Identification in Dynamic Dyadic Network Formation Models with Fixed Effects
TLDR
This paper establishes identification results for dynamic dyadic network formation models, incorporating fixed effects, time-varying covariates, and local network statistics.
Key contributions
- Establishes (set) identification for dynamic dyadic network formation models with fixed effects.
- Framework incorporates homophily, transitivity, and general local subgraph statistics.
- Introduces two novel methods for handling fixed effects: short panel integration and signed-subgraph comparisons.
- Provides conditions for point identification, including an exact conditional logit representation.
Why it matters
This paper advances the understanding of how to identify parameters in complex dynamic network models. By addressing unobserved heterogeneity through fixed effects, it provides robust methods for analyzing social and economic network evolution. The results are crucial for empirical research on network formation.
Original 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.
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