The neighborhood a child grows up in has long-run effects on the child. As is discussed in class, children who grow up in better neighborhoods on average have higher income in adulthood. We also show that there is a large variation in neighborhood quality. For example, children from low-income families in many neighborhoods in the South and the Midwest have a lower probability of achieving high-income status in adulthood than those raised in the West Coast and the Great Plains. (a) Explain, briefly in words, why the positive correlation between neighborhood quality and adulthood outcome cannot be necessarily interpreted as the causal neighborhood effect, that is, better neighborhood causes better adulthood outcomes. What are the potential confounding factors for this causal interpretation?

(b) One way to isolate causal neighborhood effects from simple correlations is to focus on those who move between different neighborhoods during childhood. Suppose children who are born and raised in city A have an average income of $50,000, and those who are born and raised in city B have an average income $30,000. Suppose there is a group of children who were born in B migrated to A immediately after birth and grew up there, and their average income in adulthood is $40,000. What can we say about the causal neighborhood effect? Why this approach is better in isolating causal effect than the simple correlation? (c) A better way to estimate the causal neighborhood effect is to look at siblings within the same family. Take neighborhoods A and B in part b. as example. Suppose there is a group of households that move from B to A when their elder children were 8-years-old and their younger children were 5-years-old. In adulthood, the average income of the elder children are $45,000, while the average income of the younger children are $39,000. What is the causal neighborhood effect for spending one additional year of childhood in neighborhood A versus in neighborhood B? Why this approach is better than that in part b.?