Exploring Spatial Patterns in Inefficiency Using a Stationary Gaussian Random Field

This article presents a semiparametric stochastic frontier model that accounts for unobserved spatial heterogeneity in inefficiency by incorporating a stationary Gaussian random field based on geographic coordinates into the inefficiency scaling function. This approach captures spatial patterns in inefficiency at a fine scale. The proposed model is validated using simulated data and applied, within a Bayesian framework, to a panel dataset of Dutch dairy farms with precise geographic coordinates. For comparison, several alternative specifications are also estimated, excluding the spatial component, the inefficiency covariates, or both. The results confirm the presence of spatial heterogeneity and indicate that spatial dependence in inefficiency persists over relatively long distances. The estimated spatial effects reveal variation across locations, including areas with relatively higher and lower inefficiency. Model comparisons further show that omitting the spatial component and/or the scaling covariates affects the distribution of inefficiency across observations and leads to a worse model fit.