Bang for the Buck

January 13, 2009, 1:04 pm
Bang for the buck (wonkish)

Mark Thoma says he was thinking about thinking about this; I was actually thinking about it. Anyway, it’s true: the cost of an effective fiscal stimulus, in terms of adding to the government’s debt, can (and should) be much less than the headline cost.

Consider an increase in government spending; assume that the interest rate is fixed (a good assumption right now, because interest rates are up against the zero lower bound). Then textbook analysis says that if the stimulus is dG, the increase in GDP is 1/(1 - c(1-t)) where c is the marginal propensity to consume out of income and t is the marginal tax rate. Suppose c is 0.5 and t is 1/3; then the multiplier is 1.5, which is more or less the conventional wisdom right now.

But if $100 billion in spending raises GDP by $150 billion, and the marginal tax rate is 1/3, $50 billion of the spending comes back in additional revenue. So bang for the buck — increase in GDP per dollar of added debt — is 3, not 1.5. Since the main concern about stimulus is that it will add to government debt, it’s this bang for the buck measure, rather than the multiplier, that’s relevant. And 3 sounds a lot better than 1.5.

Take this a bit further: $150 billion is about 1 percent of GDP, which Romer and Bernstein say means a million jobs; so this says $50,000 per job, which is a much better number than the critics have been throwing around (plus many more workers with full-time rather than part-time jobs).

Bang for the buck also heightens the contrast between effective and ineffective stimulus policies. Stay with c = 0.5, t = 1/3, and look at the effects of a tax cut; the multiplier is 0.75, half that for public investment, but bang for the buck is 1, only 1/3 that for investment.

So thinking about how stimulus comes back via revenues is important.

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