Returns to Education: an example of selection bias

How much is education worth? I personally believe that education provides you much more than just a higher income in the future, but let's simplify and focus here on how much more money you would earn if you studied a few more years. This question has interested economists for a long time (at least since Mincer in the 1950s). However, this holy number that could potentially explain whether I am (economically speaking) wasting my time doing a PhD has proved very hard to estimate.  But let's start at the beginning.

Around the end of the 1950s, Mincer proposed - after building a rather simple model of human lives - doing a regression of (log) income to years of education and years of work experience. If you did this you would basically find that one year of schooling increased your income by between 10 and 14%. However, recent analysis by Heckman (and his army of co-authors) shows that returns to education are not that easy to estimate. Particularly, the effect of each year of education may not be the same across levels (e.g. the year you finish high-school is worth a lot more than any of the previous) and that education might change your future income growth due to years of experience (e.g. if you finish high school each year of work may bring you a higher increase in income than if you did not finish high school). This is seen in Table 3a below for white men both in 1940 and 1990 (bottom row is Heckman's and top row is Mincer's). Each column refers to a different year of education: 10-12 is finishing High School and 14-16 is completing college.

Another interesting finding here is that this would suggest that finishing high school in the 1990s is worth a lot more than it used to be in the 1940s (50% vs 24% income increase). Are we learning more nowadays? Possibly. But possibly not as well. This could come from a well known issue to applied economists: selection bias.

Let me introduce this concept with a (hopefully) clearer example that comes from the health sector: the number of deaths and hospitals. For every 100 people hospitalized for diagnosis in the US more than 2 die every year. On the other hand, for every 100 people in the US only 0.8 die every year.* Hence, comparing the two pools of people, anyone ill might think: "Wow! If I go to the hospital I increase my chances of dying by more than 100%. Then, I should stay away from hospitals and try to get better on my own." But this clearly makes no sense (at least not if you have health insurance!). You are comparing a pool of people who are sick (hospitalized) with a healthy one (everyone else). If the first one stayed out of the hospital, we would expect that more of them would die. And the same logic applies to education.

Focusing on the 10-12 column, these regressions are (intuitively) comparing people who finished high school with those who did not. But are these people equal in all other terms besides having finished school? Most likely not. We can imagine that people who don't finish high school have had a worse childhood, come from worse neighborhoods and are generally raised in a more distressed environment ("sick" in the hospital example above). This would suggest that even if this people did go to school they might do differently (worse?) in the labor market later on. Similarly we can imagine that the people who did finish high school had families with a better economic background who could more easily provide job opportunities to their children, hence increasing their labor income independently of schooling choices. Basically, the two groups of people cannot be compared directly. Hence, the increase in the observed returns could be because the pool of people who don't finish High School nowadays is (relatively) worse than the one in the 1940s. Most people finish high school nowadays, while this was not the case 60 years ago. In other words, the selection bias could have gotten worse over time.

What economists might like to do to solve the enigma of schooling returns is to randomly assign people to different education levels. Someone would be flipping coins and deciding everyone's education. This way we would be able to make sure that all kinds of people are equally distributed across the different education levels. And so the income levels of the different groups could be easily compared. Fortunately, economists are not allowed to dictate people's lives that much. And the best solution so far has been to look for uncontrolled events that make (some) people more likely to go to school (but are not related to their wages in the labor market directly). And then we compare this group to some other (similar) people who were not affected by such an event. A nice example comes from Seth Zimmerman and his estimation of returns to college admission.

Zimmerman focuses on a large public university in Florida (FIU), which was particularly easy to get in when compared to other universities (kind of like a last-resort university. Apologies to any FIU students reading this!). This way he can be more confident that if someone was not admitted there, they would not be admitted by another school. But, how does he separate people randomly into the two groups (admitted versus not admitted)? His trick is to take people just around the GPA admissions threshold. Figure 4 shows that people right above it are 23% more likely to be admitted to this university than students just below it (and more likely to attend as well).

Assuming that people are not able to control their GPA at this particular university, this would provide him with people being "randomly" assigned to "admitted" and "not-admitted" groups.** Hence, we can now compare the income across the two groups worrying less about selection. Figure 8 suggests that being admitted to college (i.e. from being just above the threshold) increases your income by around 22%.

It is important to notice a few limitations of this kind of studies. These econometric techniques don't come for free. This number is the return to college admission only for people who, for various reasons, are near the threshold. And once again, this people might be very different than the ones who had no trouble being admitted. So the 22% rate should be understood as the return to this particular group of people and not for everyone else. Nevertheless, this number might be the relevant one if you are thinking about a policy that changes the requirements for admission. Such a policy would affect this particular group and not the general population. Moreover, another drawback is that this return does not consider "General Equilibrium" effects: If such a policy were applied in all the country we would expect to have lot more people graduating in the next few years, which might affect the wages of college graduates. Hence, the returns to education might change.

Economics research can (sometimes) be extremely difficult when compared to physics and other such sciences. In these sciences nature's rule is well defined. It may be hard to understand but it is there, and all the data you observe is from such a rule. In economics, data observed is driven from people's different lives, crazy personalities, complicated families and interestingly different regions of the world. And on top of these differences (which we can't observe in the data), individuals are making choices which manipulate the data we economists try to work with. Hence, understanding humans and outcomes related to them can be very complicated. Like Stephen Hawking once said,

"While physics and mathematics may tell us how the universe began, they are not much use in predicting human behavior because there are far too many equations to solve. I'm no better than anyone else at understanding what makes people tick, particularly women."

*  I would like to have the number of deaths of people not hospitalized to make the comparison with education but I wasn't able to find that number easily.
** Note that GPAs are computed differently by various universities. So students would need to preview that they want to apply to this particular school and be able to control their results very precisely to affect their result around the threshold. People way above the threshold can be easily thought to be very different, but people just above and just below the threshold are probably quite similar.

Based on an article by Heckman, Lochner and Todd and another one by Zimmerman.