On the Existence of Conditional Maximum Likelihood Estimates of the Binary Logit Model with Fixed Effects

TL;DR

This paper investigates the conditions under which conditional maximum likelihood estimates exist for the binary logit model with fixed effects, extending previous results and providing a practical algorithm to identify spurious estimates.

Contribution

It establishes a one-to-one correspondence between estimate existence and data configuration, extending prior work and enabling detection of spurious estimates in finite samples.

Findings

Existence and uniqueness linked to data point configuration

Extension of Albert and Anderson's results to fixed effects

Algorithm for detecting spurious estimates

Abstract

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.