In the second half of the 20th century, most industrialized countries experienced declining fertility, rising life expectancy and a slowdown of population growth. Standard models of R&D‐based growth predict that a decline in population growth reduces economic growth. We argue that this implication hinges on the assumption of infinitely lived individuals. The semi‐endogenous growth model with overlapping generations that we propose implies a negative relationship between population growth and economic growth during a substantial part of the transitional dynamics if the decline in population growth is accompanied by an increase in life expectancy as observed in industrialized countries.