Thursday, October 21, 2010

Tax increases as landscape perturbation?

Over at Felix Salmon's site, Justin Fox presents an interesting counter-argument to Greg Mankiw:
[T]here’s a really fascinating tale in [Sam Howe Verhovek’s Jet Age: The Comet, the 707, and the Race to Shrink the World] involving tax incentives. During the Korean War, Congress enacted an excess profits tax meant to keep military contractors from, well, profiteering. In its infinite wisdom, Congress defined excess profits as anything above what a company had been making during the peacetime years 1946-1949.

Boeing was mostly a military contractor in those days (Lockheed and Douglas dominated the passenger-plane business), and had made hardly any money at all from 1946 to 1949. So pretty much any profits it earned during the Korean conflict were by definition excess, and its effective tax rate in 1951 was going to be 82%. This was unfair and anti-business. If similar legislation were enacted today, you could expect U.S. Chamber of Commerce members to march on Washington and overturn cars on the streets.

It being 1951, Boeing instead sucked it up and let the tax incentives inadvertently devised by Congress steer it toward a bold and fateful decision. CEO Bill Allen decided, and was able to persuade Boeing’s board, to plow all those profits and more into developing what became the 707, a company-defining and world-changing innovation. Writes Verhovek:

Yes, it was a huge gamble, but for every dollar of the dice roll, only eighteen cents of it would have been Boeing’s to keep anyway. For Douglas and Lockheed, both in a much lower tax bracket, that was not so easy a call.

So that’s it! High tax rates—confiscatory tax rates—spur innovation! Well, at least once in a blue moon they do. Which is an indication that there might be some important stuff missing from the classic economists’ view of taxation, as summed up by Greg Mankiw a few weeks ago:

Economists understand that, absent externalities, the undistorted situation reflects an optimal allocation of resources. It is crucial to know how far we are from that optimum. To be somewhat nerdy about it, the deadweight loss of a tax rises with the square of the tax rate.

Somehow I don’t think that formula held true in Boeing’s case.

This leads me to wonder if this reminds anyone else of algorithms that locate superior optima by slightly perturbing fitness landscapes (processes closely related to simulated annealing). Mankiw complains that certain taxes distort the economic landscape, but if local optimization is an issue (as was apparently the case with Boeing), then mild distortion from time to time is likely to lead to a better performing economy.

For background, here's an excerpt from a post on landscapes. The subject was lab animals but the general principles remain the same:

And there you have the two great curses of the gradient searcher, numerous small local optima and long, circuitous paths. This particular combination -- multiple maxima and a single minimum associated with indirect search paths -- is typical of fluvial geomorphology and isn't something you'd generally expect to see in other areas, but the general problems of local optima and slow convergence show up all the time.

There are, fortunately, a few things we can do that might make the situation better (not what you'd call realistic things but we aren't exactly going for verisimilitude here). We could tilt the landscape a little or slightly bend or stretch or twist it, maybe add some ridges to some patches to give it that stylish corduroy look. (in other words, we could perturb the landscape.)

Hopefully, these changes shouldn't have much effect on the size and position of the of the major optima,* but they could have a big effect on the search behavior, changing the likelihood of ending up on a particular optima and the average time to optimize. That's the reason we perturb landscapes; we're hoping for something that will give us a better optima in a reasonable time. Of course, we have no way of knowing if our bending and twisting will make things better (it could just as easily make them worse), but if we do get good results from our search of the new landscape, we should get similar results from the corresponding point on the old landscape.


* I showed this post to an engineer who strongly suggested I add two caveats here. First, we are working under the assumption that the major optima are large relative to the changes produced by the perturbation. Second our interest in each optima is based on its size, not whether it is global. Going back to our original example, let's say that the largest peak on our original landscape was 1,005 feet tall and the second largest was 1,000 feet even but after perturbation their heights were reversed. If we were interested in finding the global max, this would be be a big deal, but to us the difference between the two landscapes is trivial.

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