I know there are lots of gravity models in economics that take as an input distance between countries. My understanding is distance is typically coded based on the distance between capital cities, either in $L_2$ norm or great-circle distance. Most countries are small relative to the distances between them, and so maybe it doesn't matter much how they code the center of these countries for purposes of trade. But in my application I'm looking at US states, and many states are large enough that the internal placement of the location for calculating distances between states makes a difference. Additionally, state capitals are often not the economic center of the state (Carson City, NV and Albany, NY come to mind) nor the geographic center (North Folk, CA is hours away from Sacramento, CA), so I don't know of obvious choices.
Are there any standard choices I should know about here?
As a resource to others here are some sample data:
- Average Latitude and Longitude for US States
- US Census Centers of Population
- List of geographic centers of each U.S. state
Would anyone provide a list of the economic center of each state?