We construct a model of rm dynamics with heterogenous productivity and distortions. The productivity distribution evolves endogenously as the result of the decisions of ﬁrms seeking to upgrade their productivity over time. Firms can adopt two strategies toward that end: imitation and innovation. The theory bears predictions about the evolution of the productivity distribution. We structurally estimate the stationary state of the dynamic model targeting moments of the empirical distribution of R&D and TFP growth in China during the period 2007-2012.