Levels vs. Percentages in Long-term Average Treatment Effects

Suppose that the Greater Gumville School District started a free book program back in 1976 that delivered free books to half of the children in Gumville. These books were dropped from a hot air balloon and landed randomly across town, so they had perfect balance between the children who got a book (treatment) and the children who did not (control).

Now Gumville wants to see the long-term impact of this experiment on a key statistic: did the kids with free books earn more money as adults? Because they know that rich kids tend to become rich adults, they decide to split their sample into high income and low income groups. The CATEs for each income group are below, listed in the absolute level increase (in $) in their annual salaries 30 year later:

childhood family income	CATE
high income	$6,000
low income	$3,000

You are scheduled to discuss your findings with Gumville's mayor. The mayor wants to know the best way to improve Gumville's per-capita-income (mean income). Of the options below, which one would you recommend based on the data provided?

Possible answers

The long-term CATE is larger for high-income children, so the government should offer books to high-income families.

The long-term CATE is smaller for low-income children, so the government should not offer books to low-income families.

The long-term CATE is positive for both income groups, so the government should offer books to all families, regardless of income.

Exercise

Levels vs. Percentages in Long-term Average Treatment Effects

Instructions

Possible answers