Dispersion in labor and factor productivity across firms is large and persistent, large flows of workers move across firms, and worker reallocation is an important source of productivity growth. The purpose of the paper is to provide a formal explanation for these observations that clarifies the role of worker reallocation as a source of productivity growth. Specifically, we study a modified version of the Schumpeterian model of growth induced by product innovation developed by Klette and Kortum (2002). More productive firms are those that supply higher quality products in the model. We show that more productive firms grow faster and the reallocation of workers across continuing firms contributes to aggregate productivity growth if and only if current productivity predicts future productivity. We provide evidence in support of the hypothesis that more productive firms become larger in Danish data. In addition, we provide estimates of the distribution of productivity at entry and the parameters of the cost of investment in innovation function and other structural parameters that all firms are assumed to face by fitting the model to observations on value added, employment, and wages drawn from a panel of Danish firms for the years 1992-1997.