In their paper "The Economic Effects of the 1918 Influenza Epidemic" (Working Paper, 2002), Elizabeth Brainerd and Mark V. Siegler examine a graphically powerful natural experiment. They use the 1918 Influenza Epidemic as a natural experiment on population. The dramatic loss of life and the seriousness of the epidemic can be seen in Figure 1 (click to enlarge). The fact that this flu took out middle-aged people rather than young and old people can be seen from the "W" shape in Figure 2a (click to enlarge).
The authors find a very robust impact on areas hit heavily by the flu: higher growth rates (consistent with standard neoclassical growth model predictions).