Analysing determinate components of an approximated Luenberger–Hicks–Moorsteen productivity indicator: An application to German dairy-processing firms

The Luenberger–Hicks–Moorsteen (LHM) total factor productivity (TFP) indicator has sound theoretical properties, but its decomposition yields indeterminate components of technical change and scale efficiency change that can become infeasible. The current paper decomposes the approximating Bennet indicator, which results in determinate components of technical change, technical efficiency change, scale efficiency change and mix efficiency change that are always feasible. The application focuses on the German dairy-processing sector, an important postfarm supply chain actor. We compute 558 growth rates for the period 2011–2020. The results show that the LHM-approximating Bennet indicator decreases by on average 1.14% p.a., with substantial annual fluctuations. The underlying components of output- and input-oriented technical change also fluctuate substantially, and often conflict. Moreover, output- and input-oriented TFP efficiency change fluctuate moderately on average, which is mainly driven by scale efficiency change and mix efficiency change. The components of technical efficiency change remain relatively stable on average. Indeterminateness is a relevant problem when decomposing the original LHM indicator for the current sample: depending on the specification, the proportion of infeasibilities when decomposing the original LHM indicator ranges between 6.09% and 15.95%. Our proposed determinate decomposition is thus a valuable complement. [EconLit Citations: D24, D25, Q13].