### Abstract

We discuss different estimators for logistic regression models with individual fixed effects and tackle their short-comings. A simple unconditional maximum likelihood estimator (UCL) that uses a dummy variable for each of the N cross-sectional units suffers from prohibitive computational costs if N is large. Further, it can be severely biased due to the incidental parameter problem (IPP). Using the Frisch-Waugh-Lovell theorem we derive an intuitive and computationally efficient algorithm which can be easily combined with existing bias corrections to address the IPP. The popular conditional logit estimator (CL) is fixed T consistent, but it exhibits an enormous computational burden if T is large. We therefore propose a new conditional logit estimator that alleviates the computational burden of CL at costs of efficiency. Since conditional logit estimators do not allow to estimate average partial effects, we propose a novel hybrid approach. Extensive Monte-Carlo simulations confirm that the bias-corrected UCL estimator (BCL) and CL have similar statistical properties. However, combined with the pseudo-demeaning algorithm, UCL and BCL have a much lower computational burden, especially with large T. The algorithm is implemented in the R package bife.

###### Post-Doctoral Researcher in Economics