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# Education and Income Distribution

 Timothy B. Lee's Blunder... Bastiat's Letters...

A college graduate at the 25th percentile makes \$730 per week, which is still 13.5 percent more than the median high school grad.

Here are the numbers, reproduced in tabular format.
75th percentile92810541548
50th percentile6437431043
25th percentile465516730

What Rampell is suggesting is that if the median student who had stopped after high school could have gone on to do as well as the 25th percentile of students who graduated college, then college would have been worth it. However, how likely is it that the median student who stopped after high school could have graduated college? College completion rates, once you get away from the top schools, are rather low. So a reasonable guess is that the median student who stopped after high school would have wound up somewhere in the bottom half of the "some college" distribution, and would not necessarily be earning more money.

I very much like the use of percentiles here. You can tell that the distribution of weekly earnings within education categories is approximately log-normal (the distance from the 50th to the 75th percentile is about twice the distance from the 25th to the 50th). This log-normality says that the average will be above the median and hence will not be a particularly helpful summary statistic.

Also note how large the variation is within education categories relative to the variation across categories.

Jerome Turner writes:

Do these numbers also count people who are unemployed in each group with a salary of \$0? Because if not, then I would expect the real expected values for those with no or some college to fall considerably. If not, then there is something interesting here.

writes:

Wouldn't women working part time effect the percentiles, making this less meaningful than it appears. Maybe college grad women are more like to only work part time.

E. Barandiaran writes:

Arnold, please let me know about studies of success/failure of kids trained to become professional players of high-income sports. Your point about completion of college is relevant to all projects that parents may have for their kids and it's not different from arguments about the probability of young people (with or without college) becoming entrepreneurs. If success were just a question of completing the chosen path, there would be no journalist writing about economics or anything else.

Ryan Vann writes:

Seems to me if one is trying to determine the worthiness of a degree today, they would discount degree holders from the distant past at a much higher rate than recent degree holders. If I understand it correctly, these median numbers include the salaries of all degree holders, regardless of age. A more useful matrix for degree seekers would include a) average graduation to hire periods, and b) average entry level wages.

mark writes:

Further to your observatin about the use of percentiles: the presentation also fosters a misleading impression. It's unlikely that the bottom quartile of the high school grads were as eligible for college as the top half of the high school graduate pool. But including them allows for a consistent series of improvements, left to right.

Let's be more realistic. It's likely that the college-attending pool is drawn from people who are much more like the top half of the high school graduate pool than the bottom half. So, knock out the bottom left cell, and re-cut the data in the second and third column into two, rather than three, rows to match the high school column. The argument will immediately refute itself as to the lower half of college attenders. Which, imo, is exactly the way the real world works.

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