Fragility of identification in panel binary response models

The present paper considers a linear binary response model for panel data with random effects that differ across individuals but are constant over time, and it investigates the roles of the various assumptions that are used to establish conditions for identification. The paper also shows that even for this simple model, it is always possible-including in the logistic case-to find a distribution of the random effects given the exogenous variables, such that the slopes' parameters are arbitrarily different, but the joint distributions of the binary response variables are arbitrarily close.