves instead of lending them out, paying more (or any) interest would just encourage them.
Instead, I suggest a small tweak in the other direction. Charge banks a negative interest rate to hold their reserves - even as small as 0.1%. While rational calculation implies that the difference between 0 and -0.1 is virtually no difference at all, the real world doesn't necessarily work that way.
Behavioural experiments clearly show a phenomenon called loss aversion where people are asymmetric in their valuation of profits and losses. They will typically give up twice as much to prevent a £1 loss as they would to make a £1 profit.
In this case, I would bet that loss aversion will kick in and encourage the banks to lend into the private sector instead of having their money drain away to the central bank.
Even if bank executives are entirely rational (and I'm making no comment on that) I suspect that shareholders are not, and stockmarket pressure might encourage the banks to lend. To the extent that tightness of credit is responsible for the recession, this should be a positive policy.
The negative interest suggestion is not an original proposal from me; I have seen something like it before. My addition is simply to point to the loss aversion motive as a mechanism by which this could work. Sorry not to credit it properly, but I can't recall whose idea this was (will update if I find it).
Two notes. One is that real interest rates are already negative (the UK has just cut its base rate from 1.5% to 1%, and inflation remains above either figure). However I believe that the nominal rate does make a psychological difference.
The second point is that banks, in theory, could request physical cash instead of holding central bank reserves. I don't think it's beyond the wit of the Fed to find a way of discouraging that. The security costs of holding cash are probably greater than 0.1% anyway, and no doubt some transaction fee could be imposed for withdrawing cash if necessary.