Among the rich economies of the world today, per capita output levels had typically diverged before converging to the per capita output level of the frontier economy. Since frontier economies have grown at stable rates, non-frontier economies display an S-shape aggregate transition path. Along this transition, there are "catapult effects": longer episodes of divergence are associated with faster subsequent rates of convergence to the frontier. In this paper, we construct and quantitatively assess a model of S-shaped transition with catapult effects. Deviations in per capita output from frontier economy levels are endogenous, while conventional growth accounting would classify these deviations as TFP differences