Analysing inefficiency in a non-parametric spatial-dynamic by-production framework: A k-nearest neighbour proposal

This paper accounts for spatial effects by benchmarking farms against their k-nearest neighbours (KNN) and measuring their inefficiency in a non-parametric dynamic by-production setting. The optimal number of neighbours (Formula presented.) against which farms are compared corresponds to the value of (Formula presented.) that maximises the Moran I test for spatial autocorrelation of the good and the bad output of the farms' two sub-technologies. The inefficiency scores for farms' good output, variable inputs, investments and bad outputs are then computed and compared with those calculated based on a global technology, which benchmarks all farms together. The application focuses on an unbalanced panel of specialised Dutch dairy farms over the period 2009–2016 that contains information on their exact geographical locations. The results suggest that the inefficiency scores exhibit statistically significant differences between the KNN and the global model. Specifically, the inefficiencies are generally deflated when a KNN technology is considered, suggesting that ignoring spatial effects can overestimate inefficiency.