In the long-running debate over how many administrators are too many, two economic researchers believe they have identified an ideal ratio. For colleges to operate most effectively, they say, each institution should employ three tenured or tenure-track faculty for every one full-time administrator. What the ratio is now is difficult to say, though most colleges probably would have to hire significantly more faculty or pare back on administrators if they wanted to meet a three-to-one goal. The numbers are fuzzy and inconsistent because universities report their own data. Different institutions categorize jobs differently, and the ways they choose to count positions that blend teaching and administrative duties further complicate the data. When researchers talk about "administrators," they can never be sure exactly which employees they are including. Sometimes colleges count librarians, for example, as administrators, and sometimes they do not. In their recent study, Robert E. Martin, a professor emeritus of economics at Centre College, and R. Carter Hill, a professor of economics at Louisiana State University at Baton Rouge, attempted to quantify the factors that drive costs at 137 public research institutions. They describe their findings in a working paper titled "Measuring Baumol and Bowen Effects in Public Research Universities," released in October. The study's findings demonstrate the importance of shared governance in universities' budget decisions. Sharing decisions about hiring and other spending across different types of people, including faculty, administrators, and governing-board members, acts as a natural check and balance, ensuring that no individual side's interests rise to the top. But the study highlights a staffing trend, seen over two decades, of colleges' hiring more administrators than faculty. Universities reduced costs by hiring part-time instructors instead of tenure-track faculty, while hiring relatively more full-time administrators, the study shows. In 1987, the ratio of tenure-track faculty to full-time administrators at public research universities was 0.96, a balance of about one-to-one, with a slight tilt toward administrators. By 2008, however, the ratio of faculty to administrators had fallen to 0.56, reflecting a strong shift toward administrators. Regardless of what exact ratio might make sense, some scholars see value in trying to do a better job of quantifying colleges' costs and in taking a deeper look at higher education's structure.