Of Rivalry and Synergy: Nonparametric Patents and Products Similarity Effects on R&D Investment

This paper examines how the joint effect of product and technology similarity among firms shapes R&D investment. Technological similarity creates synergies by enabling process im- provements to be shared between related firms, within the limits of patent protection. Product similarity encourages R&D for product differentiation, however it discourages R&D for process innovation because competitors can absorb process improvements and outcompete the innovator. I formalize this mechanism with a Cournot model featuring cost-reducing R&D and knowledge spillovers weighted by technological similarity and patent protection. Product similarity enters through substitutability in the demand system and R&D investment can be also used to dampen similarity. Simulations of 1,000 firms with different costs distributions yield predictions for R&D and output at the optimal intermediate patent transmission. To tests these predictions empirically, I build a network panel dataset by combining Hoberg and Phillips product similarity measures with pairwise patent portfolio similarities derived from my PatentSBERTa_V2 embeddings of all USPTO abstracts, merged with Compustat data. Consistent with prior literature, linear models fail to identify clear effects of patent and technol- ogy similarity on R&D investment. To capture the joint and nonlinear effects predicted by the model, I estimate a Generalized Additive Model (GAM), mapping the joint interaction effect on R&D of product and technology similarity. The results are in line with our theoretical simula- tions. I further validate the empirical results by using two alternative datasets, one with older patents and product similarity measures, and one with detailed semiconductor manufacturing data from the APTO NSF grant