Justice by the Numbers: Exploring Efficiency, Scale, and Scope Under Weight Restrictions Among Danish District Courts with DEA

Abstract

This study evaluates the efficiency of Danish district courts from 2016 to 2023 using data envelopment analysis (DEA) under assurance regions type I (ARI) weight restrictions (WRs), with a particular focus on identifying scale and scope effects. The analysis provides strong evidence of variable returns to scale (VRS), reveals a clear association between court size and efficiency potential, and identifies a relatively well-defined most productive scale size (MPSS), which is partially enforced by the ARI restrictions. To assess potential diseconomies of scope on the dimension of case complexity, convexity scope (CS) measures are employed to compare relatively specialized and differentiated courts. The results vary considerably depending on the application of ARI restrictions. While no consistent evidence of specialization advantages is found, results from Mann-Whitney-Wilcoxon tests comparing groups of courts, categorized by relative specialization, indicate that courts handling a higher share of complex cases tend to exhibit greater efficiency. The varying results based on the strictness of the ARI restrictions inspire a theoretical discussion of how WRs alter the shape of the efficient frontier, enhancing MPSS estimations but distorting CS values. This highlights a limitation in current methods for examining economies of scope under WRs, an issue not yet explored in the existing literature. Lastly k-Means clustering is introduced as a novel approach to search for preferable output compositions. The results suggest that output mix influences efficiency, although no single configuration proves optimal across the entire study period. Overall, the use of k-Means clustering in this context shows promise as a method to analyze and group units based on output mix.