Tuesday, October 14, 2014

Effect sizes: an often overlooked issue

This is a post by Joseph

Brad DeLong makes an argument that fits very well with a long running discussion that Mark and I have had.  Just because there is a known relation, doesn't mean that the effect size of the elements can be ignored.  So, the existence of the Laffer curve is pretty much certain, but the exact inflection point where the curve shift from more revenue to less revenue is very, very important. 

Brad Delong compares current arguments for infrastructure to the Laffer curve:
In a world where the real rate at which the U.S. Treasury can borrow for ten years is 0.3%/year and in which the tax rate t is about 30%, infrastructure investment fails to be self-financing only when the comprehensive rate of return is less than 1%/year.

Now you can make that argument that properly-understood the comprehensive rate of return is less than 1%/year. Indeed, Ludger Schuknecht made such arguments last Saturday. He did so eloquently and thoughtfully in the deep windowless basements of the Marriott Marquis Hotel in Washington DC at a panel I was on.

But Mankiw doesn’t make that argument.

And because he doesn’t, he doesn’t let his readers see that there is a huge and asymmetric difference between:
my argument that tax-rate cuts are not (usually) self financing, which at a tax rate t=30% requires only that α < 2.33; and:

his argument that infrastructure investment is not self-financing, which at a tax rate t=30% requires that ρ < 1%/year.

To argue that α < 2.33 is very easy. To argue that ρ < 1%/year is very hard. So how does Mankiw pretend to his readers that the two arguments are equivalent? By offering his readers no numbers at all.
This principle is broadly applicable to all sorts of arguments that come up on this blog.  For example, getting rid of a marginal bad teacher is probably efficient.  But constantly churning teachers might shift the efficiency function to a different place on the curve. 

So realistic estimates of parameters are critical but also they can also be hard.  How do you really tell the Comprehensive rate of return of infrastructure?  Is it different in Detroit versus San Francisco?  Can it be reliably estimated in advance or only known historically.

But it does lead to better arguments when transparent estimates (that can be discussed or tested) are placed out where they can be evaluated. 


  1. Your blog has an issue: if I write a comment and then log in, the comment is lost.

  2. I wanted to say that you've likely thought this through in longer form but there's a reason for "comprehensive" rates. You say Detroit but why focus on that? What does Detroit mean? Is the M1 line being constructed a benefit for the Metro area or some neighborhoods or some other subset? There are alway scale effects and these can be manipulated to over or understate the impact of investment.

  3. Jonanthan: you make a good point. I was using a fairly vague comparison of "growing" versus "shrinking" metro areas, but as you dig into the weeds this gets even more complex. I don't necessarily want to argue about specific thresholds and where we are, just to point out that the general shape of the distribution has to be considered in the context of plausible values for the parameters.