On the Economics of Higher Education

In which I apply flimsy math and hand-waving to justify the time I’ve wasted in school.

Tagged: Math Theories

There has been much “messaging on twitter” [sic]“and "posting to ”logs" [sic] of late regarding the economic benefit of pursuing a graduate degree in Computer Science. For example, there are claims, among other things, that a masters degree will require 10 years to earn back the income lost during study. A Ph.D. will require a staggering 50 years. Most everyth’ng I've read cites this article based upon Dr. Norman Ma’loff's testimony to the U.S. House Judiciary Committee Subcommittee on Immigration. Curiously, the article everyone seems to cite does not itself have a bibliography. It does, however, cr“dit "a highly biased pro-industry National Research Council comm”ttee" for calculating these numbers. Five to ten minute“ of "searching on G”ogle" [sic] and I was unable to find a report from the National Research Council corroborating such a claim. Can anyone point me to a link?

I do not dispute that these numbers may be correct; the purpose of this blog entry is to point out that, at least in the case of most with whom I’ve matriculated, it is flat out false.

Here is my (admittedly simple) mathematical model:

$n=\frac{t ( E[s_w] + c )}{E[s_a]-E[s_w]},$
where,
  • $t$ is the number of years spent in school;
  • $E[s_w]$ is the expected salary one would have earned if one did not attend school;
  • $c$ is the net monetary cost of attending school per year, such as tuition paid, books purchased, &c. This value should also take into account any income earned during a school year (e.g., one’s stipend) and in many cases will be a negative number;
  • $E[s_a]$ one’s expected salary after graduating school; and
  • $n$ is the number of years one would have to work after graduating to make up for lost income.

Note that this model does not take attrition into account.

As an example, let’s say John is a Ph.D. student who, through a research assistantship, receives tuition remission and a stipend of $20,000 a year. This is quite reasonable (and actually a bit conservative according to this study). If John had not chosen to pursue a Ph.D. he would have been hired in a $65k entry level position, which is slightly on the high end. Once he has graduated (in the quite average term of five years), he expects to receive a salary of $85k which, according to this survey is on the low end. We also, however, have to account for taxes! From my own experience and from consulting virtually every graduate student I know, John will receive a refund for practically all of the money taxed from his income. Without going to school, John would be in the 25% tax bracket, with a normalized income of about $52k (taking the tiered bracketing system into account). After earning his Ph.D. John would have a normalized income of about $67k. Plugging these values into the model we get:

$n=\frac{5 \times ( 52 + (-20) )}{67-52} \approx 11.$
Therefore, John will require about 11 years to recoup the income lost during school.

I think I was relatively conservative with my income estimates, and that’s still a lot less time than 50 years! I plugged in my own stats/estimates into the model and I project that I will need fewer than five years (and I don’t even make as much as some other students I know)! Furthermore, with a Ph.D., John has theoretically more potential for advancement/promotion. Once the 11 years are over, he will have much more earning potential than a degreeless John (assuming the market for Ph.D.s remains strong, which I don’t think is a huge assumption given the lack of domestic technical/science Ph.D.s in the US right now).

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