Our last important result concerned the reputation variables - one for academic reputation based on surveys of law faculty and one for lawyer/judge reputation based on a survey of lawyers and judges. U.S. News doesn't include much detail about the surveys (things like response rates would be nice), but I've filled out the academic one a few times and so know a little about it. Essentially each person who gets a survey is asked to rate all the law schools from 1-5.
We found that changes in academic reputation were associated with higher median LSAT scores for the top quartile but not for the other three quartiles.
An important question about the reputational variables is whether they are cause or effect. It seems implausible that very many law professors (or lawyers or judges) have even moderately well-informed views of the quality of more than a handful of law schools. Prof. Jeffrey Stake at Indiana, in a paper in the same symposium as ours, found evidence of an "echo" effect in reputation.
If you look at reputation across time, there is quite a bit of stability at the top and a lot of movement (especially in lawyer/judge reputation) at the bottom. (I have some nice graphs to post but haven't figured out how to do it yet. As soon as I do, I will.)