Here is a very interesting Krugman analysis of this problem. It ends up with the Fed owning all T-bills, and, in Anil Kashyap’s opinion (and mine; there’s not enough cash to cover all the required collateral) the Repo market collapsing. I do see an alternative path. Krugman writes:
What we normally say in a liquidity trap is that the Fed is keeping short-term interest rates at zero, which is as low as they can go because below that cash dominates bonds. And the Fed achieves that zero rate by being willing to buy short-term government debt whenever the rate threatens to rise above zero.
That’s a fair description, but perhaps it is a description rather than a binding equilibrium response; the Fed doesn’t have to do that and why should they if it ends in ruin? (There’s the further tricky question of whether Krugman’s assumption is holding expected fiscal policy constant.)
T-Bills are almost like money today, especially with low short rates. Think of higher default risk as like a Gesellian stamp tax on T-Bills. One equilibrium is that people spend more on durables as they shift out of liquidity, which has now been partially taxed. Another equilibrium is that everyone rushes into the truly safe asset, namely cash, and the T-Bills do truly disappear. Or heterogeneous agents may do a bit of both.
It would seem to boil down to the third derivative on the utility function. Still, empirically cash does not soak up all the periodic shifts out of other risky assets (e.g., commercial paper), so why should it soak up all the shifts out of T-Bills?
More concretely, in a liquidity trap model (which I reject, by the way, but that’s another story) an increase in default risk could have some expansionary properties.
Addendum: Brad DeLong offers comment.