What Is the Economic Meaning of FDH? A Reply to Thrall

In a recent issue of the Journal of Productivity Analysis, Thrall (1999) called for abandoning the Free Disposable Hull (FDH, Deprins et al. (1984)) approximation of production possibilities as economically meaningless in comparison to the Convex Monotone Hull (CMH; Banker et al. (1984)) approximation. This strong conclusion was solely based on Thrall's Principal Theorem, which essentially demonstrates that FDH can give a technically efficient classification to output-input vectors that are inefficient in terms of profit maximisation, i.e. at all non-negative price vectors there exists an alternative output-input vector that yields higher profit. In this short communication, we argue that the economic meaning of the competing empirical production sets cannot be inferred from this theorem. Specifically, we demonstrate that both empirical production sets are economically equally meaningful under the economic conditions that underlie Thrall's theorem. In addition, we demonstrate that FDH can be economically more meaningful than CMH under non-trivial alternative economic conditions.

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