For many years, and possibly continuing today, Law Office Management & Administration Report (LOMAR) published a cost-of-living index for about ten major US cities. As I recall it, the monthly table used prices in New York City on a certain date as the index of 100, and showed the other cities as a percentage of that index.
A legal department that studies the effective billing rates of its law firms could use the LOMAR cost index or a comparable one to see whether the rates of the various firms are comparable after adjusting their primary city’s cost of living. One difficulty with this match up is that larger firms provide services from lawyers in multiple cities. Still, cost-of-living indices serve as a tool to normalize effective billing rates.