Abstract
Factor structures or interactive effects are convenient devices to incorporate latent variables in panel data models. We consider fixed effect estimation of nonlinear panel single-index models with factor structures in the unobservables, which include logit, probit, ordered probit and Poisson specifications. We establish that fixed effect estimators of model parameters and average partial effects have normal distributions when the two dimensions of the panel grow large, but might suffer from incidental parameter bias. We also show how models with factor structures can be applied to capture important features of network data such as reciprocity, degree heterogeneity, homophily in latent variables, and clustering. We illustrate this applicability with an empirical example to the estimation of a gravity equation of international trade between countries using a Poisson model with multiple factors.
Highlights
Factor structures or interactive effects are convenient devices to incorporate latent variables in panel data models
We consider a fixed effects estimation approach that treats the factors and loadings as parameters to be estimated. As it is well-known in the panel data literature, the resulting estimators generally suffer from the incidental parameter problem coming from the high-dimensionality of the estimated parameter (Neyman and Scott, 1948)
We bring in the factor structure to model important features of network data such as reciprocity, degree heterogeneity, homophily in latent factors and clustering in a reduced form fashion
Summary
Factor structures or interactive effects are convenient devices to incorporate latent variables in panel data models. In terms of the network literature, our paper is related to the recent work on the application of panel fixed effects methods to network data including Fernandez-Val and Weidner (2016), Yan et al (2016), Cruz-Gonzalez et al (2017), Dzemski (2017), Graham (2017), and Yan (2018) These papers account for degree heterogeneity by including additive unobserved sender and receiver effects. We provide bias corrections for fixed effect estimators of model parameters and APEs. Third, we bring in the factor structure to model important features of network data such as reciprocity, degree heterogeneity, homophily in latent factors and clustering in a reduced form fashion. The proofs of the main results and other technical details are given in the Appendix
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