This paper investigates identification in binary response models with panel data. Conditioning on sufficient statistics can sometimes lead to a conditional maximum likelihood approach that can be used to identify and estimate the parameters of interest in such models. Unfortunately it is often difficult or impossible to find such sufficient statistics, and even if it is possible, the approach sometimes leads to conditional likelihoods that do not depend on some interesting parameters. Using a range of different data generating processes, this paper calculates the identified regions for parameters in panel data logit AR(2) and logit VAR(1) models for which it is not known whether the parameters are identified or not. We find that identification might be more common than was previously thought, and that the identified regions for non-identified objects may be small enough to be empirically useful.