Model Averaging for Stochastic Frontier Models with Differential Privacy

In the era of data-driven decision-making, stochastic frontier models (SFMs) have become a powerful tool for analyzing production efficiency across various domains. While model averaging is an effective strategy to mitigate model misspecification and enhance prediction accuracy, existing approaches often overlook the risks of individual privacy leakage during the model weighting process. To address this challenge, we propose a novel differentially private model averaging framework for stochastic frontier models. We develop two variants of differentially private Frank-Wolfe algorithms tailored to low-to-moderate and high-dimensional candidate model spaces, respectively, achieving a favorable trade-off between privacy protection and estimation accuracy. Our method integrates differential privacy guarantees into the weight optimization procedure via perturbation mechanisms and privacy-aware algorithms,such as a private variant of the Frank-Wolfe algorithm. We further analyze both theoretical utility bounds and empirical performance under various privacy budgets. Simulation studies demonstrate that our approach achieves a favorable balance between prediction accuracy and privacy protection, outperforming baseline regularization methods in scenarios with high model uncertainty.