Ever since the global financial crisis, economists have groped for reasons to explain why growth in the U.S. and abroad has repeatedly disappointed, citing everything from fiscal austerity to the euro meltdown. They are now coming to realize that one of the stiffest headwinds is also one of the hardest to overcome: demographics.

Next year, the world’s advanced economies will reach a critical milestone. For the first time since 1950, their combined working-age population will decline, according to United Nations projections,...