Unveiling the myth of economies of scale in local government: empirical evidence from interpretable machine learning

The issue of economies of scale in local government continues to be a subject of extensive debate within the current scholarly discourse. This paper utilizes an interpretable machine learning framework, a random forest model augmented with SHAP (SHapley Additive exPlanations) and ICE (Individual Conditional Expectation) plot, to investigate the relationship between per capita administrative costs and population size across 252 county-level governments in Hebei, Shandong, and Shanxi provinces of China. The study finds that population size appears to be a predominant factor that influences per capita administrative costs, demonstrating an “L-shaped” curve dynamic: Below a population of 450,000, increasing population size is associated with diminishing per capita administrative costs; however, the effect fades away beyond this threshold, additional increases in population size have no effect on reducing these costs. The primary contribution of this paper lies in its innovative use of an interpretable machine learning model to explore local government issues. It not only sheds light on the complexities of economies of scale with limited data but also sets a precedent for employing similar methodologies in other areas of study.