How much is a college diploma worth?

Recent weeks have produced a constant stream of articles and blog posts attacking the value of a college diploma. Given the low quality instruction my children endured at various points in their middle and high school careers, I can at least recommend many colleges as a good place to get a decent high school education. To support their assertion that college diplomas are overvalued, the blog discussions generally cite anecdotes of college graduates who are waiting tables or are otherwise underemployed. The terms of the discussion are always too vague to support a coherent argument; so, let's see if we can add clarity to the noise.

A quick internet search yields the following useful Wall Street Journal data on salaries by college major.

Undergraduate Major	Starting Median Salary	Mid-Career Median Salary		Mid-Career 10th Percentile Salary	Mid-Career 25th Percentile Salary	Mid-Career 75th Percentile Salary
Accounting	$46,000.00	$77,100.00		$42,200.00	$56,100.00	$108,000.00
Aerospace Engineering	$57,700.00	$101,000.00		$64,300.00	$82,100.00	$127,000.00
Agriculture	$42,600.00	$71,900.00		$36,300.00	$52,100.00	$96,300.00
Anthropology	$36,800.00	$61,500.00		$33,800.00	$45,500.00	$89,300.00
Architecture	$41,600.00	$76,800.00		$50,600.00	$62,200.00	$97,000.00
Art History	$35,800.00	$64,900.00		$28,800.00	$42,200.00	$87,400.00
Biology	$38,800.00	$64,800.00		$36,900.00	$47,400.00	$94,500.00
Business Management	$43,000.00	$72,100.00		$38,800.00	$51,500.00	$102,000.00
Chemical Engineering	$63,200.00	$107,000.00		$71,900.00	$87,300.00	$143,000.00
Chemistry	$42,600.00	$79,900.00		$45,300.00	$60,700.00	$108,000.00
Civil Engineering	$53,900.00	$90,500.00		$63,400.00	$75,100.00	$115,000.00
Computer Science	$55,900.00	$95,500.00		$56,000.00	$74,900.00	$122,000.00
Drama	$35,900.00	$56,900.00		$36,700.00	$41,300.00	$79,100.00
Economics	$50,100.00	$98,600.00		$50,600.00	$70,600.00	$145,000.00
Education	$34,900.00	$52,000.00		$29,300.00	$37,900.00	$73,400.00
Electrical Engineering	$60,900.00	$103,000.00		$69,300.00	$83,800.00	$130,000.00
English	$38,000.00	$64,700.00		$33,400.00	$44,800.00	$93,200.00
Film	$37,900.00	$68,500.00		$33,900.00	$45,500.00	$100,000.00
Finance	$47,900.00	$88,300.00		$47,200.00	$62,100.00	$128,000.00
Forestry	$39,100.00	$62,600.00		$41,000.00	$49,300.00	$78,200.00
Geology	$43,500.00	$79,500.00		$45,000.00	$59,600.00	$101,000.00
History	$39,200.00	$71,000.00		$37,000.00	$49,200.00	$103,000.00
Industrial Engineering	$57,700.00	$94,700.00		$57,100.00	$72,300.00	$132,000.00
Journalism	$35,600.00	$66,700.00		$38,400.00	$48,300.00	$97,700.00
Marketing	$40,800.00	$79,600.00		$42,100.00	$55,600.00	$119,000.00
Math	$45,400.00	$92,400.00		$45,200.00	$64,200.00	$128,000.00
Mechanical Engineering	$57,900.00	$93,600.00		$63,700.00	$76,200.00	$120,000.00
Music	$35,900.00	$55,000.00		$26,700.00	$40,200.00	$88,000.00
Philosophy	$39,900.00	$81,200.00		$35,500.00	$52,800.00	$127,000.00
Physics	$50,300.00	$97,300.00		$56,000.00	$74,200.00	$132,000.00
Political Science	$40,800.00	$78,200.00		$41,200.00	$55,300.00	$114,000.00
Psychology	$35,900.00	$60,400.00		$31,600.00	$42,100.00	$87,500.00
Religion	$34,100.00	$52,000.00		$29,700.00	$36,500.00	$70,900.00
Sociology	$36,500.00	$58,200.00		$30,700.00	$40,400.00	$81,200.00
Spanish	$34,000.00	$53,100.00		$31,000.00	$40,000.00	$76,800.00

One source gives the median high school salary as $32,000 for adults aged 25-34, a weak approximation to 'midcareer'. I suspect a better approximation to the Journal's midcareer category would add several thousand dollars to this.

Assuming the high school versus college data is roughly comparable, it is easy to see that for most college graduates who are now midcareer, the college degree is certainly strongly correlated with greater earning power. (Of course, we cannot exclude the possibility that for this cohort, the college degree is a proxy for a lower bound on their IQ.) With the exception of a few fields like education and religion, it should take little more than a decade or so to pay back college costs (including the cost of delaying entrance into the work force). The data becomes more interesting when we look at the bottom 10% of earners (by major) among college graduates. We see that for many majors, including Anthropology, Art History, Education, English, Film, Music, Psychology, Religion, Sociology, and Spanish, occupants of the lowest decile do not recoup the cost of the college degree.

Let's make a strong assumption that the bottom 10% of wage earners in each major are roughly the same group as the bottom 10% of students in the major (defined by some incredible nonexistent linear measure of academic ability). Of course, this assumption has terrible holes, for example, women who temporarily drop out of the workforce to raise children. Nonetheless, we will assume until otherwise informed that the correlation between poor student performance and lower subsequent wages is strong. We further assume that the majority of people who did not attend college would have been weaker students than those who did. Similar caveats obviously apply to this assumption, but I suspect it is accurate on average. We then see that the push to encourage higher rates of college attendance for students who would have been unlikely to attend otherwise, is likely to lead to poor economic results for the majority of those new students, if they major in the Arts or Humanities. On the other hand, the above data is brighter for those who choose to major in Engineering, Math, Physics, and Economics. Even the 10th percentile of earners with degrees in these majors have room to recoup the costs of college. So, if one discovers a subset of students who have strong mathematical skills but would not traditionally attend college, then perhaps they should be encouraged to attend. Otherwise, the push to continue to enlarge the population of college students does not appear likely to be economically rewarding for lower performing students.

We see that the loud corner of the blogosphere that asserts that a college degree has lost its value is obscuring the main issue. A college degree in many fields is strongly correlated with subsequent higher earnings, but our above commonsense (but unproven) assumptions suggest that the more precise statement is: for good students a college degree in many fields is likely to lead to higher earnings. For weaker students, it is likely to be a money pit.