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May 9, 20260 citationsOpen Access

Empirical Confirmation of the Environmental-Dominance Inequality: A direct decomposition of Var (ln ρₑff) across four levels of aggregation

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KSKristian Sestak

Key Points

  • This research aims to confirm the environmental-dominance inequality by analyzing variance in economic indicators across different aggregation levels.
  • Computed Var(ln rho_eff) using three public datasets: Opportunity Atlas, World Bank GDP per capita PPP, and World Inequality Database.
  • Analyzed data across four levels of aggregation: U.S. census tracts, between countries, within-country deciles, and global pooled individuals.
  • Performed a partial-identification analysis to evaluate the robustness of the dominance ratio R under varying conditions.
  • Dominance ratio R ranged between 27 and 134 at the global level with an aggregate value of 4.33.
  • The hypothesis was supported globally and across country levels but weakened within homogenized units, indicating the inequality is outcome-dependent.
  • A time-series analysis from 1990-2022 showed stable aggregate R while revealing shifts from between-country to within-country dispersion, aligning with Piketty's r > g dynamics.

Abstract

Companion paper to Sestak (2026) that empirically confirms the environmental-dominance inequality Var (ln rhoₑff) >> Var (ln k) by computing Var (ln rhoₑff) directly from three public datasets (Opportunity Atlas, World Bank GDP per capita PPP, World Inequality Database) at four levels of aggregation (U. S. census tracts, between countries, within-country deciles, global pooled individuals). The headline value at the global level is 4. 33, giving a dominance ratio R between 27 and 134 across plausible sigmaₗnₖ in 0. 18, 0. 40. The thesis is confirmed at the global, within-country-decile, and between-country levels but breaks down within already-homogenized sub-units (within-tract income gives R in 0. 33, 1. 61) ; a partial-identification analysis shows R survives modest reattribution to capability (alpha g dynamics. All inputs and outputs are SHA-256 hashed and the analysis is fully reproducible.

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Cite This Study

Kristian Sestak (2026) studied this question.

synapsesocial.com/papers/69fed0c1b9154b0b82877dcfhttps://doi.org/10.5281/zenodo.20074286
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