Panel data allow control of time-constant unobserved heterogeneity of cross-sectional units but the MLE of the structural parameters is affected by the incidental parameter problem in large n, short T panels. The source of this problem can be traced to the profiling out of these incidental prameters. In panel binary choice models, the nonlinearity also contributes to this problem.

I apply projected score methods to static and dynamic panel binary choice models, treating and interpreting these incidental parameters as constants. The chosen time dimension is deliberately small in order to examine analytically the resulting projected scores when the incidental parameters are profiled out.

The idea of projecting the score equations for the structural parameters onto the orthogonal complement of an appropriate space of functions, capturing the effects of the presence of high-dimensional nuisance parameters, is helpful in estimating these parameters and could be used to shed light on existing bias correction methods for panel binary choice models. Despite projected scores being harder to calculate, these scores are very transparent in terms of the model assumptions needed. I show that these projected scores only require predetermined regressors and may even be discrete.