What does state-level data tell us about the social value of education?

Steven Yamarik 19 September 2008



A good deal of the direct cost of education is subsidised by governments. In most Western countries, the government provides at least ten years of schooling at no cost to the student. At the university level, tuition and fees are often charged, but there is still substantial government funding. For example, James Heckman estimates that around 80% of the direct cost at major US public universities is subsidised.1

The most commonly-cited economic rationale for public investment in education is positive productivity spillovers from education. The individual student attends school in order to raise his or her earnings potential and possibly to directly increase his or her current utility. The increase in individual earnings due to educational attainment is called the private return to schooling. However, the knowledge gained by an individual can spread or "spillover" to others and thus increase aggregate productivity. The increase in income generated from the spillover is called the external return, while the sum of the private and external returns is the social return to schooling.

Mincerian wage equations

Beginning with the work of James Heckman and Peter Klenow, one approach used to determine the size of the human capital externality is to compare the estimates of the private and social return to schooling.2 Mincerian wage equations at different levels of aggregation can be used to estimate the two returns to schooling. At the microeconomic level, the Mincerian wage equation predicts that the log of earnings depends positively upon years of schooling, labour force experience, and experience squared. The coefficient in front of years of schooling is interpreted as the private return to schooling. At the macroeconomic level, the macro-Mincerian equation predicts that the log of aggregate income is positively related to physical capital, average years of schooling, and average labour force experience. By aggregating individual characteristics, the macro-Mincerian equation can capture externalities associated with schooling and thus provide estimates of the social return to schooling. Lastly, by including both individual and macroeconomic factors, the augmented micro-Mincerian equation can uniquely identify the private return to schooling and the external return to schooling. The sum of the two is the estimate for the social return to schooling.

Evidence from US states

US states provide an opportune laboratory to test for externalities in schooling. First, the educational structure and curriculum are more similar across US states than across countries. Second, state-level and individual schooling data are uniformly collected by the federal government. Third, US states share similar institutional and political backgrounds, while countries do not. As a result, state-level estimates of the return to schooling are less likely to suffer from bias introduced by measurement error, omitted variables, and parameter heterogeneity.3

Labour economists have estimated the micro-Mincerian wage equation using different time periods, samples, and econometric techniques. For the US, the private return to schooling ranges from 4% to 16% with a consensus estimate around 10%.4

The recent construction of state-level physical and human capital stock data has provided the opportunity to apply the macro-Mincerian model to US states.5 Chad Turner and his co-authors estimated a social return of 12% to 15%, while I estimated a slightly lower social return of 9% to 13%.6 The closeness of the estimates of the social return to the private return suggests that US schooling generates little to no external return.7

Researchers using the augmented micro-Mincerian equation find little evidence for the presence of external returns. These researchers match individual earnings and education data to city-level or state-level characteristics. An early study by James Rauch estimated an external return of 3% to 5%. However, more recent work by Daron Acemoglu and Joshua Angrist, Jeremy Rudd, Antonio Ciccone and Giovanni Peri, and Fabian Lange and Robert Topel find no statistically significant external return.


The lack of evidence of external returns does not automatically imply that the US government should stop subsidising education. There are other non-pecuniary externalities that can be generated from schooling. First, increased knowledge can make a person more interesting (and even more attractive) and thus raise the utility of others. Second, Lance Lochner and Enrico Moretti show that schooling reduces criminal activity and generates a substantial social effect.8 Third, Milton Friedman has argued that education enables individuals to participate more efficiently in the political process.9



1 James J Heckman, “Policies to Foster Human Capital,” Research in Economics 51 (2000), 3-56.
2 The original contribution is a working paper entitled “Human Capital Policy.” Extensive reviews of each Mincerian equation can be found in chapters 7, 8 and 11 of Erik Hanushek and F. Welch, eds., Handbook of the Economics of Education (Amsterdam: Elsevier, 2006)
3 William A. Brock and Steven N. Durlauf, “Growth Economics and Reality,” NBER Working Papers 8041 (2000) discusses the potential biases of cross-country growth regressions.
4 Dave Card, “The Causal Effect of Education on Earnings,” in Orley Ashenfelter and David Card (eds.) Handbook of Labor Economics, Vol. 3A, (Amsterdam: North Holland, 1999), 1801-1863 surveys the micro-Mincerian results. The 10% estimate is reported in James J. Heckman and Peter Klenow “Human Capital Policy” and George Psacharopoulos and Harry Anthony Patrinos, “Returns to Investment in Education: A Further Update,” Education Economics 12 (2004), 111-134.
5 Gasper Garofalo and Steven Yamarik, “Regional Growth: Evidence from a New State-by-State Capital Stock Series,” The Review of Economics and Statistics 84, (2002) 316-323 estimate physical capital data. Chad Turner, Robert Tamura, Sean E. Mulholland and Scott Baier, “Education and Income of the States of the United States: 1840-2000,” Journal of Economic Growth 12 (2007), 101-158 estimate average years of schooling and experience.
6 See Turner et al. (2007) and Steven Yamarik, “Estimating Returns to Schooling from State-Level Data: A Macro-Mincerian Approach,” Contributions in Macroeconomics 8: 1 (2008), Article 23.
7 Daron Acemoglu and Joshua Angrist, “How Large are the External Returns to Schooling? Evidence from Compulsory Schooling Laws,” NBER Macroeconomics Annual 2000, 9-59; Jeremy Rudd, “Empirical Evidence on Human Capital Spillovers,” Finance and Economics Discussion Series 2000-46 (Washington: Board of Governors of the Federal Reserve System); Antonio Ciccone and Giovanni Peri, “Identifying Human-Capital Externalities: Theory with Applications,Review of Economic Studies 73 (2006), 381-412; and Fabian Lang and Robert Topel, “The Social Value of Education” in Erik Hanushek and F. Welch, eds., Handbook of the Economics of Education (Amsterdam: Elsevier, 2006), 459-509.
8 Lance Lochner and Enrico Moretti, “The Effect of Education on Criminal Activity: Evidence from Prison Inmates, Arrests and Self-Reports,” American Economic Review 94 (1994), 155-189.
9 Milton Friedman, Capitalism and Freedom (Chicago: University of Chicago Press, 1962).



Topics:  Education

Tags:  education, positive externalities, Online Education


I'm going to write up a less rushed response to this article on my blog, but given how quickly with the internet people can move on to the next topic, with dangerous misconceptions fully intact, I think it's important that I immediately enter at least a basic response to this.

The results of this modeling and testing are being grossly and dangerously misinterpreted in the implications made for the real world. And this type of mistake is one that academia has to be careful of. As I've said before, academic social science does immensely more good than bad, and it's the only game in town for the type of highly valuable advanced technical work it does, but it certainly has flaws.

The real world conclusion of this paper is grossly and dangerously wrong. There are massive positive pecuniary (material well being) externalities to education. If there were none, then it logically follows that my pecuniary wealth (material well being) would be the same if (A), everyone in the world for the last 300 years up to today, except for myself, were completely uneducated and illiterate, as it would be if (B), everyone in the world had a bachelors, and a graduate or professional degree.

In the first case, my infrastructure would be dirt roads, and my medical care would be herbs and leaches. My lifespan would be like it was in the 1700s, early 30s, and I'd probably experience the death of at least one of my children. By the time I was 30, I'd lose most of my teeth -- very painfully. I'd freeze in the winter and swelter in the summer in a primitive dwelling. Where would I buy a modern home from? No one else in the world besides me has the education to build anything modern, from a car, to an aspirin, to toilet paper, to soap, to toothpaste, to penicillin.

In the second case, everyone besides myself in the world has had a graduate or professional degree from 1708 right up until today. Could you imagine how much science, technology, and medicine would have advanced by now if that were true. Cancer would very likely be cured, as would many diseases from Parkinson's to arthritis to diabetes to depression. Healthy lifespan would be immensely longer, with nanobots throughout the body constantly repairing cells. Robots would be extremely advanced, and we might have to a great extent robots building robots, creating immensely more material wealth. We might even have found a way to eat as much as we want without getting fat! I could go on and on.

Yeah, there's no material benefit to me when others get an education. There's no positive material externalities there. I'm exactly as materially well off in case (A) when others have no education as I am in case (B) when others are highly educated. Think about how ridiculous this conclusion sounds – and is. You need only make the most minor and realistic assumptions about the world (immensely more minor and realistic than the assumptions relied on in most models and econometric techniques) to come up with chains of logic proving the conclusion in your paper to be tremendously far from the truth.

The more other people are educated, the more they create ideas, understanding, and invention, that is to say, the more they create things which have gigantic positive pecuniary externalities. Ergo, the more they create positive pecuniary externalities.

Now, you may say that you use a definition of pecuniary which is different from quality and quantity based material wealth. If so, then you better make this very clear in your conclusions so as not to mislead in a very dangerous way.

Listen to what top growth economist Paul Romer said in an interview with Reason (at: http://www.reason.com/news/show/28243.html):

It's so striking. Evolution has not made us any smarter in the last 100,000 years. Why for almost all of that time is there nothing going on, and then in the last 200 years things suddenly just go nuts?

One answer is that the more people you're around, the better off you're going to be. This again traces back to the fundamental difference I described before. If everything were just objects, like trees, then more people means there's less wood per person. But if somebody discovers an idea, everybody gets to use it, so the more people you have who are potentially looking for ideas, the better off we're all going to be.

End Quote

"the more people you have who are potentially looking for ideas, the better off we're all going to be.", the more people are getting, the more and better they are looking for ideas, and the more I will benefit more from them. In other words, I will get a positive externality from them, and a very large pecuniary one given the nature of science, technology, and medicine.

But it's much more than that. The more educated others are, the smarter they vote. For example, as people become more educated, it has been shown they become less likely to vote Republican. In general, they will vote for far smarter economic policy, including far more government investment in extremely high social return projects of the kind that the free market will underprovide due to free market problems like externalities, etc. These projects include alternative energy, other infrastructure, and basic scientific and medical research, which can have an enormous pecuniary impact. I'm far better off from this materially, and it's due to others becoming more educated.

You mentioned that higher education correlates with lower crime. Much of this won't show up in your GDP statistic, because money spent on security, prisons, etc. is added to GDP, when in fact it should be subtracted. Likewise, GDP is flawed, because it takes technological and quality advance into account very little. $1,000 of medical care today is far better than $1,000 of it in 1920.

I could go on. Your real world conclusions from your data and tests are wrong and very dangerously misleading.

Richard H. Serlin

The main externality to getting more education is that part of one's added earnings will be taxed (and in the world of cost/benefit analysis, given to others). Without a subsidy to education, people would get too little education from a social point of view if education is purchased at its full cost. The fact that the private and social returns to education are the same suggests that the current level of educational subsidies are about right. Without them, the private return to education would fall below the social return.

Is this actually more than an elaborate way of saying that secondary US education is so shallow and inexistent that it leaves no visible imprint on those that have been subjected to it?

Henri Tournyol du Clos

... it might still make sense to subsidize education.

Education increases wages. The government taxes wages. If the expected present value of the additional taxes exceeds the present value of the government's expenditures to produce the education, then the government can increase its resources by making those expenditures.

I read somewhere that Pol Pot has a doctoral dissertation in political science on file at the University of Paris. That's a fairly clear case of harmful education externalities.

Associate Professor of Economics, California State University

Vox Talks