Boundary problems with the ‘Russell’ graph measure of technical efficiency: a refinement

In an influential paper, Färe and Lovell (J Econ Theory 19:150–162, 1978) proposed an (input based) technical efficiency index designed to correct two fundamental inadequacies of the Debreu‐Farrell index: its failure to satisfy (1) indication (the index is equal to 1 if and only if the input bundle is technically efficient) and (2) weak monotonicity (an increase in any one input quantity cannot increase the value of the index). Färe et al. (1985) extended the index to measure efficiency in the full space of input and output quantities. Unfortunately, this index fails to satisfy not only indication and monotonicity at the boundary (of output space), but also weak monotonicity. We show, however, that a simple modification of the index corrects these flaws. To demonstrate the tractability of our proposal, we apply it to baseball batting performance, in which zero outputs occur frequently.