Though I`ve been a computer science professor for a long time, and occasionally refer to my early career as a statistics professor, a little-known fact about me is that my PhD was in pure mathematics. Ah, those were days. I enjoy statistics and CS very much, but I do miss those days of pure intellectual pursuit without any application, in what I regard as a very elegant discipline.One of the mini-triumphs one can sometimes achive in pure math is the "soft analysis proof." Instead of long, intricate arguments with lots of inequalities, epsilons and deltas, with luck one might stumble onto a couple of insights and come up with a three-line proof that is very clean.In this posting, I want to apply this concept to the question of whether H-1Bs are underpaid. Lest you be misled by my somewhat lighthearted language above, let me say clearly that I`m dead serious here. Though I believe the statistical evidence, taken in its totality, shows clearly that H-1Bs are indeed on average paid less than comparable Americans (my Type I salary savings, with Type II, the age-related one, also being very important), people tend to be overwhelmed by the statistics. Even some professional analysts, astute people whom I highly respect such as Lindsay Lowell, seem not quite sure what to make of the data. In addition, statistics can be subtle, and many good number crunchers who`ve analyzed the H-1B issue who limited understanding of which numbers ought to be crunched and what the numbers mean, resulting in a lot of misleading analyses.Thus, some crisp, clean soft-analysis proofs should be useful. Here they are:Proof 1:Step A: H-1Bs, especially those being sponsored for green cards, tend to be rather immobile, not able to freely move around in the labor market.Step B: If one can`t move around in the labor market, one generally cannot get the best salary deal for oneself.Step C: Therefore, H-1Bs will typically be making less money than they ought to make, given their qualifications.QEDProof 2:Step A: Employers claim that they hire H-1Bs because they have special, hard-to-find skill sets, or are more talented than the American applicants.Step B: In the open market, employers would have to pay a premium for workers with hard-to-find skill sets, or of superior talent.Step C: According to the DOL PERM data, most tech employers pay their H-1Bs (actually green card sponsorees, most of them H-1Bs) only the official prevailing wage or just a tad higher.Step D: The official prevailing wage does not take into account special skill sets or high talent levels.Step E: Therefore, H-1Bs are typically paid less than their qualifications would command in the free market.QEDI`ve mentioned Proof 1 before. Indeed, I bring it up whenever an H-1B tells me, as for instance a former student of mine once did, that they are not underpaid. When I respond by asking whether they could make more money if they were to have full mobility in the labor market, they say "Of course," to which I reply, "Well, then, you`re underpaid after all." Please note, though, that this does not imply that I support proposals for fast-track green cards, which I`ve explained are just as injurious to U.S. citizens and permanent residents as H-1B.I brought up Proof 2 when I was interviewed by a team of researchers from the GAO a few weeks ago. They agreed that all of Steps A-D were valid, but it wasn`t clear whether they accepted Step E, the conclusion. We`ll find out when their report comes out (which won`t be soon).