Stimulus Errors

I usually enjoy reading Karl Smith over at Modeled Behavior but I think he makes a mistake here:

I agree with Matt Yglesias so often that sometimes it seems pointless for me to bother blogging... Matt echoes Noah Smith and Paul Krugman’s criticism of John Taylor

Per Smith, “Lucas, Sargent, etc. thought that government purchases wouldn’t raise GDP” which is the reverse of Taylor’s conclusion. ARRA didn’t boost GDP because a temporary boost in government purchases won’t boost GDP, and ARRA didn’t boost GDP because it didn’t lead to an increase in government purchases are incompatible positions. They’re just both criticisms of ARRA and therefore perhaps emotionally satisfying to people who dislike Barack Obama.
I actually think Taylor is making an important substantive point here. It’s that in practice fiscal stimulus doesn’t raise GDP because in practice fiscal stimulus amounts to giving money to people, who then save it – just as Lucas, Sargent etc, said they would.

Moreover, if you are using “old” models with rational expectations or Ricardian equivalence this shouldn’t happen. Matt’s basic model that if you give people more money, they will do more stuff with it should hold.

Admittedly, this is my basic model as well and Taylor’s evidence cuts against it.
If you had already accepted that its simply not possible to ramp up direct federal expenditures in a timely manner then this is an important critique. In practice fiscal stimulus means giving somebody money: tax payers, COBRA recipients, the unemployed, state and local governments, etc.

If all of these folks are simply going to save the money then fiscal stimulus doesn’t work.

Here's my comment on Smith's post:

Lucas doesn't have a point at all... not in the classical sense or the modern sense. And what you're both assuming is a situation of full employment -- which is really the only time fiscal stimulus wouldn't raise GDP. 

But fiscal stimulus can raise GDP in all models when we're not at full employment because, like unemployment transfer payments, fiscal stimulus tends to give money to people who can't readily save it. Fiscal stimulus takes some of the slack, underemployed, unemployed workers and puts them to work, thereby they're able to pay off debt and consume. That raises GDP. If you think it doesn't then you're assuming that fiscal stimulus and unemployment payments are going to independently wealthy people who will just save the money.

In reality, this is much more likely to happen with tax cuts and it's why the multiplier for the stimulative effects of tax cuts needs to be discounted heavily. A large portion of tax cuts will go to people who are already working, who will just 'save' their tax cuts. 

Finally, even in the old models with Ricardian equivalence, a fiscal stimulus should have stimulative effects on GDP, because the perfectly rational consumer will know that the stimulus is a one-time thing, funded by longer-term government debt. So the consumer can raise his consumption by the difference between the two.