Testing Cost Function Convexity under Nonconvex Variable Returns-to-Scale Technologies: Evidence from U.S. Banks

In this work, we assess the similarities between two nonconvex variable returns-to-scale nonparametric technologies: the traditional free disposal hull technology, and an alternative technology defined as the intersection of non-increasing and non-decreasing returns-to-scale technologies. The latter technology is slightly larger than the traditional free disposal hull, and it has rarely if ever been employed in empirical work. We also explore the differences between the corresponding two cost functions: the cost function based on the intersection of non-increasing and non-decreasing returns-to-scale cost functions is also larger than the traditional nonconvex variable returns to scale cost function and represents a new contribution to the literature. We define ways to compute both technologies and cost functions. We explore the empirical similarities between these two technologies and cost functions as well as their convex counterparts. We check whether both nonconvex technologies and cost functions make any differences in testing for convexity using a secondary data set: we still reject convexity under all circumstances.