Vice President Joe Biden recently got in trouble with the conservative media for claiming that cities like Camden, New Jersey and Flint, Michigan would see a rise in robberies, rapes and other violent crimes because they have had to cut police forces in half due to budget woes. Of course, Biden was arguing for Obama's new jobs bill, but I immediately thought of the more interesting data question.
The problem with determining the relationship between police force size and crime rates is "simultaneity bias." This term refers to the two events you wish to study tending to happen at the same time regardless of causality. In this case, governments tend to increase the police force when they notice a rise in crime or even in anticipation of this rise. Therefore, it is hard to see which comes first, the chicken (crime rates) or the egg (police force size).
One can overcome this problem by looking for individual events in which one factor changed for exogenous reasons--reasons outside the normal timing. There is an excellent summary of some of this research here:
The upshot is that cutting or raising the police force does have both an apparent short-term and an apparent long-term effect on crime. Nevertheless, the range of response varies significantly in the available research, some suggesting that a 50% drop in police force could mean only in the range of 10-15% rise in crime.
In a business context, simultaneity bias comes up quite a lot when looking in the rear-view mirror of one's business. For example, an increase in size of sales force is often accompanied by increase in marketing spend. This simultaneity confounds examining the effects of each investment. That is why I often recommend running experiments changing only one variable, or changing different variables in different territories or regions, before making such investments throughout the company.
Too bad Joe didn't find a source for his facts before he met the press. I hope he finds my blog.