Interpreting and Testing the Scaling Property in Models where Inefficiency Depends on Firm Characteristics

Let u ≥ 0 be technical inefficiency, let z be a set of variables that affect u, and let δ be the parameters of this relationship. The model satisfies the scaling property if u(z, δ) can be written as a scaling function h(z, δ) times a random variable u* that does not depend on z. This property implies that changes in z affect the scale but not the shape of u(z,δ). This paper reviews the existing literature and identifies models that do and do not have the scaling property. It also discusses practical advantages of the scaling property. The paper shows how to test the hypothesis of scaling, and other interesting hypotheses, in the context of the model of Wang, Journal of Productivity Analysis, 2002. Finally, two empirical examples are given.