Mobility: Educational Attainment

Monozygotic Twin Studies

There are a number of studies that use identical twins to attempt to control for ability bias. These studies generally find slopes ~20% lower than the naive slope, suggesting some (but not most) of the naive correlation isn't due to ability bias.

One wrinkle here is that adding IQ as a control variable actually reduces the slope further, which is odd given that intelligence is almost entirely genetically determined and, therefore, ought to be controlled for within twin pairs. In particular, Sandewall et al found that, in Sweden, adding the IQ control shrank the estimated slope by about 20% Sandewall. If we naively add these two adjustments together, we can estiamte that educational attainment within twin pairs is roughly ~40% lower than the naive slope among the general population after also controlling for IQ.

One hypothesis is that birth weight causes IQ and educational attainment differences in identical twins Bound. On the other hand, variables that normally correlate strongly with educational attainment (marital status, spouse educational attainment, job tenure) don't correlate within educational attainment within twin pairs, suggesting that using twin fixed-effects already controls for the bulk of relevant sociological confounders Isacsson, G. (2004). I'm unsure what to make of this.

Finally, other confounders likely remain. If, for instance, ambition has causes of the unshared environment variety, this could confound the remaining association between education and income.

Still, the fact that controlling for genes, shared environment, and IQ reduced the correlation by 40% paired with the general guidance from the socioeconomic literature that genetic causes tend to matter more than environmental causes suggest to me that most remaining confounders are probably relatively small.

Bryan Caplan's Beliefs

Bryan Caplan exclusively focuses on studies that predict earnings from education after while adjusting for various confounders. After examining the evidence, he concludes (in Chapter 3 of his book) that roughly 45% of the education-income correlation is due to ability bias. This nicely matches the twin estimates.

Quasi-Experimental Studies

As Sam Atis points out Atis, it is odd that Caplan prefers ordinary least squares studies over those with more plausible arguments for causation, particularly those employing a regression discontinuity design Regression discontinuity design. In Wikipedia. In light of this, I attempted to find all the quasi-experimental studies I could in the developed countries that link educational attainment and earnings. Here are the results.

Of the quasi-experimental studies I found, the median estimate is that a GED or high school diploma increases earnings by about 5% - a far cry from the ~30% that naive correlations suggest.

Evaluating the value of a college diploma is trickier, since colleges generally don't have final exams and since people can change colleges. However, one study looked at colleges where you were kicked out if your GPA fell below a certain value and used this to perform a regression discontinuity design. They found a ~6% effect on future earnings - about the same size as the estimated effect of graduating from high school, and still a far cry from the ~30% that naive correlations suggest.

Ultimately, whereas the twin studies and Caplan's estimates suggest roughly 60% and 55% the naive correlation is causal, respectively, these studies suggest the proportion is noticeably lower: around 20%.

There are, I think, three possible explanations for why the quasi-experimental results are lower.

First, one or more of these methodologies (twins, linear regression, quasi-experimental) is flawed and its results can simply be ignored.

Second, the quasi-experimental results, especially at the high school level, are relatively purely measuring the pure signaling value of education. The other two methods measure the combined value of signaling and gains in human capital. Hence, one explanation for this discrepancy is that roughly 40% of the correlation is due to the human capital education gives its students.

The third explanation, and the one I actually believe, is that there is significant heterogeneity in the effect of education on earnings. The regression discontinuity studies estimate the causal effect on the marginal student. So, that 5% estimate for the value of graduating high school reflects the value to someone who is 50-50 on accomplishing the feat. The twin studies and linear regression studies are considering the average person, for whom graduating from high school is very likely (~90%).

Consider a genius. If she drops out of high school, the expected effect on her earnings is probably much higher than the effect on a marginal student. The genius, for instance, is likely also forgoing college. This line of reasoning suggests the discontinuity estimates are too low for the average student, while the twins and linear-regression estimates are too high for the marginal. I should mention, though, that other people spin the opposite narrative, so take this all with a healthy helping of salt.

Note: I'm not intending to say discontinuity studies are bad - their value depends on what you're interested in. There are plenty of reasons to prefer focusing on marginal students rather than average ones - in particular, policy changes are most likely to affect the marginal students! Instead, this is simply a distinction that we need to keep in mind to fully understand the impact of education on earnings.

Conclusions

If we suppose half the 13% naive slope is causal in nature, this suggests each year of education makes you earn about 6.5% more. This is actually about the average inflation-adjusted return of the S&P 500 over the last ~150 years, which suggests that even if education is free, the economic pros and cons approximately cancel out on average.

However, there is significant heterogeneity and other factors: some degrees have larger causal effects than others, and many people derive non-economic happiness and meaning from pursuing their degree.

Ultimately, for the average student the twin studies and Caplan's preferred studies suggest about half of the the naive education correlation is causal in nature - whether due to signaling or learning. Because of this concurrence, I broadly agree with Caplan's recommendations in The Case Against Education.

However, the discontinuity designs suggest education is much less valuable to the marginal student relative to the average student. By symmetry, I intuit this means education is actually more important than average for particularly gifted students.

Caplan accounts for at least some of this heterogeneity in his book when discussing colleges by noticing that worst students attend colleges with poorer economic returns, but he doesn't account for this regarding high school graduation rates, which biases him in favor of education for marginal students and against education for high-achieving students.

Heritability

A meta-analysis found educational attainment is roughly equal parts genetic (40%) and common environment (36%) Branigan.

Evidence shows that the educational attainment of the parent you spend more time with better predicts your own future educational attainment Gould.

Appendix: Heterogeneity

One of the twin studies also examine whether the relationship between educational attainment and earnings changes by education level. They found a statistically insignificant reduction in the correlation as education level increases Rouse. This was also examined by Estimating the economic return to educational levels using data on twins and they succeeded in rejecting the null hypothesis that the true slope was equal at all levels, but I'm not really able to discern a clear trend.

The naive correlations are also pretty ambiguous on whether such a trend exists: 19% income gain from high school graduate to Associate's; 39% from Associate's to Bachelor's, 18% from Bachelor's to Master's, and 21% from Master's to PhD Education pays.

Really all we can say is that it looks, from a purely correlational perspective, like getting a Bachelor's is particularly important, and that we shouldn't expect the causal impact of education to be uniform across education levels.