Hybrid Quantile-Expectile Error Layers for Technical-Efficiency Recovery in Stochastic Frontier Analysis

This paper develops and evaluates HQER-SFA, a likelihood-based stochastic frontier specification that embeds a hybrid quantile-expectile error layer into the bilateral noise component while preserving the standard one-sided inefficiency structure. The model nests Quantile-SFA when γ=0 and extends it by normalizing the hybrid loss into a proper bilateral error density, so that likelihood inference, residual decomposition, and technical-efficiency recovery remain in a unified stochastic-frontier framework. We compare HQER-SFA with Traditional-SFA and Quantile-SFA using three processed production modules, Monte Carlo parameter-inversion experiments, an expanded R=300 robustness design, γ sensitivity and ablation checks, convergence diagnostics, and a source-assisted small-sample extension. The results demonstrate clear gains for technical-efficiency recovery: in the R=300 design, HQER-SFA attains win rates of 0.5646 for technical-efficiency RMSE and 0.5578 for technical-efficiency rank correlation, and the agricultural module shows the strongest real-data improvement under the flexible bilateral error layer. The source-assisted analysis further shows that same-domain initialization improves small-sample validation RMSE by about 2.43%, while excessive source-centered penalties should be controlled. Overall, HQER-SFA provides an interpretable and computationally feasible extension for technical-efficiency recovery, especially when bilateral noise is asymmetric, tail-sensitive, or heterogeneous across production modules.