Nonlinear Factor Models for Network and Panel Data

TL;DR

This paper develops fixed effect estimators for nonlinear panel models with factor structures, applicable to network data, and demonstrates their use in international trade analysis.

Contribution

It introduces fixed effect estimation methods for nonlinear models with latent factors, addressing incidental parameter bias and applying to network data.

Findings

Estimators are asymptotically normal with large panels.

Models capture network features like reciprocity and homophily.

Empirical example with international trade data illustrates the methods.

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 of incidental parameter bias. We show how models with factor structures can also 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.