Scandinavian Working Papers in Economics
Memorandum,
Oslo University, Department of Economics
No 14/2015: Productivity Interpretations of the Farrell Efficiency Measures and the Malmquist Index and its Decomposition
Finn. R. Førsund ()
Additional contact information
Finn. R. Førsund: Dept. of Economics, University of Oslo, Postal: Department of Economics, University of Oslo, P.O Box 1095 Blindern, N-0317 Oslo, Norway
Abstract: The ratio definition of efficiency has the form of a productivity measure. But the weights are endogenous variables and they do not function as weights in a productivity index proper. It is shown that extended Farrell measures of efficiency can all be given an interpretation as productivity measures as observed productivity relative to productivity at the various projection points on the frontier. The Malmquist productivity index is the efficiency score for a unit in a period relative to the efficiency score in a previous period, thus based on a maximal common expansion factor for outputs or common contraction factor for inputs not involving any individual weighting of outputs or inputs, as is the case if a Törnqvist or ideal Fisher index is used. The multiplicative decomposition of the Malmquist productivity index into an efficiency part and a frontier shift part should not be taken to imply causality.
Keywords: Farrell efficiency measures; Technically optimal scale; Malmquist productivity index; Decomposition of the Malmquist productivity index
26 pages, August 31, 2015
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memo-14-2015.pdf
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