US corporate concentration has been persistently rising over the past century and productivity growth has been concurrently declining. This paper builds a continuous-time Schumpeterian growth model and interprets higher concentration as a result of lower growth, rather than the reverse. A uniform decrease in R&D efficiency increases the relative growth of leading firms compared to the aggregate and endogenously thickens the Pareto tail of firms' productivity distribution. With a demand system featuring variable demand elasticities, the model explains a large part of the changes in aggregate growth, corporate concentration, markup, labor share, R&D cost, entry and exit rates, as well as job creation and destruction rates in the US since the 1980s. The model can also accommodate increasing concentration with a stable markup and labor share in the pre-1980 period by accounting for the role of economic integration