Benchmarking the performance of water companies for regulatory purposes to improve its sustainability

Access to clean drinking water and sanitation are fundamental human rights, and ensuring availability, sustainability, and sanitation for all is a key Sustainable Development Goal. Because urban water and sanitation services are natural monopolies, regulation is needed to protect consumers and incentivize utilities to improve service quality and efficiency. Regulators commonly benchmark water companies (WCs) using frontier methods such as SFA, DEA, or hybrid approaches like StoNED. While DEA is widely used in water sector benchmarking, traditional DEA allows each WC to choose its own most favorable input and output weights, creating two shortcomings for regulatory benchmarking: (i) multiple WCs may score as efficient (equal to 1), preventing clear discrimination and ranking; and (ii) results may be perceived as unfair or unacceptable since different weight sets underlie different companies’ scores. To address these limitations, common-weights approaches have been proposed. This study adopts a DEA common set of weights (DEA-CSW) model based on the satisfaction degree concept to benchmark 23 Chilean WCs. The research question is whether DEA-CSW improves discriminatory power, fairness, and acceptability of benchmarking results for regulatory purposes compared with traditional DEA.

Prior studies benchmark water and sanitation utilities using parametric (SFA), non-parametric (DEA), or combined approaches (e.g., StoNED). There remains debate about the most suitable method for regulation. Three-stage combinations of DEA and SFA have been used to incorporate environmental effects and noise, but DEA dominates the benchmarking literature for WCs. Traditional DEA’s flexibility in weights can inflate efficiency and hinder ranking. Alternatives include cross-efficiency evaluation, which replaces self-evaluation with peer evaluation, but it may yield no efficient units and lacks Pareto optimality. Common set of weights (CSW) approaches apply the same weights to all units and can be defined by maximizing average efficiency, central weights, or the number of efficient units. Wu et al. proposed a CSW model grounded in satisfaction degree and Pareto-optimal solutions, enabling unique rankings and improved acceptability. Despite these advantages, DEA-CSW has seldom been applied for WC regulatory benchmarking.

Study design and sample: The study benchmarks 23 Chilean WCs providing drinking water and sewerage services to around 95% of the urban population across all 16 regions. The sector is largely privatized but uniformly regulated by SISS under an efficient-company model that compares actual costs with a virtual efficient utility and enforces quality standards. Variables: Two inputs measured annually in local currency (converted to thousands of euros for descriptive stats) are operational expenditure (OPEX) and capital expenditure (CAPEX). Two outputs are quality-adjusted: (y1) volume of drinking water supplied multiplied by the drinking water quality index (QDW), and (y2) number of customers with wastewater treatment multiplied by the wastewater treatment quality index (QWW). QDW and QWW range from 0 to 1; values below 1 penalize output to avoid rewarding low-cost, low-quality service. Data checks: Pearson correlations among inputs and outputs were strongly positive, satisfying DEA isotonicity. An outlier test based on the median absolute deviation did not flag any WC as an outlier. Models: 1) Output-oriented DEA-CCR (Charnes-Cooper-Rhodes) is used to compute each WC’s upper efficiency target by allowing its most favorable weights, with efficiency equal to 1 indicating best practice and values below 1 indicating potential output expansion given current inputs. 2) DEA-CSW (after Wu et al.) selects a common set of weights for all WCs by maximizing the satisfaction degree. Each WC has an upper efficiency goal (its CCR score) and a lower goal determined by the least favorable peer’s weight set. The satisfaction degree for a given CSW reflects how close each WC’s CSW-based efficiency is to its upper versus lower goal. The multi-objective program maximizes the minimum satisfaction degree (and overall satisfaction) while avoiding large disparities, yielding Pareto-optimal common weights and a unique ranking. Because the CSW optimization is nonlinear, Wu et al.’s algorithms are used to obtain solutions. Orientation: An output orientation reflects the regulatory objective for WCs to improve service outputs (quality-adjusted) without increasing inputs.

Discriminatory power: DEA-CCR identified 5 of 23 WCs (22%) as efficient (score = 1), limiting ranking discrimination. DEA-CSW identified only one efficient WC (WC8), providing a clear benchmark with full discrimination across all WCs. Efficiency levels: Average efficiency was 0.747 under DEA-CCR and 0.584 under DEA-CSW. Interpreted as potential output expansion at current inputs, this implies average scope for 25.3% output increase under DEA-CCR and 41.6% under DEA-CSW. Dispersion increased with CSW: minimum efficiency 0.323 (DEA-CCR, WC23) versus 0.198 (DEA-CSW, WC19); median 0.725 vs 0.593; standard deviation 0.197 vs 0.211. Rankings: Several WCs changed positions markedly when moving from flexible to common weights (e.g., WC1: 1.000 to 0.584; WC11: 0.753 to 0.963). WC8, a small utility serving 15,571 customers and meeting all quality standards (QDW and QWW = 1), was the sole efficient benchmark under CSW. Weights: Under DEA-CSW, the common weights assigned were OPEX 18.7%, CAPEX 29.7%, quality-adjusted volume of drinking water 43.1%, and quality-adjusted wastewater-treated customers 8.5%. Inputs and outputs received comparable aggregate weights (inputs 48.4%, outputs 51.6%). Under DEA-CCR, weights varied widely across WCs; 61% of WCs set the weight on quality-adjusted drinking water volume to zero, while no WC excluded OPEX (OPEX weights ranged 7.9%–50%). Only 13% of WCs under DEA-CCR used all four variables (nonzero weights); 17% used only two variables, demonstrating bias potential with flexible weighting. Satisfaction degree and bounds: For 13 of 23 WCs (56.5%), the gap between CSW efficiency and their upper efficiency (CCR score) was below 0.1, indicating high acceptability. WC10, WC14, and WC1 experienced the largest declines (>0.5) when moving to CSW. Illustratively, WC15 would be efficient under CCR but scored 0.489 (rank 16) under CSW. Policy-relevant statistics: Tabled efficiency summary (DEA-CCR vs DEA-CSW): averages 0.747 vs 0.584; medians 0.725 vs 0.593; standard deviations 0.197 vs 0.211; minima 0.323 vs 0.198.

Adopting common weights resolves two key regulatory issues with traditional DEA: it prevents multiple ties at the efficiency frontier and produces a single, transparent ranking that is easier for utilities to accept. DEA-CSW integrates all relevant variables in performance assessment, whereas flexible DEA frequently drops poorly performing variables (assigning zero weight), leading to partial and potentially biased evaluations across different criteria. The satisfaction-degree framework anchors each WC’s CSW score between its upper and lower goals and seeks fairness by reducing disparities in satisfaction across WCs. The empirical results show that most WCs have CSW efficiencies close to their CCR upper bounds (difference < 0.1 for 56.5% of WCs), supporting the acceptability of CSW-based benchmarking. The markedly different rankings under CSW underscore the importance of weight transparency; regulators can classify WCs into optimal, moderate, and poor performers using common criteria. The approach enhances credibility and reduces disputes, aligning with the Lisbon Charter’s call for transparent and reliable regulatory information.

This study demonstrates that a DEA common set of weights (DEA-CSW) model provides superior discriminatory power and a unique, transparent ranking compared with traditional DEA-CCR for benchmarking water companies. Applying DEA-CSW to 23 Chilean WCs identified a single efficient benchmark (WC8), produced broader dispersion in efficiency scores, and ensured that all variables contributed to performance assessment. The satisfaction-degree framework enhanced acceptability by keeping CSW efficiencies near upper goals for a majority of WCs. For regulators, DEA-CSW facilitates objective classification, greater transparency, and improved acceptance of benchmarking outcomes. Future research should: (i) extend DEA-CSW to dynamic settings to measure productivity change over time; (ii) expand the variable set with additional service quality and environmental indicators (e.g., non-revenue water, unplanned interruptions, greenhouse gas emissions) including undesirable outputs; and (iii) explore policy-driven weighting schemes to reflect evolving priorities (e.g., drought resilience) while maintaining the CSW framework.

Methodologically, DEA-CSW, like DEA generally, is sensitive to outliers and does not support statistical inference. Although an outlier check found none in this dataset, this remains a known limitation. The empirical application is static and cross-sectional, not capturing performance changes over time. The number of variables was limited (two inputs, two outputs) due to the sample size; broader datasets could allow more dimensions (including undesirable outputs). Results pertain to Chilean WCs and the specific regulatory context, which may affect generalizability.