In this paper we derive a consistent estimator for the Binomial distribution in the presence of incidental parameters, or fixed effects, when the underlying probability is a logistic function of the data. The consistent estimator is obtained from the maximization of a conditional likelihood function in light of Andersen's work. We also present results of Monte Carlo runs that show the superiority of this new estimator relative to the traditional maximum likelihood estimator with fixed effects, in small samples, particularly, when the number of observations in each cross-section, T, is small. Finally, we apply this new estimator to an original dataset that allows us to model the probability of obtaining a patent.