Agreed. A city proper is definitely not an isolated social and economic "unit"; therefore limiting comparisons to it will not give you the information you really want to make decisions.

I agree, but sometimes 'metro area' is a bizarre distinction.

NYC's Metropolitan Division includes Ocean County (Jersey shore) but not Essex County (which includes Newark and all of the PATH trains).

The Metropolitan Statistical Area includes Pike County (not accessible by commuter rail from NYC) but not New Haven or Fairfield (which are).

https://en.wikipedia.org/wiki/New_York_metropolitan_area