**Note to Self: Greg Mankiw Providing Backup for Kevin Hassett Department: Larry Summers** One last time on who benefits from corporate tax cuts: "Mankiw’s blog is a fine bit of economic pedagogy...

...It asks students to gauge the impact of a corporate rate reduction on wages in a so called “Ramsey” model or equivalently in a small fully open economy, with perfect capital mobility. Even with these assumptions, he does not get answers in the range of the CEA’s estimates. As a device for motivating students to learn how to manipulate oversimplified academic models, Mankiw’s blog is terrific as one would expect from an outstanding economist and one of the leading textbook authors of his generation...

I differ. I think that the Greg we have here is not primarily (1) Greg-teaching-students-about-public-finance-issues Greg but rather (2) Greg-going-as-far-as-he-believes-he-can-to-be-helpful-to-the-Republican-Party Greg. And I wish we had (1) Greg instead.

Why do I think this? First of all, as John Maynard Keynes wrote in his obituary for Alfred Marshall:

The study of economics does not seem to require any specialised gifts of an unusually high order.... Yet good, or even competent, economists are the rarest of birds. An easy subject, at which very few excel! The paradox finds its explanation, perhaps, in that the master-economist must... reach a high standard in several different directions... be mathematician, historian, statesman, philosopher... understand symbols and speak in words... contemplate the particular in terms of the general, and touch abstract and concrete in the same flight of thought...

And the most important element of this combination needed to be a good economist is to choose the right model for one's analysis.

Greg begins his analysis of the effects of a corporate tax cut on the U.S. with "an open economy...". In so beginning he has already served his readers ill. The U.S. is not a small open economy. You choose a model that applies, not a model that does not apply.

The second most important element of this combination is that one chooses a complete model and does a complete analysis. Corporate tax cuts are cut, yes. But then what? There is a government budget constraint there somewhere—or if there isn't, that is a very important element of the situation. Is government spending cut? Is it cut now or in the future? Are other taxes raised? Which taxes? And when? Kevin Hassett called the Tax Policy Center's analysis “scientifically indefensible” and “fiction” in large part because they *had* done a complete analysis, filling in the parts of the tax cut framework that were missing with what seemed to them to be reasonable assumptions. But Mankiw doesn't do a complete analysis. The corporate tax rate is cut. Full stop.

Third, there is a math error in Greg's presentation. When in a small open economy you cut the corporate tax rate t by an infinitesimal amount dt, that tax rate cut has three first-order effects on tax revenue. It (a) reduces how much revenue is collected from each dollar of tax base, (b) reduces the tax base by reducing the pre-tax rate of profit, and (c) raises the tax base by encouraging more investment. The "static" revenue-loss calculation ignores term (c). The first-order "static" revenue loss is then:

$-𝒇'(k)kdt + \left(\frac{𝒇'(k)t}{(1-t)}\right)kdt$

But Greg misses term (b), and so he calculates the revenue loss as:

$-𝒇'(k)kdt$

This error inflates Mankiw's calculations by a factor of 1/(1-t).

He thinks that he is demonstrating that the gain in wages is greater than the "static" revenue loss because the cut in taxes calls forth extra investment and higher productivity. But you can recognize that this interpretation is wrong by considering the case in which more capital is useless and unproductive. In that case, note that Mankiw's math still claims that wages grow by a factor 1/(1-t) bigger than the corporate revenue loss *even when the tax cut does not induce any extra investment at all*.

This is the kind of math error that can happen to anyone—and does happen to me, especially in a blog post. We are all bears of very little brain, and none of us as smart individually as we are smart collectively, especially in that form of thinking that is manipulating systems of symbols.

More serious are the other two flaws. One models the behavior one wants to see students adopt. (1) Choosing an appropriate model, and (2) performing an analysis with a complete model are both very important things to, well, model. I want (1) Greg-teaching-students-about-public-finance-issues Greg, not (2) Greg-going-as-far-as-he-believes-he-can-to-be-helpful-to-the-Republican-Party Greg.