So let me essay my argument, which relies much more lightly on the liquidity trap, and a lot more heavily on the problem of long-term unemployment. Let me say in advance that I'm not necessarily endorsing this argument, only saying that I think it's a plausible way to look at our current problems. Of course, I'm sure some very smart economists will hasten to point out where I'm going wrong.
The heart of the argument is this: prolonged unemployment is basically the worst economic event that can happen to a person in America. Losing your home, declaring bankruptcy, or having your life savings stolen are awful. But as long as you are working, those things can be replaced--maybe never as good as they were, but certainly adequately. A lengthy spell of unemployment robs you of social status. It steals your piece of mind. It embezzles your accumulated skills and contacts. It beats your sense of self-worth into a bloody pulp. And like all crime victims, it leaves you permanently afraid in a way that you never were before. And that's if you get a job. Except that one of the worst parts of being unemployed for a long time is that it gets harder to get another job with each passing month.
It's also terrible for the economy. Economic output equals the labor supply times labor productivity. Long term unemployment reduces both the labor supply, and the human capital of the workforce that remains. That means lower GDP. And since Americans are not going to let other Americans starve, that means the rest of us have to get along with less, too.
That means that even if a stimulus doesn't produce anything of much lasting value, it may be good for the economy in the long term, if it interrupts this vicious cycle of human capital decay. Arguably, this is what happened in World War II: we stopped worrying about the future of the economy, and started worrying about Hitler. With labor so tight, employers had to hire anyone who could hold a hammer. Four years later, those people were rehabilitated as workers: they didn't have employers looking askance at their long employment gap, and they had gained (or at least preserved) some skills. The Forgotten Man had been rediscovered.
My argument dovetails with Krugman's to this extent: this doesn't work unless the economy has an enormous amount of slack. In normal times, there are tradeoffs: when the government does more of something, someone else has to do less of something else--now, or in the future. But in times of great slack and high unemployment, its as if we're taking a metaphorical sledgehammer to our human capital stock. There is very little short-term tradeoff, because so many resources are unemployed. And the long term tradeoff (we eventually have to pay off the debt we incur to do this) may also go away, if we're keeping our labor supply larger and more productive.
But even if this story is true, that doesn't mean that we can necessarily reproduce it--at least, not deliberately. The labor depreciation story suggests that stimulus should be tilted towards direct provision of jobs. But the government cannot simply add millions of people to its permanent payrolls--and a temporary government job may send the same signal to employers that unemployment does. Perhaps you can only get the right kind of stimulus from an exogenous event (to be fair, the example that Krugman gives is one such: changes in ozone regulations).
What we'd really like is to find an exogenous event that doesn't kill anyone. Unfortunately, I'm not aware of any non-existential threats that can mobilize an economy the way we geared up to fight the Axis.
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