A Multi-output Multi-input Stochastic Frontier System with Input and Output-Specific Inefficiency

In this paper we consider a novel stochastic frontier model with multi-output multi-input production technology that accommodates non-radial inefficiency in both inputs and outputs. These measures are also observation-specific. To identify them, we use (i) a system model consisting of the revenue and cost share equations derived from the profit function and (ii) distributional assumptions on the inefficiency components and the noise terms. The error vector of the system is shown to have a closed skew normal distribution that is used to derive the likelihood function. The ML estimator of the parameters is used to derive formulas for predicting output- and input-specific inefficiencies, which are also observation-specific. We showcase the working of our model by applying it to a farm level data with two inputs and two outputs from Norway