DOES THE AGGREGATION METHOD REALLY MATTER? A MONTE CARLO STRESS-TEST OF RANKING CONVERGENCE IN COMPOSITE WELL-BEING INDICATORS

Abstract

The selection of an aggregation functional form is a critical step in constructing composite indicators, yet its empirical consequences are often assessed using single cross-sections. We propose a Monte Carlo framework to evaluate the convergence of country rankings produced by four aggregation methods—arithmetic mean (AM), geometric mean (GM), principal component analysis (PCA), and P2-Distance (P2D)—applied to a Sustainable Human Development Index (S-HDI). We explicitly acknowledge that the structural collinearity among standard HDI dimensions (health, education, income) mechanically constrains the divergence of rankings, thereby limiting the statistical power of convergence tests. To address this, our design incorporates: (i) 10,000 simulated datasets bounded by realistic individualized intervals; (ii) complementary convergence metrics (Spearman’s ρ, Kendall’s τ, Rank-Biased Overlap, and quartile migration analysis); and (iii) a stress-test introducing a low-correlation inequality indicator (Gini coefficient). Under high collinearity, all four methods yield Spearman correlations above 0.96. However, the stress-test reveals that when compensability and weighting schemes matter —i.e., under dimensional heterogeneity—GM and P2D diverge significantly from AM and PCA. We argue that the choice of aggregation should not rely solely on rank convergence but on theoretical grounds (compensability, information redundancy, and normative weighting). Our findings suggest that for the standard S-HDI design, simpler forms (AM/GM) are statistically equivalent to more complex alternatives, but this equivalence is design-dependent, not universal.