A1794
Title: The projection solution to the incidental parameter problem
Authors: Yuanqi Zhang - University College London (United Kingdom) [presenting]
Andrew Chesher - University College London (United Kingdom)
Adam Rosen - Duke University (United States)
Abstract: An econometric approach to panel data models is introduced for settings where many observational units each deliver a small number of observations. In such models, the presence of variables that are constant within units while varying across units results in an incidental parameter problem. The approach removes these incidental parameters via projection, which delivers a correspondence specifying all combinations of observable variables and within-unit-varying unobservable heterogeneity that are achievable by choice of some value of the unit-specific incidental parameters. With unit-specific variables removed, there is no need for assumptions concerning their joint distribution with other variables. The resulting incomplete model is typically partially identifying. Identified sets are characterized via moment inequalities using tools of random set theory. Examples of application to static and dynamic models with discrete or continuous outcomes using a variety of exogeneity restrictions, including forms of weak exogeneity and distribution-free restrictions on within-unit-varying unobservable heterogeneity, are presented.
