We estimate an aggregate elasticity of substitution between capital and labor near or below one, which implies that capital deepening cannot explain the global decline in labor's share. Our methodology derives from transition paths in the neo-classical growth model. The elasticity of substitution is identified from the cross-country correlation between trends in the labor share and (a proxy for) the rental rate of capital. Trends in labor's share and the rental rate are weakly correlated across countries, and inversely related in most samples. Previous cross-country estimates of this elasticity were substantially greater than one, which we show was partly due to omitted variable bias: earlier studies used investment prices alone to proxy for the rental rate, whereas the growth model relates rental rates to investment prices and consumption growth.