A Comparative Review of Methods to Create a Composite Index for Sustainable and Inclusive Wellbeing

Technical Summary: A Comparative Review of Methods to Create a Composite Index for Sustainable and Inclusive Wellbeing

Problem Statement
The paper addresses the critical challenge of measuring Sustainable and Inclusive Wellbeing (SIW) beyond Gross Domestic Product (GDP). While the UN High-Level Expert Group on Beyond GDP (HLEG) has called for a shift toward broader progress metrics, it did not propose a specific composite index structure, highlighting the methodological difficulty of aggregating heterogeneous dimensions. Standard approaches, such as weighted arithmetic means or reducing SIW to subjective wellbeing alone, are deemed insufficient because they rely on assumptions of full substitutability (where deficits in one area can be fully offset by gains in another), linearity, and the absence of environmental or social limits. These assumptions conflict with the core nature of SIW, which involves non-linear relationships, diminishing returns, and "strong sustainability" constraints where natural capital and basic human needs are non-substitutable.

Methodology
The authors develop a normative framework to evaluate aggregation methods, deriving nine conditions for a valid SIW composite indicator based on needs theory and strong sustainability principles:

1. Formative measurement model: Indicators define the construct rather than reflecting a latent variable.
2. Distributional sensitivity: Inequality within countries must be penalized.
3. Cross-border spillovers: Wellbeing must not be achieved by degrading other nations.
4. Limited substitutability: Deficits cannot be fully compensated by surpluses elsewhere.
5. Penalisation of imbalances: Uneven performance should lower the overall score.
6. Intertemporal aggregation: Current wellbeing must not compromise future conditions.
7. Non-linear transformations: Saturation and threshold effects must be captured.
8. Respect for upper limits: Planetary boundaries act as hard constraints.
9. Respect for lower limits: Minimum thresholds for human needs must be satisfied.

The study reviews 13 aggregation methods across three categories:

• Baseline Approaches: Arithmetic/Geometric means, Linear Additive Models (LAM), and Principal Component Analysis (PCA).
• Advanced/Non-Compensatory Methods: Penalty-based indices (AMPI, MSI), UN indices (PHDI, MPI), Outranking MCDA (PROMETHEE, MCM), Data Envelopment Analysis (DEA), and Median-percentile aggregation.
• Cross-Disciplinary Insights: Principles from ecology (Liebig's law of the minimum, co-limitation), positive psychology, neuroscience, and machine learning (Neural Additive Models).

To illustrate the impact of these methodological choices, the authors constructed a fictitious dataset of 10 countries across 5 SIW domains (CO₂ emissions, material footprint, life expectancy, education, and income). They applied the 13 methods to this dataset and analyzed the resulting country rankings using Spearman rank correlations.

Key Results
The comparative analysis reveals three distinct clusters of methods with significant implications for policy narratives:

1. Compensatory Cluster: Arithmetic means, LAM, and geometric means are highly concordant (correlations up to $\rho = 0.98$). They assume full substitutability and linearity, often ranking countries with severe environmental deficits (e.g., Country C in the example) highly if they have high income.
2. Limiting-Factor Cluster: Methods like the Minimum operator, Co-limitation proxy, and Saturation variants are highly concordant among themselves ($\rho > 0.83$) but show moderate agreement with compensatory methods. These approaches penalize imbalances and enforce non-substitutability, causing countries with extreme shortfalls in one dimension to drop significantly in rank.
3. Outranking Cluster: Methods like PROMETHEE and Multi-Criteria Mapping (MCM) form a distinct group. They utilize veto thresholds to enforce hard constraints (e.g., excluding countries that fail environmental limits), resulting in rankings that diverge significantly from averaging methods ($\rho \approx 0.55–0.60$).

Diagnostic Findings:

• PCA Misalignment: PCA showed negative correlations with most other methods ($\rho$ as low as -0.67). The paper identifies this as a diagnostic warning: PCA seeks the axis of maximum variance (often a trade-off between development and environment) rather than the construct of wellbeing, making it unsuitable for formative SIW measurement.
• Rank Sensitivity: The choice of aggregation method drastically alters country rankings. For instance, a country with high income but near-zero environmental performance ranked first under PCA but last or near-last under non-compensatory methods.
• No "Silver Bullet": No single method reviewed satisfies all nine conditions. For example, while outranking methods handle veto logic well, they are resource-intensive; while DEA offers flexibility, it requires strict weight restrictions to avoid ignoring necessary dimensions.

Significance and Claims
The paper claims to provide a foundational step toward the "headline aggregated indicator" advocated by the UN HLEG. Its primary contributions are:

1. Normative Benchmarking: It establishes a set of nine conditions derived from strong sustainability and needs theory to rigorously assess aggregation methods.
2. Systematic Comparison: It offers the first systematic illustration of how 13 diverse methods (from simple averages to machine learning and ecological models) produce divergent policy narratives when applied to the same data.
3. Interdisciplinary Synthesis: It bridges gaps between statistics, economics, and fields like ecology and neuroscience to identify aggregation principles (e.g., minimum operators, saturation curves) rarely used in wellbeing measurement.

Conclusion and Recommendations
The authors conclude that a future SIW composite indicator cannot rely on a single method. Instead, they propose a hybrid framework combining:

• Non-linear normalisation (to address saturation and thresholds).
• Non-compensatory aggregation (to enforce limited substitutability and veto logic for critical dimensions like planetary boundaries).
• Measurement-level choices (to address inclusiveness and cross-border spillovers).

The paper asserts that the tools to move beyond linear averaging already exist (e.g., PHDI, median-percentile approaches, outranking MCDA). The barrier to implementation is no longer technical feasibility but political will and institutional capacity. The authors urge international bodies to pilot hybrid frameworks on real data and incorporate sensitivity analyses, emphasizing that the cost of delay is borne by current and future generations. Notably, the paper acknowledges that intertemporal aggregation (how to weigh current vs. future wellbeing) remains the most neglected condition and requires further research.