This paper investigates the construction of moment conditions in discrete choice panel data with individual-specific fixed effects. We describe how to systematically explore the existence of moment conditions that do not depend on the fixed effects, and we demonstrate how to construct them when they exist. Our approach is closely related to the numerical “functional differencing” construction introduced in a seminal paper by Bonhomme, but our emphasis is to find explicit analytic expressions for the moment functions. We first explain the construction and give examples of such moment conditions in various models. Then, we focus on the dynamic binary choice logit model and explore the implications of the moment conditions for the identification and estimation of the model parameters that are common to all individuals.

How do social networks influence the decision to migrate? Prior work suggests two distinct mechanisms that have historically been difficult to differentiate: as a conduit of information, and as a source of social and economic support. We disentangle these mechanisms using a massive “digital trace” dataset that allows us to observe the migration decisions made by millions of individuals over several years, as well as the complete social network of each person in the months before and after migration. These data allow us to establish a new set of stylized facts about the relationship between social networks and migration. Our main analysis indicates that the average migrant derives more social capital from “interconnected” networks that provide social support than from “extensive” networks that efficiently transmit information.