A Micro-Mincer regression estimates personal income as a function of personal education and controls:

ln Personal Income = a + b*Personal Years of Education + other stuff

Unless b is very large, b approximately equals the individual education premium.  b=.09, for example, indicates that an extra year of education raises earnings by about 9%.

A Macro-Mincer regression, analogously, estimates national income as a function of national education and controls:

ln National Income = a + b*Average National Years of Education + other stuff

In a pure human capital model, you would expect the Micro-Mincer and Macro-Mincer results to match.  More education makes people more productive, which increases personal income; more education makes nations more productive, which increases national income.

In a pure signaling model, in contrast, you would expect the Micro-Mincer return to be positive, but the Macro-Mincer return to be ZERO (at least at the margin).  More education makes people look more productive, which increases personal
income; at the national level, however, education is a rat race.  Only one person can be the best, and only 25% of the population can be in the top 25%.

Both cases are unrealistically extreme, but they do suggest a simple way to estimate the human capital/signaling split.*

1. Estimate Micro-Mincer regressions within countries.
2. Estimate Macro-Mincer regressions across countries.
3. Compare.

The implied human capital/signaling split is just (2) divided by (1):

Macro-Mincer coefficient/Micro-Mincer coefficient.

Of course, this computation is easier said than done.  (1) is pretty accessible: A big literature finds a global Micro-Mincer coefficient of roughly 10%.  But (2) is very difficult to get, because international education panel data is sparse, and researchers’ samples and controls vary widely.

Fortunately, after voracious but frustrating reading on the topic, I eventually hit pay dirt when the noble Ángel de la Fuente graciously emailed me an amazing appendix to his 2006 paper with Rafael Doménech.  In this appendix, they estimate the same Macro-Mincer regressions on 8 (!) different data sets for the same 21 OECD countries.  Their overall results:

 Data Set Macro-Mincer Estimate Nehru et al (1995) -0.7% Kyriacou (1991) 1.0% Barro and Lee (1993) 1.2% Barro and Lee (1996) 0.3% Barro and Lee (2000) 1.0% Cohen and Soto (2001) 4.8% de la Fuente and Doménech (2000) 2.4% de la Fuente and Doménech (2002) 4.9% Average 1.3%

Notice: The highest Macro-Mincer estimates imply a human capital/signaling split around 50/50.  The average estimate implies a split of 13/87.

If, like me, you’re a fan of transparent econometrics, you might prefer their log-levels with country fixed effects estimates.  The range is wider, but the average Macro-Mincer estimate remains very low.  In fact, it’s eerily close to my best guest of the human capital/signaling split: 20/80.

 Data Set Macro-Mincer Estimate Nehru et al (1995) 0.5% Kyriacou (1991) 0.9% Barro and Lee (1993) 2.0% Barro and Lee (1996) 0.1% Barro and Lee (2000) 1.3% Cohen and Soto (2001) 7.2% de la Fuente and Doménech (2000) -0.2% de la Fuente and Doménech (2002) 6.9% Average 2.3%

At this point, you could reasonably ask: Are some of these 8 data sets objectively better than the competition?  Researchers predictably market their own data as new-and-improved, but outside certification is very scarce.  To the best of my knowledge, only one research team with no “dog in the fight” ever weighed in.  Their conclusion based on the data sets available back in 2003: “we are not convinced that any one of the available data series is clearly preferable to the alternatives.”

Most researchers who don’t like puny Macro-Mincer results emphasize that measurement error leads to attenuation bias, so the true effect of education is larger than it looks.  As I’ve pointed out before, though, this confident claim hinges on the crazy assumption that education is the only mismeasured independent variable!  As long as other variables are mismeasured, the observed coefficients on education could be too high, too low, or just right.

What does it all mean?  If you’re a naive empiricist, the Macro-Mincer evidence is a big victory for signaling.  If you’re a human capital purist, the Macro-Mincer evidence is a big indictment of the data.  The sensible Bayesian reaction, however, lies in the middle: While the Macro-Mincer evidence settles nothing, it’s a little extra evidence in favor of an intrinsically plausible position.

* A Micro-Mincer return in excess of the Macro-Mincer return also fits a scenario where education successfully trains workers for rent-seeking or other socially unproductive jobs.  HT to David Balan for reminding me of this possibility.  In my book, I explain why I doubt this is a big deal.