Schooling, Income, and Reverse Causation
Economists normally measure the private return to education by estimating a “Micro-Mincer” regression:
(1) log(personal income in $s)= a + b1*(individual education in years)
Given crucial assumptions, b1 is the private return to education. I’ve discussed some of these crucial assumptions elsewhere. One that I’ve neglected, though, is the possibility of reverse causation. Maybe higher income (or the expectation of higher income) leads to more education in the same way that higher income leads to more plasma TVs: you buy not as a prudent investment, but because the money’s burning a hole in your pocket. If so, b1 overestimates education’s private rate of return.
Now you could object that personal income has little effect on educational attainment because individuals pay only a tiny fraction of the bill. If your income suddenly doubled, how many extra years of education would you get in response? An average answer of “one year” seems pretty high, suggesting an extremely small income–>education effect.*
Once you remember that government picks up most of the educational tab, however, another issue surfaces. When economists want to measure the social return to education, they normally estimate an analogous “Macro-Mincer” regression:
(2) log(national income in $s)= a + b2*(average national education in years)
Given crucial assumptions, b2 is the social return to education. But what if reverse causation is at work here as well? Maybe higher national income (or the expectation of higher income) leads to more
education in the same way that higher national income leads to more lavish monuments: the government’s got to spend its swelling coffers on something.
If so, b2 overestimates education’s social return.**
So far, I’ve said nothing truly original. But reflecting on reverse causation eventually led me to the following epiphany: Since government is the dominant source of funding for education, we should expect reverse causation to be a bigger deal at the national level. When a worker gets richer, he probably spends slightly more on education – and gets slightly higher credentials. When a country gets richer, it probably spends markedly more on education – and gets markedly higher credentials.
To be more concrete, if an individual gets $100 richer, he’ll probably spend about $1 on education. But if a whole society gets $100 richer, education spending will rise by more like $1 (in private spending) plus $4 (in government spending). So while both (1) and (2) yield upwardly biased estimates of b due to reverse causation, the bias in (2) is far more severe.
So what? The thrust of the signaling model is that the social return to education is smaller than the private return. Impeccable estimates of b2 (the Macro-Mincer return to education) should exceed b1 (the Micro-Mincer return to education). In practice, though, estimates of b1 and b2 are usually (though hardly always) in the same ballpark. Researchers often respond with a summary dismissal of the signaling model.
I say they’re far too quick to declare signaling empirically dead. Neither (1) nor (2) adjust for reverse causation, and reverse causation is more severe for (2) than for (1). So if the uncorrected estimates of b1 and b2 are roughly equal, we’d expect that correcting both equations for reverse causation would indeed yield b1>b2, just as the signaling model predicts.
How does this expectation hold up empirically? There is far less research on research causation than there ought to be. But the most influential piece on the topic – Bils and Klenow’s “Does Schooling Cause Growth?” (AER 2000) concludes that reverse causation is a huge deal at the macro level:
[P]ure growth in human capital accounts for a minority of the observed
relation between schooling and income, most probably less than
[F]or plausible parameter values, the reverse causality channel is strong enough to generate the empirical coefficient of 0.23 percent in the absence of any effect of schooling on the growth rate.
Hardly the final word, but definitely another reasonable doubt about the social benefits of education.
* By way of comparison, standard estimates imply that you’d need about 8 extra years of education to cause your income to double.