Identification in Dynamic Dyadic Network Formation Models with Fixed Effects

2026-04-08

AI Summary

This study addresses the identification problem in dynamic binary network formation models in the presence of individual fixed effects, time-varying covariates, and unobserved heterogeneity. The authors develop a dynamic exponential random graph model incorporating homophily, transitivity, and higher-order local subgraph statistics. They innovatively combine inequality constraints from short panels with an algebraic differencing approach to eliminate fixed effects. Under assumptions of serially independent errors and additive fixed effects, the proposed method achieves semiparametric set identification and, under specific distributional conditions, yields an exact conditional logit representation that enables point identification. This work thus establishes novel sufficient conditions and a practical pathway for identifying dynamic network models.

Abstract

This paper establishes (set) identification results in a dynamic dyadic network formation model with time-varying observed covariates, lagged local network statistics, and unobserved heterogeneity in the form of fixed effects. Our framework accommodates observed-covariate homophily, transitivity through common friends, second-order or indirect-friend effects, and more general local subgraph statistics within a single dynamic index model. The analysis combines two complementary ways of handling fixed effects: inequalities that integrate out time-invariant dyad heterogeneity by treating each dyad as a short panel, and signed-subgraph comparisons that difference out fixed effects algebraically through intertemporal variation within each dyad. We show that the semiparametric identifying restrictions can be sharpened using either or both of the following assumptions: (i) error distribution is serially independent with a known distribution, (ii) pairwise fixed effect takes the form of additive individual fixed effects. Combining (i) and (ii) under i.i.d. logit shocks, we obtain an exact conditional logit representation and provide sufficient conditions for point identification.

Problem

• dynamic dyadic network
• fixed effects
• identification
• network formation
• unobserved heterogeneity

Innovation

• dynamic dyadic networks
• fixed effects
• set identification
• conditional logit
• local subgraph statistics