Going as far back as Andrew Weiss’s survey paper, there are various attempts to argue that the two theories make the same predictions about earnings and education. A randomly elevated individual will earn more money but is this from having learned more or from being pooled with a more productive set of peers?
To explore this, let’s pursue the very good question asked by Bryan Caplan:
Our story begins with a 22-year-old high school graduate with a B average. He knows an unscrupulous nerd who can hack into Harvard’s central computer and give him a fake diploma, complete with transcript. In the U.S. labor market, what is the present discounted value of that fake diploma?
If he can fake a good interview (a big if, but let’s say), and if certification from recommenders is not important in the chosen sector (another big if), he may get a Harvard-quality job for his first placement. If you believe in the signaling theory, however, his marginal product is fairly low, much lower than the wage he will be paid. They will fire him. He’ll come out a bit ahead, if he is not too demoralized, but within a few years he will be paid his marginal product.
In most jobs they figure out your productivity within two or three months after training, if not sooner.
In a one-shot static setting, signaling and human capital theories might have the same empirical implications because the learning and pooling effects can produce similar links between education and wages (again assuming someone can fake an interview). But not over time and of course the wage dispersion for an educational cohort does very much increase with time. The workers don’t keep on receiving their “average marginal product” for very long.
Do not be tricked by those who serve up one-period examples to establish the empirical equivalence of signaling and human capital theories!
To tie this back to the academic literature, if IV-elevated workers enjoy an enduring wage effect comparable to that of the other degreed workers, you should conclude they learned something comparable at school unless you wish to spin an elaborate and enduring W > MP story.
Addendum: There is a less drastic scenario than the one outlined by Bryan. Let’s say there are fourteen classes of workers and a class nine worker is randomly elevated to class seven credentials. He might use that momentary good fortune to learn from smarter peers, work hard to establish a foothold, and so on. His lifetime earnings might end up as roughly those of other class seven workers, despite being of initial type nine. The higher earnings are still based on learning effects (not mainly pooling), though pooling gave that worker temporary access to some new learning and advancement opportunities. In most regards this works like the learning model, not the pooling model, although the period of learning extends beyond schooling narrowly construed.