I construct a model of a growing economy with pollution. The analysis of the model shows that the interactions between capital accumulation, endogenous lifetime and environmental quality determine both the long‐run growth rate and the pattern of convergence (i.e., monotonic or cyclical) towards the balanced growth path. I argue that such interactions can provide a possible explanatory factor behind the, empirically observed, negative correlation between growth and volatility. Furthermore, the model may capture the observed pattern whereby economic growth and mortality rates appear to be negatively related in the long run, but positively related in the short run.