Who Reduced Between-Country Inequality, 1990–2024? An Exact Path-Integral Decomposition of the Mean Log Deviation Across 183 Economies

Population-weighted inequality of GDP per head between 183 economies, which together hold 96.9% of world population, fell sharply between 1990 and 2024: the mean log deviation (MLD) from 0.7741 to 0.3850, the Theil index from 0.6611 to 0.3439 and the Gini coefficient from 0.6088 to 0.4520 (World Bank PPP data, constant 2021 international dollars). I derive the gradient of the MLD with respect to each country's log income, which is the country's income share minus its population share, and use the gradient theorem to split the change exactly into country contributions along a straight path in log incomes, plus a separate term for changes in population weights. Income growth lowered the MLD by 0.4471 and population reweighting raised it by 0.0580. China contributed −0.3202 and India −0.1775; together they account for 111% of the income-growth effect, because the growth of rich countries such as the United States (+0.0675) pushed the other way. Without China and India the MLD barely moved (0.5403 to 0.5169) and the Gini rose. A first-order approximation using 1990 gradients overstates the fall by 46%, because China's gradient shrank from −0.188 to almost zero as it approached the world mean; at 2024 incomes, further Chinese growth raises the index while Indian growth still lowers it.