A Two‐Stage Least Squares Estimator for Grouped Multilayer Network Autoregression With Fixed Effects

This paper investigates the parameter estimation problem for panel data with a multilayer network structure. Considering the heterogeneous behaviours or attributes exhibited by individuals, we propose a multilayer network autoregressive model with group structure. We allow individuals to have a latent group structure, whereby individuals within the same group share common slope. We assume that time‐invariant fixed effects are individually heterogeneous, which endows the model with a wide range of applications. To identify the latent group structure, we use the initial MLE for clustering purposes. Our theoretical analysis demonstrates that this two‐stage least squares (2SLS) estimator possesses desirable asymptotic normality properties. We conduct a detailed analysis of the factors influencing estimation errors and employ a jackknife method to reduce the bias of the momentum effect. Extensive simulation experiments and real data analyses validate the effectiveness of our proposed method.