In a recent paper, Jennifer Brown of Cal-Berkeley finds that when Tiger is player, the average score in tournaments increases by almost a stroke (0.8) for the field and slightly (0.2) for even the higher-skill golfers. See "Quitters Never Win: The (Adverse) Incentive Effects of Competing with Superstars."
The result, especially for the field as a whole, lines up with Sherwin Rosen's tournament theory work. It is demotivating to be forced into competition with someone out of your league. My main criticism of Brown's paper is that, like many studies on golf, course difficulty is not taken into account as well as it might be. When the variable of interest is score, using finer-tuned estimates of course difficulty matters a lot. Given the existence of slope ratings and course ratings, improving the estimates in this regard would not be all that difficult