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See update below.

Matt Yglesias reminds me of something this morning. He says:

Federal spending cuts shrink the federal budget deficit and constitute a negative shock to aggregate demand. States have to balance their budgets, so the alternative to a lower level of spending would be a higher level of taxes. In [aggregate demand] terms, it’s basically going to be a wash either way. It’s the failure of congress to enact some kind of state/local bailout appropriation that’s forcing the anti-stimulative state level stuff.

This is based on the basic GDP formula: GDP = Consumption + Investment + Government Spending – Taxes + Net Exports. If state spending goes up, that represents an increase in GDP, but if it’s matched dollar for dollar with increased taxes, then it’s a wash. Ditto for spending cuts. It’s different for the federal government, of course, because the feds can raise spending without raising taxes. States can’t.

This comes up because I posted a chart a couple of days ago showing reductions in state spending over the past four years and commented that these reductions “wiped out nearly the entire effect of the federal stimulus package.” A reader emailed to say this was wrong, that they were actually neutral if they were accompanied by reductions in tax revenue. I realized he had a point, though this depends a lot on details, especially on whether state spending reductions have outpaced declines in tax revenue; whether states can increase their bond issues instead of raising taxes; and whether states have been dipping into their rainy day funds sufficiently. Still, it’s a good point, and I’d like to hear a response from some of the economists who have said otherwise. Is there something missing here that complicates the picture?

In any case, it’s true that the real failure is the federal government’s failure to bail out the states temporarily, which would have been one of the most effective stimulus measures possible. Surely states deserve a bailout at least as much as AIG and Citigroup did?

UPDATE: Robert Waldmann writes in comments that I’m wrong. Taxes don’t show up in the GDP identity. He’s right. So this whole post is screwed up and you should ignore it.

But…..there’s still something off here. Increasing federal spending is stimulative because you can do it without raising taxes. Likewise, decreasing it is anti-stimulative if taxes stay the same. But state spending generally has to match taxes, so raising or lowering state spending has no stimulative or anti-stimulative effect except at the margins. Right?

Or not right? Somebody help! It’s true that states have a certain amount of borrowing capacity (bond issues, spending down rainy-day funds, etc.), and also true that higher spending balanced by taxes on the rich might be mildly stimulative. But that’s a fairly small effect.

Anyway, for now, ignore all this. If someone provides some kind of definitive answer, I’ll link to it.

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