Benefit of the doubt models: some issues and insights

Abstract

The Benefit of the Doubt (BoD) models offer a flexible way to construct composite indicators by endogenously aggregating performance metrics, appealing to managers who favour indices over complex DEA frameworks. While prior studies focus on BoD’s aggregation mechanism and employ weight restrictions to avoid zero weights, few leverage peer benchmarks and target values to enhance performance insights. This paper advances the BoD approach in three ways. First, we provide a comprehensive review of input- and output-oriented BoD model variations, clarifying which formulation best suits scenarios with (1) multiple outputs and a single input normalised to one, or (2) multiple inputs and single output set to one, thereby ensuring meaningful and actionable benchmarks. Second, we develop models that identify the minimum weight bounds (α) each decision-making-unit (DMU) can sustain while preserving its unconstrained efficiency score, with higher α indicating greater robustness across all performance dimensions. Third, we propose using the lowest α among top-performing (strong efficient) units as a universal weight bound, maintaining the efficiency frontier while exposing underperformance (non-radial slacks) in weaker units. These innovations strengthen the analytical rigour and policy relevance of BoD, enabling robust evaluation and targeted improvement strategies. We illustrate the approach using data from 30 large U.S. banks, evaluating performance across four prudential pillars—capital adequacy (Tier 1), earnings (ROE), operating efficiency, and funding stability—to derive interpretable scores, peer benchmarks, and actionable priorities.