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. Endogenous explanatory variables can be easily accommodated. Examples of application to some static and dynamic binary, ordered and multiple discrete choice panel data models are presented.