[O]btaining unbiased estimates of the return to college quality is difficult due to unobserved characteristics that affect both a student’s attendance at a highly selective college and their later earnings. In particular, the same characteristics (such as ambition) that lead students to apply to highly selective colleges may also be rewarded in the labor market. Likewise, the attributes that admissions officers are looking for when selecting students for college may be similar to the attributes that employers are seeking when hiring and promoting workers.I'm not sure how Dale and Krueger interpret the finding of 20% higher earnings five to ten years after graduation in (white male) students who just made the cut-off versus students who just missed it.
Early research attempted to overcome this omitted-variable bias by controlling for observed student characteristics, such as high school grades, standardized test scores, and parental background (see, for example, Monks 2000 and Brewer and Ehrenberg 1996). More recent research has tried to overcome the bias created by unobserved variables through a variety of techniques. Hoekstra (2009) uses a regression discontinuity design that compares the earnings of students who were just above the admissions cutoff for a state university to those that were just below it. He finds that attending the flagship state university results in 20 percent higher earnings five to ten years after graduation for white men, but he does not find an effect on earnings for white women.
Estimating the Return to College Selectivity over the Career Using Administrative Earnings Data
Stacy Dale, Alan B. Krueger
NBER Working Paper No. 17159
Issued in June 2011
I assume they would expect to find that the students who made the cut-off applied to a more selective group of colleges than the students who just missed the cut-off, but I don't know.