Program Results

Introduction to the event

In this paper, we analyze the equilibrium efforts of agents who seek to maximize their utility when involved in multiple, possibly overlapping projects in a bipartite network. We show that both the complementarity effect between collaborating researchers and the substitutability effect between concurrent projects of the same researcher play an important role in determining the equilibrium effort level. To estimate the structural parameters of the model, we propose a Bayesian DMH procedure that accounts for the endogenous selection of researchers into research projects. We then bring our model to the data by analyzing the collaboration network of inventors in the semiconductor and pharmaceutical industries and find empirical evidence for both complementarity and substitutability effects. 

As our model has an explicit micro-foundation, it provides a formal framework for counterfactual analysis. To illustrate the importance of correctly estimating the structural model in policy evaluation, we conduct a counterfactual analysis of the impact of the incentive program on innovation output. We find that the effectiveness of innovation incentives tends to be underestimated when the complementarity is ignored and overestimated when the substitutability is ignored. We also derive the optimal incentive scheme and show that economic gains of innovation incentives can be substantial for a firm.

The proposed bipartite network model provides a general framework to analyze complex interactions within diverse systems. By delineating the relationships between two distinct sets of nodes, the model offers a versatile structure that can be applied across various domains. Besides the direct applications of our model listed in Section 2.4, we believe that, with some modifications, this framework can also be used to analyze competition between multi-product firms (cf., Bimpikis et al. 2019, with firms and product markets depicted as two distinct sets of nodes in the bipartite network), formation of syndicated loans (cf., Berlin et al. 2020, with financial institutes and borrowing firms depicted as two distinct sets of nodes), and spillovers from science to innovations (cf., Arora et al., 2021, with scientific publications and corporate patents depicted as two distinct sets of nodes).

The network of co-inventors in the pharmaceutical industry (NAICS code 325412). Only inventors with at least one collaboration are shown. Different colors indicate different company affiliations. The network consists of 2,888 nodes and 9,164 links. The average degree is 6.36. The average clustering coefficient (i.e., the average fraction of connected neighbors of a node) is 0.86.