The data structure doesn’t help with causal inference.

Reading the abstract, it looks like the authors are trying to make a causal argument: people are more likely to improve their economic standing because they moved to a walkable city.

OP pointed out that this could be due to self-selection of people with the potential of upward mobility to walkable cities. This would lead to spurious correlation between economic mobility and walkability. That is, a third variable (a potential candidate, awareness of climate change) could explain both upward mobility (usually, climate change awareness correlates with education level) and economic mobility (education correlates with higher wages).