Semiparametric Dynamic Logit Model with Endogenous Networks
This paper studies the identification and estimation of a semiparametric dynamic logit model with nonparametric link formation, in which a time-varying index of unobserved characteristics affects outcomes and links. The outcome depends on covariates, the past outcome, a fixed effect, and an unknown function of that index. Conditioning on a switch by the same agent across waves removes the fixed effect but not the change in the unknown function. When this change is common within network types and followed by a stable period, comparing two agents of the same network type, meaning they have the same probability of linking with each of the other agents, removes it and identifies covariate effects and state dependence. The pairwise conditional likelihood estimator is consistent, including when the index is continuous, and asymptotically normal when the index takes finitely many values and matches are exact. In simulations, bias falls with sample size, and coverage is near nominal among successful fits. The fixed-effects dynamic logit and pooled logits with peer-average controls remain biased when the index moves. A second estimator, conditioning on recovered network classes, is more precise. A feasibility exercise on the Glasgow Teenage Friends and Lifestyle Study examines how past use and pocket money affect adolescents' recorded tobacco or cannabis use and documents the data requirements.