That’s what Daron Acemoglu and Pascual Restrepo document in an NBER working paper.
Figure 2 [below] provides a glimpse of the relevant pattern by depicting the raw correlation between the change in GDP per capita between 1990 and 2015 and the change in the ratio of the population above 50 to the population between the ages of 20 and 49. … even when we control for initial GDP per capita, initial demographic composition and differential trends by region, there is no evidence of a negative relationship between aging and GDP per capita; on the contrary, the relationship is significantly positive in many specifications.
In an article published in 2012 with Martín Gonzalez-Eiras (see also the VoxEU column), we provide a theory that can account for this finding.