Cost-Optimal School District Size in Pennsylvania: Comparing Cobb-Douglas Least Squares and Generalized Additive Model Estimation

School district consolidation has continued at a rapid pace in the United States, with one in every nine districts consolidating between 2000 and 2015 (Collins forthcoming). The stated aim of consolidation efforts is usually improved efficiency – growing larger to lower unit costs or improve student outcomes without spending more money (Callahan 1962). Economic theory on economies of size predicts that organizations may improve efficiency with size up to some optimal point, above which diseconomies set in and efficiency decreases (Rasmussen 2013). Least-squares Cobb-Douglas cost functions have been used to identify the optimal school district enrollment in the context of several states. This study builds upon the past research by using similar methods to estimate the optimal school district size in Pennsylvania and by comparing these results to estimates from a smoothed regression method called the generalized additive model (GAM). Findings from this study suggest the optimal school district size in Pennsylvania is between 6000 and 7000 students, with the opportunity for savings of $1000 or more per pupil in many of the smallest districts in the state. GAM estimates generally support the least-squares findings but reveal more nuance in the relationship between spending and student enrollment. These results are informative for policymakers considering mandatory consolidation and for future researchers who may benefit from the use of both parametric and semi-parametric methods.