No doubt, that has something to do with the energy boom in North Dakota, but also with the earlier tendency of young people with something on the ball in North Dakota to move to higher paying cities like Minneapolis and Denver. Until recently, North Dakota had one of the oldest populations in the country due to outflow of young career-seekers. (In Chetty's study, the younger generation are assigned to where they lived in 1996, not where they live now).
Chetty downplays the role of race for vague reasons, but in general his data suggests that income mobility is higher among white populations, as we see in Europe. Regression toward the mean can explain much of the above map of income mobility, with mostly white areas regressing toward a higher mean than heavily black areas.
A sizable methodological problem has to do with Chetty using national income percentiles, which are massively influenced by the cost of living, especially the cost of buying a home. If you grew up in New York City and stayed there, for example, you'd better be upwardly mobile relative to national average income if you want to continue to live indoors. Thus, more than a few people have left higher paying jobs in NYC for lower paying jobs (but a better standard of living) in Charlotte.
Conversely, the Eastern state with the strongest chance of a poor child getting well-to-do is West Virginia. Let me guess that most of them didn't do it by continuing to live in West Virginia, but by moving to somewhere like suburban Washington DC. Or Charlotte.
Tax and other Correlations with Intergenerational Mobility
Local Expenditure 0.215 (0.076)
State Tax 0.199 (0.141)
State EITC Rate 0.231 (0.109)
Student Expenditure 0.251 (0.094)
High-school Dropout Rate -0.639 (0.064)
Score 0.557 (0.086)
College Return -0.276 (0.137)
College Tuition -0.003 (0.060)
Colleges per capita 0.102 (0.042)
Inc. at p75 - Inc. at p25 -0.475 (0.089)
Share of Income of Top 1% 0.178 (0.068)
Share Black -0.605 (0.065)
Black Isolation -0.513 (0.065)
Segregation of Poverty -0.405 (0.063)
Migration Inflow -0.184 (0.075)
Share Foreign Born -0.016 (0.060)
Migration Outflow -0.098 (0.069)
Mean Household Income 0.109 (0.075)
Income Growth Rate 0.561 (0.066)
Share Manufacturing -0.260 (0.081)
Trade Shock -0.274 (0.124)
Social Capital Index 0.617 (0.091)
Religiosity 0.510 (0.087)
Crime Rate -0.326 (0.101)
Share Single Moms -0.763 (0.078)
Share Single Moms (kids of married) -0.652 (0.094)
Divorce Rate -0.688 (0.108)
Teen birth Rate -0.550 (0.091)
The correlations fit in well with Charles Murray's recent book Coming Apart (not to mention The Bell Curve): social capital first, then the nearly tautological income growth rate, then test scores, then religiosity, then a big drop down to school expenditures in fifth place. The highest correlation with a region's poor staying poor is share of single moms.