There are indications that business dynamism has declined in advanced economies. In particular, firm entry and exit rates have fallen, suggesting that the creative destruction process has lost some of its vitality. Meanwhile, productivity growth has slowed. Some believe that lower entry and exit rates partly explain the weaker productivity growth. However, the evidence supporting, or invalidating, this view is scarce. In the present paper, we use multi-horizon causality tests and dynamic simulations with Canadian and US data to examine the following question: Do changes to entry and exit rates provide information about, or Granger-cause, future productivity? We do not find significant evidence that entry rates Granger-cause productivity. But we do find evidence that productivity causes entry rates. Using small models with economy-wide data (but not at the sectoral level), we find some evidence that exit rates cause productivity in both countries. This suggests that the decline in productivity growth is partly caused by a decline in the productivity-based exit selection process. However, when other variables, such as measures of the business cycle and the real effective exchange rate, are controlled for, the significance of exit rates in explaining productivity tends to fall. Specifically, business-cycle measures appear to cause both productivity and the exit rate. This suggests that firm dynamics are an intermediate, not an ultimate, cause of productivity growth.