Estimating production technologies using multi-output adaptive constrained enveloping splines

Abstract

Data Envelopment Analysis (DEA) is a widely used method for evaluating the relative efficiency of decision-making units, but it often yields overly optimistic efficiency estimates, particularly with small sample sizes. To overcome this limitation, we introduce Adaptive Constrained Enveloping Splines (ACES), a non-parametric technique based on regression splines to accommodate multi-output, multi-input production contexts. ACES employs a three-stage estimation process. In the first stage, optimal output levels are estimated while incorporating essential envelope constraints, with optional monotonicity and/or concavity adjustments as needed. In the second stage, a refinement phase is carried out in which some of the estimates made are replaced by the observed values. Finally, a DEA-type technology is constructed using a new virtual data sample, ensuring adherence to usual shape constraints. Although ACES entails a higher computational cost, it achieves substantially lower mean squared error and bias than alternative methods of the literature across a wide range of simulated scenarios. This improvement is particularly pronounced in settings with complex production structures or heterogeneous returns to scale. This performance is consistent across both noise-free and noisy data environments, underscoring the method’s robustness and accuracy.