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On income being correlated with good outcomes: Francesconi and Heckman (https://onlinelibrary.wiley.com/doi/abs/10.1111/ecoj.12388) assert that it’s mostly due to confounding with SES. I haven’t dug into the citations, but here’s the key bit:

Carneiro and Heckman (2003) and Cunha et al. (2006) present evidence that child cognitive and non-cognitive skills diverge at early ages across families with different levels of permanent income during childhood.19 Levels of permanent income are highly correlated with family background factors such as parental education and maternal ability, which, when statistically controlled for, largely eliminate the gaps across income classes. The literature sometimes interprets this conditioning as reflecting parenting and parental investments, but it could arise from any or all of the correlates of permanent income associated with parental preferences and skills.

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