Robust analysis of short panels

Abstract

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. * This is a revision of the October 2023 CeMMAP working paper CWP20/23, circulated under the title "Identification analysis in models with unrestricted latent variables: Fixed effects and initial conditions." We are grateful for comments received at seminars at UCL, Duke, and the Montreal Econometrics Seminar, and at presentations at the 2023 Latin American Meeting of the Econometric Society in Bogota and the 34 th EC 2 Meeting at the University of Manchester in December 2023. Financial support from the UK Economic and Social Research Council through a grant (RES-589-28-0001) to the ESRC Centre for Microdata Methods and Practice (CeMMAP) is gratefully acknowledged.