Figure slightly corrected

I should probably not be wasting time on this. But it seems as if practically the whole wing of more or less respectable conservative economists weighing in on this subject has made a basic algebraic/conceptual error. In itself, this error isn’t at all crucial to the policy debate. Other issues matter much more, notably taxes on monopoly profits, the fact that the US isn’t a small open economy, and the near-irrelevance of long-run equilibrium conclusions given the slow pace of adjustment imposed by imperfect integration of goods markets.

But arguably what we’re seeing here is something like the famous Excel programming error in the austerity debate: it’s not so much the substantive importance of the error as the evidence it provides of sloppy thinking, of conclusions adopted without checking because they promote a political agenda.

So the claim here is that the wage gains from a corporate tax cut exceed the revenue loss by a ratio that depends only on the initial tax rate, not at all on the degree to which capital can be substituted for labor, which in turn should (in this model) determine how much additional capital is drawn in by the tax cut. This feels wrong – and it is.

I continue to think that the clearest way to do this is with a simple marginal product of capital diagram. Here MPK is the marginal product of capital, aka the demand for capital, and r* is the world rate of return.

Photo

But I do a slight transformation of variables. With perfect capital mobility, and in the long run, we must have

r(1-t) = r*

where r is the domestic rate of return and t the corporate tax rate. But we can rearrange this to write

r = r* + tau

where tau = r*t/(1-t), and corresponds to the specific tax on capital – that is, the tax paid per unit of capital.

Doing this makes things linear: we can represent a small tax change as d tau , etc.

Now I’m ready for my closeup. In the figure, I show the small-open-economy-long-run (i.e., silly) results of a small corporate tax cut, which can be represented by the areas of the two shaded rectangles (the little white triangle is second-order and can be ignored). There is a direct revenue loss, which is also the wage gain, equal to the wide, short rectangle: K dtau. Some of this revenue loss is offset by taxes on the additional capital that comes in: dK tau.

How big these secondary effects are, and therefore the ratio of wage gains to revenue losses, obviously – obviously! – depends on how much capital comes in, which depends on the sensitivity of MPK to the quantity of capital – on the slope of the MPK curve. If it’s nearly vertical, as Brad notes, there is essentially no offset.

So the claim that only the initial tax rate matters can’t be right. How could anyone imagine otherwise? I guess it’s a case of a result too good to check.

As I said, none of this is what’s really wrong with Hassettnomics. But it’s a revealing moment.