Given the rather large discontinuity in the search scope variable displayed in Figure 2, linear regression analysis is inappropriate.
The dependent variable is search scope. Control variables include indicator variables for whether the department is located in a business school or in a private university, indicator variables for whether the position is advertised as joint with another department, indicators for junior-level searches and senior-level searches (omitted category is open-rank search), a measure of department size, and year effects.
As would be expected, this measure is positively correlated with department rank (better departments are less concentrated), negatively correlated with size (larger departments are less concentrated), and negatively correlated with the search scope measure (more concentrated departments have narrower searches).
The magnitude of the effect of rank on search scope is of modest but very reasonable magnitude.
If this is the case, then the coefficient estimate for quality ranking is attenuated toward zero and we underestimate the impact of quality ranking on search scope. One correction for measurement error is to instrument the NRC ranking with a second measure of quality.
A difference in ranking of 20 places generates a difference in search scope equivalent to a major general field (six to nine subfields).