Did World Trade Stop Outgrowing World Output? The Income Elasticity of Trade 1971–2025, an Exact Identity Separating Trend from Cycle, and the Break-Even Growth Rate for Openness

The claim that world trade lost its ability to grow faster than world output after 2011 rests on a ratio of average growth rates. Using World Bank constant-price data for 1971–2025 (vintage 8 October 2026), I show that this ratio mixes two different things. I prove that the ratio of mean trade growth to mean GDP growth equals the regression slope of trade growth on GDP growth plus the intercept divided by mean GDP growth, exactly, in every sample. The ratio fell from 1.939 in 1986–2000 and 1.510 in 2001–2011 to 1.072 in 2012–2025. The regression slope, which measures how strongly trade moves with the business cycle, did not collapse: it was 2.474, 3.448 and 2.136 in the same periods, so it ended somewhat below its 1986–2000 level but far above one. The fall is in the intercept, the trend in trade that is unrelated to GDP growth. I derive the break-even rate of world GDP growth below which the trade-to-GDP ratio falls, g* = −a/(b − 1). It rose from 1.147% a year in 1986–2000 to 2.364% in 2001–2011 and 2.614% in 2012–2025, close to actual world growth of 2.791%, so world openness rose by only 0.20 log points a year. A sup-Wald test does not find a single significant break over the whole period (bootstrap p = 0.134). India's real exports moved one for one with world trade over 1971–2025 (slope 1.014) and India's share of world real exports rose from 0.45% in 1990 to 2.65% in 2025.