Per-pupil expenditures on education in the United States have grown immensely in recent decades, yet student achievement has been stagnant. An abundance of research has sought to solve this enigma, much of it centered on the incentive structure facing administrators. Some recent papers use TIMSS data to analyze the relationship between institutional arrangements—that typically do not vary within a single country—and student achievement. Similarly, we utilize TIMSS 1999 to determine if there is an indirect relationship between institutional arrangements and student achievement, via a relationship with school efficiency. Our results show that the specified link between institutional arrangements and student achievement (direct or indirect) is important in certain instances and confirms evidence found in previous research that certain arrangements are beneficial or detrimental to student achievement, regardless of the specification chosen.