The closest a nation has to equity is notes and coin, and of course, QE, which is analogous to a redeemable preference share.
I reckon - and both Taleb and Buiter are making noises along these lines - that the solution to the credit crunch lies in a debt/equity swap on a cosmic scale. Just not equity as we know it, Jim.
It could be a sort of a once and for all Jubilee, if you think about it. "Any economic unit can emit money. The serious problem is to get it accepted" Hyman Minsky