How Big a Stimulus Did We Need?

Paul Krugman writes:

But the stimulus wasn't nearly big enough to restore full employment -- as I warned from the beginning. And it was set up to fade out in the second half of 2010.

I've heard this complaint from a number of commentators, and it always surprises me.  Did anyone think we were going to get a stimulus big enough to restore full employment?

How much unemployment reduction you get for a given amount of stimulus spending is, obviously, at best an imperfect estimation. But let's take the CBO's estimates as representing a rough consensus of those who favor stimulus:  for our $800 billion, we got a reduction of 0.7 to 1.8 percentage points.

Full employment is perhaps 4.5-5%.  If we assume that stimulus benefits increase linearly, that means we would have needed a stimulus of, on the low end, $2.5 trillion.  On the high end, it would have been in the $4-5 trillion range.

I'm going to go out on a limb and say that even if Republicans had simply magically disappeared, the government still would not have been able to borrow and spend $2.5 trillion in any reasonably short time frame, much less $4-5 trillion.  The political support for that level of government expansion simply wasn't there among Democrats, much less their constituents.  Even if they had found the political will, I doubt that government institutions could have effectively channeled that much new spending.  And assuming away those two problems, would lenders really have been available to fund 18% deficits at rock-bottom rates?

The CBO's numbers imply that even if we'd gotten a much larger stimulus--$1.3 trillion, say--unemployment would at best be something under 9%.  The economy would still be underperforming. 

If course, linearly-scaling stimulus benefits is a pretty heroic assumption.  Maybe they build on each other, so that the next $800 billion delivers twice the unemployment reduction of the first.  On the other hand, maybe stimulus has diminishing marginal returns, and the next $800 billion delivers half the stimulative benefits; given that most things eventually exhibit diminishing returns, given that we hopefully did the best projects first, and given all the institutional bottlenecks on the spending, I find this at least as plausible as the notion of increasing returns to stimulus.

Which raises an interesting question:  what if Keynesian stimulus works, but no one can ever actually afford to do it, short of something like World War II, where the government can tap into a patriotic outpouring of national savings by issuing bonds with negative real yields.