This paper presents a simple formula that relates the tail index of the firm size distribution to the aggregate speed with which an economy converges to its balanced growth path. The fact that there are so many firms in the right tail implies that aggregate shocks that permanently destroy employment among incumbent firms, rather than cause these firms to scale back temporarily, are followed by slow recoveries. This is true despite the presence of many rapidly growing firms. Aggregate convergence rates are non-linear: they can be very high for economies far below the balanced growth path and very low for advanced economies.