It is still an open question whether increasing life expectancy as such causes higher health care expenditures (HCE) in a population. According to the "red herring" hypothesis, the positive correlation between age and HCE is exclusively due to the fact that mortality rises with age and a large share of HCE is caused by proximity to death. As a consequence, rising longevity-through falling mortality rates-may even reduce HCE. However, a weakness of many previous empirical studies is that they use cross-sectional evidence to make inferences on a development over time. In this paper, we analyse the impact of rising longevity on the trend of HCE over time by using data from a pseudo-panel of German sickness fund members over the period 1997-2009. Using (dynamic) panel data models, we find that age, mortality and 5-year survival rates each have a positive impact on per-capita HCE. Our explanation for the last finding is that physicians treat patients more aggressively if the results of these treatments pay off over a longer time span, which we call "Eubie Blake effect". A simulation on the basis of an official population forecast for Germany is used to isolate the effect of demographic ageing on real per-capita HCE over the coming decades. We find that, while falling mortality rates as such lower HCE, this effect is more than compensated by an increase in remaining life expectancy so that the net effect of ageing on HCE over time is clearly positive.