On the Choice of Functional Forms in the Measurement of Scale and Scope Economies: Generalized Box-Cox and Composite Cost Functions

Abstract

Abstract This paper estimates and compares generalized Box-Cox and composite cost functions to identify scale and scope economies. The robustness of the outcomes to different functional specifications was examined. Increasing returns to scale was common for product-specific and the overall measures. Generalized Leontief and composite forms yielded more robust elasticity, scale and scope measures. The generalized Box-Cox model was selected as the appropriate functional form as all the special cases were rejected. 1. Introduction The search for appropriate functional forms in production agriculture has continued to dominate the economics literature. Various functional forms have been used to more accurately explain or predict producer behavior. The parameter estimates of interest can, however, be very sensitive to the types of functional forms used because of the different restrictions and assumptions that are basically imposed by the different forms. Some of the time, researchers have failed to test the sensitivity of such estimates to different forms and under different assumptions. In some cases, general comparisons of estimates are made to other related studies without considering the differing kernels and motivations for such studies. The foregoing has implications for the recommendation and the utilization of the economic measures. Berndt and Khaled (1979) proposed a generalized Box-Cox cost function, with and without technological change, that takes on special or limiting cases of generalized Leontief (GL), generalized square-root quadratic (GSRQ), and translog (TLOG) cost 1