Estimating Models with Dynamic Network Interactions and Unobserved Heterogeneity

In this paper, we propose an approach to estimate models with network interactions in the presence of individual unobserved heterogeneity. The latter may impact the formation of ties and/or exogenous effects, thereby undermining identification of the associated parameters. In a panel setting, we devise a way to cope with these sources of endogeneity by relying on observable variations. When exogenous effects are involved, one can control for unobserved heterogeneity by including time-averages of the endogenous variables. When unobserved individual traits affect the process of network formation, it is possible to explore the role of network statistics. We derive a 2SLS estimator in order to address simultaneity bias, relying on sources of variation provided by the product between successive powers of the network matrix and the matrix of exogenous covariates; we assess the performances of the method via a Monte Carlo exercise, considering various combination of models and different ranges of parameters for both network interactions and the social multiplier. We also separately assess the cases in which unobserved sources hit the network structure only or act on exogenous effects as well. Focusing on the former case, our approach may be also applied when a simple cross-section is available. More generally, it does not require full knowledge of the spectrum of agents' interactions.