It's more which part of the country than urban vs. rural. The median household income in Mass. is $76,000 whereas the median household income in Miss. is $41,754
Income inequality was similar in the two states.
https://www.cbpp.org/press/press-releas ... ions-worst
http://www.wbur.org/bostonomix/2018/07/ ... usetts-epi
I think that you'll be hard pressed to find a significant difference in social mobility through the US. Certainly nothing that will put some states in line with Germany or Denmark.
And that's because the fundamentals regarding secondary education, health care and the social safety net are more similar across the US than they are to other OECD nations.
You raise an interesting point about rural social mobility though. Here's an interesting study on varying social mobility in rural areas.
https://www.brookings.edu/research/rura ... untryside/
the authors find that counties that had the highest rates of upward mobility also had (among other things):
higher out-migration rates, particularly among youth and young adults,
higher quality K-12 education,
improved measures of family stability,
and stronger local labor markets.
And their recommendations:
The paper lists three arenas that seem particularly promising for bolstering opportunity in rural America.
]nvest in human capital development. Improving K-12 quality in distressed areas will improve young residents’ life prospects and preparedness for adulthood.
Ensure rural communities are equipped with basic 21st century infrastructure. Technology such as broadband will enable families and schools in these areas to better connect to distant economies and opportunities.
Invest in family planning. Rural residents are less likely to have access to affordable and quality health care, which makes intentional parenthood all the more difficult.