Apologies for the long message. I got this plan to work, but encountered one major stumbling block.
Implicit in my design was assigning place points to metropolitan areas. The Place Point GISJOIN is keyed to the “place” geographic level. It took me a while to figure out (really to remember, as I have been in this situation in the past) that Census places are not necessarily contiguous with higher level Census geographies. Places can and do cross county and state boundaries. It was pretty hard to find files that assigned county or metropolitan area codes to place codes. I found a file that assigned state, county and ANSI place codes, but I ended up using this file which contains state, county, cbsa, and place codes (assigning all at the place level). I am sure this is not ideal because the lists and assignments are before 2010 (the year for which I used the Place Points and Tract Centers of Population). I used the county and
place codes to re-make GISJOIN at the place level and match to the Place Point file. A number of small CDPs did not match between the files. I just let this go as my interest is in larger metros.
I couldn’t figure out how to download population tabulations from NHGIS with GISJOIN included. I have done this in the past and found some old files that had GISJOIN, but I couldn’t remember how I had done it. Using a NHGIS file I had downloaded for a previous project with only place, total population and GISJOIN, I merged in place total population.
With state, county and cbsa codes now matched to the place points, I assigned places to metros (using state and county metro definitions). I selected the place point for the largest place in a metro. I then merged in the Tract Center of Population on metro area. Then I used the stata geodist command to measure spherical distance from each tract center of population to the lat/lon from Place Points (that I calculated with ArcGIS). After adjusting the distance measurements for metro size (both area and population), tract distance from city center (my selected place point) appeared in my models with the expected magnitude and sign, yay!
I ended up not using the stata gis utilities and I am sure there are other, easier ways to do this whole process.
I couldn’t have gotten this done without your comments Jonathan, I really appreciate it.