It doesn't scale like that, though. If the % of people with college degrees had increased by 6x, to 24%, would you expect 6/5 of students to have parents with a college degree?
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 children of degree holders got 4.7 times as many degrees as children of non-degree holders.
Which is the opposite of what the article assumes.
This is wrong. By this logic, "25% of people have degrees and 100% of degree holders have parents with degrees" is better than the 4%/20%, because it's only 4 times instead of 5 times. One of the better methods would be to calculate the "Bayes factor"(https://en.wikipedia.org/wiki/Bayes_factor) for estimating possibility of holding degree given the evidence of "parents holding degree". In this case, we need to know the parents degree percentage for both people in 1970 and 2020.
> That means that children of degree holders got 4.7 times as many degrees as children of non-degree holders.
That doesn't follow at all? You can't just divide the two percentages and get that conclusion?
In 2020 children of degree holders got twice as many degrees as children from non-degree holders; 66 vs 34. In 1970 children of degree holders got 1/4 as many degrees as children of non-degree holders; 20 vs 80.
>If you put it in absolute numbers. In 1970 among 1000 people 40 had degrees and of those 40 20% so 8 people had parents with degrees. On the other side you have 32 degree holders to 960 non degree holder parents, so just 3.3% of their kids got degrees.
>In 2020 among 1000 people 200 had degrees and of those 200 66% so 132 people had parents with degrees. On the other side you have 68 degree holders to 800 non degree holder parents, so just 8.5% of their kids got degrees.
You're confusing the total number of people who have degrees with new graduates. The only thing we can calculate with the numbers given is the ratio of new graduates who have parents with degrees to those who have parents without degrees.
> You're confusing the total number of people who have degrees with new graduates.
Yes you're right. The original data said new graduates. I got sidetracked by the formulation in your comment. I removed the false calculation.
> The only thing we can calculate with the numbers given is the ratio of new graduates who have parents with degrees to those who have parents without degrees.
Yea that ratio is 2 and 1/4 respectively? I don't even know how to put in words what we get by dividing the percentage of new grads with degree holding parents by the percentage of degree holders with college age children among the general population. Nothing useful?
- 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.
> If 4% of parents have degrees, something like 7% of the next generation has at least one parent with a degree.
Are you presuming marriage and degree-holding are independent variables? Although I presume there are fewer female degree holders, so perhaps it makes little difference.
“Something like 7%” is noticeably less than twice 4%, so no, I didn’t make that assumption. (I also explicitly stated that this was a back-of-the-napkin-quality analysis.)
It is noticeably closer to 8% than to 4% though. 7% would imply graduates exhibit a rather strong preference for marrying non-graduates over other graduates, which I find hard to believe.
At a time when only 4% of the population had graduate degrees, if 25% of married grad-degree-holders were married to another grad-degree-holder, that would constitute a large preference in favor of other graduates.
It doesn't work like that because you need to include the rates of people who have a degree and whos parent's don't.
CD = Child has a degree
PD = Parent has a degree
Your rates would be calculated with P(CD|PD)/P(CD|notPD) = [4x20/(4x80+96A)]/[4x80/(4x80+96(100-A))]
where A = Probability of parent having a degree and child not having degree
The 1970 stats are just saying that of the 4% of people who held a degree, 20% had parents who also had a degree (the 20% is a subset of the 4%, the 2 numbers are not directly comparable). This in fact means that graduates-with-degreed-parents were rarer than graduates without.
This situation has changed when we look at 2020. The overall number of degree holders is still relatively low compared to overall population (14%) but of this number a full 2/3rds now have degreed parents. The situation within this group has reversed.
% of degree holders as a population vs % parents of people with degrees is misleading - trend for getting degrees as a % of population is increasing and parents with degrees is lagging by around 10-20 years (ie. it will be 10-20 years before all the people that have degrees now can have children old enough to attain a degree).
So even if this probability reduces to 4 times more as likely, the % of population with degrees keeps increasing you'll see the pattern article is describing.
For simplicity let’s assume a static equilibrium (i.e. the rate of degree holders doesn’t change across cohorts and people don’t marry outside of their class).
Obviously in such case the probability to get a degree if your parents have a degree are 20% (in 1970) and 66% (in 2020).
Now let’s calculate the probabilities to get a degree if your parents don’t have a degree:
1970: 0.04*0.8/0.96 = 3.33%
2020: 0.14*0.34/0.86 = 5.53%
Even a “whooping” 1.7 increase doesn’t make much of a difference.
It's an oversimplification of course, but let's try another oversimplification just for argument's sake and to highlight the mechanism.
Let's say you are born without parents, and your parents get picked at random once you enter university (a completely fair system in that there is no bias involved).
If 4% of all "available" parents have a degree, your chance that you'll get at least one of those "assigned" to you is 7.84% (1 - ((1 - 0.04)^2)).
If 14% of all parents have one, this probability rises to 26.04% (1 - ((1 - 0.14)^2)).
I guess like plenty of bounded processes in nature, this is likely a sigmoid-ish function where close to zero you can approximate the function linearly. Yet yeah, there is some error.
