This paper introduces a new statistical framework, called Selection-corrected Heterogeneous Spatial Autoregressive (SCHSAR), to measure how people or firms influence each other inside a network while accounting for how they choose their connections. The key point is that links between units (for example, firms that collaborate) are not random. If those link choices are driven by traits that also affect outcomes (for example, R&D investments), standard methods can give biased estimates of peer effects. SCHSAR models link formation and outcomes at the same time and corrects for that selection.

The authors build two linked equations. One equation models the formation of dyadic links (who connects with whom) and allows the link shocks to follow a normal (probit-style) structure. The second equation models outcomes and allows people or firms to fall into a small number of latent types, or groups, each with its own peer-effect parameters. This “finite mixture” idea captures unobserved heterogeneity: different agents can respond differently to their peers. To estimate the model the authors use a fully Bayesian Markov chain Monte Carlo algorithm with data augmentation. That approach samples the unobserved quantities and parameters together, which avoids hard numerical integration and delivers posterior predictions for each unit’s latent type.

The paper checks the method with simulations. The Monte Carlo evidence reported in the excerpt shows the Bayesian implementation is computationally tractable and has good frequentist properties in their tests. The simulations also suggest the SCHSAR model performs better than simpler approaches that either ignore endogenous link formation or assume everyone responds the same way to peers.

The authors apply SCHSAR to an innovation collaboration network of 1,150 U.S. firms and focus on corporate R&D investment. After correcting for endogenous network formation, they find positive but heterogeneous peer effects. The model identifies two latent firm types. About 34% of firms are “peer-driven” with a larger estimated network effect of about 0.215 and an own-price elasticity (sensitivity to an R&D tax price) near −2.2. The remaining 66% are “self-driven” with a smaller network effect around 0.127 and a stronger own-price elasticity near −9.5. The authors also disentangle firms that are good transmitters of innovation from those that are good absorbers, and they note that targeting firms with high total spillout effects—often central firms in high-tech sectors—could speed up network-wide diffusion of innovation.

There are important caveats. The method relies on the joint specification of link formation and outcomes and on the chosen finite mixture structure for heterogeneity. Those modeling choices matter: different numbers of latent types or different link-formation assumptions could change results. The work in the excerpt is presented in a cross-sectional setting, and extensions to panel data are suggested but not shown here. Finally, while the Bayesian algorithm addresses numerical and inferential challenges, results are conditional on the model and data used; the procedure reduces, but does not eliminate, uncertainty about unobserved factors that drive both links and outcomes.