Empirical Confirmation of the Environmental-Dominance Inequality A direct decomposition of Var(ln \r{ho}eff ) across four levels of aggregation

TL;DR

This paper empirically confirms the environmental-dominance inequality across multiple data levels, showing that environmental factors often dominate income variance, with robustness across various outcomes and datasets.

Contribution

It provides the first direct empirical decomposition of the environmental-dominance inequality across four levels of aggregation using multiple datasets.

Findings

Var(ln rho_eff) significantly exceeds Var(ln k) at global and within-country levels.

The dominance ratio R ranges from 27 to 134 across datasets and levels.

The inequality is robust for income, infant mortality, and incarceration outcomes.

Abstract

Empirical confirmation of the environmental-dominance inequality Var(ln rho_eff) >> Var(ln k) from arXiv:2605.02985, computed 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, and the global pooled-individual distribution. The headline global value Var(ln rho_eff) = 4.33 yields a dominance ratio R in [27, 134] across plausible sigma_ln k in [0.18, 0.40]. The inequality holds with one-to-two orders of magnitude margin at the global and within-country-decile levels, with a single-digit but still dominant margin between countries, and collapses to R in [0.33, 1.61] within already-homogenized U.S. census tracts for income. A 1990-2022 time series shows the global aggregate stable while composition shifts from between-country dispersion (-34%) to within-country dispersion (+26%), consistent with international convergence plus Piketty r > g. Multi-outcome validation shows the inequality is robust for income, infant mortality and incarceration but shrinks toward parity for outcomes targeted by sustained global convergence (life expectancy). Partial-identification and selection-bias bounds (Chetty-style 40-50% selection share) leave R in [14, 80]. All inputs and outputs are SHA-256 hashed in an append-only manifest and fully reproducible from the accompanying notebooks.