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).
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).