A consistent estimator for the binomial distribution in the presence of “incidental parameters”: an application to patent data

In this paper a consistent estimator for the Binomial distribution in the presence of incidental parameters, or fixed effects, when the underlying probability is a logistic function is derived. The consistent estimator is obtained from the maximization of a conditional likelihood function in light of Andersenʹs work. Monte Carlo simulations show its superiority relative to the traditional maximum likelihood estimator with fixed effects also in small samples, particularly when the number of observations in each cross-section, T, is small. Finally, this new estimator is applied to an original dataset that allows the estimation of the probability of obtaining a patent.