Consistent two-stage estimation in heterogeneous network autoregressive model

Abstract

Obtaining consistent estimates of network effects in heterogeneous network autoregressive model presents significant challenges. These arise from the large number of target parameters, potential endogeneity, and non-identifiability issues. To overcome these challenges, we reformulate the model into a higher-order version. Our proposed two-stage estimation procedure first reduces parameter complexity by screening out nodes with negligible network effects. Then, we employ the ordinary least squares method and the instrumental variables technique for effective post-screening estimation. We further investigate the consistency and asymptotic normality of the estimators under appropriate assumptions and explore the case of heteroscedasticity. The finite sample performance of the two-stage method is evaluated by simulation studies and an empirical analysis.