The working age share of the population has evolved, and will continue to evolve, asymmetrically across countries. I develop a dynamic, multicountry, Ricardian trade model with endogenous labor supply to quantify how these asymmetries systematically affect the pattern of trade imbalances across 28 countries from 1970-2014. Changes in both domestic and foreign working age shares impact a country's net exports directly through the demand for net saving and indirectly through relative labor supply and population growth. Counterfactually removing demographic-induced changes to saving unveils a strong negative contemporaneous relationship between net exports and productivity growth. Demographics, thus, alleviate the allocation puzzle, and do so to a greater degree than investment distortions. Neither labor market distortions nor trade distortions systematically reconcile the puzzle.