Hoo boy! Would somebody please give Greg Mankiw an envelope, so that he can do arithmetic on the back of it before he writes again?

Greg Mankiw:

Greg Mankiw: Are stimulus skeptics logically incoherent?: Paul Krugman writes: There’s now a lot of talk about the fact that U.S. corporations are sitting on a lot of cash, but not spending it. I don’t find that particularly puzzling: with huge excess capacity, why invest in building even more capacity. But almost everyone seems to agree that if we could somehow get businesses to spend some of that cash, it would create jobs. Which then raises the question: how can you believe that, and not also believe that if the U.S. government were to borrow some of the cash corporations aren’t spending, and spend it on, say, public works, this would also create jobs?... I have never seen a coherent objection to this line of argument. A coherent objection to this line of argument might be the following: If the government borrowed the money to spend, it would need to eventually pay the money back. That means higher future taxes, on top of the future tax increases that President Obama already will need to impose to finance his spending plans. Higher future taxes reduce demand today for at least a couple reasons. First, there are Ricardian effects to the extent that consumers take future taxes into account when calculating their permanent income. Second, those future taxes are not likely to be lump-sum but will be distortionary; it is plausible that at least some of those future tax distortions may adversely affect the incentive to invest today. That is, businesses may be reluctant to invest in an economy that they expect to be distorted by historically unprecedented levels of taxation in the future. The more the government borrows, the higher taxes will need to go, the more distorted the future economy will be, and the less attractive is investment today...

Hmmm...

So Mankiw is saying that if the federal government spends an extra $1 on infrastructure today, and taxes the present value of $1 in the future to repay the debt, the excess burden of those taxes is so large as to make it optimal for consumers and businesses today to reduce their spending by $1 or more today...

To assess whether this argument is coherent or not, we need three things: an estimate of the marginal excess burden of future taxes, an estimate of the effect of lower future productivity on the desired future capital stock, and an estimate of how investment today varies with the desired capital stock.

The usual estimate of the marginal excess burden of future taxes that I use is between $0.25 and $0.50. Let's take $0.50. So each $1 of infrastructure spending now lowers after-tax future incomes in total by a present value of $1.50--amortizing over the long-term future, by $0.05 for each future year, of which 1/3 is a fall in productivity and 2/3 is the rise in tax revenues collected.

Under the (remarkably unrealistic and false) assumption of full Ricardian equivalence, consumption spending drops now: permanent after-tax income is lower by $0.05 a year, and so consumption spending this year is lower by $0.05.

The usual estimate of the effect of lower future productivity on capital is that a 1% fall in productivity produces a 1.5% fall in the desired capital stock. Since the capital stock is at most 4 times annual output, that means that the fall in the desired capital stock is 6 times the fall in productivity--so the fall in the desired long-term future capital stock of $0.10.

With standard rates of depreciation, investment in any one year is at most one-tenth of the desired capital stock. So the fall in desired investment from a $1 infrastructure boost thought likely to create a $0.50 fall in productivity which induces a $0.10 fall in the desired capital stock would be $0.01.

For these parameter values, a $1 boost to infrastructure spending crowds-out $0.01 of private investment spending and $0.05 of private consumption spending, leaving $0.94 of stimulus.

To claim that the excess burden of taxation is not $0.50 on the dollar but $20 on the dollar, or that a 1% fall in productivity produces not a 1.5% fall but a 30% fall in the desired capital stock can be called many things.

"Coherent" is not one of them.

I call this one for Paul Krugman: 6-0, 6-0, 6-0.