Firm Size, Innovation Dynamics and Growth

This paper investigates the relationship between the size of the firm and the quality of innovations of the firm. Much of the previous literature on innovation focuses on innovation frequency with an economy-wide uniform innovation quality. In contrast to the previous literature, this paper allows firms to choose not only the stochastic innovation frequency but also the innovation quality and focuses on how this heterogeneity in innovation quality is affected by the size of the firm. This paper has three distinct contributions: First, using Compustat firms and their patent applications, I document the following three reduced form facts: i) Firm sales growth (both short-run and long-run) is negatively related to the firm size. ii) Firm R&D intensity, defined as R&D expenses over sales is negatively related to the firm size. iii) The quality of innovation, proxied by the number of citations that a patent receives, is negatively related to the firm size. Second, I build a tractable general equilibrium growth model that is rich enough to investigate these empirical results. I prove the existence of the equilibrium, characterize its properties and show that the predictions of the theoretical model are consistent with the reduced form evidences mentioned above. Third, I structurally estimate the theoretical model parameters using Simulated Method of Moments on Compustat firms. Finally, I use these estimated parameters to conduct a macro policy experiment to evaluate the effects of a size-dependent R&D subsidy on different sized firms. In conclusion of this analysis, the optimal size-dependent R&D subsidy policy does considerably better than optimal uniform (size-independent) policy. More interestingly, the optimal (welfare-maximizing) policy provides higher subsidies to smaller firms.

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