NHTSA has recommendations for lots of traffic factors... why not yellow lights?
Just Googled it and it turns out that there is a manual:
Fact: Yellow light time is set to optimize safety and traffic flow. Federal
guidelines recommend yellow lights last from 3 to 6 seconds. Local authorities
set the duration based on many factors including: traffic volume, speed, roadway
grade and intersection design.
Source: “Manual on Uniform Traffic Control Devices 2009 Edition.” FHWA. Nov. 30, 2010
Found this interesting information:
ANSWER: Analysis of data in the most comprehensive study to date (Safety Evaluation of Red-Light Cameras, FHWA HRT-05-048, April 2005) from seven jurisdictions (Baltimore; Charlotte; El Cajon, CA; Howard County, MD; Montgomery County, MD; San Diego; San Francisco) at 132 intersections using red-light cameras found:
A 25 percent decrease in total right-angle crashes;
A 16 percent decrease in injury right-angle crashes;
A 15 percent increase in total rear-end crashes; and
A 24 percent increase in injury rear-end crashes.
Net result is about a wash with a slight advantage to the cameras.