A discussion of testing DMUs' returns to scale

Abstract

The issue of using Banker's most productive scale size (mpss) concept to characterize DMUs' returns to scale (RTS) is studied in this paper. It is shown that the mpss concept can always be used to estimate RTS without any adjustments unless a set of efficient DMUs exhibit linear dependency, i.e., it is the DMU itself that causes the mpss concept not to work. The mpss concept itself is independent of assuming a linear production function in the CCR model. As a result, Chang and Ghu's conclusions are erroneous. Also several other errors in Chang and Ghu's ‘proof’ and ‘illustration of proof’ are listed. The linear dependency condition in the current paper corresponds to the nonunique lambda solution situation in Banker and Thrall. Meanwhile a remedy is developed for the mpss concept so that it can still work under linear dependency. It is also shown that those DMUs which naturally exhibit increasing and decreasing returns to scale have nothing to do with linear dependency.