I always struggle to get the true essence of the incidental parameter problem. I read in several occasions that the fixed effects estimators of nonlinear panel data models can be severely biased because of the "well-known" incidental parameter problem.

When I ask for a clear explanation of this problem the typical answer is: Assume that the panel data has N individuals over T time periods. If T is fixed, as N grows the covariate estimates become biased. This occurs because the number of nuisance parameters grow quickly as N increases.

I would greatly appreciate

• a more precise but still simple explanation (if possible)
• and/or a concrete example that I can work out with R or Stata.