Hierarchical conditional forests for meta-frontier analysis under input uncertainty

Conventional meta–frontier benchmarking with Data Envelopment Analysis (DEA) treats observed inputs as exact, even though measurement is often noisy. We propose a decision-centric alternative that learns the distribution of inputs given outputs and group labels via a hierarchical conditional forest, then propagates input uncertainty by drawing nonnegative pseudo-inputs and recomputing group and meta frontiers across replications. The forest shares splits across groups and partially pools leafwise moments, stabilizing small or heterogeneous groups without imposing a common inefficiency law. This yields level uncertainty: interpretable intervals and probabilities for efficiency distances and technology-gap ratios that reflect realistic re-measurement of inputs. We emphasize that these intervals represent conditional predictive distributions under the learned input law, conceptually distinct from Bayesian posterior intervals for latent parameters or frequentist confidence intervals for population quantities. We establish measurability and Monte Carlo consistency, validate on synthetic data, and apply the method to the 2019 Penn World Table. Compared with single-shot benchmarking, our approach delivers more conservative gap assessments, particularly for the pooled middle-income group, and expresses uncertainty in a format that is directly usable for policy thresholds and cross-group comparisons.