Chief Justice Roberts and many other members of the federal judiciary say that federal judges' salaries are far too low. Scott Baker wondered what difference salary makes and put together an empirical study. Scott Baker, Should We Pay Federal Circuit Judges More?, 88 B.U. L. Rev. 63 (2008).
The obvious way to do such a study would be to take a group of high-paid federal judges and compare them with a group of low-paid federal judges. But, gee, they're all on the same pay scale (more or less).
So Prof. Baker instead calculated the opportunity cost for each court of appeals judge, comparing the salary received as a judge with the salary the judge would have received had he or she been a large firm partner in the same region over the same years. (He used law firm partners as the comparison group, even if the judge was in government or academia before appointment to the bench.)
How does that work? For example, a judge who is in Minneapolis and was appointed at age 40 would have a larger opportunity cost than a judge in Minneapolis who was appointed at 50, because he or she would forgo more years of the private sector salary. A judge in New York City would have a higher opportunity cost than a judge the same age in Seattle, because big firm partners in New York make more money than big firm partners here.
So now Baker could sort judges by how much they gave up to take the judicial salary. Now, how did he measure judicial performance? He looked at number of opinions, number of dissents, length of time to produce an opinion. For influence, he looked at number of citations by other circuits. A proxy for ideological bias was the ratio of citations to out-of-circuit opinions (i.e., persuasive precedent) by judges of the same party versus the other.
After a bunch of regression analyses, Prof. Baker concluded (as stated in his abstract):
This Article finds that low judicial salaries do not affect the nature of votes in controversial cases, the speed of controversial case disposition, the frequency of citation to outside circuit authority, or the strength of opinions as measured by citation counts. This Article does find, however, that low salaries lead to slightly fewer dissents. This effect, while statistically significant, is nonetheless practically trivial. In short, this Article finds that judicial pay is largely irrelevant to the performance of the circuit courts.