We develop a tractable dynamic model of productivity growth and technology spillovers that is consistent with the emergence of real world empirical productivity distributions. Firms can improve productivity by engaging in in-house R\&D, or alternatively, by trying to imitate other firms' technologies, subject to the limits of their absorptive capacities. The outcome of both strategies is stochastic. The choice between in-house R\&D and imitation is endogenous, and based on firms' profit maximization motive. Firms closer to the technological frontier face fewer imitation opportunities, and choose in-house R\&D, while firms farther from the frontier try to imitate more productive technologies. The equilibrium choice leads to a balanced-growth equilibrium featuring persistent productivity differences even when starting from ex-ante identical firms. The long-run productivity distribution can be described as a traveling wave with tails following a Pareto as can be observed in the empirical data.