You have probably seen the recent article by Alan Schwarz on a working paper by Joseph Price and Justin Wolfers on racial bias by officials in the NBA. Skip Sauer has some comments here. Dave Berri has some comments here. One of the problems that has been raised is that Price and Wolfers did not examine individual officials and their calls. Instead, they examined officiating crews and the calls of the crews (that issue is raised in this article). Others are concerned that the authors didn't control for the race of the player being fouled (see Brian's post below).
Econometric questions aside and assuming that Price and Wolfers have identified something that truly exists, we must ask the following: why referees would let their biases affect their calls? Orley Ashenfelter developed a model of arbitrator behavior that might be useful in understanding referee behavior.
Arbitration is a dispute resolution system in which a third party, the arbitrator, hears arguments by two disputants and renders a binding decision. The two sides are bound to honor that decision. How do arbitrators get chosen to hear particular cases? They are chosen like people are chosen for juries. Disputants are given a list of potential arbitrators and each takes turns striking names from the list. In the end, perceptibly biased arbitrators will get struck from hearing case. Because of the lucrative nature of being an arbitrator, arbitrators will have it in the back of their minds that their decisions in particular cases will be used in future selection processes. So the arbitrator will want to appear to be unbiased, at least relative to other arbitrators, in the future.
In black and white cases, the arbitrator has an incentive to make the right call. Going the other way is evidence of bias and increases the chances that the person will get struck from future lists. In the very gray cases, the decision would basically come down to a mental coin flip. But if an arbitrator is more likely to side with, say, an employer in a wage case with an employee, that is evidence of bias towards the employer and the arbitrator is more likely to be struck from future cases and to be struck by employers. Therefore, such arbitrators will have difficulty finding gainful employment as arbitrators in the future.
So it would seem to be with referees - especially in the technology age where multitudes of television cameras and other technology monitor officials constantly. Referees make calls in black and white cases and the gray cases. In such cases, if a referee makes the wrong call consistently, then he appears biased. In the gray cases, if the calls go against players of another race consistently, the referee appears biased. If so, then the referee will have difficulty finding gainful employment as referees. Moreover, referees are smart people and would know that they are officiating in a fishbowl. If bias does affect calls, it must largely occur in the subconscious mind of referees and it shouldn't appear very often.