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A GAMLSS-based Optimal Quantile estimator for Stochastic Frontiers

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Abstract

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.

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  • Francesco Vidoli & Elisa Fusco, 2025. "A GAMLSS-based Optimal Quantile estimator for Stochastic Frontiers," Econometrics Working Papers Archive 2025_12, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
    • Handle: RePEc:fir:econom:wp2025_12
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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • Q53 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Air Pollution; Water Pollution; Noise; Hazardous Waste; Solid Waste; Recycling

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