This week, my ECONS102 class is covering the economics of education. Part of that topic considers the private education decision - the decision each individual makes about the amount of education they receive. This depends on the private costs and benefits of education. Arguably the primary benefit of education is incremental income - the additional lifetime earnings that education brings.
How big are those gains? Previous studies I have seen (such as a study reported in Paul Oyer's book Everything I Ever Needed to Know about Economics I Learned from Online Dating (which I reviewed here)) have estimated effects in the order of 10 percent per additional year of education. However, that was a single study, which could easily provide a biased view if considered in isolation.
What are the effects more generally? This recent article by Gregory Clark and Christian Nielsen (both University of Southern Denmark), published in the journal Kyklos (open access), provides an answer based on a meta-analysis of 79 causal estimates of the effect of an additional year or years of compulsory schooling on earnings, drawn from 53 other papers that apply methods consistent with causal inference. Meta-analysis provides a method of combining the estimates across many studies into one overall estimate. Importantly, Clark and Nielsen apply various methods to correct for the effects of publication bias (which is the tendency for statistically significant results to be more likely to be published, while statistically insignificant results tend to be missing from the research record).
Clark and Nielsen report baseline results that are somewhat lower than I expected:
With these procedures the average percentage gain in earnings from an additional year of schooling was 8.2% for 79 independent estimates, from 53 papers... If these estimates are weighed by their precision in a random effects estimation, the gains are reduced to 6.0%, and similarly 6.2% for a fixed effects weighting.
Given that the true effect is likely to vary across populations and study settings, I would consider the random-effects estimate of 6.0 percent for each additional year of schooling as the more plausible of the three. However, Clark and Nielsen also employ meta-regression, using PET (Precision Effect Test) and PEESE (Precision Effect Estimate with Standard Error) regression models, which are designed to address imprecision and publication bias in the overall sample of results. After removing some outliers, these approaches suggest:
...a true effect of 6.1%–6.4% to an extra year of education and an insignificant effect of publication selection...
So again, it seems like the effect may be in the order of six percent per additional year of schooling. Interestingly, Clark and Nielsen themselves note that the PET-PEESE evidence for publication bias is highly model-dependent, and that these results could instead reflect genuine heterogeneity in the true effect. However, Clark and Nielsen go a little further, looking in more detail at the distribution of effects across the 79 estimates. They note that if the estimates of the earnings return were normally distributed, then there are a lot of 'missing' studies with negative returns. They also consider whether the underlying returns might be log-normally distributed. Once you consider sampling error, the log-normal distribution can still generate negative estimates, and Clark and Nielsen argue that there are fewer negative estimates in the published literature than the model would predict. Consider Figure 10 from the paper:
In the figure, the yellow bars show a histogram of the 79 estimates in the sample. The blue line shows a log-normal distribution based on the estimates. Notice that, compared with the log-normal distribution, there are more studies than expected with estimates in the 0-4 percent range, and too few in the negative range. Clark and Nielsen argue that, if the 'missing' studies were included, a better estimate of the returns to each additional year of schooling may be in the range of 0-3 percent.
However, I’m not convinced that Clark and Nielsen’s distributional assumptions are justified here. Figure 10 (like Figure 8 in the paper) shows that the observed distribution of estimates doesn’t match their chosen distribution. But they haven’t established that their chosen distribution is what we should expect in the absence of publication bias. That distribution would depend on differences in estimation methods, the precision of the estimates, and genuine differences in returns across the populations studied. A mismatch between their chosen distribution and the observed study estimates therefore does not, by itself, demonstrate that studies with negative estimates are missing. So, while publication bias remains a possible explanation, I would treat Clark and Nielsen’s proposed 0-3 percent range for the average return very cautiously.
Nevertheless, overall it does seem clear from their other results that the returns to an additional year of schooling may be somewhat lower than the 10 percent found in other studies. What would be interesting to know next is whether the estimated returns have been changing over time (which my next blog post will look at, for Australia), and what study features lead to different estimates. Clark and Nielsen do note that instrumental variable regression leads to higher estimates than difference-in-differences or regression discontinuity estimates. However, there are other contextual variables that may matter as well. Hopefully, someone else can pick up on this work and take it to the next step. That might help to distinguish publication bias from the more mundane possibility that there simply isn't a single 'true' return to an additional year of schooling.
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