Laffing Our Way To Transversal Trouble

Ok, CHB, this is what you get for that.

Over in the comments section of Jim Hamilton's excellent blog Econbrowser, Barry P asked this question:

Has anybody been able to come up with a Laffer curve for the US economy with actual, reliable, meaningful numbers attached? One guy I know swears that the maximum is at about a 90% tax rate, so we *must* be to the left of the maximum, but empirically I wouldn't know one way or another.

This topic happens to be related to my business (no, running CCM is just a hobby!). So I weighed in over there. Let me cross-post my comment there:

I'm pretty sure that the 90% number comes from Varian's Intermediate (undergrad) Micro text. But if you want to figure it out for yourself, just do the following:

1. Note that revenue is R(t) = tI(1-t), where t is the tax rate, 1-t is the take-home share, I is taxable income, which is a fctn of t if you believe in microeconomics (why this has come to be called "supply-side" rather than "utility-maximizing" is an interesting question for the intellectual historians). Of course, I am simplifying by assuming a flat tax rate. But I don't have time to write another dissertation right now.

2. Take logs and differentiate:

d ln R(t)/dt = (1/t) - I'(1-t)/I(1-t)

Note that the peak of the laffer curve occurs where this derivative equals zero. So we set

I'(1-t)/I(1-t) = 1/t.

Now multiply both sides by 1-t, and you get that the l curve peaks at t* such that

E = (1-t*)/t*,

where E is the elasticity of taxable income (E must be positive if you believe that there is an opportunity cost to revenue-generating activity). All serious arguments about the l curve's peak come down to figuring out what the value of E is, since

t* = 1/[1+E].

Now, it's only a slight caricature to say that the luskin-bush-novak-delay-kemp types seem to think that E = infinity, so that every single tax cut raises infinity. Sigh. More respectable folks think E may be as high as 3, in which case t*=0.25. For technical reasons, I think the evidence for that claim is totally dismissable. A more plausible long-run estimate is probably something in the neighborhood of 0.4, and perhaps as high as 0.6 or as low as 0.

In the 0.4 case, t*=1/[1.4]=5/7, or over 70%.

If I remember right, the 90% estimate is based on earlier estimates of the labor supply elasticity using hours worked, rather than taxable income, as the endogenous supply-side (!) variable.

In any case, t* is a hell of a lot higher than today's tax rates.

Bet you're sorry you asked, aren't you, CHB?