I’m slowly working my way through the select group of empirical papers on signaling.  One of the neatest so far: Paco Martorell and Damon Clark’s 2010 working paper, “The Signaling Value of a High School Diploma.” 

Background: There are quite a few papers on the “sheepskin effect” – the discrete earnings bump you get when you finish a degree.  In principle, sheepskin effects could reflect human capital acquisition.  Maybe academic programs are like cars: if you don’t have all four tires, you can barely drive – and if you don’t have all four years of high school, you are barely more productive than a drop-out.  But in practice, most researchers interpret sheepskin effects as evidence in favor of the signaling model.  The market rewards people who finish their degrees because finishing is a signal of determination and ambition.

Martorell and Clark admit that standard estimates of the sheepskin effect are fairly large: “estimates of the return to a high school diploma in regressions of wages on diploma receipt and other controls suggests that a diploma increases wages by between ten and twenty percent.”  That’s well in excess of standard estimates of the annual return to education.  But M&C have an amazing data set that allows them to perform stronger tests than ever before.

M&C explain that some states – including Florida and Texas – won’t give students a diploma unless they pass an exit examination.  You can finish 12th grade, but if you don’t pass the test, you don’t get a diploma.*  All students take the test at least once; those who fail can repeatedly try again.  But eventually, it’s do or die.  And M&C managed to get the following information for literally hundreds of thousands of students from Florida and Texas:

a. The usual variables – years of education, demographics, etc.
b. Exact test stores – with pass thresholds
c. Income years later

To eliminate selection issues, M&C narrow down their sample to the “do or die” students.  When they do so, the sheepskin effect basically disappears.  Earnings are a smooth function of exit exam scores, with no jump at the passing score.  If I’m reading the paper correctly, their abstract is actually overly modest.  M&C don’t just “rule out signaling values larger than five or six percent”; their point estimates are roughly zero.

Overall, it’s an extremely impressive and thought-provoking paper.  But what does it mean?  My two main thoughts:

1. As M&C explain, employers rarely verify high school diplomas; they basically just take applicants’ word for it.  My question: Suppose you ask applicants who finished 12th grade but failed their entrance exam: “Did you finish high school?”  How would they respond?

I strongly suspect the vast majority would say, “Yes” – and not consider it a lie.  In contrast, while applicants who didn’t finish 12th grade face a clear temptation to claim otherwise, I suspect that many, perhaps most, admit the unflattering truth.  (Maybe they’re afraid of getting caught; maybe they think lying is wrong; maybe they’re just not very strategic).

Notice: If my suspicions are correct, employers don’t see “high school graduates with diplomas,” “high school graduates without diplomas,” and “high school drop-outs.”  Instead, they see two main groups.  The first contains: {all high school graduates with diplomas, the vast majority of high school graduates without diplomas, and dishonest drop-outs}; the second contains {a small minority of high school graduates without diplomas, and honest drop-outs}.

In this story, there would be virtually no sheepskin effect for “passing your exit exam,” precisely as M&C report.  But there could still be a large sheepskin effect for “finishing 12th grade.”  And M&C’s exit exam data, awe-inspiring though it is, would be almost powerless to detect the latter sheepskin effect.

2. As far as I can tell, M&C have the best data set ever constructed for detecting ability bias.  After all, they’ve got measures of years of education, earnings, and initial test scores – i.e. test scores before high school has had much time to work its cognitive magic (if any). 

The upshot: I’d really like to see M&C write another paper where they simply estimate the return to education with and without the initial test score as a control.  Indeed, I’d consider this a more credible lower bound on ability bias than the whole IV literature has managed to produce.  And I strongly suspect that M&C will find that this lower bound is at least 30% of the naive return to education.

* With some exceptions, of course.