# Probit with fixed effects

Could anyone elaborate on why fixed effects (or within estimator) will not work in the probit setting? Thanks in advance.

## 1 Answer

A model with "fixed effects" has individual intercepts, say $$\alpha_{i}$$, for each individual $$i$$ in your sample. This means the number of parameters you are trying to estimate grows just as quickly as your sample size $$n$$ does. This is called the incidental parameters problem and generally causes inconsistency of the maximum likelihood estimator.

In a linear model this is not a problem because the nuisance parameters $$\alpha_{i}$$ are eliminated by first-differencing. But in a non-linear model, like probit, this is not possible.