Why empirical cost functions get scale economies wrong

Empirical applications of the translog cost function often conclude that firms operate at increasing returns to scale. From the viewpoint of economic theory, this does not make sense. We demonstrate that empirical cost functions ignore the fact that differences in firm output depends on cost differences between firms. We show graphically and mathematically that ignoring this mechanism leads to an overestimation of returns to scale. We propose a slightly altered specification and test it empirically. The empirical results show that the alternative specification yields better statistical results and is consistent with economic theory.