In 1997, Bill Shughart, Bob Tollison, and I published a piece in Economic Inquiry showing a statistically significant divergence of hit batters in the American League over the National League after the adoption of the Designated Hitter in the AL. We attributed the divergence to the reduction in personal risk faced by AL pitchers in nailing batters -- a "moral hazard" argument. A couple of thoughtful comments questioned the statistical validity of the results and moral hazard as a viable explanation. We offered a bit more evidence in rebuttal, while the original idea and the debate it spawned spilled over into a couple of Business Week columns.
The high level of aggregation (annual data) in our study made it impossible to take account of many of the specific influences on hitting batters (a recent home run, retaliation, ...). John-Charles Bradbury and Doug Drinen of the University of the South authored a piece last year that used disaggregated, pitch-by-pitch. They conclude
the lack of fear of retaliation among AL pitchers explained between 60-80% of the difference in hit batters between leagues
Details are available at Bradbury's Sabernomics website along with other intersting studies. They also have a game-by-game study for a larger time frame and a discussion of the narrowing of the difference in the 1990s.
Although Bradbury and Drinen provide powerful evidence that the moral hazard explanation is at important to the hit batter difference, the answer strikes many economists as unsatisfactory. Generally, moral hazard arises only when monitoring an agent's behavior is difficult or no mechanism exist for restraining the behavior. Since MLB managers have a pretty good idea when a pitcher is hitting batters on purpose or not and means to discipline rogue behavior, how can it be moral hazard?
I would suggest a simple "economic" answer as to why it is moral hazard -- managers weigh the cost and benefits of stamping out individual behavior that is detrimental to the team. Hitting batters, even in the AL, is a rare event and, in most cases, has little impact on team performance. On the other hand, the individual pitcher may derive quite a bit of satisfaction from doing it and be upset of actively restrained. In this way, MLB managers treat the moral hazard as an annoynance but not worth the trouble of stamping out completely -- not too disimilar to business managers who don't try to stamp out all personal use of copy machines or phones as long as it imposes little expense.