Tuesday, October 24, 2017

Delong and Krugman make "math error", while falsely accusing Greg Mankiw of making math error!

Delong and Krugman are now claiming that the Furman ratio -- defined by Furman himself to be the ratio of wage gains from a corporate-income tax cut to a "static" revenue loss defined as rate change times corporate income -- is equal to one, rather than being greater than one (namely, equal to 1/(1-t)) as Greg Mankiw showed.

They go on to claim that Mankiw made this supposed mistake as a political ploy.

But it is they who are making a mistake, in "Dem's favor" (purely accidental, I'm sure).

Specifically, Krugman says that his blue rectangle is the wage gain from a small tax cut. I agree. But it is wrong to equate that to Furman's static revenue loss, because that loss is strictly smaller than his rectangle. As Jason Furman confirms, Delong makes the same mistake algebraically by equating Furman's static revenue loss to his term "(a)" plus term "(b)" when in fact the loss is just his term "(a)".


Krugman's blue rectangle, and DeLong's (a)+(b), cannot be Furman's static revenue loss, because they incorporate an equilibrium price change in the calculation of the corporate-income tax base. The static revenue loss from the corporate-income tax must, by Furman's definition of "static," hold corporate income constant.

[Unlike DeLong, Krugman does not actually use the word "static."  He says "direct" -- it is possible that he understands Furman's static and Krugman's direct to be different, and just failed to indicate the distinction to his readers.

It's fine if he prefers his blue rectangle to Furman's "static" revenue loss, but remember that by all accounts the blue rectangle is about $400b/year -- close to CEA's estimate of the wage gain.

In other words, when you change to the blue-rectangle definition of "static" you not only reduce the theoretical Furman ratio by a factor of (1-t), you also increase the static revenue number by the same factor.  The CEA's $4k per family is fixed.

This is like measuring things in yards or meters or fathoms -- the standard you choose does not change the answer, as long as you are consistent about the standard ... let's watch to see if they are.]

Later Krugman talks about yet another concept of revenue loss, namely the actual (a.k.a., dynamic) loss.  Mankiw had already explained the static-dynamic distinction to his readers.  This morning I tried to help Mr. Krugman with this by posting on his twitter:

What @delong is seeing is that "static" revenue loss is arbitrary:

the static revenue loss from a per-unit tax cut [what Krugman shows with his blue rectangle and calls "direct"]

is different from [Furman's] static loss from an ad valorem tax cut [what a corporate-income tax cut would be],

even when those cuts are scaled so that both have the same effects on revenue and the surplus of all parties.

That is why I use actual revenue loss.

The ratio between the two "static" concepts is the (1-t) factor that has Delong and Krugman so confused.

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