Earlier quoted context omitted.
Not exactly like that, but close. As % of people with college degrees approaches 100%, all students will have parents with a college degree, so it will approach 5/5. The logic in the parent comment still stands.
What you care about is how much more likely a person with parents who had degrees is to have a degree over one who doesn't. In 1970 4% of people had degrees and 20% of degree holders had parents with degrees. That means that children of degree holders got 5 times as many degrees as children of non-degree holders. In 2020 14% of people have degrees and 66% of degree holders have parents with degrees. That means that c…
- If 4% of parents have degrees, something like 7% of the next generation has at least one parent with a degree. Because children have two parents, and only one of those two parents needs to have a degree. So the correct number to compare 20% against is ~7%, not 4%.
- Suppose a child of a degree-holder is 3 times as likely to become an economics PhD as a child of no degree-holders. Then, if 7% of children have a degree-holding parent, you would expect (7 * 3) / (7 * 3 + 93) = 21 / 114 = ~18.4% of economics PhDs to have a degree-holding parent, not 21%. If 25% of children have a degree-holding parent, you'd expect (25 * 3) / (25 * 3 + 75) = 75 / 150 = 50% of economics PhDs to have a degree-holding parent, not 75%.
Eyeballing the last few numbers, it does look like the value of having a degree-holding parent may have increased significantly, from a ~3.3x multiplier to almost 6x. But the error bars on this back-of-the-napkin analysis are pretty wide.