Longitudinal peer influence models: asymptotic colinearity and error-covariance remedies

Determine whether longitudinal models of peer influence—i.e., network-based models that analyze repeated outcomes over time—exhibit the same asymptotic colinearity of peer-effect regressors observed for cross-sectional linear-in-means models when nodal covariates are independent of network structure and the minimum degree grows, and ascertain whether imposing additional structure on the error covariance can resolve the resulting estimability challenges for peer-effect parameters.

Background

The paper proves that in cross-sectional linear-in-means models, the peer-effect design columns (contagion and interference terms) become asymptotically colinear with the intercept under mild conditions, specifically when nodal covariates are independent of the network and the minimum degree grows. This asymptotic colinearity can render common estimators (OLS, 2SLS, QMLE) inconsistent or slower than parametric rates, even when peer effects are identified in finite samples.

The authors also show that dependence between nodal covariates and network structure (e.g., via random dot product graphs) can partly alleviate colinearity. Motivated by these findings, they explicitly raise the question of whether analogous issues arise in longitudinal settings and whether stronger assumptions on the error covariance could restore estimability.