Measuring Technical Efficiency under Factor Non-Substitution: A Stochastic von Liebig Crop Response Model

The present paper develops an econometric model for measuring input-oriented technical efficiency when the underlying technology is characterized by the lack of substitution between inputs. In this instances, Farrell’s radial measure of technical inefficiency is inappropriate as it may be possible to identify a technical inefficient bundle as technical efficient. Instead Russell’s non-radial indices can adequately measure technical inefficiency in factor limitation models. To this end, a disequilibrium model augmented with a regime specific technical inefficiency term is proposed and its likelihood function derived together with the computation of technical efficiency under specific distributional assumptions. The framework under which the model is proposed is the well known von Liebig hypothesis that analyses crop response to different levels of fertilizer nutrients. Application of the proposed stochastic von Liebig crop response model to the experimental data of Heady and Pesek (1954) points out to the fact that technical inefficiency can arise for a subset of the nutrients considered.