A GAMLSS-based Optimal Quantile estimator for Stochastic Frontiers

Efficiency in public services is an equity issue: inefficiency diverts resources from vulnerable populations who depend on public provision, while inaccurate measurement risks confounding structural disadvantage with managerial failure. To reply these issues, this paper proposes a new stochastic frontier estimator that combines Generalized Additive Models for Location, Scale and Shape (GAMLSS) with a data-driven optimal quantile criterion. By modelling the full conditional distribution of production outputs/costs, the approach captures non-linearity, heteroskedasticity and asymmetric inefficiency that traditional parametric frontier models cannot accommodate. Monte Carlo experiments, spanning linear, non-linear and endogenous inefficiency designs, show that the GAMLSS optimal quantile estimator systematically outperforms standard SFA and Fan-type corrections. An application to municipal waste management in Italy confirms its empirical advantages, revealing substantial heterogeneity in cost levels and dispersion. Results demonstrate that distributional flexibility is essential for fair benchmarking and targeted policy design in heterogeneous public service sectors.