  This article deals with asimple issue: if we have grouped data with a binary
dependent variable and want to include fixed effects (group specific
intercepts) in the specification, is Ordinary Least Squares (OLS) in any way
superior to a (conditional) logit form? In particular, what are the
consequences of using OLS instead of a fixed effects logit model with respect
to the latter dropping all units which show no variability in the dependent
variable while the former allows for estimation using all units. First, we show
that the discussion of fthe incidental parameters problem is based on an
assumption about the kinds of data being studied; for what appears to be the
common use of fixed effect models in political science the incidental
parameters issue is illusory. Turning to linear models, we see that OLS yields
a linear combination of the estimates for the units with and without variation
in the dependent variable, and so the coefficient estimates must be carefully
interpreted. The article then compares two methods of estimating logit models
with fixed effects, and shows that the Chamberlain conditional logit is as good
as or better than a logit analysis which simply includes group specific
intercepts (even though the conditional logit technique was designed to deal
with the incidental parameters problem!). Related to this, the article
discusses the estimation of marginal effects using both OLS and logit. While it
appears that a form of logit with fixed effects can be used to estimate
marginal effects, this method can be improved by starting with conditional
logit and then using the those parameter estimates to constrain the logit with
fixed effects model. This method produces estimates of sample average marginal
effects that are at least as good as OLS, and much better when group size is
small or the number of groups is large. .
