  By exploiting McFadden (1974)'s results on conditional logit estimation, we
show that there exists a one-to-one mapping between existence and uniqueness of
conditional maximum likelihood estimates of the binary logit model with fixed
effects and the configuration of data points. Our results extend those in
Albert and Anderson (1984) for the cross-sectional case and can be used to
build a simple algorithm that detects spurious estimates in finite samples. As
an illustration, we exhibit an artificial dataset for which the STATA's command
\texttt{clogit} returns spurious estimates.
