Free Disposal Hull Radial Basis Function Estimation for Non-Convex Production Technologies and Efficiency Analysis

Conventional Data Envelopment Analysis (DEA) provides a widely used nonparametric framework for production-frontier estimation, but its convexity assumption may limit its ability to represent non-convex production technologies, particularly those characterized by increasing marginal returns. Artificial neural networks can approximate nonlinear production relationships without explicitly imposing convexity; however, their frontier-estimation performance can be adversely affected by inefficient observations and violations of monotonicity in the training data. This study proposes a hybrid Free Disposal Hull–Radial Basis Function (FDH-RBF) framework that uses FDH as a preprocessing technique to construct a monotonicity-consistent training dataset while preserving the non-convex structure of the observed production technology. An RBF network is subsequently employed to transform the discrete FDH frontier into a smooth and differentiable approximation, facilitating frontier-based efficiency analysis and the evaluation of marginal economic properties. Random simulation experiments are conducted under alternative production-function shapes and parameter settings to compare FDH-RBF with direct ANN, BCC/VRS, and CCR/CRS preprocessing approaches. The results demonstrate that FDH-RBF provides accurate frontier approximations across a broad range of production technologies and exhibits a clear advantage when the underlying production possibility set is non-convex. The proposed framework is further applied to a sample of 208 cities to estimate output efficiency and investigate urban agglomeration effects. The empirical results reveal a non-linear relationship between city size and output efficiency, including a medium-scale efficiency trap for cities with construction areas between 50 and 100 km². These findings highlight the potential of FDH-RBF as a flexible frontier-estimation framework for applications in which preserving non-convexity is essential.