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Bias in Conditional and Unconditional Fixed Effects Logit Estimation: A Correction

https://doi.org/10.1093/pan/mpi019
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4/4 checkable references clean · checked 2026-08-29

Every reference with a DOI in the deposited reference list resolved to a known work in Crossref or DataCite at the dated check, and none carried a retraction, withdrawal, or removal notice.

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The 4 checked references that resolve
resolves10.1111/j.1368-423X.2004.00123.x
The behaviour of the maximum likelihood estimator of limited dependent variable models in the presence of fixed effects
resolves10.2307/2297110
Analysis of Covariance with Qualitative Data
resolves10.1016/S0165-1765(97)00044-X
The equivalence of two estimators of the fixed-effects logit model
resolves10.1093/oxfordjournals.pan.a004876
Bias in Conditional and Unconditional Fixed Effects Logit Estimation
The 7 references without a DOI — listed, not checked
no DOI — not checkedInstead, one could follow Greene (2004) by generating individual specific effects that are correlated with X as follows:
no DOI — not checkedI could generate α i from N(0,1) and combine this with a randomly generated X. This leads to what economists would call a “random effect” since by construction there is no correlation between the individual specific effects and the explicative variable X. The estimation procedure in this case would be to use the random effects estimator, rather than including dummies to capture the “fixed effects.”
no DOI — not checkedThis mistake is also present in the computer program written by Katz and posted on the Political Analysis Web site (http://polmeth.wustl.edu/pa/vol9no4.html), though in a slightly different form. In the computer program, the fixed effect of the first individual is dropped, hence the formula is
no DOI — not checkedOf course, one could claim that there are fixed effects, but they just happen to be the same. However, in such a case the fixed effects are meaningless.
no DOI — not checkedItalics added.
no DOI — not checkedNote that this implies that I use a standard normal distribution for X rather than a uniform distribution (which was used by Katz). The distribution of the X generally, however, has no influence on the results (see, e.g., Greene (2004)).
no DOI — not checkedThe parameters are the same as for column 1 in Table 2 of Katz (2001): β = 0.5, γ = − 1 Tom Coupé
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