Discussion on 'Causal inference with misspecified network interference structure' by Bar Weinstein and Daniel Nevo.

The authors address the problem of misspecified interference structures arising from network misspecification. They first derive the bias of the mean potential outcome estimator under network misspecification, showing that it depends on the divergence between the misspecified and true networks, measured by disagreement in induced exposure values across units. They then develop Network Misspecification Robust (NMR) estimators, which yield unbiased estimation when at least one network correctly specifies the interference structure, provided that the exposure mapping and the extent of interference are both correctly specified. In this discussion, we first review common interference assumptions in the literature, highlighting the sources of misspecification and situating the authors' contribution within this broader context. We then consider possible relaxations of the assumptions required for the NMR estimator to be unbiased and examine the bias-variance tradeoff. This raises an open question on how to select the best pool of candidate networks. Here, we discuss possible selection strategies for candidate sets of networks for NMR estimators. Finally, we outline issues arising in real-world applications and propose several directions for future research building on this work.