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Unfortunately, indiscriminate use of the term "fixed effects" to describe any set of mutually exclusive and exhaustive dummy variables seems to be generating confusion about nonlinear models and the incidental parameters problem.
#metricstotheface
#metricstotheface
With panel data, the IPP arises when we try to include unit-specific dummies in a nonlinear model with a small number of time periods. We have few observations per "fixed effects." In other cases, IPP arises if we put in group-specific dummies with small group sizes.
But if we include, say, occupation dummies when we have lots of people in each occupation, this clearly causes no problem. Or, including interviewer "fixed effects" when we have lots of subjects per interviewer.
It's easy to find phrases such as "religion fixed effects" and "race fixed effects" and so on in published papers. Clearly the inclusion of such variables cannot cause an IPP in any nonlinear model. A clear majority knows this, but it can be confusing for the beginner.
The convention of using "fixed effects" to describe dummy variables is so ingrained that it's impossible to change now. So we probably just have to do a better job teaching what was originally meant by "fixed effects estimation" versus how "fixed effects" is now used.
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