We consider a panel model with a binary response variable that is a product of two unobservable factors, each determined by a separate binary choice equation. One of these factors is assumed to be time-invariant and may be interpreted as a latent class indicator. A simulation study shows that maximum likelihood estimates from even the shortest panel are much more reliable than those obtained from a cross-section. As an illustrative example, the model is applied to Russian Longitudinal Monitoring Survey data to estimate a proportion of the non-employed population who are participating in job search.