Well, there is the government's FHWA study. There are a couple mechanisms.

The first is that sometimes running a red light is safer. People normally don't think about red light cameras and thus their impact on behavior only comes into play when after the driver is already in a position to get caught. This leads to people making unsafe stops when it would be otherwise more advisable to just go through the light. The link above shows an increase in rear-end collisions.

More relevant to the original point is how the city reacts. The city council enjoys money and shortens yellow light timings or blocks lengthening of yellow light timings, causing more crashes.