Andrew Chesher | Searcharxiv

arXiv2026

The Projection Solution to the Incidental Parameter Problem

This paper introduces a new approach to econometric analysis of nonlinear panel data models when the number of observations per observational unit is small. In such models the presence of variables that are constant within, while varying across, units results in an incidental parameter problem. The approach taken in this paper removes these incidental parameters via projection, which produces a correspondence specifying all combinations of observed variables and within-unit-varying unobserved 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 result is an incomplete model which 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 distribution-free restrictions on within-unit-varying unobserved heterogeneity are presented.

econ.EM↗

arXiv2024

Robust Analysis of Short Panels

Many structural econometric models include latent variables on whose probability distributions one may wish to place minimal restrictions. Leading examples in panel data models are individual-specific variables sometimes treated as "fixed effects" and, in dynamic models, initial conditions. This paper presents a generally applicable method for characterizing sharp identified sets when models place no restrictions on the probability distribution of certain latent variables and no restrictions on their covariation with other variables. In our analysis latent variables on which restrictions are undesirable are removed, leading to econometric analysis robust to misspecification of restrictions on their distributions which are commonplace in the applied panel data literature. Endogenous explanatory variables are easily accommodated. Examples of application to some static and dynamic binary, ordered and multiple discrete choice and censored panel data models are presented.

econ.EM↗