Following the 2003 NASCAR season, officials changed the rules and created the Race for the Cup or Race for the Championship. What this entails is that for the last 10 races of the year are essentially a playoff where everyone can race, but only the top ten are allowed to win the overall championship. This changed racers' incentives. For instance, if you were out of the top ten, you might as well go for broke (i.e. win the race) even if this might result in you being in an accident and not finishing the race.
Sure enough, that is exactly what appears to have happened. For those racers out of the top ten in races 16-36 (I looked forward ten as well since those out of the top ten presumably also have the incentive to take chances to get into the top ten before the cut off), the likelihood of the racing ending as a result of an accident has increased.
This was found with the regression:
Accident = Intercept + B (Out of Top Ten Dummy Variable * New Rules Dummy Variable)
Variable Coefficient Standard Error t-Stat P value
|X Variable 1||0.024846||0.008633||2.878087||0.00402|
So while this is just one look and a very preliminary one at that, it does appear that when the racers were rewarded more for higher finishes, they took more chances to get the higher place. Which of course is exactly what an economist (finance person) would predict.
Hopefully I will find some time and put this into a real paper, but at least I will be using it in class.
Thanks to James Kane and Anthony Dimario for the data collection on this and to Jonathan Godbey for helpful suggestions!