The Returns to Education

Inferring the impossible

It is not possible to differentiate whether the returns from education are due to human capital growth, or from signaling, from experimental or quasi-experimental evidence. The two will appear identical to each other. In fact, it may not be possible to tell even if we include the rest of the country as a control group. 

Before anything else, a genealogy of terms. Human capital is a term for ability. It is commonly indicated by schooling, as being able to complete more schooling indicates it, but it is broader and encompasses all sorts of skills. If the returns from education are from returns to skill, then people getting more education increases social product. This need not mean that subsidizing education is socially optimal, as if each person captures their whole product a subsidy would induce an excessive level of education; nevertheless, it seems reasonable to say that people do not capture all of the social gains, and there are unaccounted for spillovers onto other people. Estimating these spillovers is extremely difficult, unfortunately, and generally finds null results. For starters, the places which have good data tend to have universal education already, which does not substantially vary in amount. What variation we have is generally due to changes in school leaving age, which can only pick up an effect in the amount of education among an incredibly marginal group. Acemoglu and Angrist (2000) use variation in state school dropout laws, and find no spillovers, but they are not able to measure spillovers from education generally.  If it is at all difficult for people to ascertain the quality of workers, then you have sufficient conditions for externalities. Production requires multiple steps, and so the returns to skill are dependent upon what other people do. (See Kremer’s O-ring paper for more). The whole reason we think cities exist is that it’s easy to transmit ideas back and forth, and ideas are almost definitionally a positive externality. So, I will say that there are spillovers from having more skilled people, and if you want to argue against that you’ll need darn good evidence. 

Signaling follows from employers not being able to perfectly tell the quality of applicants for jobs. Education is pursued because people want to prove that they are capable of doing the job, as it is costly or impossible for those with less ability to complete. The original paper outlining this is Spence (1971); it has been argued as being of prime importance in explaining why we have education by Bryan Caplan in his book “The Case Against Education”. If signaling is the reason for education’s returns, then subsidizing it would be very bad. The signal is only valuable insofar as it provides information differentiating you from others. If everyone has the signal – a college degree, a high school diploma, whatever – then it is valueless. (This need not necessarily hold – Stiglitz (1975) specifies situations under which there may be insufficient screening. The paper is interesting, and worthwhile reading, but I don’t think anyone seriously argues that there is insufficient screening – the position of people supporting subsidies for education rely upon estimating substantial returns to human capital. It is still important to remember that signaling can be positive sum insofar as it improves the quality of job matching). 

No one would argue that the returns to education are completely due to one or the other, so we would obviously like to know which effect predominates the other. It is not possible for us to separate the two out, though. To illustrate this, let’s look at notable examples of studies measuring the return to education. Duflo, Dupas, and Kremer (2021) report on a randomized controlled trial in Ghana begun in 2008. Full scholarships to high school were awarded at random to youth who had gained admission to high school, but were unable to pay the fees. The winners were naturally much more likely to go to school, and this translated into increased knowledge, scoring .16 standard deviations higher on examinations of practical math and reading comprehension. Women were substantially less likely to be pregnant, and both men and women were more likely to use modern technologies. Most importantly, wages were higher – at least among women.

And yet, problems lurk. The gains were only due to people who received education getting government jobs. In private sector jobs, there were no gains in income at all. Government jobs are rationed, and only dubiously productive. The findings are perfectly consistent with education allowing people to shuffle ahead to the front of the queue, making other people worse off. We wouldn’t be able to observe the negative effects on other people counterbalancing the gains to the treated group, because we only have a small part of the people in the sample.

So what if we had a much larger experiment, covering half the people, and had an entire nation as a control group? Esther Duflo has two papers on the Indonesian government’s expansion of school construction between 1974 and 1978. The first covers it pretty “straight”. They built 61,000 schools in that time, and caused a rise of .12 to .19 years of education for each new school per 1,000 children, with an associated return of increasing wages by 1.5 to 2.7 percent. This implies a return of 6.8 to 10.6 percent of wages for each additional year of education – simply enormous returns. The second, though, casts a shadow on the whole story. The treated group’s wages went up, yes, but the wages of the groups which did not receive more education went down. 

And yet. And yet. We can’t show that it is signaling from this. Yes, even here! It is possible that having more educated workers changed the terms of trade such that unskilled workers were worse off. If factors are immobile, this is perfectly plausible. For example, Topalova (2010) shows that the 1991 trade liberalization in India increased extreme poverty among the very poorest, even while it made the country as a whole better off. The key fact making this possible is that the poor had a difficult time adjusting to the jobs which are now better. Likewise, in America, the opening of China to trade had uneven effects, depressing employment and income in some affected areas for a decade, as Autor, Dorn, and Hanson (2016) showed. The key is that reallocation must be difficult, and Duflo shows this easily. As she writes in relation to the increasing fraction of primary school graduates in places with more schools, “this increase is strikingly similar to that which would have been predicted in the absence of any migration”. A result fully consistent with signaling explaining much or all of the return to education is also fully consistent with human capital explaining all of it. We cannot tell from experimental data what caused it, unless we have some way of truly hiding the signal from employers.

How about if we took an entirely different tack? Let’s not try and measure skill directly, but rather try to measure how fast employers learn about ability on the job. After all, there’s no plausible world in which someone can work for you, and you don’t know anything about how well they do the job. If experience definitely reveals your type, then the value of the signal from college would surely decrease. Fabian Lange (2007) estimates how fast this occurs using data from the Armed Forces Qualifying Test, or AFQT. Your score is confidential, so when employers only receive the signal from education. The AFQT reveals substantial information about your capabilities, and so people with better scores conditional upon education should see their wages rise while on the job. Lange shows that this happens extremely quickly – within three years – and so the contribution of signaling, under the most accommodating assumptions, 45%.

And yet! That intuitive claim does not suffice. Habermalz (2006) shows that faster employee learning can lead to a higher share for signaling. Up to a point, as it becomes easier for employers to suss out employees with misleading credentials, lower ability workers will find it less worthwhile to invest in education, and so the share of returns due to signaling will increase. We actually don’t know – and can’t know – which prevails. 

So what can we do? We can try and measure countries as a whole, and try to find the change in growth rate from increasing education. This is a model built entirely on faith, however. The amount of education done in a country is endogenous to so many things, and an assumption of parallel trends would be frankly ridiculous. Ed Glaeser has a debate with Bryan Caplan on whether educational subsidies should be scrapped, and he chooses to not regard the macro evidence as worthwhile at all. The best experiment would be if we could observe skill directly, and relate it to income, but vary the amount of school. The great difficulty is that intelligence is simply the best measurable component of things which cause higher income which are also correlated with school outcomes. I am not aware of any studies which are doing this – comment is appreciated. (UPDATE: Sasha Gusev points to a study estimating the effect of number of years of education on measured IQ).

I would argue we have to reason about what is most plausible. Take the “sheepskin effect”, which is the discontinuity in earnings from completing enough to graduate. It is implausible that all the gains from skill are concentrated just in the last year of school; its existence argues pretty strongly that signaling matters. We should also think critically about what skills we believe are being taught in school. Are we going to argue that learning high school Spanish made it easier to be a mechanical engineer? I would point out that “learning to learn” isn’t a thing – there are no spillover effects from learning a foreign language, playing a musical instrument, or learning chess, to pick three popular activities done for that reason. It is also striking that parenting has but a minor impact on child outcomes. If parenting doesn’t have that big of an effect, why should we expect school to? 

I tend to think that signaling explains much of the return in the developed world, that this varies profoundly by major and by subject, and that changes in human capital explain more in the developing world than in the developed, although not after accounting for the lower level. (The importance of having skills is greater when more people have them, after all. The return to skill is also greater in more cognitively demanding tasks as well). I think that society would be better off with less subsidization of higher education, and that “higher education” oughtn’t be restricted to just college, but should include high school as well. I am quite confident that making the final two years of high school non-mandatory and non-subsidized would substantially improve societal outcomes. We mustn’t think that if education is not funded, even beneficial education will not be done – it is an investment good like any other, and we should no more expect there to be profound inefficiency in the market for it than we should expect profound inefficiency in the market for steam engines. Recognizing our limitations should go both ways. We cannot definitively prove the share of returns owed to signaling, but neither can we prove the share owed to human capital accumulation. We ought not be reflexively pro increasing education spending, and neither should we take the status quo for granted as the right way to do things.