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There is substantial heterogeneity across industries in the level of interdependence between new and old technologies. I propose a measure of this interdependence–an index of sequentiality in innovation–which is the transfer rate of patents in a particular industry. I find that highly sequential industries have higher profitability, higher variance of firm growth, lower exit rates, and lower rates of patent expiry. To better understand these trends, I construct a model of firm dynamics where the productivity of firms evolves endogenously through innovations. New innovators either replace existing technologies or must purchase the rights to existing technologies from incumbents in order to produce, depending on the level of sequentiality in the industry. Estimating the model using data on US firms and recent data on US patent transfers, I can account for a large fraction of the cross-industry trends described above. Because innovation results in larger monopoly distortions in more sequential industries, there is an overinvestment of research inputs into these industries. This misallocation, which amounts to 2.5% in consumption equivalent terms, can be partially remedied using a patent policy featuring weaker protection in more sequential industries, producing welfare gains of 1.7%.