He acknowledged the flaws in the data collection in the blog posts.
Anyway, this particular flaw doesn't quite work itself out the way you describe. If you want to do out the numbers precisely, you'd multiply out the probability that a person enters a particular occupation given their degree by the lifetime earnings of that occupation, and then sum over all possible occupations.
So say (made up numbers) a CS major has an 80% chance of being a computer programmer ($1.5M), a 10% chance of being a quant ($5M), a 5% chance of being a successful entrepreneur ($20M), and a 5% chance of being a housewife ($0). The expected value of the degree would be .8 * 1.5M + .1 * 5M + .05 * 20M + 0.
Then to find the baseline you'd do the same for lifetime earnings and occupation probabilities of someone who didn't go to college. If they had a 10% chance of being a computer programmer, a 30% chance of being a barrista ($500k), a 40% chance of being a construction worker ($800k), and a 20% chance of being a househusband, that'd be .1 * 1.5M + .3 * 500 + .4 * 800 + 0. Multiply out and subtract to find the value of the degree.
Remember that statistics is about making statements about groups, not statements about any particular individual. That illustrates another pitfall of the data: the question a prospective student really wants answered is "how much will the degree be worth to me". There's at least one study out there that suggests the answer is "zero": all the difference in lifetime earnings is due to correlation and not causation. People succeed because of inborn traits like intelligence, perseverance, and the ability to delay gratitude, all of which also result in someone being able to get into an elite college and pick a challenging major. But controlling for that effect opens up a whole other can of worms, one that you could bill your client another few thousand for writing about. ;-)
You're right, I simplified for the example and assumed only one canonical job for each major. However, that doesn't undermine my criticisms. You'd still have to multiply each job by the amount that the degree helps you get that job.
So it's probably pretty hard to become a quant without a degree, so multiply that by some high number like 95%, but it's really easy to become an entrepreneur without a degree, so multiply that by some low number like 20%.
You're also right about the relevant question being "what is a degree worth to me?" That makes prediction even harder because the value of the degree is largely going to depend on the person's opportunity cost of going to school. Consider Mark Zuckerberg, Facebook was the opportunity cost of his getting a degree, which would make the degree's "value" be several billion dollars negative.
Anyway, this particular flaw doesn't quite work itself out the way you describe. If you want to do out the numbers precisely, you'd multiply out the probability that a person enters a particular occupation given their degree by the lifetime earnings of that occupation, and then sum over all possible occupations.
So say (made up numbers) a CS major has an 80% chance of being a computer programmer ($1.5M), a 10% chance of being a quant ($5M), a 5% chance of being a successful entrepreneur ($20M), and a 5% chance of being a housewife ($0). The expected value of the degree would be .8 * 1.5M + .1 * 5M + .05 * 20M + 0.
Then to find the baseline you'd do the same for lifetime earnings and occupation probabilities of someone who didn't go to college. If they had a 10% chance of being a computer programmer, a 30% chance of being a barrista ($500k), a 40% chance of being a construction worker ($800k), and a 20% chance of being a househusband, that'd be .1 * 1.5M + .3 * 500 + .4 * 800 + 0. Multiply out and subtract to find the value of the degree.
Remember that statistics is about making statements about groups, not statements about any particular individual. That illustrates another pitfall of the data: the question a prospective student really wants answered is "how much will the degree be worth to me". There's at least one study out there that suggests the answer is "zero": all the difference in lifetime earnings is due to correlation and not causation. People succeed because of inborn traits like intelligence, perseverance, and the ability to delay gratitude, all of which also result in someone being able to get into an elite college and pick a challenging major. But controlling for that effect opens up a whole other can of worms, one that you could bill your client another few thousand for writing about. ;-)