MINNEAPOLIS—When Eric Kaler became president of the University of Minnesota last year, he pledged to curb soaring tuition by cutting administrative overhead. But he hit a snag: No one could tell him exactly what it cost to manage the school.

Like many public colleges, the University of Minnesota went on a spending spree over the past decade, paid for by a steady stream of state money and rising tuition. Officials didn't keep close tabs on their payroll as it swelled beyond 19,000 employees, nearly one for every 3½ students....