The history also seems to be telling us that the recovery from (ii) is slow: the problem was that certain financial assets were grossly overvalued, and once they come back to reality there is an overall shortage of financial assets as savings vehicles or of safe financial assets that induces a shortfall of aggregate demand. A return to full employment requires that something happen to boost the economy's supply of financial assets as savings vehicles or of safe financial assets--whichever was the cause of the downturn in the first place. Only then will households and businesses be comfortable spending at a full-employment pace.
You exlain your Millian view very clearly and not (quite) for the millionth time. I remain unconvinced.
It is clear that an excess of assets which were perceived to be risky and a shortage of safe assets was a key problem (maybe the key problem) in late 2008 and very early 2009. This was shown by the tanking of the prices of assets which turned out to be risky, the TIPS spread, lots of things. Those patterns are gone.
In particular, common stock is very risky (in the short run) and yet stock market indices are at high levels. The problem just isn't the same problem it was 2 years ago.
I think the current problem is either irrational underestimates of future growth (an incorrect guess on the mean not a correct guess on the variance of returns), multiple equilibria and coordination on a bad equilibrium, or just the liquidity trap.
My first claim is that too little safe assets doesn't fit the data. The medium and long term TIPS rate isn't negative. Medium term nominal rates are well above zero. That's what should matter for investment.
My second is that firms aren't investing because they have spare capacity and their managers expect them to continue to have spare capacity -- so why invest. It could be that the managers are just wrong, roughly trend chasing. That they don't believe that the sysem is stable around a random walk *or* a trend and don't forecast normal growth. If we allow irrational pessimism (what is the antonym of exuberance intuberance esuberance ???) then we can decide not to reconcile that cliam about expectations with the implications of the model (when did either of use believe in rational expectations?).
Second just the liquidity trap. It could be that the only problem is that the inflation rate is only 1% so real interest rates can't be low enough to make firms invest even though they have spare capacity. The fact that low inflation is consistent with full employment doesn't mean that low inflation isn't consistent with high unemployment. The fact that moderate inflation has not proven to be consistent with a path with prolonged high unemployment doesn't mean that low inflation isn't consistent with such a path.
So the story is we have spare capacity so we need negative real interest rates and we can't get there.
Finally coordination. It is possible that with very low inflation, it only makes sense for firms to invest if other firms are investing (you know like implementation cycles or Cooper-John models or there are tons of them). This is really the same as explanation 2. Again I claim there is a bad equilibrium that wouldn't exist if we had 4% inflation in 2007.
None of these is a story about a shortage of safe assets. Each imply that the solution is expansionary fiscal policy (as does your model).