Law Professors and Veblen Salaries; Irrational?

At my school all salaries are a matter of public record. If you want to know who makes what, you can look it up. I did a few years ago and then I realized how little I knew. For example, all but a few get paid all year but for most only a 9 month salary is reported. In addition, there is an unreported bump associated with various chairs and professorships. The public record actually tells you very little about actual salary. (Why those actual salaries are not reported and how they are determined is too complicated to be explained, or so I have been told.)

All of this leads to a behavioral economics type of phenomenon. Recently I discussed the reported v. unreported salary matter with a couple of colleagues.  Both expressed concern that their public salaries were lower than their actual salaries. More importantly, they might be earning more than a colleague but it would not appear that way to the public.

In both cases the reasoning was that students and others might make inferences about their competence and relative competence based on salary. Moreover this halo effect could carry over to evaluations. Something like this: "Gee,  don't have any idea what professor Jones is talking about but he must be great because she makes $30,000 more than Professor Smith." When you think about it, it is no different from the institutional authority law professors and law review editors worship. You know, "OMG, she must be good, she went to Yale" or "The article must be great because the author went to Yale and thanks Professor Big Cheese for his comments on an earlier draft." Of course, we all know the Professor Big Cheese just shared a cab with the professor and said "Good luck in your job." So, the validity of institution authority must vary on whether it cuts for you against you

But the most interesting thing is this. Clearly some professors would accept less  in order to have their salaries reported as more. Presumably in a negotiation with the Dean, he or she  could say: "Bill your salary next year will be $100k but if you will take $98K I will report it as $150K. In fact, a shrewd Dean could auction off higher reported salaries. The bids would in the the form of a reduced actual salary. This is a great cost saving strategy for the Dean with budget problems.

Is this irrational? I am not sure. If a higher reported salary leads to better evaluations and a better reputation across the profession, maybe in the long run  high reported salaries have the same impact as high prices on Veblen goods -- it makes the product even more attractive.