How likely is it that children who grow up in very poor families go to college? How about children who grow up in very rich families?  If you think the chances of enrolling in college (or vocational school) are about the same for everyone, you should draw something like this: . If you think the odds are especially harsh for children from the poorest families, but higher for middle- and higher-income children, your drawing would instead look like this: . Or here is one for a situation in which chances level off after a certain income threshold: . Or for one that spikes or dips for the very richest.  When you’ve finished drawing, we’ll compare your line to the reality for children born in the early 1980s, based on research by a team of economists. We’ve started you off with one free point: 58 percent of children who were born in the early 1980s and raised in median-income families enrolled in higher education by the time they were 21. One way or another, your chart should go through that point.  Thanks for drawing. Here’s how you did:  Now let’s get to the reason for this exercise: Reality forms a remarkably straight line.  We asked you to take the trouble to draw a line because we think doing so makes you think carefully about the relationship, which, in turn, makes the realization that it's a line all the more astonishing.  In case you were wondering, here’s a chart showing the aggregate choices of other New York Times readers. (Remember, we gave you a free point at the 50th percentile, which explains why so many people were so accurate there.)  Moving up a single percentile on the family-income distribution makes enrolling in college about 0.7 percentage points more likely, up and down the distribution. Whether you’re a poor child getting a little bit less poor or a rich child getting slightly more rich, every step counts about the same.  Why would a child from the 99th percentile be more likely to go to college than a child from the 93rd? There seem to be several reasons. The rise in inequality in recent decades means that there is now quite a large income gap between the very rich and merely affluent: A tuition bill could scare off a family making $100,000 in a way it would not scare off one making $1 million. The very rich often send their children to different high schools, too, which may improve their chances of going to college. And the very rich are themselves more likely to have attended college.  Of course, the dollar differences between percentile ranks on our chart are not identical: About $2,400 in annual income separates the bottom two dots, while nearly $1 million separates the top two. So an extra dollar of income does have a greater effect on a poor child’s odds of attending college than on a rich child’s odds.  But even using ranks, we would have guessed, as many of you did, that the relationship would be more nuanced — that the very poor would have extreme difficulty sending their children to college and that the chances of going to college were basically set once a child reached upper-middle class.  Intriguingly, the relationship between parental-income rank and teen births is also quite linear, and some of the same forces are probably involved. So is the relationship between parental-income rank and a child’s future income rank.  Not every relevant relationship is linear, however. The chances that a student enrolls in the highest-quality colleges, as measured by their students’ future earnings, are a bit more complicated. These chances accelerate as incomes grow.  And enrolling is not everything. While rich children born around 1980 were nearly three times more likely to go to college than poor children, they were six times more likely to graduate, according to a study separate from the one we're showing here.  The real line above, from research by Raj Chetty, Nathaniel Hendren, Patrick Kline and Emmanuel Saez, is based on the earnings records of millions of families. Each dot – a single income percentile – represents nearly 100,000 children who were born in the early 1980s.
Draw your guess for every income level, then compare it with the actual data on college enrollment and the drawings of other readers.